Answers
Answer: 112 degrees
Step-by-step explanation:
The angles have the same measure because of the corresponding angles theorem.
[tex]\huge\boxed{112^\circ}[/tex]
To solve this problem, we need to understand the basic rules of transversals across parallel lines.
When a line crosses another line or lines, it is a transversal.
When the two lines it crosses are parallel, the eight angles formed have interesting properties that we can use.
For this question, we will look at corresponding angles. If two angles meet these two conditions, they are congruent:
Both angles are on the same side of the transversal.One angle is interior (between the parallel lines) and the other is exterior.These two conditions are met for [tex]\angle JIK[/tex] and [tex]\angle GFI[/tex], so they are congruent and their measures are equal.
This means that [tex]m\angle JIK=m\angle GFI=\boxed{112^\circ}[/tex]
Related Questions
it is math for evaluating functions please help
Answers
The domain of the given function is; (0, 2)
The range of the given function is; (-2, 6)
What is the range and domain of the given function?We want to evaluate the function f(x) = 4x - 2 for x = 0, 1 and 2.
Step 1;
f(0) = 4(0) - 2
f(1) = 4(1) - 2
f(2) = 4(2) - 2
Step 2;
f(0) = 0 - 2 = -2
f(1) = 4 - 2 = 2
f(2) = 8 - 2 = 6
The domain is the set of all possible input values which is (0, 2)
The range is the set of all possible output values which is (-2, 6)
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For a normally distributed population with a mean of 150 and standard deviation of 25, approximately what percentage of the observations should we expect to lie between 100 and 200?
Answers
The percentage of observations which we expect to lie between 100 and 200 is 3.38%
Given, the mean is 150 and
standard deviation(sd) = 25
what percentage of observation lie between 100 and 200.
x + 1sd = 175
x - 1sd = 125
x + 2sd = 200
x - 2sd = 100
x + 3sd = 225
x - 3sd = 7
observation between 100 and 200 lie from x + 1sd
Therefore P(x) = (100-175)÷25
= -3
=3.38%
Hence the percentage of observations that lie between 100 and 200 is 3.38%
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Rewrite, using the distributive
property.
4(2x + 5) = [?]x + [ ]
Answers
Step-by-step explanation:
8x+20 is the answer ......
Can someone help me with this question?
Answers
Answer:
A) y = 0.3x+24
B) 283.5 dollars
Step-by-step explanation:
A) To create an equation in slope-intercept form, we can start by using the numbers the problem gave us and represent them as coordinates. Generally, time is always our x-value.
(230,93)
(530,183)
Now that we have our two coordinates, we can plug them into the slope-intercept formula: y₂-y₁/x₂-x₁ to find our slope.
(183-93)/(530-230) = 0.3
Now that we have our slope, we can plug it into our equation.
y = 0.3x + b
To find our y-intercept, we can take either one of our 2 coordinates (x,y) and plug them into the equation to solve for b.
93 = 0.3(230) + b
93 = 69 + b
93 - 69 = b
b = 24
Now that we have found our y-intercept, we can plug it into b to complete the equation.
y = 0.3x +24
B) If 865 minutes are used, we can plug 865 into x in our equation to find the total cost.
0.3(865) + 24 = 283.5
50 POINTSS Solve for q.
s = 4p + 4q
Answers
On his road trip, Leon stops to refuel and get some snacks. He has the following purchases:
12 gallons of gas at of $2.89 per gallon
2 granola bars for $1.59 each
1 apple for $0.89
2 bottles of vitamin water for $1.39 each
Leon must pay 7.5% sales tax on everything but the gas, which already has tax included in the per gallon price. If
Leon paid $44.64, then he
for his purchase.
a. did not pay enough
b. paid the correct amount
C.
paid $2.60 too much
d.
paid $3.11 too much
Please select the best answer from the choices provided
Answers
y=12(2.89)+(2(1.59)+.89+2(1.39))+.075p
This is a function, meaning that y=output (total cost), which we are given is 44.64, so y=44.64. Also notice that there is a variable “p.” This variable “p” simply means the price disregarding gas. We substitute y in and solve the equation using PEMDAS.
44.64=34.68+(3.18+.89+2.78)+.075p
44.64=34.68+(6.85)+.075(6.85)
Now, you see that “p” was replaced with the price disregarding gas, so we need to find the sales tax (7.5%=.075) of the food products and add that to the whole equation.
44.64=34.68+6.85+.51375
44.64=34.68+7.36375
44.68≠42.043
Notice that after simplifying, the equation is an inequality; therefore, we must subtract 44.68-42.043=2.637, and rounding down to the nearest tenth of 2.60.
Your answer is that Leon overpaid by $2.60
The correct option is that;
C. Leon overpaid for his purchase by $2.60 if he paid $44.64.
What is the difference between a sales tax and a use tax?The vendor, who is acting as the state's agent, collects the sales tax and remits it to the state on behalf of the final customer. The use tax, on the other hand, is self-assessed and paid by the final customer.
Given that;
Purchase fuel = 12 Gallons per $2.89 per gallons (including Tax)
2 Granola Bar for $1.59 per bar
1 apple for $0.89
2 bottles of vitamin water for $1.39
The sales Tax rate is 7.5%
Required to calculate the difference amount of Actual Paid and Actual Purchase =?
Fuel = 12 x 2.89 = $34.68 (including tax)
Granola Bar = 2 x 1.59 = $3.18
Apple = 1 x 0.89 = $0.89
Vitamin Water = 2 x 1.39 = $2.78
Total Purchase excluding fuel without tax is,
= $3.18 + $0.89 + $2.78
= $6.85.
Adding sale tax on $6.85 at the rate of 7.5% = $7.36
Hence, Total Purchase including Tax is,
$7.36 + $34.68 = $42.04
Thus, there is a clear difference that Leon paid 2.60 more than his actual purchase. He paid $ 44.64 and his actual purchase is 42.04 the difference between that is $2.60.
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find the prime factors of 6912 and cube root
Answers
The prime factors of 6912 are 2 and 3 and the cube root of 6912 is approximately 19.05 (rounded to 2 decimal places) .
Prime numbers are numbers which do not have any factors other than 1 and itself. For example 7 is a prime number, 37 is a prime number as the factors of 7 are 1 and 7 and the factors of 37 are 1 and 37.
Prime factorization of a number is given by writing all the prime factors of as number in multiplication form.
The prime factorization of 6912 gives:
6912 = 2 × 2 × 2 ×2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 = 2⁸ × 3³
Hence the prime factors of 6912 are 2 and 3.
The cube root of 6912 = 19.0488... ≈ 19.05 (rounded to 2 decimal places)
Therefore the cube root of 6912 is approximately 19.05 .
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What size heater will be required to heat the water in a swimming pool from
70°F to 72 °F in 1 hour if the appliance is 100% efficient and the pool holds
20,000 gallons of water?
A. 166,000 Btu/h
B. 332,000 Btu/h
C. 86,000 Btu/h
D. 224,000 Btu/h
Ps. the answer is B but i want an explanation on how to work through the problem
Answers
Answer:
B
Step-by-step explanation:
the British thermal unit (BTU or Btu) is a unit of heat; it is defined as the amount of heat required to raise the temperature of one pound of water by one degree Fahrenheit.
and it is outdated. your teacher and the manufacturer should use joules as metric.
1 BTU ≈ 1055 joules
anyway, so, the solution has several parts.
we need to find how many pounds of water are in a gallon.
and then multiply by the amount of gallons (20 000) and the amount of degrees (2 from 70 to 72).
and after a little search on the internet we get
1 gallon of water = 8.34 pounds
so, we need to warm
20000×8.34 pounds of water by 2 degrees F.
that is
20000 × 8.34 × 2 = 333,600 BTU
if we use only the rounded value of pounds per gallons (8.3), this would be
20000 × 8.3 × 2 = 332,000 BTU
so in any case, B is the right answer (as being the closest to the real result), which is the situation with any size classification of devices : reality is somewhere close by, but never meets the exact specifications.
Jayden is standing in a stadium and has the option of running up a staircase or down a staircase for exercise. The function f(x)=\frac{1}{25}\big(\left|6x\right|+5x\big)f(x)= 25 1 (∣6x∣+5x) will determine how many calories Jayden will burn if he runs up xx steps. Use a negative value for xx if he runs down the stairs. Find and interpret the given function values and determine an appropriate domain for the function.
Answers
The interpretation of the value of the function, [tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex], when x = 30 is that by running up 30 steps, Jayden burns [tex] 13 \frac{1}{3} [/tex] calories.
The domain of the function is the set of all real numbers
How can the values of the function be interpreted?The given function is presented as follows;
[tex]f(x) = \frac{1}{25} \times \left( \left |6 \cdot x \right | + 5 \cdot x \right)[/tex]
Where;
f(x) = The number of calories burnt
x = The number of steps Jayden runs
The value of x is negative while running down the stairs
Therefore;
[tex]f(30) = \frac{1}{25} \times \left( \left |6 \times 30 \right | + 5 \times 30 \right) = 13 \frac{1}{3} [/tex]
[tex]f(30) = 13 \frac{1}{3} [/tex]
The interpretation of the above function equation is that the amount of calories Jayden burns when she runs 30 steps up the stairs is [tex] 13 \frac{1}{3} [/tex]
Given that 6•x > 5•x, the function is always positive, and has a minimum value of zero, the function can take any value for x.
The domain of the function is therefore, -∞ ≤ x ≤ ∞, which is the set of all real numbers.
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Two figures are said to be SIMILAR if they are the same shape. In more mathematical language, two figures are similar if their corresponding angles are congruent , and the ratios of the lengths of their corresponding sides are equal. This common ratio is called the scale factor.
This pair of figures is similar. Find the value of the missing side (x).
Answers
Answer:
The ratio is 8:1 and it is a rectangle so x is 56
If on the similar image the sides are the same the other image will be aswell
Hope thie helps!
If you have any other question feel free to ask!
What is f(3)?
-9
-1
1
9
Answers
Answer:
9
Step-by-step explanation:
Edge
Is the relation a function yes or no circle the order pairs that cause the relation to not be a function
Answers
For the relations (tables) from left to right we have:
1) Is not a function, because the input 5 is mapped into two different values.
2) Is not a function, because the input -1 is mapped into two different values.
3) It is a function.
4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).
How to know if the relations are functions or not?A relation is an operation that maps elements from one set called the domain (set of the inputs) into elements of another set, called the range (set of the outputs).
Now, a relation is a function only if each element of the domain is mapped into only one element of the range. So, if you see the same input in a table two times (related to two different outputs) then that table does not represent a function.
Then, for the tables reading from left to right, we have:
1) Is not a function, because the input 5 is mapped into two different values.
2) Is not a function, because the input -1 is mapped into two different values.
3) It is a function.
4) It is a function (the input x = 7 appears twice, but both times is mapped into the same output).
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If angle YXZ measures 90 degrees, which statement is true?
(answers are below)
segment XZ is perpendicular to segment WY
WX =XY
segment XZ is a perpendicular bisector of segment WY
X is the midpoint of segment WY
Answers
The statement that is true is: A. segment XZ is perpendicular to segment WY.
What is a Perpendicular Lines?When two lines intersect at a point to form right angles (90 degrees), both lines are said to be perpendicular to each other.
We are told that angle YXZ is equal to 90 degrees. This is the angle formed at the point where segment XZ intersects segment WY at point X.
This means that both lines are perpendicular to each other.
Therefore, the statement that is true is: A. segment XZ is perpendicular to segment WY.
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For the stem-and-leaf plot below, what are the maximum and minimum entries?
1 | 3 4
1 | 6 6 6 7 8 9
2 | 0 1 1 2 3 4 4 5 6 6
2 | 7 7 7 8 8 9 9 9
3 | 0 1 1 2 3 4 4 5 5
3 | 6 6 6 7 8 8 9 9
4 | 1 3
Answers
Min: 12
Max: 43
Write a compound inequality that represents the following phrase.
all real numbers that are between -4 and 5, inclusive
Write a compound inequality that represents the phrase. Choose the correct answer below.
A:[tex]-4\leq n\ \textless \ 5[/tex]
B:[tex]-4\ \textless \ n\ \textless \ 5[/tex]
C:[tex]-4\ \textless \ n\leq 5[/tex]
D:[tex]-4\leq n\leq 5[/tex]
Answers
The compound inequality that represents the set of real numbers that are between -4 and 5 inclusive is the option;
D: -4 ≤ n ≤ 5
How can the compound inequality be found?A compound inequality comprises of a sentence that makes two inequality statements that are joined by either the word 'and' or 'or'.
Given that the inequality represents the set of all real numbers that are between -4 and 5, and -4 < 5, the required set of numbers is therefore of the form;
[tex] - 4 \: \leftrightarrow \: 5[/tex]
The expression of the required set of numbers as inequalities is therefore;
-4 ≤ n and n ≤ 5The compound inequality is therefore;
D: -4 ≤ n ≤ 5
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The mapping diagram shows a relation.
A mapping diagram shows a relation, using arrows, between inputs and outputs for the following ordered pairs: (negative 6, 0), (2, 1), (negative 7, negative 4), (11, 2), (3, 2).
What is the domain of the relation?
{x| x = –4 , 0, 1, 2}.
{x| x = –7, –6, 2, 3, 11}.
{y| y = –4, 0, 1, 2}.
{y| y = –7, –6, 2, 3, 11}.
Answers
The domain of the given relation is: {x| x = –7, –6, 2, 3, 11}.
What is a domain?A domain can be defined as the set of all real numbers for which a particular function is defined. This ultimately implies that, a domain is the set of all possible input numerical values to a function and the domain of a graph comprises all the input numerical values which are shown on the x-axis.
Additionally, the horizontal extent of a graph represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.
In this context, we can reasonably infer and logically deduce that the domain of the given relation include the following: {x| x = –7, –6, 2, 3, 11}.
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Mr Mathes purchases 4 tickets for his family find the value of the expression when t=4
Answers
The value of the expression when t=4 is 16
How to calculate the expression?It should be noted that from the information given, it was stated that Mathes purchases 4 tickets for his family.
Therefore, the value of the expression when t=4 will be:
C = 4t
C = 4(4)
C = 4 × 4.
C = 16
Therefore, the value of the expression when t=4 is 16.
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What is the domain of the function y = 3 l n x graphed below?
On a coordinate plane, a curve starts in quadrant 4 and then increases up into quadrant 1. It crosses the x-axis at (1, 0).
Answers
The domain of the function y = 3 ln x is (0, ∞) .
In mathematics, the logarithmic function is the inverse of power.The domain of a function is the set of inputs or x-values on which the function is defined.The graph of the function y = 3ln x is given below .
Then , coordinate point (1, 0)
The logarithmic function y = log x has the domain x > 0 (or) (0, ∞).
This is a logarithmic function. An important property of logarithms is that the domain cannot be denied. The same is true for x=0, since the logarithm of negative numbers is undefined.
The image attached shows the graph of this function, there you can notice its domain restriction.
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The Andersons are planning to take a 960-mile trip. They will travel 840 miles by car. What percent of the distance will they not travel by car?
Answers
The percent of distance that the Andersons will not travel by car is 12.5%, If they are planning to take a 960-mile trip and they will travel 840 miles by car.
Total distance the Andersons are planning to take is 960-mile
They will travel 840 miles by car
Distance they will not travel by car = total distance - distance travelled by car
= 960 - 840 miles
=120 miles
Percentage formula = (value/ total value) x 100
percent of the distance will they not travel by car =
(total distance - distance travelled by car) x 100/total distance
=((960 - 840)/ 960) x100
=(120/ 960) x 100
12.5
If the Andersons are planning to take a 960-mile trip and they will travel 840 miles by car then the percentage of distance they will not travel by car is 12.5%
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In cell B16, enter a function to calculate the total attendance for the years 2018 through 2022 using the totals in the range B12:F12
Answers
The Excel formulas to enter in cell B16 is = SUM(B12 : F12)
How to determine the Excel function?From the question, we can assume the following:
Range = B12 to F12The sum of entries in cells B12 through F12 represent the required sumUsing the sum function, we have:
Total = SUM(B12 : F12)
So, the formula to enter in cell B16 is:
= SUM(B12 : F12)
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just need help with some of them at least 5 questions please already did the first one. i put 90 points please help.
Answers
2. The solution to the given system of equation is x = 1 and y = 6
3. The solution to the given system of equations is x = 1, y = 2
4. The simplified form of the expression is y²
5. The simplified form of the expression is 2
8. the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11
9. The multiplication yields x² - 4x - 96
10. The factored form of the expression is (x + 6)(x- 6)
11. The solutions to the given quadratic equation are x = 5 and x = -6
Solving system of equationsFrom the question, we are to solve the given system of equations
The given system of equation is
y = 10 - 4x --------- (1)
2x + 3y = 20 --------- (2)
Substitute equation (1) into equation (2)
2x + 3y = 20
2x + 3(10 -4x) = 20
2x + 30 - 12x = 20
2x - 12x = 20 - 30
-10x = -10
x = -10/-10
x = 1
Substitute the value of x into equation (1)
y = 10 - 4x
y = 10 - 4(1)
y = 10 - 4
y = 6
Hence, the solution to the given system of equation is x = 1 and y = 6
3.
From the question, we are to solve the system of equations using the elimination method
The given system of equations is
5x + 2y = 9
-5x + 4y = 3
Add the two equations
5x + 2y = 9
-5x + 4y = 3
----------------------
0x + 6y = 12
6y = 12
y = 12/6
y = 2
Substitute the value of y into the first equation
5x + 2y = 9
5x + 2(2) = 9
5x + 4 = 9
5x = 9 - 4
5x = 5
x = 5/5
x = 1
Hence, the solution to the given system of equations is x = 1, y = 2
4. From the question, we are to simplify the expression
y⁻⁴(y³)²
First, multiply the exponents in (y³)²
(y³)² = y ³ ˣ ²
= y⁶
Thus,
The expression becomes y⁻⁴y⁶
Applying the multiplication law of indices
y⁻⁴y⁶ = y⁻⁴ ⁺ ⁶
= y²
Hence, the simplified form of the expression is y²
5.
From the question, we are to simplify
∛8
First, express 8 in exponent form
8 = 2³
Thus,
The expression becomes
∛2³
Applying one of the laws of indices,
∛2³ = (2³)¹/³
Multiplying the exponents, we get
2¹
= 2
8.
From the question, we are to subtract the polynomial
(3x² + 5x - 8) - (2x³ - 4x + 3)
Subtracting
(3x² + 5x - 8) - (2x³ - 4x + 3)
3x² + 5x - 8 -(2x³ - 4x + 3)
Open the parentheses by distributing negative
3x² + 5x - 8 -2x³ + 4x - 3
Collect like terms
-2x³ + 3x² + 5x + 4x - 8 - 3
Simplify
-2x³ + 3x² + 9x - 11
Hence, the subtraction of the polynomials yields -2x³ + 3x² + 9x - 11
9.
From the question we are to multiply
(x + 8)(x - 12)
Applying the distributive property
x(x -12) +8(x -12)
x² - 12x + 8x - 96
Simplifying
x² - 4x - 96
10.
From the question, we are to factor
x² - 36
This can be written as
x² - 6²
From the rule of difference of two squares, we have that
a² - b² = (a + b)(a - b)
Thus,
x² - 6² = (x + 6)(x- 6)
11.
From the question, we are to find the solutions for
x² - x - 30 = 0
Solve by factoring
x² - x - 30 = 0
x² + 6x - 5x - 30 = 0
x(x + 6) -5(x + 6) = 0
(x - 5)(x + 6) = 0
∴ x - 5 = 0 and x + 6 = 0
x = 5 and x = -6
Hence, the solutions to the given quadratic equation are x = 5 and x = -6
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If 8 is 40% of N, then what does N equal?
Answers
50% equals 10
Answer:20
Step-by-step explanation:
n x 40% =8
So n = 8 / 40%
n = 20
-2x + 14y = -29
x-7y=19
elimination process
Answers
Answer:
no solution
Step-by-step explanation:
Multiplying the second equation by 2 gives 2x-14y=38.
Adding this to the first equation, we get 0=9, and thus there is no solution.
Brianna and Aisha start a small business making handmade soaps to sell at fairs and local stores.
Brianna can make 50 bars of soap in 40 hours, and Aisha can make 50 bars of soap in 75 hours. How long will it take Aisha to make 50 bars of soap?
Answers
Answer: 75 hours
Step-by-step explanation:
"Aisha can make 50 bars of soap in 75 hours"
The division is one of the four fundamental arithmetic operations. The time it will take to make 50 soap bars if they both work together is 25.4543 hours.
What is Division?The division is one of the four fundamental arithmetic operations, which tells us how the numbers are combined to form a new one.
Given that Brianna can make 50 bars of soap in 40 hours, and Aisha can make 50 bars of soap in 75 hours. Therefore, we can write,
Soaps Made Briana in an hour = 50 bars/40 hours
= 1.25 soap bars per hour
Soaps Made Aisha in an hour = 50 bars/75hours
= 0.7143 soap bars per hour
Now, together the number of soap bars they can make in an hour is,
Number of soap bars in an hour = 1.25 + 0.7143 soap bars per hour
= 1.9643 soap bars per hour
Further, the time it will take to make 50 soap bars if they both work together is,
Time is taken = Number of soaps/ Number of soaps in an hour
= 50 soap / 1.9643 soap bars per hour
= 25.4543 hours
Hence, the time it will take to make 50 soap bars if they both work together is 25.4543 hours.
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A mining company owns two mines. These mines produce an ore that can be graded into two classes: regular grade and low grade. The company must produce
at least 420 tons of regular-grade and 480 tons of low-grade ore per week. The first mine produces 6 tons of regular-grade and 16 tons of low-grade ore per
hour. The second mine produces 18 tons of regular-grade and 8 tons of low-grade ore per hour. The operating cost of the first mine is $20,500 per hour, and the
operating cost of the second mine is $10,200 per hour. The first mine can be operated no more than 55 hours a week, and the second mine can be operated no
more than 36 hours a week. How many hours per week should each mine be operated to minimize the cost?
Answers
The number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours
How to determine the number of hours?The given parameters can be represented using the following table of values
Mine 1 (x) Mine 2 (y) Available
Regular grade 6 18 420
Low grade 16 8 480
Operating cost 20500 10200
Time 55 36
From the table, we understand that we are to minimize cost
This means that:
Objective function: C = 20500x + 10200y
Subject to:
6x + 18y >= 420
16x + 8y >= 540
Next, we plot the constraints on a graph (see attachment)
From the graph, we have
(x, y) = (26.5, 14.5)
This means that
Mine 1 hour = 26.5 hours
Mine 2 hour = 14.5 hours
Hence, the number of hours to operate the mines to minimize cost are Mine 1 hour = 26.5 hours and Mine 2 hour = 14.5 hours
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The electoral college is in place so that states with a greater population have more influence in a presidential election. The higher populated states have more votes. For example, Washington is roughly 3 times as populated as Idaho, so Washigton’s number of electoral college votes is 300% of Idaho’s number. If Idaho has 4 electoral college votes, how many votes does Washington have? Percent formula
Answers
Answer: 12 electoral college votes
Step-by-step explanation:
4*100%=
4*100/100=
400/100=4
4*300%=
4*300/100=
1200/100=12 votes
Points P, Q, R, and S are collinear. Point Q is between P and R, R is between Q and S, and PQ =RS. If PS= 23 and PR = 17, what is the value of QR?
QR=
(Simplify your answer.)
Answers
Answer:
QR = 11
Step-by-step explanation:
P-Q-R-S
PQ = RS
PS = 23
PR = 17
so RS = PS - PR = 23 - 17 = 6
RS = PQ = 6
QR = PS - (RS + PQ) = 23 - (6 + 6) = 23 - 12 = 11
slope of (-8,-3) and (-1,-2)
Answers
Solution :-
As we know that,
m = y_2 - y_1 / x_2 - x_1Therefore ,
>> m = -2 - (-3) / -1 - (-8)
>> m = -2 + 3 / -1 + 8
>> m = 1 / 7
We have that the data are:
(x₁ = -8, y₁ = -3) and (x₂ = -1, y₂ = -2)
The slope is equal to the change in and with respect to change in X, or what rises when moving forward.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{Change \ in \ y}{Change \ in \ x} \ \longmapsto \ \ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} } \end{gathered}$}}[/tex]
The change in X is equal to the subtraction in the X coordinate (also called advance), and the change in and is equal to the subtraction in the coordinate and (also called elevation).
Introduce the values of x and y In the equation to find the slope.
[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{-2-(-3)}{-1-(-8) } } \end{gathered}$}}[/tex]
[tex]\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{m=\frac{1}{7} } \end{gathered}$}}}[/tex]
The slope of (-8, -3) and (-1, -2) is 1/7.Factorize the equation
Answers
Answer:
[tex]\sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]
Step-by-step explanation:
Given equation:
[tex](x^2+2)^{\frac{5}{2}}+2x(x^2+2)^{\frac{3}{2}}+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Rewrite the exponents }\frac{5}{2} \textsf{ as } \left(\frac{1}{2} \cdot 5\right)\textsf{ and }\frac{3}{2} \textsf{ as }\left(\frac{1}{2} \cdot 3\right):[/tex]
[tex]\implies (x^2+2)^{\frac{1}{2} \cdot 5}+2x(x^2+2)^{\frac{1}{2}\cdot 3}+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{bc}=(a^b)^c:[/tex]
[tex]\implies \left((x^2+2)^{\frac{1}{2}}\right)^5+2x\left((x^2+2)^{\frac{1}{2}}\right)^3+x^2\sqrt{x^2+2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{\frac{1}{2}}=\sqrt{a}:[/tex]
[tex]\implies \left(\sqrt{x^2+2}\right)^5+2x\left(\sqrt{x^2+2}\right)^3+x^2\sqrt{x^2+2}[/tex]
Factor out [tex]\sqrt{x^2+2}[/tex] from each of the three terms:
[tex]\implies \sqrt{x^2+2}\left[\left(\sqrt{x^2+2}\right)^4+2x\left(\sqrt{x^2+2}\right)^2+x^2\right][/tex]
[tex]\textsf{Factor the expression in the parentheses using} \quad a^2+2ab+b^2=(a+b)^2.[/tex]
[tex]\textsf{Let }a=\left(\sqrt{x^2+2}\right)^2 \textsf {and }b=x:[/tex]
[tex]\implies \sqrt{x^2+2}\left(\left(\sqrt{x^2+2}\right)^2+x\right)^2[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt{a^2}=a:[/tex]
[tex]\implies \sqrt{x^2+2}\left(x^2+2+x\right)^2[/tex]
[tex]\implies \sqrt{x^2+2}\left(x^2+x+2\right)^2[/tex]
The doctor has determined that one reason for the sickness is due to Cameron’s diet and that he has a protein deficiency. A change in his diet is necessary. He must increase the amount of protein that Cameron consumes. To begin this process, Cameron has to figure out how much protein he should consume in a day. Assume that he is 25 years old and weighs 132 lbs. According to the Food and Nutrition Board, Institute of Medicine, National Academies website, adults need 0.66 g/kg/d of protein.
How many grams of protein does he need each day?
Answers
Using proportions, it is found that he needs 39.5 grams of protein each day.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three. Due to this, relations between variables, either direct(when both increase or both decrease) or inverse proportional(when one increases and the other decreases, or vice versa), can be built to find the desired measures in the problem, or equations to find these measures.
First we have to convert his weight to kg. Each lb has 0.453592 kg, hence his weight in kg is given by:
132 x 0.453592 = 59.87 kg.
Each day, he needs to consume 0.66 g for each kilogram in his body, hence the amount of protein that he needs to consume each day is given by:
0.66 x 59.87 = 39.5.
More can be learned about proportions at https://brainly.com/question/24372153
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