The midpoint of the line segment with the endpoints is (4, 1)
How to determine the midpoint of the line segment with the endpoints?The endpoints are given as:
E= (-2,8) and F = (10, -6)
The midpoint of the line segment with the endpoints is calculated as
Midpoint = 0.5 * (x1 + x2, y1 + y2)
So, we have:
Midpoint = 0.5 * (-2 + 10, 8- 6)
Evaluate the sum
So, we have:
Midpoint = 0.5 * (8, 2)
Evaluate the products
So, we have:
Midpoint = (4, 1)
Hence, the midpoint of the line segment with the endpoints is (4, 1)
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What is the slope of the line passing through the points (-3, 4) and (2, - 1)?
Answer:
-1
Step-by-step explanation:
[tex]m= \frac{y2 - y1}{x2 - x1} [/tex]
put the values you will get your answer.
Marvin Co. sells pens ($6) and flashlights ($10). If total sales were $624 and customers bought 7 times as many pens as flashlights, what would be the number of pens sold?
Marvin Co. sells a total of 12 flashlights and 84 pens
Price of pen sold by Marvin Co. = $6
Price of flashlight sold by Marvin Co. = $10
Total sales = $624
Let the number of flashlights be x and the number of pens be y
Formulating the equations:
10x + 6y = 624
It is given that customer bought 7 times as many pens as flashlights, therefore:
y = 7x
Putting y = 7x in the equation we get,
10x + 6(7x) = 624
10x + 42x = 624
52x = 624
x = 12
So, the number of flashlights sold is 12 and the number of pens sold is 84
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find the area of a 36 inch tv with the aspect ratio 16:9
A ratio shows us the number of times a number contains another number. The area of the TV will be 729 inches².
What is a Ratio?A ratio shows us the number of times a number contains another number.
Given that the aspect ratio of the 36-inch tv is 16:9. Therefore, the width of the TV will be,
Length of the TV / Width of the TV = 16 : 9
36 inches / Width of the TV = 16 : 9
Width of the TV = 20.25 inches
Now, the area of the TV will be,
Area = Length of the TV × Width of the TV
= 36 inches × 20.25 inches
= 729 inches²
Hence, the area of the TV will be 729 inches².
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A 100kg bag contains peanuts and almonds. Peanuts are priced at $2 per kg and almonds are priced at $2.40 per kg. If the whole bag is priced at $2.08 per kg, how many kg of peanuts and almonds are there in the bag?
Answer:
Step-by-step explanation:x+y=100
(2x+2.4y)/100=2.08
x=80
y=20
Solve for x
(X+6)^2 = 8x+36
Answer:
x=0,x=-4
Step-by-step explanation:
(x+6)(x+6) =8x+36
x^2+12X+36-8X-36=0
X^2+4X=0
x(X+4)=0
You will get x=0 ,x=-4
Answer: x1=-4,x2=0
Step-by-step explanation:
x+6^2=8x+36
Expand the expression
x^2+12x+36=8x+36
Cancel equal terms
x^2+12x=8x
Move the variable to the left
x^2+12x-8x=0
Collect like terms
x^2+4x=0
Factor the expression
x x (x+4) = 0
Separate into possible cases
x=0
x+4=0
Solve the equation
x=0
x=-4
The equation has 2 solutions
x1=-4,x2=0
3. Mai realizes that each day her checking account is below zero, she is charged a
late fee of $5.75 per day. She realizes that she will not be paid until 10 days from
now. What will the balance of the account equal on the 10th day? Show your work.
the balance in the account at the 10th day will be equal to - $ 57.5.
Late fee for 1 day = $ 5.75
Number of days = 10
We will calculate the late fees for 10 days by using the operation of multiplication.
So, late fee will be:
Late fees = 10 × $ 5.75
Late fees = $ 57.5
Balance in the account at the 10th day = 0 - Late fees
Balance in the account at the 10th day = 0 - $ 57.5
Balance in the account at the 10th day = - $ 57.5
Therefore, the balance in the account at the 10th day will be equal to - $ 57.5.
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Please help me answer this question, I’ve tried a billion things and I keep getting it wrong
If 2 < a < 5 and 1 < b < 2 find all possible expressions a+b,ab,a-b,and a/b
The range of values for the expressions are given by these following compound inequalities:
3 < a + b < 7.2 < ab < 10.0 < a - b < 4.1 < a/b < 5.What is a compound inequality?A compound inequality is a combination of multiple inequalities, at least two, involving operations such as and and or, explained below.
The and operation between multiple sets is composed by the elements that belong to all the sets.The or operation between multiple sets is composed by the elements that belong to at least one of the sets.Hence one example of a compound inequality is:
a ≤ x ≤ b.
Which is read as follows:
x is greater or equal than a and less or equal than b.
What is the range of the addition?The smallest possible value is when both a and b are at their lower bounds, hence:
a + b = 2 + 1 = 3.
The greatest possible value is when both a and b are at their upper bounds, hence:
5 + 2 = 7.
Then the range is:
3 < a + b < 7.
Since the ranges of a and b are open intervals, the ranges of the operations will also be composed by open intervals.
What is the range of the multiplication?The smallest possible value is when both a and b are at their lower bounds, hence:
a x b = 2 x 1 = 2.
The greatest possible value is when both a and b are at their upper bounds, hence:
a x b = 5 x 2 = 10
Then the range is:
2 < ab < 10.
What is the range of the subtraction?The smallest possible value is when a is at it's lower bound and b is at it's upper bound, hence:
2 - 2 = 0
The greatest possible value is when a is at it's upper bound and b is at it's lower bound, hence:
5 - 1 = 4.
Hence the range is:
0 < a - b < 4.
What is the range of the division?The smallest possible value is when a is at it's lower bound and b is at it's upper bound, hence:
2/2 = 1.
The greatest possible value is when a is at it's upper bound and b is at it's lower bound, hence:
5/1 = 5.
Hence the range is:
1 < a/b < 5.
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Which type of statement and connective are associated with p V q?
a) Conditional; if ... then
B)Negation; not
c) Disjunction; or
d) Conjunction; and
Answer:
what will happen if we bought corrupt people
Find the equation of the line using the point-slope formula. Write the final equation using the slope-intercept form.
(x,y) =(3, 10) and (x,y) = (9, -2) are points on a line
Answer:
Step-by-step explanation:
Step 1: We must locate the slope, by using the slope formula, which is:
[tex]\frac{y2-y1}{x2-x1}[/tex]
When we plug it in we get:
[tex]\frac{-2-10}{9-3}[/tex]
Which simplifies to a -2
Step 2: We must plug in our values in the point-slope formula which is:
[tex]y-y1=m(x-x1)[/tex]
We can plug in (3,10) or (9,-2). It doesn't matter which one, we'll end up with the same answer. For this example, we'll use (3,10)
When we plug in our values we will get:
[tex]y-10=-2(x-3)[/tex]
Step 3: Now we just need to put our equation in slope-intercept form
[tex]y-10=-2(x-3)[/tex]
[tex]y-10=-2x+6\\y=-2x+16[/tex]
Therefore, our answer is [tex]y=-2x+16[/tex]
Hope this helps!!!
ind the equation of the line tangent to the graph of the given function at the point with the indicated x-coordinate.
f(x) = (x0.5 + 5)(x2 + x); x = 1
The equation of the line tangent to the curve is y = 19 · x - 7.
How to determine the equation of the line tangent to a curveIn this problem we need to find the equation of a line tangent to the function f(x) = (√x + 5) · (x² + x) for x = 1, that is, a line that only passes through one point of the entire curve. The equation of the line is introduced below:
y = m · x + b
Where:
m - Slopeb - InterceptThe slope of the line can be found by evaluating the first derivative of f(x) for x = 1:
f'(x) = (1 / 2√x) · (x² + x) + (√x + 5) · (2 · x + 1)
f'(1) = (1 / 2) · 2 + 6 · 3
f'(1) = 1 + 18
f'(1) = 19
The y-coordinate of the curve is:
f(1) = (√1 + 5) · (1² + 1)
f(1) = 6 · 2
f(1) = 12
Lastly, we determine the intercept of the tangent line:
b = y - m · x
b = 12 - 19 · 1
b = - 7
The equation of the line tangent to the curve is y = 19 · x - 7.
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Use the shape to answer the question.
7 cm
7 cm
7 cm
9 cm
9 cm
what’s the perimeter
Answer:
39cm
Step-by-step explanation:
7+7+7+9+9 = 39 - hope this works: )
Solve m–2(m–4)≤3m for m. m≤2 m≥2 m≤−2 m≥−2
Answer:
it equals 4
Step-by-step explanation:
The announcer said, ingrid won the 100 metre race in 13.9 seconds. Her time was originally measured to 2 decimal places. What was the slowest time she could have run?
Answer:
13.94 seconds
Step-by-step explanation:
The greatest number with 2 decimal places that can be rounded to 13.9 is 13.94.
Answer: 13.94 seconds
The announcer said that Ingrid has won the race in 13.9 seconds, then the slowest time she could have run is 13.94 seconds.
What is approximation?Something similar to something else but not precisely the same is called an approximation. By rounding, a number can be roughly estimated.
By rounding the values in a computation before carrying out the procedures, an estimated result can be obtained.
13.94 is the largest number that can be rounded to the nearest two decimal places and be equal to 13.9.
Because after the second decimal, that is 4 the number has to increase as per the rules of approximation. That's why the number 13.94 up to two decimal places is correct.
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Determine the total number of roots of each polynomial function.
g(x) = (x - 5)2 + 2x3
a. What is m TVZ? Show your work.
3x
120°
T
R
v (2x+15)
(2x + 5)°
Answer:
95°
Step-by-step explanation:
You want the measure of angle TVZ, when adjacent angle (2x+5)° and its supplement (2x+15)° are given. The larger of these is a vertical angle with respect to TVZ.
Linear pairThe angles marked (2x+15)° and (2x+5)° are a linear pair, hence supplementary.
((2x+15)° +(2x+5)° = 180°
4x +20 = 180 . . . . simplify
x +5 = 45 . . . . . . . divide by 4
x = 40 . . . . . subtract 5
Angle TVZ is a vertical angle with respect to the one marked (2x+15)°, so has the same measure:
∠TVZ = (2(40)+15)°
∠TVZ = 95°
__
Alternate solution
The two angles RVW (2x+15)° and ZVW (2x+5)° obviously differ by 10°. They are a linear pair, so their sum is 180°. Finding these angles is then a "sum and difference" problem. The larger of the solutions is the one we want, as (2x+15)° is a vertical angle to TVZ. We know the larger of the solutions to the sum and difference problem will be (180° +10°)/2 = 95°, the measure of TVZ.
More about sum and difference problems:
When a+b = s, and a-b = d, the larger value (a) can be found by adding these equations: (a+b) +(a-b) = s+d, or 2a = s+d, or a = (s+d)/2. This is the expression we used above to find the larger of the two angles. (You notice it is not necessary to solve for x.)
Three bags of beads have masses of 10.3 grams 5.23 grams and 3.74 grams complete the bar diagram to find the total mass of all the beads
Therefore, the total mass of all bags of beads is 19.27 grams
Given masses of three bags of beads as
Mass of beads in bag1 = 10.3 grams
Mass of beads in bag2 = 5.23 grams
Mass of beads in bag3 = 3.74 grams
We have to calculate the total mass of all the beads as below
The total mass of all bags of beads = mass of bag1 + mass of bag2 + mass of bag3
= 10.3 + 5.23 + 3.74
= 19.27 grams
Therefore, the total mass of all bags of beads is 19.27 grams
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The product of 4 and the sum of a number and is equal to the difference of twice the number and . Find the number.
The number is -4
[tex]x \times[/tex]4+4= 2[tex]x[/tex]-4
[tex]$$x \times 4+4=2 x-4$$[/tex]
Subtract 4 from both sides[tex]$x \times 4+4-4=2 x-4-4$[/tex]
Simplify
[tex]$$x \times 4=2 x-8$$[/tex]
Subtract [tex]$2 x$[/tex] from both sides [tex]$x \times 4-2 x=2 x-8-2 x$[/tex]
Simplify
[tex]$$2 x=-8$$[/tex]
Divide both sides by 2
[tex]\frac{2 x}{2}=\frac{-8}{2}$$[/tex]
Simplify
[tex]$$x=-4$$[/tex]
A strategy for teaching division is by repeated subtraction. It involves repeatedly subtracting the same integer from a big number until the result is zero. It is a fantastic approach to teach kids about division. A technique called repeated subtraction, commonly referred to as division, removes an equal amount of items from a group.
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group. Creating equal groups or determining how many people are in each group after a fair distribution is the basic objective of division.
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The difference between 4 and the sum of a number and is equal to twice that number. The number is -4.
Given that,
The difference between 4 and the sum of a number and is equal to twice that number.
Repeated subtraction is a method for teaching division. Until the result is zero, the same integer must be repeatedly subtracted from a large number. Repeated subtraction, sometimes known as division, is a method that takes an equal number of elements out of a group.
Division's opposite is multiplication. If 3 groups of 4 total up to 12, then 4 are in each group when 12 is divided into 3 equal groups. The fundamental goal of division is to produce equal groups or to determine how many individuals are in each group following a fair distribution.
x×4+4=2x-4
Subtracting 4 on both sides
4x+4-4=2x-4-4
4x=2x-8
Now, substracting 2x from both sides
4x-2x=2x-8-2x
2x=-8
x=-4
Therefore, The number is -4.
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What is the lowest form of this fraction 48/100
Answer:
12/25
Step-by-step explanation:
you have to start by reducing it by the lowest divisible numbers gradually till you get a fraction that cannot be divisible again.
start with two
48/100 = 24/50 = 12/ 25
12/25 cant be divided by any other number ahain therefore that's your final answer.
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On his first three tests, Devon scored 95, 77, and 96. What score must he get on his fourth test to have an average (mean) of 80 for all four tests?
Answer:
53
Step-by-step explanation:
Add all of number you have right now then pick a number and add it then divide it by 4 and keep going until reach 80
Cory graphed y = 100 - 50x x to represent the percentage of battery life
remaining on his phone after x hours.
What is a reasonable domain for this situation?
Percentage of battery life remaining
A. 0≤x≤ 100
Remaining Battery Life
100
Time (hours)
hr
The reasonable domain of the given situation is 0≤ x ≤2 that is 0 to 2 hours.
We see that x is represented as the number of phone hours used, therefore it has to be a number larger or equal to zero, but not a negative number. So, on one end we have that the number of phone hours used (x) must be larger or equal to zero. On the other hand, when the battery goes to zero, there are no more phone hours to use. We can find what is that other limit by making the battery percent (y variable) equal to zero, and solve the equation for x, thus giving us the upper limit of usable phone hours:
=> y = 0 = 100 - 50x
=> 100 = 50x
=> x = 100/50
=> x = 2
Therefore, the phone can be used for a maximum of 2 hours and the situation may be written as 0≤ x ≤2.
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Name a point that is collinear with points E and H.
Answer:
Point J
Step-by-step explanation:
Collinear means in a line
Point J is on the same line with E and H
Answer this question please
Answer:
Option 3
Step-by-step explanation:
[tex]|6t-7|-8 \geq 3 \\ \\ |6t-7| \geq 11 \\ \\ 6t-7 \leq -11, 6t-7 \geq 11 \\ \\ 6t \leq -4, 6t \geq 18 \\ \\ t \leq -2/3, t \geq 3[/tex]
1.09 x 10² convert to standard form
Answer:
109is the answer
Step-by-step explanation:
Hope it helps you
How many three-digit multiples of 6 have the sum of digits divisible by 6 if all digits are different?
There are 14 reams of paper in a case. How many total reams of paper are in 15 cases?
Work Shown:
1 case = 14 reams
15*(1 case) = 15*(14 reams)
15 cases = 210 reams
Answer:
There are 210 reams of paper in 15 cases
Step-by-step explanation:
1 case = 14 reams
To find out the total of reams in 15 cases, multiple both sides by 15
15 x 1 case = 15 x 14 reams
15 cases = 210 reams
The length L of a Brazilian snake m months after birth is
L(m) = 3(m - 8)-5 inches.
(a) Use function notation to give the equation that needs to be solved in order to find how old the snake is when it is 5 feet 1 inches long.
The snake would be 30 months old when his length is 5 feet 1 inches.
• Algebra is a branch in mathematics which deals with symbolic and the rule for manipulation of those symbols. Algebra is also divided into some sub branches such as advanced algebra, abstract algebra , linear algebra, elementary algebra etc.
• The basics of algebra contains numbers, variables, constants, expressions and equations. The basic operations in mathematics are addition, subtraction, multiplication, division.
The length L of an Brazilian snake m months after birth is given by
L(m) = 3(m-8) -5 inches
We need to find how much the snake is old the snake Is when it is 5 feet 1 inches long
L(m) = 5 feet 1 inches
We know that 1 feet = 12 inches
L(m) = 5*12+1
= 61 inches
61 = 3(m-8)-5
66 = 3(m-8)
m-8 = 22
m = 30
The snake would be 30 months old when his length is 5 feet 1 inches.
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The graph off (in blue) is translated a whole number of units horizontally and vertically to obtain the graph of h (in red). The functionfis defined by f(r) =/. Write down the expression for h().
Answer: the slope would be 7
Step-by-step explanation:
Find f(12) for the given piecewise function:
-18x+20, x < 19
f(x).
-16x²,
x ≥ 19
0-6478
0-5776
O-2304
0-196
Step-by-step explanation:
since 12 < 19, we have to use the first function definition :
f(12) = -18×12 + 20 = -216 + 20 = -196
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Draw a line segment with endpoints M and R. Now draw a parallel line segment that is the same length as segment MR with the endpoints M′ and R′ in the same order.
Which answer correctly describes the transformation from segment MR to segment M′R′?
Answer:
The transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)" ⇒ B
Step-by-step explanation:
Let us revise some transformationIf the point (x, y) rotated about the origin by angle 180° counterclockwise, then its image is (-x, -y) ⇒ R(180, O) (x, y) → (-x, -y) If the point (x, y) translated horizontally to the right by h units then its image is (x + h, y) ⇒ T (x, y) → (x + h, y)If the point (x, y) translated vertically up by k units then its image is (x, y + k) ⇒ T (x, y) → (x, y + k)∵ The coordinates of the point R = (-2, 4)∵ The coordinates of point R" = (3, -3)→ Both coordinates in R" have opposite signs then R∴ R rotated 180° about the origin ⇒ using the 1st rule above∴ R' = (2, -4)→ Find the difference between the x-coordinate of R" and x-coordinate of R'∵ xR" - xR' = 3 - 2 = 1→ By using the 2nd rule above∴ R' translated 1 unit to the right → Find the difference between the y-coordinate of R" and y-coordinate of R'∵ yR" - yR' = -3 - (-4) = -3 + 4 = 1→ By using the 3rd rule above∴ R' translated 1 unit up∴ The rule of translation is T(x, y) ⇒ (x + 1, y + 1)Let us use these 2 rules on S to find S"∵ The coordinates of the point S = (-4, -1)∵ S is rotated 180° around the origin→ By using the 1st rule above, opposite the signs of its coordinates∴ S' = (4, 1)∵ S' translated 1 unit right→ By using the 2nd rule above, add its x-coordinate by 1∵ S' translated 1 unit up→ By using the 3rd rule above, add its y-coordinate by 1∴ S" = (4 + 1, 1 + 1)∴ S" = (5,2)→ That means the rules of transformation of point R is rightThe transformation that map line RS to line R"S" is " rotation of 180° about the origin, followed by a translation (x, y) → (x + 1, y + 1)"
Translation
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