Answer:
x³-7x²/2-39x/2 + 10Step-by-step explanation:
Given 1/2,5, and -2 as roots of the polynomial, the function in terms of x is expressed as;
P(x) = (x - 1/2)(x - 5)(x+2)
Expand;
(x - 1/2)(x - 5) = x²-5x -x/2 + 5/2
(x - 1/2)(x - 5) = x²-11x/2 + 5/2
P(x) = (x²-11x/2 + 5/2)(x+2) = x³+2x²-11x²/2-22x+5x/2 + 10
P(x) = x³-7x²/2-39x/2 + 10
Hence the required polynomial is x³-7x²/2-39x/2 + 10
15. Write an equation and solve the equation to find the value of x so that the triangles have the same perimeter.
Triangle 1: 5,x-4,x-5
Triangle 2: 10,16,x-10
The equation is 5 + x - 4 + x - 5 = 10 + 16 + x - 10 and on solving the value of x is 20
The perimeter of a triangle is calculated by the summation of all the sides of a triangle
It is given that both the triangles have the same perimeter, so summation of all the sides of one triangle is equal to summation of all the sides of another triangle
Therefore the equation can be 5 + x - 4 + x - 5 = 10 + 16 + x - 10
Further solving the equation to calculate the unknown variable x
5 + x - 4 + x - 5 = 10 + 16 + x - 10
2x - 4 = x + 16
2x - x = 16 + 4
x = 20
The ēquation is 5 + x - 4 + x - 5 = 10 + 16 + x - 10 and on solving the value of x is 2
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there are 300 pages in a workbook. every chapter has 25 pages. which equation can be solved to find how many chapters are in the workbook?
Number of chapters in the workbook = 12
What is a linear equation?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables." from Wolfram MathWorld: linear.Total number of pages = 300
1 Chapter = 25 Pages
Divide 300 by 25 to figure out the total number of chapters in the workbook.
Number of chapters in the workbook = 300/25 = 12
Therefore, Number of chapters in the workbook = 12
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a second sheet of paper is half as long and half as wide as the one described in part a. by what factor is its area less than the area found in part a? chegg
The factor of its area less than the initial area is 1/4
How to determine the factor of its area less than the initial area?The given parameters can be represented as:
Second sheet = 1/2 * The first sheet
Assume the sheet is rectangular, the area of the sheet is calculated as:
Area = Length * Width
So, the area of the second sheet is
Second sheet = 1/2Length * 1/2Width
This gives
Second sheet = 1/4(Length * Width)
So, we have:
Second sheet = 1/4 * First sheet
Hence, the factor of its area less than the initial area is 1/4
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Can someone help me please?
Answer:
112
Step-by-step explanation:
Both angles are vertical angles
so x + 84 = 4x
3x = 84
x = 84/3 = 28
x + 84 = 28 + 84
How do i solve these types of problems?
Answer: 49 & 82
Step-by-step explanation:
*the total degrees for each triangle is 180 degrees
9) Start with the triangle furthest left- subtract 71 and 57 both from 180. That leaves you with 52 degrees for that third angle. The angles that all make a straight line or straight angle add up to 180 degrees as well. Now, subtract the 52 and 65 from 180, which leaves you with 63 degrees for the first angle in the second triangle. Now subtract the 63 and 68 from 180, which leaves you with 49 degrees for that answer.
10) For this one, you will start with the triangle further right, since it already has two angles shown. Subtract the 85 and 35 from 180, which gives you 60 degrees for that third angle. Then, you can use the vertical angles to fill in its opposite angle in the first triangle (vertical angles are equal). This means that the first triangle has angles of 38 and 60 degrees, so subtract those both from 180, giving you 82 degrees for that answer.
In a recent year, 17.3% of all registered doctors were female. If there were 41,000 female registered doctors that year, what was the total number of registered doctors?
Round your answer to the nearest whole number. PLEASE HELP DUE IN 30 MINUTES!!!
The total number of registered doctors are estimated as 236,995.
What is meant by percentage?A percentage is a relative value that represents the hundredth part of any quantity. One percent (symbolized 1%) is one hundredth part; thus, 100 percent signifies the entire amount and 200 percent specifies twice this same given amount.
The concept of cumulative percentage (percentile) is widely used in statistics. For example, a student who achieves the 83rd percentile on an investigation has outperformed 83 percent of the students with and who a comparison is made. The likelihood of an event occurring can be expressed as a percentage. (or fraction).Now, as per the given question;
It says, from all the registered doctors 17.3% is female doctors.
Now, let use assume that the total number of registered doctors be 'x'.
Then, 17.3% of this x will give 41,000 female doctors.
So, the equation will form as;
17.3% of x = 41,000
Or, (17.3×x)/100 = 41,000
x = (41,000×100)/17.3
x = 236,994.21
x = 236995 (nearest whole number)
Therefore, the total number of the registered doctors are estimated as 236995.
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now find the components nx and ny of n⃗ in the tilted coordinate system of part b. express your answer in terms of the length of the vector n and the angle θ , with the components separated by a comma.
The components are Nx= Ncosθ and Ny= -Nsinθ
What is a Vector?We know that the vector quantities are those quantities that have magnitude as well as direction.
Each vector quantity can be divided into two parts a horizontal and vertical component, the vertical component is known as the sine component while the horizontal component is known as the cosine component.
A vector component is the product of its length and the component angle.
Generally, F sinθ is the vertical component and F cosθ is the horizontal component,
Now, from the diagram the horizontal component of vector 'r' is
Nx= Ncosθ
and, the vertical component will be
Ny= -Nsinθ
this is in the opposite direction
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diamond problem for -2 and -5
Step-by-step explanation:
if I understand you correctly, then let's call the missing numbers l, r (for left and right).
and
-2 = l × r
-5 = l + r
l = -r - 5
therefore,
-2 = (-r - 5) × r = -r² - 5r
that gives us the quadratic equation
-r² - 5r + 2 = 0
for the general solutions
x = (-b ± sqrt(b² - 4ac))/(2a)
we have here
a = -1
b = -5
c = 2
and x = r, of course
r = (5 ± sqrt(25 - 4×-1×2))/(2×-1) =
= (5 ± sqrt(25 + 8))/-2 = (5 ± sqrt(33))/-2
r1 = (5 + sqrt(33))/-2 = -5.372281323...
r2 = (5 - sqrt(33))/-2 = 0.372281323...
as l = -r - 5, we see that r1 = l2, and r2 = l1.
but these are the only solutions.
there are no integer number solutions.
Correct to 2 decimal places, the volume of a solid cube is 3.37 m³. Calculate the upper bound for the surface area of the cube.
the upper bound for the surface area of the cube. is 14 m².
Volume of cube = 3.37 m³
We know the formula is:
V = a³ (where a is the side of the cube)
a³ = 3.37 m³
Cube rooting both the sides, we get that:
a = ∛3.37 m
Surface area will be:
A = 6 a²
A = 6 (∛3.37 m)²
A =6 (2.25 m²)
A = 13.5 m²
A ≈ 14 m²
Therefore, we get that, the upper bound for the surface area of the cube. is 14 m².
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When the signs are of the integers the same, 1.__________
the integers and copy the 2.) ________ sign. When the signs are
3,) ____________, subtract them and use the sign of the number
with the greater 4) _________. If we add two same numbers with
different signs, then the answer is equal to 5.) ___________.
The sum of two negative integers is a 6. )_________ integer. The
sum of two positive integers is a 7.) ___________ integer.
When the signs of the integers are the same, 1) add the integers and copy the 2) same sign. When the signs are 3) different, subtract them and use the sign of the number with the greater 4) absolute value. If we add two same numbers with different signs, then the answer is equal to 5) zero . The sum of any two negative integers is always a 6. )negative integer. The sum of any two positive integers is a 7) positive integer.
Integers are a subset of real numbers that contains all rational numbers except decimals or fractions
When the signs are the same, add the integers and copy the same sign.
Examples: (+2) + (+8) = +10
-1 + (-4 )= -5
When the signs are different, we subtract and use the sign of the number with the bigger absolute value.
Examples; +12 + (-4) = +8
-12 + (+4) = -8
If we add two same numbers with different sign then the answer is equal to zero.
Examples: +5+ (-5) = 0
-1 + +1 = 0
The sum of any two negative integers is a always a negative integer.
Examples: -3 + (-5) = -8
-16 + (-10) = -26
The sum of any two positive integers is a always a positive integer.
Examples: +12 + +56 = +68
+35 + + 15= +50
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bernardo randomly picks 3 distinct numbers from the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ and arranges them in descending order to form a 3-digit number. silvia randomly picks 3 distinct numbers from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$ and also arranges them in descending order to form a 3-digit number. what is the probability that bernardo's number is larger than silvia's number? (a) $\frac{47}{72}$ (b) $\frac{37}{56}$ (c) $\frac{2}{3}$ (d) $\frac{49}{72}$ (e) $\frac{39}{56}$
Answer:
Step-by-step explanation:
hii ,myself neha and I love animals , that's why I love my friends .
Answer:
finding if kg DJ of CM ignor
Step-by-step explanation:
Yesterday, between noon and midnight, the temperature dropped by 28.4°F. If the temperature was -1.9°F at midnight, what was it at noon?
Answer:
n= 26.5
Step-by-step explanation:
Comment
You need some sort of formula for this question. But you more or less have to invent it.
Formula
Temperature midnight = noon - temperature drop
Givens
temperature drop = 28.4
temperature midnight = -1.9
Temperature noon = x
Solution
-1.9 = x - 28.4 Add 28.4 to both sides
-1.9 + 28.4 = x-28.4+28.4 Combine
Answer
26.5 = x
Write an equation in slope intercept form for the line that is parallel to y= 2/5x-2 and passes through the point (-20,-7). Show your work (PLEASE ANSWER ASAP)
Answer:
y = 2/5x + 1
Step-by-step explanation:
If two lines are parallel, their slopes are equal
so the slope would be 2/5
if y = -7, x = -20, m = 2/5
slope-intercept form:
y = mx + b
-7 = 2/5(-20) + b
-7 = -8 + b
b = 1
then y = 2/5x + 1
Find the value of j. Show all steps to the solution and give reason to your calculations
Answer:
j=50°
Step-by-step explanation:
10x-20=5x-3+4x-2( ext angle of ∆)
10x-5x-4x=-3-2+20
x= 15
substitute the value if x
10(15)-20+ j=180 ( sum of angles in straight line)
130+j=180
j=180-130
j=50°
Which of the following data sets has the smallest standard deviation and provides correct reasoning as to why it has the smallest standard deviation?
A) {-2, -1, 0, 1, 2} because the distribution of values is symmetrical around zero.
B (99.8, 99.9, 100, 100.1, 100.2} because the range of values is clustered very close to the mean.
c {9, 9.5, 10, 10.5, 11} because the difference between successive values is constant.
(80, 93, 100, 110, 118) because the sample mean is equal to the true mean of the population
Answer: is #b
Step-by-step explanation:
A waiter earned $69.81 on a shift, and then bought himself a discounted meal for
$4.75. How much did he have left over, to the nearest dollar?
He had about $
Answer:$65
Step-by-step explanation:69.81-4.75=65.06
65.06->65
this should be EASY! just got a load of easy homework big its A LOT someone help
Answer: 1053.7225
Step-by-step explanation:
WILL GIVE BRAINLIEST need help asap
What will be the location of the y value of R' after using the translation rule (x + 4, y - 7), if the pre-image R is located at ( -17, -3)
Answer:
(-13, -10)
Step-by-step explanation:
Your original point is (-17, -13) The instruct tell you to move the point 4 units to the right and down 7 units.
-17 + 4 = -13
-3 - 7 = -10
0.5(7d+4)=7−1.5d ..............................
Answer:
d=1
Step-by-step explanation:
First let's simplify the first equation, 0.5(7d+4) by applying the distributive property
0.5(7d+4)
(0.5 x 7d) + (0.5 x 4)
3.5d+2
Now let's move all terms containing d to the left side of the equation
So add 1.5d to the left
3.5d+2 = 7-1.5d
3.5d+2+1.5d=7
5d+2=7
Move all terms not containing d to the right side of the equation
5d+2=7
5d=7 -2
5d=5
Finally, divide each term by 5 to simplify
5d/5 = 5/5
d=1
Anika spent $38 on 9.5 gallons of fruit punch. What is the cost per gallon? p= w= %=
The required cost of the punch is $4 per gallon.
Given that,
Anika spent $38 on 9.5 gallons of fruit punch.
To determine what is the cost per gallon.
The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Total volume purchased = 9.5 gallons
Total cost = $38
Now,
The ratio of the total cost of punch to the volume of fruit punch purchases the total cost will give as the cost per gallon. So,
cost per gallon = 38 / 9.5
= $4 per gallon
Thus, the required cost of the punch is $4 per gallon.
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Absolute Value
7 |dl = 49
The length of a cell phone is 1.41.4 inches and the width is 4.44.4 inches. The company making the cell phone wants to make a new version whose length will be 1.961.96 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
61.96 inches.
Step-by-step explanation:
a line passes through the points (4, 13) and (2, 5). What is it’s equation in slope intercept form
Answer:
y = 4 x - 3
Step-by-step explanation:
Find the equation of the line in slope-intercept form with the properties:
point: p_1 = (4, 13)
point: p_2 = (2, 5)
The slope of the line through points (x_1, y_1) and (x_2, y_2) is m = (y_2 - y_1)/(x_2 - x_1):
m = (5 - 13)/(2 - 4) = (-8)/(-2) = 4
Substitute the slope m = 4 and point (x_1, y_1) = (4, 13) into the point-slope equation y - y_1 = m (x - x_1):
y - 13 = 4 (x - 4)
Add 13 to both sides:
y = 13 + 4 (x - 4)
Distribute: 4 (x - 4) = 4 x - 16:
Answer: y = 4 x - 3
Write 42 900 000 in standard form
Answer:33.1
Step-by-step explanation: 3.61 × 10-3 =33.1
Step-by-step explanation:
429 × 10⁷
hopefully it will help you
8×138
I got the Answer but I'm not sure
(tell if it is true or not ,if not pls tell the answer plsss)
Answer:
Did you mean 138/8?
If so, 17.25 is correct.
Answer:
hope it helps you
Step-by-step explanation:
thankss :) if its wrong let me know
you know that your height is 5 ft 3 in. a friend measures you three times and gets these results: 5 ft 10 in, 5 ft 9.5 in, and 5 ft 10.5 in. how can these measurements be explained
The measurements can be explained as low accuracy and high precision.
Accuracy is how close or far off a given set of measurements are to their true value.
Precision is how close or dispersed the measurements are to each other.
Given,
His height = 5 feet 3 inches
Friend measures you three times and gets these results =5 ft 10 in, 5 ft 9.5 in and 5 ft 10.5 in
Here, the measurements are closely dispersed but the measurements are far from actual measurement.
Hence, the measurements can be explained as low accuracy and high precision.
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Subtracting 5 from a number and then squaring the result gives the result 16. how to solve . please help
[tex](x-5)^2=16\\x-5=4 \vee x-5=-4\\x=9 \vee x=1[/tex]
one diagonal of a rhombus has endpoints (-10, 1) and (2, 9). what are the endpoints of the other diagonal?
The endpoints of the other diagonal are (-2, 2) and (-6, 8).
Distance formula, Algebraic expression that gives the distances between pairs of points in terms of their coordinates (see coordinate system). In two- and three-dimensional Euclidean space, the distance formulas for points in rectangular coordinates are based on the Pythagorean theorem.
Given we have a rhombus with endpoints (-10, 1) and (2, 9)
So as we already know, a rhombus is a parallelogram whose sides are equal, so the distance from say (-10, 1) to either endpoint of the other diagonal must be the same.
Distance between 2 points [tex]$\mathrm{d}=\sqrt{[-2-(-10)]^2+[2-1]^2} \Longrightarrow d=\sqrt{(-2+10)^2+(2-1)^2}$$\mathbf{d}=\sqrt{\mathbf{6 4 + 1}} \Longrightarrow d=\sqrt{65}$[/tex]
While solving with other coordinate we get [tex]$\mathbf{d}=\sqrt{(-6+10)^2+(8-1)^2}[/tex]
[tex]$\mathrm{d}=\sqrt{16+49}\\\Longrightarrow d=\sqrt{65}$[/tex]
So therefore the endpoints of the other diagonal are (-2, 2) and (-6, 8) .
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The linear equation y= mx + b contains the point (-4, 3) and is perpendicular to the line 5x + 20y = 9. What is the value of m? What is the value of b?
The value of m and b of the linear equation are 4 and 19 respectively
How to represent linear equation?The linear equation is represented as y = mx + b, contains the point (-4, 3) and is perpendicular to the line 5x + 20y = 9
Linear equation can be represented as follows:
In slope intercept form,
y = mx + b
where
m = slope or gradientb = y-interceptTherefore, the linear equation y = mx + b contains the point (-4, 3) and is perpendicular to the line 5x + 20y = 9.
Perpendicular lines follows the following rules:
m₁ m₂ = -1
Therefore, let's find the slope of the second equation and use it to find the slope of the linear equation that passes through (-4, 3).
5x + 20y = 9
20y = -5x + 9
y = -1 / 4 x + 9 / 20
Hence,
- 1 / 4 m₂ = - 1
m₂ = 4
Therefore, let's find the equation since we have gotten the slope.
y = 4x + b
It's passing through (-4, 3)
3 = 4(-4) + b
3 = -16 + b
b = 3 + 16
b = 19
Therefore, the value of m and b of the linear equation are 4 and 19 respectively
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Robert is preheating his oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 25° per minute after being turned on. What is the temperature of the oven 10 minutes after being turned on? What is the temperature of the oven t minutes after being turned on?
The temperature of the oven 10 minutes after being turned on will be 315°.
The temperature of the oven t minutes after being turned on will be 65 + 25t
How to compute the value?The temperature of the oven 10 minutes after being turned on will be:
= 65 + (25 × t)
where t = number of minute
= 65 + (25t)
= 65 + 25(10)
= 65 + 250
= 315°
The temperature of the oven 10 minutes after being turned on will be 315°.
The temperature of the oven t minutes after being turned on will be:
= 65 + (25 × t)
= 65 + 25t
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