Two rectangles can be similar, but that's not always guaranteed.
In fact, similar shapes have the same angles and correspondant sides in proportion.
All rectangles will always have four right angles, so we only have to worry about the sides.
Let [tex]a,b[/tex] be the sides of a rectangle, with [tex]a\leq b[/tex]. Let [tex]c,d[/tex] be the sides of a rectangle, with [tex]c\leq d[/tex].
Then, the two rectangles are similar if and only if
[tex]a\div c=b\div d[/tex]
So, for examples, a rectangle with dimensions 3 and 7 is similar to a rectangle with sides 6 and 14 (both sides have been doubled), but it's not similar to a rectangle with sides 6 and 21 (one side has been doubled, the other has been tripled).
A set of middle school student heights are normally distributed with a mean of 150150150 centimeters and a standard deviation of 202020 centimeters. Darnell is a middle school student with a height of 161.4161.4161, point, 4 centimeters. What proportion of student heights are lower than Darnell's height?
Answer:
71.57% of student heights are lower than Darnell's height
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this question, we have that:
[tex]\mu = 150, \sigma = 20[/tex]
Darnell has a height of 161.4 centimeters. What proportion of student heights are lower than Darnell's height?
This is the pvalue of Z when X = 161.4.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{161.4 - 150}{20}[/tex]
[tex]Z = 0.57[/tex]
[tex]Z = 0.57[/tex] has a pvalue of 0.7157
71.57% of student heights are lower than Darnell's height
Answer:
0.7157
Step-by-step explanation:
Darnell's height is 161.4 - 150 = \goldD{11.4}161.4−150=11.4161, point, 4, minus, 150, equals, start color #e07d10, 11, point, 4, end color #e07d10 relative to the mean.
This is \dfrac{\goldD{11.4}}{20} = \blueD{0.57}
20
11.4
=0.57start fraction, start color #e07d10, 11, point, 4, end color #e07d10, divided by, 20, end fraction, equals, start color #11accd, 0, point, 57, end color #11accd standard deviations relative to the mean. This is Darnell's z-score.
Hint #22 / 4
We want to find the proportion of student heights below a z-score of \blueD{0.57}0.57start color #11accd, 0, point, 57, end color #11accd:
ASAP
In the expression 3x + 5, the value of 3 is the best described as:
A. The constant
B. The operation
C. The variable
D. The coefficient
Answer:
D) The coefficient
Explanation:
The coefficient is the number placed before the variable in the expression.
In 3x x is the variable and 3 is the number placed before it making it the coefficient.
26, 21, 27, 33, 24, 29
Range:
Answer:
The range is 12
Step-by-step explanation:
the range is the biggest number minus the smallest
the biggest number is 33
the smallest number is 21
so 33-21=12 so
The range is 12
Answer: 12
Step-by-step explanation: The range is the difference between the greatest number in the data set and the least number in the data set which in this case is 33 - 21 or 12.
So the range of this data set is 12.
function f whose zeros are -3 and -4 f(x) please I need help right now
Answer:
f(x) = x² + 7x + 12
Step-by-step explanation:
Given that the zeros are x = - 3 and x = - 4, then the factors are
(x - (- 3)) and (x - (- 4)), that is (x + 3) and (x + 4)
f(x) is the product of the factors, that is
f(x) = (x + 3)(x + 4) ← expand using FOIL
f(x) = x² + 7x + 12
3 POINSSSSSS
The bar graph shows the results of rolling a number cube (a die) 50 times. What is the probability of rolling an odd number? How does this compare with the theoretical probability of rolling an odd number?
Experimental Probability. Theoretical Probability
P(odd) = % P(odd) = %
Answer:
see below
Step-by-step explanation:
Experimental means what actually happened
P(odd) = (number of 1 + number of 3 + number of 5) / total
= (10+8+8) / 50
= 26/50
= 13/25 = 52%
Theoretical means what we expect to happen
P (odd) = (number of 1 + number of 3 + number of 5) / total
=(1+1+1)/6
=1/2 = 50%
We rolled an odd just a little more than the expected amount of times
Answer:
yes
Step-by-step explanation:
A total of 354 tickets were sold for the school play. They were either adult tickets or student tickets. The number of student tickets sold was two times the number of adult tickets sold. How many adult tickets were sold?
There are 118 adult tickets sold
This is because 354/3 =118
and 118+118=236
236 are the child tickets
therefore 118 are the adult tickets.
Hope this helped!
The total number of adult ticket sold is 118 tickets.
Application of linear equation.
Let's write "x" to represent how many adult tickets were sold.
The information provided indicates that there were twice as many student tickets sold as adult tickets. The quantity of student tickets sold can therefore be stated as 2x.
There were 354 total tickets sold, which includes both student and adult tickets.
We may construct an equation based on the total number of tickets to resolve this issue:
x + 2x = 354
Combining comparable variables
3x = 354
x = 354 / 3
x = 118
118 adult tickets were consequently sold.
Learn more on linear equation here: https://brainly.com/question/12788590
#SPJ2
The circumference of a circular field is 163.28 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.
Answer:
r = 26
Step-by-step explanation:
C = 2 π r
163.28 = 2 (3.14) (r)
163.28 / 2 / 3.14
26 = r
Answer:
26 yards
Step-by-step explanation:
2πr=163.28
2×3.14×r=163.28
r=163.28÷6.28=26 yards
your garden has a perimeter of 36 feet. what is the length of missing side.
Answer:
I think the answer is 3 for 1 length side. And in you need 12 for both length sides. So the total is 36 and one side is 12. Since it's a rectangle,you now know two side lengths since they are the same,just opposite from each other. So 12 + 12 = 24. You do 36 – 24 because you need to get the total number for length which is 12. 12 divided by 2 is 6 which is one length side. You can check by doing 6 + 6 + 12 + 12 and you get 36.
Hope this helped!
Can I get brainliest?
2. Suppose that
A certain circle can be represented by the following equation. x^2+y^2+8x-16y+31=0x 2 +y 2 +8x−16y+31=0x, squared, plus, y, squared, plus, 8, x, minus, 16, y, plus, 31, equals, 0 What is the center of this circle ? ((left parenthesis ,,comma ))right parenthesis What is the radius of this circle ? units
Answer:
center = [tex](-4,8)[/tex]
Radius = 7 units
Step-by-step explanation:
Given: Equation of circle is [tex]x^2+y^2+8x-16y+31=0[/tex]
To find: Radius and center of the circle
Solution:
Equation of circle is [tex](x-a)^2+(y-b)^2=r^2[/tex]
Here, [tex](a,b)[/tex] is the center and r is the radius.
[tex]x^2+y^2+8x-16y+31=0\\\left [ x^2+2(4)x+4^2 \right ]+\left [ y^2-2(8)y+8^2 \right ]+31=4^2+8^2[/tex]
Use formula [tex](u+v)^2=u^2+v^2+2uv[/tex]
[tex](x+4)^2+(y-8)^2=16+64-31\\(x+4)^2+(y-8)^2=49=7^2[/tex]
On comparing this equation with equation of circle,
center = [tex](-4,8)[/tex]
Radius = 7 units
Answer:
center: (4,-4)
Radius: 9
Step-by-step explanation:
KHAN ACADEMY
The length and width of a rectangular patio are, (x + 7) feet and (x + 9) feet, respectively. If the area of the patio is 150 square feet, what are the dimensions of the patio? Enter the dimensions to two decimal places. The equation has real solution(s). The width (shorter dimension) of the patio is feet. The length (longer dimension) of the patio is feet.
Answer:
The width of the patio is 11.29 feet while the length of the patio is 13.29 feet
Step-by-step explanation:
Mathematically, the area of the patio can be calculated by multiplying the length by the breadth of the patio
Thus we have ;
(x + 7)(x + 9) = 150
x^2 + 7x + 9x + 63 = 150
x^2 + 16x + 63 = 150
x^2 + 16x + 63 -150 = 0
x^2 + 16x -87 = 0
we can use the quadratic formula to solve this completely
x = {-b ± √(b^2 - 4ac)}/2a
where a = 1, b = 16 and c = -87
Plugging the values we have
x = {-16 ± √(16^2 - 4(1)(-87)}/2
x = {-16 ± √(256+ 348)}/2
x = {-16 ± √(604}/2
x = (-16 + 24.58)/2 or (-16-24.58)/2
x = 4.29 or -20.29
Choosing x = -20.29 will make our dimensions negative, so we ignore it and make do with the positive value only
Thus our dimensions are 4.29 + 7 and 4.29 + 9
This is equal to 11.29 feet and 13.29 feet respectively
If f(x)=5x2−3x+8, find f(0)
Answer:
8
Step-by-step explanation:
f(x)=5x^2−3x+8
Let x=0
f(0) = 5(0) -3(0) +8
= 8
A culture started with 2,000 bacteria. After 2
hours, it grew to 2,200 bacteria. Predict how
many bacteria will be present after 19 hours.
Round your answer to the nearest whole
number.
und to four
P = Aekt
Enter the correct answer
DONE
O
?
Answer:
2450
Step-by-step explanation:
First you will divide;
200÷4=50
Then you multiply;
50×9=450
Last you add;
2000+450=2450
Hope this helps :D
Answer:
4949 is your answer
Step-by-step explanation:
Christopher drove 199.5 miles in 3.5 hours. If he drove at a constant speed, how far did he drive in one hour? *
Answer:
57 miles
Step-by-step explanation:
Answer:
57 miles
Step-by-step explanation:
divide 199.5/3.5 and you will get 57 miles
Which of the following is true of the values of x and y in the diagram below? A unit circle is shown. A radius with length 1 forms angle theta = StartFraction pi Over 4 EndFraction. The radius intersects point (x, y) on the unit circle. y < x y > x y + x = 1 StartFraction y Over x EndFraction = 1
Answer:
y/x = 1 got it right on edg
Step-by-step explanation:
Answer:
y/x = 1 on E2020
Step-by-step explanation:
Have a Great Day :)
Please help, I’m so desperate for this answer. I’ve been here for two hours and no one wants to help :/ (find x)
Answer
i can't see the image can you post it again.
Step-by-step explanation:
Answer:
29 + 64 =x which is 93 for question 2
Step-by-step explanation:
Molly wants to put a fence around an area. The fence will follow the diagram of the triangle shown below. (Look at picture) About how much fencing does Molly need?
Answer:
Step-by-step explanation:
43feet
Students in another survey were asked whether they plan to attend summer camp. Out of the 56 students in the survey, 44% said yes. Use rounding and compatible numbers to estimate how many students plan to attend summer camp.
Answer:
Students to attend camp = 56 x 44/100 = 24.64
Students to attend camp = 25
Step-by-step explanation:
Answer:
≈25 students
Step-by-step explanation:
Find out 44% of 56:
(44*56)÷100=
2464÷100=
24.64
So about 25 students out of 56 said yes, they were going to attend summer camp.
solve the inequality -6(1+2 x)> 6(2x-1)+2x
Answer:
x <0Step-by-step explanation:
hello :
-6(1+2 x)> 6(2x-1)+2x
1) divide by 6 : -(1+2 x)> (2x-1)+(1/3)x
2) multiply by 3 : -3(1+2x) >3(2x-1)+x
calculate : -3-6x > 6x-3+x
now add 3 : -6x > 6x+x
-6x > 6x+x
add 6x : 0>12x+x means : 13x <0
x <0/13 but 0/13 =0
conclusion : x <0
Noah drew a triangle so that all the sides are 5 inches long. He wants to draw a new triangle, but increase the length of each side by x inches. The perimeter of the new triangle is 24 inches.
Complete question:
Noah drew a triangle so that all the sides are 5 inches long. He wants to draw a new triangle, but increase the length of each side by x inches. The perimeter of the new triangle is 24 inches. Find the value of x and length of the new side.
Answer:
x = 3 inches
The length of the new sides of the triangle is 8 inches
Step-by-step explanation:
If each of the sides of the original triangle is 5 inches, then it is an equilateral triangle.
Let the length of each of the side of the new triangle be, A, B and C.
A = 5 + x
B = 5 + x
C = 5 + x
A + B + C = 24
(5 + x) + (5 + x) + (5 + x) = 24
15 + 3x = 24
3x = 24 -15
3x = 9
x = 9/3
x = 3
A = B = C = 5 + x = 5 + 3 = 8 inches
The length of the new sides of the triangle is 8 inches
create an equation of a line that is Direct and parallel to y= 3x + 4
Hope this helps
Answer: [tex]y=3x[/tex]
Step-by-step explanation:
parallel lines have the same slope so you can have any line that is y=3x plus a number thats not 4
EXAMPLES:
[tex]y=3x-3[/tex]
[tex]y=3x+5[/tex]
[tex]y=3x-2[/tex]
(a + 3)(a - 2) (multiplying polynomials by polynomials is the assignment, i need help lol)
Answer:
a^2 +a -6
Step-by-step explanation:
(a + 3)(a - 2)
FOIL
first: a*a = a^2
outer: -2*a = -2a
inner: 3*a =3a
Last : -2*3 = -6
Add them together
a^2 -2a+3a -6
Combine like terms
a^2 +a -6
Answer:
a² + a - 6
Step-by-step explanation:
(a + 3)(a - 2) = a² - 2a + 3a - 6 = a² + a - 6
Please answer ASAP In need of help
Answer:
5/7
Step-by-step explanation:
Billy experienced a rate of catfish to toral fish of 10/14. This is 5/7. So if this rate continues, he could expect the probability of catching a catfish to be : 5/7
Simplify the equation-
x-(-2x+4)
Jason runs 440 yards in 75 seconds.at this rate,how many minutes does it take him to run a mile
Answer:
5 minutes
Step-by-step explanation:
Do a proportion
440/75= 1760/x
cross multiply
440x=1760(75)
simplify
132000/440
A bag contains 1 yellow ball and 9 red balls. A ball is chosen at random from the bag. what is the probability of drawing a yellow ball.
Answer:
1/10
Step-by-step explanation:
10 balls in the bag, there is one yellow
Answer:
answer 1/10
Step-by-step explanation:
Which ists the steps in the correct order to fnd the medan of this data set? 24 16 23 30, 18 29 1 Put the numbers in order 2. Cross off highvlow pairs 3 Add the leftover numbers 4. Divsde the sum by 1 Pt the numbers in order 2. Cross of highlow pairs 1 Cross off hightow pars 2. Add the 3 Divsle the sum by over numbers 1 Cross of highlow pars
Answer:
1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
Step-by-step explanation:
Given:
24, 16, 23, 30, 18, 29
The ordered steps involved in Calculating the median of the data set given :
1.) put the numbers in order: This involves arranging the numbers in the dataset usually in ascending order :
16, 18,23,24,29,30
2.) Cross off high/low pairs: take out equal amount of input from both the left and right hand side. Here we have (23, 34) left
3) Add the leftover numbers: Since the values left is more than one, both values are summed, we have (23+24) = 47
4.) Divide the sum by 2 : Get the average of the two numbers to obtain the median value. Here the average is (23+24)/2 = 47/2 = 23.5
Answer:
A: 1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
Step-by-step explanation:
edg2020
Find the slope of the line passing through the points (3, 8) (7, - 7)
Answer:
[tex]-\frac{15}{4}[/tex]
Step-by-step explanation:
To find the slope or the gradient of a line you have to utilise the formula
[tex]\frac{y2-y1}{x2-x1}[/tex]
Y₂ = -7
Y₁ = 8
X₂ = 7
X₁ = 3
So,
[tex]\frac{-7-8}{7-3}[/tex]
→ Simplify
[tex]-\frac{15}{4}[/tex]
By using the given points, we will see that the slope is -15/4.
How to find the slope of a line?
If we know that a given line passes through two known points (x₁, y₁) and (x₂, y₂), then the slope can be written as:
[tex]s = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here the line passes through the points (3, 8) and (7, -7).
Using the above formula, we can see that the slope is:
[tex]s = \frac{-7 - 8}{7 - 3} = \frac{-15}{4}[/tex]
If you want to learn more about linear equations, you can read:
https://brainly.com/question/4074386
The point P= (x,-1/7) lies on the unit circle shown below. What is the value of x in simplest form?
Answer:
[tex] x^2 + \frac{1}{49} =1 [/tex]
And solving for x we got:
[tex] x^2 = 1- \frac{1}{49}[/tex]
[tex] x^2 = \frac{48}{49}[/tex]
And taking square root we got:
[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]
Step-by-step explanation:
For this case we have the following point given [tex] P(x , -1/7)[/tex]
And we want to find the value of x, since P lies on the unitray circle if we find the distance from P to the center of the unitary circle (0,0) we need to get 1. Using the definition of Euclidean distance that means:
[tex] d = \sqrt{(x -0)^2 +(-1/7 -0)^2}=1[/tex]
And if we square both sides of the last equation we got:
[tex] x^2 + \frac{1}{49} =1 [/tex]
And solving for x we got:
[tex] x^2 = 1- \frac{1}{49}[/tex]
[tex] x^2 = \frac{48}{49}[/tex]
And taking square root we got:
[tex] x = \sqrt{\frac{48}{49}}= \frac{\sqrt{48}}{7} = \frac{4\sqrt{3}}{7}[/tex]
how do you write 2x - 2y = 8 in slope-intercept form ?
Answer:
y=x-4
Step-by-step explanation:
The general scaffold for the slope intercept form is y=mx+b, where m is the slope and b is the y intercept. You can rearrange the equation that you are given like this:
2x-2y=8
-2y=-2x+8
y=x-4
Hope this helps!
Answer:
Rearrange the equation so that it is written in slope intercept form:
y=mx+b.
2x+2y=8.
2y=−2x+8.
y=−x+4.
