Rectangle ABCD is graphed on the coordinate plane. The following are the vertices of the rectangle:A(2,0),B(6,0),C(6,7),D(2,7). What is the area of Rectangle ABCD

Answer:

Part 1) The measure of angle PSL is 45°

Part 2) The measure of angle XYZ is 70°

Part 3) The measure of angle HJZ is 100°

Part 4) The measure of angle PHL is 120°

Part 5) The measure of angle WXZ is 140°

Part 6) The measure of angle UTG is 62°

Step-by-step explanation:

Part 1) Find the measure of angle PSL

we know that

∠PSL+∠LSM=90° -----> by complementary angles

we have

∠LSM=45°

substitute

∠PSL+45°=90°

∠PSL=45°

Part 2) Find the measure of angle XYZ

we know that

∠WYX+∠XYZ=180° -----> by supplementary angles

we have

∠WYX=110°

substitute

110°+∠XYZ=180°

∠XYZ=70°

Part 3) Find the measure of angle HJZ

we know that

∠HJZ=∠HJK+∠KJZ

we have

∠HJK=20°

∠KJZ=80°

substitute

∠HJZ=20°+80°=100°

Part 4) Find the measure of angle PHL

we know that

∠PHL=∠PHS+∠SHL

we have

∠PHS=46°

∠SHL=74°

substitute

∠PHL=46°+74°=120°

Part 5) Find the measure of angle WXZ

we know that

∠WXZ=∠WXY+∠YXZ

we have

∠WXY=15°

∠YXZ=125°

substitute

∠WXZ=15°+125°=140°

Part 6) Find the measure of angle UTG

we know that

∠UTG=∠ATG-∠ATU

we have

∠ATG=120°

∠ATU=58°

substitute

∠UTG=120°-58°=62°

Answer:

0

Step-by-step explanation:

Example : [tex]\frac{2}{5} -  \frac{2}{5}[/tex] = 0

Answer:

Step-by-step explanation:

We have:

two trapezoids with bases 15ft and 7ft and height 5ft.

four rectangles 5ft × 11ft, 15ft × 11ft, 9.4ft × 11ft and 7ft × 11ft.

The formula of an area of a trapezoid:

[tex]A_t=\dfrac{b_1+b_2}{2}\cdot h[/tex]

b₁, b₂ - bases

h - height

Substitute:

[tex]A_t=\dfrac{15+7}{2}\cdot5=\dfrac{22}{2}\cdot5=(11)(5)=55\ ft^2[/tex]

The formula of an area of a rectangle:

[tex]A_r=lw[/tex]

l - length

w - width

The dimensions of rectangle l × w

Subtitute:

[tex]A_1=(5)(11)=55\ ft^2\\\\A_2=(15)(11)=165\ ft^2\\\\A_3=(9.4)(11)=103.4\ ft^2\\\\A_4=(7)(11)=77\ ft^2[/tex]

The surface area of the figure:

[tex]S.A.=2A_t+A_1+A_2+A_3+A_4\\\\S.A.=2(55)+55+165+103.4+77=510.4\ ft^2[/text]

Answer:

|x| + |y| = 29

Step-by-step explanation:

We have been given the expression;

|x| + |y|

We are required to evaluate the above expression if;

x = 16 and y = 13

The parallel vertical lines imply that we are dealing with the absolute value of x and y;

|x| + |y| = |16| + |13|

           = 16 + 13

           = 29

Answer:

The correct answer is 29

Step-by-step explanation:

Points to remember

|x| = x

|-x| = x

It is given an expression, |x| + |y|

To find the value of given expression

|x| + |y|  if x = 16 and y = 13

Substitute the value of x and y in the above expression,

|x| + |y| = |16| + |13|

 = 16 + 13 = 29

Therefore the correct answer is 29

Answer:

M2

Step-by-step explanation:

duh

Answer:

9/20

Step-by-step explanation:

You set the fraction up at first as 45/100. Then you know that 5 goes into each so you divide by 5 [tex]\frac{45}{100} /5[/tex]

45/5=9

100/5=20

You get 9/20, and this is in simplest form.

0.45/1

Then multiply top and bottom by 100.

45/100

Then simplify!

45/100 divide top and bottom by 5.

9/20

Answer:

Infinitely many solutions / All real numbers

Step-by-step explanation:

2(3x+5)=6x+10

Then, Distribute

6x+10=6x+10

Therefore, it is infinitely many solutions / all real numbers

For this case we must solve the following equation:

[tex]2 (3x + 5) = 6x + 10[/tex]

We apply distributive property to the left side of the equation:

[tex]6x + 10 = 6x + 10[/tex]

It is observed that we have an identity, that is, the terms on the right side are equal to the terms on the left side of the equation. Then, the equation has infinite solutions

Answer:

Infinite solutions

Answer:

c. 32

Step-by-step explanation:

Answer:

[tex]y=\frac{1}{36}x^2[/tex]

Step-by-step explanation:

The focus of the parabola is (0,9)

and the directrix is y=-9.

The equation of this parabola is given by:

[tex]x^2=4py[/tex]

The vertex of this parabola is at the origin.

The value of p is the distance from the vertex to the focus.

p=9-0=9

The equation of the parabola is

[tex]x^2=4(9)y[/tex]

[tex]x^2=36y[/tex]

Or

[tex]y=\frac{1}{36}x^2[/tex]

Answer:

1)he maximum height your feet will be above the ground is 12

2)Will you be able to dunk the ball= yes

Step-by-step explanation:

Given:

In order to dunk the basket ball, height needed to jump= 2.5 feet

The height that your feet need to be of the ground is given by the function h(t)= -16t^2+12

1) the maximum height your feet will be above the ground=?

Given function of height,h(x)=-16t^2+12

finding maximum of the above function

The maximum of any function written in form of ax^2+bx+c is given by

max= c - (b2 / 4a)

Putting values c=12, b=0 and a=16, we get

max= 12-(0^2/4(-16))

      = 12 -0

      =12 feet

he maximum height your feet will be above the ground is 12 feet.

2)  Will you be able to dunk the ball=?

As the maximum height the feet will be above the ground is 12 feet which is greater than the height needed to jump in the air to dunk the ball 2.5 feet  i.e.

12>2.25

hence yes you will not be able to dunk the ball !

Check the picture below.

[tex]\bf \displaystyle\int\limits_{-2}^{2}~[\stackrel{\textit{above function}}{(10-x^2)}~~-~~\stackrel{\textit{below function}}{(x^2+2)}]dx\implies \int\limits_{-2}^{2}~(10-x^2-x^2-2)dx \\\\\\ \displaystyle\int\limits_{-2}^{2}~(8-2x^2)dx\implies \left. 8x\cfrac{}{} \right]_{-2}^{2}-\left. \cfrac{2x^3}{3} \right]_{-2}^{2} \\\\\\ ([16]-[-16])~~-~~\left( \left[ \cfrac{16}{3} \right]-\left[ -\cfrac{16}{3} \right]\right)\implies (32)~~-~~\left( \cfrac{32}{3} \right) \\\\\\ \cfrac{64}{3}\implies 21\frac{1}{3}[/tex]

[tex]f(x)=2x\Rightarrow y=2x[/tex]

Hope this helps.

Brainly would help me.

Answer:

y=2x

Step-by-step explanation:

the slope-intercept formula is y=mx+b, where m is the slope(rise over run) and b is the y-intercept, which then becomes y=2(2/1 because it goes up by 2 and right by 1)x+0, or simply y=2x, hope this helps! :D

Answer:

[tex]\large\boxed{24\ cubes}[/tex]

Step-by-step explanation:

[tex]\bold{METHOD\ 1}\\\\\text{Calculate the volume of a prism:}\\\\V_{p}=(1)(2)\left(\dfrac{3}{2}\right)=3\ cm^3\\\\\text{Calculate the volume of a cube:}\\\\V_c=\left(\dfrac{1}{2}\right)^3=\dfrac{1}{8}\ cm^3\\\\\text{Calculate how many times the volume of the prism is greater}\\\text{than the volume of the cube:}\\\\\dfrac{V_p}{V_c}=\dfrac{3}{\frac{1}{8}}=3\cdot8=24[/tex]

[tex]\bold{METHOD\ 2}\\\\1cm:\dfrac{1}{2}m=1\cdot2=2\\\\2cm:\dfrac{1}{2}cm=2\cdot2=4\\\\\dfrac{3}{2}cm:\dfrac{1}{2}cm=\dfrac{3}{2}\cdot\dfrac{2}{1}=3\\\\2\cdot4\cdot3=24\ (cubes)[/tex]

Answer:

84 and 36

Step-by-step explanation:

The ratio of two numbers is 7:3.

We don't know what the numbers are, but since their ratio is 7:3, we can let the numbers be 7x and 3x. Notice that the ratio between 7x and 3x is 7x/3x = 7/3, so we still have the same ratio, 7:3.

The difference between the numbers is 48.

7x - 3x = 48

4x = 48

x = 12

7x = 7(12) = 84

3x = 3(12) = 36

The numbers are 84 and 36.

Check:

7/3 = 2.333...

84/36 = 2.333...

84 and 36 are int he same 7:3 ratio as 7:3.

84 - 36 = 48

The difference between 84 and 36 is 48 like the problem states.

This shows our answer, 84 and 36, is correct.

Hi, hope you’re having a good day today!!!

Answer:

84:36

(The explanation is really really long, so you may want to skip it, unless this is a test or you want a better understanding then, yeah)

So first, you have 7:3

Then, you have to multiply both by the same number to get an equal ratio to 7:3,

Let’s try 7*10=70 and 3*10=30 70-30=40, so you know that the answer is close,

Then, let’s try 7*11=77 and 3*11=33, subtract and you get 44. Nope, not the answer

So, finally let’s try 7*12=84 and 3*12=36, and 84-36=48!!!!

So, the answer is explained! Wait, but you still have to put them like ratios (if this chapter is ratios and proportions)

84:36 or 84 to 36, either way.

Answer:

0

Step-by-step explanation:

0 times anything is zero

ANSWER

x=-1.2 or x=1.6

EXPLANATION

The given equation is:

[tex] 5{x}^{2} - 2x - 10 = 0[/tex] Group and combine the constant terms:

[tex]5{x}^{2} - 2x = 10 [/tex]

Divide through by 5

[tex]{x}^{2} - \frac{2}{5} x = 2[/tex]

Add the square of the coefficient of x to both sides:

[tex]{x}^{2} - \frac{2}{5} x + \frac{1}{25} = 2 + \frac{1}{25} [/tex]

The left hand side is now a perfect square

[tex]( {x - \frac{1}{5} })^{2} = \frac{51}{25} [/tex]

Take square root:

[tex]{x - \frac{1}{5} }=\pm \sqrt{\frac{51}{25}} [/tex]

[tex]{x = \frac{1}{5} }\pm \frac{ \sqrt{51} }{5}[/tex]

[tex]{x = \frac{1}{5} } - \frac{ \sqrt{51} }{5} \: or \: \: {x = \frac{1}{5} } + \frac{ \sqrt{51} }{5}[/tex]

x=-1.2 or x=1.6

Answer:

C

Step-by-step explanation:

The square root of 39 is ~6.25 so 6 is closest

Answer:

2

Step-by-step explanation:

Think:  2.39 is sandwiched between the perfect squares 1 and 4.

The difference between 1 and 4 is 3.  From 1 to 2.39 is a step of 1.39; from 2.39 to 4 is a step of 1.61.  Therefore, 2.39 is closer to 1 than to 4, and we estimate 2.39 to be 2 (to the nearest integer).

Answer:

y=3/2and x =2

Step-by-step explanation:

Answer:

[tex]x=4+-2\sqrt{7}[/tex]

Step-by-step explanation:

To solve, we need to take square root of both sides first:

[tex](x-4)^2=28\\\sqrt{(x-4)^2} =+-\sqrt{28} \\x-4=+-\sqrt{28}[/tex]

Now we use the property of radical shown below to simplify square root of 28:

Property:  [tex]\sqrt{x*y}=\sqrt{x} \sqrt{y}[/tex]

Now, we have:

[tex]x-4=+-\sqrt{28}\\x-4=+-\sqrt{4*7}\\x-4=+-\sqrt{4}\sqrt{7}\\x-4=+-2\sqrt{7}[/tex]

Now we take 4 to the other side and isolate x:

[tex]x-4=+-2\sqrt{7} \\x=4+-2\sqrt{7}[/tex]

first answer choice is right.

The answer is:

The correct answer is the first option.

[tex](x-4)^{2}=4+-2\sqrt{7}[/tex]

To solve the problem, we must remember the following square root property:

[tex]\sqrt{ab}=\sqrt{a}\sqrt{b}[/tex]

So,

We are given the expression:

[tex](x-4)^{2}=28[/tex]

Now, isolating we have:

First, applying square root to both sides of the equation in order to simplify the quadratic term, we have:

[tex]\sqrt{(x-4)^{2} }=\sqrt{28}\\(x-4)=\sqrt{4*7}\\\\x=4+-(\sqrt{4}*\sqrt{7})\\\\x=4+-2\sqrt{7}[/tex]

Hence, the correct answer is the first option.

[tex](x-4)^{2}=4+-2\sqrt{7}[/tex]

Have a nice day!

Answer:

Paul purchased 23 pieces of pepperoni pizza

Step-by-step explanation:

Let pepperoni pizza pieces = x

and plain pizza pieces  = y

So, the equations will be:

AS pepperoni pizza piece is sold for $1.15 and plain pizza is sold for $0.90 and Paul paid $39.05

1.15 x + 0.90 y = 39.05    eq(1)

Paul bought total 37 pieces of pizza so,

x + y = 37      eq(2)

Solving eq(1) and (2)  we can find the pieces of pepperoni pizza bought by Paul.

Multiplying equation (2) with 1.15 and subtracting eq(1) and eq(2)

1.15 x + 0.90 y = 39.05

1.15 x + 1.15 y = 42.55

-         -              -

__________________

0 x - 0.25 y = -3.5

y = -3.5/-0.25

y = 14

Putting value of y in equation(2)

x+y = 37

x + 14 = 37

x = 37 - 14

x = 23

So, Paul purchased 23 pieces of pepperoni pizza as x represents pepperoni pizza pieces.

By setting up and solving a system of linear equations, we determined that Paul purchased 23 pieces of pepperoni pizza for Pam's party.

To determine how many pieces of pepperoni pizza Paul purchased for Pam's party from Perry's pizza parlor, we can set up a system of equations based on the cost of each piece and the total amount spent. Let x represent the number of pepperoni pizzas at $1.15 each and y represent the number of plain pizzas at $0.90 each. We have the following equations based on the given information:

x + y = 37 (total pieces of pizza purchased)

1.15x + 0.90y = $39.05 (total amount spent)

By solving these equations simultaneously, we can find the exact number of pepperoni and plain pizzas that Paul purchased. Multiplying the second equation by 100 to clear the decimals, we get:

115x + 90y = 3905

Now, multiply the first equation by 90:

90x + 90y = 3330

Subtract the modified first equation from the modified second equation:

(115x + 90y) - (90x + 90y) = 3905 - 3330

25x = 575

x = 23

Paul purchased 23 pieces of pepperoni pizza.

Answer:

(x - 3)(x + 1)(x + 5)

Step-by-step explanation:

I'd use synthetic division instead.  If we were to find the roots of the given polynomial, we could from them write the factors as well.

The divisor x + 5 corresponds to root x = -5.  Setting up synthetic div.,

-5   )   1    3    -13    -15

               -5     10    +15

      -----------------------------

           1   -2     -3      0

Since the remainder is 0, we know that -5 is a root and (x + 5) is a factor.  Moreover, we know that the coefficients of the quotient are 1, -2 and -3.

1x² - 2x - 3 can be factored:  the factors are (x - 3) and (x + 1).

So the end result for this problem is (x - 3)(x + 1)(x + 5).

Answer:

The time that the computer take to carry out one sum is 4.63 nanoseconds and the time that the computer take to carry out one product is 4.56 nanoseconds

Step-by-step explanation:

Let

x----> the time that the computer take to carry out one sum

y----> the time that the computer take to carry out one product

we know that

7x+10y=78 ------> equation A

4x+8y=55 -----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (4.625,4.563)

see the attached figure

therefore

The time that the computer take to carry out one sum is 4.63 nanoseconds

The time that the computer take to carry out one product is 4.56 nanoseconds

Answer:

x = 4

Step-by-step explanation:

Combining like terms, we get 4x = 16, and so x = 4.

Answer: The answer is 4.

Step-by-step explanation: The way I got my answer was by isolating the variable by dividing each side by factors that don't contain the variable. I also have a website that you can use to help you! (if you want it, just ask me and I can provide it to you!)

I hope this info helps you! :D

to translate a graph up you need to add the amount you want to move it to the end of the equation, not to the variable.

The answer would be y = sin x + π

Answer:

B

Step-by-step explanation:

y=sinx+pi

4 congruent sides, each 10 m, so perimeter 10+10+10+10 =

Answer: 40 m

Answer:

petunias, snapdragons, then pansy

Step-by-step explanation:

Ok first, lets find the percentage of 18 out of 40: 18/40= 0.45

The 21 out of 50= 21/50= 0.42

Lastly, 12/30= 0.40

And its very simple to put from least to greatest:

0.40, 0.42, 0.45

Hope this helped ;)

The answer is petunias, snapdragons, then pansies.

Hope this helps!

Answer:

144

Step-by-step explanation:

Ok. I love problems like this.

You just have to find the surface are of each part and add it up!

To find the surface area of a rectangle, you multiple the base and the height. To find the surface area of a triangle, you multiple the base and height, and divide by 2 (because its half of a rectangle).

Left rectangle: 3*ll=33

Middle rectangle: 4*ll=44

Right rectangle: 5*ll=55

Top triangle: 3*4=12

                      12/2=6

Bottom triangle: 3*4=12

                           12/2=6

ADD THEM ALL!!! 33+44+55+6+6=144

(Also can I please please please have brainliest? I need it to level up!)

radius is half the breadth of box ie 2.5 cm height of cylinder is length ie 15 cm

so volume of cylinder =pi(r^2)h

ie 93.75pi cm^3

The exact volume of the cylinder is 93.75pi cm^3.

The question is incomplete the complete question is,

What is the exact volume of the cylinder? Where radius is  5cm and height is 15cm. Enter your answer, in terms of π, in the box.

We have given that,

The radius is half the breadth of the box ie 2.5 cm height of the cylinder is length ie 15 cm.

We have to determine the  volume of a cylinder

Volume of the cylinder =pi(r^2)h

Use the given value in the above formula so we get,

[tex]V=\pi (2.5)^2(15)\\[/tex]

V= 93.75pi cm^3

Therefore the exact volume of the cylinder is 93.75pi cm^3.

To learn more about the volume of the cylinder visit:

https://brainly.com/question/9554871

#SPJ2

Answer:

D. Cluster sampling

Step-by-step explanation:

Dealing with the whole population can be cumbersome, time-consuming and very expensive. In order to make it more feasible for researchers they can employ cluster sampling. In cluster sampling, the population are divided into precincts, or gropus. The researcher then selects the groups that will be included in the study through simple random samping or systematic sampling. The researcher can opt to choose let the whole cluster or group to participate in the study or they can randomly select the individuals within the groups.

Answer:

d

Step-by-step explanation: