(THIS IS A TEST I NEED HELP)
In the rectangular prism, PQ is the diagonal. Find the length of
PQ given PR = 7, RS = 4, and QS = 4.
A 4
B 9
C 12
D 15

[tex]here \: y \: by \: itself \: means \\ \: y \: stands \: alone \: with \: \\ nothing \: nearby \: it .\\ \\ hope \: it \: helps..[/tex]

Answer/Step-by-step explanation:

✔️Using trigonometric ratio, find width of the rectangle, BD:

Thus:

[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]

Where,

[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]

Opposite = BD

Adjacent = 7 cm

Plug in the values

[tex] \sqrt{3} = \frac{BD}{7} [/tex]

Multiply both sides by 7

[tex] 7\sqrt{3} = BD [/tex]

[tex] BD = 7\sqrt{3} [/tex]

✔️Using trigonometric ratio, find height of the rectangle, BF:

Thus:

[tex] tan(\theta) = \frac{opposite}{adjacent} [/tex]

Where,

[tex] tan(\theta) = tan(60) = \sqrt{3} [/tex]

Opposite = 6 cm

Adjacent = BF

Plug in the values

[tex] \sqrt{3} = \frac{6}{BF} [/tex]

[tex] BF = \frac{6}{\sqrt{3}} [/tex]

Rationalize

[tex] BF = \frac{6 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}} [/tex]

[tex] BF = \frac{6\sqrt{3}}{3} [/tex]

[tex] BF = 2\sqrt{3} [/tex]

✔️Perimeter of rectangle BDEF:

Perimeter = 2(BD + BF)

Plug in the values

[tex] Perimeter = 2(7\sqrt{3} + 2\sqrt{3}) [/tex]

[tex] Perimeter = 2(9\sqrt{3}) [/tex]

[tex] Perimeter = 18\sqrt{3} [/tex]

✔️Area of the rectangle BDEF:

Area = BD × BF

Plug in the values

[tex] Area = 7\sqrt{3} \times 2\sqrt{3} [/tex]

[tex] Area = 7 \times 2\sqrt{3 \times 3} [/tex]

[tex] Area = 14 \times 3 [/tex]

[tex] Area = 42 [/tex]

The biggest named number that we know is googolplex, ten to the googol power, or (10)^(10^100). That's written as a one followed by googol zeroes.

Have a Merry Christmas!

Answer:

12 staples

Step-by-step explanation:

So the first thing we have to do is find the G.C.D (Greatest Common Denominator) between 21/4 and 7/16 which of course is 16 so your new fractions would be 84/16 and 7/16.

Now we have to divide both numbers I just used a fraction calculator for this but basically you multiply 84/16 by the reciprocal of 7/16 which is 16/7 and simplify which equals 12.

So it would take 12 staples to bind the booklet

Answer:

yes, the slope is the same throughout the table

Step-by-step explanation:

Answer:

Yes, the graph shown is a proportional relationship.

Step-by-step explanation:

If you divide the distance (6) by the time (1) you get the same thing (6). Repeat for all the terms in the graphs. Since 6/1 is 6, 12/2 is 6, 18/3 is 6 and 24/4 is 6, The relationship is proportional.

Answer:

69

Step-by-step explanation:

yes

Answer:

Step-by-step explanation

4-6 people left in the room

✨✨Hope it helps✨✨

Brainliest?.

Answer:

14 sweets

Step-by-step explanation:

5x+35

x=7

7*4=28

(28-10)/2=7

7+7=14

Answer:

607,420

Step-by-step explanation:

hope it is correct and helps

Answer: The point (5,7) is on the line 5x+6y = 67

=====================================================

Explanation:

(5,7) means x = 5 and y = 7 pair up

Plug in those values to get...

5x + 6y = 67

5*5 + 6*7 = 67

25 + 42 = 67

67 = 67

We get the same number on both sides after fully simplifying. This means the equation is true. A true equation in the last step means the first equation is true when (x,y) = (5,7).

Therefore, the point (5,7) is a solution and it is on the line 5x+6y = 67.

Answer:

hb=2.5

Step-by-step explanation:

base = 4

area  =  5

Answer:

A. -4< n<8 B.-4< n< 8

Step-by-step explanation:

Answer:

D.-4<n<8

Step-by-step explanation:

Answer:

7x+1

Step-by-step explanation:

Use the distributive property to multiply 7 by x−1.

7x−7+8

Add −7 and 8 to get 1.

7x+1

Answer: 100

Step-by-step explanation:

It is an alternate interior angle.

Answer:

0.3

Step-by-step explanation:

Answer:

3.0

Step-by-step explanation:

Here we have a rectangle split into ten parts with 7/10 shaded in blue. The question asks what decimal represents the portion, alright, let's go down the list.

0.003 is also known as 3 thousandths, meaning that we would need a thousand little squares as our figure. Clearly this isn't the case, so 0.003 is wrong.

0.03 is also known as 3 hundredths, meaning  that we would need a hundred little squares as our figure, this also isn't the case, so 0.03 is wrong.

0.3 is known as 3 tenths, yes this could represent our figure, but it doesn't represent the finished portion, which would be 1.0, this means that only one part will be shaded in the figure we have now, leaving it to be wrong.

This leaves us with 3.0

Answer:

In geometry, an angle can be defined as the figure formed by two rays meeting at a common end point. An angle is represented by the symbol ∠. ... Angles are measured in degrees, using a protractor.

Step-by-step explanation:

Answer: -2

Step-by-step explanation: 4-8= -4 then it ends up being -2r-4=0

Then you add 4 to 0 so -2r=4 then divide

Answer:

1 4/5 meters

Step-by-step explanation:

Juniors brother = 1 1/2 meters tall

Junior is 1 1/5 of his brother height

Junior = 1 1/5 of 1 1/2

= 6/5 × 3/2

= 6 * 3 / 5 * 2

= 18/10

= 1 8/10

= 1 4/5 meters

Junior is 1 4/5 meters tall

Answer:

1 4/5

Step-by-step explanation:

its on khan (: trust me

Answer:

2.275%

Step-by-step explanation:

We start by calculating the z-score

Mathematically;

z-score = (x-mean)SD

here, x = 70.5

mean = 65.5

SD = 2.5

Substituting these values;

z = (70.5-65.5)/2.5

= 5/2.5 = 2

So we want to calculate the probability that;

P( z> 2)

We check the standard normal distribution table for this

That will be

0.02275

In percentage, this is 2.275 %

Answer:

Anna has $1460

Betty has $1060                                                      

Step-by-step explanation:

let Anna's money be x

and Betty's money be y

If Anna gave Betty $200, then they would have the same amount of money

Anna's money will reduce by 200

x=x-200

Betty's money will increase by 200

y= y+200

if they have the same amount of money, the difference will be zero

x-200=y+200

x-200-y-200=0

x-y-400=0

x-y=400--------------1

this means that Anna has $400 more than Betty

if Betty gave Anna $220, Anna would then have twice as much as Betty.

Betty's money will reduce by 220

y=y-220

Anna's money will increase by 220

x=x+220

Anna's money will double that of Betty's

x+220=2(y-220)

x+220= 2y-440

x=2y-440-220

x=2y-660--------------------2

put x= 2y-660 in eqn 1

(2y-660)-y=400-------------------------1

2y-y=400+660

y= 1060

so Betty has $1060

put y= 1060 in eqn 1

x-y=400

x-1060=400

x=400+1060

x=1460

so Anna has $1460

[tex]\LARGE\leadsto\sf JK=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

[tex]\LARGE\leadsto\sf \sqrt {(1-1)^2+(9-5)^2}[/tex]

[tex]\LARGE\leadsto\sf \sqrt {(0)^2+(4)^2}[/tex]

[tex]\LARGE\leadsto\sf \sqrt {0+16}[/tex]

[tex]\LARGE\leadsto\sf \sqrt {16}[/tex]

[tex]\LARGE\leadsto\sf JK=4units [/tex]

Answer:

CD = 7

Step-by-step explanation:

Given that the triangles are congruent, then corresponding sides are congruent, that is

CD = AB , substitute values

3y + 1 = 15 - 4y ( add 4y to both sides )

7y + 1 = 15 ( subtract 1 from both sides )

7y = 14 ( divide both sides by 7 )

y = 2

Thus

CD = 3y + 1 = 3(2) + 1 = 6 + 1 = 7

Answer:

Quadratic polynomial can be factored using the transformation ax  

2

+bx+c=a(x−x  

1

​  

)(x−x  

2

​  

), where x  

1

​  

 and x  

2

​  

 are the solutions of the quadratic equation ax  

2

+bx+c=0.

−x  

2

−3x+5=0

All equations of the form ax  

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±  

b  

2

−4ac

​  

​  

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x=  

2(−1)

−(−3)±  

(−3)  

2

−4(−1)×5

​  

​  

Square −3.

x=  

2(−1)

−(−3)±  

9−4(−1)×5

​  

​  

Multiply −4 times −1.

x=  

2(−1)

−(−3)±  

9+4×5

​  

​  

Multiply 4 times 5.

x=  

2(−1)

−(−3)±  

9+20

​  

​  

Add 9 to 20.

x=  

2(−1)

−(−3)±  

29

​  

​  

The opposite of −3 is 3.

x=  

2(−1)

3±  

29

​  

​  

Multiply 2 times −1.

x=  

−2

3±  

29

​  

​  

Now solve the equation x=  

−2

3±  

29

​  

​  

 when ± is plus. Add 3 to  

29

​  

.

x=  

−2

29

​  

+3

​  

Divide 3+  

29

​  

 by −2.

x=  

2

−  

29

​  

−3

​  

Now solve the equation x=  

−2

3±  

29

​  

​  

 when ± is minus. Subtract  

29

​  

 from 3.

x=  

−2

3−  

29

​  

​  

Divide 3−  

29

​  

 by −2.

x=  

2

29

​  

−3

​  

Factor the original expression using ax  

2

+bx+c=a(x−x  

1

​  

)(x−x  

2

​  

). Substitute  

2

−3−  

29

​  

​  

 for x  

1

​  

 and  

2

−3+  

29

​  

​  

 for x  

2

​  

.

−x  

2

−3x+5=−(x−  

2

−  

29

​  

−3

​  

)(x−  

2

29

​  

−3

​  

)

EVALUATE

5−3x−x  

2Quadratic polynomial can be factored using the transformation ax  

2

+bx+c=a(x−x  

1

​  

)(x−x  

2

​  

), where x  

1

​  

 and x  

2

​  

 are the solutions of the quadratic equation ax  

2

+bx+c=0.

−x  

2

−3x+5=0

All equations of the form ax  

2

+bx+c=0 can be solved using the quadratic formula:  

2a

−b±  

b  

2

−4ac

​  

​  

. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x=  

2(−1)

−(−3)±  

(−3)  

2

−4(−1)×5

​  

​  

Square −3.

x=  

2(−1)

−(−3)±  

9−4(−1)×5

​  

​  

Multiply −4 times −1.

x=  

2(−1)

−(−3)±  

9+4×5

​  

​  

Multiply 4 times 5.

x=  

2(−1)

−(−3)±  

9+20

​  

​  

Add 9 to 20.

x=  

2(−1)

−(−3)±  

29

​  

​  

The opposite of −3 is 3.

x=  

2(−1)

3±  

29

​  

​  

Multiply 2 times −1.

x=  

−2

3±  

29

​  

​  

Now solve the equation x=  

−2

3±  

29

​  

​  

 when ± is plus. Add 3 to  

29

​  

.

x=  

−2

29

​  

+3

​  

Divide 3+  

29

​  

 by −2.

x=  

2

−  

29

​  

−3

​  

Now solve the equation x=  

−2

3±  

29

​  

​  

 when ± is minus. Subtract  

29

​  

 from 3.

x=  

−2

3−  

29

​  

​  

Divide 3−  

29

​  

 by −2.

x=  

2

29

​  

−3

​  

Factor the original expression using ax  

2

+bx+c=a(x−x  

1

​  

)(x−x  

2

​  

). Substitute  

2

−3−  

29

​  

​  

 for x  

1

​  

 and  

2

−3+  

29

​  

​  

 for x  

2

​  

.

−x  

2

−3x+5=−(x−  

2

−  

29

​  

−3

​  

)(x−  

2

29

​  

−3

​  

)

EVALUATE

5−3x−x  

2

Step-by-step explanation:

Answer:

I think its 5 feet

Step-by-step explanation:

I used Pythagorean theorem

Answer:

A≈50.27

Or 16π

Step-by-step explanation:

Answer:

50.24cm

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

Answer:

63

Step-by-step explanation:

21x3=63

Answer:

2<x<3

Step-by-step explanation:

the first one

Answer:

:

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The system of equations representing the rates for two duplicating companies are -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have the rates for two duplicating companies. There are two different rates as-

[1] > initial fee of $5 and $0.06 per page.

[2] > initial fee of $10.00 and $0.04 per page.

For the [1] company, we can write the equation as -

C[1] = 5 + 0.06x

For the [2] company, we can write the equation as -

C[2] = 10 + 0.04x

So, the system of equations will be -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

Therefore, the system of equations representing the rates for two duplicating companies are -

C[1] = 5 + 0.06x

C[2] = 10 + 0.04x

To solve more questions on equation modelling, visit the link below-

brainly.com/question/9144182

#SPJ2

Answer:

(-2, -8)

x = -2

y = -8

General Formulas and Concepts:

Pre-Algebra

Algebra I

Step-by-step explanation:

Step 1: Define systems

13x - 6y = 22

x = y + 6

Step 2: Solve for y

Substitution

Step 3: Solve for x

Answer:

42592

Step-by-step explanation:

Answer:42592

Step-by-step explanation: So what you do is do 88 times 88/22 and so on :)