Find the diagonal of a square whose sides are of the given measure.
Given = 3v3

Answer:

see explanation

Step-by-step explanation:

Let ∠4 be x then ∠6 is [tex]\frac{1}{8}[/tex] x

∠4 and ∠6 are same side interior angles and are supplementary, thus

x + [tex]\frac{1}{8}[/tex]x = 180

Multiply through by 8 to clear the fraction

8x + x = 1440, that is

9x = 1440 ( divide both sides by 9 )

x = 160

Hence ∠4 = 160° and ∠6 = 160° ÷ 8 = 20°

Answer:

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]

Step-by-step explanation:

From the graph, we can say that

[tex]m \angle 6 + m \angle 4 = 180 \°[/tex]

Because they are consecutive interior angles, and they sum 180° by definition. So, the reason of third statement is "by definition of consecutive interior angles".

We already know that

[tex]m \angle 6 = \frac{1}{8} \times m \angle 4[/tex]

But,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 = 180\° - m \angle 4[/tex]

Replacing this, we have

[tex]180\° - m \angle 4=\frac{1}{8}(m \angle 4)\\(\frac{1}{8}+1) (m\angle 4)=180\°\\\frac{9}{8}(m\angle 4) = 180 \°\\ m \angle 4 = \frac{180(8)}{9}= 160\°[/tex]

Then,

[tex]m \angle 6 + m \angle 4 = 180 \°\\m \angle 6 + 160\° =180\°\\m \angle 6 = 180-160=20[/tex]

Therefore, the measures of these two angles are

[tex]m \angle 4 = 160 \°\\m \angle 6 = 20 \°[/tex]

I can't really give an explanation, since it's just multiplication, so here are the answers:

1. 32

2. 12

3. 24

4. 40

5. 20

6. 12

7. 12

Answer:

wheres the answer choices

Answer:

x=60.4

Step-by-step explanation:

Add 7.6 on both sides

1/4x=15.1

Multiply both sides by 4

x= 60.4

To complete the pairs and have a difference of 3, add 4 to both sides of the equation.

To complete the pairs and have a difference of 3, the first number of the pair should be the larger number.

So, the equation ? - 4 = 3 can be solved by adding 4 to both sides of the equation.

? - 4 + 4 = 3 + 4

? = 7

Answer:The formula for variable h can be calculated by the following steps;

Step-by-step explanation:

f=8gh

f/8g=h

Or

h=f/8g

To solve for the variable h in the formula f = 8gh, divide both sides of the equation by 8g. The formula for the variable h is h = f / (8g).

To solve the formula for the variable h, we need to isolate h on one side of the equation. In this case, the equation is f = 8gh. To isolate h, we divide both sides of the equation by 8g. This gives us:

h = f / (8g)

So the formula for the variable h is h = f / (8g).

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Answer:

See step-by-step explanation

Step-by-step explanation:

Whole numbers are [tex]0,\ 1,\ 2,\ 3,\ 4,\ ...[/tex]

Integer but not whole numbers are [tex]...,\ -4,\ -3,\ -2,\ -1[/tex]

Rational numbers are fractions

Irrational numbers are numbers that are not rational

[tex]\pi[/tex] is irrational number

[tex]-100[/tex] is integer but not whole number

[tex]-34[/tex] is integer but not whole number

[tex]-4[/tex] is integer but not whole number

[tex]-\dfrac{8}{4} =-2[/tex] is integer but not whole number

[tex]0.333...=\dfrac{1}{3}[/tex] is rational number

[tex]0.456783...[/tex]  is irrational number

[tex]3[/tex] is whole number

[tex]9.23456=\dfrac{923,456}{100,000}[/tex] is rational number

[tex]\sqrt{4}=2[/tex] is whole number

[tex]\sqrt{8}=2\sqrt{2}[/tex] is irrational number

[tex]\dfrac{1}{2}[/tex] is rational number

[tex]\dfrac{49}{7}=7[/tex] is whole number

[tex]\dfrac{89}{10}[/tex] is rational number

[tex]zero[/tex] is whole number

Answer:

3:2

Step-by-step explanation:

Answer:

$960.95

Step-by-step explanation:

The question is about finding the final amount after 4 years of a $700 investment with 8% interest, compounded quarterly. This can be solved using the compound interest formula.

The subject of your question pertains to compound interest in mathematics. Given the parameters, we want to find the amount after 4 years when $700 is invested at an interest rate of 8%, compounded quarterly. To solve this, we can use the compound interest formula, A = P(1 + r/n)^(nt), where 'A' is the amount of money accumulated after n years, including interest, 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (in decimal form), 't' is the time the money is invested for in years, and 'n' is the number of times that interest is compounded per year. Plugging the values in, we get A = $700(1 + 0.08/4)^(4*4) which gives us the total amount after 4 years.

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There were 980 student desks originally.

Step-by-step explanation:

Number of desks purchased = 295

Desks bought for teacher = 50

Desks for students = No. of desks purchased - desks bought for teachers

Desks for students = 295 - 50 = 245

This is 1/4 of number of original student desks.

Let x be the number of original student desks.

According to statement;

[tex]\frac{1}{4}\ of\ x=245\\\frac{1}{4}x=245[/tex]

Multiplying both sides by 4;

[tex]4*\frac{1}{4}x=245*4\\x=980[/tex]

There were 980 student desks originally.

Keywords: subtraction, multiplication

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Cancelling out both the -6 we get 12=0 which is not true, hence the equation is incorrect.

This is an incomplete question, here is a complete question.

Debnil has 6 teaspoons of salt. The ratio of teaspoons to tablespoons is 3:1 How many tablespoons does Debnil have?

A. 1/18

B. 1/2

C. 2

D.18​

Answer : The correct option is, (C) 2

Step-by-step explanation :

As we are give that Debnil has 6 teaspoons of salt.

The ratio of teaspoons to tablespoons is 3 : 1.

It means,

if he has 3 teaspoons then he has 1 tablespoons

if he has 1 teaspoons then he has [tex]\frac{1}{3}[/tex] tablespoons

So,

if he has 6 teaspoons then he has [tex]6\times \frac{1}{3}=2[/tex] tablespoons

Therefore, Debnil have 2 tablespoons of salt.

The number of tablespoons that debnil has is;

C: 2

We are told that;

Thus, if the total spoons is x. Then;

¾x = 6

Thus;

x = (4 × 6)/3

x = 8 spoons

Thus, number of tablespoons she has = 8 - 6 = 2

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Answer:

[tex]\cos x=-\dfrac{\sqrt{21}}{5}\\ \\\tan x =-\dfrac{2}{\sqrt{21}}\\ \\\cot x=-\dfrac{\sqrt{21}}{2}[/tex]

Step-by-step explanation:

Given

[tex]\sin x=\dfrac{2}{5}\\ \\\cos x<0[/tex]

Use formula:

[tex]\cos^2x+\sin ^2x=1\\ \\\cos^2x+\left(\dfrac{2}{5}\right)^2=1\\ \\\cos^2x=1-\dfrac{4}{25}\\ \\cos^2x=\dfrac{21}{25}\\ \\\cos x=\pm \dfrac{\sqrt{21}}{5}[/tex]

Since [tex]\cos x<0,[/tex] then

[tex]\cos x=-\dfrac{\sqrt{21}}{5}[/tex]

By definition,

[tex]\tan x =\dfrac{\sin x}{\cos x}=\dfrac{\frac{2}{5}}{-\frac{\sqrt{21}}{5}}=-\dfrac{2}{\sqrt{21}}\\ \\ \\\cot x=\dfrac{1}{\tan x}=\dfrac{1}{-\frac{2}{\sqrt{21}}}=-\dfrac{\sqrt{21}}{2}[/tex]

Answer:

a is 7.5

b is 67.5

c is 100

d is let me think on d

Answer:

a is 7.5

b is 67.5

c is 100

d is for every 7.5

When trying to find the point-slope equation of a line you need to pick a point and plug it into the plain equation with your slope.

-3 = 1/3(-1) +b

Multiply your slope with your x

-3 = -1/3 +b

Move the -1/3 to the other side by doing the opposite operation, in this case being addition.

-3 +1/3 = b

-2 2/3 = b

y = 1/3x - 2 2/3

Answer:

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

Step-by-step explanation:

1. Let's review carefully all the steps taken by Noa to calculate the difference of the circumferences of the two trees.

Circumference Tree 1 = 37 5/8 inches around

Circumference Tree 2 =  45 1/3 inches around

Step 1: 45 1/3- 37 5/8

The measures are correct, no issues copying them.

Step 2: 45 8/24 - 37 15/24

Noa looked for common denominators

1/3 * 8/8 = 8 /24 is correct; 5/8 * 3/3 = 15/24 is also correct.

Step 3: 44 32/24 - 37 15/24

Noa looked for making the fraction part higher on the left side:

45 8/24 = 44 32/24 is correct because 24/24 = 1

Step 4: 44 32/24 - 37 15/24= 8 17/24

Here we can finally find out the mistake done by Noa. The result is 7 17/24 and not 8 17/24.

Answer:

step 4 is correct so D

Step-by-step explanation:

i just took the test

Answer:

h=11.3 and c=8(or 8.1 depending on what you do first)

Step-by-step explanation:

so we do the same thing like last time and 8√2 rounded is 11.3, and 7/√3, or 7√3/3 is 4( 4.04 gets rounded down). now we multiply by two because of the theorems and get 8(if this is wrong then try 8.1 because the answer differs depending on what you do first.)

The value of x is determined as 64 by solving the first equation. This value is then used to find the percentage n, which turns out to be 16%.

First, let's solve the equation 125% of x is 80. 1.25 times x equals 80. Therefore, x equals 64. Now, we can use that value to solve the second equation, x is n % of 400. This means 64 is what percent of 400. Expressing this as a proportion: 64/400 = n/100. Evaluating this gives n = 16%.

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Answer:

t=3

Step-by-step explanation:

A 6-pack of t-shirts for $3.12 because 3.12 ÷ 6 is 0.52

Answer:

the last one is the least expensive it's only $0.52

Step-by-step explanation:

$2.24 ÷ 8 = $0.56

$3.00 ÷ 3 = $1.00

$4.24 ÷ 8 = $0.53

$3.12 ÷ 6 = $0.52

Answer:

Ivan isn't the son

Step-by-step explanation:

Answer:

The height is 1343.13 meters.

Step-by-step explanation:

Air pressure may be represented as a function of height h in meters above the surface of Earth as shown below :

[tex]P(h) = P. e^{-0.000121h}[/tex] ......... (1)

In this function, P is air pressure at sea level and h is measured in meters.

Let at a height of h meters the pressure is 85% of the sea level pressure.  

Hence, from equation (1), we get

[tex]0.85 = e^{- 0.000121 h}[/tex]

Taking ln both sides, we can write

ln 0.85 = -0.000121 h (ln e) {Since [tex]\ln a^{b} = b \ln a[/tex]}

⇒ h = 1343.13 meters (Answer)

Answer:

x = -10

Step-by-step explanation:

-16 = 8x/5

-80 = 8x

x = -10

Answer:

The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Step-by-step explanation:

Given as :

The three line equation is

Line 1 : 2 y = 5 x + 6

Line 2 : y = [tex]\frac{2}{5}[/tex] x - 1

Line 3 : 10 x + 4 y = - 6

Now, The standard equation of line is

y = m x + c

where m is the slope of line

And c is the y intercept

So, From Line 1

2 y = 5 x + 6

or , y =  [tex]\frac{5}{2}[/tex] x + [tex]\frac{6}{2}[/tex]

I.e y =  [tex]\frac{5}{2}[/tex] x + 3

So,  slope of this line = [tex]m_1[/tex] =  [tex]\frac{5}{2}[/tex]

Again , From Line 2

y = [tex]\frac{2}{5}[/tex] x - 1

So, slope of this line =  [tex]m_2[/tex] =  [tex]\frac{2}{5}[/tex]

Similarly , From Line 3

10 x + 4 y = - 6

I.e 4 y = - 6 - 10 x

or, y = - [tex]\frac{6}{4}[/tex] -  [tex]\frac{10}{4}[/tex] x

I.e y =  - [tex]\frac{5}{2}[/tex] x  - [tex]\frac{6}{4}[/tex]

So, Slope of this line = [tex]m_3[/tex] = - [tex]\frac{5}{2}[/tex]

Now, If the lines are parallel , then the slope of the lines are equal

And  If the lines are perpendicular , then the product of the slopes of the lines = - 1

Now, From given lines

[tex]m_2[/tex] × [tex]m_3[/tex] = [tex]\frac{2}{5}[/tex] × ( - [tex]\frac{5}{2}[/tex] )

I.e [tex]m_2[/tex] × [tex]m_3[/tex] = - 1

So, The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3

Hence The line 2 and Line 3 are perpendicular to each others

But There is no relation between Line 1 and Line 2  , Line 1 and Line 3 Answer

Answer:

65%

Step-by-step explanation:

Cross, multiply and divide method has saved my life with these problems, heres how to do it.

Set up like this:

143 x

------- = -------

220 100

Multiply 143 by 100, then divide that by 220.

x= 65, so she has read 65%

Final answer:

Olivia has read approximately 65% of her 220-page novel by reading 143 pages.

Explanation:

To calculate the percent of the novel that Olivia has read, we use the formula: (number of pages read ÷ total number of pages) × 100%. Olivia has read 143 pages of a 220-page novel. Therefore, the calculation is (143 ÷ 220) × 100%, which simplifies to approximately 65%.

The steps to solve the problem are given below:

Step 1: 143 / 220 = 0.65

Step 2: 0.65 x 100 = 65%

So, Olivia has read about 65% of the novel.

Answer:

The total miles driven equation is [tex]y=27x[/tex]

Step-by-step explanation:

Given:

Number of gallons of gas is x.

Total miles driven is y.

Carl's new car gets 27 miles per gallon.

Hence to calculate total miles driven we need to multiply 27 with number of gallons of gas.

Hence the equation becomes.

[tex]y=27x[/tex]

Answer:

(9 x+6)   =  3( 3x + 2)

(3x+2) represent the cost of each ticket.

Step-by-step explanation:

Here, the given expression representing  the cost for three friends to go to the movies  is  : (9 x+6 )

Now,simplifying the given expression, we get:

(9 x+6)   =  3( 3x + 2)

So, the given expression represents 3 times ( 3x + 2 ).

So, here (3x+2) represent the cost of each ticket.

And the expression 3 ( 3x+2)  represent the cost 3 tickets combined.