What is the equation of the linear function represented by the table?

The length of the diagonal shown in the rectangular prism is; 9.5 ft

First of all, we have to find the length of the diagonal base to get;

x = √(4² + 7²)

x = √65

Thus;

Length of the diagonal shown = √(5² + (√65)²)

Length of the diagonal shown = √90

Length of diagonal shown = 9.4868

Length of diagonal shown ≈ 9.5 ft

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Answer:

got 100% on Plato

Step-by-step explanation:

The numbers based on the information will be 4 and 16.

Let the numbers be a and b.

Therefore, a - g = 2

(a + b)/2 - ✓ab = 2 or

(✓a - ✓b( = 4

g - h = 1.8

✓ab = 2ab/a + b = 1.8

5✓ab(✓a - ✓b)² = 8(a + b)

2a - 5✓ab + 2b + 0

✓a = 2✓b

a = 4b

b = 4.

✓a = 2✓b = 4

a = 16

Therefore, the numbers based on the information will be 4 and 16.

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[tex]\left(3\cdot8\cdot x\right)^7\\\\\left(3\cdot2\cdot4\cdot x\right)^7\\\\\left((3\cdot2)\cdot4\cdot x\right)^7\\\\\left(6\cdot4\cdot x\right)^7\\\\6^7\cdot4^7\cdot x^7\\\\[/tex]

In the second step, I rewrote 8 as 2*4. Then after that I regrouped terms so that the (3*2) can pair up together. This of course turns into 6. After that point, we have 6, 4 and x multiplied together as the base.

The last step uses the rule that [tex](a*b*c)^d = a^d*b^d*c^d[/tex], in other words, we apply the exponent d to each term inside the parenthesis. Each term inside gets its own exponent.

An example: [tex](2*4*6)^3 = 2^3*4^3*6^3[/tex]

The total amount that would be spent on all the activities is  $1605.40.

The total amount that would be spent on movies = (14/25) x 1200 x 1.55  = $1041.60

The total amount that would be spent on planetarium tickets = (7/25) x 1200 x 1.05 =352.80

The total amount that would be spent on backstage passes = (4/25) x 1200 x 1.10 =211.20

Total amount = 211.20 + 352.80 +  $1041.60 = $1605.40

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Answer:

15

Step-by-step explanation:

To find the answer, plug the values of each variable into the equation and simplify. It may be easiest to plug one variable in at a time, simplify, then plug the next variable in. Remember, if the equation is asking you to subtract a negative number, the negatives cancel and you want to add the numbers.

b = 2          c = -4

3b - c + 5                                      <----- Original expression

3(2) - c + 5                                    <----- Plug 2 in for "b"

6 - c + 5                                        <----- Multiply 3 and 2

11 - c                                              <----- Add 6 and 5

11 - (-4)                                           <----- Plug -4 in for "c"

15                                                  <----- Add 11 and 4

The function  f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

[tex]\rm f\left(x\right)=\dfrac{2}{x^2}+3x-10[/tex]

f(x) is positive for all x < -5

Plug x = -4

f(-4) = -21.875

The above statement is not true

f(x) is negative for all x < -5

Plug x = -4

f(-4) = -21.875

The above statement is true

f(x) is positive for all x < 2

Plug x = 1

f(1) = -5

The above statement is not true

f(x) is negative for all x > 2

Plug x = 3

f(3) = -0.777

The above statement is not true

Thus, the function  f(x)=2/x²+3x-10 is negative for all x < -5 option second "is negative for all x < -5" is correct.

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The (g-f)(x) is option D: - x² - 6x + 5.

Terms are added or subtracted to make a polynomial. They're composed of variables and constants all in multiplication.

Given;

f(x) = x²+2x-4

g(x) = -4x+1,

Then the subtraction of the two function;

g(x) - f(x)

= -4x+1 - (x²+2x-4 )

= -4x+1 - x²- 2x + 4

= - x² - 6x + 5

Hence, the correct option is D: - x² - 6x + 5.

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Answer:

y=-2x+8

Step-by-step explanation:

We want an equation of the form y=mx + b, where m is the slope and b is the value of y when x=0.

The slope of a line through the two given points:

(4,0) and (0,8)

Rise = (8-0) = 8

Run = (0-4) = -4

Slope = 8/-4 = -2

The y-intercept is given by the point (0,8), which tells us that b=8.

The equation is y = -2x + 8

Answer:

Which is the equation of the line passing through (0, 8) and (4, 0)?

The one that you are on is correct

Step-by-step explanation:

You're welcome.

Answer:

504 ways

Step-by-step explanation:

We know that since Sonji wants the last digit to be 7 and that numbers don't repeat, there are only 9 possibilities for the first digit, 8 possibilities for the second digit, 7 possibilities for the third digit, and 1 possibility for the fourth digit (which is 7).

Using the Fundamental Counting Principle, there are 9*8*7*1 = 504 ways for the remaining digits to be chosen.

Answer:

B. 504

Step-by-step explanation:

Have a good day!

The number of values x for which the square root of 48/x a whole number are two.

The square root of a number can be described as number that when multiplied with itself yields the number.

The first step is to determine the factors of 48. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48.

The factors of 48 that will yield a perfect square when divided by 48: 3 and 12.

48 divided by 3 would give a value of 16.

48 divided by 12 would give a value of 4.

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Answer:

Step-by-step explanation:

x²-3x+4+x=4

x²-3x+x=4-4

x²-2x=0

x²-x=0/2

x²-x=0

x=0

Answer:

5 in. = 2 mi.

Step-by-step explanation:

2.4mi  = 6in

1 mi = 2.5in

2.5 inches = 1mile

Convert to whole #'s as the question asks

5 in. = 2 mi

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

Answer:

3 inches = 1 miles

Step-by-step explanation:

The first scale you get is with the information that is given:

6 inches = 2.4 miles

Then you simplify, dividing both sides by 2.4:

2.5 inches = 1 miles

Rounding up: 3 inches = 1 miles

Hope it helps!

Answer:

0.5 =12.0095

pint   U.S Cup

I think im right but I hope this helps! ^^

Answer: B

Explanation: Key word: Atleast. This shows that you can still get 16 but it's the lowest you can get. Meaning, if you were to say, atleast get a 16% done. It'll mean that getting 16% is good but also, you'll want to get a higher number of course.

The x-intercept is (1, 0) and (-0.5, 0).

The correct option is (a)

The x-intercept is the point where a line crosses the x-axis, and the y-intercept is the point where a line crosses the y-axis.

Given function is:

f(x)= [tex]-2x^{2}+x+1[/tex]

So, The graph of this equation is attaches below.

The x- intercepts of this graph

[tex]\mathrm{X\:Intercepts}:\:\left(-\frac{1}{2},\:0\right),\:\left(1,\:0\right)[/tex]

or

X intercepts: (1, 0) and (-0.5, 0)

Hence, the x-intercept is (1, 0) and (-0.5, 0).

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Outlet A sold the greatest number of copies of album x in July and August

The tables of values are given as:

July

Album X Album Y Album Z

Outlet A 14 8 6

Outlet B 7 13 4

Outlet C 2 11 1

August

Album X Album Y Album Z

Outlet A 12 14 10

Outlet B 5 12 8

Outlet C 16 12 7

In July, the total sales of album x are:

Outlet A  = 14

Outlet B = 7

Outlet C = 2

In August, the total sales of album x are:

Outlet A  = 12

Outlet B = 5

Outlet C = 16

Add both sales

A = 14 + 12 = 26

B = 7 + 5 = 12

C = 2 + 16 = 18

26 (in outlet A) is greater than 12 and 18

Hence, outlet A sold the greatest number of copies of album x in July and August

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Answer:

Outlet D

Step-by-step explanation:

they sold 28 of album x

outlet a only sold 26

Answer:

2020

Step-by-step explanation:

(12×5×14.5+7×4×5)×2=

2020

Answer:

0, 3 , 8

Step-by-step explanation:

substitute n = 1, 2, 3 into the pattern rule

T₁ = 1² - 1 = 1 - 1 = 0

T₂ = 2² - 1 = 4 - 1 = 3

T₃ = 3² - 1 = 9 - 1 = 8

The height of the toy dinosaur will be 32 inches.

In mathematics scaling is defined as the enlarging or contracting of the size of an object by reducing or increasing the units of the measurements of the object.

Given that:-

An adult mamenchisaurus dinosaur was about 24 feet tall. if a toy model of the dinosaur is made to the scale of 1 inch to 9 inches.

The new height of the dinosaur will be calculated as:-

We know that the size of the dinosaur is scaled as 9 inches to 1 inch the actual height of the dinosaur is 24 feet so the scaled height will be:-

Actual height = 24 ft = 24 x 12 = 288 inches

9 inches  → 1 inch

288 inches  → 288 / 9 = 32 inches.

Therefore the height of the toy dinosaur will be 32 inches.

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The probability notation for choosing a blue disk or a green disk is P ( B U G).

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability = (number of blue discs / total number of discs) + (number of green discs / total number of discs)

3/8 + 5/8

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Answer:

The probability is [tex]\frac{5}{9}[/tex]

Step-by-step explanation:

First we will find the probability of having a roll that is at least 3

1 2 3 4 5 6

this means there is a [tex]\frac{4}{6}[/tex] chance we will roll at least 3

Next we will find which months of the year are applicable

January February March April May June July August September October November December

This means there is a [tex]\frac{5}{6}[/tex] chance we will pick a month that does not begin with the letter M.

Now we can multiply these chances together to see what the total probability is.

[tex]\frac{4}{6} * \frac{5}{6} = \frac{20}{36} \rightarrow \boxed{\frac{5}{9}}[/tex]

That is the answer

- Kan Academy Advance

[tex] \sqrt{29 \: - \: 12 \sqrt{5} } [/tex]

[tex] \sqrt{(3 \: - \: 2 \sqrt{5}) ^{2} } [/tex]

[tex] \boxed{ \bold{2 \sqrt{5} \: - \: 3}}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{29-12\sqrt{5}} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{20-12\sqrt{5}+9} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{4\cdot \:5-12\sqrt{5}+9} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(\sqrt{4}\right)^2\left(\sqrt{5}\right)^2-12\sqrt{5}+\left(\sqrt{9}\right)^2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{4}=2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \sqrt{9}=3 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2\cdot2\cdot3\sqrt{5}=12\sqrt{5} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{2^2\left(\sqrt{5}\right)^2-2\cdot \:2\cdot \:3\sqrt{5}+3^2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply\:the\:formula\:from\:binomial\:to\:square:(a-b)^2=a^2-2ab+b^2 \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf 2^{2}(\sqrt{5})^{2}-2\cdot2\cdot3\sqrt{5}+3^{2}=(2\sqrt{5}-3)^{2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf =\sqrt{\left(2\sqrt{5}-3\right)^2} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf Apply \ the \ laws \ of \ exponents:\sqrt[n]{a^{2} }=a \end{gathered}$}[/tex]

[tex]\sqrt{(2\sqrt{5}-3)^{2} } =2\sqrt{5 }-3.[/tex]

[tex]\red{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \red{=2\sqrt{5}-3 } \end{gathered}$}}} \ \ \red{\Rightarrow} \ \ \bf{\red{Answer}}[/tex]

↓

[tex]\red{\boxed{\boxed{\large\displaystyle\text{$\begin{gathered}\sf \bf{\red{MyHeritage}} \end{gathered}$}}}}[/tex]

Answer:

$14

Step-by-step explanation:

6 attendees divided by the cost of 12 = $2 per attendee

If 7 attendees are joining times $2 per person =$14

The half life of the radioactive isotope to the nearest tenth is  0.83 days.

The rate of radioactive decay is the rate at which a radioactive isotope is disintegrated. The half life is the time taken for half of the original amount of radioactive isotope to remain.

Given that;

t/12 = 0.693/k

Where;

t1/2 - half life

k =decay constant

t/12 = 0.693/0.84

t/12 = 0.83 days

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Answer:

13 and 30

Step-by-step explanation:

the smaller of the two numbers is 13.

If there is a 17 number difference, then that means that the second number is 30.

give brainliest, please!
hope this helps :)

Answer:

25

Step-by-step explanation:

First we add 1 to both sides :

√x = 5

Now we square both sides :

x = 5²

x = 25

To check this answer we substitute our answer back into the original equation:

√25 - 1 = 4

5 - 1 = 4

4 = 4

✅

Hope this helped and brainliest please

Answer:

See the attached graph.

Step-by-step explanation:

The most appropriate way to report a length measured by using this yardstick is to write the measurement in decimals (0.25) rather than in fraction (¼).

Measurement is a process through which the size, dimensions, or other physical quantities of magnitude that are associated with an object is taken, especially for use in a scientific research and experiment.

In Mathematics, a yardstick refers to a graduated measuring stick that has its length equal to one yard.

In this scenario, the most appropriate way to report a length measured by using this yardstick is to write the measurement in terms of decimals (0.25), so as to make easy approximations of the distance possible.

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