Use the distributive property to expand -4 (-2/5 + 3 x). Which is an equivalent expression?
A) -8/5 + 12x
B) -8/5 - 12x
C) 8/5 + 12x
D) 8/5 - 12x

Answer:

C. The vertex of the function doesn't change.

Answer:

B. 5,200

Step-by-step explanation:

Sarah's essential (fixed) expenses = $750 per month

Her essential (flexible) expenses = $500 per month

Her non-essential expenses = $250 per month

Her total monthly living expenses = 750 + 500 + 250 = $1,500

Sarah wants an emergency fund of 5 times monthly living expenses.

1500 × 5 = $7,500

Currently she is having her emergency fund savings account is = $2,300

She needs to save more = 7,500 - 2,300 = $5,200

Sarah need to save more $5,200.

Sarah need to save $5,200 to have an adequate emergency fund.

An expression is a number, or a variable, or a combination of numbers and variables and operation symbols.

Now it is given that,

Sarah's essential (fixed) expenses = $750 per month

Her essential (flexible) expenses = $500 per month

Her non-essential expenses = $250 per month

⇒ total monthly living expenses = 750 + 500 + 250 = $1,500

∵ Sarah wants an emergency fund of 5 times monthly living expenses.

∴ emergency fund = 1500 × 5 = $7,500

Currently she is having her emergency fund savings account = $2,300

Thus, Amount needs to be save = 7,500 - 2,300 = $5,200

Thus, Sarah need to save $5,200 to have an adequate emergency fund.

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Step-by-step explanation:

2X alla seconda meno 3

Answer:

What shapes can be cross sections of the rectangular pyramid?

A slice parallel to the base will take the shape of a

✔ rectangle

.

A slice perpendicular to the base and through the top vertex will take the shape of a

✔ triangle

.

A slice perpendicular to the base and not through the top vertex will take the shape of a

✔ trapezoid

.

A slice parallel to the base will take the shape of the rectangle. A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".

A slice perpendicular to the base and through the top vertex will take the shape of a .

A slice perpendicular to the base and not through the top vertex will take the shape of a .

Take a rectangle and the base. Now take four triangles such that each of them is connected to one-one side of the base rectangle and when they are taken together, they form a closed object.

That shape is called a rectangular pyramid.

A slice parallel to the base will take the shape of a "rectangle"

A slice perpendicular to the base and through the top vertex will take the shape of a "triangle".

A slice perpendicular to the base and not through the top vertex will take the shape of a "trapezoid".

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Answer:

1) x/8+ x/16= 3/4    2) 4 miles

Step-by-step explanation:

The table is an illustration of distance, rates (speed) and time.

From the question, we have:

[tex]t =45\ mins[/tex] --- total time spent

Convert to hours

[tex]t =\frac{45}{60}hr[/tex]

Reduce fraction

[tex]t =\frac{3}{4}hr[/tex]

The times spent to school and back home are given as:

[tex]t_1 = \frac x8[/tex]

[tex]t_2 = \frac x{16}[/tex]

So, we have:

[tex]t_1 + t_2 = t[/tex]

This gives:

[tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Hence, the equation that can be used to solve for x is: [tex]\frac x8 + \frac x{16} = \frac 34[/tex]

Take LCM

[tex]\frac{2x + x}{16} = \frac 34[/tex]

[tex]\frac{3x}{16} = \frac 34[/tex]

Multiply through by 16

[tex]\frac{3x}{16}\times 16 = \frac 34 \times 16[/tex]

[tex]3x = 12[/tex]

Divide both sides by 3

[tex]x = 4[/tex]

The distance to school and back home are given as:

[tex]d_1 = d_2 = x[/tex]

So, we have:

[tex]d_1 = d_2 = 4[/tex]

This means that Gerry lives 4 miles from school

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Answer:

Question 1. (2.2, -1.4)

Question 2. (1.33, 1)

Step-by-step explanation:

Equations for the given lines are

-----(1)

It is given that this line passes through two points (0, 2.5) and (2.2, 1.4).

------(2)

This equation passes through (0, -3) and (2.2, -1.4).

Now we have to find a common point through which these lines pass or solution of these equations.

From equations (1) and (2),

x =

x = 2.2

From equation (2),

y = -1.4

Therefore, solution of these equations is (2.2, -1.4).

Question 2.

The given equations are y = 1.5x - 1 and y = 1

From these equations,

1 = 1.5x - 1

1.5x = 2

x =

Therefore, the solution of the system of linear equations is (1.33, 1).

The correct approximate solution of the system of linear equations[tex]\( y = 1.5x - 1 \) and \( y = 1 \) is \( (1.33, 1) \).[/tex]

To find the solution, we need to set the two equations equal to each other since they both equal \( y \). This gives us the equation:

[tex]\[ 1.5x - 1 = 1 \][/tex]

Now, we solve for [tex]\( x \)[/tex]:

[tex]\[ 1.5x = 1 + 1 \][/tex]

[tex]\[ 1.5x = 2 \][/tex]

[tex]\[ x = \frac{2}{1.5} \][/tex]

[tex]\[ x = 1.\overline{3} \][/tex]

[tex]\[ x \approx 1.33 \][/tex]

Having found [tex]\( x \)[/tex], we can now find the corresponding [tex]\( y \)[/tex] value by substituting [tex]\( x \)[/tex] into either of the original equations. Since [tex]\( y = 1 \)[/tex] is given, we already know that [tex]\( y \)[/tex] is exactly 1. Therefore, the solution to the system is approximately [tex]\( (1.33, 1) \)[/tex].

Answer:

4+0.08 +0.0016+0.000032+ ....

Step-by-step explanation:

a+ar+ar²+ar³+ar⁴+…

the  geometric series converges if  |r| < 1

The geometric series converges:

4+0.08 +0.0016+0.000032+ ....

0.08=4*0.02

0.0016=4*(0.02)²

0.000032=4*(0.02)³

r=0.02<1

The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.

A geometric series is one where each pair of subsequent terms' ratios is a fixed function of the accumulation index. The ratio is a rational function of the accumulation index in a more comprehensive sense. creates what is known as a hypergeometric sequence.

If the common ratio is the same throughout the series, then the series is known as geometric series.

If the common ratio is less than one, then the series is known as convergence.

Let's check all the options, then we have

A. 0.02+0.02+0.02+0.02+...

Then the common ratio is given as,

r = 0.02 / 2 = 0.02 / 0.02

r = 1 = 1

B. 4+0.08 +0.0016+0.000032+....

Then the common ratio is given as,

r = 0.08 / 4 = 0.0016 / 0.08

r = 0.02 = 0.02

C. 4+80+ 1,600+ 32,000+.....

Then the common ratio is given as,

r = 80 / 4 = 1600 / 80

r = 20 = 20

D. 0.02+0.04+0.08+0.16+......

Then the common ratio is given as,

r = 0.04 / 0.02 = 0.08 / 0.04

r = 2 = 2

The common ratio of the series 4+0.08 +0.0016+0.000032+.... is less than 1 which is 0.02. Then the correct option is B.

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Answer:

2.9

Step-by-step explanation:

The mean is the average of the date It is surprisingly easy to calculate: add up all the data, then divide by how many data points there are.

Becker's data added up is 28. Kayla's data added up is 30. The total amount is 58.

The amount of data points are 20.

58/20 = 2.9

Hope this helps!

The mean number of games chess team members play per day is 2.9

Becker = 5,2,4,1,1,4,5,3,2,1

= (5 + 2 + 4 + 1 + 1 + 4 + 5 + 3 + 2 + 1) / 10

Mean average = 28 / 10

= 2.8

Kayla = 2,3,1,1,4,1,5,3,5,5

= (2 + 3 + 1 + 1 + 4 + 1 + 5 + 3 + 5 + 5) / 10

= 30 / 10

= 3

Total = Becker + Kayla

= 2.8 + 3

= 5.8

Mean average = 5.8 / 2

= 2.9

Therefore, the mean number of games chess team members play per day is 2.9

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Answer:

You are drawing a right triangle. So draw the two lines off of the right angle. Then write 5 along one line. That line is now BC, so you can start naming points and putting in lengths. Then, draw the hypotenuse (AB) going from the end of the line you were writing next to, to the other line. Make sure it is at least twice as long, because it is 13 long. Then, to find the length of the last line,  square 13, and subtract 25 from it. Take that number and find it's square root. You should get 12, which is your answer.

Step-by-step explanation:

Answer:

あなたがこれを翻訳するなら私はあなたを愛しています

Step-by-step explanation:

私は英語がわかりませんが、答えは4倍になります

Answer:

C.Lines r and s and lines t and u must be parallel.

Step-by-step explanation:

Line r s and t must be parallel and c is closest to that lol

The lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.

A straight line is a combination of endless points joined on both sides of the point.

The slope 'm' of any straight line is given by:

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

If Angle 2 is congruent to angle 4 and Angle 5 is congruent to angle 7.

From the information given we can draw lines r, s, t, and u(please attached picture)

From the picture, we can clearly see: lines r and s and lines t and u must be parallel.

Thus, the lines r and s and lines t and u must be parallel option third "Lines r and s and lines t and u must be parallel" is correct.

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Answer:

$1.50

Step-by-step explanation:

12÷8=3/2 or 1.50

Answer: the answer would be 1$ and 50 cents

Step-by-step explanation:

Answer:

Step-by-step explanation:

Recognize that the (1/2) in  4n=1/2(2n-12)  is a coefficient, the coefficient of the (2n - 12) term.

Thus, multiply both sides of this equation 4n=1/2(2n-12) by 2, to obtain:

8n = 2n - 12

Combining like terms, we get 6n = -12, so that n = -2.  

Multiplying both sides of the equation by a constant does not in any way affect your ability to find a solution and does not change the solution.

Answer:

The vertex is (6, -4)

Step-by-step explanation:

f(x) =(х – 8)(х – 4)

First find the zeros

0 = (х – 8)(х – 4)

0 = x-8      0 =x-4

x=8          x=4

The zeros are x=8 and x=4

The vertex is 1/2 way between the zeros

(8+4)/2 = 12/2 =6

To find the y value, substitute 6 into the function

f(6) = (6-8) (6-4)

     =  -2 (2) = -4

The vertex is (6, -4)

Answer:

P(2 or fewer left-handed) = 9/25 = 0.36

Step-by-step explanation:

From Chayton simulations, we can see that in 9 simulations there are 2 or fewer left-handed students in a class of 20 students. He simulated 25 classes of 20 students, then the probability to find 2 or fewer left-handed is: 9/25 = 0.36

Answer:

l=(3w-5) Inches

Step-by-step explanation:

Let the width of the rectangle =w inches

The length of a rectangle is five inches less than triple the width.

Let us break the statement down into parts.

Therefore, the length of the rectangle, l= (3w-5) Inches

Answer:22.5

Step-by-step explanation: just saying that is no the actual answer you still have to estimate it

The equation n² =45 is solved step by step. The nearest perfect squares, 36 and 49, are identified. Using a calculator, the square root of 45 is found to be approximately 6.708, satisfying the equation.

let's go through the steps to solve n² = 45 in detail:

Step 1: Find the Perfect Squares

The closest perfect squares to 45 are 6² = 36 and

7² = 49.

Since 45 is between 6² and 7², we'll use these values as reference.

Calculate the Square Root

We'll use a calculator to find the square root of 45.

√45 ≈ 6.708203932499369

So, the square root of 45 is approximately 6.708203932499369.

Step 3: Solve for n

Since we're looking for n² = 45, we have √n = 45.

Plugging in the calculated square root:

√n = 45

n ≈ 6.708203932499369

Thus, the approximate value of n that satisfies the equation n² = 45 is n ≈ 6.708.

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Answer: Cos A  = 0.96, Tan A = 0.29 and Sin A = 0.28

Step-by-step explanation: The right angled triangle can be solved by applying the trigonometric ratios given a follows;

Sin A = opposite/hypotenuse

Cos A = adjacent/hypotenuse

Tan A = opposite/adjacent

In the triangle ABC, the side AB (25) is the hypotenuse [facing the right angle], the side CB (7) is the opposite [facing the reference angle A°] while the side AC (24) is the adjacent [line between the reference angle and the right angle].

Therefore, using angle A as the reference angle;

(a) Cos A = adjacent/hypotenuse

Cos A = AC/AB

Cos A = 24/25

Cos A = 0.96

(b) Tan A = opposite/adjacent

Tan A= CB/AC

Tan A = 7/24

Tan A = 0.29

(c) Sin A = opposite/hypotenuse

Sin A = CB/AB

Sin A  = 7/25

Sin A = 0.28

Answer:

This does make a right triangle

Step-by-step explanation:

Because when you square 8 you get 64 and when you square 15 you get 225. Then you add those together and you should get 289 so when you find the square root of 289 is 17 which makes those number true

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle. This is because these side lengths satisfy the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, we have:

a² + b² = 8² + 15² = 64 + 225 = 289

c² = 17² = 289

Since a² + b² = c², these side lengths satisfy the Pythagorean theorem, and the triangle is a right triangle.

Thus,

Yes, a triangle with side lengths a = 8, b = 15, and c = 17 is a right triangle.

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Answer:

Volume of the completes tower = 160 units³

Step-by-step explanation:

Martin is using unit cubes to build a tower in the shape of rectangular prism.

Bottom layer of the prism is in the square shape.

Since number of unit cubes used in the bottom layer = 16

So, one side of the square base will measure = √16 = 4 units

Therefore, Length = width = 4 units

On this base, additional layers added on the top = 9

Therefore, height of the tower = (9 + 1) = 10 units (each layer having 16 cubes)

Volume of the tower = Volume of the rectangular prism

                                  = Length × width × height

                                  = 4×4×10

                                  = 160 cubic units.

Volume of the completed tower will be 160 cubic units.

The total volume  in cubic units of the completed tower is 160 units³.

Since number of unit cubes used in the bottom layer = 16

So, one side of the square base should be

= √16 = 4 units

Now

Length = width = 4 units

The additional layers added on the top = 9

So, height of the tower = (9 + 1)

= 10 units

Now

Volume of the tower = Volume of the rectangular prism

                                = Length × width × height

                                 = 4×4×10

                                 = 160 cubic units.

hence, The total volume in cubic units of the completed tower is 160 units³.

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Answer:

= 3

Step-by-step explanation:

4 − 5 + 9 = 5 − 9

− + 9 = 5 − 9

i hope this helps<3

:)

The value of solution of expression is,

⇒ x = 3

We have to given that;

Mathematical expression is,

⇒ 4x - 5x + 9 = 5x - 9

Now, We can simplify as;

⇒ 4x - 5x + 9 = 5x - 9

⇒ - x + 9 = 5x - 9

⇒ 9 + 9 = 5x + x

⇒ 18 = 6x

⇒ 6x = 18

⇒ x = 18 / 6

⇒ x = 3

Thus, The value of solution of expression is,

⇒ x = 3

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No, the relation isn't a function. Though positive and balanced, one input has two outputs, violating the "one input, one output" rule.

No, the relation depicted in the image is not a function. While the relation does have the same number of x values as y values, and all the values are positive, a key characteristic of a function is missing.

For a relation to be a function, each input (represented by the x -value) must correspond to exactly one output (represented by the y -value).

In the image, we see that the input value 1 has two corresponding output values, 7 and 11. Since an input value cannot have multiple outputs, this relation is not a function.

So the answer is D. No, because two points with the same x -value have different y values.

Answer:  C) 297 in2

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Surface area of a square pyramid (S) = 2 (length of the base) slant + length of the base ^2

S = 2bs + b^2

Replacing with the values given:

S = 2 (9) 12 + 9^2

S = 216 +81 = 297 square inches

Feel free to ask for more if needed or if you did not understand something.

Answer:

0.53333333333

Step-by-step explanation:

The fraction of the class that is boys is 16/30.Therefore, the decimal equivalent the fraction of boys in Daniel's class is 0.53.

The fraction of the class that is boys is obtained by dividing the number of boys by the total number of students. In this case, there are 16 boys and 30 students in total. The fraction is therefore 16/30.

To write this fraction as a decimal, divide the numerator (16) by the denominator (30). The decimal equivalent of 16/30 is approximately 0.5333.

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Answer:

B. distribution skewed to the right, mean pulled to the right, median not effected

Step-by-step explanation:

When a distribution is skewed to the right, it means that the data is positively skewed or has more positive numbers than negative numbers.

An outlier can affect the mean of a distribution since a high value outlier will make the mean be much higher than the median. In this case, since the distribution is positively skewed, a high outlier will pull the mean to the right (to higher positive values).

The high outlier  in a data set affects the mean and median is

B. distribution skewed to the right, mean pulled to the right, median not effected

At the time When a distribution is skewed to the right, so it represents the data is positively skewed or it contains more positive numbers as compared to the negative numbers. An outlier can impact the mean of the distribution.

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Answer: 397.39 cm2

Step-by-step explanation:

Hi, first we have to calculate the area of the circle:

Area of a circle = π x r^2

Replacing with the values:

A(C) =π x 12^2 = 452.39cm2

Now, we have to calculate the rectangle area:

Rectangle area = width x length = 5 x11 = 55cm2

Finally, since the shaded region is the circle and the rectangle is inside of it, we have to subtract the area of the rectangle to the area of the circle:

452.39 -55 = 397.39 cm2

Feel free to ask for more if needed or if you did not understand something.

Answer:

397.39

Step-by-step explanation:

extras...

Answer:

The value of DC is 66.34.

Step-by-step explanation:

The triangles ABC and DCA are right angled triangles.

The straight line AC is a bisector for angles C and A.

The measure of ∠C is 30°.

Then the measure of angles BCA and ACD will be 15° each.

The measure of angle DAB is 150°.

Then the measure of angles DAC and BAC will be 75° each.

Now consider the right angled triangle ABC.

The measure of side AC is:

[tex]AC^{2}=AB^{2}+BC^{2}\\AC=\sqrt{AB^{2}+BC^{2}}\\=\sqrt{4^{2}+(10\sqrt{3})^{2}}\\=\sqrt{316}[/tex]

Consider the right angled triangle DCA.

The angle DAC measure 75°.

Using the trigonometric identities compute the value of Perpendicular DC as follows:

[tex]tan\ 75^{o}=\frac{DC}{\sqrt{316}}\\\\DC=3.732\times\sqrt{316}\\\\DC=66.34[/tex]

Thus, the value of DC is 66.34.

Answer:

the mean is the midle one

we can get this by getting the average

add all of it and divide by how many it is