Read each question. Then write the letter of the correct answer on your paper.
What is the common ratio in a geometric series if a₂ = 2/5 and a₅ = 16/135 ?
(A) 2/5
(B) 2/3
(C) 6/65
(D) 8/27

The value of x in the equation -2/5 * x = 10 is x = -25

The expression is given as

-2/5 * x = 10

Express the fraction as decimal

So, we have

-0.4 * x = 10

Evaluate the product

So, we have

-0.4x = 10

Divide both sides of the equation by -0.4

So, we have

-0.4/-0.4x = 10/-0.4

Evaluate the quotient

So, we have

x = 10/-0.4

Evaluate the quotient

So, we have

x = -25

Hence, the value of x in the equation -2/5 * x = 10 is x = -25

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Answer:

7.2 units

Step-by-step explanation:

Hello, and welcome to Brainly!

You are sometimes offered to find the distances between two points on a graph. But how are we to do this you ask?

The distance formula measures the distance in units from point A to point B. The formula is d=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where Point A is depicted as [tex](x_1, y_1)[/tex] and Point B is depicted as [tex](x_2, y_2)[/tex].

To start this problem, let's label a random point as A, and the other as B.

A: (-9, 3) where [tex]x_1=-9, y_1=3[/tex]
B: (-7, -4) where [tex]x_2=-7, y_2=-4[/tex]

Let's use the distance formula to solve this distance. Fill in the known variables.

d=[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

d=[tex]\sqrt{(-7--9)^2+(-4-3)^2}[/tex]

[tex]d=\sqrt{(2)^2+(-7)^2}[/tex]                 Note that (-7--9) cancels out the two negatives and turns into (-7+9), which is 2.
[tex]d=\sqrt{4+49} \\d=\sqrt{53} \\d=7.2[/tex]

The distance between these two points is 7.2 units.

Answer:

13

Step-by-step explanation:

divide the 24 by two so you can find one side of the two right triangles. you get 12. now that you have 12 and the 5 from the other side use a^2+b^2=c^2 to solve for the missing side where a=5 b=12 and c=? so 12 squares is 144 and 5 squared is 25 so add then up and you get 169=c^2. lastly square the 169 and you end up with 13 :)

The area inside of the home is [tex]452.16 ft^2[/tex]

It is given that circular dwelling has a diameter of 24 feet then , radius will be [tex]r=\frac{24}{2} =12 \ feet[/tex]

Putting r = 12 feet in equation (1) , we get

       [tex]A=3.14\times( 12) ^2\\A=3.14\times144\\A= 452.16 ft^2[/tex]

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Answer:

Step-by-step explanation:

Givens

Let the angle = x

Let it's supplement = 180 - x

Equation

x + 9 = 2*(180 - x)                  Remove the brackets

Solution

x + 9 = 360 - 2x                     Add 2x to both sides

x + 2x + 9 = 360 - 2x + 2x     Combine

3x + 9 = 360                          Subtract 9 from both sides

3x + 9-9 = 360-9                   Combine

3x = 351                                 Divide both sides by 3

3x/3=351/3

x = 117

Answer

Given angle = 117

Supplement = 180 - 117 = 63

Answer: 122 I'm think I'm not sure tho

Step-by-step explanation:

The initial cost of the purchases is  $40.81.

The initial cost of the purchases is the sum of the total cost of each items bought. The total cost of each item bought is the product of the size of the items bought and their price.

The mathematical operations that would be used to determine the initial cost are addition and multiplication. Addition is the process of determining the product of two or more numbers. Multiplication is the process of determining the product of two or more numbers.

Total cost of cheese = 1/4 x 2.49 = $0.62

Total cost of Slice ham = 2.5 x 3.29 = $8.23

Total cost of 4 loaves of bread = 4 x 2.89 = $11.56

Total cost of 5 bags of potato chips = (2 x 3) + $1.95 = $7.95

Total cost of Salsa = 3 x 4.15 = $12.45

The initial cost of the purchase : $12.45+ $7.95 + $11.56 + $8.23 + $0.62 = $40.81

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Answer:

z = 53

Step-by-step explanation:

Comment

The three angles of any triangle add up  to 180o. There are no exceptions to this rule.

Formula

2z + z - 15 + 36 = 180                Combine like terms on the left.

Solution

3z + 21 = 180                              Subtract  21 from both sides

3z + 21 - 21 = 180 - 21                Combine

3z = 159                                      Divide both sides by 3

z = 53

Answer:

[tex]y = \dfrac{5}{2}x - 7[/tex]

Step-by-step explanation:

Step-by-step explanation:

Take any two points (x1, y1) and (x2, y2) from the table

Slope intercept equation is y = mx + b where m is slope and b = y-intercept

Slope = (y2-y1)/(x2-x1)

In this case

Let's choose the last two points

These are (6,  8) and (8, 13)

Slope = (13 - 8)/(8-6) = 5/2

So the equation is y = (5/2)x + b

To compute b, plug in x, y values for any point and solve for b

Choose the first point (0, -7)

Plug in:

-7 = (5/2)(0) + b

-7 = 0 + b or b = -7

So the equation of the line is
[tex]y = \dfrac{5}{2}x - 7[/tex]

We can verify by computing the y value for another point and seeing it agrees with table values

Choose point (4, 3)

y = 5/2 x 4 - 7

= 10 - 7 = 3

which agrees with the table value for y which is 3 when x = 4

The next two terms of the given sequence are 20 and 23. And the the formula for finding the nth term of the given sequence is [tex]T_{n+1} = T_{n} + 3[/tex].

According to the given question.

We have a sequence 5, 8, 11, 14, 17...

Since, the first term of the given sequence is 5.

The second term of the given sequence is 8.

The third term of the given sequence is 11.

Here, we can see that each term is 3 more tahn the previous term.

So, the next two terms i.e.

Fifth term = 17 + 3 = 20

Sixth term = 20 + 3 = 23

Therefore, the formula for finding the nth term of the given sequence is given by

[tex]T_{n+1} = T_{n} + 3[/tex]

Hence, the next two terms of the given sequence are 20 and 23. And the the formula for finding the nth term of the given sequence is [tex]T_{n+1} = T_{n} + 3[/tex].

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The solution of the given equation 7y + 4 = 3 - 2y is 29/2.

According to the given qestion.

We have a linear equation in one variable 7y + 4 = 3 - 2y.

So, the solution of the given linear equation in one variable  7y + 4 = 3 - 2y is given by

7y + 4 = 3 - 2y

⇒ 7y + 2y + 4 = 3    ( adding 2y both the sides)

⇒ 9y  = 3 - 4

⇒ 9y = -1

⇒ y = -1/9

Now, we will check whether y = -1/9 is the solution of the given equation 7y + 4 = 3 - 2y  or not.

Thereofore,

LHS

= 7(-1/9) + 4

= -7/9 + 4

= -7 + 36/9

= 29/9

Similarly

RHS

= 3 - 2(-1/9)

= 3 + 2/9

= (27 + 2)/9

= 29/2

Here, LHS = RHS

Hence, the solution of the given equation 7y + 4 = 3 - 2y is 29/2.

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The circumference is the perimeter of a circle or ellipse in geometry.  

If the diameter of the circle be 16 feet then the circumference of circle is 50.24

A circle's circumference is defined as the straight line distance around it. In other words, if you open a circle and draw a straight line through it, the length of that line is the circumference of the circle.

The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment.

Let the diameter of the circle, d = 16 feet

Circumference of circle, c = πd

Circumference of circle = 2 (3.14)(16)

Circumference of circle = 9.42 × 16

Circumference of circle = 50.24

Therefore, the Circumference of circle be 50.24

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Answer:

Step-by-step explanation:

a. 18² and 19² and 6³

b. 26² and 27² and 9³

c. 29² and 30²

d. 35² and 36² and 11³

Answer:

Step-by-step explanation:

This number would be between 3,300 and 3,400.  Which number would 3387 be closer to?  3350 would be right in the middle and 3387would be larger than 3350 so 3387 is closer to 3400.

The three types of congruence transformations are rotation, reflection, and translation is TRUE.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

If we rotate a triangle by any angle in any direction either clockwise or anti the dimension will remain the same so it will be congruent.

If we reflect a triangle about any axis then also it will remain the same so it will be congruent.

If we transform by any amount either horizontal or vertical then it will remain the same so it will be congruent.

Hence "The three types of congruence transformations are rotation, reflection, and translation is TRUE".

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The formula for the given cosine function is:

g(x) = 6cos(0.8(x - 0.75π)) - 8

Hence the coefficients are:

a = 6, b = 0.8, c = -0.75π, d = -8.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

In this problem, we have that the maximum value is of -2 and the minimum value is of -14(difference of 12), hence the amplitude is given as follows:

2a = 12.

a = 6.

A standard cosine function with amplitude would vary the between -6 and 6, while this one varies between -14 and -2, hence the vertical shift is of d = -8.

The minimum and maximum values form half the period, hence:

[tex]\frac{2\pi}{B} = 2\pi - \frac{3\pi}{4}[/tex]

[tex]\frac{\pi}{B} = \frac{5\pi}{4}[/tex]

B = 4π/5

b = 0.8π.

The minimum value in the standard function is at x = 0, while at this function is at x = 3π/4, hence the phase shift is of 3π/4 = 0.75π units to the right, that is, c = -0.75π.

Hence the formula for the given cosine function is:

g(x) = 6cos(0.8(x - 0.75π)) - 8

The graph of the function is given at the end of the answer.

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y varies directly with x and 1/9 is the constant of variation

y = kx                    (where k is a constant)

y = x/9

y = (1/9)x

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

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The exterior angle (∠ 5) is larger than either remote interior angle

( ∠ 7 and ∠ 8) then m ∠ 2 > m ∠ 8 and m ∠ 5 > m ∠ 8.

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles.

The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

By the Exterior Angle Inequality Theorem, the exterior angle (∠ 2) is larger than either remote interior angle (∠ 6 and ∠ 8).

Similarly, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

m ∠ 2 > m ∠ 8 and m ∠ 5 > m ∠ 8 .

Therefore, the correct answer is ∠ 2 and ∠ 5.

The complete question is:

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition

Measures greater than m ∠ 8

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$2500\\ r=rate\to 5.5\%\to \frac{5.5}{100}\dotfill &0.055\\ n= \begin{array}{llll} \textit{times it compounds per year} \end{array}\dotfill &1\\ t=years\dotfill &15 \end{cases} \\\\\\ A=2500\left(1+\frac{0.055}{1}\right)^{1\cdot 15} \implies A=2500(1.055)^{15}\implies A \approx 5581.19[/tex]

The sum of all the angles of the polygon is 8640 and each angle is measured at 172.8

The sum of all the angles of a polygon having n sides is given by the formula (n-2)* 180

To find out the sum of all the interior angles of a polygon we need to put the value of n with the number of sides of polygon which is 50

Sum of all interior angles of the given polygon = (50-2)*180

            = 48*180

            =8640

To find out the degree of each angle of the given regular polygon is the division of the sum of interior angles of the polygon with number of sides of the polygon = 8640/50  which is 172.8

The correct question is - Calculate the sum of the interior angles of a polygon with 50 sides: (i)in degrees (ii) degree of each angle of the polygon

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Answer: 6

Step-by-step explanation:

3x ÷ x = 3

27 ÷ 3 = 9

9 = x + 3
x = 6

I don't which one is the width so I just assume the smaller badge side x cm is the width

The equation of the line in standard form passing through the point (-4 , 2) with slope equal to 3 is 3x - y = -14.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values of the slope and the point to set up the equation.

(y - y1) = m(x - x1)

where m = 3 and (x1 , y1) = (-4 , 2)

(y - 2) = 3(x - -4)

y - 2 = 3(x + 4)

y - 2 = 3x + 12

To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

y - 2 = 3x + 12

3x - y = -2 -12

3x - y = -14

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A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100.

The percent of the given number 19 % of 82 is 15.58.

A percentage in mathematics is a number or ratio that can be expressed as a fraction of 100. The term percent comes from the Latin "per centum" which means per hundred. The symbol percentage is used to represent percentage.

Let the equation be 19 % of 82

Percentage = (value/total value) × 100 %.

Since, finding the fraction of a number is same as multiplying the fraction with the number, we have

19 % of 82 = 19/100 of 82

19/100 × 82 = 15.58

Therefore, the percent of the given number19 % of 82 is 15.58.

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Answer:

C

Step-by-step explanation:

hope this works for you :)