Translate the following sentence into an equation: Four times a number, plus six, is equal to 30
fasst

Given:

The two polygons are similar.

To find:

The value of [tex]a,\ b,\ m\angle C,\ m\angle D[/tex].

Solution:

We know that the corresponding side of similar figures are proportional. So,

[tex]\dfrac{5}{4}=\dfrac{5.39}{a}[/tex]

[tex]1.25=\dfrac{5.39}{a}[/tex]

[tex]a=\dfrac{5.39}{1.25}[/tex]

[tex]a=4.312[/tex]

Similarly,

[tex]\dfrac{5}{4}=\dfrac{5.83}{b}[/tex]

[tex]1.25=\dfrac{5.83}{b}[/tex]

[tex]b=\dfrac{5.83}{1.25}[/tex]

[tex]b=4.664[/tex]

We know that the corresponding angles of similar figures are congruent and their measures are equal. So,

[tex]m\angle C=99.2^\circ[/tex]

[tex]m\angle D=149^\circ[/tex]

Therefore, [tex]a=4.312\text{ units},\ b=4.664\text{ units},\ m\angle C=99.2^\circ,\ m\angle D=149^\circ[/tex].

Answer:

Step-by-step explanation:

She wins if the numbers 5 or 6 come up. There are 4 other numbers that are equally likely to be face up.

Most of the time she will lose because two out of 6 is much smaller than 4/6. If you were betting on horses, the odds are 1 in 2. That means that who ever you are playing against should put up 2 dollars for every dollar you put up.

That would be a fair game.

Answer:

the correct t answer is d

Answer:

4 inches

Step-by-step explanation:

The line that is perpendicular to the bottom of the trapezoid is the height.

Answer:

7.4 cm

Step-by-step explanation:

Volume of sphere

v = (4/3)πr³

Volume of hemisphere will be half that

v = (2/3)πr³

(2/3)πr³ = 839

multiply both sides by 3/2

πr³ = 1,258.5

Divide both sides by π

r³ = 400.5929917623

Take the cube root of both sides

r = 7.3717022001

Rounded

r = 7.4 cm

Step-by-step explanation:

Are you using a particular calculator for the class? For this class, is the payment expected to be compounded monthly?

There is a function in Microsoft Excel that will calculate the payment for you, but the answer is going to be slightly different for a business math class than a calculus-based statistics class.

The excel formula to calculate a payment is

=PMT(0.04/12,60,25000,0)

.04/12 is the interest APR on a monthly basis

60 is the number of months

25000 is the current amount owed

0 is the future balance after 60 payments

The answer from Excel is $460.41 -- ignore the negative sign for these purposes.

Multiply that number by the 60 months you pay and you get a total paid of $27,624.78

Remove the initial 25K and $2,624.78 is your interest amount.

By the way, I used the simplifying assumptions that the problem meant "interest rate" when it said "APR", and that the rate would compound monthly. In the actual loan industry, the interest rate is only part of the calculation for APR, a

146.08

Step-by-step explanation:

Let's start by figuring out the payment

effective rate: .035/12= .002916667

\begin{gathered}2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71\end{gathered}

2000=x

.002916667

1−(1+.002916667)

−48

x=44.71

then it's just

44.71*48-2000=146.08

Answer:

146.08

Step-by-step explanation:

Let's start by figuring out the payment

effective rate: .035/12= .002916667

[tex]2000=x\frac{1-(1+.002916667)^{-48}}{.002916667}\\x=44.71[/tex]

then it's just

44.71*48-2000=146.08

Answer:

Tammy initially had $4 pay.

Step-by-step explanation:

C on edge 2021

The y-intercept represent Tammy initially had $10 pay.

From the given graph, we can observe that the line passes through the points (2, 18) and (8, 42).

Using the two points on the line, the slope (m) of the line:

m = (change in y) / (change in x)

= (42 - 18) / (8 - 2)

= 24 / 6

= 4

Using slope-intercept form of a line equation: y = mx + b,

y= 4x+ b

Put x=2 and y= 18 we get

18 = 4(2)+b

18 = 8 + b

b= 18- 8

b = 10

Thus, the y-intercept represent Tammy initially had $10 pay.

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Answer:

f(6) = 82

Step-by-step explanation:

[tex]f(x) = 2x^2 + 5\sqrt{x-2}[/tex]

[tex]=> f(6) = 2(6)^2 + 5\sqrt{6-2}[/tex]

             [tex]= 2 \times 36 + 5 \times \sqrt{4}[/tex]

             [tex]= 72 + 5 \times 2[/tex]

             [tex]= 72 + 10[/tex]

             [tex]= 82[/tex]

Answer:

x < 3

Step-by-step explanation:

The graph of f(x) is above the graph of g(x) for values of x less than 3.

Answer: x < 3

Answer:

A. 115°

Step-by-step explanation:

180° - 65° = 115°

Answer:

1) (2, 1)

2) (2, -2)

3) (-1, -1)

4) (-5, -5)

Answer:

1. Pairs A(2, 5), B(6, 5), and C(6, 1)

missing coordinate is (2,1)

2. Pairs A(2, 3), B(7, 3), and C(7, -2)

missing coordinate is (2,-2)

3. Pairs A(-5, -1), B(1, -1), and C(1, -5)

missing coordinate is (-5,-5)

4. Pairs A(-1, 4), B(7, 4), and C(7, -1)

missing coordinate is (-1,-1)

Hope this is correct!! Have a nice day!!<3

Answers:

Each pair of triangles are congruent. The congruence reasoning is shown below.

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

Further Explanation:

Abbreviations:

ASA = angle side angle

SSS = side side side

HA = hypotenuse angle

9514 1404 393

Explanation:

Divide the figure into areas for which you have a surface area formula. Use the appropriate formula for each area, then add up the results.

Formulas are available for surface areas of a cone, cylinder, sphere, pyramid, rectangular prism, and for plane shapes that are circles, ellipses, triangles, rectangles, trapezoids, and regular polygons.

Most of the figures for which you are asked to find the area will decompose to some subset of these shapes. Take care to identify the relevant dimensions of each of the constituent parts of the area, and to make sure that all parts are accounted for. Do not allow your parts of the area to overlap, unless you intend to account for that overlap by subtracting the area that is counted more than once.

Also, use your common sense. A semicircle will have half the area of a circle, for example.

In some cases, it may be expedient to compute the area of a larger figure than the one you have, then subtract the part of that area that is missing from your figure.

9514 1404 393

Answer:

  448

Step-by-step explanation:

(4 pt/da)×(7 da/wk)×(16 oz/pt) = 448 oz/wk

That would be 448 fluid ounces per week.

Answer:

Step-by-step explanation:

(B). 2√2

Answer:

Step-by-step explanation:

Look at the two points and is it going up or down? The slope is 1/1 because it is going up 1 and over 1

Answer:

[tex]y=-3x+3[/tex]

Step-by-step explanation:

We start by finding the slope of the line, which is given by the formula:

[tex]m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

The points (x1, y1) and (x2, y2) are represented by the pairs given: (-2, 9) and (1, 0). WE can substitute this in and simplify.

[tex]m=\frac{0-9}{1-(-2)} =\frac{-9}{1+2} =\frac{-9}{3} =-3[/tex]

Using the point-slope formula, [tex]y-y_{1} =m(x-x_{1} )[/tex], we can find the equation. We can substitute the point (-2, 9) for (x1, y1):

[tex]y-9=-3(x+2)\\y-9=-3x-6\\y=-3x+3[/tex]

Answer:

since her score was -12 from being perfect

if she had scored 12 more points her score would have been perfect .

that is difference between her score and the perfect score o each quiz was 12

Answer:

The maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.

Step-by-step explanation:

Since Greg is installing a tile floor in a room that is 10 feet long by 15 feet wide, and he will use 1-foot square tiles, and he has two different types of tile: plain and hand-painted, and plain tiles cost $ 0.79 per tile, while hand-painted tiles cost $ 5.00 per tile, to determine what is the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200, the following calculation must be performed:

10 x 15 = 150

150 x 0.79 + 0 x 5 = 118.5

130 x 0.79 + 20 x 5 = 202.7

131 x 0.79 + 19 x 5 = 198.49

Therefore, the maximum number of hand-painted tiles that Greg can use to keep the total cost under $ 200 is 19.

Answer:

x>20

Step-by-step explanation:

Hi there!

[tex]120-5x < 20[/tex]

Subtract 120 from both sides

[tex]120-5x -120< 20-120\\-5x<-100[/tex]

Divide both sides by -5 and switch around the inequality symbol (because we're dividing by a negative number)

[tex]\frac{-5x}{-5} >\frac{-100}{-5} \\x>20[/tex]

I hope this helps!

Answer:

d.

Step-by-step explanation:

1) just to substitute the value of 'x' into the given equation and check equality:

(9;-2): -2≠ -45-1;

(5;24): 24≠-25-1;

(-1;6): 6≠5-1;

(-4;19): 19=20-1.

this contain two triangle and one rectangle

therefore total area = 2×area of triangle + area of rectangle

then refer the attachment

Answer:

Kindly check explanation

Step-by-step explanation:

Given the formula :

Pn = 25.8(1.0219)^h to predict the population of Ghana ;

The equation given is in the form of an exponential function:

The general form of an exponential distribution :

y = ab^x

a = Initial value ; b = constant multiplier or growth or Decay factor

Comparing :

The number in parenthesis = 1.0219 = b

b = Decay or growth factor :

Since b > 1 ; then We have a growth factor;

b = 1 + rate

1.0219 = 1 + rate

Rate = 1.0219 - 1

Rate = 0.0219

Hence, the population is growing at a rate of about (0.0219)*100% = 2.19%

Answer:

The center is ( -2, 7) and the radius is 6

Step-by-step explanation:

A circle is written in the form

(x-h)^2 + (y-k)^2 = r^2  where (h,k) is the center and r is the radius

(x+2)^2+(y-7)^2=36

(x -  -2)^2+(y-7)^2=6^2

The center is ( -2, 7) and the radius is 6

Answer:

x is 13°.take the triangle to find the measure of x.180° -(85°+82°)=x

180°-167°=13°

For the given triangle the measure of the angle x is = 3 degrees.

Labeling the given figure,

since angle C and angle B are alternate angles

Therefore,

For the triangle ABE

The interior angle for A = x

The interior angle for B = 180 -98

                                       = 92 degree

Since we know that,

The sum of the two interior angles of a triangle is equal to the exterior angle of the opposite side.

Therefore,

⇒ x  + 92 = 180 - 85

⇒ x  = 3 degrees.

Hence,

The measure of the angle x is = 3 degrees.

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Answer:

x = (-1 ± √21) / 2

The first choice

Step-by-step explanation:

x² = 5 - x

Put in standard form

x² + x - 5 = 0

Use quadratic equation

x = ( -b ± √( b² - 4ac) ) / (2a)

Plug in a = 1, b = 1 , c = -5

x = (-1 ± √( 1² - 4*1*(-5)) ) / 2

evaluate

x = (-1 ± √21) / 2

A. 4/7 Answer:

B. 60/7 or (8 and 4/7)

Step-by-step explanation:

A. 4 divided by 7 is the same as 4/7

B. 4/7 • 15/1= 60/7

Answer:

The width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

Step-by-step explanation:

Given that a rectangular garden covers 80 square yards, and the length is 7 yd longer than the width, to find the length and width of the rectangle the following calculation must be performed, knowing that the area of a rectangle arises from multiplying its width by its length:

X x (X + 7) = 80

5 x 12 = 60

6 x 13 = 78

8 x 14 = 112

6.1 x 13.1 = 79.91

6,105 x 13,105 = 80

Therefore, the width of the rectangle is 6,105 yards, and the length of the rectangle is 13,105 yards.

Answer:

Triangles have two meanings depending on their position. When pointing up, they represent stability and power, when pointing down they become unstable. The triangle is primarily a masculine shape, but when inverted it also represents female reproduction. Triangles possess a number of key advantages that make them ideal for both architects and curious students. The strength of a triangle derives from its shape, which spreads forces equally between its three sides.

Step-by-step explanation: