Find the missing factor BBB that makes the equality true.
21y^4=(B)(7y^3)21y
4
=(B)(7y
3
)

Answer:

Step-by-step explanation:

The number in the equation is 9.

A mathematical statement consisting of an equal symbol between two algebraic expressions with the same value is known as an equation in algebra.

Let the number be x

(2/3)x + 5 = (-2/6)x + 14 (Equation given)

x( 2/3 + 2/6 ) = 14 - 5

x( 2/3 + 1/3) = 9

x = 9

Hence, the number in the given equation is 9

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Answer:

( x + 3)² + ( y + 7)² = 361

Step-by-step explanation:

The equation of a circle written in standard form is ( x – h)² + ( y - k)² = r². The center is (h, k) and the radius is r.

With the given information of center (-3, -7) and radius 19, we get

[ x – (-3)]² + [ y - (-3)]² = (19)²

( x + 3)² + ( y + 7)² = 361

The value of Pascale's savings account at the end of the fifth year, with a 7.5% interest rate compounded annually and an additional $500 deposited each year, is approximately $3,122.00.

To calculate the value of Pascale's account at the end of the fifth year, we must use the compound interest formula which is A = P (1 + r)^t, where:

However, since Pascale deposits an additional $500 at the beginning of each year, the calculation is more complex than a single application of the formula. Our calculation should reflect the compound interest earned on each individual $500 deposit, not just the initial deposit.

Let's calculate the value at the end of year 5 step by step, adding $500 at the beginning of each year:

Therefore, the value of the account at the end of the fifth year is approximately $3,122.00.

Answer:

D

Step-by-step explanation:

sqrt(7) = about 2.6

and that divided by 2 is

0.8  which means D is the Answer

Answer:

The correct option is;

A. The mean speed and the range of the speeds of the motorists decreased

Step-by-step explanation:

Here we have the speeds given as

                  Before Sign Installation

Speed                                                   Frequency

20                                                             1

24                                                             1

25                                                             4

30                                                             2

35                                                             2

38                                                             1

40                                                             1

∑ 212                                                        12

Mean = 17.67

Median (25 + 30)/2 = 27.5

Range  = 40 - 20 = 20

                     After  Sign Installation

Speed                                                   Frequency

20                                                             1

22                                                             1

25                                                             4

28                                                             1

30                                                             3

35                                                             2

∑ 160                                                        12

Mean = 160/12 = 13.33

Median = (25+28)/2 = 26.5

Range  = 35 - 20 = 15.

Therefore, the mean speed and the range of the speeds of the motorists decreased

Answer:

119°

Step-by-step explanation:

In circle with center B, JH is diameter.

[tex]m\angle GHI = 360° - (90° + 151°)\\

m\angle GHI = 360° - 241°\\

m\angle GHI = 119°\\

\because\overset{\frown}{GHI} =m\angle GHI\\

\huge \red{ \boxed{\therefore \overset{\frown}{GHI} =119°}}\\ [/tex]

Answer:

24.

Step-by-step explanation:

The is the number of permutations of 3 digits from 4

= 4P3

= 4! / (4- 3)!

= 4 *3 *2 *1 / 1!

= 24/1

= 24.

Answer:

y = (-1/8)x^2

Step-by-step explanation:

Start with y = x^2.  When the original parabola has been reflected across the x-axis, the pertinent equation becomes y = -x^2.

Now if this is scaled vertically by a factor of 1/8, we get:

y = (-1/8)x^2

Answer:

The answer to your question is     y = -2x - 13

Step-by-step explanation:

Data

Original line    y = 1/2x - 7

Point = (-10, 7)

New line = ?

Process

1.- Find the slope of the original line

    The slope is the coefficient of the x

                     y = 1/2x - 7

    slope = 1/2

2.- Find the slope of the new line

The new line is perpendicular to the original line

    slope = -2

3.- Find the equation of the new line

          y - y1 = m(x - x1)

          y - 7 = -2(x + 10)

-Simplification

          y - 7 = -2x - 20

          y = -2x - 20 + 7

          y = -2x - 13

Answer: The equation is y = -2x - 13.

We compare the given line with y = mx + b.

So slope = m = [tex]\frac{1}{2}[/tex].

We know that the slope of the perpendicular line is negative reciprocal.

It means the slope of the required line will be -2.

Given point = (-10, 7).

So, using the point slope formula the equation of the line is:

[tex]y-7=-2(x+10)\\y-7=-2x-20\\y=-2x-13[/tex]

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Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3} - \frac{1}{2} =\frac{2x2}{3x3} -\frac{1x3}{2x3} =\frac{4}{6} -\frac{3}{6} =\frac{4-3}{6} =\frac{1}{6}[/tex]

Answer:

[tex]\frac{1}{6}[/tex]

Step-by-step explanation:

[tex]\frac{2}{3}-\frac{1}{2}=\\ \\=\frac{2*2-1*3}{6}\\ \\=\frac{4-3}{6}\\ \\=\frac{1}{6}[/tex]

Answer:

a. IT = 9.75 * X

b. GT = 4500 + 4.25 * X

c. G = 9.75 * X - 4500 - 4.25 * X

Step-by-step explanation:

With the data of the statement we can get a function. Let X be the number of pounds sold.

to. Monthly income

IT = 9.75 * X

b. Monthly expenses

GT = 4500 + 4.25 * X

c. Monthly Earnings (Monthly Income - Monthly Expenses)

G = 9.75 * X - (4500 + 4.25 * X)

G = 9.75 * X - 4500 - 4.25 * X

a. The IT function should be = [tex]9.75 \times X[/tex]

b. The GT function is = [tex]4500 + 4.25 \times X[/tex]

c. The function G is = [tex]9.75 \times X - 4500 - 4.25 \times X[/tex]

here we assume X be the number of pounds sold.

Since A coffee business should sell the coffee for $ 9.75. Monthly expenses are $ 4,500 along with $ 4.25 for each pound of coffee.

So,

a. The IT function is [tex]9.75 \times X[/tex]

b.  The GT function should be [tex]4500 + 4.25 \times X[/tex]

c. The function G should be [tex]G = 9.75 \times X - (4500 + 4.25 \times X)[/tex]

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Slope-intercept form:  y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

You know:

m = [tex]\frac{1}{3}[/tex]      So substitute/plug it into the equation

y = mx + b

[tex]y=\frac{1}{3} x+b[/tex]   To find b, plug in the point (-6, 0) into the equation, the isolate/get the variable "b" by itself

[tex]0=\frac{1}{3} (-6)+b[/tex]

0 = -2 + b         Add 2 on both sides to get "b" by itself

0 + 2 = -2 + 2 + b

2 = b

[tex]y=\frac{1}{3} x+2[/tex]       Your answer is the 4th option

The equation in slope-intercept form is y = 1/3x  + 2

The equation of the line in point slope form is expressed as:

where:

Substitute:

y - 0 = 1/3(x+6)

Write in slope-intercept form

y = 1/3(x+6)

3y = x + 6

y = 1/3x + 6/3

y = 1/3x + 2

Hence the equation in slope-intercept form is y = 1/3x  + 2

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Answer:

B, D and E.

just trust me

The angle made by the apothem and the radius would be; 30 degrees. Then the correct option is B.

The polygon is a 2D geometry that has a finite number of sides. And all the sides of the polygon are straight lines connected to each other side by side.

The apothem of a regular hexagon = 8 cm.

Then the side length of the hexagon will be

[tex]\rm x = \dfrac{8}{\sin 60^o}= 9.24\ cm[/tex]

The perimeter of the hexagon;

Perimeter = 6 × 9.24 = 55.43 cm

The area of the hexagon;

Area = 0.5 × 8 × 9.24 = 36.95 cm².

The angle made by the apothem and the radius = 30 degrees.

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Answer:

Since you provided no graphs, I just graphed y=(x+3)(x+3). I hope this helps.

Final answer:

The graph defined by the function y = (x+3)(x+3) is a parabola opening upwards with its vertex at (-3, 0), represented by a U-shaped curve on the coordinate plane.

Explanation:

The function given by y = (x+3)(x+3) represents a quadratic equation, which can be expanded to y = x^2 + 6x + 9. This is a parabola that opens upwards because the coefficient of the x^2 term is positive. The graph of this function will have its vertex at the point (-3, 0), which is obtained by setting the inside of the parentheses to zero. To visualize this function, you would plot a series of points by choosing different values for x, calculate the corresponding y values, and then plot these points on a coordinate plane. Connecting these points will reveal the U-shaped curve typical for a quadratic function.

Answer:

3/13

Step-by-step explanation:

There are 52 card in a deck of cards

12 of them are face cards   3 cards *4 suits =12

P (face card) = 12/52 = 3/13

Answer:1/3 decimal form: 0.333 repeating percent: 3.33%

Answer:

, a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero

Step-by-step explanation:

Answer:

Universal set ( U ) = Set of prime numbers

Step-by-step explanation:

Solution:-

- All even numbers are numbers that are divisible by 2 or have at-least an LCM of 2 associated with that number.

- All prime numbers are divisible by 1 and the number itself. Which 2 which is divisible by 1 and itself is a prime number and an even number.

- Considering only positive integers.

- Carrie is looking for a set of even numbers within the set of prime number.

- As stated above, the only integer, 2, is common to both prime number set and even number set.

- Hence, universal set ( U ) should be prime numbers.

- Universal set ( U ) = Set of prime numbers.

Answer:

c. prime numbers

Step-by-step explanation:

edg 2020

Answer:

The answer to your question is below

Step-by-step explanation:

Data

Equation               25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

                             25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

                              x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

                             [tex]\frac{x^{2} }{a^{2}} + \frac{y^{2}}{b^{2}} = 1[/tex]

3.- Find a, b and c

    a² = 64             a = 8

    b² = 25             b = 5

-Calculate c with the Pythagorean theorem

                   a² = b² + c²

-Solve for c

                   c² = a² - b²

-Substitution

                   c² = 8² - 5²

-Simplification

                  c² = 64 - 25

                  c² = 39

-Result

                  c = √13

4.- Find the center

          C = (0, 0)

5.- Find the vertices

          V1 = (-8, 0)     V2 = (8, 0)

6.- Find the foci

          F1 = (-√13, 0)   F2 = (√13, 0)

The center of the ellipse is (0,0), the vertices are (5.657, 0) and (-5.657, 0), and the foci are (3.317, 0) and (-3.317, 0).

The given equation of the ellipse is 25x^2 + 64y^2 = 1600.

To find the center of the ellipse, we can rewrite the equation in standard form: x^2/32 + y^2/25 = 1. The center is (0,0) since the x and y terms are squared and have the same coefficients.

To find the vertices of the ellipse, we can calculate the distance from the center to the major axis. The length of the major axis is 2*a, where a is the square root of the denominator of the x term. In this case, a = sqrt(32) ≈ 5.657. So the vertices are (5.657, 0) and (-5.657, 0).

To find the foci of the ellipse, we can calculate the distance from the center to the foci. The length of the foci is 2*c, where c is the square root of the difference between the squares of a and b (sqrt(32-25) ≈ 3.317). So the foci are (3.317, 0) and (-3.317, 0).

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Answer:

  23.6°

Step-by-step explanation:

The relevant trig relationship is ...

  Sin = Opposite/Hypotenuse

This tells you ...

  sin(Z) = XY/YZ = 6/15 = 2/5

The inverse sine (arcsine) function is used to find the angle when its sine is known.

  Z = arcsin(2/5)

  Z = 23.6°

To find the size of angle XYZ, we need additional information.

To find the size of angle XYZ, we need additional information. Typically, to determine the size of an angle, we need to know the measures of other angles or the lengths of the sides of the triangle. If we have such information, we can use the trigonometric ratios or the properties of triangles to find the size of angle XYZ. Could you please provide the missing information?

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Answer:

4 dollars and 20 cents

Step-by-step explanation:

5.00-.80=4.20

Answer:

$4.20

Step-by-step explanation:

What you bought will be subtracted from how much you paid with.

amount paid - amount bought

We paid for the cookie with $5, and bought something for 80 cents.

$5 is equal to 5.00, and 80 cents is equal to 0.8

5.00-0.8=4.2

So, you would get $4.20 back in change

Answer:

3 swimmers

Step-by-step explanation:

Answer:

The correct answer is 2.45.

Step-by-step explanation:

Probability model of an office manager regarding reports from employees is given by:

X = 0; P(X) = 0.05

X = 1; P(X) = 0.15

X = 2; P(X) = 0.35

X = 3; P(X) = 0.25

X = 4; P(X) = 0.15

X = 5; P(X) = 0.05

Now expectation of number of emails that the manager would receive is given by X × P(X)

= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05

= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25

= 2.45

The correct answer is 2.45.

X = 0; P(X) = 0.05

X = 1; P(X) = 0.15

X = 2; P(X) = 0.35

X = 3; P(X) = 0.25

X = 4; P(X) = 0.15

X = 5; P(X) = 0.05

Now the number of emalis should be

= 0 × 0.05 + 1 × 0.15 + 2 × 0.35 + 3 × 0.25 + 4 × 0.15 + 5 × 0.05

= 0 + 0.15 + 0.70 + 0.75 + 0.60 + 0.25

= 2.45

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⁵/₉ of bafter a cup would go per cupcake .

To determine how many cups of cake batter to use for each of the 18 cupcakes when you have 10 cups of batter, you need to divide the total amount of batter by the number of cupcakes.

Divide the total cups of batter (10 cups) by the number of cupcakes (18):

= 10 ÷ 18

≈ 10 / 18

Divide both sides by 2 to simplify and get:

= 5 / 9

Answer: No!

Step-by-step explanation:

Answer: No

Step-by-step explanation: If you take 944544 and divide it by 5, you will end up with 188908.8

Answer: 49

Step-by-step explanation:

If iTs half of each square its the same

Answer:

probability that the page opened will start with S

Step-by-step explanation:

14/90

0.15556

Answer:

When you are "multiplying" exponents, you're really just adding them together. So in the case of (x² ⋅ x⁴), you add the exponents:

2 + 4 = 6

[tex]x^{6}[/tex] would be the answer.

On the other hand, raising a power to a power, is actually multiplying them. So it would just be:

2 ⋅ 4 = 8

[tex]x^{8}[/tex] would be the answer.

Answer:

61 67     71 73 79

There you go:)

Answer:

53, 59, 61, 67, 71.

Step-by-step explanation:

It goes on....

53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109

, 113, 127, 131, 137, 139

I hope this helps :)

Answer:

The volume of the paper weight is 942.8 cubic cm.

Step-by-step explanation:

We are given the following in the question:

Dimensions of paperweight :

Radius, r = 10 cm

Height,h = 9 cm

Volume of paper weight = Volume of cone

[tex]V= \dfrac{1}{3}\pi r^2 h[/tex]

where r is the radius and h is the height of the cone.

Putting values, we get,

[tex]V = \dfrac{1}{3}\times \dfrac{22}{7}\times (10)^2\times 9\\\\V = 942.8\text{ cubic cm}[/tex]

Thus, the volume of the paper weight is 942.8 cubic cm.

The volume is 942.5 [tex]cm^{3}[/tex].

To calculate the volume of a cone, you can use the formula:

V = (1/3)πr²h

where:

1. For Marta's paperweight with a radius of 10 centimeters and a height of 9 centimeters, you substitute the values into the formula as follows:

V = (1/3)π(10 cm)²(9 cm)

2. First, calculate the base area:

(10 cm)² = 100 cm²

3. Then, multiply by the height:

100 cm² × 9 cm = 900 cm³

4. Finally, multiply by (1/3)π:

V = (1/3)π × 900 cm³ ≈ 942.5 cm³

Therefore, the volume of the cone is approximately 942.5 [tex]cm^{3}[/tex], rounded to the nearest tenth.

Answer:

25%(1/4)

Step-by-step explanation:

The probability of getting tails on the first flip and heads on the second flip of a coin is 25%, as each flip is an independent event.

The question pertains to the probability of an event occurring in two successive trials - flipping a coin twice. Firstly, we need to recognize that each flip is an independent event. An independent event is one in which the outcome of the first event does not affect the outcome of the second. When you flip a coin, the probability of getting tails is 1/2 or 50%, and the probability of getting heads is also 1/2 or 50%. Since these are independent events, we multiply the probabilities to get the result.

When you multiply 1/2 (probability of getting tails on the first flip) by 1/2 (probability of getting heads on the second flip), your result is 1/4 or 25%.

So, the probability of getting tails on the first flip and heads on the second flip is 25%.

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