Find the surface area of a sphere with a radius of 8 cm

Answer:

Step-by-step explanation:

4b-1=b

3b-1=0

3b=1

b=1/3

24b=

24(1/3)=

8

Equations are expression separated by an equal sign. The value of 24b if 4b-1 = b is 8

Equations are expression separated by an equal sign

Given the expresion

4b - 1 = b

Find the value of "b"

4b - b = 1

3b = 1

b = 1/3

Determine the value of 24b

24b = 24(1/3)

24b = 8

Hence the value of 24b if 4b-1 = b is 8

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To find the slope of a line passing through the origin and a point, use the formula slope = (y2 - y1)/(x2 - x1). For a line passing through origin and the point (-8,-5), the slope is 5/8.

The topic at hand revolves around the concept of slope and the algebra of straight lines. The slope is calculated by finding the change in y (vertical axis) over the change in x (horizontal axis). To find the slope of a line passing through the origin and the point (-8,-5), use the formula slope = (y2 - y1)/(x2 - x1).

In this case, the origin is point (0,0) and the given point is (-8,-5). So to find the slope, we substitute these values into the slope formula: slope = (-5 - 0)/(-8 - 0) = 5/8. Therefore, the slope of the line passing through the origin and the point (-8,-5) is 5/8.

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The slope of the line is 5/8.

The slope of a line, denoted by m, represents the rate of change between the vertical and horizontal components of two points on the line.

To find the slope of a line passing through the origin and intersecting the point (-8, -5), we can use the slope formula. The slope formula is given by: m = (y2 - y1) / (x2 - x1).

Plugging in the values from the given point gives: m = (-5 - 0) / (-8 - 0)

= -5 / -8

= 5/8.

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Answer:

[tex]\large\boxed{x=53^o}[/tex]

Step-by-step explanation:

We know: the sum of the measures of the angles of the triangle is equal to 180 °.

Therefore e have the equation:

[tex]x+45^o+82^o=180^o[/tex]

[tex]x+127^o=180^o[/tex]        subtract 127° from both sides

[tex]x=53°[/tex]

The equation doesn't provide enough context to definitively solve for 'r'. Given the original equation r16 ≥ 8, r shouldn't be less than 1 if only integer values are accepted.

In Mathematics, the original equation provided here, 'r16 ≥ 8', seems to indicate that a value 'r' is being multiplied by 16 and the product should be greater than or equal to 8. To solve for 'r', you would normally divide both sides of the equation by 16. However, each sub-question provided 'r ≥ 2', 'r ≤ 2', 'r ≥ 128', and 'r ≤ 128', indicates different potential solutions for 'r'. Without the proper context or further information it is difficult to properly solve for 'r'. Given the original equation, if only integer values are allowed, 'r' should not be less than 1 to maintain the inequality. Further clarification on the nature of 'r' and the context of the question is highly recommended.

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Answer:

The product of the slopes of line a and line is -1.

Perpendicular lines a and b intersect at a right angle, or 90 degrees. This is independent of whether they are increasing or decreasing, or their steepness on a graph.

The statement about lines a and b that is true when they are perpendicular is that they form a 90-degree angle with each other. The concept of perpendicularity in geometry refers to lines, planes, or surfaces that intersect at a right angle.

Terms like increasing or decreasing line or the steepness of a line do not apply here as they pertain to the slope of the line in the context of a graph, which is distinct from the concept of perpendicularity.

For example, saying line A is a decreasing line while line B is an increasing line, does not describe their perpendicular relationship. Instead, they intersect or meet at a right angle (90 degrees), proving their perpendicular nature.

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Answer:

Step-by-step explanation:

a1 = 3(1) - 7 = - 4

a2 = 3(2) - 7 = -1

d = a2 - a1

d = -1 - (-4)

d = -1 + 4

d = 3

a60 = 3(60) - 7

a60 = 180 - 7

a60 = 173

n = 60

Sum = (a1 + a60) * n / 2

Sum = (-4 + 173) * 60/2

Sum = (169)*30

Sum = 5070

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

Just to check, we'll use the second summation formula

d = 3

n = 60

a1 = -4

Sum = (2*a1 + (n - 1)*d )*n / 2

Sum = (2*(-4) + (60 -1)*3)* 60/2

Sum = (-8 + 59*3) * 30

Sum = (177 - 8)*30

Sum = 169 * 30

Sum = 5070

Same answer.

X is 3

Refer to picture

Answer:

0.8 cup(s)

Step-by-step explanation:

2 x 0.4 = 0.8

Answer:

0.8

Step-by-step explanation:

So to get this answer you had to mulyiply the 2 cups of flour by the size you want which is 0.4 . 2(0.4)=0.8

The answer is:

[tex]A(13)=107.37Km^{2}[/tex]

We can calculate the area of the lake after 13 years using the following equation:

[tex]A(t)=A(initial)(1-ShrinkingRate)^{t}[/tex]

Where,

A(t), is the area after t time (years)

A(Initial), is the initial area

Shrinking Rate, is the rafe of shrinking and it's 6% or 0.06.

t, is the time

So, substituting we have:

[tex]A(13)=240(1-0.06)^{13}=240*0.447=107.37Km^{2}[/tex]

So, the are after 13 years will be:

[tex]A(13)=107.37Km^{2}[/tex]

Have a nice day!

Answer:

Step-by-step explanation:

Tracey Earns in week= $102.45

Tracy=2x-12.45

102.45=2x-12.45

2x= 102.45+12.45

2x=114.90

x= 114.90/2

x=$57.45

Kayla earns 57.45 dollars

The equation is n = (102.45 + 12.45) x 2.

And Kayla earns $229.8.

Two algebraic expressions having same value and symbol '=' in between are called as an equation.

Given:

In a week, Tracey earns $12.45 less than twice the amount Kayla earns. Tracy earns $102.45.

Let n be the amount Kayla earns.

Then,

Kayla earns,

n = (102.45 + 12.45) x 2

n = $229.8

Therefore, Kayla earns $229.8.

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Answer:

$2280

Step-by-step explanation:

I see you've already found part a, which is to find the amount of interest earned. The next part is easy, to find the balance of the account after four years, just add the interest you've found back to the principal (the original size of the account or loan). $2000 + $280 equals $2280.

The interest earned on the account is $280. The balance of the account after 4 years is $2280.

To find the interest earned on the account, we use the formula for simple interest:

I = PRT

where:

Substituting the given values:

I = $2000 * 3.5/100 * 4 = $280

To find the balance of the account, we add the interest earned to the principal:

Balance = P + I = $2000 + $280 = $2280

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Answer:   c) 286.5 in²

Step-by-step explanation:

S.A.= 2π r · h

      = 2π (7.3/2) · 12.5

      = 2π (3.65) (12.5)

      = 286.5

Answer:

Step-by-step explanation:

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Answer:

Equation: $21.50•n=c

Answer: There are 180 dogs in the shelter.

Step-by-step explanation:

Let be "c" the number of cats in the shelter and "d" the number of dogs in the shelter.

You know that the total number of dogs and cats in the animal shelter is 275. Then you can express this with:

[tex]d+c=275[/tex]

If the number of cats is 5 more than one half of the number of dogs, you can express it with:

[tex]c=\frac{d}{2}+5[/tex]

Then, substitute [tex]c=\frac{d}{2}+5[/tex] into [tex]d+c=275[/tex] and solve for "d" to calculate the number of dogs that are in the shelter. Then:

[tex]d+c=275\\\\d+\frac{d}{2}+5=275\\\\d+\frac{d}{2}=275-5\\\\\frac{2d+d}{2}=270\\\\\frac{3d}{2}=270\\\\3d=270*2\\\\d=\frac{540}{3}\\\\d=180[/tex]

Answer:

x=5, y=22.36, z=11.18

Step-by-step explanation:

Use mean extremes

10^2=sqrt(20x)

Solving x = 5

for y:

y=sqrt(20(20+5))=22.36

for z:

z=sqrt(5(20+5))=11.18

5/15 or 1/3 would be the correct answer

Answer:

[tex]\large\boxed{(x+1)^2+(y-7)^2=100}[/tex]

Step-by-step explanation:

The equation of a circle in standard form:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) - center

r - radius

We have the center (-1, 7) and the radius r = 10. Substitute:

[tex](x-(-1))^2+(y-7)^2=10^2\\\\(x+1)^2+(y-7)^2=100[/tex]

Answer:

x = 14

Step-by-step explanation:

3x+2x-7=2x+35

then solve for x

Answer:

x = 14

Step-by-step explanation:

We are given that A, B and C are collinear points and B is in between A and C.

The length from A to B is [tex] 3 x [/tex], length from B to C is [tex] 2x - 7 [/tex] and AC is [tex] 2 x + 35 [/tex].

We are to find the value of x.

[tex] A B + B C = A C [/tex]

[tex] 3 x + 2 x - 7 = 2 x + 3 5 [/tex]

[tex] 3 x + 2 x - 2 x = 3 5 + 7 [/tex]

[tex] 3 x = 4 2 [/tex]

[tex] x = \frac { 4 2 } { 3 } [/tex]

x = 14

Answer: 20

Step-by-step explanation:

6/30 = 0.2

0.2 times 100 = 20

Final answer:

After setting up a proportion and solving the equation 0.30x = 6, we find that there are 20 students in Mrs. Rutherford's class.

Explanation:

To determine how many students are in Mrs. Rutherford's class when 30% like chocolate ice cream and we know that 6 students like chocolate ice cream, we can set up a proportion where 30% (or 0.30) of the total number of students (which we will call x) is equal to 6. Therefore, the equation to find x is 0.30x = 6.

To solve for x, we divide both sides of the equation by 0.30:

0.30x = 6

x = 6 / 0.30

x = 20

So, there are 20 students in Mrs. Rutherford's class.

Answer: GCF = x

Step-by-step explanation:

x(x^3/x + x^2/x + -6x/x)

x(x^2 + -6)

x(x - 2)(x + 3)

Answer:

x(x + 3)(x - 2)

Step-by-step explanation:

Factor out x from each term

= x(x² + x - 6)

To factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x - term (+ 1)

The factors are + 3 and - 2, since

+ 3 × - 2 = - 6 and + 3 - 2 = + 1, hence

x² + x - 6 = (x + 3)(x - 2)

---------------------------------------

x³ + x² - 6x = x(x + 3)(x - 2) ← in factored form

Answer:

145°

Step-by-step explanation:

The angle is 90°+55°=145°

Answer: 145°

Step-by-step explanation:

The angle of straight lines is always 180°, so I took 180 and subtracted 55 from it, and then 90 to get 35. I got 90 because the x and y axis are perpendicular to each other, and the angle between perpendicular lines is always 90. 35° is the angle of the small un marked section to the left of the circles, so to get the angle of the circle-like line, I did 180-35 to get 145°.

ANSWER

A. (x+4)

EXPLANATION

The given binomial is

[tex] {x}^{2} + 12x + 32[/tex]

Split the middle term:

[tex] {x}^{2} + 8x + 4x + 32[/tex]

Factor;

[tex]x(x + 8) + 4( x + 8)[/tex]

Factor further;

[tex](x + 8)(x + 4)[/tex]

Therefore

[tex](x + 4)[/tex]

is a factor.

To simplify the expression, combine the exponents and evaluate the values to get the simplified expression 1/12.

To simplify the expression, we can combine the exponents of the same base. Let's break it down step-by-step:

So, the simplified expression is 4-1 * 3-1 * 40. Any number raised to the power of 0 is equivalent to 1, so the expression can be further simplified to 4-1 * 3-1 * 1. Finally, we can evaluate the values: 4-1 = 1/4, and 3-1 = 1/3.

Therefore, the simplified expression is (1/4) * (1/3) = 1/12.

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The expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex] simplifies to [tex]\(\frac{4}{3}\).[/tex]

To simplify the expression [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex], follow these steps:

So the simplified expression is [tex]\(\frac{4}{3}\)[/tex] .

Corrected question:

What is the simplified expression for [tex]\(\frac{4^{-3} \times 3^4 \times 4^2}{3^5 \times 4^{-2}}\)[/tex]

Answer:

x=1

Step-by-step explanation:

8x+4y=12y

-4y         -4y

8x=8y

x=1

Answer:

2

Step-by-step explanation:

3(2)+30=36

Answer:

The answer to 4-3 is 1.

Step-by-step explanation:

The quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

The quadratic equation '4 - 3' is a simple algebraic equation that can be decoded as follows:

Start with the number 4.

Subtract 3 from it.

So, the decoded mathematical expression is:

4 - 3 = 1

The result is 1.

Therefore, the quadratic code '4 - 3' corresponds to the mathematical expression "4 minus 3," which equals 1.

This demonstrates how to decode and interpret a simple algebraic expression, showing that when you subtract 3 from 4, the result is 1.

It's a basic example of performing arithmetic operations on numbers.

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The probable question may be:

Decode the quadratic expression '4 - 3​' to reveal the mathematical expression it represents. Provide the complete mathematical expression that corresponds to the given quadratic code.

Answer:

9/5 = 9 x  1/ 5

Answer:

9/5 = 9 * 1/5

Step-by-step explanation:

p(x) * r(x) = ab^x * cd^x

p(x) * r(x) = (a*c)*(b^x*d^x)

p(x)*r(x) = ac(bd)^x

For the last step, I used the rule that (ab)^x = a^x*b^x

The product of two exponential functions p(x) = ab^x and r(x) = cd^x is calculated by following the rules of exponents in mathematics, resulting in p(x) * r(x) = a * c * (bd)^x

The student is asking for the product of two exponential functions. If p(x) = ab^x and r(x) = cd^x, their product can be calculated as follows:

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