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7.1.21
Graph the equation. Select integers for x from – 3 to 3, inclusive.
y=x2-3
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\(\textit{surface area of a sphere}\\\\ SA=4\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies SA=4\pi (4)^2\implies SA\approx 201.1~in^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=4 \end{cases}\implies V=\cfrac{4\pi (4)^3}{3}\implies V\approx 268.1~in^3\)

Answer:

Minimum = -1

Maximum = 3

Step-by-step explanation:

∛-10+9 = ∛-1 = -1

∛18+9 = ∛27 = 3

Answer:

21/7 and 72/12

Step-by-step explanation:

As the "?" are both at the numerator we just multiply by the denominator of the question mark (that is 1) so they remain the same.

Step-by-step explanation:

given points,

(-5,-3) and (5,4)

we know,

slope = (y2 - y1/ x2 - x1)

→ 4 - (-3) / 5 - (-5)

→ 4+3/ 5 + 5 = 7/10

therefore,

slope of the line is 0.7

hope this answer helps you dear! take care

Answer:

Step-by-step explanation:

(4 + 3)/(5 + 5)= 7/10

Step-by-step explanation:

The lateral surface area of a pyramid is the area of each side of a right rectangular prism. The lateral area of a right pyramid can be calculated by multiplying half of the perimeter of the base by the slant height. The lateral surface area can also be found using this equation (see attachment.)

Answer:

Step-by-step explanation:

Answer:

D. -3 + 2i and E. 3+2i are the zeroes for the equation.

Step-by-step explanation:

The total value of the loan with quarterly compounded interest is approximately $45,288.38, while the total value of the loan with monthly compounded interest is approximately $45,634.84. The difference in total interest accrued is approximately $346.46.

Part A: To determine the total value of the loan with quarterly compounded interest, we can use the formula for compound interest:

A = P(1 + r/n)^(nt),

where:

A is the total value of the loan,

P is the principal amount (initial loan amount),

r is the interest rate (in decimal form),

n is the number of times interest is compounded per year,

and t is the number of years.

Given:

P = $20,000,

r = 9% or 0.09,

n = 4 (quarterly compounding),

t = 10 years.

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/4)^(4*10).

Calculating this value, we find:

A ≈ $45,288.38.

Therefore, the total value of the loan with quarterly compounded interest is approximately $45,288.38.

Part B: To determine the total value of the loan with monthly compounded interest, we follow the same formula but with a different value for n:

n = 12 (monthly compounding).

Substituting the values into the formula, we have:

A = 20000(1 + 0.09/12)^(12*10).

Calculating this value, we find:

A ≈ $45,634.84.

Therefore, the total value of the loan with monthly compounded interest is approximately $45,634.84.

Part C: The difference between the total interest accrued on each loan can be calculated by subtracting the principal amount from the total value of each loan.

For the loan with quarterly compounding:

Total interest = Total value - Principal

Total interest = $45,288.38 - $20,000

Total interest ≈ $25,288.38.

For the loan with monthly compounding:

Total interest = Total value - Principal

Total interest = $45,634.84 - $20,000

Total interest ≈ $25,634.84.

The difference between the total interest accrued on each loan is approximately $346.46.

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Answer:

Alt. Ext. Angles Theorem.

m∠1 = 150

Step-by-step explanation:

∠1 and ∠8 are alternate exterior angles formed when the transversal line cuts across the 2 parallel lines. According to the alternate exterior angles theorem, both are congruent. Therefore,

m∠1 = m∠8

m∠1 = (50x)°

m∠8 = 150

Set both equal and solve for x

50x = 150

Divide both sides by 50

50x/50 = 150/50

x = 3

Unknown angle:

m∠1 = (50x) = 50*3 = 150°

Explanation:

We assume your question is "why is that name given to these three numbers?"

There are many names in mathematics that are given to sequences or sets of numbers having a particular characteristic. The term "Pythagorean triple" is usually reserved for three positive integers that satisfy the relation "the sum of the squares of the smaller two is equal to the square of the largest."

This relationship exists between the side lengths of a right triangle, which is the point of the Pythagorean theorem. So, integer side lengths of a right triangle constitute a "Pythagorean triple."

_____

If your question is "why do right triangle side lengths have the relationship specified by the Pythagorean theorem?", that demands a different answer. In general, the sides and angles of a triangle obey the Law of Sines and the Law of Cosines.

One of the expressions of the Law of Cosines is ...

  c² = a² +b² -2ab·cos(C)

where C is the angle opposite side c in the triangle. You may recall that the cosine of 90° is zero, so the cosine term in this equation vanishes when angle C is a right angle. The remaining equation is ...

  c² = a² +b²

This is an expression of the Pythagorean theorem, and it is true only for right triangles.

Answer:

C. 1/3<b<3/2

D. 1/6<x<2

Step-by-step explanation:

Hope this helps

Answer:

In the photos

Step-by-step explanation:

Integer numbers are whole numbers that can be positive or negative.

Find the range and try to draw an interval set notation for each question.

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The equation 2 log₅ x = log₅ 4 + log₅ 9 has two solutions: x = 6.

To solve the equation 2 log₅ x = log₅ 4 + log₅ 9, we can use logarithmic properties to simplify and find the value of x.

Using the properties of logarithms, we can rewrite the equation as follows:

2 log₅ x = log₅ (4 * 9)

Next, we simplify the right side:

2 log₅ x = log₅ (36)

Now, we can use the property of logarithms that states logₐ b = c is equivalent to aᶜ = b. Applying this property, we have:

x² = 36

Taking the square root of both sides, we get:

x =  √36

Since the square root of 36 can be either positive or negative, we have two possible solutions:

x = 6

It's important to note that when working with logarithmic equations, we must always check if the obtained solutions satisfy the domain restrictions of the original equation. In this case, since the logarithm has a base of 5, the solution x = 6.

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Since the growth rate is linear and constant over time, it means that the sequence formed is an arithmetic sequence. The formula for finding the nth term of an arithmetic sequence is expressed as

an = a1 + d(n - 1)

where

a1 is the first term of the sequence

n = number of terms

d = common difference

In this case, n would be t(number of years

From the information given,

a1 = 3

Since the first term is at t = 0 and it represents 2010, six years letter would be represented by t = 7. Thus, we would took for d given that a7 = 24

We have

24 = 3 + d(7 - 1)

24 = 3 + 6d

6d = 24 - 3 = 21

d = 21/6 = 3.5

The linear model would be

an = 3 + 3.5(t - 1)

Substituting H for an, the linear model is

H = 3 + 3.5(t - 1)

At 2020, t = 11

H = 3 + 3.5(11 - 1) = 3 + 35

H = 38

Plane ADF is another way to label Plane J.

In order to determine which of the given options is another way to label Plane J, we need to first identify the key characteristics of Plane J.

These characteristics are its points, lines, and planes that it contains. We can then use these characteristics to compare and match them with the given options.

Here are the key characteristics of Plane J: Points: J, A, D Lines: JA, JD, AD Planes: Plane J Now let's examine each option to see which one matches the characteristics of Plane J: Option A: Plane h This option is not a match since Plane h is not one of the planes that contain the points J, A, and D.

Option B: Plane ABD This option is not a match since Plane ABD contains points A, B, and D but not point J.

Option C: Plane EFG This option is not a match since Plane EFG contains points E, F, and G but not point J.

Option D: Plane ADF This option is a match since Plane ADF contains points A, D, and F which are all points that are contained in Plane J.

Therefore, Plane ADF is another way to label Plane J.

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Answer:

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Linear function that relates y to x.

y = x

coordinates of y = x

\(| \ \ x \ | -2 \ | \ -1 | \ \ 0 \ | \ \ 1 \ | \ \ 2 \ | \ \ 3 \ \ \ | \\ --------------\\ | \ \ y \ \ | -2 \ | \ -1 | \ \ 0 \ | \ \ 1 \ | \ \ 2 \ | \ \ 3 \ \ |\)

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

A linear function is a straight line following equation: y = mx + b

                                                              where m is slope, b is y-intercept

⚘ Refer to the attachment for graph and below for some details!~

It is a linear function. Since, the line is straight when it's plotted and the linear function is (y=x)

Some X and Y coordinates are:

\(\begin{gathered}\boxed{\begin{array}{c|c}\boxed{\sf x} &\boxed{\sf y} \\ \sf -2 &\sf -2 \\ \sf -1 &\sf -1\\ \sf 0 &\sf 0 \\ \sf 1 &\sf 1\\ \sf 2 &\sf 2 \end{array}}\end{gathered}\)

Answer: 34,650 permutations

Answer:

3

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Since square rooting (√) is the opposite function of squaring a number (exponent of 2), to approximate √10 to the nearest whole number, determine the two squares it is in between.

If you square 3, you will get 9 (3 x 3 = 9) and if you square 4, you will get 16 (4 x 4 = 16). Since 10 is in between 9 and 16, √10 will be in between 3 and 4.

The difference between 9 and 10 is only 1, while the difference between 10 and 16 is 6. Therefore, √10 is closest to 3.

Answer:

 \(\dfrac{x^2+8x+8}{2x+4}\\\\\)

Step-by-step explanation:

Simplify:

        \(\dfrac{3x + 4}{x +2}+\dfrac{x^2+2x}{2x+ 4}\)

Multiply the denominator and the numerator of the first term by 2,

                        \(=\dfrac{2*(3x +4)}{2*(x+ 2)}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{2*3x+2*8}{2*x +2*2}+\dfrac{x^2+2x}{2x+4}\\\\\\=\dfrac{6x+8}{2x+4}+\dfrac{x^2+2x}{2x+4}\)

                       \(\sf = \dfrac{6x+8+x^2+2x}{2x+4}\\\\\text{\bf Combine like terms,}\\\\=\dfrac{x^2+8x+8}{2x+4}\\\\\)

The initial temperature of the soda is 22 degrees Celsius, and its temperature after 20 minutes is approximately 10 degrees Celsius.

To find the initial temperature of the soda, we need to evaluate the temperature function T(x) at x = 0.

T(x) = -5 + 27e^(-0.03x)

T(0) = -5 + 27e^(-0.03(0))

T(0) = -5 + 27e^0

Since any number raised to the power of 0 is 1, we have:

T(0) = -5 + 27(1)

T(0) = -5 + 27

T(0) = 22

Therefore, the initial temperature of the soda is 22 degrees Celsius.

To find the temperature of the soda after 20 minutes, we evaluate the temperature function at x = 20.

T(x) = -5 + 27e^(-0.03x)

T(20) = -5 + 27e^(-0.03(20))

T(20) = -5 + 27e^(-0.6)

Using a calculator, we can compute e^(-0.6) ≈ 0.5488.

T(20) = -5 + 27(0.5488)

T(20) = -5 + 14.8152

T(20) ≈ 9.8152

Therefore, the temperature of the soda after 20 minutes is approximately 10 degrees Celsius (rounded to the nearest degree).

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Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current amount.

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Answer:

\(\huge\boxed{\sf 16}\)

Step-by-step explanation:

Given expression is:

= 10 + 3(12 ÷ (3x))

Put x = 2 nd use PEDMAS [Parenthesis Exponents Division Multiplication Addition Subtraction "in that order"]

= 10 + 3(12 ÷ (3)(2))

Solve Parenthesis

= 10 + 3(12 ÷ 6)

Now, Divide

= 10 + 3(2)

Now, Multiply

= 10 + 6

Now, Add

= 16

\(\rule[225]{225}{2}\)

Hope this helped!

Answer:

\(\huge\boxed{ \boxed{\tt \: 16}}\)

Step-by-step explanation:

Evaluate :

\(10 + 3(12 \div 3x)\)

When,

\(x = 2\)

Solution:-

\(\sf \implies10 + 3(12 \div 3x)\)

This expression may be rewritten as,

\(\sf \implies10 + 3 \bigg(\cfrac{12}{3x} \bigg)\)

Put 2 instead of x as x = 2 :-

As we know that x is multiplied with 3 on this expression so,

\(\sf \implies10 + 3 \bigg(\cfrac{12}{3 \times 2} \bigg)\)

\(\sf \implies10 + 3 \bigg(\cfrac{12}{6} \bigg)\)

Cancel off 12 and 6(By 6) :-

\(\sf \implies10 + 3 \bigg({\cfrac{ \cancel{12}}{ \cancel{6}} ^{2} }\bigg)\)

\(\sf \implies10 + 3 (2)\)

According to BODMAS Rule we know that, First Multiplication and then addition.(According to this expression)

So,Multiply 3 and 2 :-

\(\sf \implies10 + 3 \times 2\)

\(\sf \implies10 + 6\)

Simply add :-

\(\sf \implies16\)

Hence, the answer of the given expression would be 16.

_____________________________________

I hope this helps!

Let me know if you have any questions.

Answer:

The table represents a nonlinear function because the rate is not constant.

Step-by-step explanation:

As shown in the picture below, the x side of the table has the same rate of change of +1. However, due to the fact that the y side does not have the same rate of change, +6 and +3, the table represents a non linear function. If the rate on the y side of the table were all the same, then this would be a Linear function.

Answer:

5+x=y

Step-by-step explanation:

If she has already knit 5 cm you will always have to factor that in. If x is the number of nights adding the number of nights she does 1 cm of knitting will give you the length she has knit so far (y). I hope this helped! Good luck

Answer:

y=5x

Step-by-step explanation:

i did the ixl

Answer:

a

Step-by-step explanation:

the data is represented in the dot plot

Answer:

answer is 77.67

Step-by-step explanation:

explain by the x axis is 68 to y axis is 84 so the median is 77.67

The total volume is the one in option C, 708 cubic centimeters.

We know that this prism can be divided into two prisms, and remember that the volume of a prism is equal to the product between its dimensions.

Then the volume of the first prism is:

V = 8cm*6cm*13cm = 624 cm³

And the volume of the second prism is:

v' = 3cm*4cm*7cm = 84 cm³

Adding that we will get:

total volume =  624 cm³+  84 cm³ = 708 cm³

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Answer:

Step-by-step explanation:

Answer:

72

Step-by-step explanation:

-6 times -12