Fill in the blank
To solve an equation when the coefficient is a decimal, you
each side by the coefficient

Answer:

B  t = 9(5)

Step-by-step explanation:

for each mile the time increased by 9 minutes. So you can find the time in minutes by multiplying the number of miles by 9.

A: (x^a) / (x^a) = x^(a - a) = x^0

B: Anything divided by itself is 1, so x^a / x^a = 1.

C: If x^a / x^a = x^0 from Part A and x^a / x^a = 1 from Part B, then x^0 = 1.

Reflect: 1. To complete Part A, we used the quotient rule for exponents.

Hope this helps!

Answer:

Step-by-step explanation:

A

\(\frac{x^{a} }{x^{a} } = x^{a-a} =x^{0}\)

B

Anything divided by itself is 1, so \(\frac{x^{a} }{x^{a} } = 1\)

C

If \(\frac{x^{a} }{x^{a} } = x^{0}\) from part A, and \(\frac{x^{a} }{x^{a} } =1\) from part B, then \(x^{0} = 1\)

Reflect:

Properties of exponents

Answer: See below

Step-by-step explanation:

1.    x²-y²=55           or         (x+y)(x-y)=55  

2.   x-y=5

Solution      (1)    (x+y)5=55

______      (2)    x+y=55/5

______      (3)    x+y=11

______      (4)    x+y+x-y=11+5       The equation we got before we can use now

______      (5)    2x+y-y=16            see this y-y=0

______      (6)    2x=16                   2x+0=16 that's mean 2x=16

______      (7)    x=8                       Got the answer

Hope that help

9514 1404 393

Answer:

  6

Step-by-step explanation:

You will recognize that these points both have the same x-coordinate, so are on the vertical line x=2. The distance between them will be the difference of the y-coordinates:

  6 - 0 = 6

The points are 6 units apart.

__

If you like, you can use the distance formula.

  d = √((x2 -x1)² +(y2 -y1)²)

The values of these parameters are ...

  x1 = 2, y1 = 0

  x2 = 2, y2 = 6

Then the distance is ...

  d = √((2 -2)² +(6 -0)²) = √(0 +36) = 6

The distance between the points is 6 units.

less than zero

Step-by-step explanation:

when the discriminant is less than zero, then it has no real solutions. this can be written as

b²-4ac<0 has no real solutions.

Answer:

C. 150 degrees

Step-by-step explanation:

Angles 2 and 4 are opposite angles which means that they are congruent to each other

Answer:

150

Step-by-step explanation:

∠2 and ∠4 are vertically opposite angles and they are congruent.

There is a directly proportional relationship between the weight and total cost of bag of of lemons.

The ratio connecting two given numbers in what is known as a proportional relationship is the constant of proportionality. The constant of proportionality may also be referred to as the constant ratio, constant rate, unit rate, constant of variation, or even the rate of change.

When two variables are directly or indirectly proportional to one another, their relationship may be expressed using the formulas y = kx or y = k/x, where k specifies the degree of correspondence between the two variables. The proportionality constant, k, is often used.

As an illustration, we may write y = kx, where x is the amount of gas in gallons, y is the price in dollars, and k is the proportionality constant.

Given data :

One bag weighs 2.4 pounds and cost $5.28.

Another bag weighs 2.7 pounds and cost $5.94

2.4k = 5.28

k= 2.2

2.7k = 5.94

k = 2.2

k > 1

The weight and total cost of bag of of lemons is directly proportional, so when weight of lemon increases, the cost of lemon also increases.

Therefore, there is a directly proportional relationship between the weight and total cost of bag of of lemons.

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For the given function f(x) = x⁸(3-2x³) then

a. The roots of the function f(x) are x= 0 or ∛3/2.

b. When x →∞ then f(x) →∞

c. And x→-∞ then f(x) →-∞.

As given in the question,

Given function is equal to :

f(x) = x⁸(3-2x³)

a. Simplify the given function f(x) = x⁸(3-2x³) to get the roots of the f(x) we get,

f(x) =0

x⁸(3-2x³) = 0

⇒ x =0 or 3 -2x³ =0

⇒ x=0 or x = ∛3/2

b. When x → ∞

⇒x⁸ →∞ and (3-2x³) → ∞

⇒ x⁸(3-2x³) → ∞

When x →∞ then f(x) →∞

c. When x → -∞

⇒x⁸ →∞ and (3-2x³) →- ∞

⇒ x⁸(3-2x³) →- ∞

When x →-∞ then f(x) →-∞

Therefore, for the given function f(x) = x⁸(3-2x³) then

a. The roots of the function f(x) are x= 0 or ∛3/2.

b. When x →∞ then f(x) →∞

c. And x→-∞ then f(x) →-∞.

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\(\left| \log_7(x^8)\cfrac{}{} \right|~~ - ~~\left( ~~ \log_{49}(x^2) ~~ \right)^2 = 7 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \left| \log_7(x^8)\cfrac{}{} \right|\implies \pm\log_7(x^8)\implies \pm 8\log_7(x) \\\\[-0.35em] ~\dotfill\\\\ \left( ~~ \log_{49}(x^2) ~~ \right)^2\implies \left( ~~ \cfrac{\log_7(x^2)}{\log_7(49)} ~~ \right)^2\implies \left( ~~ \cfrac{\log_7(x^2)}{\log_7(7^2)} ~~ \right)^2\)

\(\left( ~~ \cfrac{\log_7(x^2)}{2} ~~ \right)^2\implies \left( ~~ \frac{1}{2}\log_7(x^2) ~~ \right)^2\\\\\\ \left( ~~ \log_7(x^{2\cdot \frac{1}{2}}) ~~ \right)^2 \implies \left( ~~ \log_7(x) ~~ \right)^2 \\\\[-0.35em] ~\dotfill\\\\ \left| \log_7(x^8)\cfrac{}{} \right|~~ - ~~\left( ~~ \log_{49}(x^2) ~~ \right)^2=7 \implies \pm 8\log_7(x)~~ - ~~\left( ~~ \log_7(x) ~~ \right)^2=7 \\\\[-0.35em] ~\dotfill\\\\ \textit{now let's make }\hspace{5em}\log_7(x)=Z \\\\[-0.35em] ~\dotfill\)

\(\mp 8Z-Z^2=7\implies 0=Z^2\pm 8Z+7\implies 0= \begin{cases} Z^2+ 8Z+7\\ Z^2 - 8Z+7 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ 0=Z^2+8Z+7\implies 0=(Z+7)(Z+1)\implies 0=[\log_7(x)+7][\log_7(x)+1] \\\\\\ 0=Z^2-8Z+7\implies 0=(Z-7)(Z-1)\implies 0=[\log_7(x)-7][\log_7(x)-1]\)

now, let's process for each case to get its roots

\(0=\log_7(x)+7\implies -7=\log_7(x)\implies 7^{-7}=7^{\log_7(x)}\implies \boxed{7^{-7}=x} \\\\\\ 0=\log_7(x)+1\implies -1=\log_7(x)\implies 7^{-1}=7^{\log_7(x)}\implies \boxed{7^{-1}=x} \\\\\\ 0=\log_7(x)-7\implies 7=\log_7(x)\implies 7^{7}=7^{\log_7(x)}\implies \boxed{7^{7}=x} \\\\\\ 0=\log_7(x)+1\implies 1=\log_7(x)\implies 7^{1}=7^{\log_7(x)}\implies \boxed{7=x}\)

Answer:

8 is the number

Step-by-step explanation:

I don't know why it took me so long to figure it out, 4 x 8 = 32 32 + 15 = 47

It probably took me a really long time because I am tired, and I am not using a calculator.

Answer:

10 years old

Step-by-step explanation:

lets break it down:

6 more means +6

four times means *4

so if her son is x years old, she is 4x+6

since we know she's 46, we know that 4x+6=46

now we just solve the equation

4x+6=46

-6 on both sides

4x=40

/4 on both sides

x=10

There was 4 dollar of discount on the total amount.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.

At the counter, he received a discount. If he only paid 22 dollars total, then

Total cost 11 + 15 = 26

But 26 - 22 = 4

Therefore, the discount was 4 dollar.

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when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

When the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse remains the same as in the original triangle. In a right triangle, the side opposite ∠A is referred to as the "opposite" side, and the hypotenuse is the longest side.

The ratio of the side length of the side opposite ∠A to the length of the hypotenuse is commonly known as the sine of angle A (sin A). So, when the scale factor is 1, the ratio of the side length of the side opposite ∠A to the length of the hypotenuse is equal to sin A.

In mathematical terms, when the scale factor is 1, we have:

(side length of side opposite ∠A) / (length of hypotenuse) = sin A

It's important to note that this ratio holds true for any right triangle, regardless of its size or dimensions, as long as the angle A remains the same.

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The polynomial -8m²n - 7m²n can be factored using the common factor -m²n. The complete factored form of the polynomial is (-m²n) (8 + 7a).

To find the complete factored form of the polynomial -8m²n - 7m²n, we can factor out common terms from both the terms. The common factor in the terms -8m²n and -7m²n is -m²n. We can write the polynomial as:

-8m²n - 7m²n = (-m²n) (8 + 7a)

Therefore, the complete factored form of the polynomial -8m²n - 7m²n is (-m²n) (8 + 7a). This expression represents the original polynomial in a multiplied form. We can expand this expression using distributive law to verify that it is equivalent to the original polynomial.

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The equation that models the path of the football released from the given position is h(t) = -10 + 25.37t - 16.1t².

The initial velocity of the ball is determined by applying third kinematic equation as shown below;

Vf² = V₀² - 2gh

0 = V₀² - 2gh

V₀² = 2gh

V₀ = √(2gh)

V₀ = √(2 x 32.17 x 10)

V₀ = 25.37 ft/s

The equation of the ball's motion can be modelled as follows;

h = V₀t - ¹/₂gt²

10 = 25.37t - ¹/₂(32.17)t²

10 = 25.37t - 16.1t²

h(t) = -10 + 25.37t - 16.1t²

Thus, the equation that models the path of the football at any given position is h(t) = -10 + 25.37t - 16.1t².

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Answer:

If x = 3, then y = -2 since the corresponding value of y for x=3 is -2 in the given table.

Step-by-step explanation:

Answer:

272

Step-by-step explanation:

It is 5%

63-60=3

60 divided by 3 = 5

5%

Answer:

5(x-1)>5/4x

If you mean (5/4)x, then

Divide by 5

x-1 > (1/4)x

x-1 > x/4

Multiply by 4

4x-4 > x

Add 4

4x > x+4

Subtract x

3x > 4

Divide by 3

x > 4/3

I hope its help u dear

The best description of the graph is "a quadratic function with a constant difference of 2."

A quadratic function is a function of the form f(x) = ax^2 + bx + c, where a, b, and c are constants. In a quadratic function, the graph forms a parabola.

In the given graph, if the differences between consecutive points on the graph are constant and equal to 2, it indicates a constant difference in the y-values (vertical direction) as the x-values (horizontal direction) increase. This is a characteristic of a quadratic function.

On the other hand, an exponential function with a growth factor of 2 would result in a graph that increases at an increasing rate, where the y-values grow exponentially as the x-values increase. This is not observed in the given graph.

Therefore, based on the information provided, the graph best represents a quadratic function with a constant difference of 2.

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Based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

To determine the distance between Houston, TX and Dallas, TX using the given scale, we can set up a proportion using the distances on the map and the actual distances.

Let's denote the distance between Houston and Dallas as "x" (in miles).

According to the scale provided, 2.3 centimeters on the map represents a distance of 348 miles. This can be expressed as:

2.3 cm / 348 miles = 1.6 cm / x miles

To find the value of "x," we can cross-multiply and solve the equation:

(2.3 cm) * (x miles) = (1.6 cm) * (348 miles)

2.3x = 556.8

Divide both sides by 2.3 to isolate "x":

x = 556.8 / 2.3

x ≈ 242.0869565

Therefore, based on the given scale, if Houston and Dallas are 1.6 centimeters apart on the map, the estimated distance between the two cities is approximately 242.1 miles.

Please note that this is an approximation based on the given scale and the assumption that the scale is linear and consistent throughout the map. Actual distances may vary and should be verified using more accurate measurements or reliable sources.

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The compound interest rate of the investment is 1.10%

The given parameters about the compound interest are

Principal, P = $11,000

Amount, A = $20,000

Time, t = 9

Number of times, n = 12 i.e. monthly interest

To calculate the amount, we have:

A = P(1 + R/n)^nt

Substitute the known values in the above equation, so, we have the following representation

20000 = 11000 * (1 + r/12)^(12 * 9)

This gives

1.82 = (1 + r/12)^108

Take the 108th root of both sides

1 + r/2 = 1.0055

Subtract 1 from both sides

r/2 = 0.0055

Multiply by 2

r = 0.011

Express as percentage

r = 1.10%

Hence, the value of the interest rate is 1.10%

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Answer:

6.66%

Step-by-step explanation:

Compounded Monthly:

�

=

�

(

1

+

�

�

)

�

�

A=P(1+

n

r

​

)

nt

Compound interest formula

�

=

20000

�

=

11000

�

=

9

�

=

12

A=20000P=11000t=9n=12

Given values

20000

=

20000=

11000

(

1

+

�

12

)

12

(

9

)

11000(1+

12

r

​

)

12(9)

Plug in values

20000

=

20000=

11000

(

1

+

�

12

)

108

11000(1+

12

r

​

)

108

Multiply

20000

11000

=

11000

20000

​

=

11000

(

1

+

�

12

)

108

11000

11000

11000(1+

12

r

​

)

108

​

Divide by 11000

1.8181818

=

1.8181818=

(

1

+

�

12

)

108

(1+

12

r

​

)

108

(

1.8181818

)

1

/

108

=

(1.8181818)

1/108

=

[

(

1

+

�

12

)

108

]

1

/

108

[(1+

12

r

​

)

108

]

1/108

Raise both sides to 1/108 power

1.0055509

=

1.0055509=

1

+

�

12

1+

12

r

​

−

1

−1=

−

1

−1

Subtract 1

0.0055509

=

0.0055509=

�

12

12

r

​

12

(

0.0055509

)

=

12(0.0055509)=

(

�

12

)

12

(

12

r

​

)12

Multiply by 12

0.0666108

=

0.0666108=

�

r

6.66108

%

=

6.66108%=

�

r

Convert to percent (multiply by 100)

�

≈

r≈

6.66

%

6.66%

Round to the nearest hundredth of a percent

Answer:

negative association

Step-by-step explanation:

3a. An equation in slope-point for this line is y + 2 = 1/2(x - 0).

3b. The equation in slope-intercept form is y = 1/2(x) - 2.

4a. An equation in slope-point form to represent this function is y - 3875 = -1/695(x - 19375).

4b. The cost of operating a car that has been driven 31250 km is $3892.086.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Part 3.

First of all, we would determine the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (0 + 2)/(4 - 0)

Slope (m) = 1/2

At data point (0, -2) and a slope of 1/2, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y + 2 = 1/2(x - 0)

y = 1/2(x) - 2

Part 4a.

Based on the information provided about Jay's business, we would determine the slope of the line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (3900 - 3875)/(2000 - 19375)

Slope (m) = 25/-17375

Slope (m) = -1/695

At data point (19375, 3875) and a slope of -1/695, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 3875 = -1/695(x - 19375)

Part 4b.

For the cost when x = 31250 km, we have:

y - 3875 = -1/695(31250 - 19375)

y = 17.086 + 3875

y = $3892.086.

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Answer:

2,3,5

Step-by-step explanation:

Answer:

2, 3 and 5 are the prime numbers

Step-by-step:

k-3+3<5+3 is the explanation and the answer is k<8