What is the sum of the polynomials? (6x + 7 + x2) + (2x2 - 3)

Answer:

19 -  8√3

Step-by-step explanation:

(-4 + √2)^2

= (-4)^2 + 2(-4)(√3) + √3)^2

= 16 - 8√3 + 3

= 19 -  8√3

Answer:

D

Step-by-step explanation:

note that ([tex]\sqrt{3}[/tex] )² = 3

Given

(- 4 + [tex]\sqrt{3}[/tex] )² = (- 4 + [tex]\sqrt{3}[/tex])(- 4 + [tex]\sqrt{3}[/tex])

Expand using (a + b)² = a² + 2ab + b²

= (- 4 )² + 2(- 4[tex]\sqrt{3}[/tex] ) + ( [tex]\sqrt{3}[/tex] )²

= 16 - 8[tex]\sqrt{3}[/tex] + 3

= 19 - 8[tex]\sqrt{3}[/tex]

The answer is:

The correct option is:

A) The function g(x) has a higher y-intercept.

To solve the problem, we need to find the y-intercept of the g(x) function, and then, compare to the y-intercept of the f(x) function which is equal to -1 (we can see it on the picture).

Also, we need to remember the slope-interception form of the line:

[tex]y=mx+b[/tex]

So,

Finding the y-intercept of the g(x) function, we have:

Calculating the slope of the function, using the first two points (4,9) and (6,13), we have:

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{13-9}{6-4}=\frac{4}{2}=2[/tex]

Now,

Calculating the value of "b", we have:

Using the first point (4,9), the slope of the function, and the slope-intercept form of the function, we have:

[tex]y=mx+b[/tex]

[tex]y=2x+b[/tex]

[tex]9=2*(4)+b[/tex]

[tex]9=8+b[/tex]

[tex]9-8=b[/tex]

[tex]b=1[/tex]

So, the equation of the line will be:

[tex]y=2x+1[/tex]

We know that "b" represents the y-intercept, so, the function g(x) has its y-intercept at y equal to 1.

Comparing, we have that the function f(x) has a y-intercept located at y equal to "-1" and the g(x) function has a y-intercept located at y equal to "1".

Hence, the correct option is:

A) The function g(x) has a higher y-intercept.

Have a nice day!

To express the area of a rectangle as a monomial, multiply the length and width. This gives 30m6.

The area of a rectangle is calculated by multiplying its length and width. For a rectangle with length 5m4 and width 6m2, to express the area as a monomial, you multiply these two together. So, the area A = 5m4 * 6m2.

In terms of exponents, when we multiply terms with the same base (in this case, m), we add up the exponents. Thus, A = 30m4+2 = 30m6. Therefore, the area of the rectangle expressed as a monomial is 30m6.

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Answer:

64% as a fraction and decimal: 16/25 and .64

1/8 as a percent and decimal: 12.5% and .125

1.4 as a percent and fraction: 140% and 1 2/5

2 3/4 as a percent and decimal: 275% and 2.75

8 percent as a decimal and fraction: .08 and 2/25

Step-by-step explanation:

Answer: 1,760 centimeters

Step-by-step explanation: Your Answer is above

sqrt (b^2 -4ac ) =sqrt (4-4•3•4) = sqrt (-44) so the parabola does not have real solutions. Answer C)

Answer:

c

Step-by-step explanation:

To find the monthly rate of decay, we convert the annual decay rate of 8% to a monthly rate using the formula for compound interest. The monthly rate comes out to be approximately -0.6734%, which is closest to the provided option of -0.667%.

To find the monthly rate of decay for a car that depreciates 8% annually, we should convert the annual decay rate to a monthly decay rate assuming compound interest. This calculation involves using the formula for converting an annual percentage rate to a monthly rate when compounded monthly:

Monthly rate = [tex](1 + Annual rate)^(1/12)[/tex] - 1

Substitute the given annual rate of decay (-0.08 or -8%) into the formula:

Monthly rate = [tex](1 - 0.08)^(1/12)[/tex] - 1

This calculation gives us:

Monthly rate = [tex](0.92)^(1/12)[/tex] - 1
Approximately -0.006734

Expressed as a percentage, the monthly rate of decay is approximately -0.6734%, which means the correct answer is not exactly presented in the choices. However, the closest value from the options provided is -0.667%.

Answer:

[tex]\boxed{0.2}[/tex]

Step-by-step explanation:

Convert [tex]\dfrac{12}{60}[/tex] to a decimal

Step 1. Reduce the fraction to its lowest terms.

Divide both numerator and denominator by their greatest common factor (12)

[tex]\dfrac{12}{60} =\dfrac{1}{5}[/tex]

Step 2. Convert the denominator to a power of 10

Multiply both numerator and denominator by 2.

[tex]\dfrac{1}{5} \times \dfrac{2}{2} = \dfrac{2}{10}[/tex]

Step 3. Divide the numerator by the denominator

Dividing by 10 moves the decimal point one place to the left.

[tex]\dfrac{2}{10} = \boxed{0.2}[/tex]

Answer: Third option

[tex]V_s=14\ m^3[/tex]

Step-by-step explanation:

The volume of a sphere is:

[tex]V_s=\frac{4}{3}\pi r^3[/tex]

Where r is the radius of the sphere

The volume of a cylinder is:

[tex]V_c = \pi r ^ 2 h[/tex]

Where h is the height of the cylinder and r is the radius

We assume that the height of the sphere is its diameter or 2 times its radius.

Then [tex]2r = h[/tex]

[tex]V_c= 21\ m^3=\pi r ^ 2 h[/tex]

[tex]V_c= 21\ m^3=\pi r ^ 2(2r)[/tex]

We solve the equation for r

[tex]\frac{21}{2\pi}=r ^ 3\\\\r= \sqrt[3]{\frac{21}{2\pi}}\\\\r=1.495\ m[/tex]

The radius of the cylinder is equal to the radius of the sphere

Finally

[tex]V_s=\frac{4}{3}\pi (1.495)^3[/tex]

[tex]V_s=14\ m^3[/tex]

2y^2- 14y+ 20

By splitting the middle term:

2y^2 -10y -4y +20

By taking the common outside:

2y(y-5) -4(y-5)

=(2y-4)(y-5)

=2(y-2)(y-5)

Therefore D is the right answer

Answer:

D

Step-by-step explanation:

Given

2y² - 14y + 20 ← factor out 2 from each term

= 2(y² - 7y + 10)

To factor the quadratic

Consider the factors of the constant term (+ 10) which sum to give the coefficient of the y- term (- 7)

The factors are - 2 and - 5, since

- 2 × - 5 = 10 and - 2 - 5 = - 7, so

y² - 7y + 10 = (y - 2)(y - 5) and

2y² - 14y + 20 = 2(y - 2)(y - 5) → D

Answer:

[tex]f(15)=525\ ft^{2}[/tex]

f(15) is the area of the rectangular garden for a width of 15 ft

Step-by-step explanation:

we know that

[tex]f(x)=x(2x+5)[/tex]

where

x----> is the width of the rectangular garden

(2x+5) ----> is the length of the rectangular garden

so

f(15) -----> is the value of f(x) for x=15 ft

That means

f(15) is the area of the rectangular garden for a width of 15 ft

substitute the value of x and solve

[tex]f(15)=15(2(15)+5)[/tex]

[tex]f(15)=525\ ft^{2}[/tex]

Answer:f(15) is the area of the rectangular garden for a width of 15 ft

Step-by-step explanation:

we know that

where

x----> is the width of the rectangular garden

(2x+5) ----> is the length of the rectangular garden

so

f(15) -----> is the value of f(x) for x=15 ft

That means

f(15) is the area of the rectangular garden for a width of 15 ft

substitute the value of x and solve

Step-by-step explanation:

Answer:

0.42

Step-by-step explanation:

There are 12 different paths to the end. Five of those paths lead to money.

p(winning money) = 5/12 = 0.42

Answer:

=53 seconds.

Step-by-step explanation:

24ft=7sec

180

180 x 7

_______=52.5=53

24

Answer:

[tex](f + g) (2) = -4[/tex]

Step-by-step explanation:

We have the functions

[tex]F(x) =-3x^2-2[/tex]

And

[tex]g(x)=4x+2[/tex]

We want to find [tex](f + g) (x)[/tex]

Then

[tex](f+g)(x) = f(x) + g(x)\\\\(f+g)(x) = -3x^2-2 + 4x+2\\\\(f+g)(x)= -3x^2 +4x[/tex]

finally we find [tex](f + g) (2)[/tex]

[tex](f + g) (2) = -3(2)^2 + 4(2)\\\\(f + g) (2) = -3*4 + 8\\\\(f + g) (2) = -12+ 8\\\\(f + g) (2) = -4[/tex]

Answer:

(f+g)2 = 20

Step-by-step explanation:

18. if F(x) =-3x2-2 and g(x)=4x+2 what is value of (f+g)(2)?

We know, (f+g)2= f(2) + g(2)

We will put 2 in the place of x for f(x) and g(x) and then find their result.

Solving:

(f+g)2= f(2) + g(2)

         =3(2)^2 -2 + 4(2) +2

         = 3(4) -2 + 8 +2

         = 12 -2 +8 +2

         = 20

So, (f+g)2 = 20

Answer:

[tex]\large\boxed{x=-\dfrac{1}{5}}[/tex]

Step-by-step explanation:

[tex]\dfrac{a-x}{x-a}=5x\\\\\dfrac{(a-x)}{-(a-x)}=5x\qquad\text{cancel}\ (a-x)\\\\-1=5x\qquad\text{divide both sides by 5}\\\\-\dfrac{1}{5}=\dfrac{5x}{5}\to\boxed{x=-\dfrac{1}{5}}[/tex]

The mean is the average, add the numbers together and divide by the quantity of numbers:

10 + 12 + 15 + 12 + 13 + 11 + 10 + 13 = 96

96 / 8 = 12

The mean is 12

The median is the middle value.

Rearrange the numbers from smallest to largest:

10 , 10 , 11 , 12 , 12 , 13 , 13 , 15

There are an even amount of numbers, so find the middle two values, add together and divide by 2:

12 + 12 = 24 /2

Median = 12

Check the picture below.

Check the picture below.

Answer:

800 meters

Step-by-step explanation:

y is inversely proportional to x is the same as y is inversely proportional to [tex]\frac{1}{x},[/tex] that means

[tex]y=\dfrac{k}{x}.[/tex]

If a wave with a frequency of x=720 kilohertz has a length of y=500 meters, then

[tex]500=\dfrac{k}{720}\\ \\k=500\cdot 720=360000.[/tex]

Hence, the length of a wave y with a frequency of x=450 kilohertz is

[tex]y=\dfrac{360000}{450}=800[/tex]

The relationship between the frequency and wavelength of a wave is given by the formula:
\[ c = f \times \lambda \]
where:
- \( c \) is the speed of light (or the speed of the wave in another medium, but for radio waves in the air or vacuum, it's approximately the speed of light),
- \( f \) is the frequency of the wave,
- \( \lambda \) is the wavelength of the wave.
Given that the relationship is inverse, when the frequency goes up, the wavelength goes down, and vice versa.
We are given that a wave with frequency 720 kilohertz has a length of 500 meters. We can represent this with the equation:
\[ c = 720 \times 500 \]
We are asked to find the wavelength when the frequency is 450 kilohertz. Since the speed of light doesn't change, we set up the proportion using the formula, keeping \( c \) constant:
\[ 720 \times 500 = 450 \times \lambda_{\text{new}} \]
Now we solve for \( \lambda_{\text{new}} \):
\[ \lambda_{\text{new}} = \frac{720 \times 500}{450} \]
To simplify this, we can divide both the numerator and the denominator by a common factor. In this case, let's divide by 90:
\[ 720 \div 90 = 8 \]
\[ 450 \div 90 = 5 \]
\[ 500 \text{ remains unchanged} \]
Now we can substitute these simplified numbers back into our equation:
\[ \lambda_{\text{new}} = \frac{8 \times 500}{5} \]
\[ \lambda_{\text{new}} = \frac{4000}{5} \]
\[ \lambda_{\text{new}} = 800 \]
So the length of a wave with a frequency of 450 kilohertz is 800 meters.

To determine which equations have a lower unit rate than the rate in the table, calculate the unit rate or slope from the table and compare it to the slopes of the other equations. Equations with a smaller slope have a lower unit rate.

To answer this question, we need to calculate the unit rate of the original equation. The unit rate is the ratio of the increase in the dependent variable (usually represented by y) to the increase in the independent variable (usually represented by x).

For example, if the table shows x increasing by 2 and y increasing by 4, then the unit rate is 4/2 = 2 which is the slope.

The equations with a lower unit rate than this would have a smaller ratio of the increase in y to the increase in x. For instance, if the slope of another equation is 1, that means for each unit increase in x, y increases by only 1, which is less than the original rate of 2.

Therefore, to decide which equations have a lower unit rate, compare the slopes of the equations to the unit rate calculated from the original table. Any equation with a smaller slope has a lower unit rate.

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Answer:

1. Simple random sampling

2. Systematic random sampling

Answer:

A) x+y=4

B) x-y=-6​

We add both equations and get

2x = -2 so x = -1

and y = 5

So the ordered pair (-1, 5) is the solution to the equations.

Step-by-step explanation:

Answer:

k = 2cw

Step-by-step explanation:

1. 11cw + 2k = 15cw

2. Subtract 11cw from both sides:

2k = 4cw

3. Divide by 2 on both sides:

k = 2cw

Answer:

She would need to complete 5.57 each noght to reach her goal of 100%.

Step-by-step explanation:

39/7 is equal to 5.57

Answer:

[tex]m=\frac{3}{4}[/tex]

Step-by-step explanation:

We can use the slope formula in order to find the slope of the line

[tex]m=\frac{-2-2}{0-(-3)} \\m=\frac{-4}{3}[/tex]

For a line to be perpendicular, it must have a slope that is the negative reciprocal, so that means that we swap the numerator and denominator and then multiply it by -1, this means that

[tex]m=\frac{-4}{3}\\\\m=\frac{3}{-4} \\\\m=\frac{-3}{-4} \\\\m=\frac{3}{4}[/tex]

Answer:

The square root of 130 would be 11.4017543. Rounding to the nearest tenth, we would get 11.4, because the value 0 is below 5. Rounding 11.4 to the nearest whole number, we would get 11, because the value 4 is below 5. So either 11 or 11.4 works, depending on if you are looking for a decimal or a whole number.

Hope this helps ya :D

Final answer:

The simplified square root of 130 is √130 and cannot be further simplified using integers as 130 does not have pairs of identical prime factors.

Explanation:

The question asks for the simplified form of the square root of 130. To simplify a square root, you want to factor the number under the square root into its prime factors and look for pairs of identical factors, because the square root of a pair of identical factors is just that number. In this case, 130 = 2 x 5 x 13, and since there are no pairs of identical factors, we cannot simplify it further without using a decimal or fractional answer. Therefore, the simplified square root of 130 is √130, which cannot be further simplified using integers.

The area of a kite is half the product of the diagonals.  

Area = ½(d1 x d2)  

Plug in the values of the diagonals.

Area = ½(7.8 * 6)  

Multiply, and you should get -

Area = 23.4 ft²

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

Diagonals of kite are as follows:

7.8 ft and 6 ft

As we know the formula for "Area of kite":

Area of kite is given by

[tex]\dfrac{1}{2}\times d_1\times d_2\\\\=\dfrac{1}{2}\times 7.8\times 6\\\\=3\times 7.8\\\\=23.\ ft^2[/tex]

Hence, Option 'A' is correct.

.25 is the answer because the next number should be half of the previous number and the opposite sign of the previous number.

0.25 is the best answer for the sequence :D

Answer:

It would take them 6.667 minutes to paint 50 square feet together.

Step-by-step explanation:

This is a classic work problem.  If Sam can do the job in 10 minutes, she can get done 1/10 of the job in one minute.  If you can do the job in 5 minutes, you can 1/5 of the job done in one minute.  To find out how many minutes it will take them together to paint 25 square feet, set the addition of their times equal to 1/x:

[tex]\frac{1}{10}+\frac{1}{5}=\frac{1}{x}[/tex]

x is how long it takes them to get the job done together.  Find the common denominator and multiply it through be everything to get rid of the denominators altogether.  That denominator is 10x:

[tex](10x)\frac{1}{10}+(10x)\frac{1}{5}=(10x)\frac{1}{x}[/tex]

Simplify to get the simple equation x + 2x = 10 and 3x = 10.  That means that x=3 1/3.  That's how long it takes to do 25 square feet.  Double that time for 50 square feet.

-35

First, add the contents of the parentheses. 3 + 4 = 7. This gives you -5 * 7.

Now, just multiply. -5 * 7 = -35, so -35 is the answer.