which of the expressions are equivalent to the one below? check all that apply.
5 x (8+3)
A. 55
B. 5 x 24
C. 43
D. 5 x 8 + 5 x 3

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Given:

The two functions are:

[tex]f(x)=2x^2+1[/tex]

[tex]g(x)=3x-6[/tex]

To find:

The correct statement about the function [tex]f+g[/tex].

Solution:

We have,

[tex]f(x)=2x^2+1[/tex]

[tex]g(x)=3x-6[/tex]

Adding both functions, we get

[tex]f+g=f(x)+g(x)[/tex]

[tex]f+g=2x^2+1+3x-6[/tex]

[tex]f+g=2x^2+3x-5[/tex]

It is a quadratic function. So, option A is incorrect and option B is correct.

The domain of [tex]f+g[/tex] is all real numbers because it is defined for all real values of x. So, option C is incorrect.

The range of [tex]f+g[/tex] cannot be the all real numbers because it has a minimum value of y as the leading coefficient is positive. So, option D is incorrect.

Therefore, the correct option is B.

The answer to your question is 137

Answer:

Correct Answer: A.

Step-by-step explanation:

A) The height of the water increases 2 inches per minute.

Step-by-step explanation:

Slope is the rate of change of height

m = (16 - 12)/(4 - 2) = 4/2 = 2

2 inch per min

Positive slope implies increase

The angles represented by (2x - 60) and (60 - 2x) cannot be supplementary because their sum add up to zero instead of 180°.

Answer:

π × d

Step-by-step explanation:

The relationship between the diameter and circumference is that the circumference is equal to π multiplied by the diameter. This means that our answer is π × d, or the third option

Answer:

The answer is below

Step-by-step explanation:

The endpoints of AB are A(2, 3) and B(8, 1). The perpendicular bisector of AB is CD, and point C lies on AB. The length of CD is (root of 10) units.

The coordinates of point C are (-6, 2) (5, 2) (6, -2) (10, 4) . The slope of is -3 -1/3 1/3 3 . The possible coordinates of point D are (4, 5) (5, 5) (6, 5) (8, 3) and (2, 1) (4, -1) (5, -1) (6, -1) .

Solution:

Since CD is the perpendicular bisector of AC, hence line CD is perpendicular to AB and divides line AB into two equal parts.

Point C(x, y) is the midpoint of AB.

hence:

x = (2 + 8) / 2 = 5

y = (3 + 1)/2 = 2

The coordinates of point C = (5, 2)

The slope of line AB is:

slope of AB = (1 - 3) / (8 - 2) = -1/3

Since CD is perpendicular to AB, hence the product of the slope of AB and the slope of CD is -1

slope of AB * slope of CD = -1

slope of CD * -1/3 = -1

slope of CD = 3

Line CD has slope of 3 and pass through C(5, 2). The equation of line CD is:

y - 2 = 3(x - 5)

y = 3x - 13

The possible coordinates of point D are (6, 5) and (4, -1), because this point lie on line CD.

Answer:

7x

or 7*x

Step-by-step explanation:

Answer:

if you add 14 to 1750 you will get 1764 which equals 42²

Step-by-step explanation:

Answer:

40.2

Step-by-step explanation:

To better analyze this problem, we can first draw a picture. Looking at the one attached, we can see that the stake is represented by the point in the bottom right of the screen, and the kite is 45 meters away from it, representing the 45. Then, the height is 38, and this is directly above the 45 meters away from the stake.

This forms a right triangle, and we can use sohcahtoa to help use. As we don't have the hypotenuse, we can use tan. Tan(θ) = opposite/adjacent, or 38/45. Thus, arctan(38/45) = θ, and plugging that into a calculator, we get 40.2 as our answer

Answer:

x = - 52

Step-by-step explanation:

Given

[tex]\frac{1}{3}[/tex] x - [tex]\frac{2}{3}[/tex] = - 18 ( multiply through by 3 to clear the fractions )

x - 2 = - 54 ( add 2 to both sides )

x = - 52

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf {b. \:-52}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {STEP-BY-STEP\:\:EXPLANATION:}}}[/tex]

[tex] \frac{1}{3} x - \frac{2}{3} = - 18\\[/tex]

➺[tex] \: \frac{1}{3} x = - 18 + \frac{2}{3}\\ [/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 18 \times 3}{1 \times 3} + \frac{2}{ 3} \\[/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 54 + 2}{3}\\ [/tex]

➺[tex] \: \frac{1}{3} x = \frac{ - 52}{3} \\[/tex]

➺[tex] \: x = \frac{ - 52 \times 3}{3}\\ [/tex]

➺[tex] \: x = - 52\\[/tex]

[tex]\sf\pink{Therefore, \:the \:value \:of\: x\:is \:-52.}[/tex]

[tex]\sf \bf {\boxed {\mathbb {TO\:VERIFY:}}}[/tex]

[tex] \frac{1}{3} \times ( - 52) - \frac{2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 52}{3} - \frac{2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 52 - 2}{3} = - 18\\[/tex]

➼[tex] \: \frac{ - 54}{3} = - 18\\[/tex]

➼[tex] \: - 18 = - 18\\[/tex]

➼ L. H. S. = R. H. S.

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

option C

Step-by-step explanation:

Answer:

isosceles triangle

Step-by-step explanation:

Answer:

A, B, and, D

Step-by-step explanation:

I'm not 100% sure but i'm pretty sure these are it.

Hope thus helps!

Answer:

1. reflection- a figure is flipped over

2. translation- a figure is slide

3. rotation- a figure is turned

Answer:

Ox-12

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

(4x - 6) - (3x + 6)              Remove the brackets

4x - 6 - 3x - 6                   Collect like terms

4x - 3x - 6 -6

x - 12

The answer   is A

Answer:

There is no answer

Step-by-step explanation:

because 3√5=6,7082039232 > 6

So 6-3√5 < 0

But √x always >0

So there is no answer

Step-by-step explanation:

profit = sold price - bought price

= 140,000 - 60,000 k

= 80,000 k

% profit = (80,000/60,000)×100

= 133.33 %

the answer is on the picture

Answer:8

Step-by-step explanation:

0.5*10=5

3+5=8

a. Montserrat runs 7.5 kilometers in her 10th training week.

b. by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

To find how many kilometers Montserrat runs in her 10th training week, we can use the arithmetic sequence formula to find the nth term:

[tex]a_n = a_1 + (n - 1) * d[/tex]

where:

[tex]a_n[/tex] is the nth term (the number of kilometers in the nth week),

[tex]a_1[/tex] is the first term (the number of kilometers in the first week, which is 3 km),

n is the number of weeks (in this case, 10), and

d is the common difference (the amount by which the distance increases each week, which is 0.5 km).

[tex]a_{10} = 3 + (10 - 1) * 0.5\\a_{10} = 3 + 9 * 0.5\\a_{10} = 3 + 4.5\\a_{10 }= 7.5 km[/tex]

So, Montserrat runs 7.5 kilometers in her 10th training week.

b. Next, to calculate the total number of kilometers Montserrat will have run by her 15th training week, we use the sum of the first n terms formula:

[tex]S_n = (n / 2) * (a_1 + a_n)[/tex]

where:

[tex]S_n[/tex] is the sum of the first n terms (the total number of kilometers run by the nth week),

[tex]a_1[/tex] is the first term (3 km),

[tex]a_n[/tex] is the nth term (which we found to be 7.5 km in her 10th week),

n is the number of weeks (15 in this case).

[tex]S_{15} = (15 / 2) * (3 + 7.5)\\S_{15} = 7.5 * 10.5\\S_{15} = 78.75 km[/tex]

So, by her 15th training week, Montserrat will have run a total of 78.75 kilometers.

To know more about training:

https://brainly.com/question/28942187

#SPJ3

Answer: F. is a linear relation.

Step-by-step explanation:

Answer:

G

Step-by-step explanation:

Equation of the eventual line:

(y-4)/(5-4) = x

y-4 = x

y = x + 4

this equation can’t be used to determine the last three values. In fact, for examples:

7 = 2 + 4

7 = 6 (false)

So the relation is non linear

Answer:

f (4) = 8

Step-by-step explanation:

f (x) =2

2 x 4 = 8

Answer:

What is 5/8 x 128? Answer: This is the same as working out 5/8 of 128. Do this by dividing by the bottom numbers, and multiplying by the top number. So 128 divided by 8 is 16, 16 times 5 is 80.

Answer:

The rate (or speed) of the wind is 40 meters per minute.

Step-by-step explanation:

Let's define:

S = speed (or rate) of the duck alone

S' = speed (or rate) of the wind.

When the duck travels with the wind, its speed is:

(S + S')

While when the duck travels against the wind, its speed is:

(S - S')

Also, remember the relation:

Distance = Speed*Time

ok, we know that the duck can travel a distance of 2400 m in 10 minutes with the wind, then:

2400m = (S + S')*10 min

And against the wind, it can travel 2/3 of that distance, then we can write:

(2/3)*2400m = (S - S')*10 min

Then we have a system of 2 equations:

2400m = (S + S')*10 min

(2/3)*2400m = (S - S')*10 min

We want to find the speed of the wind, then we want to find the value of S'.

To solve this, we first need to isolate S in one of the equations.

Let's isolate S in the first one:

2400m = (S + S')*10 min

2400m/10min = (S + S')

240 m/min = S + S'

240 m/min - S' = S

Now we can replace this in the other equation:

(2/3)*2400m = (S - S')*10 min

(2/3)*2400m = ( 240 m/min - S' - S')*10 min

Now let's solve this for S'

(2/3)*2400m/10min = 240 m/min - 2*S'

(2/3)*240 m/min = 240 m/min - 2*S'

2*S' = 240 m/min - (2/3)*240 m/min

2*S' = (1/3)*240 m/min

2*S' = 80 m/min

S' = (80 m/min)/2

S' = 40 m/min

The rate (or speed) of the wind is 40 meters per minute.

Answer:

57

Step-by-step explanation:

5|x^³-2|+7

let x=-2

5|(-2)^3-2|+7

work inside the absolute value first

5|-8-2|+7

5|-10|+7

Take the absolute value, which make it positive

5 *10+7

multiply

50+7

=57

nakita ko lng po yan but hope that helpsツ

Answer:

[tex]x = \frac{7}{2}[/tex]

Step-by-step explanation:

[tex]6^{x-1} = 36 \sqrt6\\\\6^{x-1} = 6^2 \times 6^{\frac{1}{2}}\\\\6^{x-1} = 6^{2 + \frac{1}{2} }[/tex]                        [tex][ \ a^x \times a^ y = a^{x+ y} \ ][/tex]

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

[tex]x = 2 + \frac{1}{2} + 1\\\\x = 3 + \frac{1}{2} \\\\x = \frac{6+ 1}{2} \\\\x = \frac{7}{2}[/tex]

Answer:

x = 3.5

Step-by-step explanation

Using the rules of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] ⇔ [tex]a^{(m+n)}[/tex] and [tex]\sqrt{a}[/tex] = [tex]a^{\frac{1}{2} }[/tex]

Then

36[tex]\sqrt{6}[/tex] = 6² × [tex]6^{\frac{1}{2} }[/tex] = [tex]6^{(2+0.5)}[/tex] = [tex]6^{2.5}[/tex]

Thus

[tex]6^{x-1}[/tex] = [tex]6^{2.5}[/tex]

Since the bases on both sides are equal, both 6, equate the exponents

x - 1 = 2.5 ( add 1 to both sides )

x = 3.5

Answer:

y >= x/2 - 1

Step-by-step explanation:

the slope (rise/run) is 1/2 and the y-intercept is -1 so in point-slope form

y = x/2 - 1 but everything above the line (unshaded part) is valid so y is equal to or greater than.