What is the GCF of the expression 4x2 + 3x?


A.x


B.3x


C.4x


D.x2

Number of Horses in Avery's farm, after t years from now is given by function H(t); where  [tex]H(t) = 25(2)^{t}[/tex]

The amount of hay, in tons, that is produced on her farm t years from now is given by function A(t); where  [tex]A(t) = 150(1.5)^{t}[/tex]

The predicted yearly supply of hay, in tons, available to each horse in Avery's farm t years from now is given by function F(t); where F(t) = A(t)/H(t)

So, F(t) = [tex]\frac{150(1.5)^{t}}{25(2)^{t}}[/tex] = [tex]6 (\frac{1.5}{2}) ^{t}[/tex] = [tex]6 (0.75)^{t}[/tex] tons/horse

The formula for F(t) in terms of H(t) and A(t) is F(t) = (150(1.5)^t) / (25(2)^t).

To find the formula for F(t), we need to divide the amount of hay produced, A(t), by the number of horses, H(t). So, the formula for F(t) is F(t) = A(t) / H(t). Substituting the given functions, we have F(t) = (150(1.5)^t) / (25(2)^t).

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6 on the sq rt 5 - 4 on the sq rt 7

To simplify the given expression, substitute the values of each square root and simplify the expression to get the final result of 1.416.

To simplify the given expression:
3 times the square root of 5 - 2 times the square root of 7 + the square root of 45 - the square root of 28

We can simplify each square root separately:

√5 = 2.236 (approx.)

√7 = 2.646 (approx.)

√45 = 6.708 (approx.)

√28 = 5.292 (approx.)

Substituting these values in the expression:

3(2.236) - 2(2.646) + 6.708 - 5.292

This simplifies to:
6.708 - 5.292 = 1.416

Therefore, the simplified expression is 1.416.

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i THINK its 2 1/2 ?????

Remark

You are dealing with a right angle triangle. You can use one of Sin(x) Cos(x) or Tan(x). Since the Hypotenuse is involved and since you are given the adjacent side, Cos(71) is what you will need.

Solution

H = BC

Cos(x) = adjactent / hypotenuse

Cos(71) = 6.3 / H            Multiply both sides by H

H * Cos(71) = 6.3            Divide by Cos(71)

H = 6.3 / cos(71)             Cos(71) = 0.32557

H = 6.3 / 0.32557          Divide

H = BC = 19.351                       Answer

Oh this is easy.I completed the table. C) 40%

THE ANSWER IS C (◡ ‿ ◡ ✿)

Answer:

Domain = R

Range =(0,infinity)

Step-by-step explanation:

Given a function as

y = 4(1/3)^x

The function does not have x or y in the denominator or any square root sign.

Hence we can assign any values to x.

Domain = R = Set of all real numbers = (-infinity, infinity)

Let us consider range.

We find that 4(1/3)^x is a multiple of 4 and powers of 1/3

Since power of 1/3 is always positive, y cannot take any negative value.

When x=0 y =4.

When x tends to -infinity, y tends to 0

So y cannot take the value 0 except at -infinity.

Range =(0,infinity)

B) 5 mph

hope this helped

Answer:

Its 16

100% Correct

Step-by-step explanation:

USA TEST PREP

The weight of the body when the distance is 750 miles if it is inversely proportional is 3,920 pounds.

w = k/d²

Where,

k = constant of proportionality

w = 180 pound

d = 3,500 miles

w = k/d²

180 = k/3500²

180 = k/12,250,000

cross product

k = 180 × 12,250,000

k = 2,205,000,000

Therefore, when d = 750 miles

w = k/d²

w = 2,205,000,000 / 750²

= 2,205,000,000 / 562,500

= 3,920 pounds

Hence, the weight of the body is 3,920 pounds.

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The sum of the measures of the angles of a hexagon is equal 720°.

Therefore we have the equation:

[tex]160^o+75^o+132^o+113^o+108^o+x^o=720^o\\\\588^o+x^o=720^o\ \ \ \ |-588^o\\\\x^o=132^o[/tex]

Answer: x = 132

ANSWER

[tex]x=4[/tex]

EXPLANATION

We have[tex]6x-8=16[/tex]

We add 8 to both sides of the equation

[tex]6x-8+8=16+8[/tex]

We simplify

[tex]6x=24[/tex]

We divide both sides by 6

[tex]x=\frac{24}{6}[/tex]

[tex]x=4[/tex]

Using the base and the acute angle on the base, to find the height of the dam, you would need to multiply the base by the tangent of the angle.

Height = 100 * tan(40)

Answer:

Sali's speed was 18.75 km/h.

Step-by-step explanation:

Jane took 3.5 hours to cycle the 63 km.

As,  [tex]Speed= \frac{Distance}{Time}[/tex] , so the speed of Jane will be:  [tex]\frac{63}{3.5} km/h = 18 km/h[/tex]

Suppose, the speed of Sali is  [tex]x[/tex] km/h

Sali caught up with Jane when they had both cycled 30 km.

So, the time required for Jane to cycle 30 km [tex]= \frac{30}{18}=\frac{5}{3} hours[/tex] and the time required for Sali to cycle 30 km  [tex]=\frac{30}{x} hours[/tex]

Given that, Sali started to cycle 4 minutes or [tex](\frac{4}{60}) or (\frac{1}{15}) hours[/tex] after Jane started to cycle. So, the equation will be.......

[tex]\frac{5}{3}-\frac{30}{x}= \frac{1}{15}\\ \\ \frac{30}{x}= \frac{5}{3}-\frac{1}{15}\\ \\ \frac{30}{x}= \frac{24}{15}\\ \\ 24x=450\\ \\ x= \frac{450}{24}= 18.75[/tex]

Thus, the speed of Sali was 18.75 km/h.

Answer:Thus, the speed of Sali was 18.75 km/h.

Step-by-step explanation:

Sali's speed was 18.75 km/h.

675 : 5 = 135

135 : 5 = 27

27 : 3 = 9

9 : 3 = 3

3 : 3 = 1

675 = 5 · 5 · 3 · 3 · 3 = 5² · 3³

6. vertical

7. LSM and MSN are vertical angles

8. MSN

Answer:

6. Which type of angle pair are LSM and OSN?

Answer - D. Vertical angles

Vertical angles are pairs of opposite angles made by two intersecting lines.

7. Which of the following statements are false?

Answer - C. LSM and MSN are vertical angles.

Vertical angles are pairs of opposite angles made by two intersecting lines.

8. Which angle is supplementary to LSM?

Answer - D. MSN

Two angles are supplementary when they add up to become 180 degrees.

Here adding both we will get angle S as 180 degrees.

Answer: Single deposit by Edward=$3594 to make it  amount for college=$50,000 in 10 years.

Step-by-step explanation:

Here Compound amount =$50,000

Time=10 years

Rate of interest=4.3%

By the Daily compound  interest formula ,we have

[tex]Amount=Principal(1+rate/365)^{365\times\ time}\\\Rightarrow\ Amount=Principal(1+4.3/365)^{365\times\ 10}\\\Rightarrow\ 50000=P(1+.011)^{3650}\\\Rightarrow\ 50000=P(1.011)^{3650}\\\Rightarrow\ 50000=P(13.911)...........(approx)\\\Rightarrow\ P=\frac{50000}{13.911}=3594......(approx)[/tex]

Therefore Principal amount deposited by Edward is $3594.

Answer:

$32,526.67

Step-by-step explanation:

Let the Principle be P

amount here A= $50,000

time n= 10 years n= 10*365=3650 days

rate of interest= 4.3% compounded daily= 4.3/365

let us use compound interest formula to calculate the principle

[tex]A= P(1+\frac{r}{100})^n[/tex]

putting all the values we get

[tex]50000=P(1+\frac{4.3}{100\times365})^10times365[/tex]

on solving we get P= $32,526.67

therefore he need to deposit $32,526.67

Answer:

Option B) 5    

Step-by-step explanation:

We are given the following information:

A scatter plot is given which shows the number of hats and scarves each knitter sold at a knitting show.

In the scatter plot the x-axis shows the number of hats sold and the y-axis shows the number of scarves sold.

We have to find the number of hats sold by the knitter when he sold 8 scarves.

In order to find this we have to find the x-values corresponding to the y-values of 8 scarves in the scatter plot.

Corresponding to 8 on y-axis we have a point that have a corresponding value of 5.

Hence, 5 hats were sold by the knitter when he sold 8 scarves.

Option B) 5 is the correct answer.

The scatter plot that shows the number of hats and scarves each knitter sold at a knitting show is Option B) 5    

To find the number of hats sold when 8 scarves were sold, you can look at the scatter plot and observe that there is a data point on the plot where the y-value (number of scarves) is 8, and the corresponding x-value (number of hats) is 5.

In the scatter plot the x-axis shows the number of hats sold and the y-axis shows the number of scarves sold. In order to find this we have to find the x-values corresponding to the y-values of 8 scarves in the scatter plot.

Hence, 5 hats were sold by the knitter when he sold 8 scarves.

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Area of Bull's Eye:

A = π r²

   = π (1)²

   = π

Area of Inner Ring:

A = π r²

   = π (3-1)²

   = 4π

Ratio between Inner Ring and Bull's Eye:

[tex]\frac{InnerRing}{Bull's Eye} = \frac{4\pi }{\pi} = 4[/tex]

Answer: It is 4 times harder to hit the Bull's Eye than it is to hit the Inner Ring

Final answer:

The Inner Ring is 8 times larger than the Bull's Eye.

Explanation:

To determine how much harder it is to hit the Bull's Eye compared to the Inner Ring, we can compare their areas.

The area of a circle is calculated using the formula A = πr^2, where A is the area and r is the radius of the circle.

The area of the Bull's Eye can be calculated as A = π(1)^2 = π square inches.

The area of the Inner Ring can be calculated as A = π(3)^2 - π(1)^2 = 9π - π = 8π square inches.

Therefore, the Inner Ring is 8 times larger than the Bull's Eye.

The value of the expression 2d + 32 is 48 when d equals 8.

The student has provided an expression 2d + 32 and the value for d is given as 8. In order to evaluate the expression, we simply need to substitute the value of d into the expression.

Evaluating the expression:
2d + 32
= 2(8) + 32
= 16 + 32
= 48.

So, the value of the expression when d = 8 is 48.

[tex]1.\\\dfrac{9}{2}(8-x)+36=102-\dfrac{5}{2}(3x+24)\ \ \ \ |\text{multiply both sides by 2}\\\\\not2^1\cdot\dfrac{9}{\not2_1}(8-x)+2\cdot36=2\cdot102-\not2^2\cdot\dfrac{5}{\not2_1}(3x+24)\\\\9(8-x)+72=204-5(3x+24)\ \ \ \ |\text{use distributive property}\\\\(9)(8)+(9)(-x)+72=204+(-5)(3x)+(-5)(24)\\\\72-9x+72=204-15x-120\ \ \ \ |\text{use commutative and associative property}\\\\-9x+(72+72)=-15x+(204-120)\\\\-9x+144=-15x+84\ \ \ \ |\text{subtract 144 from both sides}[/tex]

[tex]-9x=-15x-60\ \ \ \ |\text{add 15x to both sides}\\\\6x=-60\ \ \ \ |\text{divide both sides by 6}\\\\\boxed{x=-10}[/tex]

[tex]2.\\-12x-0.4 > 0.2(36.5x+80)-55\ \ \ \ |\text{use distributive property}\\\\-12x-0.4 > (0.2)(36.5x)+(0.2)(80)-55\\\\-12x-0.4 > 7.3x+16-55\ \ \ \ |\text{use associative property}\\\\-12x-0.4 > 7.3x+(16-55)\\\\-12x-0.4 > 7.3x-39\ \ \ \ |\text{add 0.4 to both sides}\\\\-12x > 7.3x-38.6\ \ \ \ |\text{subtract 7.3x from both sides}\\\\-19.3x > -38.6\ \ \ \ \ |\text{change the signs}\\\\19.3x < 38.6\ \ \ \ |\text{divide both sides by 19.3}\\\\\boxed{x < 2}[/tex]

2)

-12x - 0.4 > 0.2(36.5x + 80) - 55

Distributive property

-12x - 0.4 > 7.3x + 16 - 55

Combine like terms

-12x - 0.4 > 7.3x -39

Subtract both sides by 7.3x

-19.3x - 0.4 > - 39

Add 0.4 to both sides

-19.3x > -38.6

Divide both sides by -19.3 (remember when dividing a negative number, the sign will be flipped)

x < 2

1)

9/2(8 -x) + 36 = 102 - 5/2(3x+24)

Multiply both sides by 2

9(8 -x) + 72 = 204 - 5(3x+24)

Distributive propery

72 - 9x + 72 = 204 - 15x - 120

Combine like terms

- 9x + 144 = -15x + 84

Add 15x to both sides

6x + 144 = 84

Subtract 144 from both sides

6x = -60

 x = -10

Hope they help.

answer is equal to2:1/2=4:1

4 cups are required

Final answer:

For every cup of butter in the recipe, 4 cups of flour are needed. This is found by analyzing the ratio of flour to butter given in the recipe, which is 2 cups flour to 0.5 cup butter.

Explanation:

The question asks how many cups of flour are needed to mix with each cup of butter according to a given recipe. To determine this, we look at the provided ratios and find that the recipe calls for 2 cups of flour and 0.5 cup of butter. This results in the ratio of 4 cups of flour for every 1 cup of butter.

To calculate the amount of flour required for each cup of butter, we use a simple proportion:

0.5 cup butter : 2 cups flour
1 cup butter : x cups flour

To solve for x (the amount of flour needed for 1 cup of butter), we cross-multiply and get:

0.5x = 2
x = 2 / 0.5
x = 4

So, for every cup of butter, 4 cups of flour are needed.

Point slope form says the line through (a,b) with slope m is

y - b = m(x - a)

Here that's

y - - 1 = -2(x - -4)

Answer: y + 1 = -2(x + 4)

Point-Slope equation: y - y₁ = m(x - x₁)  ; m is slope and (x₁ ,y₁) is the coordinate

y - (-1) = -2(x - (-4)

y + 1 = -2(x + 4)     simplified (two negatives make a positive)

Distance covered in 12 gallons tank of gas = 420 miles

So, distance covered in 1 gallon tank of gas = [tex]\frac{420}{12}[/tex] miles

Now, distance covered in 8 gallons will be =

[tex]8*\frac{420}{12}[/tex] =280 miles

Hence, distance covered by Mr.Fink's economy car in 8 gallons tank of gas is 280 miles.

Answer:

Only one solution

Step-by-step explanation:

Given that there is a coordinate plane (say xy)

Two lines are given.

One line crosses the y axis at 3 and has a slope of negative 1.

hence equation of I line is y = -x+3

The other line crosses the y axis at 3 and has a slope of two thirds.

So equation is y = 2x/3 +3

Since the two lines lie in the same plane and are having different slopes, they intersect at one point.

Eliminate y to get

-x+3=2x/3+3

Or x=0

y=3

Hence solutionis (0,3) for the system.

Answer:

One solution

Step-by-step explanation:

we know that

The solution of the system of equations  is equal to the intersection point both graphs

we have

[tex]y=-x+3[/tex] ------> equation A

[tex]y=-(2/3)x+3[/tex] ------> equation B

Using a graphing tool

see the attached figure to better understand the problem

In this problem the intersection point is only one

therefore

The system of equations has one solution

The solution is the point [tex](0,3)[/tex]

Answer:

it is PRIME

Step-by-step explanation:

It has 2 factors: 1 and 5

Yes, there was a mistake in applying the distributive property. If you have to perform

[tex] 3(2x-5) [/tex]

you have to multiply both terms in the parenthesis by 3, not just the first one.

So, the correct expansion would be

[tex] 3(2x-5) = 3\cdot 2x - 3 \cdot (-5) = 6x-15 [/tex]

Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 4x=7+3(2x-5).

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Now, 4x=7+6x-15

4x=6x-8

4x-6x= -8

-2x=-8

x=4

Leeza made an error she did not multiply 3 into the bracket correctly. Therefore, the solution to an equation is 4.

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answer:  [tex]-15 - x[/tex]

work:

[tex]5-(x+4)[/tex]  | distribute the negative into the parentheses, which means multiply   into the parentheses.

[tex]5 - x - 20[/tex]  | combine like terms

[tex]-15 - x[/tex]  | final answer

correct me if anything is wrong, otherwise hope this helps! ❤ from peachimin

Hello there!

Distributive property you had to used their formula like:

↓

a(b+c)=ab+ac

5-(x+4)

First you had to distribute by the negative signs.

5+-1(x+4)

5+-1x+(-1)(4)

5+-x+-4

Then you combine like terms of

↓

5+-x+-4

(-x)+(5+-4)

Simplify

=-x+1

Answer⇒⇒⇒⇒-x+1

Hope this helps!

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-Charlie