If the sides of a triangle MNP are MN= 4x+9, NP= x+5, MP= 7x-20, find the range of possible values for x. Please show steps!

[tex]3\times9^{x+1}=27^{x-1}\\\\3\times(3^2)^{x+1}=(3^3)^{x-1}\qquad\text{use}\ (a^n)^m=a^{nm}\\\\3\times3^{2(x+1)}=3^{3(x-1)}\\\\3\times3^{2x+2}=3^{3x-3}\qquad\text{use}\ a^n\times a^m=a^{n+m}\\\\3^{1+2x+2}=3^{3x-3}\\\\3^{2x+3}=3^{3x-3}\iff2x+3=3x-3\qquad\text{subtract 3 from both sides}\\\\2x=3x-6\qquad\text{subtract 3x from both sides}\\\\-x=-6\to\boxed{x=6}[/tex]

Final answer:

To divide 65.2 by 26, you perform the division to find that 26 goes into 65.2 exactly 2.5 times. Therefore, the answer, when rounded to the nearest tenth, is 2.5.

Explanation:

To divide 65.2 by 26, start with the division process. Place a decimal point directly above the decimal point in the dividend within the answer area. Since 26 does not go into 6, but goes into 65 twice, write 2 above the 5 in the dividend. Multiply 2 by 26 to get 52, and subtract this from 65, which leaves a remainder of 13. Bring down the 2 from the dividend to get 132.

Now, divide 26 into 132, which goes exactly 5 times. Multiplying 5 by 26 gives 130, subtract this from 132 to get a remainder of 2. Because we are left with no more numbers to bring down and our remainder is less than 26, we stop. The answer to 65.2 divided by 26 when rounded to the nearest tenth is 2.5.

Answer:

slope = [tex]\frac{9}{7}[/tex]

Step-by-step explanation:

to calculate the slope m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 6, - 3) and (x₂, y₂ ) = (1,6) ← 2 points on the line

m = [tex]\frac{6+3}{1+6}[/tex] = [tex]\frac{9}{7}[/tex]

Answer: x = 45

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Work Shown

x/y = 10/4

x/18 = 10/4 ... replace y with 18

x*4 = 18*10 ... cross multiply

4x = 180

4x/4 = 180/4 ... divide both sides by 4

x = 45

Final answer:

By cross-multiplying the given proportion x/y=10/4 with y=18, we determine that the value of x is 45.

Explanation:

To find the value of x given that x/y=10/4 and y = 18, we can use the method of cross-multiplication. This method involves multiplying the numerator of one fraction by the denominator of the other fraction and setting the two products equal to each other. So, we set up the equation:

[tex]\(\frac{x}{y} = \frac{10}{4}\)[/tex]

Let's substitute y with 18:

[tex]\(\frac{x}{18} = \frac{10}{4}\)[/tex]

We then cross-multiply and solve for x:

[tex]4x = 10 \times 18[/tex]

4x = 180

[tex]x = \frac{180}{4}[/tex]

x = 45

Therefore, the value of x is 45 when y is 18.

Answer:

20/9 sq.feet

Step-by-step explanation:

The width is 4/3 ft because 1/3 times 4 is 4/3 and the length is 5/3 because 1/3 times 5 is 5/3.

Then to find the area you do length times width.

5/3 ×4/3= 20/9 sq. feet

I hope this helps! :)

Answer:

The labor fee is $14.25, each quart of oil costs $2.25.

Step-by-step explanation:

Let $x be thee price of each quart of oil and $y be a flat fee for labor.

1. If the oil change for one car required 5 quarts of oil, then these 5 quarts cost $5x and together with a flat fee for labor it cost $25.50. Thus,

5x+y=25.50.

2. If the oil change for another car required 7 quarts of oil, then these 7 quarts cost $7x and together with a flat fee for labor it cost $30.00. Thus,

7x+y=30.00.

3. Subtract from the second equation the first one, then

[tex]7x+y-(5x+y)=30.00-25.50,\\ \\7x+y-5x-y=4.50,\\ \\2x=4.50,\\ \\x=\$2.25.[/tex]

Substitute it into the first equation:

[tex]5\cdot 2.25+y=25.50,\\ \\y=25.50-11.25,\\ \\y=\$14.25.[/tex]

The labor fee is $14.25, each quart of oil costs $2.25.

The labor fee is $14.25 and the cost per quart of oil is $2.25.

To find the labor fee and cost per quart of oil, we can set up a system of equations using the given information. Let x represent the cost of each quart of oil and y represent the labor fee.

We have the equations:

5x + y = 25.50
7x + y = 30.00

We can solve this system of equations using substitution or elimination. Substituting y from the first equation into the second equation, we get:

7x + (25.50 - 5x) = 30.00

2x = 4.50

x = 2.25

Substituting x back into the first equation, we get:

5(2.25) + y = 25.50

11.25 + y = 25.50

y = 14.25

Therefore, the labor fee is $14.25 and the cost per quart of oil is $2.25.

Answer: choice A

f(x) = (1/4)x^2, f(x) = -0.5x^2, f(x) = x^2

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The coefficient in front of the x^2 term tells us how wide or narrow the parabola will be. It turns out that the further the coefficient value is from 0, in either direction, this will make the parabola more narrow.

Notice how 1/4 = 0.25 which is less than |-0.5| = 0.5 meaning that f(x) = (1/4)x^2 is wider than f(x) = -0.5x^2

Then comparing f(x) = -0.5x^2 to f(x) = 1x^2, we see that 0.5 is smaller than 1, so f(x) = -0.5x^2 is wider than f(x) = 1x^2

That is why the order from widest to narrowest is f(x) = (1/4)x^2, f(x) = -0.5x^2, f(x) = x^2

A graph shown below helps confirm the answer (note the color coding). In figure 1 is the graph of all three functions together. In figure 2, I reflect the second function help show the comparison of why it's the middle-most in terms of how wide it is (it is the orange parabola, which is the reflection of the red parabola)

Answer: 35

Step-by-step explanation: 48 - 13 = 35

Answer:

35 ants left

Step-by-step explanation:

The solutions to the equation 7x(x+1.8)=0 are x = 0 and x = -1.8.

The highest power of the polynomial function is defined as the degree.

The Fundamental Theorem of Algebra asserts that a polynomial has n roots if its degree is n.

The equation is 7x(x+1.8)=0.

To solve this equation, we can use the property that if the product of two factors is equal to zero, then at least one of the factors must be zero.

Therefore, we set each factor equal to zero and solve for x:

7x = 0

x = 0

x + 1.8 = 0

x = -1.8

So, the solutions to the equation 7x(x+1.8)=0 are x = 0 and x = -1.8.

To solve the equation 7x(x+1.8)=0, set each factor equal to zero to find the two possible solutions for x, which are 0 and -1.8.

To solve the equation 7x(x+1.8)=0, we need to set each factor equal to zero and solve for x.

Setting 7x=0, we find x=0. Setting x+1.8=0, we subtract 1.8 from both sides to get x=-1.8. Therefore, the solutions to the equation are x=0 and x=-1.8.

SEO Keywords: quadratic equation, solve, factor, solutionsThe given equation is 7x(x+1.8)=0. This is a quadratic equation that can be easily solved by setting each factor equal to zero. Here's how you can find the value(s) of x:

Therefore, the two possible values for x are 0 and -1.8.

Answer:

x=49

Step-by-step explanation:

First multiply 4 on both sides

(4) x/4+7=14(4)

the fours cross out leaving x by itself

x+17=14(4)

x+7=56

subtract 7 on both sides leaving:

x=49

Hi There!

Step-by-step explanation:

Solve: x/4 + 7 = 14 (x/4 = 1/4x)

Simplify: 1/4x + 7 = 14

Subtract 7 to both sides of the equation: 1/4x + 7 - 7 = 14 - 7

Simplify: 1/4x = 7

Multiply 4 to both sides of the equation: 1/4x * 4 = 7 * 4

Answer:

x = 28

Hope This helps :)

Answer:

There is one solution

Step-by-step explanation:

You can tell by looking at it that 2x and 3x are different. Both are obtained once the brackets have been removed. So you will get just one answer.

2(x -1) = 3(x - 4)                  Remove the brackets.

2x - 2 = 3x - 12                  Subtract 2x from both sides.

2x - 2x - 2 = 3x - 2x - 12   Combine

-2 = x -12                           Add 12 to both sides.

-2 + 12 = x -12 +12             Combine

10 = x

The slope-intercept form:

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

m - slope

b - y-intercept

We have the equation in standard form.

[tex]2x-3y=6[/tex]      subtract 2x from both sides

[tex]-3y=-2x+6[/tex]      divide both sides by (-3)

[tex]y=\dfrac{2}{3}x-2[/tex]

Answer:

Match the following:

1. An angle that measures more than 0° but less than 90°:

Acute angle.

2. Two angles that have a common vertex and side but are not overlapping:

Adjacent angles.

3. Two angles whose sum is 90°

Complementary angles.

4. An angle that measures more than 90° but less than 180°:

Obtuse angle.

5. An angle that measures exactly 90°:

Right angle.

6. An angle that measures exactly 180°:

Straight angle.

7. Two angles whose sum is 180°:

Supplementary angles.

8. The point where two line segments, lines, or rays meet to form an angle:

Vertex.

9. Angles that are opposite from one another at the intersection of two lines:

Vertical angles.

Step-by-step explanation:

Match the following:

1. An angle that measures more than 0° but less than 90°:

Acute angle.

2. Two angles that have a common vertex and side but are not overlapping:

Adjacent angles.

3. Two angles whose sum is 90°

Complementary angles.

4. An angle that measures more than 90° but less than 180°:

Obtuse angle.

5. An angle that measures exactly 90°:

Right angle.

6. An angle that measures exactly 180°:

Straight angle.

7. Two angles whose sum is 180°:

Supplementary angles.

8. The point where two line segments, lines, or rays meet to form an angle:

Vertex.

9. Angles that are opposite from one another at the intersection of two lines:

Vertical angles.

The terms such as acute angle, adjacent angles, complementary angles, obtuse angle, right angle, straight angle, supplementary angles, vertex, and vertical angles are correctly matched with their respective definitions.

The correct matching for the provided terms are as follows:

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Answer:

7.49

Step-by-step explanation:

1.07x7=7.49

check the picture below.

Answer:

[tex]\dfrac{1}{24}[/tex]

Step-by-step explanation:

1. The student is allowed to choose white, blue, green or black Polo shirts. So the student has 4 possibilities to select shirt and the probability of wearing the blue shirt is [tex]\dfrac{1}{4}.[/tex]

2. The student is allowed to choose khaki, black or plaid skirts/pants. So the student has 3 possibilities to select skirt and the probability of wearing the plaid skirt is [tex]\dfrac{1}{3}.[/tex]

3. The student is allowed to choose black or brown shoes. So the student has 2 possibilities to select shoes and the probability of wearing black shoes is [tex]\dfrac{1}{2}.[/tex]

Now use the product rule for probabilities:

[tex]Pr=\dfrac{1}{4}\cdot \dfrac{1}{3}\cdot \dfrac{1}{2}=\dfrac{1}{24}.[/tex]

Answer:

He needs to drive for 2 more days to get to his aunt's house.

Step-by-step explanation:

Answer:

hello

Step-by-step explanation:

Answer:

So, 36 completes perfect square

Step-by-step explanation:

we are given

trinomial as

[tex]x^2-12x+......[/tex]

we can square formula

[tex]a^2-2ab+b^2=(a-b)[/tex]

we can see that middle term is 2ab

so, we will factor middle term in 2ab form

[tex]12x=2\times x\times 6[/tex]

We can see that b is 6

so, if we could add 6^2 , then we will get perfect square

[tex]x^2-12x+6^2......[/tex]

[tex]x^2-12x+36......[/tex]

So, we should add 36

so, 36......Answer

Answer:  The correct option is

(C) 36.

Step-by-step explanation:  We are given to select the value that completes the square or creates a perfect square trinomial for the following incomplete expression :

[tex]E=x^2-12x+?[/tex]

We will be using the following square formula :

[tex]a^2-2ab+b^2=(a-b)^2.[/tex]

Let the required value be represented by c.

We have

[tex]E\\\\=x^2-12x+c\\\\=(x^2-2\times x\times 6+6^2)+c-6^2\\\\=(x-6)^2+c-36.[/tex]

So, for the given expression to be a perfect square trinomial, we must have

[tex]c-36=0\\\\\Rightarrow c=36.[/tex]

Thus, the required value is 36.

Option (C) is CORRECT.

The United States was at war with Spain in Cuba and the Philippines. Hawaii was of importance to the military effort because of its location. ... It was at this time that Congress annexed Hawaii because of the economic and military benefit the islands offered.

mark brainliest  :)

hope this helped

Answer:

Because of the oceans and all of the undiscovered stuff there. The fact it was an island and could be used as a navy base. Very dessolite. Not a lot of people the time it was a territory

Step-by-step explanation:

The point-slope form:

[tex]y-y_1=m(x-x_1)[/tex]

We have:

[tex]slope:m=\dfrac{4}{3}[/tex]

[tex]the\ point\ (-2,\ 11)\to x_1=-2,\ y_1=11[/tex]

SubstituteL

[tex]y-11=\dfrac{4}{3}(x-(-2))\\\\\boxed{y-11=\dfrac{4}{3}(x+2)}[/tex]

Answer:

Exponential growth; percentage rate of growth is 4%.

Step-by-step explanation:

The function,

[tex]f(x)=3.6.(1.04)^x[/tex]

represents an exponential growth function because the growth factor is greater than 1.

The general form of an exponential growth function is,

[tex]y=a(1+r)^t=(a).(ar)^t[/tex], where 'r' is the percentage rate of growth.

If we compare the given equation with the standard form of the equation we can see that, we have,

[tex]f(x)=3.6(1+0.04)^x[/tex]

Therefore, the percentage rate of growth is = [tex]0.04 \times 100=4\%[/tex] .

To calculate the cost of the vegetable oil used by Lucy in three weeks, we need to determine the cost per ounce and then multiply it by the quantity used. In this case, the approximate cost of the oil used is $5.00.

To find out the approximate cost of the amount of vegetable oil Lucy used in three weeks, we first need to figure out how much of the 40-ounce bottle she used. As the question states that she used 65% of it, we can calculate it as follows:

So, the approximate cost for the amount of vegetable oil Lucy used in three weeks is $5.00, rounded to the nearest cent.

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To find the approximate cost for the amount of vegetable oil Lucy used in three weeks, calculate 65% of the total cost of the 40-ounce bottle of vegetable oil, and the approximate cost is $4.99.

To find the approximate cost for the amount of vegetable oil Lucy used in three weeks, we need to calculate 65% of the total cost of the 40-ounce bottle of vegetable oil.

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Answer:

The percent increase is 34.48276%

Step-by-step explanation:

we are given

original price =$2900

new price =$3900

now, we can find change in price

change in price = (new price)-(original price)

change in price =3900-2900

change in price =1000

percent increase = (change in price)/(original price) *100

percent increase is

[tex]=\frac{1000}{2900}\times 100[/tex]

[tex]=34.48276[/tex]

Answer:

The correct answer is A. 1.6

Step-by-step explanation:

1.6x50= 80 minutes per song.

1.6x106= 169.6 minutes per song.

If you don't believe me, then grab yourself a calculator, punch the #'s  (above^) in, and you'll get the answer.

Hope this helped ya out! (:

Answer:

ans is C. 0.8 of a minute per song

Step-by-step explanation:

x represents the number of songs he wants to download to his music player,

and y represents the total amount of time, in minutes, it will take him to download the songs.

(100, 80) and (212, 169.6)

subtracting: he DL 212-100=112 songs in 169.6-80=89.6 minutes

so the rate of change = 89.6/112 = 0.8 minute per song

Answer:

a 3 quarts

b 6 quarts

c thats in the step by step

d yes

Step-by-step explanation:

c since they have to make 9 quarts of violet paint if you add the number of red and blue paint mixed together you get 1 quart meaning you have to multiply both by nine and if you simply you get what i have above

This is a proportional relationship because you decide whether two quantities are in a proportional relationship, by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

-hope this helps :D

Answer:

-3

Step-by-step explanation: