Which ordered pair is a solution to the system of linear equations Negative 4 x + y = 8 and x minus 5 y = 17?

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Explanation:

Check out figure 1 which is one of the attached images below.

In this diagram, I have angle A as 75 degrees and angle B as 51 degrees.

Angle C is therefore, C = 180-A-B = 180-75-51 = 54 degrees.

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Point D is somewhere between A and B such that it is on segment AB.

Figure 2 (also attached as an image) shows segment CD forming two angles DCB and ACD.

These are the blue and red angles respectively, such that the blue angle is twice as large as the red angle.

blue angle = 2*(red angle)

This is what it means when it says the ratio of the two angles is 2:1.

I have 2x as the blue angle and x as the red angle. We don't know what x is yet, but we do know that the x and 2x combine back to angle C = 54 degrees.

So,

(angle DCB) + (angle ACD) = angle C

(2x) + (x) = 54

3x = 54

x = 54/3

x = 18

Since x = 18, this means 2*x = 2*18 = 36

Therefore,

angle DCB = 2x = 36 degrees

angle ACD = x = 18 degrees

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Focus solely on triangle DCB. We found angle DCB = 36 degrees and we know that angle DBC = 51

The remaining angle y = angle BDC is...

(angle BDC)+(angle DCB)+(angle DBC) = 180

(y)+(36)+(51) = 180

y+87 = 180

y+87-87 = 180-87

y = 93

angle BDC = 93 degrees

Figure 3 shows the angles we found (basically I replaced x, 2x and y with their respective numbers).

The size of angle BDC is 0 degrees.

To find the size of angle BDC, you can use the fact that the sum of the angles in a triangle is always 180 degrees. Since angle ACD is 1 part and angle DCB is 2 parts, we can express their sizes as:

Angle ACD = x degrees

Angle DCB = 2x degrees

Now, you know that the sum of the angles in triangle ABC is 180 degrees. So, you can write the equation:

x (angle ACD) + 2x (angle DCB) + 180 degrees (angle BDA) = 180 degrees

Now, simplify and solve for x:

x + 2x + 180 = 180

Combine like terms:

3x + 180 = 180

Now, subtract 180 from both sides of the equation:

3x = 0

Finally, divide by 3:

x = 0

Now that you know the value of x, you can find the size of angle BDC (2x):

Angle BDC = 2x = 2(0) = 0 degrees

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Answer: -13x^2 + 10x + 4

Step-by-step explanation:

group all of the same variables together to simplify the equation.

-7 - 6 = -13 // the x^2 value

-5 + 15 = 10 // the x value

4 is the only number without an exponent so leave it alone.

Answer:

-13x²+10x+4

Step-by-step explanation:

You need to group all of the same variables together:

-7x² - 5x - 6x² + 4 + 15x

-7x²-6x²-5x+15x+4

-13x²+10x+4

Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]

Step-by-step explanation:

Given,

Distance walked by Addie = [tex]2\frac{1}{2}=\frac{5}{2}\ miles[/tex]

Time taken by Addie = 45 minutes

Converting the time into hours;

1 hour = 60 minutes

45 minutes = [tex]\frac{45}{60}=\frac{3}{4}\ hour[/tex]

Distance = Speed * Time

Speed = Distance/Time

Speed = [tex]\frac{5}{2} / \frac{3}{4}[/tex]

Speed = [tex]\frac{5}{2}*\frac{4}{3} = \frac{10}{3}\ mph[/tex]

Speed = [tex]3\frac{1}{3}\ mph[/tex]

Addie's speed was [tex]3\frac{1}{3}\ mph[/tex]

Keywords: speed, distance

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Answer:

vertex=?

Step-by-step explanation:

given data:

g(x)=-3x^2+18x+2

from the given equation

a=-3,b=18,c=2

x=-b/2a

x=-(18)/2(-3)

x=3

put value of x in the given equation

y=-3(3)^2+18(3)+2

y=-27+54+2

y=29

x=3    y=29

(3,29)

Answer:

Area of trapezoid = 144 cm²

Step-by-step explanation:

The length of parallel sides are,

a = 8 cm

b = 16 cm

h = 12 cm

Formula area of trapezoid:-

[tex]A=\dfrac{1}{2}(a+b)\times h[/tex]

[tex]A=\dfrac{1}{2}(8+16)\times 12[/tex]

[tex]A=144[/tex]

Hence, the area of trapezoid is 144 cm²

Answer:

Hence, the area of trapezoid is 12 cm²

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

yes it b because it goes origion and it not a zero pair

Answer: Order if operations

Step-by-step explanation:

15-10n+12n

15+12n

Answer:

The three points for the line  y = -6x + 12 ...Red color line

point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)

point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)

point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)

The Graph is attached below.

Step-by-step explanation:

Given:

[tex]y = -6x +12[/tex]  ........... equation of a line

Let the points be point A, point B, and point C  

To Find:

point A( x₁ , y₁) ≡  ?

point B( x₂ , y₂) ≡ ?

point C(x₃ , y₃ ) ≡ ?

Solution:

For Drawing a graph we require minimum two points but we will have here three points.

For point A( x₁ , y₁)

Put x = 0 in the given equation we get

y = 0 + 12

y = 12

∴ point A( x₁ , y₁) ≡ ( 0 , 12)

For point B( x₂ , y₂)

Put y= 0 in the given equation we get

0 = -6x + 12

6x = 12

[tex]x=\dfrac{12}{6}=2[/tex]

∴ point B( x₂ , y₂)  ≡ (2 , 0)

For point C(x₃ , y₃ )

Put x = 1 in the given equation we get  

y = -6 × 1 + 12

y = 6

∴ point C(x₃ , y₃ )≡ (1 , 6)

Therefore,

The three points for the line  -2y = -x + 8 are

point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)

point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)

point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)

The Graph is attached below..

Answer:

6(x+5)

Step-by-step explanation:

Answer: 6 x (x+5)

Step-by-step explanation: Since it is six times a number AND five, you want to do the addition equation first. To show this you place parentheses around a variable (x) plus 5. You add six in front of this because it comes first in the word problem.

The fraction 43/200 is evidently between 1/5 and 1/4 from equivalent fractions.

Im essence, since 43 lies between, 40 and 50;

The fraction 43/200 in turn lies between fractions 1/5 and 1/4.

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Answer:

x = 5/4

y = 15/16

Step-by-step explanation:

We are given y = 3/4x

and 5/2x +2y = 5

Substituting the value y=3/4 x in second equation we get

5/2x + 2(3/4)x = 5

8/2x = 5

4x = 5

and so , x = 5/4

substituting value of x in y = 3/4x we get,

y = 3/4 (5/4)

So, y = 15/16

which are the required values of x and y on solving the two given equations.

The solution to the equation is (5/4, 15/16)

Given the system of equations

Substitute equation 1 into 2 to have:

5/2x  + 2(3/4x) = 5

5/2x + 3/2x = 5

8/2x = 5

4xx = 5

x = 5/4

Snce y = 3/4x

y = 3/4(5/4)

y = 15/16

Hence the solution to the equation is (5/4, 15/16)

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Answer:

2/3

Step-by-step explanation:

parallel lines have the same slope

given that a line has a slope of 2/3

a line that is parallel to this line would also have a slope of 2/3

y=-2/3x+5

Step-by-step explanation:

From the scattered plot, it is evident that the line of best fit will have a negative slope from the way the plots are aligned.

Selecting the line of best fit that will cut the y axis at +5, the points can be estimated as;

(5,1.5) and (3.5,2.5)

The slope can be found as;

m=Δy/Δx

m=2.5-1.5/3.5-5 =1.0/ -1.5 = -0.67

Finding the equation as;

m=Δy/Δx

-0.66 = y-2.5/x-3.5

-0.66(x-3.5) = y-2.5

-0.66x+2.3=y-2.5

-0.66x+2.3+2.5=y

-0.66x+4.7=y

⇒⇒  y= -0.66 x + 4.7

⇒⇒y= -2/3 x + 5

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Keywords: best trend line, data set

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a = amount invested at 9%

b = amount invested at 11%

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hfill \stackrel{\textit{9\% of "a"}}{\left( \cfrac{9}{100} \right)a\implies 0.09a}~\hfill \stackrel{\textit{11\% of "b"}}{\left( \cfrac{11}{100} \right)b\implies 0.11b}[/tex]

we know she has a total of $40,000 to invest, so, if she invested "a" amount in one, the other quantity must be the slack left from 40,000 and "a", namely b = 40000 - a.

we also know that the yield or earned interest from both amounts is 4300, thus

[tex]\bf \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11b}~~=~~\stackrel{\textit{annual income from both}}{4300} \\\\\\ \stackrel{\textit{yield of "a"}}{0.09a}~~+~~\stackrel{\textit{yield of "b"}}{0.11(40000-a)}~~=~~4300 \\\\\\ 0.09a+4400-0.11a = 4300\implies -0.02a+4400 = 4300 \\\\\\ 4400=4300+0.02a\implies 100=0.02a\implies \cfrac{100}{0.02}=a\implies \boxed{5000=a} \\\\\\ \stackrel{\textit{we know that}}{b = 40000-a}\implies \boxed{b = 35000}[/tex]

Answer:

The width of the red tile would be [tex]2.25[/tex] inches.

Step-by-step explanation:

Given blue tile has a length of [tex]4.25[/tex] inches, and a width of [tex]6.75[/tex]inches.

Also, length of similar tile is [tex]12.75[/tex] inches.

Let us assume [tex]x[/tex] as the width of red tile.

It is given in the question that both tiles are similar.

So, their area will be the same.

Area of blue tile would be [tex]4.25\times 6.75=28.6875\ inch^2[/tex]

Area of red tile would be [tex]12.75\times x[/tex]

The area of blue tile would be equal to area of red tile.

[tex]28.6875=12.75\times x[/tex]

[tex]\frac{28.6875}{12.75}=x\\\\x=2.25[/tex]

So, the width of the red tile would be [tex]2.25[/tex] inches.

Answer:

[tex]k=54[/tex]

Step-by-step explanation:

Find the coordinates of points M and N in terms of k. Solve the system of two equations:

[tex]\left\{\begin{array}{l}y=3x^2\\ \\y=-3x^2+k\end{array}\right.\Rightarrow \left\{\begin{array}{l}y=3x^2\\ \\y=-y+k\end{array}\right.\\ \\2y=k\\ \\y=\dfrac{k}{2}\\ \\\dfrac{k}{2}=3x^2\\ \\x^2=\dfrac{k}{6}\\ \\x=\pm\sqrt{\dfrac{k}{6}}[/tex]

Two points have the coordinates [tex]M\left(\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex] and [tex]N\left(-\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex]

Find the distance between M and N:

[tex]MN=\sqrt{\left(\sqrt{\dfrac{k}{6}}-\left(-\sqrt{\dfrac{k}{6}}\right)\right)^2+\left(\dfrac{k}{2}-\dfrac{k}{2}\right)^2}=\sqrt{4\dfrac{k}{6}}=\sqrt{\dfrac{2k}{3}}[/tex]

Since MN = 6, you have

[tex]\sqrt{\dfrac{2k}{3}}=6\\ \\\dfrac{2k}{3}=36\\ \\2k=108\\ \\k=54[/tex]

Answer:

Step-by-step explanation:

6c + 5

term : 6c and 5....coefficient : 6......constant : 5

a coefficient is the number multiplied by the variable (the letter)....a constant is just a number with no variables (letters)

The term described by the phrase 'the cost of 6 pizzas, c being the cost of each pizza, and a delivery charge of $5' is 6c. The coefficient is 6 and the constant is 5.

The term described by the phrase 'the cost of 6 pizzas, c being the cost of each pizza, and a delivery charge of $5' is 6c. The coefficient is 6 because it is the number multiplying the variable c. The constant is 5 because it is a fixed value that does not involve any variables.

So the correct answer is option A: Term: 6c, coefficient: 6, constant: 5.

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[tex]\text{Solve for x:}\\\\-4x-6=-5y+9\\\\\text{Add 6 to both sides}\\\\-4x=-5y+15\\\\\text{Divide both sides by -4}\\\\\boxed{x=\frac{5}{4}y-\frac{15}{4}}[/tex]

The number of teachers required for the 425 students that enrolled at the school is 25.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

At Elmwood Middle School there are 4 teachers for every 68 students.

There are 425 students enrolled at the school.

Let the number of teachers be x required for the 425 students will be

[tex]\rm \dfrac{x}{4} = \dfrac{425}{68}\\\\x \ = \dfrac{425*4}{68}\\\\x \ = 25[/tex]

The number of teachers required for the 425 students that enrolled at the school is 25.

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Approximately 25 teachers are needed at Elmwood Middle School. So the correct option is c) 25.

To find out how many teachers are needed at Elmwood Middle School, we can set up a proportion using the given ratio of teachers to students.

Given:

- There are 4 teachers for every 68 students.

Let's set up the proportion:

[tex]\[\frac{\text{Number of teachers}}{\text{Number of students}} = \frac{4}{68}\][/tex]

We know there are 425 students enrolled at the school, so let's find out how many teachers are needed:

[tex]\[\text{Number of teachers} = \frac{4}{68} \times 425\][/tex]

[tex]\[\text{Number of teachers} = \frac{4 \times 425}{68}\][/tex]

[tex]\[\text{Number of teachers} = \frac{1700}{68}\][/tex]

[tex]\[\text{Number of teachers} \approx 25\][/tex]

So, approximately 25 teachers are needed at Elmwood Middle School.

Therefore, the answer is option C. 25.

The complete question is:

At Elmwood Middle School there are 4 teachers for every 68 students. There are 425 students enrolled at the school. How many teachers are needed? A. 17 B. 21 C. 25 D. 28

Answer:B

Step-by-step explanation:

Final answer:

A quadratic function with zeros at -5 and -6 can be written as f(x) = (x + 5)(x + 6), which expands to f(x) = x² + 11x + 30.

Explanation:

To write a quadratic function whose zeros are -5 and -6, you start by remembering that if α and β are the zeros of a quadratic function, the function can be written as f(x) = a(x - α)(x - β) where a is a nonzero coefficient. In this case, -5 and -6 are the zeros, so our function is f(x) = a(x + 5)(x + 6).

For simplicity, if we choose a to be 1, the quadratic function simplifies to

f(x) = (x + 5)(x + 6)

f(x) = x² + 11x + 30.

Therefore, the quadratic function with zeros at -5 and -6 is f(x) = x² + 11x + 30.

x° = 10°

Solution:

In the given figure the angle L represents 90°.

The center ray splits 90° into two angles.

(3x + 6)° + (5x + 4)° = 90°

⇒ 3x° + 6° + 5x° + 4° = 90°

Combine like terms together.

⇒ 3x° + 5x°+ 6° + 4° = 90°

⇒ 8x°+ 10° = 90°

Subtract 10° on both sides of the equation.

⇒ 8x°+ 10° – 10° = 90° – 10°

⇒ 8x° = 90° – 10°

⇒ 8x° = 80°

Divide by 8 on both sides of the equation.

⇒ x° = 10°

Hence, the value of x° = 10°.

Answer:

3k+5a=45

Step-by-step explanation:

It says write an equation. It doesn't specify that you have to solve. That means you can use variables like (k) and (a).

That allows for more flexibility and the equation 3k+5a=45.

3k means that 3 dollars per ticket times (k) tickets equals the total price for kid's tickets

5a means that 5 dollars per ticket times (a) tickets equals the total price for adult's tickets

The equation to represent the cost based on the combination of kids' and adult tickets purchased by Larry is 3k + 5a = 45, where k represents the kids' tickets and a represents the adult tickets.

The problem can be translated into a simple algebraic equation where the number of kids' tickets (k) and the number of adult tickets (a) are the variables. Given the cost per ticket for each category (kids at $3 and adults at $5), we can define a equation where 3k + 5a = 45. This equation represents the cost distribution of the ten tickets that Larry purchased for the state fair, 3 multiplied by the number of kids' tickets plus 5 multiplied by the number of adult tickets.

Therefore, if Larry knows how many of each ticket he bought, he can insert the values for k and a into the equation to see if it equals to 45, the total amount of money he spent.

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Answer:

See explanation!

Step-by-step explanation:

Let us first give some principle theory to aid our solution.

Considering two functions [tex]A(x)[/tex] and [tex]B(x)[/tex], in order to show that function

which is the inverse of [tex]y=ax[/tex].

Now let as solve our problem. We are given the following:

[tex]f(x)=3x-4\\g(x)=\frac{x+4}{3}[/tex]

Method A: Show that these are inverse functions by finding f^-1 (x) and showing that it is the same as g(x).

Let us take [tex][f(x)=y]=3x-4[/tex] and "exchanging" our variables we have

[tex]x=3y-4\\x+4=3y\\\\y=\frac{x+4}{3}[/tex]

which is exactly the same with our given function of [tex]g(x)=\frac{x+4}{3}[/tex], so proved!

Method B: Show that these are inverse functions by showing that when the output of one function is used for the input of the other function, the final output is equal to the original input value. (you may choose any initial input)

For this case we will use a simple input let us say [tex]x=1[/tex]. Thus taking the [tex]f(x)[/tex] function and plugging in we have:

[tex]f(x=1) = 3(1)-4\\f(1)=3-4\\f(1)=-1[/tex]

Now let us take the output of [tex]f(1)[/tex] which is [tex]-1[/tex] and use it the input to our second function of [tex]g(x)[/tex], so we have:

[tex]g(x=-1) = \frac{(-1)+4}{3}\\ \\g(-1)=\frac{3}{3}\\ \\g(-1)=1[/tex]

so the output of the second function is equal to the original input value of the first function, hence proved!

Method C: Verify that these are the inverse function by showing that f(g(x)) = x AND g(f(x)) = x.

Basically we are asked to prove that both [tex]f(g(x))=g(f(x))=x[/tex]

To do so, we just replace one function into the [tex]x[/tex] value of the other function as follow:

[tex]f(g(x))=3(\frac{x+4}{3} )-4\\\\f(g(x))=x+4-4\\\\f(g(x))=x[/tex]

Lets repeat now for the opposite as follow:

[tex]g(f(x))=\frac{(3x-4)+4}{3}\\ \\g(f(x))=\frac{3x}{3}\\ \\g(f(x))=x[/tex]

Hence proved!

Answer:

22.77

Step-by-step explanation:

39.95 * 1.14 (tax + markup) * 0.5 (discount) = 22.77 (rounded)

Answer:

There are 24 gumballs, 6 of which are yellow.

P(yellow) = 6/24 = 1/4

Answer:

x=3/8, y=-7/8. (3/8, -7/8).

Step-by-step explanation:

y=-5x+1

y=3x-2

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-5x+1=3x-2

-5x-3x+1=-2

-8x+1=-2

-8x=-2-1

-8x=-3

8x=3

x=3/8

y=3(3/8)-2=9/8-2=9/8-16/8=-7/8

Answer:

6.2

Step-by-step explanation:

sin 20 = x/18

solve for x

Answer:

  A.  ∠ABC ≅ ∠DBE

Step-by-step explanation:

The whole proof is not shown, but in order to show the triangles similar, one would need to (a) show the sides are proportional, and (b) show the included angle is the same. The portion of the proof that is shown is on the way to showing side lengths are proportional. The missing part for showing triangle similarity is the congruence statement for angle B, as shown above.

__

Once the triangles are shown to be similar, additional work is needed to show DE║AC. At least one pair of corresponding "base" angles must be shown congruent, too.