solve 4x-3y=-1 and 2x+3y=13 using the elimination method

Answer:

The number of trucks and sedans can be

(0 trucks ,26 sedans)

(8 trucks ,21 sedans)

(24 trucks ,11 sedans)

(25 trucks ,1 sedans)

(32 trucks ,6 sedans)

(16 trucks ,16 sedans)

Step-by-step explanation:

Given:

The  cost for trucks =$5

The cost for sedans  =$8

The total amount collected = $208

To Find:

Number of trucks and sedans passed through the toll booth =?

Solution:

Let the number of trucks be x and the number of sedans be y

Then

5x + 8y = 208-------------------------------(1)

By Trail and error method

5(0) + 8(26) = 208

5(8) + 8(21) = 208

5(24) +8(11) =208

5(25) + 8(1) = 208

5(32) + 8(6) =208

5(16) + 8(16) = 208

Answer:

Hence Proved AB = DF

Step-by-step explanation:

In the Figure:

Given;

CD = EF

AB = CE

We need to prove AB = DF

Solution:

CD = EF    ⇒ (Given)

Now Adding both side by DE we get;

CD + DE = EF + DE   ⇒by the (Addition) Property of Equality.

CE=CD + DE and DF = EF + DE ⇒(Segment Addition)

Now we know that if [tex]a=b \ and \ b =c \ so \ a=c[/tex]

CE = DF           ⇒by the (transitive) Property of Equality.

Now Given:

AB = CE

CE = DF

Now we know that if [tex]a=b \ and \ b =c \ so \ a=c[/tex]

AB  = DF    ⇒by the (Transitive) Property of Equality)

The correct options to fill in the gaps are:

From the diagram given, we have that;

We are to show that the segment AB is congruent to DF

Also from the diagram

Similarly, given that:

AB = CE and CE = DF implies AB = DF by the Transitive Property of Equality.

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Answer:

y=-2/3x+2

\\\\\\\\\\\\\\\\\\\\\

STEPS:

First distribute the 5 through the parentheses to get 5q + 135. So the problem now reads 5q + 135 - (-30) = 95.

Now, minus a negative can be changed to plus a positive so - (-30) can be changed to +30 so our equation now reads 5q + 135 + 30 = 95.

Before adding or subtracting anything from both sides of the equation, make sure you simplify the left side as much as possible. Notice that we can add 135 and 30 to get 165 so the left side simplifies to 5q + 165 = 95.

Now we can simply subtract 165 from both sides of the equation to get 5q = -70.

Now simply divide both sides of the equation by 5 to get q = -14.

Answer:

The fraction of trip completed by Andre is  [tex]\frac{31}{24}[/tex] km

Step-by-step explanation:

Given as :

The Total distance between the home to a festival = 1 [tex]\frac{5}{8}[/tex] km

I.e The total distance between the home to a festival =  [tex]\frac{13}{8}[/tex] km

The distance cover by Andre before taking rest =  [tex]\frac{1}{3}[/tex] km

Let The fraction of trip completed by Andre = x km

So, According to question

The fraction of trip completed by Andre = The Total distance between the home to a festival - The distance cover by Andre before taking rest

or, x =  [tex]\frac{13}{8}[/tex] km - [tex]\frac{1}{3}[/tex] km

or, x =  [tex]\frac{39 - 8}{24}[/tex] km

∴ x = [tex]\frac{31}{24}[/tex] km

Or, The fraction of trip completed by Andre = x = [tex]\frac{31}{24}[/tex] km

Hence , The fraction of trip completed by Andre is  [tex]\frac{31}{24}[/tex] km Answer

Answer:

[tex]\frac{4}{15}[/tex]

Step-by-step explanation:

We know that the total distance is

[tex]1\frac{5}{8}km[/tex] which is standard fraction would be [tex]\frac{13}{8}km[/tex].

So, Andre walks [tex]\frac{1}{3}km[/tex], that means he needs to walk the following distance to get to the festival

[tex]\frac{13}{8}-\frac{1}{3}=\frac{39-8}{24}=\frac{31}{24}km[/tex]

Now, to find the fraction of the tripe that represents the distance he already completed, we have to divide

[tex]\frac{1}{3} \div \frac{13}{8}=\frac{1}{3} \times \frac{8}{13}=\frac{8}{30}=\frac{4}{15}[/tex]

Therefore, we completed a [tex]\frac{4}{15}[/tex] part of the total distance.

Answer:

See the explanation

Step-by-step explanation:

Given function

[tex]Y=3x+1[/tex]

We need to find [tex]y[/tex] value corresponding to each [tex]x[/tex] value.

So, plug each [tex]x[/tex] value in equation we get,

[tex]plug\ x=4\\y=3(4)+1\\y=12+1\\y=13\\\\plug\ x=6\\y=3(6)+1\\y=18+1\\y=19\\\\plug\ x=10\\y=3(10)+1\\y=30+1\\y=31[/tex]

Now in next part of question it ask us to check each ordered pair.

Let us plug each [tex]x[/tex] value and [tex]y[/tex] value in the function [tex]y=-3x-5[/tex]

[tex]plug\ (1,-8)\\-8=-3(1)-5\\-8=-3-5\\-8=-8\\\\plug(-5,0)\\0=-3(-5)-5\\0=15-5\\0\neq10\\\\plug\ (-2,1)\\1=-3(-2)-5\\1=6-5\\1=1\\\\plug\ (-1,-2)\\-2=-3(-1)-5\\-2=3-5\\-2=-2\\[/tex]

we can see ordered pair [tex](1,8),(-2,1)and(-1,-2)[/tex] true for function [tex]y=-3x-5[/tex]

Answer:12

Step-by-step explanation:bcs in 1/3 it  has the same denominatoor

Answer:

640 cm²

Step-by-step explanation:

The ratio between the area two similar polygon are the ratio between their sides squared.

Given side S₁ and side S₂, you can find the area of the second shape by multiplying the area of the first shape by a factor of (S₂/S₁)².

This might sound confusing if you're not used to hearing math terms so lets solve it in this problem.

The side of the first trapezoid is 5cm, so S₁ = 5

The side of the second trapezoid is 20cm so S₂ = 20.

The ratio between them is 20/5=4

To find the area of the second shape, we just have to multiply the area of the first one by the ratio², ie. (S₂/S₁)².

40(4)² = 40(16) = 640 cm²

Answer:

The coordinates of the mid-point are :

[tex](\frac{1}{2}, \frac{5}{2})[/tex]

Step-by-step explanation:

We know that, the coordinates of the mid-point (x, y) of a line segment joining the points (x₁, y₁) and (x₂, y₂) is given by

[tex](x, y) = (\frac{x_{1} +x_{2} }{2},\frac{y_{1}+y_{2} }{2} )[/tex]

Now, we have the given points as (3, 5) and (-2, 0).

By using the above formula, coordinates of the mid-point (x, y) of the line-segment joining the points (3, 5) and (-2, 0) is given by,

[tex]x = \frac{3+(-2)}{2} = \frac{3-2}{2} = \frac{1}{2}[/tex]

[tex]y = \frac{5+0}{2} = \frac{5}{2}[/tex]

∴ coordinates of the mid-point of the line-segment joining the points (3,5) and (-2,0) is [tex](\frac{1}{2}, \frac{5}{2})[/tex].

Answer:

Step-by-step explanation:

ΔABC ≅ ΔABD  by ASA

Answer: 14ft > 41/2

Step-by-step explanation:

Your answer is:

14ft > 41/2yd

I hope this helped! If so, please mark brainliest!

Answer:

1) up

2) correct

3) left

4) down

Step-by-step explanation:

do you not have a graphing calculator, it really helps you with these.

The parabola opens by matching an equation are as follows,

The standard equation of a regular parabola exists [tex]y^{2} = 4ax.[/tex] Some of the important representations below are helpful to understanding the features and parts of a parabola. Focus: The point (a, 0) is the focus of the parabola.

A parabola is a plane curve that exists mirror-symmetrical and is approximately U-shaped. It fits several superficially various mathematical descriptions, which can all be established to define the same curves.

The parabola opens by matching an equation are as follows,

To learn more about Parabola refer to:

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Answer:

1/392 cubic yard

Step-by-step explanation:

 V = Bh = (1/28 yd²)·(1/14 yd) = 1/(28·14) yd³ = 1/392 yd³

Answer:

1/392

Step-by-step explanation:

i was foing this test and turns out this is right.

Answer: see attached file

Step-by-step explanation: see attached file for explanation. Thanks!

Answer:

(∞,-5)

Step-by-step explanation:

For a line to have a slope of 0, it has to be horizontal.

Any point that has a y value of -5 could form a horizontal line along with (0,-5).

Answer:

Theo Should use 1.3 cups of Sugar to make 24 cookies.

Step-by-step explanation:

Given;

Number of cookies required by recipe = 36 cookies

Number of cookies Theo wants to use = 24 cookies

Number of cups sugar recipe requires = 2 cups

We need to find Number of cups sugar Theo should use to make cookie according to recipe.

Now,

For 36 cookies = 2 cups of sugar

So For 24 cookies = Number of cups of sugar required for 24 cookies.

By Using Cross Multiplication we get;

Number of cups of sugar required for 24 cookies = [tex]\frac{24\times2}{36}= 1.33\ cups[/tex]

Hence Theo Should use 1.3 cups of Sugar to make 24 cookies.

The question is incomplete. Here is the complete question:

The triangle will be rotated 180° clockwise around the point (3, 4) to create A A'B'C.Which

characteristics of AA'B'C' will be the same for the corresponding characteristics of AABC? Select ALL that  apply.

(A) The coordinates of A'.

(B) The coordinates of B'.

(C) The perimeter of Δ A'B'C'.

(D) The area of Δ A'B'C'.

(E) The measure of ∠B'.

(F) The length of segment A'B'.

Answer:

(C) The perimeter of Δ A'B'C'.

(D) The area of Δ A'B'C'.

(E) The measure of ∠B'.

(F) The length of segment A'B'.

Step-by-step explanation:

Given:

A triangle ABC rotated by 180° clockwise around the vertex C(3,4) to create Δ A'B'C.

Now, a rotation is a rigid motion transformation. In rigid transformation, the  size, length, angle measures, perimeter and area of the figure doesn't change and remains the same as the original figure.

Rotation only changes the position of the points on the figure.

Here, as the triangle ABC is rotated about vertex C, the position of vertex A and B will change. But, the angles made by each of the vertices will remain same. Also, the side lengths of the triangle will remain the same. So, the perimeter and area will also not change. As the point of rotation is point C, the vertex C' will be same as vertex C.

So, the correct options are (C), (D), (E), and (F).

Answer:

The probability of selecting the given event = [tex]\frac{25}{52}[/tex]

Step-by-step explanation:

A card is drawn at random from a standard 52-card deck.

We have to find the probability of selecting an odd numbered card(3,5,7,9) or spade or both.For this we have to find the number of favourable cases.

Favorable cases = 13 (all the spades) + 12(4 odd numbered cards from each of the remaining 3 )

                         = 25

Final probability = [tex]\frac{number of favourable cases}{total number of cases}[/tex]

                             = [tex]\frac{25}{52}[/tex]

Hence the probability = [tex]\frac{25}{52}[/tex]

Answer:

[tex]P=4x\sqrt{26}\ units[/tex]

Step-by-step explanation:

we know that

The sides of a rhombus are all congruent and the diagonals are perpendicular bisectors of each other

so

Applying the Pythagorean Theorem

[tex]c^2=a^2+b^2[/tex]

where

c is the length side of the rhombus      

a and b are the semi-diagonals

we have

[tex]a=2x/2=x\ units\\b=10x/2=5x\ units[/tex]

substitute the values

[tex]c^2=x^2+(5x)^2[/tex]

[tex]c^2=26x^2[/tex]

[tex]c=x\sqrt{26}\ units[/tex]

To find out the perimeter of the rhombus multiply the length side by 4

[tex]P=(4)(x\sqrt{26})[/tex]

[tex]P=4x\sqrt{26}\ units[/tex]

Answer:

For [tex](2x^2 + 8x - 8)[/tex], the group is CLOSED as it a polynomial.

Step-by-step explanation:

Here, the given polynomials are:

[tex]P(x)=(5x^2+2x-6)\\Q(x)=(3x^2-6x+2)[/tex]

Now, a group G is said to be CLOSED UNDER SUBTRACTION if,

a and b are he elements of G ⇒ (a-b) is ALSO AN ELEMENT of G

Now, here:

[tex]R(x)  = P(x) - Q(x) = (5x^2+2x-6) - (3x^2-6x+2) = (2x^2 + 8x - 8)[/tex]

or, [tex]R(x)  = (2x^2 + 8x - 8)[/tex]

Also, R(x) is a POLYNOMIAL.

So, R(x) is an Element of group G.

So, the set G of polynomials.

Hence, for the polynomial  [tex](2x^2 + 8x - 8)[/tex], it will be a polynomial the group is CLOSED.

Answer:

The answer would be C

Step-by-step explanation:

Answer:

968 ways

Step-by-step explanation:

This is a question of permutation and combination.

Each equation can have two different answers.

Thus the total number of cases will be (for 10 questions) :

[tex]2*2*2*2*.....10times=2^{10}[/tex] cases.

Now to find the number of ways to at least answer 3 questions False will be total minus the number of question with at most 2 False answers.

Total ways (at most 2 answers false) = [tex]1+10_C_1+10_C_2[/tex] ;

∴

The number of ways in which at least 3 have False as the answer is :

[tex]2^{10}-(1+10_C_1+10_C_2)\\=968[/tex] WAYS.

Answer:

They both have 3 up ig

Step-by-step explanation:

Answer:

m = -1/2

Step-by-step explanation:

As we move from the point (-1, 7) to the point (3, 5), x increases by 4 (this is the "run") and y decreases by 2 (this is the "rise").

Thus, the slope of the line connecting these two points is

m = rise / run = -2/4, or m = -1/2.

Answer:

1/2

Step-by-step explanation:

Using linear combination method, the solution to given system of equations are (-7, -15)

Linear combination is the process of adding two algebraic equations so that one of the variables is eliminated

Addition is used when the two equations have terms that are exact opposites, and subtraction is used when the two equations have terms that are the same.

Given system of equations are:

2x - y = 1  ---- eqn 1

3x - y = -6 ------ eqn 2

Subtract eqn 2 from eqn 1

2x - y = 1

3x - y = -6

(-) -------------

-x = 7

Substitute x = -7 in eqn 1

2(-7) - y = 1

-14 - y = 1

y = -14 - 1 = -15

Thus the solution to given system of equations are (-7, -15)

Answer:

120 ways

Step-by-step explanation:

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✉️ If any further questions, inbox me! ✉️

Answer:

56

Step-by-step explanation:

add

Answer:

You have to simplify the equation and find the answer

Step-by-step explanation:

[tex]4x + ( - 4) = - 2x + 8 \\ \\ 4x + 2x = 4 + 8 \\ \\ 6x = 12 \\ \\ x = 2[/tex]

Answer:

Step-by-step explanation:

4x+(-4) = -2x+8

4x - 4 = -2x + 8

Collecting like terms

4x + 2x = 8 + 4

6x = 12

Dividing through by 6

x = 12/6

x = 2

$120 +$144 =$264

Alexndra earns $264

Answer:

f(g(x))=(x-2)^2 - 7

(x-2)(x-2) - 7

x^2-2x-2x+4-7

x^2-4x-3

g(f(x))=x^2-2-7

x^2-9

(x+3)(x-3)

Step-by-step explanation:

To evaluate functions, you substitute x with the given value in the function and perform the calculation. For example, evaluating f(3) for the function f(x)=x^2-7 gives f(3)=2, while evaluating g(3) for the function g(x)=x-2 gives g(3)=1.

The functions given are f(x)=x^2-7 and g(x)=x-2. To evaluate these functions, we substitute a value for x into the function and perform the calculation. For example, if we want to evaluate f(3), we replace x in the function f(x) with 3.

So for f(3)=3^2-7, we do the following: f(3)=9-7=2.

For g(3), we substitute x in the function g(x) with 3: g(3)=3-2=1

It's important to note that the value you're evaluating might change depending on the question, but this is the basic process for evaluating a function at a given value or values.

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Answer:

272,100

This is because 62 rounds up

Answer:

272,100

You get this answer by looking at the hundreds place and then looking at the right of it. The hundreds place is the 0 and the the right of it is 6, so 5 and up round up 4 and down round down and in this case, 6 is above 5, so it rounds up to 272,100!

Hope this helped!

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3x + 5 + 4x = 5x + 27

7x + 5 = 5x + 27

- 5

7x = 5x + 22

- 5x

2x = 22

/2

x = 11

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Answer:

Step-by-step explanation:

3x + 5 + 4x = 5x + 27

collect like terms

7x - 5x = 27 -5

2x = 22

divide both side by 2

x = 11