A line having a slope 3/4 passes through the point (-8,4). Write the equation of this line.

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:

6.4 meters per second

Step-by-step explanation:

Rate of Change

If two variables x and t are to be related as the rate x changes when t changes, it can be expressed as:

[tex]\displaystyle v=\frac{x}{t}[/tex]

Hans takes a ride in the elevator down from the 86th floor to the first floor, a distance of x=320 meters in t=50 seconds. The rate of descent is

[tex]\displaystyle v=\frac{320}{50}[/tex]

[tex]v=6.4\ m/s[/tex]

Answer: 14ft > 41/2

Step-by-step explanation:

Your answer is:

14ft > 41/2yd

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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).

Triangle with sides RS=19, SQ = 20, AND QR = 18 must have unequal angles as triangles with unequal sides have unequal angles.

A triangle with unequal sides is known as the Scalene triangle. As mentioned in the question triangle QRS has unequal sides of length RS = 19, SQ = 20, and QR = 18.

Then we can say that triangle Δ QRS is a Scalene triangle.

A scalene triangle has unequal angles. It has no line of symmetry present in a  scalene triangle.

In a scalene triangle, the angle opposite to the longest side is the greatest.

Hence, we can say that the angles of  Δ QRS are unequal.

For more details about Triangles,

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The correct statement is that at least two angles of ΔQRS are equal, and one angle is different.

Here,

In a triangle, the sum of the measures of the three interior angles is always 180 degrees.

This is known as the triangle angle sum property.

Therefore, if we know the lengths of two sides of a triangle, you can determine the measure of the third angle using the Law of Cosines or the Law of Sines.

In the case of ΔQRS, we can use the Law of Cosines to find the measure of angle ∠Q:

Cos(∠Q) = (RS² + QR² - SQ²) / (2 * RS * QR)

Cos(∠Q) = (19² + 18² - 20²) / (2 * 19 * 18)

Cos(∠Q) = (361 + 324 - 400) / (2 * 19 * 18)

Cos(∠Q) = 285 / 684

Cos(∠Q) ≈ 0.416667

Now, to find the measure of ∠Q, we take the inverse cosine (arccos) of 0.416667:

∠Q ≈ arccos(0.416667) ≈ 65.392°

Now that we know the measure of ∠Q, we can find the measures of the other angles:

∠R = 180° - ∠Q - ∠S

∠R = 180° - 65.392° - ∠S

And

∠S = 180° - ∠Q - ∠R

∠S = 180° - 65.392° - (180° - 65.392° - ∠S)

∠S = 180° - 65.392° - 180° + 65.392° + ∠S

∠S = 2 * 65.392° - ∠S

2 * ∠S = 2 * 65.392°

∠S = 65.392°

So, the measures of the angles in ΔQRS are approximately:

∠Q ≈ 65.392°

∠R ≈ 49.608°

∠S ≈ 65.392°

As we can see, two of the angles (∠Q and ∠S) are equal, while the third angle (∠R) is different.

Therefore, the correct statement is that at least two angles of ΔQRS are equal, and one angle is different.

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Final answer:

The area of triangle ABC with vertices A(-1, -1), B(3, -1), and C(-1, 2) is calculated using the determinant method and results in 6 square units.

Explanation:

To find the area of a triangle with vertices on a coordinate plane, you can use the formula that requires knowing the coordinates of all three vertices.

For triangle ABC with vertices A(-1, -1), B(3, -1), and C(-1, 2), we can use the determinant method:

The area of triangle ABC is ½ |x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂)|. Substituting our given coordinates into this formula, we get:

Area = ½ |(-1)(-1 - 2) + 3(2 - (-1)) + (-1)((-1) - (-1))|

Area = ½ |(-1)(-3) + 3(3) + (-1)(0)|

Area = ½ |3 + 9 + 0|

Area = ½ × 12

Area = 6 square units

The area of triangle ABC is therefore 6 square units.

Answer:

Step-by-step explanation:

Summation means that you are adding together all the numbers that result from putting in the numbers 5-11 for i:

(-7 - 6(5)) + (-7 - 6(6)) + (-7 - 6(7)) + ( -7 - 6(8)) + ( -7 - 6(9)) + ( -7 - 6(10)) + ( -7 - 6(11)) which gives you the numbers:

-37 + -43 + -49 + -55 + -61 + -67 + -73 = -385

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:

The first picture is a function and the second picture is not.

Step-by-step explanation:

Reason - In the first picture, there is no repeating value of x. In other words, every x value has a y value. However, in the second picture, the x value, 2 goes to 2 and -3.

Answer:

C

Step-by-step explanation:

Answer:

Matt bought 7 packages of hot dogs and 5 packages of hamburger.

Step-by-step explanation:

We are given the following in the question

Let x represent the number of packages of hot dogs.

Cost of one packet of hot dog = $2.75

Let y represent the number of packages of hamburgers

Cost of one packet of hamburgers = $3.20

Then, we can write the following equations:

[tex]x + y = 12\\2.75x + 3.2y = 35.25[/tex]

Solving the two equations,

[tex]2.75x + 2.75y = 33\\2.75x + 3.2y = 35.25\\\Rightarrow 0.45y = 2.25\\y = 5\\x = 7[/tex]

Thus, Matt bought 7 packages of hot dogs and 5 packages of hamburger.

The solution is viable.

Constraints to the system of equation:

[tex]x,y \geq 0 \\x + y = 12\\2.75x + 3.2y = 35.25[/tex]

answer:C=10+10n

proof: 10+10 (1)=20

10+10 (.6)=16

10+10 (-.4)=6

Answer: The numbers are 10 and 23

Step-by-step explanation:

Let the smaller number be x

And the larger number be y

Ist sentence;

1. The sum of two numbers is 33.

X + y= 33 .........eqn 1

2. second sentence

the larger number is 3 more than two times the smaller number.

Y = 3 +2x

Put y into eqn 1

X+ 3 +2x = 33

3x= 33- 3

3x= 30

X = 30/3

X= 10 and y= 3+ 2x

Y= 3+ 2(10)

Y = 3+ 20

Y= 23

Therefore the two numbers are 10 and 23

Answer:

x=-3y

Step-by-step explanation:

-2x-6y=0

x+3y=0

x=-3y

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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

Answer:

18,000

Step-by-step explanation:

because its closer to 18,000 then 19,000.

Answer:

[tex]time=1.2\times 10^{-1}\ second[/tex]

Step-by-step explanation:

Given:

The speed of the radio is [tex]3\times 10^{8}[/tex] meters per second.

The distance of the satellite from the earth is [tex]3.6\times 10^{7}[/tex] meter

The formula of the speed is

[tex]speed = \frac{distance}{time}[/tex]

For time the formula is.

[tex]time = \frac{distance}{speed}[/tex]

put distance and speed value in above equation.

[tex]time = \frac{3.6\times 10^{7}}{3\times 10^{8}}[/tex]

[tex]time = \frac{1.2 x 10^{7}}{10^{8}}[/tex]

[tex]time=1.2\times 10^{7}\times 10^{-8}[/tex]

[tex]time=1.2\times 10^{7-8}[/tex]

[tex]time=1.2\times 10^{-1}\ second[/tex]

Therefore, the radio will be take the time is [tex]1.2\times 10^{-1}\ second[/tex] or 0.12 seconds.

Answer:

y=-2/3x+2

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

Answer:

2i: 169.71

2ii: 0.17L

3a: 4×10⁻⁵

3b: 110011

Step-by-step explanation:

2i. The surface of the top and bottom of the tin is two times (top and bottom) π·r² = 2·π·3² = 18π cm².

The circumference of the circle is 2·π·r = 6π cm².

The area of the material connecting top and bottom is a rectangle of the tin height times the circumference: 6·6π = 36π cm².

This gives a total of  18π + 36π = 54π  cm².

With π approximated by 22/7 the total surface area is 54*22/7 ≈ 169.71.

Notice how the calculation is simple by waiting until the very last moment to substitute π.

2ii. The volume is the area π·r² of the circle times the height of the tin: 9π*6 = 54π cm³ ≈ 169.71 cm³.

Since 1L = 1000 cm³ the volume is 0.16971 litres, which should be rounded to 0.17 L.

3a: If we rewrite P as 36 x 10⁻⁴ and realize that 36/2.25 = 16, then the fraction can be written as

16 x 10⁻⁴⁻⁶ = 16 x 10⁻¹⁰.

The square root of that is taking it to the power of 1/2, so (16x10⁻¹⁰)^0.5 = 4x10⁻⁵ = 0.00004

3b: 1111 1111 is 255 in decimal. 101 is 5 in decimal. 255/5 is 51 in decimal. 51 in binary is 110011.

Answer:

8 1/4

Step-by-step explanation:

20 2/4

-

12 3/4

__________

8 1/4

7 1/4

You subtract 20 and 2/4 by 12 3/4 and you get 8 1/4

The sides are 7 inches and 5 inches. To get the perimeter, it's 7 +7 +5 + 5, which equals 24, and then 7 x 5 = 35 for the area.

Answer: they lost 20 yards.

Step-by-step explanation

Answer:

A -20

Step-by-step explanation:

Answer:

0

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(-2-(-2))/(5-(-3))

m=(-2+2)/(5+3)

m=0/8

m=0

Answer:

Step-by-step explanation:

We need to find the option for which the value of the function will be increasing, with the increasing variable.

Vertical line means the value of the x is constant, for any y. Hence, it is not the answer.

Horizontal line represents constant functions. Hence option B can not be the answer.

The data having a positive slope represents a increasing function with the increasing variable. Vice-versa for the data having a negative slope.

That is why option D will be the answer.

The correct option is d, which is the data canvas be modeled by a line with a negative slope.

A scatter plot is also known as a scatter chart, a scatter graph that uses dots to represent values for two different numeric variables. Each dot on the graph represents a particular on both the axis.

the Y values are decreasing as the x-values are increasing

As we can see in the graph below with the decreasing value of y and increasing value of x, therefore, it will be a negative slope.

Hence, the correct option is d, which is the data canvas be modeled by a line with a negative slope.

Learn more about Scatter plots:

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Answer:

Step-by-step explanation:

Complete the square to do this.  This one is a bit of a pain because of the 7 as our linear term, but a little hard work never killed anyone!

The rules for completing the square are very strict and cannot be strayed from.  The first rule is that the leading coefficient HAS to be a positive 1; ours is a positive 6 so we have to factor it out.  Let's do that first then we can get to rule number 2.

Set the quadratic equal to 0, then move the constant over to the other side.  This is not a rule, per se, but I teach it this way to avoid unnecessary confusion in an already confusing process.  

[tex]6x^2+7x=-2[/tex] and to factor out the 6:

[tex]6(x^2+\frac{7}{6}x)=-2[/tex]

Now for rule #2:  take half the linear term, square it, and add it to both sides.  Our linear term is 7/6.  Half of that is 7/12, and 7/12 squared is 49/144.  BUT we cannot forget about that 6 hanging around out front, refusing to be ignored.  It is a multiplier, so when we add 49/144 inside the parenthesis on the left, we have to add 6(49/144) to the right, giving us:

[tex]6(x^2+\frac{7}{6}x+\frac{49}{144})=-2+\frac{294}{144}[/tex]

We will rewrite now by simplifying.  The left side can be written into a perfect square binomial (which is why we did this in the first place) and the right side can be added.  The left side becomes

[tex]6(x+\frac{7}{12})^2[/tex]

The 7/12 comes from the square root of 49/144, and the x comes from the square root of x-squared.  The right side requires a common denominator:

[tex]-2+\frac{294}{144}=-\frac{288}{144}+\frac{294}{144}=\frac{6}{144}=\frac{1}{24}[/tex]

So now we have

[tex]6(x+\frac{7}{12})^2=\frac{1}{24}[/tex]

Put evertyhing back onto the left side and set it back to equal y and you're done!

[tex]y=6(x+\frac{7}{12})^2-\frac{1}{24}[/tex]

Because the vertex form of a quadratic does not allow us to stray from the format "x -", we have to interpret our h coordinate as "x - (-7/12))" which is movement to the left.  This gives us a vertex of

[tex](-\frac{7}{12},-\frac{1}{24})[/tex]

Answer:

Step-by-step explanation:

The basic concept for both is the same, except with grouping you have more than 3 terms and after factoring out what is common in each group, you are left with identical terms in a set of parenthesis that can then also be factored out.  For example, this would be factoring by grouping (then I will show you a factoring by GCF to better illustrate the idea):

If our polynomial is

[tex]x^3-x^2+3x-3=0[/tex]

we could group those terms into groups of 2 (without changing their order at all) to get:

[tex](x^3-x^2)+(3x-3)=0[/tex]

and we factor out what's common in each group to get:

[tex]x^2(x-1)+3(x-1)=0[/tex]

You can see that the (x - 1) is common now and can be factored out, leaving us with

[tex](x-1)(x^2+3)[/tex] (the secod term now can be factored if you need the complete linear factorization, but it will lead to imaginary numbers).  

An example of factoring out the GCF is to factor out what's common in all the terms.  It HAS TO BE COMMON IN ALL THE TERMS to do it this way.  For example, in the polynomial

[tex]6x^3-4x^2+2x-8=0[/tex] the GCF for all the terms is a 2, so that's all we can factor out.  It has to factor out of every term every time, no exceptions:

[tex]2(3x^3-2x^2+x-4)=0[/tex]

The method of GCF factoring often just serves to simplify the polynomial down a bit, but sometimes will still require factoring.

Final answer:

Factoring by grouping is used for polynomials with four or more terms, arranging them into groups with common factors, while factoring by GCF involves finding the largest common factor for all terms in an expression.

Explanation:

Factoring by grouping and factoring by the Greatest Common Factor (GCF) are two methods used in algebra to simplify expressions or solve equations.

Factoring by GCF involves finding the largest factor that is common to all terms in an expression.

For example, in the expression 4x + 8, the GCF is 4, so we can factor it as 4(x + 2).

Factoring by grouping, on the other hand, is used when an expression has four or more terms.

The method involves grouping terms so that each group has a common factor that can be factored out.

For instance, with the polynomial x^3 + 3x^2 + 4x + 12, we group the terms into (x^3 + 3x^2) + (4x + 12).

We then factor out the GCF from each group, yielding x^2(x + 3) + 4(x + 3).

Recognizing that (x + 3) is common between the groups, we can then factor further to get (x^2 + 4)(x + 3).

Answer:

Step-by-step explanation:

3y + 8 +(-7y) + 9 =

3y + 8 - 7y + 9 =

-4y + 17

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:

Step-by-step explanation:

ΔABC ≅ ΔABD  by ASA

Answer:

2 cups of sugar

Step-by-step explanation: