The measure of angle b is three times the measure of angle
a. the sum of the angle measures is 128°. find the value of x.

Given two lines are parallel, their slopes are equal. After calculating the slopes of the two lines and solving the equation, we find that the value of 'k' in the question is 4.

In the realm of Mathematics, when two lines are parallel, their slopes are equal. The line y = x + 1 has a slope of 1. To find the slope of the line through (−7,−2) and (−1, k), use the formula for slope, which is m = (y2 - y1) / (x2 - x1). Here, (x1,y1) is (−7,−2) and (x2,y2) is (−1, k). Hence, the equation for slope would look like this: m = (k - (-2)) / (-1 - (-7)).

As the slopes are equal, we can form an equation 1 = (k + 2) / 6. Solving this equation will give us the value of k. By multiplying both sides by 6, we obtain 6 = k + 2. Consequently, subtracting 2 from both sides, we get k = 4.

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The given expression in its simplest form is 8.

The given expression is (-11x/2+3)-2(-11x/4-5/2).

We need to write the given expression in the simplest form.

A simplified expression is one in which each base is written only once, there are no negative exponents and no parentheses. Simplifying an expression makes it easier to solve complex problems, and using the rules for exponents makes simplifying expressions easier.

Now, the given expression can be simplified as follows:

(-11x/2+3)-2(-11x/4-5/2)

=-11x/2+3+22x/4+10/2

=-11x/2+22x/4+3+5

=-22x/4+22x/4+8

=8

Therefore, the given expression in its simplest form is 8.

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Answer:

[tex]C=2.5d[/tex]

Step-by-step explanation:

Your variable is always the number of drinks that you are going to drink, and the independent clause is the cost of the drink, which is $2.5.

Drinks     Cost

1                 2.5

2                  5

3                 7.5

4                  10

5                 12.5

SO now you know that the cos of 3 drinks is 7.5 and that can be escalated to any number that you want just by puttin the number of drinks that are going to be bought and multiply it by the cost.

Answer:

y - 9 = 22(x - 3)

Step-by-step explanation:

The rate of using water per minute will be 8.5 gallons per minute.

The rate of flow of water is defined as the amount of water or any liquid flowing in a unit of time. If the gallons of water are flowing in some minutes the rate will be measured in the gallons of water.

Given that Kim learned in her science class that every 2 minutes she spends in the shower, she uses 17 gallons of water.

The rate of flow of water will be calculated as:-

Rate of flow = Volume of water / Time

Rate of flow = 17 / 2

Rate of flow = 8.5 gallons per minute

Therefore, the rate of using water per minute will be 8.5 gallons per minute.

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Answer:

B.

Step-by-step explanation:

when trying to calculate the volume when being given the M or the mass, and the D or density, hears is the calculations needed for that: P=M/V, which also means volume is the mass divided by the volume, or density. Hence, the answer would be mass divided by density. hope this helps!!! (also, please give me brainliest.)

Volume is calculated given mass and density is Mass divided by density.

Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic meter and liter) or by various imperial units (such as the gallon, quart, cubic inch).

Mass is the quantity of matter in a physical body. It is also a measure of the body's inertia, the resistance to acceleration (change of velocity) when a net force is applied.

Density is defined as a measure of how compact the mass in a substance or object is.

Since, density of a substance is measure as the ratio of its mass to its volume,

Density =  Mass/Volume

or, Density x volume =  mass

or, Volume =  Mass/Density

Hence,Volume is calculated given mass and density is Mass divided by density.

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To solve the inequality -8x - 10 > 7x + 20, combine like terms, isolate the variable term, and solve for x. The correct answer is D) x < -2.

We need to solve the inequality -8x - 10 > 7x + 20.

Therefore, option D.) x < -2 is the correct answer.

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we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

[tex]G(-1,3)\ H(1,2)\ J(-3,-1)[/tex]

Step 1

Find the slope GH

[tex]G(-1,3)\ H(1,2)[/tex]

substitute in the formula

[tex]m=\frac{2-3}{1+1}[/tex]

[tex]m=\frac{-1}{2}[/tex]

[tex]mGH=-\frac{1}{2}[/tex]

Step 2

Find the slope HJ

[tex]H(1,2)\ J(-3,-1)[/tex]

substitute in the formula

[tex]m=\frac{-1-2}{-3-1}[/tex]

[tex]m=\frac{-3}{-4}[/tex]

[tex]mHJ=\frac{3}{4}[/tex]

Step 3

Find the slope JG

[tex]J(-3,-1)\ G(-1,3)[/tex]

substitute in the formula

[tex]m=\frac{3+1}{-1+3}[/tex]

[tex]m=\frac{4}{2}[/tex]

[tex]mJG=2[/tex]

Step 4

Verify if triangle GHJ is a right triangle

we know that

if two lines are perpendicular, then the product of their slopes is equal to minus one

so

[tex]m1*m2=-1[/tex]

compare slope GH with slope JG

we have

[tex]mGH=-\frac{1}{2}[/tex]

[tex]mJG=2[/tex]

[tex]-\frac{1}{2}*2=-1[/tex] -----> side GH and side JG are perpendicular

The triangle GHJ is a right triangle

The answer in the attached figure

Answer:

- 1/2, 3/4, 2, is, two of these slopes have a product of -1

Step-by-step explanation:

The factors of a quadratic equation will be (qx + r) and (sx+t). If the solutions are all integers, you may be able to quickly find q, r, s and t. The advantage of this method is that factoring can be very fast. The disadvantage is that factoring may not work; for instance, factoring will not find solutions that are not integers.

Completing the square is a multistep process. The main idea is to convert the original equation into one of the form (x + a)^2 = b, where a and b are constants. The advantage of this method are that it always works and that completing the square gives some insight into how algebra works more generally. The disadvantage is that this method is complex.

The quadratic formula is x = (-b +- (b*2 - 4ac)^.5))/2a. The advantages of this method are that the quadratic formula always works and is straightforward. The disadvantages are that the formula provides no insight and can become a rote technique.

Sometimes, you can guess an approximate solution. Then, you can increase or decrease your guess, depending on whether the result from your first guess is too big or too small. The advantages of this method are that guessing can be very fast if you guess right, and can get an approximate answer quickly, if that is all you need. The disadvantage is that sometimes you won't be able to make a good guess .

For an expression equivalent to, let's say, -8, you could do: -2 + -6.