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4 years ago

5a+7=4a+4 solve for a.

Mathematics

2 answers:

stich3 [128]4 years ago

8 0

Answer:

a=-3

Step-by-step explanation:

Combine the variable: 5a+7=4a+4

Combine the constants: a+7=4

a=-3

Zarrin [17]4 years ago

3 0

Answer:

5a+7=4a++4

solution

54-4a=4-7

a= -2

1a/1=-2/1

a=-2

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In a ∆ABC , angle A + Angle B = 125° and Angle B + Angle C = 150° . Find all the angles of ∆ABC.

mel-nik [20]

$\large\underline{\sf{Solution-}}$

Given that,

<em>In triangle ABC</em>

$\purple{\rm :\longmapsto\:\angle A + \angle B = 125 \degree \: - - - (1) }$

$\purple{\rm :\longmapsto\:\angle B + \angle C = 150 \degree \: - - - (2)}$

We know,

Sum of all interior angles of a triangle is supplementary.

$\purple{\rm :\longmapsto\:\angle A + \angle B + \angle C = 180\degree }$

<u>On adding equation (1) and (2), we get </u>

$\purple{\rm :\longmapsto\:\angle A + \angle B + \angle B + \angle C = 125\degree + 150 \degree \:}$

$\purple{\rm :\longmapsto\:\angle A + \angle B + \angle C + \angle B = 275\degree \:}$

$\purple{\rm :\longmapsto\:180\degree + \angle B = 275\degree \:}$

$\purple{\rm :\longmapsto\:\angle B = 275\degree - 180\degree \:}$

$\purple{\rm :\longmapsto\:\angle B = 95\degree \:}$

On substituting the value in equation (1) and (2), we get

$\purple{\rm :\longmapsto\:\angle A + 95\degree = 125\degree }$

$\purple{\rm :\longmapsto\:\angle A = 125\degree - 95\degree }$

$\purple{\rm :\longmapsto\:\angle A = 30\degree }$

Also, from equation (2), we get

$\purple{\rm :\longmapsto\:95\degree + \angle C = 150\degree }$

$\purple{\rm :\longmapsto\:\angle C = 150\degree - 95\degree }$

$\purple{\rm :\longmapsto\:\angle C = 55\degree }$

Hence,

$\begin{gathered}\begin{gathered}\bf\: \rm\implies \:\begin{cases} &\sf{\angle A = 30\degree } \\ \\ &\sf{\angle B = 95\degree } \\ \\ &\sf{\angle C = 55\degree } \end{cases}\end{gathered}\end{gathered}$

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3 years ago

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Which two statements contradict each other?

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The answer is C. To contradict something is to say or do the opposite of what is stated. If point S lies on plane PQR, it cannot not lie on plane PQR.

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3 years ago

The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative

madam [21]

The true statement is:

"The range of the function is all real numbers less than or equal to 9."

<h3>Which statements are true?</h3>

Here we have the quadratic function:

$f(x) = -x^2 - 4x + 5$

And we want to see which of the given statements are true.

The first one is:

"The domain is al real numbers less than or equal to -2"

This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).

The second statement is:

" The domain of the function is all real numbers less than or equal to 9."

Also false

Third one:

" The range of the function is all real numbers less than or equal to −2"

The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.

In this case, the quadratic function is:

$f(x) = -x^2 - 4x + 5$

So the vertex is at:

$x = 4/(2*-1) = -2\\$

Then the y-value of the vertex is:

$f(-2) = -(-2)^2 - 4*(-2) + 5 = -4 + 8 + 5 = 9$

So the range is the set of all real numbers less than or equal to 9.

So the above statement is false, and the final one:

"The range of the function is all real numbers less than or equal to 9."

Is the true statement.

If you want to learn more about quadratic functions:

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2 years ago

Which of the following statements could be true regarding the bar

Ray Of Light [21]

What are the statements

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3 years ago

You want to buy a new winter coat that originally costs $115. The coat was marked down to $86.25 so you bought it. What percent

romanna [79]

Answer:

Step-by-step explanation:

The regular price is $62.50.

Explanation:

If the sale price is $50, and the sale is 20% off, that means the $50 represents the other 80% of the regular price—the part that you do pay. So then we ask ourselves, okay, $50 is 80 percent of... what? In math speak, that would be written as

$50(is)80%(of)(regular price)

$50=80% × r

Solving this for r, we get

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We remind ourselves that the "percentage" symbol is just a shorthand for "divide this number by 100." The equation becomes

r=$5080/100=$500.8=$62.50

So the regular price is $62.50.

Bonus:

A general formula can be used for any regular price r, any percent discount p, and any sale price s:

p%off of reg.price is sale price

(100−p)%× r = s

As long as we know two of the three variables {p,r,s}, we can solve for the third one.

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3 years ago

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5a+7=4a+4 solve for a.​

5a+7=4a+4 solve for a.