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3 years ago

Factorize: Challenge problem: x^2+19x+78 help :)

Mathematics

2 answers:

mezya [45]3 years ago

4 0

$\bold{ x^2+19x+78 }$

$\bold{ x^2+13x+6x+78 }$

$\bold{ x(x+13)+6(x+13) }$

$\bold{(x+6)(x+13) }$

Trava [24]3 years ago

3 0

Answer:

(x + 6)(x + 13)

Step-by-step explanation:

Given

x² + 19x + 78

Consider the factors of the constant term (+ 78) whuch sum to give the coefficient of the x- term (+ 19)

The factors are + 6 and + 13 , since

6 ×13 = + 78 and 6 + 13 = + 19 , then

x² + 19x + 78 = (x + 6)(x + 13) ← in factored form

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Which of the following rotational symmetry is applied to the isosceles triangle

ioda

Answer:

Rotational symmetry of 180° about the origin: Yes.

Rotational symmetry of 270° about the origin: No.

Explanation:

A figure is a rotationally symmetrical if it look the same after a given turn.

We have to analyze if the parallelogram has rotational symmetry of 180° or 270°. picture the figure rotating a given amount of degrees to see if it looks the same or not.

180 degree rotation:

We can see that the figure looks the same after a 180° rotation.

270 degree rotation:

We can see that the figure does not look the same after a 270° rotation.

So the answer will be:

Rotational symmetry of 180° about the origin: Yes.

Rotational symmetry of 270° about the origin: No.

7 0

3 years ago

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A man has 32 coins in his pocket, all of which are dimes and quarters. If the total value of his change is 545 cents, how many d

inn [45]

A dime is worth 10 cents and a quarter is worth 25 cents.

Let D be the number of dimes and Q be the number of quarters.

Since the total amount of coins in the pocket is 32, then:

$D+Q=32$

On the other hand, the total value of D dimes is 10D, while the total value of Q dimes is 25Q. Then, the total value of D dimes and Q cuarters is 10D+25Q, which must be equal to 545. Then:

$10D+25Q=545$

Notice that we have found a 2x2 system of equations:

$\begin{gathered} D+Q=32 \\ 10D+25Q=545 \end{gathered}$

Solve the system using the substitution method. To do so, isolate D from the first equation and replace the expression for D into the second equation to obtain a single equation in terms of Q:

$\begin{gathered} D+Q=32 \\ \Rightarrow D=32-Q \\ \\ 10D+25Q=545 \\ \Rightarrow10(32-Q)+25Q=545 \\ \Rightarrow320-10Q+25Q=545 \\ \Rightarrow25Q-10Q=545-320 \\ \Rightarrow15Q=225 \\ \Rightarrow Q=\frac{225}{15} \\ \\ \therefore Q=15 \end{gathered}$

Replace back Q=15 into the expression for D to find the amount of dimes:

$\begin{gathered} D=32-Q \\ =32-15 \\ =17 \end{gathered}$

Therefore, the amount of dimes that the man has is 17.

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1 year ago

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faltersainse [42]

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3 years ago

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Rus_ich [418]

Answer:

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Step-by-step explanation:

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Hope this helps and have a great day!

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Step-by-step explanation:

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3 years ago

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