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2 years ago

Marcus wants to save $378 in order to buy a new electronic

Mathematics

1 answer:

melomori [17]2 years ago

7 0

Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

<h3>Define the meaning of the equation?</h3>

A mathematical assertion in which you use mathematical symbols to demonstrate that two sums are equal.

As per specified data-

Marcus wishes to save $378 so that he can purchase a new electronic keyboard.
Every week, he saves $15.75 from his paycheck.

Let 'x' be the number of weeks required to complete the amount.

The equation becomes.

378 = 15.75x

For the number of week required.

x = 378/15.75

x = 24

Thus, Marcus would need to save for 24 weeks in order to purchase a new electronic keyboard.

To know more about the equation, here

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Find all zeros of the polynomial P(x) = x3 − 2x2 − 3x + 10. Express any non-real roots in the form a + bi.

Strike441 [17]

Answer:

$x = - 2 \: or \: x = 2 - i \: or \: x = 2 + i$

Step-by-step explanation:

The given equation is

$p(x) = {x}^{3} - 2 {x}^{2} - 3x + 10$

We can see that:

$p( - 2) = {( - 2)}^{3} - 2 {( -2) }^{2} - 3( - 2)+ 10$

$p( - 2) = - 8- 8 + 6+ 10 = 0$

This means x=-2 is a zero of p(x).

From the long division in the attachment,

We can rewrite the polynomial as:

${x}^{3} - 2 {x}^{2} - 3x + 10 = (x + 2)( {x}^{2} - 4x + 5)$

We now find solution to the quadratic part:

${x}^{2} - 4x + 5 = 0$

This is given by:

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

We plug in the values to get:

$x = \frac{ - - 4 \pm \sqrt{ {( - 4)}^{2} - 4 \times 1 \times 5} }{2 \times 1}$

$x = \frac{ 4 \pm \sqrt{ 16 - 20} }{2 }$

$x = \frac{ 4 \pm \sqrt{ - 4} }{2 }$

$x = \frac{ 4 \pm2i}{2 } \\ x = 2 \pm \: i \\ x = 2 - i \: or \: x = 2 + i$

Therefore all solutions are:

$x = - 2 \: or \: x = 2 - i \: or \: x = 2 + i$

4 0

3 years ago

Solve the system of equations using the substitution method. check the solution.

Gennadij [26K]

Hello there!

To solve this system using substitution, notice that you already have one variable, x, solved for:
x=5-3y

Now, plug 5-3y in place of x in the other equation, -6x+5y=16:
-6(5-3y)+5y=16

Now simplify:
-6(5-3y)+5y=16
-30+18y+5y=16
-30+23y=16
23y=46
y=2

Now that you have y=2, plug this value in place of y into any of the two equations to solve for x:
x=5-3(2)
x=4-6
x=-1

Therefore, your final answers are that x=-1 and y=2 or (-1,2)

6 0

4 years ago

Multiply: k+3 4k−2 ×(12 k 2 +2k − 4)

Dmitriy789 [7]

K+3 * 4k=12k
2(12k * 2 + 2k - 4) = 2(26k - 4)
= k + 12k - 2 (26k - 4)
- 2 (26k - 4) : -52k+8
=k + 12k - 52k = -39k
FINAL ANSWER = -39k + 8

7 0

3 years ago

PLZ help now i need help n

vichka [17]

Answer:

Step-by-step explanation:

<em>hey there,</em>

<em />

< Here's how you do subtraction in fractions!

Make sure you find a least common denominator. Here, it's given to you to be 15. Usually, you can just multiply the two denominators but then it would be quite large at times, so you kind of just have to guess.

How did they go from $\frac{4}{5} x-\frac{1}{3} x$ to $\frac{?}{15} x$ ?

Well, they used a least common denominator. 5 was multiplied by 3 to create 15, and 3 was multiplied by 5. But when you multiply the bottoms, you have to multiply the tops of the fraction too (the numerators).

So 4/5x was multiplied by 3. Denominator turned out to be 15, and now the top is 4x3 = 12. So the fraction is 12/15.

1/3x, on the other hand, was multiplied by 5. Denominator was also 15 so they're the same, and top is 1x5 = 5. So the fraction is 5/15.

Now, let's put them together.

$\frac{12}{15}x-\frac{5}{15} x$

When subtracting x, the x just stays there, so if it was 10x-4x, the answer would've been 6x. So now let's subtract!

12-5 = 7, and the denominator stays the same.

The answer is $\frac{7}{15} x$ . So the numerator, or answer to your question, would be 7.

<u>Hope this helped! Feel free to ask anything else.</u>

5 0

3 years ago

Can someone help me ‼️

vazorg [7]

Answer:

A) 6

Step-by-step explanation:

The angle 12x is the same angle as the one below 108 degrees. They are supplementary angles so they add up to 180 degrees. 180-108 = 72, 12x = 72 divide each side by 12, x = 6 :)

8 0

3 years ago