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3 years ago

What is the simplified form of this expression?

Mathematics

1 answer:

Rasek [7]3 years ago

3 0

Answer:

B. -7 $x^{2}$ + 3x + 5

Step-by-step explanation:

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

-3 $x^{2}$ + x + 5 - 4 $x^{2}$ - 2x

Combine like terms

-3 $x^{2}$ - 4 $x^{2}$ = -7 $x^{2}$

x - -2x = x + 2x = 3x

-7 $x^{2}$ + 3x + 5

I hope this helps :))

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Even numbers between 27 and 39

lianna [129]

Even numbers are numbers that can be divisible by 2, so in this case
28, 30, 32, 34, 36, 38
^ are even numbers because they can be divided by 2

6 0

3 years ago

The room can hold a maximum of 400 people. If there are already 134 people

Olegator [25]

Answer:

x+ 134 is less than or equal to 400 is the answer

6 0

3 years ago

Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and ro

Helga [31]

Answer:

Part 1) The shape is a trapezoid

Part 2) The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

Part 3) The area is $937.5\ units^2$

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

The shape is a trapezoid

see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

$P=AB+BC+CD+AD$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

we have

A(-28,2),B(-21,-22)

substitute in the formula

$d=\sqrt{(-22-2)^{2}+(-21+28)^{2}}$

$d=\sqrt{(-24)^{2}+(7)^{2}}$

$d=\sqrt{625}$

$d_A_B=25\ units$

Find the distance BC

we have

B(-21,-22),C(27,-8)

substitute in the formula

$d=\sqrt{(-8+22)^{2}+(27+21)^{2}}$

$d=\sqrt{(14)^{2}+(48)^{2}}$

$d=\sqrt{2,500}$

$d_B_C=50\ units$

Find the distance CD

we have

C(27,-8),D(-4,9)

substitute in the formula

$d=\sqrt{(9+8)^{2}+(-4-27)^{2}}$

$d=\sqrt{(17)^{2}+(-31)^{2}}$

$d=\sqrt{1,250}$

$d_C_D=25\sqrt{2}\ units$

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

$d=\sqrt{(9-2)^{2}+(-4+28)^{2}}$

$d=\sqrt{(7)^{2}+(24)^{2}}$

$d=\sqrt{625}$

$d_A_D=25\ units$

Find the perimeter

$P=25+50+25\sqrt{2}+25$

$P=(100+25\sqrt{2})\ units$

simplify

$P=25(4+\sqrt{2})\ units$ ----> exact value

$P=135.4\ units$

therefore

The perimeter is $25(4+\sqrt{2})\ units$ or approximately $135.4\ units$

step 3

Find the area

The area of trapezoid is equal to

$A=\frac{1}{2}[BC+AD]AB$

substitute the given values

$A=\frac{1}{2}[50+25]25=937.5\ units^2$

4 0

3 years ago

In triangle NQL, point S is the centroid, NS = (x + 10) feet, and SR = (x + 3) feet.

olya-2409 [2.1K]

Where R is the median between Q and L:

From my understanding of a triangle's centroid, it divides an angle bisector into parts of 2/3 and 1/3. In the given problem, these divisions are NS and SR. Therefore, twice SR would be equal to NS. From here, we can get the value of X, to solve for SR.

NS = 2SR
(x + 10) = 2(x + 3)
x + 10 = 2x + 6
x = 4

Therefore, SR = (x + 3) = 7

4 0

3 years ago

Read 2 more answers

A 1.5m wire carries a 7 A current when a potential difference of 54 V is applied. What is the resistance of the wire?

borishaifa [10]

Answer:

R = 7.71 ohms

Step-by-step explanation:

By ohm's law: R= V/I

where, R = resistance of wire, V = potential difference, I = electric current

Given: V = 54 and I = 7 A

Plug in the above values in the ohm's law, we get

R = 54 V/7 A

R = 7.71 ohms

Hope this will helpful.

Thank you.

6 0

3 years ago

Read 2 more answers