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2 years ago

Simplify the expression: –2b + 7 – 2a + 5b – 6a

Mathematics

2 answers:

satela [25.4K]2 years ago

8 0

Answer:

A. -8 + 3b + 7

Step-by-step explanation:

GalinKa [24]2 years ago

6 0

Answer: A. -8a + 3b + 7

Step-by-step explanation: To answer this we have to combine like terms so we have to things being multiplied by a and two things being multiplied by b so we have to combine those to numbers,

So the first number (-2b) is a negative so when we add it to the positive (5b) we get 3b, (-2b + 5b = 3b)

Now onto the a's, both of them are negative so we can add them together then put the negative sign after them, -2a + -6a = -8b,

Finally we have the 7 but it is still just adding 7 to the equation so from what we just did A. -8a + 3b + 7 is the best answer.

If you need any further instruction or help let me know!

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A cone is cut out of the center of a pyramid with a rectangular base. The rectangular base has side lengths of 15 and 10 units.

Mekhanik [1.2K]

Answer:

Volume of shaded portion = (600 - 36π) units³

Step-by-step explanation:

Volume of the shaded portion = Volume of pyramid - Volume of cone

Volume of pyramid = ⅓*l*w*h

Where,

l = length of base of pyramid = 15 units

w = width of base of pyramid = 10 units

h = height of pyramid = 12 units

Plug in the values to find the volume of the pyramid

Volume of pyramid = ⅓*15*10*12 = 5*10*12 = 600 units³

Volume of Cone = ⅓πr²h,

Where,

r = radius = ½ of diameter = ½ of 9 = 3 units

h = height = 12 units

Volume of Cone = ⅓*π*3²*12 = ⅓*π*9*12

= π*3*12 = 36π units³

Volume of shaded portion = (600 - 36π) units³

3 0

2 years ago

The square of a number decreased by 3 times the number 28 find all possible values for the number

stealth61 [152]

Question:

The square of a number decreased by 3 times the number is 28 find all possible values for the number

Answer:

The possible values of number are 7 and -4

Solution:

Given that the square of a number decreased by 3 times the number is 28

To find: all possible values of number

Let "a" be the unknown number

From given information,

square of a number decreased by 3 times the number = 28

$a^2 - 3a = 28$

$a^2 - 3a - 28 = 0$

Let us solve the above quadratic equation

$\text {For a quadratic equation } a x^{2}+b x+c=0, \text { where } a \neq 0$

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

Using the above formula,

$\text { For } a^{2}-3 a-28=0 \text { we have } a=1, b=-3, c=-28$

$\begin{aligned}&a=\frac{-(-3) \pm \sqrt{(-3)^{2}-4(1)(-28)}}{2 \times 1}\\\\&a=\frac{3 \pm \sqrt{9+112}}{2}\\\\&a=\frac{3 \pm \sqrt{121}}{2}=\frac{3 \pm 11}{2}\\\\&a=\frac{3+11}{2} \text { or } a=\frac{3-11}{2}\\\\&a=7 \text { or } a=-4\end{aligned}$

Thus the possible values of number are 7 and -4

5 0

2 years ago

A falcon flying 55 mph crosses a lake in 1 minute. How long would it take a hummingbird flying 45 mph to cross the same lake?

OverLord2011 [107]

Answer:

1 2/9 minutes

Step-by-step explanation:

55 mph

55 / 60 = 11/12

11/12 of a mile = 1 minute

45 mph

45 / 60 = 3/4

3/4 of a mile = 1 minute

11/12 divided by 3/4

11/12 * 4/3

We can cross-cancel

11/3 * 1/3 = 11/9 = 1 2/9

It takes 1 2/9 minutes for the hummingbird to cross the lake

Hope this helps!

(Please let me know if I did something wrong!)

7 0

2 years ago

Read 2 more answers

What are the solution(s) to the quadratic equation 40 – x2 = 0?

Anna35 [415]

Answer:

$x=-2\sqrt{10}, \\x= 2\sqrt{10}$

Step-by-step explanation:

6 0

2 years ago

△XYZ was reflected over a vertical line, then dilated by a scale factor of , resulting in △X'Y'Z'. Which must be true of the two

Igoryamba

Answer:

correct option is △XYZ ~ △X'Y'Z'.

Step-by-step explanation:

since ΔXYZ is dilated by some scale factor so, the resulting triangle can not be congruent to the ΔXYZ. so option 2 is wrong.

as we have explained that the two triangles are not congruent then it's sides and angles also can't be congruent so, option 3 is also incorrect.

As we don't know by what factor the triangle XYZ is dilated so we can't say anything about correctness of option 4 and 5.

ΔXYZ was reflected over a vertical line and then dilated so the resulting ΔX'Y'Z' is similar to ΔXYZ.

i.e., △XYZ ~ △X'Y'Z'.

5 0

2 years ago

Read 2 more answers