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3 years ago

Which statement represents 8 more than 6 times a number is 5 less than 3 times that number

Mathematics

1 answer:

riadik2000 [5.3K]3 years ago

3 0

6n+8+3n-5 because you have to flip the numbers when a question says less than or more than

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1. Drag and drop an answer to each box to correctly complete the derivation of a formula for the area of a sector of a circle.

N76 [4]

Answer:-

Central angle , Ф/2π , A = Ф/2 r²

The ratio is 1/3 , V = 1/3 Bh

The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

Step-by-step explanation:

* Lets revise the rules of the area of the sector of a circle

- The area of the sector which has a central angle Ф° is

(Ф°/360°) × πr², where 360° is the measure of the circle and r is

the radius of the circle

- The area of the sector which has a central angle Ф radians is

(1/2) r²Ф

* Lets complete the missing in the 1st picture

- The ratio of the sector's area A to the circle's area is equal to the

ratio of the central angle to the measure of a full rotation of the circle

- A full rotation of a circle is 2π. This proportion can written as

A/πr² = Ф/2π

- Multiply both sides by πr² to get A = Ф/2 r² where Ф is the measure

of the central angle and r is the radius of the circle

* Lets revise the rules of the volume of the prism and the volume

of the pyramid, where they have the same base and height

- The volume of the prism = area of the base × its height

- The volume of the pyramid = 1/3 × area of the base × its height

- From them the ratio of the volume of the pyramid to the volume

of the prism is 1/3

- The formula of the volume of the prism is V = Bh, where B is the

area of the base and h is the height, the formula of the volume

of the pyramid is V = 1/3 Bh

* Lets revise the standard form of the equation of a circle with

center (h , k) and radius r

- The equation is: (x - h)² + (y - k)² = r²

∴ x² - 2hx + h² + y² - 2ky + k² - r² = 0

∵ x² - 8x + y² - 2y - 8 = 0

- Lets equate the two equation

∴ x² - 2hx + h² + y² - 2ky + k² - r² = x² - 8x + y² - 2y - 8 = 0

∵ -2h = -8 ⇒ ÷ -2

∴ h = 4

∵ -2k = -2 ⇒ ÷ -2

∴ k = 1

∵ h² + k² - r² = -8

∴ (4)² + (1)² - r² = -8

∴ 16 + 1 - r² = -8

∴ 17 - r² = -8 ⇒ subtract 17 from both sides

∴ -r² = -15 × -1

∴ r² = 25

* Substitute the values of h , k , r in the equation of the standard

form of the circle

∴ (x - 4)² + (k - 1)² = 25

* The equation of the circle in standard form is (x - 4)² + (k - 1)² = 25

8 0

3 years ago

Three fourths of x increased by 5 is - 7

Finger [1]

Answer:

$x=\frac{8}{3}$

Step-by-step explanation:

$\frac{3}{4} x+5=7$

Subtract 5 from both sides.

$\frac{3}{4}x+5-5=7-5$

Simplify.

$\frac{3}{4}x=2$

Multiply both sides by 4.

$4*\frac{3}{4} x=2*4$

Simplify.

$3x=8$

Divide both sides by 3.

$\frac{3x}{3} =\frac{8}{3}$

Simplify.

$x=\frac{8}{3}$

7 0

3 years ago

(answer with "sometimes, always, or never true") An integer is a whole number.

Pani-rosa [81]

Answer:

An integer is always a whole number

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Which equation has a slope

Dominik [7]

All the choices are in the slope-intercept form where,

y=mx+b

so, the number before the x is the slope. The given slope is -34. We just have to look for the -34 number before the x. So mong the choices, it is the letter a choice that has the slope -34. So the answer is A.

7 0

4 years ago

Read 2 more answers

Write the fraction or mixed number as a decimal. 1. 8 4/100 2. 4/10 3. 4 7/100 4. 6/10 5. 8 3/100 6. 8/10 7. 4/100 8. 10 14/100

damaskus [11]

8 4/100 = 8.04, as the ".00" is out of 1.00.
4/10 = 0.40
4 7/100 = 4.07
6/10 = 0.60
8 3/100 = 8.03
8/10 = 0.80
4/100 = 0.04
10 14/100 = 10.14
The quick way to determine what the decimal is, is to divide 100 by the denominator. That way, each time the numerator goes up, you can multiply how many times it goes up by the denominator.
I hope this helps!

5 0

3 years ago