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4 years ago

3/9=21/k proportion

1 answer:

7 0

$\frac{3}{9} = \frac{21}{k}\\\\\frac{1}{3}= \frac{21}{k}\\\\\sf Cross~multiply\\\\1(k) = 21(3)\\\\k = 21(3)\\\\\boxed{k = 63}$

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find the length of side X in simplest radical form with a rational denominator (giving brainliest and thanks to all!)

irina1246 [14]

Answer:

x= √10/2

Step-by-step explanation:

if you use trig. functions:

sin 45° = opposite side /hypothenuse = x/√5

sin 45° = √2/ 2

√2/2 = x/√5 multiply both sides by √5

x= (√2*√5)/2 = √10/2

if you use that is a 45-45-90 special triangle

the sides are x, and hypothenuse must be x√2 in this type of triangles so in our case:

x√2 = √5 divide both sides by √2

x= √5/√2 multiply by √2/√2 which =1 and help us get rid of the radical from the denominator

x= (√5*√2)/ (√2*√2) = √10/2

6 0

3 years ago

Does anyone know to do this

neonofarm [45]

Answer:

Step-by-step explanation:

The questions asks you to work out what her annual salary is with benefits included. The health insurance, paid holidays, retirement contributions, paid vacation are all benefits as well as is the supplied uniform.

You need to add together all the figures in the chart=)

3 0

2 years ago

Read 2 more answers

Find the value of x. 1) m angle2=3x-6 120° 2 B) 10 D) 6 A) 12 C) -11

Kamila [148]

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4 0

3 years ago

Two roads are represented by lines on a coordinate grid. Two points on each of the roads are shown in the tables.

stellarik [79]

Answer:

(A) y - 7 = 2(x -2)

(B) y = -x + 6; y - 5 = -1(x + 1)

(D) (1, 5)

Step-by-step explanation:

(A) Road 1

(a) Slope

The <em>point-slope formula</em> for a straight line is

y₂ - y₁ = m(x₂ - x₁) Insert the points

3 - 7 = m(0 - 2)

-4 = m(-2) Divide each side by -2

m = -4/(-2) Divide numerator and denominator by-2,

m = 2

=====

(b) y-intercept

y₂ - y₁ = m(x₂ - x₁)

y₂ - 7 = 2(x₂ -2)

y - 7 = 2(x -2)

===============

(B) Road 2

(a) Slope

y = mx + b

Choose point (3,3)

m = (3 - 5)/(3 - 1)

m = -2/2

m = -1

=====

(b) y-intercept

y = mx +b

Choose point (3,3).

3 = -3 + b Add 3 to each side

b = 6

=====

(c) Equation of line (point-slope form)

y = mx + b

y = -x + 6

=====

(d) Equation of line (slope-intercept form)

y - 5 = -1(x - 1)

===============

(C) Consistency

The two roads intersect.

There is only one point of intersection, so this is a consistent, independent system of equations

===============

(D) Point of intersection

(1) y - 7 = 2(x - 2)

(2) y = -x + 6 Substitute (2) into (1)

-x + 6 – 7 = 2(x – 2) Remove parentheses

-x - 1 = 2x – 4 Add 4 to each side

-x +3 = 2x Add x to each side

3 = 3x Divide each side by 3

x = 1 Substitute into 2

=====

y = -1 + 6

y = 5

The point of intersection is (1, 5).

5 0

3 years ago

What is the diameter of a sphere with a volume of 332\text{ cm}^3,332 cm 3 , to the nearest tenth of a centimeter?

Korvikt [17]

Answer:

The diameter is 8.6cm

Step-by-step explanation:

Given

Shape: Sphere

$Volume = 332cm^3$

Required

Determine the diameter of the sphere

First, calculate the radius using:

$Volume = \frac{4}{3} \pi r^3$

Substitute: $Volume = 332cm^3$

$332= \frac{4}{3} \pi r^3\\$

Solve for r

$r^3 = \frac{332 * 3}{4 * \pi}$

$r^3 = \frac{996}{4 * \pi}$

$r^3 = \frac{249}{\pi}$

$r^3 = \frac{249}{3.142}$

$r^3 = 79.25$

Take cube roots

$r = \sqrt[3]{79.25}$

$r = 4.3$

Diameter (D) is calculated as:

$D = 2r$

$D = 2 * 4.3$

5 0

3 years ago