which equation could use the find the length of the hypotenuse
0 6² + 11² - c²
0 6²+c² - 11²
Oc²-6²-11²
0 11²-6²-c²

Answer:

B

Step-by-step explanation:

Answer:

he total number of people who use at least two facilities is 4 + 45 = 49

Step-by-step explanation:

To find the number of people who use at least two facilities, we can find the number of people who use all three facilities and add the number of people who use only two facilities.

The number of people who use all three facilities is 4, and the number of people who use only two facilities is 27 + 23 + 31 - 3 * 4 = 45.

Therefore, the total number of people who use at least two facilities is 4 + 45 = 49.

Answer:

The greatest common factor of 70 and 15 is 5.

Step-by-step explanation:

First, list the prime factors for each individual number

Next, circle each common prime factor. This means that you must find the prime factors that are the same as each other. For example, if it's 1 3 4 and 2 3 5, the common prime factor would be 3.

Finally, you must multiply all of the common prime factors. Your answer will be the greatest common factor!

So, the greatest common factor of 70 and 15 is 5.

1. When we simplify sec² x + tan² xsec² x, the result obtained is sec⁴x

2. When we simplify (sec² x - 1) / sin² x, the result obtained is sec² x

3. When we simplify (1/sec² x) + (1/csc² x), the result obtained is 1

4. When we simplify (sec x / sin x) - (sin x / cos x), the result obtained is cot x

5. When we simplify (1 + sin x)(1 - sin x), the result obtained is cos² x

6.  When we simplify cos x + sin xtan x, the result obtained is sec x

We can simplify the trig identities as follow:

1. Simplification of sec² x + tan² xsec² x

sec² x + tan² xsec² x = sec² x(1 + tan² x)

Recall

sec² x = 1 + tan² x

Thus,

sec² x(1 + tan² x) = sec² x × sec² x

sec² x(1 + tan² x) = sec⁴x

Therefore, the simplified is written as

sec² x + tan² xsec² x = sec⁴x

2. Simplification of (sec² x - 1) / sin² x

(sec² x - 1) / sin² x

Recall,

sec² x - 1 = tan² x

Thus,

(sec² x - 1) / sin² x = tan² x / sin² x

Recall

tan² x = sin² x / cos² x

Thus,

tan² x / sin² x = (sin² x / cos² x) / sin² x

tan² x / sin² x = 1/ cos² x

Recall

1/ cos² x = sec² x

Therefore, the simplified expression is written as:

(sec² x - 1) / sin² x = sec² x

3. Simplification of (1/sec² x) + (1/csc² x)

(1/sec² x) + (1/csc² x)

Recall

sec² x = 1/cos² x

Thus,

cos² x = 1/sec² x

Also,

csc² x = 1/sin² x

Thus,

sin² x = 1/csc² x

Therefore, we have

(1/sec² x) + (1/csc² x) = cos² x + sin² x

Recall

cos² x + sin² x = 1

Thus, the simplified expression of (1/sec² x) + (1/csc² x) is:

(1/sec² x) + (1/csc² x)  = 1

4. Simplification of (sec x / sin x) - (sin x / cos x)

(sec x / sin x) - (sin x / cos x) = (sec xcos x - sinx sinx) / sinx cos x

Recall

sec x = 1/cos x

sinx sinx = sin² x

Thus,

(sec x / sin x) - (sin x / cos x) = [(cos x/cos x) - sin² x] / sinx cos x

(sec x / sin x) - (sin x / cos x) = [1 - sin² x] / sinx cos x

Recall

1  - sin² x = cos² x

Thus, we have

[1 - sin² x] / sinx cos x = [cos² x] / sinx cos x

[1 - sin² x] / sinx cos x = cos x / sin x

Recall

cos x / sin x = cot x

Thus, the simplified expression of (sec x / sin x) - (sin x / cos x) is:

(sec x / sin x) - (sin x / cos x) = cot x

5. Simplification of (1 + sin x)(1 - sin x)

(1 + sin x)(1 - sin x)

Clear bracket

1 - sin x + sin x - sin² x

1 - sin² x

Recall

1 - sin² x = cos² x

Thus, we have

(1 + sin x)(1 - sin x) = cos² x

6. Simplification of cos x + sin xtan x

cos x + sin xtan x

Recall

tan x = sin x / cos x

cos x + sin xtan x = cos x + sin x (sin x / cos x)

cos x + sin xtan x = cos x + (sin² x / cos x)

cos x + sin xtan x = (cos² x + sin² x) / cos x

Recall

cos² x + sin² x = 1

cos x + sin xtan x = 1 / cos x

1/cos x = sec x

Thus,

cos x + sin xtan x = sec x

The simplified expression of cos x + sin xtan x is sec x

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Answer:

Either \(\frac{11}{2}\) or \(\frac{11}{4}\).  See explanation.

Step-by-step explanation:

So, I'm not exactly sure what the equation looks like.

If it's \(\frac{2x+3}{2}=7\):

\(2(\frac{2x+3}{2})=(7)2\\2x+3=14\\(2x+3)-3=(14)-3\\2x=11\\(\frac{2x}{2})=(\frac{11}{2})\\x=\frac{11}{2}\)

If it's \(2x+\frac{3}{2}=7\):

\((2x+\frac{3}{2})-\frac{3}{2}=(7)-\frac{3}{2}\\2x=\frac{14}{2}-\frac{3}{2}\\2x=\frac{11}{2}\\(\frac{2x}{2})=(\frac{11}{2})(\frac{1}{2})\\x=\frac{11}{4}\)

Hopefully one of these answers works for you.

Answer:

4.5

Step-by-step explanation:

4 * 1.5 = 6

3* 1.5 = 4.5

Answer: 180 gallons needed

Step-by-step explanation:

Zykeith,

Assume x gallons of 50% antifreeze is needed

Final mixture is x + 60 gallons

Amount of antifreeze in mixture is 0.4*(x+60)

Amount of antifreeze added is .5x + .1*60 = .5x + 6

so .5x + 6 = .4(x + 60)

.5x -.4x = 24 -6

.1x = 18

x = 180

Let x be the number of gallons of the 50% antifreeze solution needed. We know that the resulting mixture will be 70 + x gallons. To get a 40% antifreeze mixture, we can set up the following equation:

\({\implies 0.5x + 0.1(70) = 0.4(70 + x)}\)

Simplifying the equation:

\(\qquad\implies 0.5x + 7 = 28 + 0.4x\)

\(\qquad\quad\implies 0.1x = 21\)

\(\qquad\qquad\implies \bold{x = 210}\)

\(\therefore\) We need 210 gallons of the 50% antifreeze solution to mix with 70 gallons of 10% antifreeze to get a mixture that is 40% antifreeze.

\(\blue{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}\)

Step-by-step explanation:

Angle measures:

Supplementary angles for a linear pair and sum to 180°.

Examples are:

Solution:

Given:

Using the given measure of an angle, we can identify all the angles.

We can tell that:

Supplementary angles are pairs of angles that sums up to 180°.

Example of supplementary angle:

Answer:

Step-by-step explanation:

A = L x W

so you know that the length is 3m longer than the width, so you could use a formula to represent that

w = L + 3

you then substitute the second equation into the first to solve for L

70 = L x (l +3)

70 = L^2 + 3l

you could then rearrange the formula and solve for l using the quadratic formula  

0 = L^2 + 3l - 70

l = -3 +- (square root (3)^2 - 4(1)(70)) / 2(1)

l = -3 +- (square root 9 + 280) / 2

l = -3 +- (square root 289) / 2

l = -3 +- 17 / 2

then you solve for the two separate roots

l = -3 + 17 /2

l = 14 / 2

l = 7

or  

l = -3 - 17 / 2

l = -20 / 2

l = -10

since a length cannot be negative, this root is not viable. therefore l = 7

to solve for w you would use

w = l + 3

w = 7 + 3

w = 10  

hope this helps. :)))

1. The Fill ups are as follow:

AB² +  BC² = AC. AD + AC. CD

2. Segment addition postulate

The relationship between the three sides of a right-angled triangle is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The Pythagoras theorem states that the square of a triangle's hypotenuse is equal to the sum of its other two sides' squares.

Given:

BC/ AC = CD/ BC and AB/ AC = AD/ AB

Now, BC² = AC. CD  and AB² = AC. AD

Using, Addition Property of Equality

AB² +  BC² = AC. AD + AC. CD

and, AB² +  BC² = AC (AD + CD)  [factor]

AD + CD = AD (segment addition postulate)

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PLATO

i got it correct :)

Answer:

See below

Step-by-step explanation:

Answer: 22

Step-by-step explanation:

Solve for x

   1/2x + 7 = 18

Combine 1/2 and x.

  x/2+ 7 = 18

Move all terms not containing x to the right side of the equation.

Subtract 7 from both sides of the equation.

  x/2= 18 − 7

  x/2 = 11

Multiply both sides of the equation by 2.

  2 ⋅ x/2 = 2 ⋅ 11

Simplify both sides of the equation.

Cancel the common factor of 2.

  x = 2 ⋅ 11

Multiply 2 by 11.

  x = 22

Answer:

2/6; 3/9

Step-by-step explanation:

Multiply both the numerator and the denominator by the exact same number to find equivalent fractions

For example, I will randomly choose to multiply both by 2

Example 1:

1 × 2 / 3 × 2

2/6

Now, I'll do 3

Example 2:

1 × 3 / 3 × 3

3/9

You can check your work by dividing both the numerator and the denominator by the original fraction (1/3) to see if you get the number 1

Example 1:

2/6 ÷ 1/3

Copy dot flip

2/6 × 3/1

2 × 3 / 6 × 1

6/6

1

Example 2:

3/9 ÷ 1/3

Copy dot flip

3/9 × 3/1

3 × 3 / 9 × 1

9/9

1

Answer:

Solve for x: x = 4 - 4y/3

Solve for y: y = 3 - 3x/4

X intercept(s): (4, 0)

Y intercept(s): (0, 3)

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

Answer:

m > 4

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Step-by-step explanation:

Step 1: Define

11 + m > 15

Step 2: Solve for m

Here we see that any value m greater than 4 would work as a solution to the inequality.

Answer:

1.17

Step-by-step explanation:

You have to divide the cost/number of people who paid. This would be 7/6. 7/6 is equal to 1.16666666667. Since this is cost we round up to 1.17.

Answer:

The rectangle is 7.9 meters by 2.9 meters.

Step-by-step explanation:

Let l be the length and w be the width

l = w + 5

A = 23 m²

Formula: A = lw

Solve for the dimensions

23 = (w+5)w

23 = w² + 5w

w² + 5w - 23 = 0

Use quadratic formula to find the possible value/s of w

\(w = \frac{-b+-\sqrt{b^2-4ac} }{2a}\\ w = \frac{-5+-\sqrt{5^2-4(1)(-23)} }{2(1)} \\w = \frac{-5+-\sqrt{25+92} }{2}\\ w = \frac{-5+-\sqrt{117} }{2} \\w = \frac{-5+-\sqrt{9(13)} }{2} \\w = \frac{-5+-3\sqrt{13} }{2}\\ w = \frac{-5+3\sqrt{13} }{2} = 2.9\\ w = \frac{-5-3\sqrt{13} }{2} = -7.9\)

Since we're dealing with dimensions, take the positive value which is 2.9.

w = 2.9 m

Substitute the value to l = w + 5

l = 2.9 + 5

l = 7.9 m

An equation in slope-intercept form that represents the amount of solution y in the beaker x minutes after the start of the experiment is y = 9.65x + 2.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (50.25 - 2)/(5 - 0)

Slope (m) = 48.25/5

Slope (m) = 9.65.

At data point (0, 2) and a slope of 9.65, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 2 = 9.65(x - 0)

y = 9.65x + 2

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Answer:

Step-by-step explanation:

To find the product of the given fractions in lowest terms, we can multiply the numerators and denominators together, and then simplify the resulting fraction:

(24/18) * (2/17) * (34/3)

First, we can simplify the fractions by reducing any common factors in the numerators and denominators:

24/18 = (212)/(29) = 12/9 = 4/3

2/17 = 2/17

34/3 = (2*17)/3 = 34/3

Now we can multiply the simplified fractions:

(4/3) * (2/17) * (34/3) = (4234)/(3173) = 272/153

The product of the given fractions in lowest terms is 272/153.

Answer:

a, c and d

Step-by-step explanation:

the answer was not sufficient so writing.

Answer:

Height of cone = 5 cm

Step-by-step explanation:

Volume of rectangular prism with a cone hole = 163.22 cm³

Volume of rectangular prism - volume of the cone = 163.22 cm³

L*W*H - ⅓πr²h = 163.22

Where,

L = 5 cm

W = 5 cm

H = 7 cm

r = ½(3) = 1.5 cm

h = ?

Plug in the values into the equation and solve for h (height of the cone)

5*5*7 - ⅓*π*1.5²*h = 163.22

175 - 2.36*h = 163.22

-2.36*h = 163.22 - 175

-2.36*h = -11.78

Divide both sides by -2.36

-2.36*h/-2.36 ° -11.78/-2.36

h = 4.99152542

h = 5 cm (nearest tenth)

The perimeter of the regular polygon with 15 sides, each measuring 11 cm and an apothem of 18.4 cm, is approximately 166.05 cm.

What is polygon?

A polygon is a two-dimensional geometric shape that is made up of straight lines connecting a sequence of points, which are called vertices.

To find the perimeter of a regular polygon with 15 sides, we need to know the length of each side. However, we are given the apothem, which is the distance from the center of the polygon to the midpoint of any side.

We can use the apothem and the number of sides to find the length of each side using the formula:

length of each side = 2 × apothem × tan(π/n)

where n is the number of sides and π is the mathematical constant pi (approximately equal to 3.14159).

Substituting the given values, we get:

length of each side = 2 × 18.4 cm × tan(π/15)

length of each side ≈ 11.07 cm

Now that we know the length of each side, we can find the perimeter by multiplying it by the number of sides:

perimeter = number of sides × length of each side

perimeter = 15 × 11.07 cm

perimeter ≈ 166.05 cm

Therefore, the perimeter of the regular polygon with 15 sides, each measuring 11 cm and an apothem of 18.4 cm, is approximately 166.05 cm.

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Answer: it’s d

Step-by-step explanation:

Answer: C. 124

Step-by-step explanation:

In parallelograms, any two consecutive interior angles add to 180 degrees. CDA and BCD are consecutive interior angles. Since the measure of angle CDA is 56 and the sum of CDA and BCD equal 180, then to find the value of BCD, evaluate 180-56.

180 - 56 = 124

Answer:

Equation

Step-by-step explanation:

an equation is a statement of equality of two algebraic expressions involving one or more unknown quantities.

To find the distance between points A and B, we can use trigonometry and the given information.

Let's label the distance between A and B as "d". We know that point C is 94.4 meters away from point A. From angle A, we have the measure of 72°, and from angle C, we have the measure of 30°.

Using trigonometry, we can use the tangent function to find the value of "d".

tan(72°) = d / 94.4

To solve for "d", we can rearrange the equation:

d = tan(72°) * 94.4

Using a calculator, we can evaluate the expression:

d ≈ 4.345 * 94.4

d ≈ 408.932

Therefore, the distance between points A and B is approximately 408.932 meters.

The angle at which the ball takes off, distance the ball in the air, the ball's speed is mathematically given as

Generally, the equation for the verticle component   is mathematically given as

\(y=xtan\theta-\frac{16x^2}{v0cos^2\theta}\\\\Therefore\\\\\theta=tan^{-1}(1.8)\)

theta=60

b)

hmax=vo^2sin^2\theta/2g

vo=116.486

Therefore, distance the ball in the air

\(d=\frac{2*114.486*0.874*2}{32}\)

d=6.3658

c)

The ball's speed when it hits the ground will be vo

vo=116.486

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