Determine which set of side measurements could be used to form a right triangle.

square root of 18, square root of 32, 50
square root of 14, 6, square root of 50
4, 8, 20
4, 5, 6

The exact value of tan(F) in the simplest radical form for the given triangle is (√29)/8.

We are given a triangle. The vertices of the triangle are F, G, and H. The lengths of the sides of the triangle are given. The lengths of FG, GH, and HF are 8 units, √29 units, and √93 units, respectively. The triangle is a right-angled triangle. The measure of the angle ∠G is 90°. We must find the value of tan(F) in its most basic radical form. A radical expression is one that contains a square root.

Considering the angle ∠F, the base and the perpendicular of the triangle are FG and GH. The trigonometric ratio tan (F) is calculated as follows.

tan(F) = GH/FG

tan(F) = (√29)/8

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To solve for a variable, simply isolate it.

f + 32 = -2
f + 32 - 32 = -2 - 32
f = 34

Answer:

The correct answer is -34.

The number of students per teacher is 23.

The number of students per tutor is 8.

The number of tutors needed for 72 students is 9.

In order to determine the number of students per teacher, divide the total number of teachers by the total number of students.

Students per teacher = total number of students / total number of teachers

115 /5 = 23 students per teacher

In order to determine the number of students per tutor, divide the total number of tutors by the total number of students.

Students per tutor = total number of students / total number of tutors  

54 / 6 = 9 students per tutor

The number of tutors needed for 72 students = total number of students / students per tutor

72 / 9 = 8 tutors

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Answer:

y = 122

x = 58

Step-by-step explanation:

Parallel line angle rule, corresponding angle are equal

so y = 122

A flat line has 180degree angle

to get x, flat line - y = 180 - 122 = 58

For function, f(-4)=20, f(0)=4, f(2)=16 and f(3)=26

a relationship between two expressions or values that are not equal to each other is called 'inequality.

The given function is

f(x)= { -4x +4 for x <= 0

{ 10x - 4 for x > 0

We need to find f(-4),f(0),f(2) and f(3)

f(-4) is -4x +4 as x<=0

-4(-4)+4

16+4=20

f(-4)=20

f(0) is -4x +4 as x<=0

-4(0)+4=4

f(0)=4

f(2) is 10x - 4 as x>0

10(2)-4

20-4

f(2)=16

f(3) is 10x - 4 as x>0

10(3)-4

30-4

f(3)=26

Hence f(-4)=20, f(0)=4, f(2)=16 and f(3)=26

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Answer:

C ≈ 207.3 ft

Step-by-step explanation:

the circumference (C) of a circle is calculated as

C = 2πr ( where r is the radius ) , then

C = 2π × 33 = 66π ≈ 207.3 ft ( to the nearest tenth )

Answer:

103.67 feet

Step-by-step explanation:

using C = pi d

Answer:62

Step-by-step explanation:

let x=number of marbles Rasheed has
let 7x+6 = number of marbles Lacey has
x+7x+6=70
8x+6=70
8x=64
x=8
Plug 8 into 7x+6 and you get 62

The discount amount is $213.6

The sale price for the exercise machines is $676.4

The first step is to calculate the discount amount

890 × 24/100

= 890 × 0.24

= 213.6

The next step is to calculate the sale price

890(1-0.24)

890(0.76)

676.4

Hence the discount amount is $213.6 and the sale price of the exercise machine is $676.4

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Step-by-step explanation:

please recheck your question..

There is no question attached.

hope it helps..

The amount paid to vehicle A is less than to vehicle B so, Vehicle A is suitable to purchase based on a monthly payment.

When the loan is given to you, then some amount is charged to you for the principal amount and that is called interest.

Given:

For vehicle A,

The Principal amount of the car, P = $25000,

The rate of interest, r = 5% = 5/100 = 0.05,

The tenure, n = 60 months = 60/12 = 5 years,

Calculate the amount by the formula given below,

A = P (1 + r)ⁿ

Here A is the amount,

Substitute the values,

A = 25000 (1 + 0.05)⁵,

A = $31907.03

Similarly,  for vehicle b

A = 29000 (1 +0.04)⁶

A = $36694.25

As the amount of vehicle A is less than the of vehicle B Therefore, vehicle A is suitable to buy.

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Answer: The probability that more than 12 of the entry forms will include an order is 0.624.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

The Magazine Mass Marketing Company has received 16 entries in its latest sweepstakes.

The probability that more than 12 of the entry forms will include an order can be found as:

P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P( X = 3) - P(X = 4)

P(X > 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4)

P(X > 4) = 1 - 0.0009 - 0.0097 - 0.043 - 0.117 - 0.205

P(X > 4) =  0.624

Thus, the probability that more than 12 of the entry forms will include order is 0.624.

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Step-by-step explanation:

True. You can look at the direction of the line and automatically know if the slope is a positive or negative number.

The linear equation with positive value of slope goes upwards from left to right and linear equation with negative value of slope goes downwards from left to right.

Thus, it is true that you can look at the direction of the line and automatically know if the slope is a positive or negative number.

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The probability that C and D would be odd according to the given task content is; 1/4.

It follows from the task content that the probability that C and D would be odd be determined.

Given that the C and D are each chosen from a set 1, 2, 3, 4.

The probability that C is odd would be;

P (C is odd) = 2/4 = 1/2

Also; P ( D is odd) = 1/2

Consequently, the probability that C and D would be odd is;

= 1 / 2 × 1 / 2

= 1 / 4.

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The number sentence 4.8 < √32 is true

A number sentence is an arrangement of numbers and mathematical operation symbols

Given:

For 3 1/3 < √7

3 1/3 = 3.33 and √7 = 2.65

3.33 < 2.65

This is not true

For 4.8 < √32

√32 = 5.66

4.8 < 5.66

This is true

For |-3.2| < |-3.1|

|-3.2| = 3.2                Note: when you see sign | | you neglect the sign

|-3.1| = 3.1

3.2 < 3.1

This is not true

For 5.3×10⁵ < 9.76× 10⁴

5.3×10⁵ = 5.3×100000 = 530000

9.76× 10⁴ = 9.76×10000 = 97600

530000 < 97600

This is not true

Therefore, the number sentence 4.8 < √32 (4.8 < 5.66) is true. So option B is the answer

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Answer:A

Step-by-step explanation:

N is a lie, its increasing

Q is linear

R is linear

P must be true

Answer:

The answer is A) In Section P, the function is linear and increasing.

Step-by-step explanation:

B is false because it is not decreasing

C is false because it is considered linear (linear is a line). Non-linear is typically a curved line.

D is false because it's not increasing or decreasing, so when it states decreasing it isn't even right.

Hope this helps!!!

Answer:

Step-by-step explanation:

7

The axis of symmetry of function y = -|x + 10| is at y = 0

Axis of symmetry is an imaginary straight line which divide the function into two equal parts.

Axis of symmetry creates a mirror image of other part.

If we fold the two parts then the parts will superimposed.

Given function,

y = -|x + 10|

is in form y = a |x - h| + k

here , (h, k) is vertex

Comparing the form to the given equation

(h, k) = (-10 , 0)

which means graph is opens upward

and a = -1

Hence, the equation of axis of symmetric is at y = 0

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Aanya will now buy each at the cost below

A cherry muffin costs 350 shillings

A blueberry muffin costs 210 shillings

An apple costs 140 shillings

damson ones costs 70 shillings

The information given in the question is interpreted as below

A cherry muffin = 350 shillings

A blueberry muffin = 3 * damson ones

An apple + a blueberry muffin = 1 cherry muffin

A cherry muffin + 2 damson ones = 2 apple + 1 blueberry

from: 1 blueberry muffin, B = 3 * damson ones, D

D = B / 3

Also, An apple, A + B = 1 cherry muffin, C

A = C - B

C + 2D = 2A + B

substituting the values

350 + 2 * (B/3) = 2 * (350 - B) + B

350 + 2B/3 = 700 - 2B + B

collecting like terms

2B/3 + B = 700 - 350

5B/3 = 350

5B = 1050

B = 1050/5

B = 210

Solving for cost of apple

A = C - B = 350 - 210 = 140

Solving for the cost of the damson ones

D = B / 3 = 210 / 3 = 70

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Answer:

Even and Positive

Step-by-step explanation:

Answer:

(15x+3)° = 108 (vertically opposite angles)

15x = 108-3

15x = 105

x = 105/15

x =7

Answer:

x = 8. y = 21

Step-by-step explanation:

x + 8x + 18 = 90

combine like terms

9x + 18 = 90

-18 both sides

9x = 72

divide by 9 both sides

x = 8

______

3y + 27 = 90

-27 both sides

3y = 63

divide by 3 both sides

y = 21

The quadratic functions in this problem are listed as follows:

The definition of a quadratic function is presented as follows:

y = ax² + bx + c.

In which the leading coefficient a has to assume a value different of zero.

Another format to represent a quadratic function is making the input variable y and the output variable x, which is an exchange of the conventional notation, hence:

x = ay² + by + c.

The non-quadratic functions in this problem are:

All the other functions are quadratic functions, as they have two as the highest exponent, with a leading coefficient different of zero.

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The critical values for the chi-square distribution, with a sample size of 4 and a confidence level of 98 percent, are of:

0.2971 and 13.2767.

The critical value for the chi-square distribution is obtained inserting these following information into a calculator:

In the context of this problem, with a sample size of 4 and a confidence level of 98 percent, the parameters are given as follows:

Inserting these information into the calculator, the critical values are given as follows:

0.2971 and 13.2767.

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The cups of flour required for 2 cups of cashew is 2.6667

The proportion given in the problem is 3 cups of cashews for 4 cups of flour.

From the given proportion we calculate for the quantity of flours required for 2 cups of cashew

3 cups of cashew = 4 cups of flours

2 cups of cashew = ?

cross multiplying

3 * ? = 4 * 2

? = 4 * 2 / 3

? = 8 / 3

? = 2.6667

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Explanation:

To find x we need to find the unknown side that connects the two triangles using the Pythagorean theorem:

a² + b² = c² (c is always hypotenuse)

So:

a² + 6² = 9²

a² = 9² - 6²

a² = 81 - 36

a² = 45

a = sqrt45

Now we do the same thing for the other triangle:

x² + 5² = sqrt45²

x² + 25 = 45

x² = 20

x = 2√5 or 4.5...

Answer:

Domain: (negative infinity, positive infinity)

Range: (negative infinity,-4]

Step-by-step explanation:

infinity always has parentheses

domain is seen from left to right

range is seen from bottom to top

Answer:

[tex]\frac{8}{31}[/tex]

Step-by-step explanation:

the reciprocal of a number n is [tex]\frac{1}{n}[/tex]

given

3 [tex]\frac{7}{8}[/tex] ← express as an improper fraction

= [tex]\frac{31}{8}[/tex] , then

reciprocal = [tex]\frac{1}{\frac{31}{8} }[/tex] = [tex]\frac{8}{31}[/tex]

Answer:

[tex]\displaystyle \frac{8}{31}[/tex]

Step-by-step explanation:

First, we will turn 3 ⅞ into an improper fraction.

   [tex]\displaystyle (3*\frac{8}{8} )+(\frac{7}{8} )=\frac{24}{8} +\frac{7}{8} = \frac{31}{8}[/tex]

Next, we will find the reciprocal. This means we flip the numerator and the denominator.

[tex]\displaystyle \frac{31}{8} \rightarrow \frac{8}{31}[/tex]

Answer:30%

Step-by-step explanation:

Step-by-step explanation:

so,

100% = $130

1 % = 100%/100 = 130/100 = $1.30

the price changed by 169 - 130 = $39.

how many % are that ?

as many % and times 1% fits into $39 :

39 / 1.3 = 30%

the price increase was 30%.