One morning in Atlanta, Tina observed that the temperature was 72 degrees. Later the temperature rose 21 degrees and then dropped 11 degrees. She then flew to New York where the temperature was 67 degrees.
What was the change in temperature from when Tina left Atlanta and arrived in New York?
A:5°
B:6°
C:14°
D:15°

SOLUTION:

Case: Pythagoras Triple

Method:

The Pythagorean triple:

(8, 15, 17) can be formed with factor integers

8----> 4

15---->3.

Final answer:

x=4, y= 3

With the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

So, h(t) = 24:

Then, calculate as follows:

Therefore, with the help of the quotient, we know that the time the water balloon dropped from the rooftop is 1.3sec.

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Based on the dimensions of the right triangle, the equation to be used to find the missing lengths is hypotenuse² = Known leg² + Unknown leg².

To find the missing length of a right-angled triangle, you should use Pythagoras theorem.

This theorem allows you to find the dimensions of missing leg as:

hypotenuse² = Known leg² + Unknown leg²

When you solve for the missing length, the length is:

9² = 6² + Unknown leg²

81 = 36 + Unknown leg²

Unknown leg² = 81 - 36

Unknown leg = √(81 - 36)

Unknown leg = 6.7

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[tex]21+a=90 \implies a=69^{\circ} [/tex]

This is because the angles are complementary.

Answer:
domain: [-1,4]
range: [-2,4]
the graph is not a function, this is proven by using the vertical line test.

hope this helps :)

Answer:

We need to determine 50% of 100 now and the procedure explaining it as such

Step 1: In the given case Output Value is 100.

Step 2: Let us consider the unknown value as x.

Step 3: Consider the output value of 100 = 100%.

Step 4: In the Same way, x = 50%.

Step 5: On dividing the pair of simple equations we got the equation as under

100 = 100% (1).

x = 50% (2).

(100%)/(x%) = 100/50

Step 6: Reciprocal of both the sides results in the following equation

x%/100% = 50/100

Step 7: Simplifying the above obtained equation further will tell what is 50% of 100

x = 50%

Therefore, 50% of 100 is 50

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Remember that the domain is the numbers that x can take

x=5 has a domain of only 5

y = 1/x cannot have a value of x=0 because 1/0 is undefined

t = sqrt(x) cannot have negative values because sqrt( negative numbers) is not defined in the real number system

y = |x| is defined for all values of x so it has a domain of all real numbers

We want to find the value of the expression;

When x = 4 and y = 2.

All we have to do is substitute these values; when we do that, we have;

Therefore, the answer is 30.

[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{op ens~\cap}\qquad \stackrel{"a"~is~positive}{op ens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} h=-1\\ k=9 \end{cases}\implies y=a(~~x(-1)~~)^2 +9\implies y=a(x+1)^2 + 9 \\\\\\ \textit{we also know that} \begin{cases} x=-2\\ y=-8 \end{cases}\implies -8=a(-2+1)^2 + 9 \\\\\\ -17=a(-1)^2\implies -17=a\hspace{9em}\boxed{y=-17(x+1)^2 + 9}[/tex]

Answer:

D. infinite

Step-by-step explanation:

2(x+4) -1 = 2x + 7

To solve for x

Distribute

2x+8 -1 = 2x+7

Combine like terms

2x +7 = 2x + 7

Subtract 2x from each side

2x+7-2x = 2x+7-2x

7 = 7

This is always true, so there are infinite solutions

Answer:

75

Step-by-step explanation:

Answer:

75. ..... ............................

The result of the function f(3) is 3.

Given:

f(x) = -x² + 8x - 12

x = 3

Putting the value of x in the given function to obtain the outcome of the function,

f(3) = -(3)² + 8 × 3 - 12

     = -9 + 24 - 12

     = 24 - 21

     = 3

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Step-by-step explanation:

1 m = 4 cm

therefore,

A = 2.5 m = 2.5×1 m = 2.5×4 cm = 10 cm

B = 2.75 m = 2.75×1 m = 2.75×4 cm = 11 cm

D = 3.75 m = 3.75×1 m = 3.75×4 cm = 15 cm

The solution to 1/4(n - 6) = 1/4n - 3/2 is infinite many solutions

The equation is given as

1/4(n - 6) = 1/4n - 3/2

Multiply through the fraction equation by 4

So, we have the following equation

4 x 1/4(n - 6) = 4 x 1/4n - 4 x 3/2

Evaluate the products in the equation

So, we have the following equation

n - 6 = n - 6

Evaluate the like terms

0 = 0

The equation cannot be solved further

If the solution to an equation is 0 = 0, then the equation has infinite many solutions

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Answer: infinite many answers

Step-by-step explanation:

-3x - 4y = -5

12x - 3y = -18

Multiply the first equation by 4, and add both

-12x - 16y = -20

+

12x - 3y = -18

___________

-19y = -38

Solve for y:

y = -38/-19

y= 2

Replace y on any equation and solve for x

-3x - 4(2)=-5

-3x -8 = -5

-3x = -5+8

-3x = 3

x=3/-3

x=-1

Solution = (-1,2)

Solution

Number 6

for this case we can see that we have two common angles and one equal side. By the way we have also a common side and then since we have right triangles the correct postulate would be:

SSS

Number 9

The probability that the student will be prepared for exactly 4​ questions is; 0.3427

Hypergeometric distribution is defined as a discrete probability distribution that expresses the probability of k successes in n draws, done without replacement, from a finite population of size N that contains exactly K objects with that feature. In this disdtribution, each draw is either a success or a failure.

The probability mass function of Hypergeometric distribution is given by the formula;

P(K = k) = KCk * N-KCn-k ]/NCn

Now, the probability that the student will be prepared for exactly 4​ questions will be;

P(K = 4) where;

N = 16

K = 9

n = 8

Solving P(K = 4) = 9C4* 16-9C8-4 ]/16C8 = 0.3427

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Answer:

the first answer option : all lengths and angles stay the same.

Step-by-step explanation:

imagine you have a piece of plastic or glass of a triangular shape on your table.

now, lower your hand on the table, so that your thumb touches the table and one of your other fingers touches the triangle on the top.

and now twist your hand that your thumb stays at the same point, and your finger holding the triangle starts making a circular motion.

that finger is dragging the triangle along.

what happens to the triangle ? it keeps its original shape, and changes only its location and orientation.

that is what a rotation is.

The total number of strawberries needed for making all the smoothies can be represented by the expression -

y = 15x

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is Amy who is making all three smoothies for each of her x number friends. The first recipe uses 4 strawberries per smoothie, the second recipe uses 5, and the third recipe uses 6.

Number of friends [n] = x

Each of the three friends will get smoothies made from recipe 1, recipe 2 and recipe 3.

Then -

Number of strawberries needed for smoothie made from recipe 1 for x friends = n[1] = 4x

Similarly, for smoothies made from recipe 2 and 3 will need -

n[2] = 5x and n[3] = 6x number of strawberries.

Assume that total number of strawberries needed for making all the smoothies are y. Then, we can write -

y = 4x + 5x + 6x

y = 15x

Therefore, the total number of strawberries needed for making all the smoothies can be represented by the expression -

y = 15x

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Solution:

Given;

The z-score is calculated using;

Thus;

(b) The z-score of 99.7 probability is between -3 and 3. Thus;

ANSWER: Approximately 99.7% of men have cranial capacities between 560 cc and 1760 cc

The amount of times that 14 goes into 78 is; 5 times

We want to find how many 14 goes into 78.

Now, it is pertinent to note that this expression is used in our common daily lives for basic things of life. For example, if i want to know how many 10 dollars can go into 100 dollars, i will just divide 100 by 10.

Similarly another example is if i want to know how many 5 liters container of fuel would go into a 60 liters tank, i will just divide 60 by 5 to get the number.

In a similar vein, we can solve this question by dividing 78 by 14 to get;

78/14 = 5 ⁸/₁₄

This means 14 can only go in 5 full times as we will not count the fraction.

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Solution

A

Using pythagorean theorem

The final answer

The height of window A is

Answer: $4.20

Step-by-step explanation:

The sale price is $12 * .35 = 4.2

The table of values of the relationship between time and earnings is a linear relation

From the question, we have the following parameters:

Number of hours = 2 hours

Total earnings in this time = $35

Also from the question, we understand that:

She makes a constant hourly wage

A constant hourly wage implies that the table of values has a linear relationship

In this case, the linear relationship is represented as

A(t) = constant hourly wage * t

Where

A(t) represents the earnings

t represents the number of hours

So, we have

constant hourly wage * 2 = 35

Divide both sides of the equation by 2

So, we have

constant hourly wage = 17.5

Substitute constant hourly wage = 17.5 in A(t) = constant hourly wage * t

A(t) = 17.5 * t

Evaluate

A(t) = 17.5t

Using the values of t as:

t = 0, 2, 4, 6

We have the following table of values

Number of hours (t) || Amount earned

0                                              0

2                                              35

4                                              70

6                                              105

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The plane containing point B and parallel to the plane CDH is plane ABF.

As, from the diagram we can see that there are two plane passing from point B; plane ABF and ABC.

But plane ABC is intersecting the given plane CDH, while plane ABF is not.

Thus, plane ABF is parallel to the plane CDH.

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Answer: 31.25%

Step-by-step explanation:

Draw a Ven diagram in a rectangle with 2 circles one for F and the other for C. The intersection overlap will have the 10 who play both outside the circles but within the rectangle the 7 who do neither so then fill the rest of F with 4 to give a total of 14 and 11 for the C to total 21. When you add all the numbers you’ll get a class total of 32. Then the % who play both F and C is = (10/32)*100 = 31.25%

The pairs of angles that are linear pairs involving point F are:

A. ∠DFC and ∠CFG

D. ∠HFD and ∠CFD

E. ∠GFH and ∠GFC

F. ∠HFG and ∠DFH

When two angles that are adjacent to each other, (that is, they share the same vertex and the same side), are located on a straight line, these angles are linear pairs and are also supplementary angles.

Making reference to the image given, angles DFC and CFG share a common vertex F and a common side CF. Also, they lie on a straight line. Therefore, angle DFC and angle CFG are a linear pair.

Angles HFD and CFD share a common vertex F and a common side FD. They lie on a straight line. Thus, angle HFD and angle CFD are also a linear pair.

The same thing applies to angle GFH and angle GFC, as well as angle HFG and angle DFH.

The linear pairs are:

A. angle DFC and angle CFG

D. angle HFD and angle CFD

E. angle GFH and angle GFC

F. angle HFG and angle DFH

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In total, he spend $510 after discount.

A deduction taken from the gross amount or worth of anything, such as  a price decrease made from the standard or list price, giving clients a 10% discount to purchase tickets. A proportionate withdrawal from a loan account, typically done in exchange for cash or quick payment.

Given Data

Coats are discounted 30%

Suits are discounted 25%

Joe purchased a coat of $300

= 300 - [tex]\frac{30}{100}[/tex] × 300

= 300 - 90

= 210

He purchased coat for $210.

He purchased a suit $400.

Suits are discounted 25%

= 400 - [tex]\frac{25}{100}[/tex] × 400

= 400 - 100

= 300

He purchased suit for $300.

In total, he spend $510 after discount.

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