Which equation represents a function?
A) x = 4y + 7
B) y2 = -5x - 8
C) x2 + y2 = 16
D) y = ±2x + 3

Step-by-step explanation:

We know that tan=sin/cos, so tan(x+π/2)=

[tex]\frac{sin(x+pi/2)}{cos(x+pi/2)}[/tex]

Then, we know that sin(u+v)=sin(u)cos(v)+cos(u)sin(v),

so our equation is then

[tex]\frac{sin(x)cos(\pi/2)+cos(x)sin(\pi/2)}{cos(x+\pi/2)} = \frac{cos(x)}{cos(x+\pi/2) }[/tex]

Then, cos(u+v)=cos(u)cos(v)-sin(u)sin(v), so our expression is then

[tex]\frac{cos(x)}{cos(x)cos(\pi/2)-sin(x)sin(\pi/2)} = \frac{cos(x)}{-sin(x)} = -cot(x)[/tex]

Answer:

-1 2/6

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

#4

Step-by-step explanation:

p+n=26

.01p+.05n=.34

graph it out by desmos...?

you'll get the coordinates (24,2)

The number of pennies and nickels chiara has is 24 pennies and 2 nickels; the correct option is 4

The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.

Let;

p = the number of penny coins

n = the number of nickel coins

Remember;

1 penny = $0.01

1 nickel = $0.05

Chiara has 26 coins that equal 34 cents

so, p + n = 26

isolate the variable x;

p = 26 - n...equation(1)

34 cents=$0.34

0.01p + 0.05n = 0.34

Multiply by 100 both sides;

1p + 5n =$34

isolate the variable x;

p = 34 -5n...equation(2)

Create a table  to guess;

Assume  different values of n and determine the value of p in equation 1 and equation 2

The solution is when the value of p in the equation 1 must be equal to the value of p in equation 2

For n=1;

equation 1; p = 26-1 = 25

equation 2; p = 34-5(1)= 29

29 is not equal to 25

For n=2

equation 1; p= 26-2 = 24

equation 2; p= 34-5(2) = 24

24=24

Hence, the answer is (2,24)

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Answer:

Minimum-35

Maximum-50

Step-by-step explanation:

Sally can solve 35 questions in 5 hours and at most 70 question in 5 hours.

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that,

Minimum number of questions sally can solve in 1 hour = 7

Maximum number of questions sally can solve in 1 hour = 10

Now minimum of of question sally can solve in 5 hour,

= 5x7

= 35 questions

And Maximum number of question she can solve in 5 hour,

= 5x10

= 50 questions.

Hence,

In 5 hours she can solve,

Minimum 35 questions

Maximum 50 questions.

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Answer:

a. 85.5 sq ft

b. 3 bottles

Step-by-step explanation:

a. The cardboard is rectangular in shape. How much he needs to paint is the same as the cardboard that he needs to paint.

The area of a rectangle is given as:

A = L * B

where L = length and B = breadth

Therefore, the area of the cardboard having dimensions 14 1/4 feet by 6 feet is:

A = 14 1/4 * 6

A = 57 / 4 * 6 = 85.5 sq feet

He needs to paint 85.5 sq feet of the cardboard.

b. On bottle of paint covers 40 sq feet. The number of bottles he will need for his backdrop will be the area he needs to paint divided by the amount of paint that can cover 40 sq feet:

85.5 / 40 =  2.14

Since the number of bottles he will need is a whole number and its greater than 2, then it must be 3.

To paint the entire cardboard, he must have 3 bottles of paint.

Answer:

75 feet

Step-by-step explanation:

Answer:

1800

Step-by-step explanation:

Answer:

c you choose 5 out of 6 people

Answer:

90

Step-by-step explanation:

[tex]$f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = e^{x} + 1$[/tex]

[tex]\text{Range}(f) = \{y \in \mathbb{R} \vert x \in \mathbb{R}, f(x) = y\}[/tex]

[tex]\text{Suppose $f(x) = a$}\\e^{x} + 1 = a \implies e^{x} = a - 1 \implies x = \ln(a-1)\\[/tex]

[tex]\text{For the logarithm to be real, it must be true that $a - 1 > 0$}\\\text{But then we have that } a > 1. \implies \boxed{\text{Range}(f) = (1, \infty)}[/tex]

Answer:

The answer is D. y > 1 on edge

Answer:

K'(2, 1 )

Step-by-step explanation:

Under a reflection in the y- axis

a point (x, y ) → (- x, y ), thus

K(- 2, 1 ) → K'(2, 1 )

A - Trust me, its A

The people above are wrong

Answer:

B y=-2/3x+3

Step-by-step explanation:

y=mx+b

y=-2/3x+3

Answer:

Step-by-step explanation: y= -2/3x+3

Answer:

its B

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The data set up lowest to highest is: 6, 8, 8, 14, 18. Median is the middle number of the data, so the answer would be 8

Answer:

1 and 1/4

Step-by-step explanation:

40/32 divided by 8 = 5/4

5 divided by 4 = 1 R1

5/4 = 1 1/4

Answer:

B

Step-by-step explanation:

Answer:

x ≥ -15/2

Step-by-step explanation:

-2x - 4 ≤ 11

Add 4 to each side

-2x - 4+4 ≤ 11+4

-2x   ≤ 15

Divide each side by -2, remembering to flip the inequality since we are dividing by a negative

-2x/-2 ≥ 15/-2

x ≥ -15/2

Answer:

x≤-7.5

Step-by-step explanation:

-2x - 4 ≤ 11

Add 4 to both sides

-2x≤15/-2

Divide

x≤-7.5

Answer:

Step-by-step explanation:

The box plot shows all three quartiles, where the first one is 45, the second quartile is 50 and the third quartile is 67 (remember that there are only three quartiles in a dataset).

Now, the interquartile range is defined as the difference between the third and first quartile, which in this case is 67 - 45 = 22.

Therefore, the interquartile range is 22.

Answer:

The distance from station A to the fire is 90.4 miles

The distance from station B to the fire is 95.6 miles

Step-by-step explanation:

Given that 2 fire stations are 100 miles apart.

Station A = N 55°E

Station B = S 60°E

To find the distance of the fire from each station, let's use the law of sines,

From the diagram, our values are:

A = 55°

B =  60°

Let's take C as point of fire.

Since the total sum of angle in a triangle is 180,

A+B+C=180

C = 180 - A - B

C = 180 - 55 - 60 = 65°

For station A.

[tex] \frac{Sin A}{a} = \frac{Sin C}{c} [/tex]

[tex]\frac{Sin55}{a} = \frac{Sin65}{100}[/tex]

[tex]a = \frac{Sin55 * 100}{Sin65}[/tex]

[tex]a = 90.38[/tex]

The distance from station A to the fire is 90.4 miles

For station B:

[tex] \frac{Sin B}{b} = \frac{Sin C}{c} [/tex]

[tex]\frac{Sin60}{b} = \frac{Sin65}{100}[/tex]

Solving for b, we have:

[tex]a = \frac{Sin60 * 100}{Sin65}[/tex]

[tex]a = 95.6[/tex]

The distance from station B to the fire is 95.6 miles

The expression into an equivalent form [tex]5^{10} \times 5^5[/tex] is  [tex]5^{15}[/tex].

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expressions, we can either make it look more complex or simple. Usually, we simplify it.

We need the expression into an equivalent form.

This expression could also be given by;

[tex]5^{10} \times 5^5[/tex]

Now plug the values then we get;

[tex]5^{10} \times 5^5\\\\= 5^{10+ 5} \\\\= 5^{15}[/tex]

Hence, the expression into an equivalent form [tex]5^{10} \times 5^5[/tex] would be; [tex]5^{15}[/tex]

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parallogram it has exactly 2 pairs of congruent angles

Answer:

Parallelogram.

Step-by-step explanation:

Answer:

denominator is 100

Answer:

The demominator is 100

Step-by-step explanation:

0.85 is pronounced eighty-five hundreths therefore the denominator is 100!

Answer: She can buy up to 2 bags of nuts

Step-by-step explanation:

Hi, to answer this question we have to write an inequality:

The product of the number of bags of nuts bought (n) and the price per bag (5.70); plus the price of one box of cookies (4.25) must be less or equal to Annie's money (18).

5.70n +4.25 ≤18

Solving for x:

5.70n ≤18 -4.25

5.70n ≤13.75

n ≤13.75/5.70

n ≤2.41  

n ≤2 (rounded)

She can buy up to 2 bags of nuts

Answer:2

Step-by-step explanation:

The formula for area of a circle is r² x π.

Since we know the diameter, we can firstly divide by 2 to find our radius.

4/2 = 2

Now that we know the radius, we can substitute it in and square the value.

(2)² x π

(4) x π

Since we're finding the area in terms of pi, we won't multiply by pi, giving us the answer of 4π.

Therefore, the area of the circle is equal to 4π.

Hope this helped! :)

Answer:

If the diameter of the circle is 4 in. then the radius of the circle is 2

the formula for the circle area is

A = πr^2

r = radius

A = π * 2 * 2

A = 12.57 if solved

Step-by-step explanation:

Answer:

Step-by-step explanation:

Two groups of subjects were divided in an experimental study. One group was given a drug to help speed up

their metabolism and result in weight loss. The other group was given a placebo (a pill that looks identical to the one given to the other group, but without the weight loss drug). After a month of the experiment, the weight loss of each individual in each of the two groups were measured. In general, people in the group who took the metabolism drug did lose more weight, although there were differences in the amount each lost. There are two main types of variability occurring in this study. Describe each type below in the context of this study.

Induced Variability-

Natural Variability-

------------------------------------------------------------------------

Induced Variability - It is the kind of variability that is introduced by the one conducting the experiment. The decision to give one group the drug and othe other group a placebo was deliberate to check the merit of the drug on its own and was introduced by the one conducting the study. Hence the, the observation that the group that took the drug lost more weight as compared to the group that took the placebo is an induced variability.

Natural Variability - It is classified as a natural fluctuation in the observations that is not influenced by the one conducting the study. Even though the group that took the drug lost more weight, the exact amount that each of them lost was not constant. Hence this was a variability that did not introduce itself through the one conducting the study, and rather was unexplained and natural. Hence it is a natural variability.

Answer:

your answer is -9,-4,0,2,7 so your answer is d

Step-by-step explanation:

by looking on the number line you can see that -9 is farthest to the left ,so meaning it would go first and 7 which is the farthest right meaning it should be last giving you the order -9 as first -4 as second and 0 as third and so on.

Answer:

8

Step-by-step explanation:

23 + (-7) =16

16/2 = 8

Answer: 8

Step-by-step explanation:

23+(-7) = 16/2 = 8

Answer:

r = 1.0 cm to the nearest tenth

Step-by-step explanation:

The formula for the area of a circle of radius r is A = (pi)r².  So, from the given information we need to determine the radius of the orange.  The volume formula is V = (4/3)(pi)r³ and in this case V = 113.1cm³.  Thuis,

(4/3)(pi)r³ = 113.1cm³

                                                3                              3(113.1 cm³)

Multiplying both sides by ------------ , we get r³ = --------------------- , and so

                                              4(pi)                                12.57

r³ = 339.3 cm³ / 12.57 ≈ 0.997, so that r ≈ ∛(0.997 cm³) ≈ 0.9999, or

r = 1.0 cm to the nearest tenth.