The point where the graphs of two equations intersect has y-coordinate 2. One equation is y=-3x+5. Complete the other equation in the
form y = mx + b if its graph has a slope of 1.

The trigonometric function equation obtained for the graph is y = 4 sec (πx) - 2.

What is trigonometric function?

Simply put, trigonometric functions also referred to as circular functions are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle.

The upper waver have a value of y = 2 and the lower waves have a value of  y = -6.

Add the points and divide by 2 -

[2 + (-6)] / 2

(2 - 6) / 2

-4 / 2

-2

Therefore, the midline is y = -2.

The vertical asymptotes are drawn and they intersect the midline at certain points.

Then the sinusoidal function is drawn using the intersection point.

There is one period of sinusoidal function that is starting from x = 0 and goes upto x = 2.

This pattern tells that the function is of cosine.

Then the graph will be of trigonometric function secant .

The value of C = -2 , A = 4, D = 0

Here C is the midline value, A is the points above and below the midline, D is the horizontal shift and 2π/B is the period.

Now, 2π/B = 2

2B = 2π

B = π

Now, use the formula -

y = A cos (B(x - D)) + C

y = 4 cos (π(x - 0)) - 2

y = 4 cos (πx) - 2

y = 4 sec (πx) - 2

Now plot the graph for the obtained function.

The graph is same as given in the question.

Therefore, the function is y = 4 sec (πx) - 2.

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To find the sum of the Xm'f column, we first need to calculate the midpoint (Xm) for each class interval and then multiply it by the frequency (f) for that interval. The midpoint of each class interval can be calculated as the average of the lower and upper bounds of the interval.

For the first class interval 50-52:

Xm = (50 + 52) / 2 = 51

Xm'f = Xm * f = 51 * 5 = 255

For the second class interval 53-55:

Xm = (53 + 55) / 2 = 54

Xm'f = Xm * f = 54 * 8 = 432

For the third class interval 56-58:

Xm = (56 + 58) / 2 = 57

Xm'f = Xm * f = 57 * 12 = 684

For the fourth class interval 59-61:

Xm = (59 + 61) / 2 = 60

Xm'f = Xm * f = 60 * 13 = 780

For the fifth class interval 62-64:

Xm = (62 + 64) / 2 = 63

Xm'f = Xm * f = 63 * 11 = 693

Finally, we can add up the Xm'f values for each interval to get the sum of the Xm'f column:

Sum of Xm'f = 255 + 432 + 684 + 780 + 693 = 2954

So the sum of the Xm'f column is 2954.

Answer: [tex]533 yd^{2}[/tex]

Step-by-step explanation:

The surface area of the base is:

(20 x 17.3) / 2

= 346 / 2

= 173

The surface area of one of the three identical triangles is:

(20 x 12) / 2

= 240 / 2

= 120

So in total, your answer would be one base plus three of those identical triangles:

173 + (3 x 120)

= [tex]533 yd^{2}[/tex]

The height of the cell phone tower in feet is solved to be 23 feet

The height of the cell phone tower is calculated using the concept of similar triangle and the equation is as follows

A ​2-ft vertical post casts a 10​-in shadow

2 / 10

nearby cell phone tower casts a 115​-ft shadow

let the height be x

x / 115

equating the proportions

2 / 10 = x / 115

cross multiplying

10x = 2 * 115

x = 2 * 115 / 10

x = 23 ft

The height of the tower is 23 feet

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Answer:

B=B1B2B3/B1B2+B2B3+B1B3

Step-by-step explanation:

B1 B2 B3=B2B3B+B1B3B+B1B2B

B2B3B+BB1B3B+B1B2B=B1B2B3

(B2B3+B1B3+B1B2)B=B1B2B3

B=B1B2B3/B2B3+B1B3+B1B2

B=B1B2B3/B1B2+B2B3+B1B3

The required probability is 0.8945 that a sample of 29 smoke detectors will have a mean lifetime between 57 and 64 months.

To find the probability that a sample mean is between 57 and 64 months, we need to find the standard deviation of the sample mean, which is given by the standard deviation of the population divided by the square root of the sample size.

The standard deviation of the sample mean = standard deviation of the population / square root of sample size = 8 / √(29) = 8 / 5.385 = 1.48

Next, we need to standardize the interval of 57-64 months by subtracting the mean and dividing it by the standard deviation of the sample mean.

z₁ = (57 - 60) / 1.48 = -2.03

z₂ = (64 - 60) / 1.48 = 1.35

Finally, we can use a standard normal table to find the area under the normal curve between z₁ and z₂, which gives us the probability of a sample mean falling in the interval (57, 64).

P(57 < X < 64) = P(-2.03 < Z < 1.35) = 0.9790 - 0.0845 = 0.8945

Therefore, the final answer is 0.8945, rounded to four decimal places.

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The statements that are true about the two given functions intersections are; D. II and III

The functions we are working with are;

f(x) = ²/₃x - 4

g(x) = ¹/₄x + 1

I) f(4) = ²/₃(4) - 4 = -4/3

g(4) = ¹/₄(4) + 1 = 2

II)  f(12) = ²/₃(12) - 4

f(12) = 4

g(12) = ¹/₄(12) + 1

g(12) = 4

III) The coordinates of their intersection is; 12, 4

IV) This is incorrect

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Answer:The range is all number greater than -10, so the values that are elements of the range of f(x) are c) -9, d) -6, and e) -2

Step-by-step explanation:

Answer: The answer is 101

Answer: you need to do it on your own

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

cos 13 x 2 = 26

13 is a factor that is more than 4 and less then 26

The factor of the number 26 that is between 4 and 26 is 13. Factors are the numbers that can divide into a number without leaving a remainder. In this case, the factors of 26 are 1, 2, 13, and 26.

In mathematics, a factor of a number is a number that divides into another number without leaving a remainder. In the case of the number 26, its factors include 1, 2, 13, and 26. The factor of 26 that is between 4 and 26 is 13.

To find this, you can go through the factors of 26 one by one. The factors are found by dividing 26 by all the numbers up to 26, and the numbers that give a remainder of 0 are the factors. In this case, 1, 2, 13, and 26 divide evenly into 26, and so are the factors of 26. Of these, only 13 lies between 4 and 26.

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She made 12 out of 25 free throws, so in fraction it is expressed as 12/25. A fraction is useful here to show how many of her throws are successful compared to all the attempted throws.

A fraction is defined to be a part of a whole. It can also be defined as a numerical quantity that's not an integer. The parts of a whole or collection of things can be represented by a fraction. For instance, to cut a pie in half means we cut the pie so that there will be 2 halves of the pie.

A common fraction has two parts, which are the numerator and the denominator. The number above the line is the numerator, while the number under the line is the denominator. The numerator represents the parts and the denominator represents a whole collection.

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The expected phenotypes for the offspring is All tall.

Mendel came to the conclusion that some features predominated over other inherited traits when he noticed that a heterozygote offspring might exhibit the same phenotype as the parent homozygote. However, the connection between genotype and phenotype is rarely as straightforward as Mendel's descriptions of dominant and recessive patterns.

Given:

One is short and one is tall, Tall is dominant.

When two plants that are tall and short are crossed. They would all produce tall plants as a result, T.

The first crossing produced these children.

As a result of their parents' TT and SS genes, they all now have TS genes.

There will be some towering and some short off springs when these off springs are crossed. TS and TS will cross at this location. Given that they are all genetically tall and short.

So, The ratio of tall to short children they would have according to Mendel is 3:1.

Hence, almost All are tall.

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Answer:

x = 3.5

Step-by-step explanation:

x/2 + 2 = 9

x/2 = 7

x = 3.5

The volume of the composite figure  is: 2,412 millimeters cubed.

How to find the Volume of the composite figure?

Dimension of top rectangular prism:

Volume of top rectangular prism = 13× 12× 12

Volume of top rectangular prism = 1872 mm³

Dimension of bottom rectangular prism:

Volume of bottom rectangular prism = 15× 12× 3

Volume of bottom rectangular prism = 540 mm³

Volume of the composite figure = 1872 + 540

Volume of the composite figure   = 2412 mm³

Therefore the volume of the composite figure is 2412 mm³.

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If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Mr. Olsen has a PC business wherein he sells everything at 44.5% above the wholesale price. On the off chance that he bought a printer for $80 wholesale.

Then the retail price is given as,

⇒ $80 x (1 + 0.445)

⇒ $80 x 1.445

⇒ $115.60

If he purchased a printer for $80 wholesale. Then the retail price will be $115.60.

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Answer:

Step-by-step explanation:

2 hrs 12 mins

Answer:-200

Step-by-step explanation:

The translation means that the x coordinate is moving 4 units to the right and the y coordinate is moving9 units to the right.

A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions. The shape just shifts from one place to another, therefore there is no change in the shape.

The translation is T(x,y) (x+4,y+9).

The translation means that the x coordinate is moving 4 units to the right and the y coordinate is moving9 units to the right.

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x = 112 degrees.

A full triangle is 180 degrees total so do 180 - (39 + 29) = 112.

y = 220 degrees.

The sum of exterior angles are 360 degrees so 360 - 140 = 220.

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The percent decrease in the boiling point of water from sea level to 7,500 feet is equal to 18.7%.

In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.

In order to determine the percent decrease in the boiling point of water from sea level to 7,500 feet, we would determine the difference in temperature as follows;

Difference in temperature = 212°F - 198°F

Difference in temperature = 14°F

Percentage decrease = 14/7500 × 100

Percentage decrease = 0.00187 × 100

Percentage decrease = 18.7%.

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Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = [tex]\frac{1}{2}[/tex] x + 3 ← is in slope- intercept form

with slope m = [tex]\frac{1}{2}[/tex]

• Parallel lines have equal slopes , then

y = [tex]\frac{1}{2}[/tex] x + c ← is the partial equation

to find c substitute (2, - 4 ) into the partial equation

- 4 = [tex]\frac{1}{2}[/tex] (2) + c = 1 + c ( subtract 1 from both sides )

- 5 = c

y = [tex]\frac{1}{2}[/tex] x - 5 ← equation of parallel line

The equation of line is y = -50x + 150

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the

change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Points:(1, 100) (2, 50) (4, 25), (5, 20)

so, the slope is

= (50-100)/ (2-1)

= -50 /1

= -50

using slope intercept form

y - 100 = m (x- 1)

y- 100 = -50(x-1)

y- 100 = -50x + 50

y = -50x + 50 + 100

y = -50x + 150

Hence, the equation of line is y = -50x + 150.

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Answer: -1.5, -4/3, 3/2, 3/2

Step-by-step explanation:

First, convert the numbers to decimals or fractions.

-1.5

3/2 = 1.5

3/2 = 1.5

-4/3 = -1.3

Therefore, on a number line, the numbers would be in the following order:

-1.5, -4/3, 3/2, 3/2

Answer:

X=7

Step-by-step explanation:

To solve this equation, we need to use the logarithmic properties. First, we can use the property loga(bx) = x loga(b) to rewrite the equation:

log3(5) + log3(x) = log3(35)

This can be rewritten as:

log3(5x) = log3(35)

Using the property loga(b) = c, we can re-write the equation as:

x = 35/5

Now, we can calculate the value of 35/5:

35/5 = 7

Therefore, the solution to the equation is x = 7.

The total time that it took Pat and Rich to get to the beach is given as 3 hours.

Let's call the time it took Pat and Rich to drive to the beach "t".

Since it took them twice as long to get back, it took them 2t to get back.

The total time they spent traveling was 9 hours, so we can set up an equation:

t + 2t = 9

Combining like terms:

3t = 9

Finally, dividing both sides by 3:

t = 3

So it took them 3 hours to drive to the beach, and 6 hours to drive back.

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Answer:

In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.

Step-by-step explanation:

Answer: A) 2 and a half B) 5 pints

Step-by-step explanation:

in 1 cup there are 16 table spoons.

a) 4tbsp (2 servings) times 10 (to reach 20 servings) =40 tbsp

40/16 =2.5

ANSWER A= 2 and a half cups of lemon juice.

in 1 pint there are 2 cups.

b)

1 cup = 1/2 a pint,

1/2 pint (2 servings) times 10 (to reach 20 servings) = 5 pints

ANSWER B= 5 pints of olive oil

To obatin the graph of y=(x-8)^2 shifts the graph of y=x^2 8 units right

From the question, we have the following parameters that can be used in our computation:

y=(x-8)^2

y = x^2

In the above equations, we can see that

The value of 8 is subtracted from x in y = x^2 to get y = (x - 8)^2

This represents a right translation by 8 units

Hence, the translation is 8 units to the right

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Answer:

working on a answer one second

Step-by-step explanation: