What value of x will satisfy the equation:cos( x) = sin( 2x+ 57 )

Answer:

The piecewise model of the function is

[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]

[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]

Step-by-step explanation:

we know that

The general form of absolute value equation is

[tex]f\left(x\right)=a\left|x-h\right|+k[/tex]

where

The variable a, tells us how far the graph stretches vertically, and whether the graph opens up or down

(h,k) is the vertex of the absolute value

In this problem we have

[tex]f\left(x\right)=0.7\left|x-4\right|+2[/tex]

we have

[tex]a=0.7[/tex]

The coefficient a is positive ----> the graphs open up

The vertex is the point (4,2)

Find the piecewise model

case 1) positive value

[tex]f(x)=0.7[(x-4)]+2[/tex]

[tex]f(x)=0.7x-2.8+2\\f(x)=0.7x-0.8[/tex]

Is a linear equation with positive slope

[tex](x-4)\geq 0\\x\geq 4[/tex]

The domain is the interval [4,∞)

case 2) negative value

[tex]f(x)=0.7[-(x-4)]+2[/tex]

[tex]f(x)=-0.7x+2.8+2\\f(x)=-0.7x+4.8[/tex]

Is a linear equation with negative slope

[tex](x-4)< 0\\x<4[/tex]

The domain is the interval (-∞,4)

[tex]x<4[/tex]

therefore

The piecewise model of the function is

[tex]f(x)=-0.7x+4.8[/tex] -----> For [tex]x<4[/tex]

[tex]f(x)=0.7x-0.8[/tex] -------> For [tex]x\geq 4[/tex]

Answer:

X= -5

Step-by-step explanation:

Expression: 2.8X+12=-1.4X-9

Order it: 12+9=-1.4X-2.8X

Simplification: 21=-4.2X

Results: x=-5

Answer:

9

Step-by-step explanation:

Answer:

3/7 and 4/14

Step-by-step explanation:

a) 3/7 is not an equivalent of 6/21 because when you multiply the numerator and the denominator by 2 you get: 6/14

b) 4/14 is not an equivalent

Answer:

3/7

Step-by-step explanation:

6/21 = 6 ÷ 3 / 21 ÷ 3 = 2 / 7

6 / 21 = 4 ÷ 2 / 14 ÷ 2 = 2 / 7

6/21 = 12 ÷ 6 / 42 ÷ 6 = 2 / 7

Step-by-step explanation:

y+5-5=-2(x-4)

-5, first let's put it in the form y=mx+b.

y+5-5=-2(x-4)-5

y=-2x+3, so in this, m=slope and b=y-intercept. On your graph, plot three on the y line, and the slope is negative two, so go down two then over one to the left side, because it is decreasing. Also slope is rise over run or just rise/run.

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! As well as a great Valentines Day! :-)  

- Cutiepatutie ☺❀❤

Answer:

Step-by-step explanation:

3(x + 1) + 4x + 3 = 34......distribute thru the parenthesis

3x + 3 + 4x + 3 = 34....combine like terms

7x + 6 = 34....subtract 6 from both sides

7x = 34 - 6

7x = 28....divide by 7

x = 28/7

x = 4 <====

Answer:

look at the picture shown

Answer:

[tex]200.96sq.ft.[/tex]

Step-by-step explanation:

Given:

            Circumference= 50.24 ft.

We have to find the area of the circle.

Finding the radius with the help of given circumference

            Circumference of a circle= [tex]2\pi r[/tex]

                           [tex]50.24=2*\pi* r\\\\50.24=2*(3.14)*r\\\\50.24=6.28*r\\\\r=\frac{50.24}{6.28} \\\\r= 8ft.[/tex]

Area of a circle=  [tex]\pi r2[/tex]

                     [tex]=\pi *8*8\\\\=64*\pi \\\\=64*3.14\\\\=200.96sq.ft.[/tex]

Answer:

114

Step-by-step explanation:

the answer is not geomatic but you just have to think harder not smarter. ;)

Answer:

104

Step-by-step explanation:

80 = 8 * 10

88 = 8 * 11

? = 8 * x

128 = 8 * 16

160 = 8 * 20

11 - 10 = 1

x - 11 = 2

16 - x = 3

20 - 16 = 4

x = 13

13 * 8 = 104

Answer:

Step-by-step explanation:

Answer:103

Step-by-step explanation:

The value of n from the equation 7n = 28 is n = 4

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

7n = 28   be equation (1)

On simplifying the equation , we get

Divide by 7 on both sides of the equation , we get

n = 28/7

n = 4

Another equation which satisfies the relation is 4n = 16

n = 4

Therefore,  the value of n is 4

Hence , the value of the equation is 4

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Answer:

135m^2

Step-by-step explanation:

length = l

width = w

l + l + w + w = 48

l = w+6

w+6 + w+6 + w + w = 48

4w + 12=48

4w=36

w=9

l=15

15*9=135

Answer:

A = 135m²

Step-by-step explanation:

Write equations to represent the problem.

l = w + (6m)        The length is 6m more than the width

P = (48m)        Perimeter is 48m

***We put brackets around numbers with the "m" to avoid confusing the units with a variable.

The formula for perimeter of a rectangle is P = 2(l + w)

Substitute "l" and "P" into the perimeter formula with the equations above. Simplify, then isolate "w".

P = 2(l + w)        

(48m) = 2(w + (6m) + w)        Collect like terms (w + w = 2w)

(48m) = 2(2w + (6m))        Distribute over brackets

(48m) = 4w + (12m)        Start isolating "w"

(48m) - (12m) = 4w + (12m) - (12m)        Subtract 12m from both sides

(36m) = 4w        

4w/4 = (36m)/4        Divide both sides by 4

w = 9m        Width of rectangle

Find "l" using the formula for length. Substitute the width.

l = w + (6m)        

l = (9m) + (6m)        Add

l = 15m        Length of rectangle

Use the formula for the area of a rectangle A = lw.

Substitute the values we found for length and width.

A = lw        

A = (15m)(9m)        Multiply

A = 135m²        Area of rectangle

Therefore the area of the rectangle is 135m².

Answer:

The area of Andrew's tree house must be greater than or equal to 117 square feet

Step-by-step explanation:

Let

x -----> the area of Andrew's tree house in square feet

y ---->  the area of Cynthia's tree house in square feet

we know that

Cynthia plans to make the area of her tree house at least 13 square feet.

The word "at least" means "greater than or equal to"

so

[tex]y\geq 13[/tex] ----> inequality A

Cynthia plans to build a tree house that is 1/3 the size of Andrew's tree house

so

Remember that

When two figures are similar, the ratio of its areas is equal to the scale factor squared

In this problem the scale factor is given

The scale factor is 1/3

The scale factor squared is 1/9

That means

The area of Andrew's tree house is 9 times greater than the area of Cynthia's tree house

or

The area of Cynthia's tree house is 9 times smaller than the area of Andrew's tree house

[tex]y=\frac{1}{9}x[/tex] ----> equation B

substitute equation B in the inequality A

[tex]\frac{1}{9}x\geq 13[/tex]

solve for x

[tex]x\geq 117\ ft^2[/tex]

so

The area of Andrew's tree house must be greater than or equal to 117 square feet

we know that Andrew's tree house is larger than  Cynthia's tree house, because the problem states that Cynthia's tree house is 1/3 the size of Andrew's tree house

That means

The size of Andrew's tree house is 3 times greater than the size of Cynthia's tree house, without solving the inequality

Final answer:

To find the size of Andrew's treehouse, let's assume the area as x square feet. Using the given information, we can write and solve the inequality (1/3)x ≥ 13 to find the area of Andrew's treehouse. Without solving the inequality, we know that Andrew's treehouse is larger because the area must be greater than or equal to 39 square feet.

Explanation:

To find the area of Andrew's tree house, let's assume that his tree house has an area of x square feet.

According to the information given, Cynthia plans to build a treehouse that is 1/3 the size of Andrew's tree house. Therefore, the area of Cynthia's tree house would be (1/3)x square feet.

We are told that Cynthia plans to make the area of her tree house at least 13 square feet. So we can write the inequality as follows:

(1/3)x ≥ 13

To solve the inequality, we need to multiply both sides by 3 (since the coefficient of x is 1/3). This will give us:

x ≥ 39

This means that the area of Andrew's tree house must be greater than or equal to 39 square feet.

Without solving the inequality, we can see that Andrew's tree house is indeed larger than Cynthia's tree house because the area of Andrew's tree house must be greater than or equal to 39 square feet.

Answer:

  see below

Step-by-step explanation:

The five linear equations produce five parallel contour lines. The value of z increases as the lines shift to the right.

Final answer:

Level curves for the function f(x, y) = 5x - y for different values of c are straight lines with a slope of 5. They can be plotted on the same coordinate axes to form a contour map, with each line corresponding to one value of c.

Explanation:

Level Curves for the Function f(x, y) = 5x - y

To find the level curves of the function f(x, y) = 5x - y for the given values of c, we set f(x, y) equal to each constant and solve for y in terms of x:

For c = -2: -2 = 5x - y → y = 5x + 2

For c = -1: -1 = 5x - y → y = 5x + 1

For c = 0: 0 = 5x - y → y = 5x

For c = 1: 1 = 5x - y → y = 5x - 1

For c = 2: 2 = 5x - y → y = 5x - 2

These equations represent lines with a slope of 5 and various y-intercepts. The level curves can be drawn on a set of coordinate axes by plotting the lines according to their y-intercepts. Each line represents a different level curve and the set of these lines can be referred to as a contour map.

Because the triangles are congruent we know that NM = ST = 50.

answer: 50

The length of NM line segment for the considered situation is given by: Option D: 50 mi

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF\\[/tex]

(|AB| denotes length of line segment AB, and so on for others).

For these cases, the two triangles in the image are congruent.

So their corresponding sides must be of same measures.

The three sides of triangle RST are of measures 75, 67 and 50 miles

The two sides of triangle NLM are 67 miles and 75 miles. So obviously third one can be nothing except 50 miles so that the triangle NLM also have sides of same measure as of the triangle RST.

Thus, the length of NM line segment for the considered situation is given by: Option D: 50 mi

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Marco can watch TV for at most 56 minutes each day.

Step-by-step explanation:

Given,

Time of screen each week = 7 hours

1 hour = 60 minutes

7 hours = 60*7 = 420 minutes

Length of movie = 1 hour + 20 minutes = 60 + 20 = 80 minutes

Time left for other days = 420 - 80 = 340 minutes

Number of days = 6

Let,

x be the time per day for remaining 6 days.

Number of days * Time per day ≤ Time remaining

[tex]6x\leq 340[/tex]

Dividing both sides by 6

[tex]\frac{6x}{6}\leq \frac{340}{6}\\x\leq 56.66[/tex]

Marco can watch TV for at most 56 minutes each day.

Keywords: inequality, division

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Answer:

[tex]f^{-1}[/tex](x) = 9x + 18

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y = [tex]\frac{1}{9}[/tex] x - 2 ( add 2 to both sides )

y + 2 = [tex]\frac{1}{9}[/tex] x

Multiply through by 9 to clear the fraction

9y + 18 = x

Change y back into terms of x

[tex]f^{-1}[/tex] (x) = 9x + 18

The inverse of the function is 9y+18

An inverse is a function that serves to “undo” another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.

Given:

f f (x) = one-ninth x minus 2

f(x)= 1/9 x - 2

let f(x)=y

Now, solve for x

y = 1/9x -2

y+2 = 1/9x

9y+18 = x

Hence, the inverse of the function is 9x+18.

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Answer:

His commission on the boat he sells is $6250.

Step-by-step explanation:

Given:

Mr. Norris is paid a 5% commission on each boat he sells.

Now, to find his commission on a boat that he sells for $125,000.

Commission = 5%.

Boat he sell for = $125,000.

Now, to get the commission on the boat he sells:

5% of $125,000.

[tex]=\frac{5}{100} \times 125000[/tex]

[tex]=0.05\times 125000[/tex]

[tex]=\$6250.[/tex]

Therefore, his commission on the boat he sells is $6250.

Final answer:

Mr. Norris's commission on a boat sold for $125,000, with a commission rate of 5%, is $6,250.

Explanation:

Mr. Norris earns a commission based on a fixed percentage of the sales price. To calculate his commission for selling a boat priced at $125,000, we apply the 5% commission rate to the sale price.

Here's the calculation:
Commission = Sale Price × Commission Rate
Commission = $125,000 × 0.05
Commission = $6,250

Hence, Mr. Norris's commission for selling a boat that he sells for $125,000 is $6,250.

Answer:

She needs to buy 4.25 m cloth

Step-by-step explanation:

Add the length of one piece to the length of the other piece. Subtract the sum from the length needed.

2.3 + 3.45 = 5.75

10 - 5.75 = 4.25m

Answer:

4.25, B

Step-by-step explanation:

2.3+3.45= 5.75 you need 4.25 more to have 10 meters

The domain of a graph is the set of input values the function can take

The domain of the graphed function is (c) {x | x is a real number}

The equation of the graph is given as:

[tex]y = \sqrt[3]{x -1} + 3[/tex]

The above function is a cubic function, and a cubic function can take any real number as its input

This means that, the input values of the function [tex]y = \sqrt[3]{x -1} + 3[/tex] is the set of real numbers

Hence, the domain of the graphed function is (c) {x | x is a real number}

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The domain of the translated cube root function y = ∛(x - 1) + 3 is {x | x is a real number}, since cube root functions accept all real numbers.

The graph of the function y = ∛(x - 1) + 3, which is a cube root function, is a translated version of the parent function y = ∛x. The translation involves shifting the graph to the right by 1 unit and up by 3 units. Given that a cube root function, like y = ∛x, can accept any real number as an argument because there are real cube roots for all real numbers, the domain of the translated function would also be all real numbers. This remains true even after the function is translated. Hence, the domain of the graphed function is {x | x is a real number}.

Answer:

Is the equation that you need answered

y = 4x - 3 ?

That is not a real equation, therefore you can not answer that/show work

Answer:

Step-by-step explanation:

Not sure what they are looking for here.

you can plug in different x and get a y

x = 0 y = -3

x = -3 y = -15

x = 4 y = 13

Simple interest formula: A= P(1+Ryan)

A = 12000(1+ 0.07x4) = 15,360.00

Amount of interest = 15360-12000= 3,360.00

A= 12000(1+0.08x5) = 16,800.00

Interest = 16,800-12,000 = 4,800.00

Difference in interest = 4800 - 3360 = $1,440.00

Answer:

1440

Step-by-step explanation:

Answer:

Triangle 1 line segment AB and triangle 2 line segment BA correspond to each other

Step-by-step explanation:

Point b and point a don't correspond to anything else

triangle 1 and 2 are congruent my answer would be a 50/50 guess between C and D If it were me id risk it and go D but it is up to you.

Given the provided conditions which are a known population standard deviation and a sample size (n = 40) greater than 30, the critical value of Za/2 is appropriate for calculating the margin of error in a skewed population.

In this scenario, a 95% confidence interval is being constructed for a population that is skewed. Given a sample size, n, of 40, the population standard deviation (σ) is 2.6. When we construct confidence intervals for such a scenario, we refer to either a Z-distribution (critical value of Za/2) or a T-distribution (critical value of ta/2) based on certain conditions.

A critical value of Za/2 is used when the population standard deviation is known, and the sample size is large enough (typically n > 30). A critical value of ta/2 is referred to when the population standard deviation is unknown, or the sample size is too small (typically n < 30).

In this case, the population is skewed, the standard deviation is known, and the sample size (n = 40) is larger than 30. Therefore, we should use the critical value of Za/2 for calculating the margin of error.

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A roller coaster can usually be considered a function if each time point corresponds to exactly one location of the car. However, there may be exceptions, such as during loops. The roller coaster also demonstrates conversions between potential and kinetic energy.

In mathematical terms, a roller coaster can be described as a function if each input (in this case, time) corresponds to exactly one output (the position of the roller coaster car). For a typical roller coaster, this would be the case, as at each moment in time during the ride, the car is at one specific location.

However, there might be exceptions. For example, if the roller coaster has a loop, there's a point in time where the car reaches the top of the loop, descends, goes around the loop, and ends up at the same vertical location as before but upside down. Two different positions correspond to the same 'height' input, hence it wouldn't be considered a function in regards to height.

The physics of roller coasters also involves conversions between potential and kinetic energy. The car gains potential energy as it climbs to the top of a hill then it loses potential energy but gains kinetic energy as it descends a hill.

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Answer:

D.)<-50.5, 58.1>

Step-by-step explanation:

The vector can be decomposed into its x and y components using trigonometry.

The x and y components of the vector, together with the vector length forms a right triangle, as shown in the figure attached.

The x-component of the vector is given by

[tex]sin (-41^o)=\dfrac{x}{77}[/tex]

[tex]x=77*sin (-41^o)[/tex]

[tex]x=-50.5[/tex]

And the y-component of the vector is given by

[tex]cos(-41^o)=\dfrac{y}{77}[/tex]

[tex]y=77*cos(-41^o)[/tex]

[tex]y=58.1[/tex]

Thus, the vector as an ordered pair is represent by

[tex]\boxed{ (-50.5, 58.1)}[/tex]

which is choice D.

Final answer:

The combined probability of the coin landing tails-up and the number cube landing on a 4 is 8.33%.

Explanation:

The question involves calculating the probability of two independent events: the coin landing tails-up and the dice landing on a 4. The probability of a coin landing on tails is 0.5, and the probability of a dice landing on a particular number, say 4, is 1/6 since a dice has six faces. Since these two events are independent, their combined probability is found by multiplying the probabilities of each event.

The probability of the coin landing tails-up is 0.5, and the probability of the number cube (dice) landing on a 4 is 1/6. So, the combined probability of both events occurring is (0.5) × (1/6) = 0.0833, or 8.33% when expressed as a percentage.

Answer:

The slope of the line is 2.

Step-by-step explanation:

slope = y2 - y1/x2 - x1

= -8 - 6/3 - (-4)

= 14/3 + 4

= 14/7

= 2

Answer:  Use the slope formula to find the slope  m .

m = -2

Step-by-step explanation:

Final answer:

To find the percentage of weight lost, calculate the difference in weight and then divide by the original weight, multiplying by 100%. The patient has lost approximately 5.88% of their original weight.

Explanation:

To determine the percentage of weight lost by a patient who weighed 102 kg and now weighs 96 kg, we use the following steps:

So, the patient has lost approximately 5.88% of their original weight.