solve for x
help me pls

Answer:

5 compact discs on sale.

Step-by-step explanation:

To solve this you'll need to set up a system of equations. Let's use x or the original price and y for sale price. Here's what your equations will look like:

14.95x + 12.95y = 139.50

x + y = 10

Now, cancel out x so you can solve for y. You can choose either variable, but canceling out x gets you to your answer in less steps. Remember to multiply by a negative so you can cancel out the variable.

Here's what your work will look like:

14.95 + 12.95y = 139.50

-14.95 (x + y = 10)

Here's what your new equations will look like after distributing:

14.95x + 12.95y = 139.50

-14.95x - 14.95y = -149.5

Now, add these two equations together. When you do that, x cancels out and you can solve for y.

Here's what your new equation will look like after adding:

-2y = -10

Now, divide both sides by -2. After doing so, you should get y = 5. This means that you bought 5 compact discs on sale.

Hope this helps!

The 42 grams of aluminum implies that the chemist has 0.06429ml of aluminum

The density of material shows the denseness of that material in a specific given area. A material’s density is defined as its mass per unit volume. Density is essentially a measurement of how tightly matter is packed together. It is a unique physical property of a particular object. The principle of density was discovered by the Greek scientist Archimedes. It is easy to calculate density if you know the formula and understand the related units The symbol ρ represents density or it can also be represented by the letter D.

How to determine the amount of aluminum?

The mass is given as:  Mass = 42 grams

The density of aluminum is: Density = 2.7 g/cm³

So, we have: Volume = Density/Mass

This gives, Volume = 2.7/42

Evaluate : Volume = 0.06429cm³

Convert to ml

Volume = 0.06429ml

Hence, the chemist has 0.06429ml of aluminum

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The optimal solution for the given linear programming problem is x = 20 and y = 80

The given linear programming problem is:

Minimize g = 44x + 13y

Subject to:  

x + y ≥ 100

-x + y ≤ 20

-2x + 3y ≥ 30

Where x, y ≥ 0

To solve this problem, we need to determine the feasible region for x and y. The first constraint is x + y ≥ 100, which gives the inequality x + y - 100 ≥ 0.

The second constraint is -x + y ≤ 20, which gives the inequality x - y + 20 ≥ 0.

The third constraint is -2x + 3y ≥ 30, which gives the inequality 2x - 3y + 30 ≥ 0. The feasible region for x and y can be represented by the three inequalities x + y - 100 ≥ 0, x - y + 20 ≥ 0 and 2x - 3y + 30 ≥ 0.

To minimize g = 44x + 13y, we need to use the graphical method. First, draw the feasible region. Then, we draw the line corresponding to the objective function g = 44x + 13y. We will be looking for the point where the line intersects the feasible region with the lowest possible value of g. The intersection point is the optimal solution.

In conclusion, the optimal solution for the given linear programming problem is x = 20 and y = 80, with the minimum value of g being g = 44*20 + 13*80 = 3200.

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Answer:

y - 8 ≤ -27

Step-by-step explanation:

The difference of y and 8 is less than or equal to -27

y - 8 ≤ -27

The most accurate comparison is that a gamma ray has more energy than a radio wave because it has a shorter wavelength and higher frequency.

The most energetic and high frequency particles are gamma rays. On the other side, radio waves are the EM radiation types with the lowest energies, longest wavelengths, and lowest frequencies.

All electromagnetic radiation travels in a vacuum at the speed of light (c), which is the same for all electromagnetic radiation types, including microwaves, visible light, and gamma rays.

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The number of stamps given for the books in question are :

To find the number of stamps needed for 1 book, the formula is :

= Stamps needed for 19 books / Number of books

= 380 / 19

= 20 stamps

For 7 books :

= 7 books x 20 stamps per book

= 140 stamps

For 12 books :

= 12 books x 20 stamps per book

= 240 stamps

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Claire will be 20 years old in 16 years. To solve this problem, we use algebra.

Let's represent Claire's current age with the variable x. According to the problem, in 8 years, Claire will be three times her current age. We can write this as an equation:

x + 8 = 3x
Next, we can rearrange the equation to solve for x:

8 = 2x
x = 4
This means that Claire is currently 4 years old. To find out when she will be 20 years old, we can subtract her current age from 20:

20 - 4 = 16

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The midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).

To find the exact distance between the points (9.6,-19.7) and (6.6,-23.7), we can use the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given values:

distance = sqrt((6.6 - 9.6)^2 + (-23.7 - (-19.7))^2)

Simplifying:

distance = sqrt((-3)^2 + (-4)^2)

distance = sqrt(9 + 16)

distance = sqrt(25)

distance = 5

Therefore, the exact distance between the points is 5.

To find the midpoint of the line segment whose endpoints are the given points, we can use the midpoint formula:

midpoint = ((x1 + x2)/2 , (y1 + y2)/2)

Substituting the given values:

midpoint = ((9.6 + 6.6)/2 , (-19.7 + (-23.7))/2)

Simplifying:

midpoint = (16.2/2 , -43.4/2)

midpoint = (8.1 , -21.7)

Therefore, the midpoint of the line segment whose endpoints are the given points is (8.1 , -21.7).

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Answer:

Please review the trigonometric proof below

Step-by-step explanation:

Given

[tex]\csc x -\sin x=\cos x \cot x[/tex]

Apply the reciprocal identity to [tex]\csc x[/tex].

[tex]\frac{1}{\sin x} -\sin x=\cos x \cot x[/tex]

Write [tex]-\sin x[/tex] as a fraction then multiply by [tex]\frac{\sin x}{\sin x}[/tex].

[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} =\cos x \cot x[/tex]

[tex]\frac{1}{\sin x} + \frac{-\sin x}{1} *\frac{\sin x}{\sin x}=\cos x \cot x[/tex]

[tex]\frac{1}{\sin x} + \frac{-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]

Combine the numerators over the common denominator.

[tex]\frac{1-\sin x\sin x}{\sin x}=\cos x \cot x[/tex]

Multiply [tex]\sin x[/tex] by [tex]\sin x[/tex].

[tex]\frac{1-\sin^2 x}{\sin x}=\cos x \cot x[/tex]

Apply the Pythagorean identity [tex]1-\sin^2 x=\cos^2 x[/tex]

[tex]\frac{\cos^2 x}{\sin x}=\cos x \cot x[/tex]

Factor [tex]\cos x[/tex] out of [tex]\cos^2 x[/tex].

[tex]\frac{\cos x\cos x}{\sin x}=\cos x \cot x[/tex]

Separate into two fractions.

[tex]\frac{\cos x}{1} *\frac{\cos x}{\sin x}=\cos x \cot x[/tex]

Apply the quotient identity [tex]\frac{\cos x}{\sin x}=\cot x[/tex].

[tex]\frac{\cos x}{1} *\cot x=\cos x \cot x[/tex]

Anything over 1 is just itself.

[tex]\cos x\cot x=\cos x \cot x[/tex]

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, = space

Answer:

csc x − sin x

= [tex]\frac{1}{sin, x}[/tex] - sin x

= [tex]\frac{1 - sin^{2}, x }{sin, x}[/tex]

= [tex]\frac{cos^{2}, x }{sin, x}[/tex]

= [tex]\frac{cos, x}{sin, x}[/tex] * cos x

= cot x cos x

∴csc x - sin x - cot x cos xQED

It is the most " explanation " I can think of.

Thus the answer is shown above..

Answer:

3.5 * 10²

Step-by-step explanation:

In standard form, the number before the point has to be less than ten so

0.035 = 3.5 *10²

The system of inequalities is correctly graphed on Shannon's graph.

Here we have the following system of inequalities:

y ≥ (1/2)*x - 1

x - y > 1

We can rewrite the second inequality as:

y < x - 1

Then the system becoimes:

y ≥ (1/2)*x - 1

y < x - 1

The first line will be one with positive slope, it is solid (due to the symbol ≥) and the shaded area is above the line.

For the second we will have a dashed line, and now the shaded area is below the dashed line.

From that, we caonclude that Shannon's graph is the correct one.

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Answer:

  100°

Step-by-step explanation:

You want the missing arc measure in the geometry where two chords cross at 85° and they intercept one arc of measure 70°.

The angle where chords cross is the average of the two arcs that they intercept. Here, that means ...

  85° = (AE +BC)/2

Solving for BC, we get ...

  2(85°) = AE +BC

  BC = 170° -AE = 100°

The missing arc measure is 100°.

Answer:

1/4

Step-by-step explanation:

Fractions have two parts, the numerator and the denominator. The denominator is the bottom number and it tells us what unit of fraction we are working with (ie: it denotes fourths, halves, etc.)

Hope it helps! :D

Answer:

The possible number of hours Yolanda could rent the boat is 6 hours. I hope this isn't too late, and it's not incorrect lol

Step-by-step explanation:

7t - 3 ≤ 39

*We add 3 to both sides, which will cancel out the 3.*

7t ≤ 42

*We divide 42 by 7 to isolate the variable*

t ≤ 6

The value of the constant of variation for the direct variation is k = -1/2.

Variation depicts the relationship between two variables and how it changes. Often, a ratio is used to illustrate this connection. When we remark that a variation is continuous, we are referring to how consistently the ratio changes. Hence, whenever you read the phrase "constant of variation," just keep in mind that it refers to the stability of the relationship between the variables.

The direct variation is given by the following relations:

y = kx

Now, using the table substitute the value of y = f(x) and x:

y = kx

-2 = k(4)

k = -2/4

k = -1/2

Hence, the value of the constant of variation for the direct variation is k = -1/2.

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Answer:

Below

Step-by-step explanation:

The graph of the linear inequality y ≥ −2x − 1 is the region _______ the graph of the line y= - 2x -1

≥  is greater than or equal to and translates to 'on or above'

McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.

If McKenzie and Lindy can complete the landscaping job in 4 hours working together, it means their combined work rate is 1/4 of the job per hour. Let x be the number of hours it takes Lindy to complete the job alone, then McKenzie can complete the job in x-6 hours.

Using the formula for their individual work rates, we have:

[tex]1/x + 1/(x-6) = 1/4[/tex]

Multiplying both sides by [tex]4x(x-6)[/tex], we get:

[tex]4(x-6) + 4x = x(x-6)[/tex]

Expanding and simplifying, we get:

[tex]2x^2 - 12x - 48 = 0[/tex]

Dividing both sides by 2 and using the quadratic formula, we get:

[tex]x = (12 ± \sqrt{12^2 + 4248}) / (2*2)[/tex]

x = (12 ± 18) / 4

x = 7.5 or -1.5

Since we cannot have a negative time, the answer is that it would take Lindy 7.5 hours to complete the job alone, and McKenzie would take 1.5 hours less, or 6 hours, to complete the job alone if Lindy calls in sick.

Therefore, McKenzie would take 6 hours to complete the landscaping job alone if Lindy calls in sick.

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Answer:

y = -1/35x + 71/35

Step-by-step explanation:

slope of the perpendicular line = -1/35  (the negative reciprocal of 35)

use the point (1,2) and the point-slope form:

y - 2 = -1/35(x - 1)  now put it in slope-intercept form

y = -1/35x + 1/35 + 2

y = -1/35x + 71/35

0r,  y = -1/35(x - 71)

The equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.

To find the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2), we need to follow these steps:

y - 2 = (-1/35)(x - 1)

y - 2 = (-1/35)x + 1/35
y = (-1/35)x + 1/35 + 2
y = (-1/35)x + 71/35

So, the equation of the line perpendicular to y = 35x − 4 and passing through the point (1, 2) is y = (-1/35)x + 71/35.

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if we take a peek at the tickmarks on the sides, that means that the line that cuts the side is the median, so we have three medians meeting at the centroid of the triangle, bearing in mind that the centroid cuts all three medians in a 2 : 1 ratio, then we can say that line AC is being cut by it in a 2 : 1 ratio, the hell all that means?  well, it means

[tex]\cfrac{AB}{BC}=\cfrac{2}{1}\implies \cfrac{10}{BC}=\cfrac{2}{1}\implies 10=2BC\implies \cfrac{10}{2}=BC\implies \boxed{5=BC} \\\\\\ \stackrel{AB+BC}{10+5}\implies \stackrel{ AC }{\boxed{15}}[/tex]

Answer:

See below.

Step-by-step explanation:

We are asked to identify BC and AC.

Before we start, we should know that this triangle has a center called a Centroid.

A Centroid is a point that is formed by 3 concurrent medians.

A Median is a line segment that connects the vertex of a triangle to the midpoint of the opposite side.

The top part of a Median is 2/3 of the entire line segment. The bottom part of a Median is 1/3 of the entire line segment.

Using the information from above, we can identify that AB (10) is 2/3 of AC, and that BC is 1/3 of AC.

Divide 10 by [tex]\frac{2}{3}[/tex] to find AC.

[tex]10 \div ( \frac{2}{3} )=15 \ (AC)[/tex]

Since we know AC, we can now find BC by simply subtracting AC - AB.

[tex]15-10=5 \ (BC)[/tex]

Therefore, AC = 15; BC = 5.

Below, you will learn how to solve the problem.

(a) To find the linear relationship y = mx + b between x = year and y = profit, we first need to find the slope (m) and the y-intercept (b).

The slope (m) is the change in y (profit) divided by the change in x (year):
m = (17 - 5)/(6 - 2)

m = 12/4

m = 3

Next, we can use one of the data points (2, 5) and the slope (3) to find the y-intercept (b):
5 = 3(2) + b
b = 5 - 6

b = -1

So the linear relationship between x = year and y = profit is:

y = 3x - 1

(b) To find the company's profit at the end of 3 years, we can plug in x = 3 into the equation:
y = 3(3) - 1

y = 8

So the company's profit at the end of 3 years is $8 million.

(c) To predict the company's profit at the end of 8 years, we can plug in x = 8 into the equation:

y = 3(8) - 1 = 23

So the company's profit at the end of 8 years is predicted to be $23 million.

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The graph of this function is a sine curve with amplitude 3√2 and phase shift π/4.

The k cos(ϕ) would be 3 and k sin(ϕ) would be 3.

The combined sound is given by:

f(t) = f1(t) + f2(t)

f(t) = 3 sin(t) + 3 cos(t)

To find k and ϕ, we can use the following trigonometric identity:

k sin(t + ϕ) = k sin(t) cos(ϕ) + k cos(t) sin(ϕ)

Comparing this with the equation for f(t), we can see that:

k cos(ϕ) = 3

k sin(ϕ) = 3

Squaring both equations and adding them gives:

k^2 = 3^2 + 3^2 = 18

k = √18 = 3√2

Dividing the two equations gives:

tan(ϕ) = 3/3 = 1

ϕ = π/4

Therefore, the combined sound has the form:

f(t) = 3√2 sin(t + π/4)

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(5g^(2)+6g-10)-(2g^(2)+2g+9) = 3g^(2) + 4g - 19

To subtract the two polynomials, we will use the vertical form. This means that we will line up the like terms and subtract them.

Step 1: Line up the like terms in the vertical form.

5g^(2) + 6g - 10

- (2g^(2) + 2g + 9)

Step 2: Distribute the negative sign to each term in the second polynomial.

5g^(2) + 6g - 10

- 2g^(2) - 2g - 9

Step 3: Subtract the like terms.

5g^(2) - 2g^(2) = 3g^(2)

6g - 2g = 4g

-10 - 9 = -19

Step 4: Write the final answer.

3g^(2) + 4g - 19

Therefore, the answer is 3g^(2) + 4g - 19.

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Answer:

See below.

Step-by-step explanation:

This is the correct formula for simple interest, but be careful with the numbers.

a = 6 000(1 + 0. 028t)

0.028 means 2.8% interest rate.

For 2.9% interest rate it should be

a = 6 000(1 + 0. 029t)

Answer and Explanation:

The expression [tex](3y + 5) + \frac{1}{2}(3y + 5)[/tex] is equivalent to the expression [tex]1.5(3y + 5)[/tex] because of the distributive property and the equivalence of [tex]1 \frac{1}{2}[/tex] and [tex]1.5[/tex].

In other words:

We know that

[tex]1 + \frac{1}{2} = 1 \frac{1}{2} = 1.5[/tex],

and that

[tex](B + C)(A) = BA + CA[/tex].

Therefore,

[tex]1A + \frac{1}{2}A = 1 \frac{1}{2}A = 1.5A[/tex]

and

[tex](3y + 5) + \frac{1}{2}(3y + 5) = 1.5(3y + 5)[/tex].

To simplify [tex]1.5(3y + 5)[/tex], we can distribute the 1.5.

[tex]1.5(3y + 5) = (1.5) (3y) + (1.5)(5)[/tex]

[tex]= \boxed{4.5y + 7.5}[/tex]

Answer:

x intercept

Step-by-step explanation:

please give brainliest

Answer:

Step-by-step explanation:

W = w

L = 3w

H = w+4

Now V = LHW

          = (3w)(w+4)(w)

         = (3w²+12w)(w)

        = 3w³+12w²

The man has 7 shirts in total, so he can take 3 of those shirts on his 3-day trip without repetition. This means that he can make 7 different combinations of shirts, since each shirt has only one choice. For example, he could take shirts A, B, and C; or he could take shirts D, E, and F; or he could take shirts G, A, and B. In total, he has 7 different combinations of shirts to choose from.
The number of combinations of shirts that the man can take without repetition can be found using the formula for combinations, which is:
C(n, r) = n! / (r! * (n-r)!)

In this case, n = 7 (the total number of shirts) and r = 3 (the number of shirts he will take with him).

Plugging in these values into the formula, we get:

C(7, 3) = 7! / (3! * (7-3)!)

C(7, 3) = 7! / (3! * 4!)

C(7, 3) = 5040 / (6 * 24)

C(7, 3) = 5040 / 144

C(7, 3) = 35

Therefore, the man can take 35 different combinations of shirts without repetition.

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Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test).

If the researcher does not reject a null hypothesis that is actually wrong in the population, this is known as a type II error (false-negative). Notwithstanding the fact that type I and type II mistakes cannot be completely prevented, the researcher can lessen their risk by increasing the sample size.

from the question:

Part A: In this situation, a Type II error would take place if the council failed to reject the null hypothesis even if it was untrue (i.e., less than 40% of children under the age of 5 could pass a swim test). This would result in a lost chance to provide these kids with more swim safety training, perhaps placing them in danger of drowning or other swimming-related mishaps.

Part B: We are unable to reject the null hypothesis since the p-value (0.8438) exceeds the significance level (0.05). This indicates that there is insufficient information to draw the conclusion that less than 40% of children under the age of five can pass a swim test. But, since the test only looked at the alternative hypothesis that the fraction is less than 40%, we cannot draw the conclusion that it is exactly 40%.

Part C: One possible defect in the study is the use of a volunteer sample. The children who volunteered to take the swimming test may not be representative of the entire population of children under 5 in Bloomburg City. For example, parents who are more concerned about their children's swimming abilities may be more likely to volunteer their children for the test, leading to a biased sample. To obtain a more representative sample, a random sample of children under 5 could be selected from the population and asked to take the swimming test.

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The value of the expression a + 4 when a = 7 is 11.

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

We are given that;

Function= a+4

Now,

By algebra

If a = 7, then we can substitute this value into the expression a + 4 to get:

=a + 4

= 7 + 4

= 11

Therefore, by algebra the answer will be 11.

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The complete question is;

Evaluate the expression a+4 when a=7?

Mariam will have purchased 3.5 pounds of fruit if she purchases 3 pounds of apples and 0.5 pounds of strawberries.

Mariam will purchase a total of (x + y) pounds of fruit if she purchases x pounds of strawberries and y pounds of apples.

The arithmetic operations were used to arrive at the answer.

The four basic operations—often referred to as "arithmetic operations"—are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.

We are given that Mariam buys 0.5 pounds of strawberries and 3 pounds of apples.

So, the total pounds of fruit bought = 0.5 + 3 = 3.5

Similarly, if she buys x pounds of strawberries and y pounds of apples, then the total amount of pound of fruits  = (x + y)

Hence, the required solution has been obtained.

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