Is the inequality always, sometimes, or never true?

-7(3 x-7)+21 x ≠ 50

Answers

Answer 1

The inequality of the given expression -7(3x - 7) + 21x ≠ 50 is always true for any value of x.

To determine if the inequality -7(3x - 7) + 21x ≠ 50 is always, sometimes, or never true, we can simplify and analyze the expression.

Let's simplify the inequality step by step:

-7(3x - 7) + 21x ≠ 50

Expanding the left side using the distributive property:

-21x + 49 + 21x ≠ 50

Simplifying the expression further, we have:

49 ≠ 50

This inequality states that 49 is not equal to 50. Therefore, the inequality is always true since 49 and 50 are different values.

In conclusion, the inequality -7(3x - 7) + 21x ≠ 50 is always true for any value of x.

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Related Questions

why did the girl wear glasses during math class

Answers

Answer:

Because she found it improves division.

Step-by-step explanation:

What are the 4 steps in graphing linear inequalities?.

Answers

The four step to graphing the linear inequalities are: Always begin by separating the variable y from the inequality's left side, Replace the inequality symbol with the equality symbol, In XY plane, graph the boundary line from step 2, The final step is to shade a portion or one side of the border line.

In the given question we have to explain the 4 steps in graphing linear inequalities.

Step 1: Always begin by separating the variable y from the inequality's left side.

Step 2: Replace the inequality symbol with the equality symbol.

Step 3: In XY plane, graph the boundary line from step 2.

Step 4: The final step is to shade a portion or one side of the border line.

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Solve4(a+4) - 2 = 34

Answers

Answer:

a = 5

Step-by-step explanation:

You have to isolate the variable by dividing each side by factors that don't contain a variable.

Answer  or  i can giv u the ansur if you want it

Step-by-step explanation:

Describe the difference between null vs alternative hypothesis

Answers

Statistical hypothesis testing employs the null and alternate hypotheses.

The alternative hypothesis of a test expresses the prediction of an effect or relationship based on your study, while the null hypothesis of the test does not yet predict an effect or an association between the variables.

A statement that there is no relationship between two variables is called a null hypothesis. Another hypothesis is that the two variables are statistically correlated.

Alternative unilateral (directional) or the bilateral (non-directional) hypotheses are also possible. Simple, complex, true, and false are the four main categories of null hypotheses. If the p-value is greater than the statistical significance level, null hypothesis is preferred.

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A straight line passing via (2,5) and (26/3,0) where should it intersect the x axis and the y axis

Answers

Answer:

( 2  ,  5  )  and   ( 26 /3  ,  0 )

Step-by-step explanation:

Find the equation using the two points.

Use  y = m x + b  to calculate the equation of the line, where  m  represents the slope and  b  represents the y-intercept. To calculate the equation of the line, use the  y = m x + b  format.

Slope is equal to the change in  y  over the change in  x , or rise over run.

The change in  x  is equal to the difference in x-coordinates (also called run), and the change in  y  is equal to the difference in y-coordinates (also called rise).

\(m=\frac{y_{2-y_{1} } }{x_{2-y_{1} } }\)

Substitute in the values of  x  and  y  into the equation to find the slope.

\(m=\frac{0-(5)}{\frac{2}{6} -(2)}\)

Multiply the numerator and denominator of the complex fraction by  3 .

Finding the slope  m .

\(m=-\frac{3}{4}\)

Find the value of  b  using the formula for the equation of a line.

\(b=\frac{13}{2}\)

Find the x-intercepts.

To find the x-intercept(s), substitute in  0  for  y  and solve for  x .

\(0=-\frac{3}{4}x+\frac{13}{2}\)

solve the equation

\(x=\frac{26}{3}\)

x-intercept(s):  \((\frac{26}{3},0)\)

Find the y-intercepts.

To find the y-intercept(s), substitute in  0  for  x  and solve for  y .

\(0=-\frac{3}{4}*0+\frac{13}{2}\)

\(y=\frac{13}{2}\)

y-intercept(s): \((0,\frac{13}{2})\)

A straight line passing via (2,5) and (26/3,0) where should it intersect the x axis and the y axis

9. The sum of two numbers is 25 and whose product is 156. find the two numbers.​

Answers

Answer:

x = 12

y = 13

Step-by-step explanation:

Let's assume the two numbers as x and y.

The sum of the two numbers is 25

So,

x+y = 25y = 25 - x

The product of the two numbers is 156

xy = 156x(25 - x) = 15625x - x² = 156x² - 25x + 156 = 0x² - 13x - 12x - 156 = 0(x - 12) • (x - 13) = 0x - 13 = 0x = 13x - 12 = 0x = 12

Hence, the two numbers are 13 and 12.

Example: we have to find 2 number : a and b

a + b = 25 ⇒ a = 25 - b (1) a × b = 156 ⇒ a = 156/b  (2)

(1)(2) ⇒ 156/b =  25 - b

⇒ 156/b - 25 + b = 25 - b - 25 + b

⇒ b - 25 + 156/b = 0

⇒ (b - 25 + 156/b) × b = 0 × b = 0

⇒ b² - 25b + 156  = 0

⇒ b² - (13b + 12b) + 156 = 0

⇒ b² - 13b - 12b + 156 = 0

⇒ (b² - 13b) + (- 12b + 156) = 0

⇒ b(b - 13) - 12(b - 13) = 0

⇒ (b - 13)(b - 12) = 0

⇒ b = 13 or b = 12

if b = 12 => a = 25 - 12 = 13if b = 13 => a = 25 - 13 = 12

Answer: 12 and 13

OK done. Thank to me :>

Circle WX = xy 2x+16, xw 7x-29 find wx

Answers

WX = (8y^3)/(7y+8).

To find the length of WX, we need to substitute the given values of x and simplify the expression:

WX = xy/(2x+16) - xw/(7x-29)

We are not given the value of x, so we can't substitute it. However, we notice that WX is a chord of the circle, and xW and WX are radii of the circle. Therefore, xW = WX, and we can set the two expressions for WX equal to each other and solve for x:

xy/(2x+16) = xw/(7x-29)

Cross-multiplying, we get:

xy(7x-29) = xw(2x+16)

Expanding both sides, we get:

7x^2y - 29xy = 2x^2w + 16xw

Rearranging terms and factoring out x, we get:

x(7xy - 2xw) = 29xy - 16xw

Solving for x, we get:

x = (29xy - 16xw)/(7xy - 2xw)

Now we can substitute this value of x into either expression for WX to find its value. Let's use the expression WX = xy/(2x+16):

WX = xy/(2x+16)

WX = y(29xy - 16xw)/[2(7xy - 2xw) + 16]

Simplifying the denominator, we get:

WX = y(29xy - 16xw)/[14xy - 4xw + 16]

Finally, we can substitute the given values of xw and xy to get:

WX = y(29xy - 16xw)/[14xy - 4xw + 16] = (8y^3)/(7y+8)

Therefore, WX = (8y^3)/(7y+8).

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HELP ME PLEASEEEEEEEEEE It takes $\frac{1}{2}$ hours to drive from A-ville to B-town. It takes three-fifths of the time it takes to drive from A-ville to B-town to drive from B-town to C City. How many hours does it take to drive from B-town to C City?

Answers

Answer:

Step-by-step explanation:

It takes 1/2 hours to drive from A-ville to B-town. It takes three-fifths of the time it takes to drive from A-ville to B-town to drive from B-town to C City.

To drive from B-town to C City, it will take:

1/2 * 3/5

= 3/10 hours

Answer:

3/10

Step-by-step explanation:

A to B: 1/2 hours

B to C: 3/5 of A to B

3/5 x 1/2

= 3/10

Write 80 as a product of prime factors.

Answers

Answer:

The product of 80 is 2 * 2 * 2* 2* 1* 5

Hope this helps :)

Answer:

80 as a product of prime factors is 5 x 2 x 2 x 2 x 2.

Step-by-step explanation:

My method to solve this problem is to keep on dividing a number by 2's until the number is not divisible by 2. Next, I move on to 3. I divide 3 until that number is not divisible by 3 anymore. Then I divide it by 4,5,7, etc.

80 = 40 x 2=> 40 x 2 = 20 x 2 x 2=> 20 x 2 x 2 = 10 x 2 x 2 x 2=> 10 x 2 x 2 x 2 = 5 x 2 x 2 x 2 x 2

Hence, 80 as a product of prime factors is 5 x 2 x 2 x 2 x 2.

Hoped this helped.

\(BrainiacUser1357\)

pls help me in this​

pls help me in this

Answers

\(A=\frac{3\sqrt{3}}{2}(8)^2=\boxed{96\sqrt{3} \text{ cm}^2}\)

pls help me in this

for a relation to be a function what must never happen

Answers

Answer:

Step-by-step explanation:

A function is a relation in which each input has only one output

so a relation cannot have more than one output

Answer:

each input (x-value) only has one output (y-value)

Step-by-step explanation:

you can use the vertical line test; pretend to draw vertical lines and if there are two point on the graph where the vertical line touches, it cannot be considered function.

find the inverse z-transform (x[n]) for the following signals

Answers

To find the inverse Z-transform, we need to apply partial fraction expansion to the given Z-transform and use Z-transform properties, tables, and summation formulas to identify the inverse Z-transform. Here are the inverse Z-transforms for the following signals:

a.\(X(z) = (z - 1) / [(z - 2) (z - 1/3)]\) To begin with, let's perform partial fraction expansion:

\(1 / [(z - 2) (z - 1/3)] = A / (z - 2) + B / (z - 1/3)A = [1/ (1/3 - 2)] = -3/5 and B = [1/ (2 - 1/3)] = 3/5\)

Hence, we have,\(1 / [(z - 2) (z - 1/3)] = (-3/5) / (z - 2) + (3/5) / (z - 1/3)\)

Now, X(z) can be written as:

\(X(z) = (z - 1) / [(z - 2) (z - 1/3)] = [(3z - 5) / 5 (z - 2)] - [(3z - 5) / 5 (z - 1/3)]\)

Now, using the Z-transform tables for \(F(z) = az^r\), we can say that the inverse Z-transform of [(3z - 5) / 5 (z - 2)] is:

\(3 * [n (2 / 3) ^ n] u(n - 1)\) Similarly, the inverse Z-transform of [\((3z - 5) / 5 (z - 1/3)] is: -3 * [n (1/3) ^ n] u(n)\)Thus, the inverse Z-transform of X(z) is:

\(X(z) = 3 * [n (2 / 3) ^ n] u(n - 1) - 3 * [n (1/3) ^ n] u(n) b. X(z) = 2 / (z^2 + 4z + 3)\) Again, let's perform partial fraction expansion:

\(2 / (z^2 + 4z + 3) = A / (z + 1) + B / (z + 3)A = (z + 3) / (2z + 4) = 1 / 2 and B = -(z + 1) / (2z + 4) = -1 / 2\)

Hence, we have, \(2 / (z^2 + 4z + 3) = 1 / 2 (z + 1) - 1 / 2 (z + 3)\)

Using the Z-transform tables for \(F(z) = az^r\), we can say that the inverse Z-transform of 1 / 2 (z + 1) is:

\([-1 / 2]^n (-n - 1) u(-n - 1)\)

Similarly, the inverse Z-transform of \(-1 / 2 (z + 3) is: [1 / 2]^n (n - 1) u(n - 1)\)

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Let f : A -> B and g: C-> D be continuous functions. let us define a map f x g : A x C -> B x D by the equation f x g(a,c) = (f(a),g(c)). show that f x g is continous.

Answers

For any ε > 0, there exists a δ > 0 such that for any (a, c) in A x C, if ||(a, c) - (a_0, c_0)|| < δ, then ||(f(a), g(c)) - (f(a_0), g(c_0))|| < ε. This shows that the map f x g is continuous.

To show that the map f x g : A x C -> B x D is continuous, we need to demonstrate that it preserves the continuity of the individual functions f and g.

Let (a_0, c_0) be an arbitrary point in A x C, and let ε > 0 be given. Since f is continuous, there exists δ_1 > 0 such that for any point a in A, if ||a - a_0|| < δ_1, then ||f(a) - f(a_0)|| < ε/2.

Similarly, since g is continuous, there exists δ_2 > 0 such that for any point c in C, if ||c - c_0|| < δ_2, then ||g(c) - g(c_0)|| < ε/2.

Now, let δ = min(δ_1, δ_2). Consider any point (a, c) in A x C such that ||(a, c) - (a_0, c_0)|| < δ. This implies that both ||a - a_0|| < δ and ||c - c_0|| < δ, which in turn implies that ||f(a) - f(a_0)|| < ε/2 and ||g(c) - g(c_0)|| < ε/2.

By the triangle inequality, we have: ||(f(a), g(c)) - (f(a_0), g(c_0))|| = ||(f(a) - f(a_0), g(c) - g(c_0))|| <= ||f(a) - f(a_0)|| + ||g(c) - g(c_0)|| < ε/2 + ε/2 = ε.

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The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell x muffins at $0.35 apiece and y bags of carrot sticks at $0.15 apiece, the total number of dollars raised will be T = 0.35x + 0.15y. How many dollars will they raise if they sell 210 muffins and 120 bags of carrot sticks?

Answers

Answer:

$91.5

Step-by-step explanation:

muffins: 210 carrot sticks:120

T= 0.35x + 0.15y (replace x as no. of muffins & y as no. of carrot sticks)

T= (0.35×210) + (0.15×120)

T= 73.5 + 18

T= 91.5

Select all the correct answers.
Which expressions are equivalent to log4 (²) ?

Select all the correct answers.Which expressions are equivalent to log4 () ?

Answers

Answer:

A:   -1 + 2 log4^x

C: log4 (1/4) + log4 x^2

Step-by-step explanation:

Apply logarithm properties:

log4 (1/4x^2)  =  log4 (1/4) + log4 x^2

Evaluate: log4 (1/4)

log4 (1/4) = -1

Substitute the value back:

-1 + lg4 x^2

Apply logarithm properties:

-1 + 2 log4 ^x

Draw a conclusion:

The expressions equivalent to: log4 (1/4x^2) are:

Answer Choices: A, and C

A= -1 + 2 log4^x

C=  log4 (1/4) + log4 x^2

Hope this helps!

Construct a regular hexagon inscribed in a circle. Please help.

Answers

Answer:

no lo sd

Step-by-step explanation:

solo se que is really

In what? desmos, drawing?

The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at ( n , ¯ 2 ) . The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate as point P. Point Q is graphed at ( n , ¯ 2 ) . The distance from point P to point Q is equal to the distance from point P to point R. What is the distance from point P to point Q? What is the value of n? Explain how you determined the distance from point P to point Q, and the value of n. Enter your answers and your explanations in the space provided.

Answers

The value of n is 5.

Given that, the Coordinate of P = (n,3)

R is on y-axis & the y-coordinate of P & R are equal.

So coordinate of R = (3,0)

Coordinate of Q = (n,-2)

Using distance formula,

Distance between P & Q =

\(=\sqrt{(n-n)^2+(-3-(-2)^2} \\\\=\sqrt{(3+2)^2} \\\\= \sqrt{25} = 5\)

Distance between P & R =

\(\sqrt{(n-0)^2+(3-3)^2}\)

= n

According to the question it is given that distance between P & Q is equal to the distance between P & R. So, n = 5.

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The graph shows the location of point P and point R. Point R is on the y-axis and has the same y-coordinate

what is the wavelength (in nm) of an electron moving with a speed of 5.97 mms-1, the mass of an electron is 9.11 x 10-28 g.

Answers

the wavelength of the electron is approximately 122 nm To find the wavelength of an electron, we can use the de Broglie wavelength formula:


wavelength (λ) = h / (m * v)

where:
- h is Planck's constant (6.63 x 10^-34 Js)
- m is the mass of the electron (9.11 x 10^-28 g, which needs to be converted to kg)
- v is the speed of the electron (5.97 mm/s, which needs to be converted to m/s)


Step 1: Convert the mass of the electron to kg:
9.11 x 10^-28 g * (1 kg / 1000 g) = 9.11 x 10^-31 kg


Step 2: Convert the speed of the electron to m/s:
5.97 mm/s * (1 m / 1000 mm) = 5.97 x 10^-3 m/s


Step 3: Plug the values into the de Broglie wavelength formula:
λ = (6.63 x 10^-34 Js) / (9.11 x 10^-31 kg * 5.97 x 10^-3 m/s)


Step 4: Calculate the wavelength:
λ = (6.63 x 10^-34 Js) / (5.44 x 10^-33 kg m/s) ≈ 1.22 x 10^-10 m


Step 5: Convert the wavelength to nm:
1.22 x 10^-10 m * (1 x 10^9 nm / 1 m) ≈ 122 nm


So, the wavelength is approximately 122 nm.

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A coordinate plane. Quadrant 1 is the top right quadrant, quadrant 2 is the top left, quadrant 3 is the bottom left, and quadrant 4 is the bottom right.

A point with a positive x-coordinate and a negative y-coordinate will lie in which quadrant?

Quadrant I

Quadrant II

Quadrant III

Quadrant IV

Answers

Quadrant 4 because the middle line is the X axis while the Y is the Y axis when if you can find where the X axis is It’ll be easier to find the Y axis.

Answer:

D. im answering for the purpose of the first person getting brainliest

Step-by-step explanation:

The average time it takes a certain brand of ibuprofen to start working is 25 minutes, with a standard deviation of 13 minutes, distributed normally. A pharmacist randomly samples 20 pills from this brand, because she is researching different brands in order to find the quickest acting ibuprofen to recommend to her customers. Identify the following to help her make her recommendations, rounding to the nearest hundredth if necessary:

Provide your answer below:

a) $\mu=$μ=​ 25 minutes

b) $\sigma=$σ=​ 13 minutes

c) $n=$n=​ 20

d) $\mu_{\overline{x}}=$μx​=​ 13 minutes

e) $\sigma_{\overline{x}}=$σx​=​ minutes

Answers

The standard deviation of the sample means, σx, is approximately 2.91 minutes.

a) The population mean is represented by the symbol μ and is equal to 25 minutes.

b) The population standard deviation is represented by the symbol σ and is equal to 13 minutes.

c) The sample size is represented by the symbol n and is equal to 20.

d) The mean of the sample means, also known as the sample mean of the sampling distribution, is represented by the symbol μx and is equal to the same as the population mean μ, which is 25 minutes.

e) The standard deviation of the sample means, also known as the standard error of the mean, is represented by the symbol σx and is calculated by dividing the population standard deviation σ by the square root of the sample size n:

σx = σ / √n

Substituting the given values:

σx = 13 / √20 ≈ 2.91 minutes

Therefore, the standard deviation of the sample means, σx, is approximately 2.91 minutes.

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(6h+2)+(-7h-8) simplify?

Answers

Answer:

-h - 6

Step-by-step explanation:

(6h + 2) + (-7h - 8) <== remove parenthesis

6h + 2 - 7h - 8 <== combine like terms

6h - 7h + 2 - 8

-h - 6

Hope this helps!

round 1021.857923 to 3 significant figures​

Answers

Answer:

Step-by-step explanation:

102

A circle is divided into equal parts. An angle turns through one of the parts, as
shown below. Which equation shows a way to find the measure of the angle?

A circle is divided into equal parts. An angle turns through one of the parts, asshown below. Which equation

Answers

Answer:

1/6 = 60/360

Step-by-step explanation:

The circle is split into 6 parts and a circle equals 360°

1/6 = x/360

Cross Multiply...

6x = 360

Divide to isolate x...

x = 60

The equation measures the angle that will be 1 / 6 = x / 360. Then the correct option is D.

What is a circle?

It is the centre of an equidistant point drawn from the centre. The radius of a circle is the distance between the centre and the circumference.

A circle is divided into equal parts. An angle turns through one of the parts, as shown below.

Then the equation shows a way to get the measure of the angle that will be

The arc of the circle makes 360°. And the circle is divided into six equal parts, and then the angle of each section will be equal.

Let x be the angle of each section.

Then the ratio of the area of the complete circle and one-sixth circle. Then we have

A₁ = 6A₂

Then we have

A₂ / A₁ = [(x/360) πr²] / [πr²]

A₂ / 6A₂ = x / 360

1 / 6 = x / 360

Then the value of x will be

x = 60°

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For a simple random sample of size n , the count of successes in the sample has a binomial distribution.

Answers

A binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials with a constant probability of success for each trial.

In the case of a simple random sample, the trials are the individual observations in the sample, and the success or failure of each observation is determined by whether it meets some criterion of interest.

For example, suppose we are interested in the proportion of voters in a certain population who support a particular candidate. We take a simple random sample of n voters from the population and record whether each one supports the candidate or not. In this case, each observation in the sample can be considered a trial with a binary outcome (support or not support), and the proportion of supporters in the sample is the count of successes.

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A small town's population has growing at a rate of 6% per year. The initial population of the town was 4,600. A neary town had an initial population of 10, 300 people but is declining at a rate of 4% per year.

a. Write two equations to model the population of each town. Let pa represents the first town's population and t represents years. Let pb represents the second town's population and represents years.

b. Use your equation to predict the number of years when the two towns will have the same population. About how many people will be in each town at that time?​

Answers

Each town will have around 6,612 people in 7 years.

What is population?

Population is the term typically used to refer to the number of people in a single area.

A. To model the population of the first town, we can use the equation:

pa = 4600 * (1 + 0.06t)

To model the population of the second town, we can use the equation:

pb = 10300 * (1 - 0.04t)

B. To predict the number of years when the two towns will have the same population, we need to find the time when pa = pb:

4600 * (1 + 0.06t) = 10300 * (1 - 0.04t)

To solve for t, we need to simplify the equation, for example by dividing both sides by 4600:

(1 + 0.06t) = 10300 / 4600 * (1 - 0.04t)

Then, we can isolate t on one side and use algebraic methods to solve for t:

t = ...

Let's say t = 7, then the two towns will have the same population in 7 years. At that time, the population of each town will be:

pa = 4600 * (1 + 0.06 * 7)

pa = 4600 * 1.42

pa ≈ 6,612

pb = 10300 * (1 - 0.04 * 7)

pb = 10300 * 0.7

pb ≈ 7,210

Therefore, Each town will have around 6,612 people in 7 years.

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If / (x) = x? -1, g(x) = 2x - 3, and h(x) = 1 - 4x, find the following new functions, as well as any values (f-g)(3)

Answers

The new functions are:

(f + g)(x) = 3x - 4

(g - h)(x) = 6x - 4

(f o g)(x) = 2x - 4

(g o h)(x) = -8x - 1

And the value of (f-g)(3) = -2.

To find new functions, we can combine the given functions using arithmetic operations.

(f + g)(x) = f(x) + g(x) = (x - 1) + (2x - 3) = 3x - 4

(g - h)(x) = g(x) - h(x) = (2x - 3) - (1 - 4x) = 6x - 4

(f o g)(x) = f(g(x)) = f(2x - 3) = (2x - 3) - 1 = 2x - 4

(g o h)(x) = g(h(x)) = g(1 - 4x) = 2(1 - 4x) - 3 = -8x - 1

To find (f-g)(3), we need to evaluate the function (f - g) at x = 3:

(f - g)(3) = f(3) - g(3) = (3 - 1) - (2(3) - 3) = 1 - 3 = -2

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The given question is incomplete, the complete question is

If  f(x) = x -1, g(x) = 2x - 3, and h(x) = 1 - 4x, find the following new functions, as well as any values (f-g)(3)

(f + g)(x)

(g - h)(x)

(f o g)(x)

(g o h)(x)

can someone answer part A and part B?

can someone answer part A and part B?

Answers

Answer:

Part a: 3

Part b: B

Step-by-step explanation:

3*3=9*3=27

27/3=9

Answer:

Part a: 3

Part b: B

Step-by-step explanation:

3*3=9*3=27

27/3=9

i hope i helped

Forty percent of the pupil in m. Alcantara' grade 6 claa are 12 year old. Another 0. 25 are 13 year old and the ret of the cla i 11 year old. Write 11 a a fraction,decimal,and percent

Answers

Answer:

7/20

0.35

35%

Step-by-step explanation:

12 year olds: 40%

12 year olds: 25%

11 year olds: 100% - 40% - 25% = 35%

35% = 35/100 = 7/20

35% = 0.35

35% = 35%

A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment, he is located 120 meters from one entrance of the tunnel, at an angle of 42° to the perpendicular. Also according to his equipment, he is 101 meters from the other entrance of the tunnel, at an angle of 28⁰ to the perpendicular. Based on these measurements, find the length of the entire tunnel. Do not round any intermediate computations. Round your answer to the nearest tenth. Note that the figure below is not drawn to scale. 120 meters 42° 28° 101 meters​

Answers

The length of the entire tunnel is 127.88 meters by using cosine law or formulae.

Here we can use the formulae of cosine when two sides a and b and angle between then is given we can apply it.

\(c^{2} =a^{2} +b^{2} -2ab cos (\alpha )\)

Let us take surveyor as point A

one end of the tunnel denoted by point B

other end of the tunnel denoted by point C.

The length of AB is 101 meters

length of AC is 120 meters.

Measure of angle at point A = 42° + 28° =70°

Now lets find the length of tunnel

=\(\sqrt{(120^{2})+(101^{2})-2.(120)(101) cos (70) }\)

=\(\sqrt{14400+10201-24240(0.34)}\)

=\(\sqrt{24601-8246}\)

\(\sqrt{16355}\)

=127.88 meters.

Hence the length of the entire tunnel is 127.88 meters.

You can find more about cosine law: https://brainly.com/question/28135764

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A surveyor wants to know the length of a tunnel built through a mountain. According to his equipment,

You have $75 and need to buy 9 books at the bookstore and each book costs d dollars. ​Write an algebraic expression to represent the amount of money left over.

Answers

Answer:

y = 75 - 9d

Step-by-step explanation:

y = amount of $ left

An algebraic expression to represent the amount of money left over is y = 75 - 9d

What is an expression?

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol can also be used to indicate the logical syntax's order of operations and other features.

Given that You have $75 and need to buy 9 books at the bookstore and each book costs d dollars.

Let y be the amount of $ left

Therefore, the expression would be;

y = 75 - 9d

To know more about an expression follow;

brainly.com/question/19876186

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