Given the figure below find the values of x and z.

Step-by-step explanation:

[tex] \because \: \cos \theta = \sin \theta = - 15 \\ \\ \therefore \: \: \: \cos \theta = - 15 \: \: \\ \: \: \: \: \: \: \: and \: \: \\ \: \: \: \: \: \: \: \: \sin \theta = - 15 \\ \therefore \: \frac{\sin \theta }{\cos \theta} = \frac{ - 15}{ - 15} \\ \therefore \: \huge \purple{ \boxed{\tan \theta = 1}}[/tex]

Answer:

Helicopter have traveled  5.55 units of distance approximately  if it went directly from one location to the other.

Step-by-step explanation:

We are given the following in the question:

A traffic helicopter travels due north and then due east to get to the location at (-3,4) to the location at (7,13).

The attached image shows the path of helicopter.

Distance Formula:

[tex](x_1,y_1), (x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]

Distance traveled by helicopter =

[tex]d((-3,4),(-3,13)) + d((-3,13),(7,13))\\\\=\sqrt{(-3+3)^2 + (13-4)^2} + \sqrt{(7+3)^2 + (13-13)^2}\\= 9+10\\= 19 \text{ units}[/tex]

If the helicopter goes directly:

[tex]d((-3,4),(7,13))\\\\=\sqrt{(7+3)^2+(13-4)^2}\\\approx 13.45 \text{ units}[/tex]

Difference in distances =

[tex]19 - 13.45 = 5.55\text{ units}[/tex]

Thus, helicopter have traveled  5.55 units of distance approximately  if it went directly from one location to the other.

Answer:

i had this question in a quiz on edge and got a 100% on the quiz

here is your answer

Step-by-step explanation:

Answer: 27

Step-by-step explanation:

Answer:

Step 1: 14x − 21 = 1; Step 2: 14x = 22

Explanation:

7(2x−3)=1

Step 1: Simplify both sides of the equation

7(2x−3)=1

(7)(2x)+(7)(−3)=1(Distribute)

14x+−21=1

14x−21=1

Step 2: Add 21 to both sides

14x−21+21=1+21

14x=22

Step 3: Divide both sides by 14

14x / 14 = 22 / 14

x = 22 / 14: x = 11/7

Answer:

The last option.

Step-by-step explanation:

When distributed, 7 times 2x becomes 14x and 7 times -3 is -21.

Once you add -21 to both sides, 14x is left alone on one side while 22 is on the other

Answer:75

Step-by-step explanation: 50 + 25

Answer: x = 75

Step-by-step explanation: The first thing to note is that what we have here is a quadrilateral. In other words, all the internal angles sum up to 360°. Also take note that the figure is a parallelogram, which means two sides are parallel to each other. Line AD is parallel to BC, and line DC is parallel to AB. That makes angle D equal to angle B (alternate angles), and angle A equals Angle C.

If the sum of the interior angles of a quadrilateral equals 360, then

x + (x + 30) + x + (x + 30) = 360

x + x + 30 + x + x + 30 = 360

Collecting like terms, we have

x + x + x + x + 30 + 30 = 360

4x + 60 = 360

Subtract 60 from both sides of the equation

4x = 300

Divide both sides of the equation by 4

x = 75.

The slope of the line that passes through two points is

(the difference in 'y') divided by (the difference in 'x').

The two points are:  (3, -4) and (5, -7)

The difference in 'y' is . . . (-7) - (-4) = -3

The difference in 'x' is . . . (5) - (3) = 2

The slope of the line through those two points is (-3) / (2) .

That's the 3rd choice on the list.

Answer:

The slope of the line that passes through two points is

(the difference in 'y') divided by (the difference in 'x').

The two points are:  (3, -4) and (5, -7)

The difference in 'y' is . . . (-7) - (-4) = -3

The difference in 'x' is . . . (5) - (3) = 2

The slope of the line through those two points is (-3) / (2) .

That's the 3rd choice on the list.

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34% of the scores lie between 433 and 523.

Solution:

Given data:

Mean (μ) = 433

Standard deviation (σ) = 90

Empirical rule to determine the percent:

(1) About 68% of all the values lie within 1 standard deviation of the mean.

(2) About 95% of all the values lie within 2 standard deviations of the mean.

(3) About 99.7% of all the values lie within 3 standard deviations of the mean.

[tex]$Z(X)=\frac{x-\mu}{\sigma}[/tex]

[tex]$Z(433)=\frac{433-\ 433}{90}=0[/tex]

[tex]$Z(523)=\frac{523-\ 433}{90}=1[/tex]

Z lies between o and 1.

P(433 < x < 523) = P(0 < Z < 1)

μ = 433 and μ + σ = 433 + 90 = 523

Using empirical rule, about 68% of all the values lie within 1 standard deviation of the mean.

i. e. [tex]((\mu-\sigma) \ \text{to} \ (\mu+\sigma))=68\%[/tex]

Here μ to μ + σ = [tex]\frac{68\%}{2} =34\%[/tex]

Hence 34% of the scores lie between 433 and 523.

Using the Empirical Rule for normally distributed scores, about 34% of SAT verbal scores lie between 433 (mean) and 523 (mean plus one standard deviation).

The Empirical Rule, also known as the 68-95-99.7 rule, applies to a normally distributed set, as we have here with SAT verbal scores. This rule states that approximately 68% of the data falls within one standard deviation from the mean in a normal distribution.

In this scenario, the mean (average) SAT verbal score is 433, the standard deviation is 90. We're going to find what percent of the scores lie between 433 (mean) and 523 (mean plus one standard deviation).

According to the Empirical Rule, approximately 68% of the scores fall within one standard deviation of the mean (both above and below). So about 34% of the scores fall between the mean and one standard deviation above the mean. Thus, about 34% of the students scored between 433 and 523 on the SAT verbal section.

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Answer:b = 81

Step-by-step explanation:

perimeter = 2(l+b)

344= 2(91 + b)

344 =182 + 2b

344 -182 =2b

162 = 2b

b = 162/2

b= 81

Answer:

perimeter = 2(l+b)

344= 2(91 + b)

344 =182 + 2b

344 -182 =2b

162 = 2b

b = 162/2

b= 81

Step-by-step explanation:

Answer:

3x

Step-by-step explanation:

2x--x is the same thing as 2x+x which equals 3x. Hope that helped. ;P

2x minus negative x simplifies to 2x + x, which further simplifies to 3x.

To simplify 2x - (-x), we can apply the concept of subtracting a negative number, which is equivalent to adding its positive counterpart.

The expression -(-x) can be rewritten as +x, since double negation cancels out. Therefore, the expression becomes 2x + x.

Combining like terms, we have 2x + x = 3x.

So, 2x - (-x) simplifies to 3x.

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Answer:

4

Step-by-step explanation:

15 = 7 - /2x/

Subtract 7 from both sides ( if it was negative you would add it)

(15-7) = (7 - 7) -/2x/ now the seven is no longer there

8 = -/2x/

Now divide 2 from both sides

( 8 / 2 ) = - /(2 / 2)x/

4 = -/x/

4 = -x

Now the two is no longer there but the x would still be there because you divided it by 2 and not 2x

To solve the equation 15 = 7 - |2x|, consider two cases: 2x ≥ 0 and 2x < 0. In case 1, x = -4. In case 2, x = 4.

To solve the equation 15 = 7 - |2x|, we need to eliminate the absolute value. To do this, we can consider two cases: when 2x is positive and when 2x is negative.

Case 1: 2x ≥ 0

In this case, the equation becomes 15 = 7 - 2x, which simplifies to 2x = -8. Solving for x, we get x = -4.

Case 2: 2x < 0

In this case, the equation becomes 15 = 7 + 2x, which simplifies to 2x = 8. Solving for x, we get x = 4.

Therefore, the solution to the equation 15 = 7 - |2x| is x = -4 or x = 4.

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Answer:4 divided by  x hours

Step-by-step explanation:

The number of hours that Daniel gets paid for on each paycheck will be 4x.

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

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

Every 4 weeks, Daniel receives a paycheck. He puts in x hours a week at work.

The number of hours that Daniel gets paid for on each paycheck is given as,

⇒ 4 · x

⇒ 4x

The number of hours that Daniel gets paid for on each paycheck will be 4x.

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Answer:

3,840 calories

Step-by-step explanation:

a = an avocado's calories

Given: 1/2a = 160 calories

Multiply both sides of the equation by 2

a = 320 calories

We need to find the amount of calories in a dozen (12) avocados so multiply both sides of this equation by 12

12a = 3,840 calories

Hope this helps :)

Answer:

car C gets the best gas mileage

Step-by-step explanation:

Final answer:

To find the car with the best gas mileage, the miles driven are divided by the gallons used for each car. Car A gets 25 MPG, Car B gets 28 MPG, Car C gets 31 MPG, and Car D gets 20 MPG. Car C has the best gas mileage with 31 MPG.

Explanation:

The student's question is about calculating and comparing the gas mileage (miles per gallon or MPG) of different cars to determine which one is the most fuel-efficient. To answer this, we calculate the MPG for each car by dividing the number of miles driven by the gallons of gas used and then compare the results.

Car A: 200 miles / 8 gallons = 25 MPG

Car B: 28 miles / 1 gallon = 28 MPG

Car C: 279 miles / 9 gallons = 31 MPG

Car D: 140 miles / 7 gallons = 20 MPG

Upon comparison, Car C has the highest MPG at 31 miles per gallon, making it the most fuel-efficient car among those listed.

Step-by-step explanation:

let’s start with the positive number because it’s easier :

84x12 = 1 008

84×24 = (84×12)×2 = 1008×2 = 2 016

-84x12 = -(84x12) = -1 008

-84x24 = -(84x24) = -2016

Final answer:

The product of the given expressions is found by multiplying the numbers together. The product of -84x12 is -1008, -84x24 is -2016, 84x12 is 1008, and 84x24 is 2016.

Explanation:

The product of -84x12 is -1008. To find the product, simply multiply the two numbers together. In this case, -84 multiplied by 12 gives us -1008.

The product of -84x24 is -2016. Similarly, multiplying -84 by 24 gives us -2016.

The product of 84x12 is 1008. When multiplying a positive number and a negative number, the product will be negative. In this case, 84 multiplied by -12 gives us -1008.

Finally, the product of 84x24 is 2016. When multiplying two positive numbers, the product will also be positive. Therefore, 84 multiplied by 24 equals 2016.

Answer:

x=5

Step-by-step explanation:

15÷5=3

that is the right answer

Answer:

  5

Step-by-step explanation:

Put 3 where x is, and do the arithmetic.

  [tex]\dfrac{15}{x}=\dfrac{15}{3}=5[/tex]

Answer:

Yes

Step-by-step explanation:

The tablecloth is large enough as when you multiply 4×8=32 square feet. Thus meaning a 56 square foot table cloth would be enough.

4×8=32

Answer:

69

Step-by-step explanation:

step 1: 6 x 9 =54

step 2: 54 + 6 = 60

step 3: 60 + 9 = 69

Answer:

x=-1

Step-by-step explanation:

2-8x=10   subtract both sides by 2

-8x=8   divide both sides by -8

x=-1

Answer:

x = -1

Step-by-step explanation: 2 - 8x = 10

-2. -2

-8x. 8

Divide -8. -8

x = -1

Answer:

What Do You Mean

Step-by-step explanation:

The value of x is 81

Step-by-step explanation:

The sum of the interior angles of any quadrilateral is 360°

∵ The figure have 4 sides

∴ The figure is a quadrilateral

∵ The sum of the measures of the interior angles of a

    quadrilateral is 360°

- Add the four angles and equate the sum by 360

∴ m∠1 + m∠2 + m∠3 + x = 360

∵ m∠1 = 40% of the sum of the angle measures of the quadrilateral

∴ m∠1 = 40% × 360 = [tex]\frac{40}{100}[/tex] × 360 = 144°

∵ m∠2 = 12.5% of the sum of the angle measures of the quadrilateral

∴ m∠2 = 12.5% × 360 = [tex]\frac{12.5}{100}[/tex] × 360 = 45°

∵ m∠3 = 25% of the sum of the angle measures of the quadrilateral

∴ m∠3 = 25% × 360 = [tex]\frac{25}{100}[/tex] × 360 = 90°

- Substitute these values in the equation above

∴ 144 + 45 + 90 + x = 360

- Add the like terms in the left hand side

∴ 279 + x = 360

- Subtract 279 from both sides

∴ x = 81°

The value of x is 81

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Answer:

The number of acres of corn planted was 230 and the number of acres of wheat planted was 140

Step-by-step explanation:

Let

c ----> the number of acres of corn

w ----> the number of acres of wheat

we know that

Farmer Brown planted corn and wheat on 370 acres of his land

so

[tex]c+w=370[/tex] -----> equation A

The cost and planting and harvesting corn,c,is $280 per acre

The cost of planting and harvesting wheat,w,is $135 per acre

The Farmer Brown's total cost was $83,300

so

[tex]280c+135w=83,300[/tex] ----> equation B

solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

The solution is the point (230,140)

see the attached figure

therefore

The number of acres of corn planted was 230 and the number of acres of wheat planted was 140

Farmer Brown planted 230 acres of corn and 140 acres of wheat.

To determine how many acres of corn and wheat Farmer Brown planted, we can set up a system of equations. Let x be the number of acres of corn and y be the number of acres of wheat. From the given information, we have the following equations:

Cost of planting and harvesting corn: 280x

Cost of planting and harvesting wheat: 135y

Total cost: 280x + 135y = 83,300

We also know that the total number of acres planted is 370 acres, so we have the equation:

x + y = 370

To solve this system of equations, we can use substitution or elimination. Let's use substitution:

From the second equation, we can solve for x in terms of y: x = 370 - y

Substitute this expression for x in the first equation:

280(370 - y) + 135y = 83,300

Simplify and solve for y:

103,600 - 280y + 135y = 83,300

-145y = -20,300

y = 140

Substitute the value of y back into the second equation:

x + 140 = 370

x = 230

Therefore, Farmer Brown planted 230 acres of corn and 140 acres of wheat.

Answer:

117.3 feet per second.

Step-by-step explanation:

Velocity is the speed of an object in a definite direction. In mechanics, velocity is a vector quantity. It requires magnitude and direction to make any sense. Velocities are expressed per unit time.

The SI unit of time is the second.

Now, suppose we need the velocity in feet per second. A simple calculation will help:

feet per second = miles per hour × 1.466667 [ in other words, one mile per hour equals 1.466667 feet per second]

For a space capsule moving at 80 miles per hour, the velocity is given by

                           = 80 × 1.466667

                           = 117. 3 ft/s [feet per second]

Answer:

80 miles

Step-by-step explanation:

it is 80 miles bc it asked for its speed and  that is 80 also i did this on iready a while ago :)

Answer:

Remember, perimeter means addition. And area means multiplying. I see 16 and 12, so do you want me to add 16 and 12 because I see x in. But, 16 plus 12 equal 28. So, 28 in.

Option C: -4, -2, 3 are the roots of the polynomial.

Explanation:

The equation is [tex]x^{3} -10x=-3x^{2} +24[/tex]

Now, Adding [tex]3x^{2}[/tex] on both sides, we have,

[tex]x^{3} +3x^{2} -10x=24[/tex]

Subtracting 24 from both sides of the equation, we have,

[tex]x^{3} +3x^{2} -10x-24=0[/tex]

Solving the equation using synthetic division, we have,

[tex](x-2)(x^{2} +x-12)=0[/tex]

Now, we shall factor [tex](x^{2} +x-12)[/tex], we have,

[tex](x+4)(x-3)[/tex]

Thus, we have,

[tex](x+2)(x-3)(x+4)=0[/tex]

Solving each factor, we have,

[tex]$\begin{aligned} x+2 &=0 \\ x &=-2 \end{aligned}$[/tex]  and  [tex]\begin{array}{r}{x-3=0} \\{x=3}\end{array}[/tex]  and  [tex]\begin{aligned}x+4 &=0 \\x &=-4\end{aligned}[/tex]

Thus, the roots are -2,3 and 4.

Final answer:

To determine the original price of the shirt, divide the sale price of $27.20 by 85% (0.85 in decimal form) because Ben paid this amount after a 15% discount. The original price was $32.00.

Explanation:

To find the original price of the shirt before the 15% off sale, we can follow these steps:

Therefore, the original price of the shirt was $32.00 before the 15% discount was applied.

Answer:

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Answer:

-17

Step-by-step explanation:

-4 - 3 - 10 = -17

Answer:

[tex] 3^{-2} = \dfrac{1}{9} [/tex]

Step-by-step explanation:

Definition of negative exponent:

[tex] a^{-n} = \dfrac{1}{a^n} [/tex]

In our case, a = 3 and -n = -2.

[tex] 3^{-2} = \dfrac{1}{3^2} [/tex]

Now we just evaluate the power in the denominator.

[tex] 3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{9} [/tex]

Answer:

294.71

Step-by-step explanation:

298.8-4.09=294.71

Combine the whole number and the decimal parts to get the final answer: 294.71.

Final answer:

Prime numbers are numbers that are only divisible by 1 and themselves. The prime numbers in the list are 19, 29, 17, and 23.

Explanation:

In mathematics, prime numbers are numbers that are only divisible by 1 and themselves. They have exactly two distinct positive divisors. To determine if a number is prime, you can check if it is divisible by any number less than itself.

Using the list of numbers given, we can determine which ones are prime:

19 - Prime

29 - Prime

17 - Prime

23 - Prime

25 - Not prime (divisible by 5)

Therefore, the prime numbers in the list are: 19, 29, 17, and 23. The correct statement is: none of the above.