Twenty more than four times a number is equal to the difference between −71 and three times the number. Find the number.

The value of \(f\) is \(0\), by using the concept of slope of a line.

The equation to find the slope of a line is given by:

\(\(\text{slope} = \frac{{y_2 - y_1}}{{x_2 - x_1}}\)\)

Given that the slope is -8 and the points (-7, f) and (-6, -8) lie on the line, we can substitute the coordinates into the equation:

\(\(-8 = \frac{{-8 - f}}{{-6 - (-7)}}\)\)

Simplifying the equation:

\(\(-8 = \frac{{-8 - f}}{{1}}\)\)

Multiply both sides by 1:

\(\(-8 = -8 - f\)\)

Rearranging the equation:

\(\(-8 + 8 = -f\)\(0 = -f\)\)

The concept used in this problem is finding the slope of a line using two given points. The slope represents the rate of change of the line, indicating how much the line rises or falls for each unit of horizontal distance.

By substituting the coordinates of the two given points (-7, f) and (-6, -8) into the formula, we can calculate the slope.

Thus, the value of \(f\) is \(0\).

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Answer:Can somebody also help me with this. i'm confused please hurry!

Step-by-step explanation:

Using the scale factor given, the amount of fence, to the nearest foot, that they will have to purchase is: 297 feet.

Let P be the perimeter of your yard. We know that P = 339 feet.

Let k be the scale factor for your friend's yard. We know that the perimeter of your friend's yard is 7/8 times the perimeter of your yard, so the perimeter of your friend's yard is:

7/8 * P = 7/8 * 339 = 296.625 feet

Since your friend's yard is similar to yours, the ratio of corresponding sides is k. Since the perimeter is the sum of all sides, we can write:

k * P = 296.625

Solving for k, we get:

k = 296.625 / P = 296.625 / 339 = 0.875

So the scale factor for your friend's yard is 0.875.

Now we can use the scale factor to find the length of fence your friend will need to purchase. The length of fence for your yard is P, so the length of fence for your friend's yard is:

k * P = 0.875 * 339 = 296.625 feet

Therefore, your friend will need to purchase approximately 297 feet of fence.

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Answer:

x = 2

Step-by-step explanation:

The given triangle is a (30 - 60 - 90) triangle (this refers to the angle measurements). One property of a (30 - 60 - 90) triangle is that its side follows the following ratio,

\(x:x\sqrt{3}:2x\)

Where the side opposite the (30) degree angle measures (x), the side opposite the (60) degree angle measures (\(x\sqrt{3}\)) and the side opposite the (90) degree angle measures (2x).

One can use this ratio in the given triangle. Since it is given that the side opposite the (90) degree angle measures (4), and the side opposite the (30) degree angle measures (x), one can form an equation and solve for the unknown,

(2x) = (4)

Inverse operations,

x = 2

Answer:

the answer is 4

Step-by-step explanation:

none of the options are right

The straight-line distance between Akira's house and Cooper's house is 6.13 kilometers (rounded to the nearest tenth)

Given that,To get from home to his friend Akira's house, Jaden would have to walk 2.8 kilometers due east.The straight-line distance between Akira's house and Cooper's house is given by the distance between two points in a coordinate plane. Let the home be the origin (0, 0) of the coordinate plane and Akira's house be represented by the point (2.8, 4.7). Similarly, let Cooper's house be represented by the point (8.3, 7.4).The distance formula between the two points (2.8, 4.7) and (8.3, 7.4) is given by:distance = √[(8.3 - 2.8)² + (7.4 - 4.7)²]= √[5.5² + 2.7²]= √(30.25 + 7.29)= √37.54= 6.13 km (rounded to the nearest tenth)

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Answer:

y + 9 = 0

Step-by-step explanation:

Line is passing through the point (14,-9).

\(\implies x_2=14\:\&\:y_1=-9\)

Slope m = 0

Equation of line in point-slope form is given as:

\(y-y_1=m(x-x_1)\)

\(\implies y-(-9)=0(x-14)\)

\(\implies\huge{\red{\boxed{ y+9=0}}}\)

Answer:

4/10 = 2/5

Step-by-step explanation:

It's asking you what's an equivalent fraction to 4/10. 4/10 is equivalent to 2/5 because the size of 2 parts out of 5 is the same size as 4 parts out of 10.

Answer:

the solution to the system of equations is (x, y) = (3, -2).

Step-by-step explanation:

y = -2x + 4 (Equation 1)

y = x - 5 (Equation 2)

To solve for x, we can equate the right sides of the equations:

-2x + 4 = x - 5

Now, we can solve for x:

-2x - x = -5 - 4

-3x = -9

x = (-9) / (-3)

x = 3

Substituting the value of x back into Equation 2, we can solve for y:

y = 3 - 5

y = -2

a. The number of ways that this is done, if the order of the choices is relevant is 12 ways.

b. The number of ways that this be done, if the order of the choices is irrelevant is 6 ways

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

= n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

When the orders are relevant, this will be:

= 4! / (4 - 2!)

= 4! / 2!

= 12

When orders are irrelevant, this will be:

= 4! / (4 - 2!)2!

= 6 ways

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The zeros of a function are the values of x that, when evaluated in the function, make the output of the function to be zero.

A function is written in general form as y = f(x)

That notation says that, when we use the input "x" in a given function, that function "transforms" that input x into an output "y"

So y = f(x) is the value that the function takes for the input x.

A zero is an input of the function such that:

0 = f(x)

So the zeros are the inputs that have an output of zero, in this case you know that the function has a zero at 3, and as you can see, when x = 3, the function intercepts the x-axis, which is the axis defined by y = 0.

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Answer:

No(im not totally sure though because its slanted.)

Step-by-step explanation:

desmos.

Answer:

only one time that is the answer

Answer:

1.2

Step-by-step explanation:

The situation from above will likely make the bank seize the car and likely sell it to pay off Jason’s loan.

Option B is the correct answer.

Collateral is an item of value that a lender can take away from a borrower when he or she fails to repay a loan according to the terms that were agreed upon while borrowing.

We have,

Collateral is an item that a lender can seize when the borrower is unable to pay the loan.

Collateral for Jason was his car.

Thus,

The situation from above will likely make the bank seize the car and likely sell it to pay off Jason’s loan.

Option B is the correct answer.

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Answer:

(L-6)(L+2)

Step-by-step explanation:

Let L be the length of the flower garden.

Then the width will be L-4.

The area of the flower garden = L*(L-4) =L²-4L

The area of the birdbath is 3*4 = 12 ft²

The area of the remaining space for planting is

= Area of flower garden - area of birdbath

We can factor the expression as follows:

taking common frome each two terms

Therefore, the number of feet left for planting is (L-6)(L+2) in factored form.

Answer:

The 90% confidence interval is   \( 87.95   <  \mu < 92.05  \)

Step-by-step explanation:

From the question we are told that

   The sample size is  \(n = 28\)

    The  sample mean is  \(\= x = 90\)

    The standard deviation is  \(s= 60\)

Generally given that the sample size is not large enough i.e  n <  28 then we will make use of the t distribution table  

Generally the degree of freedom is mathematically represented as

         \(df = n- 1\)    

=>      \(df = 28 - 1\)  

=>      \(df = 2 7\)

From the question we are told the confidence level is  95% , hence the level of significance is    

      \(\alpha = (100 - 95 ) \%\)

=>   \(\alpha = 0.10\)

Generally from the student t  distribution table the critical value  of  \(\frac{\alpha }{2}\) at a degree of freedom of \(df = 2 7\)  is  

   \(t_{\frac{\alpha }{2} , 27  } =  2.052\)

Generally 95% confidence interval is mathematically represented as  

      \(\= x -E <  \mu <  \=x  +E\)

=> \(90  - 2.052  <  \mu < 90  + 2.052  \)

=> \( 87.95   <  \mu < 92.05  \)

Answer:

Lola used 3/4 more ink cartridges than her friends

Step-by-step explanation:

Subtract 2(first equation) from the second, and 3(first equation) from the third to eliminate x :

(2x + 3y + z) - 2(x + y + z) = 16 - 2*9

y - z = -2

(3x - 4y + 2z) - 3(x + y + z) = 1 - 3*9

-7y - z = -26

Now subtract either equation with y and z from the other to eliminate z. If we take the first from the second, we get

(-7y - z) - (y - z) = -26 - (-2)

-8y = -24

y = 3

Then

y - z = 3 - z = -2

z = 5

And lastly,

x + y + z = x + 3 + 5 = 9

x = 1

Using Pythagorean theorem, the length of the ladder is 10ft

In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:

x² = y² + z²

In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.

To calculate the length of the ladder, we can write the formula as;

x² = 8² + 6²

x² = 64 + 36

x² = 100

x = √100

x = 10

The length of the ladder is 10 feet

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The required angles (corresponding, vertical and alternate) in relation to the Parallel lines are attached accordingly.

Parallel lines are coplanar infinite straight lines that do not cross at any point in geometry. Parallel planes are planes that never intersect in the same three-dimensional space.

When two parallel lines cross by any other line (i.e. the transversal), corresponding angles are generated in matching corners or corresponding corners with the transversal.

When two parallel lines are sliced by a transversal, the resulting alternate exterior angles are congruent, according to the Alternate Exterior Angles Theorem.

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Answer: 1152wx^2y^2

Step-by-step explanation:

By solving a quotient, we will see that there are 13.33 servings of pasta on Lois' dish.

We know that one serving of pasta is 0.4 cups, and we know that Lois made a dish with (5 + 1/3) cups of pasta.

To see how many servings are in that dish, we need to take the quotient between the total number of cups used and the cups of a single serving.

So we need to solve:

N = (5 + 1/3)/0.4

We can write the numerator as:

5 + 1/3 = 15/3 + 1/3 = 16/3

The denominator as:

0.4 = 4/10 = 2/5

Then the quotient becomes:

N = (16/3)/(2/5)

N = (16/3)*(5/2) = (16*5)/(3*2) = 80/6 = 13.33

There are 13.33 servings on Lois' dish.

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Angle WZY is 50 degrees, angle WZX is also 50 degrees, and angle XZW is 160 degrees.

What is the inscribed angle theorem?

The inscribed angle theorem, also known as the central angle theorem, states that an angle formed by two chords in a circle is half the measure of the arc they intersect, or subtend, inside the circle.

To find all other angles in the circle with quadrilateral WXYZ inscribed in it and WY going through the center Q:

Since WY goes through the center, angle WYZ and angle WXY are both right angles (90 degrees)

By the inscribed angle theorem, angle WZY is equal to half the measure of the arc WX.

Since angle XYZ is given as 50 degrees, the measure of the arc WX is 2 times 50 degrees, which is 100 degrees.

Therefore, angle WZY is 50 degrees.

By the same logic, angle WZX is also 50 degrees.

Since angles WYZ and WXY are right angles, angles XZY and WZX are also right angles.

Finally, we can find angle WZY + angle XYZ + angle XZW + angle WZX = 360 degrees (sum of angles in a quadrilateral), and we can solve for angle XZW which is 160 degrees.

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Answer:

i don't understand the last one?

The amount of tax that is added to the cost of the computer is 159.72

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

Computer cost = 968

Tax percentage = 16.5%

Using the above as a guide, we have the following:

Tax amount = Computer cost * Tax percentage

substitute the known values in the above equation, so, we have the following representation

Tax amount = 968 * 16.5%

Evaluate

Tax amount = 159.72

Hence, the amount of tax that is added to the cost of the computer is 159.72

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The formula to be used is

Therefore,

Thus, the answer is t=20.4hr

Suggested method.

The answer is t=20.4 hours