Given the equations of two lines, describe how to determine if the lines are parallel.

The work done in pushing the car along the level road from point A is found to be 8147 foot-pounds.

The work done in pushing a car along a level road can be calculated using the formula,

work = force × distance × cos(angle) where the angle between the force and the direction of motion is 0 degrees (since the force is parallel to the level road). The force is given as 103 pounds, and the distance is 79 feet. Therefore,

work = 103 × 79 × cos(0) = 8147 foot-pounds

Rounding to the nearest foot-pound, the work done in pushing the car from point A to point B is 8147 foot-pounds.

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Answer:

78/97

Step-by-step explanation:

First, add up all the balls to find the total amount of balls in the bag (19+28+21+29). Then determine how many balls are not blue (you could either take the total and subtract 19 or add up all the colors that are not blue). There are 97 balls total and 78 of them are not blue which is shown as 78/97. 78/97 cannot simplify further.

Answer:A=OE+L

Step-by-step explanation:

880000=51000+L

Liabilities=370000

680000=2x

The amount of its equity of 340000 for the second problem

Answer:3,000

Step-by-step explanation:

Answer:no image

Step-by-step explanation:

Step-by-step explanation:

No image is overe there please add the image

Answer:

Step-by-step explanation:

You want the tangent and secant of the angle θ the line x-3y=0 makes with the negative x-axis.

The relations between the angle and its trig functions are ...

  Tan = Opposite/Adjacent

  Sec = Hypotenuse/Adjacent

We have shown the angle of interest in a unit circle with the "adjacent" side equal to the radius of the circle (1). Then the values of interest are ...

  tan(θ) = opposite side = 1/3 . . . . . . . equal to the slope of the line

  sec(θ) = hypotenuse = √(1 +(1/3)²) = √(10/9) = (√10)/3

The tangent is 1/3; the secant is (√10)/3.

__

Additional comment

A third-quadrant angle measured from the +x axis has a negative secant. The tangent is positive there.

Since this angle is measured from the -x axis, it isn't clear whether it is supposed to be considered a 3rd-quadrant angle or not. For the given acute angle θ shown, the trig functions are both positive. YMMV

Answer:

The expanded notation of -6⁷ means writing the number -6⁷ as a sum of its place values.

-6⁷ can be written as:

-6 × 6 × 6 × 6 × 6 × 6 × 6

or

-6 × (6 × 6 × 6 × 6 × 6 × 6)

or

-6 × 6⁶

In expanded notation form, it can be written as:

-6 × (6 × 6 × 6 × 6 × 6 × 6)

= -6 × (46656)

= -279936

Therefore, the expanded notation of -6⁷ is -279936.

Step-by-step explanation:

The value of the function is 136

It is important that we note that functions are described as expressions that are used to explain the relationship between two variables.

From the information given, we have that;

g(x)=2x

h(x)=x^(2)+4

To determine the composite function, we would need to substitute the value of h(-8) as x in the function g(x)

Then, we have that;

h(-8) = (-8)^2 + 4

Find the values

h(-8) = 68

Now, substitute the value as x , we have that;

g(h(-8)) = 2(68)

expand the bracket and multiply

g(h(-8)) = 136

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Answer:

240 8018

Step-by-step explanation:

two hundred forty eight thousand and eighteen

There would be 35 more defective bean seeds than pumpkin seeds in the shipment.

Calculate the number of defective bean seeds:

Defective bean seeds = Total bean seeds * Defect rate for bean seeds

Defective bean seeds = 1,750 * 0.05 = 87.5

Since we can't have half a seed, we'll round it up to the nearest whole number.

Defective bean seeds = 88

Calculate the number of defective pumpkin seeds:

Defective pumpkin seeds = Total pumpkin seeds * Defect rate for pumpkin seeds

Defective pumpkin seeds = 1,750 * 0.03 = 52.5

Similarly, we'll round it up to the nearest whole number.

Defective pumpkin seeds = 53

Calculate the difference in defective seeds:

Difference in defective seeds = Defective bean seeds - Defective pumpkin seeds

Difference in defective seeds = 88 - 53 = 35

So, there would be 35 more defective bean seeds than pumpkin seeds in the shipment.

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In a shipment of 1,750 seeds of each type, with a defect rate of 5% for bean seeds and 3% for pumpkin seeds, how many more defective bean seeds would be expected than pumpkin seeds?

The measure of angle IHE is 23°.

Since DF and GI are parallel, we know that angle HJF is congruent to angle GHJ. Therefore, we have:

mHJF = mGHJ = 134°

We can now use this information to find the measure of angle IHE. To do this, we need to use the fact that the sum of the angles in a straight line is 180°. Since H, J, F, and I lie on a straight line, we have:

mHJF + mFJI + mIHE = 180°

Substituting the values we know, we get:

134° + mFJI + mIHE = 180°

Simplifying the equation, we get:

mFJI + mIHE = 46°

We still need to find the measure of angle FJI. To do this, we can use the fact that the angles in a triangle add up to 180°. Triangle GHJ is a straight line, so its angles add up to 180°. Therefore, we have:

mGHJ + mHJF + mFJI = 180°

Substituting the values we know, we get:

134° + mFJI + mFJI = 180°

Simplifying the equation, we get:

2mFJI = 46°

Dividing both sides by 2, we get:

mFJI = 23°

Finally, we can substitute this value back into our earlier equation to find the measure of angle IHE:

mFJI + mIHE = 46°

23° + mIHE = 46°

Subtracting 23° from both sides, we get:

mIHE = 23°

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Complete Question:

If DF and GI are parallel lines and mGHJ = 134°, what is mIHE?

Answer:

  B. CPCTC

  D.  opposite sides are congruent

Step-by-step explanation:

You want to know the necessary claims for proving opposite angles are congruent in a parallelogram.

Given parallelogram ABCD and diagonal AC, you can prove opposite angles congruent in this way:

  AB≅CD and BC≅DA . . . . . opposite sides are congruent

  AC≅CA . . . . . . . . . . . . . . reflexive property of congruence

  ∆ABC≅∆CDA . . . . . . . . . . . SSS congruence

  ∠B ≅ ∠D . . . . . . . . . . . . Corresponding parts of congruent triangles

When doing the proof, the necessary claims are ...

  B. Corresponding parts of congruent triangles are congruent

  D. Opposite sides are congruent.

<95141404393>

The missing side measure is equal to: A. 14.

In Mathematics and Geometry, the scale factor of a geometric figure can be calculated by dividing the dimension of the image (new figure) by the dimension of the pre-image (original figure):

Scale factor = Dimension of image (new figure)/Dimension of pre-image (original figure)

By substituting the given parameters into the formula for scale factor, we have the following;

Scale factor = Dimension of image/Dimension of pre-image

4/5.6 = 10/x

4x = 56

x = 56/4

x = 14

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

  $640

Step-by-step explanation:

You want to know the income tax reduction resulting from investing $3200 in a defined-contribution account when the marginal tax rate is 20%.

The money invested in a defined-contribution account is not subject to income taxes when it is invested. The tax savings is ...

  20% × $3200 = $640

Jermaine lowered his taxes by $640.

Answer: D

Step-by-step explanation:

The equation for a linear function is y = mx + b

We first need to find the slope of the object, we can see here than it perfectly lands on the point, (0, -3) and (6,0). We can use this formula to determine the slope:

(y2 - y1)/(x2 - x1)

Now let's plug in the numbers.

(0 + 3) / (6 - 0)

3/6

1/2

Now we know the slope is 1/2 and the y-intercept is -3, so let's make it into a slope-intercept form.

y = 1/2x - 3

The answer is 11 or at least i think it is

Answer:

Step-by-step explanation:

Use the vertical line test. If you can draw a vertical line that cuts more than one point then the graph is not a function.

The only one that is incorrect is graph 4. It is a function (no vertical line will cut the graph more than once).

The row operation performed to obtain  [0    0     -3     9] is R₃ - R₂.

A row operation in a matrix involves making a change to one or more rows of the matrix. The three elementary row operations are, interchanging rows, rows addition, and rows multiplication.

The given matrix;

[9  -2  -9  9]            [9  -2  -9  9]

[1   2  -6   -1]  into   [1   2  -6   -1]

[1  2  -9    8]            [0  0  -3    9]

If we perform R₃ - R₂, that is row 3 minus row 2, we will have the following;

[1  2  -9    8] - [1   2  -6   -1]

= [(1-1)  (2-2)   (-9 + 6)   (8 + 1)]

= [0    0     -3     9]

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Answer:

Step-by-step explanation:

To find the margin of error for a 98% confidence level, we need to use the z-score that corresponds to this confidence level, which is 2.33 (found in a z-table or using a calculator).

The formula for the margin of error (E) is:

E = z*(sqrt(p*q/n))

Where:

z is the z-score for the desired confidence level (2.33 for 98% confidence)

p is the sample proportion (0.4, or 40%)

q is the complement of the sample proportion (1 - 0.4 = 0.6)

n is the sample size (800)

Substituting these values into the formula, we get:

E = 2.33*(sqrt(0.4*0.6/800)) = 0.045

So the margin of error for a 98% confidence level, with a sample size of 800 and a sample proportion of 40%, is 0.045 or approximately 4.5%. This means that we can be 98% confident that the true population proportion is within 4.5% of the sample proportion.

The total surface area of the pyramid is:260 ft²

The area of a triangle is expressed as:

A = ¹/₂bh

where:

b denotes the base of the triangle

h denotes the height of the triangle

Area of rectangle is:

A = l * w

where:

l denotes the length of the rectangle

w denotes the width of the rectangle

Thus, the total surface area of the given pyramid is:

Total Surface Area =  4(¹/₂(10 * 12)) + (10 * 10)

Total Surface Area  = 240 + 20

Total Surface Area  = 260 ft²

Therefore, we can conclude that is the calculation of the total surface area of the composite figure.

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The expression to find the angle BGC is 11x + 34.

The equation that would help us find the angles of AGB and BGC is 90 = 11x + 46.

The correct equation that would help us find the angles of ABG, AGF, and AGE is 15x + 120 = 180.

In Mathematics and Geometry, a complementary angle refers to two (2) angles or arc whose sum is equal to 90 degrees (90°).

By substituting the given parameters into the complementary angle formula, the sum of the angles is given by;

∠AGB + ∠BGC = 90.

12 + 11x + 34 = 90

11x + 46 = 90

90 = 11x + 46.

Additionally, the sum of all of the angles on a straight line is always equal to 180 degrees. In this scenario, we can reasonably infer and logically deduce that the sum of angles ABG, AGF, and AGE are supplementary angles:

12 + 90 + 15x + 18 = 180°

120 + 15x = 180°

15x + 120 = 180

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Answer:

51/4 quarters

Step-by-step explanation:

To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator for 4 and 2 is 4x2=8.

So we need to convert both fractions to have a denominator of 8:

31/4 = (31/4) x (2/2) = 62/8

41/2 = (41/2) x (4/4) = 164/8

Now we can add the fractions:

62/8 + x/4 = 164/8

Subtracting 62/8 from both sides:

x/4 = 102/8

Simplifying:

x = 51/4

Therefore, we need to add 51/4 quarters to 31/4 to get 41/2

Answer:

Step 1:

Let x = number of years

Let y = Value of the laptop after x years

Step 2:

Write an equation that expresses the value of the laptop after x years y = 0.8((4700)x)

Step 3:

Set the equation equal to 1000 and solve for x

1000 = 0.8((4700)x)

1 = 0.8(4700)x

1/0.8 = 4700x

1.25 = 4700x

x = (1.25/4700)

Answer: The laptop will be worth $1000 or less after 0.0026608 years.

Answer:

1 year

Step-by-step explanation:

4700 x .8= 3760

4700 - 3760 = 940$

In 1 year the laptop will be $940

Answer:

$17,204.28

Step-by-step explanation:

So first of all you want to start by finding what P, r and t would be.

Once I found all of those I put them into the equation (l = Prt) and solved (by putting it into a calculator obviously). That is how I came up with my answer. Check the screenshot provided to see what P, r and t would be and to see all my work! :)

Hope this helps! :)

Have a great day!

The sine of angle θ is given as follows:

sin(θ) = -8/17.

For an angle [tex]\theta[/tex] the unit circle is a circle with radius 1 containing the following set of points: [tex](\cos{\theta}, \sin{\theta})[/tex].

The point in this problem has the coordinates given as follows:

(15/17, -8/17).

Hence the trigonometric ratios are given as follows:

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For circle O, For circle O, m CD=125° and m∠ABC = 55°. In the figure, ∠ ABO and ∠ BCO have measures equal to 35°.

For circle O, m(arc CD) = 125° and m∠ABC = 55°.

First, we use central angle to find that ∠COB is 125°,

give that ∠COB = arc CD

Next, we use complementary angles to find that ∠BCA is 35°,

given that ∠ABC +  ∠BCA = 90°.

Then, we use the sum of interior angles in a triangle to find that ∠CBO is 20°; given that:

∠CBO + ∠COB + ∠BCO = 180°.

∠BCO = ∠BCA = 35°

∠COB = 125°

125° + 35° = 160°

180° +  160° =  20°

Finally, we use angle addition postulate to find that ∠ABO is also 35°.

Therefore, <ABO and <BCO both have measures of 35° in the figure.

The above answer is in response to the question below;

For circle O, and m∠ABC = 55°. In the figure, ∠_____ and ∠____ have measures equal to 35°.

a. the first could be AOB, ABO, or BOA

b. the second could be BCO, OBC, or BOC

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A graph of the parabola with five points on the parabola is shown below.

In Mathematics and Geometry, the vertex form of a quadratic equation is given by this formula:

y = a(x - h)² + k

Where:

For the given quadratic function, we have;

y = x² - 2x + 4

When x = 0, we have:

y(0) = 0² - 2(0) + 4

y(0) = 4

When x = 2, we have:

y(2) = 2² - 2(2) + 4

y(2) = 4

When x = -2, we have:

y(-2) = -2² - 2(-2) + 4

y(-2) = 12

When x = 4, we have:

y(4) = 4² - 2(4) + 4

y(4) = 12

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The result of the carrying out the operation, Add -4(row 1) to row 3, on the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

From the question, we are to perform the given row operation on the given matrix

From the given information, the given matrix is:

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\4&-1&6&-8\end{array}\right][/tex]

We are to carry out the operation

Add -4(row 1) to row 3

This means we should multiply row 1 by -4

-4 × [ 1     2    1   | -5

       -4   -8   -4  | 20

Now, we will add the result to row 3

4    -1     6  |  -8

-4   -8   -4  | 20

------------------------

0    -9    2  |  12

Hence,

The resulting matrix becomes

[tex]\left[\begin{array}{ccc|c}1&2&1&-5\\0&4&-2&3\\0&-9&2&12\end{array}\right][/tex]

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Answer:

7 seeds will go into each bag

Given:

56 flower seeds need to be put into 8 separate bags.

To find out how much go into each bag you will divide the number of seeds by the number of bags

56/8=7

So 7 seeds will go into each of the 8 bags