Which reason is the justification for the statement that angle A ≅ angle B?

A) Vertical angles are congruent.
B) Linear angles are equal.
C) Intersecting lines form opposing angles.
D) Lines intersect at one point.

Answer:

936m3

Step-by-step explanation:

6×6×2=72m3

9×16×6=864m3

72+864=936m3

Answer:

Question 1 : Pierre is right

Question 2 : 0.85 (because 1 - 0.15 = 0.85)

Question 3 : Less than 1

Step-by-step explanation:

Answer:

4x+1

Step-by-step explanation:

3x-1+(x+2)

3x-1+x+2

Collect Like Terms: 3x+x-1+2

= 4x+1

The woman will withdraw $300 given 6%   interest rate annually.

We can use the formula for simple interest to solve this problem:

I = Prt

where I is the interest earned, P is the principal (initial deposit), r is the annual interest rate as a decimal, and t is the time in years. Since the interest rate is given as an annual rate, we need to convert it to a daily rate by dividing by 365:

r = 0.06/365 = 0.00016438356

The time in years is 120/365 = 0.3287671233 years. Now we can plug in the values and solve for I:

I = 300 * 0.00016438356 * 0.3287671233 = 0.01699999999

The interest earned is $0.017, which is negligible. Therefore, the woman will withdraw the entire principal plus any interest earned, which is:

300 + 0.017 = $300.02

Rounding to the nearest dollar, the woman will withdraw $300.

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Step-by-step explanation:

The real-world situation that can be represented by 4m+2 is option D, where a music download website has a membership fee of $4 and charges $2 for each download.

Here, "4m" represents the total cost of downloading "m" songs at a cost of $2 per song, and "2" represents the fixed cost of the membership fee. So, the total cost of downloading "m" songs along with the membership fee can be represented by the expression 4m + 2.

Part A: The GCF of the expression 12x² + 18x - 12 is 6x.

Part B: The factored form of the expression 12x² + 18x - 12 is 6x(2x + 3) - 12x.

Part C: The result matches the original expression, which means our factoring is correct.

Part A: Finding the Greatest Common Factor (GCF)

To find the greatest common factor (GCF) of the given expression, we need to identify the largest term or number that can divide evenly into all the terms of the expression. In this case, we are dealing with three terms: 12x², 18x, and -12.

The coefficients of the three terms are 12, 18, and -12. The common factor of these coefficients is 6, as it can divide evenly into all of them.

The variable 'x' is present in both the first and second terms, and 'x' is also a common factor.

Combining the common factors of the coefficients and variables, we find that the GCF of the expression 12x² + 18x - 12 is 6x.

Part B: Factoring the Expression Completely

Now that we have determined the GCF of the expression, we can proceed to factor it completely.

We already found that the GCF is 6x. Factoring it out from each term, we get:

6x(2x + 3) - 6x(2)

We can simplify the expression further by multiplying the GCF with the remaining terms inside the parentheses:

6x(2x + 3) - 12x

Part C: Checking the Factoring

To check if our factoring is correct, we can multiply the factored expression back and see if it matches the original expression.

Multiplying the factored expression:

6x(2x + 3) - 12x

= 12x² + 18x - 12

The result matches the original expression, which means our factoring is correct.

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Answer:

To sum up, 162/9 = 18.

Step-by-step explanation:

Step 1:

Start by setting it up with the divisor 9 on the left side and the dividend 162 on the right side like this:

9 ⟌ 1 6 2

Step 2:

The divisor (9) goes into the first digit of the dividend (1), 0 time(s). Therefore, put 0 on top:

0

9 ⟌ 1 6 2

Step 3:

Multiply the divisor by the result in the previous step (9 x 0 = 0) and write that answer below the dividend.

0

9 ⟌ 1 6 2

0

Step 4:

Subtract the result in the previous step from the first digit of the dividend (1 - 0 = 1) and write the answer below.

0

9 ⟌ 1 6 2

- 0

1

Step 5:

Move down the 2nd digit of the dividend (6) like this:

0

9 ⟌ 1 6 2

- 0

1 6

Step 6:

The divisor (9) goes into the bottom number (16), 1 time(s). Therefore, put 1 on top:

0 1

9 ⟌ 1 6 2

- 0

1 6

Step 7:

Multiply the divisor by the result in the previous step (9 x 1 = 9) and write that answer at the bottom:

0 1

9 ⟌ 1 6 2

- 0

1 6

9

Step 8:

Subtract the result in the previous step from the number written above it. (16 - 9 = 7) and write the answer at the bottom.

0 1

9 ⟌ 1 6 2

- 0

1 6

- 9

7

Step 9:

Move down the last digit of the dividend (2) like this:

0 1

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

Step 10:

The divisor (9) goes into the bottom number (72), 8 time(s). Therefore put 8 on top:

0 1 8

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

Step 11:

Multiply the divisor by the result in the previous step (9 x 8 = 72) and write the answer at the bottom:

0 1 8

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

7 2

Step 12:

Subtract the result in the previous step from the number written above it. (72 - 72 = 0) and write the answer at the bottom.

0 1 8

9 ⟌ 1 6 2

- 0

1 6

- 9

7 2

- 7 2

0

You are done, because there are no more digits to move down from the dividend.

The answer is the top number and the remainder is the bottom number.

Therefore, the answer to 162 divided by 9 calculated using Long Division is:

18

0 Remainder

The total cost of an apple pie and a blueberry muffin is €3. An apple pie costs €1 and a blueberry muffin costs €2.

To tackle this issue, we can utilize an arrangement of conditions. We should let "a" address the expense of one fruity dessert, and "b" address the expense of one blueberry biscuit.

Then we can compose two conditions in light of the data given:

8a + 3b = 14

6a + b = 8

The principal condition addresses the expense of 8 fruity desserts and 3 blueberry biscuits, which is equivalent to €14. The subsequent condition addresses the expense of 6 fruity desserts and 1 blueberry biscuit, which is equivalent to €8.

Presently we can tackle this arrangement of conditions utilizing replacement. We can detach b in the subsequent condition:

b = 8 - 6a

We can then substitute this articulation for b into the primary condition:

8a + 3(8 - 6a) = 14

Working on this situation, we get:

8a + 24 - 18a = 14

Joining like terms, we get:

-10a + 24 = 14

Deducting 24 from the two sides, we get:

-10a = - 10

Partitioning by - 10, we get:

a = 1

Now that we know the expense of one fruity dessert, we can substitute this worth back into the second condition to settle for b:

6(1) + b = 8

Improving on this situation, we get:

6 + b = 8

Taking away 6 from the two sides, we get:

b = 2

Consequently, a fruity dessert costs €1 and a blueberry biscuit costs €2. The complete expense of a fruity dessert and a blueberry biscuit is €3.

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Answer

I think its a

Step-by-step explanation:

Answer:y=-4x-1

Step-by-step explanation:

The equation of the line in slope-intercept form that is perpendicular to the line passing through (-2,6) and (-3,2) and passes through point (-1,3) is

x - 4y = -11

We have,

From the figure,

(-2, 6) and (-3, 2)

So,

The slope of the given line.

slope = (change in y) / (change in x)

slope = (2 - 6) / (-3 - (-2))

slope = -4 / -1

slope = 4

Since the two lines are perpendicular, the slope of the new line will be the negative reciprocal of the slope of the given line.

The slope of the new line = -1/4

Now that we know the slope of the new line, we can use the point-slope form of the equation of a line to find the equation of the line that passes through point J(-1,3):

y - y1 = m(x - x1)

where m is the slope and (x1,y1) is the point through which the line passes.

Substituting the values.

y - 3 = (-1/4)(x - (-1))

Simplifying.

y - 3 = (-1/4) (x + 1)

Multiplying by -4 to get the equation into slope-intercept form.

-4y + 12 = x + 1

Simplifying:

x - 4y = -11

Therefore,

The equation of the line in slope-intercept form that is perpendicular to the line passing through (-2,6) and (-3,2) and passes through point (-1,3) is

x - 4y = -11

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The rectangular form of the complex number z = 3√2 cis (7π/4) is

z = -3 - 3i

We have,

To convert a complex number from polar form to rectangular form, we use the following formulas:

x = r cos(theta)

y = r sin(theta)

where r is the modulus of the complex number, and theta is its argument.

In this case, we have:

r = 3√2

theta = 7π/4

So:

x = 3√2 cos(7π/4) = 3√2 (-1/√2) = -3

y = 3√2 sin(7π/4) = 3√2 (-1/√2) = -3

Therefore,

The rectangular form of the complex number z = 3√2 cis (7π/4) is

z = -3 - 3i

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Answer:

Michigan: 32.8

Nebraska: 23.6

Step-by-step explanation:

Answer:

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

The formed triangles are similar right triangles.

They have equal ratios of corresponding sides.

Let the tree is t feet high, then we have ratios:

Solve it for t:

Answer:

10.8 feet

Step-by-step explanation:

The problem involves using proportions to find the height of the tree, based on the height of the child and the lengths of the two shadows.

To set up the proportion, first recognize that the ratio of the height of the child to the length of their shadow is the same as the ratio of the height of the tree to the length of its shadow.

This can be written mathematically as:

[tex]\boxed{\sf \dfrac{height\;of\;the\;child}{child\;shadow\;length}=\dfrac{height\;of\;the\;tree}{tree\;shadow\;length}}[/tex]

Let the height of the tree be x.

Given the height of the child is 4.5 feet, the length of the child's shadow is 10 feet, and the length of the tree's shadow is 24 feet:

[tex]\begin{aligned}\sf \dfrac{height\;of\;the\;child}{child\;shadow\;length}&=\sf \dfrac{height\;of\;the\;tree}{tree\;shadow\;length}\\\\\dfrac{4.5}{10}&=\dfrac{x}{24}\end{aligned}[/tex]

To solve for x, multiply both sides of the equation by 24 and simplify:

[tex]24 \cdot \dfrac{4.5}{10}=24 \cdot \dfrac{x}{24}[/tex]

     [tex]\dfrac{108}{10}=x[/tex]

     [tex]10.8=x[/tex]

Therefore, the height of the tree is 10.8 feet.

The angle of sinθ between the horizontal vector (1, 0) and the slant vector (15/17, -8/17) is sin⁻¹(8/17), which is approximately 29.11 degrees.

To find the angle of sinθ between a horizontal vector and a slant vector, we can use the dot product formula:

a · b = |a| |b| cos(θ)

where a and b are vectors, |a| and |b| are their magnitudes, and theta is the angle between them.

In this case, the horizontal vector is (1, 0) and the slant vector is (15/17, -8/17).

The magnitude of the horizontal vector is 1, and the magnitude of the slant vector is:

|b| = sqrt((15/17)² + (-8/17)²) = sqrt(225/289 + 64/289) = sqrt(289/289) = 1

The dot product of the two vectors is:

a · b = (1)(15/17) + (0)(-8/17) = 15/17

So we have:

15/17 = (1)(1) cos(θ)

cos(θ) = 15/17

To find sin(θ), we can use the trigonometric identity:

sin²(θ) + cos²(θ) = 1

sin²(θ) = 1 - cos²(θ) = 1 - (15/17)² = 64/289

Taking the square root of both sides, we get:

sin(theta) = sqrt(64/289) = 8/17

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The volume of the rectangular prism is 31.2 [tex]m^{3}[/tex].

To find the volume of a rectangular prism, we multiply the length, width, and height of the prism.

Given that the length of the rectangular prism is 4m, the width is 6.5m, and the height is 1.2m, we can find the volume as follows:

Volume = length x width x height

= 4m x 6.5m x 1.2m

= 31.2 cubic meters

Therefore, the volume of the rectangular prism is 31.2 cubic meters.

To understand what this means, imagine filling the rectangular prism with cubic blocks, each having a volume of 1 cubic meter. We would need to place 31.2 of these blocks to completely fill the prism. Another way to think about it is that the prism could hold 31.2 cubic meters of water, if filled to the brim without any spillage.

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[tex]\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] ~\dotfill[/tex]

[tex]\stackrel{\textit{"z" varies inversely with "t"}}{z = \cfrac{k}{t}}\hspace{5em}\textit{we also know that} \begin{cases} z=10\\ t=12 \end{cases} \\\\\\ 10=\cfrac{k}{12}\implies 120 = k\hspace{9em}\boxed{z=\cfrac{120}{t}} \\\\\\ \textit{when t = 5, what's "z"?}\qquad z=\cfrac{120}{5}\implies z=24[/tex]

Answer:

Step-by-step explanation:

I'd suggest a bar graph. Some may suggest a pie chart, but it can be visually difficult to quickly tell the difference in sizes between slices of the pie in pie charts when there are a lot of options. With a bar graph, it is usually very easy to see which bar is the tallest.  

Answer:

Both.

Step-by-step explanation:

They both are the same diagram. Just rearranged.

Graph B represents the system of linear inequalities the best.

Hence the correct option is (B).

Let Tami needs to work x hours per week as server and y hours per week as tutors.

So it is given that she can work at most 20 hours a week.

So, the suitable inequality to describe the situation:

x + y [tex]\le[/tex] 20 ............. (i)

Now the corresponding equation of this above inequality is,

x + y = 20

x/20 + y/20 = 1

comparing to inception form of straight line we can say that the equation says about a line which cuts axes at (20, 0) and (0, 20) respectively.

since (0, 0) gives 0 + 0 = 0 [tex]\le[/tex] 20 is true.

So the solution area towards origin.

It is also given that she makes $6 per hour as server and makes $12 per hour as tutor and she needs to earn at least $150.

The best suited inequality for this condition,

6x + 12y [tex]\ge[/tex] 150 .................(ii)

The corresponding equation of the above inequality:

6x + 12y = 150

6x/150 + 12y/150 = 1

x/25 + y/(12.5) = 1

So it is the line cuts the axes at (25, 0) and (0, 12.5) respectively.

since (0, 0) gives 6*0 + 12*0 = 0 [tex]\ge[/tex] 150 is not true so the solution area for this inequality towards opposite of origin along the straight line.  

So Graph B represents the system of linear inequalities the best.

Hence the correct option is (B).

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Answer:

[tex]y =\dfrac{1}{2}x[/tex]

Step-by-step explanation:

General slope-intercept form of a straight line is
y = mx + b
where m = slope, b = y-intercept

The diagonals of a rhombus bisect each other at 90°

The equation of diagonal AC can be found as follows

Slope of AC = [tex]\dfrac{4 - (-4)}{-2 - 2} = \dfrac{8}{-4} = - 2\\[/tex]

Therefore the diagonal AC has the equation
y = -2x + b

where b is the y intercept

We can find b by plugging in (-2, 4) into the above equation:
4 = -2(-2) + b

4 = b + b

b = 0

So the equation of the diagonal is y = -2x

This passes through the origin (0,0)

Since A and C are equidistant from the origin, the origin is the midpoint of the diagonal AC

Since the other diagonal BD has to bisect this diagonal at 90°, it too has to pass through the midpoint (0, 0)

The slope of a line perpendicular to y = mx + b is -1/m

Therefore the slope of the perpendicular line to y = -2x is - (1/-2) = 1/2 and the y-intercept is 0 since it passes through the origin

Therefore the equation of diagonal BD is
[tex]y =\dfrac{1}{2}x[/tex]

The ΔABC is dilated with scale factor 1/2 followed by

a 180° clockwise rotation about the origin.

Hence option (C) is correct.

From the given figure;

The image shrinks while moving ABC to DEF.

And the scale factor is defined as the proportion of the new image's size to that of the previous image.

Since we know

The image contracts if the scale factor is between 0 and 1.

To acquire the position of DEF we have to rotate the triangle 180 degree in clockwise direction about the origin.

Since 1/2 lies between 0 and 1.

Therefore,

It dilated clockwise at 180 degree with scale factor 1/2.

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Answer:

Therefore, $28.20 is added as gratuity to the $141 bill for a party of 6.

Step-by-step explanation:

If a party has 6 or more people, a 20% gratuity is automatically charged. So in this case, the gratuity is:

20% of $141 = (20/100) x $141 = $28.20

Therefore, $28.20 is added as gratuity to the $141 bill for a party of 6.

Answer:

$3000

Step-by-step explanation:

22×10=220

15×20=300

8×10=80

220+300+80=600ft²

5×600=$3000

Answer:

Step-by-step explanation:

To determine the actual length represented by a given length on a drawing, you need to use the scale ratio. In this case, the scale is 1 cm : 50 km. This means that 1 cm on the drawing represents 50 km in actual length.

To find the actual length represented by a length of 8.6 cm on the drawing, we can set up a proportion:

1 cm : 50 km = 8.6 cm : x

To solve for x, we can cross-multiply:

1 * x = 50 * 8.6

x = 430 km

Therefore, the actual length represented by a length of 8.6 cm on the drawing is 430 km.

The numeric value of f(a) + f(h) for f(x) = x² - 5x + 3 is given as follows:

A. f(a) + f(h) = a² + h² - 5a - 5h + 6.

To calculate the numeric value of a function or of an expression, we substitute each instance of any variable or unknown on the function by the value at which we want to find the numeric value of the function or of the expression presented in the context of a problem.

The function for this problem is defined as follows:

f(x) = x² - 5x + 3.

Hence the numeric values are given as follows:

The only like term is the 3 for both expressions, hence the addition is given as follows:

f(a) + f(h) = a² + h² - 5a - 5h + 6.

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The limiting reactant in the reaction between 35.2 grams of Ca(OH)₂ and 20.7 grams of H₂SO₄ is H₂SO₄. This was determined by calculating the moles of each reactant and comparing them to the stoichiometric ratio of the reaction.

To determine the limiting reactant, we need to calculate the amount of product that can be formed from each reactant.

First, let's write the balanced chemical equation for the reaction between Ca(OH)₂ and H₂SO₄

Ca(OH)₂ + H₂SO₄ → CaSO₄ + 2H₂O

Next, let's calculate the amount of product that can be formed from each reactant

For Ca(OH)₂:

Molar mass of Ca(OH)₂ = 74.09 g/mol

1 mole of Ca(OH)₂ reacts with 1 mole of H₂SO₄ to produce 1 mole of CaSO₄

Moles of Ca(OH)₂ = 35.2 g / 74.09 g/mol = 0.475 mol

Moles of H₂SO₄ = 20.7 g / 98.08 g/mol = 0.211 mol

Moles of CaSO₄ that can be formed from Ca(OH)₂ = 0.475 mol

Moles of CaSO₄ that can be formed from H₂SO₄ = 0.211 mol

For H2SO4

Molar mass of H₂SO₄ = 98.08 g/mol

Moles of CaSO₄ that can be formed from H2SO4 = 0.211 mol

Since the amount of CaSO₄ that can be formed from Ca(OH)₂ is greater than the amount that can be formed from H₂SO₄, Ca(OH)₂ is the excess reactant and H₂SO₄ is the limiting reactant.

Therefore, H₂SO₄ is the limiting reactant

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Answer:

[tex]6 \sqrt{8} \sqrt{2} = 6 \sqrt{16} = 6(4) = 24[/tex]

B is the correct answer.

The standard form of the equation of a circle and the location of where Millie lives indicates;

12) The equation of the circle is; (x - 6)² + (y - 2)² = 25/π

13) Dave does not deliver to Millie

The equation for the area of a circle is A = π × Radius²

12) The length of a block = 250 inches

The distance of the post office = 6 blocks east and 2 blocks north

The area the postal carriers delivers mail = 25 square blocks

The coordinates of the location of the post office = (6, 2)

The radius of the circle ias therefore, r = √(25/π) ≈ 2.82

The equation of a circle is; (x - h)² + (y - k)² = r²

Where; (h, k) = (6, 2)

13) The coordinates of the location where Millie lives is (3, -3)

The distance of Millie's address 3 blocks south of the city hall, whereby the carrier Dave reaches about south 2.82 blocks, from 2 blocks north from the city hall, which is about 0.82 blocks south from the city hall.

Therefore, Dave's area does not extend to Millie's location and Dave does not deliver mail to Millie

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