What is the inverse of the following statement?

"If the corresponding angles are congruent, then the lines are parallel."

If the corresponding angles are not congruent, then the lines are not parallel.
If the lines are parallel, then the corresponding angles are congruent.
If the lines are not parallel, then the corresponding angles are not congruent.
If the corresponding angles are congruent, then the lines must be parallel.

Answers

Answer 1

The true statement is that proves the congruence of both triangles is:

∠ABC ≅ ∠DCB;

alternate interior angles of parallel lines are congruent.

Here, we have

to prove that angles are congruent

From the complete question, we have the following highlights

Angles B and C are alternate interior angles

The triangles are bounded by parallel lines

The above highlights mean that:

Angles ABC and DCB are congruent, by the theorem of alternate interior angles of parallel lines

Hence, the true statement is (c)

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complete question:

Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used? ∠ABC ≅ ∠BAC; corresponding angles of parallel lines are congruent. ∠CAB ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent ∠ACD ≅ ∠ABD; corresponding angles of parallel lines are congruent.


Related Questions

PLEASE HELP!!! MARKING BRAINLIST

Answers

Answer:

P = (3^2)/(4^2) = 9/16 = .5625 = 56.25%

This probability is about .56.

A child that is 4.5 feet tall is standing in the playground. The sun is shining and the child casts a shadow 10 feet long. At the same time, a tree casts a shadow that is 24 feet long. How tall is the tree?

Answers

Answer:

The tree is 10.8 feet

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

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:

t/4.5 = 24/10

Solve it for t:

t/4.5 = 2.4t = 4.5*2.4t = 10.8

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.

Please help test is due in 1 hour will mark brainiest and get points
Suppose one of the following numbers is chosen at random.



1 2 3 4 5 6



What is the probability the number chosen is even, give that it is greater than 1?

Answers

The probability the number chosen is even, give that it is greater than 1 is 1/2.

The numbers include 1,2,3,4,5,6,

Let P (E) = probability of chosing even number is

P (E) = (Required outcome)/(Total outcome)

Required outcome = numbers of even number

Total outcome = total numbers

P (E) = 3/6

P (E) = 1/2

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Your teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each. Let x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators. Write an inequality that represents the number of each type of calculator she can buy.

Answers

The inequality that represents the number of each type of calculator she can buy will be 25x + 65y ≤ 800

Given that teacher needs to purchase some scientific calculators for $25 each and some graphing calculators for $65 each.

Consider that x equal the number of scientific calculators and y equal the number of graphing calculators she buys She can only spend up to $800 for the calculators.

The inequality that represents the situation becomes as;

25x + 65y ≤ 800

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A cylinder has a height of 8 feet and a diameter of 12 feet. Which of the following is a true statement?

A- All of the answers listed
B- A cone with the same height and radius would have a volume of 96π ft³
C- The volume of the cylinder is 288π ft³
D- The area of the base is 36π ft²

Answers

Answer:

A- All of the answers listed

Step-by-step explanation:

Let's consider each choices:-

B- A cone with the same height and radius would have a volume of 96π ft³.

In this case, we are replaced with the cone figure that has diameter of 12 feet and height of 8 feet. We know that the formula of cone's volume is:

[tex]\displaystyle{\dfrac{1}{3}\pi r^2 h}[/tex]

Our radius is half of diameter which is 12/2 = 6 feet. Therefore:

[tex]\displaystyle{V = \dfrac{1}{3}\pi \cdot 6^2 \cdot 8}\\\\\displaystyle{V = \dfrac{1}{3}\pi \cdot 36 \cdot 8}\\\\\displaystyle{V = \pi \cdot 12 \cdot 8}\\\\\displaystyle{V=96\pi \ \: \text{ft}^3}[/tex]

Therefore, the statement B is true.

C- The volume of the cylinder is 288π ft³

Finding the volume of cylinder, the volume's formula is [tex]\displaystyle{V = \pi r^2 h}[/tex]. Substitute known values:

[tex]\displaystyle{V = \pi \cdot 6^2 \cdot 8}\\\\\displaystyle{V = \pi \cdot 36 \cdot 8}\\\\\displaystyle{V=288\pi \ \: \text{ft}^3}[/tex]

Therefore, the statement C is also true.

D- The area of the base is 36π ft²

Finding the base's area, our base of cylinder is a circle shape. Therefore, the area of circle is [tex]\displaystyle{A=\pi r^2}[/tex]. Thus:

[tex]\displaystyle{A=\pi \cdot 36}\\\\\displaystyle{A=36\pi \ \: \text{ft}^2}[/tex]

Hence, the statement D is also true.

Therefore, every statements are true. Hence, All of the answers listed are correct answers.

Find an equation of the line.Write the equation in the standard form.
Through (7,3)​; parallel to 8x−y=9.

Answers

As the line is parallel to the given line, the slopes of both lines are equal.

The given line 8x − y = 9 can be written in slope-intercept form as:

y = 8x - 9

Comparing with y = mx + b, we get slope m = 8.

Therefore, the slope of the line we need to find is also 8.

Using the point-slope form of the equation of a line, we have:

y - y1 = m(x - x1)

where (x1, y1) = (7, 3) and m = 8.

Substituting the values, we get:

y - 3 = 8(x - 7)

y - 3 = 8x - 56

y = 8x - 53

This is the equation of the line in slope-intercept form. To convert it to standard form, we move all the variables to the left-hand side:

-8x + y = -53

Therefore, the equation of the line in standard form is:

8x - y = 53.

Write the equation of the line in slope intercept form, that is perpendicular to the line shown and passes through the point J(-1,3).

Answers

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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can someone please do #7

Answers

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.

How to calculate the numeric value of a function or of an expression?

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:

f(a) = a² - 5a + 3.f(h) = h² - 5h + 3.

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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ABCD is a rhombus. A has coordinates (2,- 4) and C (-2, 4). Find the equation of the diagonal
BD.

Answers

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]

8 apple pies and 3 blueberry muffins cost €14.
6 apple pies and a blueberry muffin cost €8.
Work out the total cost of an apple pie and a blueberry
muffin.

Answers

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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AABC DEF. What sequence of transformations will move AABC onto ADEF?

A. A dilation by a scale factor of 2, centered at the origin, followed by
a 90° clockwise rotation about the origin

B. A dilation by a scale factor of centered at the origin, followed by
the translation (x, y) - (x+4, y-2)

C. A dilation by a scale factor of, centered at the origin, followed by
a 180° clockwise rotation about the origin

D. A dilation by a scale factor of 2, centered at the origin, followed by
a reflection over the y-axis

Answers

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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What is the sine of 0?
(Need help)

Answers

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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Firm A calculates the cost of a job using the formula=500+30t,where t represents the number of days to complete the job. Firm B calculates the cost of a job using the formula=260+48t​

Answers

Answer

I think its a

Step-by-step explanation:

In one to two sentences, describe one similarity and one difference between a quota and an embargo.

Answers

A quota is a limit on the number of goods that a country can import or export during a specific time period, while an embargo is an official ban on trade with a particular country or good or service. Unlike a quota, an embargo is much more strict as it completely shuts down the trade, but a quota simply limits the amount of trade.

A quota limits the quantity of a specific product that can be imported, while an embargo prohibits the import or export of a particular product entirely.

The primary similarity between quotas and embargoes is that they both restrict the flow of goods between countries. Both policies are designed to protect domestic industries by limiting foreign competition and promoting local production.

The main difference between quotas and embargoes is the way they achieve their objectives. A quota sets a limit on the quantity of a particular product that can be imported into a country during a specified period. In contrast, an embargo prohibits the import or export of specific goods altogether, typically for political reasons such as national security concerns or human rights violations.

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find the square root of 7

Answers

The value of the square root of 7 is,

⇒ √7 = 2.645

What is mean by Function?

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

WE have to given that;

To find the value of the square root of 7 .

Since, the square root of 7 is,

⇒ √ 7

⇒ 2.645

Thus, The value of the square root of 7 is,

⇒ √7 = 2.645

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logan is buying his baby sister a stacking toy with his allowance. the cost of a wooden stacking toy is $25.50. a plastic stacking toy costs 1/3 the price of the wooden toy. sales tax on either would be 6%. how much more will logan pay if he buys the wooden toy instead of the plastic toy?

Answers

Logan will pay $18.02 more if he buys the wooden stacking toy instead of the plastic stacking toy.

The cost of the plastic stacking toy is 1/3 the cost of the wooden stacking toy:

Cost of plastic toy = (1/3) x $25.50 = $8.50

If Logan buys the wooden toy, he will pay:

Cost of wooden toy = $25.50

To find the amount of sales tax on either toy, we can multiply the cost of the toy by the tax rate of 6%:

Sales tax = 6% x cost of toy

Sales tax on the wooden toy = 6% x $25.50 = $1.53

Sales tax on the plastic toy = 6% x $8.50 = $0.51

If Logan buys the wooden toy, he will pay an extra:

Total cost difference = Cost of wooden toy - Cost of plastic toy + Sales tax on wooden toy - Sales tax on plastic toy

Total cost difference = ($25.50 - $8.50) + ($1.53 - $0.51)

Total cost difference = $17 + $1.02

Total cost difference = $18.02

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A dressmaker just created dresses to be sold. There is a 1/5
chance that they will be sold today, in which case the profit
will be $76. There is a 6/11 chance that they will not be sold, in which case the dressmaker will lose $31. Find the
dressmaker's expected value. Round to the nearest penny.

Answers

Step-by-step explanation:

The dressmaker's expected value can be calculated as follows:

E(X) = (1/5) x $76 + (6/11) x (-$31)

E(X) = $15.20 - $16.36

E(X) = -$1.16

Therefore, the dressmaker's expected value is -$1.16, which means that on average, the dressmaker can expect to lose $1.16 for each dress they create.

If f(x) and g(x) are inverse functions of each other, which of the following shows the graph of f(g(x))?

Answers

Answer:

f(g(x)) = x is the correct graph.

A woman deposits $300 in a savings account that pays 6% annually. If she withdraws all the money in the account after 120 days, how much does she withdraw (rounded to the nearest dollar)?

Answers

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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What are the domain and range for the cube root function graphed below? Justify your answer in complete sentences.

Answers

The domain and range of the cube root function is all real numbers because the cube root of any real number is defined.

The domain of the cube root function is all real numbers because the cube root of any real number is defined. However, in certain situations, such as when the function is being used in a real-world context, there may be practical restrictions on the domain of the function.

The range of the cube root function is also all real numbers because every real number has a unique real cube root. Specifically, the range of the cube root function includes negative and positive real numbers, as well as zero.

It's important to note that the domain and range of a function can be affected by any restrictions or conditions that apply to the function, which may depend on the specific context in which the function is being used. However, for the cube root function as a mathematical concept, the domain and range are as stated above.

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please help me with theses!! need to get it done asap.

Answers

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:

GRADE O7 MATHEMATICS MCA / MATHEMATICS MCA / 22 OF 49
42%
The table shows the average annual precipitation over a 30-year period for 7 states. The values for Michigan and Nebraska are missing.
• When the missing values are included, the range for the data is 18.1.
• The mean of the values for Michigan and Nebraska is 28.2 inches.
• Michigan has a greater amount of annual precipitation than Nebraska.
• Indiana has the greatest average annual precipitation.
What are the missing values?
Drag the numbers into the table.

Answers

Answer:

Michigan: 32.8

Nebraska: 23.6

Step-by-step explanation:


The table shows the average annual precipitation over a 30-year period for 7 states. The values for Michigan and Nebraska are missing.
• When the missing values are included, the range for the data is 18.1.
• The mean of the values for Michigan and Nebraska is 28.2 inches.
• Michigan has a greater amount of annual precipitation than Nebraska.
• Indiana has the greatest average annual precipitation.
What are the missing values?
Drag the numbers into the table.

Answers

The missing values of the average annual precipitation over a 30-year period for Michigan and Nebraska are:

Michigan = 32.8 inchesNebraska = 23.6 inches

What are the average annual precipitations over a 30-year period for Michigan and Nebraska?

The average annual precipitations over a 30-year period for Michigan and Nebraska are calculated as follows:

The range of the data is 18.1 inches

Indiana has the greatest average annual precipitation of 41.7 inches

Hence, the smallest value = 41.7 - 18.1

The smallest value = 23.6 inches

From the table, this would be the value of either Michigan or Nebraska.

Also, the mean of the values for Michigan and Nebraska is 28.2 inches.

Let the unknown value be y

Hence; (23.6 + y) / 2 = 28.2

y = 56.4 - 23.6

y = 32.8 inches

Since Michigan has a greater amount of annual precipitation than Nebraska, the average annual precipitation over a 30-year period for Michigan and Nebraska is 32.8 inches and 23.6 inches respectively.

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Help out, Algebra 1 Math Nation Section 8

Answers

The function g(x)=3a²-4x-1 given represents the quadratic function family.

A quadratic polynomial in mathematics is a polynomial of degree two in one or more variables. The polynomial function defined by a quadratic polynomial is known as a quadratic function.

Prior to the twentieth century, the distinction between a polynomial and its related polynomial function was hazy, therefore "quadratic polynomial" and "quadratic function" were nearly equivalent.

This is still the case in many elementary courses, where both names are sometimes shortened as "quadratic". A quadratic equation is formed when a quadratic function is equated with zero.

The zeros of the appropriate quadratic function are the solutions of a quadratic equation. A quadratic function may have an infinite number of variables.

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If the reaction starts with 35.2 grams of Ca(OH)2 and 20.7 grams of H2SO4, find the limiting reactant and show your work to support your decision.

Answers

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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You're at a clothing store that dyes your clothes while you wait. The store offers
4 different articles of clothing and 3 colors.
If you randomly choose the article of clothing and the color, which of these diagrams can be used to find all of the possible outcomes?
Choose all answers that apply:

Answers

Answer:

Both.

Step-by-step explanation:

They both are the same diagram. Just rearranged.

*WILL GIVE BRAINLIEST!!*
What is m

Answers

Answer: 70

Step-by-step explanation: The circles total angles will be 360. From here we just subtract 360-140-150 to get our answer of 70.

The school asked students to help decide what to name the school gym. Each student was given a list of six names and asked to choose one. What type of graph would be the most appropriate to graph the results?

Answers

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.  

what is the actual lenght if length of drawing is 8.6cm and scale is 1cm of 50km?

Answers

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.

what is the answer? –162 ÷ (–9)

Answers

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

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