Suppose you have fewer than 10 place value blocks. How many different ways could you show 1214?

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Explanation:

We'll need to find the slope of the line through the two given points.

[tex](x_1,y_1) = (-3,17) \text{ and } (x_2,y_2) = (2,-3)\\\\m = \text{slope} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}\\\\m = \frac{\text{y}_{2} - \text{y}_{1}}{\text{x}_{2} - \text{x}_{1}}\\\\m = \frac{-3 - 17}{2 - (-3)}\\\\m = \frac{-3 - 17}{2 + 3}\\\\m = \frac{-20}{5}\\\\m = -4\\\\[/tex]

The slope is -4.

Think of -4 as -4/1. The reciprocal is -1/4, and it flips in sign to +1/4 or simply 1/4.

The original slope -4 leads to the perpendicular slope 1/4. The two slopes multiply to -1. This is true of any perpendicular lines where neither is vertical nor horizontal.

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In short, the answer equation will involve a slope of 1/4. This points us directly to choices A and E as two answers so far.

Something like choice B is not an answer since it has slope 4. Choice C is ruled out because 4x+y = -8 solves to y = -4x-8. It has a slope of -4.

Choice D on the other hand has x-4y = 2 solve to y = (1/4)x - 1/2, and this has a slope of 1/4 that we want. This means choice D is another answer.

Choice F and choice G are ruled out because they involve slopes of 4 and -4 respectively.

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Summary: The 3 answers are choices A, D and E

Step-by-step explanation:

the slope of a line is the ratio

y coordinate change / x coordinate change

when going from one point on the line to another.

so for (-3, 17) and (2, -3) we get

x changes by +5 (from -3 to 2).

y changes by -20 (from 17 to -3).

the slope is

-20/+5 = -4/1 = -4

now, a perpendicular slope (90° to the original slope) is putting the slope fraction upside-down and flips the sign :

+1/4 or simply 1/4.

the slope in an equation of the form "y = ..." is always the factor of x.

y + 2 = (1/4)(x - 1)

yes, there are only some constant additions or subtractions to get to a or "y = ..." form, so 1/4 is indeed the factor of x and the slope of this line.

y = 4x + 12

4 <> 1/4, so, no, it is not.

4x + y = -8

y = -4x - 8

-4 <> 1/4, so, no, it is not.

x - 4y = 2

-4y = -x + 2

y = (1/4)x - 2/4

1/4 is indeed 1/4, so, yes, it is.

y = (1/4)x - 15

1/4 is indeed 1/4, so, yes, it is.

y + 3 = 4(x - 2)

similar to the first one, but 4 <> 1/4, so, no, it is not.

y = -4x + 3

-4 <> 1/4, so, no, it is not.

Answer:

b is increased by 17% : A and E

b is decreased by 17%: H and J

Step-by-step explanation: Took the test hope this helps

Answer:

Step-by-step explanation:

Answer:

97611 is the correct answer

Answer:

$2,631.20

Step-by-step explanation:

We are told that the loan has a simple interest rate of 8% per year. This means that every year that goes on without Kyle paying back the money, he will have to pay an extra 8% of $32,890 as interest.

After one year, he only has to pay back one lot of interest, just 8% of $32,890.

To find that number we can change 8% into a decimal: 8%/100% = 0.08

And then multiply this by the amount of loan money:

0.08 x 32,890 = 2,631.20

Kyle has to pay $2,631.20 of interest at the end of one year.

Hope this helped!

Answer:

4 6/7

Step-by-step explanation:

Part A

Reason:

Divide the side lengths of B over A to get B/A = 3/5. The order is important. The fraction 3/5 is smaller than 1 to indicate a size reduction. There are no units involved with the scale factor.

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Part B

Reason:

The linear scale factor is 3/5. The area scale factor is (3/5)^2 = 9/25. It means if figure A had area 25, then figure B would have area 9.

Let's use that idea to set up the following:

(area of figure B)/(area of figure A) = 9/25

B/A = 9/25

x/15 = 9/25

25x = 15*9

25x = 135

x = 135/25

x = 5.4 represents the area of figure B

Answer:

Step-by-step explanation:
Step 1: Subtract 8cx from both sides of the equation to get

10ax + 9b - 8cx = d

Step 2: Subtract 9b from both sides of the equation to get

10ax - 8cx = d - 9b

Step 3: Multiply both sides of the equation by (-1/10) to get

-8cx/10 = -(d - 9b)/10

Step 4: Add (d - 9b)/10 to both sides of the equation to get

-8cx/10 + (d - 9b)/10 = 0

Step 5: Simplify the left side of the equation to get

x = (9b - d)/80

Therefore, x = (9b - d)/80 is the solution to the equation 10ax + 9b = 8cx + d.

The rate of growth or decay, r, is equal to 0.10.

Population in math refers to the set of all items of interest in a given context. It is the target or focus of a statistical study, and the objects described by the population's characteristics are known as population elements. It is important to define the population in detail before analyzing data and drawing conclusions. Examples of populations can include all students at a school, all people living in a particular country, or all people who bought a particular product.

So each year the number of residents in the town is 1.10 times the number in the previous year.

There were around 14,641 residents in the town 14 years after 2005.

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Answer:

x=-1

Step-by-step explanation:

y=kx

18=-3*k

k=-6

6=x*-6

x=-1

Answer:

x=-+1

Step-by-step explanation:

Answer:

-1

Step-by-step explanation:

Night: -4
Morning: -4 + 3 = -1

Answer:

6). x + 70° + 70° = 180°

x + 140° = 180°

x = 180° - 140° = 40°

Therefore x is equal to 40°

7). y + 55° +60° = 180°

y + 115° = 180°

y = 180° - 115° = 65°

Therefore x is equal to 65°

8). n + n + 50° = 180°

2n + 50° = 180°

2n = 180° - 50° = 130°

n = 130°/2 = 65°

Therefore both the angles are 65°

Explaination:

All the angles of a triangle always add up to 180°

Answer:

x = (3/5, -3/5)

Answer:

60%

Step-by-step explanation:

Answer:

The answer is 60%

Step-by-step explanation:

The question tells us to find the probability of male sophomore students. From the question we know that the total number of sophomore students are 10 (6 male + 4 female). The probability is # of male student over the total # of sophomore students which is 6/10 = 0.6 now we multiply is it by 100% which gives us 60% (0.6 x 100% = 60%) as our answer.

Answer:

✔ 1

5-foot by 4-foot face(s)

✔ 2

5-foot by 3-foot face(s)

✔ 2

4-foot by 3-foot face(s)

Step-by-step explanation:

EDGE 2021

The faces that must be included are two faces that measure 5ft*3ft = 15 ft², another two faces that measure 4ft*3ft = 12ft², and one face that measures 5ft*4ft = 20ft².

For the pool, we need to consider the four lateral face and the bottom face . (not the top, as it is a hole actually).

So if we have:

Then we have two faces that measure 5ft*3ft = 15 ft², another two faces that measure 4ft*3ft = 12ft², and one face that measures 5ft*4ft = 20ft².

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Answer:

d=12.5

Step-by-step explanation:

.......................................

Answer:

0.44, or 8/18

Step-by-step explanation:

The probability of it being blue is 8/18 or 0.444... (0.44)

Answer:

125.54%

Step-by-step explanation:

160.7/128 = 1.2554

1.2554 *100 = 125.54%

Answer:

4

Step-by-step explanation:

The coefficient is 4 because it is the amount placed before a variable. The variable is the x, therefore, the coefficient is the 4, the amount placed before the x.

Hope this helps! :)

Answer:

350(6) / 48 = 43.75

Step-by-step explanation:

40$ per hour.

Answer:

the answer is 7

Step-by-step explanation:

because 7×31=217 so that means she wrote 7 pages each day for 31 days

Answer: a lot

Step-by-step explanation:

Answer:

ummmm none? maybe

Step-by-step explanation:

Answer: 130

Step-by-step explanation:

The original price of the sweater is $303.

A discount is the reduction of either the monetary amount or a percentage of the normal selling price of a product or service.

Given that, June is buying a sweater using a coupon offering a 30% discount on items over $99.

The discounted price is $91

Let the original price of the sweater be x.

So, 30% of x=91

30/100 ×x=91

0.3x=91

x=91/0.3

x=$303

Therefore, the original price of the sweater is $303.

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Answer: Simplify the expression.

6.1b − 4.9

Answer:

a) Angle XBC = 55° because it is a corresponding angle to 55°

b) angle BXC = 70°

Step-by-step explanation:

ΔXBC is an isosceles triangle because XB = XC

∠XCB = ∠XBC because ΔXBC is an isosceles triangle

∠BXC = 180° - 55° - 55° = 70° because the sum of all the interior angles of a triangle - 180°

Answer:

b) BXC=70

Step-by-step explanation:

a)

Angle XBC = 55° as XY and BD are parallel lines, the interior angles on the same side of a transversal are supplementary hence the same.

b)

Triangle BXC is isosceles when XBC and XCB are both 55°

XBC+XCB+BXC= 180° (sum of angles of triangle)

55°+55°+BXC=180°

110°+BXC= 180°

BXC= 180°-110°

BXC= 70°

Radical form is rather simple. It refers to the form of a number or algebraic expression where the number or expression is contained under a radical. The answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].

Simply put, simplifying a radical eliminates the need to find any more square roots, cube roots, fourth roots, etc. when expressing it in its simplest radical form. Additionally, it entails eliminating any radicals from the denominator of a fraction.

A radical notation is an expression that makes use of a root, such as the square or cube root.

The fundamentals of radical form are simple. When a numerical or algebraic expression is under a radical, the term refers to that version of the expression. To improve that, we can manipulate a number or an algebraic expression in radical form to convert it to simplest radical form.

[tex]\text { Simplify }-x \sqrt{2} 8+10 \sqrt{6} 3 x^2:-\\\\8 \sqrt{2} x+30 \sqrt{6} x^2 -x \sqrt{2} \cdot 8+10 \sqrt{6} \cdot 3 x^2 \\\\& =-8 \sqrt{2} x+30 \sqrt{6} x^2\end{aligned}$$[/tex]

Therefore, the answer is [tex]$-8 \sqrt{2} x+30 \sqrt{6} x^2$[/tex].

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Answer:

a + b

Step-by-step explanation:

Theorem:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the remote interior angles.

x = a + b

Answer:

It is a solution

Step-by-step explanation:

Given

[tex]y + 4 > 3x-1[/tex]

Required

Is [tex](-1,4)[/tex] a solution

[tex](-1,4)[/tex] implies that:

[tex]x=-1\ \ \y = -4[/tex]

Substitute in:

[tex]y + 4 > 3x-1[/tex]

[tex]-4 + 4 > 3 * -1 -1[/tex]

[tex]-4 + 4 > -3 -1[/tex]

[tex]0 > -4[/tex]

The above inequality is true.

Hence, [tex](-1,4)[/tex] is a solution y + 4 > 3x-1