what is the length of a short leg of a 30-60-90 triangle shown below?

Answer:

the Answer is:

△DEF is congruent to △D′E′F′ because the rules represent a translation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

I got 100% on the quiz

The two triangles ΔPQR and ΔP'Q'R' are congruent.

A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.

The statement that correctly describes the relationship between △PQR and △P′Q′R′ is:

2. △PQR is congruent to △P′Q′R′ because you can map △PQR to △P′Q′R′ using a reflection across the y-axis, which is a rigid motion.

From the attached graph we can observe that the given Triangle PQR is reflected across the y-axis.

In this case, a translation, a reflection across the x-axis, but a reflection across the y-axis can map △PQR onto △P′Q′R′. Therefore, the two triangles are congruent.

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Answer:

-3

Step-by-step explanation:

Solution of the equation is y = -3.

What is the solution of the equation?

A solution to an equation is a value of a variable that makes a true statement when substituted into the equation. The process of finding the solution to an equation is called solving the equation.

Given expression (3/4)y+1/4= 1+y.

simplify each term,

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

Move all terms not containing y to the right side of the equation,

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

(-1/4)y = 3/4

Since  both side of the expression has the same denominator, the numerators must be equal.

y = -3

Solution of the equation is y = -3.

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Answer:

[tex]\frac{7}{10} ,0.7[/tex]

Reasoning:

Do the inverse of adding 4/5 to isolate and find a.

[tex]1\frac{1}{2} - \frac{4}{5} =\frac{7}{10}[/tex]

Decimal Form:

[tex]1.5-0.8=0.7[/tex]

Answer:

  a = 0.7 = 7/10

Step-by-step explanation:

Subtract 4/5 from both sides.

  a + 4/5 = 1 1/2

  a + 0.8 = 1.5

  a + 0.8 -0.8 = 1.5 -0.8 . . . . subtract 4/5 from both sides

  a = 0.7 = 7/10

_____

If you like, you can solve this a couple of other ways:

1) Solve it as an integer problem.

  10a +8 = 15 . . . . . . multiply the given equation by 10 to clear fractions

  10a = 7 . . . . . . . . subtract 8

  a = 7/10 . . . . . . divide by 10

2) Use a common denominator

  a +8/10 = 1 5/10

  a = 1 5/10 -8/10 . . . . . subtract 8/10

  a = 15/10 -8/10 = (15 -8)/10 = 7/10 . . . . . convert to improper fraction

__

Additional comment

It is a good idea to get comfortable working with numbers in any form in which they are presented: decimal, fraction, mixed number, scientific notation, percentage. Knowing how to convert between forms is essential.

Answer:

The answer is B

Answer:

100,000 × 1,000,000 = 1.E11

Answer:

100000000000

Step-by-step explanation:

Step-by-step explanation:

it's 42.85 percent that you can say 42 or maybe 43

Answer:

Step-by-step explanation:

Let the numbers are x and y.

Their difference is:

Sum of their squares:

Substitute y = x - 6 into sum equation:

We observe this is a quadratic expression. It has minimum value at vertex, which is when x = -b/2a or:

Then the value of y is:

Answer:

x=6.7

Step-by-step explanation:

In relation to the given angle, we are given the triangle's opposite side and hypotenuse. Therefore, we use the sine function to set up a proportion and solve for x:

[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]

[tex]sin(31^\circ)=\frac{x}{13}[/tex]

[tex]13sin(31^\circ)=x[/tex]

[tex]x=13sin(31^\circ)[/tex]

[tex]x\approx6.7[/tex]

So, the opposite side is about 6.7 inches

42 square inches.

Step-by-step explanation:

A = 1/2 b × h

A = 1/2 x 12 x 7

A = 6 × 7

A = 42

Answer:

See answer below.

Step-by-step explanation:

Pick any two ordered pairs that is on the given graph line.

The  Slope = (the change in the y-values)/(the change in the x-values) or

Answer:

Step-by-step explanation:

If the copy made by Xerox's machine is same size as the original, the scale factor will be 1.

Recall:

Let's assume that one of the dimension of the original copy is 4 inches.

If the new copy is of exact same size as the original copy, therefore the new copy will still have a dimension of 4 inches.

Thus:

Scale factor = 4/4 = 1

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Answer:

Answer: -7

Step-by-step explanation:

The roots at which the graph of f(x) =(x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] cross the x axis are -4 and -7.

In mathematics, a root is a solution to an equation that is usually stated as a number or an algebraic formula.

A quadratic equation's roots are the variable values that fulfil the equation. They are also referred to as "solutions" or "zeroes" of the quadratic equation.

We have If(x) = (x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] cross the x-axis then y = f(x) = 0.

Now, if f(x) = 0

then (x + 4[tex])^6[/tex](x + 7[tex])^5[/tex] = 0

Now, calculating in separate the value of x as

x +4 =0 and x+ 7= 0

x = -4 and x = -7

Thus, the roots cross x axis at -4 and -7.

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Answer:

2 and 3

Step-by-step explanation:

20/12 = 1.6666666

15/9 = 1.6666666

Answer:

3/4 or 0.75

Step-by-step explanation:

[tex] \frac{3 }{8} + \frac{3}{8} [/tex]

transform the equation

[tex] \frac{3 + 3}{8} [/tex]

calculate

[tex] \frac{6}{8} [/tex]

simplify

[tex] \frac{3}{4} [/tex]

or 0.75

Answer:

Step-by-step explanation:

Let pineapple  = x, orange = y

A pineapple is 7 times as heavy as an orange:

The pineapple also weighs 870 grams more than the orange:

Compare the two equations above:

Find the value of x:

[tex]\huge \bf༆ Answer ༄[/tex]

Weight of pineapple :

[tex] \boxed{ \sf1015 \: g}[/tex]

Weight of Orange :

[tex] \boxed{ \sf145 \: g}[/tex]

[tex]꧁  \:  \large \bf{ Kaul } \: ꧂[/tex]

Answer: $459 each month

Step-by-step explanation:

Paisley's mom is paying the loan of $22,032 in 48 equal monthly payments.

In order to find how much each month's payment would be you divide the loan by 48.

22,032 ÷ 48 = 459

Paisley's mom would need to pay $459 each month for 48 months to pay off her loan.

The polynomial that gives the interest earned after a year will have variables, exponents and constants that are joined by operators.

Reasons:

The amount Paul has to invest = $900

The annual interest rate from the savings account = 1.8%

The amount the money market account pays per year = 4.2 %

Required: The polynomial for the interest Paul earned by investing x dollars in the savings account.

Solution:

The interest earned is found using the compound interest formula as follows;

[tex]\displaystyle A = \mathbf{P \cdot \left(1 + \frac{r}{n} \right)^{n \cdot t}}[/tex]

Where;

A = The amount in the account after one year

P = The original amount invested = x

r = The interest rate offered on the investment = 1.8% = 0.018

t = The time of the investment = 1 year

n = The number of times of application of the interest per period = Once per year

Which gives;

Interest = Amount earned = A - P

Therefore;

[tex]\displaystyle Interest, \ I = \mathbf{P \cdot \left(1 + \frac{r}{n} \right)^{n \cdot t} - P}[/tex]

Plugging in the values gives;

[tex]\displaystyle I = x \cdot \left(1 + \frac{0.018}{1} \right)^{1 \times 1} - x = x \cdot 1.018^1 - x = 1.018 \cdot x - x = 0.018 \cdot x[/tex]

The polynomial equation is therefore;

Interest, I = 0.018·x

Using the simple interest formula, we have;

[tex]\displaystyle Interest = \mathbf{\frac{P \times r \times t}{100}}[/tex]

Which gives;

[tex]\displaystyle Interest = \frac{x \times 1.8 \times 1}{100} = 0.018 \cdot x[/tex]

Interest earned by investing in the savings account for one year, I = 0.018·x

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Answer:

We write it as $1841.67 (Rounded)

Step-by-step explanation:

The 7 will round up to the hundredths (0.01) place.

Hoped this helped.

Answer:Frogs

I think so…If it’s wrong and you can tell me and I’ll try correct it

Hope its correct!

;)

Have a great day!

Answer:

n + 23

24,25,26,27,28,29,30,...

Based on the information given the new balance is $283.15.

Using this formula

New balance=Principal+ [Principal ×(APR/12)]+New transaction

Where:

Principal=$200.15

APR=15%

New transaction=$80.50

Let plug in the formula

Let plug in the formula

New balance=$200.15+($200.15×(0.15/12)+$80.50

New balance=$200.15+$2.50+$80.50

New balance=$283.15

Inconclusion  the new balance is $283.15.

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Answer:

perimeter=32t units

Step-by-step explanation:

let:

a=8t-2

b=8t+2

perimeter=2(a+b)

Subtitute values of a and b:

=2(8t-2+8t+2)

=2(16t)

=32t units

Answer:

The answer I'd 28464835383637533

Answer:

No, does not pass the vertical line test

Step-by-step explanation:

Answer:

No.

Step-by-step explanation:

A function is a relation in which that one x-value (input) is related to exactly one y-value (output). For relations shown on graphs, we can use the vertical line test.

Since the line would intercept at 2 points in the graph at one point, it is not a function.

Hope this helps.