What is the area of this triangle?
y
5
D
4
F
Enter your answer in the box.
3
2
1
E
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The expressions are irrational 1/3 + √216 and √64+ √353 and the expressions √100 × √100, 13.5 + √81, √9 + √729, and 1/5 + 2.5 are rational number.

If the value of a numerical expression is terminating then they are the rational number then they are called the rational number and if the value of a numerical expression is non-terminating then they are called an irrational number.

1.  √100 × √100

→ √100 × √100

→ 10 × 10 = 100

This is a rational number.

2.  13.5 + √81

→ 13.5 + √81

→ 13.5 + 9 = 22.5

This is a rational number.

3.  √9 + √729

→ √9 + √729

→ 3 + 27 = 30

This is a rational number.

4.  √64+ √353

→ √64 + √353

→ 8 + √353

This is an irrational number.

5.  1/3 + √216

→ 1/3 + √216

→ 1/3 + √216

This is an irrational number.

6.  1/5 + 2.5

→ 1/5 + 2.5

→ 0.2 + 2.5 = 2.7

This is a rational number.

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Answer:

A, B, C, F

Step-by-step explanation:

edge

The number of days Ashley ate Mexican food while on vacation is 20 days.

The first step is to determine the fraction of the number of days Ashley atae Mexican food. In order to do this, divide 4 by 7

4/7.

The second step is to multiply 4/7 by 35

4/7 x 35= 20 days

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Answer:

Side A is 4

Step-by-step explanation:

Answer:

A.4

Step-by-step explanation:

a = √(c² - b²)

a= √(5² -3b²)=4

Answer:

x=7   y= -3

Step-by-step explanation:

When you ADD both the x variable is cancelled

since -3x + 3x = zero

then you solve for y  And when you plug the value of y you will solve x

     2y-3x =-27

     5y+3x =6

   ADD BOTH

    7y = -21

    y = -3

     PLUG y

5(-3)+3x  = 6

 -15 + 3x = 6

     3x = 21

      x=7

Answer: pretty sure the answer is D

Step-by-step explanation:

Answer:

1440 ounces

Step-by-step explanation:

there are 16 ounces in a pound so multiply 90 by 16 and you get 1440 hope this helps!

Answer:

x = 17.82

Step-by-step explanation:

6x + 8% = 107    

      -8%    -8%

or

107 - 0.08 = 106.92

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

6x = 106.92

÷6      ÷6

x = 17.82

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

I hope this helps!

Answer:

62.5 miles per hour

Step-by-step explanation:

Assuming she had the same speed the whole time and never stopped, just divide the miles driven by the time to get miles per hour. 437.5/7 = 62.5, so she drove 62.5 miles per hour.

Hopefully this helps- let me know if you have any questions!

Answer:

d 115.9

Step-by-step explanation:

The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D)

In this question we must apply the concept of compound interest to derive the initial investment to be done by Calvin. According to the statement, Calvin invests money five years later than Marquez.

To determine the initial investment to be deposited by Calvin such that his investment equals Marquez's investment at any time we resort to the following expression:

[tex]1500\cdot (1+0.03)^{t+5} = C_{C}\cdot (1+0.03)^{t}[/tex]     (1)

Then, we simplify the required initial investment:

[tex]C_{C} = 1500\cdot (1+0.03)^{5}[/tex]

[tex]C_{C} = 1738.911[/tex]

And the increase factor is:

[tex]r_{C} = \frac{1738.911}{1500}\times 100\,\%[/tex]

[tex]r_{C} = 115.927\,\%[/tex]

The initial investment of Calvin must be increased by a factor of 115.927 % to equal Marquez's investment at any time. (Correct choice: D) [tex]\blacksquare[/tex]

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Answer:

[tex]\frac{1}{2}x[/tex]

Step-by-step explanation:

If the greater number is x and it is two times greater than the other number then the other number is half as big.  This is true because 2*[tex]\frac{1}{2}[/tex]x = x

The other number is equal to x/2.

A fraction in mathematics represents a portion or element of the whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator.

As per the given data:

We are given the relationship between 2 numbers, It's given that One number is two times greater than another number.

The greater number = x

Let's assume that the smaller number is y.

From the given data in the question:

One number is two times greater than another number

= x = 2y ...(i)

The other number that is the smaller number is given by:

By dividing eq (i) by 2 from both sides.

y = x/2

The other number is equal to x/2

Hence, The other number is equal to x/2

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Answer:

5 feet

Step-by-step explanation: 60 divided by 12 inches is 5 feet

Step-by-step explanation:

288÷60(60 minutes in an hour) = 4.8

is this what you asked for?

Answer:

Step-by-step explanation:

A set of factors of a number (N) is a set of integers {f1, f2, f3, ...} whose product is the number:

  f1 × f2 × f3 × ... = N

Often the term "factors" is used to mean "prime factors," the set of prime numbers whose product is N.

When N = 25, the prime factors are {5, 5}. That is ...

  5×5 = 25

__

A "divisor" of a number is a sub-multiple of N. That is, the quotient N/k is an integer for some divisor k of N. Usually, we're interested in integer divisors. All prime factors will be integer divisors of N. The term "factor" is often used when the term "divisor" is meant.

Divisors of N = 25 include 1, 5, and 25. There will be an odd number of integer divisors (as here) if the number N is a perfect square.

__

For an integer k, the value k×N is called a multiple of N, often, the k-th multiple of N.

Multiples of 25 include 25, 50, 75, 100, 125, and any other decimal number ending in 25, 50, 75, or 00.

__

Another example

When N=30, the prime factors are {2, 3, 5}. The divisors are {1, 2, 3, 5, 6, 10, 15, 30}. (Note there are an even number of divisors.) Multiples of 30 include 30, 60, 90, 120, ....

Answer:

2, 0.2, 0.02

The first number is 2000.  The term to term rule is 'divide by 10'.

Step-by-step explanation:

To calculate the next term, divide the previous term by 10:

2000 ÷ 10 = 200

200 ÷ 10 = 20

Therefore, the next three terms will be:

20 ÷ 10 = 2

2 ÷ 10 = 0.2

2 ÷ 10 = 0.02

Term to term rule

To work out the term to term rule, give the initial number of the sequence and then describe the pattern:

The first number is 2000.  The term to term rule is 'divide by 10'.

Answer:

0.125 = ⅛

Step-by-step explanation:

Both are equal.......

Answer:

94%

Step-by-step explanation:

400-24=376

Find 376 out of 400 as a decimal:

376/400 = 0.94

0.94x100 = 94%

Based on the equidistant chords theorem, the value of m and n in the circle are:

m = 7/4 = 1.75

n = 1/2 = 0.5

The equidistant chords theorem states that, two chords are congruent if they are equidistant to the center of the same circle.

Given:

Thus, since US = RU, therefore chords PO and EW are congruent based on the equidistant chords theorem.

Therefore:

3m + 2 = -m + 9

Add like terms

3m + m = -2 + 9

4m = 7

m = 7/4

m = 1.75

20n - 14 = -2(2n + 1)

20n - 14 = -4n - 2

20n + 4n = 14 - 2

24n = 12

n = 12/24

n = 1/2 = 0.5

Therefore, based on the equidistant chords theorem, the value of m and n in the circle are:

m = 7/4 = 1.75

n = 1/2 = 0.5

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Answer:

Min = 2

Q1 = 4

Median = 11

Q3 = 16

Max = 18

Step-by-step explanation:

2, 4, 4, 7, 10, 11, 12, 13, 16, 17, 18

       Q1         Q2           Q3

Min (minimum value) = 2

Q1 = 4

Median (middle value Q2) = 11

Q3 = 16

Max (maximum value) = 18

Answer:

[tex]\frac{5}{36}[/tex]

Step-by-step explanation:

the total number of possible combinations of rolling two dice is 36 because a side has 6 sides and [tex]6^{2}=36[/tex]

and possible combinations that sum to 8 are

which are 5 possible combinations which gives [tex]\frac{5}{36}[/tex]

Answer:

[tex]x < -3\quad \mathrm{or}\quad \:x > 3[/tex]

Step-by-step explanation:

Given:

[tex]9-x^2 < \:0[/tex]

Solve:

[tex]\mathrm{Subtract\:}9\mathrm{\:from\:both\:sides}[/tex]

[tex]9-x^2-9 < 0-9[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-x^2 < -9[/tex]

[tex]Multiply\:both\:sides\:by\:-1\:[/tex]

[tex]\left(-x^2\right)\left(-1\right) > \left(-9\right)\left(-1\right)[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]x^2 > 9[/tex]

[tex]\mathrm{For\:}u^n\: > \:a\mathrm{,\:if\:}n\:\mathrm{is\:even}\mathrm{\:then\:}u\: < \:-\sqrt[n]{a}\:or\:u\: > \:\sqrt[n]{a}[/tex]

[tex]x < -\sqrt{9}\quad \mathrm{or}\quad \:x > \sqrt{9}[/tex]

[tex]\sqrt{9}=3[/tex]

[tex]x < -3\quad \mathrm{or}\quad \:x > 3[/tex]

~lenvy~

Answer:

78.1428571429

Step-by-step explanation:

Answer:

t = 9

Step-by-step explanation:

the sum of the exterior angles of a polygon is 360°

sum the exterior angles and equate to 360

10t + 16t + 53 + 73 = 360 , that is

26t + 126 = 360 ( subtract 126 from both sides )

26t = 234 ( divide both sides by 26 )

t = 9

So

Now

The required probability

[tex]\\ \rm\rightarrowtail P(A')^{10}\times P(A)^5\times ^{15}C_{10}[/tex]

[tex]\\ \rm\rightarrowtail (0.33)^{5}\times (0.67)^{10}\times \dfrac{15!}{5!10!}[/tex]

[tex]\\ \rm\rightarrow 0.0039(0.0182)\times\dfrac{15(14)(13)(12)(11)10!}{5!10!}[/tex]

[tex]\\ \rm\rightarrowtail 0.00007098\times \dfrac{360360}{120}[/tex]

[tex]\\ \rm\rightarrowtail 0.00007098(3003)[/tex]

[tex]\\ \rm\rightarrowtail 0.213[/tex]

So probability

Option B

Answer:

b.  21.4 % (nearest tenth)

Step-by-step explanation:

P(lose) = 33% = 0.33

P(win) = 1 - 0.33 = 0.67

Using binomial distribution X ~ B(n, p)

where n is the number of trials and p is the probability of success

⇒ X ~ B(15, 0.67)

Binomial probability formula:

[tex]\sf P(X=x)= \ _nC_x\cdot p^x \cdot(1-p)^{n-x}[/tex]

[tex]\sf \implies P(X=10)=15C10\cdot 0.67^{10} \cdot(1-0.67)^{15-10}[/tex]

                       [tex]\sf =3003 \cdot 0.67^{10} \cdot 0.33^5[/tex]

                       [tex]\sf =0.214226434...[/tex]

Converting to percentage:

0.214266434... x 100% = 21.4 % (nearest tenth)

rate of change:

[tex]\sf \bold{\dfrac{y_2-y_1}{x_2-x_1} }[/tex]

coordinates taken: (0, 0), (2, 1)

[tex]\rightarrow \dfrac{1-0}{2-0}[/tex]

[tex]\rightarrow \dfrac{1}{2}[/tex]

Take 2 points

[tex]\\ \rm\rightarrowtail m=\dfrac{1+1}{2+2}[/tex]

[tex]\\ \rm\rightarrowtail m=\dfrac{2}{4}[/tex]

[tex]\\ \rm\rightarrowtail m=\dfrac{1}{2}[/tex]

The length of the diagonal of Bob’s TV will be 50 in.

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

Bob’s rectangular TV is 40 inches wide and 30 inches high.

Now,

Since, TV is in rectangular shape.

Hence, It satisfy the Pythagoras theorem.

Let the length of the diagonal of Bob’s TV = x

So, We can formulate;

⇒ x² = 40² + 30²

⇒ x² = 1600 + 900

⇒ x² = 2,500

⇒ x = √ 2,500

⇒ x = 50 in

Thus, The length of the diagonal of Bob’s TV = 50 in.

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Answer:

91 degrees

Step-by-step explanation:

Angle RT = 46 degrees

Angle RU = 180 degrees

Angle RS = 89 degrees

So 46 + 89 = 135

180 - 135 = 45

So Angle UT = 45 degrees

Which means that Angle QR = 45 degrees also because they are vertical from each other

So you add 45 + 46 = 91

Angle TQS = 91 degrees

By defining that h(t) = 0 means that the ball is in the ground, we conclude that the ball is thrown at t = 0, and hits the ground again at t = 2.

The height equation is:

h(t) = -14*t^2 + 28*t

When t = 0, we have: h(0)  = 0

So it is in the ground, meaning that it is thrown at the time t = 0.

We need to find the other root of the quadratic equation, so we need to solve:

-14*t^2 + 28*t = 0

We can rewrite this as:

t*(-14*t + 28) = 0

The parenthesis is zero when:

-14*t + 28 = 0

t = 28/14 = 2

So at t = 2, the ball hits the ground.

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solution:

[tex]\frac{299}{6}=49\frac{5}{6}[/tex]

decimal result:

[tex]49.833[/tex]

1. Simplify the expression

[tex]26/3*23/4[/tex]

Multiply the fractions:

[tex]\frac{\left(26\cdot23\right)}{\left(3\cdot4\right)}[/tex]

Cancel terms:

[tex]\frac{\left(13\cdot23\right)}{\left(3\cdot2\right)}[/tex]

Simplify the arithmetic:

[tex]\frac{299}{\left(3\cdot2\right)}[/tex]

Simplify the arithmetic:

[tex]\frac{299}{6}[/tex]

Simplify the fraction:

[tex]\frac{299}{6} =49\frac{5}{6}[/tex]

[tex]==========================================[/tex]

First, let's convert the mixed numbers into improper fractions:-

[tex]\bf{8\displaystyle\frac{2}{3}[/tex]

[tex]\displaystyle\frac{26}{3}[/tex]

Now, do the same for the second fraction:-

[tex]\displaystyle\frac{23}{4}[/tex]

Now, the formula for the area is

[tex]\bold{A=bh}[/tex]

We know both b and h, so we can just plug in the values and solve:

[tex]\bold{A=\displaystyle\frac{26}{3} *\frac{23}{4} }}[/tex]

Actually, we can reduce some fractions here (we can divide 26 and 4 by 2)

[tex]\bold{\displaystyle\frac{13}{3} *\frac{23}{2}}[/tex]

Multiplying 13 times 23 is easier than multiplying 26 times 13.

Now, this can only be done if the numbers do have some common factors. Both fractions are now in simplest form; 13, 23, 3 & 2 don't have common factors.

Multiply:

[tex]\bold{\displaystyle\frac{13*23}{3*2}}}[/tex]

The answer is

[tex]\bold{\displaystyle\frac{299}{6}}[/tex]

Convert to a Mixed Number:-

[tex]\bold{49\displaystyle\frac{5}{6}}[/tex]

[tex]==================================[/tex]

Nickname:- [tex]\mathbb{DiAmOnD}[/tex]

[tex]\boxed{An~emotional~helper}[/tex]

Answer:

the correct answer is the second