Catalina and Morgan are finding the length of the third side of the right triangle. Who is correct? Explain your reasoning.

Answer:

20

Step-by-step explanation:

Plug in -4 for n:

(-4)^2 - (-4) = 16 + 4 = 20

Applying the negative exponent, it is found that the equivalent expression to [tex]3^{-3}[/tex] is [tex]\frac{1}{27}[/tex].

When we have a negative exponent, we use a fraction, with the term with the exponent going to the denominator, as follows:

[tex]a^{-b} = \frac{1}{a^b}[/tex]

Hence, in this problem, the equivalent expression is:

[tex]3^{-3} = \frac{1}{3^3} = \frac{1}{27}[/tex]

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Let the numbers be x and x/7

Now

The numbers are

Answer:

7x+X=824

8X/8=834/8

x=108

Step-by-step explanation:

hope I helped

When reflected over ry-axis (x, y) (-x, y) , rx-axis (x, y) (x,-y) , Option A and D is the correct answer.

The rule for reflection is when an object or a coordinate point is reflected over x axis then the coordinate of the x axis remains the same while the y coordinate changes to be additive inverse.

Vice Versa happens when reflected over y axis.

So,

rx-axis (x, y) - (-x, y) --> (x,-y)

ry-axis (x, y) (-x, y)

Therefore Option A and D is the correct answer.

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Answer: its A not A & D

Step-by-step explanation:

The number ab², where a and b are prime numbers, has 6 divisors.

Remember that any number can be written as a product of primes, for example, 15 can be written as:

15 = 3*5

Where 3 and 5 are primes.

Such that the divisors of 15 are the factors made with the primes on the right side.

So for the number:

N = a*b^2 = a*b*b

The divisors are:

a, b, a*b, b*b

And trivially, itself and 1, so there are a total of 6 divisors.

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The average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.

Since the arrival rate and service rate follow a Poisson distribution, we can use the Poisson arrival rate formula to calculate the average queue length.

Average queue length = (arrival rate * service time) / (1 - arrival rate * service time)

For the given problem, the average queue length is:

Average queue length = (50 * 35) / (1 - 50 * 35)

= 175

Since the average queue length is greater than 10 students, the introduction of an extra checkpoint is justifiable.

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Answer:

7 units

Step-by-step explanation:

The short leg is opposite the 30 degree angle

sin 30 = opposite side/ hypotenuse

Hypotenuse * sin 30 = opposite side = 14 * 1/2 = 7 units

The annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.

It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount of borrowed amount.

We have:

You have loaned a friend $100 and will charge him 5% annually.

As we know:

A = P(1 + rt)

P = $100

r = 5% = 0.05

t = 1 years

A = 100(1 + 0.05×1)

A = $105

I = A - P = 105 - 100 = $5

Thus, the annual interest would be $5 if you have loaned a friend $100 and will charge him 5% annually and the total amount would be $105.

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Answer:

$324

Step-by-step explanation:

let x be the amount of money she had at first , then

[tex]\frac{1}{3}[/tex] x + [tex]\frac{1}{9}[/tex] x = 144 ( multiply through by 9 to clear the fractions )

3x + x = 1296

4x = 1296 ( divide both sides by 4 )

x = 324

she had $324 at first

[tex]5(1-x)=20\\5-5x=20\\5x=-15\\x=-3[/tex]

Hii!

__________________________________________________________

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Answer}}}\circ\leftharpoonup[/tex]

The value of x is -3! ^^

[tex]\stackrel\star{\rightsquigarrow\circ\boldsymbol{\underbrace{Explanation}}}\circ\leftharpoonup[/tex]

[tex]\bullet[/tex] First multiply 5 times 1 and -x

[tex]\twoheadrightarrow\sf 5(1-x)=20[/tex]

[tex]\twoheadrightarrow\sf 5-5x=20[/tex]

[tex]\bullet[/tex] Now subtract 5 from both sides

[tex]\twoheadrightarrow\sf -5x=15[/tex]

[tex]\bullet[/tex] Now divide both sides by -5

[tex]\twoheadrightarrow\sf x=-3[/tex]

--

Hope that this helped! Best wishes.

--

[tex]{\huge \underline{{ \fbox \color{red}{A}}{\fbox \color{green}{n}}{\fbox \color{purple}{s}}{\fbox \color{brown}{w}}{\fbox \color{yellow}{e}}{\fbox \color{gray}{r } }}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bf \red{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{3}{4} }[/tex]

Step by step explanation :-

The only thing you have to do is add the numerator to the denominator, in this case you have to add the first ones from the front, which can be these 2+1/4, which would result in 3/4, and this is called the Commutative Property.

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \gray{ \dfrac{1}{2} + \dfrac{1}{4} = \dfrac{1}{4} + \dfrac{1}{2} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \bf \green{\dfrac{2 + 1}{4} = \dfrac{1 + 2}{4} }}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{3}{4} = \dfrac{3}{4}} }[/tex]

Answer :- The answer is 3/4

¿What is commutative property?

It is to change different ways in order of the addends the result would be the same.

Example :-

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed {\bf \blue{\dfrac{a}{b} + \dfrac{c}{d}} = {\dfrac{c}{d} + \dfrac{a}{b}} }[/tex]

I hope I've helped : )

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: Final \:\: value = \cfrac{3}{4}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{1}{2} + \cfrac{1}{4} [/tex]

[ take LCM ]

[tex]\qquad \tt \rightarrow \: \cfrac{2}{4} + \cfrac{1}{4} [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{2 + 1}{4} [/tex]

[tex]\qquad \tt \rightarrow \: \cfrac{3}{4} [/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex]4x + 7 - (x + 6) = 68 \\ \\ 4x + 7 - x - 6 = 68 \\ \\ 3x + 1 = 68 \\ \\ 3x = 68 - 1 \\ \\ 3x = 67 \\ \\ x = \frac{67}{3} \\ \\ x = 22.3[/tex]

The value of x is 67/3 or 22.3 .

Hi!

__________________________________________________________

[tex]\rightsquigarrow\circ\boldsymbol{Answer}\circ\leftharpoonup[/tex]

x=

[tex]\rightsquigarrow\circ\boldsymbol{Explanation}\circ\leftharpoonup[/tex]

First let's distribute the minus sign.

[tex]\twoheadrightarrow\sf 4x+7-x-6=68[/tex]

[tex]\bullet[/tex] Add 6 to both sides

[tex]\twoheadrightarrow\sf 4x+7-x=74[/tex]

[tex]\bullet[/tex] Subtract the x's

[tex]\twoheadrightarrow\sf 3x+7=74[/tex]

[tex]\bullet[/tex] Subtract 7 from both sides

[tex]\twoheadrightarrow\sf3x=67[/tex]

[tex]\bullet[/tex] Divide both sides by 3

[tex]\twoheadrightarrow\sf x=\cfrac{67}{3}[/tex]

[tex]\bullet[/tex] Great job! We solved for the variable

--

Hope that this helped! Best wishes.

[tex]\textsl{Reach far. Aim high. Dream big.}\\\boldsymbol{-Greetings!-}[/tex]

--

Step-by-step explanation:

simply count them.

there are 7 little rectangles building the whole.

from these 7, 4 are gray and 3 are white.

so, 3 of 7 are white.

that means,

3/7 of all the parts are white.

Answer:

Yes, she passes with 80%

Step-by-step explanation:

4 divided by 5 = 0.8

0.8 multiplied by 100 = 80%

80% is greater than the required 75% needed to pass

Answer:

Yes

Step-by-step explanation:

First lets establish the key points

We know she needs 75% to pass and she gets 4/5 of the marks

Lets make 4/5 a decimal 4/5 X 2/2 is 8/10 better know as .8

.75 = 75%

.8 = 80%

80% > 75%

Meaning She PASSED!!!

Answer: the +2

Step-by-step explanation: PEMDAS. Exponents are before addition in the sequence. I hope this helps!

(The E standing for exponents and the A standing for addition)

Answer:

simple interest is $281(nearest whole number)

Step-by-step explanation:

S. I=PXTXR

100

P=$6609

T=5

R=8.5 or 85/10

S. I=6609X5X85

100X10

=280.8825

=281

Answer:

10

Step-by-step explanation:

3+2-1+6=5-1+6=4+6=10

The subtraction of the expression will be 238 cubic feet, 551 cubic inches.

It simply implies subtracting something from an entity, group, location, etc. Subtracting from a collection or a list of ways is known as subtraction.

The expressions are given below.

9 cubic yd 113 cubic in and 4 cubic ft 129 cubic in

1 cubic yard = 27 cubic feet

1 cubic feet = 1728 cubic inches

Then the subtraction will be

    242 cu ft 1841 cu in

   −   4 cu ft 1290 cu in

   238 cu ft 551 cu in

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Two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.

The relation between two expressions that are not equal, employing a sign such as ≠ ‘not equal to’, > ‘greater than, or < ‘less than.

Given inequality is:-

We will check all the points for the inequality:-

(−8,−1) →  x + 5y  <  2.  →  -8 +(5 x -1) < 2  →  -13 < 2 It is inequality

(−1,0)   → x + 5y  <  2   →   -1 < 2 It is inequality

(4,2)    → x + 5y  <  2   →    14 < 2  wrong

(9,6)    → x + 5y  <  2   →    39 < 2 wrong

(0,10)  →  x + 5y  <  2  →    50 < 2 wrong

Therefore the two points ( -8,-1) and ( -1,0) are the solutions and the other points are not the solution to the inequality.

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Answer:

3qr - 6q²

Step-by-step explanation:

3q(r - 2q) ← multiply each term inside the parenthesis by 3q

= 3qr - 6q²

Answer:

3qr – 6q²

Step-by-step explanation:

3q(r – 2q)

E X P A N D I N G :-

3qr – 6q²

An equation is formed of two equal expressions. If x is increased by 5 then the value of y is increased by 10.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Given that y=2x+1, now if the value of x increased by 5. then the value of y will be,

[tex]y_1=2(x+5)+1\\y_1 = 2x + 11[/tex]

Now if we compare y and y₁, then it can be said that if x is increased by 5 then the value of y is increased by 10.

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Answer:

3 + a/2

Step-by-step explanation:

3 + a/2

Answer:

B: 25 and 35

Step-by-step explanation:

25 product 35 875

Answer:

5 units

Step-by-step explanation:

to find out the answer for this you must first find the distance between 7 and 4 and then 6 and 10

then you would square them and then add them

lastly you would take the square root of that and youd have your answer

so

7 - 4 = 3

6 - 10 = -4 (just use 4)

3^2 + 4^2 = 9  + 16 = 25

then you take the square root of this

sqrt(25) = 5

that is your answer

To solve this problem, you will use the Distance Formula to find the distance between two coordinate points.

The Distance Formula is defined as follows:

[tex]d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

We must title our points by the standard coordinate naming system:

[tex](x_1, y_1) \ \text{and} \ (x_2, y_2)[/tex]

Therefore, our points can be labeled:

Now, substitute the known values as the variables in the Distance Formula:

[tex]d=\sqrt{(4 - 7)^2 + (10 - 6)^2}[/tex]

You must know the BPEMDAS acronym, which stands for:

Brackets

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

Simplify the expression using BPEMDAS:

[tex]d=\sqrt{(-3)^2 + (4)^2}[/tex]

Remember that when a number is raised to the 2nd power, it is the same thing as multiplying the number by itself:

[tex]-3\times-3 = 9[/tex]

[tex]4\times4=16[/tex]

Simplify further by removing the parentheses:

[tex]d=\sqrt{9+16}[/tex]

Compute the additive operation:

[tex]d=\sqrt{25}[/tex]

The number that is placed inside of a square root symbol (or a radical symbol) is referred to as the radicand.

In this situation, the radicand is 25.

To simplify the radicand, you may either use a calculator to compute the result, or you can determine which number raised to the 2nd power will result in a final answer of 25.

In this case, we can determine that 5² will result in a final answer of 25.

[tex]5^{2} = 25[/tex]

The final answer is 5 units.

The word problem for given equation is : When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .

The complete equation will be 3x - 2y =13

When an algebraic expression is equated by an equal sign to a constant or any other algebraic expression , then an equation is formed .

The equation given in the question is

3x-2y =13

When 3 is multiplied with x and subtracted by 2 multiplied by y , the number obtained is 13. Solve the equation for x =1 .

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The value of the variable x is 30° and the value of the variable y is 10°.

The missing diagram is attached below.

The angle is the distance between the intersecting lines or surfaces.

Corresponding angle – If two lines are parallel, then the third line. The corresponding angles are equal angles.

Vertically opposite angle – When two lines intersect, then their opposite angles are equal.

Linear angle – If the total of two angles is 180 degrees, they are said to be linear angles.

If angle ∠1 = 105°, angle ∠12 = (3x + 15)°, and angle ∠7 = (8y-5)°.

∠1 = ∠5 = ∠9 = 105° (corresponding angles)

∠1 = ∠4 = 105° (Vertical opposite angles)

∠1 + ∠2 = 180° (linear angle)

       ∠2 = 75°

∠2 = ∠3 = 75° (Vertical opposite angles)

∠3 = ∠8 = ∠12 = 75° (corresponding angles)

Then the value of x and y will be

   ∠9 = ∠12

   ∠1 = ∠12

105° = (3x + 15)°

  3x = 90°

    x = 30°

∠6 = ∠7

75° = (8y – 5)°

8y = 80°

  y = 10°

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The fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.

We know that fraction is an expression in mathematics used to denote the division of two whole numbers.

Given that the total distance = 48 km.

The distance Sapna traveled by car = 18 km.

So, the fraction is = distance traveled by car/total distance = 18/48 = 3/8

The distance Sapna traveled by train = 48 - 18 km = 30 km.

So, the fraction is = distance traveled by train/total distance = 30/48 = 5/8

Therefore the fraction of the journey Sapna traveled by car and train is 3/8 and 5/8 respectively.

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