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Consider right triangle DEF below.

Answer:

That is the answer for you step 2

20 hot dogs was eaten by the 10 people who attended the hot dog eating contest.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that there were 10 people at the hot dog eating contest. If each person eats 2 hot dog, hence:

Number of hot dogs eaten = 2 hot dog per person * 10 people = 20 hot dogs.

20 hot dogs was eaten by the 10 people who attended the hot dog eating contest.

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When we simplify (3 + √5)(3 + √2), the result obtained is:

9 + 3√2 + 3√5 + √10

a√b × c√d = (a × c)√(b × d)

(3 + √5)(3 + √2)

Expand by clearing the bracket

3(3 + √2) + √5(3 + √2)

9 + 3√2 + 3√5 + √10

Thus,

(3 + √5)(3 + √2) = 9 + 3√2 + 3√5 + √10

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Answer:

-3/2 ≤ x < 5

Decimal form:

-1.5 ≤ x < 5

(hope this helps)

Answer:

Step-by-step explanation:

b+9≤2

Subtract 9 from both sides:

9+b≤2

subtract 9 on each side which will be -7

the answer will be b≤-7

Answer:

7/9

Step-by-step explanation:

Divide the numerator and denominator by 4.

28/36 = 7/9

Answer:

7/9

Step-by-step explanation:

28 and 36 are both divisible by 4.

28÷4 is 7 and

36÷4 is 9

28/36 = 7/9

The equation that represents Camille's profit p as a function of the number of doughnuts sold, n is P = 1.35n - 60

She bought 120 doughnuts for $60.

Therefore,

cost  = $60

Her profit was $48 once she sold 80 doughnuts.

p = profit

n = number of doughnuts sold.

Therefore,

let

x = amount she is selling each doughnuts

p = nx - 60

Using the information given we have:

48 = (80x) - 60

Therefore,

x = $1.35

Hence, for any number of doughnuts then, we have the profit equation as follows:

P = 1.35n - 60

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Answer:

7+45/n or 5

Step-by-step explanation:

45 divided by n or technically 5 is 9 plus 7 is 16 :)

Answer:7+45/n or 5

Step-by-step explanation:

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Answer:  [tex]\textsf{x = 1000}[/tex]

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Given: [tex]\textsf{log(x) = 3}[/tex]

Find: [tex]\textsf{The value of x}[/tex]

Solution:  In order to solve for x we need to get rid of the log which means that we need to put it to the power of the same number as the base.  When a base isn't displayed it defaults to 10 so we raise everything to the base of 10.

Get rid of log

Therefore, the final answer would be that x is equal to 1000.

The x-coordinate of the point (50, 55) is 50

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The distance of point (50, 55) perpendicular to y-axis

Thus, perpendicular distance = 50 units

The x-coordinate of the point (50, 55) is 50

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Answer:

[tex]\textsf{B.} \quad (f \cdot g)(x)=10x[/tex]

Step-by-step explanation:

Given:

[tex]\begin{cases}f(x)=\sqrt{50x}\\g(x)=\sqrt{2x}\end{cases}[/tex]

[tex]\begin{aligned}\textsf{As }(f \cdot g)(x) & = f(x) \cdot g(x)\\\implies (f \cdot g)(x)& = \sqrt{50x} \cdot \sqrt{2x}\end{aligned}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a}\sqrt{b}=\sqrt{ab}:[/tex]

[tex]\begin{aligned}\implies (f \cdot g)(x) &= \sqrt{50x2x}\\& = \sqrt{100x^2}\end{aligned}[/tex]

Rewrite 100 as 10²:

[tex]\implies (f \cdot g)(x)=\sqrt{10^2x^2}[/tex]

[tex]\textsf{Apply exponent rule} \quad a^bc^b=(ac)^b:[/tex]

[tex]\implies (f \cdot g)(x)= \sqrt{(10x)^2}[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:[/tex]

[tex]\implies (f \cdot g)(x)=10x[/tex]

Answer:

36 problems

Step-by-step explanation:

so let's say x = how many problems Marcela was assigned

she completed half of them so the amount of problems left is x/2

She then completed 7 more so now we can subtract 7. We then set this to 11 to solve for x

x/2 - 7 = 11

x/2 = 18

x = 36

Answer:

To solve the answer, you can do it in 2 ways:

1) you could take the square root on both sides and solve for x

OR

2)you could multiply 3x-5 times itself and subtract 19 on both sides and use the grouping or quadratic formula method to find x.

Hope it helps.

Answer:

6 : 1

Step-by-step explanation:

The length is the longer side compared to the width.

Hence, the length is 42 inches and width is 7 inches.

Taking the ratio :

Answer:

1 : 6

Step-by-step explanation:

42 /7 = 6

We will have to simply the ratios in order to get the answer.

The smallest digit of the smallest number is at the thousands place.

The system of representing numbers is called Number System.

The given numbers are 6895 , 4875 , 5689

The smallest number among these is 4875

The smallest digit in this number is 4

4 is at thousands place

Therefore , The smallest digit of the smallest number is at the thousands place.

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Answer:

B

Step-by-step explanation:

given the graph of y = 0.5x

Then any point on the line satisfies y = 0.5x

consider the points given

x = 1 then y = 0.5 × 1 = 0.5 ⇒ (1, 0.5 ) is on the line

x = 4 then y = 0.5 × 4 = 2 ⇒ (4, 2 ) is on the line

Answer:

A

Step-by-step explanation:

Comment (and answer)

Both start with the plus x axis as one of the arms. The other arm of 110o goes anti clockwise until it is 30 degrees into the second quadrant.

The answer can be found by using 110 - 360 = negative angle.

So 110 - 360 = - 250 which goes clockwise from the plus x axis. The answer must be A.

Make sure you understand the concept of clockwise and anti clockwise. If you don't know, ask your teacher, write it down, and try not to forget it. The distinction comes up a lot.

Answer:

x = -2

Step-by-step explanation:

2x^3 +16 = 0

We are solving for x

Subtract 16 from each side

2x^3 +16- 16 = 0-16

2x^3 = -16

Divide each side by 2

(2x^3 ) /2 = -16/2

x^3 = -8

Take the cube root of each side

[tex]\sqrt[3]{x^3} = \sqrt[3]{-8}[/tex]

x = -2

Answer:

[tex]x=-2[/tex]

Step-by-step explanation:

Given equation:

[tex]2x^3+16=0[/tex]

To solve for the unknown variable x, apply arithmetic operations to isolate the variable.

Subtract 16 from both sides:

[tex]\implies 2x^3+16-16=0-16[/tex]

[tex]\implies 2x^3=-16[/tex]

Divide both sides by 2:

[tex]\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}[/tex]

[tex]\implies x^3=-8[/tex]

Take the cube root of both sides:

[tex]\implies \sqrt[3]{x^3}=\sqrt[3]{-8}[/tex]

[tex]\implies x=-2[/tex]

When taking the cube root of a negative number, the result will be negative.  To understand why, examine what happens when we cube a negative number.

When a number is cubed, it is multiplied by itself, then by itself again.

When multiplying a negative number by another negative number, the result is always positive.

When multiplying a positive number by a negative number, the result is always negative.

Therefore:

[tex]\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}[/tex]

So if -8 is cube rooted, the result is -2.

Let's take this problem step by step:

To find the ordered pair of the system:

 ⇒ must set both equations equal to each other

     ⇒ solve for 'x'

Let's solve:

 [tex]x^2-2x+3=-2x+12\\x^2-2x+2x+3-12\\x^2-9=0\\(x+3)(x-3)=0[/tex]

Let's find the x-values:

 [tex](x+3)=0\\x=-3\\\\(x-3)=0\\x+3[/tex]

Let's find f(x)'s value for each 'x':

 [tex]x=-3\\f(-3)=-2(-3)+12=6+12=18\\\\x=3\\f(3)=-2(3)+12=-6+12=6[/tex]

Answer: (3, 6), (-3,18)

Hope that helps!

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

[tex]\qquad \tt \rightarrow \: Add \:\: -6 \hat i - 6\hat j \:\:with \:\; Vector \:\; c[/tex]

____________________________________

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

Vector d can be represented as :

[tex]\qquad \tt \rightarrow \: - 2 \hat i - 2 \hat j[/tex]

Vector c can be represented as :

[tex]\qquad \tt \rightarrow \: 4 \hat i + 4\hat j[/tex]

we have to create vector d from vector c

So, let's assume a vector x, such that sum of vector x and vector c equals to vector d

[tex]\qquad \tt \rightarrow \: x + ( 4 \hat i + 4 \hat j) = - 2 \hat i - 2 \hat j[/tex]

[tex]\qquad \tt \rightarrow \: x = - ( 4 \hat i + 4 \hat j) - 2 \hat i - 2 \hat j[/tex]

[tex]\qquad \tt \rightarrow \: x = (- 4 \hat i - 2 \hat i) + ( - 4 \hat j - 2 \hat j)[/tex]

[tex]\qquad \tt \rightarrow \: x = - 6 \hat i -6 \hat j[/tex]

Henceforth, in order to get vector d, we need to add (-6i - 6j) in vector c

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find the length using the Pythagorean theorem.

Length = sqrt(20^2 - 12^2)

Length = 16 feet

area = 12 x 16 = 192 square feet

The solution to the inequality 5x - y > -3 is shown in the graph.

An equation is an expression that shows the relationship between two or more numbers and variables.

An inequality shows the non equal comparison of two or more variables and numbers.

The solution to the inequality 5x - y > -3 is shown in the graph.

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Answer:

3 and 4

Step-by-step explanation:

well you can approximate by squaring values

2^2 = 4

3^2 = 9

4^2 = 16

the value should fall somewhere between 3 and 4 since the square root of 9 is 3 and the square root of 16 is 4

Answer:

4 secs

Step-by-step explanation:

Since they have to be synchronized, their parabolic equations must be equal to one another

3(t^2 + 9 - 6t) - (t^2 + 25 - 10t) - t + 2 = 0

2t^2 - 9t + 4

(2t - 1)(t - 4) = 0

t = 1/2, 4

From the options, the answer is 4

The gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.

so, correct option is: C.

Here, we have,

To determine when the gymnasts will be at the same height during their flips, we need to find the time (x) at which the equations for y are equal.

The given equations are:

y = –(x – 5)² + 3

y = –3(x – 3)² + x + 1

Setting the two equations equal, we have:

–(x – 5)² + 3 = –3(x – 3)² + x + 1

Expanding the squared terms:

–(x² – 10x + 25) + 3 = –3(x² – 6x + 9) + x + 1

Simplifying the equation:

–x² + 10x – 25 + 3 = –3x² + 18x – 27 + x + 1

Combining like terms:

–x² + 10x – 22 = –3x² + 19x – 26

Rearranging the equation:

2x² - 9x + 4 = 0

To solve this quadratic equation, we can factor it:

(2x - 1)(x - 4) = 0

Setting each factor equal to zero:

2x - 1 = 0 or x - 4 = 0

Solving for x:

2x = 1 or x = 4

Dividing by 2:

x = 1/2 or x = 4

Therefore, the gymnasts will be at the same height during their flips at two different times: 1/2 seconds and 4 seconds.

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Answer:

A

Step-by-step explanation:

both numbers are negative, you can rearrange them in any order provided you keep the sign

Reason:

An expression in the form -a-b is the same as -a + (-b)

Recall we can add two numbers in any order we want. For instance, 2+3 = 3+2 since both sides are equal to 5. This is the commutative property of addition.

Therefore, the -a + (-b) is the same as -b + (-a) which in turn becomes -b - a

In short:  -a - b = -b - a

This rule lets us say that -71n - 29 = -29 - 71n

Answer:

PA = [tex]\sqrt{29}[/tex]

AC =[tex]\sqrt[2]{5}[/tex]

Step-by-step explanation:

distance formula : if [tex](x_{1},y_{1}) and (x_{2},y_{2})[/tex] are two points on a line segment then distance between both the points is given by distance formula.

[tex]d = \sqrt{[(x_{2} - x_{1} )^2 +(y_{2} - y_{1})^2]}[/tex]

therefore ,

given points are , A(2, 5),  P(0, 0), C(-2, 7).

so PA = [tex]\sqrt{[({2} - {0} )^2 +({5} - {0})^2]} = \sqrt{({2} )^2 +({5} )^2}[/tex]

    PA = [tex]\sqrt{\229}[/tex]

similarly,

AC = [tex]\sqrt{[({-2} - {2} )^2 +({7} - {5})^2]} = \sqrt{({4} )^2 +({2} )^2}[/tex]

AC = [tex]\sqrt{20} = \sqrt[2]{5}[/tex]

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The adjustment of thicker fur will be selected over thinner fur, and the population will develop. Then the correct option is D.

Determining the proper option, acquiring evidence, and exploring various options are all steps in the decision-making process.

In a mouse population, some mice have thicker fur than others, but there are more mice with thinner fur.

The climate in which these mice live has slowly gotten colder.

The change in the environment most likely affect the mouse population will be

The adjustment of thicker fur will be selected over thinner fur, and the population will develop.

Then the correct option is D.

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Answer:

P =2(x+ y) [tex]ft[/tex].

A =xy [tex]ft^{2}[/tex]

Step-by-step explanation:

perimeter of rectangle (P)= 2(L+B

Area of rectangle (A)        =    L×B

Given,

width = 'x'

length = y = x+20

therefore using above formula

P = 2(x+20 + x) = 2(2x+20)

A = (x+20)(x)

cost of land per square foot = $12

cost of land per linear foot   = $8

total cost of land                   = $10560

now,

P×8 + A×12   = 10560

2(2x+20)×8 +  (x+20)(x)×12 = 10560

32x + 320 + 12x²+ 240x     = 10560

12x² + 272x                         = 10240

12x² + 272x - 10240           = 0

solving this quadratic equation using Discriminant method

x = [-b ±√(b² - 4ac)]/2

where b is the coefficient of x

a is the coefficient of x²

and c is the constant term

by replacing values in the above formula

x = 19.5  , x = -42.24

as the area cannot be negative therefore -42.24 is neglected

hence x = 19.5ft

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