Four friends had dinner togethere.
The total cost was $65.60.
The four friends shared the cost eaually between them.
How much did each person pay

Answer:

? = 45

Step-by-step explanation:

the inner and outer triangles are similar ( AA postulate )

Then the ratios of corresponding sides are in proportion, that is

[tex]\frac{56}{56+24}[/tex] = [tex]\frac{105}{105+?}[/tex]  , that is

[tex]\frac{56}{80}[/tex] = [tex]\frac{105}{105+?}[/tex] ( divide numerator/denominator by 8 to simplify left side )

[tex]\frac{7}{10}[/tex] = [tex]\frac{105}{105+?}[/tex] ( cross- multiply )

7(105 + ? )  = 1050 ← distribute parenthesis on left side

735 + 7? = 1050 ( subtract 735 from both sides )

7? = 315 ( divide both sides by 7 )

? = 45

Option A and D. The statements that are correct here are

If the two points UT and QP are parallel, then UT is going to be the half of QP. This would be due to a scale factor of 1/2.

Then at a midpoint T is that of PR. SU is parallel to RP. SU is half of RP due to as scale factor of 1/2.

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Answer: A and D E2020

Step-by-step explanation:

E2020 geometry B!! :)

ΔRSP ≅ ΔQSP by SAS. Therefore, PR ≅ PQ by CPCTC theorem.

If two triangles are congruent, the CPCTC theorem states that all corresponding parts of the two triangles would also be congruent to each other.

Since S is the midpoint of QR, therefore, RS ≅ QS (one pair of congruent sides)

∠RSP ≅ ∠QSP [right angles] (one pair of congruent included angles)

SP ≅ SP based on the reflexive property (one pair of congruent sides)

Therefore, ΔRSP ≅ ΔQSP by SAS.

Conclusively, PR ≅ PQ by CPCTC theorem.

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⊱________________________________________________________⊰

Answer:

Step-by-step explanation:

Take the cube root of both sides. That way, you'll get rid of the ³ next to x and leave x by itself

[tex]\large\boldsymbol{\rm{x=\sqrt[3]{13} }}[/tex]

done !!

⊰________________________________________________________⊱

The product of the mathematical expression √10 · √10 is 10 option first 10 is correct.

It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.

We have given a mathematical expression:

= √10 · √10

As we know,

√a² = a

or

√a×√a = a

By applying the above rule:

= √10×√10

= √10²

= 10

Thus, the product of the mathematical expression √10 · √10 is 10 option first 10 is correct.

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Answer: Second option from the top

Step-by-step explanation:

   First, we will simplify the given inequalities.

2x + 7 ≥ 1

2x ≥ -6

   x ≥ -3

-

8 - [tex]\frac{x}{3}[/tex] ≤ 5

- [tex]\frac{x}{3}[/tex] ≤ 5

- [tex]\frac{x}{3}[/tex] ≤ -3

   x ≥ 9

   Now, we will graph them. See attached.

Jorge will receive 9 hours in time off from work.

How many hours will Jorge get to take time off?

It is given that, Jorge has done overtime for 6 hours in this week. As per the Fair Labor Standards Act, for 6 hours of overtime work, he must be paid one and a half times the pay he gets per hour.

Instead of receiving an overtime pay for working 6 hours extra, Jorge decides to receive paid leaves from work, that is, he will get one and a half of the total hours for which he worked overtime.

As a result, the time off he receives from work = [tex]1\frac{1}{2} (6)[/tex] hours

[tex]=\frac{3}{2}(6) = 9 hours[/tex]

Thus, Jorge gets 9 hours in time off from work in return. The time that he earns for the overtime is equivalent to the pay he was supposed to receive for the overtime work.

What is Fair Labor Standards Act?

The Fair Labor Standards Act (FLSA) specifies standards for minimum wage, over-time compensation, recordkeeping, and youth employment that are applicable to workers in the private sector and in federal, state, and municipal governments.

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The transformation that's illustrated in the diagram is translation.

It should be noted that transformation simply means the manipulation of that moves a shape from a space to another.

In this case, the transformation that's illustrated in the diagram is translation. This is the sliding of try shape across certain number of spaces.

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Answer:

Step-by-step explanation:

Let "a number" be x.

"3/7 of a number" means (3/7)x

"32 less" means - 32

Thus, "32 less than 3/7 of a number" means (3/7)x -32

"is 11/35 of that number" means = (11/35)x

Put these together and we get:

(3/7)x -32 = (11/35)x

(3/7)x - (11/35)x = 32   Rearrang to get the x on one side

We need to change "(3/7)x - (11/35)" so that the two terms have a common denominator.

If we multiply the first term by (5/5) [which is equal to 1], we get:  

(5/5)(3/7)x or

(15/35)x

We can now write:

(15/35)x - (11/35)x = 32

(4/35)x = 32

Multiply both sides by (35/4)

(35/4)(4/35)x = (35/4)(32)

x = (35)(8)

x = 280

Closed-end

You can answer "yes" or "no" to the completed question. Or, the number of answers is limited (eg A, B, C, or all of the above). Closed-end questions are often suitable for voting, as response rates are high when users don't have to type too much.

Closed-end questions are defined as question types that require respondents to choose from a specific set of predefined answers. B. Between "yes/no" or fixed multiple-choice questions. In a typical scenario, closed-end questions are used to collect quantitative data from respondents.

An indefinite definition represents a situation or question with a predetermined number of results. An example of a closed ending is the question "Do you need help?" This usually has only four answers-yes, no, maybe, or not.

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Answer: x = 15

Step-by-step explanation:

Hi!

These are supplementary angles, which means they both add up to 180°

Therefore,

9x+10 + 1x + 20 = 180

to solve, combine like terms

10x + 30 = 180

Then subtract 30 from both sides

10x = 150

now divide 10 from both sides leaving x by itself

x = 15

Hope this helps and have a nice day!

Answer: x = 15

Step-by-step explanation:

Hi!

These are supplementary angles, which means they both add up to 180°

Therefore,

9x+10 + 1x + 20 = 180

to solve, combine like terms

10x + 30 = 180

Then subtract 30 from both sides

10x = 150

now divide 10 from both sides leaving x by itself

x = 15

Hope this helps and have a nice day!

Here use general math mind

F(x) has more than one x inetercept .

Domain is for real numbers

Four unique numbers?

Lets see

[tex]\sf f(x)=\begin{cases}\sf (x+2)²,x\neq \left\{0,-1,1,2,3\right\}\\ \sf 0,x=0\\ \sf 1,x=-1\\ \sf 9,x=1\\ \sf 16,x=4\\ \sf 25,x=5\end{cases}[/tex]

For -2

For 0 it's (0,0)

And for extra ,it's discontinuous on x=0

Step-by-step explanation:

13.6 is the answer because 1cm is 10 cm

Answer:

13.6 cm

Is the second requested unit mm?  The value is already in mm.

Step-by-step explanation:

Use conversion factors for the metric system.

By definition:  1cm = 10mm

We can write this as a conversion factor.  Either:

 1)  1cm/10mm, or

 2) 10mm/1cm

We are given 136 mm.  Convert that by using either conversion factor.

(136mm)*(1cm/10mm) = 13.6 cm  Note how the mm unit cancels.

To use the other conversion factor, do a division:

(136mm)/(10mm/1cm) = 13.6 cm

====

136 mm is already 136 mm.  

Answer:

How To Protect Against Predatory Lending

1) Consider alternatives to borrowing

2) Borrow federal first

3) Check your credit before applying for private loans

4) Shop around when looking for a loan

Explanation:

Definition: "Imposing unfair and abusive loan terms on borrowers." - FDIC

Answer:

1/5

Step-by-step explanation:

The slope-intercept form looks like [tex]y=mx+b[/tex] where b is the y-intercept and m is the slope. m is the slope because if you increase x by 1, the value y increases by m, and if you increase x by 1 again, the y-value will increase by the value of m, because it's being multiplied. b is the y-intercept since the y-intercept is when x=0 so mx will become m(0) which is just 0 leaving b by it self. In this case you have y=1/5x so if you were to start with 0 as x the value of y is 0. Now increase it by 1 so x becomes 1, the value of y becomes 1/5x, now increase it by 1 again so x becomes 2, the value of y is 2/5x, so as you can see the function is just increasing by 1/5 so that's the slope, so essentially whatever the coefficient of x is (the number in front of the variable x), is the slope

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Answer:  [tex]\textsf{Slope = 1/5}[/tex]

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Given:  [tex]\textsf{y = 1/5x}[/tex]

Find: [tex]\textsf{The slope of the line}[/tex]

Solution:  In order to determine the slope of the line we need to see how the slope-intercept form compares to this expressions.  The slope-intercept form is y = mx + b where m is the slope and b is the y-intercept.  In this case we have no y-intercept therefore we do not have a b. However, our slope is equal to 1/5 as it fits perfectly with the form that was provided.

Answer:

13

Step-by-step explanation:

f(-3)=2(-3)-5(-3)+4. = -6+15+4= 13. f(a)=13

The points on the graph of the inverse variation are of the form:

(x, 8/x)

An inverse variation function is written as:

y = k/x.

Here we know that k = 8.

y = 8/x

Then the points (x, y) on the graph of the function are of the form:

(x, 8/x).

So evaluating in different values of x, we can get different points on the graph:

And so on.

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Hello and Good Morning/Afternoon

Let's take this problem step by step.

        [tex]5=\frac{1}{3}(5x-15)\\ 5=\frac{5}{3}x-5\\ 5+5= \frac{5}{3}x-5 +5\\10=\frac{5}{3}x\\ 10 * 3 = 3* \frac{5}{3}x\\30=5x\\\frac{30}{5} =\frac{5}{5}x\\ 6=x\\x=6[/tex]

What did we do in this problem

                  [tex]5=\frac{1}{3}(5(6)-15)\\ 5=\frac{1}{3} (30-15)\\5=\frac{1}{3}*15\\ 5=5 \checkmark\\[/tex]

Answer: x = 6

Hope that helps!

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Solution :-

⇒ 5 = 1/3 (5x - 15)

⇒ 5 × 3 = 1 (5x - 15)

⇒ 15 = 1 (5x - 15)

⇒ 15 = 1 × (5x - 15)

⇒ 15 = 5x - 15

⇒ 5x = 15 + 15

⇒ 5x = 30

⇒ x = 30 / 5

⇒ x = 6

Probability helps us to know the chances of an event occurring. The probability of selecting an even number or multiple of 13 is 13/25.

Probability helps us to know the chances of an event occurring.

[tex]\rm Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]

Number of even numbers between 1 to 25 = 22

Number of multiple of 13 between 1 to 25 = 1

The probability of selecting an even number or multiple of 13 is,

Probability = (12+1)/25 = 13/25

Hence, The probability of selecting an even number or multiple of 13 is 13/25.

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The value of x will be 33 units approximately. Thus, option A is correct.

Trigonometric identities are the functions that include trigonometric functions such as sine, cosine, tangents, secant, and, cot.

We need to find the value of x

so first

Tan 60 = Perpendicular / 11√6

Perpendicular = 1.732 (11√6)

Perpendicular = 46.66

Then,

Sin 45 = Perpendicular / x

Sin 45 = 46.66/ x

x = 33.00

So, the value of x will be 33 units approximately.

Thus, option A is correct.

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Answer:

38

Step-by-step explanation:

Let x be the number of pencils bought.

Let y be the number of pens bought.

Given information from the question:

x = y - equation 1

2.9y - 1.2x = 32.30 - equation 2

From here we can use the substitution method in solving simultaneous equations to find x and y. We will substitute equation 1 into equation 2.

2.9y - 1.2y = 32.30

1.7y = 32.30

y = [tex]\frac{32.3}{1.7} \\= 19[/tex]

Now since we know number of pens = number of pencils,

x = 19

Total Pencils and Pens bought = x + y = 19 + 19 = 38

Answer:

19

Step-by-step explanation:

hope it helps.good day.

Answer: $13361.76

Step-by-step explanation:

Amount = initial balance(1 + annual rate/periods per year)^(periods per year*years)

A = 3000(1+0.1/12)^12*15

A = 3000(1.0083)^180

A = 3000(4.4275)

A = 13361.76

Hope this helps!

#1

No

#2

We can see f(1) has 3 values so it's not a function as it's failed in vertical line test

#3

f(10) has two values -2 and 11

So not a function

#4

As per definition of function

So it's not a function

The probability that a randomly selected customer will order a chicken sandwich or french fries is 36%

The given parameters are:

P(Chicken) = 56%

P(Sandwich) = 43%

P(Both) = 30%

The required probability is:

P = P(Chicken) + P(Sandwich) - P(Both)

This gives

P = 56% + 43% - 30%

Evaluate

P = 36%

Hence, the probability that a randomly selected customer will order a chicken sandwich or french fries is 36%

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[tex]10^2 + b^2=15^2\\\\100+b^2=225\\\\b^2=125\\\\b =\sqrt{125}\\\\b \approx \boxed{11.2}[/tex]

The area of a right-angle triangle is half the product of the base of the triangle and the height of the triangle. The area of the triangle is 90 units².

The area of a right-angle triangle is half the product of the base of the triangle and the height of the triangle.

[tex]\rm{ Area \triangle = \dfrac{1}{2} \times base \times height\\[/tex]

For the given triangle if the hypotenuse is assumed as the base, and the altitude is assumed as the height of the triangle, then the area of the triangle will be,

Area of the triangle = 0.5 × 15 units × 12units

                                 = 90 units²

Hence, the area of the triangle is 90 units².

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Answer:

A. y<-1/5x+1

Step-by-step explanation:

First, find the slope of the line

delta y / delta x = slope (delta means "change in", so delta y would the the change in y)

the change in y is 1, and the change in x is -5, so the slope is -1/5

we now know that the equation of the line is
y=-1/5x+1

The answer can't be c or d, because the line is dotted and not solid (solid lines signify ≥ or ≤, and dotted > and <)
To test if it is > or <, we can plug in some numbers to see if the equation is true

Right now, we have:

y[?]-1/5x+1, where "[?]" is either > or <

we see that the point 0,0 is a solution, since it is in the shaded region of the graph, because of this, we know that if we plug x=0 and y=0 into the equation, it must be true

plug in:

0[?]-(1/5)*0+1

0[?]1

clearly, [?] should be <, as 0<1
so, now that we know [?], we can replace it in our equation

y<-1/5x+1 , or "A"

Answer:

I don't see a list of equations.  See the attached image for an equation that works well.

Step-by-step explanation:

Answer:

P = 55°

K = 27°

Step-by-step explanation:

55° + 98° + c = 180°

153° + c = 180°

c = 27°

since C is opposite K, K = 27°

Since 55° is opposite P, P = 55°

We can check this by adding up the values of P, K, and 98

27°+55°+98° = 180°