Since V is between R and T, then:

[tex]RT=VR+VT\text{.}[/tex]Substituting VR=3x, VT=5x+9, RT=33, and solving for x we get:

[tex]\begin{gathered} 33=3x+5x+9, \\ 33=8x+9, \\ 33-9=8x, \\ 8x=24, \\ x=3. \end{gathered}[/tex]Substituting x=3 in VR we get:

[tex]\text{VR}=3\cdot3=9.[/tex]**Answer:**

The value of x is **3**.

The length of VR is **9**.

a group of six people has 10 pizzas to share if they divide the pizzas evenly how much does each person get

We will have that if they divide them evenly they will end up with:

[tex]\frac{10}{6}=\frac{5}{3}[/tex]So, each one will end up with option D.

An item is regularly priced at $43. It is on sale for 15% off the regular price.Use the ALEKS calculator to find the sale price.

Answer:

**$36.55**

Explanations:

**Given **the following parameters

Regular price of a ticket = $43

Sales discount = 15%

**Determine the** **discounted price**

Discount price = 0.15 * 43

Discount price = $6.45

**Determine the sales price**

Sales price = Regular price - discount

Sales price = $43 - $6.45

Sales price = $36.55

Hence the **sales price **for the item will be ** $36.55**

Suppose y varies directly with x.When x is 7,y is 21 Write the equation that relates x and y

Answer:[tex]y=3x[/tex]Explanation:

Given that y varies directly with x, we have:

[tex]\begin{gathered} y\propto x \\ \Rightarrow y=kx \end{gathered}[/tex]Where k is constant.

When x = 7, y = 21. From here, we can obtain the value of k

21 = 7k

k = 21/7 = 3

Since k = 3, the equation that relates x and y is:

[tex]y=3x[/tex]When Mr. Jackson got in his car yesterday, the odometer read 187,198.9 km. When he got home, the reading was 187,399.4 km. How far did Mr. Jackson drive?

The **distance **Mr. Jackson **drove **from when he got in his car to when he got home is 200.5 **km**.

Given:

The **odometer **reading when Mr.Jackson got in his car = 187,198.9 km

The odometer reading when Mr.Jackson got home = 187,399.4 km

An **odometer** is a **device** used to calculate the distance traveled by a **vehicle.**

To determine the **distance** Mr.Jackson drove we subtract the odometer readings from when he got home minus when he got into his car.

⇒ (187,399.4 - 187,198.9) km

⇒ 200.5 km

Therefore, Mr. Jackson **drove **220.5 km from when he got in his car to when he got home.

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What property is used to solve 9x + 5 = 21 and 9x + 5 -5 = 21 - 5

**Problem**

What property is used to solve 9x + 5 = 21 and 9x + 5 -5 = 21 - 5

**Solution**

9x +5 =21

If we subtract 5 in both sides we got:

**9x +5-5 =21-5**

**Subtraction property of equality**

What is the value of sin^-1(0)

a= -1

b= 0

c = 1

d = pi

**Answer:**

B: 0

**Step-by-step explanation:**

At the unit circle, we can see that sin(x) = 0 for x = 0 and for x = pi

This gives us directly that sin^-1(0) = 0 or x = pi

However, the function sin^-1(x) is only defined for -pi/2 \leq 0 \geq pi/2, since otherwise it is very unclear which answer is the right one.

By this definition, we directly see that the only right aswer is 0

What is the solution to the rational inequality?

3 - x / 2x + 1 ≥ 2

( - 1/ 2 , 1 / 5)

( - ∞ ; - 1 /2)

( - 1 / 2 , 1 / 5)

( - ∞ , - 1/ 2 ) ∪ ( 1 /5 , ∞ )

The **solution **to the** rational inequality **given in this problem is as follows:

(-1/2, 1/5].

Rational inequalityThe rational inequality is **defined **as follows:

[tex]\frac{3 - x}{2x + 1} \geq 2[/tex]

The first step to solve the inequality is **isolate 0 **on the right side of the inequality, hence:

[tex]\frac{3 - x}{2x + 1} - 2 \geq 0[/tex]

Then the least common multiplied is applied to represent the left side of the inequality as a **single fraction,** as follows:

[tex]\frac{3 - x - 2(2x + 1)}{2x + 1}\geq 0[/tex]

[tex]\frac{3 - x - 4x - 2}{2x + 1}\geq 0[/tex]

[tex]\frac{-5x + 1}{2x + 1}\geq 0[/tex]

There are **two cases** for the solution to the inequality:

The solution is the **union **of the solution of each of these cases.

-5x + 1 ≥ 0

-5x ≥ -1

5x ≤ 1

x ≤ 1/5

2x + 1 > 0 (only > as the denominator cannot be zero)

2x > -1

x > -1/2

The **intersection **of these solutions is given by the following interval:

(-1/2, 1/5].

Case 2-5x + 1 ≤ 0

-5x ≤ -1

5x ≥ 1

x ≥ 1/5

2x + 1 < 0

2x < -1

x < -1/2.

The **intersection **of these two cases is empty, hence the **solution **to the inequality is given by the following interval:

(-1/2, 1/5].

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EFG and GFH are a linear pair, mEFG = 2n +17, and mGFH = 4n +31. What are mEFG and mGFH?

mEFG and mGFH is 61 and 119 respectively.

What is **linear pair **of angle**?**

**Linear pair** of angle are formed when two lines intersect each other at a single point and sum of angles of linear pair is always 180.

given, mEFG = 2n+17 and mGFH = 4n+31 and they both are linear.

Hence,

mEFG+mGFH = 180

2n+17+4n+31 = 180

6n+48=180

6n = 132

n = 22

hence, mEFG = 2(22)+17= 61 and mGFH = 4(22)+31 = 119

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f(a)=-3a-5; Find ƒ(-7)

**Step-by-step explanation:**

the answer is attached

hope it helps

If figure, angle ABE & angle DBC are right angles. Prove that angle ABD ≊ angle EBC

Hurry and answer please

**Angle** ABE & angle DBC are** right angles** then ∠ABE≅ ∠EBC

**What is complementary angle theorem?**

If two angles are complementary to the same angle, then they are congruent.

1.∠ABE and ∠DBC are right angles(Given)

2. m∠ABE=90⁰

m∠DBC=90⁰

By definition of **right angles**

3.∠ABE and ∠DBE are** complementary.**

∠DBE and ∠EBC are complementary.

(By complementary theorem)

two angles are complementary to the **same angle**, then they are **congruent.**

4. ∠ABE≅ ∠EBC (is **complementary** to same)

Hence ∠ABE≅ ∠EBC.

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Find the maximum value of

C = x + 4y

subject to the following constraints:

x ≥ 0

x≤ 12

y ≤ 10

2x + 3y ≥ 24

The** maximum value **of the **linear equation** is obtained as 52.

For the given question;

The** linear equation** is defined as;

C = x + 4y

The constraints are-

x ≥ 0

x≤ 12

y ≤ 10

2x + 3y ≥ 24

From the **constraints**, the maximum value for x and y are taken as;

x = 12 and y = 10.

Put the the equation, to find the maximum value.

C = x + 4y

C = 12 + 4×10

C = 52

Thus, the** maximum value **of the function is obtained as 52.

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Find the value of the expression: 12 ÷ 2 + ( 6 − 4 ) 2

**Given:**

**Required:**

To find the value of the given expression.

**Explanation:**

Consider the given expression,

[tex]\begin{gathered} 12\div2+(6-4)\times2 \\ =6+(6-4)2 \\ =6+2\times2 \\ =6+4 \\ =10 \end{gathered}[/tex]**Final Answer**:

The value of the given expression is 10.

Hello! I need some help with this homework question, please? The question is posted in the image below. Q3

As given by the question

There are given that the function:

[tex]f(x)=x^2+3[/tex]Now,

From the given formula:

[tex]\frac{f(x+h)-f(x)}{h}[/tex]Then,

First find the equation for f(x + h)

So,

[tex]\begin{gathered} f(x)=x^2+3 \\ f(x+h)=(x+h^{})^2+3 \\ f(x+h)=x^2+h^2+2xh+3 \end{gathered}[/tex]Then,

Put both values into the given formula:

So,

[tex]\frac{f(x+h)-f(x)}{h}=\frac{x^2+h^2+2xh+3-x^2-3}{h}[/tex]Then,

[tex]\begin{gathered} \frac{f(x+h)-f(x)}{h}=\frac{h^2+2xh}{h} \\ =\frac{h(h^{}+2x)}{h} \\ =h+2x \\ =2x+h \end{gathered}[/tex]Hence, the difference quotient is **2x + h.**

I only need the answer

THANK YOU!!

After simplifying the expression to a singles** complex number**, it becomes 1+√3i.

A **complex number** is a unique kind of number in the number system, it has two parts. One it called the **real part** which is a real number and an **imaginary part** which is also a real part but accompanied by the specific notation called **iota.**

Here a complex number Z is provided to us,

Z = [2+√(-12)]/2

As we can see,

Here we have √-12

We can write it as,

√(-2×2×3)

= 2√(-3)

Here, √-1 is given that special notation** "IOTA (i)"** which we mentioned earlier.

=2√3i

So, Z becomes,

Z = (2+2√3i)/2

Z= 1+√3i

So, the simpler form of Z = [2+√(-12)]/2 is Z= 1+√3i.

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determine the maximum or minimum of the quadratic function. express your answer in the form (x,y) and using decimals rounded to the hundredths.f(x)=2x^2+7-10

We are given the following quadratic equation

[tex]f(x)=2x^2+7x-10[/tex]The **vertex** is the maximum/minimum point of the quadratic equation.

The x-coordinate of the vertex is given by

[tex]h=-\frac{b}{2a}[/tex]Comparing the given equation with the general form of the quadratic equation, the coefficients are

**a =** **2**

**b =** **7**

**c =** **-10**

The y-coordinate of the vertex is given by

[tex]\begin{gathered} f(x)=2x^2+7x-10 \\ f(-1.75)=2(-1.75)^2+7(-1.75)-10 \\ f(-1.75)=2(3.0625)^{}-12.25-10 \\ f(-1.75)=6.125^{}-12.25-10 \\ f\mleft(-1.75\mright)=-16.13 \end{gathered}[/tex]This means that we have a **minimum** point.

Therefore, the **minimum** point of the given quadratic equation is

**Answer:**

Exact Form:x=±√6/2

Decimal Form:x=1.22474487,−1.22474487

**Step-by-step explanation:**

If you travel southeast from one city to another city that is 314 km away, and the trip takes you 4.00 hours, what is your average velocity?

**Answer:**

78.5

**Step-by-step explanation:**

i just know

Good morning I could really use some help with this question please!!

Answer: [tex](x\text{ - 3\rparen}^2\text{ + \lparen y + 2\rparen}^2\text{ = 16 \lparen option B\rparen}[/tex]Explanation:

**Given:**

center of the circle = (3, -2)

radius = 4

**To find:**

the standard form of the equation of a circle

The standard form of the equation of circle is given as:

[tex]\begin{gathered} (x\text{ - h\rparen}^2\text{ + \lparen y - k\rparen}^2\text{ = r}^2 \\ center\text{ = \lparen h, k\rparen} \end{gathered}[/tex][tex]\begin{gathered} h\text{ = 3, k = -2, r = 4} \\ \\ substitute\text{ the values into the formula:} \\ (x\text{ - 3\rparen}^2\text{ + \lparen y - \lparen-2\rparen\rparen}^2\text{ = 4}^2 \\ (x\text{ - 3\rparen}^2\text{ + \lparen y + 2\rparen}^2\text{ = 16} \end{gathered}[/tex]**The equationof the circle in standard form:**

f(x) = 2^3x-1 - 2find the inverse function of f(x)

**Given the function**

Substitute y = f(x) into the function above

[tex]y=2^{3-x}-2[/tex]**Make 'x' the subject of the formula**

Take the log₂ of both sides

[tex]\begin{gathered} \log _2(y+2)=\log _22^{(3-x)} \\ \log _2(y+2)=3-x\log _22 \\ \end{gathered}[/tex]Note:

[tex]\log _22=1[/tex]Therefore,

[tex]\begin{gathered} \log _2(y+2)=(3-x)\times1 \\ \log _2(y+2)=3-x \end{gathered}[/tex]Isolating 'x'

[tex]x=3-\log _2(y+2)[/tex]**Replace 'x' with 'y'**

**Hence,**

**The correct option is ****Option 2****.**

Marian purchased a home valued at $465,000. She purchased homeowner insurance for 75% of the value of the home. If the annual premium on the policy was $0.74 perhundred-dollar unit, how much did she pay to the nearest whole cent)?$2,875.50$2,695.00$2,580.75$3,050.74None of these choices are correct.

The value of the police if fot the 75% of the total value of the home value. The 75% of $465000 is:

[tex]465000\cdot0.75=348750[/tex]The value of the insurance is then for $348750. The annual premium of the policy is $0.74 per hunder-dollar unit. Then, we need to estimate the hundred-dollar units in $348750. To estimate them, we need to divide the value by 100:

[tex]\frac{348750}{100}=3487.5[/tex]The value of the policy is then by 3487.5 hundreds of dollars. Now, we can estimate the amount to be paid yearly:

[tex]0.74\cdot3487.5=2580.75[/tex]Then, the amount to pay, according to the given conditions is $2580.75. Correct answer is the third option.

What is the solution of the following system? {6x+2y=−10 5x−5y=5

Answer below:

Step-by-step explanation:

6x+2y=-10

(-5/3,0) x-int

(0,5) y-int

slope= -3

5x-5y=5

slope= 1

(1,0) x-int

(0,-1) y-int

Martin charges $10 for every 5 bags of leaves

**Answer: each bag is 2$ **

**Step-by-step explanation: 2+2= 4 4+2 = 6 6+2=8 8+2= 10**

If **Martin charges $10 for every 5 bags of leaves**, *then we* **divide the total price by the number of bags, **then

**Answer:** In total, each bag of leaves counts $2**✅ .**

MotoWin Auto Superstore is thinking about offering a two-year limited warranty for $928 on all new cars of a certain model. The terms of the warranty would be that MotoWin would replace the car free of charge under certain, specified conditions. Replacing the car in this way would cost MotoWin 13,800 . Suppose that under the warranty, there is a 7% chance that MotoWin would have to replace the car one time and a 93% chance they wouldn't have to replace the car.

**MotoWin** can expected to make **money** from offering these warranties.

In the long-run, they should expect to make** 514 dollars** from each **warranty** sold

**What is expected value of replacement?**

The expected value to **MotoWin Auto Superstore** of a replacing a car is the sum of the costs to be incurred when there is replacement multiplied by its probability of occurrence plus the cost of no **replacement **multiplied by its likelihood of occurrence expressed in percentage terms

expected value of replacement=(cost of replacement*its probability)*(cost of no replacement*its probability)

cost of replacement=$13,800

probability of replacement=7%

cost of no replacement=$0(when there is no to replace no cost is incurred)

probability of no replacement=93%

expected value of replacement=($13,800*3%)+($0*97%)

expected value of replacement=$414

profit on replacement=replacement price-expected value of replacement

profit on replacement=$928-$414

profit on replacement=$514

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what the slope of the following equations y y equals -1/2x+4

the form or the slope-intercept form of the equation of the line is

[tex]y=mx+b[/tex]where m is the slope and b is the y-intercept

we have the next equation

[tex]y=-\frac{1}{2}x+4[/tex]**as we can see the slope is m=-1/2, because we have the same form of the slope-intercept form**

why do trees have wood (fre3 po1nts

**Answer: The tree takes the Carbon dioxide from the air and converts it to wood.**

*THIS IS AN ANSWER BECAUSE I CAN'T ANSWER SOMEONE'S QUESTION*

Bob can do a job in 5 hours, while Bill can do the same job in 8 hours. How many hours would it take them, working together, to do this job?

ANSWER:

The one in the following equation stands for ONE WHOLE JOB.

[tex]\frac{1}{5}x+\frac{1}{8}x=1\\\\[/tex]

[tex]x=\frac{40}{13} hours[/tex]

hence, this is the answer.

**Answer:**

x=40/13

**Step-by-step explanation:**

tex]\frac{1}{5}x+\frac{1}{8}x=1\\\\[/tex]

[tex]x=\frac{40}{13} hours[/tex]

Kira, Justin, and Reuben have a total of $82 in their wallets. Kira has $10 more than Justin. Reuben has 2 times what Kira has. How much do they have in their wallets?

Kira have $23 in his **wallet**.

Justin have $13 in his wallet.

Reuben have $46 in his wallet.

Given,

There are three persons, Kira, Justin, Reuben.

The **total amount **in their wallet = $82

The amount in Justin's wallet = x

The amount in Kira's wallet = x + 10

The amount in Reuben's wallet = 2(x + 10)

We have to find the** amount** in their wallets.

Here,

x + x + 10 + 2(x + 10) = 82

2x + 10 + 2x + 20 = 82

4x + 30 = 82

4x = 82 - 30

x = 52/4 = 13

Now,

The amount in Justin's** wallet** = x = $13

The amount in Kira's wallet = x + 10 = 13 + 10 = $23

The amount in Reuben's wallet = 2(x + 10) = 2(13 + 10) = 2 × 23 = $46

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Redondea 5,951 a la decena más cercana

the answer to the question is 5950

Answer:

6

Step-by-step explanation:

5.951

porque 1 no es mas o menos que 5, no vamos arriba

5.95

porque 5 es igual o mas que 5, vamos arriba

1 mas 9, es 10

pero este diez en el .9 is basicamente 1.0

entonces se combireta a uno entero

dejando nos con

6

You order seventeen burritos to go from a Mexican restaurant, eight with hot peppers and nine without. However, the restaurant forgot to label them. If you pick three burritos at random, find the probability of the given event.

The probability of at most two hot peppers = **0.918**

**Total** number of burritos ordered = 17

Number of burritos **with hot peppers** = 8

Number of burritos** without hot pepper** = 9

Number of burritos** picked **= 3

We need to find the **probability** of the event that** at most two **have hot peppers.

At most two have hot peppers means either there is one with hot pepper or there are two with hot pepper. So there should not be 3 burritos all with hot peppers.

Thus we can rewrite the **probability** that at most 2 out of 3 burritos are with hot peppers as, Total probability - the probability that all 3 burritos are with hot peppers.

So the** probability** that all three burritos are with hot peppers = P(3 with hot peppers) = (8C3x9C0)/17C3

= 56 x 1/680

= 0.082

Then the **probability** that at most two burritos out of three are **with hot peppers** = 1 - P(3 with hot peppers)

= 1 - 0.082

= **0.918**

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If a 45-gal hot water tank holds 375 lb of water, what weight of water will a 55-gal tank hold? (Round to the nearest pound.)

Given:

A 45-gal hot water tank holds 375 lb of water.

[tex]\begin{gathered} 45\text{ gal }\rightarrow375\text{ lb} \\ 55\text{ gal}\rightarrow x?\text{ lb} \end{gathered}[/tex]To find the values of x,

[tex]\begin{gathered} \frac{45}{375}=\frac{55}{x} \\ 45x=55\cdot375 \\ 45x=20625 \\ x=458.33\text{ lb} \end{gathered}[/tex]Answer: The weight of water which will hold 55 gal tank is 458 lb.

If Z is a standard normal variable, find P(-1.2 < Z < 0.4). Round your answer to 3 decimal places.

If Z is a **standard normal variable**, The value of P(-1.2 < Z < 0.4) is

0.5403

This is further explained below.

What isGenerally, A** random variable **with a **normal distribution** and mean equal to zero and standard deviation equal to one is referred to as a standard normal random variable. The letter Z will never be used to represent it in any context.

Given that, we have to find, P(-1.2<z<0.4)

P(-1.2<z<0.4) =P(z<0.4)-P(z<-1.2)

Using, the** z-distribution table **determine the values

=0.6554-0.1151

=0.5403

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Your parents said you could purchase a new car for graduation. Youwant to show them that you can be responsible and take thenecessary steps in purchasing a car. Make a list of the steps youneed to take to make your big purchase. Make sure to addresseconomics questions and concepts.
how many moles of HCL are required to prepare 0.80L of a 0.5M HCL solution
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