Mathematics College

## Answers

**Answer 1**

The given equations are

y = x^2 + 2x + 7

y = x + 7

We would substitute y = x + 7 into the first equation. It becomes

x + 7 = x^2 + 2x + 7

Collecting like terms, it becomes

x^2 + 2x - x + 7 - 7 = 0

x^2 + x = 0

By factorising x, it becomes

x(x + 1) = 0

Thus,

x = 0 or x + 1 = 0

x = 0 or x = - 1

Substituting x = 0 into y = x + 7, it becomes

y = 0 + 7

y = 7

Thus, one solution set is (0, 7)

Substituting x = - 1 into y = x + 7, it becomes

y = - 1 + 7

y = 6

Thus, another solution set is (- 1, 6)

Therefore, **the solution sets are **

**{(0, 7), (- 1, 6)}**

**Option A is correct**

## Related Questions

Order these numbers from least to greatest 7.15 , 7 18/25 , 7.134 , 77/10

### Answers

7.134 , 7.15 , 77/10 , 7 18/25

what is the simplified form of the expression x^2+4x-21 over 4(x+7)

### Answers

**Answer:**

x-3 over 4

Let me know if you need elaboration

f(x)=3x+4 Evaluate f(2)=

### Answers

We will look at how to evaluate a function for one of the value from a defined domain.

Domain is a set of values over which the function is defined. These are set of values of ( x ) that serves as an input to the function.

Function expresses an input -> output relationship usually expressed as an amalgam of different mathematical expressions. The function evaluates the output for every set value of ( x ) from the domain. The mathematical expressions ( relationships ) are given in terms of the input variable(s).

We are given the following function as follows:

[tex]f\text{ ( x ) = 3x + 4}[/tex]

The above functions isd efined for all the real values. Hence, the domain of the above function is defined as:

[tex]\text{\textcolor{#FF7968}{Domain:}}\text{ x :-> ( -}\infty\text{ , }\infty\text{ )}[/tex]

We will evaluate the above function for one of the values from the domain. We will plug in the value of input ( x = 2 ) into the function. Then we will evaluate the function f ( x ) as follows:

[tex]\begin{gathered} f(2)\text{ = 3}\cdot(2)\text{ + 4} \\ f(2)\text{ = 6 + 4} \\ \textcolor{#FF7968}{f(2)}\text{\textcolor{#FF7968}{ = }}\textcolor{#FF7968}{10} \end{gathered}[/tex]

Hence, the function is evaluated for the input value of ( x = 2 ) and the ouput is:

[tex]\textcolor{#FF7968}{10}[/tex]

2. The following triangle is an isosceles triangle. What is the length of the missing side? ? 11 in. 37 ? 4 in. 11 in 37° 4 in 530

### Answers

An ISOSCELES triangle has two sides equal, and two base angles are also equal.

The two sides on the left and the right are equal. The right side measures 11 inches, therefore the left side also measures 11 inches.

The correct answer option is 11 inches

How to graph inequalities y + 6 < 10 or 2y - 3 > 9

### Answers

We need to graph on the number line the solution to the compounded inequality

[tex]\begin{gathered} y+6<10 \\ \text{or } \\ 2y-3>9 \end{gathered}[/tex]

In order to do so, let's work with each inequality separately. The final solution will be the union of the two solutions since it can be one "or" the other.

**Step 1**

Subtract 6 from both sides of the first inequality:

[tex]\begin{gathered} y+6<10 \\ \\ y+6-6<10-6 \\ \\ y<4 \end{gathered}[/tex]

So, the solution to the first inequality is all real numbers less than 4 (not included). Therefore, we graph this solution using an empty circle:

**Step 2**

Add 3 to both sides of the second inequality, and then divide both sides by 2:

[tex]\begin{gathered} 2y-3+3>9+3 \\ \\ 2y>12 \\ \\ \frac{2y}{2}>\frac{12}{2} \\ \\ y>6 \end{gathered}[/tex]

Thus, the solution to this inequality is all the real numbers greater than 6 (not included: empty circle):

**Answer**

Therefore, the solution to the compounded inequalities is the union of both solutions:

Hello. I am trying to help my 9th grade daughter with text corrections. It has been over 20 yrs since I had Algebra 1 and Im a bit rusty. She gets easily frustrated especially in math so Im trying to do some of the leg work before going over how to do it with her. I appreciate your help in advance.

### Answers

The half-life of a radioactive substance is given 3 hours.

Given the initial amount of substance is 800 grams. After 3 hours, the substance becomes half that is 400 grams. Then again after 3 more hours, the substance becomes half again that is 200 grams. Again after three hours, the substance becomes half that is 100 grams.

Thus, the amount of radioactive material after 9 hours is 100 grams.

In a study of 200 students under 25 years old one-fifth have not yet learned to drive. What percentage can drive?

### Answers

[tex]\begin{gathered} \text{Total number of students is }\Rightarrow200 \\ \frac{1}{5}\text{ can't drive}\Rightarrow200\times\frac{1}{5}=40\text{ students can't drive} \\ Number\text{ of students tthose can drive}\Rightarrow200-40=160\text{ students} \\ So, \\ \text{percentage}\Rightarrow\frac{160}{200}\times100=80\text{ \% students can drive.} \end{gathered}[/tex]

Mantinum What is 92,119 rounded to the nearest thousand?

### Answers

We will have that 92,119 rounded to the nearest thousand is:

[tex]92,119[/tex]

This is since there are not smaller decimals on the number to be able to round it.

which of the triangles cannot be proved congruent? so a different tutor gave me the answer which is D. But he told me to ask another tutor to tell me how to type out how I got the answer.

### Answers

The triangles that cannot be proved congruent are the triangles in option D. We are not told that the other side is congruent to the corresponding side of the other triangle.

To prove they are congruent, we need to know the other side is congruent and prove this using the SSS postulate.

In the other cases, we can be proved they are congruent by:

• Case A ---> SAS postulate.

,

• Case B ---> ASA postulate.

,

• Case C ---> SSS postulate (the triangles share a common side)

In summary, *we only have that **the triangles in D cannot be proved congruent** since we have two corresponding congruent sides, and one angle (vertical angle) to be congruent corresponding parts. It would be an SSA method. However, this method is not Universal, and it is not enough to demonstrate they are congruent.*

A door to playhouse is 50 inches tall.Which of the following is another measure eaqual to the height?A.4 ft 2 in.B.4 ft 1 in.C.4 ft 1/2 in.D.5 ft

### Answers

Dereo, this is the solution:

All we need to do is to convert inches to feet, as follows:

Let's recall that:

12 inches = 1 feet

In consequence,

50 inches = 50/12 feet

50 inches = 4 feet + 2 inches

**The correct answer is A. **

I need help converting to logarithmic equation e^-t = 125

### Answers

Apply ln to both sides:

Ln e^-t = ln 125

Ln e (125) = -t

how do i find the volume to the nearest 1 decimal place?

### Answers

**Solution:**

The volume of a cylinder is expressed as

[tex]\begin{gathered} V=\pi\times r^2\times h \\ where \\ V\Rightarrow volume\text{ of the cylinder} \\ r\Rightarrow radius\text{ of its circular ends} \\ h\Rightarrow height\text{ of the cylinder} \end{gathered}[/tex]

Given the cylinder below:

we have

[tex]\begin{gathered} height\text{ of the cylinder = 4 cm} \\ diameter\text{ of the circular end = 2 cm} \end{gathered}[/tex]

but

[tex]\begin{gathered} radius=\frac{diameter}{2} \\ \Rightarrow r=\frac{d}{2}=\frac{2cm}{2}=1\text{ cm} \end{gathered}[/tex]

Thus, the volume of the cylinder is evaluated by substituting the values of 4 cm and 1 cm for h and r respectively into the volume formula.

[tex]\begin{gathered} V=\pi\times1cm\times1cm\times4cm \\ =12.56637 \\ \approx12.6\text{ cubic centimeters} \end{gathered}[/tex]

**Hence, the volume of the cylinder, to the nearest 1 decimal place is **

[tex]12.6\text{ cubic centimeters}[/tex]

4+(6x2²)-9 use pemdas

### Answers

**Given:**

[tex]4+(6\times2^2)-9[/tex]

**Required:**

To solve the given expression.

**Explanation:**

Consider

[tex]\begin{gathered} =4+(6\times2^2)-9 \\ \\ =4+(6\times4)-9 \\ \\ =4+24-9 \\ \\ =28-9 \\ \\ =19 \end{gathered}[/tex]

**Final Answer:**

[tex]4+(6\times2^2)-9=19[/tex]

Which number line shows points are to represent the opposite of P

### Answers

**Explanation**

The given image marks point p at -3 . Therefore, the opposite of -3 is +3. The corresponding number line that marks R as +3 is given as

**Answer: Option 2**

The number of dogs per household in a neighborhood is given in the probabilitydistribution. Find the mean and the standard deviation. Round to 1 decimal.# of Dogs0123stP(x)0.620.240.070.05.02a) What is the mean rounded to 2 decimal place?b) What is the standard deviation rounded to 2 decimal place?

### Answers

[tex]\sum ^n_{i\mathop=1}\frac{\text{xiP(x)}}{N}=\frac{0\cdot0.62+1\cdot0.24+2\cdot0.07+3\cdot0.05+4\cdot0.02}{0.62+0.24+0.07+0.05+0.02}=\frac{0.61}{1}=0.6[/tex]

[tex]s=\sqrt[]{\frac{(x-\mu)^2p(x)}{n}}[/tex]

[tex]\begin{gathered} \sum ^n_{i\mathop=1}(x-\mu)^2p(x)=(0-0.61)^20.62+(1-0.61)^20.24+(2-0.61)^20.07+.. \\ \text{ (3-0.61)}^20.05+(4-0.61)^20.02=0.9179 \\ \end{gathered}[/tex][tex]s=\sqrt[]{\frac{0.9179}{1}}=0.958\approx0.96[/tex]

The answers to choose from are -40, 130, 53, -63, -140, 265, 234

### Answers

First we need to know how to convert radians to degrees

[tex]d=\text{r}\cdot\frac{180}{\pi}[/tex]

where r is the measure in radians and d is the measure in degrees

for A.

r=53pi/36

[tex]d=\frac{53\pi}{36}\cdot\frac{180}{\pi}=265[/tex]

the measure in degrees is** 265°**

for B.

r= 13pi/18

[tex]d=\frac{13\pi}{18}\cdot\frac{180}{\pi}=130[/tex]

the measure in degrees is **130°**

for C.

r=-7pi/20

[tex]d=-\frac{7\pi}{20}\cdot\frac{180}{\pi}=-63[/tex]

the measure in degrees is **-63°**

for D.

r=-2pi/9

[tex]d=-\frac{2\pi}{9}\cdot\frac{180}{\pi}=-40[/tex]

the measure in degrees is **-40°**

Nintendo previously projected that it would sell 19 million units of the console for the year ending in March. If it ended up selling 26.5 million after several upward versions to the forecast. How many selling off were their estimate

### Answers

[tex]\begin{gathered} 26.5-19=7.5 \\ \\ \text{ They were 7.5 million selling off!} \end{gathered}[/tex]

Suppose that the dollar value v(t) of a certain car that is t years old is given by the following exponential function. v(t) = 21, 300 * (1.24) ^ t

### Answers

**Given:-**

[tex]v(t)=21300(1.24)^t[/tex]

**To find the initial value, does the fucnction represent growth or decay.**

Here the value of a is **21300.**

So we get,

[tex]1+r=1.24[/tex]

So the value of r is,

[tex]r=0.24[/tex]

So now we get percentage is,

[tex]24\%[/tex]

Rate of change is **24%.**

So the required solution is,

[tex]initial\text{ value =21300}[/tex]

So the percentage range is,

[tex]24\%[/tex]

How many radians are equal to 180 degrees 2piPi 1 2

### Answers

**Given: **An angle of 180 degrees.

**Required: **To find the measure of the given angle in radians.

**Explanation: **The degree and radians measure of an angle is related by the following relation

[tex][/tex]

Write the point-slope form of the equation of the line that passes through the point (-1, 5) and has a slope of -1.

a. Using variables, write out the formula for the point-slope form of the equation.

b. Identify the values for m, x1, and y1.

c. Fill these values into the point-slope form of the equation from part (a), and simplify as needed.

Use the box provided to submit all of your calculations and final answers. Simplify the answer as needed.

### Answers

[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{5})\hspace{10em} \stackrel{slope}{m} ~=~ - 1 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{5}=\stackrel{m}{- 1}(x-\stackrel{x_1}{(-1)}) \implies {\large \begin{array}{llll} y -5= -(x +1) \end{array}}[/tex]

A store had 896 swimsuits that were marked to sell at $40.99. Each suit was marked down $17.90. Find the reduced price using the formula M=S-N, where M is the markdown, S is the original selling price, and N is the reduced price. The reduced price is?

### Answers

Let us assumed that each of the swimsuit is marked to sell at $40.99, and each suit was marked down $17.90 (given).

With the given formula below, we solve for the reduced price

[tex]M=S-N[/tex][tex]\begin{gathered} M=\text{ \$17.90(given)} \\ S=\text{ \$40.99(given)} \\ N=\text{reduced price} \end{gathered}[/tex]

Substitute the value of M and S in the given formula to solve for N as shown below:

[tex]\begin{gathered} 17.90=40.99-N \\ 17.90+N=40.99-N+N \\ 17.90+N=40.99 \\ 17.90+N-17.90=40.99-17.90 \\ N=23.09 \end{gathered}[/tex]

**Hence, the reduce price is $23.09**

For which value of x does p(x)=-4 in the graph below

### Answers

You have to identify which dot in the graph corresponds to p(x)=-4

**p(x)=-4 → this expression indicates that the value of the "output" is -4, in the graph, it will correspond to the dot that has y-coordinate= -4**

The dots in the graph have the following coordinates:

The coordinates are always given in the following order (x,y), the first coordinate corresponds to the value of x (input) and the second coordinate corresponds to the value of y (output)

From the dots, the only one that has the y-coordinate -4 is the one located in the fourth quadrant with coordinates** (2,-4)**

hurry and anwser please im dying

### Answers

**Answer:**

the answers to your question would be 65 aka D

is 1,000 feet greater than 300 yards

### Answers

hello

to solve this question, we have to know the the dimensions or

Pls help with this math problem pl

### Answers

Using the **slope intercept equation**, the equation of the line in fully simplified slope intercepted form is y=4x−4.

In the given question we have to write the **equation** of the line in fully simplified **slope intercepted** form.

As we know that slope intercept form of equation of line is given by

y=mx+c

where m=**slope **

c=intercept of the line (i.e point where line cut y-axis )

From graph we can easily find two point of the line that is (1,0)(0,−4).

From the point x(1)=1, y(1)=0, x(2)=0, y(2)=−4

Slope (m)=(y(2)−y(1))/(x(2)−x(1))

m=(−4−0)/(0−1)

m=-4/−1

m=4

As we know that c is a point where line cut y axis so c=−4

Hence, slope-intercept form of** equation** is y=4x−4.

To learn more about **slope intercept equation** link is here

brainly.com/question/28947895

#SPJ1

If 8% of the sheet aluminum is lost to scrap when forming a fuel tank, what is the weight of the tank if the raw sheets of aluminum weigh 200 pounds?

### Answers

**Solution**:

**Step 1**: Calculate 8% of the raw sheets of aluminum :

[tex]200\text{ x 0.08 = 16}[/tex]

This is the weight that is lost in the production of the fuel tank.

**Step 2**: Calculate the weight of the tank :

200 pounds - 16 pounds = 184 pounds.

So that, we can conclude that** the correct answer is:**

**184 pounds.**

How do I solve these?If f(x)=3xsquared + 9x-4 then evaluate the following:f(1)=3x^2+9x-4f(x+h)=3x^2+9x-4

### Answers

[tex]\begin{gathered} a)\text{ }f(1)\text{ = 8} \\ b)\text{ }f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]

Explanation:[tex]\begin{gathered} The\text{ given function:} \\ f(x)=3x^2\text{ + 9x - 4} \end{gathered}[/tex]

a) We need to evaluate when x = 1

**f(1): this means we will replace x with 1 in the given function**

[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f\mleft(1\mright)=3(1)^2+9(1)-4 \\ f(1)\text{ = 3(1) + 9 - 4 = 3 + 9 - 4} \\ f(1)\text{ = 8} \end{gathered}[/tex]

b) We need to evaluate the function when x = x + h

[tex]\begin{gathered} f\mleft(x\mright)=3x^2+9x-4 \\ f(x\text{ + h): we will replace x with x + h in the given function} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]

**Expanding:**

[tex]\begin{gathered} f(x\text{ + h) }=3(x^2+2xh+h^2)\text{ + 9(x + h) - 4} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \text{Since there are no like terms we can simplify, we can leave it in expanded form:} \\ f(x\text{ + h) }=3x^2+6xh+3h^2\text{ + 9x + 9h - 4} \\ \\ or\text{ the non expanded form:} \\ f(x+h)=3(x+h)^2\text{ + 9(x + h) - 4} \end{gathered}[/tex]

The following table is a function.х15725354 9у-3 27-4 5971 0

### Answers

a For any relation to be a function, an independent variable x cannot produce different dependent varible y

From the table,

when x = 5, y = 2

Also, when x = 5, y = 5

and when x = 5, y = 7

We can see that x= 5 produces 3 different values of y ( that is 2, 5, and 7). This has disobeyed the rule of a function

Hence, the table is not a function

**The answer is False**

AХХ14DС1016BABBCCDAD0-14=1016 Х10x= 224x= 22.4

### Answers

we get that

[tex]\frac{10}{16}=\frac{x}{14}\rightarrow x=14\cdot\frac{10}{16}=\frac{35}{4}=8.75[/tex]

The sales tax rate is 10%. If Lindsey buys a fountain priced at $125.40, how much tax will she Inay? $

### Answers

We have to calculate the sales tax over a purchase of $125.40.

The sales tax rate is 10%, so we can calculate:

[tex]\text{Sales tax}=\frac{10}{100}\cdot125.40=0.1\cdot125.40=12.54[/tex]

**Answer: the sales tax on this purchase is $12.54,**