What Is The Solution Set Of Y Equals X Squared Plus 2X + 7 + Y Equals X + 7 (2024)

Answer:

x-3 over 4

Let me know if you need elaboration

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]

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

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:

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.

[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]

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.

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.

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.

Apply ln to both sides:

Ln e^-t = ln 125

Ln e (125) = -t

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]

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]

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

[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]

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°

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

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]

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]

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

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)

Answer:

the answers to your question would be 65 aka D

hello

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

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

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.

[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]

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

we get that

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

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,