Could you guys help me answer this question.

Answer:

4.   2x^2 - 2x.

Step-by-step explanation:

Adding the 2 functions:

Area of the 2 triangles = x^2 + x + x^2 - 3x

= .2x^2 - 2x

Answer:

OPTION 4

Step-by-step explanation:

Let be f(x) the function that represents the area of Triangle A:

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

Let be g(x) the function that represents the area of Triangle B:

[tex]g(x)=x^2 - 3x[/tex]

Then, you need to add the area of Triangle A and the area of Triangle B in order to find the sum of the areas (Let be h(x) the function that represents the sum of the the areas of triangles A and B):

Therefore, this is:

[tex]h(x)=(x^2 + x)+(x^2 - 3x)=x^2 + x+x^2 - 3x=2x^2-2x[/tex]

You can notice that this matches with the option 4.

Answer:

x = 500.

Step-by-step explanation:

log20x^3 - 2logx = 4

By the laws of logs:

log20x^3 - logx^2 = 4

log(20x^3 / x^2) = 4

20x^3 / x^2 = 10^4

20x = 10,000

x = 10,000 / 20

x = 500.

The solution of the given logarithmic equation is x = 500.

Any equation in the variable x that contains a logarithm is called a logarithmic equation.

Given logarithmic equation

[tex]log20x^{3} -2logx=4[/tex]

Using [tex]mloga=loga^{m}[/tex]

[tex]log20x^{3} -logx^{2}=4[/tex]

Using [tex]loga-logb=log(\frac{a}{b})[/tex]

[tex]\frac{log20x^{3} }{x^{2} }=4[/tex]

[tex]log20x=4[/tex]

[tex]20x=10^{4}[/tex]

[tex]x=\frac{10000}{20}[/tex]

[tex]x=500[/tex]

The solution of the given logarithmic equation is x = 500.

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Answer:

9 ^ (-15)

Step-by-step explanation:

9^-3/9^12

We know that a^b/ a^c = a^(b-c)

9^-3/9^12 = 9 ^(-3-12)

                  =9^(-15)

The expression [tex]\frac{9^{-3}}{9^{12} }[/tex] written in the form  [tex]9^{n}[/tex] is [tex]9^{-15}[/tex]

From the question,

we are to rewrite the given expression (9^-3/9^12) in the form 9^n

First, write the expressions properly.

The given expression is

[tex]\frac{9^{-3}}{9^{12} }[/tex]

To rewrite the given expression in the form [tex]9^{n}[/tex], we will use the division law of indices

From the division law of indices, we have that

[tex]x^{y} \div x^{z}= x^{y-z}[/tex]

Then, the given expression becomes

[tex]\frac{9^{-3}}{9^{12} } = 9^{-3} \div 9^{12}[/tex]

[tex]= 9^{-3-12}[/tex]

[tex]=9^{-15}[/tex]

Hence, the expression [tex]\frac{9^{-3}}{9^{12} }[/tex] written in the form  [tex]9^{n}[/tex] is [tex]9^{-15}[/tex]

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Using the Pythagorean theorem a^2 + b^2 = c^2 where a and b are the side and bottom of the triangle and c is the hypotenuse ( length of rope).

Let the tent pole = a

Lhe distance from the pole be b = 10 ft.

The length of rope would vce c = 26 ft.

Now you have:

a^2 + 10^2 = 26^2

Simplify:

a^2 + 100 = 676

Now subtract 100 from each side:

a^2 = 576

To get a, take the square root of both sides:

a = √576

a = 24

The tent pole is B. 24 ft

Answer:

[tex]\$620.07[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=2\ years\\A=\$700\\ r=0.0625\\n=1[/tex]  

substitute in the formula above  and solve for P

[tex]700=P*(1+\frac{0.0625}{1})^{2}[/tex]  

[tex]700=P*(1.0625)^{2}[/tex]  

[tex]P=700/(1.0625)^{2}[/tex]  

[tex]P=\$620.07[/tex]  

Answer:B, C, D, E.

Step-by-step explanation:

The third side of a triangle with two sides measuring 10 and 14 units must be greater than 4 and less than 24 units. This is determined using the Triangle Inequality Theorem.

The possible values for the third side of a triangle with sides of lengths 10 and 14 can be found using the Triangle Inequality Theorem.

Add the two given side lengths: 10 + 14 = 24.

To find the range of possible values for the third side, subtract the two given side lengths from the total: 24 - 10 = 14, and 24 - 14 = 10.

Therefore, the third side of the triangle must have a length greater than 4 but less than 24.

Answer:

-10.2n - 1

Step-by-step explanation:

−2.4n − 3 + (−7.8n + 2) =

= -2.4n - 7.8n - 3 + 2

= -10.2n - 1

Answer:

-10.2n -1

Step-by-step explanation:

−2.4n−3 + −7.8n+2

Combine like terms

−2.4n −7.8n -3+2

-10.2n -1

Answer:

5.75

Step-by-step explanation:

[tex]3 + 11 + 4 + 3 + 10 + 6 + 4 + 5 = 46 \\ 46 \div 8 = 5.75[/tex]

The total amount of numbers are : 8

To find the mean, we calculate the sum of all values and divide that sum by the amount of numbers there are.

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Answer:

[tex]-6x+15< 10-5x[/tex]

Step-by-step explanation:

we have

[tex]-3(2x-5) < 5(2-x)[/tex]

solve for x

eliminate the parenthesis (apply the distributive property)

[tex]-3*2x+3*5 < 5*2-5*x[/tex]

[tex]-6x+15< 10-5x[/tex] ---> correct representation of the inequality

Adds (5x-15) both sides

[tex]-6x+15+5x-15< 10-5x+5x-15[/tex]

[tex]-x< -5[/tex]

Multiply by -1 both sides

[tex]x>5[/tex]

Answer:

-23 = x

Step-by-step explanation:

-(-9) = 9

The thing with double negatives is that they form a plus sign, so that is really a POSITIVE nine. Therefore you do the inverse to find x: -14 - 9 = -23.

I am joyous to assist you anytime.

Answer:

[tex]\Huge \boxed{X=-23}[/tex]

Step-by-step explanation:

[tex]\displaystyle x+9=-14[/tex]

[tex]\Large\textnormal{First, subtract by 9 from both sides of equation.}[/tex]

[tex]\displaystyle x+9-9=-14-9[/tex]

[tex]\Large\textnormal{Simplify, to find the answer.}[/tex]

[tex]\displaystyle -14-9=-23[/tex]

[tex]\Large\textnormal{x=-23, which is our answer.}[/tex]

[tex]\tt 4c-d-c-3d=3c-4d[/tex]

Answer:

3c -4d

Step-by-step explanation:

4c -d -c -3d

Combine like terms

4c -c     -d -3d

3c -4d

Answer:

Step-by-step explanation:

[tex]x^2-2x-3=0\\\\x^2+x-3x-3=0\\\\x(x+1)-3(x+1)=0\\\\(x+1)(x-3)=0\iff x+1=0\ \vee\ x-3=0\\\\x+1=0\qquad\text{subtract 1 from both sides}\\x=-1\\\\x-3=0\qquad\text{add 3 to both sides}\\x=3[/tex]

Answer:

I prefer to express solutions to inequalities using interval notation. Both formats are are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

To express solutions to inequalities using interval notation.

I prefer to express solutions to inequalities using interval notation. Both formats are important but I think interval notation is easier to understand and represents better the solutions.

For example, if you have the following inequation:

x-2> 1

x>3

Therefore, the solution could be written either x>3 OR (3, +inf). But what happens if the solution to the system of equation is x>3 or x<-3? The solution can be easily written as: (-inf, -3) U  (3, inf) instead of 'x>3 or x<-3' which can be confusing.

Hence, To express solutions to inequalities using interval notation.

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Answer:

f(x) = 4.5x + 3/8

Answer: Third Option

[tex]f(x) = \frac{3}{8}x + 54[/tex]

Step-by-step explanation:

We want to propose an equation that models the distance traveled by the caterpillar as a function of time, we have a constant initial quantity of 4.5 feet and then we know that every minute the caterpillar advances 3/8 of an inch

Then the distance that the caterpillar to advanced after x minutes is:

[tex]f(x) = \frac{3}{8}x[/tex]

Then we know that initially the caterpillar was at a distance of 4.5 feet or 54 inch

Then the equation for the distance in inch is:

[tex]f(x) = \frac{3}{8}x + 54[/tex]

Answer:

The correct answer is the second one

Step-by-step explanation:

Line BE and ED are congruent because they are the same length and E is the mid line.

Answer:

second option is correct

Step-by-step explanation:

By the given

ΔDEC≅ΔBEC

which means triangle DEC is congruent to triangle BEC

then by CPCTC (corresponding parts of congruent triangle are congruent)

there every side and angle of DEC will be equal to BEC

⇒BE= DE (by CPCTC)

hence second option is correct

Answer:

[tex]a_n=-\frac{1}{n}[/tex]

[tex]a_6=-\frac{1}{6}[/tex] is our sixth term.

[tex]a_7=-\frac{1}{7}[/tex]  is our seventh term.

[tex]a_8=-\frac{1}{8}[/tex] is our eighth term.

Step-by-step explanation:

So every number in this sequence is -.

If you write 1 as 1/1, then you should see the numerator is constant one while the denominator is going up by 1 each time.

So the patter is

[tex]a_n=-\frac{1}{n}[/tex]

Test if you like:

n=1 gives us [tex]a_1=-\frac{1}{1}=-1[/tex] which is our first term.

n=2 gives us [tex]a_2=-\frac{1}{2}[/tex] which is our second term.

n=3 gives us [tex]a_3=-\frac{1}{3}[/tex] which is our third term.

n=4 gives us [tex]a_4=-\frac{1}{4}[/tex] which is our fourth term.

n=5 gives us [tex]a_5=-\frac{1}{5}[/tex] which is our fifth term.

Now we are going to use [tex]a_n=-\frac{1}{n}[/tex]

to write our next three terms:

n=6 gives us [tex]a_6=-\frac{1}{6}[/tex] which is our sixth term.

n=7 gives us [tex]a_7=-\frac{1}{7}[/tex] which is our seventh term.

n=8 gives us [tex]a_8=-\frac{1}{8}[/tex] which is our eighth term.

Answer:

x=3 or x= 1/3

Step-by-step explanation:

Let the number = x

The reciprocal of the number = 1/x

According to the given statement:

x+1/x=10/3

x²+1/x=10/3

3(x²+1)=10x

3x²+3=10x

Move 10x to the L.H.S

3x²-10x+3=0

Break the middle term:

3x²-9x-x+3=0

3x(x-3)-1(x-3)=0

(x-3)(3x-1)=0

x-3=0 , 3x-1=0

x=0+3 ,  3x=0+1

x=3    , 3x=1

x=3    ,x = 1/3

So x=3 or x= 1/3 ....

Answer:

f⁻¹(x) = (4x)/5

Step-by-step explanation:

f(x) = 2x - 3x/4.

Assume y=f(x). Therefore:

y = 2x - 3x/4.

Make x the subject in the above equation.

y = (2x(4) - 3x)/4.

y = 5x/4.

4y = 5x.

(4y)/5 = x.

x = (4y)/5.

Therefore:

f(y) = (4y)/5.

Replace y with x.

f⁻¹(x) = (4x)/5.

Therefore, the inverse of f(x) = 2x - 3x/4 is f⁻¹(x) = (4x)/5!!!

Answer:

[tex]\boxed{\text{3; is not}}[/tex]

Step-by-step explanation:

[tex]\begin{array}{rcl}p(x) & = & (x - 7)(x^{2} - 2x + 4) + 3\\\\\dfrac{p(x)}{x - 7} & = &x^{2} - 2x + 4 + \dfrac{3 }{x-7 }\\\\\end{array}\\\\\text{The number }\boxed{\mathbf{3}}\text{ is the remainder when $p(x)$ is divided by $(x - 7)$,}\\\\\text{so $(x - 7)$ }\boxed{\textbf{is not}} \text{ a factor of $p(x)$.}[/tex]

(q+8)(2n^2-1)

I think this is the correct form.

Answer:

Third graph

Step-by-step explanation:

We are determine whether which of the given graphs is that of the linear inequality [tex]2y>x-2[/tex].

We know that, on the graph the greater than sign ([tex]>[/tex]) represents the shaded part above the line and less than sign ([tex]<[/tex]) represents the shaded region below the line.

While the signs [tex]\leq[/tex] or [tex]\geq[/tex] is denoted by a solid line on the graph.

Therefore, the third graph represents the given inequality.

Answer:

The graph in the attached figure

Step-by-step explanation:

we have

2y > x-2

The solution of this inequality is the shaded area above the dotted line 2y=x-2

The graph in the attached figure

Answer: 5.

Step-by-step explanation:

6+9 = 15

10 + x = 15

-10 -10

x = 5

Answer:

x=5

Step-by-step explanation:

6+9=10+x

15=10+x

x=15-10

x=5

Answer:

12 is the best estimate

Answer:

option A.

Step-by-step explanation:

We have to find the circumference of the given circle with radius 2 units.

Since formula to calculate circumference of a circle is = 2πr

Where r = radius of the circle.

Circumference = 2 × (3.14) × (2)

                        =  4 × 3.14

                        = 12.56

So approximate value will be option A.

Answer:

D. G(x) = (x+2)^2

Step-by-step explanation:

We can easily solve this problem by graphing each case with a graphing calculator or any plotting tool.

The equations are

A. G(x) = (x-2)^2

B. G(x) = (x)^2 + 2

C. G(x) = (x)^2 -2

D. G(x) = (x+2)^2

Se attached image.

The correct option is

D. G(x) = (x+2)^2

Answer:

C. G(x)=x²-2

Step-by-step explanation:

The midpoint of the graph has been displaced from x=0 to x=-2. this is a negative displacement.

Therefore the new equation G(x)=x²-2

This is because there is no tilt in the graph so it is a replica of the red graph.

Answer:

37

Step-by-step explanation:

Substitute x = 10 into g(x), then substitute the result into f(x)

g(10) = 10 - 4 = 6, then

f(6) = 6² + 1 = 36 + 1 = 37

Answer:

Width=4.7 ft

Length=16.1 ft

Step-by-step explanation:

Let the width of the table to be x ft

Then the length should be two more than three times the width= 2+3x ft

The area of the serving table should be 75 ft²

But you know the area of this table is calculated by multiplying the length by the width of the table

Hence, Area= length× width

Length=x ft  and width =2+3x ft

75ft²= (x ft) × (2+3x ft)

[tex]75=x*(2+3x)\\\\75=2x+3x^2\\\\3x^2+2x-75=0[/tex]

Apply the quadratic formula to solve this quadratic equation

The formula is ;

x= (-b ±√b²-4ac)÷2ac

where a=3, b=2 and c=-75

x= (-2 ± √2²-4×3×-75)÷(2×3)

x=(-2±√4+900)÷6

x=(-2±√904)÷6

x=(-2±30.1)÷6

x=(-2+30.1)÷6=4.683⇒4.7(nearest tenth)

or

x=(-2-30.1)÷6= -32.1÷6=-5.35⇒ -5.4

Taking the positive value

x=width =4.7 ft

2+3x= length= 2+3(4.7)=16.1 ft

Answer:

A 3

Step-by-step explanation:

y-9 = 3(x-9)

This is in point slope form

y-y1 = m(x-x1)

where (x1,y1) is the point and m is the slope

A point on the line is (9,9) and the slope is 3

Answer:

y=0.01179/w

Step-by-step explanation:

First understand that the fuel consumption in miles per gallon is inversely proportional to the weight of a car.

If y is the fuel consumption in miles per gallon and w is weight of car in pounds . you can write the first statement as;

y∝1/w

Introduce a constant value for proportionality, k

y=k/w....................make k subject of the formula by multiplying both sides by 1/w

k=y/w

Given in the question that ;

w=2800

y=33

k=?

To find k , apply the formula that you derived above

k=y/w

k=33/2800 =0.011785⇒0.01178(4 significant figures)

Rewrite the formula as

y=k/w  ⇒ y=0.01179/w

The equation that relates y and w is;

y=0.01179/w

The fuel consumption in miles per gallon for a car varies inversely with its weight and can be represented mathematically by the inverse proportionality relationship y = k/w. Substituting the given values gives us the constant k = 92400, so the final equation is y = 92400/w.

This problem can be defined mathematically by an inverse proportionality relationship, expressed as y = k/w, where k is a constant, y is the fuel consumption in miles per gallon, and w is the weight of the car in pounds.

To find the value of k, we can substitute the given values into the equation. This gives us 33 = k/2800, which simplifies to k = 33 * 2800, or k = 92400.

So, the equation that relates the mileage per gallon, y, to the weight of the car, w, is y = 92400/w. This means the fuel efficiency of a car decreases as its weight increases, thus heavier cars tend to have lower miles per gallon.

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