Find a ⋅ b. a = 4i - 4j, b = 4i + 5j

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:

[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: 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:

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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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]

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:

-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]

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:

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:

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:

[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.

[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:

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

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:

(f+g)(x)= 5x-11

(f-g)(x)= x-3

The value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

It is required to find the value of   (f+g)(x) and (f-g)(x).

A function is defined as a relation between a set of inputs having one output each. function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input.

Given:

The functions are

f(x) = 3x - 7

g(x) = 2x - 4

We have to find the value of the function (f + g)(x) and  (f-g)(x) we get

According to given question we have,

The value of the function (f +g)(x)

(f + g)(x) = f(x) + g(x)

(f + g)(x) = 3x - 7 + 2x - 4

(f + g)(x) = 5x - 11

The value of the function (f - g)(x)

(f - g)(x) = f(x) - g(x)

(f - g)(x) = 3x - 7 - (2x - 4)

(f - g)(x) = 3x - 7 - 2x + 4

(f - g)(x) = x - 3

Therefore,  the value of the functions (f + g)(x) and (f - g)(x) will be 5x - 11 and x - 3.

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The line segment drawn from point A to point A′, after reflecting the triangle over the y-axis, is perpendicular to the y-axis. This is because the reflection mirrors the image across the y-axis resulting a right-angle formation between the line segment and the axis.

The line segment drawn from point A to point A′, after a reflection of Triangle HAM over the y-axis, would be perpendicular to the y-axis. This is because in a reflection over the y-axis, the x-coordinates of the points change sign and the y-coordinates stay the same. This procedure mirrors the image over the y-axis and creates a segment from A to A′ that is perpendicular to the y-axis and bisects the distance between A and A′.

This idea correlates to the vector concept in physics where components of the vector may be viewed as sides of a right triangle. Much like in that context, the line segment from A to A′ and the y-axis form a right angle, hence they are perpendicular.

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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:

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:

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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[tex]\huge{\boxed{\frac{1}{20}}}[/tex]

To convert from a decimal to a percentage, multiply the decimal by [tex]100[/tex].  [tex]0.05*100=5[/tex], so the percentage equivalent is [tex]5\%[/tex].

Percentages are fractions when you use a denominator of [tex]100[/tex], so [tex]5\%[/tex] is the same as [tex]\frac{5}{100}[/tex].  Divide the numerator and denominator each by [tex]5[/tex] to get the fraction in simplest form, which is [tex]\frac{1}{20}[/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:

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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9m = 4.5

divide by 9 for 9m and 4.5

9m/9= 4.5/9

m= 0.5

3v= -105

divide by 3 for 3v and -105

3v/3=- 105/3

v= -35

17m = 85

divide by 17 for 17m and 85

17m/17= 85/17

m= 5

Answers: 0.5,-35 and 5

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:

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:

[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:

see below

Step-by-step explanation:

g(x) = x^3 − x^2 − 4x + 4

We know the graph will have up to 3 zero's because it is a cubic

g(x) = x^3 − x^2 − 4^x + 4

I will factor by grouping, taking an x^2 from the first 2 terms and -4 from the last 2 terms

  g(x)=  x^2(x-1) -4(x-1)

Now factor out x-1

  g(x)= (x-1)(x^2 -4)

We can factor the (x^2-4) as a difference of squares

g(x) = (x-1) (x-2)(x+2)

Using the zero product property

0= (x-1) (x-2)(x+2)

x-1 =0   x-2 =0   x+2=0

We have zeros at x=1   x=2  and x=-2

Then we can plot points to determine where the function is between the points We will pick negative infinity 0 1.5 and infinity

at g(-inf) =  -inf  because x^3 dominates and that goes to -infinity

at g(0) = 0+000+4 =4

at g(1.5) =-.875

at  g(inf)=because x^3 dominates and that goes to infinity

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!!!