Determine the factors of 5x2 + 6x − 8. (5x − 1)(x + 8) (5x − 8)(x + 1) (5x − 4)(x + 2) (5x − 2)(x + 4)

Answer:

11/12

Step-by-step explanation:

18/36 + 15/36= 33/36 = 11/12

The  probability that the chosen animal feeds on seeds or insects or both is:

                [tex]\dfrac{3}{4}[/tex]

Let A denote the event that the animal feed on seeds.

B denote the event that the animal feed on insects

and A∩B denote the event that the animal feed on both seed and insects.

and A∪B denote the event that the animal feeds on seeds or insects or both.

Let P denote the probability of an event.

Now, based on the information from the question we have:

[tex]P(A)=\dfrac{18}{36}\\\\P(B)=\dfrac{15}{36}\\\\P(A\bigcap B)=\dfrac{6}{36}[/tex]

Now, we know that:

[tex]P(A\bigcup B)=P(A)+P(B)-P(A\bigcap B)[/tex]

Hence, on putting the values we have:

[tex]P(A\bigcup B)=\dfrac{18}{36}+\dfrac{15}{36}-\dfrac{6}{36}\\\\\\P(A\bigcup B)=\dfrac{18+15-6}{36}\\\\\\P(A\bigcup B)=\dfrac{27}{36}=\dfrac{3}{4}[/tex]

the answer is

10 × (4+3) = 70

Answer:

the solution is (40, 21)

Step-by-step explanation:

Let the two numbers be x and y.

Then x + y = the sum = 61, and

         x - y = the difference = 19.

Solve the system of linear equations

x + y = 61

x - y  = 19

Combining these two equations:

x + y = 61

x - y  = 19

---------------

2x    =  80, so x must be 40.

Substituting 40 for x in the first equation, we get 40 + y = 61.  

Combining the constants, we get y = 21.

Then the solution is (40, 21).

The numbers whose sum is 61 and difference 19 are 40 and 21. This is obtained by using algebraic expression for the given condition.

Given that sum of numbers is 61 and difference is 19.

Let the larger number be x and smaller number be y.

Then we can write that, x+y=61 (sum) and x-y=19 (difference)

By solving the algebraic equations we can find the numbers.

(19+y) + y = 61

19+2y = 61

2y = 61 - 19 = 42

y=42/2=21 ⇒ y=21 is the smaller number

x = 19+y = 19+21 =40 ⇒ x=40 is the larger number

Hence the numbers whose sum is 61 and difference 19 are 40 and 21.

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For this case it is observed that the border of the region is not dotted, then the inequality includes an equal.

Thus, we discard options C and D.

We substitute the point (0,0) and see if it is fulfilled:

[tex]y\geq\frac {3} {2} x-3\\0 \geq\frac {3} {2} (0) -3\\0 \geq0-3\\0 \geq-3[/tex]

It is fulfilled, so the correct option is A.

Answer:

Option A

Answer:

A. [tex]y\geq \frac{3}{2} x-3[/tex]

Step-by-step explanation:

We are given a graph and we are to determine which inequality is described by the graph.

Since the graph has a solid line that means that the inequality includes the points on the line and must contain an equal sign.

So we will substitute the point (0, 0) to find the correct inequality.

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

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

[tex]0\geq 3[/tex] - true

[tex]y\leq \frac{3}{2} x-3[/tex]

[tex]0\leq \frac{3}{2} (0)-3[/tex]

[tex]0\leq 3[/tex] - false

Therefore, the correct inequality is [tex]y\geq \frac{3}{2} x-3[/tex].

Answer:

There's no string in your question so zero. If you find out how long the string is just subtract it from the ribbon

Step-by-step explanation:

Answer:

It is A.

Step-by-step explanation:

In function A we see that there are 2 ordered pairs with value 2 in the first position with y values 6 and 2. So this is not a function.

A function is a relation in which each input pairs with exactly one output. In the given relations, option A is not a function because the input 2 pairs with both 6 and 2, contradicting the definition of a function.

In mathematics, a function is a relation in which every input, also known as the domain, corresponds to exactly one output, called the range. Looking at the following relations, we determine if a relation is not a function by seeing if any input values are paired with more than one output.

Option A: {(2, 6), (- 4, 0), (2, 2), (3, 5)} is NOT a function because the input 2 corresponds to both 6 and 2, which violates the definition of a function.

Options B, C, and D each pair every input with exactly one output, thus they are all functions. In conclusion, the relation provided in option A is the only one that is not a function.

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Answer:

CD = 9.2 cm

Step-by-step explanation:

The arc of any circle is calculated as

arc = circumference × fraction of circle

     = 2πr × [tex]\frac{66.4}{360}[/tex]

     = 2π × 7.9 × [tex]\frac{66.4}{360}[/tex]

     = [tex]\frac{2(7.9)(66.4)\pi }{360}[/tex] ≈ 9.2

arc CD is approximately 9.2 cm

Answer:

∠PQR=30°

Step-by-step explanation:

I assuming that the measure of angle PQR is the third internal angle of the triangle

Remember that

The sum of the internal angles of a triangle must be equal to 180 degrees

80°+70°+∠PQR=180°

150°+∠PQR=180°

∠PQR=180°-150°

∠PQR=30°

Answer:

The answer is 30 degrees

Step-by-step explanation:

(80+70) - 180 = 30

because all the angles should add up to 180 degrees so to double check your answer you do 30+70+80=180

Answer:

Ben has mixed up the digit for millions and hundred thousands: he wrote 5 in the place for millions and 6 in the place for hundred thousands, but it should be the other way. I think that he should exchange those two digits in the faulty report.

Answer:

4 quarts

Step-by-step explanation:

Answer:

according to the equation it is 158.330917...

Step-by-step explanation:

put w as 64 and solve for t

Answer: 158.331 minutes.

Step-by-step explanation: To solve this problem we need to replace the given level of water (64 cups) in the equation, and isolate and calculate the time (t):

W=-0.414t+129.549

isolating t:

W-129.549=-0.414t

t=(W-129.549)/-0.414

replacing W=64

t=(64-129.549)/-0.414

t=-65.549/-0.414

t=158.331 minutes.

Answer:

15 yards

Step-by-step explanation:

1 balloon = 2.5 feet

18 balloons = 2.5 x 18 = 45 feet

1 yard = 3 feet

[tex]\frac{3 feet}{1 yard}=\frac{45 feet}{x yard}[/tex]

45 = 3x

x = 15 yards

The answer is -- 29,524

Answer:

29,524

Step-by-step explanation:

This is a geometric sequence; notice how each new term is 3 times the previous term.  Thus, a(n) = 1 · 3^(n-1).  The 10th term is a(10) = 3^(9) = 19683.

a(4) = 27 (given)

a(5) = 81 (calculated)

a(6) = 243

a(7) = 729

a(8) = 2107

a(9) = 6561

a(10) = 19683 (previously calculated)

So the sum of the first 10 terms is 29,524.

1 + 3 + 9 + 27 + 81 + ... + 6561 + 19683 =

The change in variables s=x+3y, t=y to find the area of the ellipse x²+6xy+10y²≤1 yields; s² +t²≤ 1.

It follows from the equations given that;

Hence, it follows from substitution that;

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By applying a change of variables to the ellipse equation x2+6xy+10y2≤1, this simplifies to the standard ellipse equation from which the area, π*sqrt(10), can be determined using the standard formula for the area of an ellipse.

To find the area of the ellipse defined by the equation x2+6xy+10y2≤1, we can begin by using the provided change of variables, s = x + 3y and t = y. This transformation simplifies the equation of the ellipse to: (s^2) / 10 + (t^2) ≤ 1.

Now the expression looks like the standard equation of an ellipse, where 'a' (the radius on the x-axis) is sqrt(10) and 'b' (the radius on the y-axis) is 1. The area 'A' of an ellipse is given by 'A=πab'. Substituting 'a' and 'b' into the formula gives us 'A = π*sqrt(10)*1 = π*sqrt(10)'

This indicates that the area of the ellipse with the change of variables s=x+3y, t=y for the equation x2+6xy+10y2≤1 is π*sqrt(10).

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Answer:

tan(Sin^-1 x/2)=  [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]

Step-by-step explanation:

Let sin^-1 x/2= θ

then sinθ= x/2

on the basis of unit circle, we have a triangle with hypotenuse of length 1,   one side of length x/2 and opposite angle of θ.

          tan(Sin^-1 x/2) = tanθ

           tanθ= sinθ/cosθ

as per trigonometric identities cosθ= √(1-sin^2θ)

           tanθ= sinθ/ √(1-sin^2θ)

substituting the value sinθ=x/2 in the above equation

             tanθ= [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]

now substituting the value sin^-1 x/2= θ in above equation

             tan(sin^-1 x/2) =  [tex]\frac{x/2}{\sqrt{1-x^{2}/4 } }[/tex]

!

Answer: “A”

Step-by-step explanation: Your Answer Would Be “A”

Answer:

A

Step-by-step explanation:

THAT IS THE BEST ANWSER OPTION

hence angle between vectors is option a ,173 degree

When an equation has both direction as well as magnitude it refers to vector equation.

Formula used [tex]\alpha =cos^{-1} (\frac{u.v}{|u||v|})[/tex]

u.v=1*(-1)+[tex]\sqrt{7} *(-4)[/tex]

|u|=[tex]\sqrt{ 1^{2} +\sqrt{7} ^{2}}[/tex]=[tex]2\sqrt{2}[/tex]

|v|=[tex]\sqrt{ (-1^{2}) +(-4^{2})[/tex]=[tex]\sqrt{17}[/tex]

[tex]\alpha =cos^{-1} (\frac{-1-4\sqrt{7} }{|2\sqrt{2} ||\sqrt{17} |})[/tex]

[tex]\alpha =cos^{-1} (\frac{-1-10.58}{2.82*4.12})[/tex]

[tex]\alpha =cos^{-1} (\frac{-11.58}{11.61})[/tex]

[tex]\alpha =cos^{-1} (-0.99)[/tex]

hence option a 173 degree is correct

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Answer:

Chris is correct. (Choice letter C)

Step-by-step explanation:

We can eliminate choices A and B from the get-go because the problem stated that both hikers are traveling at 1mi/hr. This means that the slope of the equation would equate to 1, so just x.

That leaves us with C and D. The two equations both have a slope of 1, but C has a y-intercept of -2 and D has a y-intercept of 2, which represents the starting location of the second hiker. The first hiker is the one who is ahead by 2 miles, so it can't be D. This leaves us with choice C. Chris is correct.

Answer:

C. Chris said, “The equation y = x – 2 represents the distance traveled by the second hiker.”

Step-by-step explanation:

Answer:

option c

amplitude 1 ; period 2π/3

Step-by-step explanation:

Given in the question a function,

f(t)=-cos3t

Standard form of cosine function is

f(t)=acos(bt)

Amplitude is given by = |a|

Period of function is given by = 2π/b

So the amplitude is |-1| = 1

    the period is 2π/3 = 2π/3

Answer:

c. The amplitude is 1.

The period is [tex]\frac{2\pi}{3}[/tex]

Step-by-step explanation:

The given cosine function is ;

[tex]f(t)=-\cos 3t[/tex]

This function is of the form;

[tex]f(t)=a\cos bt[/tex]

The amplitude is given by |a|

|-1|=1

The period of this function is given by;

[tex]T=\frac{2\pi}{|b|}[/tex]

[tex]T=\frac{2\pi}{|3|}=\frac{2\pi}{3}[/tex]

The amplitude is 1.

The period is [tex]\frac{2\pi}{3}[/tex]

Answer:

a) h(x)

b) q(x)

c) w(x)

Step-by-step explanation:

Finding the answers for this is easy.  Take two values for x that shows a different Y-value for each function on the graph and place them in the equations suggested to see which equation match their Y-value on the graph.

Let's take x = -1 and x = 1.

a) h(x) = | -x + 3 |

| - (-1) + 3| = | 4 | = 4

| - 1 + 3 | = | 2 | = 2

h(x) passes through (-1,4) and (1,2)

b)  q(x) = | x | + 3

|-1| + 3 = 4

| 1 | + 3 = 4

q(x) passes through (-1,4) and (1,4)

c) w(x)  = | x+ 3 |

| -1 + 3 | = | 2 | = 2

| 1 + 3 | = | 4 | = 4

w(x) passes through (-1,2) and (1,4)

The probability that the die will land with a value less than 3 and on a red square, given an equal number of black and red squares, is 1/6.

The subject of this question is probability, a branch of Mathematics. In the given scenario, Gabrielle is tossing a die onto a black-and-red checkerboard. There are two separate events here - the roll of the die and the colour of the square where the die lands.

Firstly, the probability that the die will land with a value less than 3 is 2/6, or 1/3, as there are two sides of a six-sided die that have values less than 3 (1 and 2).

Secondly, assuming the checkerboard has an equal number of red and black squares, the probability that the die will land on a red square is 1/2.

Since these are separate events, we can calculate the combined probability by multiplying the probabilities of the individual events: (1/3) * (1/2) = 1/6. So, the answer is 1/6.

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Answer:

a

Step-by-step explanation:

Answer:

1. C

2. A

3. C

Step-by-step explanation:

1. The equation is most easily solved through the quadratic formula since it’s a term is greater than 1.

2. The equation is most easily factored since it’s a term is 1.

3. The equation is most easily solved by the quadratic formula since it’s a term is greater than 1.

Answer:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

y = tan(2x - π)

y = tan (2*(x-π/2))

We can compare it to its parent function

g(x) = tan(x)

The answer is

Option a.

Horizontal shrink by 1/2 and horizontal shift of π/2 to the right

about 19 percent (~19%)

Answer:

  6

Step-by-step explanation:

There are 2 service choices and 3 grade choices for each, a total of 2×3 = 6 choices.

Answer:

50%

Step-by-step explanation:

Answer:

the answer is he rode 17 miles in the morning and 40 miles in the afternoon

Step-by-step explanation:

so in the afternoon, it says that 6 more than twice as many miles in the afternoon as in the morning. this means that if the morning is x then in the afternoon it will be 2x+6 but it says altogether it is 57 miles so the you have to add x too.

so the equation is 2x+6+x=57

then this should be easy to solve.

2x+6+x=57

3x+6=57

3x=51

x=17

so if the morning is 17 miles then the afternoon will be:

2(17)+6

this equals to 40.

I hope that this is helpful!

Answer:

C

Step-by-step explanation:

Answer:

option c is the answer

hope it helps

and ur welcm

Answer:

$129.04

Step-by-step explanation:

Gross pay:  $815.70

The following will be deducted as

 (0.062 · $815.70 + 0.0145 · $815.70 + 0.19 · $56  +  $56,  or:

         $50.57         +         11. 83            +     $10.64 + $56, or

$129.04

His pay will be reduced by $129.04.

Next time, please share ALL of the possible answer choices.  Thx.

The amount that Chuck's gross pay will reduce by as a result of the items withheld is d. 273.38

The items withheld from Chuck's pay are:

= Federal tax + Social security tax + Medicare tax + State tax

Solving gives:

= 56 + (6.2% x 815.70) + (1.45% x 815.70) + (19% x 815.70)

= 56 + 50.57 + 11.83 + 154.98

= $273.38

In conclusion, the total reduction will be $273.38

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