Question
Find the values for x and y .

Answer:

See attachments.

Step-by-step explanation:

Given inequality:

[tex]-2x\leq 4(x-6)[/tex]

Solve the inequality by first expanding the brackets:

[tex]\implies -2x\leq 4x-24[/tex]

Subtract 4x from both sides:

[tex]\implies -2x-4x\leq 4x-24-4x[/tex]

[tex]\implies -6x\leq -24[/tex]

Divide both sides by -6 (remembering to reverse the inequality sign as we are dividing by a negative number).

[tex]\implies \dfrac{-6x}{-6}\leq \dfrac{-24}{-6}[/tex]

[tex]\implies x\geq 4[/tex]

When graphing inequalities on a coordinate plane:

Therefore, to graph the given inequality on a coordinate plane:

(See attachment 1).

When graphing inequalities on a number line:

Therefore, to graph the given inequality on a number line:

(See attachment 2).

The domain and range of the logarithmic function are

Therefore, if

We require that

Notice that the -8 term does not affect the range of function g(x); thus,

Set g(x)=-8; then,

Therefore, y=-8 is not an asymptote of g(x), and, as shown above, the domain and range of g(x) are x>4, y->all real numbers.

Calculate the limit when x->4 as shown below,

Therefore, there is a vertical asymptote at x=4

Answer:

Hope this helps ;)

Step-by-step explanation:

Answer

Check Explanation

Explanation

The laws of logarithms will come in handy in helping to obtain the points for the log from its inverse.

Before we commence, the two laws of logarithms that we will be using is that

log₄ 4ᶜ = c (log₄ 4)

And

log₄ 4 = 1

So, no matter the value of inverse given, a simple mathematical evaluation will give the log points.

when x = 1

f(x) = log₄ x

f(1) = log₄ 1 = log₄ 4⁰ = 0 log₄ 4 = 0 × 1 = 0

when x = 4

f(x) = log₄ x

f(4) = log₄ 4 = log₄ 4¹ = 1 (log₄ 4) = 1 × 1 = 1

when x = 16

f(x) = log₄ x

f(16) = log₄ 16 = log₄ 4² = 2 (log₄ 4) = 2 × 1 = 2

when x = 64

f(x) = log₄ x

f(64) = log₄ 64 = log₄ 4³ = 3 (log₄ 4) = 3 × 1 = 3

Hope this Helps!!!

The numbers under consideration are:

Converting all the numbers to decimal:

Therefore, the numbers can be written as:

48.4, 48.5, 48.09, and 48.6

Out of these numbers, only 48.6 is closest to 49

If s is between r and t, then:

RS + ST = RT

Where RS = 2z + 6

ST = 4z - 3

RT = 5z + 12

So, we get:

(2z + 6) + (4z - 3) = 5z + 12

Solving for z, we get:

2z + 6 + 4z - 3 = 5z + 12

6z + 3 = 5z + 12

6z + 3 - 5z = 12

z + 3 = 12

z = 12 - 3

z = 9

Answer: z = 9

Problem N 2

we have

12x-14=8x+16

solve for x

subtract 8x both sides

12x-14-8x=8x+16-8x

4x-14=16

Adds 14 both sides

4x-14+14=16+14

4x=30

divide by 4 both sides

x=30/4

x=7.5

Problem N 4

we have

12x-14=6x+16

solve for x

subtract 6x both sides

12x-14-6x=6x+16-6x

6x-14=16

adds 14 both sides

6x=16+14

6x=30

divide by 6 both sides

x=30/6

x=5

We proved that formula using the trigonometry relations sin3A + sinA = 4sinAcos^2A.

In the given question,

We have to prove the formula sin 3A+sin A = 4sinAcos^2A

The given expression is sin 3A+sin A = 4sinAcos^2A

To prove the formula we take the left side terms to the right side terms

The left side is sin 3A+sin A.

As we know that sin 3A = 3sinA − 4sin^3A

To solve the left side we put the value of sin 3A in sin 3A+sin A.

=sin 3A+sin A

=3sinA − 4sin^3A+sin A

Simplifying

= (3sinA+sin A) − 4sin^3A

= 4sinA − 4sin^3A

Taking 4sinA common from both terms

= 4sinA(1 − sin^2A)

As we know that cos^2A=1 − sin^2A. So

= 4sinAcos^2A

We proved the right hand side.

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The slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3

The first point = (-5,6)

The second point = (-9,-6)

The slope of the line defined as the change in y coordinates with respect to the change in x coordinates.

The slope of the line m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where m is the slope of the line

[tex](x_1,y_1)[/tex]  is the coordinates of the first point

[tex](x_2,y_2)[/tex] is the coordinates of the second point

Substitute the values in the equation

The slope of the line m = [tex]\frac{-6-6}{-9-(-5)}[/tex]

= -12/-4

= 3

Hence, the slope of the line that passes through the points (-5,6) and (-9,-6) is m = 3

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Answer:

Height = 13.5cm

Explanation:

The area of a parallelogram is obtained using the formula below:

Substituting the given values:

The first face is a triangle with height 5in and base 12in

Traingular face area = 1/2 x bh

=1/2 x 12 x 5

= 30 in^2

The area of the other triangular base = 30 in^2

Area of left side face = Length x breadth

= 5 x 4 = 20in^2

Area of the slant face = Length x breadth

= 13 x 4 = 52in^2

Area of the bottom face = Length x breadth

= 12 x 4 = 48in^2

Total surface area = 30 in^2 + 30 in^2 + 20in^2 + 52in^2 + 48in^2

=180in^2

according to the equation and information given we can see that the equation is in the form

in which k is the constant of proportionality

use one of the points to find the constant

replace withone of the points to see if its true in all the points

according to this the equation for the table will be

Answer:

The number of shirts sewn at most, when there is just 1 spool of thread left is;

Explanation:

Given a graph that relates the number of spools of thread left to the number of shirts sewn.

We want to find the number of shirts sewn at most, when there is just 1 spool of thread left.

To get that, let us draw a straight horizontal line from y=1 (spools of thread remaining =1) to join the line of the graph and also trace it down.

Tracing the line down we can observe that it is at shirt sewn equals 5.

So, the number of shirts sewn at most, when there is just 1 spool of thread left is;

exactly For sentence A "The grade-point average of a student who does not play video games is 2.9408" we can verify as follows:

That means this sentence "The grade-point average of a student who does not play video games is 2.9408" is true.

For sentence B "The average number of video games played in a week by students is 2.9408" is not exactelly correct because the average number of hours of video game played is not specified.

For sentence C "It cannot be interpreted without more information" let's look over an illustration.

We can see, we can interpret the y-intercept as the moment where x = 0 which means when the student does not play a video game. So this sentence is false.

I mean the correct sentence is sentence A.

The solution of the linear system of three simultaneous equations is presented as follows; x = 2, y = 1 and z = 4

Simultaneous system of equations consists of a finite set of equations for which a solution to the equation system is required.

The linear system of three equations can be presented as follows;

13•x - 17•y + 16•z = 73...(1)

-11•x + 15•y + 17•z = 61...(2)

46•x + 10•y - 30•z = -18...(3)

The above system of equations can be solved using common multiples of the coefficients as follows;

Multiply equation (2) by 2 and equation (3) by 3 to get;

2 × (-11•x + 15•y + 17•z) = 2 × 61 = 122

3 × (46•x + 10•y - 30•z) = 3 × (-18) = -54

Subtracting equation (4) from equation (5) gives;

138•x + 30•y - 90•z - (-22•x + 30•y + 34•z) = -54 - 122 = -176

138•x - (-22•x) + 30•y - 30•y - 90•z - 34•z = -176

160•x - 124•z = -176

40•x - 31•z = 44

[tex] \displaystyle {z = \frac{(44 + 40\cdot x)}{31}}[/tex]

Plugging in the value of z in equation (1) and (2) gives;

1043•x - 527•y + 704 = 73 × 31 = 2236...(6)

Which gives;

[tex] \displaystyle {y = \frac{(1043\cdot x - 1559)}{527}}[/tex]

339•x + 465•y + 748 = 61 × 31 = 1891...(7)

Which gives; [tex] \displaystyle {y = \frac{(381 - 113\cdot x )}{155}}[/tex] which gives;

[tex] \displaystyle { \frac{(1043\cdot x - 1559)}{527}= \frac{(381 - 113\cdot x )}{155}}[/tex]

Therefore; 221216•x - 442432 = 0

x = 442432 ÷ 221216 = 2

x = 2

y = (1043×2 - 1559)÷527 = 1

y = 1

z = (44 + 40×2) ÷ 31 = 4

z = 4

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Remember that

The volume of a sphere is equal to

N 1

we have

D=9 units

r=9/2=4.5 units

substitute

N 2

we have

r=2 units

N 3

we have

D=14 units

r=14/2=7 units

N 4

we have

r=9 units

Answer: -$0.26, -$0.7, $0.65, and -$1.6

The number of days = 5

Average price = Total change in price / the number of days

For Stock A

Total change in price = -$1.30

Average price = - 1.30 / 5

Average price = -$0.26

STOCK B

Average change in price = -$0.14

From, Average price = Total price / number of days

Total price = Average price x number of days

Total price = -0.14 x 5

Total price = - $0.7

For stock C

Average price = 3.25 / 5

Average price = $0.65

Stock D

Average price = Total price / number of days

Total price = Average price x number of days

Total price = -0.32 x 5

Total price = - $1.6

The answer are -$0.26, -$0.7, $0.65, and -$1.6

The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters.

To subtract in mathematics is to take something away from a group or a number of objects.

The group's total number of items decreases or becomes lower when we subtract from it.

It is known that East and West are the opposite of each other.

So, 15 2/3 towards the east let's take it positively.

And 21 3/4 towards left let's consider it negative.

So, the distance from the home

⇒ | ( 15 + 2/3) - (21 +3/4) |

⇒ | 15 -21 + 2/3 - 3/4 |

⇒ | -6 + (8 - 9)/12 |

⇒ | -6 - 1/12 |

⇒ | -(6 +1/12) |

⇒ 6 1/12

Hence "The distance between Joey and his home was such that joey walked east for 15 2/3 meters from home. Then, he walked west for 21 3/4 meters is 6 1/12 meters".

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for right angles triangle,

hyposenuse square should be equal to sum of square of other two sides

it fails that law so its not right angled triangle

To find a value of θ theta given a value of sin(θ) we must use the arcsin function, it receives a value of an sin as argument and returns the value of the angle θ. Then we must use a calculator and input

The result is already rounded to the nearest degree. Therefore, one value of θ that satisfies sin θ = −0.966 is θ= -75°

Now to find the other value we will look at the symmetry in the trigonometric circle:

Then, the other value of theta will be

Final answer:

1 sample t-test

Calculating t test statistic

Plugging in the values, we have:

t test statistic = 2.9207

degrees of freedom = n - 1 = 50 - 1 = 49

Using a calculator, we can calculate the p-value.

Since p value is less than significance level (p value < alpha), then we will reject H_0 and take the alternate hypothesis.

Thus the test suggests that the new batteries do last more than 45 hours.

E)

We could've done Type I error here.

Type I error or α: Reject the null when it’s true.

Given:

The trinomial equation is given as,

The objective is to choose the correct value for which the factors are to be obtained for factorization.

Explanation:

From the step 1, to perform the factorization the values of a and c has to be multiplied.

Then in step 2, the factors need to be calculated for the product of a and c.

Product of a and c :

The product of a and c will be,

Thus, factors are to be listed for the number 21.

Hence, option (1) is the correct answer.

ANSWER

EXPLANATION

The roots are the x values where the equation intercepts the x-axis.

288 u²

1) Let's calculate the area of that trapezoid by plugging into the formula below the measures of the altitude, larger base, smaller one:

2) So that trapezoid has an area of 288 u²

Given:

Jim baked 48 cookies with 4 scoops of flour.

So, the unit rate will be = 48/4 = 12 cookies/scoop of flour

So, for 96 cookies, the number of scoops of flour will be =

96/12 = 8

So, the answer will be 8 scoops of flour

We need to simplify the like terms.

"The like terms are whose with the same variable and exponent"

Therefore, the like terms are:

21v - 12v = 9v

8 - 7 = 1

3t - t = 2t

Now, the result is :

9v + 2t + 1

Hence, the correct answer is option D.

Answer:

[tex]f^{-1}[/tex](x) = x/2 - 3/2

Step-by-step explanation:

Swap x and y and solve for y.

Original equation:

y = 2x + 3

Swapped equation:

x = 2y + 3

Now, solve for y:

x -3 = 2y

y = (x-3)/2

If it's wrong, it might just be the way you format your answer, since Pearson (what I assume you're using) is specific about that.

Maybe, [tex]f^{-1}[/tex](x) = x/2 - 3/2 or [tex]f^{-1}[/tex](x) = (x-3)/2

to solve this we need to convert the number 4 to a fraction with denominator 100 and add both fractions

to do that we can multiply 4 and 1 by 100, like this:

now we can add the fractions

So the answer is: 419/100

A dilation means an elongation of the sides of a figure

So in a dilation the sides are bigger than at the original figure

A key formula for found dilation is Pithagoras theorem

For calculate T'R'

T'R' is the exact diagonal of OT' and OR', that means

OT' + OR' = T'R' in vectorial sum

OT'^ 2 + OR'^ 2 = T'R'^2. In numerical sum

So then T'R'^2 = 5^2 + 5^2 = 50.

and T'R'= √50

Now find TR to find the factor of dilation that is

T'R'/TR

2 (8x+4) -x =

Simplify the equation:

2(8x)+2(4) -x

16x +8 -x

15x +8

If both sides of the equation are equal o equivalent, there is an infinite number of solutions.

2 (8x+4) -x = 15x + 8

Answer:

y intercept= (0,-3)

slope= 2/1 or simplified 2

Step-by-step explanation: