log(2t+4)=log(14-3t)

Answer:

18

Step-by-step explanation:

Using order of operations:

[tex] \frac{15 - 9}{3} (19 - 10)[/tex]

[tex] \frac{6}{3} (9)[/tex]

[tex]2(9) = 18[/tex]

The area of a triangle with vertices (-4,-5), (3,-3), and (3,-7) will be 7 square units.

The vertices of the triangle are (x₁, y₁), (x₂, y₂), and (x₃, y₃).

Then the area of the triangle will be

Area = 1/2 |[(x₁y₂ + x₂y₃ + x₃y₁) - (y₁x₂ + y₂x₃ + y₃x₁)]|

We have

(x₁, y₁) ⇒ (-4, -5)

(x₂, y₂) ⇒ (3, -3)

(x₃, y₃) ⇒ (3, -7)

Then the area will be

Area = 1/2[{(-4) x (-3) + (3) x (-7) + (3) x (-5)} – {(-5) x (3) + (-3) x (3) + (-7) x (-4)}]

Area = 1/2 [(12 – 9 – 21) – (- 15 – 9 + 28)]

Area = 1/2[-18 + 4]

Area = 1/2 × 14

Area = 7 square units

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Answer:  [tex]\textsf{x = 6}[/tex]

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Given:  [tex]\textsf{The image provided with 2 angles and one side}[/tex]

Find:  [tex]\textsf{Solve for the unknown side of x}[/tex]

Solution:  In order to determine the length of x we need to use some trigonometric functions.  Using Soh Cah Toa we can see that we can either use 30 degrees or 60 degrees.  We will stick to 60 and we can see that the opposite side is 3 and the hypotenuse is x meaning that we need to use sin.  Plug in the values and solve for the unknown.

Plug in the values

Multiply both sides by x

Divide both sides by sin(30)

Simplify

Therefore, the value of the unknown variable x is 6 units.

The plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

Scatter plots are graphs that represent individual points of data and are labeled with quantitative values on both the co-ordinate axes, meaning that there is only one projection on the x-axis and one projection on the y-axis for each point.

We have a scatter plot shown in the table:

1) As we can see in the scatter plot all data are within 3 standard deviations of the mean:

Standard deviation = SD

6SD(x) = 40

SD(x) = 40/6 = 6.67

6SD(y) = 20

SD(y) = 20/6 = 3.37

2) Slope of the line:

= SD(x)/SD(y) = (20/6)/(40/6) = 1/2 = 0.5

3) It is plausible to take the slope of the line as 0.5 because the slope of the line is the ratio of the change in y to the change in x.

Thus, the plausible values for the SD(x) are 6.67 and for SD(y) is 3.37, and the slope of the line is 0.5.

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Answer:

Step-by-step explanation:

Using slope m = y_2-y_1/x_2-x_1 to find the solution slope that passes through those two-point.

Point-slope form into y-intercept form.

Answer:

For finding slope

we have the formula

m = y2 - y1/ x2 - x1

x1 = (-2)

x2. = ( 8)

y1. = (-1)

y2 =(-3)

putting the value of this in the formula we get,

m = (-3)-(-1)/8-(-2)

m = (-3+1)/8 + 2.

m = (-2)/10

m = (-1)/5.

m = (-1)/5

Answer:

l

Step-by-step explanation:

Answer:

Lines L and n are parallel

Explanation -

In the question it is given that angle 7 and angle 5 are supplementary.

which means that sum of this angle is 180°

so line L and n are parallel

Answer:

6587

Step-by-step explanation:

Formula is

A= P(1+r/n)^nt

A = 11303.34

r = .09

n = 365 compounded daily

t = 6 years

solve for P

Answer:

the answer is 24

Step-by-step explanation:

6x - 48 = 4x

6x - 4x - 48 = 0

2x - 48 = 0

2x = 0 + 48

2x = 48

x = 24

Answer: It is possible to draw different lines to approximate the same data. The line of best fit is only an estimate.

The equation would be  y+ 3/8x+9/4.

Lets try to explain in the further steps to calculate the equation,

Slope formula: (y₂ - y₁) / (x₂ - x₁)

First, plug in these values of the two given points.

[tex]= > (-5+2) / (4+4)\\= > -3/8[/tex]

Slope = -3/8

To find the equation of the line, (y- y1) = m* (x-x1)

So by putting the values into the above equation we get,

[tex]= > (y-4) = -3/8(x+5)\\= > y-4 = -3/8x - 15/8\\= > y + 3/8x + 4 - 15/8\\= > y + 3/8x + 9/4[/tex]

Hence the equation is [tex]y+ 3/8x+9/4.[/tex]

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Answer:

[tex]\frac{1}{18}[/tex]

Step-by-step explanation:

The best way to solve this problem is to simplify each factorial one by one!

Starting at the numerator, the factorial for 2! is just 2, while the factorial for 5 is 120.

At the denominator, the factorial of 6! is 720, while the factorial for 3 is 6.

To write this out, we're given: [tex]\frac{(2) (120)}{(720) (6)}[/tex]

Just simply multiply and then divide, and we are given 1/18

Answer:

Line LM

Step-by-step explanation:

First, we need to know what the slope is of a line that would be perpendicular to a line with a slope of -5/6. To find this, we take the reciprocal and multiply it by -1. Therefore, the line we are looking for needs to have a slope of 6/5.

Based on the fact that the slope is positive, we can eliminate lines PQ and JK as they have a negative slope. This leaves us with lines LM and NO.

To find out whether or not it is between LM and NO, you could eyeball it by looking at the graph and simply counting which might be faster if you understand how to do that (rise/run), or you can use the pair of coordinates given to you on each line to calculate for slope.

Line LM - [tex]\frac{-3-3}{-5-0}=\frac{-6}{-5}=\frac{6}{5}[/tex]

Line NO - [tex]\frac{-5-0}{-6-0}=\frac{-5}{-6}=\frac{5}{6}[/tex]

Based on this, we know that line LM is perpendicular to a line that has a slope of -5/6.

If you need help on calculating slope from two points, I'd suggest watching this video: https://www.brightstorm.com/math/algebra/linear-equations-and-their-graphs/finding-the-slope-of-a-line-from-2-points-problem-1/#:~:text=Use%20the%20slope%20formula%20to,second%20points%20are%20x2%2C%20y2.

Answer:

h(-1) is -1, h(-0.5) is 0 and h(1) is 1.

Step-by-step explanation:

functions :- an expression, rule or law that defines relationship between one variable and another variable. When a certain condition is fulfilled, then the result is corresponding to that condition.

In the function it is given that when x∈(-2,-1] then we get -1. Now here x=-1 satisfies the given condition. So, the answer will be -1.

In the function it is given that when x∈(-1,0] then we get 0. Now here x=-0.5 lies in the range (-1,0]. So, the answer is 0.

In the function it is given that when x∈(0,1] then we get 1. Clearly, x=1 satisfies this range of values. So, we get 1.

Hence, the Answer is h(-1) = -1, h(-0.5) = 0 and h(1) = 1.

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Answer:

60°

Step-by-step explanation:

since angle on straight line is 180° you take the sum of the exterior angle of R and its interior angle then divide both sides by the coefficient of y to find y then things get easier from there

Answer:

Step-by-step explanation:

Plan

7y and 5y are made on the same straight line. Therefore they are supplementary and add to 180 degrees. <s has to be found by finding 3x and 5y first. Find <s by solving 3y + 5y + x = 180 degrees.

Solution

7y + 5y = 180 degrees               Combine the left

12y = 180 degrees                      Divide by 12

12y/12 = 180/12

y = 15

3y + 5y + x = 180                         Combine the left side

8y + x = 180                                  Substitute 15 for y

8*15 + x = 180                               Combine

120 + x = 180                                Subtract 120 from both sides

120 -120 +x =180 - 120                 Combine

x  = 60

Answer

s = 60 degrees

<TRS = 5y = 75

James receives a pay increase of 100% per month and has a starting salary of $500.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let b represent the rate of pay increase and a represent the initial pay.

Let us assume that he had received 128000 after the 8 months. hence:

128000 = ab⁸   (1)

Also in the 10th month, he had received 512000, hence:

512000 = ab¹⁰    (2)

From the both equations:

a = 500, b = 2

rate of increase = 200% - 100% = 100%

James receives a pay increase of 100% per month and has a starting salary of $500.

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The true option about the system of linear equation is that the system can only be independent and consistent.

It should be noted that the system is consistent as it can illustrate more than a solution.

Also, it can't be independent and dependent at the same time as depicted in some of the option given.

In this case, true option about the system is that the system can only be independent and consistent.

The complete question is:

Given that (1, 0, 1) is a solution to a system of three linear equations, which of the following is true about the system?

The system can be either inconsistent or consistent.

The system can be either independent or dependent.

The system can only be independent and consistent.

The system can only be dependent and inconsistent.

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The value of the probability P(decaf or sugar) is 0.41

From the table, we have:

P(decaf) = 0.05 + 0.08 + 0.09 = 0.22

P(sugar) = 0.19 + 0.08 = 0.27

P(decaf and sugar) = 0.08

The required probability is:

P = P(decaf) + P(sugar) - P(decaf and sugar)

This gives

P = 0.22 + 0.27 - 0.08

Evaluate

P = 0.41

Hence, the value of the probability P(decaf or sugar) is 0.41

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From the given study, we can tell that the conclusion is; The frequency of eating breakfast is associated with lower BMI in adolescent girls.

From the study in the question, we see that a national institute is trying to examine the association of breakfast intake and body mass index (BMI).

Now, in the research we saw that the frequency is being counted about the type of foods being eaten by those surveyed to find out the impact on BMI.

From the study, we see that girls who ate breakfast more often tended to have a lower BMI. Thus, we can say that the conclusion is that The frequency of eating breakfast is associated with lower BMI in adolescent girls.

The missing options are;

A. The frequency of eating breakfast is associated with lower BMI in adolescent girls.

B. There is no relationship between eating breakfast and BMI in adolescent girls.

C. Eating breakfast makes adolescent girls thinner.

D. Skipping breakfast can contribute to obesity in adolescent girls.

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That is the length in terms of p and x.

L = p/2 - x

For a rectangle of length L and width W, the perimeter is:

P  = 2*(L + W).

Here we know that the perimeter is p, so P = p, and let's say that the width is x.

Then we can write:

p = 2*(L + x)

Solving for L:

L = p/2 - x

That is the length in terms of p and x.

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The sequence of transformations used to obtain figure A'B'C'D'from figure ABCD are a reflection across the y-axis followed by a horizontal translation 1 unit right

Figure ABCD is transformed to figure A'B'C'D', as shown below: (see attachment)

Which of the following sequences of transformations is used to obtain figure A'B'C'D'from figure ABCD?

From the attached figure, we can see that:

ABCD and A'B'C'D' are on either sides of the y-axis.

This means that ABCD is first reflected across the y-axis.

ABCD is 2 units from the y-axis, while A'B'C'D' is 1 unit from the y-axis.

This means that the reflection is followed by a translation.

The unit of translation is:

Unit = 2 - 1

Evaluate

Unit = 1

1 represents a right translation

Hence, the sequence of transformations are a reflection across the y-axis followed by a horizontal translation 1 unit right

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Answer:

the length of the fence = 420 ft

The total area = 8000 ft²

Step-by-step explanation:

the fence has the same length as the perimeter of the rectangle

then

the length of the fence = 2×(160+50) = 420 ft

………………………………………………………………

The total area enclosed by the fencing = the area of the rectangle

Then

The total area = 160×50 = 8000 ft²

Answer:

see explanation

Step-by-step explanation:

the perimeter (P) of a rectangle is calculated as

P = 2(length + width)

  = 2(160 + 50)

  = 2 × 210

  = 420 ft ← amount of fencing needed

the area (A) of a rectangle is calculated as

A = length × width = 160 × 50 = 8000 ft²

Step-by-step explanation:

Easy buddy....

_________________________________

Remember, from now on, wherever the function domain is asked

They mean the same inputs or xs of the function.

Now you can answer them yourself but I like to help you to do it buddy.

_________________________________

The first function's domain is :

D = { -6 , -1 , 0 , 3 }

°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°

The second function's domain is :

D = { -7 , -6 , -2 , -1 , 0 , 1 , 3 , 9 }

_________________________________

And we're done.

Thanks for watching buddy good luck.

♥️♥️♥️♥️♥️

The domain of the function in the table given is:

A. {x|x = -6, -1, 0, 3}.

In any given function, all x-values (input) make up the domain of the function, while corresponding y-values (output) make up the range of the function.

In the table given, the x-values (input) are -6, -1, 0, and 3.

Therefore, the domain of the function in the table given is:

A. {x|x = -6, -1, 0, 3}.

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In order of blank boxes going from left to right then down will be 1, 9, 5, 75, 35.

The missing table is given below.

A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.

Shawn is collecting money from students at his school for a charity.

The table gives the ratios of the number of students who have donated and the amount of money he has collected from them.

Since 30 is 1/3 of 90, we know the ratio is 1:3.

In order of blank boxes going from left to right then down

1, 9, 5, 75, 35

The complete table is attached below.

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A function assigns the values. The correct option is C, x=-6.

A function assigns the value of each element of one set to the other specific element of another set.

A.) When the value of x is -12,

f(-12) = 2/3(-12) + 7 = -1

g(-12) = 2(-12) + 15 = -9

B.) When the value of x is -9,

f(-9) = 2/3(-9) + 7 = 1

g(-9) = 2(-9) + 15 = -3

C.) When the value of x is -6,

f(-6) = 2/3(-6) + 7 = 3

g(-6) = 2(-6) + 15 = 3

D.) When the value of x is -3,

f(-9) = 2/3(-3) + 7 = 5

g(-9) = 2(-2) + 15 = 11

Hence, the correct option is C, x=-6.

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The standard error will be equal to 0.75.

The standard deviation of a statistic's sample distribution, or an approximation of that standard deviation, is the statistic's standard error. The term "standard error of the mean" is used when referring to a statistic that is the sample mean.

The standard error will be calculated by using the formula:-

SE = [tex]\sigma[/tex] / √n

Here [tex]\sigma[/tex] is the standard deviation and n is the sample number.

SE = 6.5 / √75

SE = 0.75

Therefore the standard error will be equal to 0.75.

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Answer:

56x² + 8x

(second option listed)

Step-by-step explanation:

area: length × width

length: 7x + 1

width: 8x

(8x)(7x + 1)

{distribute 8x}:

(8x)(7x):  8x × 7x = 8 · 7 · x · x = 56 · x · x = 56x²

(8x)(1) = 8x

area = 56x² + 8x

so, the area of this rectangle is 56x² + 8x

Answer:

56x² + 8x

[answer B]

In logarithmic form, we get In(2e^9)= ln(2)+9.

We are given,

 ln(2[tex]e^{9}[/tex])

We know that, ln(ab) = ln(a) + ln(b)

So we get,

 ln(2[tex]e^{9}[/tex]) = ln(2)+ln([tex]e^{9}[/tex])

Since ln(m^n)=n ln(m)  

And ln(e)= 1, we will get,

ln(2[tex]e^{9}[/tex]) = ln(2) +9 ln(e)

          = ln(2) +9

Hence, the logarithmic form, we get In(2e^9)= ln(2)+9.

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Answer:

C

Step-by-step explanation: