What equation would you set up to solve for X?

Let,

B = the speed of the boat in still water

S = the speed of the stream

Use the equation for distance.

Rate * Time = Distance

Upstream:

(B-S)6 = 282

Downstream:

(B+S)6 = 402

Simply first:

(B-S)6 = 282

(B-S) = 282/6

B-S=47

(B+S)6 = 402

(B+S) = 402/6

B+S=67

Solve by elimination. Add the two equations.

B-S=47

+ B+S=67

2B = 114

B = 114/2

B = 57 km/hr (the speed of the boat in still water)

Substitute this into either equation and solve for S.

B+S=67

57 + S = 67

S = 67 - 57

S = 10 km/hr (the speed of the stream)

Answer:

see explanation

Step-by-step explanation:

(a)

the 2 angles are same- side interior angles and are supplementary.

(c)

since they are supplementary , they sum to 180° , that is

6x + 14 + 10x - 10 = 180

16x + 4 = 180 ( subtract 4 from both sides )

16x = 176 ( divide both sides by 16 )

x = 11

(d)

then

6x + 14 = 6(11) + 14 = 66 + 14 = 80

10x - 10 = 10(11) - 10 = 110 - 10 = 100

note 80 + 100 = 180 ( supplementary angles )

To write the sentence:

Number k is 4/5 of the number t in algebraic language, we can proceed as follows:

We need to express that k is equal to the four-fifths of t.

Then, the answer is k = (4/5)*t.

Using proportional relationships, it is found that:

Brown 12 10 14 30

Green 20 25 35 75

Total 32 35 49 105

In a direct proportional relationship, the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

For the first question, we have that out of a total distance of 8 miles, they:

Hence the proportional relationships for the distances are given as follows:

For a total distance of 32 miles, the distances walked and ran are given as follows:

For the second question, we have that the table has to following the given ratios of the first row to the second row, with the third row being the sum of the first two rows, hence the third table is correct.

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Consider the relation,

Let the distance between Trent and Austin is 'd' kilometers.

Then the time taken by Trent to reach Austin is given by,

Similarly, the time taken by Trent on his return trip is given by,

Given that the trip to Austin was 1 hour less than the return trip,

Solve for the total time of the trip as,

Thus, the total time required for complete trip is 5 hours.

If Connor edits 34 pages in 8 hours. Using the equivalent ratios, the table has been completed.

The equivalent ratios are the ratios that has same value when we compare them. We can check two or more ratios and check whether they are equivalent or not.

Connor edits 34 pages in 8 hours

Number of pages he edits in 8 hours = 34 pages

Number of pages he edits in 1 hour = 34/8 = 17/4 pages

Number of pages he edits in 12 hours = (17/4)×12

= 51 pages

Complete the table

Hence, if Connor edits 34 pages in 8 hours, using the equivalent ratios, the table has been completed

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When solving an inequality, treat it like an equal sign while solving.

y - 4 ≤ -13
y - 4 + 4 ≤ -13 + 4
y ≤ -9

Answer:

TRUE

Step-by-step explanation:

an integer is a whole number from the set of negative, non-negative, positive and 0 numbers.

ex : -1, -2, -3, -4, -5, 0, 1, 2, 3, 4, 5

-17 is a negative whole number

so yes, -17 is an integer

Simone, these are the steps to calculate Q1, Q2, and Q3.

Step 1: You need to put all the values in order from the lowest to the greatest.

Step 2: The tenth value from left to right is the median or Q2.

Step 3: The

Answer:

[tex] - \frac{1}{3} \geqslant - \frac{4}{5} x[/tex]

[tex] \frac{1}{3} \leqslant \frac{4}{5} x[/tex]

[tex]5 \leqslant 12x[/tex]

[tex]12x \geqslant 5[/tex]

[tex]x \geqslant \frac{5}{12} [/tex]

The input value x when the output value f( x ) = 4 in the function f( x ) = 5x - 7 is 11/5.

A function is simply a relationship that maps one input to one output, each x-value can only have one y-value.

Given the data in the question;

To determine the input value x when the output value f( x ) = 4, replace f( x ) by 4 in the function and solve for x.

f( x ) = 5x - 7

4 = 5x - 7

Collect like terms

4 + 7 = 5x

5x = 11

Divide both sides by 5

5x/5 = 11/5

x = 11/5

Therefore, the input value x is 11/5, this forms an ordered pair of ( 11/5, 4 ).

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Answer:

  3(n +5)

Step-by-step explanation:

You want the math expression that means "three times the sum of a number and five."

A sum is represented using a plus sign. "A number" is represented using a variable. "x" is a variable commonly used for an unknown value. "n" can also be used to represent "a number."

The sum of a number and 5 will be ...

  n + 5

We want an expression that is 3 times that sum, so we multiply it by 3:

  3(n +5) . . . . . . 3 times the sum of a number and 5

__

Additional comment

Note that the expression above is not the same as 3n+5, which would represent "the sum of 3 times a number and 5".

By cross multiplying the given equation, we have

By multiplying the right hand side, we get

Then, by subtracting 6x to both sides, we have

or equivalently,

Since the left hand side is a conjugate binomial, it can be expressed as

Then, we have the equation

Therefore, the values of x that make the equation true are x= 4 and x= -4

The equation of the blue line is y = 2(2 - x).

Equation of A(1,0) and B(0, -2)

Use y = mx + c,

m = change of x axis ÷ change of y axis

The difference in x-coordinates equals the difference in y-coordinates, and the difference in y-coordinates equals the difference in y-coordinates.

m = (y2 - y1) ÷ (x2 - x1)

To get the slope, plug in the parameters of both x and y into to the equation.

m = (2 - 0) ÷ (0 - 1)

m = -2

The value of b calculated using the expression of a line formula.

b = 2

Now that you have the measurements of m (slope) and b (y-intercept), plug them into y = m x + b to determine the equation of the line.

y = −2x+2

Because the line is two primary components to the left, the parallel line's equation is,

y = -2x + 2 + 2

y = -2x + 4

y = 2(2 - x)

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The total amount that must be repaid will be $26,015.

Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.

A = P + (PRT)/100

Where P is the principal, R is the rate of interest, and T is the time.

For $21,500, Norman buys a brand-new vehicle. The loan amount (plus simple interest) must be repaid in full within five years, and the simple interest rate is 4.2%.

The total amount that must be repaid will be given as,

A = $21,500 + ($21,500 x 4.2 x 5)/100

A = $21,500 + $4,515

A = $26,015

The total amount that must be repaid will be $26,015.

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In linear equation, 4 is the Simplify your answer .

What is a linear equation example?

2y-9 ............1

-3y-2=4 .............2

From equation  (2)

                  - 3y = 4 + 2

                  - 3y = 6

                     y = 6/-3  ⇒ -2

value of y put in equation 2

                         -3y-2=4

                       - 3 * -2 - 2 = 4 ⇒ 6 - 2 ⇒ 4

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Answer:

|2x - 3| ≥ 1

Step-by-step explanation:

Since the absolute value function is always ≥ 0 we can conclude that                
|2x - 3| ≥ 0 so we can eliminate choices 2 and 4

That leaves two possibilities:
|2x - 3| ≥ 1  and |2x - 3| ≤  1

There are two ways to go about solving this

Pick a point in the given graph on each side of the segment marked in red and see which of the two inequalities both points satisfy

Two points which are on both segments are x = 0 and x = 1

Plug x = 0 into |2x - 3|
|2x - 3| at x = 0
=> | 2 ·0 - 3|  
=> |0 - 3|
=> |-3|
= 3  

Since 3 ≥ 1,  point x = 0 satisfies |2x - 3| ≥ 1

But it does not satisfies |2x - 3| ≤  1 since 3 is not less than or equal to 1

So the correct inequality is |2x - 3| ≥ 1

By using division, when the restaurant needs at least 736 knives and there are currently 155 knives, if each set on sale contains 12 knives then he minimum number of sets of knives Kaj should buy is 49 sets

The total number of knife that restaurant needs = 736 knives

Number of knives that restaurant has = 155 knives

The number of knife that he want to buy = 736-155

= 581

Number of knives on one set = 12

To find the number of set he wants to buy, we have to use division

Number of sets he wants to buy = 581/12

= 48.41

≈49 sets

Hence, by using division, when the restaurant needs at least 736 knives and there are currently 155 knives, if each set on sale contains 12 knives then he minimum number of sets of knives Kaj should buy is 49 sets

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The shape of the distribution for the given dot plot is as follows:

The data is skewed right, with fewer values on the right end of the graph. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.

A dot plot shows the number of times that each measure appears in the data-set.

In the context of this problem, we have that from the given dot plot, the measures are as follows:

62, 68, 68, 68, 69, 70, 70, 72, 72, 72, 75, 75, 76, 78, 78, 80, 80, 80, 89, 89.

The mean is the sum of all observations divided by the number of observations, hence, applying it's formula, it is given by:

74.55.

The median is the middle value of the data-set, the value of which 50% of the measures are greater and 50% are less. The data-set in this problem has 20 elements, hence the median is the mean of the 10th and the 11th elements, which are 72 and 75, respectively, hence:

Median = (72 + 75)/2 = 73.5.

The median is less than the median, hence the distribution is skewed to the right, which means that the third option is correct.

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Answer:

The data is not symmetrically distributed, with most values clustered from 68 to 80 beats per minute. The values at 62 and 89 are possible outliers. The data fits within the average of 60 to 100 beats per minute.

Step-by-step explanation:

its not skewed right and this is the next one that makes sense

The value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].

Relationships between two variables that are proportional occur when their ratios are equal. Another way to consider them is that in a proportionate relationship, one variable is consistently equal to the other's constant value. The "constant of proportionality" is the name of this constant. The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k. Any relationship that has a constant ratio is said to be proportionate. For instance, the ratio of proportionality is the average number of apples per tree, and the amount of apples in a crop is proportional to the number of trees in the orchard.

Given Data

X 5 6 7 8

Y 1 2/3 2 2 1/3 2 2/3

Yes, the table shows proportional relationship.

Value of Y when X will be 10 is

x = 10

= 3[tex]\frac{1}{3}[/tex]

the value of y when x is 10 is 3[tex]\frac{1}{3}[/tex].

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Given that tanθ = 3.2603 where π < θ < 3π/2

From the calculation the value of θ = 72.95, hence the correct the error by adding 180

because it dint dnt fall in the range of

And to correct the error add 180 to their answer,

Hence the value of θ = 180 + 72.95 = 252.95 degree

Answer:

Either. They are both correct

Step-by-step explanation:

So 7+4(1-8p): 7+4-32p => 11-32p => -32p+11.

Answer:

11-32p

Step-by-step explanation:

The answer is 11-32p because your only distributing the 4 to the 1 and 8p.

the monthly deposit that will be required will be equal to $ 1214 by compound interest.

We are given the information that:

Amount (A) = $ 30,000

Time = 18 years

Compound interest rate = 4.1 %

Now, let the principal amount be x.

So, by using the formula for compound interest, we get that:

30,000 = x ( 1+ 0.041)¹⁸

30,000 = x (1.041)¹⁸

30,000 = x × 2.06

x = 30,000 / 2.06

x = 14563 ( approx.)

Monthly deposit = 14563 / 12 = 1214 (approx.)

Therefore, the monthly deposit that will be required will be equal to $ 1214 by compound interest.

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Answer:

Step-by-step explanation:

Let David will need m months to save to able to afford his birthday party.

Then 43m>=250 that is m>=5.814 .

But since months are whole numbers

So We take m>=6.

He will need at least 6 months to save to able to afford his birthday party.

The answer is 6 months .

Let's classify the angles.

The angles are alternate interior angles.

The

The value of the numbers that are given will be:

1. 6

2. 12

3. 42

It should be noted that based on the information given, PEDMAS is important. This implies that multiplication will come first before addition. This will be illustrated thus:

1. 2 + 2 × 2

= 2 + 4

= 6.

2. 3 + 3 × 3

= 3 + 9

= 12

3. 6 + 6 × 6

= 6 + 36

= 42..

Therefore, it should be noted that we multiplied first before adding.

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Answer:

greater

Step-by-step explanation:

if it wasn't bidmas then the product would be 5.104 which is greater than 2.324

a) the two angles are supplementary, then:

(3x - 45) + (2x + 25) = 180

(3x + 2x) + (-45 + 25) = 180

5x - 20 = 180

5x = 180 + 20

5x = 200

x = 200/5

x = 40

Then, the measure of the angles are:

3x - 45 = 3*40 - 45 = 75°

2x + 25 = 2*40 + 25 = 105°

b) the two angles are complementary, then:

(2y) + (6y - 30) = 90

(2y + 6y) - 30 = 90

8y = 90 + 30

8y = 120

y = 120/8

y = 15

Then, the measure of the angles are:

2y = 2*15 = 30°

6y - 30 = 6*15 - 30 = 60°

c) the two angles are vertical angles, then they are congruent, that is,

2z + 7 = 5z - 23

7 + 23 = 5z - 2z

30 = 3z

30/3 = z

10 = z

Then, the measure of the angles are:

2z + 7 = 2*10 + 7 = 27°

5z - 23 = 5*10 - 23 = 27°

d) the two angles are alternative exterior angles, then they are congruent, that is,

4x - 5 = 3x + 15

4x - 3x = 15 + 5

x = 20

Then, the measure of the angles are:

4x - 5 = 4*20 - 5 = 75°

3x + 15 = 3*20 + 15 = 75°