Two cars start at the same point and simultaneously drive in opposite directions.
The speed of the first car is s miles per hour. The speed of the second car is 5
miles per hour less than the speed of the first car.
How far apart are the cars 1.5 hours after they start moving?

A rhombus is a parallelogram because the opposite sides are parallel but every parallelogram is not a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

We need to identify the properties of the given figure in order to answer why one figure can not be the other one:

A rhombus has all sides equal as well as parallel but all angles might not be right angles.

A square has all four sides equal and has 4 right angles.

A rectangle has equal opposite sides and 4 right angles.

A parallelogram has opposite parallel sides.

Hence, a rhombus can be a parallelogram because the opposite sides are parallel but every parallelogram can not be a rhombus because all sides may not be equal. Every square is a rectangle because opposite sides are equal but not every rectangle is a square because all sides might not be equal. Every square is rhombus because all sides are equal but not every rhombus is a square because the angles might not be right angles.

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The solution to the system of equations y = x − 5 and y = 5x − 17 is x = 3 and y = -2

The system of equations is given as

y = x − 5

y = 5x − 17

Substitute y = x − 5 in the equation y = 5x − 17

So, we have

x - 5 = 5x − 17

Evaluate the like terms

4x = 12

Divide both sides by 4

x = 3

Substitute x = 3 in y = x − 5

y = 3 − 5

So, we have

y = -2

Hence, the solution is x = 3 and y = -2

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Answer:

6 pizzas

Step-by-step explanation:

12.99 times 3 which is the 3 pitchers of soda is 38.97

38.97 subtracted from 75 which is our total amount is 36.03

36.03 which is what we have left divided by 6 since each pizza is 6$ is 6.

Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:

m= (4 - (-4))÷ (0 - (-5))

m= (4 + 4)÷ (0 +5)

m= 8÷ 5

m= 8/5

Considering point 2 and the slope m, you obtain:

4= 8/5×0 + b

4= 0 +b

4= b

Finally, the equation of the line is y=8/5x + 4.

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The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

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Answer:

1,198 cm

Step-by-step explanation:

To find the diameter, use the formula d = 2r.

d = 2(599)

d = 1,198

Numerous other sorts of numbers exist, including natural, whole, rational, real, and integers. Positive and negative numbers, but not decimals or fractions, make up the category of integers.

Q      What are integers in mathematics?
ANS An integer is a whole number without any fraction or decimal part.

The traits of each group of numbers are as follows:

The values indicated trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) =  0.14 and csc(β) = 1.01

Trigonometric functions are the periodic functions that denote the relationship between angle and sides of a right-angled triangle e.g sine, cosine, tangent, etc.

Given: tan(β) = 7

Thus, β = arc tan 7 = 81.87

(a) cot(β) = 1/tan(β) = 1/7 = 0.14

(b) cos(β) = cos 81.87 = 0.14

(c)  tan(90-β) =  tan(90-81.87) = tan 8.13 = 0.14

(d) csc(β) = 1/sinβ = 1/sin(81.87) = 1.01

Therefore, the value of the trigonometric functions are cot(β) = 0.14, cos(β) = 0.14, tan(90-β) =  0.14 and csc(β) = 1.01

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Answer:

-73 +n

the first term is -73+1

the secound is -73+2

and so on

Answer:

[tex]a_{n}[/tex]= n - 73

Step-by-step explanation:

there is a common difference between consecutive terms , that is

- 71 - (- 72) = - 70 - (- 71) = - 69 - (- 70) = 1

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 72 and d = 1 , then

[tex]a_{n}[/tex] = - 72 + 1(n - 1) = - 72 + n - 1 = n - 73

The distance that Evan has left to hike is 13/30 mile.

From the information, Eva is hiking a real that has a length of 5/6 miles.

He has also hiked 2/5 miles. Therefore, in this situation, the distance that he has left will gotten by subtracting the fractions.

This will be:.

Distance left = Total distance - Distance hiked

Distance left = 5/6 - 2/5

= 25/30 - 12/30

= 13/30

The distance is 13/30 miles.

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The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.

What is synthetic division?

In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

The divisor is x - 1.The dividend is (x³-15).

Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.

Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).

Step 2:Write down the first coefficient without changes:

Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum

Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.

We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)

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Answer:

8p - 9

Step-by-step explanation:

→ Expand brackets

6p - 15 + 2p + 6

→ Collect like terms

8p - 9

Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]

The number of revolutions taken by a wheel will be 353.68 millimeters.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Given data as:

The radius of the wheel r = 45 millimeters

Circumference of wheel = Circumference of a circle

Circumference of wheel = 2πr =2π(45) = 282.74 millimeters

The distance traveled by wheel = 100,000 millimeters

Now, the number of revolutions taken by a wheel will be

⇒ distance traveled by wheel / Circumference of wheel

⇒ 100,000 / 282.74

⇒ 353.68

Thus, the number of revolutions taken by a wheel will be 353.68 millimeters.

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The value of the inequality when the sum of two consecutive integers is less than -9 is x < - 5.

It is vital to note that an inequality simply shows that the expressions aren't equal.

In this case, the sum of two consecutive integers is less than -9.

Let the integers be x and x + 1.

Therefore, x + x + 1 < -9

2x + 1 < -9

Collect like terms

2x < -9 - 1

2x < -10

Divide

x < - 10 / 2

x < - 5

The value is x < - 5.

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If a₁ = 9 and aₙ = 4 + (aₙ - 1) in an arithmetic sequence, then the value of fifth term a₅ is equal to 25.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

From the information provided, we know that the common difference is equal to 4.

Substituting the given parameters into the formula, we have;

a₅ =  9 + (5 - 1)4

a₅ =  9 + 4(4)

a₅ =  9 + 16

a₅ =  25

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Complete Question:

If a₁ = 9 and aₙ = 4 + (aₙ - 1), then find the value of a₅.

Answer:

42 workers

Step-by-step explanation:

27 divided by 9 = 3 (how much we need to multiply workers by)

14x3=42

One-sided confidence interval which have the smallest margin of error.

Given that;

Researchers want to decrease the margin of error by adjusting the confidence level.

You cannot be completely certain of the true value of a parameter, such as the mean, if your confidence interval is too broad. However, there are a number of methods you may do to narrow a confidence interval and improve the accuracy of your estimate. The following characteristics have an impact on the confidence interval's width.

one-sided confidence interval:

The margin of error is lower for a one-sided confidence interval than a two-sided confidence interval. A one-sided interval, however, merely shows whether a parameter is larger or less than a cut-off number. A one-sided interval does not reveal anything regarding the parameter's value when viewed from the other direction. Therefore, only use a one-sided confidence interval to boost an estimate's precision when you are concerned that it will either be higher or lower than a cut-off value, but not both.

Hence, we use one-sided confidence interval which have the smallest margin of error.

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Answer:

True

Step-by-step explanation:

f'(3) = 0 says the tangent line at x = 3 is horizontal.

f"(3) = 0 means the graph of  f  is concave up at x = 3.

Together, these tell you the graph has a local minimum at x = 3.  The graph is  U-shaped at the point where x = 3.

Answer:

Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

40/5 then x the answer by 2 and you get 16 with now deposits or withdraws

The solution to the equations is y = -7

From the question, we have the equation to be given as

3x - 2y = 5

The above equation is a linear equation

The domain or the replacement set is given as

{-3}

Rewrite properly as

Domain  = {-3}

or

x = -3

So, we replace the variables using the elements in the replacement set

When x = -3, we have

3 x -3 - 2y = 5

Evaluate the products

This gives

-9 - 2y = 5

Add 9 to both sides

-2y = 14

Divide both sides by -2

y = -7

So, we have

x = -3 and y = -7

Hence, the solution to the equation is y = -7

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Answer: i think its -18

Step-by-step explanation:

5*(4-9*2)-2*(3*2+4)+7

= 5*(4-18)-2*(3*2+4)+7

= 5*(-14)-2*(3*2+4)+7

= 5*-14-2*(3*2+4)+7

= 5*-14-2*(6+4)+7

= 5*-14-2*(10)+7

= 5*-14-2*10+7

= -70-2*10+7

= -70-20+7

= -90+7

= -83

The null and alternative hypothesis of the pctrush are explained below.

Given that;

By performing a partial F-test;

In hypothesis testing, the F test is a statistical test that is used to determine whether or not the variances of two populations or two samples are equal. The data in a f test follows a f distribution. In this test, two variances are divided and compared using the f statistic. Depending on the problem's characteristics, a f test can be either one- or two-tailed.

The one-way ANOVA (analysis of variance) test is run using the f value discovered after running the f test. More information on a f test, the f statistic, its critical value, formula, and how to perform a f test for hypothesis testing will be provided in this article.

The f test statistic is used in a test called the f test to determine if the variances of two samples (or populations) are equal. An f test needs a f distribution in the population and independent events for the samples in order to be valid. The null hypothesis can be rejected after conducting the hypothesis test if the f test results are statistically significant; otherwise, it cannot be rejected.

Null hypothesis:

The idea that there is no influence on the population is known as the null hypothesis.

We can reject the null hypothesis if the sample contains sufficient data to refute the assertion that there is no effect in the population (p). If not, we are unable to rule out the null hypothesis.

Although it may sound odd, statisticians only accept the phrase "fail to reject." Avoid using words like "prove" or "accept" when referring to the null hypothesis.

Alternative hypothesis:

The alternate response to your research question is the alternative hypothesis (Ha). It asserts that the populace is affected.

Your research hypothesis and your alternate hypothesis are frequently identical. It is, in other words, the assertion that you anticipate, or hope will be accurate.

The complement of the null hypothesis is the alternative hypothesis. The exhaustive nature of null and alternative hypotheses ensures that they account for all potential outcomes. Additionally, they are mutually exclusive, so only one of them can be true at once.

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Lamp that can be bought with $12 is 21

What is an example of a unitary method?

A single or distinct unit is referred to by the word unitary. Therefore, the goal of this strategy is to establish values in reference to a single unit. The unitary technique, for instance, can be used to calculate how many kilometers a car will go on one litre of gas if it travels 44 km on two litres of fuel.

How is the unitary method divided?

This can be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees. In order to determine the value of one unit, we essentially divide the total value of a set of items by the number of units. The unitary approach is this.

Given that

Kwai bought 15 lamp for $8.25

$8.25 = 15 lamp

$1 = 15/8.25

$12 = (15/8.25)*12 = 21 approx.

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The equation of the function graphed for 0 ≤ x ≤ 360 is

Transformation is a term used in mathematics to refer to the movements made by objects.

Transformation that took place in the graph is of two types namely

The translation involves moving the graph downward by 1 unit. This movement shifts the graph from running across the x axis to making x axis the crest

The vertical stretch is by a factor of 2. A complete cycle would have been rom 0 to 180. however two cycles are now covered within this period.

The graph is of showing cos x (blue) and y = -1 + cos 2x (red) is attached

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Answer:

SAS

Step-by-step explanation:

∠CBA ≌ ∠DBA are equal by SAS

sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.

Given,

sin 0 = -1

We have  to find the value of 0.

Lets see the trigonometric table for sin.

From the above table we get the value of sin 0

The value -1 is for sin 270° which is equal to sin 3π/2

That is,

sin 270° = sin 3π/2 = -1, the value of 0 is 270° or 3π/2.

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