When you adjust one number and change another number in the problem to make a computation easier you use ?

Answer:2.5

Step-by-step explanation:

5/2=2.5

The domain, range and  x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.

Given the function in the question;

g(x) = −4x + 4

The domain of the expression is all real numbers except where the expression is undefined.

For -4x + 4, there is no real numbers that makes the expression undefined.

Hence, domain is (-∞,∞).

Also, the range is the set of all valid y-values.

The range is (-∞,∞).

For the x-intercept, substitute 0 in place of y or g(x) in the given function and solve for x.

g(x) = −4x + 4

0 = −4x + 4

4x = 4

x = 4/4

x = 1

Hence, the x-intercept in point form is (1,0)

Therefore, the domain, range and  x-intercept of the given function are (-∞,∞), (-∞,∞) and (1,0) respectively.

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The expression is f(y) = 80y.

We have a school canteen.

We have to write down an expression for the cost in pence of y cups of tea.

A function in mathematics is a relation involving two variables, such that one variable is dependent on the other for its value.

According to the question -

Number of cups of tea = y

Cost of one cup = 80 pence.

Therefore, the function representing the cost in pence of y cups of tea =

f(y) = 80y

Hence, the expression is 80y.

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Answer:

Step-by-step explanation:

=the highest common factor is [tex]3b^{3}[/tex]

therefore you can divide each and every term of the expression and take it out of the brackets.

[tex]=3b^{3} (3+8)\\=3bx^{3} (11)[/tex]

Although I still see no use of factorising because there are only like times that is what I put on table. Please ask if you have questions

Answer: 13.7

Step-by-step explanation:

First you do 16.6 - 2 = 14.6 then you subtract 0.9 from 14.6, your equation would be 14.6 - 0.9 = 13.7

Hope This Helps!

Answer:

13.7

Step-by-step explanation:

The distance between pair of parallel lines with the  following equation

y=2x+3 y=2x-7 [tex]2{\sqrt 5}[/tex] units

​

Parallel lines are any two or more lines that lie in the same plane but never cross one another. Both have the same slope and are equally distant from one another. No matter how far we extend a parallel line, it will always remain straight.

The fundamental characteristics listed below make it simple to recognize parallel lines.

The slope of a line which is perpendicular to both the lines will be [tex]-\frac{1}{2}[/tex].

Check what are the y-intercept of any one of the two lines & write the equation of the perpendicular line through it.

The y-intercept of line y = 2x-7 is (0, -7).

So, the equation of any line with slope [tex]-\frac{1}{2}[/tex] and a y-intercept of −7 is

y = [tex]-\frac{1}{2}x-7[/tex]

The perpendicular intersects or meets the line y = 2x -7 at (0,-7).

Now, to find the point of intersection of the perpendicular & the other line, solve the two equations.

Solve for x:

                    2x + 3 =    [tex]-\frac{1}{2}x-7[/tex]

                          [tex]\frac{5}{2} x[/tex] = -10                                        (combine them like terms)

                            x = -4                                         (multiply each side by 2\5)              

Find y:

               y = [tex]-\frac{1}{2}.(-4)-7[/tex]

                  = -5

so, the point is (-4,-5).

Now using the Distance Formula, find the distance between the points (-4,-5) and (0,−7).

​

[tex]{\displaystyle d={\sqrt {\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}}[/tex]

  [tex]={\sqrt {\left(0-(-4\right)^{2}+\left(-7-(-5\right))^{2}}}[/tex]

  [tex]={\sqrt {4^2 +(-2)^2}}[/tex]

  [tex]=2{\sqrt 5}[/tex]

​

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​

The value of the greater integer is -8.

Given,

The sum of an integer and 6 times the next consecutive integer = -50

We have to find the value of the greater integer:

Let's take x as the integer.

Next consecutive integer be (x + 1)

Now,

x + 6(x + 1) = -50

x + 6x + 6 = -50

7x + 6 = -50

7x = -50 - 6

7x = -56

x = -56/7

x = -8

The value of x is -8.

Now,

x + 1 = -8 + 1 = -7

That is,

-8 + (6 × -7) = -50

-8 -42 = -50

Here, the integers are of negative values.

So, the value of greater integer be -8.

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The total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y

The given parameters are:

Leroy made 9 more penalty kicks than he missed

Represent the penalties made with x and the penalties missed with y

So, we have

x = 9 + y

The total number of penalty kicks is then calculated as

Total = x + y

This gives

Total = 9 + y + y

Evaluate

Total = 9+ 2y

Hence, the total number of penalty kicks is 9+ 2y where the penalties made is x and the penalties missed is y

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The expression is written as 2 × 10 =  2 x 10^ 1  = 20

The index form of a number  can be defined as that number written as an exponential expression.

It is also said to be a single number that is  raised to another number.

Given the expression;

2x _____ = 2 x 10^ 1 = ______

Note that a number raised to the power 1 is that same number, so we have;

2 × 10

2 x 10^1 = 2 × 10

2 × 10  = 20

Thus, we have the expression to be written as 2 × 10 =  2 x 10^ 1  = 20

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The projectile motion equation [tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex], gives;

First part;

Second part;

Third part;

The quadratic equation that represents the projectile motion can be presented as follows;

[tex]h(t) = - g \cdot {t}^{2} + v_{0}\cdot {t} + h_{0}[/tex]

g = 16 ft./s² or 9 m/ s²

First part;

When

[tex] v_{0} = 0 \: and \: h_{0} = 100 \: ft.[/tex]

We have;

h(t) = -16•t² + 100

When the object hits the ground, we have;

h(t) = 0, which gives;

0 = -16•t² + 100

Therefore;

16•t² = 100

t² = 100 ÷ 16 = 25/4

t = √(25/4) = 5/2 = 2.5

Second part;

The direction in which the object is thrown = Upwards

Initial height of the object, [tex] h_{0} = 6 \: ft[/tex]

Initial speed of the object, [tex] h_{0} = 30 \: ft/sec[/tex]

The equation of the projectile motion is therefore;

h(t) = -16•t² + 30•t + 6

Which gives;

When the object is at its starting height of 6 feet, h(t) = 6, which gives;

6 = -16•t² + 30•t + 6

-16•t² + 30•t = 0

A solution to the above equation is t = 0

The other solution is found as follows;

-16•t² + 30•t = 0

-16•t + 30 = 0

30 = 16•t

t = 30/16 = 1.875

Third part;

When the object hits the ground, we have;

h(t) = 0, which gives;

0 = -16•t² + 30•t + 6

Which gives;

t ≈ 2.06

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LM is the perpendicular bisector, median, and altitude of Δ JKL.

Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.

CPCTC is an abbreviation for "corresponding parts of congruent triangles are congruent," and it states that if two or more triangles are congruent, their corresponding angles and sides are also congruent.

CPCTC is frequently used at or near the end of a proof in which the student is asked to demonstrate that two angles or two sides are congruent. It means that if two triangles are proven to be congruent, the three pairs of sides that correspond must also be congruent, as must the three pairs of angles that correspond.

Since Δ JLM ≅ ΔKLM, we can prove JM ≅ MK and [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK. Since [tex]\angle[/tex] LMJ ≅ [tex]\angle[/tex] LMK and they are a linear pair, then we know they are right angles and LM ⊥ JK.

Therefore, we know that JM ≅ MK by CPCTC, making M the midpoint of JK. Therefore, LM is the perpendicular bisector, median, and altitude of ΔJKL.

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Answer:

3.36

Step-by-step explanation:

→ How much is a dozen

12

→ Multiply by 14

168

→ Divide by 50

168 ÷ 50 = 3.36

The sum of the polynomials is [tex]\bold{4.5t^3 + 12.3t^2-132t+24}[/tex].

Given polynomials are:

[tex]1.3t^3+t^2-42t+8\\ 1.3t^3+t^2-6t+8 \\1.9t^3+8.4t^2-42t \\1.9t^2-42t+8[/tex]

To find the sum of the polynomials, add the coefficients of the terms of same degree in each polynomials. That is add the terms containing [tex]t^3[/tex] , then terms of [tex]t^2[/tex], then terms of t and finally the constant terms of the polynomials.

So we get, [tex](1.3t^3+t^2-42t+8)+(1.3t^3+t^2-6t+8 )+(1.9t^3+8.4t^2-42t )+(1.9t^2-42t+8)\\ = (1.3+1.3+1.9)t^3+(1+1+8.4+1.9)t^2+(-42-6-42-42)t+(8+8+8)\\=\bold{4.5t^3 + 12.3t^2-132t+24}[/tex]

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Answer:

The recipe with 14 cups of tomatoes requires more tomatoes. This is because it needs 10 cups more of tomatoes than the recipe with 4 cups.

The Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .

Harmonic mean for 2 numbers "a" and "b" is denoted by

[tex]HM=\frac{2}{\frac{1}{a} +\frac{1}{b} }[/tex].

In the given question ;

Given that ;

the length of the first string is 3/4

Length of the second string is  3/5.

Substituting the values in the formula of harmonic mean

we get,

HM=[tex]\frac{2}{\frac{1}{\frac{3}{4} }+\frac{1}{\frac{3}{5} } }[/tex]

[tex]=\frac{2}{\frac{4}{3} +\frac{5}{3} }[/tex]

Taking LCM of denominator as 3 and solving further we get ;

[tex]=\frac{2}{\frac{5+4}{3} }\\ \\ =\frac{2}{\frac{9}{3} }[/tex]

Rewriting the complex fraction

=2*(3/9)

=6/9

On further simplifying we get ;

=2/3

Therefore , the Harmonic Mean for the length of strings 3/4 and 3/5 is 2/3 .

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Igor has not been skiing in 10 years. however, when he gets on his skis, his body remembers exactly how to ski. the kind of memory that makes it possible for him to remember how to ski is procedural.

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The value of x in the equation 3/7 = 12/x is equal to 28.

Proportion is a type of mathematical equation that is used to determine the value of the quantities that are not known by forming two equal ratios.

Ratios can be defined as an expression that is used to compare the size of two numbers in relationship to each other to determine how big is one number from the other.

The given proportion can be solved as follows:

3/7 = 12/x

3x = 12 × 7

3x = 84

If 3x is equal to 84, then x will be equal to:

x = 84/3

x= 28

Therefore, the proportion is solved as the value of x is found to be 28.

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The sequence can be expressed by the formula: v(n) = 5000 . (3/4)ⁿ⁻¹. Helium left at the start of the 10th day is 375.42 cm³

1st day:

Helium is filled with 5000 cm³ of helium.

We can write v(1) = 5000 cm³

2nd day:

The balloon losses 1/4 of helium volume. In other word, the remaining volume of helium is:

(1 - 1/4) = 3/4 of its initial volume.

We can write:

v(2) = 3/4 . 5000 = 3750  cm³

We can continue this process:

v(3) = 3/4 . 3750 = 2812.5

Notice that each day remaining volume of helium forms a geometric sequence, with v(1) = 5000 and a common ratio (r) = 3/4.

Recall the formula for the nth term of a geometric sequence:

v(n) = v(1) . rⁿ⁻¹

To find the explicit formula, substitute v(1) = 5000 and (r) = 3/4:

v(n) = 5000 . (3/4)ⁿ⁻¹

Tenth day means n = 10. Substitute these parameters into the formula:

v(10) = 5000 . (3/4)¹⁰⁻¹

v(10) = 5000 . (3/4)⁹

        = 375.42 cm³

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It is proved that CM will be perpendicular to AB if M is midpoint of AB.

It is given that ΔABC is a right isosceles triangle with hypotenuse AB and M is midpoint of AB.

We have to prove that CM is perpendicular to AB.

What is an isosceles triangle ?

An isosceles triangle ΔABC is a triangle that has at least two sides of equal length i.e., AC= BC

As per the question ;

ΔABC is a right isosceles triangle with hypotenuse AB.

⇒ AC = BC (by the definition of isosceles triangle)

Also ;

M is midpoint of AB.

⇒ CM = CM  (reflexive property)

So ;

ΔACM ≅ Δ BCM (by SSS)

∠A = 45° and ∠B = 45° because of right isosceles triangle.

Also ;

∠ACM = ∠BCM

because they are corresponding angles of congruent triangles

i.e.,

∠ACB = 90°

Now ;

∠ACM + ∠BCM = ∠ACB

because they are adjacent angles.

∵

∠ACM = ∠BCM , so ;

∠ACM + ∠ACM = ∠ACB

2∠ACM = 90°

∠ACM = 45 °

∵

∠A = 45 ° and ∠ACM = 45°

⇒ ∠AMC = 90°

because the sum of angles in a triangle is 180°.

So ,

If ∠AMC = 90° , then CM is perpendicular to AB because perpendicular lines form 90° angles.

Thus , CM will be perpendicular to AB if M is midpoint of AB.

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Answer:

in image

Step-by-step explanation:

The mean of the probability distribution is 21.35 and the variance of the probability distribution is 51.3275

Given the probability distribution with values of x and corresponding P(x). We need to find the values of [tex]x^2[/tex], x P(x), [tex]x^2[/tex] P(x) to calculate mean and variance.

x       P(x)          [tex]x^2[/tex]      x P(x)      [tex]x^2[/tex] P(x)

7       0.10         49       0.7         4.9

14     0.20        196      2.8         39.2

21     0.25         441     5.25       110.25

28     0.45        784     12.6       352.8

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

∑x P(x) = 21.35

∑[tex]x^2[/tex] P(x) = 507.15

Mean = ∑x P(x) = 21.35

and variance = ∑[tex]x^2[/tex] P(x) - [tex](\sum x\ P(x) )^2[/tex] = 507.15 - 455.8225 = 51.3275

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According to the question, a project has a duration of [tex]20[/tex] weeks and a standard deviation of[tex]4[/tex] weeks. And the calculated weeks to complete the [tex]35[/tex] percent work is [tex]18.4[/tex].

As per question, the critical path is the longest path from start to finish. It tells the minimum time required to finish the assigned project.

As per the question, the given data is as follows:

Time Duration = [tex]20[/tex] weeks, Standard Deviation = [tex]4[/tex] weeks, Completion = [tex]35[/tex] percent

[tex]Z = \frac{S-T}{var} =18.4[/tex]

The solution for the given question is [tex]18.4[/tex].

What is the critical path?

The critical path is the path for the assigned work and it is the longest path. This phenomena is used to calculate the minimum time for the project completion.

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say Steve is x ,then jenny will be x + 12

five years ago Steve's age was x - 5 and Jenny's age was x + 12 - 5= x + 7

since jenny was four times Steve's age 5 years ago the equation will be

x + 7 = 4(x - 5)

= x + 7 = 4x - 20

putting like terms together, we will have

4x - x = 20 + 7

= 3x = 27

this means 3x ÷ 3= 27 ÷ 3

x = 9

this means Steve is 9 years old and Jenny is 21 years old

Answer:

Explanation:

a) To work out the average or mean age we must first calculate the total age.

19 x 2 = 38

20 x 3 = 60

21 x 1  = 21

22 x 4 = 88

23 x 1 = 23

Total = 230

Then... Divide the number of players with this figure

Number of players =  2 + 3 + 2 + 4 + 1 = 11

230/11 = 20.9 is the average age of the players

b) We know the average will now be 22 and we know the number of players is now 12.

So... 22 x 12 = 264 (This will be the new total age of all the players)

We know the previous total was 230

So 264-230 = 34 (years old)

I hope this helps you! :)

The value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that:

0.83 = F

0.83 is a repeating decimal

Multiply by 10 on both sides:

10x0.83 = Fx10

8.33 = ? F

Plug F = 0.833

8.33 = ? (0.833)

? = 0.833/0.833

? = 10

8.33 = (10) F

Thus, the value in the missing place is 10 after plugging the value of F = 0.833; the answer is 10.

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Answer:

kribble

Step-by-step explanation:

Answer: rftyguhjiomnbvfdswertyio

Step-by-step explanation:

pyploliguatd

Person B recovers their investment in a shorter amount of time.

In order to determine the recovery time, divide the total cost of college by the salary that is earned after graduating from college.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Recovery time = cost of college / salary after college

Recovery time for person A  = $45,000 / $33,000 = 1.36

Recovery time for person B  = $30,000 / $37,000 = 0.81

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The total asset is $4750

The worth of the car is valued at the worth of  has $4000 and you he have a baseball card collection valued at $750.

The capital is also know as the equity which means the net worth.

Liabilities are everything a business owes, now and in the future.

Assets are everything a business owns. Assets may be current or fixed assets

Therefore,

Total Assets - Total Liabilities = Capital

Where

Base ball card collection = $750

Total assets = ?

Capital = $4000

Hence,

Total Assets  =  $4000 + $750

Total Assets  = $4750

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the bottles were sold equal x / 45