My age if I am half as old as two more than twice Mack's age if Mack is m years old.

Answer:

Step-by-step explanation:

Given

u = 14 , a = 8 , t = 4

Now, let's find the value of s

[tex]s = ut + \frac{1}{2} a {t}^{2} [/tex]

plug the values

[tex] = 14 \times 4 + \frac{1}{2} \times 8 \times {4}^{2} [/tex]

Reduce the numbers with G.C.F 2

[tex] = 14 \times 4 + 4 \times {4}^{2} [/tex]

Multiply the numbers

[tex] = 56 + 4 \times {4}^{2} [/tex]

Calculate the product

[tex] = 56 + {4}^{3} [/tex]

Evaluate the power

[tex] = 56 + 64[/tex]

Add the numbers

[tex] = 120[/tex]

Hope this helps..

best regards!!

Answer:

It takes Carrie and James an hour and a half to finish the job.

Step-by-step explanation:

assuming they have to inspect ONE case of watches.

Carrie can inspect 1/5 case in one hour.

James can inspect 1/3 case in one hour.

Carrie worked alone for 1 hour, so she finished 1/5 of a case.

She leaves 4/5 case to finish.

She had lunch.

After that, Carrie and James worked together for x hours to finish the job.

When they work together, the finish 1/5+1/3 = 8/15 case per hour.

So time to finisher the remaining case

Time = 4/5 / (8/15)

= 4/5 * 15/8

= 3/2 hours

= an hour and a half.

Answer:

Afful is 21 and Naomi is 13.

Step-by-step explanation:

Let [tex]A[/tex] represent the age of Afful and [tex]N[/tex] represent the age of Naomi.

The sum of their ages is 34. In other words:

[tex]A+N=34[/tex]

In 5 years time, Afful will be two times the age of Naomi now. In other words:

[tex]A+5=2N[/tex]

Solve for the system. Substitute.

[tex]A+N=34\\A=34-N\\34-N+5=2N\\39=3N\\N=13\\\\A=34-N\\A=34-(13)\\A=21[/tex]

Afful is currently 21 and Noami is currently 13.

Answer:

Naomi=x

Afful=2x

In 5 years time= +5

So Naomi=x+5

and and Afful=2x+5

=x+5+2x+5=34

=3x+10=34

Subtract 10 on both sides

3x=24

Divide 3 on both sides

X=8

Check:

X=8

Naomi=16

In 5 years

=16+5=21

Naomi=8+5=13

13+21=34

Hope this helps

Step-by-step explanation:

Answer:

1: C) y = -x + 1

2: D) y = -3x + 8

Step-by-step explanation:

Well number 1,

c is the correct option because,

-2 -> 2

2+1 - 3

This rule applies for all the x values.

2,

X: -2, -1, 0, 1, 2

Y: 14, 11, 8, 5, 2

d is the correct option because -3*-2 is 6 + 8 = 14.

this rule applies for all x values.

Thus,

the answers are C and D.

Hope this helps :)

Answer:

a) A quadrilateral with 4 right angles

Answer:

I think the answer is b

I'm sorry if I'm not correct

Answer: it is =4176000000000000

Step-by-step explanation:

(2.9)(100000)(7.2)(10^2)

5(10^−8)

=

(290000)(7.2)(10^2)

5(10^−8)

=

2088000(10^2)

5(10^−8)

=

(2088000)(100)

5(10^−8)

=

208800000

5(10^−8)

=

208800000

5(1/100000000)=

208800000/1

20000000

=4176000000000000

hope i helped

-lvr

Answer:

140 toy cars

Step-by-step explanation:

The ratio of Ed's toy car to Pete's toy car is initially given as 5:2

Ed gave Pete a total number of 30 cars

Let x represent the greatest common factor that exists between both number

Number of Ed's car is represented as 5x

Number of Pete car is represented as 2x

Since they each have an equal number of cars which is 30 then we can solve for x as follows

5x-30=2x+30

Collect the like terms

5x-2x= 30+30

3x= 60

Divide both sides by the coefficient of x which is 3

3x/3=60/3

x=20

Ed's car is 5x, we substitute 20 for x

5(20)

= 100 cars

Pete car is 2x,we substitute 20 for x

2(20)

= 40 cars

Therefore, the total number of cars can be calculated as follows

= 100+40

= 140 toy cars

Hence they have 140 toy cars altogether

Answer:

140

Step-by-step explanation:

Answer:

(5, 11) and (2, 2)

Step-by-step explanation:

y = (x-2)² + 2

y + 4 = 3x

(x-2)² + 2 + 4 = 3x

x² - 4x + 4 + 6 = 3x

x² - 7x + 10 = 0

(x - 5)(x - 2) = 0

x - 5 = 0, x = 5

x - 2 = 0, x = 2

y = (5-2)² + 2 = 11

(5, 11)

y = (2-2)² + 2 = 2

(2, 2)

Answer:

[tex]\large \boxed{\sf \bf \ \text{ The solutions are } x=2, y=2 \text{ and } x=5, y=11.} \ \ }[/tex]

Step-by-step explanation:

Hello, please consider the following.

We want to solve this system of equations.

[tex]\begin{cases}&y=(x-2)^2+2\\&y+4=3x\end{cases}[/tex]

This is equivalent to (subtract 4 from the second equation).

[tex]\begin{cases}&y=(x-2)^2+2\\&y=3x-4\end{cases}[/tex]

Then, we can write y = y, meaning:

[tex](x-2)^2+2=3x-4\\\\\text{*** We develop the left side. ***}\\\\x^2-4x+4+2=3x-4 \\\\\text{*** We simplify. *** }\\\\x^2-4x+6=3x-4\\\\\text{*** We subtract 3x-4 from both sides. ***}\\\\x^2-4x+6-3x+4=0\\\\\text{*** We simplify. *** }\\\\x^2-7x+10=0[/tex]

[tex]\text{*** The sum of the zeroes is 7 and the product 10 = 5 x 2 ***}\\\\\text{*** We can factorise. ***}\\\\x^2-5x-2x+10=x(x-5)-2(x-5)=(x-2)(x-5)=0\\\\x-2 = 0 \ \ or \ \ x-5 = 0\\\\x= 2 \ \ or \ \ x=5[/tex]

For x = 2, y =0+2=2 (from the first equation) and for x = 5 y=3*5-4=15-4=11 (from the second equation)

So the solutions are (2,2) and (5,11)

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

Answer:

y>9x+6

Step-by-step explanation:

y-9x+(9x)>6+(9x)

y>9x+6

Answer:

(C) 1809 in.2

Step-by-step explanation:

Took the test on edg :3

Answer:

The width is 23.5 ft and the length is 47 ft

Step-by-step explanation:

The perimeter of a rectangle is given by

P = 2(l+w)

141 = 2(l+w)

The length is twice the width

l = 2w

141 = 2 ( 2w+w)

141 = 2( 3w)

141 = 6w

Divide each side by 6

141/6 = 6w/6

23.5 = w

l = 2w = 2(23.5) = 47

The width is 23.5 ft and the length is 47 ft

Answer:

[tex]\boxed{Width = 23.5 \ feet}[/tex]

[tex]\boxed{Length = 47 \ feet}[/tex]

Step-by-step explanation:

Let Length be l and Width be w

Perimeter = 2(Length) + 2(Width)

Condition # 1:

2l+2w = P

=> 2 l + 2 w = 141

Condition # 2:

=> l = 2w

Putting the second equation in the first one

=> 2(2w)+2w = 141

=> 4w + 2w = 141

=> 6w = 141

Dividing both sides by 6

=> Width = 23.5 feet

Given that

=> l = 2w

=> l = 2(23.5)

=> Length = 47 feet

Answer:

(10, 17)

Step-by-step explanation:

It might be easier to explain with a picture or drawing, but I am new to this, so I would try using words.

Assuming the fruit market is on that straight line from Tia's home to Lei's, So we look at both address (coordinates)

From Tia to Lei, x coordinate is from 4 to 12, that's increased by 8, divide by 4, one step is 2.

y coordinate is from 8 to 20, an increase of 12, divide by 4 again, one step is 3.

The fruit market is at 3/4 distance, so 3 steps, on both x and y coordinates.

x: 4+6 = 10

y: 8+9=17

The fruit market is at point (10,17)

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The point (x,y) which divides the segment AB with endpoints at A(x₁,y₁) and B(x₂,y₂) in ratio m:n has cordinates

[tex]x= \dfrac{nx_1+nx_2}{m+n}[/tex]

[tex]y= \dfrac{ny_1+ny_2}{m+n}[/tex]

Tia is at P(4, 8) and Lei is at Q(12, 20).

The fruit market (F) is three-fourths the distance from Tia’s home to Lei's home, then PM : PQ = 3:4 or PM : MQ = 3:1

So,

[tex]x= \dfrac{1.4+3.12}{3+1} = \dfrac{4+36}{4} = \dfrac{40}{4} = 10 \\y= \dfrac{1.8+3.20}{3+1} = \dfrac{8+60}{4} = \dfrac{68}{4} = 17[/tex]

Hence, the fruit market is at point (10,17) which means it is placed at the corner of 10th Street and 17th Avenue.

Learn more about graph here:

brainly.com/question/16608196

#SPJ5

Answer: The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Step-by-step explanation:

There are three measures of the center: 1) Mean   2) Median  3) Mode

Mean : Average value of the data

Mode = The most repeated value.

Median is the middlemost value in a well-ordered data.

It measures the center of the data.

Hence, the completed statement would be:

The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.

Answer:

First ____ is median

Second ____ is center

Step-by-step explanation:

The median is the middle value of a set of numbers, and is found in the center.

Answer: x = -2 , y = 3

Step-by-step explanation:

4x-y=-11

2x+3y=5

Solve 4x-y=-11 for y

Add -4x to both sides

4x-y+-4x=-11+-4x

-y=-4x-11

Divide both sides by -1

-y/-1=-4x-11/-1

y=4x+11

Substitute 4x+11 for y in 2x +3y=5

2x+3y=5

2x+3(4x+11)=5

Simplify both sides of the equation

14x+33=5

Add -33 to both sides

14x+33+-33=5+-33

14x=-28

Divide both sides by 14

14x/14=-28/14

x=-2

Substitute -2 for x in y= 4x+11

y=4x+11

y=(4)(-2)+11

Simplify both sides of the equation

y=3

Answer:

130

Step-by-step explanation:

just did test on plato/edmentum..it was correct

84 (the answer above) is incorrect

Answer:

Hi sorry for late respond but the answer in 130!!

Step-by-step explanation:

Answer:

45°

Step-by-step explanation:

[tex]tan^{-1}(1)[/tex] = 45°

Answer:

[tex]\huge\boxed{\theta=45^o\ \vee\ \theta=225^o}[/tex]

Step-by-step explanation:

[tex]\tan\theta=1[/tex]

[tex]\bold{METHOD\ 1}\\\\\text{Use the table in the attachment}\\\\\tan45^o=1\to\theta=45^o\ \vee\ \theta=45^o+180^o=225^o\\\\\bold{METHOD\ 2}\\\\\tan\theta=1\to\tan^{-1}1=\theta\to\theta=45^o\ \vee\ \theta=225^o[/tex]

Answer: It represents that 2 will be divided into 3 equal parts.

Step-by-step explanation:

The given fraction : [tex]\dfrac{2}{3}[/tex]

here, Numerator = 2

Denominator = 3

It represents that 2 will be divided into 3 equal parts.

Answer:

x = 4 or x = - [tex]\frac{5}{7}[/tex]

Step-by-step explanation:

Given

(2x - 8)(7x + 5) = 0

Equate each factor to zero and solve for x

2x - 8 = 0 ⇒ 2x = 8 ⇒ x = 4

7x + 5 = 0 ⇒ 7x = - 5 ⇒ x = - [tex]\frac{5}{7}[/tex]

Answer:

k= l/3 - 14/3j

Step-by-step explanation:

l = 14j + 3k

Solve for k

l = 14j + 3k

Subtract 14j from both sides

l - 14j =14j + 3k - 14j

l - 14j = 3k

Divide both sides by 3

l - 14j / 3=3k / 3

k= l/3 - 14/3j

Or

1/3(l - 14j) = k

Answer:

Which expression is equivalent to ‐10

k

‐

10

?

Step-by-step explanation:

Answer:

$320

Step-by-step explanation:

Let the total sum of money be $x.

Therefore,

12 1/2% of x = 40

25/2% * x = 40

0.125 * x= 40

x = 40/0.125

x = $320

Thus, total sum of money is $320.

Answer:

$2,500 was invested in the first account while $7,500 was invested in the second account

Step-by-step explanation:

Here in this question, we want to find the amount which was invested in each of the accounts, given their individual interest rates and the total amount that was accorded as interest from the two investments

Now, since we do not know the amount invested , we shall be representing them with variables.

Let the amount invested in the first account be $x and the amount invested in the second account be $y

Since the total amount invested is $10,000, this means that the summation of both gives $10,000

Mathematically;

x + y = 10,000 ••••••(i)

now for the $x, we have an interest rate of 5%

This mathematically translates to an interest value of 5/100 * x = 5x/100

For the $y, we have an interest rate of 6% and this mathematically translates to a value of 6/100 * y= 6y/100

The addition of both interests, gives 575

Thus mathematically;

5x/100 + 6y/100 = 575

Multiplying through by 100, we have

5x + 6y = 57500 •••••••••(ii)

From 1, we can have x = 10,000-y

let’s substitute this into equation ii

5(10,000-y) + 6y = 57500

50,000-5y + 6y = 57500

50,000 + y = 57500

y = 57500-50,000

y = 7,500

Recall;

x = 10,000-y

so we have;

x = 10,000-7500 = 2,500

=======================================================

If a < 7, then |a-7| = -(a-7) = -a+7 based on how absolute value functions are constructed. We're using the idea that

[tex]|x-k| = \begin{cases}x-k \ \text{ if } \ x \ge k\\ -(x-k) \ \text{ if } \ x < k\end{cases}[/tex]

Also, if a < 7, then |a-9| = -(a-9) = -a+9. This is true whenever 'a' is less than 9 for similar reasoning as above.

---------

So we have,

|a-7| - |a-9| = -a+7 - (-a+9) = -a+7+a-9 = -2

As long as a < 7, the result of |a-7| - |a-9| will always be -2.

---------

As an example, let's say a = 0

|a-7| - |a-9| = |0-7| - |0-9|

|a-7| - |a-9| = |-7| - |-9|

|a-7| - |a-9| = 7 - 9

|a-7| - |a-9| = -2

I recommend you try out other values of 'a' to see if you get -2 or not. Of course only pick values that are smaller than 7.

Answer:

B

Step-by-step explanation:

C is too little and D is too much

Answer:

93107

Step-by-step explanation:

add all of the numbers together

divide by 5 since there are 5 numbers

you would get 92106.8

so round that up since you cannot have 1/8 of a squirrel

Hope this helps!!

Answer:

52 students

Step-by-step explanation:

From the question above, we have the following information:

a) Vidya ranks 7th from the top.

Mathematically,

Vidya = 7th student

b) Divya 3 ranks behind Vidya.

Divya = Vidya + 3

Hence, Mathematically:

Divya = 7 + 3 = 10

Divya = 10th student

c) Also, Divya is 7 ranks ahead of Medha.

Mathematically,

Medha = 10 + 7= 17

Medha= 17th student

d)Sushma is 32 ranks behind Medha

Mathematically,

Sushma = Medha + 32

= 17 + 32 = 49

Sushma is the 49th student

Therefore, since, Sushma is 4th from the bottom, total number of students is:

49 + 3 = 52 students

Answer: (upside down fancy u) q5

Step-by-step explanation:

Simply apply the law of conservative (upside down fancy u)

Answer:

divide the number by 8 and write the remainder like this 10 r 5.Then you get your answer by going through the remainders in an upward direction. So the answer is 125

Answer:

Step-by-step explanation:

[tex]x^2+\frac bax+\frac ca=0\\\\ ax^2+bx+c=0\\\\x_1=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\qquad\quad x_2=\dfrac{-b+\sqrt{b^2-4ac}}{2a}\\\\\\x_1+x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}+\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\dfrac{-2b}{2a}=\dfrac{-b}a\\\\\\x_1\cdot x_2=\dfrac{-b-\sqrt{b^2-4ac}}{2a}\cdot\dfrac{-b+\sqrt{b^2-4ac}}{2a}=\\\\{}\ \ =\dfrac{b^2-b\sqrt{b^2-4ac}+b\sqrt{b^2-4ac}-(\sqrt{b^2-4ac})^2}{2a}=\dfrac{b^2-(b^2-4ac)}{4a^2}=\\\\{}\ \ =\dfrac{b^2-b^2+4ac}{4a^2}=\dfrac{4ac}{4a^2}=\dfrac{c}{a}[/tex]

[tex]x_1-x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}-\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-2\sqrt{b^2-4ac}}{2a}=\frac{-\sqrt{b^2-4ac}}{a}\\\\\\x_1\div x_2=\frac{-b-\sqrt{b^2-4ac}}{2a}\div\frac{-b+\sqrt{b^2-4ac}}{2a}=\frac{-b-\sqrt{b^2-4ac}}{2a}\,\cdot\,\frac{2a}{-b+\sqrt{b^2-4ac}}=\\\\=\frac{-b-\sqrt{b^2-4ac}}{-b+\sqrt{b^2-4ac}}=\frac{b+\sqrt{b^2-4ac}}{b-\sqrt{b^2-4ac}}=\frac{b^2+2\sqrt{b^2-4ac}+b^2-4ac}{b^2-b^2+4ac}=\frac{2b^2+2\sqrt{b^2-4ac}-4ac}{4ac}=[/tex]

[tex]=\frac{b^2+\sqrt{b^2-4ac}-2ac}{2ac}[/tex]

Work Shown:

sin(angle) = opposite/hypotenuse

sin(35) = 10/x

x*sin(35) = 10

x = 10/sin(35)

x = 17.434467956211 make sure your calculator is in degree mode

x = 17.4

Answer:

[tex]\boxed{17.4}[/tex]

Step-by-step explanation:

sin [tex]\theta[/tex] = [tex]\frac{opposite}{hypotenuse}[/tex]

sin (35) = [tex]\frac{10}{x}[/tex]

x = [tex]\frac{10}{sin(35)}[/tex]

x = 17.4344679562...

x ≈ 17.4

Answer:

B

Step-by-step explanation:

sqrt30 -6^2 doesn't work

2.5 sqrt18 and 5 do work