The side of a square is 3 cm smaller than one of the sides of a rectangle and 2 cm greater than its other side. Find the side of the square, if it’s known that the area of the square is 30 cm^2 less than the area of the rectangle.

Answer:

The ratio given is part to part. The total number of parts in the whole is 1 + 3 = 4.

Step-by-step explanation:

I like to call the numbers in the ratio 1 : 3 "ratio units".

That is, the short length is 1 ratio unit long, and the longer length is 3 ratio units long. The total (whole) length is 1+3 = 4 ratio units long. Then the short length (1 ratio unit) is 1/4 of the whole length (4 ratio units).

_____

Coment on the answer wording

I think you need to be careful with terminology. The word "part" has a different meaning in the first answer sentence "... part to part" than it does in the second answer sentence "... parts in the whole ...".

In the first sentence, it refers to "a piece of the line, no matter its length." In the second sentence, it refers to "that length of the line represented by 1 in the ratio."

Answer:

The correct answer would be A) (4, 49.6)

Step-by-step explanation:

In order to find the equation, we first have to start with the base form of direct variation.

y = kx

Now we input the k value.

y = 12.4x

Now that we have this, we can try the ordered pairs and look for which satisfies the equation.

y = 12.4x

49.4 = 12.4(4)

49.4 = 49.4

Since this is the true statement, this is the ordered pair that works.

Answer:

(4,49.6)

Step-by-step explanation:

Answer:

x = 2/5

Step-by-step explanation:

[tex]x^3=\dfrac{0.008}{0.125}=\dfrac{8}{125}=\dfrac{2^3}{5^3}\\\\x=\sqrt[3]{\dfrac{2^3}{5^3}}=\dfrac{\sqrt[3]{2^3}}{\sqrt[3]{5^3}}=\dfrac{2}{5}[/tex]

The value of x is 2/5.

Answer:

x = 2/5

Step-by-step explanation:

x^3 = .008/.125

Take the cubed root on each side

x^3 ^ (1/3)  = (.008/.125) ^ 1/3

Using ( a/b) ^c = a^c / b^c  and a^b^c = a^ (b*c)

x^(3 *(1/3))  = (.008) ^ 1/3 / (.125) ^ 1/3

x = (.008) ^ 1/3 / (.125) ^ 1/3

x = .2/.5

x = 2/5

Answer:

Point

Step-by-step explanation:

If you are referring to geometry

Answer:

Step-by-step explanation:

We have been given an equation:

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

(a) Related equation means the equation that are equivalent to the given equation.

We can shift 3 on the right hand side of the equation:

(1)[tex]x=3+2\frac{1}{2}[/tex]

We can solve the mixed fraction [tex]2\frac{1}{2}=\frac{5}{2}[/tex] we get.

(2)[tex]x=3+\frac{5}{2}[/tex]  

We can solve the right hand side of the equation [tex]x=3+\frac{5}{2}[/tex]    we get:

(3)[tex]x=\frac{11}{2}[/tex]

Hence, above three expressions are the related equations of the given equation.

(b) We have to find the related equations that isolates the variable and simplify.

So, basically we can solve for x.

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

[tex]x=1+3[/tex]

[tex]x=4[/tex].

Answer:

{x = 1/7 ,y = 1

Step-by-step explanation:

Solve the following system:

{-5 y = -5 | (equation 1)

{7 x + 6 y = 7 | (equation 2)

Swap equation 1 with equation 2:

{7 x + 6 y = 7 | (equation 1)

{0 x - 5 y = -5 | (equation 2)

Divide equation 2 by -5:

{7 x + 6 y = 7 | (equation 1)

{0 x+y = 1 | (equation 2)

Subtract 6 × (equation 2) from equation 1:

{7 x+0 y = 1 | (equation 1)

{0 x+y = 1 | (equation 2)

Divide equation 1 by 7:

{x+0 y = 1/7 | (equation 1)

{0 x+y = 1 | (equation 2)

Collect results:    Answer:    {x = 1/7 ,y = 1

Answer:

No

Step-by-step explanation:

Answer:

Each hiker gets [tex]\frac{7}{3}[/tex]  cups of mixed nuts.

Step-by-step explanation:

First, we need to find the total amount of cups by multiplying the number of bags with the amount of cups in each bag:

8 * 3.5 = 28

Now, we divide this by 12 to find the amount of cups per hiker:

28 ÷ 12 = [tex]\frac{7}{3}[/tex] or 2.3333

So each hiker gets  [tex]\frac{7}{3}[/tex]  cups of mixed nuts.

Answer:

f(x)= -x²-4x-2

Step-by-step explanation (this way is not the shortest one):

1. for intercept (-2-√2;0): a(-2-√2)²+b(-2-√2)+c=0

for intercept (-2+√2;0): a(-2+√2)²+b(-2+√2)+c=0

for the point (-1;1): a(-1)²+b(-1)+c=1

2. using the three record written above, it is possible to make up the system of equations and calculate 'a', 'b' and 'c':

[tex]\left \{ \begin{array}{ccc}a-b+c=1\\a(-2- \sqrt2)^2+b(-2- \sqrt2)+c=0\\a(-2+ \sqrt2)^2+b(-2+ \sqrt2)+c=0\end{array}[/tex]

[tex]\left \{ \begin{array}{ccc}a=-1\\b=-4 \\c=-2\end{array}[/tex]

3. the required equation is: -x²-4x-2

Answer:

Question 39: False

Question 43: True

Step-by-step explanation:

Question 39

|-4| is a solution of x ≤ 4

|-4| ⇒ This mean the absolute value of 4. The sign s are neglected.

So, |-4| is not a  solution of x ≤ 4.

Question 43

The point (5, -1) is a solution of the equation: y = 2x − 11.

To prove this we are to substitute the point (5, -1) in the equation y = 2x − 11.

y = -1 and x = 5

y = 2x − 11   ⇒   -1 = 2(5) -11

                         -1 = 10 - 11

                         -1 = -1

Answer:

Point (1,8)  

Step-by-step explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

[tex][x=\frac{mx_2+nx_1}{m+n},y= \frac{my_2+ny_1}{m+n}][/tex]

Let us substitute coordinates of point P and Q as:

[tex]x_1=-8[/tex],

[tex]y_1=-4[/tex]

[tex]x_2=4[/tex]

[tex]y_2=12[/tex]

[tex]m=3[/tex]

[tex]n=1[/tex]

[tex][x=\frac{(3*4)+(1*-8)}{3+1},y=\frac{(3*12)+(1*-4)}{3+1}][/tex]

[tex][x=\frac{12-8}{4},y=\frac{36-4}{4}][/tex]

[tex][x=\frac{4}{4},y=\frac{32}{4}][/tex]

[tex][x=1,y=8][/tex]

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.

Answer:

Step-by-step explanation:

1,8

Answer:

Total tax paid by Bruce = $2477.62

Step-by-step explanation:

Bruce banner taxable income last year = $43,467

State's income tax rate = 3.9%

State's income tax = 43467*3.9% = 43467*0.039 = $1695.21

City income tax rate is = 1.8

City income tax = 43467*1.8% = 43467*0.018 =$782.41

Total tax = $1695.21 + $782.41

= $2477.62

Thank you.

Answer:

2.5 min

Step-by-step explanation:

The tortoise takes 1 min/3 m.

7.5 × 1/3  = 2.5 min

Answer:

Length of Charlie's brother's room  = 8 2/5 feet

Area of Charlie's brother's room  = 60 9/10 feet²

Step-by-step explanation:

Width Charlie's room = 7 1/4 = (7 x 4 +1)/4 = 29/4  feet

Length Charlie's room =  10 1/2 = (10 x 2 +1)/2 = 21/2 feet

Length brother's room = 4/5 x 21/2 = (4 x 21)/(5 x 2) = 84/10 = 8 2/5 feet

Area = Length x Width = (42/5 x 29/4) feet² = 1218/20 feet² = 60 9/10 feet²

[tex]\textit{\textbf{Spymore}}[/tex]

The "rate of change" is presumed to refer to the rate at which the balance in the bank account changes as dues are collected from Art Club members. It increases by $15 for each new collection, so we can say ...

... the rate of change is $15 per member.

We further presume that the problem intends the "initial value" to refer to the fact that the 17 × $15 = $255 does not match the full amount of the current Art Club account balance ($300). So, there must have been some balance in the account before collection started. We can interpret that $45 "initial value" as ...

... the account balance before dues collection started is the initial value.

Answer:

it should be 4x^3 y-4xy^2+xy+3x^2

Step-by-step explanation:

Answer:

X = 37

Y = 29

Step-by-step explanation:

X + Y = 66

X - Y = 8

------

Solve second equation for X

X = Y + 8

Substitute for X in first equation

Y + 8 + Y = 66

2 * Y = 58

Y = 29

___

X - 29 = 8

X = 37

X = 37

Y = 29

Good Luck,

- I.A. -

Answer:

x = 37 and y = 29

Step-by-step explanation:

x + y = 66

x - y = 8

solve second equation for x

x = y + 8

substitute for x in first equation

y+8 +y = 66

2y = 58

y = 29

x - 29 = 8

x = 37

x = 37 and y = 29

Answer:

Probability that a vehicle is white, given that the vehicle is a car :

0.2222

Step-by-step explanation:

A: vehicle is white

probability that a vehicle is white =P(A)= 0.25

B:vehicle is a car

probability that it is a car =P(B)= 0.36

A∩B:vehicle is a white car

P(A∩B)=probability that it is a white car = 0.08

A/B:vehicle is white,given that vehicle is a car

to find P(A/B)

baye's theorem says that

P(A∩B)=P(A/B)×P(B)

⇒   0.08=P(A/B)×0.36

⇒  P(A/B)=0.2222

Hence, probability that a vehicle is white, given that the vehicle is a car is :

0.2222

Answer: 0.22

Step-by-step explanation:

confirmed

Answer:

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

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

                                      2+1

Step-by-step explanation:

To find the average rate of change

ave rate of change = f(x2) - f(x1)

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

                                   x2-x1

We know that x2 = 2 and x1 = -1

ave rate of change = f(2) - f(-1)

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

                                   2--1

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

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

                                      2+1

Answer:

ave rate of change = (-6)^(2+2) +3 -  (-6)^(-1+2) +3

Step-by-step explanation:

Answer:

[-5/2, 1/2] is the correct answer

Step-by-step explanation:

Subtract the left side to compare to zero:

... 4x^2 +8x -5 ≤ 0

... (2x +5)(2x -1) ≤ 0 . . . . factor

... x = -5/2 . . . or . . . x = 1/2 . . . . are the zeros

The factors will differ in sign (the product will be negative) when x is between the zero values. Hence the solution set is ...

... x ∈ [-5/2, 1/2]

_____

Check

When you normalize the leading coefficient of the quadratic to 1, it becomes ...

... x² +2x -5/4 ≤ 0

Now, you know the sum of zeros must be -2 and the product of zeros must be -5/4. The zeros associated with the answer given in your key have a sum of -4.5 and a product of -5/2. It cannot be right.

Answer:

b. 3x - (5y -7)

Step-by-step explanation:

Let x represent "a number". Let y represent "another number."

The "3 times a number" is represented by 3x.

And "5 times another number less 7" is represented by 5y -7.

The difference between these quantities is the second subtracted from the first:

... 3x - (5y -7) . . . . matches selection b.

The number 9.36×10-4 in standard form is 0.000936. You convert from scientific notation to standard form by moving the decimal point to the left by the number equivalent to the exponent when the exponent is negative.

Explanation:

When asked what is 9.36×10-4 in standard form, we are being asked to convert a number from scientific notation to its regular number format. Scientific notation is a method of writing numbers that are too big or too small to be conveniently written in decimal form. To convert this to standard form, we move the decimal point to the left if the exponent is negative (or to the right if the exponent is positive) as many times as the value of the exponent.

In this case, we have a negative exponent (-4), so we move the decimal four places to the left:

9.36 -> 0.936 -> 0.0936 -> 0.00936 -> 0.000936

Therefore, 9.36×10-4 in standard form is 0.000936.

E. 168 sq units

The legs of this right triangle have length 24 and 14, so the area is ...

... A = (1/2)bh = (1/2)(24)(14) = 168 . . . . sq units

Answer:

Step-by-step explanation:

Numerical reasoning

If all questions were 2-point, the total score would be 80. It is 20 more than that. Each 4-point question that replaces a 2-point question will add 2 points to the score, so there must be 20/2 = 10 of them.

There are 10 4-point questions and 30 2-point questions.

_____

With an equation

Let x represent the number of 4-point questions. Then 40-x is the number of 2-point questions. The total number of points is ...

... 2(40-x) +4x = 100

... 2x +80 = 100 . . . . simplify

... 2x = 20 . . . . . . . . .subtract 80

... x = 10 . . . . . . . . . . divide by 2.

There are 10 4-point questions and 40-10=30 2-point questions.

Answer:

D) 75%

Step-by-step explanation:

75% of 24 = 0.75 x 24 = 18

Answer:

-1,81

Step-by-step explanation:

Multiplicity of a number can be written as power

for example

-1(multiplicity 3) can be written as

[tex]-1^{3}[/tex]= -1

similiarly 3(multiplicity 4) can be written as

[tex]3^{4}[/tex]=81

The eleventh-degree polynomial (x + 3)4(x – 2)7 has the same zeroes as did the quadratic, but in this case, the x = –3 solution has multiplicity 4 because the factor (x + 3) occurs four times (that is, the factor is raised to the fourth power) and the x = 2 solution has multiplicity 7 because the factor (x – 2) occurs ... Can you do the rest on your own?

Attached pictures shows the answers in RED.

B. (5, -2)

Try the points in the inequalities and see what works. Here, we evaluate the point in the first inequality, and if that works, then the second inequality.

A. 2 ≤ -(-5) -5 . . . ⇒ . . . 2 ≤ 0 . . . false

B. -2 ≤ 5 -5 . . . true

... -2 ≥ -(5) -4 . . . true . . . . . . selection B is a viable choice

C. we know from A that the first inequality will be satisfied

... -2 ≥ -(-5) -4 . . . ⇒ . . . -2 ≥ 1 . . . false

D. 2 ≤ 5 -5 . . . . false

Since QC and BR are parallel, triangles CDQ and BDR are similar.

This means that corresponding sides are in proportion, so we have

[tex] BD \div QD = RD \div CD [/tex]

Substituting numbers, we have

[tex] 26+39 \div 39 = 18+x \div x \iff \dfrac{65}{39} = \dfrac{18+x}{x} [/tex]

Multiply both sides by [tex] 39x [/tex]

[tex] 65x = 39(18+x) [/tex]

Expand right hand side:

[tex] 65x = 702 + 39x [/tex]

Subtract 39x from both sides:

[tex] 26x = 702 [/tex]

Divide both sides by 26

[tex] x = \dfrac{702}{26} = 27 [/tex]

Just took the test and got the the correct answer *\(♡°▽°♡)/*

Look at the image down below!!

Answer:

7:10 (boys to girls)

10:7 (girls to boys)

7:17 (boys to everyone combined)

10:17 (girls to everyone combined)

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