A rectangular box has the length of [tex]\sqrt{90}[/tex] inches, width of [tex]\sqrt{14}[/tex] inches, and height of [tex]\sqrt{70}[/tex] inches.

a. What is the volume of the box?
b. What is the area of the top of the box?
c. What is the ratio of the height of the box to the length of the box?

Don't answer in decimals.

Answer:

w = ±[tex]\sqrt{1/2}[/tex] or w= ±[tex]\sqrt{2}[/tex]

Step-by-step explanation:

if we say some variable y = w^2, we can rewrite the equation to:

2y^2 - 5y + 2 = 0

this can be factored into (2y-1)(y-2) = 0

putting w^2 back in the place of y, that's (2w^2 - 1)(w^2 - 2) = 0

The equation is a fourth degree polynomial, so there are four roots, or four values of w that will cause the equation to equal 0.

If 0 is multiplied by anything, the result is 0, so we set 2w^2 - 1 = 0 and solve for w, which is ±√1/2, then set w^2 - 2 = 0 to get w = ±√2 as our roots

the four solutions are ±√1/2 and ±√2

(because the positive counts as one solution and the negative another solution)

Answer:

y=0.75x+3.75

Step-by-step explanation:

The slope is

[tex] \frac{6 - 4.5}{3 - 1} = \frac{3}{4} [/tex]

Substituting into point-slope form,

y - 6 = 0.75(x - 3)

y - 6 = 0.75x - 2.25

y = 0.75x + 3.75

The quadrants of the points are

The points are given as:

A(2, 4)    B(0, -3)   C(1, -1)

E(-4,1)     G(-3,-2)   I(0, 2)

D(3, 3)     F(2,0)    H(-2, 3)

J(-1,-4)

Next, we plot each coordinate on a graph (see attachment)

From the attached graph, we have the following categories

Quadrant 1: Points A and D

Quadrant 2: Points E and H

Quadrant 3: Points G and J

Quadrant 4: Points C

x-axis: Point F

y-axis: Point B and I

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Answer:

3

Step-by-step explanation:

slope = (y_2 - y_1)/(x_2 - x_1)

slope = (1 - 7)/(3 - 5)

slope = -6/(-2)

slope = 3

Parallel lines have equal slopes.

Answer: 3

Answer:

The speed of the boat in still water is 18 mph.

The speed of the current is 2 mph

Step-by-step explanation:

Let x constitute the charge of the boat in nonetheless water.

Let y constitute the rate of the contemporary.

When the boat is going against the modern-day, the rate is sixteen mph. Assuming it traveled against the modern at the equal time as going upstream, its general speed may be (x - y) mph. It way that

x - y = 16  (equation 1)

Going downstream, the boat averages 20 mph. Assuming it traveled with the current, its standard pace would be (x + y) mph. It way that

x + y = 20  (equation 2)

Adding each equation, it becomes

2x = 36

x = 36/2

x = 18 mph

Substituting x = 18 into equation 1, it will become

18 - y = 16

y = 18 - 16

y = 2 mph

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Answer:

C)  x = 3

Step-by-step explanation:

Given equation:

[tex]5^x=125[/tex]

Rewrite 125 with base 5:  125 = 5³

[tex]\implies 5^x=5^3[/tex]

[tex]\textsf{Apply the one-to-one property of exponents}: \quad a^{f(x)}=a^{g(x)} \implies f(x)=g(x)[/tex]

[tex]\implies x=3[/tex]

The problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

The weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

We assume the weight of the cow to be x kg.

The weight of a full-grown dog is given to be one-eight of a cow, that is, the weight of a full-grown dog = (1/8)*x = x/8 kg.

Thus, the sum of the weights of the full-grown dog and the cow = x/8 + x kg.

But, we are given that together, they weigh 360 kg.

This can be shown as the linear equation in the one variable:

x/8 + x = 360.

Thus, the problem could be solved using the linear equation in one variable, x/8 + x = 360, where x kg is the weight of a cow.

To solve the problem, we solve the equation as follows:

x/8 + x = 360,

or, (9/8)x = 360 {Simplifying},

or, x = 360*8/9 {Cross-Multiplying},

or, = 320.

Thus, the weight of the cow, on solving the equation, is found to be 320 kg.

The weight of the full-grown dog = (1/8)*320 kg = 40 kg.

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No digit with the format 90x0y07 is divisible by 2017

The given parameters are:

Dividend = 90x0y07

Divisor = 2017

The dividend is a 7-digit number, and the divisor is a 4-digit number

So, the quotient must be 3 to 4 digits.

Comparing the first and last digits of 90x0y07 and 2017;

The first and last digits of the quotient must be 4 and 1, respectively

So, we have:

90x0y07 = 2017 * 4a1

Assume a = 9.

So, we have:

90x0y07 = 2017 * 491

90x0y07 = 990347

The above is 6-digit.

So, we make use of a 4-digit quotient

This gives

90x0y07 = 2017 * 4ab1

Next, we make use of trial by error.

After several attempts, we conclude that no digit with the format 90x0y07 is divisible by 2017

The closest attempt is

90x0y07 = 2017 * 4471

90x0y07 = 9018007

Where:

x = 1, y = 0 and the digit between x and y is 8, not 0

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The area of Entire roof is 12 feet².

The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs (the side opposite the right angle)

Given:

As, the roof peak with a 3 and the roof overhang the sides is 4.

Now, Using Pythagorean theorem.

a² + b² = c ²

15² + 13² = c²

c² = 225+ 169

c = 19.8 (or 20)

So, the length of diagonal is 24.

Roof Dimension 36 x 24 or (

Area of Roof = 3 x 2

                      = 6 unit²

and, area of the entire roof = 2 x6 = 12 ft²

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Answer:

The system of equations y=14-2x and 6x+3y=42.

Step-by-step explanation:

Please see attachment to see the answer as a graph.

Hope this helps!

Answer:

True

Step-by-step explanation:

Answer:

222

Step-by-step explanation:

Hey there!

250 - {(135 + 34) ÷ (46 - 33)} - 15 

= 250 - 169/(46 - 44) - 15

= 250 - 169/13 - 15

= 250 - 13 - 15

= 237 - 15

= 222

Therefore, your answer should be:

222

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

The result of the evaluation of the equation given in the task content is; x =-2.

It follows from the task content that the equation given whose solution is to be determined is;

3[-x + (2 x +1)]=x-1

The equation can be solved as follows;

-3x + 6x +3 = x-1

2x = -4

x = -2

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Each junior  receives 93 score on the test. It is also the average score of the juniors.

Given Information

It is given that 10% of the strength of the class consists of juniors and 90% consists of seniors.

Let us assume the total strength of the class is 100, then,

Number of seniors = 90

Number of juniors = 10

It is also given that the average score of the class = 84

And, average score of the seniors = 83

Another given information is that all the juniors all received the same score, which is their average score. Let it be x.

Average Score of Juniors

Total marks obtained by the seniors = Number of seniors × Average score of seniors

= 90 × 83

= 7470

Total marks obtained by the juniors = Number of juniors × Average score of juniors

= 10x

Average marks on the test = Total marks / Total number of students

⇒ 84 = (7470 + 10x)/100

⇒ 84 × 100 = 7470 + 10x

⇒ 10x + 7470 = 8400

⇒ 10x = 8400-7470

⇒ 10x = 930

⇒ x = 930/10

⇒  x = 93

Thus, each junior scores 93 on the test.

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Answer:

-500

Step-by-step explanation:

since 501 has a negative sign,add 1 to to the number,the next number will be -500

-501 +1 = -500

successor in this case means a number that succeeds another

The expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

A square is a quadrilateral with all four sides equal, and all four angles at 90°, whereas a rectangle is a quadrilateral with opposite pair of sides equal, and all four angles at 90°.

In the question, we are informed that Melissa is planning a rectangular vegetable garden with a square patch for tomatoes.

The side of the square is given to be x feet.

We are asked to write expressions for the length and width of the rectangular garden.

For the length of the rectangle:-

We are informed that she wants the length of the garden to exceed three times the length of the tomato patch by 2 feet.

Thus, the length of the garden can be shown as the expression 3x + 2 feet.

For the width of the rectangle:-

We are informed that she also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Thus, the width of the garden can be shown as the expression x + 5 feet.

Thus, the expressions for the length and the width of the rectangular garden are 3x + 2 feet, and x + 5 feet respectively where x is the length of the square patch for tomatoes.

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The provided question is incomplete. The complete question is:

"Melissa is planning a rectangular vegetable garden with a square patch for tomatoes. She wants the length of the garden to exceed three times the length of the tomato patch by 2 feet. She also wants the garden's width to exceed the width of the tomato patch by 5 feet.

Let x represent the length, in feet, of the square tomato patch.

Write expressions to represent the length and width of Melissa's vegetable garden in terms of x.

Enter the correct answer in the box."

Answer: [tex]110^{\circ}[/tex]

Step-by-step explanation:

[tex]m\angle 20=62^{\circ}[/tex] (linear pair)

[tex]m\angle 11=70^{\circ}[/tex] (angle sum in a triangle)

[tex]m\angle 12=110^{\circ}[/tex] (linear pair)

Answer:

One side is 40 cm and the adjacent side is 50 cm

Step-by-step explanation:

We can use a rectangle because a rectangle is a parallelogram.  Draw a rectangle.  Write the width as x and the length as x + 10.  We find the perimeter by adding all 4 side lengths.

Two side lengths are x and two side lengths are x + 10.  If we add all of this together we get 180

x +x +x+10+x+10 = 180

4x + 20 = 180  Combine the like terms.  There are 4 x's and 10+10 is 20

4x = 160  Subtract 20 from both sides

x  = 40  Divide both sides by 4

So, two sides are 40 and two sides are 50, this will add up to 180

Answer:

40 cm & 50 cm

Step-by-step explanation:

one side = X cm (??)

the other side =X+10 cm

Solve

2(x+x+10)=180

x+x+10=90

2x=80

x = 80/2

x=40

therefore

x+10=50cm

Using a system of equations, the weight of 5 apples, 2 oranges are 4 bananas is given as follows:

B. 1147 gm.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are:

Considering the data given, the equations are:

From the first equation:

3x = 928 - 5y.

x = 309.33 - 1.667y.

From the second equation:

6z = 1088 - 4y

z = 181.33 - 0.667y

Replacing in the third equation:

5x + 3z = 799

5(309.33 - 1.667y) + 3(181.33 - 0.667y) = 799

10.336y = 12961.64

y = 1291.64/10.336

y = 125 gm.

The other weights are:

The weight of 5 apples, 2 oranges are 4 bananas is:

5x + 2y + 4z = 5 x 101 + 2 x 125 + 4 x 98 = 1147 gm, option B.

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Answer:

  (c)  5y -17x +99 = 0

Step-by-step explanation:

The median of a triangle is the line through a vertex and the midpoint of the opposite side. The median of ΔXYZ from vertex Y will be the line through point Y and the midpoint of XZ.

The midpoint of XZ is the average of the coordinates of X and Z.

  M = (X +Z)/2

  M = ((1, -2) +(8, -7))/2 = (9, -9)/2 = (4.5, -4.5)

The slope of the median can be found using the slope formula:

  m = (y2 -y1)/(x2 -x1)

The slope of line YM is ...

  m = (-4.5 -4)/(4.5 -7) = -8.5/-2.5 = 17/5

The point-slope form of the equation of a line is ...

  y -k = m(x -h) . . . . . . line with slope m through point (h, k)

The line with slope 17/5 through point Y(7, 4) is ...

  y -4 = 17/5(x -7)

Subtracting the right side, and multiplying by 5 gives ...

  5(y -4) -17(x -7) = 0

  5y -17x +99 = 0 . . . . equation of the median through Y

Answer:

c = 10

Explanation:

Use Pythagoras theorem: a² + b² = c²

where 'a' and 'b' are legs and 'c' is the hypotenuse (the longest side)

Here given: a = 8 cm, b = 6 cm, c = ?

Substituting values:

8² + 6² = c²

c² = 64 + 36

c² = 100

c = √100

c = 10

Answer:

10 cm

Step-by-step explanation:

[tex]a^2=b^2+c^2[/tex]

[tex]a^2=6^2+8^2[/tex]

[tex]a^2=100[/tex]

[tex]\sqrt{a^2}=\sqrt{100[/tex]

a=10

The distance of the top of the building from a is 163m and that from b is 115m .

Calculating the Perpendicular Distance of the Top From Ground

It is given that the angle of elevations of the building top from a and b are 25° and 37° respectively.

ab = 57m

Let the top of the building be point c and the distance between the building and the point b be x. Then, from the figure, we can deduce the following,

In Δacd, tan 25° = cd/ad

⇒ 0.4663 = cd /(x+57)

⇒ cd = 0.4663(x+57)             ......................... (1)

In Δbcd, tan 37° = cd/x

⇒ 0.7536 = cd/x

⇒ x =cd / 0.7536                   .......................... (2)

Solving for the Distance cd

Substitute the value of in equation (2) to equation (1) to get,

cd = 0.4663 ((cd/0.7536)+57)

cd = 0.4663(cd+42.9552)/0.7536

0.7536cd = 0.4663cd + 20.03

0.7536cd - 0.4663cd = 20.03

0.2906cd = 20.03

cd = 20.03/0.2906

Thus, the distance cd ≈ 68.93m

Finding the Distance cb and Distance ca

In Δacd, sin25° = cd/ca

⇒ 0.4226 = 68.93/ca

ca = 68.93/0.4226

ca = 163.10

∴ The distance ca ≈ 163m

Similarly, in Δbcd, sin37° = cd/cb

⇒ 0.6018 = 68.93/cb

cb = 68.93/0.6018

cb =114.54m

∴ The distance cb ≈ 115m

Therefore, the points a and b are at a distance of 163m and 115m respectively from the top of the building.  

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The number of times that Derrick batted last season is 188 times.

Percentage can be described as a fraction out of an amount that is usually expressed as a number out of hundred. Percentage is a measure of frequency. The sign used to denote percentage is %.

A percentage of 25% here means that twenty five times out of hundred times, Derrick hit the ball. In order to convert a percentage to a decimal, divide the percentage by 100.

Number of times Derrick bat last season = Number of hits last season / percentage of his batting average

47 / 25%

47 / 0.25 = 188

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Answer:  [tex]\frac{2}{9}[/tex]

Step-by-step explanation:

[tex]\frac{\sqrt{4} }{3^{3} }[/tex]
The square root of 4 can be written as 2
3 to the third power can be written as 9

So, the answer is [tex]\frac{2}{9}[/tex]

Answer:

8(3j - 2).

Step-by-step explanation:

24j-16

GCF = 8

so the answer is

8(3j - 2).

Answer:

1) [tex]x_1=-1-2\sqrt{2},\ x_2=-1+2\sqrt{2}[/tex]

2) [tex]x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

Step-by-step explanation:

[tex]{\large \textsf{ Quadratic Formula: }}x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\ \Bigg{\|}\ \textsf{when }ax^2+bx+c=0[/tex]

Given quadratic equations:

1. [tex]x^2+2x-7=0[/tex]

2. [tex]4x^2-3=x^2-5x-4[/tex]

1. x² + 2x - 7 = 0

[tex]\implies a=\textsf{1},b=\textsf{2},c=\textsf{-7}[/tex]

Step 1: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{2})\pm \sqrt{(\textsf{2})^2-4(\textsf{1})(\textsf{-7})}}{2(\textsf{1})}\\\implies x&=\dfrac{-2\pm \sqrt{4-4(-7)}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{4+28}}{2}\\\implies x&=\dfrac{-2\pm \sqrt{32}}{2}\end{aligned}[/tex]

Step 2: Simplify the radicand (under the square root).

[tex]\begin{aligned}x&=\dfrac{-2\pm \sqrt{16\times2}}{2}\\x&=\dfrac{-2\pm 4\times\sqrt{2}}{2}\\x&=\dfrac{-2\pm 4\sqrt{2}}{2}\end{aligned}[/tex]

Step 3: Separate into two solutions and simplify them.

[tex]\implies x_1&=\dfrac{-2 - 4\sqrt{2}}{2},\ x_2&=\dfrac{-2 + 4\sqrt{2}}{2}[/tex]

[tex]\begin{aligned}\implies x_1&=\dfrac{-2}{2}+\dfrac{- 4\sqrt{2}}{2},\ x_2=\dfrac{-2 + 4\sqrt{2}}{2}\\\implies {x_1&=\boxed{-1-2\sqrt{2}},\ x_2=\boxed{-1+2\sqrt{2}} \end{aligned}[/tex]

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

2. 4x² - 3 = x² - 5x - 4

Step 1: Set the equation to zero (by moving the "x² - 5x - 4" to the left).

4x² - 3 - x² + 5x + 4 = 0 [ Combine like terms. ]

3x² + 5x + 4 = 0

[tex]\implies a=\textsf{3},b=\textsf{5},c=\textsf{1}[/tex]

Step 2: Substitute the given values into the formula and simplify.

[tex]\begin{aligned}\implies x&=\dfrac{-(\textsf{5})\pm \sqrt{(\textsf{5})^2-4(\textsf{3})(\textsf{1})}}{2(\textsf{3})}\\\implies x&=\dfrac{-5\pm \sqrt{25-12}}{6}\\\implies x&=\dfrac{-5\pm \sqrt{13}}{6}\end{aligned}[/tex]

Step 3: Separate into two solutions.

[tex]\implies x_1=\dfrac{-5 - \sqrt{13}}{6},\ x_2=\dfrac{-5 + \sqrt{13}}{6}[/tex]

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Answer:

The water in pot X is hoter than that of pot Y

Answer:

A is the answer

Step-by-step explanation:

The center and radius of the circle is (b) center: (-5, 1) radius: 2

The circle equation is given as:

(x-5)^2 + (y+1)^2 = 4

The circle equation is represented as:

(x-a)^2 + (y-b)^2 = r^2

Where:

Center = (a,b)

Radius = 4

By comparison, we have:

(a, b) = (-5, 1)

r^2 = 4

This gives

(a, b) = (-5, 1)

r = 2

Hence, the center and radius of the circle is (b) center: (-5, 1) radius: 2

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Answer:

Step-by-step explanation:

(7x-3)(12x-7)

we are solving for x and we are multiplying.

we start with the x's 7x*12x=  84x

-3*-7=21

so now we have

84x+21=0

the 0 is a placer for answering the question

we minus 21 to both sides

84x=-21

now we divide

84/-21= -4

x=-4

Answer:

y = |x + 8|

Explanation:

Please see the table attached below.

Answer:y=|x+8|

Step-by-step explanation: