The base area of a rectangular water tank is 1000cm². If the tank has a height of 100cm' a) Find the capacity of the water tank.​

Answer:

[tex]x = \dfrac{21}8[/tex]

Step-by-step explanation:

[tex]~~~~~~~~\dfrac 1 2 -x + \dfrac 34 = x-4\\\\\\\implies \dfrac 24 + \dfrac 34 - x =x-4\\\\\\\implies \dfrac 54+4=x+x\\\\\\\implies 2x = \dfrac{21}{4}\\\\\\\implies x = \dfrac{21}{4 \cdot 2}\\\\\\\implies x = \dfrac{21}8[/tex]

Answer:

−5(x+2)=−4x−12−x+2

Step-by-step explanation:

1) −5(x+2)=−4x−12−x+2

−5x−10=−4−10−x

-5x= -5x

0=0

so, it is true for all values

Fish fed during night  is equal to  1/6 tons

Let the weight of the fish fed at night = X tons

In the morning, the weight of the fish fed Wm = 2/15 tons.

In the afternoon, 1/15 ton more fish fed during the morning.

∴ Weight of fish fed in afternoon Wa

= 2/15 + 1/15

= 3/15 tons

Given that,

Wm + Wa + Wn = 1/2 tons

∴ 2/15 + 3/15 + Wn = 1/2

∴Wn = 1/2 - 5/15

∴ Wn = 3/6 - 2/6

∴ Wn = 1/6 tons

Fish fed during night = 1/6 tons.

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Answer:

I think it's 35x^2 +16x-24 listen I'm not sure yet I could be wrong

Answer:

There were 67 coins in the bag, 36 of which were 50-cent coins and 31 of which were 20-cent coins.

Let x be the number of 50-cent coins in the bag,

And y be the number of 20-cent coins.

From the problem,

we know that y = x - 5,

Since there were 5 fewer 20-cent coins than 50-cent coins.

We can also set up an equation for the total value of the coins in the bag,

⇒ 0.5x + 0.2y = 24.20

Now we can substitute y = x - 5 into the equation,

⇒ 0.5x + 0.2(x - 5) = 24.20

Simplifying, we get,

⇒ 0.7x - 1 = 24.20

⇒ 0.7x = 25.20

⇒ x = 36

So there were 36 50-cent coins in the bag.

Using y = x - 5,

We can find that there were 31 20-cent coins.

Therefore, there were a total of 67 coins in the bag (36 + 31 = 67).

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The sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.

It is defined as the diagram that shows a logical relation between sets.

The Venn diagram consists of circles to show the logical relation.

We have:

From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa, 30 took all the three beverages, 70 took coffee and cocoa, 110 took coffee only, and 185 took cocoon only.

We can represent the above data by the Venn diagram as shown in the picture.

From the Venn diagram:

The number of customers who took none of the beverages

= 800 - 580 = 220

The number of customers who took tea only = 95

The number of customers who took tea and cocoa only = 70

The number of customers who took tea and coffee only = 50

The number of customers who took none of the beverages = 220

Thus, in the sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa are shown in the picture by the Venn diagram.

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Answer:

IUOIUJUIYIYIYUYUYUYIYUYUY

The dimension of the original photo is 11 inches by 11 inches.

Given that, the area of the reduced photo is 64 square inches.

In the equation [tex](x -3)^{2} = 64[/tex], x represents the side measure of the original photo.

We have to determine the dimensions of the original photo.

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Now, solve the equation for the value of x.

By square rooting on both the side, we get

[tex]\sqrt{(x-3)^{2} } =\sqrt{64}[/tex]

⇒[tex](x-3)=[/tex]±[tex]8[/tex]

⇒[tex]x=8+3=11[/tex] and [tex]x=-8+3=-5[/tex]

The length and width can not be negative.

Therefore, the dimension of the original photo is 11 inches by 11 inches.

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Answer: A) 11 inches by 11 inches

Step-by-step explanation:

Edg 2022

Answer:

0.75gal.

Step-by-step explanation:

(4gal.) (2qt) - (3gal.) (3qt) =

the easiest way to solve this would be get everything in the same units,

lets make the qt to gallons

2qt = 0.5gal                          divide the volume value by 4

3qt = 0.75gal

 (4gal.) + (0.5gal.) - (3gal.) + (0.75gal.)

= (4.5gal.) - (3.75gal.)

= 0.75gal.

Notice that the left side of the third equation is 2 times the left side of the first equation:

6x - 8y + 2z = 2 (3x - 4y + z)

The first equation says

3x - 4y + z = -5

while the third equation would reduce to

2 (3x - 4y + z) = 10   ⇒   3x - 4y + z = 5

but -5 ≠ 5, so there is no solution to the system.

The functions that are one to one are the set of ordered pairs.

It should be noted that the set of ordered pairs simply means an object that the pairs are significant.

On the other hand, a mapping diagram simply consists of two parallel columns that represents the domain and the range.

In this case, the functions that are one to one are the set of ordered pairs.

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Answer:

Option 4

Step-by-step explanation:

                h = x units

   diameter = x units

                 r = (x/2) units

    [tex]\sf \boxed{\text{ \bf Volume of cone = $\dfrac{1}{3} \pi r^2h$}}[/tex]

                                   [tex]\sf =\dfrac{1}{3}*\pi * (\dfrac{x}{2})^2*x\\\\=\dfrac{1}{3}*\pi*\dfrac{x^2}{4}*x\\\\=\dfrac{1}{12}\pi x^3[/tex]

The point that is not included in the solution set for the inequality in the graph is (-1, 3).

In the information given, (h, k) is the vertex point. In the graph, the vertex point will be (1, 2). The equation will be:

y = a(x + 1)² + 2

By the point of the graph(0, 3) the value of a will be:

3 = a(0 - 1)² + 2

3 = a + 2

a = 3 - 2

a = 1

The equation this becomes:

y = 1(x - 1)² + 2.

y = x² - 2x + 1 + 2

y = x² - 2x + 3

Therefore, the point that is not included in the solution set for the inequality is (-1, 3).

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Radhika attempted 8 questions incorrectly, while Mohini attempted 13 questions incorrectly.

The given parameters are:

Correct = +3

Wrong = -2

Let the correct attempt be x and the incorrect attempt be y.

The equation that represents the total score is:

Total = 3x - 2y

She scored a total of 20.

So, we have:

3x - 2y = 20

She got 12 correctly.

So, we have:

3 * 12 - 2y = 20

Evaluate the product

36 - 2y = 20

Subtract 36 from both sides

-2y = -16

Divide by -2

y = 8

Hence, Radhika attempted 8 questions incorrectly.

In (a), we have the equation that represents the total score is:

Total = 3x - 2y

She scored a total of -5

So, we have:

3x - 2y = -5

She got 7 correctly.

So, we have:

3 * 7 - 2y = -5

Evaluate the product

21 - 2y = -5

Subtract 21 from both sides

-2y = -26

Divide by -2

y = 13

Hence, Mohini attempted 13 questions incorrectly.

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Answer:

19i

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

[tex]\sqrt{-361}[/tex]

= [tex]\sqrt{361(-1)}[/tex]

= [tex]\sqrt{361}[/tex] × [tex]\sqrt{-1}[/tex]

= 19 × i

= 19i

Answer: The equation of a linear relationship is y = mx + b, where m is the rate of change, or slope, and b is the y-intercept (The value of y when x is 0).

Step-by-step explanation:

The correct number line which represents the solution set for the inequality is shown in option 2.

A relation by which we can compare two or more mathematical expression is called an inequality.

We have to given that;

Inequality is,

⇒ 2x - 6 ≥ 6 (x - 2) + 8

Now, We cam simplify as;

⇒ 2x - 6 ≥ 6 (x - 2) + 8

⇒ 2x - 6 ≥ 6x - 12 + 8

⇒ 2x - 6x ≥ - 12 + 8 + 6

⇒ - 4x ≥ 2

⇒ 4x ≤ - 2

⇒ x ≤ - 1/2

⇒ x ≤ - 0.5

Hence, The correct number line which represents the solution set for the inequality is shown in option 2.

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Answer:

The answer is A

Step-by-step explanation: if 4 is the radius you take 4 and square it

(4 times 4= 16)

16 times pie

(in this case 3.14)

equals: 50.24

Answer:

If using a calculator, you can calculate one number as a percentage of another by dividing the numbers and multiplying by 100.

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

I got it right on the test

Answer:

B

Step-by-step explanation:

The line of the best fit is shown in the picture which is approximate near the dots.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

The slope and y-intercept can be found using the formula below:

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2} \\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

We have a given a scatter plot shows the data for NCAA quarterbacks comparing their attempted passes to completed passes.

We can draw a line of best fit y = mx + c

Thus, the line of the best fit is shown in the picture which is approximate near the dots.

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Deena is 420 miles from home in 12 hours.

The graph is shown below. The graph is linear

From the question, we are to determine how far Deena is from home in 12 hours

From the given linear equation,

y = 35x

We are to determine how far Deena is from home in 12 hours

That is,

x = 12 hours

Put x = 12 into the equation,

∴y = 35(12)
y = 420 miles

Hence, Deena is 420 miles from home in 12 hours.

The graph is shown below. The graph is linear

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Answer:

The answer should be D.

Answer:

d

Step-by-step explanation:

Answer:

A=l*w

Step-by-step explanation:

so We Derive Their Formula

L=A/w

Step-by-step explanation:

we can see that this is an absolute value function. we know that for the graph to be shifted to the left the value of the constant inside the absolute value should be positive. and the fact that it is shifted down means that there is a negative constant outside the absolute value. the equation is:

| X + 5 | - 1

Answer:

m = 50h, where m is the distance traveled in miles

Answer:

a = 4

b = 7

c = 0

4n² + 7n = 0

4/4n² + 7n/4 = 0/4

= n² + 7/4n = 0

a = 1

b = 7/4

c = 0

b = 7/4

(b/2)² = (7/4 ÷ 2)²

Use fraction rule.

7/4 ÷ 2² = 7/4² / 2²

square the numbers

7/4² / 2² = 49/16 ÷ 4

49/16 ÷ 4 = 49/16 × 1/4

49/16 × 1/4 = 49/64

Add to both sides of the equation using 49/64

b = 7/4

b/2 = 7/4 ÷ 2

simplify

b/2 = 7 ÷ (4 × 2)

simplify(arithmetic)

b/2 = 7/8

n² + 7/4n + 49/64 = 49/64

(n + 7/8)² = 49/64

[tex](n+\frac{7}{8})^2=\frac{49}{64}\\\sqrt{(n+\frac{7}{8})^2}=\sqrt{\frac{49}{64}}\\[/tex]

Next, cancel out the square on the left side.

[tex]n+\frac{7}{8}=+/-\sqrt{\frac{49}{64}}[/tex]

Subtract 7/8 from both of the sides.

[tex]n+\frac{7}{8}-\frac{7}{8}=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}[/tex]

Simplify the left side.

[tex]n=-\frac{7}{8}+/-\sqrt{\frac{49}{64}}\\n=-\frac{7}{8}+/-\frac{\sqrt{49}}{\sqrt{64}}\\n=-\frac{7}{8}+/-\frac{7}{8}\\n_1=0\\n_2=-\frac{7}{4}[/tex]

That wraps it up for this equation. Hope it helped!