Caitlin creates an architectural blueprint of a rectangular dining room. The area of the actual dining room is 900 times as large as the area of the dining room on the blueprint. The length of the dining room on the blueprint is 4 inches. What is the length of the actual dining room?

The Weight on Venus is 3.64 pounds

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

They need to find out how much a rock that weights 4 pounds on earth would weight on Venus.

So, the Weight on Venus

= 4 x 0.91

= 4x 0.9+ 4 x 0.01

= 3.6+ 0.04

= 3.64

Hence, the Weight on Venus is 3.64 pounds

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There is 4 roll of coins of nickel and 3 rolls of coins of dimes.

Given that,

Joanna has a total of 7 rolls of coins worth $23.

She has rolls of dimes worth $5 each and rolls of nickel worth $2.

We have to determine,

How many rolls of each kind does she have?

According to the question,

Let the number of coins of dimes be x

And the number of coins of nickel be y.

Then,

The number of coins of dimes + Number of coins of nickel = Total number of coins.

[tex]\rm x+ y =7[/tex]

And the total price of the coins is equal to the price of each coin of dimes and nickel.

[tex]\rm 5x+2y=23[/tex]

Solving both the equation,

From equation 1,

[tex]\rm x+ y = 7\\\\x = 7-y[/tex]

Substitute the value of x in equation 2,

[tex]\rm 5x+2y = 23\\\\5(7-y) +2y = 23\\\\35-5y+2y=23\\\\-3y = 23-35\\\\-3y = -12\\\\y = \dfrac{-12}{-3}\\\\y = 4[/tex]

Substitute the value of y in equation 1,

[tex]\rm x+y = 7\\\\x+4 = 7\\\\x = 7-4\\\\x =3[/tex]

Hence, there is 4 roll of coins of nickel and 3 rolls of coins of dimes.

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It would take the computers 12 minutes and 36 minutes respectively to individually update the software

An equation is an expression that shows the relationship between two or more numbers and variables.

Let t represent the time it takes the fastest computer. Hence:

[tex](\frac{1}{t}+\frac{1}{t+24})9=1\\ \\ t=12 \ minutes[/tex]

It would take the computers 12 minutes and 36 minutes (12 + 24) respectively to individually update the software

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Answer:31.88

Step-by-step explanation:

answer and explanation:

g(x)=(x^2+4x-12)(x-3)

(x+6)(x-2)(x-3)

x+6=0

-6 -6

x= -6

~~~~~~~~~~~~~~~~~~~

x-2=0

+2 +2

x=2

~~~~~~~~~~~~~~~~~~~

x-3=0

+3 +3

x=3

~~~~~~~~~~

answer: -6, 2, 3.

a. The height of the ball when it leaves the child's hand is 3 feet, as [tex]\(x = 0.[/tex]

b. The maximum height of the ball is 195 feet, calculated by finding the vertex of the parabolic function.

c. The distance from the child where the ball strikes the ground is approximately 47.24 feet, using the quadratic formula.

Given the equation representing the height y of a ball as a function of the horizontal distance x :

[tex]\[y = \frac{1}{16} x^2 + 4x + 3\][/tex]

Part (a): Height of the ball when it leaves the child's hand

The ball leaves the child's hand when x = 0.

Substituting x = 0 into the equation:

[tex]\[y = \frac{1}{16} \cdot 0^2 + 4 \cdot 0 + 3 = 3\][/tex]  

Thus, the height of the ball when it leaves the child's hand is 3 feet.

Part (b): Maximum height of the ball

The given function represents a parabola, and since [tex]\(a = \frac{1}{16}[/tex] is positive, it opens upward.

To find the maximum height, we need the x-coordinate of the vertex, which can be found using:

[tex]\[x = -\frac{b}{2a} = -\frac{4}{2 \cdot \frac{1}{16}} = -\frac{4}{\frac{1}{8}} = -32\][/tex]

However, the correct derivation is:

[tex]\[x = -\frac{4}{2 \cdot \frac{1}{16}} = -\frac{4}{\frac{1}{8}} = -32 \cdot 8 = -64\][/tex]

But the correct value for x should be:

[tex]\[x = -\frac{4}{2 \times \frac{1}{16}} = -4 \times 8 = -32[/tex]

Considering this, let's correct the previous explanation and use the correct approach:

1. Find the x-coordinate of the vertex:

[tex]\[x = -\frac{4}{2 \times \frac{1}{16}} = -8 = 32\][/tex]

With the x-coordinate of the vertex, find the maximum height (the y-coordinate of the vertex):

[tex]\[y = \frac{1}{16} \cdot 32^2 + 4 \cdot 32 + 3 = \frac{1024}{16} + 128 + 3 = 64 + 128 + 3 = 195\][/tex]

Thus, the maximum height is 195 feet

Part (c): How far from the child does the ball strike the ground?

To find out when the ball strikes the ground, we need to set \(y = 0\) and solve for \(x\):

[tex]\[0 = \frac{1}{16} x^2 + 4x + 3\][/tex]

Using the quadratic formula, where[tex]\(a = \frac{1}{16}\), \(b = 4\), and \(c = 3\):[/tex]

[tex]\[x = \frac{-4 \pm \sqrt{4^2 - 4 \cdot \frac{1}{16} \cdot 3}}{2 \cdot \frac{1}{16}} = \frac{-4 \pm \sqrt{16 - \frac{12}{16}}}{\frac{1}{8}} \][/tex]

To find the x-coordinates where the ball strikes the ground, you can set (y = 0) and solve for (x):

[tex]\[0 = \frac{1}{16} x^2 + 4x + 3\][/tex]

Using the quadratic formula, where [tex]\(a = \frac{1}{16}\), \(b = 4\), and \(c = 3\) :[/tex]

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

Substitute the given values of a ,b , and c into the quadratic formula:

Calculate [tex]\(b^2 - 4ac\) :[/tex]

  - [tex]\(b^2 = 4^2 = 16\),[/tex]

  - [tex]\(4 \cdot \frac{1}{16} \cdot 3 = \frac{12}{16} = \frac{3}{4}\),[/tex]

  - So [tex]\(b^2 - 4ac = 16 - \frac{3}{4} = \frac{64}{4} - \frac{3}{4} = \frac{61}{4}\).[/tex]

Calculate the roots :

  - The value for [tex]\(a\) is \(\frac{1}{16}\), so \(2a = \frac{1}{8}\),[/tex]

  - Now we can find \(x\):

   [tex]\[ x = \frac{-4 \pm \sqrt{16 - \frac{3}{4}}}{\frac{1}{8}} = \frac{-4 \pm \sqrt{61/4}}{1/8} = -32 \pm 2 \sqrt{61}. \][/tex]

Simplifying the roots :

  - The roots for x are:

   [tex]\[ x_1 = -32 + 2 \sqrt{61}, \, x_2 = -32 - 2 \sqrt{61}. \][/tex]

However, we consider only the positive root, as it represents the distance from the point where the ball is thrown to where it lands.

Thus, the value of [tex]\(x_1\)[/tex] is:

[tex]\[x = -32 + 2 \sqrt{61} \approx -32 + 15.6 = -16 + 16 \cdot \sqrt{61} \approx 47.24\][/tex]

Thus, the correct answer with [tex]\(x\approx 47.24\).[/tex]

The complete question is : The height y (in feet) of a ball thrown by a child is

[tex]y = (1)/(16) {x}^{(2)}+ 4x + 3[/tex]

where x is the horizontal distance in feet from the point at which the ball is thrown

a).how high is the ball when it leaves the child's hand ?

b).what is the maximum high of the ball ?

c).how far from the child does the ball strike the ground ?

The answer provides step-by-step explanations for finding the initial height, maximum height, and horizontal distance at which the ball strikes the ground, given the equation of the ball's height as a function of the horizontal distance.

To find the height of the ball when it leaves the child's hand (a), we need to determine the value of y when x is 0. Substituting x = 0 into the equation, we get:

y = -1/14(0)² + 2(0) + 3

y = 3 feet

Therefore, the ball is 3 feet high when it leaves the child's hand.

let's find the maximum height of the ball (b), we need to find the vertex of the quadratic equation. The vertex can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation. In this case, a = -1/14, b = 2, and c = 3. Substituting these values into the formula, we get:

x = -2 / (2 * (-1/14))

x = 7 feet

Substituting x = 7 into the equation, we can find the maximum height:

y = -1/14(7)² + 2(7) + 3

y = 10.5 feet

Therefore, the maximum height of the ball is 10.5 feet.

let's find how far from the child the ball strikes the ground (c), we need to find the x-coordinate when y = 0. Setting y = 0 in the equation, we get:

0 = -1/14x² + 2x + 3

Solving this quadratic equation,

hence we find two possible values for x: x = -7 and x = 28. Since the ball is thrown in a positive direction, the ball strikes the ground 28 feet away from the child.

57+95=152

180-152=28

56+95+28=180

Third angle  =28

Answer: –18 feet

Step-by-step explanation:

Given: Garrett begins 18 feet above water level to inspect the lighting, descends 32 feet to inspect the base of the bridge underwater, then descends another 4 feet to check on the concrete anchoring the base.

Then using integers, the expression which represents Garrett’s position with respect to the water level is given by :-

[tex]+18-32-4=-18[/tex]

Hence, Garrett’s position with respect to the water level =-18 feet.

The whole bottle of olive oil contains 7920 calories.

To find the total number of calories in the entire bottle of olive oil, one must multiply the number of calories in one serving by the total number of servings in the bottle.  

Given that one tablespoon serving of olive oil contains 120 calories, and the bottle contains 66 servings, the calculation is as follows:

 Total calories in the bottle = Calories per serving [tex]\times[/tex] Number of servings

Total calories in the bottle = 120 calories/serving [tex]\times[/tex] 66 servings

Total calories in the bottle = 7920 calories

Therefore, the whole bottle of olive oil contains 7920 calories.

Final answer:

A multiple of 1/10 is any fraction obtained by multiplying 1/10 by an integer. For example, 1/10 multiplied by 2 is 2/10, which simplifies to 1/5. Dividing by powers of 10 shifts the decimal point left, making 1.9436 divided by 1,000 equal to 0.0019436.

Explanation:

In mathematics, when identifying a multiple of a fraction, you look for fractions that can be created by multiplying the original fraction by an integer. In the case of 1/10, a multiple would be any fraction where 1/10 is multiplied by a whole number.

For instance:

Multiplying 1.9436 by powers of 10 shifts the decimal point accordingly:

Conversely, dividing by powers of 10 will shift the decimal point to the left, making the number smaller:

The fraction 15 can be simplified by dividing both the numerator and the denominator by the greatest common factor, in this case, 15, yielding a value of 1.