On a scale drawing the scale is 1/2 inch=1 foot what are the dimensions on the scale drawing for a room that is 22 feet by 17 feet

Question:

How fast should the ant walk to go around the rectangle in 4 minutes if the sides are 12 inches and 16 inches

Answer:

The ant should walk 14 inches per minute

Solution:

Given that,

Dimensions of rectangle are 12 inches and 16 inches

Find the perimeter of rectangle

Perimeter = 2(length + width)

Perimeter = 2(12 + 16)

Perimeter = 2(28) = 56

Thus perimeter of rectangle is 56 inches

Time taken = 4 minutes

We have to find the speed at which ant covers 56 inches in 4 minutes

The speed is given by formula:

[tex]speed = \frac{distance}{time}[/tex]

[tex]speed = \frac{56}{4} = 14[/tex]

Thus the ant should walk 14 inches per minute

Answer:

The dimensions of the wall are 100 ft x 100 ft

Step-by-step explanation:

we know that

The perimeter of a rectangular wall is

[tex]P=2(x+y)[/tex]

where

x is the length

y is the width

we have

[tex]P=400\ ft[/tex]

so

[tex]400=2(x+y)[/tex]

simplify

[tex]200=x+y[/tex]

[tex]y=200-x[/tex] ----> equation A

The area of a rectangular wall is equal to

[tex]A=xy[/tex] ----> equation B

substitute equation A in equation B

[tex]A=x(200-x)\\A=-x^2+200x[/tex]

This is the equation of a vertical parabola open downward (because the leading coefficient is negative)

The vertex represent a maximum

Convert the quadratic equation in vertex form

[tex]A=-x^2+200x[/tex]

Factor -1

[tex]A=-(x^2-200x)[/tex]

Complete the square

[tex]A=-(x^2-200x+100^2)+100^2[/tex]

[tex]A=-(x^2-200x+10,000)+10,000[/tex]

Rewrite as perfect squares

[tex]A=-(x-100)^2+10,000[/tex] ----> equation in vertex form

The vertex is the point (100,10,000)

The x-coordinate of the vertex represent the length of the wall for a maximum area

so

[tex]x=100\ ft[/tex]

Find the value of y

equation A

[tex]y=200-(100)=100\ ft[/tex]

therefore

The dimensions of the wall are 100 ft x 100 ft

To find the dimensions of a rectangular wall that maximizes the area enclosed by 400 feet of brick, you can use the formula for the area of a rectangle and find where the derivative of the area equation equals zero. By solving the resulting equations, you can determine the dimensions of the wall that will maximize the enclosed area.

To find the dimensions of a rectangular wall that maximizes the enclosed area with 400 feet of brick, we need to use the formula for the area of a rectangle, which is length times width. So, let's represent the width of the wall as x and the length as y. Since we have 400 feet of brick, we can write the equation 2x + 2y = 400. We can rearrange this equation to solve for y: y = (400 - 2x)/2. Now we have the area equation A = x * y,

which becomes A = x * ((400 - 2x)/2). To find the maximum area, we can take the derivative of A with respect to x and set it equal to zero: (400 - 4x)/2 = 0. Solving for x, we get x = 100. Substituting this back into the y equation, we find y = 100 as well. Therefore, the dimensions of the rectangular wall that maximize the area enclosed by the brick are 100 feet by 100 feet.

Answer:

[tex]x = 6[/tex] and [tex]y = 236[/tex]

Step-by-step explanation:

[tex]y = 296 - 10x[/tex]

[tex]y = 200 + 6x[/tex]

By equating both equations, we get:

[tex]296 - 10x = 200+6x[/tex]

[tex]16x = 96[/tex]  [Separate variables and constants]

[tex]x = 6[/tex]

By substituting [tex]x = 6[/tex] to the above equation, we get:

[tex]y = 296 - 10(6)[/tex]

[tex]y = 296 - 60[/tex]

[tex]y = 236[/tex]

Hence, [tex]x = 6[/tex] and [tex]y = 236[/tex]

Answer:1

Step-by-step explanation:just divide numerator by denominator

Answer:

x=-y/2

Step-by-step explanation:

1. The value of a variable that makes an equation true.

2. In chemistry, a solution is a homogeneous mixture composed of only one phase

Answer:

1   7/20   mixed= 27/20

Step-by-step explanation:

Answer:

Step-by-step explanation:

i think its b or c

The confidence interval of the mean weight of all the coins is 8.0518g. The correct option is B.

A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specified confidence level; the 95% confidence level is most commonly used, but other levels, such as 90% or 99%, are occasionally used.

Given that a sample of 20 silver dollar coins is weighed. The mean of the sample is 8.0710 g and the standard deviation of the sample is 0.0411 g.

The confidence interval is calculated by the formula:-

CI = X ± z (S / √n)

CI = 8.0710 ± [ (1.96 x 0.0411) / √20 ]

CI = 8.0710 - 0.018

CI = 8.053 g

To know more about confidence intervals follow

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Answer:

60 hours

Step-by-step explanation:

you multiply 5×12 and then you get 60

Answer:

it's B

Step-by-step explanation:

a triangle cannot two obtuse angles

A traingle does not contain two obtuse angles. Option B is correct.

The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°.

Here,
A triangle cannot contain two obtuse angles.

A triangle cannot have the two obtuse angle, becaue for a triangle sum of the iternal angle must not exceeds 180°

Thus, A traingle does not contain two obtuse angles. Option B is correct.

Learn more about triangles here:

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Answer:5/12

Step-by-step explanation:

If you cut 10 ( the numerator) in half you get 5 and if you cut 24(the denominator) in half you get 12

Answer:

Step-by-step explanation:

Measure of the smaller angle is 75°

Step-by-step explanation:

Let angles be 5x and 7x.

⇒ 5x + 7x = 180

⇒ 12x = 180

⇒ x = 15

⇒5x = 5 [tex]\times[/tex] 15 = 75°

To find the measure of the smaller supplementary angle, when the ratio of the two angles is 5:7, you need to set up an equation with 5x and 7x as the angle measures. Solve this equation to find the value of 'x', and then use 'x' to calculate the measure of the smaller angle, which amounts to 75 degrees.

In this mathematics problem, we know that two angles are supplementary if their measures add up to 180 degrees. If the ratio of the two supplementary angles is 5:7, we can set up an equation to solve for the unknowns.

Let 5x represent the measure of the smaller angle and 7x represent the measure of the larger angle. We know that the sum of these two angles should be 180 degrees, thus:

5x + 7x = 180

Combining like terms, we get:

12x = 180

Now, we can solve for 'x' by dividing both sides of the equation by 12:

x = 180 / 12, which equals 15

Now that we know the value of 'x', we can plug it back in to find the measures of the two angles. The smaller angle, which is 5x, is then:

5x = 5 * 15, which equals 75 degrees

So the measure of the smaller angle is 75 degrees.

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8.2is the answer

Step-by-step explanation:

|CB|+8

Answer:

4

Step-by-step explanation:

√10  is a irrational number

Final answer:

The square root of 10 is an irrational number because it is a non-terminating, non-repeating decimal that cannot be expressed as a simple fraction. It lies between the integers 3 and 4 on the number line.

Explanation:

The square root of 10 is an example of an irrational number. Unlike integers and whole numbers, which are exact and do not have an ending decimal or fraction, and unlike rational numbers which can be written as a ratio of two integers (like 1/2 or 3/4), an irrational number cannot be expressed as a simple fraction.

The square root of 10 cannot be precisely written as a fraction because it is a non-terminating, non-repeating decimal. In other words, if we were to write out the decimal form of the square root of 10, it would have an infinite number of digits after the decimal point without any repeating pattern.

For a real-world example, consider that knowing whether a number is rational or irrational can influence how we represent that number in various contexts, such as in engineering or architecture, where precision is paramount.

Step-by-step explanation:

[tex]5 \times 5= 25[/tex]

Answer:

B

Step-by-step explanation:

Because, according to the graph, they are making the most sells.

Final answer:

To solve the quadratic equation 2x² + 9x - 5 = 0, the quadratic formula is used, and after calculating the discriminant and applying the formula, one of the roots is found to be 1/2, which is option C.

Explanation:

To solve the quadratic equation 2x2 + 9x - 5 = 0, we can use the quadratic formula which is x = (-b ± √(b2 - 4ac)) / (2a). In this equation, a equals 2, b equals 9, and c equals -5.

Firstly, we need to calculate the discriminant: b2 - 4ac which is 92 - 4 * 2 * (-5) = 81 + 40 = 121.

Since the discriminant is a perfect square, we can proceed with the formula: x = (-9 ± √(121)) / (2*2). The square root of 121 is 11, so we have:

Thus, one of the roots of the equation is 1/2, which corresponds to option C.

Answer:

$14

Step-by-step explanation:

if Gerald's coins have the same value as his brothers, then that means they have exactly the same amount

Answer:

Position 12.

Step-by-step explanation:

It will be n the center of the bottom 23 numbers ( when the data is arranged in ascending order).

That is in position 12.

Hello there n ÷ 5 - 9  = 2!

Here's how i solved it:

The quotient of a number and -5, decreased by 9, is 2

"is 2" means the result is 2, so we can have one side of the equation set up to look like this: = 2.

The quotient of a number and -5, decreased by 9, is 2

This looks like: n ÷ 5

The quotient of a number and -5, decreased by 9, is 2

We are taking 9 away from the previous expression, so n ÷ 5 - 9

Putting it all together, we have: n ÷ 5 - 9  = 2

The algebraic mathematical problem is to solve the equation x/-5 - 9 = 2. Simplifying this equation through a series of algebraic steps gives the result x=-55.

The subject of your question is algebra, a branch of mathematics. You are looking for a number which, when divided by -5 and then decreased by 9, equals 2. The equation that represents this problem is x/-5 - 9 = 2.

To solve for x, we would first get rid of the -9 from the left side of the equation. We do this by adding 9 to both sides of the equation. We then have x/-5 = 2 + 9, which simplifies to x/-5 = 11.

Next, we isolate x by multiplying both sides of the equation by -5. We now get x= -5*11, which gives x = -55. Thus, the number x that satisfies this equation is -55.

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Answer:

d

step-by-step explanation:

The ratio of boys to girls (3:4) and girls to adults (5:7) leads to a combined ratio of children to adults at the holiday camp of 5:4 after aligning the ratios on the common term for girls and simplifying.

To determine the ratio of children to adults at the holiday camp, we can use the given ratios:

First, express both ratios with a common term for girls to combine them accurately:

Since the ratio of girls to adults is 5:7, we can align this with the boys to girls ratio by multiplying the boys to girls ratio by 5 (the common term for girls). This gives us:

So, we have 15 boys and 20 girls for every 28 adults. The total number of children (boys and girls) is 15 + 20 = 35.

Therefore, the ratio of children to adults at the camp is 35:28, which simplifies to 5:4 after dividing both terms by 7.

Answer:L F and K G

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The answer is not A because:

lines gk and kg are the same line

The answer is not B because:

lines il and gk are perpendicular if they were to touch

The answer is not C because:

line fl and il are perpendicular

The answer IS D because:

lines fl and gk are parallel because they will never touch

Answer:

B. 52 beats/min

Step-by-step explanation:

while resting her heart beats : 36×2 = 72 beats/min

while running her heart beats : 1 860÷15 = 124 beats/min

difference = 124-72 = 52 beats/min

:)

Answer:

B. 52 beats/min

Step-by-step explanation:

To find the answer you have to find the bpm of each time that Chandra recorded her heart rate. So when she recorded her heart rate when running, you simply divide 1850 by 15, and you should get 123.333 (repeating) I am assuming by the answers that we are rounding, so we are going to round that answer up. Next to find her heart rate while resting, you take her heart rate in 30 seconds, which is 36, and multiply it by 2, because it was her heart rate in half of the time that we are measuring it in. So when you multiply 36 by 2 you should get 72. The next step is to subtract 124 from 72. You answer is 52.

Step-by-step explanation:

Jose need at least 94 more points in order to get an A on this semester

133 is the Answer bc that is a supplementary angle and supplementary angles always sum up to 180 hope this helps please mark brainliest

Step-by-step explanation:

Answer:

An example of a situation that you might not be able to use an equation with a single unknown is

[tex]x = \ln{e^x}[/tex]

Step-by-step explanation:

An example of a situation that you might not be able to use an equation with a single unknown is

[tex]x = \ln{e^x}[/tex]

The identity on both sides which results in 1 = 1 and thus the equation is not usable.

A situation where an equation with a single unknown cannot be effectively used is when you need to explore or solve multiple variables or dimensions, like best represented by physics-related problems. The number of unknowns should not exceed the number of equations for correct problem-solving. Equations with a single unknown may not always suffice, especially for problems involving various dimensions or variables.

An example of a situation where you may not be able to use an equation with a single unknown to understand is a problem that involves multiple elements or dimensions needing exploration. For instance, in physics, if you're calculating an object's motion, you may need to take into account various forces acting on it, its initial velocity, its acceleration, and the time. No single equation with just one unknown can solve this problem; you would need multiple equations to represent each of these dimensions.

Remember that the number of unknowns should not be larger than the number of equations. Otherwise, the problem can't be solved. Therefore, the complexity of your problem can sometimes make it impossible to use an equation with a single unknown. Physics is often an area where this is true, due largely to the dimensional consistency of equations.

Nevertheless, equations with a single unknown can often be combined together or manipulated to solve specific problem-solving strategies. Overall, while an equation with a single unknown is a powerful tool, it may not always be sufficient to understand every situation, especially those involving multiple dimensions or variables.

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Answer:

x>7

Step-by-step explanation:

2x+6>20

2x>20-6

2x>14

x>14/2

x>7

The given question have mistake.

Question:

Which expression is not a polynomial?

(1) x – 1

(2) 4 + p

(3) [tex]5x^2-\sqrt x[/tex]

(4) [tex]8x-z^3[/tex]

Answer:

[tex]5x^2-\sqrt x[/tex] : Not a polynomial

Solution:

Definition of polynomial:

A polynomial can have constants, variables and exponents.

Constants = 2, 5

Variables = x, y, z

Exponents = [tex]x^2[/tex]

Not a polynomial:

Roots, fractions in power, negative powers and dividing by a variable are not polynomials.

Given expressions:

(1) x – 1 : Polynomial

(2) 4 + p : Polynomial

(3) [tex]5x^2-\sqrt x[/tex] : Not a polynomial

(4) [tex]8x-z^3[/tex] : Polynomial

Hence in the given expressions [tex]5x^2-\sqrt x[/tex] is not a polynomial.