a rectangle has a width-to-height ratio of 8:5. The perimeter of the rectangle is 208 inches. what is that area of the rectangle, in square inches?

Answer:

x = 11/90 = 0.122

Step-by-step explanation:

7[tex]\frac{1}{2}[/tex]x - [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{3}[/tex]

15/2x - 1/4 = 2/3

90/12x - 3/12 = 8/12

90/12x = 8/12 + 3/12

90/12x = 11/12

x = (11/12)(12/90) = 132/1080 = 11/90

The engine's speed at which the vehicle's estimated horsepower at the wheels is greatest is given as follows:

1905 rpm.

The equation of a quadratic function, of vertex (h,k), is given by the following rule:

y = a(x - h)² + k

In which:

The value of h for this problem is given as follows:

h = 1905 rpm.

As the leading coefficient is negative, for h = 1905, the output has the maximum value.

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The possible set of dimensions for the container

radius = 8 inches, height = 21 inches:

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

A) radius = 21 inches, height = 21 inches:

The inequality h > 0.3r² is satisfied (21 > 0.3 * 21^2).

The height must be no more than 15 inches greater than the radius

=21 - 21 <= 15), which is satisfied.

The area of the base must be at least 36pi square inches

= πr² ≥ 36pi, which is not satisfied ( πr² < 36π).

So, option A is not a possible set of dimensions.

B) radius = 8 inches, height = 21 inches:

The inequality  h > 0.3r² is satisfied (21 > 0.3 x  8²).

So, The height must be no more than 15 inches greater than the radius (21 - 8 ≤ 15), which is satisfied.

The area of the base must be at least 36π square inches

= π(8²) ≥ 36π

So, option B is a possible set of dimensions.

C) radius = 7 inches, height = 23 inches:

The inequality h > 0.3r^2 is satisfied (23 > 0.3 x 7^2).

The height must be no more than 15 inches greater than the radius

= (23 - 7 ≤ 15), which is satisfied.

and, Area of the base

= (π (7)² < 36pi) not satisficed.

So, option C is not a possible set of dimensions.

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The solution of the given expression will be 1.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbol; which can also be used to indicate the logical syntax's order of operations and other features.

We are given the expression as;

[tex][(2/5)^{12}(3/16)^{-8}] \times [(2/5)^{12}(3/16)^{-8}]^{-1}[/tex]

Therefore, we can write as the fraction form;

[tex][(2/5)^{12}(3/16)^{-8}] \times [(2/5)^{12}(3/16)^{-8}]^{-1}\\\\[/tex]

[tex]\dfrac{[(2/5)^{12}(3/16)^{-8}] }{ [(2/5)^{12}(3/16)^{-8}]}[/tex] = 1

Then it will cancel out so,

= 1

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Answer:

-3

Step-by-step explanation:

-3×(-3)×(-3)= 9×(-3)

= -27

For the triangle ABC the interior angles measures ∠A = 48°, ∠B = 82°, and ∠C = 50°.

What are triangles?

Triangles are a particular sort of polygon in geometry that have three sides and three vertices. Three straight sides make up the two-dimensional figure shown here. An example of a 3-sided polygon is a triangle. The total of a triangle's three angles equals 180 degrees. One plane completely encloses the triangle.

According to the angles of a triangle theorem, the sum of angles of a triangle is 180°.

The measure of ∠A = 4x.

The measure of ∠B = 7x - 2.

The measure of ∠C = 5x - 10.

The equation is -

∠A + ∠B + ∠C = 180°

Substitute the values into the equation -

4x + 7x - 2 + 5x - 10 = 180

Collect the like terms -

4x + 7x + 5x = 180 + 2 + 10

16x = 192

x = 192/16

x = 12°

So, the measure of ∠A = 4(12) = 48°.

The measure of ∠B = 7(12) - 2 = 82°

The measure of ∠B = 5(12) - 10 = 50°

The interior angles of the triangle are 48°, 82° and 50°.

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Answer:

B

Step-by-step explanation:

We always look original price for 1 or 100%, now increase 1/2, that is 50%

So now it is 100%+50%=150%

Equating both equations, Nayati and Tatiana will have the same amount of savings after 21 weeks.

Equations are mathematical statements that show that there is equality between two or more mathematical expressions.

Equations are depicted using the equation symbol (=).

                       Nayati   Tatiana

Savings            $240     $450

Weekly savings $40       $30

Nayati total savings = 40w + 240

Tatiana total savings = 30w + 450

To determine the number of weeks when their savings will be equal, the two equations will be equated as follows:

40w + 240 = 30w - 450

10w = 210

w = 21

= 21 weeks

Thus, we expect Nayati and Tatiana to embark on their road trip after 21 weeks.

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The  slope and the y-intercept of the line are -1 and 5 respectively

It is important to note the general formula for the equation of a line is expressed with the formula;

y = mx+ c

Where the noted parameters of the equation are;

From the information given, we have the equation of the line as;

y = -x + 5

Now, we can have the parameters as;

Intercept, c = 5

Slope of the line, m = -1

Hence, the values are 5 and -1

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Answer:

MN = 15.5 units

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

The triangles are similar since all three angles are equal on both.

We know corresponding sides of similar triangles are proportional.

Set up proportions and find the missing side length:

In the given choices, both (D) n = 300 and (E) n = 312 satisfies the inequality. So for both these options, the inequality is true.

We can solve for n by adding 93 to both sides of the inequality:

n - 93 > 175

Adding 93 on both sides

n - 93 + 93 > 175 + 93

n > 268

Therefore, the value of n that makes the inequality true is greater than 268.In the given options, n = 300 and n = 312 satisfy this condition. So this is inequality is true for both cases. The answer choice that fits this is (D) n = 300 and (E) n =312.

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The equivalent of the rate is $2750 per month

From the question, we have the following parameters that can be used in our computation:

The equivalent rate of $33,000/1year

There are 12 months in a year

So, we have the following representation

Rate =  $33,000/12 months

Evaluate the quotient

Rate =  $2750 per month

Hence, the equivalent rate is $2750 per month

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There are 56 possible ways to make a selection of coins so that the value is at least 25 cents.

The total number of possible ways to make a selection of coins so that the value is at least 25 cents is calculated using the formula:

# of ways = (n+r-1Cr-1)

Where n is the number of coin denominations available and r is the number of coins needed to make the selection.

In this case, n = 5 (1 cent, 5 cents, 10 cents, 25 cents, 50 cents) and r = 4. Therefore, the number of ways to make a selection of coins so that the value is at least 25 cents is calculated as:

of ways = (5+4-1C4-1)

of ways = (8C3)

of ways = 56

Therefore, there are 56 possible ways to make a selection of coins so that the value is at least 25 cents.

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Answer:

what we should do when we leave for every 25minutes

The image showing the locus points equidistant from X, Y, and Z is B. See the attached image.

If the distances between a point and each object in the set are equal, the point is said to be equidistant from the set.

When a point is equidistant from two other points, it is at the same distance from both of them. The distance between two points may be computed using the distance formula and the coordinates of the two points.

In geometry, a locus is a set of points that satisfy a specific condition or circumstance for a form or figure. The locus is pluralized as loci. The region is the location of the locus. The term locus comes from the word location.

Thus, the point that is equidistant from X, Y, and Z is B.

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Answer:

599 and 550

Step-by-step explanation:

I'm not sure but I think it's 599 and 550

The proof for UX || VW is shown below.

According to the midpoint theorem, "The line segment in a triangle joining the midpoint of any two of the triangle's sides is said to be parallel to its third side and is also half the length of the third side."

Given:

As, TUX and TVW are similar.

So, the ratio of their corresponding sides are equal.

So, TU/ TV = UX/ VW = TX / TW = 1/2  {TU/ TV = 1/2}

By using mid point Theorem

UX = 1/2 VW

Then, UX || VW.

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Answer:

V = πr^2h = πr^2(2r) = 2πr^3

Volume of the cone: The volume of a cone with height h and base radius r is given by the formula V = (1/3)πr^2h. In this case, the height of the cone is equal to the radius of the hemisphere, so h = r. Substituting this into the formula, we have:

V = (1/3)πr^2h = (1/3)πr^2r = (1/3)πr^3

Volume of the hemisphere: To estimate the volume of the hemisphere, we'll average the volumes of the cylinder and cone.

So:V = (2πr^3 + (1/3)πr^3) / 2 = (5/3)πr^3 / 2 = (5/6)πr^3

So the volume of the hemisphere is approximately equal to (5/6)πr^3, where r is the radius of the hemisphere (and equal to the radius of the cylinder).

Step-by-step explanation:

Answer: Perimeter because A=L X W and P= L+W+L+W

Step-by-step explanation:

Answer:-12x

Step-by-step explanation:

just trust me on this

The perimeter of scale drawing of rectangular classroom floor is 42 inches.

Based on the mentioned information, let us first calculate the width of floor of classroom according to the scale drawing.

Length/width of original classroom floor = length/width of scale drawing

30/33 = 10/width

As we know, 1 foot = 12 inches

So, length = 360 inches and width = 396 inches

Width = (396 × 10)/360

Cancelling zero as it is common in both numerator and denominator

Width = 396/36

Performing division on Right Hand Side of the equation

Width = 11 inches

Perimeter of scale drawing = 2 (length + width)

Perimeter = 2( 10 + 11)

Performing addition

Perimeter = 2 × 21

Performing multiplication

Perimeter = 42 inches

Thus, perimeter of the rectangle is 42 inches.

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The value 0.00073 feet per millisecond. in scientific notation is 7. 3 × 10⁴ feet per millisecond

Index forms are described as mathematical methods of writing or representing numbers that are too large or two small in more convenient forms.

They are written in the forms of exponents of numbers or variables,

There are other names for index forms which are scientific notation and standard forms.

From the information given, we have that;

The seahorse moves 0.5 miles per hour, or 0.00073 feet per millisecond

In converting 0.00073 feet per millisecond into index forms

count the number of zeros to the first significant number

7. 3 × 10⁴ feet per millisecond

Hence, the value is 7. 3 × 10⁴ feet per millisecond

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Answer:

40 days

Step-by-step explanation:

We know

A certain insect eats 1/8 gram of food each day.

How many days would the insect take 5 grams of the food?

We take

5 divided by 1/8 = 40 days

So, it would take the insect 40 days to eat 5 grams of the food.

Answer:40 days

Step-by-step explanation: first, how many days would it take for the insect to eat 1 gram of food? it would take 8 days so if it wants to eat 5 grams of food 8x5=40 so it would take 40 days for the insect to eat the food

The probability that Nomusa will not take two of the same type of sweet is 0.35

To find the probability that Nomusa will not take two of the same type of sweets, we need to find the total number of combinations of two sweets she can take, and then find the number of combinations where the two sweets are different.

First, let's find the total number of combinations of two sweets:

C(30, 2) = 435

This means there are 435 different combinations of two sweets she can take from her collection of 30 sweets.

Next, let's find the number of combinations where the two sweets are not the same:

C(18, 2) + C(7, 2) + C(5, 2) = 153

This means that there are 153 combinations where the two sweets are different fruit sweets, different aniseed sweets, or different mint sweets.

So, the probability that Nomusa will not take two of the same type of sweet is:

153 / 435 = 0.35

This means that there is a 35% chance that the two sweets she takes will not be the same type of sweet.

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The table in the question which the values from the graph of the parabola is inputed is presented as follows;

Name [tex]{}[/tex]                     Key Feature             Name           Key Feature
x-intercepts[tex]{}[/tex]             (-1, 0), (3, 0)                Increasing      (-∞, 1)      

y-intercept[tex]{}[/tex]               (0, 3)                          Decreasing     (4, ∞)

Vertex[tex]{}[/tex]                      (1, 4)                            Positive           (-1, 3)

Axis of symmetry[tex]{}[/tex]     x = 1                           Negative        (-∞, 1), (3, ∞)

Domain[tex]{}[/tex]                    (-∞, ∞)                         Range            (-∞, 4]

The graph of a parabola is a u (or n) shaped curve obtained by the intersection of a cone and a plane which is parallel to the slant of the cone.

The x-intercepts are the point the graph intersects the x-axis, where the y-value is zero, y = 0. From the graph, the x-intercepts are;(-1, 0), and (3, 0)

The y-intercept is the point at which the graph intersects the y-axis, which is the point the x-value is 0, (x = 0). The graph indicates that the y-intercept is (0, 3)

The vertex of the parabolic graph is the highest (or lowest) point on the graph, therefore, from the graph in the question, the vertex point is; (1, 4)

The axis of symmetry is the line that divides the graph into two mirror halves, which is the line passing through the vertex and parallel to the y-axis. The axis of symmetry is therefore the line; x = 1

The domain is the set of the possible input values of the graph of the function, which is the set of the possinble x-values.

The graph indicates that the x-values can decrease and increase to -∞ and ∞. The domain is therefore; (-∞, ∞).

The region where the graph is increasing is fro x = -∞ to just before x = 1. The interval where the graph is increasing is therefore; (-∞, 1)

Similarly, the interval the graph is decreasing is; (4, ∞)

The graph is positive in the region above the x-axis. The interval over which the graph is positive is therefore between the x-intercepts, which is; (-1, 3)

The graph is negative in the region below the x-axis. The interval in which the graph is negative are; (-∞, 1), and (3, ∞)

The range is the set of possible output of the graph, therefore, the range is the set of the possible y-values, which is; (-∞, 4]

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The solution to the system of linear equations using the Equal Value Method is Y = -(8y / 6) - 21.

The Equal Value Method is a technique used to solve a system of linear equations. To solve a system of linear equations using the Equal Value Method, we first write out the two equations. In this case, we have the two equations:

Y = -8x - 21

y = 6x + 7

Next, we need to solve one of the equations for one of the variables. We can solve for x in the first equation, giving us x = (-21 - Y) / -8. We can then substitute this into the second equation, giving us y = (6(-21 - Y) / -8) + 7. We can then expand and simplify this equation, giving us y = (126 + 6Y) / -8.

Finally, we can set the two equations equal to each other and solve for Y. This will give us 126 + 6Y = -8y, which simplifies to 6Y = -8y - 126. We can then divide both sides by 6 to get Y = -(8y / 6) - 21.

Therefore, the solution to the system of linear equations using the Equal Value Method is Y = -(8y / 6) - 21.

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The ordered pair that can be plotted together with these four points is (0, 3). Option C is the correct answer.

A relationship between inputs and outputs in which each input is connected to only one output is called a function.

For instance, f(x) = 2x + 1; f(1) = 2 + 1; f(2) = 2 x 2 + 1; 4 + 1; and so on.

The functions' 3 and 5 outputs are

The function's arguments are 1 and 2.

We've got

The graph's coordinates are as follows.

(3, -1), (2, 3), ), (-4, 2), and (-2, -3) (-2, -3)

Having said that,

Many-to-one but not one-to-many can exist in a function.

We therefore cannot have (-2, 0), (-2, 3). because we already had (-2, 3) and (3, 0). (3, -1).

This indicates an impossibility of a one-to-many function.

It is feasible (0, 3).

As a result, the ordered pair that can be plotted together with these four points is (0, 3). Option C is the correct answer.

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Answer:

5.2

Step-by-step explanation:

9×3 and the root of that is 5.1961524