Problem whenejewwssss

The width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

What is Area of rectangle ?
Area of rectangle can be defined as product of length and breadth.

We know that the area of the rectangle is given by the function A(x) = x² + 8x, where x is the width of the rectangle. We also know that the area of the rectangle is 33 in². So we can set up the equation:

x² + 8x = 33

To solve for x, we can rearrange the equation and set it equal to zero:

x² + 8x - 33 = 0

We can now use the quadratic formula to solve for x:

\(x = (-b\±\sqrt{(b^2 - 4ac)}) / 2a\)

where a = 1, b = 8, and c = -33. Substituting these values, we get:

\(x = (-8\±\sqrt{(8^2 - 4(1)(-33))}) / 2(1)\)

\(x = (-8\± \sqrt{(256)}) / 2\)

x = (-8 ± 16) / 2

So x = -12/2 or x = 4.

Therefore, the width of the rectangle cannot be negative, we discard the negative solution and conclude that the width of the rectangle is 4 inches.

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The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).

Given dimensions:

Length (L) = 9 cm

Width (W) = 7 cm

Height (H) = 4 cm

a) Area of the top face of the cuboid:

The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

b) Area of the bottom face of the cuboid:

The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).

Area = Length × Width

Area = 9 cm × 7 cm

Area = 63 square centimeters (cm²)

Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).

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By using trigonometric relations, we will see that the angle that the ladder makes with the ground is 64.2°, so we conclude that the ladder is safe.

Notice that the ladder makes a right triangle with the wall.

Such that the hypotenuse (the ladder itself) measures 15 ft, and one of the catheti (distance between the ground and top of the ladder) measures 13.5ft

If we considerate the angle that the ladder makes with the ground, the known cathetus is the opposite cathetus.

Then we can use the relation:

sin(x) = (opposite cathetus)/(hypotenuse)

Then:

sin(x) = (13.5ft)/(15ft)

If we use the inverse sine function on both sides, we get:

Asin(sin(x)) = Asin( 13.5ft/15ft)

x = Asin(13.5/15) = 64.2°

So the angle is less than 75°, which means that in fact, the ladder is safe.

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We may predict that, when rοunded tο the clοsest whοle number, 185 persοns οught tο be present at Sοcial Prοblems οn Sunday.

Detailed numbers the set οf integers that cοntains zerο and the natural numbers. nοt a decimal and fractiοn. Integer 0 thrοugh 2, 3, 4, 5, 6, 7, 8, 9, 10, and sο οn. a cοunting number, a negative number, οr zerο.

The library saw a sum οf 416 + 448 + 341 = 1205 visitοrs οn Saturday. By dividing the entire number οf visitοrs by the number οf visitοrs whο visited Sοcial Prοblems, and then multiplying the result by 100% tο represent the results as a percentage, we can determine what percentage οf these visitοrs visited Sοcial Issues:

Percentage οf visitοrs whο went tο Sοcial Issues = (448 ÷ 1205) x 100%

Percentage οf visitοrs whο went tο Sοcial Issues ≈ 37.18%

We may assume that a similar percentage οf Saturday's visitοrs will return οn Sunday in οrder tο estimate the number οf persοns whο can be expected tο attend Sοcial Prοblems οn that day. Tο determine hοw many peοple will visit Sοcial Prοblems οn Sunday, we can utilize the prοpοrtiοn mentiοned abοve:

Estimated number οf visitοrs tο Sοcial Issues οn Sunday = (37.18% οf 500 visitοrs)

Estimated number οf visitοrs tο Sοcial Issues οn Sunday ≈ 185

We may calculate that, if we rοund tο the next whοle number, 185 persοns shοuld be anticipated tο attend Sοcial Prοblems οn Sunday.

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Answer:

96 square units

Step-by-step explanation:

The surface area of the prism can be calculated using its net.

The net consists of 3 rectangles and 2 triangles.

The surface area = area of the 3 rectangles + area of the 2 triangles

Area of 3 rectangles:

Area of 2 rectangles having the same dimension = 2(L*B) = 2(7*3) = 2(21) = 42 squared units

Area of the middle triangle = L*B = 7*6 = 42 square units.

Area of the 3 triangles = 42 + 42 = 84 square units.

Area of the 2 triangles:

Area = 2(½*b*h) = 2(½*6*2) = 6*2

Area of the 2 triangles = 12 square units

Surface area of the triangular prism = 84 + 12 = 96 square units.

Answer:

It's 96 unit2

Step-by-step explanation:

I just do it in khan and it's correct

The final distance is 31 km.

Time, t = Distance, d/Velocity, v

Let's assume the ambulance drives a distance of x along the road, which leaves us 50-x on the road, after which it has reached the road.

It forms a triangle, after which we can use Pythagoras Theorem.

Using it, we get distance down the hill, d1, and we can calculate distance on the road remaining till the hospital, d2.

t = d1/v1 + d2/v2

 = \(\frac{\sqrt{x^{2} + 30^{2} } }{30} + \frac{50 - x}{120}\)

We need to minimise t. Therefore, we have to differentiate.

On differentiating and equating it to 0, we get the value of x as \(\sqrt{60} = 7.75\)

How far down the road should the vehicle aim to reach the road to reach the hospital at the minimum time?

\(= \sqrt{900 + 7.75^{2} } = 31 km\)

Thus, the final distance is 31 km.

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The correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3)

For the first question:

The table shows a proportional relationship between x and y. To describe what the graph of this proportional relationship would look like, we can examine the given data points.

The data points are (12, 3), (8, 26), and (24, ?). We can observe that as x increases, y also increases. This indicates a positive correlation between the variables. Additionally, we can see that the ratio of y to x remains constant for each data point.

Now, let's analyze the answer options:

A. A line passes through the point (0, 0) and continues through the point (3, 12).

This answer option does not align with the given data because there is no data point with an x-value of 3 and a corresponding y-value of 12.

B. A line passes through the point (0, 0) and continues through the point (2, 8).

This answer option aligns with the given data because (2, 8) is a valid data point from the table, and the line passes through the origin (0, 0).

C. A line passes through the point (0, 0) and continues through the point (6, 24).

This answer option does not align with the given data because there is no data point with an x-value of 6 and a corresponding y-value of 24.

D. A line passes through the point (0, 0) and continues through the point (12, 3).

This answer option aligns with the given data because (12, 3) is a valid data point from the table, and the line passes through the origin (0, 0).

Based on the analysis, the correct answer is option D: A line passes through the point (0, 0) and continues through the point (12, 3). This accurately represents the graph of the proportional relationship given in the table.

For the second question, I'm sorry, but you didn't provide the multiple-choice options or the complete question. Could you please provide the question and options so that I can assist you further?

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\(\stackrel{\textit{\huge P~\hfill E~\hfill M~\hfill D~\hfill A~\hfill S}}{\cfrac{3.5(3.7-2.2)}{4(-1.75)}\implies \cfrac{3.5(1.5)}{4(-1.75)}\implies \cfrac{5.25}{4(-1.75)}\implies \cfrac{5.25}{-7}\implies -0.75}\)

Step-by-step explanation:

Answer

a - 8

------------+

2

Answer: 133/408 or 0.2769607843

Step-by-step explanation:

Answer:

27

Step-by-step explanation:

=4(3)^2-3(3)

=4(9)-9

=3(9)

=27

Step-by-step explanation:

step 1 find thd equation of line PI

step 2 find the equation of line AD

step 3 solve the two equations of the 2 lines

step 4 the valued of x and y obtained from step 3are yhe coordinates of the intetcept

A polynomial function f(x) of degree 3 with given zeros, 2, -3 , 5 and condition f(3)=6 is given by f(x) = -1/2 (x-2)(x+3)(x-5).

Degree of the polynomial function is equal to 3.

Zero's of the polynomial function is equal to 2, -3 , 5 .

And f(3) = 6

If 2, -3, and 5 are zeros of f(x), then we can write function as,

f(x) = a(x-2)(x+3)(x-5)

where a is some constant.

To determine the value of a, we can use the fact that f(3) = 6.

Substituting x = 3 into the equation above, we get,

f(3) = a(3-2)(3+3)(3-5)

     = -12a

Here we have,

f(3) = 6, so we can set these two expressions equal to each other and solve for a,

⇒ -12a = 6

⇒ a = -1/2

Now we can substitute this value of a back into the equation for f(x) that we found earlier,

⇒ f(x) = -1/2 (x-2)(x+3)(x-5)

Therefore, a polynomial function f(x) of degree 3 with zeros 2, -3, 5, and f(3) = 6 is equal to f(x) = -1/2 (x-2)(x+3)(x-5).

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The slope-intercept equation of the line with a slope of 8 and a y-intercept of (0, 9) is y = 8x + 9.

To find the slope-intercept equation of a line, we use the form y = mx + b, where m represents the slope and b represents the y-intercept.

Given:

Slope (m) = 8

Y-intercept (0, 9)

We can substitute these values into the slope-intercept form:

y = mx + b

y = 8x + 9

Consequently, y = 8x + 9 represents the slope-intercept equation for the line with a slope of 8 and a y-intercept of (0, 9).

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The value of the cash flows four years from today is $22,609.26.

The value of a set of cash flows can be calculated using the present value of an annuity formula. This formula takes into account the time value of money, which states that money has a different value at different points in time due to the opportunity cost of the money. In other words, the money you have today is more valuable than the money you will have in the future.

The present value of an annuity formula is PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the interest rate, and n is the number of periods. In this example, the cash flows are $3,000, $4,040, $5,885, and $7,975, the interest rate is 5.4%, and the number of periods is 4. Plugging these numbers into the formula, the present value is $22,609.26. This is the value of the cash flows four years from today.

The value of the cash flows four years from today is $22,609.26.

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Answer:

x = 2

Step-by-step explanation:

Given equation,

→ 4x - 22 = -14

Now the value of x will be,

→ 4x - 22 = -14

→ 4x = -14 + 22

→ 4x = 8

→ x = 8/4

→ [ x = 2 ]

Hence, the value of x is 2.

Answer:

Solution/answer is in the explanation.

Step-by-step explanation:

Let's check a for fun.

a)

\(\frac{7}{x}-\frac{1}{y}=6\)

I will rewrite so I can use power rule and chain rule on the first two terms.

\(7x^{-1}-y^{-1}=6\)

Now let's begin.

\(7(-1)x^{-1-1}-(-1)y^{-1-1}y'=0\)

Let's simplify:

\(-7x^{-2}+y^{-2}y'=0\)

Add \(7x^{-2}\) on both sides:

\(y^{-2}y'=7x^{-2}\)

Divide both sides by \(y^{-2}\):

\(y'=\frac{7x^{-2}}{y^{-2}}\)

Using law of exponents we can rewrite this as:

\(y'=\frac{7y^2}{x^2}\).

So a) does look good (Great job!).

b)

We need to solve for \(y\) first since we want to do this explicitly. That is what that means by the way.

\(\frac{7}{x}-\frac{1}{y}=6\)

Subtract \(\frac{7}{x}\) on both sides:

\(-\frac{1}{y}=6-\frac{7}{x}\)

Multiply both sides by \(-1\):

\(\frac{1}{y}=-6+\frac{7}{x}\)

Multiply both sides by \(y\):

\(1=y(-6+\frac{7}{x})\)

Divide both sides by \((-6+\frac{7}{x})\):

\(\frac{1}{-6+\frac{7}{x}}=y\)

Symmetric property:

\(y=\frac{1}{-6+\frac{7}{x}}\)

Multiply the right hand side be \(\frac{x}{x}\):

\(y=\frac{x}{-6x+7}\) (the is the explicit equation since it is solved for \(y\).

Now we are to differentiate this.

Let's use quotient rule \((\frac{f}{g})'=\frac{f'g-g'f}{g^2}\):

\(y'=\frac{(1)(-6x+7)-x(-6)}{(-6x+7)^2}\)

\(y'=\frac{-6x+7+6x}{(-6x+7)^2}\)

\(y'=\frac{7}{(-6x+7)^2}\)

c) So we need to see if a) and b) are actually the same now.

For a) we go \(y'=\frac{7y^2}{x}\) and we solve for \(y\) in b) we go \(y=\frac{x}{-6x+7}\).

I'm going to find \(y^2\) so I can just replace

\(y=\frac{x}{-6x+7}\)

Squaring both sides:

\(y^2=(\frac{x}{-6x+7})^2\)

\(y^2=\frac{x^2}{(-6x+7)^2}\)

I will leave it as this because we may not have to do further work such as expanding the bottom.

Let's plug this into our solution for a):

\(y'=\frac{7y^2}{x^2}\)

\(y'=\frac{7(\frac{x^2}{(-6x+7)^2})}{x^2}\)

Division by a number is the same as multiplication by the reciprocal of that number. So let's rewrite:

\(y'=\frac{7x^2}{x^2(-6x+7)^2}\)

Now we can cancel the common factor \(x^2\) from the top and bottom:

\(y'=\frac{7}{(-6x+7)^2}\)

We see this is the same solution we got for b).

We have completed the objective for c).

Using differentiation, it is found that:

a)

The implicit derivative is:

\(y^{\prime} = \frac{7y^2}{x^2}\)

b)

The explicit derivative is:

\(y^{\prime} = -\frac{7}{x^2}\)

c)

Substituting into part a, we have that:

\(y^{\prime} = \frac{7}{x^2}\left[\frac{49}{x^2} - \frac{84}{x} + 36\right]\)

The expression given is:

\(\frac{7}{x} - \frac{1}{y} = 6\)

Item a:

Applying implicit differentiation, we have that:

\(-\frac{7}{x^2}\frac{dx}{dx} + \frac{1}{y^2}\frac{dy}{dx} = 0\)

\(\frac{1}{y^2}\frac{dy}{dx} = \frac{7}{x^2}\)

\(\frac{dy}{dx} = \frac{7y^2}{x^2}\)

Item b:

First, we solve the expression for y, then:

\(\frac{1}{y} = \frac{7}{x} - 6\)

\(\frac{1}{y} = \frac{7 - 6x}{x}\)

\(xy = 7 - 6x\)

\(y = \frac{7 - 6x}{x}\)

Applying the quotient derivative rule:

\(y^{\prime} = \frac{x(7-6x)^{\prime} - x^{\prime}(7-6x)}{x^2}\)

\(y^{\prime} = \frac{-6x -7 + 6x}{x^2}\)

\(y^{\prime} = -\frac{7}{x^2}\)

Item c:

We have that the expression for the derivative is is:

\(y = \frac{7 - 6x}{x}\)

Substituting into part a, using \(y = \frac{7}{x} - 6\):

\(y^{\prime} = \frac{7y^2}{x^2}\)

\(y^{\prime} = \frac{7\left[\frac{7}{x} - 6]^2}{x^2}\)

\(y^{\prime} = \frac{7}{x^2}\left[\frac{49}{x^2} - \frac{84}{x} + 36\right]\)

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Answer:

33 , 39

Step-by-step explanation:

given

9 , 15 , 21 , 27

there is a common difference between consecutive terms, that is

15 - 9 = 21 - 15 = 27 - 21 = 6

to obtain terms in the sequence add 6 to the preceding term

27 + 6 = 33

33 + 6 = 39

the next two terms are 33 and 39

Answer:

864 grams

Step-by-step explanation:

540 divided by 5=108 grams per cupcake

108 times 8=864 grams

Answer:

too difficult 99%(95%) fraction and decimal of 26.5 and (-36)

Answer:

Both A and B

Step-by-step explanation:

Both a and b. A three-way intersection can be referred to as a T-intersection or a Y-intersection, depending on the shape of the intersection. In a T-intersection, one road intersects another road perpendicularly, forming a T-shape. In a Y-intersection, one road splits into two branches, forming a Y-shape.

Each function on the left should be matched to all points on the right that would be located on the graph of the function as follows;

f(x) = 2x + 2         ⇒   (0, 2).

f(x) = 2x² - 2        ⇒   (-1, 0).

\(f(x) = 2\sqrt{x+1}\)   ⇒   (0, 2).

In Mathematics and Geometry, a function is a mathematical equation which defines and represents the relationship that exists between two or more variables such as an ordered pair in tables or relations.

Next, we would determine the point or ordered pair that represent a solution on the graph of each of the function as follows;

For the ordered pair (0, 2), we have:

f(x) = 2x + 2

2 = 2(0) + 2

2 = 2 (True).

For the ordered pair (-1, 0), we have:

f(x) = 2x² - 2

0 = 2(-1)² - 2

0 = 2 - 2

0 = 0 (True).

For the ordered pair (0, 2), we have:

\(f(x) = 2\sqrt{x+1}\\\\2= 2\sqrt{0+1}\\\\2 = 2\sqrt{1}\)

2 = 2 (True).

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Answer:

1/25

Step-by-step explanation:

5^4/5^6

Since we are dividing exponents with the same base, we subtract the exponents

5^( 4-6)

5^-2

We know that a^-b = 1/a^b

1/5^2

1/25

Answer:

C. No, the program is not statistically significant because the results are likely to occur by chance.

Step-by-step explanation:

At a significance level that is smaller than 0.2, the effect is not significant.

We have a P-value of 20%, which means that we have 20% chances of getting this sample given that the method has no effect.

We then can conclude that there is not enough evidence to support the claim that the method is effective.

The ratio of a to d can be expressed by multiplying the ratio of a to b, b to c, and c to d. Therefore, a to d = (a to b) x (b to c) x (c to d).

The ratio of a to d can be determined by using the given ratio of a to b, b to c, and c to d. To begin, the ratio of a to b can be expressed as a:b, the ratio of b to c can be expressed as b:c, and the ratio of c to d can be expressed as c:d. Then, the ratio of a to d can be determined by multiplying the ratios of a to b, b to c, and c to d. This can be written as (a:b) x (b:c) x (c:d). Therefore, the ratio of a to d can be expressed as (a:b) x (b:c) x (c:d). For example, if the ratio of a to b is 2:3, the ratio of b to c is 4:5, and the ratio of c to d is 6:7, then the ratio of a to d would be (2:3) x (4:5) x (6:7) or 24:35.

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Answer:

The linear equation satisfying the given condition is,

\(x=t+15\)

where x is Ravi's age and t is the number of years

(after 10 years (t=10) his age becomes 25)

Step-by-step explanation:

Let x be Ravi's age

Now, his  current age is unknown, but if you add 10 to it, then it becomes 25, so

x + 10 =25

so, his current age is x = 25 =10

x = 15

Now, we find the linear equation satisfying the given condition,

Let t be the number of years that have passed since the present time

so, if 0 years have passed, his age will be 15 years

after 1 year, his age will be 16 years

after 10 years, his age will be 25 years and so on

so

\(x = t + 15\)

this satisfies the given condition, since if we add ten years i.e t = 10,

then we get 25

The equation is:

Work/explanation:

Here's the linear equation for Ravi's age.

Ravi's age is x.

If you add 10 to x you get x + 10.

That gives 25.

So the linear equation is x + 10 = 25.

Answer:

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

Use the given values in the table and find the missing ones.

The first two rows add up to the last row and same for the columns.

1) Find the Row total for Males:

2) Find the number of Males not enrolled in Composition 1:

Correct choice is A.

Answer:

  3 fish, 2 dogs

Step-by-step explanation:

You want a point on the grid representing the solution to the relations, Kingston has 5 pets, and the number of fish is 1 more than the number of dogs.

Each relation can be plotted as a line on the graph:

  f + d = 5 . . . . . . . . the total number of pets is 5

  f = d + 1 . . . . . . . . there is 1 more fish than dogs

The attached plot shows these lines cross at coordinates ...

  (fish, dogs) = (3, 2)

The red circle is the point on the grid that represents the numbers of pets Kingston has.

__

Additional comment

The equations are plotted only for their respective practical domains. It makes no sense to plot numbers of pets in a range outside 0 to 5.