how wide can a 5 m load be to fit under a parabolic underpass that is 7 m wide and 7 m at its highest point

Answers

Answer 1

Answer:

[tex]\boxed{\text{3.74 m}}[/tex]

Step-by-step explanation:

This is equivalent to finding the equation of a parabola from three points.

Let's call the ground-level points (-3.5, 0) and (3.5, 0).

The axis of symmetry will be the y-axis, so the vertex is at (0, 7).

Part 1. Find the equation of the parabola

The vertex form of the equation for a parabola is

y = a(x - h)² + k

where (h, k) is the vertex of the parabola.

If the vertex is at (0, 7),  

h = 0 and k = 7

The equation is

y = ax² + 7

Insert the point (0, -3.5)

0 = a(0 + 3.5)² + 7

0 = a(3.5)² + 7

0 = 12.25a + 7

-7 = 12.25a

a = -0.5714

The equation in vertex form is

y = -0.5714x² + 7

Part 2. Calculate the width when y = 5

 5 = -0.5714x² + 7

-2 = -0.5714x²

x² = 2/0.5714

x² = 3.5

x = ±√3.5 = ±1.87  

So, on the graph, the coordinates of the truck at ground level are x = -1.87 and x = +1.87.

The maximum width of the load is 1.87 – (-1.87) =[tex]\boxed{\textbf{3.74 m}}[/tex]

In the diagram below, the red parabola represents the underpass, and the blue box is the truck going through it.

How Wide Can A 5 M Load Be To Fit Under A Parabolic Underpass That Is 7 M Wide And 7 M At Its Highest

Related Questions

Given: f(x) = x - 7 and h(x) = 2x + 3

Write the rule for h(f(x)).


h(f(x)) = 2x - 11

h(f(x)) = 2x - 7

h(f(x)) = 2x - 4

h(f(x)) = 3x - 4

Answers

Answer:

h(f(x)) = 2x - 11

Step-by-step explanation:

Answer:

h(f(x)) = 2x - 11 and the next one is f(h(x)) = 2x - 4 or A and B

Which represents the decimal 0.071

A 71 tenths
B 71 thousandths
C 71 hundredths
D 71 ten thousandths

Answers

Answer:

The answer is B

Step-by-step explanation:

In the decimal (base ten) system, the value of the digits is based on the number ten. Each position in a decimal number has a value that is a power of 10.

Answer is B

The last digit (1) is on the thousandths place value

PLEASE HURRY
A 5 inch × 7 inch photograph is placed inside a picture frame. Both the length and width of the frame are 2x inches larger than the width and length of the photograph. Which expression represents the perimeter of the frame?

Answers

Answer:

48in

Step-by-step explanation:

We know that the photograph is

Width photo = 5in

Lenght photo = 7in

The length and width of the frame are 2x inches larger than the width and frame of the photograph so:

Width frame = 5in x 2 = 10 in

Lenght frame = 7in x 2 = 14 in

The perimeter is the distance around a two-dimensional shape. Then, the perimeter of the frame is:

Perimeter = 10 in + 14 in + 10 in + 14 in = 48in

If the radius of a flying disc is 7.6 centimeters, what is the approximate area of the disc?

Answers

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} r=7.6 \end{cases}\implies A=\pi 7.6^2\\\\\\ A=57.76\pi \implies A\approx 181.46[/tex]

Answer: OPTION C

181.3664 square centimeters

Step-by-step explanation:

What is 5 to the fith power

Answers

5×5×5×5×5=3125

Hope this helped :)

Plzzzzzzzz help meeeee

Answers

Answer:

38 in²

Step-by-step explanation:

The area (A) of a trapezium is calculated using the formula

A = [tex]\frac{1}{2}[/tex] h (a + b)

where a, b are the parallel bases and h the perpendicular height

here a = 12, b = 7 and h = 4, hence

A = 0.5 × 4 × (12 + 7) = 2 × 19 = 38 in²

Answer:

38 in²

Step-by-step explanation:

What is the base of the largest triangular flag can make?

Answers

Answer:

9.36cm

Step-by-step explanation:

We can add up all the sides to find the perimeter.

[tex]x+2x+2x=5x[/tex]

So the perimeter, 46.8, is equivalent to 5x.

Solve.

[tex]5x=46.8 \\ \\ x=9.36[/tex]

So [tex]x[/tex] is 9.36.

Since the base is [tex]1x[/tex], the base is 9.36cm.

We can plug back in to check our answers.

[tex]2x=18.72\\9.36+18.72+18.72 = 46.8[/tex]

The answer is 9.36cm hope u do well :)

how many possible outcomes are there when flipping a coin 9 times​

Answers

Answer: 512

=======================================================

Explanation:

If you had one coin, then there are 2 outcomes because of the two sides heads or tails, which I'll shorten to H and T respectively.

With two coins, there are 2*2 = 4 outcomes (HH, HT, TH, or TT)

Having 3 coins there are 2*2*2 = 2^3 = 8 outcomes

4 coins and we have 2^4 = 2*2*2*2 = 16 outcomes

and so on

With 9 coins there are 2^9 = 512 different outcomes

Answer:

There are 2 outcomes per flip.

Therefore the answer is 2^9 which equals 512 outcomes.

Step-by-step explanation:

Which ordered pairs are solutions to the inequality 2x-y>-4

Answers

Answer:

well these are all the possible solutions that make the inequality statement correct.

Step-by-step explanation:

you can recheck by placing the pairs into the equation

hope that helps

Tasha is decorating a rectangular bulletin board by putting ribbon around its outer edge. The bulletin board is 14 in wide and 18 in tall how many inches of ribbon does she need?​

Answers

Answer: tasha needs at least 252 inches of ribbon

your exact answer should be 252 inches

Step-by-step explanation: multiply the width times height to find the area of a rectangle

Final answer:

Tasha requires 64 inches of ribbon to decorate the outer edge of her bulletin board. To determine this, we use the formula for the perimeter of a rectangle, 2*(length+breadth), substituting the dimensions of the board.

Explanation:

To calculate the amount of ribbon Tasha requires, you need to find the perimeter of the bulletin board. The perimeter of a rectangle (which is the shape of the bulletin board) is calculated by the formula 2*(length+breadth).

In this instance, the length is 18 in, and the width (or breadth) is 14 in. Substituting these values into the formula we get: 2*(18 in + 14 in) = 2*32 in = 64 inches. Thus, Tasha needs 64 inches of ribbon to decorate the entire outer edge of the bulletin board.

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Write your answer as a fraction or as a whole mixed number 16 2/3 - 9 1/3=

Answers

16 2/3 - 9 1/3=7 1/3 or 22/3

Or

50/3 - 28/3= 22/3 or 7 1/3

The result of the given mixed fraction subtraction 16 2/3 - 9 1/3 is 22/3 or 7 1/3.  

What is the result of the given mixed fraction subtraction ?

Given equation of mixed fraction is 16 2/3 - 9 1/3

Thus, we have

= 16 2/3 - 9 1/3

= 50/3 - 28/3

= 22/3

Thus, the result of the given mixed fraction subtraction 16 2/3 - 9 1/3 is 22/3 or 7 1/3.

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can someone please help me out

Answers

Answer:

c

Step-by-step explanation:

i think is right because i got most of the answers correct

40 points Please help, answer and explain, please. Thank you!
Which expression is arranged by decreasing powers of x for the given polynomial? 6x^2 - 2x^4+4+3x

A. -2x^4+3x+6x^2+4

B.6x^2+4+3x-2x^4

C. -2x^4+6x^2+3x+4

D.4+3x+6x^2-2x^4

Answers

Answer:

C. 6x² + 6x² + 3x + 4

Step-by-step explanation:

[tex]6x^2-2x^4+4+3x\\\\\text{Look at the power of variables.}\\\text{Arrange the terms in order from the largest exponent to the smallest.}\\\\-2x^4+6x^2+3x+4[/tex]

Convert 346.5 lb. to kg.

Answers

Answer:

157.5

Step-by-step explanation:

346.5 lb = 157.16976 kg

346.5 lbs. = 157.16976 kg

Can anyone help me please

Answers

Answer:

$55.24

Step-by-step explanation:

Add $32.78 + $27.24 + $5.22

= 65.24

Subtract 10

= $55.24

Answer:

55.24

Step-by-step explanation:

Shoes                            32.78

Dress                             27.24

Shipping                         5.22

Total                               65.24

Less Gift Certificate      10.00

Her Payment                  55.24

Find the highest common factor of 32, 48, 72

Answers

Answer:

8

Step-by-step explanation:

8 x 4 = 32

8 x 6 = 48

8 x 9 = 72

Help anyone please!!

Answers

Answer:

2/9 of a chance

Step-by-step explanation:

If she only spun the spinner twice and had to land on a 2 and a 3 in order to get a sum or 5.  The possible results of the spinners would be

1 & 1          2 & 1          3 & 1

1 & 2          2 & 2         3 & 2

1 & 3         2 & 3         3 & 3

only two of those possibilities equal 5.  So it would be 2/9 of a chance.

To the nearest foot, how many feet is the object in front of the whale? (image included)

Answers

[tex]\bf \begin{array}{ccll} feet&seconds\\ \cline{1-2} 4752&1\\ x&0.8 \end{array}\implies \cfrac{4752}{x}=\cfrac{1}{0.8}\implies 3801.6=x\implies \stackrel{\textit{rounded up}}{3802=x}[/tex]

so, we can conclude that since the wave went and came back in 0.8 seconds, it travelled the distance of 3802 feet, however that's the whole trip, we want to know how far the object is, and that'd be only the distance it took on its way forth, namely half the trip, namely 3802/2 = 1901.

∠1 and ∠2 are complementary. If m∠1 = 4m∠2, find m∠1

Answers

Answer:

∠1 = 72°

Step-by-step explanation:

Complementary angles sum to 90°, thus

∠1 + ∠2 = 90, substitute ∠1 = 4∠2 , thus

4∠2 + ∠2 = 90

5∠2 = 90 ( divide both sides by 5 )

∠2 = 18°

Hence ∠1 = 90 - 18 = 72°

Bob brought 40% of the collected canned goods to the food pantry, 11
Bob brought 160 cans to the pantry, how many cans were collected?

Answers

Final answer:

To find the total number of cans collected, when Bob brought 40% to the pantry equaling 160 cans, we set up the equation 0.40 * x = 160 and solve for x to get 400 cans.

Explanation:

The student has asked to calculate the total number of canned goods collected if Bob brought 40% of them to the pantry and that amounted to 160 cans. To find the total, we can set up a proportion where 40% of the total number of cans equals to 160 cans, and then solve for the total.

First, express 40% as a decimal, which is 0.40. Then, let the total number of cans be represented by x. According to the problem, 0.40 times x equals 160 cans.

So the equation is:

0.40 * x = 160

To solve for x, divide both sides of the equation by 0.40:

x = 160 / 0.40

x = 400

Therefore, a total of 400 cans were collected.

Write 7 over 10 as a percentage

Answers

70%

A percentage is the same thing as a fraction with a denominator of 100. To make our current denominator change to 100, we must multiply it by 10. So, we must do the same thing to the numerator. 7 times 10 is 70, and 10 times 10 is 100. This means 7/10 equals 70/100, which is 70%.

can someone help me pls

the options are

A.78.23 to 115.43

B.74.23 to 113.43

C.72.3 to 103.3

D 76.3 to 118.3​

Answers

The mean is the average.

Add the number of contacts and divide by the number of people:

112 + 104 + 96 + 54 +98 +120 = 584

584 / 6 = 97.3

The mean = 97.3

Now add the standard deviation to the mean for the higher value and subtract the standard deviation from the mean for the lower value:

97.3 - 21 = 76.3

97.3 +21 = 118.3

The answer would be D.

Solve this inequality for x.

81 - 1 1/5x <_ 55

Answers

Answer:

A

Step-by-step explanation:

On solving the given inequality, we get x > 11.81

What is inequality? What is a mathematical equation? What do you mean by domain and range of a function?A relationship between two expressions or values that are not equal to each other is called 'inequality.A mathematical equation is used to equate two expressions.Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

Given is the following inequality -

81 - 11/5x ≤ 55

We have -

81 - 11/5x ≤ 55

(11/5)x ≥ 81 - 55

(11/5)x ≥ 26

(11/5)x ≥ 26

x ≥ = (26 x 5)/11

x > 11.81

Therefore, on solving the given inequality, we get x > 11.81

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A go-cart has a maximum weight limit of 240 pounds. Which inequality correctly represents this weight limit,w?

Answers

Answer:

w<240 pounds

Step-by-step explanation:

The inequality of weight is w≤250 pounds.

What is inequality?

A statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions

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), larger than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

A go-cart has a maximum weight limit of 240 pounds.

let the weight is represented by 'w'

We can use inequality sign here as ≤.

Now, in the given situation weight should be less than or equal to 250 pounds.

Hence, the equality is w≤250 pounds.

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Write a similarity statement for the triangles.

Answers

Answer:

[tex]\large\boxed{c.\ \triangle CDE\sim\triangle FGH}[/tex]

Step-by-step explanation:

[tex]\text{Calculate the maeasure of the angle}\ E:\\\\180^o-(60^o+53^o)=180^o-113^o=67^o\\\\\angle C\cong\angle F\\\\\angle E\cong\angle H\\\\\angle D\cong\angle G\\\\\text{Therefore:}\\\\\triangle CDE\sim\triangle FGH[/tex]

Answer:  The correct option is

(c) [tex]\triangle CDE\sim \triangle FGH.[/tex]

Step-by-step explanation:  We are given to write a similarity statement for the triangles shown in the figure.

In the given triangles, we have

m∠C = 60°,  m∠D = 53°,  m∠F = 60°  and  m∠H = 67°.

Fist, we have to fin d the measures of angles E and G.

From angle sum property of a triangles, we can write

[tex]m\angle C+m\angle D+m\angle E=180^\circ\\\\\Rightarrow 60^\circ+53^\circ+m\angle E=180^\circ\\\\\Rightarrow 113^\circ+m\angle E=180^\circ\\\\\Rightarrow m\angle E=180^\circ-113^\circ\\\\\Rightarrow m\angle E=67^\circ.[/tex]

Similarly, we have

[tex]m\angle F+m\angle G+m\angle H=180^\circ\\\\\Rightarrow 60^\circ+m\angle G+67^\circ=180^\circ\\\\\Rightarrow 127^\circ+m\angle G=180^\circ\\\\\Rightarrow m\angle G=180^\circ-127^\circ\\\\\Rightarrow m\angle G=53^\circ.[/tex]

So, we get

m∠C  =  m∠F,

m∠D  =  m∠G

and

m∠E  = m∠H.

Therefore, by angle-angle-angle similarity postulate. we get

[tex]\triangle CDE\sim \triangle FGH.[/tex]

Thus, option (c) is CORRECT.

how many raffle ticket numbers are possible if they contain two letters followed by three digits

Answers

more information is needed

To determine the total number of possible raffle ticket numbers with two letters followed by three digits, we multiply the number of possibilities for each position (26 for each letter and 10 for each digit): 26 x 26 x 10 x 10 x 10 = 676,000 possible combinations.

To calculate how many raffle ticket numbers are possible with the given format—two letters followed by three digits—we need to consider the total number of options for each position in the sequence. Each letter in the raffle ticket can be one of 26 possible letters (assuming we're using the English alphabet), and each digit can be one of 10 digits (0-9).

For the two letters, the number of possibilities for each letter is 26. Since there are two letters, the total number of possibilities for the letters is 26 times 26. For the three digits, assuming each digit can be any number from 0-9, the number of possibilities for each digit is 10. The total number of possibilities for the digits is 10 times 10 times 10.

Thus, to find the total number of possible raffle ticket numbers, we multiply the possibilities for the letters and the digits together:

26 (for the first letter) times 26 (for the second letter)times 10 (for the first digit)times 10 (for the second digit)ttimes 10 (for the third digit)

Total possibilities = 26 times 26 times 10 times 10 times 10 = 676,000.

I need help for question 8

Answers

It’s 6, wow that question was really worded weird.

Answer:

3/4 pound or less , thinks this is the answord

Step-by-step explanation:

7x-2y=37 4x+y=19 soliving system by elimation

Answers

Answer:

x=5  y=-1

Step-by-step explanation:

7x-2y=37

[2(4x+y=19)]=

8x+2y=38

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

15x/15=75/15

x=5

[4(5)+y=19]

y=-1

Final answer:

The solution to the given system of equations using elimination is x = 5 and y = -1. This was achieved by multiplying the second equation by 2 and then adding both equations to eliminate y.

Explanation:

We are given a system of linear equations and are asked to solve it using the method of elimination. We have the following equations:

1) 7x - 2y = 37

2) 4x + y = 19

To eliminate one of the variables, we can multiply the second equation by 2 to make the coefficient of y the same in both equations (but with opposite signs). After this step, our system looks like:

1) 7x - 2y = 37

2) 8x + 2y = 38

Now, adding the two equations will eliminate y, and we get:

7x + 8x = 37 + 38

15x = 75

x = 5

We can then substitute the value of x into one of the original equations to solve for y:

4x + y = 19

4(5) + y = 19

20 + y = 19

y = -1

So, the solution to the system is x = 5 and y = -1.

A lender will verify and carefully consider your income before approving you for a loan because _____.

Answers

They need to make sure you will be able to pay the loan back

Hope this helps :)

Lenders verify income before approving loans to assess borrowers' creditworthiness and ensure they have the means to repay. They use income information, credit checks, cosigners, and collateral to mitigate the risks associated with uncertain future income and potential default.

A lender will verify and carefully consider your income before approving you for a loan because income indicates your ability to repay the loan. In a financial capital market, banks assess the creditworthiness of a borrower to manage uncertainty and the risk of default. They require information about income sources, perform credit checks, and might ask for additional security measures such as a cosigner or collateral. Collateral could include property or equipment that the bank has the right to seize if the loan is not repaid. This scrutiny is crucial because lenders face imperfect information and cannot predict with certainty whether the borrower will fulfill their repayment obligations.

A parallelogram has vertices at (5, 3), (8, 4), (7, 8), and (4, 7). What is the approximate area of the parallelogram?

12 Unit

13 Units

17 Units

27 Units

Please help and show work!!!!! Will mark brainliest!!!!!

Answers

Answer:

13 square units.

Step-by-step explanation:

We can find the area of the parallelogram using the formula:

[tex]Area=2\times \frac{1}{2}[|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|][/tex]

where [tex]A(x_1,y_1)[/tex], [tex]B(x_2,y_2)[/tex]. and [tex]C(x_3,y_3)[/tex] are the vertices of one of the triangles created by the diagonals.

[tex]Area=[|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|][/tex]

We use A(5, 3), B(8, 4), C(7, 8) to obtain:

[tex]Area=[|5(4-8)+8(8-3)+7(3-4)|][/tex]

[tex]Area=[|-20+40-7|][/tex]

[tex]Area=|13|=13[/tex]

The area of the parallelogram is 13 square units.

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