For a project in her Geometry class, Chloe uses a mirror on the ground to measure
the height of her school's football goalpost. She walks a distance of 10.65 meters from
the goalpost, then places a mirror on flat on the ground, marked with an X at the
center. She then steps 1.2 meters to the other side of the mirror, until she can see the
top of the goalpost clearly marked in the X. Her partner measures the distance from
her eyes to the ground to be 1.75 meters. How tall is the goalpost? Round your answer
to the nearest hundredth of a meter.

The roots of the polynomial are the solutions to that equation.

If you consider the original equation, \(y=x^2-7x+10\), and the equation you're solving, \(x^2-7x+10=0\), the connection is that y=0.  

In terms of the graph, you're looking where the graph crosses the line y=0, which is the x-axis.

In short, the solutions to that equation are the x-values where your graph crosses the x-axis: 2 and 5.

You can double check this by substituting in 2 and 5 (one at a time) to verify that they are solutions to the equation.

Part A: To find the total surface area of the rectangular prism, we need to calculate the areas of all six faces and then add them together.

Given dimensions:

Length = 7 feet

Width = 3 feet

Height = 4.8 feet

Surface Area of each face:

Front and back faces: Length * Height

= 7 feet * 4.8 feet

= 33.6 square feet

Top and bottom faces: Width * Length

= 3 feet * 7 feet

= 21 square feet

Side faces: Width * Height

= 3 feet * 4.8 feet

= 14.4 square feet

Total Surface Area:

2 * (Front and back faces) + 2 * (Top and bottom faces) + 2 * (Side faces)

= 2 * 33.6 square feet + 2 * 21 square feet + 2 * 14.4 square feet

= 67.2 square feet + 42 square feet + 28.8 square feet

= 137 square feet

Therefore, the total surface area of the bench is 137 square feet.

Part B: To calculate the cost of covering the bench with ceramic tiles, we need to multiply the total surface area by the cost per square foot.

Cost per square foot = $0.89

Total Surface Area = 137 square feet

Total cost to cover the bench:

= Cost per square foot * Total Surface Area

= $0.89 * 137 square feet

= $121.93

Therefore, it will cost $121.93 to cover the bench with ceramic tiles.

Answer:

Step-by-step explanation: bép lép sép tao tât sgayx dép ok

To determine how long it takes for Martin and Gordon to complete the maintenance when working together, we can use the concept of their combined work rates.

Martin takes 4 hours to complete the work, so his work rate is 1/4 of the job per hour (1 job / 4 hours = 1/4 job/hour).

Similarly, Gordon takes 2 hours to complete the work, so his work rate is 1/2 of the job per hour (1 job / 2 hours = 1/2 job/hour).

When they work together, their work rates are additive. Therefore, the combined work rate is:

Combined work rate = Martin's work rate + Gordon's work rate

Combined work rate = 1/4 job/hour + 1/2 job/hour

Combined work rate = 3/4 job/hour

To find the time it takes for them to complete the maintenance when working together, we can use the formula:

Time = 1 / Combined work rate

Time = 1 / (3/4 job/hour)

Time = 4/3 hours

Therefore, the correct option is:

Four thirds

The maintenance takes 4/3 hours (or 1 hour and 20 minutes) when Martin and Gordon work together.

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How long it takes for Martin and Gordon to complete the maintenance when working together, we can use the concept of their combined work rates.

Martin takes 4 hours to complete the work, so his work rate is 1/4 of the job per hour (1 job / 4 hours = 1/4 job/hour).

Similarly, Gordon takes 2 hours to complete the work, so his work rate is 1/2 of the job per hour (1 job / 2 hours = 1/2 job/hour).

When they work together, their work rates are additive. Therefore, the combined work rate is:

Combined work rate = Martin's work rate + Gordon's work rate

Combined work rate = 1/4 job/hour + 1/2 job/hour

Combined work rate = 3/4 job/hour

The time it takes for them to complete the maintenance when working together, we can use the formula:

Time = 1 / Combined work rate

Time = 1 / (3/4 job/hour)

Time = 4/3 hours

Therefore, the correct option is:

Four thirds

The maintenance takes 4/3 hours (or 1 hour and 20 minutes) when Martin and Gordon work together.

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Answer: 4x² + 4xy - 3y²

Concept:

When encountering questions that ask for simplifying algebraic expressions, using the FOIL method would be easier:

Solve:

Given

(2x - y) (2x + 3y)

Expand parentheses and apply the FOIL method

=4x² + 6xy - 2xy - 3y²

Combine like terms

=4x² + (6xy - 2xy) - 3y²

=\(\boxed{4x^2+4xy-3y^2}\)

Hope this helps!! :)

Please let me know if you have any questions

The 95% confidence interval for the population proportion of picky eaters is given as follows:

(0.4, 0.46).

The z-distribution is used to obtain a confidence interval of proportions, and the bounds are given according to the equation presented as follows:

\(\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}\)

The parameters of the confidence interval are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The parameter values for this problem are given as follows:

\(n = 1009, \pi = \frac{435}{1009} = 0.4311\)

The lower bound of the interval is obtained as follows:

\(0.4311 - 1.96\sqrt{\frac{0.4311(0.5689)}{1009}} = 0.40\)

The upper bound of the interval is obtained as follows:

\(0.4311 + 1.96\sqrt{\frac{0.4311(0.5689)}{1009}} = 0.46\)

The problem states that in the sample, 435 out of 1009 adults were picky eaters.

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Step-by-step explanation:

"which is the measure of angle L?"

the total angle measures of all angles on a triangle should always equal 180

72 + 36 = 108

180 - 108 = 72!

angle L is 72 degrees!

"which angle is the vertex angle?"

from my understanding, the angle opposite the base would be the vertex angle

since j and k are equal, we can only assume 36 is the vertex angle!

hope this helps! if so, pls give brainliest!

Answer:

hi. I'm so sorry I just need to answer some questions. I'm sorry

I substituted x' value as square numbers so we don't get irrational or decimal number as y's value.

Now,

plot (9,3) , (4,2), (36,6), (25,5) and (49,7) in the graph and join them.

Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.

Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.

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Answer:

here is the required answer hope it help u

Step-by-step explanation:

−2(−5n+6)+5(2−7n)

10n-12+10-35n

-25n-2

Answer:

A = (1, 10)

B = (4,10)

C = (4, 14)

D = (1, 16)

Step-by-step explanation:

Okay, so first, we move, or translate the quadrilateral PQRS down -8 spaces on the graph, turning old points:

P (1, -2) = (1, -10)     Q (4, -2) = (4, - 10)     S (1, -8) = (1, -16)     and R (4, -6) = (4, -14)

Now, we need to rotate this new box into -x, y. So our new points are:

(1, -10) = (-1, 10)     (4, -10) = (-4, 10)     (1, -16) = (-1, 16)     and (4,-14) = (-4, 14)

Now we're reflecting off the y-axis, making our x change. So for our final points:

A(1, 10)   B (4,10)    D(1, 16)    and C(4, 14)

Hope this helps! Please check my math and comment wether this worked or not! :)

Answer:

hi

Step-by-step explanation:

Answer:

When you divide the amount you have by the total amount and then multiply the quotient by 100, you are calculating the percentage of the total amount that the amount you have represents.

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

A percentage is a fraction expressed as a part per hundred.

It is calculated by dividing the number you want to express as a percentage by the total number and then multiplying by 100%.

This can be expressed using the formula:

The quantitative data is the value of data in the form of counts or numbers where each data set has a unique numerical value.

Data in math is a collection of facts and figures that can be in any form numerical or non-numerical. Numerical data is the one you can calculate, and it is always collected in number form, such as scores of students in class, wages of workers in an organization or height of players on a football team, etc.

Quantitative data is the value of data in the form of counts or numbers where each data set has a unique numerical value. This data is any quantifiable information that researchers can use for mathematical calculations and statistical analysis to make real-life decisions based on these mathematical derivations.

Therefore, the quantitative data is the value of data in the form of counts or numbers where each data set has a unique numerical value.

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The total number of ways the winning number can be drawn using the combination is 45.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

We have,

The Total numbers, n = 10

The Numbers to select, r = 2

The following combination formula is used to determine the potential winning numbers.

Total = ⁿCᵣ

Where,

n = 10 and r = 2

Substitute the values in the above equation,

Total = ¹⁰C₂

Using the combination formula,

ⁿCᵣ = n!/(n - r)!r!

So, we have

Total = 10! / 8! 2!

Total = 10 × 9 / 2

Total = 45

Hence, the number of ways is 45.

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The time and distance traveled during the duration described are 5.56 seconds and 77.15 meters respectively.

Given the parameters:

Acceleration (a) = 5 m/s²

Initial velocity (u) = 0 m/s

Final velocity (v) = 100 km/h

Converting the final velocity to m/s:

100 km/h = (100 × 1000) / 3600 m/s = 27.78 m/s

Using the equation of motion:

v = u + at

Rearranging the equation to solve for time (t):

t = (v - u) / a

Substituting the values:

t = (27.78 - 0) / 5

t = 27.78 / 5

t ≈ 5.556 seconds

Therefore, it takes approximately 5.556 seconds to reach a merging speed of 100 km/h.

b)

Using motion equation

Distance (s) = ut + (1/2)at^2

Substituting the values:

s = 0 * 5.556 + (1/2) * 5 * 5.556^2

Calculating:

s = 0 + (1/2) * 5 * 30.86

s = (1/2) * 5 * 30.86

s = 77.15 meters

Therefore, you would travel approximately 77.15 meters in that length of time.

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The systems of inequalities that must be true is \(363b + 6c > = 1,500,000.\)The correct is D

The system of inequalities that must be true if b is the number of beams and c is the number of connector plates is \($\mathbf{D. 363b + 6c \geq 1,500,000}$ and $\mathbf{2b \geq c}$.\)Explanation:Let's find out the weight of one beam and one connector plate:

Weight of one beam = 363 kgWeight of one connector plate = 6 kgLet's represent the number of beams by b and the number of connector plates by c.Each beam weighs 363 kg, and each connector plate weighs 6 kg.There must be at least 2 connector plates for each beam.

Using the above information, we can represent the total weight of the steel pieces by:Total weight of steel pieces = (Weight of each beam) × (Number of beams) + (Weight of each connector plate) × (Number of connector plates)Inequality:

(Weight of each beam) × (Number of beams) + (Weight of each connector plate) × (Number of connector plates) < 1,500,000 kg (Given)Substituting the values:Number of beams = bWeight of each beam = 363 kgNumber of connector plates = cWeight of each connector plate = 6 kgThen, we get:\($$363b + 6c < 1,500,000$$\)

Since there must be at least 2 connector plates for each beam, we can write another inequality as:\($$c \geq 2b$$\) Simplifying, we get:\($$2b \leq c$$\) Combining these two inequalities, we get the required system of inequalities as:\($$\boxed{363b + 6c \geq 1,500,000 \text{ and } 2b \geq c}$$\) Hence, option D is the correct answer.

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Answer:

29.) y = -1.5x - 20

30.) y = 6 - 3x

Step-by-step explanation:

29.) For parallel lines; M1 = M2

put the equation in the form y = mx + c

the equation becomes 2y = 14 - 3x

therefore y = 7 - 1.5x.

For the points, introduce another point; (x,y) and the initial (-6,-11)

(y - - 11) ÷ ( x - - 6) = -1.5

y+11 = -1.5x - 9

y= -1.5x - 20

30.) still following the same procedure, only that M1 × M2 = -1

M1 = 1/3, M2 = -3

(y + 9)/(x - 5) = -3

y + 9 = 15 - 3x

y = 6 - 3x

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

1/8

The probability of getting a head or a tail when flipping a coin is 1/2.  

Therefore, the probability of getting two heads when tossing two coins is 1/2 x 1/2 = 1/4.

The probability of getting three heads when tossing three coins is 1/2 x 1/2 x 1/2 = 1/8.

Since each person is tossing three coins, the probability that they both obtain the same number of heads is 1/8.

The probability of getting n heads when tossing n coins is 1/2^n. Therefore, the probability of getting the same number of heads when two people toss n coins is 1/2^n. This means that if two people each toss a coin, the probability that they both get heads is 1/4; if they each toss two coins, the probability that they both get two heads is 1/16; if they each toss three coins, the probability that they both get three heads is 1/64; and so on.

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Answer: I got this answer from the internet hopefully this helps

Resultant force will act on 65° N of W.

Step-by-step explanation:

The direction of the resulting force upon the piling, to the nearest degree is gotten as; A = 60°

As given in the question one bulldozer exerts force of 1850 pounds in western direction and another pushes with a force of 3250 pounds in northern direction.

Now, we have to find angle A which is an angle between 1850 pounds of force and resultant force F.

Thus;

tan A= Force on North direction/ Force on west direction

tan A = 3250/1850

tan A = 1.7568

A = tan⁻¹1.7568

A = 60.35°

To the nearest degree is A = 60°

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Answer:

Andy :

36+35 = 71 cards.

- I hope this helps:)

The Solution:

We want to find the equation of a line S, which passes through point (6,2).

Let the required equation of line S be

Where m = the slope of line S, and

We are told that line S is parallel to line r, which is, y = 56x + 1. This implies that both lines have the same slope (m).

So, to find the slope (m) of line S, we shall compare y=56x+1 to the general form of equation of a line as given below:

Comparing both equations below:

Substituting 56 for m, and the given point (6,2) in the formula above, we get

Clearing the bracket, we get

Thus, the equation of line r is: y = 56x - 334

The ordered pairs for the system of equations f(x) = x^2 -2x + 3 and f(x) = -2x + 12 are (3, 6) and (-3, 18)

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax2 + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠ 0)

f(x) = x^2 -2x +3 and f(x) = -2x + 12

which means

x^2 -2x +3  = -2x + 12

x^2 -2x +3  + 2x - 12 = 0

x^2 -9 = 0

by factorizing we have

(x-3)(x+3) = 0

x = 3 or -3

when x = 3

f(x) = -2x + 12

f(3) = -2(3) + 12 which is 6

when x = -3

f(-3) = -2(-3) + 12 which is 18

ordered pairs are (3, 6) and (-3, 18)

In conclusion, (3, 6) and (-3, 18) are the ordered pairs

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The equation to describe the relationship between the number of lilies (ll) and the number of roses (rr) is ll/6 = 303030 and rr/6 = 787878.

To write an equation that describes the relationship between the number of lilies (ll) and the number of roses (rr), we need to consider the information provided. Flannery used 303030 lilies and 787878 roses to create six identical flower arrangements.

Since there are six identical arrangements, we can divide the total number of lilies and roses by six to find the number used in each arrangement.

So, the number of lilies used in each arrangement can be represented by ll/6, and the number of roses used in each arrangement can be represented by rr/6.

Therefore, the equation that describes the relationship between ll and rr is:
ll/6 = 303030
rr/6 = 787878

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Answer:

122.5 People

Step-by-step explanation:

4500-90 = 4410

4410 divided by 36 equals 122.5

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

Explanation:

n = number of people invited

n+2 = total number of people after adding Oscar and Julie

36(n+2) = total cost before the $90 fee

36(n+2)+90 = total cost after the $90 fee

Set that equal to the budget of 4500 and isolate n

36(n+2)+90 = 4500

36n+72+90 = 4500

36n+162 = 4500

36n = 4500-162

36n = 4338

n = 120.5

n = 120

We round down so that we don't go over budget

Oscar and Julie can invite 120 people.

-----------

Check:

If n = 120 then 36(n+2)+90 = 36(120+2)+90 = 4482 which is under budget

If n = 121 then 36(n+2)+90 = 36(121+2)+90 = 4518 which is over budget

This confirms that 120 is the answer.

Answer:

Answer is A the highest number we can get is 12 so its potion A

The both highest numbers are 6 and, 6 6 +6 is 12 so its 0

Answer;

(7,9)

Hope you could understand.

If you have any query, feel free to ask.

Answer:

Step-by-step explanation:

35*27%=9.45 mark up

35+9.45= 44.45 total cost

Answer:

The answer is $44.45

Step-by-step explanation:

You change the percent into a decimal so it would be .27 then multiply the .27 to the $35 and you will get $9.45. Then you add the $9.45 to the $35 and you will get the answer.

The total area of the composite figure is 228 sq cm

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

The composite figure with 6 sides

The total area of the composite figure is the sum of the areas of the individual shapes

So, we have

Area = Area of Rectangle + Area of Rectangle

Using the above as a guide, we have the following equation

Area = 12 * 14 + (22 - 12) * 6

Evaluate the products

Area = 228

Hence, the total area of the figure is 228 sq cm

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Answer:

distance between -5 to 0 = 5 units