Please help answer this question also with explanation

Answer:

Positive integer

Step-by-step explanation:

A parabola is the locus of a point which is equidistant from a fixed point and a fixed line. The fixed line is known as the directrix, while the fixed point is known as the focus.

The axis of a parabola passes through the focus and is perpendicular to the directrix. The axis touches the parabola at a point known as the vertex.

The standard form of a parabola that opens up is:

4ay = x²;

where the focus is at (0, a), the equation of the axis is x = 0 and the equation of the directrix is y = -a (parallel to the y axis).

Hence, the leading coefficient of the equation of a parabola that opens up will be a positive integer.

Answer:683 km

Step-by-step explanation:

Using trigonometric ratio and Pythagoras theorem, the value of the sides TS, TV, TW and TU are 10.2m, 15.2m, 12.2m and 9.4m respectively.

Using trigonometric ratio, we can find the value of the unknown sides in the figure.

Using cosine ratio;

cosθ = adjacent / hypothenuse

cos 64 = 4 / TS

TS = 4 / cos 64

TS = 10.2m

TV = TS + SV

TV = 10.2 + 5 = 15.2m

To find TW, we can apply Pythagoras theorem;

TV² = VW² + TW²

15.2² = 9² + TW²

TW² = 15.2² - 9²

TW = 12.2m

The value of TU can be found using Pythagoras theorem;

TS² = US² + TU²

10.2² = 4² + TU²

TU² = 10.2² - 4²

TU = 9.4m

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According to the equation for the maximum speed, it is found that the height at the top of the swing of the rider is of 0.8 m.

As stated in the problem, it is given by:

v = 2gh.

In which:

In this problem, the parameters are g = 9.8, v = 15. Hence we can solve for h to find the height.

v = 2gh

2 x 9.8h = 15

19.6h = 15

h = 15/19.6

h = 0.8.

The height at the top of the swing of the rider is of 0.8 m.

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Jack and Jills' speed in miles per hour is 4

The given parameters are:

Jack speed = x^2-11x-22

Jill distance = x^2-3x-54 and time = x + 6

Speed is calculated as:

Speed = Distance/time

So, we have:

Jill speed = x^2-3x-54/x + 6

Factorize the numerator

Jill speed = (x + 6)(x - 9)/x + 6

Cancel the common factor

Jill speed = x - 9

Both speeds are equal.

So, we have:

x^2-11x-22 = x - 9

Collect like terms

x^2-11x - x -22 + 9 = 0

Evaluate

x^2 - 12x - 13 = 0

Factorize the expression

(x + 1)(x - 13) = 0

Solve for x

x = -1 or x = 13

x cannot be negative.

So, we have:

x =13

Substitute x =13 in Jill speed = x - 9

Jill speed = 13 - 9

Evaluate

Jill speed = 4

Hence, their speed in miles per hour is 4

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Solution:

Given:

Therefore, to the nearest hundredth, the value of t for which the rocket's height is 82 feet is;

0.42 seconds or 12.21 seconds.

Answer: x = -2

Step-by-step explanation:

Given expression

(1/2) (2 - 6x) - 4 (x + 3/2) = - (x - 3) + 4

Expand parentheses and apply the distributive property when there is a constant outside of the parentheses

(1/2) · 2 - (1/2) · 6x - 4 · x - 4 · (3/2) = - x + 3 + 4

1 - 3x - 4x - 6 = -x + 3 + 4

Combine like terms

(1 - 6) - (3x + 4x) = -x + (3 + 4)

-5 - 7x = -x + 7

Add x on both sides

-5 - 7x + x = -x + 7 + x

-5 - 6x = 7

Add 5 on both sides

-5 - 6x + 5 = 7 + 5

-6x = 12

Divide -6 on both sides

-6x / -6 = 12 / -6

\(\boxed{x=-2}\)

Hope this helps!! :)

Please let me know if you have any questions

Answer:

B

Step-by-step explanation:

given

tanΘ = \(\frac{3\sqrt{5} }{2}\) = \(\frac{opposite}{adjacent}\)

this ratio relates to a right triangle, with hypotenuse h and

legs 3\(\sqrt{5}\) and 2

using Pythagoras' identity in the right triangle

h² = (3\(\sqrt{5}\) )² + 2² = 45 + 4 = 49 ( take square root of both sides )

h = \(\sqrt{49}\) = 7

then

cosΘ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{2}{7}\)

Look I saw you post like a million of these. Functions are time consuming, especially rate of change, I suggest you ask a tutor!

The value of cos\((x \ + \frac{2\pi }{3})\) with x in quadrant 2, if sin x = \(\frac{8}{17}\) is \(\frac{(15 - 8\sqrt{3} )}{34}\).

To evaluate cos\((x \ + \frac{2\pi }{3})\) in quadrant 2 with sin x = \(\frac{8}{17}\), we can use the following trigonometric identity:

cos\((x \ + \frac{2\pi }{3})\) = cos(x)cos\((\frac{2\pi }{3} )\) - sin(x)sin\((\frac{2\pi }{3} )\)

We know that sin x = \(\frac{8}{17}\), and in quadrant 2, sin x is positive and cos x is negative. Therefore, we can determine that:

sin² x + cos² x = 1

\((\frac{8}{17})\)² + cos² x = 1

cos² x = 1 - \((\frac{8}{17})\)²

cos x = \(- \frac{15}{17}\) (since cos x is negative in quadrant 2)

Now we can substitute the values into the identity:

cos\((x \ + \frac{2\pi }{3})\) = cos(x)cos\((\frac{2\pi }{3} )\) - sin(x)sin\((\frac{2\pi }{3} )\)

= \((- \frac{15}{17})\)\((- \frac{1}{2})\) - \((\frac{8}{17} )(\frac{\sqrt{3}}{2} )\)

= \(\frac{15}{34} - \frac{4\sqrt{3} }{17}\)

= \(\frac{(15 - 8\sqrt{3} )}{34}\)

Therefore, cos\((x \ + \frac{2\pi }{3})\) in quadrant 2 with sin x = \(\frac{8}{17}\) is \(\frac{(15 - 8\sqrt{3} )}{34}\).

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Answer:

x = 1.56

Step-by-step explanation:

so what you have to do is isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

-1

Step-by-step explanation:

\(\frac{10-8}{-7- - 5}\) =\(\frac{2}{-7+5}\) = \(\frac{2}{-2}\) = -1

Ordered pairs are written (x,y)  The first number is the x coordinate and the second number is the y coordinate.

(-5,8)  and (-7,10)  You take the y's and subtract them that is your numerator.  Take the x's and subtract them.  That is your denominator.

Answer:

all 3 options are true : A, B, C

Step-by-step explanation:

warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.

they say that A and C are correct.

but I am going to show you that if A and C are correct, then also B must be correct.

therefore, my given answer above is the actual correct answer (no matter what the test systems say).

originally the information about the alignment of the point F in relation to point E was missing.

therefore, I considered both options :

1. F is on the same vertical line as E.

2. F is not on the same vertical line as E.

because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :

the vertical line of EF is like a mirror between the left and the right half of the picture.

A is mirrored across the vertical line resulting in B. and vice versa.

the same for C and D.

this leads to the effect that all 3 given congruence relationships are true.

if we consider assumption 2, none of the 3 answer options could be true.

but if the assumptions are true, then all 3 options have to be true.

now, for the "why" :

remember what congruence means :

both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.

for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.

so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.

therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.

but do you notice something ?

both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.

now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.

therefore, AC must be equal to BD.

and that means that AC is congruent to BD.

because lines have no other congruent criteria - only the lengths must be identical.

Answer:

I think the answer is 35x⁴-10

Step-by-step explanation:

3x × 4x=12x²

3x × 5=15x

2 × 4x=8x

2 × -5=-10

15x+8x=23x²

12x²+23x²=35x⁴

35x⁴-10

Answer:

-9

Step-by-step explanation:

Since 5 can go into 40 9 times, the answer would be nine, but by following negative rules, since we have an odd amount of negative numbers in this equation, the answer is -9

Answer:-8

Step-by-step explanation:

5 goes into -40 8 times. 5 goes into 45 9 times.

Answer:

5.82.384.8+9×8=8×99+8×6×8+9×

Answer: They are equivalent

Step-by-step explanation:

2.2x+3.8x=6x

5.5-4.1=1.4

Answer:108 houses

Step-by-step explanation:

Step 1: ratio of flats to bungalows is 10:5 and the bungalows are 30, therefore:

(10*30)/5 = 60 flats

Step 2: the ratio of houses to flats is 9:5 and the number of flats is 60, therefore

9*60/5 = 108 houses

Answer:

270 girls

Step-by-step explanation:

Total number of students = 380

Play musical instrument = 70%

Boys who play musical instrument = 60%

Number of girls who play musical instrument = 200

How many girls are in the class?

Number of play musical instrument = 70% of 380

(0.7 * 380) = 266

Since number of girls who play musical instrument = 200

Then number of boys who play = (266 - 200) = 66

Hence, 66 boys is equivalent 60% of the boy's population

Let population of boys = b

0.6b = 66

b = 110

Number of girls in class :

Number of boys + number of girls

110 + number of girls = 380

Number of girls = 380 - 110

Number of girls = 270

Answer:

Step-by-step explanation:

They're both right angle triangles and have the same length and size , hence congruency

If the population is known to be exponential, or the sample size is less than 10, the t distribution should not be used.

The t distribution can be used when the population is not normal, as long as certain assumptions are met. Let's examine each of the conditions you mentioned to see whether they meet these assumptions:

"The population distribution is not badly skewed": The t distribution assumes that the population is approximately normally distributed. If the population is not normal, but is not badly skewed, then the t distribution may still be used. However, the more the population deviates from normality, the less reliable the t distribution becomes.

"The sample size is less than 10": If the sample size is less than 10, the t distribution is generally not recommended. Instead, a small sample size can be better analyzed using non-parametric tests or exact tests, which do not assume any particular population distribution.

"The population distribution is known to be exponential": If the population distribution is known to be exponential, then the t distribution should not be used, as it assumes normality. Instead, an appropriate distribution, such as the exponential distribution, should be used to analyze the data.

"The sample size is not too small": The t distribution can be used when the sample size is not too small. Typically, a sample size of at least 30 is recommended for the t distribution to be reliable. However, if the population is not normal or if the sample is highly skewed, a larger sample size may be required.

In summary, using the t distribution requires certain assumptions to be met. If the population is not normal, but is not badly skewed, and the sample size is not too small, the t distribution can be used. However, if the population is known to be exponential, or the sample size is less than 10, the t distribution should not be used.

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Based on the table, the minutes a person has to run to burn 100 calories is 20 minutes

Ratio shows the equivalent relationship that exists between two or more numbers. A ratio table can be described as table that shows equivalent relationship between two numbers.

The first step is to determine the ratio between the minutes run and the calories burned. To do this, divide any of the minutes run on the table by the corresponding calories burned.

Ratio = minutes run / calories burned

8 / 40 = 1/5

Now, multiply this ratio by 100

1/5 x 100 = 20 minutes

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Answer:

6

Step-by-step explanation:

The triangles SAT and SAO are congruent by the Side-Angle-Side (SAS) congruence theorem.

The Side-Angle-Side congruence theorem states that if any of the two sides on a triangle are the same, along with the angle between them, then the two triangles are congruent.

For the triangles SAT and SAO in this problem, we have that:

The common angle are between the common sides, hence the SAS congruence theorem was used to determine the congruence of the two triangles.

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Answer:

x= 30

Step-by-step explanation:

3x + 50 = 140

3x = 140 -50

3x = 90

x = 90/3

x = 30

Answer:

x = 30

Step-by-step explanation:

The given angles are vertical and congruent , then

3x + 50 = 140 ( subtract 50 from both sides )

3x = 90 ( divide both sides by 3 )

x = 30

The amount of money that I will have at the end of 20 years would be =$4,480. That is option D

Compound interest is defined as the interest that is being earned on an account which is based on the rate and the time the investment was made.

The total amount invested (p)= $2,000

The rate of investment (r) = 5%

The time of investment(t)= 12 year

The compound interest warm from that account;

= P×T×R/100.

= 2,000×12×5/100

= 120000/100

= $1200

For the next 8 years with the rate of 8% ;

= 2,000×8×8/100

= 128000/100

= $1280

The total compound interest = $1200+$1280= $2,480

Therefore, the amount of money that I will have at the end of 10 years would be = 2000+2480 = $4,480

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A homogeneous system in parametric vector form:

(x1,x2,x3) = (s,s,-0.25s)

Parametric vector Form:

Any equation expressed as a parameter is a parametric equation. The general equation y = mx + b (where m and b are parameters) of a straight line in the form of a slope intersection is an example of a parametric equation. Example: one of the variables to t(x = t). Then we can rewrite this equation as y = t²+5.

So the set of parametric equations is x = t and y=t²+5.

According to the Question:

We are to solve them in parametric form.

X₁ + 2X₂ + 12X₃ = 0     ----------------------- (1)

2X₁ + X₂ + 12X₃ = 0     ----------------------- (2)

-X₁ + X₂ = 0                  ----------------------- (3)

From equation 3 we get

x₁ = x₂

Substitute in 1 and 2 to get

3x₁ + 12x₃ = 0 and

3x₁ + 12x₃ = 0

Thus, we find these two equations are dependent.  So we can have infinite solutions in parametric form only.

No unique solution is possible

Let x₁ = x₂ = s

Since 3x₁ +12x₃ = 0

x₁ = -4x₃

Or x₃ = -0.25s

So solution in parametric form is

(x1,x2,x3) = (s,s,-0.25s) for all real values.

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Answer:

at first count solution set

6 feet 7 inches

1 feet = 12 inches

6 feet = 6(12) = 72 inches

6 feet 7 inches = 72 + 7 = 79 inches

Answer:

79 inches