How much time will it take for a car to travel 250meters if it is traveling at 70 m/s?

The values of tht missing part of the triangle are;

A= 20.9°

a = 13.06

c = 33.6

The sine rule states that if a, b and c are the lengths of the sides of a triangle, and A, B and C are the angles in the triangle; with A opposite a, etc., then a/sinA=b/sinB=c/sinC.

To find side c

sinB/b = sinC/c

sin45.9/26.30 = sin113.2/c

csin 45.9 = 26.30 × sin113.2

0.718c = 23.90

c = 23.90/0.718

c = 33.6

Angle A = 180-(113.2+ 45.9)

angle A = 20.9°

sinA/a = sinB/b

sin20.9/a = 0.718/26.30

0.357 × 26.30 = 0.718a

a = 9.389/0.718

a = 13.06

Therefore A = 20.9°

a = 13.06

c = 33.6

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Answer:

13

Step-by-step explanation:

In the figure provided,

∠(9y + 7) = ∠(2y + 98)                     [vertically opposite angles]

7y + 7 = 98                                      [subtracting 2y from both sides]

7y = 91                                             [subtracting 7 form both sides]

y = 13                                               [dividing both sides by 7]                              

Answer:

min: 56

lower quartile: 70

median: 74

upper quartile: 80

max: 86

9514 1404 393

Answer:

  Syed

Step-by-step explanation:

Expressed as decimal numbers, the portions read were ...

Syed read the most.

The function g(x) increases at a faster rate and has a greater initial value.

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Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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Answer:

b and d

Step-by-step explanation:

14

the secant- secant angle CEG is half the difference of the measures of the intercepted arcs, that is

∠ CEG = \(\frac{1}{2}\) (CG - DF)

44° = \(\frac{1}{2}\)( 170 - DF) ← multiply both sides by 2 to clear the fraction

88° = 170 - DF ( subtract 170 from both sides )

- 82 = - DF ( multiply both sides by - 1 ) , then

DF = 82°

15

the tangent- tangent angle PQR is half the difference of the measures of the intercepted arcs.

the intercepted arcs are PSR and RP

the sum of the arcs in a circle = 360° , so

PSR = 360° - RP = 360° - 121° = 239°

then

∠ PQR = \(\frac{1}{2}\) ( 239 - 121)° = \(\frac{1}{2}\) × 118° = 59°

Answer:

A multiple is a number that can be divided by another number a certain number of times without a remainder. A factor is one of two or more numbers that divides a given number without a remainder. ... This number sentence tells us that 20 is a multiple of 5 and is also a multiple of 4.

Step-by-step explanation:

Answer:

D=221 m

Step-by-step explanation:

In order to solve this problem, we can start by drawing a diagram of the given situation. (see attached picture)

As you may see, we have a right triangle there, so we can use trigonometric functions to solve this. Specifically, the sine function.

\(sin \theta = \frac{OS}{Hyp}\)

in this case we need to find the hypotenuse, so we solve the equation above for the Hyp, so we get:

\(Hyp= \frac{OS}{sin \theta}\)

in this case, the opposite side (OS) is the heght of the helicopter, the angle is the 42° and the Hyp is the direct distance between the helicopter and Jackson, so we substitute the given data to get:

\(Distance=\frac{148m}{sin 42^{o}}\)

Which yields:

D=221m

The given equation is

y = - 3x + 6

We would find the x and y intercepts.

The x intercept is the value of x when y = 0. Substituting y = 0 into the equation, we have

0 = - 3x + 6

Adding 3x to both sides of the equation, we have

0 + 3x = - 3x + 3x + 6

3x = 6

x = 6/3 = 2

x intercept = (2, 0)

The y intercept is the value of y when x = 0. Substituting x = 0 into the equation, we have

y = - 3(0) + 6

y = 0 + 6

y = 6

y = intercept = (0, 6)

The graph is plotted as shown below with the intercepts

An image of triangle NOG after a rotation 90° clockwise about the origin is shown below.

In Mathematics and Geometry, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anticlockwise) direction.

Next, we would apply a rotation of 90° clockwise about the origin to the coordinate of this triangle NOG in order to determine the coordinate of its image;

(x, y)                →            (y, -x)

Point N = (-4, -1)          →     Point N' (-1, 4)

Point O = (-4, -3)          →     Point O' (-3, 4)

Point G = (0, -1)          →     Point G' (-1, 0)

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Answer:

ok

Step-by-step explanation:

Answer:

Constant of proportionality

K= 16.5 gallons per minute

Step-by-step explanation:

Time t (minutes) Water g (gallons)

For t= 1, g= 16.50,

for t= 1.5 ,g= 24.75

For t= 2,g= 33

Let the function be

Gallons g= k(time t)

Where k is the constant of proportionality

16.5= k(1)....for when t= 1

24.75= k(1.5) ..for when t= 1.5

Solving gives

8.25=k(0.5)

8.25/0.5= k.

16.5 = k

K= 16.5 gallons per minute

Width x Length

X = Length

\(\frac{1}{3}\) = 507

\(x^{2}\) = 1521 \(ft^{2}\)

X = 39\(ft\)

Answer:

180

Step-by-step explanation:

120 divide by 2

then times by 3

Answer:

Step-by-step explanation:

Well, since the length of a month can vary in the number of days, this answer can also vary.

For example, February is only 28 days long, while December is 31 days long.

That being said, the average length of all 12 months is 30.436875 days, so if Denny left to another country on June 20th, he would most likely be back   July 19th of July 20th.

I hope this helps!

The graph of the linear function y = -4 - 2x is given at the end of the answer.

The slope-intercept representation of a linear function is presented by the equation below:

y = mx + b.

The parameters of the equation, and their meaning, are explained as follows:

In this problem, the function is given as follows:

y = -4 - 2x.

Hence the intercept is:

b = -4.

Meaning that point (0,-4) is on the graph of the function.

The x-intercept of the function is given as follows:

-4 - 2x = 0

2x = -4

x = -2.

Hence point (-2,0).

A decreasing line, due to the negative slope, is plotted through the two points, and when x increases by 1, y decays by 2.

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Answer:  13.2

In fraction form, this is 66/5

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

Explanation:

The five values are in the ratio 1:2:3:4:5 which scales up to 1x:2x:3x:4x:5x for some positive number x.

Add up the pieces of the second ratio and set that sum equal to 198. Then solve for x.

1x+2x+3x+4x+5x = 198

15x = 198

x = 198/15

x = 66/5

x = 13.2 is the smallest number since 1x = 1*13.2 = 13.2 was the smallest value of the ratio 1x:2x:3x:4x:5x.

The probability that the first success occurs on trial number n = 3 is 0.032

Given:

probability of success on a single trial p = 0.80

trial number, n = 3

Recall the formula for the Geometric Probability Distribution

P(n) = p(1 - p)ⁿ⁻¹

where n is the number of the binomial trial on which the first success occurs and p is the probability of success on each trial

P(n) = p(1 - p)ⁿ⁻¹

P(3) = 0.8(1-0.8)³⁻¹

P(3) = 0.8(0.2)²

P(3) = 0.032

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The interest paid for the loan is $1748

Given that there is a 6.1% interest rate for a loan of $28,654 in student loan debt pay in the first year,

We need to find the interest paid for the same.

So,

Simple Interest = principal × time × rate / 100

= 28654 × 1 × 6.1 / 100

= 28654 × 0.061

= 1747.894

= 1748

Hence the interest paid for the loan is $1748

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Answer:

144

Step-by-step explanation:

im right:D have  a good day or night

Answer:

x=8,y=-2/3

Step-by-step explanation:

make x the subject of formula

x=7+3y

substitute into the first equation

4(7+3y)+3y=18

28+12y+3y=18

28+15y=18

15y=18-28

15y=-10

y=-10/15=-2/3

since y=-2/3, substitute y into x=7+3y

x=7+3(-2/3)

x=7-2

x=5

Multiplication of the given matrix is not possible by definition of matrix multiplication.

Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

We have to given that;

Expression for multiply,

⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]

Since, We can see that;

First matrix have order 1 x 6

And, Second matrix have order 1 x 4

We know that;

Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.

Hence, By given matrices we get;

Number of column in first matrix (6) ≠ number of rows in second matrix (1)

So, Multiplication of the given matrix is not possible by definition of matrix multiplication.

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Answer:

The answer is 275 students.

Step-by-step explanation:

In 75 students, 33 students attend.

So the ratio is 33/75.

so multiply with 625.

625 x 33/75 = 275

Answer:

1

Step-by-step explanation:

(m+1-m)/(n-n)

answer is 1

The width of the field is 230 feet and the length is 310 feet.

Let's denote the width of the field as "x" feet.

The length of the field is 80 feet longer than the width, so it can be represented as "x + 80" feet.

To find the total amount of fencing material needed, we sum up the lengths of all four sides of the rectangular field:

2(length) + 2(width) = perimeter

Substituting the given values:

2(x + 80) + 2(x) = 1080

2x + 160 + 2x = 1080

4x + 160 = 1080

4x = 920

x = 920/4

x = 230

Therefore, the width of the field is 230 feet.

Now we can find the length by adding 80 feet to the width:

Length = Width + 80 = 230 + 80 = 310 feet.

So, the width of the field is 230 feet and the length is 310 feet.

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Answer: Most part-time jobs are worked 10 to 20 hours per week.

Answer:

part-time

Step-by-step explanation:

most part time jobs work shorter hours than 40

Answer: 142825

Step-by-step explanation:

If \(t\) is the number of years, then the population is \(P(t)=100000(1.02)^t\).

Setting \(t=18\). \(P(18)=100000(1.02)^{18} \approx 142825\).