Evaluate the cosine if the angle of rotation which contains the point (9, -3) on its terminal side

Answer:

A' will be located 10 units from point A along ray PA

Step-by-step explanation:

we know that

The scale factor is equal to 3

To obtain PA', multiply PA by the scale factor

so

PA'=PA*3

PA=5 units

substitute

PA'=(5)*3=15 units

AA'=PA'-PA=15-5=10 units

therefore

A' will be located 10 units from point A along ray PA

Answer:10 units

Step-by-step explanation:

Answer:x + 10

Step-by-step explanation:

Answer:

J=x+10

Step-by-step explanation:

We know the equation is about Jenna's money. We can use J to represent Jenna and X to represent Alyssa's Dollars.

We know that J has 10 more than A. We can say J=X+10

Answer: I believe the answer is the second choice.  

81y^4 - 16x^2, the difference of squares.

Step-by-step explanation:

For this case we must find an expression equivalent to:

[tex]log_ {5} (\frac {x} {4}) ^ 2[/tex]

So:

We expanded [tex]log_ {5} ((\frac {x} {4}) ^ 2)[/tex]by moving 2 out of the logarithm:

[tex]2log_ {5} (\frac {x} {4})[/tex]

By definition of logarithm properties we have to:

The logarithm of a product is equal to the sum of the logarithms of each factor:

[tex]log (xy) = log (x) + log (y)[/tex]

The logarithm of a division is equal to the difference of logarithms of the numerator and denominator.

[tex]log (\frac {x} {y}) = log (x) -log (y)[/tex]

Then, rewriting the expression:

[tex]2 (log_ {5} (x) -log_ {5} (4))[/tex]

We apply distributive property:

[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]

Answer:

An equivalent expression is:

[tex]2log_ {5} (x) -2log_ {5} (4)[/tex]

Answer: the answer is c

Step-by-step explanation: 2log5x-2log54

Answer:

x = 75

Marta's jump rope is 75 inches long

Step-by-step explanation:

Hello!! This is how you solve it:

x + ( x - 10 x 3 ) = 120

2x - 10 x 3 = 120

2x - 30 = 120

+ 30. + 30

2x = 150

--- ------

2. 2

x = 75

Final answer:

Marta's jump rope is 87.5 inches long. This was determined by setting up an equation based on the information that Marta's rope is 10 inches shorter than three times Dilbert's rope length, and together they measure 120 inches.

Explanation:

The question involves finding the length of Marta's jump rope when it is known to be 10 inches shorter than three times the length of Dilbert's rope, and when both ropes laid end-to-end measure 120 inches long. Let's denote the length of Dilbert's jump rope as D inches. Therefore, the length of Marta's jump rope can be expressed as 3D - 10 inches. Since the combined length of both ropes is 120 inches, we can write the equation: D + (3D - 10) = 120.

Combining like terms, we get 4D - 10 = 120. Adding 10 to both sides gives 4D = 130, and dividing both sides by 4 yields D = 32.5 inches. Thus, Dilbert's rope is 32.5 inches long, and Marta's rope, being 3(32.5) - 10, calculates to 87.5 inches long.

Answer:

279 ft^2

Step-by-step explanation:

The area of a rectangle of length L and width W is A = LW.

Here, that area is (19.25 ft)(14.5 ft) = 279.125 ft^2, or approx. 279 ft^2

Final answer:

0.64 is a finite decimal with zero repeating digits as it does not have digits that continue infinitely after the decimal.

Explanation:

The number 0.64 is a decimal that has two digits after the decimal point. These digits (6 and 4) do not repeat infinitely, making them non-repeating decimal digits. Therefore, there are zero repeating digits in 0.64. A repeating decimal would have one or more digits after the decimal point that continue infinitely, often denoted by a bar over the repeating digits. Since 0.64 does not exhibit this pattern, it is a finite decimal.

Answer:

20.922

Step-by-step explanation:

Evaluate ln 7.2 on a calculator; the correct result is 1.974.

Multiply that by 3, obtaining 5.922.

Finally, add 15 to that result:  y = 15 + 3 In 7.2 = 20.922

1 = C      2 = I     3 = B  have a good day

By moving the decimal according to the number of places expressed by the exponents, we can see the real value of each answer choice.

A. .0008 lbs not a realistic weight for an 18-wheeler

B. 800 lbs closer but still not enough weight

C. .08 nope not this one either.

D. 80,000 lbs. this is probably in the range we are looking for.

If the exponent is negative, move the decimal that many spaces left. If the exponent is positive, move the decimal that many space right.

The correct answer is D.

Answer:

The reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]

Step-by-step explanation:

The average and legally maximum weight of an 18-wheeler is 80,000 pounds.

From option a through d, we check which of the measurement is close or equivalent to 80,000 pounds

By converting this, we have

[tex]= 8 * \frac{1}{10000} lb[/tex]

[tex]= \frac{8}{10000} lb[/tex]

[tex]= 0.0008 lb[/tex]

By converting this, we have

[tex]= 8 * 100 lb[/tex]

[tex]= 800 lb[/tex]

By converting this, we have

[tex]= 8 * \frac{1}{100} lb[/tex]

[tex]= \frac{8}{100} lb[/tex]

[tex]= 0.08 lb[/tex]

By converting this, we have

[tex]= 8 * {10000} lb[/tex]

[tex]= {80000} lb[/tex]

From the 4 conversions, only  [tex]8 * 10^{4} lb[/tex] is equivalent to the average and legally maximum weight of an 18-wheeler, 80,000 pounds.

Hence, the reasonable estimate for the weight of an 18-wheeler is [tex]8 * 10^{4} lb[/tex]

Answer: The number is 8

Step-by-step explanation:

 Let be "x" the certain number. Then "3 times a certain number" means that the number "x" is multiplied by 3. This is:

[tex](3)(x)=3x[/tex]

Now, "3 times a certain number is increased by 4" means that the we must add 4 to [tex]3x[/tex], in other words, this indicate an addition:

 [tex]3x+4[/tex]

And finally "3 times a certain number is increased by 4 the result is 28" means that  [tex]3x+4[/tex] is equal to 28. Then the expression is:

 [tex]3x+4=28[/tex]

To find the number "x", subtract 4 from both sides of the equation:

[tex]3x+4-4=28-4[/tex]

[tex]3x=24[/tex]

Dividing both sides of the equation by 3, you get that the number is:

[tex]\frac{3x}{3}=\frac{24}{3}\\\\x=8[/tex]

Multiply the bracket by 3

3(2f+g+4)

My answer is 6f+3g+12

Answer is true

This is true. You applied the Distributive Property authentically.

Answer:

-4

Step-by-step explanation:

(1/4)*x-(1/8) = (1/2)*x+7/8

First rearrange the numbers

(1/4)*x-((1/2)*x)-(1/8)-(7/8)

1/4*x ((-1/2)*x)-(1/8)-(7/8)

-1/4*x-1 = 0 + 1

-1/4*x = 1  -1/4

x = 1/(-1/4)

x = -4

x = -4

Answer:

Step-by-step explanation:

[tex]x^2+11=36\qquad\text{subtract 11 from both sides}\\\\x^2=25\to x=\pm\sqrt{25}\\\\x=-5\ or\ x=5\\============================\\\\\dfrac{x^2-25}{x+5}=0\qquad Domain:\ x+5\neq0\to x\neq-5\\\\\dfrac{x^2-25}{x+5}=0\to x^2-25=0\qquad\text{add 25 to both sides}\\\\x^2=25\to x=-5\notin D\ or\ x=5\in D[/tex]

Answer:

It is angle 4 because they make 90 degrees together. This is if there are choices for the problem.

It would be ∠4

Angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

We have:

From the angle diagram, angle 4 makes the complete right angle.

The sum of the complementary angles is 90 degree

Angle 3 + Angle 4 = 90 degree

Thus, angle 4 is the complementary angle of 3 because the sum of these angles is 90 degrees.

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Answer:

[tex]\large\boxed{x=-1\ \vee\ x=1}[/tex]

Step-by-step explanation:

[tex]8x^2+4=12\qquad\text{subtract 4 from both sides}\\\\8x^2+4-4=12-4\\\\8x^2=8\qquad\text{divide both sides by 8}\\\\\dfrac{8x^2}{8}=\dfrac{8}{8}\\\\x^2=1\to x=\pm\sqrt1\\\\x=-1\ \vee\ x=1[/tex]

Answer:

444

Step-by-step explanation:

the x value of point a is 5

The x value of point A is; 5

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line.

We have been given a graph representing the point A.

therefore, we need to find the coordinate of the given point.

So, we can see that the coorddinate of the point A is (5, 5)

The value x in the point A would be 5.

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Answer:

Hello :))

Step-by-step explanation:

You should set this up as a proportion equation. 8.1kg /1hr =x/7hr You would cross multiply here and end up getting the equation... 1x=8.1*7 (x=56.7 kg)

Hope this helps! :))

Answer:

the answer would be 3.25 meters

Answer:

3 meters and 25 centimeters of ribbon

Step-by-step explanation:

Battery is down currently = 2/5

Battery drains at the rate of 1/9 every hour.

Remaining battery life of Vera = 1 -2/5 = 3/5

Let y we the number of hours battery will last.

So, 1/9 y = 3/5

y = 27/5

y = 5 + 2/5 hours

y = 5 hrs and 24 mins

So battery will last another 5 hrs and 24 mins.

hope this helps:)

Answer:

16, 26, 36

Step-by-step explanation:

In order to solve this problem, you MUST find the number that is making the pattern flow. The first method you should try is to subtract the first number from the second. That means -24 - (-14), which equals 10. If you continue to do this is every number, 10 will be the answer. Now that we have the number add 10 to the number and the next number, to find the answers.

Ex.

[tex]6 + 10 = 16\\16 + 10 = 26\\26 + 10 = 36[/tex]

This is how you solve this problem.

Answer:

Measure B= 121

Measure C=59

Step-by-step explanation:

10x-19=7x+23

3x=42

x=14

plug in x to the problem and you'll find Measure B is 121 so to find Measure C you'll have to subtract 180 and 121 to get 59.

The value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B

It is defined as the four-sided polygon in geometry having four edges and four corners and two pairs of congruent sides. It has one pair of opposite congruent angles.

We have a quadrilateral in which angle B and angle D are given.

As we know the opposite angles in the quadrilateral are same in measure.

10x - 19 = 7x + 23

3x = 42

x = 14

Angle B =  10x - 19 = 10(14) - 19 = 121 degree

Angle C =  7x + 23 = 7(14) + 23 = 121 degree

Angle A + Angle C = 360 - 121 -121 = 118

Angle C = 118/2 = 59

Thus, the value of angle B is 121 degree and Angle C is 59 degree, and Angle D has the same measure as the angle B

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See the attached picture:

I hope to understood my writing

To determine at what time the two lorries will meet, we can use the concept of relative speed. Since the lorries are moving towards each other, their relative speed is the sum of their individual speeds.
The speed of the first lorry is 63 km/h and the speed of the second lorry is 67 km/h. Together their combined speed is:
63 km/h + 67 km/h = 130 km/h
Now we need to calculate how long it will take for them to cover the distance of 520 km between the two towns at their combined speed.
The time taken to cover a distance is equal to the distance divided by the speed, so the time taken \( t \) in hours can be found by:
\( t = \frac{distance}{speed} \)
Substituting the known values into this formula gives us:
\( t = \frac{520 km}{130 km/h} = 4 \) hours
Now we know the lorries will meet after 4 hours of travel.
Given that the lorries start to travel at 7:30 am, we add 4 hours to that time to find the meeting time.
7:30 am + 4 hours = 11:30 am
Therefore, the two lorries will meet at 11:30 am.

Answer:

C

Step-by-step explanation:

The shape consists of a cylinder and a hemisphere.

The volume of a cylinder is:

V = πr²h

where r is the radius (half the diameter) and h is the height.

The volume of a hemisphere is:

V = ⅔ πr³

where r is the radius (half the diameter).

The cylinder and hemisphere both have a diameter of 8 cm, or a radius of 4 cm.  The cylinder has a height of 17 cm.

So the total volume is:

V = π(4 cm)²(17 cm) + ⅔ π(4 cm)³

V = π (272 + 128/3) cm³

V ≈ 988.6 cm³

Answer:

z = 24°

Step-by-step explanation:

The 3 angles 48, x and x form a straight angle and sum to 180°, thus

x + x + 48 = 180

2x + 48 = 180 ( subtract 48 from both sides )

2x = 132 ( divide both sides by 2 )

x = 66

The 3 angles in a triangle sum to 180°

sum the 2 known angles and subtract from 180

z = 180° - (66 + 90)° = 180° - 156° = 24°

Answer:

z=24

Step-by-step explanation:

Mary is 10 yrs old now.

Explanation:

10+20=30

30÷3=10

So, Mary has to be 10yrs old now.

Mary is currently 10 years old.

Given that in coming 20 years Mary's age will be 3 times her present age, we need to calculate her present age,

Let's assume Mary's current age is represented by "x". According to the given information, in 20 years, Mary will be three times as old as she is now. Therefore, her age in 20 years will be 3 times her current age, which can be expressed as 3x.

So, we can set up the equation:

x + 20 = 3x

To solve this equation, we can subtract x from both sides:

20 = 2x

Then, we can divide both sides by 2:

x = 10

Therefore, Mary is currently 10 years old.

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Answer:

3y² + 7y + 4 = (3x + 4)(x + 1)

Step-by-step explanation:

* To factor a trinomial in the form ax² ± bx ± c:

- Look at the c term

# If the c term is positive

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will have the same sign (sign of b)

∵ a = h × k ⇒ h , k are the factors of a

∴ rk + hs = b

∴ (hx + r)(kx + s) ⇒ if b +ve  OR  (hx - r)(kx - s) ⇒ if b -ve

# If the c term is negative

∵ c = r × s ⇒ r and s are the factors of c

∴ r and s will not have the same sign

∵ a = h × k ⇒ h and k are the factors of a

∴ rk - hs = b OR hs - rk = b

(hx + r)(kx - s) OR (hx - r)(kx + s)

* Now lets solve the problem

∵ 3y² + 7y + 4

∵ ax² + bx + c

∴ a = 3 , b = 7 , c = 4

∵ a = h × k

∵ 3 = 3 × 1

∴ h = 3  , k = 1

∵ c = r × s

∵ 4 = 4 × 1

∴ r = 4 , s = 1

∵ c is positive

∴ hs + rk = b

∴ 3(1) + 4(1) = 7 ⇒ same value of b

∴ 3y² + 7y + 4 = (3x + 4)(x + 1)

Answer:

The factors of 3y^2 + 7y + 4 are

(y +1) and (3y + 4)

Step-by-step explanation:

It is given a quadratic equation in variable y

3y^2 + 7y + 4

To find the factors using splitting method

3y^2 + 7y + 4 can be written as,

3y^2 + 7y + 4 = 3y^2 + 3y + 4y + 4

 = 3y(y + 1) + 4(y + 1)

 = (y + 1)(3y + 4)

Therefore the factors of 3y^2 + 7y + 4 are

(y +1) and (3y + 4)

Answer:

-(√5)/3

Step-by-step explanation:

The tangent being negative means the sine and cosine have opposite signs. Using the identity ...

cos(o) = ±√(1 -sin(o)^2)

we find ...

cos(o) = -√(1 -(2/3)^2) = -√(5/9)

cos(o) = -(√5)/3