The elongation α
of a planet is the angle formed by the planet, earth, and sun. it is known that the distance from the sun to venus is 0.723au
(see exercise 65 in section 6.2 ). at a certain time the elongation of venus is found to be 39.4∘.
find the possible distances from the earth to venus at that time in astronomical units (au).

Answer:

15x^2 + 14x - 8.

Step-by-step explanation:

(3x + 4)(5x - 2)

= 3x(5x - 2) + 4(5x - 2)

= 3x*5x + 3x*-2 + 4*5x + 4*-2

= 15x^2 - 6x + 20x - 8

= 15x^2 + 14x - 8.

Answer:

hi! this is (insert your name) what does this sybol/mathematical term mean?

√

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Greetings Mrs.(name here)!

I got my recent test back and I was wondering why this question was incorrect.

For #4, I was sure that you had to find the square root and then multiply by pi, but apparently that's not what some people did and they got it correct.

How do I properly do this question?

-*name here*

Answer:

Step-by-step explanation:

Answer:

2,945 feet

Step-by-step explanation:

Find the circumference.

C = dπ

C = 67(3.14)

C = 210.38

Since there are 14 revolutions, multiply the circumference by 14.

210.38 x 14 = 2945.32

Round

2,945

Answer:

96

Step-by-step explanation:

Answer:

the answer of this question

is 96

In order to solve this inequality, we should divide both sides by 9:-

[tex]\sf{9x < 72}[/tex]

Why 9? Because x is multiplied by 9, and we need to isolate x in order to find its value.

[tex]\sf{x < 8}[/tex]

Hence, that's the solution to the inequality.

It also means that the numbers less than 8 will satisfy the given inequality (make the inequality true)

(Option C is correct :) )

Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)

x < 8

solving steps:

The average amount of time it takes a professional football player to run a mile is = 18.96 seconds

The total number of players that made up the sample data = 20

The average time for the whole players was = 6.32minutes.

If 20 players = 6.32 mins

∴ 1 player = ?

Make the unknown the subject of formula,

? =  1 × 6.32/20

? = 6.32/20

? = 0.316 mins

To converted to seconds multiply by 60,

Therefore, 0.316 × 60 = 18.96 seconds.

Learn more about time conversion here:

https://brainly.com/question/11947673

The selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.

The target profit is the profit that is expected by a manufacturer from the sale of its product.

The target profit can be established and used to determine the selling price.

When the target profit is added to the fixed cost per unit and the variable cost per unit, the resultant figure is the selling price.

Fixed costs per print = $15,000

Number of Bibles per print = 5,000

Fixed costs per Bible = $3 ($15,000/5,000)

Variable costs per Bible = $25

Expected profit per Bible = $10

The selling price = $38

Thus, the selling price to earn $10 per Bible if 5,000 Bibles are printed when the fixed costs per print is $15,000 and variable costs are $25 per Bible, is $38.

Learn more about determining the selling price at https://brainly.com/question/1153322

Answer:

Step-by-step explanation:

Let the missing length is x.

According to Pythagorean, we have the following equation

Answer:

Missing length = 4 in

Step-by-step explanation:

Pythagoras' Theorem: a² + b² = c²

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

Given:

Substitute given values into the formula and solve for ?:

⇒ 3² + ?² = 5²

⇒ 9 + ?² = 25

⇒ ?² = 25 - 9

⇒ ?² = 16

⇒ ? = √16

⇒ ? = 4 in

Using the vertex of the quadratic equation, it is found that the profit will be maximized when each cookbook is sold for $8.25.

A quadratic equation is modeled by:

[tex]y = ax^2 + bx + c[/tex]

The vertex is given by:

[tex](x_v, y_v)[/tex]

In which:

[tex]x_v = -\frac{b}{2a}[/tex]

[tex]y_v = -\frac{b^2 - 4ac}{4a}[/tex]

Considering the coefficient a, we have that:

In this problem, the function is modeled as follows, considering x as the price divided by $0.05.

P(x) = -0.1x² + 15x + 120.

The coefficients are a = -0.1 < 0, b = 15, c = 120, hence the x-value of the vertex is given by:

[tex]x_v = -\frac{15}{2(-0.1)} = \frac{15}{0.2} = 75[/tex]

75 increases of $0.05, hence the price will be of:

4.5 + 75 x 0.05 = $8.25.

Hence, the profit will be maximized when each cookbook is sold for $8.25.

More can be learned about the vertex of a quadratic equation at https://brainly.com/question/24737967

Answer:

32 +x+x=180(Sum of angles of a triangle)

32+2x=180

2x=180-32

2x=148

x=148/2

Therefore,X=74

Answer:

the answer for x is 74°

Step-by-step explanation:

[tex]32 + x + x = 180 \\ 2x + 32 = 180 \\ 2x = 180 - 32 \\ 2x = 148 \\ x = 74 \: degrees[/tex]

Answer:

$31

Step-by-step explanation:

295 minus 16 is 279

that's how much they were all together

and divide 279 by 9 and you get 31

Step-by-step explanation:

1) 35×23 = 805

2) 800/40=20

3)170/10=17

4) 2000-805-800-170=225

5)225/15=15

Hence answers

1)805

2)20

3)17

4)225

5)15

Answer:

C. 76 degrees.

Step-by-step explanation:

n = 180 - 104

= 76.

Answer:

C

Step-by-step explanation:

a straight line is 180 degrees

so we can say that n is equal to 180 - 104

n is equal to 76 degrees

Answer:

80 cubic inches

Step-by-step explanation:

Hey there!

In order to find the volume, you need to split this shape in two parts

We are going to take the big rectangle and the small rectangle as our two shapes

The bigger rectangle has dimensions 5.5 x 6 x 2 which is 66 cubic inches

So now we need to get the volume of the smaller rectangle which has the dimensions: 2x2x3.5 which is 14 cubic inches

Now we add both volumes

66+14 is 80

So the total volume is 80 cubic inches

Answer:

30th percentile = 105 90th percentile = 176

Step-by-step explanation:

Arrange the data set in order from smallest to largest:

100, 100, 105, 113, 129, 132, 146, 152, 176, 200

30th percentile

r = number of data values = 10

q = percentile = 30

q/100 = 30/100 = 0.3

q/100 × r = 0.3 × 10 = 3

Therefore, count the 3rd number in the ordered set.

⇒ 30th percentile = 105

90th percentile

r = number of data values = 10

q = percentile = 90

q/100 = 90/100 = 0.9

q/100 × r = 0.9 × 10 = 9

Therefore, count the 9th number in the ordered set.

⇒ 90th percentile = 176

30th percentile = 105, 90th percentile = 176

Explanation:

data {129, 113, 200, 100, 105, 132, 100, 176, 146, 152}

arrange in ascending order:

{100, 100, 105, 113, 129, 132, 146, 152, 176, 200}

Answer:

I'm not 100% sure but I think it is 200.96 in (201 in if rounded)

Step-by-step explanation:

Answer:

200.96 inches squared

Step-by-step explanation:

The radius of the pizza is 8(half of the diameter).

The formula for are of a circle is pie*radius^2.

So you would do 3.14 * 8^2.

8^2 is equal to 64.

Your new equation is 3.14 * 64, which equals 200.96.

Answer:

[tex]g\geq 17[/tex]

[tex]g > -10[/tex]

[tex]g > -1[/tex]

Step-by-step explanation:

[tex]7(g-19)\geq -14[/tex]

Divide both sides by 7:

[tex]g-19\geq -2[/tex]

Add 19 to both sides:

[tex]g\geq 17[/tex]

[tex]3(7g+17) > -19+14g[/tex]

Expand brackets:

[tex]21g+51 > -19+14g[/tex]

Subtract 14g from both sides:

[tex]7g+51 > -19[/tex]

Subtract 51 from both sides:

[tex]7g > -70[/tex]

Divide both sides by 7:

[tex]g > -10[/tex]

[tex]6(-6g+6) > -2(19g-17)[/tex]

Expand brackets:

[tex]-36g+36 > -38g+34[/tex]

Add 38g to both sides:

[tex]2g+36 > 34[/tex]

Subtract 36 from both sides:

[tex]2g > -2[/tex]

Divide both sides by 2:

[tex]g > -1[/tex]

Answer:24/3/7/5 = 8/ 35 ≅ 0.2285714

Step-by-step explanation:

Divide: 24/3: 7 = 24/3· 1/7

= 24 · 1/3 · 7

= 24/21

= 3 · 8/3 · 7= 8/7

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 7/1 is 1/7) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, cancel by a common factor of 3 gives 8/

7

.

In other words - twenty-four thirds divided by seven = eight sevenths.

Divide: the result of step No. 1 : 5 = 8/7 : 5 = 8/7 · 1/5

= 8 · 1/7 · 5

= 8/35

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 5/1

is 1/5

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the following intermediate step, it cannot further simplify the fraction result by canceling.

In other words - eight-sevenths divided by five = eight thirty-fifths.

Answer:

T is not a function.

Step-by-step explanation:

The definition of a function is a relationship where only one x value has a specific y value. So if an x-value has more than one y value, it is not a function due to its rule. This can also be checked by using a graph, graphing the function, and checking if it fits the vertical line test.

We see all of them work except T, where 2 x values are stated that are the same but have different y values.

So T is not a function.

I hope this helped!

It would be greatly appreciated if you marked this answer as brainliest!

Answer:

17x+7

Step-by-step explanation:

(10x+3)-(-7x-4)

Done!

Answer:

3\sqrt(5)

or 6.71

Step-by-step explanation:

Answer:

Step-by-step explanation:

First find the number of students who stayed home.

# students who stayed home = Total number - the choir members.

Total number = 126

Choir members = 94

Stay at homes = 126 - 94 = 32

Formula

Stay at home % = (32 / 126) * 100

Stay at home %= 0.25397 * 100

Stay at home % = 25.397

To the nearest whole %, the answer is 25

Answer:

126/94 = 1.34

1% of the students stayed at school

Step-by-step explanation:

Answer: 13%

Step-by-step explanation:

Step 1:

5000

10% of 5000=500

5% of 5000=250

25%=500+500+250= 1250 rupees

so...

5000-1250= 3750 INR, which is the original price, BEFORE THE 25% WAS ADDED

but..

They only want a 10% discount of the price which is 25% above the cost (5000). So essentially we want to find  15%, because 25%-10%=15%

so if...

10%=500

5%=250

15%=750 INR

this means the price with the 10% discount off 25%= 4250 INR (5000-750)

now we need to find the percentage change. For this we need to subtract the price with the 15% discount with the price BEFORE THE 25% was added

e.g 4250-3750= 500INR

Then.. divide this price with the original price before the 25% was added

e.g 500/3750= 2/15=0.13

So...

Convert 0.13 into a percentage=13%

The PERCENTAGE PROFIT of the owner is 13%

P.S Please could someone double check this answer as I am only 15 years old and may have gotten some working out wrong! Thank you

Answer:

Below in bold.

Step-by-step explanation:

The triangle ABC is a right triangle as BCD is a tangent.

So m < y = 90 - 30 = 60 degrees

The angle at the centre O = 2*30 = 60 degrees  (angle subtended at centre theorem)
m < x =  180 - 90 - 60 = 30 degrees

Step-by-step explanation:

y = 60

x= 30

these are the answer s

The questions are illustrations of combination and probability

The given parameters are:

Monitors = 4

Keyboard = 2

CPU = 4

Printer = 3

The number of systems to choose from is:

n = 4 * 2 * 4 * 3 = 96

Hence, Patrick can choose from 96 systems

The given parameters are:

Containers = 2

Flavors = 4

The number of total combination to choose from is:

n = 2 * 4C3 = 8

Hence, the number of total combination is 8

The given parameters are:

Blouse = 5

Skirt = 3

Shoes = 4 pairc

The number of ways to dress up:

n = 5 * 3 * 4 = 60

Hence, Emma can dress up in 60 ways

The given parameters are:

Students = 6

Members of committee = 3

The number of ways to form a committee is:

n = 6C3 = 20

Hence, there are 20 ways to form the committee

We have:

Letters = 11

Consonnats = 7

The probability of selecting a consonant is:

P = 7/11

P = 0.636

Hence, the probability of selecting a consonant is: 0.636

We have:

Total students = 34

Students not in grade 8 = 25

The probability that a student is not in grade 8 is:

P = 25/34

P = 0.735

Hence, the probability that a student is not in grade 8 is 0.735

Not enough details to solve

There are 9 prime numbers in a total number of 31 numbers from 4 to 34.

So, the probability that a number is prime is:

P = 9/31

P = 0.290

Hence, the probability that a number is prime is 0.290

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The bag of chips for $2.25 and a 5-pack of juice bottles each bottle of juice costs $1.54.

Let's break down the information given in the problem:

Henry bought a bag of chips for $2.25.

He also bought a 5-pack of juice bottles.

The total cost before tax was $9.95.

Let's represent the cost of each bottle of juice as "x" dollars.

The total cost of the chips and the juice bottles is given as $9.95. So, we can write the equation:

Cost of chips + Cost of 5 juice bottles = Total cost

$2.25 + 5x = $9.95

Now, we can solve for the value of "x" (the cost of each bottle of juice):

5x = $9.95 - $2.25

5x = $7.70

Dividing both sides by 5:

x = $7.70 / 5

x = $1.54

To know more about costs here

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#SPJ3

Answer:

160

Step-by-step explanation:

72=0.45x

72/0.45=x

x=160

Step-by-step explanation:

First, Join OB and OC.

∠BOC = 2∠BAC

(∵ angle subtended by an arc at the centre = double the angle subtended by it at any point on the remaining part of the circle)

=> ∠BOC = 2 x 30°...(∵ ∠BAC = 30°, Given)

=> ∠BOC = 60°

In, ΔOBC, OB = OC...(radii of same circle)

∴ ∠OCB = ∠OBC...(∠s opp. equal sides of a triangle are equal)

As the sum of angles of a traingle is 180°,

∠OBC + ∠OCB + ∠BOC = 180°

∠OBC + ∠OBC + 60° = 180°...(∵∠BOC = 60°,proved above)

2∠OBC = 120° => ∠OBC = 60°

Thus, we have ΔABC such that,

∠BOC = ∠OBC = ∠OCB = 60°

ΔOBC is an equilateral triangle

BC = OB i.e. BC is equal to the radius of circle.