Charles has 24 marbles. He has 6
more yellow marbles than blue marbles.
Which equation represents this situation?

Answer:

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Step-by-step explanation:

Given equation is:

[tex]15sin^2 x+11cosx-17=0[/tex]

To find:

Values of [tex]x[/tex] in the range [tex]0^\circ\leq x\leq180^\circ[/tex].

Solution:

First of all, let us recall one identity of square of sine and square of cosine.

Sum of square of sine of an angle and square of cosine of the same angle is equal to 1.

[tex]\bold{sin^2\theta+cos^2\theta=1}[/tex]

So

Putting [tex]sin^2x=1-cos^2x[/tex] in the given equation.

[tex]15(1-cos^2x)+11cosx-17=0\\\Rightarrow 15-15cos^2x+11cosx-17=0\\\Rightarrow -15cos^2x+11cosx-2=0\\\Rightarrow 15cos^2x-11cosx+2=0\\\Rightarrow 15cos^2x-5cosx-6cosx+2=0\\\Rightarrow 5cosx(3cosx-1)-2(3cosx-1)=0\\\Rightarrow (5cosx-2)(3cosx-1)=0\\\Rightarrow cosx=\dfrac{2}{5}, \dfrac{1}{3}[/tex]

So, in the range [tex]0^\circ\leq x\leq180^\circ[/tex]

[tex]\bold{x = 66.42^\circ, 70.53^\circ}[/tex]

Answer:

1) increases on all interval of x = only g(x)

2) approaches an integer as x approaches -∞ = only f(x)

3) y-intercept at (0, 4) = only g(x)

4) x-intercept at (1, 0) = f(x) and h(x)

Step-by-step explanation:

1) The functions that increases on all interval of x are;

f(x) = -2(3)ˣ + 6 decreases on all interval of x

The function g(x) which is 4 × 4ˣ  increases on all interval of x

The function h(x) is observed to be decreasing as x increases, therefore, the only function that increases on all interval of x = g(x)

2) The function that approaches an integer as x approaches -∞ = -2(3)ˣ + 6

-2(3)ˣ + 6 approaches 6 as x approaches -∞ which is only f(x)

3) The functions that have a y-intercept at (0, 4) is only g(x)

4) The function that have a x-intercept at (1, 0) are f(x) and h(x).

Answer:

A) f(x) and g(x)

B) only g(x)

C) All three functions

D) f(x) and h(x)

Step-by-step explanation:

In my uploaded image on the test I have gotten C) wrong but if you graph all three functions, you can see that all three functions have the same style of -∞

end behavior so I think that would be the most logical answer.

Answer:

x=-3

y=3

(-3-3i)(3+5i)

Step-by-step explanation:

[tex](x-yi)(3+5i)\\=3x+5xi-3yi+5y\\=(3x+5y)+(5x-3y)i\\[/tex]

and we have that must equal

6-24i

3x+5y=6

5x-3y=-24 and if we work it we found out that the solutions are

x=-3 and

y=3

1) 3 is the Coefficient.

2) 10 is the constant.

3) 10.8 is the ans.

Answer: y=18+4x

Step-by-step explanation:  Let y stand for the number of customers the business has in total, and x stand for the number of weeks that have passed. If the business increases by 4 clients per week as described by the scenario, then the range will go as followed: 18, 22, 26, 30...

Answer:

.6

Step-by-step explanation:

First find < ABC

Since this is a right triangle, we can use trig functions

tan < ABC = opp / adj

tan < ABC = 2/4

Take the inverse tan of each side

tan ^-1 tan < ABC =  tan ^-1 2/4

< ABC = 26.56505118

Multiply by 2

53.13010235

Take the cos

cos (53.13010235)

.6

Answer:

y=90 degree

Step-by-step explanation:

bcz this triangle is drawn in the semi-circle and the greatest angle of triangle in a semi-circle is always right angle.

Answer:

6.11km/hr

Step-by-step explanation:

Let the speed that Kelli swims be represented by Y

Speed of the river = 5km/hr

Distance = Speed × Time

Kelli swam upstream for some distance in one hour

Swimming upstream takes a negative sign, hence:

1 hour ×( Y - 5) = Distance

Distance = Y - 5

She then swam downstream the same river for the same distance in only 6 minutes

Downstream takes a positive sign

Converting 6 minutes to hour =

60 minutes = 1 hour

6 minutes =

Cross Multiply

6/60 = 1/10 hour

Hence, Distance =

1/10 × (Y + 5)

= Y/10 + 1/2

Equating both equations we have:

Y - 5 = Y/10 + 1/2

Collect like terms

Y - Y/10 = 5 + 1/2

9Y/10 = 5 1/2

9Y/ 10 = 11/2

Cross Multiply

9Y × 2 = 10 × 11

18Y = 110

Y = 110/18

Y = 6.1111111111 km/hr

Therefore, Kelli's can swim as fast as 6.11km/hr still in the water.

PT.1     Kelli swam upstream for some distance in one hour. She then swam downstream the same river for the same distance in only 6 minutes. If the river flows at 5 km/hr, how fast can Kelli swim in still water?

Choose the most logical value for the variable to represent.

Let x = Kelli's swimming speed in still water

PT.2    Which expression represents the distance Kelli traveled upstream?

1(x – 5)

PT.3     Which expression represents the distance Kelli traveled downstream?

0.1(x + 5)

PT.4     Solve the equation x – 5 = 0.1(x + 5) for x. Round your answer to the nearest hundredth.  Kelli can swim about 6.11  km/hour.

Answer:

10 incorrect answers

Step-by-step explanation:

From the information given, you can say that 5 marks for the number of correct answers minus two marks for the number of incorrect answers is equal to 30 that is the score that Radhika got:

(5*10)-2x= 30, where x is the number of incorrect answers.

Now, you can solve for x:

50-2x=30

50-30=2x

20=2x

x=20/2

x=10

According to this, the answer is that they attempted 10 incorrect answers.

Answer:

Below

Step-by-step explanation:

6)

The sum that we have is 85 +99

We want to express it as the product of a whole number thar is greater than 1 and a sum of two whole numbers.

Notice that: 85 = 84+1

● 85 + 99 = 84 + 1 + 99 = 84 + 100

84 and 100 are even numbers so we can factor using 2.

● 84 + 100 = 2(42 +50)

2 is greater than one and 42+50 is the sum of two whole numbers so all the conditions are satisfied.

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7)

Dasha go on business trips every 9 months while Charlie go every 6 months.

They came back at the same time.

So Charlie has to wait 6 months before going and Dasha nine months.

Dasha will be alone home for 3 months so she doesn't need to hire someone.

Here is what happens:

● Both Dasha and Charlie are home.

● After 6 months Charlie go and Dasha is at home

● after 3 months Dasha goes also and Charlie is home

● after 3 months charlie go and Dasha is home

● after 3 months both are home.

● aftet 3 months they both go

So the period is:

● 6+3+3+3+3 = 18

So after 18 months they should hire someone.

The picture below makes the understanding easier. ( x is Charlie and y is Dasha)

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8)

Pime factorisation

● 96÷2= 48

● 48÷2= 24

● 24 ÷ 2 = 12

● 12 ÷ 2 = 6

● 6÷2 = 3

● 3÷3 = 1

=> 96 = 2 × 2 ×2×2×2 ×3 =2^5 ×3

● 80÷ 2 = 40

● 40 ÷ 2 = 20

● 20÷2 = 10

● 10÷2 = 5

● 5÷5 = 1

=> 80 = 2×2×2×2×5 = 2^4 × 5

So the GCF is 2^4 wich is 16

He can make 16 party

● 80÷16 = 5

There will be 5 boxes of raisin in each one

● 96÷16 = 6

There will be 6 pencils in each party

Answer:

162.5 Cedis

Step-by-step explanation:

Cost Price= 125

Profit % = 30%

Selling price=?

Selling price= Cost price+ profit

Profit = ?

[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]

[tex]30 \% = \frac{x}{125} \times 100[/tex]

[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]

[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]

Profit = 37.5 gh Cedis

Selling price= 125+37.5

Selling price= 162.5 gh Cedis

The selling price of a bag is 162.5Cedis.

It is required to find the selling price.

The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.

Given that :

Let the profit be x.

Cost Price= 125

Profit % = 30%

profit%=profit/cp*100

30=profit/125*100

3750=100x

x=37.5

profit=37.5

Selling price= Cost price+ profit

Selling price=125+37.5

Selling price=162.5ghcedis

So, the selling price of a bag is 162.5Cedis.

Learn more about profit here:

https://brainly.com/question/17189085

#SPJ2

Answer:

A. 2.24

Step-by-step explanation:

Multiply 56 by 0.04

56(0.04)

= 2.24

Answer:

Option A

Step-by-step explanation:

4% * 56 =

0.04 * 56 = (Convert the percent into a decimal.)

2.24 (Multiply)

Hope this helps.

Answer:

4 pints

Step-by-step explanation:

30 quarts ÷ 15 kids = 2 quarts per kid

there are 2 pints in a quart so..

2 quarts per kid x 2 pints per quarter = 4 pints

Answer:

Step-by-step explanation:

A line from the center of the circle to bisect  a chord is perpendicular to the chord.

Therefore, OA⊥ AS

Join O & R

OR is radius of the circle

ΔOAR is right angled triangle.

Use Pythagorean theorem to find OR

OR² = OA² + RA²

       = 3² + 4²

       = 9 +16

OR² = 25

OR = √25

OR = 5 cm

OP  is radius. Therefore, OP = OR = 5 cm

PA = OP + OA

     = 5 + 3

PA = 8 cm

Answer:

A & C

Step-by-step explanation:

A and C have a value of 1.4142 as does the problem in the question.

Answer:

x1 = 0.64575

x2 = -4.64574

Step-by-step explanation:

Step 1: We want to rearrange the equation so all the variables are on one side

0 = -x² - 4x + 3

Step 2: We take out -1 in the first 2 terms so a = 1

0 = -(x² + 4x) + 3

Step 3: Force a square, take the 'b' value and divide it by 2 and square the result. Add it and subtract it from the inside of the brackets

b = 4

4/2 = 2

2² = 4

0 = -(x² + 4x + 4 - 4) + 3

Step 4: Move the -4 out remembering to apply the -

= -(x² + 4x + 4) + 4 + 3

Step 5: We notice is inside the brackets is a perfect square

0 = -(x + 2)² + 7

Therefore the vertex form of the equation is

y = -(x + 2)² + 7

Step 6: We want to solve the equation (find the x intercepts) so we set y to 0 and solve for x

0 = -(x + 2)² + 7

-7 = -(x + 2)²

7 = (x + 2)²

[tex] \sqrt{7 } = x + 2 [/tex]

[tex]x = \sqrt{7} - 2[/tex]

1st Solution:

x = +2.64575 - 2

x = 0.64575

2nd Solution:

x = -2.64575 - 2

x = -4.64574

Answer:

its a mnemonic

Oh  Heck  Another  Hour Of  Algebra

(O = opposite side, H = hypotenuse ) = sine

(A = adjacent side,  H = hypotenuse ) = cosine

(O = opposite side,  A = adjacent ) = tangent

Answer:

The correct option is;

C. Marginal frequency

Step-by-step explanation:

The objective of comparison of two distributions is to check the significant difference from each other

The general measures used to compare the difference between distributions are the measures of centers such as the mean, the measures of spread such as the standard deviation and the shape of the compared distribution curves

Marginal frequencies are the values found in the total row and total column portion of a two way frequency distribution table

The marginal frequency is used to calculate the marginal relative frequency

The values of the marginal frequency, which is a sum, does not characterize the details of a distribution to a large extent.

Answer:

C. Marginal frequency

Step-by-step explanation:

Answer:

Hey there!

Part A. This is a proportional relationship because the amount of dollars she earns per hour is constant. We can divide her total income by the number of hours she works to find that she earns 12.50 dollars per hour.

Part B. Joslyn will always earn more money than Kate because she earns more money per hour, and the slope of Joslyn's line is greater.

Let me know if this helps :)

0.75x+0.8(x + 10) = 101

Answer:

0.75x+0.8(x+10)=101

Step-by-step explanation:

Jared attempted x shots and made 75% of them, or 0.75x. Zach attempted 10 more shots than Jared did, which is represented as x + 10. He made 80% of them, or 0.8(x + 10). Together, they made 101 shots. So, add the two expressions and set the sum equal to 101:

0.75x + 0.8(x + 10) = 101.

Answer:

24

Step-by-step explanation:

What you have here is a permutation, seeing as each element can only be used once.

We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter

However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.

Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.

Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.

Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter

The way to calculate how many permutations we have without repetition is using factorials

N!

Where N is the number of elements you have.

In this case, it would be 4!

4! is 4 * 3 * 2 * 1

Which equals 24

If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on

Answer:

see below

Step-by-step explanation:

The formula for a geometric sequence is

an = a1 * r^ (n-1)  where a1 is the first term and r is the common ratio

The common ratio is  found by taking the second term and dividing it by the first term

a) 1, 2,4.........

a1 = 1

r = 2/1 = 2

an = 1 * ( 2) ^ (n-1)

Let n = 4

a4 = 1 * 2^ (4-1) = 1 * 2^3 = 8

b)50, 20, 8.........

a1 = 50

r = 50/20= 5/2

an = 50 * ( 5/2) ^ (n-1)

Let n = 4

a4 = 50 * (5/2)^ (4-1) = 50 * (5/2)^3 = 3125/4

Using proportions, it is found that Lennox gets 2.5 dollars per kilogram.

During each week:

Hence, the amount of kilograms delivered each week are:

[tex]A = 3(50)(12) = 1800[/tex]

He sells 4500 dollars each week(1800 kilograms), hence, the amount of dollars per kg is:

[tex]D = \frac{4500}{1800} = 2.5[/tex]

Lennox gets 2.5 dollars per kilogram.

To learn more about proportions, you can take a look at https://brainly.com/question/24372153

Answer:0.50

Step-by-step explanation:

Answer:

The answer looks correct.

Step-by-step explanation:

All the other option doesn't match the above question's statement.

The last answer is the correct (in my opinion)

Answer:

Absolutely Correct

Step-by-step explanation:

Based on the definition of midpoint;

It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.

meaning the distance from the midpoint to one end is the same as the distance to the other end

Answer:

8

Step-by-step explanation:

Calculate the distance d using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = z₁(6, 2) and (x₂, y₂ ) = z₂(6, 10)

d = [tex]\sqrt{(6-6)^2+(10-2)^2}[/tex]

   = [tex]\sqrt{0^2+8^2}[/tex]

   = [tex]\sqrt{64}[/tex] = 8

Answer:

x = 4.5

y = 3.25

Step-by-step explanation:

Use elimination

5x + 2y = 29

x + 4y = 13 (-5)

4y(-5) = 13(-5)

2y = 29

-20y = -65

y = 3.25

Sub it back into the equation

5x + 6.50 = 29

5x = 22.5

x = 4.5

Answer:

The answer is

Step-by-step explanation:

To solve the fraction reduce the fraction with d

That's we have

Next simplify the expression using the rules of indices to simplify the letters in the fraction

For c

Since they are dividing we subtract the exponents

We have

For e

Substituting them into the expression we have

Reduce the fraction by 3

We have the final answer as

Hope this helps you

Answer:

[tex]=\left(-\frac{9}{2},\:-\frac{11}{2}\right)[/tex]

Step-by-step explanation:

[tex]\mathrm{Midpoint\:of\:}\left(x_1,\:y_1\right),\:\left(x_2,\:y_2\right):\\\quad \left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)\\\\\left(x_1,\:y_1\right)=\left(-12,\:-3\right),\:\left(x_2,\:y_2\right)=\left(3,\:-8\right)\\\\=\left(\frac{3-12}{2},\:\frac{-8-3}{2}\right)\\\\=\left(-\frac{9}{2},\:-\frac{11}{2}\right)[/tex]

Answer:

positive 35

Step-by-step explanation:

x2 + 3(x + y)        given

4(2) + 3(4+5)         problem

4(2) + 3(9)

8 + 27= 35