In a child's bank are 11 coins that have a value of S1.85. The coins are either
quarters or dimes. How many coins each does child have?
a. Define your variables:
b. Write the equations:
d. Check:
c. Solve:

Use the fact that the co/sine functions are [tex]2\pi[/tex]-periodic and that the tangent function is [tex]\pi[/tex]-periodic. Also, recall that [tex]\cos x[/tex] is even (so that [tex]\cos(-x)=\cos x[/tex]) and [tex]\sin x[/tex] is odd (so that [tex]\sin(-x)=-\sin x[/tex].

15.

[tex]\cos\left(-\dfrac{13\pi}3\right)=\cos\dfrac{13\pi}3=\cos\left(\dfrac\pi3+4\pi\right)=\cos\dfrac\pi3=\boxed{\dfrac12}[/tex]

16.

[tex]\sin\dfrac{23\pi}4=\sin\left(\dfrac{3\pi}4+5\pi\right)=\sin\left(\dfrac{3\pi}4+\pi\right)=\sin\dfrac{7\pi}4=-\dfrac1{\sqrt2}[/tex]

[tex]\implies\csc\dfrac{23\pi}4=\boxed{-\sqrt2}[/tex]

17.

[tex]\cos\left(-\dfrac{7\pi}2\right)=\cos\dfrac{7\pi}2=\cos\left(\dfrac\pi2+3\pi\right)=\cos\left(\dfrac\pi2+\pi\right)=\cos\dfrac{3\pi}2=0[/tex]

[tex]\implies\sec\left(-\dfrac{7\pi}2\right)=\boxed{\text{undefined}}[/tex]

18.

[tex]\tan\left(-\dfrac{29\pi}6\right)=\dfrac{\sin\left(-\frac{29\pi}6\right)}{\cos\left(-\frac{29\pi}6\right)}=-\dfrac{\sin\frac{29\pi}6}{\cos\frac{29\pi}6}[/tex]

[tex]\sin\dfrac{29\pi}6=\sin\left(\dfrac{5\pi}6+4\pi\right)=\sin\dfrac{5\pi}6=-\dfrac12[/tex]

[tex]\cos\dfrac{29\pi}6=\cos\dfrac{5\pi}6=\dfrac{\sqrt3}2[/tex]

[tex]\implies\tan\left(-\dfrac{29\pi}6\right)=-\dfrac{-\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}[/tex]

[tex]\implies\cot\left(-\dfrac{29\pi}6\right)=\boxed{\sqrt3}[/tex]

Answer:

The function has a maximum

The maximum value of the function is

[tex]f (-1) = 11[/tex]

Step-by-step explanation:

For a quadratic function of the form:

[tex]ax ^ 2 + bx + c[/tex] where a, b and c are the coefficients of the function, then:

If [tex]a <0[/tex] the function has a maximum

If [tex]a> 0[/tex] the function has a minimum value

The minimum or maximum value will always be at the point:

[tex]x=-\frac{b}{2a}\\\y=f(-\frac{b}{2a})[/tex]

In this case the function is: [tex]f(x) = -5x^2 - 10x + 6[/tex]

Note that

[tex]a = -5,\ a <0[/tex]

The function has a maximum

The maximum is at the point:

[tex]x=-\frac{-10}{2(-5)}[/tex]

[tex]x=-1[/tex]

[tex]y=f(-1)[/tex]

[tex]y= -5(-1)^2 - 10(-1) + 6[/tex]

[tex]y= 11[/tex]

The maximum value of the function is

[tex]f (-1) = 11[/tex]

The function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum value at the vertex of its parabola. The maximum value is f(x) = 11 when x = -1.

To determine whether the quadratic function [tex]f(x) = -5x^2 - 10x + 6[/tex] has a maximum or a minimum value, we need to examine the coefficient of the [tex]x^2[/tex]term. The general form of a quadratic function is [tex]f(x) = ax^2 + bx + c.[/tex] If 'a' is negative, the parabola opens downwards, and the function has a maximum value at its vertex. In this case, 'a' is -5, which is negative, so the function has a maximum value.

To find the vertex of the parabola, we use the formula for the x-coordinate of the vertex, which is given by -b/(2a). Here, a = -5 and b = -10. Plugging these values into the formula gives us:

x = -(-10) / (2 * (-5))

x = 10 / -10

x = -1

Now that we have the x-coordinate of the vertex, we can find the y-coordinate (the maximum value) by substituting x = -1 into the original function:

[tex]f(-1) = -5(-1)^2 - 10(-1) + 6[/tex]

f(-1) = -5(1) + 10 + 6

f(-1) = -5 + 10 + 6

f(-1) = 5 + 6

f(-1) = 11

Therefore, the maximum value of the function [tex]f(x) = -5x^2 - 10x + 6[/tex] is 11 when x = -1. This is the value at the vertex of the parabola, confirming that it is the maximum value since the parabola opens downwards.

Answer:

38.72 change

Step-by-step explanation:

153.6 x 1.05 = 161.28

100 x 2 = 200

200-161.28 = 38.72

Answer:

42.36

Step-by-step explanation:

Answer:

$97.24

Step-by-step explanation:

You can use a direct proportion.

175 is to $52.36 as 325 minutes is to x.

Use two ratios of minutes/dollars:  

175/52.36 = 325/x

Cross multiply.

175x = 52.36 * 325

175x = 17,017

x = 17,017/175

x = 97.24

Answer: $97.24

Answer:

Step-by-step explanation:

Recall that an equilateral triangle has three equal interior angles, all 60°.  Let b represent the length of the base.  Draw a dashed line from the upper vertex to the base, perpendicularly.  This dashed line represents the height or altitude of the triangle.  

Now construct a triangle whose opposite side is this altitude, whose hypotenuse is b (and whose base is (1/2)b).

The altitude (opp) is then given by sin Ф = opp / hyp = opp / b.  Solving this for the altitude (opp), we get b·sin 60°:

alt (opp)       √3

------------- = ------

  hyp             2

                                                b·√3    

so that 2 alt = b·√3, or alt = ------------

                                                    2

Thus, for any equilateral triangle of side length b, the height of the triangle is

                             √3

alt = height = b · ------

                               2

Please note:  Your problem statement refers to "the equilateral triangle below."  It's important that you share such illustrations, along with all instructions.  In this case your question was general enough so that I could use the definitions of "sine," "equilateral," etc., to come up with a general answer.

Answer:

do u have a pic i can see

Step-by-step explanation:

Answer:

x+7

Step-by-step explanation:

let x= the amount of money he got that day

he gains $7/day

x+7

Answer: he spends 2.5 hours in the weight room each week.

Step-by-step explanation: 2.5 multiplied by 2 (which is the twice amount of time spent working out in the pool) is 5.

So the answer is 2.5

Answer:

135 degrees

Step-by-step explanation:

Coterminal means it ends at the same spot around the circle.

To calculate the resulting angle we need to reduce/increase the started value to arrive to a value between 0 and 359 degrees.  

If the starting angle is greater or equal to 360, we subtract 360 until we get below 360.

If the starting angle is below 0, we add 360 until we get equal or greater than 0.

So, starting with 495, we subtract 360 a first time....

A = 495 - 360 = 135

We're already in the desired range (0-359)... so we have our answer.

Answer:

Step-by-step explanation:

15/27 - 5/9

5:9

5 to 9 ratio

Answer:

Step-by-step explanation:

It’s is a because if you divide 4.41 divide by 3 you will get 1.47

Step-by-step explanation:

1 yard = 3 feet

So 3 yards = 9 feet

$4.41 / 9 feet = $0.49 per foot

$1.05 / 3 feet = $0.35 per foot

The second one is cheaper, so that's the better buy.

Answer:

33.75

Step-by-step explanation:

find 35 % of 25 then add that to 25.

He sold the ticket at $33.75.

Markup is the amount by which a product is sold above its cost price.

It is given that

Cost Price of the ticket is $25

Selling price = ?

Markup = 35%

Selling Price = 1.35 * 25 = $33.75

Therefore he sold the ticket at $33.75.

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Answer:

B 78 students

Step-by-step explanation:

The answer is d. 132 students

Answer:

151

Step-by-step explanation:

because 225-74 =151

151 books

There are 225 books, and 74 have already been placed on the shelf. Subtract 225 minus 74 to find that Ivan needs to place 151 more books on the shelf.

Answer: The system of equations has no solutions.

Step-by-step explanation:

Identify the equation as:

[tex]x + 2y - z=3[/tex]   [Equation 1]

[tex]2x -y + 2z=6[/tex]    [Equation 2]

[tex]x - 3y + 3z=4[/tex]    [Equation 3]

Multiply  [Equation 1]  by -2 and add this to [Equation 2] :

[tex](-2)(x + 2y - z)=3(-2)[/tex]

[tex]\left \{ {{-2x - 4y +2z=-6} \atop {2x -y + 2z=6}} \right.\\ ..........................\\-5y+4z=0[/tex]

 Find another equation of two variables: Multiply  [Equation 3]  by -2 and add this to [Equation 2]:

[tex](-2)(x - 3y + 3z)=4(-2)[/tex]  

[tex]\left \{ {{2x -y + 2z=6} \atop {-2x +6y -6z=-8}} \right.\\........................\\5y-4z=-2[/tex]

Then you get this new system of equations. When you add them, you get:

[tex]\left \{ {{-5y+4z=0} \atop {5y-4z=-2}} \right.\\..................\\0=-2[/tex]

Since the obtained is not possible, the system of equations has no solutions.

The solution to the system of equations x + 2y - z = 3, 2x - y + 2z = 6, and x - 3y + 3z = 4 is (-1, 1, 2) utilizing substitution method.

The subject of this question is to find a solution to the system of linear equations. We can solve this system by methods of either substitution, elimination or matrix - but let's use substitution. First, let's isolate x in the first equation: x = 3 - 2y + z. Then we substitute x into the second and the third equation:

After simplifying these equations, we find y = 1 and z = 2. Plugging these back into x = 3 - 2y + z, we get x = -1. Therefore, the solution to the system is (-1, 1, 2).

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Answer:

44

Step-by-step explanation:

0.5 m - 0.75 n = 16

Substitute n = 8 into the equation  

0.5 m - ( 0.75 × 8 )  = 16

0.5 m - 6  = 16

( Add 6 to both sides )

0.5 m = 26

( Divide by 0.5 )

m = 52

Answer:

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

The equation of a proportional relation is of the form

y = kx,

where k is a number.

Here you have

3 - 6x = y,

which can be rewritten as

y = -6x + 3

Because of the +3, your equation is not for the form y = kx, and it is not a proportional relation.

There are 50 degrees in angle c

Answer: A. 50°

Step-by-step explanation:

Since the measure angles of a triangle add up to 180° and the right triangle=90°, therefore when you subtract 180-90-40, you get 90-40, which then equals to 50°.

Answer:

2. The correct answer option is 25%.

3. The experimental probability is 3% greater than the theoretical probability.

Step-by-step explanation:

2. We are given that a number cube is rolled 20 times out of which 5 times it lands on the number 2.

We are to find the experimental probability of getting the number 2.

P (2) = [tex]\frac{5}{20} \times 100 =\frac{1}{4} \times 100[/tex] = 25%

3. The theoretical Outcomes are: HH HT TH TT

So theoretical probability of getting HH = [tex]\frac{1}{4} \times 100[/tex] = 25%

Total number of outcomes = [tex]28+22+34+16[/tex] = 100

So experimental probability of getting HH = [tex]\frac{28}{100} \times 100[/tex] = 28%

Therefore, the experimental probability is 3% greater than the theoretical probability.

Answer:

The probability that the candy picked is not grape flavored would be 4/5

Step-by-step explanation:

We are given that a bag contains 10 pieces of flavored candy. 4 lemon, 3 strawberry, 2 grape and 1 cherry. The probability that the candy picked is not grape flavored is calculated as;

(number of candy that are not grape flavored)/ ( total number of candy in the bag)

= (4+3+1)/(10)

= 8/10

=4/5

Therefore, the probability that the candy picked is not grape flavored would be 4/5

To find the probability that a randomly picked candy is not grape flavored, we will follow these steps:

1. Count the total number of pieces of candy in the bag. This is the sum of all the different flavors of candy:
  - 4 lemon candies
  - 3 strawberry candies
  - 2 grape candies
  - 1 cherry candy
  The total number is 4 + 3 + 2 + 1 = 10 candies.

2. Count the number of candies that are not grape flavored. Since there are 2 grape candies, the number of candies not grape flavored is the total minus the grape candies:
  10 (total candies) - 2 (grape candies) = 8 candies that are not grape flavored.

3. Calculate the probability of picking a non-grape flavored candy. Probability is the number of favorable outcomes divided by the total number of possible outcomes. In our case, the favorable outcomes are the instances where we pick a non-grape flavored candy, and the total possible outcomes are picking any candy from the bag:
  Probability (not grape flavored) = Number of non-grape flavored candies / Total number of candies
  Probability (not grape flavored) = 8 / 10

4. Simplify the fraction, if needed. In this case, the fraction 8/10 can be simplified to 4/5 by dividing both the numerator and denominator by the greatest common divisor, which is 2.

Therefore, the probability of picking a candy that is not grape flavored from the bag is 4/5, or 80% if expressed as a percentage.

The answer is:

The piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]

To find the correct option, we need to look for the piecewise function that contains the following functioncs existing in the determined domains (inputs).

From the graph, we know that we need the following functions:

- A horizontal line, which exists from -∞ to -1, givind as input 8.

The function will be:

[tex]y=8[/tex]

Then, the piecewise function it will be:

[tex]8; x\leq -1[/tex]

- A quadratic function (convex parabola) which y-intercept is equal to 1, exists from -1 to 5, and it vertex (lowest point for this case) is located at (2,-3)

The function will be:

[tex]y=x^{2}-4x+1[/tex]

Finding the y-intercept, we have:

[tex]y=0^{2}-4*80)+1[/tex]

[tex]y=1[/tex]

Finding the vertex of the parabola, we have:

[tex]x_{vertex}=\frac{-b}{2}\\\\x_{vertex}=\frac{-(-4)}{2}=\frac{4}{2}=2[/tex]

[tex]y_{vertex}=x_{vertex}^{2}-4x_{vertex}+1[/tex]

[tex]y_{vertex}=2^{2}-4*2+1=4-8+1=-3[/tex]

The vertex of the parabola is located at the point (2,-3).

Then, for the piecewise function it will be:

[tex]x^{2} -4x+1;-1<x<5[/tex]

- A negative slope function, which evaluated at x equal to 5 (input), gives as output -4.

The function will be:

[tex]y=-x+1[/tex]

Proving that it's the correct equation by evaluating "x" equal to 5, we have:

[tex]y=-5+1[/tex]

[tex]y=-4[/tex]

It proves that the equation is correct.

Then, for the piecewise function it will be:

[tex]-x+1\geq 5[/tex]

Hence, we have that the piecewise function that represents the graph, is the option A (first option):

f(x) (piecewise function):

[tex]8; x\leq -1\\\\x^{2} -4x+1;-1<x<5\\\\-x+1\geq 5[/tex]

Have a nice day!

Answer:

C. 3.3 • 10^-7

Step-by-step explanation:

(1.1•10^-5)(3 •10^-2)

Multiply the numbers out front of the powers of ten, then add the exponents on the powers of 10

1.1 * 3   * 10 ^(-5+-2)

3.3 ^ (-7)

Answer:

C

Step-by-step explanation:

Do you mean irrational?

X^2-4x+4 is the answer, to save you points next time, use an app called M8thw8y

First you want to drop the parenthesis. If there is a “+” sign, you do not have to change anything. If there is a “-“ sign, you have to distribute the negative in order to simplify, so imagine you are distributing -1 to 7x + 3 to make it -7x -3.

So, you now have x^2 + 3x - 4 + 16 -5 - 7x -3. (I evaluated the 4^2 to 16)

Now, what you want to do now is to combine like terms. Notice that there is only one x^2, so it is the same. There are two terms that have “x”. 3x and -7x react like normal numbers and they form -4x. The numbers who don’t have x on them you combine like terms.

Answer is x^2 - 4x - 12

Answer:

SSS, SAS, ASA, AAS, and HL. These tests describe combinations of congruent sides and/or angles that are used to determine if two triangles are congruent.

Step-by-step explanation:

[tex]\bf \cfrac{7^2}{2x+6}\div \cfrac{3x-5}{x+3}\implies \cfrac{7^2}{2x+6}\cdot \cfrac{x+3}{3x-5}\implies \cfrac{49}{2~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}}\cdot \cfrac{\begin{matrix} x+3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix} }{3x-5}\implies \cfrac{49}{2(3x-5)}[/tex]

(540 + 540 + 900 + 900) + (2160) = (Surface area of Lateral faces) + (Top) = 5040 sq cm.

5040 / 720 = dishes of craft paint = 7 dishes

Answer:

7 dishes

Step-by-step explanation:

It’s the first one and the third one

Answer: A and C

Step-by-step explanation:

It an expression or a way of saying f(x)=6x2+12-7

Answer:

[tex]x=-1+\frac{\sqrt{78} }{6}[/tex] and

[tex]x=-1-\frac{\sqrt{78} }{6}[/tex]

Step-by-step explanation:

[tex]f(x) = 6x^2 + 12x - 7[/tex]

To find out the zeros of the quadratic function, we apply quadratic formula

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

From the given f(x), the value of a=6, b=12, c=-7

Plug in all the values in the formula

[tex]x=\frac{-12+-\sqrt{12^2-4(6)(-7)}}{2(6)}[/tex]

[tex]x=\frac{-12+-\sqrt{312}}{2(6)}[/tex]

[tex]x=\frac{-12+-2\sqrt{78}}{2(6)}[/tex]

Now divide each term by 12

[tex]x=-1+-\frac{\sqrt{78} }{6}[/tex]

We will get two values for x

[tex]x=-1+\frac{\sqrt{78} }{6}[/tex] and

[tex]x=-1-\frac{\sqrt{78} }{6}[/tex]

Answer: 500 dollars

You just plug in 100 to the x’s in the equation

The company's profit be if 100 games are sold is $41100

The profit function is given as:

[tex]p(x) = -0.3x^2 + 45x - 1000[/tex]

When the number of games is 100, it means that

x = 100

So, we substitute 100 for x in the profit function

[tex]p(x) = -0.3x^2 + 45x - 1000[/tex] becomes

[tex]p(100) = -0.3(100)^2 + 45(100) - 1000[/tex]

Evaluate the exponents

[tex]p(100) = -0.3(10000) + 45(100) - 1000[/tex]

Open all brackets

[tex]p(100) = -3000 + 45100 - 1000[/tex]

Evaluate like terms

[tex]p(100) = 41100[/tex]

Hence, the company's profit be if 100 games are sold is $41100

Read more about quadratic functions at:

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Answer:

11 units

Step-by-step explanation:

Since ∆ABC is isosceles, it means that at least two sides are congruent/equal in length.

Sides CA and AB are congruent, since BC is the base. So, CA = 4.

That means the perimeter is 4 + 4 + 3 = 11 un