The baseball team sold $1,340 in tickets one Saturday. The number of $12 adult tickets was 15 more than twice the number of $5 child tickets. How many of each were sold?

Answer:

[tex]\log_4{(16384)}=7[/tex]

Step-by-step explanation:

The base of the exponent is the base of the logarithm. The exponent is the logarithm. The value the exponential expression is equal to is the argument of the logarithm.

Answer:3 percent because

Answer:

Percent = 62.5%

Step-by-step explanation:

Answer:

true statement

Step-by-step explanation:

Substituting a solution back into the original equation will make the equation true.

Answer: 7/8

Step-by-step explanation:

think of each faction as a pie or pizza.

each one will have the number of slices as the bottom number of the fraction.

now shade in the top numbers and see if it more than your 1/2

you will see 7/8 is the answer since it will be one piece left from being complete or "gone"

hope this helped angel!!

Answer:

Step-by-step explanation:

Answer:

The problem can not be solved since  information is missing.

The coldest surface temperature of the moon needs to be given in the text.

THIS IS THE ACTUAL ANSWER

NO JOKE

Answer:

y=-6

Step-by-step explanation:

y=-4(2)+2

y=-8+2

y=-6

(2,-6)

Answer:

y = - 6

Step-by-step explanation: You have to substitute 2 for x in order for you to get your solution.

y = - 4x + 2

y = - 4(2) + 2

y = - 8 + 2

y = - 6

Hope this helps you!!! :)

Answer:

x<=11

Step-by-step explanation:

2(x-3 ) <= 16

Distribute the 2

2x -6 <= 16

Add 6 to each side

2x -6+6<= 16+6

2x <= 22

Divide by 2

2x/2 <= 22/2

x<=11

This can be represented by the inequality:

3x + 0.75 ≥ 4.5

Inequality shows the non-equal comparison between two numbers or mathematical expressions.

Let x represent the price of milk per gallon.

Since the price of milk tripled, and then rose another $0.75 per gallon, hence:

Price of milk = 3x + 0.75

The price is now is AT LEAST $4.50 per gallon, hence this can be represented by the inequality:

3x + 0.75 ≥ 4.5

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Answer:

its called line FGH

Step-by-step explanation:

its because the line is FGH

Hope this helps :)

A line is named by two of the points on the line, with a line drawn above the letters.

For the line in the attached image, the answer would be the first choice.

Answer:

[tex]\sqrt{3} * /sqrt{16} = 4\sqrt{3}[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

square root of 3 times the square root of 16 looks like this

[tex]\sqrt{3} .\sqrt{16}[/tex]

we try to break the numbers inside the radical to there prime factors

so

[tex]\sqrt{3} .\sqrt{2.2.2.2}[/tex]

the prime factors which are in pair , comes out of the radical so

[tex]\sqrt{3} .2.2[/tex]

which simplifies to

[tex]4\sqrt{3}[/tex]

Answer:

B

Step-by-step explanation:

i took a test with this question

We want to see which one of the given relations is a function.

The correct options are:

B and C.

To see this, we first need to define what a function is.

A function is a relationship that maps elements from one set, the domain, into another set, the range.

Such that each element in the domain can be mapped into only one element on the range.

The standard notation to these relations is (x, y).

This means that x, from the domain, is being mapped into y, from the range.

Now let's analyze the given options:

A) {3,7,-7,9}

This is just a set of values, no relation there, so this is not a function.

B)  { (3,9), (7,-4), (-7,7) }

Here we have a relation, and we can see that each element on the domain is being mapped into only one element from the range, so this is a function.

C)  { (3,9), (7,-4), (-7,7) }

This is the exact same set as the one on B.

D)  { (3,9), (7,-4), (7,6), (-7,7) }

Here we can see that the element x = 7 is mapped into two different values, so this is not a function.

Then the options that represent functions are B and C.

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Answer:

I would say A. 7.8 x 10^-5

Step-by-step explanation:

7.8 x 10^-5 can also be written as 7.8 times 10 to the negative fifth power or the exponent of negative five. But, if you solve it you would get 0.000078 as the real number.

Answer:

Yes she did

Step-by-step explanation:

There is .75 yards and she cut .1125 of it, it make it 15% as .75 x .15 = .1125

None of these questions have anything to do directly with the polynomial remainder theorem. The theorem says that the remainder upon dividing a polynomial [tex]p(x)[/tex] by [tex]x-c[/tex] is given by the value of [tex]f(c)[/tex].

For these questions, all you really have to do is evaluate the given polynomials at the given points, and IMO is much less work.

Question 2: [tex]f(5)=4(5)^2-5(5)+2=77[/tex]

Question 3: [tex]f(4)=3(4)^4-8)4)^2-2(4)+12=644[/tex]

Question 4: Here you have check the value of [tex]h(x)[/tex] and 2 and -2, then interpret them as points in the coordinate plane, [tex](x,h(x))[/tex].

[tex]h(-2)=2(-2)^5-4(-2)^4-2(-2)^2+15=-121[/tex]

[tex]h(2)=2(2)^5-4(2)^4-2(2)^2+15=7[/tex]

Question 5: Same as in question 4, but you have to check [tex]h(x)[/tex] at -4, -3, -2, -1.

[tex]h(-4)=72[/tex]

[tex]h(-3)=46[/tex]

[tex]h(-2)=26[/tex]

[tex]h(-1)=12[/tex]

- - -

If you insist on using the polynomial remainder theorem, it's a question of polynomial division. For instance, in question 2 you'd compute

[tex]\dfrac{4x^2-5x+2}{x-5}=4x+15+\dfrac{77}{x-5}\implies4x^2-5x+2=(4x+15)(x-5)+77[/tex]

so the remainder is 77, as we found by simply computing [tex]f(5)[/tex].

Answer:

f(x) = 3x-8

Step-by-step explanation:

y −4 = 3 (x − 4)

We want to write the equation in y = mx+ b form

Distribute the 3

y-4 = 3x -3*4

y-4 = 3x -12

Add 4 to each side

y -4+4 = 3x-12+4

y = 3x-8

Since the want it in function form,  f(x)

f(x) = 3x-8

Answer:

Option A is correct.

Inequality represents the sale s in dollars:

[tex]0.025s\geq 100[/tex]

[tex]s> 4000[/tex]

Step-by-step explanation:

Let s represents the sales in dollars.

Given :A salesperson at a clothing store earns a commission of 2.5% on all the sales he makes.

Earns a  Commission = 2.5% of s = [tex]\frac{2.5}{100} \times s = \frac{25s}{1000} = 0.025s[/tex]

It is also given that he needs to make to earn a commission of more than $100

then, we have an inequality:

[tex]0.025s\geq 100[/tex]

divide both sides by 0.025 we get;

[tex]s> 4000[/tex]

Therefore, an inequality represents the sales in dollar ; [tex]0.025s\geq 100[/tex] or [tex]s> 4000[/tex]

Answer:

s > 4,000, s > 4,000

Step-by-step explanation:

Since he needs to make $100 the choices that give him $100 or more are correct.

Answer:

option: A is correct

Step-by-step explanation:

kaisa's claim is incorrect. clearly the sum of the three angles is 180 degrees therefore we could easily create a triangle with the help of this information but we can't say that this traingle will be unique so we need to know some more information regarding its side.hence multiple triangles could be drawn with these angle measures.

hence option A is correct.

Answer:

A

Step-by-step explanation:

Answer:

the answer is d

Step-by-step explanation:

you can tell because it's past 2 and close to 3. it's -5 because it's past -4. so their is your answer to why it's d

The ordered pair that represents point P on the graph is **D) (3, -5)**. Point P lies in the fourth quadrant, where both the x-coordinate (3) and the y-coordinate (-5) are positive.

Answer:

[tex]\frac{3\sqrt{13} }{2}[/tex]

Step-by-step explanation:

First we have to identify the parallel sides of the trapezium.

We know that the slopes are equal for parallel lines.

Slope of (x₁,y₁) and (x₂,y₂) is given by

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Slope of AB:

[tex]m_{AB} = \frac{3-5}{3-0}=-\frac{2}{3}[/tex]

Slope of BC:

[tex]m_{BC} = \frac{-2-3}{5-3}=-\frac{5}{2}[/tex]

Slope of CD:

[tex]m_{CD} = \frac{2+2}{-1-5}=-\frac{4}{6}=-\frac{2}{3}[/tex]

Slope of DA:

[tex]m_{DA} = \frac{2-5}{-1-0}=3[/tex]

We see that the slopes of AB and CD are equal, so, AB and CD are the parallel sides.

The length of the midsegment = (1/2)*(length of base1 + length of base2 )

Length of the bases can be calculated using distance formula,

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

AB = [tex]\sqrt{(3-0)^{2}+(3-5)^{2}}= \sqrt{9+4} =\sqrt{13}[/tex]

CD = [tex]\sqrt{(-1-5)^{2}+(2+2)^{2}}= \sqrt{36+16} =\sqrt{52}=2 \sqrt{13}[/tex]

Length of the midsegment = (1/2) (√13 + 2√13) =3√13/2

Answer:

Step-by-step explanation:

factor the trinomial: (3x-1)(2x+1)=0

x = 1/3 or -1/2

Answer:

The number of black ink pen are 15 pens.

Step-by-step explanation:

As given

Jared bought a package of pens containing 20 pens.

[tex]if\ \frac{3}{4}\ of\ the\ pens\ have\ black\ ink.[/tex]

Thus

[tex]Number\ of\ black\ ink\ pens = \frac{3}{4}\times Total\ number\ of\ pens[/tex]

Putting the value

[tex]Number\ of\ black\ ink\ pens = \frac{3}{4}\times 20[/tex]

Number of black ink pens = 3 × 5

                                          = 15 pens

Therefore the number of black ink pen are 15 pens.

Jared has 15 pens with black ink, which is calculated by multiplying 3/4 by the total number of pens he has (20 pens).

To determine the number of pens with black ink that Jared has, you need to multiply the total number of pens by the fraction representing the pens with black ink. Jared has a package containing 20 pens, and 3/4 of these have black ink. Here's how you calculate it:

Find the fraction of pens with black ink: 3/4 of the pens.

Multiply this fraction by the total number of pens: 3/4 × 20 pens.

Calculate the product to find the number of pens with black ink: 3/4 × 20 = 15 pens.

Therefore, Jared has 15 pens that contain black ink.

The number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.

Suppose that a function is defined as;

[tex]y = f(x)[/tex]

Then, suppose that we want to know the instantaneous rate of the growth of the function with respect to the change in x, then its instantaneous rate is given as:

[tex]\dfrac{dy}{dx} = \dfrac{d(f(x))}{dx}[/tex]

Assuming that the bacterial growth can be approximated by a continous and differentiable function y = f(x), where x represents the number of hours spent from the initial time, we're given that:

Supposing the proportionality constant be k, then we get:

[tex]\dfrac{dy}{dx} = ky[/tex]

Solving this differential equation, we get:

[tex]\dfrac{dy}{y} = kdx\\\\\text{Integrating both the sides without limits}\\\\\int \dfrac{dy}{y} = \int x dx\\\\\ln(y) + \ln(c) = kx\\\\\ln(yc) =kx\\ yc = e^{kx}\\y = \dfrac{e^{kx}}{c}[/tex]

where ln(c) represents the integration constant. (we took ln(c) because, firstly, ln's range is whole real number (which gives us the access to use it as integration constant), and secondly that it can merge with ln(y) to simplify the work)

Since we're given that:

At x = t (for some value of t in hours), we're given that y = 500,

and for x = t+2, y = 1000,

so we get two equations as:

[tex]\\500 = \dfrac{e^{kt}}{c}\\\\1000 = \dfrac{e^{k(t+2)}}{c}\\[/tex]

Thus, we get:

[tex]\dfrac{e^{kt}}{500} = \dfrac{e^{k(t+2)}}{1000} \\\\kt = \ln(0.5) + k(t+2)\\\\k = \dfrac{-\ln(0.5)}{2}} \approx 0.3465[/tex]

Thus, we get:

[tex]\\500 = \dfrac{e^{kt}}{c} \\\\c = \dfrac{e^{0.3465t}}{500}[/tex]

Thus, we get:

[tex]y = \dfrac{e^{0.3465x}}{\dfrac{e^{0.3465t}}{500}} = 500e^{0.3465(x-t)[/tex]

Let from the initial given time t, it takes h hours more for bacterias to be 2500, then we get:

[tex]2500 = 500 \times e^{0.3465 (t+h - t)}\\0.3465(h) = \ln(5)\\\\h = \dfrac{\ln(5)}{0.3465} = 4.644 \: \rm hours \: approx.[/tex]

Thus, the number of hours from the initial given time that will take for the bacteria to grow to 2500 number is 4.64 hours approx.

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Look at the picture.

(x, y) → (x + 2, y)

Translate the graph of f(x) 2 units right.

-------------------------------------------------------------

(x, y) → (x, y + n) - translate the graph n units up

(x, y) → (x, y - n) - translate the graph n units down

(x, y) → (x - n, y) - translate the graph n units left

(x, y) → (x + n, y) - translate the graph n units right

Answer: 200 messages

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

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Plan A's cost equation is y = 0.10x + 30

Plan B's cost equation is y = 50

Equate the two right hand sides, then solve for x

0.10x + 30 = 50

0.10x = 50-30

0.10x = 20

x = 20/0.10

x = 200

If you send/receive 200 messages, then the two plans will both cost the same ($50) per month.

Answer:

C

Step-by-step explanation:

using the cosine ratio to find p

cos 45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{p}[/tex]

cross- multiplying gives

p × cos45° = 6 → [ cos 45° = [tex]\frac{1}{\sqrt{2} }[/tex]]

p × [tex]\frac{1}{\sqrt{2} }[/tex] = 6

multiply both sides by [tex]\sqrt{2}[/tex]

⇒ p = 6[tex]\sqrt{2}[/tex] ( third option on list )

To determine the value of p in simplest radical form, solve the equation by simplifying the denominator and taking the square root of both sides. The value of p is 2.

To identify the value of p, we need to solve the equation and simplify it to the simplest radical form. Let's start by simplifying the denominator and expressing it as a perfect square.

Next, we can take the square root of both sides of the equation to eliminate the square. This will help us isolate p. Once we do that, we can solve for p by getting rid of the square root on the left side of the equation. After simplifying, we find that p = 2.

So, the value of p is 2.

Answer:3/5

Step-by-step explanation:

First we change 500% to fractions

Changing percentage to fraction is dividing the number by 100

500% = 500/100

Putting this we get 3/(500/100)

Then when a number is being divided by a fraction, to get the answer, we multiply the number by the inverse of the fraction

3/(500/100) = 3 x 100/500 = 300/500 = 3/5

If contaminant is found in a solution at a level of 3/500%. Then 3/5  is fraction of the solution

A fraction represents a part of a whole.

Given,

A contaminant is found in a solution at a level of 3/500%

Let us convert five hundred percentage to a fraction.

500% is converted to fraction by dividing 500/100

So let us divide three by 500/100

3/ (500/100)

When a fraction is divided with another fraction, then the denominator is multiplied inversely with numerator

3×100/500

=300/500

3/5

Hence if contaminant is found in a solution at a level of 3/500%. Then 3/5  is fraction of the solution

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Answer:

We are given that a fair coin is tossed 3 times.

We know that if a fair coin is tossed 3 times, then there are 8 possible outcomes.

(a) what is the sample space for this chance process?

The sample space associated with tossing a fair coin three times are:

Ω = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

Where:

H denotes the head and T denotes the tail.

(b) what is the assignment of probabilities to outcomes in this sample space?

We are given that a fair coin is tossed 3 times, which means that all the possible outcomes in the above mentioned sample space has equal chance being selected. Therefore, the assignment of probabilities to outcomes in this sample space is same for all outcomes and is given below:

[tex]p= \frac{1}{8}[/tex]

Answer:

A. 33

B. k=32

C. 1

D. [tex]\pm 1,\ \pm 2,\ \pm 4[/tex]

E. [tex]B=-2,\ D=5[/tex]

Step-by-step explanation:

In all parts for the quadratic equation [tex]ax^2+bx+c=0[/tex] use Vieta's formulas

[tex]x_1+x_2=-\dfrac{b}{a},\\ \\x_1\cdot x_2=\dfrac{c}{a},[/tex]

where [tex]x_1,\ x_2[/tex] are the roots of the quadratic equation.

A. For the equation [tex]x^2-5x-4=0,[/tex]

[tex]x_1+x_2=5,\\ \\x_1\cdot x_2=-4.[/tex]

Then

[tex](x_1+x_2)^2=x_1^2+2x_1\cdot x_2+x_2^2,\\ \\5^2=x_1^2+x_2^2+2\cdot (-4),\\ \\x_1^2+x_2^2=25+8=33.[/tex]

B. One of the roots of [tex]x^2+12x+k=0[/tex] is twice the other root, then [tex]x_2=2x_1.[/tex] By the Vieta's formulas,

[tex]x_1+x_2=3x_1=-12,\\ \\x_1\cdot x_2=2x_1^2=k.[/tex]

Then [tex]x_1=-4[/tex] and [tex]k=2x_1^2=2\cdot (-4)^2=2\cdot 16=32.[/tex]

C. The sum of the roots of the quadratic  [tex]4x^2-4x-4[/tex] is [tex]-\dfrac{b}{c}=-\dfrac{-4}{4}=1.[/tex]

D. Note that

[tex](Ax+B)(Cx+D)=ACx^2+x(AD+BC)+BD,[/tex]

then [tex]AC=a=4.[/tex] If [tex]A,\ B,\ C,\ D[/tex] are integers, then you should check [tex]A=\pm 1,\ \pm 2,\ \pm 4.[/tex]

E. Consider [tex]3x^2 - x - 10 = (x + B)(3x + D).[/tex] Note that

[tex]x_1+x_2=\dfrac{1}{3},\\ \\x_1\cdot x_2=-\dfrac{10}{3}.[/tex]

Then

[tex]x_1=2,\ x_2=-\dfrac{5}{3}.[/tex]

Then [tex]3x^2 - x - 10 = (x -2)(3x+5),[/tex] hence [tex]B=-2,\ D=5.[/tex]

A. The sum of the squares of the roots is 33, B. k = 32, C. The sum of the roots is 1, D. The possible values he should check are ±1, ±2, ±4, E. The ordered pair (B, D) is (2, -5).

Let's solve each part of the problem step-by-step:

A. First, find the roots of the quadratic equation using Vieta's formulas:

Now, the sum of the squares of the roots is given by: (α² + β²) = (α + β)² - 2αβ. Substituting the known values:
Hence, α² + β² = 25 - (-8) = 25 + 8 = 33.

B. Let the roots be α and 2α. Using Vieta's formulas again:

C. The sum of the roots is given by -b/a:

D. The quadratic can be written as 4x² + bx + c. The coefficient of x² on the right-hand side must be AC. Since a = 4:

E. The quadratic can be factored as (x + B)(3x + D). Let's determine B and D:

Thus, the ordered pair (B, D) is (2, -5).