Match the expression with its name 3x^2 -6x +10

Answer:

Option C. [tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] , [tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]

Step-by-step explanation:

we know that

If cosine of angle theta is positive  then angle theta belong to the I or IV quadrant

and

If co secant of angle theta is negative then angle theta belong to the III or IV quadrant

therefore

angle theta belong to the IV quadrant (common solution)

Part 1) Find [tex]sin(\theta)[/tex]

we know that

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

we have

[tex]cos(\theta)=4/7[/tex]

substitute the value

[tex]sin^{2}(\theta)=1-(4/7)^{2}[/tex]

[tex]sin^{2}(\theta)=1-(16/49)[/tex]

 [tex]sin^{2}(\theta)=(33/49)[/tex]

[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex] ----> is negative because the angle belong to the IV quadrant

Part 2) Find [tex]tan(\theta)[/tex]

we know that

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

we have

[tex]sin(\theta)=-\frac{\sqrt{33}}{7}[/tex]

[tex]cos(\theta)=4/7[/tex]

substitute the values

[tex]tan(\theta)=\frac{-\frac{\sqrt{33}}{7}}{4/7}[/tex]

[tex]tan(\theta)=-\frac{\sqrt{33}}{4}[/tex]

Answer:

23 Cards were given to your brother.

Step-by-step explanation:

12 + 24 = 36

36 - 13 = 23

Answer:

you gave him 23 cards

Step-by-step explanation:

12+24=36, 36-13=23

Answer:

Step-by-step explanation:

A diameter of a rhombus is an angle bisector. Therefore we have the equation:

[tex]3x-11^o=x+23^o[/tex]              add 11° to both sides

[tex]3x=x+44^o[/tex]                subtract x from both sides

[tex]2x=44^o[/tex]             divide both sides by 2

[tex]x=22^o[/tex]

Answer:

You cant solve this without one more number.

Step-by-step explanation:

You need the length of the blue piece because it could be smaller or larger at this point. I may be wrong but unless I am missing something, and I totally might be if this is a kind of math I've never done, then please feel free to ignore me :) and have a lovely day!

Factor out the common term 6

6(x^2 - 11x + 24) = 0

Factor x^2 - 11x + 24

6(x - 8)(x - 3) = 0

Solve for x;

x = 8,3

Answer:

The measure of angle R is [tex]22.62\°[/tex]

Step-by-step explanation:

we know that

In the right triangle PQR

The cosine of angle R is equal to divide the adjacent side angle R by the hypotenuse

so

[tex]cos(R)=\frac{QR}{PR}[/tex]

substitute the values

[tex]cos(R)=\frac{12}{13}[/tex]

[tex]<R=arccos(\frac{12}{13})=22.62\°[/tex]

see the attached figure to better understand the problem

Answer:

16 pounds

Step-by-step explanation:

Total cereal she ate = 256 ounces

How many pounds she ate = ?

Given that (16 ounces = 1 pound)

Therefore, we have to divide the total ounces by 16 to calculate the cereal she ate in pounds = 256/16 = 16 pounds

Answer:

A. 16

Step-by-step explanation:

The second one should be it

I’m not sure bc I’m going off of my head

Answer:

Step-by-step explanation:

A rectangular prism has 12 edges. In geometry, a prism is a solid figure with parallel ends or bases that are the same size and shape, with each side representing a parallelogram. The parallelograms in a rectangular prism are all rectangles.

The rectangular prism also has six faces, or flat sides. The surface area of a rectangular prism is determined by multiplying the length by the width of each of the six rectangles and by then adding the products together.

Answer:

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up → (x, y + n)

f(x) - n - shift the graph of f(x) n units down → (x, y - n)

f(x - n) - shift the graph of f(x) n units to the right → (x - n, y)

f(x + n) - shift the graph of f(x) n units to the left → (x + n, y)

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

(x, y) → (x - 3, y + 6)

x - 3 → shift the graph 3 units to the right

y + 6 → shift the graph 6 units up

Answer:

the right answer is left 3 units and up 6 units

Step-by-step explanation:

Answer:

Step-by-step explanation:

r = [tex]\frac{a_n}{a_{n-1}} = \frac{896}{3584} =  \frac{1}{4}[/tex]

Using the geometric series formula for the nth term:

[tex]S_n = a \cdot \frac{1-r^n}{1-r} => S_{6} = 3584 \cdot \frac{1 - (\frac{1}{4})^{6} }{1 - \frac{1}{4} }  = 4777\frac{1}{2}[/tex]

Final answer:

The equation for the nth term of the geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio. The sixth term of the sequence is 14.

Explanation:

The given sequence is a geometric sequence. In a geometric sequence, each term is found by multiplying the previous term by a common ratio. To find the equation for the nth term of the geometric sequence, we need to find the common ratio. We can do this by dividing any term in the sequence by the previous term.

For example, dividing the second term 896 by the first term 3584 gives us a common ratio of 1/4.

So, the equation for the nth term of the sequence is:

an = a1 × r(n-1)

where a1 is the first term and r is the common ratio.

To find the sixth term, we can substitute n = 6 into the equation:

a6 = 3584 × (1/4)(6-1)

a6 = 3584 × (1/4)5

a6 = 14

Answer: 6 teaspoons of sugar

Step-by-step explanation: Create a proportion

4 ounces of frosting = 2 teaspoons of sugar

8 ounces of frosting = 4 teaspoons of sugar

12 ounces of frosting = 6 teaspoons of sugar

To make 12 ounces of frosting, you would need 6 teaspoons of sugar.

To find out how much sugar is needed to make 12 ounces of frosting, we can set up a proportion using the given information. The recipe calls for 2 teaspoons of sugar for 4 ounces of frosting. We can set up the proportion: 2 teaspoons / 4 ounces = x teaspoons / 12 ounces.

To solve the proportion, we can cross multiply and divide. So, (2 teaspoons)(12 ounces) = (4 ounces)(x teaspoons). This simplifies to 24 = 4x. Dividing both sides by 4, we find that x = 6 teaspoons.

Therefore, you would need 6 teaspoons of sugar to make 12 ounces of frosting.

To determine when Tyron's savings will surpass Linda's, we can set up an inequality using their daily saving rates and the fact that Linda started 3 days earlier. Solving for the number of days Tyron needs to save, we find that Tyron will surpass Linda's savings after saving for 2 full days.

Linda and Tyron are saving money on a daily basis, but Linda started saving 3 days earlier than Tyron. To find out on which day Tyron's savings will be more than Linda's, we need to set up an equation.

Let's define x as the number of days after which Tyron starts saving. Since Linda starts 3 days earlier, she has been saving for x + 3 days by the time Tyron starts saving.

Linda's daily savings: $1.55
Tyron's daily savings: $3.90

 Linda's total savings after x + 3 days: $1.55(x + 3)
Tyron's total savings after x days: $3.90x

We want to find the value of x at which Tyron's total savings exceed Linda's, so we set up the inequality:
$3.90x > $1.55(x + 3)

Now, solve for x:

$3.90x > $1.55x + $4.65
$3.90x - $1.55x > $4.65
$2.35x > $4.65
x > $4.65 / $2.35
x > 1.978

Since x represents the number of days and we cannot have a fraction of a day in this context, x must be at least 2 days. Therefore, Tyron's savings will be more than Linda's after he has saved for 2 days.

Answer:

a:  That the mean weight of the trials is 10 kg

b:  See attached photo for work

Step-by-step explanation:

We want to see if the scale is weighing properly and are using a 10 kg weight to calibrate it.  That means our hypothesis test is that the mean weight of the trails (in this case 25) is 10 kg.

The hypothesis we will use are

H0:  µ = 10

Ha:  µ ≠ 10

The alternate hypothesis has a not equals to sign because if the scale weighs too much or to little, then it needs to be better calibrated, so it's a two tailed test.

The calibration of the scale follows a normal distribution.

The given parameters are:

[tex]\mathbf{\sigma = 0.200}[/tex]

[tex]\mathbf{\mu = 10}[/tex]

[tex]\mathbf{n = 25}[/tex]

[tex]\mathbf{\bar x = 9.85}[/tex]

(a) The null and the alternate hypotheses

The true average weight is to be tested.

So, the null and the alternate hypotheses are:

[tex]\mathbf{H_o: \mu = 10}[/tex]

[tex]\mathbf{H_a: \mu \ne 10}[/tex]

(b) The p-value when [tex]\mathbf{\bar x = 9.85}[/tex]

First, we calculate the test statistic

[tex]\mathbf{t = \frac{\bar x - \mu}{\sigma/\sqrt n}}[/tex]

So, we have:

[tex]\mathbf{t = \frac{9.85 - 10}{0.2/\sqrt{25}}}[/tex]

[tex]\mathbf{t = \frac{9.85 - 10}{0.2/5}}[/tex]

[tex]\mathbf{t = \frac{-0.15}{0.04}}[/tex]

[tex]\mathbf{t = -3.75}[/tex]

Using p-value calculator, we have:

[tex]\mathbf{p=0.000494}[/tex]

The critical regions of [tex]\mathbf{t = -3.75}[/tex] are t >2.797 and t < -2.797

Because -3.75 < -2.797, we reject the null hypothesis.

This means that, the scale needs to be calibrated

(c) Probability that recalibration is judged when [tex]\mathbf{\mu = 10.2}[/tex]

First, we calculate the test statistic

[tex]\mathbf{t = \frac{\bar x - \mu}{\sigma/\sqrt n}}[/tex]

So, we have:

[tex]\mathbf{t = \frac{9.85 - 10.2}{0.2/\sqrt{25}}}[/tex]

[tex]\mathbf{t = \frac{-0.35}{0.04}}[/tex]

[tex]\mathbf{t = -8.75}[/tex]

Using p-value calculator, we have:

[tex]\mathbf{p<0.00001}[/tex]

The probability that  recalibration is judged unnecessary is less than 0.00001

Read more about probabilities using test statistics at:

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Graph of constant function is a horizontal line

It’s a horizontal line because all of the x’s must be different

Answer:

It can't be simplified.

Answer:

The area of the triangle = 31.5 feet² ⇒ answer (c)

Step-by-step explanation:

∵ Area of any Δ = 1/2 (side 1)(side 2)(sin the angle between them)

∴ The area of the Δ = 1/2 (b)(c) sin(∠A)

∵ b = 11 feet

∵ c = 10 feet

∵ m∠A = 35°

∴ Area of the Δ = 1/2 (11)(10) (sin(35)) = 31.547 feet²

∴ The area of the triangle = 31.5 feet²

∴ The answer is (c)

h = 12.

See the attached picture:

Answer:

[tex]\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)[/tex]

Step-by-step explanation:

The given logarithmic expression is

[tex]log_{3}(x^4y)[/tex]

Recall and use the product property of logarithm: [tex]\log_a(MN)=\log_a(M)+\log_a(N)[/tex];

This implies that;

[tex]\log_{3}(x^4y)=\log_{3}(x^4)+\log_{3}(y)[/tex]

Recall again that; [tex]\log_a(M^n)=n\log_a(M)[/tex];

We apply this property to get;

[tex]\log_{3}(x^4y)=4\log_{3}(x)+\log_{3}(y)[/tex]

he has 84 hockey cards total

Answer:

The slope is undefined

Step-by-step explanation:

x = -4 is a vertical line.  Slope is defines as the change in y divided by the change in x.  

(change in y)/(change in x)

All the points on this line have the same x value, so the change in x is zero.  This means we have

(change in y)/0, which is undefined.

Answer:

UNDEFINED

Step-by-step explanation:

Any initial value set to equal x is considered an undefined rate of change [slope], which is a vertical line.

I am joyous to assist you anytime.

Answer:

This is correct, Carolyn will make $7.70 for each necklace but she loses $3.20 most likely for the suplices for the making of the necklace so she really earns $4.50.

Step-by-step explanation:

a. The series is

[tex]\displaystyle\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-4-\frac43-\frac4{3^2}-\frac4{3^3}-\cdots[/tex]

(first four terms are listed)

b. The series converges because this is a geometric series with [tex]r=\dfrac13<1[/tex].

c. Let [tex]S_N[/tex] be the [tex]N[/tex]-th partial sum of the series:

[tex]S_N=\displaystyle\sum_{n=1}^N-4\left(\frac13\right)^{n-1}[/tex]

[tex]S_N=-4-\dfrac43-\dfrac4{3^2}-\cdots-\dfrac4{3^{N-1}}[/tex]

Multiplying both sides by [tex]\dfrac13[/tex] gives

[tex]\dfrac13S_N=-\dfrac43-\dfrac4{3^2}-\dfrac4{3^3}-\cdots-\dfrac4{3^N}[/tex]

Subtracting this from [tex]S_N[/tex] gives

[tex]S_N-\dfrac13S_N=\dfrac23S_N=-4+\dfrac4{3^N}[/tex]

[tex]\implies S_N=-6+\dfrac6{3^N}[/tex]

As [tex]N[/tex] gets larger and larger [tex](N\to\infty)[/tex] the rational term converges to 0 and we're left with

[tex]\displaystyle\lim_{N\to\infty}S_N=\sum_{n=1}^\infty-4\left(\frac13\right)^{n-1}=-6[/tex]

Answer:

 √48 could not be M.

Step-by-step explanation:

M must be  between - 2 and 6, so:

a. √48 = 6.93 so this can't be M.

b.   √18 = 4.24 so this could be M.

c and d could also be M.

The coordinate of point M can be any of the given options.

To determine the possible coordinates of point M, we need to find the values between X (-2) and Y (6) on the number line provided. Starting from X (-2) and moving towards Y (6), the numbers that lie between them are -2, 0, 2, 4, and 6. We can see that all the given options for the coordinate of point M can be found on the number line. Therefore, none of the given numbers could not be the coordinate of point M.

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Answer:

Ella's Grade: 15

Minh's Grade: 16

Step-by-step explanation:

If each grade has 20 girls in the grade, then that implies effectively that the ratios would apply via fractions, which are 3:4 and 4:5. As such, take both Fractions and increase them both to 20: 15:20 and 16:20.

The number of boys in Ella's grade is 15 and Minh's grade is 16

Given that,

The ratio of  boys to girls in Ella's grade is 3:4

And the ratio of  boys to girls in Minh's grade is 4:5

The total number of girls is 20

Computation:

Let the number of boys be [tex]x[/tex]

So in the case of  Ella's,

[tex]\frac{3}{4}=\frac{x}{20}\\x=\frac{20\times3}{4}\\x=15[/tex]

And in case of Minh's,

[tex]\frac{4}{5}=\frac{x}{20}\\x=\frac{20\times4}{5}\\x=16[/tex]

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Answer:

The correct option is D) All real numbers.

Step-by-step explanation:

Consider the provided function.

Range: Range is the set of output value produce by the function, or the range is the set of all possible y values.

Now consider the provided graph of the function.

The graph of the function is a straight line and function produces the positive and negative value of y.

By interpreting the graph it can be concluded the the range of the function is all real numbers.

Thus, the correct option is D) All real numbers.

Answer:

[tex]\frac{g}{8}-17[/tex] games

Step-by-step explanation:

Employees: 8

Sales last month: g

Average: [tex]\frac{totalGames}{Employees}[/tex]

To find out how many games Chris sold, we have to take the average and subtract 17.

[tex]\frac{g}{8}-17[/tex]

Since there are no more values we can use, this is as simple as we can get it. If we knew how many games they sold last month, we could get an exact answer for Chris using this expression.

Answer:

g over 8 -17

Step-by-step explanation:

Answer:

3rd group of possible answers is the correct set

Step-by-step explanation:

Each of the three points in the 3rd line of possible answers is a solution of the given equation, as can be verified by substitution:

If x = -2, y = -8(-2) = +16

If x = 3, y = -8(3) =  -24

If x = -4, y = -8(-4) = +32

Answer:

c

Step-by-step explanation:

Answer: [tex]x=\frac{41}{10}[/tex]

Step-by-step explanation:

Descompose the denominators into their prime factors to calculate the Least Common Denominator (LCD):

[tex]5x=5*x[/tex]

[tex]2=2*x[/tex]

Choose the common and non-common numbers and varibles with the largest exponents and multiply them:

[tex]LCD=5*2*x=10x[/tex]

Divide eac originl denominator by the LCD and multiply the resul by each numerator. Then, make the addition and solve for x:

[tex]\frac{3(2)+7(5)}{10x}=1\\\\\frac{6+35}{10x}=1\\\\\frac{41}{10x}=1\\\\41=10x\\x=\frac{41}{10}[/tex]

Answer:

[tex]x=4.1[/tex]

Step-by-step explanation:

The given equation is;

[tex]\frac{3}{5x}+\frac{7}{2x}=1[/tex]

Multiply through by the Least Common Denominator which is [tex]-10x[/tex]

[tex]10x(\frac{3}{5x})+10x(\frac{7}{2x})=10x[/tex]

Cancel the common factors to obtain;

[tex]2(3)+5(7)=10x[/tex]

[tex]6+35=10x[/tex]

[tex]41=10x[/tex]

Divide by 10

[tex]x=\frac{41}{10}[/tex]

[tex]x=4.1[/tex]