If sine theta equals three over four, what are the values of cos θ and tan θ?

cosine theta equals plus or minus square root of seven over four, tangent theta equals plus or minus two times square root of seven over seven

cosine theta equals plus or minus seven over four, tangent theta equals negative three over seven

cosine theta equals plus or minus square root of seven over 4, tangent theta equals plus or minus three over seven

cosine theta equals plus or minus seven over four, tangent theta equals negative one over seven

Answer:

1)3/5=60%

2)7/8=87.5%

3)4/25=16%

4)27/50=54%

fractions

1)50%=0.5

2)34%=0.34

3)56%=0.56

4)331/3%=1.1033

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Answer : The true statements are:

The equation [tex]c+d=58[/tex] represents the sum of two numbers.

The equation [tex]c=\frac{d}{2}-8[/tex] represents the relationship between the two numbers.

The number c is, 14

The number d is, 44

Step-by-step explanation :

Given:

Let 'c' represent the first number. Let 'd' represent the second number.

The sum of two numbers is 58. The equation will be:

[tex]c+d=58[/tex]      .........(1)

The first number is 8 less than half the second number. The equation will be:

[tex]c=\frac{d}{2}-8[/tex]      .........(2)

Now by solving the two equations, we get the value of c and d.

As, [tex]c+d=58[/tex]

or, [tex]c=58-d[/tex]          ..........(3)

Now put equation 3 in 2, we get the value of d.

[tex]58-d=\frac{d}{2}-8[/tex]

[tex]58-d=\frac{d-16}{2}[/tex]

[tex]2(58-d)=d-16[/tex]

[tex]116-2d=d-16[/tex]

[tex]3d=132[/tex]

[tex]d=44[/tex]

Now put the value of 'd' in equation 3, we get the value of 'c'.

[tex]c=58-d[/tex]

[tex]c=58-44[/tex]

[tex]c=14[/tex]

Thus, the value of c and d is, 14 and 44 respectively.

Answer:

ABGH

Step-by-step explanation:

Answer:

11

Step-by-step explanation:

Ok so we aren't looking to maximize profits which is equivalent to finding the vertex of the parabola.

But we want to know what is the highest number of x so that our we aren't losing money.  We aren't losing money when our profit is 0.

So we are asked to solve P(x)=0 for x and take the highest x of that equation.

[tex]P(x)=0[/tex]

[tex]-10x^2+120x-150=0[/tex]

I'm going to divide both sides by -10 to make the numbers easier to work with later.

[tex]x^2-12x+15=0[/tex]

I'm going to use the quadratic formula.

[tex]x^2-12x+15=0[/tex] when compared to [tex]ax^2+bx+c=0[/tex] gives us [tex]a=1,b=-12,c=15[/tex].

We are going to plug this into our quadratic formula:

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

[tex]x=\frac{12\pm \sqrt{(-12)^2-4(1)(15)}}{2(1)}[/tex]

[tex]x=\frac{12\pm \sqrt{144-60}}{2}[/tex]

[tex]x=\frac{12\pm \sqrt{84}}{2}[/tex]

[tex]x=\frac{12}{2} \pm \frac{\sqrt{84}}{2}[/tex]

[tex]x=6 \pm \frac{\sqrt{84}}{2}[/tex]

I'm ready to put this into my calculator.

The one with the plus gives me 10.5826 approximately.

The one with the minus gives me 1.4174 approximately.

The 10.5826 is the higher number.

So about 11 dollars.

Answer:

C $11

Step-by-step explanation:

If a company found that its monthly profit, P, is  given by P = -10x2 + 120x - 150 where x is the  selling price for each unit of the product, the best estimate of  the maximum price per unit that the company  can charge without losing money is $11.

Answer:

12

Step-by-step explanation:

For our problem since we only in 10 am:

I'm going to let x=4 represent the time 10:04 am

which means I'm going to let x=17 represent 10:17am.

So when x=4, y=23 miles and when x=17,y=179 miles.

You have two points.

You can use the formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex].

Or just line the points up vertically and subtract them vertically, then put 2nd difference over first difference. Like this:

(    17  ,   179)

-(     4 ,      23)

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

   13          156

So the slope is 156/13=12 miles/hour.

the equation is S=30w+450

to find the answer just replace the w by 14

multiply 30 by 14 to get 420 and add 450 to it to get 870

The equation relating the total amount of money 'S' in the savings account to the number of weeks 'W' that Ryan has been saving is S = 450 + 30W. By substituting W with 14 in this equation, we find that Ryan will have $870 in his savings account after 14 weeks.

In this case, Ryan had started with $450 in his savings account. His weekly contribution to the savings is $30. So the total amount of money 'S' in the savings account after 'W' weeks could be represented by the equation S = 450 + 30W.

Now, if you want to find out the total amount of money in the savings account after 14 weeks, just substitute W = 14 into the equation. Thus the equation becomes S = 450 + 30*14 = 450 + 420 = $870.

Therefore, Ryan will have $870 in his savings account after 14 weeks.

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Answer:

c. a reflection in the x-axis.

Step-by-step explanation:

All values of log x are made  negative by the transformation so it is a reflection in the x axis.

The graph of [tex]f(x) =-log x[/tex] is the reflection in the x-axis of the graph of [tex]g(x)=log x[/tex].

" Graph is defined as a pictorial representation of the relation between the variables in the coordinate plane along x-axis and y-axis."

According to the question,

Given function on the graph,

[tex]f(x) =-log x[/tex]

[tex]g(x)=log x[/tex]

[tex]'x'[/tex] represents the concentration of hydrogen ions, in moles per liter.

value of [tex]'x'[/tex] remain the same in both cases.

[tex]f(x)[/tex] value is negative.

[tex]g(x)[/tex] value is positive.

The graph of [tex]f(x)[/tex] lying in the first quadrant and the graph of  [tex]g(x)[/tex] lying in the fourth quadrant.

Therefore, the graph of [tex]f(x)[/tex] is the reflection in the x-axis of the graph of [tex]g(x)[/tex].

Hence, Option(C) is the correct answer.

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The graph that represents y = -|x + 4| + 1 is graph (a)

The equation is given as:

y = -|x + 4| + 1

The above equation is a transformation from the parent function, which is represented as:

y = |x|

First the function is reflected across the x-axis, then translated 4 units left, and lastly 1 unit up.

The graph that represents this transformation is graph (a)

Hence, the graph that represents y = -|x + 4| + 1 is graph (a)

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Answer:

t x 6=c or      c divided by 6= t

Step-by-step explanation:

Answer: [tex]c=6t[/tex]

Step-by-step explanation:

You need to analize the information provided in the exercise:

-  "c" represents the number of chairs in the conference room.

- "t" represents the number of tables in the conference room.

- "6 times the number of tables" indicates a multiplication. This is:

[tex]6t[/tex]

Therefore if the number of chairs in the conference room is equal to 6 times the number of tables, you can write this equation that matches the information provided:

[tex]c=6t[/tex]

Answer:

y=-2x+4

Step-by-step explanation:

2x+y-1=0

2x+y=0+1

2x+y=1

y=1-2x

y=-2x+1

y=mx+b where m=slope and b=y-intercept

parallel means same slope,

so the slope would still be -2.

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

y-y1=m(x-x1)

y-2=-2(x-1)

y=-2x+2+2

y=-2x+4

Answer:

5 jumps

Step-by-step explanation:

Personally I would write it out, although there surely is a formula for it.

3 fall to 2 - 5 fall to 4 - 7 fall to 6 - 10 fall to 9 - 12.

This makes 5 jumps, since once he is out he won't fall back in.

Answer:

A 6/7

Step-by-step explanation:

3/4 ÷ 7/8

Copy dot flip

3/4 * 8/7

The numerator is 3*8 = 24

The denominator is 4*7 = 28

24/28

Divide the top and botto by 4

6/7

Answer:

71°

Step-by-step explanation:

The equation should be 19+90+x=180

Step 1: Add 19+90=109

Step 2: Subtract 180-109=71

So, you're answer is 71°

Final answer:

To find the measure of the other angle in a right triangle when one angle is given, subtract the given angle and the right angle from 180 degrees to get the third angle, which is the measure of the other angle.

Explanation:

One angle of a right triangle measures 19∘. In a right triangle, one angle is always 90 degrees. Therefore, to find the measure of the third angle, you need to subtract the sum of the given angle and the right angle from 180 degrees.

Third angle = 180° - 90° - 19° = 71°. So, the measure of the other angle in the right triangle is 71 degrees.

Let

x--------> volume of 50​% fertilizer

y--------> volume of 30% fertilizer

we know that

x+y=160-----> x=160-y-----> equation 1

x*0.5+y*0.3=160*0.4-----> equation 2

substitute equation 1 in equation 2

[160-y]*0.5+0.3*y=63.8----> 77-0.35*y+0.25*y=63.8

0.10*y=13.2------> y=13.2/0.10----> y=132 gal

x=220-y----> x=220-132----> x=88 gal

the answer is

88 gal of 50​% fertilizer

132 gal 30​% fertilizer

To obtain a 40% fertilizer mixture, the landscaping company should mix 80 gallons of 50% fertilizer with 80 gallons of 30% fertilizer.

To solve this problem, we can set up an equation based on the amount of fertilizer needed and the percentage of fertilizer in each type. Let's call the amount of 50% fertilizer x and the amount of 30% fertilizer y. We know that the total amount of fertilizer needed is 160 gallons, so we can write the equation x + y = 160. We also know that the amount of fertilizer in the 50% type is 0.5x and the amount of fertilizer in the 30% type is 0.3y. Since we want a total of 40% fertilizer, we can write the equation 0.5x + 0.3y = 0.4 * 160. Solving this system of equations will give us the amounts of each type of fertilizer needed.

First, let's rearrange the first equation to solve for x: x = 160 - y. Substituting this into the second equation, we get 0.5(160 - y) + 0.3y = 0.4 * 160. Simplifying the equation, we get 80 - 0.5y + 0.3y = 64. Combining like terms, we have 80 - 0.2y = 64. Subtracting 80 from both sides, we get -0.2y = -16. Dividing both sides by -0.2, we get y = 80. Now we can substitute this value back into the first equation to solve for x: x = 160 - 80 = 80. Therefore, they should mix 80 gallons of the 50% fertilizer with 80 gallons of the 30% fertilizer to obtain the desired 40% mixture.

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Answer:

B.

Step-by-step explanation:

Let's plug in and find out.

A. y-4<3x-5 with (x,y)=(0,0)

   0-4<3(0)-5

     -4<-5

This is false because -5 is not bigger than -4.

B. y-5<3x-4 with (x,y)=(0,0)

   0-5<3(0)-4

     -5<-4

This is true because -4 is bigger than -5.

C. y+5<3x+4 with (x,y)=(0,0)

   0+5<3(0)+4

       5<4

This is false because 4 is not bigger than 5.

D. y+5<3x-4 with (x,y)=(0,0)

    0+5<3(0)-4

        5<-4

This is false because -4 is not bigger than 5.

The only true inequality I got from plugging in (0,0) for (x,y) was B so that your answer.

Answer: B

Step-by-step explanation:

This is because it is just a statement, and may be true for some people, but not others.

Answer:

$300

Step-by-step explanation:

Let's say that L is the amount of money Luisa had in the beginning, and C is the amount of money Connor had in the beginning.

C + L = 360

C - 2/5 C = L + 2/5 C

Simplifying the second equation:

3/5 C = L + 2/5 C

1/5 C = L

Substituting into the first equation:

C + 1/5 C = 360

6/5 C = 360

C = 300

Connor originally had $300, and Luisa $60.  Connor gave Luisa $120, and they both had $180.

Answer:

64.7%

Step-by-step explanation:

Write a proportion:

275 / 425 = x / 100

x = 64.7

64.7% of the tickets were adult tickets.

Answer:

Number line graph with closed circle on 30 and shading to the left

Step-by-step explanation:

we know that

The algebraic expression of the phrase " An unknown number x is at most 30" is equal to

[tex]x\leq 30[/tex]

The solution is the interval ------> (-∞,30]

All real numbers less than or equal to 30

Number line graph with closed circle on 30 and shading to the left

see the attached figure

Final answer:

To graph the scenario where the number of loaves of bread on hand (L) minus the number of reservations (R) must be greater than 5, one would represent this inequality on a two-dimensional graph with L on the horizontal axis and R on the vertical axis, shading the region above the line L - R = 5.

Explanation:

The subject of the question is Mathematics, with a focus on inequalities and graphical representation of constraints. The scenario describes the requirement that the number of loaves of bread on hand minus the number of reservations must be greater than 5. To represent this mathematically, let's define the variable L as the number of loaves of bread on hand and R as the number of reservations. The inequality can, therefore, be expressed as L - R > 5.

This inequality needs to be represented on a graph. To do this, one typically uses a two-dimensional coordinate system where the horizontal axis, often labeled as x, could represent the number of loaves of bread (L), and the vertical axis, often labeled as y, could represent the number of reservations (R). The region that satisfies the inequality L - R > 5, would be shaded above the line L - R = 5 (since we are looking for L being greater than R by more than 5 units). This line will have a slope of 1 and a y-intercept at R = -5.

Answer:

Step-by-step explanation: just did it on apex

The pairs of triangles appear to be congruent are Triangles 1 and 4,  Triangles 1 and 3 and  Triangles 3 and 4, that is option B, option C and option E. This can be obtained by understanding the concept of congruence.

In the question, Triangle 2 is larger than the other triangles.

Triangle 1, Triangle 3 and Triangle 4 appears to have the same size and shape.

Thus Triangle 1, Triangle 3 and Triangle 4 appears to be congruent to each other.

Hence the pairs of triangles appear to be congruent are Triangles 1 and 4,  Triangles 1 and 3 and  Triangles 3 and 4, that is option B, option C and option E.

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[tex]\displaystyle\\\int \limits_2^a(3x^2+x-1)\, dx=52\\\left|x^3+\dfrac{x^2}{2}-x\right|_2^a=52\\a^3+\dfrac{a^2}{2}-a-(2^3+\dfrac{2^2}{2}-2)=52\\a^3+\dfrac{a^2}{2}-a-(8+2-2)=52\\a^3+\dfrac{a^2}{2}-a-8=52\\a^3+\dfrac{a^2}{2}-a=60\\2a^3+a^2-2a=120\\2a^3+a^2-2a-120=0[/tex]

Now you need to solve the resulting equation, but it's not easy. The approx. solution is [tex]a\approx 3.8[/tex]

The exact solution is

[tex]a=\dfrac{1}{6}\left(-1+\sqrt[3]{6461-78\sqrt{6861}}+\sqrt[3]{6461+78\sqrt{6861}}\right)[/tex]

Answer:

a = 3.84

Step-by-step explanation:

Let's integrate the function

3x^2 becomes 3x^3/3 =x^3

x becomes x^2/2

-1 becomes -x

The intergral is x^3 +x^2/2 -x

We take the upper limit minus the lower limit

a^3 +a^2/2 -a - (2^3 + 2^2/2 -2) and that is equal to 52

Simplify

a^3 + a^2/2 -a - (8+2-2) = 52

a^3 +a^2/2 -a -(8) = 52

Subtract 52 from each side

a^3 +a^2/2 -a -8-52 = 52-52

a^3 +a^2/2 -a -60 =0

Multiply by 2

2a^3 +a^2 -2a -120 = 0

Using a graphing system, we see it only has 1 real root

This is at approximately

3.84

Answer:

[tex] \frac { 8 6 5 } { 2 6 7 8 } [/tex]

Step-by-step explanation:

We are given the following information for year 2015:

Number of arrests = 8625  

Number of robberies = 2678

Number of assaults = 865

Number of murders = 20

Population of Buffalo = 258959

We are to find the ratio of number of assaults to the number of robberies in simplest form.

Ratio of number of assaults to number of robberies = [tex]\frac{865}{2678}[/tex]

Answer:

[tex]\large\boxed{A.\ \sqrt{-4}}[/tex]

Step-by-step explanation:

[tex]A.\ \sqrt{-4}=\sqrt{(4)(-1)}=\sqrt4\cdot\sqrt{-1}=2i\ -\ \text{complex number}\\\\i-\text{imaginary unit}[/tex]

[tex]B.\ \sqrt{13}\approx3.61\ -\ \text{real number}\\\\C.\ \sqrt{16}=4\ -\ \text{real number}\\\\D.\ \sqrt1=1\ -\ \text{real number}[/tex]

A Vertex is the point that 2 or more lines connect.

When an angle is written given the letters of the lines/ points, the point where the lines connect are always the middle letter.

For ∠XYZ, the vertex would be point Y, because it is the middle letter.

An angle is formed by two rays that have a common endpoint which is known as the vertex of the angle

The vertex of the angle ∠XYZ is point Y

The reason the above selection is correct is as follows;

There are three methods used in naming an angle, including;

. The given angle is ∠XYZ, therefore, the middle letter, Y, is the vertex

The vertex point is Y

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Answer:

$2700.00

Step-by-step explanation:

6000 x 3% =180.00

180.00 x 15= 2700.00

Answer:

(1, 2 )

Step-by-step explanation:

Given the 2 equations

y = - 3x + 5 → (1)

y = 4x - 2 → (2)

Substitute y = 4x - 2 into (1)

4x - 2 = - 3x + 5 ( add 3x to both sides )

7x - 2 = 5 ( add 2 to both sides )

7x = 7 ( divide both sides by 7 )

x = 1

Substitute x = 1 into (2) for corresponding value of y

y = (4 × 1) - 2 = 4 - 2 = 2

Solution is (1, 2 )

Answer:

.08 feet

Step-by-step explanation:

So slope=rise/run.

You are given slope is 2% or .02.

You are also given run is 4 ft.

Plug these into the formula

.02=rise/4

To solve this for rise multiply both sides by 4:

4(.02)=rise

.08=rise

The rise is .08 feet.

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} A=113.04 \end{cases}\implies 113.04=\pi r^2\implies \cfrac{113.04}{\pi }=r^2 \\\\\\ \stackrel{using~\pi =3.14}{36}=r^2\implies \sqrt{36}=r\implies 6=r[/tex]

Explanation

We can use pythagorean theorem to solve for the value of x:

45^2 + x^2 = 53^2

2025 + x^2 = 2809

We now subtract 2025 from both sides:

2809 - 2025 = 784

x^2 = 784

Square both sides

[tex]\sqrt{784}[/tex] = 28

x = 28

Answer

The value of x is 28