If 0 < x < 2π, find the sum of all solutions to the equation 2cos^2(x)-7 cos(x)-4=0.
Show how to do it on a ti-84 if possible.

The solutions to the equation 1x² - 16x = 20 are x = 8 + 2√21 and x = 8 - 2√21.

To solve the quadratic equation 1x² - 16x = 20, we need to rearrange it into the standard form ax² + bx + c = 0. Let's simplify the equation step by step:

1x² - 16x = 20

First, move all terms to one side of the equation:

1x² - 16x - 20 = 0

Now we have a quadratic equation in the standard form. To solve it, we can use factoring, completing the square, or the quadratic formula. In this case, factoring may not be straightforward, so let's use the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

For our equation, a = 1, b = -16, and c = -20. Substituting these values into the quadratic formula:

x = (-(-16) ± √((-16)² - 4(1)(-20))) / (2(1))

Simplifying further:

x = (16 ± √(256 + 80)) / 2

x = (16 ± √336) / 2

x = (16 ± √(16 * 21)) / 2

x = (16 ± 4√21) / 2

Simplifying:

x = 8 ± 2√21

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Step-by-step explanation:

y=107(vertically opposite angles)

x=180-107=73(angles on a straight line)

z=73(vertically opposite angles)

Answer:

\({ \sf{y = 107 \degree}} \: \{ \sf{alternate \: angles} \}\)

\({ \sf{z + 107 \degree = 180 \degree}} \: \{ \sf{straight \: line \: angles \}} \\ z = 180\degree - 107\degree \\ z = 73\degree\)

\({ \sf{x = z}} \: \{ \sf{alternate \: angle \}} \\ x = 73\degree\)

Step-by-step explanation:

Edit:

a is 18

b is 36

c is 18

d is 18 times sqr root of 3

Answers:

sqrt is shorthand for "square root"

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

Explanation:

The smaller triangle on the left is a 45-45-90 triangle (aka isosceles right triangle). One special property of such triangles is that the legs are the same length, meaning a = c. Another special feature is that the hypotenuse is exactly sqrt(2) times that of the leg.

In other words, if x is the leg length, then x*sqrt(2) is the length of the hypotenuse. That means mean a = 18 in order for the hypotenuse to be 18*sqrt(2). This then leads to c = 18 as well.

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The smaller triangle on the right side has a = 18 as the shorter leg, opposite the smallest angle (30 degrees). The hypotenuse b is twice that of the short leg, and this works because we're dealing with a 30-60-90 triangle. Therefore b = 2a = 2*18 = 36.

The longer leg d is equal to sqrt(3) times the short leg, ie,

d = a*sqrt(3)

d = 18*sqrt(3)

You could use the pythagorean theorem to solve for d like so:

a^2 + d^2 = b^2

18^2 + d^2 = 36^2

d^2 = 972

d = sqrt(972)

d = 18*sqrt(3)

I skipped a bunch of steps, but you get the idea.

Answer:

With polar coordinates this isn’t true. In polar coordinates there is literally an infinite number of coordinates for a given point. For instance, the following four points are all coordinates for the same point. Here is a sketch of the angles used in these four sets of coordinates.

Step-by-step explanation:

Answer:

if its a 90 degree angle u will  say 90 -46 to get m<2

if is a 180 degree angle u will say 180-46 to get m<2

hope this helped :) brainliestn pls

The value of side EA is,

EA = 16.9

We have to given that;

Circle E with diameter CD and radius EA.

And, AB is tangent to E at A.

Here, AB = 34 and EB = 38

Hence, By using Pythagoras theorem we get;

AB² + AE² = EB²

34² + AE² = 38²

1156 + AE² = 1444

AE² = 1444 - 1156

AE² = 288

AE = √288

AE = 16.9

Thus, The value of side EA is,

EA = 16.9

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Step-by-step explanation:

There are 24=16 total possible outcomes of which only one outcome gives rise to all heads. Thus the probability that all coins land heads is 1/16.

Answer:

80 square units

Step-by-step explanation:

The figure given can be decomposed to have two trapezoids of equal dimensions and a rectangle.

Area of the figure = (2*area of a trapezoid) + (area of a rectangle)

Area of the 2 trapezoids:

Area of the two trapezoid = 2(½(a + b)*h)

Where,

a = 2 + 6 + 2 = 10 units

b = 6 units

h = 2 units

Plug in the values:

Area of the two trapezoid = 2(½(10 + 6)*2)

= 2(½(16)*2)

Area = 32 units²

Area of the rectangle:

Area = length × width

Length = 8 units

Width = 6 units

Area = 8 × 6 = 48 units²

✔️Area of the figure = 32 + 48 = 80 units²

Answer:

Blake's car gets better mileage

Step-by-step explanation:

In order to find how many miles you get per gallon, you would do miles/gallons

As I'm typing this I realize it makes no sense but pretty much you just do 300/20 which is 15 mpg, and 495/15 which is 33 mpg, therefore Blake's car is better

Answer:

multiple 18 x 8, then minus 6 from your answer

Answer:

1pack=6cans

18packs=x

=108canspacks=1xpack

Dividing both sides by 1 pack

X=108cans

The length of the school bus is 45 feet.

Given, School bus has a scale of 1/2 inch to 5 feet.

Length of the school bus is 4 1/2 inches on the scale drawing.

Actual length of the bus = ?

Given scale = 1/2 inch = 5 feet

⇒ 1 inch = 1/2 inch ₊ 1/2 inch

⇒ 1 inch = 5 feet ₊ 5 feet

⇒ 1 inch = 10 feet

Length of school bus = 4 1/2 inches = 4.5 inches.

Actual length:

length of school bus = length in inches × length in feet

4.5 inches = (4.5 × 10) feet

4.5 inches = 45 feet.

Hence we get the actual length of the school bus as 45 feet.

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Answer:

Step-by-step explanation: 5.) Circular shape.

     6.) Feet.

     7.) Circle.

     8.) The circumference is 9 and the radius is 18.

     9.)  By the way we would need to use The Circumference as 2 and the radius to be 9 to equal 18 for the radius circle.

Answer:

-5/8

Step-by-step explanation:

13/ -56   -x = 11/28

Add 13/56 to each side

13/ -56   + 13/56  -x = 11/28+ 13/56

-x = 11/28 + 13/56

Get a common denominator

-x = 11/28 *2/2 +13/56

-x = 22/56 + 13/56

-x = 35/56

Divide top and bottom by 7

-x = 5/8

Multiply both side by -1

x = -5/8

The equation with an infinite number of solutions is 12x-x+8+3x=14x+8.

An equation is a formula in mathematics that expresses the equality of two expressions by connecting them with the equals sign =. In its most basic form, an equation is a mathematical statement that shows that two mathematical expressions are equal. 3x + 5 = 14, for example, is an equation in which 3x + 5 and 14 are two expressions separated by a 'equal' sign. A mathematical equation that depicts the relationship between two expressions on opposite sides of the sign. It mostly consists of one variable and one equal to symbol. 2x - 4 = 2 is an example.

Here,

12x-x+8+3x=14x+8

The equation so that it has infinitely many solution is 12x-x+8+3x=14x+8.

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Using the z-distribution, it is found that:

The confidence interval is:

\(\overline{x} \pm zs\)

In which:

In this problem, we have a 95% confidence level, hence\(\alpha = 0.95\), z is the value of Z that has a p-value of \(\frac{1+0.95}{2} = 0.975\), so the critical value is z = 1.96.

The estimate and the standard error are given by:

\(\overline{x} = 0, s = 0.69\)

Hence the bounds of the interval are given by:

\(\overline{x} - zs = 0 - 1.96(0.69) = -1.38\)

\(\overline{x} + zs = 0 + 1.96(0.69) = 1.38\)

1.74 is outside the interval, hence:

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The equivalent expression will be;

⇒ 12 (2m + 3) + 6 (2m + 3)

Option D is true.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The expression is,

⇒ (24m + 36) + (12m + 18)

Now,

Since, The expression is,

⇒ (24m + 36) + (12m + 18)

it can be written as;

⇒ (24m + 36) + (12m + 18) = 12 (2m + 3) + 6 (2m + 3)

Thus, The equivalent expression after solving,

⇒ 12 (2m + 3) + 6 (2m + 3)

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Answer:

8*(3a+2b)

Step-by-step explanation:

Im really not sure if this is right since the question is basically incomplete!

Answer:

30

Step-by-step explanation:

Answer:

3 times 10 + 5 times 1

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

x = total amount of gumballs

let's start subtracting the balls she's giving away

\(\stackrel{total}{x}-\stackrel{\textit{to jaysen}}{\cfrac{x}{2}}\implies \stackrel{\textit{what's left}}{\cfrac{x}{2}}~\hfill \stackrel{\textit{half of what's left to Marinda}}{\cfrac{~~ \frac{x}{2}~~}{2}\implies \cfrac{x}{4}} \\\\\\ \stackrel{\textit{what was left minus Marinda's}}{\cfrac{x}{2}-\cfrac{x}{4}\implies \stackrel{\textit{what's left}}{\cfrac{x}{4}}}~\hfill ~\hfill \stackrel{\textit{a third of what's left to Zack}}{\cfrac{~~ \frac{x}{4}~~}{3}\implies \cfrac{x}{12}}\)

\(\stackrel{\textit{what was left minus Zack's}}{\cfrac{x}{4}-\cfrac{x}{12}\implies \stackrel{\textit{what's left}}{\cfrac{x}{6}}}~\hfill \stackrel{\textit{her sister gets 5 balls of what's left}}{ \cfrac{x}{6}-5 }\)

and we also know that after all that has been subtracted, she's only left with 5, so we can say that

\(\stackrel{\textit{what's finally left}}{\cfrac{x}{6}-5}~~ = ~~\stackrel{\textit{what's finally left}}{5}\implies \cfrac{x}{6}=10\implies \boxed{x = 60}\)

Refer to the attached images.

Answer:

5(2 + y)

Step-by-step explanation:

The sum of 2 and y is 2 + y and 5 times this sum is

5(2 + y)

(i)  The partial fraction decomposition of\(100/(x^7 * (10 - x))\) is\(100/(x^7 * (10 - x)) = 10/x^7 + (1/10^5)/(10 - x).\) (ii) The expression for t in terms of x is t = 10 ± √(100 + 200/x).

(i) To express the rational function 100/(\(x^7\) * (10 - x)) in partial fractions, we need to decompose it into simpler fractions. The general form of partial fractions for a rational function with distinct linear factors in the denominator is:

A/(factor 1) + B/(factor 2) + C/(factor 3) + ...

In this case, we have two factors: \(x^7\) and (10 - x). Therefore, we can express the given rational function as:

100/(\(x^7\) * (10 - x)) = A/\(x^7\) + B/(10 - x)

To determine the values of A and B, we need to find a common denominator for the right-hand side and combine the fractions:

100/(x^7 * (10 - x)) = (A * (10 - x) + B * \(x^7\))/(\(x^7\) * (10 - x))

Now, we can equate the numerators:

100 = (A * (10 - x) + B * \(x^7\))

To solve for A and B, we can substitute appropriate values of x. Let's choose x = 0 and x = 10:

For x = 0:

100 = (A * (10 - 0) + B * \(0^7\))

100 = 10A

A = 10

For x = 10:

100 = (A * (10 - 10) + B *\(10^7\))

100 = B * 10^7

B = 100 / 10^7

B = 1/10^5

Therefore, the partial fraction decomposition of 100/(\(x^7\) * (10 - x)) is:

100/(\(x^7\) * (10 - x)) = 10/\(x^7\) + (1/10^5)/(10 - x)

(ii) Given the differential equation: dx/dt = (1/100) *\(x^2\) * (10 - x)

We are also given x = 1 when t = 0.

To solve this equation and obtain an expression for t in terms of x, we can separate the variables and integrate both sides:

∫(1/\(x^2\)) dx = ∫((1/100) * (10 - x)) dt

Integrating both sides:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) + C

Where C is the constant of integration.

Now, we can substitute the initial condition x = 1 and t = 0 into the equation to find the value of C:

-1/1 = (1/100) * (10*0 - (1/2)*\(0^2\)) + C

-1 = 0 + C

C = -1

Plugging in the value of C, we have:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

To solve for t in terms of x, we can rearrange the equation:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Multiplying both sides by -1, we get:

-1/x = (1/100) * (10t - (1/2)\(t^2\)) - 1

Simplifying further:

1/x = -(1/100) * (10t - (1/2)\(t^2\)) + 1

Now, we can isolate t on one side of the equation:

(1/100) * (10t - (1/2)t^2) = 1 - 1/x

10t - (1/2)t^2 = 100 - 100/x

Simplifying the equation:

(1/2)\(t^2\) - 10t + (100 - 100/x) = 0

At this point, we have a quadratic equation in terms of t. To solve for t, we can use the quadratic formula:

t = (-(-10) ± √((-10)^2 - 4*(1/2)(100 - 100/x))) / (2(1/2))

Simplifying further:

t = (10 ± √(100 + 200/x)) / 1

t = 10 ± √(100 + 200/x)

Therefore, the expression for t in terms of x is t = 10 ± √(100 + 200/x).

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Note that the table of budget is attached accordingly, and steps 1-4 have been completed. See the table.

4) Since the emergency fund for that month was $200, it means that they are in the short for $105. They can only affod it if they take from their savings.

5) they had a balance of $800 for the month. This is miscellaneous funds. They can make use of this for the trip to NASA. This way, they won't have to touch the savings or entertainment.

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Full Question:
See attached image.

Reflect

4. Analyze Relationships One month, the family must make an

emergency car repair for $305. Are they able to pay for it out of the

fixed emergency fund for that month? If not, how can they afford it?

5. The family wants to make a trip to Houston to visit the NASA Space

Center. What are some ways they can save without using all of the

allotted $160 for entertainment

The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of \($\triangle QRS$\), we can use the formula:

\($Area = \frac{1}{2} \times base \times height$\)

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side \($QR$\). We can use the Law of Cosines:

\($QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$\)

where \($R$\) is the angle at vertex \($R$\). Substituting the given values, we get:

\($QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$\)

\($QR \approx 8.02$\)

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex \($R$\) to side \($QS$\). We can use the sine function:

\($\sin(R) = \frac{opposite}{hypotenuse}$\)

\($\sin(57^\circ) = \frac{height}{8.02}$\)

\($height \approx 6.51$\)

Now we can find the area of the triangle:

\($Area = \frac{1}{2} \times QR \times height$\)

\($Area = \frac{1}{2} \times 8.02 \times 6.51$\)

\($Area \approx 26.10$\) square units

Therefore, the area of \($\triangle QRS$\) is approximately \($26.10$\) square units.

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Answer:

6

Step-by-step explanation:

Assuming C lies on segment BD, we know that by the segment addition postulate,

\(BC+CD=BD \\ \\ 2+2x-6=x+2 \\ \\ 2x-4=x+2 \\ \\ x=6\)

The values of BC = 2, CD = 2x - 6 and BD = x + 2 then the value of x = 6.

The algebraic expression should be any one of the conditions such as addition, subtraction, multiplication, and division.

In mathematics, an algebraic expression exists as an expression built up from integer constants, variables, and algebraic operations. For example, 3x² − 2xy + c exists as an algebraic expression.

To estimate the value of x, bring the variable to the left side and bring all the remaining values to the right side. Simplify the values to estimate the result.

Given: BC = 2, CD = 2x - 6 and BD = x + 2 then

BC+CD= BD

2+2x-6=x+2

Simplifying,

2x-4=x+2

Thus,

x=6

Therefore, the value of x = 6.

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Answer:

First blank - SSS congruent condition

Second blank - Congruent

Answer: This looks famiiar to me btw which school do u go to? :)

Given :

Maximum capacity of fuel tank , M = 14 gallon .

It can travel approximately 26 miles with one gallon of  gas.

To Find :

A function d(x), that gives the distance the Escape can travel with x gallons of gas in  the tank.

Solution :

Car can travel 26 miles in one gallon of gas.

So , distance covered in x gallon of gas :

\(D(x)=26x\)

( Here,  0 ≤ x ≤ 14 ) or x ∈ [ 0 , 14 ] .

Hence , this is the required solution.

Answer:

64%

Step-by-step explanation:

Answer:

64%

Step-by-step explanation:

Answer:

Step-by-step explanation:B