What is the solution with steps?
2cosx=-sin^2x

Answer:

First one is 64

Step-by-step explanation:

Answer:

x=30

Step-by-step explanation:

53+97+x=180

150+x=180

x=30

The sum of all the angles of a triangle is 180 degrees.

Add all the angles together and set it equal to 180, then solve for x

53 + 97 + x = 180

(150-150) + x = 180 -150

x = 30

Hope this helped!

Answer:

Part 1) The measure of arc EHL is [tex]108\°[/tex]

Part 2) The measure of angle LVE is [tex]54\°[/tex]

Step-by-step explanation:

step 1

Let

x-----> the measure of arc EHL

y----> the measure of arc EVL

we know that

The measurement of the outer angle is the semi-difference of the arcs it encompasses.

so

[tex]m<EYL=\frac{1}{2}(y-x)[/tex]

we have

[tex]m<EYL=72\°[/tex]

substitute

[tex]72\°=\frac{1}{2}(y-x)[/tex]

[tex]144\°=(y-x)[/tex]

[tex]y=144\°+x[/tex] ------> equation A

Remember that

[tex]x+y=360\°[/tex] -----> equation B ( complete circle)

substitute equation A in equation B and solve for x

[tex]x+(144\°+x)=360\°[/tex]

[tex]2x=360\°-144\°[/tex]

[tex]x=216\°/2=108\°[/tex]

Find the value of y

[tex]y=144\°+x[/tex]

[tex]y=144\°+108\°=252\°[/tex]

therefore

The measure of arc EHL is [tex]108\°[/tex]

The measure of arc EVL is [tex]252\°[/tex]

step 2

Find the measure of angle LVE

we know that

The inscribed angle measures half that of the arc comprising

Let

x-----> the measure of arc EHL

[tex]m<LVE=\frac{1}{2}(x)[/tex]

we have

[tex]x=108\°[/tex]

substitute

[tex]m<LVE=\frac{1}{2}(108\°)=54\°[/tex]

Answer:

  200.3 in²

Step-by-step explanation:

The area of the top of the cylinder is precisely the area of the cube that the cylinder covers. In other words, the total of that area and the visible area of the cube is precisely equal to the area of the cube with no added parts.

So, the added cylinder only increases the total area by the area of its curved surface. That area is the product of its circumference and height.

  cylinder lateral area: π·d·h = π·(4 in)(4 in) = 16π in² ≈ 50.3 in²

  cube surface area: 6·(5 in)² = 150 in²

__

total surface area = cube surface area + cylinder lateral area

total surface area = (150 +50.3) in²

total surface area =200.3 in²

Answer:

15 cm^2

Step-by-step explanation:

Simply multiply the base times the height of the cross section. So 3 x 5 is 15

Answer:

The letters in the word glacier can be arranged in 5040 different ways

Step-by-step explanation:

As there are 7 letters in the word glacier, that means that the number of ways would be 7!

This can also be written as

[tex]7*6*5*4*3*2*1=5040[/tex]

The letters in the word glacier can be arranged in 5040 different ways.

When the order of the arrangements counts, a permutation is a mathematical technique that establishes the total number of alternative arrangements in a collection. Choosing only a few items from a collection of options in a specific sequence is a common task in arithmetic problems.

A permutation of a set exists, loosely articulating, an arrangement of its members into a sequence or linear order, or if the set exists already contained, a rearrangement of its elements.

Given,

As there are 7 letters in the word glacier, that means that the number of ways would be 7!

This can also be written as

7*6*5*4*3*2*1 = 5040

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a and b are matrices

Answer:

There is few equation that has a solution of all real numbers like this picture

,

The net represents a square pyramid is a net with a square base and 4 triangular sides.

A square pyramid is a pyramid with a square base in geometry. A right square pyramid is one with the tip perpendicular to the square's centre.

There will be five surfaces in the pyramid the base is square and the remaining four will be triangular.

Hence net represents a square pyramid is a net with a square base and 4 triangular sides.

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Answer:

Step-by-step explanation:

25%:  640 X .25 =160

         640-160= $480

10%:   640 X .10= 64

        640- 64= $576

5%:     640 X .05 =32

        640- 32= $608

Answer:

the discount with rate 25%=$160,the discount with rate 10%=$64,the discount with rate 5%=$32

Step-by-step explanation:

Hello, I think I can help you with this

the discount is a percentage, a proportion of the real value, we can find that proportion using a simple rule  of three

let

100% =$640

Step 1

If

$640= 100%

x? %  = 25%    

($640/100%)=(x/25%)

isolating x

x=($640*25%)/(100%)

x=$160

the discount with rate 25%=$160

Step2

If

$640= 100%

x? %  = 10%

($640/100%)=(x/10%)

isolating x

x=($640*10%)/(100%)

x=$64

the discount with rate 10%=$64

Step 3

If

$640= 100%

x? %  = 5%

($640/100%)=(x/5%)

isolating x

x=($640*5%)/(100%)

x=$32

the discount with rate 5%=$32

Have a nice day

Answer: Your answer would be 59.5

Answer:

  y = 2x +1

Step-by-step explanation:

The given line is in "slope-intercept" form, where the slope is the coefficient of x, 2, and the intercept is the added constant, 3. The parallel line will have the same slope, but its constant will be different. We can find the constant by putting the given point into an equation with the constant as the unknown:

  y = 2x + b

  -1 = 2(-1) +b . . . substitute for x and y

 2 -1 = b . . . . . . add 2

  1 = b

So the equation for the parallel line is ...

  y = 2x + 1

To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, calculate the mean stem weight for each group, the sample standard deviation, the standard error, and the margin of error. Then, calculate the lower and upper bounds of the confidence interval.

To construct a 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen, we will use a t-distribution and the formula for calculating a confidence interval for the difference in means. First, we find the mean stem weight for each group and calculate the sample standard deviation. Then, we calculate the standard error and the margin of error. Finally, we calculate the lower and upper bounds of the confidence interval.

Therefore, the 95% confidence interval for the difference in mean stem weight between seedlings that received no nitrogen and seedlings that received 368 ppm of nitrogen is approximately (-0.292, -0.052). This means we can be confident that the mean stem weight of seedlings that received no nitrogen is lower than the mean stem weight of seedlings that received 368 ppm of nitrogen.

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Final answer:

The number of cats in the neighborhood can be found by using the given ratio of dogs to cats, 3 to 7, and the total number of animals, 210. The calculations lead to a result of 147 cats.

Explanation:

To find the number of cats in the neighborhood, we can set up a proportion using the given ratio of dogs to cats, which is 3 to 7. We know that the total number of dogs and cats is 210. Let's assume the number of cats is 7x and the number of dogs is 3x.

So, 3x + 7x = 210. Combining like terms, we get 10x = 210. Dividing both sides by 10, we find that x = 21. Now, to find the number of cats, we multiply 7x by 21, which gives us 147 cats.

Therefore, there are 147 cats in the neighborhood.

Answer:

  AB = 4

Step-by-step explanation:

Since point P bisects AB, we have ...

  AP = PB

  y/2 = y - 2

  0 = y/2 - 2 . . . . subtract y/2

  0 = y - 4 . . . . . . multiply by 2

  4 = y . . . . . . . . . add 4

Now, we can find AB:

  AB = 2(AP) = 2(1/2y) = y

  AB = 4

Answer:

The distribution of data is (approximately normal-skewed left-skewed right) , with a mode of (7 ) , and a range of (8 )

Step-by-step explanation:

The data distribution is a normal skewed right with a range of (8) and a mode of (7).

Mode is the most frequently used number.

From the dot plot, it is observed that on the data 7th player took 6 attempts. Which is the greatest. The mode of the data distribution is 7.

The range of the data is the difference between the maximum and the minimum value.

Range = 9-1

Range=8

From the dot plot, it is observed that the maximum value is toward the right. So that it is right-skewed.

Hence, the data distribution is a normal skewed right) with a range of (8) and a mode of (7).

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Answer:

102.1

102.10 <--- 0 can be rounded down, so it is 102.1.

Answer:

x^3 +9x^2 +27x +27

Step-by-step explanation:

The expansion of a power of a binomial looks like ...

  (a +b)^n = nC0·a^n·b^0 + nC1·a^(n-1)·b^1 + nC2·a^(n-2)·b^2 + ... + nC(n-1)·a^1·b^(n-1) + nCn·a^0·b^n

Of course, nCk = n!/(k!·(n-k)!) and a^0 = b^0 = 1. The list of coefficients nCk corresponds to a row of Pascal's triangle (see attached).

For n=3, this is ...

  (a +b)^3 = a^3 +3a^2b +3ab^2 +b^3

You have a=x and b=3, so the expansion is ...

  (x +3)^3 = x^3 +3·x^2·3 +3·x·3^2 +3^3

  = x^3 +9x^2 +27x +27

x and y  are supplementary angles

x - y = 27

x + y = 180

--------------------- We add the equations:

2x   / = 207

2x = 207

x = 207/2

Final answer:

To find the angle measure, set up the equation 2x - (180 - x) = 27, simplify to 3x = 207, and solve to find that x = 69 degrees.

Explanation:

The question asks to find the measure of an angle where the difference between twice the angle's measure and its supplement is 27. To solve this, let's designate the measure of the angle as x. Since the angle's supplement will be 180° - x, we can set up the equation 2x - (180° - x) = 27. Simplifying this equation, we get 2x - 180° + x = 27, which simplifies further to 3x = 207°. Dividing both sides of the equation by 3, we find that x = 69°. Therefore, the measure of the angle is 69 degrees.

the answer is -8, the 9 is negative and -9+1= -8

By the substitution property of equality, substitute all x's with ¹/₂ and all y's with -5.

1. -2xy = -2(¹/₂)(-5) = 5

2. 4x² - 3y = 4(¹/₂)² - 3(-5) = 1 + 15 = 16

3. 10y/(12x + 4) = 10(5)/(12(¹/₂) + 4) = -50/10 = -5

4. 11x - 8(x - y) = 11(¹/₂) - 8(¹/₂ - -5) = ¹¹/₂ - 8(¹¹/₂) = -7(¹¹/₂) = -⁷⁷/₂ = -38.5

Substitute a's with -9 and b's with -4

5. 3ab = 3(-9)(-4) = 108

6. a² - 2(b + 12) = (-9)² - 2(-4 + 12) = 81 + 8 - 24 = 65

7. 4b²/(3b - 7) = 4(-4)²/(3(-4) - 7) = 64/-19

8. 7b² + 5(ab - 6) = 7(-4)² + 5((-9)(-4) - 6) = 112 + 150 = 262

9. x = 7.25, y = 3.25 --> 4x: people w/o popcorn, 2(x + y): people w/ popcorn; 4x + 2(x + y) = 4(7.25) + 2(7.25 + 3.25) = 29 + 21 = $50

To find the number of hours, divide the total distance by the speed.

Hours = 76 km / 14 km per hour

Hours = 4.529

Round the answer as needed.

X = 1/2(76 + 78)

x = 1/2(154)

x = 77

Answer:

-8x(2x - 9)

Step-by-step explanation:

-16x² + 72x

GCF = 8x

8x(16x² / 8x, -7x/8x)

-8x(2x - 9)

hope this helps!!

The answer would be -8x(2x-9)

Answer:

cos∠FHE = 4/5

Step-by-step explanation:

* Lets revise the trigonometry functions

- In ΔABC

# m∠B = 90°

# Length of AB = a , length of BC = b and length of AC = c

# The trigonometry functions of angle C are

- sin(C) = a/c ⇒ opposite side to ∠C ÷ the hypotenuse

- cos(C) = b/c ⇒ adjacent side to ∠C ÷ the hypotenuse

- tan(c) = a/b ⇒ opposite side to ∠C ÷ adjacent side to ∠C

* Now lets solve the problem

- To find cos∠FHE , we must find the length of the adjacent

 side HF and the length of the hypotenuse HE

- We can find the length of HF from ΔFGH

- In ΔFGH

∵ m∠G = 90°

∵ GF = √8

∵ m∠GHF = 45°

∵ sin∠GHF = GF/HF

∴ sin45° = √8/HF ⇒ by using cross-multiplication

∴ HF × sin45° = √8

∵ sin45° = 1/√2

∴ HF × 1/√2 = √8 ⇒ multiply each side by √2

∴ HF = √2 × √8 = √16 = 4

* Lets find the length of HE from ΔHFE

- In ΔHFE

∵ m∠HFE = 90°

∵ EF = 3 ⇒ given

∵ HF = 4

- By using Pythagoras theorem

∵ HE = √(FH² + FE²)

∴ HE = √(4² + 3²) = √(16 + 9) = √25 = 5

* Now we can find cos∠FHE

∵ cos∠FHE = HF/HE

∵ HF = 4 and HE = 5

∴ cos∠FHE = 4/5

Answer:

Part B shaded below first line and above second line.

Step-by-step explanation:

The first inequality corresponds to the second line (-3 = -4+1, for example) The ≥ symbol in that inequality tells you it will be satisfied by y values above those on the line.

The second inequality corresponds to the first line (-4+3 = -1, for example) The ≤ symbol in that inequality tells you it will be satisfied by y values below those on the line.

Hence the solution set is those values shaded below the first line and above the second line — matching Part B.

Answer:

$248.03

Step-by-step explanation:

The formula you use for this is as follows:

[tex]A(t)=P(1+\frac{r}{n})^{nt}[/tex]

where A(t) is the amount after the compounding is done, P is the initial amount invested, r is the interest rate in decimal form, n is the number of times the compounding is done per year, and t is the time in years.  Using that information and filling in our equation gives us this:

[tex]A(t)=75(1+\frac{.08}{12})^{(12)(15)}[/tex]

which simplifies down to

[tex]A(t)=75(1+.0066667)^{180}[/tex]

which simplifies further to

[tex]A(t)=75(3.307118585)[/tex]

which multiplies to $248.0338938.  Round to the nearest cent to get your answer.

The amount of money is $248.02.

Principal amount = P=75

Interest rate = r = 8% = 0.08

Number of years = t = 15

Number of times compounded in a year = n = 12

A = Amount after t years.

After 15 years there will be:

[tex]A=P\left(1+\frac{r}{n}\right)^{nt}\\ A=75\left(1+\frac{0.08}{12}\right)^{\left(12\cdot15\right)}\\ A=248.019110806\\ A \approx 248.02[/tex]

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Answer:

30 ft

Step-by-step explanation:

Let the height of the tree be x ft. There are two right triangles:

1. Tree and its shadow are two legs of the first triangle;

2. Man and his shadow are two legs of the second triangle.

A tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet. This means these two triangle are similar. Similar triangles have proportional sides' lengths. Hence,

[tex]\dfrac{\text{tree}}{\text{tree shadow}}=\dfrac{\text{man}}{\text{man's shadow}}\\ \\\dfrac{x}{24}=\dfrac{5}{4}\\ \\4\cdot x=5\cdot 24\\ \\x=\dfrac{5\cdot 24}{4}=5\cdot 6=30\ ft[/tex]

Answer:

30 feet

Step-by-step explanation:

We are given that a tree casts a shadow of 24 feet at the same time as a 5-foot tall man casts a shadow of 4 feet.

We are to find the height of the tree.

Using their proportions to compare the height of each object to the length of the shadow.

[tex]\frac{h}{24} =\frac{5}{4}[/tex]

[tex]h=\frac{5\times24}{4}[/tex]

[tex]h=30[/tex]

Therefore, the height of the tree is proportion comparing the height of each object to the length of the shadow 30 feet.

To solve the system of equations, graph the linear equation y = x - 1 and the quadratic equation y = 1/3(x + 2)(x - 4) on the same axes. Look for intersection points between the line and the parabola, which represent the solution(s) to the system. The number of intersections can vary, indicating how many solutions exist.

The question involves solving a system of equations:

To find the solution(s), we plot both equations on the same graph and look for intersection points. The first equation, y = x - 1, represents a straight line with a slope of 1 and a y-intercept of -1. For the second equation, y = 1/3(x + 2)(x - 4), it represents a parabola that opens upwards because the coefficient of the x^2 term (which is derived from expanding the equation) is positive. The roots (zeroes) are at x = -2 and x = 4, giving us points where the parabola crosses the x-axis.

To graph these, start with the linear equation by plotting the y-intercept (0, -1) and then using the slope to find another point (for example, (1, 0)). Plot these points and draw a straight line through them. For the quadratic equation, plot the roots (-2, 0) and (4, 0) and find the vertex by computing the axis of symmetry and the maximum or minimum value of y by substituting back into the equation. Sketch the parabola based on these points.

The solution(s) to the system are where the line and the parabola intersect. Depending on the exact shape of the parabola, there might be two, one or no intersection points, representing the solution(s).

Answer:

The solutions to the system of equations are (-0.85, -1.85) and (5.85, 4.85).

Step-by-step explanation:

The system of equations is a set of multiple equations. The solution to a system of equations is the set of all points which make all equations in the system true. The greatest amount of solutions possible in a system is equal to the highest degree present in it.

To find the solutions of a system of equations through graphing, graph all equations in the system and note the locations where they intersect. These are the points where all equations are true, aka the solutions. In this system, there are two points of intersection at (-0.85, -1.85) and (5.85, 4.85).

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Answer:

• 109 lb 1 oz

• 115 gal 3 qt 1 pt

• 111 yd 8 in

Step-by-step explanation:

The relevant unit relationships are ...

1 lb = 16 oz

1 gal = 4 qt

1 qt = 2 pt

1 yd = 3 ft = 36 in

To convert from one unit to another, multiply by a fraction that has ...

(to unit)/(from unit)

For example, to convert (13 oz)×5 = 65 oz to pounds, multiply by (1 lb)/(16 oz). This will give you ...

(65 oz)·(1 lb)/(16 oz) = 65/16 lb = 4 1/16 lb

Now, if you don't already recognize that 1/16 lb = 1 oz, you can multiply the fraction by the unit conversion from lb to oz: (16 oz)/(1 lb). Doing that gives ...

(1/16 lb)·(16 oz)/(1 lb) = 16/16 oz = 1 oz

When the same units are in the numerator and denominator, they cancel, as do any factors that appear in both numerator and denominator.

___

1. (21 13/16 lb)×5 = 105 65/16 lb = 109 1/16 lb = 109 lb 1 oz

__

2. (12 7/8 gal)×9 = 108 63/8 gal = 115 7/8 gal = 115 gal 3 qt 1 pt

__

3. ((15 2/3 +8/36) yd)×7 = (105 14/3 + 56/36) yd = 109 yd 2 ft + 1 yd 20 in

= 111 yd 8 in

_____

Additional explanation

7/8 gal = 7 pt = 1 pt + 3·2 pt = 1 pt + 3 qt

__

14/3 yd = 4 2/3 yd = 4 yd 2 ft

56/36 yd = 1 20/36 yd = 1 yd + (12 +8)/36 yd = 1 yd + 1 ft + 8 in

Then 14/3 yd + 56/36 yd = (4 yd + 2 ft) + (1 yd + 1 ft + 8 in) = 6 yd + 8 in

[tex] \frac{ - 1}{3} (6x + 15) - 3 \\ \\ 1. \: \frac{ - 6x + 15}{3} - 3 \\ 2. \: \frac{ - 3(2x + 5)}{3} - 3 \\ 3. \: - (2x + 5) - 3 \\ 4. \: - 2x - 5 - 3 \\ 5. \: - 2x + ( - 5 - 3) \\ 6. \: - 2x - 8[/tex]

Final answer:

To simplify -1/3 (6X +15) -3, distribute the -1/3 across the parentheses to get -2X - 5, and then subtract 3 to get the equivalent expression: -2X - 8.

Explanation:

The student's question is asking for the equivalent expression of -1/3 (6X +15) -3. To find the equivalent expression, we start by distributing the -1/3 across the parentheses:

-1/3 × 6X = -2X

-1/3 × 15 = -5

Next, we combine this result with the -3 that is outside of the parentheses:

-2X - 5 - 3 = -2X - 8

Therefore, the equivalent expression is -2X - 8.