please help me solve this' 2x − 4y = 6 2x + 4y = -10 (-1, -4). (-1, -2). (2, 4). (1, -2).

Answer: 40/41

Step-by-step explanation:

The cosine can be represented as adjacent/hypotenuse.  Thus, the cosine of C is 40/41

Answer:

Solution,

BC = 40

AC = 41

Now,

[tex]cos \: theta \: = \frac{adjacent}{hypotenuse} [/tex]

[tex]cos \: c \: = \frac{bc}{ac} [/tex]

Plugging the values

[tex]cos \: c \: = \frac{40}{41} [/tex]

Hope this helps..

Good luck on your assignment..

Answer:

B. 1296 in.^2

Step-by-step explanation:

The rectangles are similar, and sides ST and YZ are corresponding sides.

The linear scale factor is k = YZ/ST = 24/8 = 3

The area scale factor is k^2 = 3^2 = 9

A = 144 sq in. * k^2 = 144 sq in. * 9 = 1296 sq in.

Answer: B. 1296 in.^2

Answer:

4)1,296in^2

5)510.4ft

Step-by-step explanation:

4)

24/8=3 This is the dilation

144/8=18 This is the side length for QRST

18*3=54 The side length for WXYZ

24*54=1296 The area of WXYZ

5)

319*8/5 Your fence with a scale factor of 8/5

319*1.6 Changing 8/5 into fraction form

319*1.6=510.4 The length of the friend's fence.

Hope this helps. I could not see the end of the last question so I am sorry if it is not written properly.

Have a good day!

Answer:

108

Step-by-step explanation:

To find x, you need the geometric mean. First, find the second part of 225 by doing 225 - 144 = 81. Now, to find geometric mean, do 81 x 144 = 11,664; [tex]\sqrt{11,664} = 108[/tex].

The missing length in the right triangle as given in the task content is; 108.

It follows from the complete question that the triangle given is a right triangle and the missing length can be calculated as;

First, find the second part of 225 by

225 - 144 = 81.

Now, to find geometric mean,

81 × 144 = x²

11,664 = x²

x = 108

Thus, The missing length in the right triangle as given in the task content is; 108.

Read more on missing length;

https://brainly.com/question/28040679

#SPJ2

Answer:

The correct answer is D.

Step-by-step explanation:

Giving the following information:

R = 90x

Total cost= 35x + 17,000

x= is the number of units produced and sold

Now, we know that:

Unitary variable cost= 35

Fixed costs= 17,000

Selling price per unit= 90

To calculate the break-even point in units, we need to use the following formula:

Break-even point in units= fixed costs/ contribution margin per unit

Break-even point in units= 17,000 / (90 - 35)

Break-even point in units= 309 units

Answer:

work is shown and pictured

Answer:

C

Step-by-step explanation:

Brainliest?

Answer:

For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:

[tex] arctan(tan(\frac{2\pi}{3}))[/tex]

Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:

[tex]  arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]

Step-by-step explanation:

For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:

[tex] arctan(tan(\frac{2\pi}{3}))[/tex]

Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:

[tex]  arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]

Answer: 26 games in total.

Step-by-step explanation:

If in each game we have one winner and one loser, then after each game we have one less player.

first, out of 37 players, we can write it as 36 players  + 1 player that does not play in the first round

the 36 players play games. Because in each game we need 2 players, we have a total of 36/2 = 18 games

in those 18 games, we eliminate 18 players, so now we have 37 - 18 = 19 players.

Now, we can write 19 = 18 players + 1 player that does not play this round.

From the 18 players, we have 18/2 = 9 games.

And from those 9 games, we lose 9 players, so now we have:

19 - 9 = 10 players.

Now from those 10 players, we have 10/2 = 5 games, so after those 5 games we have 10 - 5 = 5 players.

Now we can write 5 = 4 players + 1 player that does not play this round.

from the 4 players we have 4/2 = 2 games, after those 2 games we end with 5 - 2 = 3 players.

And from those last 3 players, we have two games, where in each game one player is eliminated until we have only one winner.

Then the total number of games is:

18 + 9 + 5 + 2 + 2 = 26 games

Answer: m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Given: Circle k(O), m NM =65° ∠PNO≅∠PMO

To find: m∠PNO, m∠ONM.

Since, central angle is equal to the measure of minor arc.

⇒∠MON = m NM =65°

In Δ MON , ON = OM [Radii of circle]

⇒ ∠ONM = ∠NMO   (i)   [Angle apposite to equal side of triangle are equal]

In Δ MON , ∠ONM + ∠NMO+∠MON =180°

⇒ ∠ONM + ∠ONM+65°=180°  [from (i)]

⇒ 2∠ONM=115°

⇒ ∠ONM=57.5°

⇒ ∠ONM = ∠NMO =57.5°

Also, an inscribed angle is half of a central angle that subtends the same arc.

⇒∠MPN =half of∠MON

=  [tex]\dfrac{65^{\circ}}{2}=32.5^{\circ}[/tex]

Also, ∠PNO≅∠PMO  [Given]

⇒∠PNO =∠PMO

⇒ ∠PNO +∠ONM =∠PMO+∠NMO   [∵∠ONM = ∠NMO]

⇒∠PNM=∠PMN

In ΔNPM

⇒ ∠MPN +∠PNM+∠PMN = 180°

⇒ 32.5° +∠PNM + ∠PNM= 180°

⇒ 2(∠PNM)= 147.5°

⇒ ∠PNM = 73.75°

Also,  ∠PNM = ∠PNO+∠ONM

⇒73.75°= ∠PNO+57.5°

⇒ ∠PNO =16.25°

Hence, m∠PNO =16.25°  , m∠ONM=57.5°

Answer:

Answer: m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Given: Circle k(O), m NM =65° ∠PNO≅∠PMO

To find: m∠PNO, m∠ONM.

Since, central angle is equal to the measure of minor arc.

⇒∠MON = m NM =65°

In Δ MON , ON = OM [Radii of circle]

⇒ ∠ONM = ∠NMO   (i)   [Angle apposite to equal side of triangle are equal]

In Δ MON , ∠ONM + ∠NMO+∠MON =180°

⇒ ∠ONM + ∠ONM+65°=180°  [from (i)]

⇒ 2∠ONM=115°

⇒ ∠ONM=57.5°

⇒ ∠ONM = ∠NMO =57.5°

Also, an inscribed angle is half of a central angle that subtends the same arc.

⇒∠MPN =half of∠MON

=  

Also, ∠PNO≅∠PMO  [Given]

⇒∠PNO =∠PMO

⇒ ∠PNO +∠ONM =∠PMO+∠NMO   [∵∠ONM = ∠NMO]

⇒∠PNM=∠PMN

In ΔNPM

⇒ ∠MPN +∠PNM+∠PMN = 180°

⇒ 32.5° +∠PNM + ∠PNM= 180°

⇒ 2(∠PNM)= 147.5°

⇒ ∠PNM = 73.75°

Also,  ∠PNM = ∠PNO+∠ONM

⇒73.75°= ∠PNO+57.5°

⇒ ∠PNO =16.25°

Hence, m∠PNO =16.25°  , m∠ONM=57.5°

Step-by-step explanation:

Answer:

The shortest altitude = 8 cm

Step-by-step explanation:

Where we have the sides given by

15 cm, 17 cm, 8 cm

From cosine rule, we have;

a² = b² + c² - 2×b×c×cos(A)

We have

For the side 15 cm,

15² = 17² + 8² - 2×17×8 cos A

-388 = -612×cos×A

A = 61.93°

17² = 15² + 8² - 2×15×8 ×cos B

0 = -240·cos B

B = 90°

Therefore, 17 is the hypotenuse side and 15 and 8 are the legs, either of which can be the height which gives the shortest altitude as 8 cm

Answer:

Her Verticle ramp support was 5.5 ft tall.

Step-by-step explanation:

In this type of question, you would need to use the saying "soh cah toa".

Soh Cah Toa is a saying that people use for Sin, Cosine, and tagent. Each of those mean

Sine: opposite/hypotenuse Cosine: Adjacent/hypotenuse and Tagent: Opposite/Adjacent

In this specific question to figure out how tall or high her support is or needs to be have to 20 degree  angle off the ground, you will need to use Sin which is opposite over Hypotenuse or x/16

To find the answer in your calculator you would do:

Sin(20)=x/16

First thing you do is the get the x on one side by itself so you would multiply 16 on both sides giving you:

16 × Sin(20)= x

You would then follow to put Sin(20) in your calculator giving you 0.34202014332

After that you multiply that number by 16

5.47232229321

Rounding to the nearest tenth you get answer:

5.5

Answer:

see explanation

Step-by-step explanation:

1) 6c + 15(1) = 75

6c = 60

c = 10 packs of cupcakes

2) 6c + 15(7) = 75

6c + 105 = 75

6c = -30

c = -5, since he bought more brownies than needed, he does not need to buy any cupcakes.

Answer:

6c+15b=75

1)If the treasurer buys 1 package of brownie bites

6(1)+15b=75

15b=75-6

b=69/15=4.6 ( means the treasure needs to buy 5 packages).

2): If the treasurer buys 7 packages of brownie bites,

6c+15(7)=75

6c+105=75

c=-30/6=-5( you can not buy negative amount)

the treasure does not need to buy, because brownies are enough and more.

Answer:

The answer is option B.

Explanation:

A rule that uniquely associates elements of one set A with the elements of another set B and each element in set A maps to only one element in set B.

Each element from X is related to only one element in Y. But it is okay for two different elements in X to be related to the same element in Y. So its  still a function. Let suppose

{ (1,a) , (2, b) , (2, c) , (3, d) }

This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c.

Answer:

6 ft and 8 ft

Step-by-step explanation:

let x be the length of one leg then (x + 2) is the other leg.

Using Pythagoras' identity in the right triangle, that is

x² + (x + 2)² = 10² ← expand left side and simplify

x² + x² + 4x + 4 = 100 ( subtract 100 from both sides )

2x² + 4x - 96 = 0 ( divide all terms by 2 )

x² + 2x - 48 = 0 ← in standard form

(x + 8)(x - 6) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 8 = 0 ⇒ x = - 8

x - 6 = 0 ⇒ x = 6

But x > 0 ⇒ x = 6

Thus the 2 sides are 6 ft and x + 2 = 6 + 2 = 8 ft

Answer:

[tex]\boxed{D = 15.8\ units}[/tex]

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance Formula = [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

D = [tex]\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

D = [tex]\sqrt{(-8)^2+(-13)^2}[/tex]

D = [tex]\sqrt{81+169}[/tex]

D = [tex]\sqrt{250}[/tex]

D = 15.8 units

Answer:

15.3

Step-by-step explanation:

The coordinates are (0,9) and (-8,-4)

Distance of two points formula:

[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Plug in the values.

[tex]D=\sqrt{(-8-0)^2+(-4-9)^2}[/tex]

[tex]D=\sqrt{(-8)^2+(-13)^2}[/tex]

[tex]D=\sqrt{64+169}[/tex]

[tex]D=\sqrt{250}[/tex]

[tex]D= 15.264338...[/tex]

[tex]D \approx 15.3[/tex]

Answer:

14,7

Step-by-step explanation: if it is being divided by 2 it is 14 and 7

Answer:

[tex] s = 14.1 [/tex]

Step-by-step explanation:

Find s using the Law of Cosines:

m < S = 31°

SR = q = 21

SQ = r = 9

QR = s = ?

Thus,

[tex] s^2 = r^2 + q^2 - 2(r)(q)*cos(S) [/tex]

[tex] s^2 = 9^2 + 21^2 - 2(9)(21)cos(31) [/tex]

[tex] s^2 = 81 + 441 - 378*0.8572 [/tex]

[tex] s^2 = 522 - 324.0216 [/tex]

[tex] s^2 = 197.9784 [/tex]

[tex] s = \sqrt{197.9784} [/tex]

[tex] s = 14.07 [/tex]

[tex] s = 14.1 [/tex] (to the nearest tenth)

Answer:

[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]

Step-by-step explanation:

Part 1: Rewriting equation to match ax² + bx + c = 0 (quadratic function)

The given equation is not written in quadratic form. To rewrite the equation:

To overcome this difficulty, follow these mathematical steps:

[tex]2x^2=8x-7\\2x^2-8x=-7\\2x^2-8x+7=0[/tex]

Subtract 8x from both sides of the equation to rearrange it to the left side. Then, add 7 to rearrange it as well. Finally, set the three values on the left of the equation equal to zero.

Part 2: Using the quadratic formula

The quadratic formula is defined as [tex]\boxed{x=\frac{-b\pm\sqrt{b^2-4ac} }{2a} }[/tex].

Using the parent quadratic function, the values are easy to find in the given equation. [tex]\boxed{a=2, b=-8, c=7}[/tex]

Substitute these values into the quadratic formula and solve for x.

[tex]x=\frac{8\pm\sqrt{(-8)^2-4(2)(7)}}{2(2)} \\\\x=\frac{8\pm\sqrt{64-4(14)}}{4}\\\\x=\frac{8\pm\sqrt{64-56}}{4} \\\\x=\frac{8\pm\sqrt{8}}{4}\\\\x= 2\pm\frac{\sqrt{8}}{4}\\ \\x=2\pm\frac{\sqrt{2}}{2}[/tex]

Part 3: Solving for x with the values from the quadratic formula

Now that x is set equal to the simplified version of the equation, the operations have to be followed through with.

This equation will have two zeros/roots to solve for by setting x equal to zero.

Operation 1: Addition

[tex]x=2+\frac{\sqrt{2} }{2}\\\\x=\frac{4+\sqrt{2}}{2}[/tex]

Operation 2: Subtraction

[tex]x=2-\frac{\sqrt{2}}{2}\\ \\x=\frac{4-\sqrt{2}}{2}[/tex]

Because both values are the exact same (minus the operations), the roots can be simplified even further to one value:

[tex]\boxed{x=\frac{4\pm\sqrt{2}}{2}}[/tex]

Answer: Friday

Step-by-step explanation:

Answer:you got this

Step-by-step explanation:

Answer:

4%

Step-by-step explanation:

We can write the following equation:

20 * (x / 100) + 60 * 0.12 = 80 * 0.10 (Note that since we're writing the percentages as decimals, x% becomes x / 100 as a decimal.)

x / 5 + 7.2 = 8

x / 5 = 0.8

x = 4%

Answer:

Its B. on edge

Step-by-step explanation:

got it right on my test

Answer:

B.

Step-by-step explanation:

Well we know that

[tex]224=2^{5} *7[/tex]

so we can get the 2 outside of the radical

[tex]x^{11} =(x^{5} )^{2} *x[/tex]

and we can get the x^2 outside too.

[tex]y^8=y^5*y^3[/tex]

and we also can get y outside.

so we have:

[tex]2x^{2}y\sqrt[5]{7xy^3}[/tex]

Answer:

Our set of data is:

A. their first choice (12 people)

B their second choice (7 people)

C their third choice (3 people)

D their last choice (3 people)

The total number of people is:

12 + 7 + 3 + 3 = 25.

You already know the number of people for each situation, but let's calculate the percentage:

1st choice: The first choice of 12 people winned, and the total number of people is 25.

Now, 25 is our 100%, then 12 is equivalent to x;

Then we have

12*100% = 25*x

x = (12/25)*100% = 48%

This is:

The quotient between

Second choice:

Same reasoning as above, here the percentage is:

(7/25)*100% = 28%

Third choice:

Same reasoning as above, here the percentage is:

(3/25)*100% = 12%

Fourth/Last choice:

Same reasoning as above, here the percentage is:

(3/25)*100% = 12%

Answer:

m<R=48.2 to the nearest tenth

Step-by-step explanation:

1. sin(m<T)=2/3

m<T=arcsin(2/3)=41.81 degrees

m<R=180-90-m<T=180-90-41.81=48.19 degrees

Answer:

X= 618079825.9

Y= 6.18 crystals

Step-by-step explanation:

It takes Lily a crystal to raise 999 zombies.

It will take her x crystals to Raise 617461746174 zombies

Mathematically

One crystal= 999 zombies

X = 617461746174

X=( 617461746174*1)/999

X= 617461746174/999

X= 618079825.9

Again

It took one crystal to raise 999 zombies

It will take y crystal to raise 6174 zombies

Mathematically

One = 999

Y =( 6174*1)/999

Y= 6.18 crystals

Answer: f(x) = -3x^2 + 3x - 2

Explain: x of vertex: [tex]x[/tex] = [tex](-\frac b{2}{a} )[/tex]  = [tex]-\frac{3}{-6} = \frac{1}{2}[/tex]

y of vertex: y = [tex]f (\frac{1}{2} ) = - \frac{3}{4} + \frac{3}{2} -2=-\frac{5}{4}[/tex]

y-intercept: y = -2

x-intercept: y = 0

D = b[tex]^[/tex]^2 - 4ac = 9 - 24 = - 15 <0. There are no real roots (no x-intercepts) because D<0.

Since a <0, parabola opens downward. The parabola is below the x-axis

[tex] {3x}^{2} - 4x - 12 = 0[/tex]

[tex]a = 3[/tex]

[tex]b = - 4[/tex]

[tex]c = - 12[/tex]

Formula:

[tex] \boxed{x = \dfrac{ - b \pm \: \sqrt{ {b}^{2} - 4ac} }{2a} }[/tex]

Replacing:

[tex]x = \dfrac{ -( - 4) \pm \sqrt{ { (- 4)}^{2} - 4(3)( - 12)} }{2(3)} [/tex]

Option: C).

Answer:

39 students

Step-by-step explanation:

let x represent the number of students taking both current event and foreign language

there are : 70 eight grader taking current event and 54 taking foreign

70+54-x=93

-x=93-124

x= 31 students taking both

number of eighth graders take only a current events class and not a foreign language class: 70-31=39 students

Answer:

Area of the triangle = 469.4 ft²

Step-by-step explanation:

By applying Sine rule in the given triangle WXY,

[tex]\frac{\text{SinW}}{\text{XY}}=\frac{\text{SInY}}{\text{WX}}=\frac{\text{SinX}}{\text{WY}}[/tex]

Since m∠X + m∠Y + m∠W = 180°

m∠X + 40° + 27° = 180°

m∠X = 180° - 67°

m∠X = 113°

Now substitute the measures of sides and angles given in the picture,

[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}=\frac{\text{Sin113}}{\text{WY}}[/tex]

[tex]\frac{\text{Sin27}}{\text{XY}}=\frac{\text{SIn40}}{38}[/tex]

XY = [tex]\frac{38\text{(Sin27)}}{\text{Sin40}}[/tex]

XY = 26.84

Area of the triangle = [tex]\frac{1}{2}(\text{XY})(\text{XW})(\text{SinX})[/tex]

                                = [tex]\frac{1}{2}(26.84)(38)(\text{Sin113})[/tex]

                                = 469.42

                                ≈ 469.4 ft²

Answer:

x = -7

Step-by-step explanation:

5x+8=3x-6

Subtract 3x from each side

5x-3x+8=3x-3x-6

2x+8 = -6

Subtract 8 from each side

2x+8-8 = -6-8

2x = -14

Divide by 2

2x/2 = -14/2

x = -7

Answer: x= -7

Step-by-step explanation:

[tex]5x+8=3x-6[/tex]

[tex]\mathrm{Subtract\:}8\mathrm{\:from\:both\:sides}[/tex]

[tex]5x+8-8=3x-6-8[/tex]

[tex]5x=3x-14[/tex]

[tex]\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}[/tex]

[tex]5x-3x=3x-14-3x[/tex]

[tex]2x=-14[/tex]

[tex]\mathrm{Divide\:2\:\:on\:\:both\:sides\:}[/tex]

[tex]-14/2=-7[/tex]

[tex]x=-7[/tex]

Answer:

38.5°

Step-by-step explanation:

Given that the height of the building is 8 yard and the distance between Jonathan and the building is 10 yards.

The sun is at the top of the building, let the distance between Jonathan laying on the ground and the top of the building be x. Using Pythagoras:

x² = 10² + 8²

x² = 100 + 64

x² = 164

x = √164 = 12.86 yards

For a triangle with sides a, b, c and their respective opposite angles A, B, and C. The sine rule is given as:

[tex]\frac{a}{sin(A)} =\frac{b}{sin(B)}=\frac{c}{sin(C)}[/tex]

Let the angle that the sunlight hit the ground be y°. The andle between the building and the ground is 90°. Therefore using sine rule:

[tex]\frac{8}{sin(y)}=\frac{12.86}{sin(90)}\\\\sin(y)=\frac{8*sin(90)}{12.86}\\\\sin(y)=0.622\\\\y=sin^{-1}0.622\\\\y = 38.5^0[/tex]

Answer:

The answer is option 2.

Step-by-step explanation:

First, you have to find the length of CD using Tangent Rule, tanθ = opposite/adjacent:

[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]

[tex]let \: θ = 48[/tex]

[tex]let \: oppo. = cd[/tex]

[tex]let \: adj. = ad = 110[/tex]

[tex] \tan(48) = \frac{cd}{110} [/tex]

[tex]cd = 110 \tan(48)[/tex]

[tex]cd = 122.17 \: feet[/tex]

Next, you have to find the length of BC using Sine Rule:

[tex] \sin(θ) = \frac{oppo.}{hypo.} [/tex]

[tex]let \: θ = 65[/tex]

[tex]let \: oppo. = cd = 122.17[/tex]

[tex]let \: hypo. = bc[/tex]

[tex] \sin(65) = \frac{122.17}{bc} [/tex]

[tex]bc = \frac{122.17}{ \sin(65) } [/tex]

[tex]bc = 134.8 \: feet \: (near.tenth)[/tex]

Answer:

[tex]\boxed{134.8 \: \mathrm{ft}}[/tex]

Step-by-step explanation:

Let’s take triangle ACD.

Find length CD.

tan θ = [tex]\frac{opposite}{adjacent}[/tex]

tan (48) = [tex]\frac{CD}{110}[/tex]

110 tan (48) = CD

CD ≈ 122.167

Let’s take triangle BCD.

Find length BC.

sin θ = [tex]\frac{opposite}{hypotenuse}[/tex]

sin (65) = [tex]\frac{122.167}{BC}[/tex]

BC = [tex]\frac{122.167}{sin(65)}[/tex]

BC ≈ 134.796