What is the solution to the system of equations? 3x-6 = -12
x-2y = -8

(a) Use the substitution method to justify that the given system of equations has no solution.
(b) What do you know about the two lines in this system of equations?

Check the picture below.

so, the reference angle, will be the angle made by it with the x-axis, namely 75°.

Answer:

the answer for this is 57 I believe

Step-by-step explanation:

I cue the shape into a small rectangle with sides of 3, 3, and 1 which comes out to 9 cubic feet, and then I took the rest of the shape which became a bigger rectangle with sides of 2, 6, and 4 which comes out to 48 cubic feet. 48+9=57. Sorry if I am wrong, I tried my best. Hope this helps!

Answer: 36

Step-by-step explanation:

1) Chop the image like a hamburger, leaving the top part sticking out. You can draw a line.

2) Find the length, width, and height. 2*3*4=24

3) Find the top part that was separated from the bottom part with the line that you drew. The height of the bottom prism was 2 and the height on the other side of the prism was 3. 3-2=1

4) So, you got the height of the piece that is cut out like a small square on the top left corner of the shape. That height will be used as the height for the top part now.

5) You found the height, which was 1. Now the length is shown at the bottom of the bottom prism, which is 3. All that's left is to find the width. The width is the same as the bottom prism, which is 4. 1*3*4=12

6) Add the two volumes together to find the whole volume. 24+12=36

1 Use Integration by Parts on \int \sec^{3}x \, dx∫sec

​3

​​ xdx.

Let u=\sec{x}u=secx, dv=\sec^{2}xdv=sec

​2

​​ x, du=\sec{x}\tan{x} \, dxdu=secxtanxdx, v=\tan{x}v=tanx

2 Substitute the above into uv-\int v \, duuv−∫vdu.

\sec{x}\tan{x}-\int \tan^{2}x\sec{x} \, dxsecxtanx−∫tan

​2

​​ xsecxdx

3 Use Pythagorean Identities: \tan^{2}x=\sec^{2}x-1tan

​2

​​ x=sec

​2

​​ x−1.

\sec{x}\tan{x}-\int (\sec^{2}x-1)\sec{x} \, dxsecxtanx−∫(sec

​2

​​ x−1)secxdx

4 Expand (\sec^{2}x-1)\sec{x}(sec

​2

​​ x−1)secx.

\sec{x}\tan{x}-\int \sec^{3}x-\sec{x} \, dxsecxtanx−∫sec

​3

​​ x−secxdx

5 Use Sum Rule: \int f(x)+g(x) \, dx=\int f(x) \, dx+\int g(x) \, dx∫f(x)+g(x)dx=∫f(x)dx+∫g(x)dx.

\sec{x}\tan{x}-\int \sec^{3}x \, dx+\int \sec{x} \, dxsecxtanx−∫sec

​3

​​ xdx+∫secxdx

6 Set it as equal to the original integral \int \sec^{3}x \, dx∫sec

​3

​​ xdx.

\int \sec^{3}x \, dx=\sec{x}\tan{x}-\int \sec^{3}x \, dx+\int \sec{x} \, dx∫sec

​3

​​ xdx=secxtanx−∫sec

​3

​​ xdx+∫secxdx

7 Add \int \sec^{3}x \, dx∫sec

​3

​​ xdx to both sides.

\int \sec^{3}x \, dx+\int \sec^{3}x \, dx=\sec{x}\tan{x}+\int \sec{x} \, dx∫sec

​3

​​ xdx+∫sec

​3

​​ xdx=secxtanx+∫secxdx

8 Simplify \int \sec^{3}x \, dx+\int \sec^{3}x \, dx∫sec

​3

​​ xdx+∫sec

​3

​​ xdx to 2\int \sec^{3}x \, dx2∫sec

​3

​​ xdx.

2\int \sec^{3}x \, dx=\sec{x}\tan{x}+\int \sec{x} \, dx2∫sec

​3

​​ xdx=secxtanx+∫secxdx

9 Divide both sides by 22.

\int \sec^{3}x \, dx=\frac{\sec{x}\tan{x}+\int \sec{x} \, dx}{2}∫sec

​3

​​ xdx=

​2

​

​secxtanx+∫secxdx

​​  

10 Original integral solved.

\frac{\sec{x}\tan{x}+\int \sec{x} \, dx}{2}

​2

​

​secxtanx+∫secxdx

​​  

11 Use Trigonometric Integration: the integral of \sec{x}secx is \ln{(\sec{x}+\tan{x})}ln(secx+tanx).

\frac{\sec{x}\tan{x}+\ln{(\sec{x}+\tan{x})}}{2}

​2

​

​secxtanx+ln(secx+tanx)

​​  

12 Add constant.

\frac{\sec{x}\tan{x}+\ln{(\sec{x}+\tan{x})}}{2}+C

​2

​

​secxtanx+ln(secx+tanx)

​​ +C

To integrate sec³(x), use integration by parts and trigonometric identities, ultimately resulting in the integral: 1/2 * (sec(x) * tan(x) + ln|sec(x) + tan(x)|) + C.

To integrate sec³(x), we can use integration by parts. Let’s denote the integral by I:

I = ∫ sec³(x) dx

First, we use the identity:

We know that sec²(x) = 1 + tan²(x), so:

Now, we use integration by parts:

Then, du = sec(x) * tan(x) dx and v = tan(x).

Using integration by parts formula ∫ u dv = uv - ∫ v du, we get:

Which simplifies to:

We already know sec²(x) = 1 + tan²(x), so:

Answer:

angle 2 is 43 as the opposite side of the angle is always equal angle 1 and 3 are:

step 1

43+43=86

step 2

360-86=274

step 3

274÷4=68.5

we subtracted 86 with 360 because 360 is the sum of all the angles we then divided  the answer by 2 as we were suppose to find two angles angle 1 and 3 are opposite angles so they both will be same

      hope this information helps u :)

Answer:

see explanation

Step-by-step explanation:

∠1 and 43° form a straight angle = 180°, hence

∠1 = 180° - 43° = 137°

∠2 = 43° ( vertical to 43° )

∠3 = 137° ( vertical to ∠1 )

Answer:

2, 29

Step-by-step explanation:

The prime numbers are 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89, and 97.

Answer: 2:1

Step-by-step explanation:

Answer:   (5n - 8)(n² - 3)

Step-by-step explanation:

You can factor this using the Grouping Method (hint: rearrange the terms)

   5n³ - 8n² - 15n + 24

=  5n³ - 15n   -8n² +24

=  5n(n² - 3)   -8(n² - 3)

= (5n - 8)(n² - 3)

Answer:

[tex]y=\frac{1}{4p}x^{2}[/tex]

Step-by-step explanation:

∵ The directrix is y = -p

∵ The focus is (0 , p)

∵ (x , y) is a general point on the parabola

∵ The distance between (x , y) and the directrix = the distance

   between (x , y) and the focus

By using the rule of distance:

∵ (y - -p)² = (x - 0)² + (y - p)²

∴ (y + p)² = x² + (y - p)²

∴ y² + 2py + p² = x² + y² - 2py + p²

∴ 2py + 2py = x²

∴ 4py = x² ⇒ ÷ 4p in both sides

∴ [tex]y=\frac{1}{4p}x^{2}[/tex]

Answer:

80 is the volume

Step-by-step explanation:

l*b*h

5*2*8

80

L*W*H

8*5 = 40

40*2 = 80

The volume is 80 cm^3

Answer:

(0, 15) and (11, 48)

Step-by-step explanation:

Given the 2 equations

y = x² - 8x + 15 → (1)

y = 3x + 15 → (2)

Substitute y = x² - 8x + 15 into (2)

x² - 8x + 15 = 3x + 15 ( subtract 3x + 15 from both sides )

x² - 11x = 0 ← in standard form

x(x - 11) = 0 ← in factored form

Equate each factor to zero and solve for x

x = 0

x - 11 = 0 ⇒ x = 11

Substitute these values into (2) for corresponding values of y

x = 0 : y = 0 + 15 = 15 ⇒ (0, 15)

x = 11 : y = 33 + 15 = 48 ⇒ (11, 48)

Solutions are (0, 15), (11, 48)

Answer:

100

Step-by-step explanation:

sqrt[y] = 10

Apply both side a ^2

then

y = 100

Best regards

Answer:   b. 100

Step-by-step explanation:

[tex]\sqrt y-7=3\\\\\sqrt y=10\qquad added\ 7\ to\ both\ sides\\\\(\sqrt y)^2=(10)^2\\\\y=100\\\\\\Check:\\\sqrt{100}-7=3\\\\10-7=3\ \checkmark[/tex]

9514 1404 393

Answer:

  A (and C)

Step-by-step explanation:

A relationship that is a direct proportion is described by the equation ...

  y = kx

for some constant k.

You can examine the tables to see what the value of k is by looking at ...

  k = y/x

__

In table A, the values of k are 125/5 = 250/10 = 500/20 = 25.

In table B, the values of k are 100/50 = 2, 250/20 = 125, 50/10 = 5. These are not constant, so the relation is not a proportional one.

In table C, the values of k are -125/5 = -250/10 = -500/20 = -25.

In table D, the values of k are 8/2 = 4, 10/4 = 2.5, 12/6 = 2. These values are not constant, so the relation is not a proportional one.

__

We see that the tables of A and C both represent proportional relationships. We usually expect the value of k to be positive, but there is nothing in the definition of a proportional relationship that demands that be the case.

If this is a single-answer question, choose A.

If this is an "all that apply" question, choose A and C.

Answer:

54

Step-by-step explanation:

add all of the numbers then subtract from 100

Answer: Bonnie went to a meadow to pick flowers there was 20 flowers in one area and had decided to pick 18 of the flowers, how many flowers are left?

Step-by-step explanation: I don't know.... Just something random, hope I was able to help!

A Number story was written to describe the given mathematical equation.

Mercy had 20 balls, 6 were of green color, 6 were of blue color, 6

were of red color, 2 were of yellow colors. One day six of her friends came

to her home and each of them liked the balls Mercy had. All of them

requested Mercy to offer one ball of each color i.e. green, blue, and red. Since they were the best friends of Mercy so Mercy couldn't deny it.

She offered each friend 3 balls of green, blue, and red color each. Since She offered 3 balls to each of her friends i.e 18 balls, she was left with

20-(3*6) = 2 yellow color balls.

Thus, a number story was written to describe the given mathematical equation.

Answer:

In my opinion I would say Tax Dollars

Hope This Helps!     Have A Nice Day!!      

Whether public goods should be paid for through taxes or individual fees depends on various factors, including the nature of the good and one's income level. For many public goods and services, a combination of tax funding and user fees is used. The decision between the two is a matter of public policy and individual preference.

The decision on whether to pay for public goods through taxes or individual fees depends on various factors. In essence, this relates to the discussion on public provision versus personal pay-per-use. Some public goods, like parks, are free to use, but the government charges for certain services, such as parking or reserving picnic areas. This is a mixture of public provision at no charge along with fees for some purposes.

On the other hand, taxes are paid by most working people and by consumers when they buy goods and services. These taxes fund public services like roads, bridges, schools, and public safety functions. Thus, some may prefer public goods to be funded through taxes so everyone contributes to these community-supporting services.

Nonetheless, there are also 'toll goods', like cable TV and private schools, that are open to everyone but require users to pay a fee. The choice between taxes versus individual fees can also depend on one's income level, as those with more discretionary income might prefer pay-per-use to avoid potential higher taxes.

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Answer:

y = 1/2 x

Step-by-step explanation:

slope = 1/2 and y-intercept = 0

so equation

y = 1/2 x

Answer:

x = 32/7, or 4 4/7 meals

Step-by-step explanation:

Write and solve an equation of ratios, as follows:

 7/8 lb           4 meals

------------        -------------

    1 lb                   x

x will be the number of meals necessary for the dog to eat 1 lb of food.

Cross-multiplying, (7/8)x = 4.

Multiplying both sides by 8/7 is an easy way to isolate x:

(8/7)(7/8)x = (8/7)(4)

or

              x = 32/7, or 4 4/7 meals

the measure is 140, I basically summed all of the angles of a polygon of “n”, which is 7, then I did 7-2 times 180 (900) so I can finally add up all of your measurements

The seventh angle of the given Heptagon is 140 degrees.

A heptagon is a polygon that has seven sides. It is a closed figure having 7 vertices. A heptagon is also sometimes called Septagon.

Given, six angles of a heptagon measure 107, 139, 131, 110, 145. and 128.

Since, Sum of all angles of Heptagon is 900°

Let "x" be the seventh angle of Heptagon

thus,

107 + 139 + 131  + 110 + 145 + 128 + x = 900

760 + x = 900

x = 140

Therefore, The seventh angle of the given Heptagon is 140 degrees.

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Answer:

The diagonal  is about 14 m

Step-by-step explanation:

A = s^2

98 = s^2

so

s = √98

diagonal c^2 = 98 + 98

c^2 = 196

c = √196

c  ≈ 14

Answer:

The diagonal  is about 14 m

Answer:

C= 14

Step-by-step explanation:

The side is the square root of the area

S × S = A

S = √98

The diagonal is the hypotenuse of a right triangle formed by the two sides so

a²  + b² = c²

Where C = the diagonal A = √98 , B = √98

so C²= (√98)² + (√98)²

This gives: C²= 98 + 98 or

C² = 196

√C² = √196

C= 14

1.50 waters 2.80 nachos

hope this helps :)

The cost of each nachos is $2.50 and the cost of each water bottle is $1.50.

A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.

Let x be the cost of each water bottle and y be the cost of each nachos.

Two bottled water and an order of cheese nachos costs $5.50.

So, 2x+y=5.50 -------(I)

Three bottled water and two orders of cheese nachos costs $9.50​

3x+2y=9.50 -------(II)

Multiply equation (I) by 2, we get

4x+2y=11 -------(III)

Subtract equation (II) from equation (III), we get

4x+2y-(3x+2y)=11-9.50

x=$1.50

Substitute x=1.50 in equation (I), we get

2(1.50)+y=5.50

y=$2.50

Therefore, the cost of each nachos is $2.50.

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"Your question is incomplete, probably the complete question/missing part is:"

Two bottled waters and an order of cheese nachos costs $5.50. Three bottled waters and two orders of cheese nachos costs $9.50​. How much money does the nachos cost.

Answer:

The total surface area = 10956 m²

Step-by-step explanation:

∵ The pyramid is rectangular pyramid

∴ It has a rectangular base with dimensions of 50 m and 78 m

∴ It has four faces each two opposite are congruent

* to find the total surface area, we will find the area of

  each face and add them together

- Area base = L × W

∴  Area base = 50 × 78 = 3900 m² ⇒ (1)

- Area of triangular face of dimensions:

 base = 50 m and height = 60 m

∵ Area triangle = 1/2 × base × height

∴ Area triangle = 1/2 × 50 × 60 = 1500 m²

∵ We have another triangle congruent to this triangle (opposite faces)

∴ Area of the two congruent faces = 1500 × 2 = 3000 m² ⇒ (2)

- Area of triangular face of dimensions:

 base = 78 m and height = 52 m

∵ Area triangle = 1/2 × base × height

∴ Area triangle = 1/2 × 78 × 52 = 2028 m²

∵ We have another triangle congruent to this triangle (opposite faces)

∴ Area of the two congruent faces = 2028 × 2 = 4056 m² ⇒ (3)

∴ Add (1) , (2) and (3)

∴ The total surface area = 3900 + 3000 + 4056 = 10956 m²

Answer:

The total answer is : 10956 m²

Step-by-step explanation:

Answer:

The answer is 195 :)))

Step-by-step explanation:

Step-by-step explanation:

Divide the circumference by pi to get diameter, which is 14. Divide 14 by 2 for the radius, which is 7. Now square the radius to get 49, and multiply by pi for the area.

Area is 49pi.

The area of the circle in terms of π with a circumference of 14π is 49π units².

Given a circle.

Also, given that:

Circumference of the circle = 14π

It is required to find the area of the circle.

It is known that:

Circumference of a circle is:

C = 2πr, where r is the radius.

So, here,

2πr = 14π

2r = 14

r = 7

So, the radius of the circle is 7.

So, the area of the circle is:

A = πr²

  = π(7)²

  = 49π

Hence, the area is 49π.

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Answer:

The next step is to put all terms into the left side of the equation and group the like trems

Step-by-step explanation:

The first step in determining the solution to the system of equations, [tex]y =-x^2-4x-3[/tex] and [tex]y = 2x + 5[/tex], algebraically is to set the two equations equal as [tex]-x^2-4x-3 = 2x + 5.[/tex]

The next step is to put all terms into the left side of the equation and group the like trems:

[tex]-x^2-4x-3-2x-5=0,\\ \\-x^2+(-4x-2x)+(-3-5)=0,\\ \\-x^2-6x-8=0.[/tex]

Now you can multiply this equation by -1:

[tex]x^2+6x+8=0[/tex]

and solve it using quadratic formula:

[tex]x_{1,2}=\dfrac{-6\pm \sqrt{6^2-4\cdot 8\cdot 1}}{2\cdot 1}=\dfrac{-6\pm\sqrt{4}}{2}=\dfrac{-6\pm 2}{2}=-4,\ -2.[/tex]

Answer:

The answer is $7.50.

Step-by-step explanation:

First you have to find the price of the souvenirs which were $2.25, just by doing each common price. Then you just do the answer you got divided by two.

The one ticket for this basketball game is $ 7.50, and one ticket for a souvenir is $2.25.

It is defined as the relation between two variables if we plot the graph of the linear equation we will get a straight line.

If in the linear equation one variable is present then the equation is known as the linear equation in one variable.

Let's suppose the price of the one ticket = $x

And the price of the one souvenir = $y

We have:

2x + y = 17.25 ....(1)

5x + 2y = 42.00 ....(2)  (from the quetion)

From the equation (1):

y = 17.25 - 2x

Put the value of y in the equation (2), we get:

5x +2(17.25 -2x) = 42

5x + 34.5 - 4x = 42

x = 42 - 34.5

x = $ 7.50

and y = 17.25 - 2x ⇒ 17.25 - 2(7.5) ⇒ $2.25

Thus, the one ticket for this basketball game is $ 7.50, and one ticket for a souvenir is $2.25.

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Answer: Objects have the same velocity only if they are moving at the same speed and in the same direction. Objects moving at different speeds, in different directions, or both have different velocities.

Answer:

Step-by-step explanation:

There are 4 quarts in a gallon.

So, that is $32 a gallon.

2 gallons is $64

So y = 1/3x + 7, therefore the gradient is 1/3 and the y-intercept is 7.