what’s the solution to x-4y=-8 and 2x-3y=-16

Answer:

x + y = -1

Step-by-step explanation:

To write the equation of a line, find the slope and use it with a point in the point slope form.

You can find the slope using the slope formula.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{5--3}{-6-2} = \frac{8}{-8}=-1[/tex]

Substitute m = -1 and the point (2,-3) into the point slope form.

[tex]y - y_1 = m(x-x_1)\\y --3 = -1(x-2)\\y+3=-1(x-2)[/tex]

Convert to standard form by applying the distributive property and rearranging the terms.

y+3 = -1(x-2)

y + 3 = -x + 2

x + y + 3 = 2

x + y = -1

Answer:

All are True

a) 30a^6-24a^2=3à^2(10a^4-8)

b) 24a^4+18=6(4a^⁴+3)

c) 16a^5-20a^3=4a^3(4a^2-5)

D) 12a^3+8a=4(3a^3+2a)​

Step-by-step explanation:

a) 30a^6-24a^2=3à^2(10a^4-8)

since; 3à^2(10a^4-8)

        = 30a^6 - 24a^2

b) 24a^4+18=6(4a^⁴+3)

Since; 6(4a^⁴+3) opening the brackets

           = 24a^4 + 18

c) 16a^5-20a^3=4a^3(4a^2-5)

Since; 4a^3(4a^2-5) , opening the brackets we get

         = 16a^5 - 20^3

D) 12a^3+8a=4(3a^3+2a)​

Since;4(3a^3+2a)​, opening the bracket we get;

        = 12a^3 + 8a

have a good day!!!!!!!!!

The total cost of the regular price for a group of x people is represented by the equation C = 22x, while the total cost of the group special is represented by C = 18x + 24.

Equations for Total Cost

1. Total Cost of Regular Price: Ms. Chen can calculate the total cost for x people with the regular price by using the equation C = 22x. Here, C represents the total cost, and x is the number of people in the group.

2. Total Cost of Group Special: To calculate the total cost for x people with the group special, Ms. Chen would use the equation C = 18x + 24. C is still the total cost, x is the number of people, and 24 represents the additional fee for the private room.

By comparing the results of both equations for a specific number of people, Ms. Chen can determine which option is more cost-effective.

Final answer:

To factor the expression 3x² - 19x + 20, we find two numbers that multiply to 60 and add up to -19, which are -4 and -15. The expression can then be rewritten and factored by grouping to obtain the factors (x - 5)(3x - 4).

Explanation:

The question asks to factor the quadratic expression

3x² - 19x + 20

To factor this expression, we need to find two numbers that multiply to give the product of the coefficient of x² (which is 3) and the constant term (which is 20), and at the same time, add up to give the coefficient of x (which is -19). The two numbers that satisfy these conditions are -4 and -15, as (-4) * (-15) = 60 and (-4) + (-15) = -19.

Now, we can rewrite the expression by splitting the middle term:

3x² - 4x - 15x + 20

Factor by grouping: x(3x - 4) - 5(3x - 4)

The factors are: (x - 5)(3x - 4)

Answer:

Approx. 39.7%

Step-by-step explanation:

All you have to do is

17,892÷45,128

Answer:

40 %

Step-by-step explanation:

Percent = Responses/total surveys × 100 %

             = 17 892/45 128 × 100 %

             ≈ 40 %

Approximately 40 % of people responded to the survey.

Answer:

35 ft²

Step-by-step explanation:

We set up a system of linear equations describing this rug and then solve it:

Perimeter:  P = 2L + 2W

L = (1  2/5)W = 1.4W

Going back to the Perimeter equation, and knowing that P here is 24 ft, we have:

24 ft = 2(1.4W) + 2W, or 2.8W + 2W, or 4.8W.

Solve for W (width) by dividing both sides of this equation by 4.8:

W = 24 ft  / 4.8  = 5

The width of the rug is 5 ft; the length is 1.4(5 ft), or 7 ft.

Thus the area of the rug is A = L * W, or A = (7 ft)(5 ft) = 35 ft²

Option B is correct since both the lines given in option B have same slope so both the lines do not intersect each other and hence have no common solution.

The given equations are of the form

ax + by = c ......(1)

Slope for the equation of line is given by [tex](\dfrac{-a}{b} )[/tex]

We can  clearly see that in option B the lines given are

4x + 2y = 12 .......(2)

20x + 10y = 30....... (3)

Slope of equation (2)

[tex](\dfrac{-4}{2} )= -2[/tex]

Similarly slope of equation (3)

[tex](\dfrac{-20}{10} )= -2[/tex]

Which concludes that both are parallel to each other.

Since parallel lines can not have any common solution so  they never intersect each other. Hence option B is correct.

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False, .0034 is 1/10 of .034

The statement that 0.034 is 1/10 of 0.0034 is incorrect. In fact, 0.034 is 10 times larger than 0.0034. Thus, it's correct to say 0.0034 is 1/10 of 0.034.

No, the statement that 0.034 is 1/10 of 0.0034 is not correct. When comparing the two numbers, we can see that 0.034 is actually 10 times larger than 0.0034, not 1/10. To confirm this, we can perform the division operation: 0.034 ÷ 0.0034 = 10. Therefore, we can say that 0.0034 is 1/10 of 0.034, but not the other way around.

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Answer: OPTION C

Step-by-step explanation:

By definition you know that:

[tex]\sqrt[n]{a^n}=a[/tex]

and by the exponents properties you also know that:

[tex]a^n*a^m=a^{(n+m)}[/tex]

Now, descompose 18 into its prime factors:

18=2*3*3=2*3²

Rewrite the expression and simplify (Keep on mind that: [tex]\sqrt{x^4}=x^{(\frac{4}{2})}=x^{2}[/tex]). Then, you obtain:

[tex]\sqrt{2*3^2*x^4*y*y^2}=3x^2y\sqrt{2y}[/tex]

Answer:

C. [tex]3x^2y\sqrt{2y}[/tex].

Step-by-step explanation:

The given radical expression is  [tex]\sqrt{18x^4y^3}[/tex].

We can rewrite this radical expression to obtain;

[tex]\sqrt{2\times9 \times (x^2)^2\times y^2\times y}[/tex].

This will give us;

[tex]\sqrt{2y} \times \sqrt{9(x^2)^2 y^2}[/tex].

[tex]3x^2y\sqrt{2y}[/tex].

The correct choice is C

Answer:

<3 and <6 are Vertical angle and is the correct answer

Step-by-step explanation:

1) Vertical angle is The angles opposite each other when two or more line intersect each other or crosses each other.

Hopes this helps.

Answer:

Step-by-step explanation:

Vertical angles: each of the pairs of opposite angles made by two intersecting lines.

The vertical angles from the picture:

∡1 and ∡4

∡2 and ∡5

∡3 and ∡6

Answer:

number 16 is correct nice job!  number 17 is J=PM/300

Step-by-step explanation:

For 16 the answer is option D

For 17 the correct option is D

See the attached figure

Answer:

The inequality is

6+4r>17

The miminum number of runs per inning is  

3.

Step-by-step explanation:

Answer:

[tex]S.A=96\pi m^2[/tex]

Step-by-step explanation:

The surface area of a right circular cylinder is given by the formula;

[tex]S.A=2\pi r(r+h)[/tex]

where [tex]h=8m[/tex] is the height of the cylinder and

[tex]r=4m[/tex] is the radius of the cylinder.

We plug in these values into the formula to obtain;

[tex]S.A=2\pi \times4(4+8)[/tex]

[tex]S.A=8 \times12 \pi[/tex]

[tex]S.A=96\pi m^2[/tex]

Answer:

-2

Step-by-step explanation:

slope is equal to:       y2-y1

                                _______ =

                                   x2-x1

  6-2            4

______ = _____ = -2

-7-(-5)          -2

The unit rate in the equation 64t = 384 is 64.

The unit rate in the equation 64t = 384 is 64.

To find the unit rate, we divide the total value by the number of units. In this case, the total value is 384 and the number of units is 64. When we divide 384 by 64, we get the unit rate of 6.

Therefore, the unit rate in the equation is 64.

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The unit rate in the equation 64t = 384 is 6.

The unit rate in the equation 64t = 384 is 6.

To find the unit rate, divide both sides of the equation by 64:

t = 384/64 = 6.

Therefore, the unit rate is 6, which means that Steve drove at a constant rate of 6 hours to reach the beach.

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To round 7/11 to three decimal places, you divide 7 by 11 to get 0.63636..., and then round the result to 0.636 since the fourth decimal place is 6, which mandates rounding up.

To convert 7/11 as a decimal rounded to 3 decimal places, you can either use a calculator or do long division. After dividing 7 by 11, you will get a result that must be rounded to maintain only three digits after the decimal point. To round off a decimal number, look at the digit after the place you want to round to. In this case, if you want to round to three decimal places, you will look at the fourth place after the decimal. If this digit is 5 or higher, you round up the third-place digit. If it's lower than 5, you leave the third-place digit as it is.

So, converting 7/11 into a decimal, you get approximately 0.63636... Looking at the fourth decimal place, we see that the digit is 6, which means we round up the third decimal place. So, 7/11 rounded to three decimal places is 0.636.

Answer:

You can make one triangle with these lengths

Step-by-step explanation:

we know that

The Triangle Inequality Theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side

Verify if the lengths satisfy the triangle inequality theorem

1) 2+1 > 2

3 > 2 ------> is true

2)2+2 > 1

4 > 1 -----> is true

so

The lengths  satisfy the triangle inequality theorem

therefore

You can make one triangle with these lengths

Answer:

You can make 11 recipes with 7 1/2 cups of walnuts

Answer:

Step-by-step explanation:

11 1/4 but it says the number of full recipes so it would be 11

Answer:

Step-by-step explanation:

f(x) = - 4x + 3

x = - 5

f(- 5) = - 4.(- 5) + 3

f(- 5) = 20 + 3

f(- 5) = 23

Alternative D

I hope I helped you.

Answer:

the answer is D

Step-by-step explanation:

Answer:

radius=3.5 Diameter=7 Circumference=21.99 area=38.48

Step-by-step explanation: These are the answers, hope you found them helpful :)

Answer:B.

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

it is C because A, B, and D are triangular prisms.

Answer:

a.) is 36 square meters

b.) 400 square meters

Step-by-step explanation:

to find the Volume you must multiply the length, width, and the hight. so to find a.) V = lwh

6 x 2 x 3 = 36

36 square meters.

and you can use the same formula for b.)

Hope this helps!

Please mark as brainliest! Thanks!

Volume of a) 36 cubic meter

Volume of b) 400 cubic feet

Let, Length of the rectangular solid = l unit

Width of the rectangular solid = w unit

And height of the rectangular solid = h unit

Then volume of rectangular solid = l × w × h cubic unit

Given, Length of the rectangular solid = 6 meters

Width of the rectangular solid = 2 meters

And height of the rectangular solid = 3 meters

∴ Volume of the rectangular solid = (6×2×3) cubic meter

                                                        = 36 [tex]m^{3}[/tex]

Given, Length of the rectangular solid = 5 feet

Width of the rectangular solid = 10 feet

And height of the rectangular solid = 8 feet

∴ Volume of the rectangular solid = (5×10×8) cubic feet

                                                        = 400 cubic feet

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this is the answer to your equation

The solutions to the equation x² = -63 in simplified, rationalized form are:

x = 3√7 * i

x = -3√7 * i

Isolate x²: In this case, x² is already isolated on one side of the equation.

Apply the Square Root Property: Take the square root of both sides of the equation to eliminate the exponent on x²:

√(x²) = √(-63)

Simplify and Introduce Imaginary Unit: Recall that the square root of a negative number is an imaginary number. We introduce the imaginary unit 'i,' defined as √(-1):

x = ±√(63) * √(-1)

x = ±√63 * i

Simplify and Rationalize: √63 cannot be simplified further, but we can rationalize it by multiplying both the numerator and denominator by √3:

x = ±√63 * i * √3 / √3

x = ±3√7 * i

Answer:

Step-by-step explanation:

(1/4) (2-5x+6)

=(1/4)(8-5x)

= 8/4 - 5x/4

=1/2 - 5x/4

[tex]AB\: is \:the \:diameter\Rightarrow \widehat{ACB}=90°\Rightarrow \widehat{ABC}=180°-90°-30°=60° \: (1) \\ \bigtriangleup OBC \: has \: OB=OC=R\Rightarrow \bigtriangleup OBC \: is \: an \: isosceles \: triangle \: (2) \\ (1),(2)\Rightarrow \bigtriangleup OBC \: is \: an \: equilateral \: t riangle \Rightarrow \widehat{COB} =\widehat{COD} = 60° \\ CD \: tangents \: (O) \: at \: C\Rightarrow OC\perp OD \: at \: C\Rightarrow \widehat{OCD}=90° \\ \widehat{CDO}=180°-\widehat{OCD}-\widehat{COD}=180°-90°-60°=30° \\ In\: \bigtriangleup ACD,\widehat{CAD}=\widehat{CDA}=30°\\\Rightarrow \bigtriangleup ACD\: is\: an\: isosceles\: triangle\: at\: C[/tex]

Triangle ACD is an isosceles triangle, with AC = AD.

A triangle is a 2-D figure with three sides and three angles.

The sum of the angles is 180 degrees.

We can have an obtuse triangle, an acute triangle, or a right triangle.

We have,

Let O be the center of the circle, and let E be the point where the tangent line to the circle at point C intersects diameter AB.

Since OC is perpendicular to CE (tangent line at C), and OD is perpendicular to AB, angle ECD and angle OAD are alternate angles, and hence congruent.

Now,

Since the measure of the angle between diameter AB and chord AC is 30°, the measure of angle AOC is 60°.

The measure of angle OAD is also 60°.

Now,

Since angles ACD and OAD are congruent, and angle AOC is 60°,

we have:

angle ACD = angle OAD = 60°

Also,

Since OC is perpendicular to AC (radius of the circle),

we have angle OCA = 90°.

Now,

angle ACB

= angle OCA - angle AC0

= 90° - 30°

= 60°

Since angle ACD is equal to angle ACB, and angle AOC is also equal to 60°,

We have:

angle ACD = angle ACB = 60°

angle AOC = 60°

Therefore,

Triangle ACD is an isosceles triangle, with AC = AD.

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Answer:

1. Area = 113.1 square units

2. Area = 28.27 square units

3. Area of Shaded = 22.27 square units

Step-by-step explanation:

1.

Area of the circle is given by the formula   [tex]A=\pi r^2[/tex]

where A is the area and r is the radius

In our case the radius is 6 units, thus we have:

[tex]A=\pi r^2\\A=\pi (6)^2\\A=\pi *36\\A=113.1[/tex]

Area = 113.1 square units

2.

When we have the angle given in radians, the area of sector is given by the formula   [tex]A=\frac{1}{2}r^2\theta[/tex]

Where  [tex]\theta[/tex]  is the central angle ( in our case [tex]\theta = \frac{\pi}{2}[/tex] and r is the radius (it is 6)

Plugging in these info into the formula we have area of sector:

[tex]A=\frac{1}{2}r^2\theta\\A=\frac{1}{2}(6)^2(\frac{\pi}{2})\\A=\frac{1}{2}*36*\frac{\pi}{2}\\A=28.27[/tex]

Area = 28.27 square units

3.

Area of shaded region = Area of Sector - Area of Triangle

We know area of sector is 28.27

Since the angle is 90 degrees, we have a right triangle, we can use the pythagorean theorem to find the height of the triangle, CE.

Thus

[tex]DC^2+CE^2=DE^2\\3^2+CE^2=5^2\\9+CE^2=25\\CE^2=25-9\\CE^2=16\\CE=4[/tex]

The area of triangle is  [tex]A=\frac{1}{2}bh[/tex]

where b is the base (in our case it is DC = 3 ) and h is the height (in our case it is CE, which is 4). Plugging into the formula we have the area of triangle as:

[tex]A=\frac{1}{2}bh\\A=\frac{1}{2}(3)(4)\\A=6[/tex]

Area of Shaded = 28.27 - 6 = 22.27 square units

Answer:

2

Step-by-step explanation:

Answer:

it is 5/6

Step-by-step explanation:

it's easy. There are 5 numbers that are greater than 2.

Answer: the answer is 2/3 i took the test

The car would be about 90 ft

The Answer is hundredths