What is the solution to this equation?
8 - 2x + 6x = 24
A. X= 4
B. x = 8
C. x= -4
D. x = -8

Answer:

~1.8 mile

Step-by-step explanation:

Michael lives at the closest  point to the school (the origin) on Maple Street,  which can be represented by the line  y = 2x – 4.

This means Michael's house will be the intersection point of line y1 (y = 2x - 4) and line y2 that is perpendicular to y1 and passes the origin.

Denote equation of y2 is y = ax + b,

with a is equal to negative reciprocal of 2 => a = -1/2

y2 pass the origin (0, 0) => b = 0

=> Equation of y2:

y = (-1/2)x

To find location of Michael's house, we get y1 = y2 or:

     2x - 4 = (-1/2)x

<=> 4x - 8 = -x

<=> 5x = 8

<=> x = 8/5

=> y = (-1/2)x = (-1/2)(8/5) = -4/5

=> Location of Michael' house: (x, y) = (8/5, -4/5)

Distance from Michael's house to school is:

D = sqrt(x^2 + y^2) = sqrt[(8/5)^2 + (-4/5)^2) =  ~1.8 (mile)

Answer:

4(x+8)

Step-by-step explanation:

4x+32

x+8 in parentheses

and put the 4 on the outside of the parentheses

like this 4(x+8)

Answer:

4(x+8)

Step-by-step explanation:

4x + 32

Rewriting

4*x + 4*8

Factor out 4

4(x+8)

Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

Answer:

Option (C)

Step-by-step explanation:

Given expression is 4(x + x + 7) - 2x + 8 - 4

When x = 1,

Value of the expression will be,

= 4(1 + 1 + 7) - 2(1) + 8 - 4

= 4(9) - 2 + 8 - 4

= 36 - 2 + 8 - 4

= 38

For x = 2,

= 4(2 + 2 + 7) -2(2) + 8 - 4

= 44 - 4 + 8 - 4

= 44

Now we will check the same for the given options.

Option (A). For x = 1,

6x + 11 = 6(1) + 11

           = 17

For x = 2,

6x + 11 = 6(2) + 11

          = 23

Option (B). For x = 1,

3(x + 7) = 3(1 + 7)

            = 24

For x = 2,

3(x + 7) = 2(2 + 7)

            = 18

Option (C), x = 1

2(3x + 16) = 2[3(1) + 16]

                = 38

For x = 2,

2(3x + 16) = 2[3(2) + 16]

                = 44

Option (D), For x = 1,

            = 19

For x = 2,

2(3x + 16) = 2[3(2) + 16]

                = 44

Since value of the expression for x = 1 and 2 matches with the value in option (C)

Therefore, Option (C) will be the answer.

Answer:

The measures of the two angles are 80 and 100

Step-by-step explanation:

Let [tex]m_1[/tex] and [tex]m_2[/tex] represent the two angles such that

[tex]m_1 = m_2 - 20[/tex]

Required

Find [tex]m_1[/tex] and [tex]m_2[/tex]

The two angles of a same-side interior angle of parallel lines add up to 180;

This implies that

[tex]m_1 + m_2 = 180[/tex]

Substitute [tex]m_2 - 20[/tex] for [tex]m_1[/tex]

[tex]m_1 + m_2 = 180[/tex] becomes

[tex]m_2 - 20 + m_2 = 180[/tex]

Collect like terms

[tex]m_2 + m_2 = 180 + 20[/tex]

[tex]2m_2 = 180 + 20[/tex]

[tex]2m_2 = 200[/tex]

Divide both sides by 2

[tex]\frac{2m_2}{2} = \frac{200}{2}[/tex]

[tex]m_2 = \frac{200}{2}[/tex]

[tex]m_2 = 100[/tex]

Recall that [tex]m_1 = m_2 - 20[/tex]

[tex]m_1 = 100 - 20[/tex]

[tex]m_1 = 80[/tex]

Hence, the measures of the two angles are 80 and 100

Answer:

8.6

Step-by-step explanation:

The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6

The square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

The square root of the value 74 will be calculated as below:-

D = √74

D = 8.602325267

D = 8.6

Therefore, the square root of 74 is 8.602325267. If you round this number to the nearest tenth you get 8.6.

To know more about expression follow

https://brainly.com/question/723406

#SPJ2

Answer:

Option (4)

Step-by-step explanation:

To solve this question we will try to factor the expressions given in each option.

Option (1)

g⁵ - g = g(g⁴ - 1)

         = g(g² - 1)(g² + 1)

         = g(g - 1)(g + 1)(g² + 1)

Option (2)

4g³ + 18g² + 20g = 2g(2g² + 9g + 10)

                            = 2g[2g + 5g + 4g + 10]

                            = 2g[g(2g + 5) + 2(g + 5)]

                            = 2g(2g + 5)(g + 2)

Option (3)

24g² - 6g⁴ = 6g²(4 - g²)

                 = 6g²(2 - g)(2 + g)

Option (4)

2g² + 5g + 4

This expression is the in the completely factored form.

Answer:

yes its D :)

Step-by-step explanation:

other guy has the math, i just know the answer, sorry lol

Answer:

Statement                                   Reason

1. [tex]4x+5x-2=6[/tex]                 1. Distributive Property

2. [tex]9x-2=6[/tex]                        2. Combine like terms

3. [tex]9x=8[/tex]                              3. Addition Property of Equality

4. [tex]x=\dfrac{8}{9}[/tex]                               4. Division Property of Equality

Step-by-step explanation:

The given equation is

[tex]4x+\dfrac{1}{2}(10x-4)=6[/tex]

Using distributive property, we get

[tex]4x+\dfrac{1}{2}(10x)+\dfrac{1}{2}(-4)=6[/tex]

[tex]4x+5x-2=6[/tex]

[tex]9x-2=6[/tex]         (Combine like terms)

Using Addition Property of Equality, add 2 on both sides.

[tex]9x=6+2[/tex]

[tex]9x=8[/tex]

Using Division Property of Equality, divide both sides by 9.

[tex]x=\dfrac{8}{9}[/tex]

Answer:

let me know when you have the anwser

Step-by-step explanation:

Answer:

£380

Step-by-step explanation:

Consider the initial win of £4750

Sum the parts of the ratio, 1 + 4 = 5 parts

Divide the win by 5 to find the value of one part of the ratio.

£4750 ÷ 5 = £950 ← value of 1 part of the ratio

Thus Jim's share is £950

Sum the parts of the ratio shared in his family, 2 + 6 + 2 = 10 parts

Divide his share by 10 to find the value of one part

£950 ÷ 10 = £95 , thus

2 parts = 2 × £95 = £190 ← sons share

6 parts = 6 × £95 = £570 ← wife's share

£570 - £190 = £380

Wife gets £380 more than the son

Answer:

134-35/16-4 (A)

Step-by-step explanation:

I just know

Answer

A)  134-35/16-4

Step-by-step explanation:

Answer:

This is modelling the exterior angle formula which states that the measure of an exterior angle is equal to the sum of the measures of its two remote interior angles. Therefore, the answer is x = a + b.

Answer:

x = a+b

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the opposite interior angles

x = a+b

Answer:

Step-by-step explanation:

Givens

Petri Dish A sees a double ever 10 minutes

Petri Dish B sees a double ever 6 minutes

Consequences

A doubles 60 / 10 = 6 times.

B doubles 60 / 6 = 10 times.SolutionIf you work best with numbers then suppose there are 100 bacteria in both dishes at the beginningA = 100 * 2^6B = 100 * 2^10A will have 100 * 64 = 6400 bacteria growing inside AB will have 100 * 1024 = 102400 bacteria growing inside BB/A = 102400 / 6400 = 16There are 16 times as many in B than in A

Answer:

x^2+y^2=25

Step-by-step explanation:

x^2+y^2=25 graphs a circle. A relation is a function if every x only has one y value. This is not true in a circle.

Answer:

d) x^2 + y^2 = 25.

Step-by-step explanation:

D is the equation of a circle so it fails the vertical line test for a function. If a relation is a function then any vertical line passing through it's graph will only intersect it once. This is not true of a circle.

Answer:

Step-by-step explanation:

The formula is

[tex]y=45(4)^x[/tex]

which models the exponential function

[tex]y=a(b)^x[/tex] where a is the initial amount of whatever it is you have (in our case it's bacteria), b is the growth rate (ours is 4 which means that every day the number from the day before increases by a factor of 4), and x is the number of days. We plug into the formula the values we have, starting with x = 1:

[tex]y=45(4)^1[/tex]

Always raise what's inside the parenthesis first, then multiply in the 45. 4 to the first is 4, and 4 multiplied by 45 is 180. After the first day, there are 180 bacteria present in the culture.

Next, x = 2:

[tex]y=45(4)^2[/tex] which simplifies to

y = 45(16) so

y = 720.

Next, x = 3:

[tex]y=45(4)^3[/tex] which simplifies to

y = 45(64) so

y = 2880

Answer:

24,429.0245 square units

Step-by-step explanation:

The volume of a sphere can be found using the following formula.

[tex]V=\frac{4\pi r^3}{3}[/tex]

The radius is 18 units. Therefore, we can substitute 18 units in for r.

[tex]V=\frac{4\pi (18units)^3}{3}[/tex]

First, evaluate the exponents.

18 units^3= 18 units * 18 units * 18 units= 5832 units^3

[tex]V=\frac{4\pi (5832 units^3)}{3}[/tex]

Multiply 4 and pi.

[tex]V=\frac{12.5663706*5832 units^3}{3}[/tex]

Multiply in the numerator.

[tex]V=\frac{73287.0733 units^3}{3}[/tex]

Divide

[tex]V=24429.0245 units^3[/tex]

The volume of the sphere is 24,429.0245 units^3

Answer:

-3 + 12x

Step-by-step explanation:

3 - 2(-6x + 3)

3 + 12x - 6

-3 + 12 x

Hope this helped! :)

Answer:

[tex]4 \frac{1}{10}[/tex]

Step-by-step explanation:

=> [tex]\frac{1305}{31828} * 100[/tex]

=> 0.041 * 100

=> 4.1

=> [tex]4 \frac{1}{10}[/tex]

Answer:

16.66cm²

Step-by-step Explanation:

Given:

∆LMN with m<N = 38°

Length of side NL = 7.2cm

Length of side ML = 4.8cm

Required:

Area of ∆MNL

Solution:

Step 1: Find Angle LMN using the sine rule sin(A)/a = sin(B)/b

Where sin(A) = Sin(M) = ?

a = NL = 7.2cm

sin(B) = sin(N) = 38°

b = ML = 4.8cm

Thus,

Sin(M)/7.2 = sin(38)/4.8

Cross multiply

4.8*sin(M) = 7.2*sin(38)

4.8*sin(M) = 7.2*0.6157

4.8*sin(M) = 4.43304

Divide both sides by 4.8

sin(M) = 4.43304/4.8

sin(M) = 0.92355

M = sin-¹(0.92355) ≈ 67.45°

Step 2: Find m<L

angle M + angle N + angle L = 180 (sum of angles in a triangle)

67.45 + 38 + angle L = 180

105.45 + angle L = 180

Subtract 105.45 from both sides

Angle L = 180 - 105.45

Angle L = 74.55°

Step 3: Find the area of ∆MNL using the formula ½*a*b*sin(C)

Where,

a = NL = 7.2 cm

b = ML = 4.8 cm

sin(C) = sin(L) = sin(74.55)

Thus,

Area of ∆MNL = ½*7.2*4.8*0.9639

= ½*33.31

= 16.655

Area of ∆MNL ≈ 16.66cm²

[tex]\boxed{ \bf The~answer~is~$2,350.69.}[/tex]The answer is $2,350.69.

First, we must find the area of the rectangular driveway.

A = l × w

A = 15.75 × 3

A = 47.25

So, the area of the driveway is 47.25 yd².

Next, we need to multiply the cost of each square yard by the area.

49.75 × 47.25 = 2350.6875

This can be rounded to 2,350.69.

Answer:

[tex] \sqrt{9} \times \sqrt{16} [/tex]

Step-by-step explanation:

[tex] \sqrt{9} \times 16 = \sqrt{9} \times \sqrt{16} = 3 \times 4 = 12[/tex]

Hope this helps ;) ❤❤❤

Answer:

sqrt(9) * sqrt(16)

Step-by-step explanation:

sqrt( 9*16)

We know that sqrt(a*b) = sqrt(a) sqrt(b)

sqrt(9) * sqrt(16)

3*4

12

Answer:

Coin A : [tex]V(t)=25(1.07)^t[/tex]

Coin B : [tex]V(t)=40(1.05)^t[/tex]

Step-by-step explanation:

Consider the given formula is  

[tex]V(t)=P(1+r)^t[/tex]

where, P is current value, V(t) is the value of the coin in t years, and r is annual appreciation rate.

For coin A, current value is 25 dollars and annual appreciation rate is 7%.

[tex]V(t)=25(1+0.07)^t[/tex]

[tex]V(t)=25(1.07)^t[/tex]

For coin B, current value is 40 dollars and annual appreciation rate is 5%.

[tex]V(t)=40(1+0.05)^t[/tex]

[tex]V(t)=40(1.05)^t[/tex]

Therefore, the required equations for coin A and B are [tex]V(t)=25(1.07)^t[/tex] and [tex]V(t)=40(1.05)^t[/tex] respectively.

Answer:

Step-by-step explanation:

A monomial is an expression containing just one term. Given the monomial 1000000m¹⁸, to get the monomial we need to raise to the power of 2 to get this given monomials, the following steps must be taken using the laws of indices.

In indices, [tex](a^m)^n = a^m^n[/tex], applying this rule to the question we have;

1000000m¹⁸

= (10*10*10*10*10*10)m¹⁸

= 10⁶m¹⁸

= 10⁶*(m³)⁶

= (10*m³)⁶

= (10m³)⁶

= (10m³)²ˣ³

= (10³m⁹)²

= (1000m⁹)²

The last result gives the required expression

Answer:

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex].

Step-by-step explanation:

If a point is [tex]P=(r,\theta)[/tex], the all polar coordinates are defined as

In radian : [tex](r,\theta +2n\pi)\text{ and }(-r,\theta +(2n+1)\pi)[/tex]

In degree : [tex](r,\theta +360^{\circ}n)\text{ and }(-r,\theta +(2n+1)180^{\circ})[/tex]

where, n is any integer.

The given point is

[tex]P=(2,14^{\circ})[/tex]

So, all polar coordinates are  

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +(2n+1)180^{\circ})[/tex]

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,14^{\circ} +360^{\circ}n+180^{\circ})[/tex]

[tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex]

Therefore, the required polar coordinates are [tex](2,14^{\circ}+360^{\circ}n)\text{ and }(-2,194^{\circ} +360^{\circ}n)[/tex], where n is any integer.

Answer:

Option (C)

Step-by-step explanation:

Since FJ is the bisector of AD,

AL ≅ DL

And it's given that BL ≅ LC

Length of BL is 10 less than the length of AB.

m(BL) = m(AB) - 10

m(AD) = 220 [Since m(AD) = 2m(AL)]

2m(AL) = 220

m(AL) = 110

m(AB) + m(BL) = 110

m(AB) + [m(AB) - 10] = 110

2m(AB) = 110 + 10

m(AB) = 60

Therefore, m(BL) = m(AL) - m(AB)

                            = 110 - 60

                            = 50

Since, m(AL) = m(DL)

m(AB) + m(BL) = m(LC) + m(CD) [Since BL = LC]

m(AB) = m(CD) = 60

Now m(BD) = m(BL) + m(LC) + m(CD)

                   = 50 + 50 + 60

                   = 160

Therefore, option (C) will be the answer.

Answer:

B: (3x + 81)(x - 1)

Step-by-step explanation:

Answer: 25.71

Step-by-step explanation:

The area of a triangle is b*h/2. First, focus on finding the missing height. To find the height, use the pythagorean theorem. The pythagorean theorem only works on rights triangles. If you divide the triangle in half (vertically), you end up with two right triangles. From there, use the pythagorean theorem. The equation for the theorem is a²+b²=c². a and b are the sides and c is the hypotenuse(longest side).

1. For this triangle, you have the base and hypotenuse. Because there are technecally two right triangles, divide the base into two. 7.2/2 is 3.6.

2. Going back to what I said about a²+b²=c² , fill in the variables. The pythagorean theorem is used to find a missing side in a right triangle, so in this case, you would use it to find the height. 3.6²+X²=8². X represents the height which is 7.14

3. Finally, 7.14*7.2= 51.43.

4. Divide 51.43 by 2. 51.43/2 is 25.72.

I hope this wasn't too difficult to understand bc it's harded to explain without visuals. Hope this helped!

Answer:

[tex]\boxed{25.72 \: units^2}[/tex]

Step-by-step explanation:

Split the triangle into two triangles.

The base of one triangle is 3.6 and hypotenuse (longest side) is 8.

Use Pythagorean theorem to find length of one leg.

a² + b² = c²

3.6² + b² = 8²

b = 7.144228

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

The base and height both are given now.

[tex]\frac{1}{2} (7.144228)(3.6)[/tex]

[tex]12.85961[/tex]

Multiply by 2 because there are two triangles.

[tex]12.85961 \times 2[/tex]

[tex]25.719221[/tex]

Answer:

Step-by-step explanation:

The answer is B, the solution to your equation is at (2,1). Your solution is where the two lines meet.

Answer:

The second option.

Step-by-step explanation:

When two lines intersect, they usually intersect at just one point (unless they are parallel, where they never intersect; or no solutions when they infinitely intersect).

According to the graph provided, the lines are intersecting at one point: (2, 1).

So, your answer will be the second option!

Hope this helps!

Answer: 7 packages

Step-by-step explanation:

From the question, we are told that a truck is to be filled with packages that weigh 5.8kg. The maximum capacity of the truck is 48000 grams(48kg) and there is a 5500 gram(5.5kg) package already in the truck.

First, we need to subtract 5.5kg from 48kg to know the amount of space left. This will be:

= 48kg - 5.5kg

= 42.5kg

To get the number of 5.8kg packages that can be loaded, we divide 42.5kg by 5.8kg. This will be:

= 42.5kg/5.8kg

= 7.3

= 7 approximately

Therefore, 7 packages will be loaded.

N.B: 1000 grams = 1 kilogram