How do you prove that lines are similar in triangles if it is parallel? (look at photo)

Answer:

x=4

AB=19

Step-by-step explanation:

in such a parallelogram the length of AD must be equal to the length of BC.

=>

18x = 17x + 4

x = 4

AB = 4x + 3 = 4×4 + 3 = 19

Answer:

Step-by-step explanation:

It's a cubic.

It has 1 root that cuts the x axis at x = -4

It has 2 roots that are the same. The reason you know this is because the curve touches the x axis, but does not go through the x axis, at 3.

y = (x + 4) (x - 3)(x - 3)

Notice the sign change. x has to have sign change when going from a root to a binomial

The root is - 4. The binomial is (x + 4)

The same argument works for x = 3

Answer:

The author sold a total of 30240 books following this trend.

Step-by-step explanation:

Let's find 5% of 14400 first;

14400 * 5%

14400 * 5/100

144 * 5

720 (So now we know that they are decreasing by 720 each month; therefore thats the constant)

=> aₙ = a₁ + r(n - 1)

=> a₂₃ = 14400 + 720(23 - 1)

=> a₂₃ = 14400 + 720(22)

=> a₂₃ = 14400 + 15840

=> a₂₃ = 30240

Hope this helps!

The author sold a total of 30240 books following this trend.

Let's find 5% of 14400 first;

[tex]14400 * 5\%\\14400 * 5/100\\144 * 5=720[/tex]

A, is a type of numerical sequence studied by Mathematics, where each term or element counting from the second is equal to the sum of the previous term with a constant.

So using the arithmetic progression we have:

[tex]a_n = a_1 + r(n - 1)\\a_{23} = 14400 + 720(23 - 1)\\ a_{23} = 14400 + 720(22)\\ a_{23} = 14400 + 15840\\a_{23} = 30240[/tex]

See more about arithmetic progression at brainly.com/question/20385181

Answer:

20a

Step-by-step explanation:

26a+4a-10a=30a-10a=20a

Answer:

20a

Step-by-step explanation:

26a+4a-10a

since they are like terms u can add and subtract them

=30a-10a

=20a

Answer: [tex]\dfrac{6}{26}[/tex]

Step-by-step explanation:

Given

Denominator is 4 more than twice its numerator

Suppose the numerator is x. So, it follows above condition, fraction becomes

[tex]\Rightarrow \dfrac{x}{2x+4}[/tex]

If both numerator and denominator are reduced by 6, they become equal

[tex]\Rightarrow 12(x-6)=2x+4-6\\\Rightarrow 12x-72=2x-2\\\Rightarrow 10x=70\\\Rightarrow x=7[/tex]

The fraction is

[tex]\Rightarrow \dfrac{x}{4x+2}=\dfrac{6}{4\times 6+2}\\\\\Rightarrow \dfrac{6}{26}[/tex]

Answer:

8

Step-by-step explanation:

7 x 8 = 56 56 - 4 = 52.

3 x 8 = 24 24 + 28 = 52

Step-by-step explanation:

1) [tex](-4)^2{\cdot}(-4)[/tex]

We know that, [tex]a^x{\cdot}a^y=a^{x+y}[/tex]

[tex](-4)^2{\cdot}(-4)=(-4)^{2+1}\\\\=(-4)^3\\\\=64[/tex]

2) [tex](-2)^5{\cdot} (-2)^3[/tex]

Again using above property,

[tex](-2)^5{\cdot} (-2)^3=(-2)^8\\\\=256[/tex]

3) [tex]5^{-3}[/tex]

We know that,

[tex]a^{-x}=\dfrac{1}{a^x}[/tex]

So,

[tex]5^{-3}=\dfrac{1}{5^3}\\\\=\dfrac{1}{125}[/tex]

4) [tex]2.5^2=2.5\times 2.5\\\\=6.25[/tex]

Hence, this is the required solution.

Answer:

x = 12.2

Step-by-step explanation:

to solve for 'x', we can use the sine ratio of opposite/hypotenuse

we need to find the angle opposite side 'x', which can be found by:

180-(44+90) = 46

sin46° = x/17

x = 17·sin46°

x = 12.2

Answer:

240,000

Step-by-step explanation:

standard form means the way you would write it

Answer:

y = -2x - 3

Step-by-step explanation:

A standard equation written in slope-intercept form looks like this:

y = mx + b

m is the slope and b is the y-intercept.

First let's identify the y-intercept.

This is the point where the line crosses the y-axis. That point is (0, -3); therefore, our y-intercept is -3.

y = mx - 3

Now let's find the slope.

This is the rate of change of the line. It is represented by rise over run. "Over" means the number will be presented as a fraction.

We can see that from Point 2 (on the right), we rise 2 units to the level of Point 1 (on the left). This is expressed as 2.

To get directly to Point 1, we run backwards 1 unit. This is expressed as -1.

rise: 2

run: -1

rise/run = 2/-1 = -2

-2 is our slope.

y = -2x - 3

This is your equation.

Hope this helps!

Answer:

They are different because they are not similar and they have different answer at the end

Answer:

0.0152 probability

Step-by-step explanation:

first there are 12 marbles: odds are 2/12 = 1/6

Then, there are 11 marbles: odds are 1/11

So the odds of both of them being blue are: 1/6 * 1/11 = 0.0152

Please give brainliest thanks!

Answer:

x = 19

Step-by-step explanation:

5x - 26 = x + 50

Subtract x on both sides of the equation.

4x - 26 = 50

Add 26 on both sides.

4x = 76

Now, divide by 4 on both sides.

x = 19

Answer:

x = 19

Step-by-step explanation:

5x-26=x+50

5x = 76 +x

4x = 76

x = 19

Answer:

Step-by-step explanation:

The answer is B.

It's a line that shows every point that satisfies the equation

y = 3x + 4  which is what I think you meant (but I'm not sure). If I am correct then there are a million possible points that could be the answer to this question.

If I am not correct, leave a comment that tells me so, and I'll revise my answer.

Never mind the question has the right equation. And my answer remains as given.

Given:

The image of a lens crosses the x-axis at –2 and 3.

The point (–1, 2) is also on the parabola.

To find:

The equation that can be used to model the image of the lens.

Solution:

If the graph of polynomial intersect the x-axis at c, then (x-c) is a factor of the polynomial.

It is given that the image of a lens crosses the x-axis at –2 and 3. It means (x+2) and (x-3) are factors of the function.

So, the equation of the parabola is:

[tex]y=k(x+2)(x-3)[/tex]          ...(i)

Where, k is a constant.

It is given that the point (–1, 2) is also on the parabola. It means the equation of the parabola must be satisfy by the point (-1,2).

Putting [tex]x=-1, y=2[/tex] in (i), we get

[tex]2=k(-1+2)(-1-3)[/tex]

[tex]2=k(1)(-4)[/tex]

[tex]2=-4k[/tex]

Divide both sides by -4.

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

[tex]-\dfrac{1}{2}=k[/tex]

Putting [tex]k=-\dfrac{1}{2}[/tex] in (i), we get

[tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex]

Therefore, the required equation of the parabola is [tex]y=-\dfrac{1}{2}(x+2)(x-3)[/tex].

Note: All options are incorrect.

Given:

The equation is:

[tex]270=3e^{2.4K}[/tex]

To find:

The solution for the given equation to the nearest hundredth.

Solution:

We have,

[tex]270=3e^{2.4K}[/tex]

Divide both sides by 3.

[tex]\dfrac{270}{3}=e^{2.4K}[/tex]

[tex]90=e^{2.4K}[/tex]

Taking ln on both sides, we get

[tex]\ln (90)=\ln e^{2.4K}[/tex]

[tex]\ln (90)=2.4K[/tex]                  [tex][\because \ln e^x=x][/tex]

Divide both sides by 2.4.

[tex]\dfrac{\ln (90)}{2.4}=K[/tex]

[tex]\dfrac{4.4998}{2.4}=K[/tex]           [tex][\because \ln (90)\approx 4.4998][/tex]

[tex]1.874916667=K[/tex]

Round the value to the nearest hundredth (two decimal place)

[tex]K\approx 1.87[/tex]

Therefore, the value of K is 1.87.

Answer:

x=3  x = -1/2  x=1

Step-by-step explanation:

y = (x - 3)(2x + 1)(x - 1)

Set the function equal to zero

0 = (x - 3)(2x + 1)(x - 1)

Using the zero product property

x-3 =0   2x+1 =0  x-1 =0

x=3   2x = -1  x=1

x=3  x = -1/2  x=1

Answer: 1. equal to - having the requisite qualities for; "equal to the task"; "the work isn't up to the standard I require" adequate to, up to, capable.

Step-by-step explanation:Glad Too Help :))

Answer:

B

Step-by-step explanation:

Answer:

third side = 4

Step-by-step explanation:

third side is hypoenuse as it is opposite to 90 degree.

using pythagoras theorem

(perpendicular)^2 + (base)^2 = (hypotenuse)^2

2^2 + (2[tex]\sqrt{3[/tex] )^2 = hypotenuse^2

4 + 4*3 = hypotenuse^2

16 = hypotenuse^2

[tex]\sqrt{16}[/tex] = hypotenuse

4 = hypotensue

Answer:

785.4

Step-by-step explanation:

The formula to find the surface area of a cylinder is

2* pi* radius* height + 2* pi* 2radius.

2( 3.14) (5) (20)= 628

2 (3.14* 5*5)= 157

628+ 157= 785.

Answer:

22 grams

Step-by-step explanation:

loses 50% of it's mass per 22 years

so after 22 years the mass would be 44 grams

22 years later would leave 50% of 44 grams = 22 grams

Answer:

7.61 miles

Step-by-step explanation:

Given that,

Haley hikes 3 miles north and 7 miles east.

We need to find the shortest distance from the campground to the waterfall. Let the distance is D.

It can be calculated as follows :

[tex]D=\sqrt{3^2+7^2}\\D=7.61\ miles[/tex]

So, the shortest distance from the campground to the waterfall is 7.61 miles.

Answer: [tex]-6,13[/tex]

Step-by-step explanation:

Given

The sum of the two numbers is 20

and the difference of the two is -6

Suppose, the numbers are x and y

[tex]\therefore x+y=20\quad \ldots(i)\\\Rightarrow x-y=-6\quad \ldots(ii)\\\text{Solving} (i)\ \text{and}\ (ii)\ \text{we get}[/tex]

[tex]\Rightarrow 2x=14\\\Rightarrow x=7[/tex]

[tex]\therefore y=13[/tex]

Therefore, the numbers are [tex]-6,\ \text{and}\ 13[/tex]

Answer:

60

Step-by-step explanation:

Note that angle ZXY is the bisected angle which was split into angle 1 and 2

Also note that bisectors split angles into to separate congruent angles ( So if angle ZXY was bisected into angle 1 and angle 2 then angle 1 = angle 2 )

If angle 2 = 30 then angle 1 also = 30

Like stated multiple times angle ZXY is made up of angle 1 and 2

Hence, Angle ZXY = Angle 1 + Angle 2

Angle ZXY = 30 + 30 = 60

Answer:

Lauren tutors 42 students in total

Step-by-step explanation:

She tutors for 6 hours and she teaches 7 students an hour , so we just have to multiply 7 by 6 which is 42

Hope it helps:)

Answer:

x = 51, y = 17

Step-by-step explanation:

Consecutive angles sum to 180° , so

x + 129 = 180 ( subtract 129 from both sides )

x = 51

-------------------------------------

Opposite angles are congruent, so

3y = x = 51 ( divide both sides by 3 )

y = 17

Step-by-step explanation:

x + 129° = 180°

x = 180°- 129°

x = 51°

3y + 129° = 180°

3y = 180° - 129°

3y = 51°

y = 51°/3

y = 17°