What is the value of x that makes l1||l2?

A. 14
B. 11.6
C. 10
D. 26.7

Answer:

1. AC is perpendicular to BD

1. Given

2. ACB is a right angle

2. Definition of perpendicular lines

3. Triangle ACB is a right triangle

3. Definition of right triangles

4. Angles 1 and 3 are complementary

4. Interior angles of a triangle add up to 180 degrees (Triangle Interior Angle Sum Theorem), and m<ACB = 90 degrees (definition of right angles), so m<1 + m<3 = 90 degrees (subtraction property of equality). By the definition of complementary angles, angles 1 and 3 are complementary.

The equation of the circumference of a circle in terms of [tex]\pi[/tex] is [tex]2\pi r[/tex] or [tex]\pi d[/tex].

The circumference for a circle with diameter 10 is [tex]10\pi[/tex].

The circumference for a circle with diameter 19 is [tex]19\pi[/tex].

The circumference for a circle with diameter 30 is [tex]30\pi[/tex].

The circumference for a circle with diameter 16 is [tex]16\pi[/tex].

Relatively easy, right?

The equation of the area of a circle in terms of [tex]\pi[/tex] is [tex]\pi r^2[/tex].

The area of a circle with radius 5 is [tex]25\pi[/tex].

The area of a circle with radius 9.5 is [tex]90.25\pi[/tex].

The area of a circle with radius 15 is [tex]225\pi[/tex].

The area of a circle with radius 8 is [tex]64\pi[/tex].

Hope this helped!

(By the way, I don't know why you're using hard formulas for trying to find the radius or diameter. The diameter is simply twice the radius, and the radius is simply half the diameter.)

Answer:

Circumference = 10[tex]\pi[/tex], 19[tex]\pi[/tex], 30[tex]\pi[/tex], 16[tex]\pi[/tex]

Area = 25[tex]\pi[/tex], 90.25[tex]\pi[/tex], 225[tex]\pi[/tex], 64[tex]\pi[/tex]

Step-by-step explanation:

For the first row we have the radius which is 5, the diameter is 10. The formula for circumference is 2[tex]\pi[/tex]r. So for this one its gonna be 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

radius = 5

diameter = 10

circumference = 2[tex]\pi[/tex]5 or 10[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]5^{2}[/tex] or 25[tex]\pi[/tex]

for the second row

radius = 9.5

diameter = 19

circumference = 2[tex]\pi[/tex]9.5 or 19[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]9.5^{2}[/tex] or 90.25[tex]\pi[/tex]

for the third row

radius = 15

diameter = 30

circumference = 2[tex]\pi[/tex]15 or 30[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]15^{2}[/tex] or 225[tex]\pi[/tex]

for the fourth row

radius = 8

diameter = 16

circumference = 2[tex]\pi[/tex]8 or 16[tex]\pi[/tex]

area = [tex]\pi[/tex][tex]8^{2}[/tex] or 64[tex]\pi[/tex]

The required percentage increase is 36%. So, a number increased by 36% is the same as the number multiplied by 1.36.

The formula for calculating the percentage increase of a number is

%increase = 100 × (Final - initial)/initial

Consider the number as 'x'

The result when the number is multiplied by 1.36 is 1.36x

So, the percentage increase is calculated as follows:

%increase = 100 × (Final - initial)/initial

Where Initial = x and Final - 1.36x

⇒ %increase = 100 × (1.36x - x)/x

⇒ %increase = 100 × x(1.36 - 1)/x

⇒ %increase = 100 × 0.36

⇒ %increase = 100 × 36/100

∴ %increase = 36

Thus, when a number is multiplied by 1.36, the result obtained is equal to the 36% increase in the number.

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The general terms for the given arithmetic sequences are given as follows:

1. [tex]a_n = -2 -3(n - 1)[/tex]

2. [tex]a_n = 22 - 2(n - 1)[/tex]

In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.

The general term of an arithmetic sequence is given by:

[tex]a_n = a_1 + (n - 1)d[/tex]

For sequence 1, given by -2, -5, -8, -11, the first term and the common ratio are given as follows:

[tex]a_1 = -2, d = -3[/tex]

Hence the general term that defines sequence 1 is presented below:

[tex]a_n = -2 -3(n - 1)[/tex]

For sequence 2, represented by 22, 20, 18, 16, the first term and the common ratio are given as follows:

[tex]a_1 = 22, d = -2[/tex]

Hence the general term that defines sequence 2 is presented below:

[tex]a_n = 22 - 2(n - 1)[/tex]

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[tex]\frac{(-12)(3)+(-5)(9)}{3^2 + 9^2} \langle 3, 9 \rangle \\ \\ =-\frac{9}{10} \langle 3, 9 \rangle \\ \\ =\langle -\frac{27}{10}, -\frac{81}{10} \rangle[/tex]

So, the correct answer is Option 1.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textsf{Equation:}[/tex]

[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]

[tex]\huge\textsf{Solving:}[/tex]

[tex]\mathsf{2[(8 \div 4)-(-5)] + 6}[/tex]

[tex]\mathsf{= 2[((2 - (-5)] + 6}[/tex]

[tex]\mathsf{= 2(7) + 6}[/tex]

[tex]\mathsf{= 2 \times 7 + 6}[/tex]

[tex]\mathsf{= 14 + 6}[/tex]

[tex]\mathsf{= 20}[/tex]

[tex]\huge\textbf{Therefore, your answer should be: }[/tex]

[tex]\huge\boxed{\frak{20}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {SOLUTION:}}}}[/tex]

▪ [tex] \sf{2[(8 ÷ 4)-(-5)] + 6}[/tex]

First, we will start with the division:

[tex]\longrightarrow \sf{2[(2) − (−5)] +6}[/tex]

Now we will resolve what is inside the bracket:

[tex]\longrightarrow \sf{2[2+5] +6}[/tex]

[tex]\longrightarrow \sf{2 \times 7 +6}[/tex]

Now we will solve the multiplication:

[tex]\longrightarrow \sf{14 +6= 20}[/tex]

[tex]\huge\underline{\underline{\boxed{\mathbb {ANSWER:}}}}[/tex]

[tex] \bm{2[(8 ÷ 4)-(-5)] + 6 = \boxed{\bm {20}}}[/tex]

Answer:

I am not 100% confident, but I think that she is 11.

Step-by-step explanation:

Answer:

14 years old

Step-by-step explanation:

Define the variable

Let x be the actual age of Zeba (in years).

Create an equation using the give information and the variable x:

[tex](x - 5)^2=5x+11[/tex]

To find Zeba's age now, solve the equation for x.

Expand the brackets:

[tex]\implies x^2-10x+25=5x+11[/tex]

Subtract 5x from both sides:

[tex]\implies x^2-10x+25-5x=5x+11-5x[/tex]

[tex]\implies x^2-15x+25=11[/tex]

Subtract 11 from both sides:

[tex]\implies x^2-15x+25-11=11-11[/tex]

[tex]\implies x^2-15x+14=0[/tex]

Factor the found quadratic

To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex], then rewrite [tex]b[/tex] as the sum of these two numbers:

[tex]\implies x^2-14x-x+14=0[/tex]

Factor the first two terms and the last two terms separately:

[tex]\implies x(x-14)-1(x-14)=0[/tex]

Factor out the common term (x - 14):

[tex]\implies (x-1)(x-14)=0[/tex]

Apply the zero product property:

[tex]\implies (x-1)=0 \implies x=1[/tex]

[tex]\implies (x-14)=0 \implies x=14[/tex]

Therefore, Zeba's age now is either 1 or 14 years.

As the question states "If Zeba were younger by 5 years" then 1 must be an extraneous solution since 1 - 5 = -4 and Zeba cannot be -4 years old.

Therefore, Zeba's age now is 14 years old.

Check

Given the actual age of Zeba is 14 years old.

Therefore, If Zeba were younger by 5 years, she would be 9 years old as:  14 - 5 = 9

The square of 9 is:  9² = 81.

5 times her actual age:  5 × 14 = 70

81 is 11 more than 70, hence verifying that her actual age is 14 years old.

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Answer: b. the two triangles are similar by SAS

Step-by-step explanation:

       These two triangles (ABC and ADE) both share angle A. This means that one angle is congruent.

       Next, we will look at the sides. Triangle ADE has side lengths of 6, 9, and x. Triangle ABC has side lengths of 8+6, 12+9, y. Let us see how these side lengths compare.

[tex]\frac{8+6}{12+9} =\frac{14}{21} =0.6666[/tex]

[tex]\frac{6}{9} = 0.6666[/tex]

       THey are similar. This means the triangles can be prooven similar with SAS.

⟨A = 7•x + 40° and ⟨B = 3•x + 112°

From a possible diagram of the question, ⟨A = ⟨B, which gives;

Given;

⟨A = 7•x + 40°

⟨B = 3•x + 112°

In the diagram from a similar question posted online, we have;

Corresponding angles formed by parallel lines having a common transversal are congruent, therefore;

Which gives;

7•x + 40° = 3•x + 112°

7•x - 3•x = 112° - 40° = 72°

7•x - 3•x = 4•x = 72°

x = 72° ÷ 4 = 18°

Therefore;

Which gives;

⟨A = 7•x + 40°

⟨A = 7 × 18 + 40° = 166°

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Answer:d

Step-by-step explanation:

khan

The lower and the upper class limit are as follows

interval  lower limit  upper limit

10-14          10                14

15-19          15                19

20-24         20              24

25-29           25            29

This is further explained below.

Generally, The lower class limit and the upper-class limits are just the minima and maximum values that are allowed in each class, respectively: The gap that exists between the upper-class limit and the lower class limit is referred to as the class interval.

In conclusion, The lower and the upper class limit are as follows

interval  lower limit  upper limit

10-14          10                14

15-19          15                19

20-24         20              24

25-29           25            29

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In quadrant IV, [tex]\cos(A)[/tex] is positive. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258[/tex]

Then by the definition of tangent,

[tex]\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}[/tex]

Step-by-step explanation:

since the 2 arc angles cover the full circle, we know their sum must be 360°.

so,

23x - 5 + 37x + 5 = 360

60x = 360

x = 6

and so the angle at V = 5×6 + 17 = 30+17 = 47°

Answer:

(-5, 2)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}-2x-5y=20\\y=\dfrac{4}{5}x+2\end{cases}[/tex]

Both equations are linear equations.

Rearrange Equation 1 to make y the subject:

[tex]\implies -2x-5y=20[/tex]

[tex]\implies -5y=2x+20[/tex]

[tex]\implies y=-\dfrac{2}{5}x-4[/tex]

Therefore, the graph of this equation is a straight line with a negative slope and a y-intercept of (0, -4).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0\implies y=-\dfrac{2}{5}(0)-4=-4 \implies (0,-4)[/tex]

[tex]x = 5 \implies y=-\dfrac{2}{5}(5)-4=-6 \implies (5,-6)[/tex]

Plot the found points and draw a straight line through them.

The graph of this equation is a straight line with a positive slope and a y-intercept of (0, 2).

Find two points on the line by substituting two values of x into the equation:

[tex]x = 0 \implies y=\dfrac{4}{5}(0)+2=2 \implies (0,2)[/tex]

[tex]x = 5 \implies y=\dfrac{4}{5}(5)+2=6 \implies (5,6)[/tex]

Plot the found points and draw a straight line through them.

The solution(s) to a system of equations is the point(s) of intersection.

From inspection of the graph, the point of intersection is (-5, -2).

To verify the solution, substitute the second equation into the first and solve for x:

[tex]\implies \dfrac{4}{5}x+2=-\dfrac{2}{5}x-4[/tex]

[tex]\implies \dfrac{6}{5}x=-6[/tex]

[tex]\implies 6x=-30[/tex]

[tex]\implies x=-5[/tex]

Substitute the found value of x into one of the equations and solve for y:

[tex]\implies \dfrac{4}{5}(-5)+2=-2[/tex]

Hence verifying that (-5, -2) is the solution to the given system of equations.

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First simplify first one

Another one is

On first line

at x=0

At x=5

On second line

At x=0

At x=5

Graph attached

Solution is (-5,-2)

Answer:

$0.17425/Km

Step-by-step explanation:

8.5L/100Km*$2.05/L

= $0.17425/Km

Answer:

I think the answer is 12 because 8/6 is 1.3333.... Continously so the smaller traingel is 1.33333 times smaller then the bigger one. So you jus do 9 x 1.3333... To get the bigger angels side

Answer:

1.78 feet.

Step-by-step explanation:

If they cost $20 each and its $2 per square foot, the area of the spheres

is 20 / 2 = 10 ft^2.

Area of sphere = 4 π r^2 = 10   (where r = the radius)

---> r^2 = 10 / 4π

            =   0.796

---> r = 0.892 ft

So the diameter = 2 * r  

                           =  1.78 feet to nearest hundredth.    

Answer:

The function is increasing from x = 0 to x = 1.

Step-by-step explanation:

A function is increasing when the y-value increases as the x-value increases.

A function is decreasing when the y-value decreases as the x-value increases.

From x = -2 to x = -1 the function is decreasing as the y-value decreases as the x-value increases:  

From x = -1 to x = 0 the function is increasing as the y-value increases as the x-value increase:  

From x = 0 to x = 1 the function is increasing as the y-value increases as the x-value increase:  

The reliability of two components in series is 0.996.

To find the reliability of the engine, we need all the two components to work. Each components has a reliability of 0.998, so to find the reliability of the engine we need to find the probability of all two components working.

Reliability is defined as the probability that a product, system, or service will perform its intended function adequately for a specified period of time, or will operate in a defined environment without failure.

We can find this probability multiplying all the ten reliabilities:

P = 0.998^2 = 0.996004

Rounding to three decimal places, we have P = 0.996

The reliability of the engine is 0.996.

Hence,

The reliability of two components in series is 0.996.

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Answer:

7

Step-by-step explanation:

The start this question by looking at two important things, how much money we have and how much money it costs per person. The friends have a total of $284.25 and we don't know how much it costs per person. To find this we must set up an equation and solve it!

Because each person must pay for parking and a ticket, we can find the cost for one person by adding the parking and ticket cost together.

$9.25 + $27.50 = $36.75

Now that we have solved this equation, we know that it costs $36.75 for one person. To find how many total people can go we dived the total amount of money we have by how much it costs per person. Let's call the number of people that can go 'p'.

p = [tex]\frac{284.25}{36.75}[/tex]

Once we simplify/solve this equation we get 7 [tex]\frac{36}{49}[/tex] so essentially, we get the whole number 7 and a long decimal, but the only important part is the 7. We take the whole number from our answer which is 7.

We now know the answer: 7.

Let's check our work!

7 * 36.75 = 257.75

284.25 - 257.75 = 26.5

26.5 < 36.75 so we are correct!

The final answer is 7!

Have an amazing day!

Use BODMAS and algebra to arrive at the values of P = 5/2, q = -25/4 and r = -9/2.

Then substitute the values of p and q into p+2q to get -10

Answer:

Future Amount ≈ 32

Step-by-step explanation:

substitute x = 8 into the given formula , that is

future amount = 16[tex](1.09)^{8}[/tex] = 16 × 1.99256.. ≈ 32 ( nearest whole number )

Answer:51 crates could have 12 oranges and one crate could hold 11 oranges.

Step-by-step explanation: 623 / 12 is 51.9... 51 x 12 is 612. 612 + 11 is 623 math checks out.

Answer: A) 23,00

Step-by-step explanation:

A=23,00

B=8,600

C=12,00

D=3,600

Answer:

I forgot the name but I can show you how to do it lol

Step-by-step explanation:

x+5(-2)-1

x-10-1 we multiplied 5 and -2

x-11

x=11

how I did the last one is there is a non-existent 0 with an equal sign like my teacher says  so we added 11 to both sides.

The distance the bird has flown by the time Alice and Bob meet is 40 feet.

Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.

Distance equals speed multiplied by time.

Distance between Alice and Bob=1000 feet.

Distance between the bird and Bob=1000 feet.

Speed of Alice and Bob=10 feet per second.

The combined speed of Alice and Bob=20 feet per second.

Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)

The time covered at the meeting point=20 second (1000/50)

Speed of the bird=20 feet per second.

The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).

Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.

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Answer:

[tex]\sf \dfrac{4}{9}x^8[/tex]

Step-by-step explanation:

       [tex]\sf (a*b)^m = a^m *b^m\\\\(a^m)^n =a^{m*n}[/tex]

  16 = 4 *4 = 4²

 81  = 9 *9 = 9²

[tex]\sf\left (\dfrac{16}{81}x^{16}\right)^{\frac{1}{2}}= \left(\dfrac{4^2}{9^2}x^{16}\right)^{\frac{1}{2}}[/tex]

                [tex]\sf =\dfrac{4^{2*\frac{1}{2}}}{9^{2*\frac{1}{2}}}*x^{16*\frac{1}{2}}\\\\=\dfrac{4}{9}x^8[/tex]

Answer:

[tex]\huge\boxed{\sf a_{400}=1276}[/tex]

Step-by-step explanation:

79, 82, 85, 88, ....

[tex]a_n=a_1+(n-1)d[/tex]

Where,

Put the givens in the above formula

[tex]a_{400}=79 +(400-1)3\\\\a_{400}=79 + 399\times3\\\\a_{400}=79+ 1197\\\\a_{400}=1276\\\\\rule[225]{225}{2}[/tex]

Answer: B

Step-by-step explanation: what I did was I drew a square and folded it if both sides matched i knew that that was a line of symmetry

Answer:

Speed of the plane in still air: [tex]779\; {\rm km \cdot h^{-1}}[/tex].

Windspeed: [tex]100\; {\rm km \cdot h^{-1}}[/tex].

Step-by-step explanation:

Assume that [tex]x\; {\rm km \cdot h^{-1}}[/tex] is the speed of the plane in still air, and that [tex]y\; {\rm km \cdot h^{-1}}[/tex] is the speed of the wind.

The question states that when going against the wind ([tex]v = (x - y)\; {\rm km \cdot h^{-1}}[/tex],) the plane travels [tex]6111\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex]. Hence, [tex]9\, (x - y) = 6111[/tex].

Similarly, since the plane travels [tex]7911\; {\rm km}[/tex] in [tex]9\; {\rm h}[/tex] when travelling in the same direction as the wind ([tex]v = (x + y)\; {\rm km \cdot h^{-1}}[/tex],) [tex]9\, (x + y) = 7911[/tex].

Add the two equations to eliminate [tex]y[/tex]. Subtract the second equation from the first to eliminate [tex]x[/tex]. Solve this system of equations for [tex]x[/tex] and [tex]y[/tex]: [tex]x = 779[/tex] and [tex]y = 100[/tex].

Hence, the speed of this plane in still air would be [tex]779\; {\rm km \cdot h^{-1}}[/tex], whereas the speed of the wind would be [tex]100\; {\rm km \cdot h^{-1}}[/tex].

The terms of this series may be arranged without changing the value of the series. The sum of the reciprocals of the squares of the odd positive integers is [tex]\pi ^{2} /8[/tex].

In mathematics, a sequence is the cumulative sum of a given collection of terms. Usually, those phrases are actual or complicated numbers, but plenty of extra generalities are feasible.

A series is described as an arrangement of numbers in a specific order. then again, a chain is described as the sum of the factors of a sequence.

In mathematics, a series is, more or less speaking, a description of the operation of including infinitely many quantities, one after the alternative, to a given beginning quantity. The look at of series is a primary part of calculus and its generalization, mathematical analysis.

k=1

1/(1)2+1/(2)2+1/(3)2+1/(4)2+1/(5)2+1/(6)2+1/(7)2+.

up to ∞ terms = 2/6

[1/(1)2+1/(3)2+1/(5)2+1/(7)2+]+[1/(2)²+1/(4)²+1/(6)²+

..∞0] = T²/6

→ [1/(1)² + 1/(3)² + 1/(5)2+1/(7)2+......00] + [1/4 (1)² + 1/4(2)²+

1/4(3)²+....0] =²/6

[1/(1)²+1/(3)²+1/(5)2+1/(7)2+.......)] + 1/4[1/(1)² + 1/(2)²+

1/(3)²+....x] = 2/6

⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+..] + 1/4 [π²/6] = 2/6

⇒ [1/(1)² + 1/(3)² + 1/(5)²+1/(7)²+] = (1-1/4)/6

⇒ [1/(1)²+1/(3)2+1/(5)2+1/(7)2+..∞ = 3/4 x π²/6

=

↑

[1/(1)2+1/(3)2+1/(5)2+1/(7)²+] = 2/8

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