Use a paragraph, flow chart, or two-column proof to prove the angle congruence. Given: CXY ≅ BXY CAX ≅ BAX AC≅ AB Prove: XCY ≅ XBY

Answer:

The correct answer is B. y = 5

Step-by-step explanation:

Let's recall that two are triangles are similar when its side lengths are proportional. That is in our case, if Δ ABC is similar to Δ DEF , then the following equation holds:  

EF/BC = DF/AC

Replacing with the real values:

6/12 = y/10

Cross multiplication:

12 * y = 10 * 6

12y = 60

y = 60/12

y = 5

The correct answer is B. y = 5

Answer:

Step-by-step explanation:

The product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.

Simplification of an expression is the process of writing an expression in the most efficient and compact form without affecting the value of the original expression. It involves, multiply out the brackets and then simplify the resulting expression by collecting the like terms.

For the given situation,

The expression is [tex](\sqrt{14} -\sqrt{3})( \sqrt{12} +\sqrt{7} )[/tex]

⇒ [tex]\sqrt{14}\sqrt{12} +\sqrt{14} \sqrt{7} -\sqrt{3} \sqrt{12} -\sqrt{3} \sqrt{7}[/tex]

⇒ [tex]\sqrt{168}+\sqrt{98}-\sqrt{36}-\sqrt{21}[/tex]

⇒ [tex]\sqrt{2^{2}(42) } +\sqrt{7^{2}(2) } -\sqrt{6^{2} }-\sqrt{21}[/tex]

⇒ [tex]2\sqrt{42 } +7\sqrt{2 } -6-\sqrt{21}[/tex]

Hence we conclude that the product of this expression is option (A) (2√42 + 7√2 - 6 - √21) is the correct answer.

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Answer:

Therefore the slope of the line shown on the graph is option  D)

[tex]-\dfrac{2}{3}[/tex]

Step-by-step explanation:

Given:

Let the Two points on the line be

point A( x₁ , y₁) ≡ ( 0 , 0)  one as a Origin  

point B( x₂ , y₂) ≡ (-3, 2)  

To Find:

Slope AB = ?

Solution:

For a slope  we require two points i.e

[tex]Slope=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex]

Substituting the given values we get

[tex]Slope(AB)=\frac{2-0}{-3-0}\\\\Slope(AB)=-\dfrac{2}{3}[/tex]

Therefore the slope of the line shown on the graph is option  D)

[tex]-\dfrac{2}{3}[/tex]

The expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is [tex]\frac{n + 14}{7n + 49}[/tex]

Solution:

Given that,

Hose A, when turned on alone, can extinguish the fire in 7 minutes

Hose B takes "n" minutes more time than hose A

Hose takes (n + 7) minutes to extinguish the fire

STEP 1: Calculate how much work (here work is to extinguish the fire) each person does in one minute

[tex]Hose A = \frac{1}{7}th \text{ of the work }\\\\Hose B = \frac{1}{n+7}th \text{ of the work }[/tex]

STEP 2: Add up the amount of work done by each person in one minute

Work done in one minute when both are working together:

[tex]\rightarrow \frac{1}{7} + \frac{1}{n + 7}\\\\\rightarrow \frac{n + 7 + 7}{7n + 49}\\\\\rightarrow \frac{n + 14}{7n + 49}[/tex]

Therefore, the expression in terms of "n" for how much of the fire they will extinguish in 1 minute when both hoses are turned on together is:

[tex]\frac{n + 14}{7n + 49}[/tex]

The total rate in 1 minute is [tex]\frac{1}{7} + \frac{1}{7+n}[/tex].

To find the expression for how much of the fire they will extinguish in 1 minute when both Hose A and Hose B are turned on together, we need to determine their individual rates first.

Hose A can extinguish the fire in 7 minutes, so its rate is:

⇒ Rate of Hose A = 1 fire ÷ 7 minutes = [tex]\frac{1}{7}[/tex].

Hose B takes 'n' minutes more than Hose A. Therefore, it takes (7 + n) minutes to extinguish the fire, so its rate is:

⇒ Rate of Hose B = 1 fire ÷ (7 + n) minutes = [tex]\frac{1}{7+n}[/tex].

When both hoses are operating together, their combined rate is the sum of their individual rates:

⇒ Combined Rate = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]

We need the combined rate per minute:

⇒ Combined Rate per Minute = [tex]\frac{1}{7} + \frac{1}{7+n}[/tex]

This fraction represents the portion of the fire they will extinguish in 1 minute when both hoses are used together.

Yes!

This would be in-fact a linear equation!

This equation is set up in y=mx+b form, therefore we know it is a linear equation.

y=12x+2

The 12 is the mx in the equation.

And the 2 is the B in the equation! :)

That is how we solve that.

Any questions?

Have a great day!

The x - intercept is (9, 0) and y - intercept is (0, -6)

Solution:

Given that the equation is: 2x - 3y = 18

We have to find the x and y intercepts of the equation

The x-intercept is the point at which the line crosses the x-axis. At this point, the y-coordinate is zero.

The y-intercept is the point at which the line crosses the y-axis. At this point, the x-coordinate is zero.

Finding x - intercept:

Substitute y = 0 in given equation

2x - 3y = 18

2x - 3(0) = 18

2x = 18

x = 9

Thus the x - intercept is (9, 0)

Finding y - intercept:

Substitute x = 0 in given equation

2(0) - 3y = 18

-3y = 18

y = -6

Thus the y-intercept is (0, -6)

Answer:

19/2

Step-by-step explanation:

8 3/2=19/2

Answer:

19/2

Step-by-step explanation:

Answer:

3.0 kg

Step-by-step explanation:

Momentum before collision = momentum after collision

m₁ u₁ + m₂ u₂ = m₁ v₁ + m₂ v₂

(1.0 kg) (5.0 m/s) + m (-2.0 m/s) = (1.0 kg) (-4.0 m/s) + m (1.0 m/s)

5.0 kg m/s + m (-2.0 m/s) = -4.0 kg m/s + m (1.0 m/s)

9.0 kg m/s = m (3.0 m/s)

m = 3.0 kg

Final answer:

2 × 3 × 4, which equals 24.

Explanation:

To find equivalent expressions, we need to think about numbers that can multiply together to reach 24, while also keeping in mind the properties of operations and exponents.

Answer:

Seawater

Step-by-step explanation:

I just took a quiz on this and it said the correct answer is sea water

Answer:

your answer is down below

Step-by-step explanation:

Check the picture below.

Answer:

X2-13X-18=0

Step-by-step explanation:

x-2(x+3)=4(2x+3)-x(x-4)

Multiply through the equations

x-2x-6=8x+12-x2+4x

Equate all to zero

x-2x-6-8x-12+x2-4x=0

x2-4x+x-2x-8x-6-12

x2-13x-18=0

Answer:

A. x minus 2 x minus 6 = 8 x + 12 minus x minus 4

E. Negative x minus 6 = 7 x + 8

Step-by-step explanation:

i took the unit test review on edg

Answer:

Dimensions of printed area

x   =  7.58     the length

y   =  31.40  cm   the height

Step-by-step explanation:

Printed region    P(a)  =  238 cm²

Let call x  and y dimensions of printed area then:

A  =  238  =  x*y       ⇒    y  = 238/x

And the area of the advertisement   is

A(a)  =  L *  W        where     L  =  x  + 6       and   W  =  y  + 5

A(x)  =  (x  +  6  ) * (  y  +  5 )

Area as a function of x                         y  =  238/ x

A(x)  =  (x  +  6  ) * ( 238/x  +  5 )

A(x)  = 238  + 5x  + 1428/x  +  30

A(x)   =  268  +   5x    + 1428/x

Taking derivatives on both sides of the equation

A´(x)   =   5  -  1428/x²

A´(x)   =  0         ⇒   5x²   =  1428       ⇒ x²   =  57.12

x  = 7.58 cm         and         y  =  238/ 7.58       y  =  31.40 cm

Answer:

8.83%

Step-by-step explanation:

Using compound interest formula

A = P ( 1+ r) ^t where A = amount = 530 × 36 = $ 19080, P = the amount of the loan = $ 14800, t = 36 / 12 = 3 years

substitute the values into the equation

19080 = 14800 (1 + r) ^3

19080 / 14800 = (1 + r) ^3  

1.2892 = (1 + r) ^3  

∛(1.2892) = 1 + r

1.0884 = 1 + r

r = 1.0884 - 1 = 0.0884 × 100 = 8.83%

Answer:

d 8,5%, the most probable, provided the error in the question is confirmed!!!

Step-by-step explanation:

Mason has an offer to buy an item with a sticker price of P= $14,800.

He is to pay $8530 a month for 36 months.

Total amount paid by Mason will be

$8530*36= $307,080

This will be very outrageous compared to the sticker price!!!

If we presume he is paying yearly 8530 for 36 months or 3 years.

Then total amount paid will be 8530*3 = $25590

Also very high in my opinion.

Perhaps the dollar sign was wrongly typed as '8' in the question and he pays only $530 monthly,

Then the total amount paid will be $19,080

This is quite reasonable.

If the interest rate is compounded for n (n=3, 36 months = 3 years)

years, thus

19080= ((P*(1+i)^n) , meaning

19080 =((14800(1+i)^3), which when evaluated yields

i=8.8%

Answer:

The sign of h must be negative, and the sign of k must be positive.

Answer:

No solution

Step-by-step explanation:

we have

[tex]7x-7(x+6)=10[/tex]

Solve for x

Apply distributive property left side

[tex]7x-7x-42=10[/tex]

Combine like terms left side

[tex]-42=10[/tex] ----> is not true

therefore

The equation has no solution

Answer:

v<=-3

Step-by-step explanation:

-3(v-3)-6>=12

-3v+9-6>=12

-3v+3>=12

-3v>=12-3

-3v>=9

v>=9/-3

v>=-3

Answer:

1. The ladder forms 71.8° with the ground.

2. The top of the ladder will reach 18.79 feet up the wall.

3. Height = 8.66 cm and area = 21.65 sq. cm.

Step-by-step explanation:

1. If the angle of elevation of the ladder is [tex]\theta[/tex] then we can write  

[tex]\sin  \theta = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} = \frac{19}{20}[/tex]

⇒ [tex]\theta = \sin ^{-1}(\frac{19}{20}) = 71.8[/tex] Degrees.

Therefore, the ladder forms 71.8° with the ground. (Answer)

2.  Now, if the ladder formed a 70 degree angle with the ground and the length of the ladder remains the same as 20 feet, then we can write  

[tex]\sin 70 = \frac{\textrm {Perpendicular}}{\textrm {Hypotenuse}} =  \frac{x}{20}[/tex]

⇒ x = 20 sin 70 = 18.79 feet.

Therefore, the top of the ladder will reach 18.79 feet up the wall.

3. See the attached figure.

We have, [tex]\tan 60 = \frac{BC}{CD} = \frac{BC}{5}[/tex]

⇒ Height = BC = 5 tan 60 = 8.66 cm.

Therefore, the area of the triangle BCD will be = [tex]\frac{1}{2} \times CD \times BC =  \frac{1}{2} \times 5 \times 8.66 = 21.65[/tex] sq. cm. (Answer)

Answer:

Step-by-step explanation:

Answer:

The cost of producing 50 blu-rays will be $1337.5

Each blu-rays must be sold of $26.75

Step-by-step explanation:

The cost of producing x number of blu-rays is given by the relation  

B(x) = 1250 + 1.75x ........... (1)

Therefore, the total cost for producing 50 blu-rays will be  

B(50) = 1250 + 1.75 × 50 = $1337.5 (Answer)

Now, Alexis does not want to make a profit by selling the blu-rays to her friends and wants just to cover her costs.

Therefore, the selling price of 50 blu-rays will be $1337.5.

Hence, each blu-rays must be sold of [tex]\frac{1337.5}{50} = 26.75[/tex] dollars. (Answer)

Answer:

the rule is:

75x + 1000

Step-by-step explanation:

after 18 months

plug 18 in for x.

75(18) + 1000

= 1350

1350 + 1000

= 2350

$2350 after 18 months

Answer:

Part (A)  1000+(n-1)75

Part (B)   2,275

subtract the 1 it's not 2350

Step-by-step explanation:

The correct solution for the equation 3x + 6 = 34 is x = 9.33 (repeating). The provided options do not match this solution, indicating an error in the given choices.

To solve the equation 3x + 6 = 34, start by subtracting 6 from both sides to isolate the term with the variable x on one side. You get 3x = 28. Next, divide both sides by 3 to solve for x, which gives you x = 28 / 3 or 9.33 (repeating). None of the provided options A, B, C, or D matches the solution, indicating a potential error in the question or the options provided.

The value of y is 28

y = 28

Answer:

f(5) = 3200

Step-by-step explanation:

Using the recursive formula to generate the terms, that is

f(2) = 2 × f(1) = 2 × 200 = 400

f(3) = 2 × f(2) = 2 × 400 = 800

f(4) = 2 × f(3) = 2 × 800 = 1600

f(5) = 2 × f(4) = 2 × 1600 = 3200

Answer: 6400

Step-by-step explanation:

Given :

f(1) = 200

f(n) = 2.f(n-1) , for n = 2 ,3 , 4 , ...

To find the 5th term

when n = 2 , the sequence becomes

f(2) = 2 .f(2-1)

f(2) = 2 f(1)

since f(1) = 200

therefore:

f(2) = 2 x 200

f(2) = 400

When n = 3

f(3) = 2f(2)

f(3) = 2 x 400

f(3) = 800

When n = 4

f(4) = 2 f(3)

f(4) = 1600

When n =5

f(5) = 2f(4)

f(5) = 3200

When n = 6

f(6) = 2f(5)

f(6) = 6400

Since n = 2 , 3 , 4 ... this means that the 5th term if f(6) , therefore ,the 5th term is 6400

Answer:

[tex]\$52.50[/tex]

Step-by-step explanation:

we know that

The simple interest formula is equal to

[tex]A=P(1+rt)[/tex]

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

[tex]t=1\ year\\ P=\$50\\ A=?\\r=5\%=5/100=0.05[/tex]

substitute in the formula above

[tex]A=50(1+0.05*1)[/tex]

[tex]A=50(1.05)[/tex]

[tex]A=\$52.50[/tex]

Answer:

.85 or 85/100

Step-by-step explanation:

Answer:

0.85 is your decimal. 85 / 100 - not simplified.

17 / 20 - simplified.

Step-by-step explanation:

For the decimal, all you gotta do is move your decimal to the left 2 times.

-Hope this helps.

For the fraction, 85% is per 100, so it's 85 / 100. To simplify, the answer is 17 / 20.

Answer:

Step-by-step explanation:

4/7 - (-4/7) = 4/7 + 4/7 = 8/7 or 1 1/7......a negative times a negative is a positive...so those two negatives turn into a positive...so ur basically just adding them

Answer:

x=0.8, y=2.2 (0.8, 2.2).

Step-by-step explanation:

y+x=3

y=1.5x+1

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

1.5x+1+x=3

2.5x=3-1

2.5x=2

x=2/2.5

x=0.8

y+0.8=3

y=3-0.8

y=2.2

To solve the given system of equations by substitution, we substitute the second equation into the first, solve for x, and then substitute x back into the second equation to solve for y, which yields x=0.8 and y=2.2 as the solution.

To solve the system of equations using substitution, we start by isolating one variable in one of the equations. Here, the second equation already gives us y in terms of x: y = 1.5x + 1.

Next, we substitute this expression for y into the first equation y + x = 3. This gives us:

Combine like terms to solve for x:

Now that we have the value of x, we can find the value of y by substituting x back into the equation y = 1.5x + 1:

Hence, the solution to the system of equations is x = 0.8 and y = 2.2.

As a final step, you may want to check your solution by plugging the values back into the original equations to confirm that they satisfy both equations.

Answer:

x³ - 5x² + 81x - 405 = 0

Step-by-step explanation:

Complex roots occur in conjugate pairs.

Thus given x = - 9i is a root then x = 9i is also a root

The factors are then (x - 5), (x - 9i) and (x + 9i)

The polynomial is the the product of the roots, that is

f(x) = (x - 5)(x - 9i)(x + 9i) ← expand the complex factors

    = (x - 5)(x² - 81i²) → note i² = - 1

    = (x - 5)(x² + 81) ← distribute

    = x³ + 81x - 5x² - 405, thus

x³ - 5x² + 81x - 405 = 0 ← is the polynomial equation

The required polynomial equation is x³ - 5x² + 81x - 405 = 0 with roots 5 and -9i.

A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.

As we know that complex roots occur in conjugate pairs.

Thus given x = - 9i is a root then x = 9i is also a root

The factors are then (x - 5), (x - 9i) and (x + 9i)

The polynomial is the product of the roots, that is

f(x) = (x - 5)(x - 9i)(x + 9i)

Expand the complex factors in the above equation

f(x) = (x - 5)(x² - 81i²)   [∵ i² = - 1]

f(x) = (x - 5)(x² + 81)

f(x) = x³ + 81x - 5x² - 405

This is equating to zero.

f(x) = 0

Thus, the required polynomial is x³ - 5x² + 81x - 405 = 0

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