solve the following simultaneous equation graphically 2x-y=1 and 3x+y=9

Answer:

EF = 32

Step-by-step explanation:

since the base angles D and F are congruent then the triangle is isosceles with both legs congruent , that is

EF = DE = 32

Answer:

32 units

Step-by-step explanation:

It is an isosceles triangle so two sides will be the same length opposite the equal angles     EF = 32

Answer:

8 boys.

Step-by-step explanation:

Lets say b is the number of boys and g is the number of girls.

We know that:

23 = b + g

g = b + 7

So then lets solve for b:

23 = b + g

23 = b + ( b + 7)

Simplify.

23 = 2b + 7

Subtract 7 from both sides to isolate the b.

16 = 2b

Divide both sides by 2.

8 = b

So there are 8 boys in the class.

We can check our work by substituting the value of b into our equation.

23 = b + ( b + 7)

23 = 8 + ( 8 + 7 )

23 = 8 + 15

23 = 23

So therefore our answer is correct.

Answer:

[tex]2a^2b*(3a^2-5ab-3b^2)[/tex]

Step-by-step explanation:

Attempt factorization by grouping

(((6•(a^4))•b)-((10•(a^3))•(b^2)))-((2•3a^2)•b^3)

(((6•(a^4))•b)-((2•5a^3)•b^2))-(2•3a^2b^3)

(((2•3a^4) • b) -  (2•5a^3b^2)) -  (2•3a^2b^3)

6a^4b - 10a^3b^2 - 6a^2b^3  =  2a^2b • (3a^2 - 5ab - 3b^2)

Pull out the leading term and put it with the original equation

= 2a^2b • (3a^2 - 5ab - 3b^2)

This would be one of the quicker ways to factor this equation.

Hope this helps.

Answer: S = K/4 - 790

Step-by-step explanation:

the problem tells us Ken = Sam times 4 + 790.

So you need to reverse it (or solve for Ken to find Sam).

Ken/4 = Sam + 790

Ken/4-790 = Sam

Answer:

9

Step-by-step explanation:

We can determine the number of bowls that can be made by dividing the size of the bowl by the amount of soup. 1 1/8 can be expressed as 8/8 + 1/8, or 9/8. (9/8)/(1/8) = 9. The chef can fill 9 bowls of soup.

Mushroom soup sounds pretty good right now ngl

[tex]~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{-22})\qquad B(\stackrel{x_2}{8}~,~\stackrel{y_2}{4}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ 8 +3}{2}~~~ ,~~~ \cfrac{ 4 -22}{2} \right) \implies \left(\cfrac{ 11 }{2}~~~ ,~~~ \cfrac{ -18 }{2} \right) \implies (5.5~~,~~\stackrel{\stackrel{y}{\downarrow }}{-9})[/tex]

Answer:

is it is 10^4 - 11^2 + 6 then the answer will be 4

Step-by-step explanation:

The 100th line segment by using the nth term of a sequence is equal to 20200.

A sequence can be defined as a series of real and natural numbers in which each term or list of elements are ordered in a particular order and repetitions are allowed.

Next, we would determine the differences between the terms in this sequence until all the differences are the same:

12 - 4 = 8

24 - 12 = 12

40 - 24 = 16

12 - 8 = 4

16 - 12 = 4

Since the differences are the same, the sequence is a quadratic function and it contains an n² term. Also, the coefficient of n² is one-half of the equal difference. This ultimately implies that, the coefficient of n² is equal to 2.

In order to determine the nth term of this sequence, we would develop a table to model increment:

n                    1       2       3      4

2n²                2       8      18    32

Operation    +2     +4     +6    +8

Sequence     4       12     24   40

By critically observing the table above, we can logically deduce that the nth term of this sequence is given by:

aₙ = 2n² + 2n

a₁₀₀ = 2(100)² + 2(100)

a₁₀₀ = 2(10000) + 2(100)

a₁₀₀ = 20000 + 200

a₁₀₀ = 20200.

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Answer:

3. 7

5. 8

7. 15

9. 6

10. 1

Step-by-step explanation:

In order to be able to compensate to get the exact sum of the two prices, Kayla should subtract $0.05 from $55.75.

In order to be able to get the price of $55.75, Kayla rounded $34.95 up to $35 and then added $20.75.

To compensate for the rounding up and then get the exact sum of the prices of the sweaters, Kayla should subtract the difference between the $35 and the $34.95.

That difference is:

= 35 - 34.95

= $0.05

In conclusion, Kayla should subtract $0.05 from $55.75 to get $55.70.

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The cost of the washer based on the total cost of $1,800 of all three items is $442.86

How do represent the cost of the washer?

If we assume that the cost of the washer is x, based on that we can determine the cost of the refrigerator and the dryer while deriving from the cost of the washer as denoted below:

cost of washer=x

The cost of the refrigerator is $250 more than the cost of washer i.e. x+250

cost of dryer=0.5*x

cost of dryer=0.5x

total cost=x+x+250+0.5x

total cost=3.5x+250

total amount spent=1800

1800=3.5x+250

1800-250=3.5x

1550=3.5x

x=1550/3.5

x=$442.86

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Answer:

The answer is not that clear: But for 16.4 it isn't correct because you need to round it from 16.468 to 16.5. so therefore the answer is <

Answer:

n= -35 .................................

Using the numeric value of functions, it is found that:

To find the numeric value of a function, we replace each instance of the variable by the desired value.

The formula for the velocity is given as follows:

[tex]v = 8\sqrt{h}[/tex]

In which h is the height.

For this problem, we have that the height is of h = 9.8, hence:

v = 8sqrt(9.8) = 25 feet per second.

The holder was running at a rate of 25 feet per second.

Then, in two seconds, the distance is given as follows:

d = 25 x 2 = 50 feet.

The pole vaulter will run 50 feet in 2 seconds.

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Answer:

The answer will be A.

Answer:

2

Step-by-step explanation:

f(-3) represents f(x) evaluated at x=3.

[tex]f(-3)=(-3)^2+2(-3)-1 \\ \\ =9-6-1 \\ \\ =2[/tex]

Answer:

x = 4

Step-by-step explanation:

x - 6 = 2x - 10

-2x     -2x

-x - 6 = -10

    +6    +6

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

-x = -4

÷-1   ÷-1

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

x = 4

I hope this helps!

The value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)

The function definition is given as

f(x) = √(x - 9) + 6

We start by calculating the function f(x + a)

So, we have

f(x + a) = √(x + a - 9) + 6

The function definition f(x + a) - f(x) is calculated as

f(x + a) - f(x) = √(x + a - 9) + 6 - (√(x - 9) + 6)

Open the bracket

So, we have

f(x + a) - f(x) = √(x + a - 9) + 6 - √(x - 9) - 6

Evaluate the difference

So, we have

f(x + a) - f(x) = √(x + a - 9) - √(x - 9)

Hence, the value of the function f(x + a) - f(x) is √(x + a - 9) - √(x - 9)

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Answer:

16

Step-by-step explanation:

4n -4 (pattern rule)

4x2 = 8-4 = 4

The monthly finance charge for the credit card transaction is $51.70.

We need to calculate the monthly finance charge for the given credit card transaction.

Credit card transaction means the purchase of goods or obtaining of services or cash against the use of the Credit Card, the Card number or in any manner authorised by the Cardholder for debit to the Credit Card Account or utilising of any services made available to the Cardholder by the Bank from time to time in respect.

Given that, $3,000 balance, 21% rate, 150 payments, average daily method

The particular month in question is 30 days long.

Your balance at the start of the month is $3,000.

Annual interest rate = 21%.

Payment = $150.00

When the payment is made in the month, it reflects on the tax amount you pay on both the average daily balance.

The average daily balance is $3000 from day 1 until day 10 (10 days)

The average daily balance is $2850 from day 11 until day 30 (20 days)

Average daily balance for the month = 10 × 3000 + 20 × 2850

= 87000 / 30

= $2900

Interest charge for the month = (0.21 × 2900× 30) / 365

The interest charge for the month = $50.05 rounded to the nearest penny

The average daily balance is $3000 from day 1 until day 29 (29 days)

The average daily balance is $2850 from day 30 until day 30 (1 day)

Average daily balance for the month = 3000 × 29 + 1 × 2850

= 89850 / 30

= $2995

Interest charge for the month = (0.21 × 2995 × 30) / 365

=51.6945≈$51.70

Therefore, the monthly finance charge for the credit card transaction is $51.70.

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D. (x + 5)

 We have to find the factor of this expression which matches to the options.

The number of employees decreased by 18 percent

The formular for percent decrease is

old value-new value/old value × 100

old value= 1500

new value= 1230

1500-1230/1500 × 100

= 270/1500 × 100

= 0.18 × 100

= 18

Hence the number of employees decreased by 18 percent

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The number of concert shows that singer A and singer B attended will be 41 and 18 shows respectively.

Based on the information, the equation for last year will be:

A = 2B + 5

The number will be illustrated as:

A = B + 23

Therefore, it should be noted that we will equate the expression. This will be:

2B + 5 = B + 23.

Collect like terms

2B - B = 23 - 5

B = 18.

A = 23 + B = 23 + 18 = 41

Therefore, the number of concert shows that singer A and singer B attended will be 41 and 18 shows respectively.

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Last year, Singer A performed two times as many shows during concert tours than Team B. The number of Singer A concert tour shows exceeded the number of shows by Team B by 23. How many concert shows did each perform?

Answer:

  (a) height: 44.5 m

  (b) shadow: 71.2 m

Step-by-step explanation:

You want building height and shadow length for angles of elevation 56° and 32°, given the shadow is 30 m when elevation is 56°.

The building height and shadow length are the sides opposite and adjacent (respectively) to the elevation angle in the right triangle that models the geometry. The trig function that relates these sides to the angle is the tangent function:

  Tangent = Opposite/Adjacent

(a) building height

Using the tangent relation, we have ...

  tan(56°) = (height)/(30 m)

  height = (30 m)(tan(56°)) ≈ 44.4768 m

The height of the building is about 44.5 meters.

(b) shadow length

Using the same relation with the building height known, we have ...

  tan(32°) = (44.4768 m)/(shadow)

  shadow = (44.4768 m)/tan(32°) ≈ 71.1778 m

The length of the shadow at an angle of 32° is about 71.2 m.

Answer:

x=3

Step-by-step explanation:

3 times (2x+5)-23=10 can be rewritten as 3(2x+5)-23=10

6x+15-23=10 ----> Use distributive Property

6x-8=10 ------------> Combine Like Terms

6x=18 -----------------> Use inverse operations; add 8 on both sides; simplify

x=3 ---------------------> Use inverse operations, divide by 3, simplify

Answer:

X=3!

Step-by-step explanation:

1) 6x - 8 = 10

2) + 8 +8

3) 6x = 18

Solution: X=3

The ways to know know which school has higher athletic achievements relative to budget per student are:

Analia thought of two different ways to define this quantity. Identify these two definitions among the following options.

% of students in sports club divided by SAT average

the number of sports medals won divided by SAT average

To determine which school has higher athletic achievements relative to the SAT average, according to the two definitions will be that Did you get the same result for both definitions?

No. The definitions have opposite results.

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Analia wants to know which school has higher athletic achievements relative to the SAT average. 1) Analia thought of two different ways to define this quantity. Identify these two definitions among the following options. Choose 2 answers: Choose 2 answers: (Choice A) A % of students in sports club divided by SAT average (Choice B) B Graduation rate divided by SAT average (Choice C) C Number of sports medals won (Choice D) D Number of sports medals won divided by SAT average 2) Determine which school has higher athletic achievements relative to the SAT average, according to the two definitions. Did you get the same result for both definitions? Choose 1 answer: Choose 1 answer: (Choice A) A Yes. According to both definitions, School A has higher athletic achievements relative to the SAT average. (Choice B) B Yes. According to both definitions, School B has higher athletic achievements relative to the SAT average. (Choice C) C No. The definitions have opposite results.

Answer:

66

Step-by-step explanation:

he will pay 66 dollars

Step-by-step explanation:

1. divide 10 with 5

2. using law indices, simplify the rest of the equation

3. you're done!

Answer: 5m³n³

Step-by-step explanation:

[tex]\frac{10m^5n^4}{2m^2n}[/tex] = [tex]\frac{5m^5n^4}{m^2n}[/tex]  

          = [tex]\frac{5m^3n^4}{n}[/tex]
          = 5m³n³

or
[tex]10m^{5} n^{4}[/tex] ÷[tex]2m^{2}n[/tex] = [tex]5m^{5-2} n^{4-1}[/tex]
                       = [tex]5m^{3} n^{3}[/tex]