if angle 2=6x+8 and angle 4=4x+11 what is the value of angle 2?

Adam invested $350 at 6% and $450 at 10%

Amount invested by Adam = $800

Interest paid by one account = 6%

Interest paid by another account = 10%

Let the amount invested in one account be x and the other be y

The formula for simple interest is given by:

Simple interest = (P*R*T)/100

where P = Principal

R = rate of interest

T = number of years amount is invested

Substituting the value in the formula we get:

Simple interest in one account = (x*6*1)/100-------(1)

Simple interest in another account = (y*10*1)/100--------(2)

The question states that interest earned would be the same when $800 is invested at 8.25%, therefore

Simple interest = (800*8.25*1)/100

= 66----(3)

Equating (1), (2) and (3) we get:

x + y = 800-----(4)

6x/100 + 10y/100 = 66

6x + 10y = 6600-----(5)

Multiplying (4) with 6 and equating it with (5)

6x + 6y = 4800

6x + 10y = 6600

4y= 1800

y = 450

x = 350

So, Adam invested $350 at 6% and $450 at 10%

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Answer:

1, 2, 3, 6, 13, 26, 39, and 78

Step-by-step explanation:

:)

Answer:

Step-by-step explanation:

( g ° f )(x) = ( x + 7 )² = x² + 14x + 49

20 + 3(x² + 14x + 49) = - 34

20 + 3x² + 42x + 147 = - 34

3x² + 42x + 201 = 0 ⇔ x² + 14x + 67 = 0

D = 196 - 268 = - 72 < 0

There is no any roots in set of real numbers.

The values of x in set of complex numbers are:

[tex]x_{12}[/tex] = [tex]\frac{- 14 }{2}[/tex] ± [tex]\frac{6\sqrt{2}i }{2}[/tex]

[tex]x_{12}[/tex]  = - 7 ± 3√2 i  

Based on the results shown in the dot plot on the number of pets owned by students in Ileana's grade, the mean number of pets owned by students is 2.5 pets

The number of pets owned per student home according to the dot plot is:

= 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 8

The total number of pets owned is:

= 0 + 0 + 0 +1 + 1 + 1 + 1 + 1 + 2 + 2 + 2 + 3 + 3 + 3 + 4 + 4 + 4 + 5 + 5 +8

= 50 pets

The mean number of pets owned is:

= 50 / 20 students

= 2.5 pets

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Step-by-step explanation:

but please where is the question I'm eager to answer and win the pizza

Given is the quadratic function by its graph..

At the start point, when time is zero, the height is not zero because the cannon was shot above the ground level.

The domain is the time from the point the cannon was shot and to the point the ball lands.

The range is the height from zero to the maximum height the ball reaches.

Answer:

A. 0

Step-by-step explanation:

[tex]2 \frac{3}{4} + ( - 2 \frac{3}{4}) \\ = \frac{11}{4} - \frac{11}{4} \\ = \frac{11 - 11}{4} \\ = \frac{0}{4} = 0 \\ hope \: this \: would \: help[/tex]

Answer:

A. 0

Explanation:

Given:

[tex]2\dfrac{3}{4} +(-2\dfrac{3}{4} )[/tex]

In improper fractions:

[tex]\dfrac{11}{4} +(\dfrac{-11}{4} )[/tex]

Simplify:

[tex]\dfrac{11}{4} -\dfrac{11}{4}[/tex]

Evaluate:

[tex]0[/tex]

Tip:

As the integers are alike, when subtracted they simplify to zero as a result.

Answer: x=24

Step-by-step explanation:

-1/3x+1= -7

you move the negative one to the other side of the equation to get x by itself and get -1/3x= -8

then you divide both sides by -1/3 and get 24

The function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18

Coordinate points are mathematical statements that are used to represent the location of points on a coordinate plane

The coordinate point is given as

(-5, 18)

The above coordinate point can be represented as

(x, y) = (-5, 18)

The above coordinate point can further be rewritten as

(x, f(x)) = (-5, 18)

So, we have

x = -5

f(x) = 18

Substitute x = -5 in the equation f(x) = 18

f(-5) = 18

Hence, the function notation of the coordinate point where the coordinate point is given as (-5, 18) is f(-5) = 18

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The value of cscθ is 1/y

In this question, we have been given that the terminal side of angle θ intersects the unit circle in the first quadrant at (7/17, y).

We know that the point on the unit circle is of the form (cosθ, sinθ)

Comparing (cosθ, sinθ) with point (7/17, y) we get,

cosθ = 7/17, and sinθ = y

also, we know that cscθ = 1/sinθ

So, cscθ = 1/y

Therefore, the value of cscθ is 1/y

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2(14m-8)=180

24m-16=180

24m=196

m= 8 and 1/6

The mean absolute deviation is 5.4.

The mean absolute deviation tells us that the variance of each data set is 5.4.

The mean absolute deviation is a measure of variance that determines the average distance between each data point in the dataset and its mean.

The mean absolute deviation = 1/n ∑ l x - m(x) l

The first step is to determine the mean of the data set: (18 + 15 + 25 + 17 + 13 + 15 +  23 + 27 + 30 +  27) / 10

= 210 / 10

= 21

The second step is to determine the absolute difference between the mean and each data point. Then add the result together.

|(18 - 21) + (15 - 21)+ (25- 21) + (17- 21) + (13- 21) + (15- 21) +  (23- 21) + (27- 21) + (30- 21) +  (27- 21)| = 54

Now, divide the sum by the total numbers in the data set : 54 / 10 = 5.4

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Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

First, convert R as a percent to r as a decimal

r = R/100

r = 5.65/100

r = 0.0565 per year,

Then, solve the equation for P

P = A / (1 + r/n)^(nt)

P = 22,450.15 / (1 + 0.0565/12)^{(12)(3.7)}

P = 22,450.15 / (1 + 0.0047)(44.4)

P = $18,223.97

The principal investment required to get a total amount of $22,450.15 from compound interest at a rate of 5.65% per year compounded 12 times per year over 3.7 years is $18,223.97.

Therefore, Roman should invest $18,223.97 in order to withdraw $22450.15 in exactly 3.7 years from now if interest rate is 5.65 % compounded monthly.

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Expanding out the equation, we get

[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]

Considering the discriminant,

[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]

This is always non-negative, meaning the roots are real.

The roots are equal if and only if the discriminant is 0, which is when a=b=c.

Answer:

x + 3/7=2x-25/7 ​

X=4

Answer:

0.36

Step-by-step explanation:

Applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.

In the problem given, we have the following information:

Material needed for one t-shirt = 1 3/8 yards

We want to find how many 1 3/4 we would find in 41 1/4.

Applying the knowledge of fraction, we are to divide 41 1/4 by 1 3/8. Convert both mixed fractions to improper fractions then divide:

41 1/4 ÷ 1 3/8

165/4 ÷ 11/8

165/4 × 8/11

165/4 × 8/11

15/1 × 2/1

= (15 × 2)/(1 × 1)

= 30/1

= 30.

Therefore, applying the knowledge of fractions, the number of t-shirts that can be made is: 30 t-shirts.

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12) Z ∪ N = {Set of Integers}

13)  H ∪ Q = R which is a set of real numbers

We are told that;

R = U represents the set of real numbers

N is the set of natural numbers

W is the set of whole numbers

Z is the set of integers

Q is the set of rational numbers

H is the set of irrational numbers

12) We want to find Z ∪ N. This is a set union of the set of integers and the set of natural numbers.

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero. Thus, an integer is also a rational number and all natural numbers are positive integers and as such;

Z ∪ N = {Set of Integers}

13) We want to find H ∪ Q. This is a set union of the irrational numbers and the set of rational numbers. Now, we know that all real numbers are classified as either rational or irrational numbers

Thus; H ∪ Q = R which is a set of real numbers

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The coordinates of the resulting point after the reflection are (-5, -5)

When we do a reflection over a given line, the perpendicular distancee between the line and the point is invariant.

In this case, we want to reflect the point (-5, -1) over the line y = -3

The distance between the y-value of the point and the line is:

D = |-1 - (-3)| = | -1 + 3| = 2

The point is at 2 units (above) from the line, then after the reflection, the point will be 2 units below the line.

So the new y-value is:

y = -3 - D = -3 - 2 = -5

The coordinates of the resulting point are (-5, -5).

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Answer: can u finish the question

Step-by-step explanation:

The value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.

Given expression: |-3d - 6| + |-5 - d²|, and d = -3

Substitute the value of d: |-3(-3) - 6| + |-5 - (-3)²|

Calculate the values inside the absolute value signs:

|-(-9) - 6| + |-5 - 9|

Simplify the inside calculations:

|9 - 6| + |-5 - 9|

Continue simplifying:

|3| + |-14|

Calculate the absolute values:

3 + 14

Add the values together:

3 + 14 = 17

So, the value of the expression |−3d − 6| + |−5 − d²| when d = -3 is 17.

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Answer:

[tex]\textsf{a)} \quad f(t) = 4+0.2t \:\: \textsf{ and }\:\:A(t)=2(1.03)^t[/tex]

b)  77 years

c)  86 years

d)  110 years

Step-by-step explanation:

Given:

As the food supply grows at a constant rate of being adequate for an additional 0.2 million people per year, it can be expressed as a linear function:

[tex]f(t) = 4+0.2t[/tex]

where:

Given:

As the annual attendance increases by 3% per year, it can be expressed as an exponential function:

[tex]A(t)=2(1.03)^t[/tex]

where:

Graph the two functions (see attached) and locate the value of t for which A(t) > f(t) for the first time.

From inspection of the graph, the two functions intersect at t ≈ 77.  So after approximately 77 years the food supply will not be enough for the number of people attending the amusement park.  Therefore, after approximately 77 years, the park will first experience shortages of food.

If the park doubles its initial food supply and maintains the rate of increase of 0.2 million people per year, the new equation would be:

[tex]f(t) = 8+0.2t[/tex]

Again, graph the new function against A(t) and find the point where the two functions intersect.  A(t) = f(t) at approximately t = 86 so the park will first experience food shortages after 86 years.  So doubling the initial food supply delays the eventual food shortage by only c. 9 years.

If the park doubled the rate at which its food supply increases in addition to doubling its initial food supply, the new equation would be:

[tex]f(t) = 8+0.4t[/tex]

Again, graph the new function against A(t) and find the point where the two functions intersect.  A(t) = f(t) at approximately t = 110 so the park will first experience food shortages after 110 years.  So doubling the initial food supply and doubling the rate delays the eventual food shortage by only c. 33 years compared to the initial parameters.  Shortages would still occur, but it would be later in approximately 110 years' time.

The line skewed to AT is HB

As a general rule, skew lines are nonparallel lines that do not intersect

This means that the lines are in different planes

From the given figure, we can see that lines HB and AT do not intersect and they are not parallel

Hence, the line skewed to AT is HB

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Answer:

£980

Step-by-step explanation:

3 portions = 210

1 portion = 70

so 70

70 × 4 = would be 280

70 × 7 = 490

490 + 280 + 210 = 980

hope this works : )

Answer: k=0,-5

Step-by-step explanation:

Your GCF is 5k, as you're able to take it out of both terms.

Once you've taken out a 5k, this will leave you with an equation that looks like this;5k(k+5)=0.

Set your 5k equal to 0 and divide to get k=0

Set your k+5 equal to 0 and subtract on both sides to get k=-5

Hope this helps you, dawg.

Answer:

1672.50 = 37.75x + 1068.50

x = 16

There were 16 players brought to the tournament.

Step-by-step explanation:

y = mx + b

y= the total cost

m = cost of each meal

x = the number of players

b = cost of the bus

Plug in what you know and solve for x

1672.50 =  37.75x + 1068.50  Subtract 1068.50 from both sides.

604 = 37.75x  Divide both sides by 37.75

16 = x

Equation: 1068.50 + 37.75x =1,672.50

Answer: X= 16

If 1,672.50 is our total it will go behind the equal sign. 37.75x and 1068.50 must be added together to help us receive our total.

Our written equation should look like this

1068.50 + 37.75x =1,672.50

X is the number of players on the team.To find out we must first subtract the amount of money spent on the bus, from the total amount spent.

1,672.50-1068.50 is 604. This means our equation now looks like this

37.75x=604. The next and final step is to divide 37.75 into 604.

604/ 37.75 is 16. Which means that there are 16 players on the team.

I hope this helps & Good luck.

Answer:

6ft

Step-by-step explanation:

180cm=5ft10in=70in

So it's closer to 6ft

(0,5) is that equations y intercept so it WILL pad through that point.

[tex]Answer:\ y=3x+5\ pass\ throught\ the\ (0,5)[/tex]

Step-by-step explanation:

[tex]y=3x+5\ \ \ \ \ (0,5)\\5=3*0+5\\5=0+5\\5\equiv5\\Hence,\\y=3x+5\ pass\ throught\ the\ (0,5)[/tex]

According to the solving the total and the difference of the numbers:

total = 136 + 64

difference  = 64

Mathematical difference is the outcome of one of the key operations, which is the subtraction of two numbers. It reveals the margin of difference between two numbers.

Subtract the largest number from the lowest number to determine the difference between two integers. The difference between these two numbers is the product of this sum. As a result, there are 55 between the numbers 45 and 100.

Let the numbers be x and y

Given,

x+y = 200_____(1)

x-y = 72_____(2)

Add above 2 eq.

2x= 272

x= 136

Substitute the value of x in eq 1,we get

136+y = 200

y = 64

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Answer:

Step-by-step explanation: