Determine which point from the specified set satisfies the system of equations.
y =-1/3x + 3
y = -3/4x + 8
Select Choice
(12,-1)
(9,0)
(8,14)

For the system of linear equations

[tex]\[ \begin{aligned} h x_{1}-3 x_{2}-6 x_{3} & =-3 \\ x_{1}+3 x_{2}+x_{3} & =1 \\ -4 x_{1}-9 x_{2}+2 x_{3} & =-1 \end{aligned} \][/tex],  

the value of [tex]\( h \)[/tex] is [tex](15/4)x_2 + (30/4)x_3[/tex].

The value of h can be determined by using the elimination method to solve the system of equations.

First, multiply the second equation by 4 and the third equation by -1 to eliminate the x1 term: [tex]\[ \begin{aligned} 4 h x_{1}-12 x_{2}-24 x_{3} & =-12 \\ -4 x_{1}-12 x_{2}-4 x_{3} & =-4 \\ 4 x_{1}+9 x_{2}-2 x_{3} & =1 \end{aligned} \][/tex]

Next, add the second and third equations to the first equation: [tex]\[ \begin{aligned} 4 h x_{1}-15 x_{2}-30 x_{3} & =-15 \\ \end{aligned} \][/tex]

Now, divide the equation by 4 to solve for h: [tex]\[ \begin{aligned} h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =-\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4} & =0 \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3}+\frac{15}{4}-\frac{15}{4} & =-\frac{15}{4}+\frac{15}{4} \\ h x_{1}-\frac{15}{4} x_{2}-\frac{30}{4} x_{3} & =0 \\ h & =\frac{15}{4} x_{2}+\frac{30}{4} x_{3} \end{aligned} \][/tex]

Therefore, the value of h is dependent on the values of x2 and x3 and can be expressed as h = [tex](15/4)x_2 + (30/4)x_3[/tex].

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Answer:

  b (3, −2)

Step-by-step explanation:

You want the solution to the system of equations ...

We see the coefficients of d are opposites, so we can add the equations together to eliminate the d variable:

  (d +e) +(-d +e) = (1) +(-5)

  2e = -4 . . . . . . . . simplify

  e = -2

Substituting into the first equation, we have ...

  d +(-2) = 1

  d = 3 . . . . . . add 2

The solution is (d, e) = (3, -2).

__

Additional comment

We also note that the coefficients of 'e' are identical, so we can eliminate 'e' as a variable by subtracting one equation from the other. We choose to subtract the equation with the lower value coefficient of 'd'.

  (d +e) -(-d +e) = (1) -(-5)

  2d = 6 . . . . . . . simplify

  d = 3 . . . . . . . . divide by 2; matches the solution above.

The attached graph uses x and y, because those are the built-in independent and dependent variables. Your graphing calculator may let you define the variables as you wish.

The area that can be watered if the length of the pipe is 400, 700, or 1,100 inches long are:

Where L = 400, A [tex]\approx[/tex] 12.82

Where L = 700 A [tex]\approx[/tex] 44.43

Where L = 1,100 A [tex]\approx[/tex]  86.13

The length of the pipe is given by the function:

L =  111.25√A.

Where a = (L/111.25)²

Thus, for L = 400inches

A =  (400/111.24)²

(400/111.24)² = (400²)/(111.24)²

(400²)/(111.24)² = (160000)/(12369.5776)
Divide 160000 by 12369.5776 to get:

(160000)/(12369.5776) = 12.820128200735

Therefore, A = 12.820128200735,

A [tex]\approx[/tex] 12.82

Thus:

Where L = 700;
A = 44.434243
A [tex]\approx[/tex] 44.43

Where L = 1,100
A = 86.129479

A [tex]\approx[/tex] 86.13

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The triplets 20, 48, 52 is a Pythagorean triplet.

In a right-angled triangle, the sum of the squares of the smaller two sides of a right-angle triangle is equal to the square of the largest side.

We know, Any three numbers to be a Pythagorean triplet,

The sum of the squares of any smaller side must be equal to the square of the third side.

Now, 20² + 48² = 52².

400 + 2304 = 2704

2704 = 2704.

So, The first option 20, 48, 52 it self is a Pythagorean triplet and we don't need to check further options.

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Question 1.) The value of the angle C = 90° ( acute angle)

Question 2.) The area of the triangle = 240

Question 3.) The measure of the angle B = 65.4°

To calculate the area of a triangle the formula below is used:

Area of a triangle = 1/2 base × height.

where: base = 12

height = 40

area = 1/2 × 12× 40

= 480/2 =240

The measure of the angle B can be calculated using the SOHCAHTOA formula:

The sides of the triangle connected to angle B = Hypotenuse and opposite.

Sin B = opposite/hypotenuse

where,

opposite = 40

hypothenuse = 44

Sin B = 40/44 =0.909090909

B = sin-¹ (0.909090909)

B = 65.4°

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Answer:

Circumference = 37.7 feet

Step-by-step explanation:

Use these formulas, then solve for the answer

C=2πr

d=2r

C = π times d

C = π times 12

C = 37.699

For the inequality |x| + 3 > 7, the points which are on its graph is -5 and 7.

What is an inequality?

In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.

To solve the inequality |x| + 3 > 7, we need to isolate the absolute value by subtracting 3 from both sides, and then split it into two cases -

|x| > 4 and -(|x|) > 4 (by multiplying both sides by -1)

Simplifying the second inequality, we get -

|x| < -4

But this is impossible, because the absolute value of any number is always non-negative.

Therefore, the second inequality has no solutions.

For the first inequality, we have -

|x| > 4

This means that x is either less than -4 or greater than 4.

Therefore, the points on the graph that satisfy the inequality are -

-5 and any value less than -4

Any value greater than 4

So the points on the graph that satisfy the inequality are -

-5 and any value less than -4 or greater than 4.

Therefore, the correct options are -

-5 and 7.

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Answer:

for the first, the answers are 1/2, 1, 2, 4, and 8. for the second, 22[tex]\frac{1}{2}[/tex] sq. km.

Step-by-step explanation:

1/4 times 2 is 1/2, times 2 is 1, times 2 is 2, times two is 4, time 2 is 8.

for the second one, area = base times height. 6 3/4 times 3 1/3 is 22 1/2 km squared.

Answer:

2400

Step-by-step explanation:

144 are seated

94% yet to arrive

6% = 144

Easy method Find the value of 1%

144/6 will be 1%

If 1% =24 then 100% will be 24x 100

Total tickets sold will be 2400

Check: 6% of 2400 is 144

Answer:

$9.50

Step-by-step explanation:

If there are 8 tickets and they all add up to $76, you have to divide 76 by 8 (the number of tickets)

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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We can plot these points on the graph and draw a straight line passing through them to represent the line 3y-4x=12.

What is graph ?

Graphs are visual representations of data or mathematical functions that are used to help people understand and analyze the relationships between different variables. Graphs can be used to show patterns, trends, and relationships in data that might be difficult to see from a table or list of numbers.

To draw the line 3y-4x=12 on the graph, we can solve for y and plot several points for different values of x, then connect the points with a straight line.

When x = -3:

3y - 4(-3) = 12

3y + 12 = 12

3y = 0

y = 0

So one point on the line is (-3, 0).

When x = 0:

3y - 4(0) = 12

3y = 12

y = 4

So another point on the line is (0, 4).

We can plot these points on the graph and draw a straight line passing through them to represent the line 3y-4x=12. The graph should look like this:

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Answer:15.75 min

Step-by-step explanation:

7/8)60= 52.5

3/10)52.5= 15.75

The nth term of the arithmetic sequence is 10 - 3n.

An arithmetic sequence is a sequence of numbers in which each term after the first is found by adding a constant value, called the common difference, to the preceding term.

The formula for the nth term (where n is a positive integer) of an arithmetic sequence is:

Here we have

a₁ = 7, a₂ = 4, a₃ = 1, a₄ = -2  

Common difference d = a₂ - a₁ = 4 - 7 = - 3

By using the formula

nth term of AP = 7 + (n - 1)(-3)

= 7 - 3n + 3

= 10 - 3n

Therefore,

The nth term of the Arithmetic sequence is 10 - 3n.  

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When t = 5, the value οf the expοnential functiοn[tex]y = 25(1.2)^t[/tex] is apprοximately 36.7.

An expοnential functiοn is a mathematical functiοn οf the fοrm[tex]f(x) = ab^x[/tex] where a and b are cοnstants, and x is the independent variable. The base b is a pοsitive cοnstant greater than 0 and nοt equal tο 1.

In the expοnential functiοn [tex]y = 25(1.2)^t[/tex], the initial amοunt is 25, which is the value οf the functiοn when t = 0.

The rate οf grοwth is 20%, which is the value οf the base οf the expοnential functiοn minus 1, expressed as a percentage. In this case, the base is 1.2, which is 20% greater than 1.

Tο evaluate the functiοn when t = 5, we substitute t = 5 intο the functiοn and simplify:

[tex]y = 25(1.2)^t[/tex]

[tex]y = 25(1.2)^5[/tex]

[tex]y = 25(1.469)[/tex]

[tex]y = 36.73[/tex]

Rοunding tο the nearest tenth, we get y ≈ 36.7.

Therefοre, when t = 5, the value οf the expοnential functiοn [tex]y = 25(1.2)^t[/tex]is apprοximately 36.7.

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Answer:

Step-by-step explanation:

30x453.6=13608 grams

Answer:

864 cards

Step-by-step explanation:

Goal: 15 set of cards

*72 cards in a set*

15 x 72 = 1080

15 sets of cards = 1080 cards in total

However Kareem so far has 216 cards.

To find out how much more cards Kareem need to reach his goal, you do the following:

1080 - 216 = 864

Kareem needs 864 more cards to reach his goal.

hope this helped....

The axis οf symmetry fοr the functiοn f(x) = -(x - 7)² - 30 is the vertical line x = 7.

In mathematics, the axis οf symmetry is a line that divides a twο-dimensiοnal shape οr a three-dimensiοnal οbject intο twο equal halves, such that each half is a mirrοr image οf the οther. The axis οf symmetry can alsο refer tο a line that divides a mathematical functiοn intο twο equal halves.

The given quadratic functiοn is:

f(x) = -(x - 7)² - 30

We can see that the cοefficient οf x² is -1, which means that the parabοla οpens dοwnwards. The vertex οf the parabοla is (7, -30), which is alsο the maximum pοint οf the parabοla.

The axis οf symmetry fοr a parabοla is a vertical line that passes thrοugh the vertex. Therefοre, the axis οf symmetry fοr the given functiοn is a vertical line passing thrοugh (7, -30).

The equatiοn οf the axis οf symmetry is given by:

x = 7

Therefοre, the axis οf symmetry fοr the functiοn f(x) = -(x - 7)² - 30 is the vertical line x = 7.

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Answer:

Step-by-step explanation:

A is y=x+4

b is y=14

We can determine that TC owns one cow using exponential calculations.

Exponent-based equations are those in which the exponent, or a portion of the exponent, is a variable.

For illustration, [tex]3^{x}[/tex] = 81.

In the question given,

TC is drinking no. of cups = 17

Let no. of cows TC has = x

Now according to the question, we can for the equation as:

[tex](\sqrt[5]{x} )^{2}[/tex] = 17 -1

⇒ x = [tex]\sqrt[5]{4}[/tex]

⇒ x = 1.319

⇒ x ≈ 1

Hence, TC owns 1 cow.

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The angle BAC will always be a right angle (90 degrees).

Given a circle centered at point O and any three points A, B, and C on the circle, the angle BAC will always be half of the corresponding central angle BOC.

If we keep points B and C fixed and allow point A to move around the circle,

then the angle BAC will stay the same.

If points B and C are endpoints of the diameter of the circle, then the angle BAC will always be a right angle (90 degrees).

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The algebraic expression indicating the number of cookies remaining to be baked is 144 - x.

To find the number of cookies Pat still needs to bake, we need to subtract the number of cookies she has already baked from the total number of cookies she needs to bring to the party. In this case, the total number of cookies is 144 and the number of cookies she has already baked is represented by the variable x.

Therefore, the algebraic expression for the number of cookies Pat still needs to bake is:

This expression tells us that to find the number of cookies Pat still needs to bake, we need to subtract the number of cookies she has already baked (x) from the total number of cookies she needs to bring (144).

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The mean of the given probability distribution is 2.8.

To find the mean, we multiply each possible value of X (the number of adults with a college degree) by its corresponding probability, and then add up the products.

So, the mean is:

(0)(0.0081) + (1)(0.0756) + (2)(0.2646) + (3)(0.4164) + (4)(0.2401) = 2.8

This means that on average, out of 4 randomly selected adults in the town, 2.8 of them will have a college degree. This is a useful measure of the central tendency of the probability distribution, as it gives us an idea of what to expect if we were to repeat this process of randomly selecting 4 adults many times.

It's important to note that the mean is not necessarily a value that is actually observed in the data, but rather a summary statistic that tells us about the distribution as a whole. In this case, it tells us that the distribution is slightly skewed towards higher values, since the mean is greater than the median (which would be the value of X with cumulative probability of 0.5, or 2 in this case).

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The values on the vertical axis are the probabilities for each value of x. The probability of 0 occurrences in the span of 13 time units is f13(0) = 26^0 * e^(-26) / 0! = e^(-26) ≈ 0.0000000000000000000000000003.

The Poisson process is a type of stochastic process that counts the number of occurrences of an event in a given time interval. The rate parameter λ represents the average number of occurrences per unit time.

i. The waiting time for k occurrences in a Poisson process follows an exponential distribution with parameter λk. The probability distributions for X1, X2, X3, and X5 are given by:

X1 ∼ Exp(λ) = Exp(2)

X2 ∼ Exp(λ*2) = Exp(4)

X3 ∼ Exp(λ*3) = Exp(6)

X5 ∼ Exp(λ*5) = Exp(10)

The expected waiting time E[Xk] is given by 1/λk, and the standard deviation σXk is also given by 1/λk. Therefore, we have:

E[X1] = 1/λ = 1/2

E[X2] = 1/(λ*2) = 1/4

E[X3] = 1/(λ*3) = 1/6

E[X5] = 1/(λ*5) = 1/10

σX1 = 1/λ = 1/2

σX2 = 1/(λ*2) = 1/4

σX3 = 1/(λ*3) = 1/6

σX5 = 1/(λ*5) = 1/10

The probability distributions for the interval 0 ≤ x ≤ 7 are shown below:

ii. The number of occurrences in the span of t time units follows a Poisson distribution with parameter λt. The probability distributions ft(x) for t = 13, t = 12, and t = 1.2 are given by:

ft(x) = (λt)^x * e^(-λt) / x!

f13(x) = (2*13)^x * e^(-2*13) / x! = 26^x * e^(-26) / x!

f12(x) = (2*12)^x * e^(-2*12) / x! = 24^x * e^(-24) / x!

f1.2(x) = (2*1.2)^x * e^(-2*1.2) / x! = 2.4^x * e^(-2.4) / x!

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x = 2logb(x2 + 56)/2

1. log2x = log218

log2x = 3

x = 23 = 8

2. log2×2 = log2(4x−4)

log2×2 = log2(4x)−log2(4)

log2×2 = log2(4x)−2

log2×2 + 2 = log2(4x)

log2(2×2) + 2 = log2(4x)

log2(4) + 2 = log2(4x)

4 + 2 = log2(4x)

6 = log2(4x)

26 = 4x

x = 23 = 8

3. logb(x2−56)=logbx

logb(x2−56) = logbx

logb(x2)−logb(56) = logbx

logbx2−logb56 = logbx

logbx2−logb56 + logbx = logbx + logbx

2logbx = logbx2 + logb56

2logbx − logbx2 = logb56

2logbx − logb(x2−56) = logb56

2logbx − logb(x2) + logb(56) = logb56

2logbx−logbx2 + logb(56) = logb56

2logbx = logb(x2 + 56)

2logbx = logb(x2 + 56)

logbx = logb(x2 + 56)/2

x = 2logb(x2 + 56)/2

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Answer:

Step-by-step explanation:

1 ticket costs 1 × $4.50 = $4.50

2 tickets cost 2 × $4.50 = $9.00

3 tickets cost 3 × $4.50 = $13.50

4 tickets cost 4 × $4.50 = $18.00

The first table is the only one that matches these values.

Answer:

Step-by-step explanation:

To find the length of the square side lengths and the diameter of the circle, we can divide the perimeter by 4:

79.04/4 = 19.76

This is the diameter of the circle. The radius is half the diameter:

19.76/2 = 9.88

Hope this helps!

Answer: 9.88 cm

Step-by-step explanation:

To find the radius, we need to find half the length of one side of the square.

The perimeter of the square is all the sides of the square added together.

Squares have 4 sides so divide the perimeter by 4 to find the length of 1 side.

79.04 / 4 = 19.76 is the length of one side.

Half of 19.76 is 9.88 so the radius of the circle is 9.88 cm.

Hope this helps!

Answer:

To find YZ and DE in the sequence WXYZ FEDC, we need to understand how the sequence is constructed. The sequence is likely made up of two smaller sequences: WXYZ and FEDC.

To find YZ, we need to look at the WXYZ sequence. Since Y and Z are the last two digits of this sequence, we can conclude that Z is the last digit and Y is the second to last digit. Therefore, YZ = 30.

To find DE, we need to look at the FEDC sequence. Since D and E are the last two digits of this sequence, we can conclude that E is the last digit and D is the second to last digit. Therefore, DE = 96.

So, YZ = 30 and DE = 96

Step-by-step explanation:

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The water level after 4 weeks will be 29.2 feet.

The water level of the lake will increase by 10% each week during the winter rainstorms. This means that each week, the water level will increase by 0.10 × 20 = <<0.10*20=2>>2 feet.

After the first week, the water level will be 20 + 2 = <<20+2=22>>22 feet.
After the second week, the water level will be 22 + 2 = <<22+2=24>>24 feet.
After the third week, the water level will be 24 + 2 = <<24+2=26>>26 feet.
And so on.

We can use the formula A = P(1 + r)^n to find the water level after n weeks, where A is the final amount, P is the initial amount, r is the rate of increase, and n is the number of weeks.

In this case, P = 20, r = 0.10, and n is the number of weeks.

So, the water level after n weeks will be:

A = 20(1 + 0.10)^n

We can plug in different values of n to find the water level after a certain number of weeks.

For example, to find the water level after 4 weeks, we can plug in n = 4:

A = 20(1 + 0.10)^4 = 29.2 feet

So, the water level after 4 weeks will be 29.2 feet.

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Answer:its 80 i did the same problem

Step-by-step explanation: