Solve the following system of equations by using the substitution method.
x – y = 3
2x + 2y = 2

(3, 4)

(-4, 5)

(2, -1)

[tex]x^3-4^3 = (x-4)(x^2+4x+16)=(x-4)(x+4)(x+4)[/tex]

area = 98 cm²

the area of a rectangle = length × width

here length = 14 and width = 7

area = 14 × 7 = 98 cm²

Perimeter = 2*14 + 2x   where x is length of the adjacent side

46 = 28 + 2x

2x =  18

x = 9 inches Answer

Answer-

The total interest after 3 years is Rs.5760 .

Solution-

Total money borrowed = Rs.12000

Out of those Rs.4000 is of 18% interest rate and remaining 12000-4000=8000 is of 15% interest rate.

[tex]\text{Total interest}=\frac{P_1\times r_1\times t}{100}+\frac{P_2\times r_2\times t}{100}[/tex]

Where,

P₁ = principal amount = Rs.4000

P₂ = principal amount = Rs.8000

r₁ = rate of interest of P₁ = 18%

r₂ = rate of interest of P₂ = 15%

t = time period  = 3 years

[tex]\text{Total interest}=\frac{4000\times 18\times 3}{100}+\frac{8000\times 15\times 3}{100}=2160+3600=5760[/tex]

Remark

The diameter of the circle is AC. The hypotenuse of the right triangle is also AC. This assumes that A,B and C all lie on the circumference of the circle.

Answers

One

The center of the circle is on the diameter of the circle. In fact, the center bisects the diameter. So the center lies on AC and if the center is labeled O then AO = BO.

Answer 1: AC

Two

The answer is the single word diameter.

The ____ is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

When largest exponent of the polynomial is even and leading coefficient is positive , then left hand and right hand ends of the graph goes up

When largest exponent of the polynomial is even and leading coefficient is negative , then left hand and right hand ends of the graph goes down

When largest exponent of the polynomial is odd and leading coefficient is positive , then left hand graph goes down and right hand ends of the graph goes up

When largest exponent of the polynomial is odd and leading coefficient is negative , then left hand graph goes up and right hand ends of the graph goes down

Hence, Leading coefficient test is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

The leading coefficient test is used to determine the left-hand and right-hand behavior of the graph of a polynomial function.

The correct choice to fill in the blank is Leading coefficient test.

The leading coefficient, which is the coefficient of the highest power term in a polynomial function, helps determine the behavior of the graph. If the leading coefficient is positive, the graph will have an upward (right-hand) behavior, while if the leading coefficient is negative, the graph will have a downward (left-hand) behavior.

For example, in the polynomial function f(x) = 3x^3 - 2x^2 + 5x - 1, the leading coefficient is 3. Therefore, the graph of this function will have an upward (right-hand) behavior.

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The unemployment rate is calculated as the number of unemployed divided by the labor force, resulting in approximately 9.6%, which is the closest to 9.3% as listed. It is higher than the historical average and the February 2015 rate.

The unemployment rate of an economy is calculated by taking the number of unemployed persons and dividing it by the total labor force, and then multiplying the result by 100 to get a percentage.

In this case, using the given figures, the unemployment rate is calculated as follows: 14.8 (unemployed) / 153.9 (labor force) = approximately 9.6%.

This indicates that the correct answer is not explicitly listed, but the closest answer given is 9.3%, which seems to be a typo.

Furthermore, this current unemployment rate is significantly higher than the February 2015 rate of 5.5% and above the historical average unemployment rate, which tends to range between 4% to 6% over time, according to Federal Reserve Economic Data.

Answer:

Option 3 (7,2) is right answer.

Step-by-step explanation:

Given two equations

3x-2y=17    ... i

x-3y=1         ... ii

We can solve this by elimination.

coefficients of x are 3 and 1 with LCD = 3

Hence multiply ii equation by 3

3x-9y = 3  ... iv

3x-2y = 17  ... i

Subtract i from iv

-7y = -14

Divide by -7

y =2

Substitute in ii

x-3(2) = 1

x=7

Hence solution is (7,2)

Verify:

We can verify our solution by substituting in i and ii.

3(7)-2(2) = 17 and 7-6 =1

Verified

Remark

How does this poor soul survive?

Solution

Let the number of faults he has in his teens = x

1/7 of (of means multiply) those faults were there at birth.

1/7 x = 326     Solve for x by multiplying by 7

7* (1/7 x) = 326 * 7

x = 2282 is the number of faults Patrick has. Answer

answer=3.20/16=0.20 is cost per ounce

The equation is y = 2x - 12

Equation in slope intercept form is

[tex]y = mx + b[/tex]

Where,

m = slope

b = y-intercept

Putting the value of slope in this equation:

[tex]y = 2x + b[/tex]

From this we can solve the equation for b

[tex]b = y - 2x[/tex]

[tex]b = -2 - 2(5)[/tex]

[tex]b = -12[/tex]

Now, the equation of y-intercept becomes

[tex]y = 2x - 12[/tex]

The dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.

To solve this problem, we can use the kinematic equation that relates initial velocity, final velocity, acceleration, and displacement:

vf² = vi² + 2ad

The positive value of d indicates that the dolphin's friend is 8.63 meters below the surface of the water relative to the dolphin's jumping point.

The dolphin's friend is 5.3 meters below the surface of the water.

Let's reassess the problem with the given constraints more carefully.

We need to find the position of the dolphin's friend relative to the surface of the water.

1. Dolphin's height above the water:

[tex]\[ 4.5 \text{ meters above the surface} \][/tex]

2. Distance between the dolphin and her friend:

[tex]\[ 9.8 \text{ meters below the dolphin} \][/tex]

Since the friend is swimming below the dolphin, we need to subtract this distance from the height of the dolphin above the surface to find the position of the friend relative to the water surface.

3. Calculate the position of the dolphin's friend:

[tex]\[ \text{Position of friend} = 4.5 \text{ meters} - 9.8 \text{ meters} \][/tex]

[tex]\[ \text{Position of friend} = -5.3 \text{ meters} \][/tex]

This means the dolphin's friend is 5.3 meters below the surface of the water.

We have been given the dimensions of the rectangular prism.

Lets say that the length, width, and height of the rectangular prism are:

Length [tex]= x+1[/tex]

Width [tex]=x-1[/tex]

Height[tex]=x[/tex]

Volume of a rectangular prism is given by:

[tex]length \times width\times height[/tex]

Plugging the values of length, width, and height, we get:

Total volume of the prism [tex]= (x+1)\times(x-1)\times x[/tex]

[tex]=(x^2-1)x=x^3-x[/tex]   (we have used [tex](a+b)\times (a-b)=a^2-b^2[/tex])

So, the expression for the total volume of the prism is:

[tex](x^3-x)[/tex]

96 square yards would complete the room

The function that models the total cost of the repair service as a function of the number of hours, [tex]\( h \),[/tex] is given by:  [tex]\[ C(h) = 75 + 55h \][/tex]

  In this situation, the appliance repair service charges a fixed amount of  [tex]75[/tex] for making a service call, regardless of how long the repair takes. This is the flat fee component of the cost. Additionally, the service charges [tex]55[/tex] for each hour of work performed by the technician. This is the hourly rate component of the cost.

 To model the total cost as a function of the number of hours [tex]h[/tex] that the repair takes, we start with the flat fee of [tex]75[/tex]. We then add the product of the hourly rate [tex]55\\[/tex] and the number of hours [tex]\( h \)[/tex]. This gives us the total cost function:

[tex]\[ C(h) = \text{Flat Fee} + (\text{Hourly Rate} \times h) \][/tex]

[tex]\[ C(h) = 75 + 55h \][/tex]

 Here, [tex]\( C(h) \)[/tex] represents the total cost in dollars as a function of the number of hours [tex]\( h \)[/tex] spent on the repair. The term [tex]\( 75 \)[/tex] is the fixed cost, and [tex]\( 55h \)[/tex] represents the variable cost that depends on the number of hours worked.

 This linear function correctly models the total cost of the repair service based on the given rates and the time spent on the repair.

Answer:

The answer is Daniel is correct, but Kelly is not.

Step-by-step explanation:

Answer:

(D) Daniel is correct, but Kelly is not.

Step-by-step explanation:

It is given that Line segment NT intersects line segment MR forming four angles. Angles 1 and 3 are vertical angles. Angles 2 and 4 are vertical angles.

Kelly's Proof:∠2 = ∠4 (Vertical angles are congruent)

∠1 = ∠3 (Vertical angles are congruent)

Using Vertical Angle Theorem  the vertical angles are equal.

since, we cannot use the direct information given in the question in order to prove the same.

Thus, the justification given by Kelly is incorrect.

Now, Daniel's proof:

∠1 + ∠2 = 180°(Definition of Supplementary Angles)

and ∠1 + ∠4 = 180° (Definition of Supplementary Angles)

⇒∠1 + ∠2 = ∠1 + ∠4(Transitive Property of Equality)

Hence,  ∠2 = ∠4(Subtraction Property of Equality)

Thus, the justification of Daniel is correct.

Hence, option (D) is correct.

Answer:  b. $3,374.65

Step-by-step explanation:

The exponential equation of growth (continuously) is given by :-

[tex]y=Ae^{rx}[/tex], where A is the initial amount, r is the rate of growth ( in decimal) and x is the time period.

Given : You invest $2,500 in an account that grows 5% each year.

i.e.  A= $2,500  and r= 5%=0.05

Then, the equation model this situation will be :-

[tex]y=2500e^{0.05x}=2500(1.05)^x[/tex]

Now, At x= 6

[tex]y=2500e^{0.05\times6}\\\\\Rightarrow\ y=2500e^{0.3}=3374.64701894\approx3374.65[/tex]

Hence, the investment amount after 6 years will be $3,374.65.

The amount of the investment after 6 years is $3,374.65

From the question, we have the following parameters that can be used in our computation:

Inital value, a = $2500

Rate of increase, r = 5%

Using the above as a guide, we have the following:

The function of the situation is

f(x) = a * (1 + r)ˣ

Substitute the known values in the above equation, so, we have the following representation

f(x) = 2500 * (1 + 5%)ˣ

So, we have

f(6) = 2500 * (1 + 5%)⁶

Evaluate

f(6) = $3,374.65

Hence, the amount is $3,374.65

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Answer:

Step-by-step explanation:

A vertical stretch by a factor of k means that the point (x, y) on the graph of f (x) is transformed to the point (x, ky) on the graph of g(x), where k <1.

If k =1, then same graph we obtain and if k>1 we get a vertically shrink graph.

In our question, there is a vertical stretch of 3. This means new graph would have points as (x,y/3)

i.e. instead of f(x) = y, we have now f(x) = y/3

So transformation is g(x) = 3f(x)

Option A is correct.

2) Here f(x) = 3x+8 is transformed to g(x) =3x+6

i.e. y intercept is reduced by 2 units.  Hence there is a translation of 2 units down.

I did not have the answer to the second question but here is the first.

There would be 4 groups of 8 coins. 32/8=4 Hope I could help!!!

A and A

the equation of a parabola in vertex form is

y = a(x - h)² + k

where ( h, k ) are the coordinates of the vertex and a is a multiplier

y = - 2(x + 3)² + 2  is in this form

with vertex = ( - 3, 2)

To find the y-intercept let x = 0

y = - 2(3)² + 2 = - 18 + 2 = - 16

Similarly

y = - 2(x + 2)² + 2 is in vertex form

vertex = ( - 2 , 2)

x = 0 : y = - 2(2)² + 2 = - 8 + 2 = - 6 ← y- intercept

That would be FALSE

They have the same angles, so they're similar triangles.  For them to be congruent, the corresponding sides must have equal length.  Here we have two sides of length 7, but they're not corresponding sides.  If on the second triangle the 7 was the length of the side between the 60 and 62 degree vertices then we'd have equal corresponding sides and congruent triangles.

Answer: no

Step-by-step explanation: this answer would be FALSEEE

Answer: sin2y =240/289 where 0<y <π/2

Step-by-step explanation:

Given  sin(x) = 1/3 and sec(y) = 17/15 , where x and y lie between 0 and π/2.

We now that

[tex]cosy = \frac{1}{secy} =\frac{15}{17} \\and\\\text{using identity } sin^2y+cos^2y=1\\\text{we have}\\siny=\sqrt{1-cos^2y}=\sqrt{1-(\frac{15}{17} )^2}=\sqrt{1-\frac{225}{289} }=\sqrt{\frac{64}{289} }=\frac{8}{17} \\\Rightarrow\ siny=\frac{8}{17} \\\text{Now we are using identity sin2A=2sinAcosA we have}\\sin2y=2\cdot\ siny\cdot\ cosy=2\cdot\ \frac{8}{17} \cdot\ \frac{15}{17} =\frac{240}{289}[/tex]

To solve the question, we firstly find cos(y) from 'sec(y) = 17/15' because secant is the reciprocal of cosine. Then, we use the Pythagorean identity to find sin(y). Finally, we substitute these values into the double angle identity 'sin(2y) = 2sin(y)cos(y)' to find the final answer.

In this high school level mathematics problem, 'sin(x) = 1/3' and 'sec(y) = 17/15' are given. From 'sec(y) = 17/15', we can calculate cos(y) because secant is the reciprocal of cosine. Hence, 'cos(y) = 15/17'. The question asks for the evaluation of the expression 'sin(2y)'. Here, we can use a trigonometric identity for double angles, which states 'sin(2y) = 2sin(y)cos(y)'.

However, we are only given secant of y, not sine. To find sin(y), we can use the Pythagorean identity. According to this identity, 'sin^2(y) = 1 - cos^2(y)'. So, 'sin(y) = sqrt[1 - (15/17)^2]'.

So, the final answer becomes 'sin(2y) = 2 * √[1 - (15/17)²] * 15/17'. It's useful to note that you should always check that your angle lies within the given range when using a square root in trigonometry, to ensure your answer is correct.

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Answer:

Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]

Step-by-step explanation:

Given : A card is chosen from a standard deck of cards.

To find : What is the probability that the card is a queen, given that the card is a club?

Solution : It is the conditional probability

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

Let A is probability that card is queen.

Let B is the probability that card is a club.

Probability that card is queen given card is club [tex]P(A\cap B)=\frac{4}{52}=\frac{1}{13}[/tex]

Probability that card is club from deck of 52 cards [tex]P(B)=\frac{13}{52}=\frac{1}{4}[/tex]

To find probability that card is queen given that card is club [tex]P(A|B)[/tex]

[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]

[tex]P(A|B)=\frac{\frac{1}{13}}{\frac{1}{4}}[/tex]

[tex]P(A|B)=\frac{1\times4}{13\times 1}=\frac{4}{13}[/tex]

Therefore, Option A is correct.

Probability that card is queen given that card is club is [tex]\frac{4}{13}[/tex]

Answer:

the correct answer was 1/13

Step-by-step explanation:

i took my test and put 4/13 which was wrong and said that 1/13 is the right answer