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Answer:

To graph the equation y=-x^2+12x-35, we need to find the vertex and the roots of the equation.

The equation can be written in vertex form as y=-(x-6)^2+1, where the vertex is (6,1).

To find the roots, we need to set y=0 and solve for x:

0=-x^2+12x-35

x^2-12x+35=0

(x-5)(x-7)=0

x=5 or x=7

So the roots are (5,0) and (7,0).

The vertex is at (6,1) and the roots are at (5,0) and (7,0). The curve is a downward-facing parabola.

Answer:

The perimeter of a square is four times the length of one side, so we can write:

4s = 24x + 36

Dividing both sides by 4, we get:

s = 6x + 9

Therefore, the length of one side of the fence is 6x + 9 units.

Step-by-step explanation:

Answer:

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Applying the inscribed angle theorem, we have the missing measures as: 15. m<DEF = 127°         16. m(PL) = 62°

15. Angle DEF is an inscribed angle while arc FGD is the intercepted arc. Thus, according to the inscribed angle theorem, we have:

m<DEF = 1/2(m(FGD)

Plug in the values:

6x + 37 = 1/2(19x - 31)

2(6x + 37) = 19x - 31

12x + 74 = 19x - 31

12x - 19x = -74 - 31

-7x = -105

x = 15

m<DEF = 6x + 37 = 6(15) + 37 = 127°

16. m<LMP = m<LNP

Plug in the values:

5x - 19 = 2x + 11

5x - 2x = 19 + 11

3x = 30

x = 10

m(PL) = 2(LMP) [based on the inscribed angle theorem]

Plug in the values:

m(PL) = 2(5x - 19)

Plug in the value of x:

m(PL) = 2(5(10) - 19)

m(PL) = 62°

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The volume of the tank that will be filled with water through which the given relation is satisfied is [tex]22.5ft^{3}[/tex]

What about volume of cuboid?

The volume of a cuboid is the amount of space occupied by the three-dimensional solid figure known as a cuboid. A cuboid is a box-shaped object with six rectangular faces, where each face has a pair of parallel sides, and opposite faces are equal in size and shape.

The formula for calculating the volume of a cuboid is:

Volume = length x width x height

where length, width, and height are the three dimensions of the cuboid.

The unit of measurement for the volume of a cuboid will depend on the unit of measurement used for each dimension. For example, if the length, width, and height are measured in centimeters, then the volume of the cuboid will be expressed in cubic centimeters (cm³). Similarly, if the dimensions are measured in meters, the volume will be expressed in cubic meters (m³).

According to the given information:

As, we know that volume of cuboid is = length x breath x height

Here, length = 5 feet, breath = 3 feet and height = 1.5 feet

Volume of the aquarium = 5 x 3 x 1.5 =  [tex]22.5ft^{3}[/tex]

So, the given result is  [tex]22.5ft^{3}[/tex]

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Answer:

The probability that atleast one ticket labeled 2-6 is drawn is 0.94

Numbered ticket = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}

Number of draws = 4

Required picks = {2, 3, 4, 5, 6}

Recall :

Probability = required outcome / Total possible outcomes

Probability of choosing a required ticket :

5/10 = 1/2

Therefore, the probability that none of the required tickets is chosen :

(1/2 × 1/2 × 1/2 × 1/2) = 1/16

The probability that atleasr one ticket labeled 2-6 is drawn is :

1 - P(none is chosen) = 1 - 1/16 = 15/16 = 0.9375

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A graph of the transformed function [tex]y=\frac{1}{(x+2)^2} +5[/tex] is shown in the image attached below.

In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image;

g(x) = f(x + N)

On the other hand, the translation a geometric figure upward simply means adding a digit to the value on the positive y-coordinate (y-axis) of the pre-image;

g(x) = f(x) + N

Since the parent function is [tex]y = \frac{1}{x^{2} }[/tex], it ultimately implies that the transformed function would be created by translating the parent function to the left by 1 units and 5 units upward as shown below.

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This stock trade generated a profit of $600 and a 7.69% return on investment.

The total amount received from selling the shares, after commission.

The total cost of purchasing the shares = $7800

Total amount received from selling the shares = $8400

The commission paid for purchasing the shares and for selling the shares will cancel out since they will both be subtracted, so we do not need to consider them.

Profit on this stock transaction = Total amount received - Total cost of purchasing

= $8400 - $7800

= $600

To calculate the percentage return on investment, we need to divide the profit by the total cost of purchasing the shares, and then multiply by 100 to express it as a percentage.

Percentage return on investment = (Profit / Total cost of purchasing) x 100%

= ($600 / $7800) x 100%

= 7.69%

Therefore, the profit on this stock transaction was $600 and the percentage return on investment was 7.69%.

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Answer:

Step-by-step explanation:

Z:

the angle b/n z and  65 is 90 b/c its a square and they are found on a straight line (180)

- 65 + 90 + z = 180

-155 + z = 180

-z= 180 - 155= 25

x:

-x + 90 = 180

- x= 180 - 90 = 90

y:

in this case now we have an inner triangle which has only one missing angle so as we know for any triangle ABC; <A + <B + <C = 180 so

- y + x + 65=180

-y+ 90 + 65= 180

-y=180 - 155

- y = 25

Answer:

110.5

Step-by-step explanation:

The first step is to find the measure of angle RVT

Angle Formed by Two Chords= 1/2(SUM of Intercepted Arcs)

RVT = 1/2 ( 97+42)

RVT =1/2 ( 139)

RVT = 69.5

Now RVT and RVU equals a straight line so they add to 180

RVT + RVU = 180

69.5 + RVU = 180

RVU = 110.5

There are 1140 different possible ways to select 3 restaurants out of 20 for the promotional program.

Combination and permutation are two alternative strategies in mathematics to divide up a collection of components into subsets. The subset's components can be listed in any order when combined. The components of the subset are listed in a permutation in a certain order.The combination formula, which is: can be used to resolve this issue.

n C r = r! * (n-r)!

where r is the number of restaurants to be chosen, and n is the total number of restaurants (20 in this case). (3 in this case).

By replacing these values, we obtain:

20 C 3 = 20! / (3! * (20-3)!) = 20! / (3! * 17!) = (20 * 19 * 18) / (3 * 2 * 1) = 1140

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The values  of x and y that make the triangles congruent by HL are:

x = 3 and y = 1

From the question, we are to determine the values of x and y that make the triangles congruent by HL.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure.

Thus,

For the triangles to be right congruent by HL

x = y + 2

and

x + 1 = 4y

Solve the equations simultaneously

Substitute x = y + 2 in the second equation

x + 1 = 4y

y + 2 + 1 = 4y

y + 3 = 4y

3 = 4y - y

3 = 3y

Divide both sides by 3

3/3 = 3y/3

1 = y

Therefore,

y = 1

Substitute the value of y into the first equation

x = y + 2

x = 1 + 2

x = 3

Hence,

The values are:

x = 3 and y = 1

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Fro the one to one functions g and h defined, the value of :

g⁻¹(6) = 2

h⁻¹(x) = 7x + 8

(h⁻¹ o h)(1) = 1

Given one to one functions h and g.

We have that,

g(2) = 6

So, g⁻¹(6) = 2

We have,

y = (x - 8) / 7

Switch x and y.

x = (y - 8) / 7

7x = y - 8

y = 7x + 8

So, h⁻¹(x) = 7x + 8

(h⁻¹ o h) (x) = h⁻¹ (h(x))

                  = h⁻¹ ((x - 8) / 7)

                  = 7 ((x - 8) / 7)) + 8

                  = x - 8 + 8

                  = x

(h⁻¹ o h) (1) = 1

Hence the functions are found.

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The population predicted after two hours is approximately 666.5 bacteria as they have exponential growth.

The continuous exponential growth model is given by the formula:

P(t) = P0 * [tex]e^{(rt)[/tex]

where P0 is the initial population, r is the relative growth rate (expressed as a decimal), t is the time in hours, and P(t) is the predicted population after t hours.

In this case, P0 = 535, r = 0.12 (12% per hour), and t = 2. Plugging in these values, we get:

P(2) = 535 * [tex]e^{(0.12*2)[/tex] ≈ 666.5

Therefore, the population predicted after two hours is approximately 666.5 bacteria (rounded to the nearest tenth).

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In linear equation, The graph in option 3 models the length of the new rectangle.

What is a linear equation in mathematics?

A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.

                         Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.

According to the problem,

width of the rectangle is  x units

Area of the rectangle is 10 square units

Length of the rectangle is given by f(x) = 10/x

Now if width becomes (x+1) units

∴ Length will be represented as 10/(x+1)

Now from the given options we need to find the exact graph of              f(x) = 10/(x +1)

Here if x = 4 , y =2

So the point (4 , 2) is satisfied which is only happening in the graph of option 3

Option 3 represents the correct graph.

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Answer:

If only 60% of the seeds planted by the class grow into plants, we can find the number of plants by multiplying the total number of seeds planted by the percentage of seeds that grow, expressed as a decimal.

To do this, we can start with the total number of seeds planted, which is 20, and multiply by 0.6:

20 x 0.6 = 12

Therefore, the class has 12 plants.

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Answer:

[tex]\dfrac{137}{3}\approx 45.7\; \sf m[/tex]

Step-by-step explanation:

To find the velocity function, integrate the acceleration function (and add a constant of integration).

[tex]\begin{aligned}\displaystyle v(t)=\int a(t) &= \int (2t + 2)\; \text{d}t\\\\&=\int 2t \; \text{d}t+\int 2\; \text{d}t\\\\&=\dfrac{1}{2} \cdot 2t^{(1+1)}+2t+\text{C}\\\\&=t^2+2t+\text{C}\end{aligned}[/tex]

To find the constant of integration, C, substitute v(0) = -15 into the velocity function and solve for C:

[tex]\begin{aligned}v(0)=(0)^2+2(0)+\text{C}&=-15\\0+0+\text{C}&=-15\\\text{C}&=-15\end{aligned}[/tex]

Therefore, the velocity function (in m/s) is:

[tex]v(t)=t^2+2t-15[/tex]

As we want to find the distance travelled during the given time interval 0 ≤ t ≤ 5, we first need to determine if the particle momentarily stops at any point in the given interval (and therefore changes direction). The particle will stop when its velocity is zero, so when v(t) = 0:

[tex]\begin{aligned}v(t)&=0\\\implies t^2+2t-15&=0\\t^2+5t-3t-15&=0\\t(t+5)-3(t+5)&=0\\(t-3)(t+5)&=0\\\\\implies t&=3, -5\end{aligned}[/tex]

As time is positive only, the velocity is zero at t = 3 seconds.

Therefore, at t = 3, the particle changes direction and begins to move in the opposite direction. Therefore, the displacement between 0 ≤ t ≤ 5 consists of two parts: 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5.

To find the distance travelled, first find the displacement function by integrating the velocity function:

[tex]\begin{aligned}\displaystyle s(t)=\int v(t) &= \int (t^2+2t-15)\; \text{d}t\\\\&= \int t^2\; \text{d}t+\int 2t\; \text{d}t-\int 15\; \text{d}t\\\\&=\dfrac{1}{3}t^3+t^2-15t\left(+\text{C}\right) \end{aligned}[/tex]

Distance is the absolute value of displacement.

As we want to find the distance travelled for the intervals 0 ≤ t ≤ 3 and 3 ≤ t ≤ 5, we need to add the absolute values of displacement for these intervals. So, the absolute values of the definite integrals for these intervals:

[tex]\begin{aligned}\textsf{Distance}&=\left|\int^3_0 v(t)\right|+\left|\int^5_3 v(t)\right|\\\\&=\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^3_0\right|+\left|\left[\dfrac{1}{3}t^3+t^2-15t\right]^5_3\right|\\\\&=\left|\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)-\left(\dfrac{1}{3}(0)^3+(0)^2-15(0)\right)\right|+\\&\left|\left(\dfrac{1}{3}(5)^3+(5)^2-15(5)\right)-\left(\dfrac{1}{3}(3)^3+(3)^2-15(3)\right)\right|\\\\&=\left|(-27-0)\right|+\left|\left(-\dfrac{25}{3}-(-27)\right)\right|\end{aligned}[/tex]

             [tex]\begin{aligned}&=27+\dfrac{56}{3}\\\\&=\dfrac{137}{3}\end{aligned}[/tex]

Therefore, the total distance travelled during the given time interval is 137/3 ≈ 45.7 meters.

The percent of the parcels weighed between 16 ounces and 40 ounces is 81.9%.

To solve this problem, first, find the z-scores for the weights of 16 ounces and 40 ounces using the given mean and standard deviation:

z1 = (16 - 32) / 8 = -2

z2 = (40 - 32) / 8 = 1

Next, we need to find the area under the standard normal distribution curve between these two z-scores. We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we get:

P(-2 < Z < 1) = 0.8186

So, approximately 81.9% of the parcels weighed between 16 ounces and 40 ounces.

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The statement that shows the quantity of gallons of gas that he can buy would be =g≤11.82. That is option A.

The total number of money he has to spend on his vehicle = $230

The amount of money he wishes to save = $160

The remaining amount he can spend = 230+160 = $70

The amount he wishes to spend on oil change = $24.95

The remaining amount = 70-24.95

= $40.05

The cost per gallon of gas = $3.81 per gallon.

The quantity of gallons of gas he can purchase = 40.05/3.81 = 10.51 gallons.

Therefore the quantity of gallons of gas he can purchase would be g≤11.82

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The median is the average that is most representative of the data.

The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.

In this problem, we have that smaller values have a higher number of observations, meaning that the data-set is not symmetric.

As the data-set is not symmetric, it means that the median is the average that is most representative of the data.

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Answer: it is more probable that Peter will finish ahead of Francis and Christopher than that both Anthony and Peter will receive ribbons.

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Step-by-step explanation:

Answer:

Parameter= 98ft

Area=180ft^2

Step-by-step explanation:

Parameter= Length times 2 plus width times 2 or

L2+W2=P 4(2)+45(2)=8+90=98

Area= LxW=A^2

4x45=180^2

Answer:

  A

Step-by-step explanation:

You want to know which inequality must be true regarding the side lengths of a triangle.

The triangle inequality requires the sum of any two side lengths be greater than the length of the third side:

  a + b > c . . . . . choice A

__

Additional comment

This means it must also be true that ...

  a + c > b

  b + c > a

Of course, this means the sum of the two shortest sides must be more than the longest side. It also means any side length must lie between the sum and difference of the other two side lengths:

  |a - b| < c < a + b

The version of this inequality most often seen uses the > or < symbol. Some authors use the ≥ or ≤ symbol instead. This allows triangles that look like a line segment and have zero area.

Answer:

The y-intercept represents Adam's base salary

Step-by-step explanation:

Since it's y = 0.28x + 38,000, when x is 0, the salary is 38,000 without commission.

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Answer:

264π

Step-by-step explanation:

The midpoint of the line joining the endpoints (-1, 5) and (-8, -4) will be (-4.5, 0.5).

Given that:

Endpoints, (-1, 5) and (-8, -4)

The coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The midpoint is calculated as,
(x, y) = [(-1 - 8) / 2, (5 - 4) / 2]

(x, y) = (-9 / 2, 1 / 2)

(x, y) = (-4.5, 0.5)

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we know that,

[tex] \sf \dashrightarrow \: cos(a - b) = cos a \times cos b + sin a \times sin b[/tex]

Therefore,

[tex] \sf \leadsto \: cos \: 15 \degree[/tex]

[tex] \sf \leadsto \: cos \: (45 \degree - 30 \degree)[/tex]

[tex] \sf \leadsto \: cos \: 45 \degree . \: cos \: 30 \degree + \: sin \: 45 \degree . \: sin \: 30 \degree[/tex]

[tex] \sf \leadsto \: \frac{1}{ \sqrt{2} } \: . \: \frac{ \sqrt{3} }{2} + \: \frac{1}{ \sqrt{2} } \: . \: \: \frac{1}{2} \\ [/tex]

[tex] \sf \leadsto \: \frac{1. \: \sqrt{3} }{ \sqrt{2} \: . \: 2} \: + \: \frac{1 \: .\: 1}{ \sqrt{2} \: .\: 2} \\ [/tex]

[tex] \sf \leadsto \: \frac{ \: \sqrt{3} }{ 2\sqrt{2} \: } \: + \: \frac{1}{ 2\sqrt{2} \: } \\ [/tex]

[tex] \sf \leadsto \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: \\ [/tex]

Therefore Value of cos 15° is [tex] \sf \: \frac{ \: \sqrt{3} + 1 }{ 2\sqrt{2} \: } \: [/tex]

Answer:

To find the monthly payments, we can use the PMT function in Excel or a financial calculator. The formula is:

PMT(rate, nper, pv)

where rate is the interest rate per period, nper is the total number of periods, and pv is the present value (i.e. loan amount).

For this problem, the interest rate is 8%/12 = 0.0066667 per month, the number of periods is 4 years * 12 months/year = 48 months, and the present value is $10,000. Therefore, the formula becomes:

PMT(0.0066667, 48, 10000)

Evaluating this formula gives a monthly payment of $242.42.

To find the total interest for the loan, we can multiply the monthly payment by the number of periods (i.e. 48) and subtract the loan amount. This gives:

total interest = monthly payment * number of periods - loan amount

total interest = $242.42 * 48 - $10,000

total interest = $2,678.16

Therefore, the monthly payments are $242.42 and the total interest for the loan is $2,678.16.

Step-by-step explanation: