Match each point of intersection with the system of equations whose solution is at that point

Answer:

The area is 92 square yards.

Step-by-step explanation:

We can decompose this figure into a rectangle and a triangle.

First, we can find the area of the rectangle.

A(rect) = length × width

A(rect) = 10 × 8

A(rect) = 80 yd²

Next, we can find the area of the triangle.

A(triangle) = (1/2) × base × height

[tex]A(\text{triangle}) = \dfrac{1}{2} \, (13 - 10) \times 8[/tex]

[tex]A(\text{triangle}) = \dfrac{3}{2} \times 8[/tex]

[tex]A(\text{triangle}) = 12 \text{ yd}^2[/tex]

Finally, we can add the two shapes' areas to get the area of the entire figure.

A = A(rect) + A(triangle)

A = 80 yd² + 12 yd²

A = 92 yd²

Answer: 92 yd²

Step-by-step explanation:

Decomposition means to break the shape into parts, but it's not necessary to break apart.

This is a trapezoid turned sideways A=1/2(b1+b1)h

b1=10

b2=13

h=8

A=1/2(10+13)8 =92 yd²

if you decompose, you can make the top a triangle and bottom a rectangle.

A(triangle) = 1/2(b)(h)     b=3   h=8

                 1/2(b)(h)

                 = 12

A(rectangle)=bh     b=10     h=8

                  =10*8

                   =80

Add the 2 and you get 92 again

Answer: x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.

Step-by-step explanation: To determine if `x + 10` is a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`, we can use the Factor Theorem. The Factor Theorem states that if `f(a) = 0`, then `x - a` is a factor of `f(x)`.

In this case, we want to determine if `x + 10` is a factor of `f(x)`, so we can let `a = -10` and evaluate `f(-10)`:

`f(-10) = 5(-10)^3 + 60(-10)^2 + 109(-10) + 90`

`= -5000 + 6000 - 1090 + 90`

`= -1000`

Since `f(-10) ≠ 0`, we can conclude that `x + 10` is **not** a factor of `f(x) = 5x^3 + 60x^2 + 109x + 90`.

Answer:  The sum of the integers is equal to $\frac{14}{3}$ times the largest of the seven integers. What is the smallest integer that pearl wrote down?.

Step-by-step explanation:

Angle B, in the triangle ABC is solved to be 116 degrees

Angle B is solved using the concept of triangles and exterior angle relationship. This helps to know that addition of exterior angle to ∠B to angle B results to 180 degrees. Hence we have that:

exterior angle to ∠B + ∠B = 180

given data:

∠B = (15x − 19)°

exterior angle to ∠B is (9x − 17)°

plugging in gives

9x − 17 + 15x − 19 = 180

9x + 15x = 180 + 19 + 17

24x = 216

x = 9

For m∠B = (15x − 19)°

= 15 * 9 - 19

= 116 degrees

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The range of the cosine function is [-1, 1], there are no real solutions for θ in the given range.

We have,

We can solve the given quadratic equation for cos(θ) using the quadratic formula:

cos(θ) = (-b ± sqrt(b^2 - 4ac)) / 2a

Here, a = 1, b = 7, and c = 4.

Substituting these values, we get:

cos(θ) = (-7 ± √(7² - 4(1)(4))) / 2(1)

cos(θ) = (-7 ± √(41)) / 2

Since 0 ≤ θ < 2π, we need to consider only the solutions that lie in this range.

Using a calculator, we get:

cos(θ) ≈ -3.03 or -0.65

Since the range of the cosine function is [-1, 1], there are no real solutions for θ in the given range.

Therefore,

None of the given options (4.03, 2.65, 1.65, 2.25, 1.43) is correct.

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Possible strategic initiatives for the strategic objective to satisfy clients:

• Implement additional training course on serving and interacting with clients

a. client review and client growth percentage metrics likely relate to a strategic objective to satisfy and increase clients. The market share and profit margin metrics likely relate to a strategic objective to increase profits.

b.

New clients during the month

7

Lost clients during the month

(4)

Increase in clients

3

Total clients at the beginning of last month

÷ 72

Client growth percentage last month

4.17%

target met

c.

Number of 5-star reviews

55 × 5 =

275

Number of 4-star reviews

10 × 4 =

40

Number of 3-star reviews

3 × 3 =

9

Number of 2-star reviews

1 × 2 =

2

Number of 1-star reviews

1 × 1 =

1

Sum total of stars

327

Total number of reviews

÷ 70

Average online client satisfaction rating

4.67

stars, target

not met

d.

Possible strategic initiatives for the strategic objective to satisfy clients:

• Implement additional training course on serving and interacting with clients

• Invite clients to provide additional feedback through a brief online survey

• Have the company owner send a personal apology to any clients providing a review of 2 stars or less, and offer them some kind of compensation; also ask for their feedback regarding what caused them dissatisfaction

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The area of the composite figure is 136 sq. units.

Given that a composite figure we need to find it area,

The figure is composed of a triangle and a rectangle,

So to find its area we will simply calculate the areas of both the polygons and add them,

So, the area of a triangle = 1/2 x base x height

The area of a rectangle = length x width

So,

The required area = 1/2 x (16-8)(13-7) + 7 x 16

= 1/2 x 8 x 6 + 112

= 24 + 112

= 136

Hence, the area of the composite figure is 136 sq. units.

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The nth term of the sequence 4/5, 1/5, 1/20. 1/80..... is an = 4/5(1/4)^(n - 1)

The definition of the function is given as

4/5, 1/5, 1/20. 1/80.....

The above definitions imply that we simply multiply 1/4 to the previous term to get the current term

Using the above as a guide, we have

First term, a = 4/5

Ratio, r = 1/4

So, we have the following equation

an = 4/5(1/4)^(n - 1)

Hence, the value of the nth term is an = 4/5(1/4)^(n - 1)

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Answer:

5cm

Step-by-step explanation:

According to Pythagoras Theorem:

a^2+b^2=c^2

Given,

a=3, b=4, c=x

3^2+4^2=x^2

9+16=x^2

25=x^2

25 sqrt= 5

Therefore the answer is 5cm.

The required ratio of the lengths EF and AD is 2:1 for the given circle.

Given that a circle A with points B, C, D, E, F, and I on its circumference.

A chord of the circle is a line that connects any two locations on the circumference of any circle. The circle chords are BC, EF, and HI in this case.

The radius of the circle is defined as the line connecting center A with any point on the circle's perimeter. AD indicates the radius of the circle.

The diameter of the circle is any chord that passes through the center of the circle. The diameters of the circle are represented by EF and HI.

A diameter is usually twice as long as a radius.

As a result, the diameter-to-radius ratio will be 2:1.

Therefore, the required ratio of the lengths EF and AD is 2:1

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The missing figure has been attached below.

The quadratic equation shown in the graph is:

y = (x + 2)*(x - 1)

Remember that if h and k are the zeros of a quadratic equation of leading coefficient a, we can write it as:

y = a*(x - h)*(x - k)

Here we can see that the zeros are:

x = -2

x = 1

Then we can write it as:

y = a*(x + 2)*(x - 1)

And the y-intercept is -2, then we can write:

-2 = a*(0 + 2)*(0 - 1)

-2 = a*-2

-2/-2 = a

1 = a

The quadratic equation is:

y = (x + 2)*(x - 1)

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Answer:

  D.  5 +9i

Step-by-step explanation:

You want to simplify the expression ...

  √(-16) +√(-25) +5

We know that the value of √(-1) is represented by the constant i. This means we can simplify the expression like this:

  [tex]\sqrt{-16}+\sqrt{-25}+5\\\\=\sqrt{-1(4^2)}+\sqrt{-1(5^2)}+5\\\\=4i+5i+5\\\\=\boxed{5+9i}\qquad\text{matches choice D}[/tex]

<95141404393>

Answer:

76

Step-by-step explanation:

the second number = the first one + 3

the third number = the second one + 5

the fourth number = the third one + 7

the fifth number = the fourth one + 9

because of this, we can know that we add an odd number to the left number

so

sixth = 20+11=31

seventh = 31+13=44

eighth = 44+15=59

ninth = 59+17=76

Answer:

Step-by-step explanation:

34.0 degrees, 29.6 feet in Diameter.

This is a right triangle trigonometry question.

Use half of the diameter to form the base of the triangle (19.3 ft) with a height 0f 13.

Use Inverse Tangent function to find the angle of repose

round to 34.0

then use the angle of repose to solve trigonometric function of the tangent for the radius of the other cone.

switch denominator and tangent

multiply by 2 to get diameter of second cone

14.82*2≈29.6

Answer: 22√3

Step-by-step explanation:

When finding perimeter you take l+l+w+w, or 2l + 2w.

Answer:

[tex]22\sqrt{3}[/tex]

Step-by-step explanation:

To find the perimeter, we have to add up all four sides.

[tex]5\sqrt{3} +3\sqrt{12} +5\sqrt{3} +3\sqrt{12}[/tex]

write this on your calculator then you'll get [tex]22\sqrt{3}[/tex]

Hope this helps

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Using a system of equations, the number of different rolls of yarn that Laura bought is as follows:

A system of equations refers to simultaneous equations.

Simultaneous equations are two or more equations solved concurrently.

The total number of rolls of yarn bought = 25 rolls

The unit cost of multi-colored yarns = $4

The unit cost of solid-colored yarns = $3

The total cost paid for the 25 rolls of yarn = $88

Let the number of rolls of multi-colored yarns = x

Let the number of rolls of solid-colored yarns = y

Equation 1: x + y = 25

Equation 2: 4x + 3x = 88

Multiply Equation 1 by 3:

3x + 3y = 75 ... Equation 3

Subtract Equation 3 from Equation 2:

4x + 3x = 88

-

3x + 3y = 75

x = 13

Substitute x = 13 in either equations 1 or 2:

x + y = 25

13 + y = 25

y = 12

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The exponential function that passes through the points (0,19) and (2,1539) is y = 19(9)ˣ.

We can use the two given points to form a system of two equations in two unknowns (a and b) to find the exponential function in the form y = abˣ that passes through those points.

Using the point (0,19), we get

19 = ab⁰

19 = a

Using the point (2,1539), we get

1539 = ab²

Substituting a = 19 from the first equation, we get

1539 = 19b²

Solving for b, we get

b² = 81

b = 9 or b = -9

Since we are dealing with an exponential function that models a growth, we will choose the positive value for b. Thus, b = 9.

Now that we know a and b, we can write the exponential function in the form y = abˣ

y = 19(9)ˣ

Therefore, the exponential function is y = 19(9)ˣ

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--The given question is incomplete, the complete question is given

" Write an exponential function in the form y=ab^x that goes through points ( 0 , 19 ) (0,19) and ( 2 , 1539 ) (2,1539)."--

There is no correlation between age and the cost of a used car

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

The scatter plot

Where

x = Age

y = cost of used car

From the graph, we can see that

The points on the graph are scattered and they do not follow a definite pattern

This means that the scatter plot shows no correlation

And as such the correct option is (d)

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The expected value of a $2 ticket is $0.63

To calculate the expected value of a $2 ticket, we need to multiply the probability of winning by the value of the prize, then sum those products:

The Probability of winning the grand prize = 1/2000

Product: (1/2000) x $500 = $0.25

The Probability of winning a secondary prize: 3/2000

Product: (3/2000) x $200 = $0.30

The Probability of winning a third level prize: 8/2000

Product: (8/2000) x $20 = $0.08

The sum of the products:

$0.25 + $0.30 + $0.08 = $0.63

So the expected value of a $2 ticket is $0.63, meaning that on average, a person can expect to win $0.63 for every $2 they spend on a ticket.

The charity is expected to make a profit, which is why the answer is negative.

That is -$2 + $0.63 = -$1.37

So the expected profit for the charity per ticket sold is -$1.37, which is approximately the same as the given answer of negative $1.358(rounding off)

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Answer:

Step-by-step explanation:

even function is symmetric along the y-axis

the y-axis acts like a mirror

f(x) = f(-x) for any real x

odd function is similar to even function except

one side is up-side-down. (rotational symmetric by 180 degree)

odd function is nice property since the definite integral

from -a to a always equals to 0

f(x) = -f(-x) for any real x

top-left:

even

top-right:

odd

bottom-left:

Neither

bottom-right:

odd

Ceci should give Fluffles 26 grams of food each day after the 15% reduction.

Given that the original amount of food: 30 grams/day

Now, calculate the 15% reduction:

30 grams/day x 0.15 = 4.5 grams/day

Subtract the reduction from the original amount:

30 grams/day - 4.5 grams/day = 25.5 grams/day

Round the answer to the nearest gram:

25.5 grams/day ≈ 26 grams/day

Thus, she should give Fluffles 26 grams of food each day after the 15% reduction.

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Answer:

[tex](x-7)^2+(y+2)^2=49[/tex]

Step-by-step explanation:

A tangent of a circle is a straight line that touches the circle at only one point.

Since the circle is tangent to the horizontal line y = 5, the distance between the center of the circle and the line y = 5 is equal to the radius of the circle.

Given the center of the circle is C(7, -2), the y-coordinate of the center is y = -2. Therefore, the radius of the circle is the difference between y = 5 and y = -2:

[tex]\implies r=5-(-2)=7[/tex]

The equation of a circle is:

[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]

where (h, k) is the center and r is the radius.

Substitute the given center (7, -2) and found radius, r = 7, into the equation of circle:

[tex](x-7)^2+(y-(-2))^2=7^2[/tex]

Simplify:

[tex](x-7)^2+(y+2)^2=49[/tex]

Therefore, the equation of the circle that has center C(7, -2) and is tangent to the line y = 5 is:

[tex]\boxed{(x-7)^2+(y+2)^2=49}[/tex]

The appropriate intervals to use when creating a histogram of the data are:

0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74.

Given information:

The following is a list of movie tickets sold each day for 10 days.

7, 18, 23, 41, 34, 12, 48, 65, 57, 52.

When creating a histogram, you want to group the data into intervals or bins.

The intervals should be chosen so that they are of equal size, and they should also include all the data values.

In this case, the data values range from 7 to 65, so we need to choose intervals that cover this range.

The appropriate intervals to use when creating a histogram of the data are:

0 – 14, 15 – 29, 30 – 44, 45 – 59, 60 – 74

These intervals capture the range of values in the data set and have equal widths, making it easy to create a histogram.

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Answer:

Answer: 9,924.966.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Sorry it is hard to explain the process by typing!

The correct statement regarding the values is given as follows:

The values are opposite from each other, and they are both 5/2 units from zero.

The absolute value function is defined by the following piecewise rule, depending on the input of the function:

It measures the distance of a point x to the origin, hence, for example, |-2| = |2| = 0.

The values for this problem are given as follows:

The numbers are the same, with the opposite signal, hence they are opposites.

Additionally, both numbers have the same absolute value of 5/2, hence they are both at a distance of 5/2 units from the origin.

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Answer: The cost of a single ticket is £6.30.

Step-by-step explanation: The group bought 4 tickets and got one for free, which means they paid for 3 tickets. If each of them paid £6.30, then the total amount paid is 4 x £6.30 = £25.20.

To find the cost of a single ticket, we can divide the total paid by the number of tickets bought, which is 4:

£25.20 ÷ 4 = £6.30

Therefore, the cost of a single ticket is £6.30.

Answer:

Area of shaded portion= (θ/360º) × πrr

32/360°×22/7×3cm×3cm

(Simplify)

=2.514cm×cm

To nearest tenth= 2.500cm×cm

Answer: A cylindric section is the intersection of a plane with a right circular cylinder.

If we cut a cylinder perpendicularly to its base, the figure formed is a rectangle with a length equal to the height of the cylinder and a length equal to its diameter.