Two boats depart from a port located at (–8, 1) in a coordinate system measured in kilometers and travel in a positive x-direction. The first boat follows a path that can be modeled by a quadratic function with a vertex at (1, 10), whereas the second boat follows a path that can be modeled by a quadratic function with a vertex at (0, –7). Which system of equations can be used to determine whether the paths of the boats cross?
StartLayout Enlarged Left-Brace 1st Row y = negative one-ninth (x minus 1) squared + 10 2nd Row y = one-eighth x squared minus 7 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = one-ninth (x + 8) squared + 1 2nd Row y = Negative one-eighth (x + 8) squared + 1 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = negative StartFraction 9 Over 49 EndFraction (x + 1) squared + 10 2nd Row y = one-eighth x squared minus 7 EndLayout
StartLayout Enlarged Left-Brace 1st Row y = negative 17 (x minus 1) squared + 10 2nd Row y = 17 x squared minus 7 EndLayout

Answer:

-3

Step-by-step explanation:

a² = 64

Taking the square root of both sides, we get:

a = ±√64

a = ±8

Therefore, the solutions to the equation a² = 64 are a = 8 and a = -8.

2x-2 = 16

Adding 2 to both sides, we get:

2x = 18

Dividing both sides by 2, we get:

x = 9

Therefore, the solution to the equation 2x-2 = 16 is x = 9.

3y² = 27

Dividing both sides by 3, we get:

y² = 9

Taking the square root of both sides, we get:

y = ±√9

y = ±3

Therefore, the solutions to the equation 3y² = 27 are y = 3 and y = -3.

The length of the diagonal of the rectangle is 66

Here we have the rectangle WXYZ.

In that notation, we would have:

WX

XY

YZ

ZW

As the sides

And:

WY

XZ

as the diagonals.

We know that the values of the two diagonals must be the same ones, then we can write:

WY = XZ

14x + 10 = 11x + 22

Now we can solve that for x.

14x - 11x = 22 - 10

3x = 12

x = 12/3 = 4

then the length of the diagonal is:

WY = XZ = 14*4 + 10 = 66

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At 90% confidence, the lower confidence limit for the proportion students passing with 3 decimal places is  0.563.

To find the lower confidence limit for the proportion of students passing, we need to use the formula for confidence interval of a proportion:

Lower limit = sample proportion - z*standard error

where z is the z-score associated with the confidence level, and standard error is the standard deviation of the sampling distribution of the proportion.

First, let's calculate the sample proportion of students passing:

proportion passing = 82.0% = 0.820

Next, we need to calculate the standard error:

standard error = sqrt(p*(1-p)/n)

where p is the sample proportion, and n is the sample size.

standard error = sqrt(0.820*0.180/19) = 0.154

Now we need to find the z-score associated with the 90% confidence level. We can use a standard normal distribution table or a calculator to find that the z-score is 1.645.

Finally, we can plug in the values to find the lower confidence limit:

Lower limit = 0.820 - 1.645*0.154 = 0.563

Rounding to 3 decimal places, the lower confidence limit for the proportion of students passing is 0.563.

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There are 64 cups in 8 gallons.

To find the number of cups in 8 gallons, you can use the conversion rate of 8 cups per gallon. This means that the formula to find the number of cups in 8 gallons is:

Cups = 8 x Gallons

Thus, the calculation to find the number of cups in 8 gallons is:

Cups = 8 x 8

Cups = 64

Therefore, there are 64 cups in 8 gallons. This calculation shows that for every gallon, there are 8 cups. To find the number of cups in any number of gallons, you can multiply the number of gallons by 8. This calculation can be seen in the formula:

Cups = 8 x Gallons

By using this formula, you can easily find the number of cups in any number of gallons.

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The factored form of the expression 25a² - 30a + 9 is (5a - 3)².

Given the expression in the question;

25a² - 30a + 9

To factor completely, first rewrite the expression as as follows;

25a² - 30a + 9

rewrite 25a² as ( 5a )²

( 5a )² - 30a + 9

rewrite 9 as 3²

( 5a )² - 30a + 3²

Now, check that the middle term is two times the product of the numbers being squared in the first and third term.

30a = 2 × ( 5a ) × 3

Next, rewrite the polynomial;

( 5a )² - 2 × ( 5a ) × 3 + 3²

( 5a )² - 2( 5a )3 + 3²

Factor using the perfect square trinomial rule.

a² - 2ab + b² = ( a - b )²

Here; a = 5a and b = 3

Hence, we have;

(5a - 3)²

Therefore, the factored form is (5a - 3)².

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The line on the graph will be a straight line passing through the points (3,5) and (-3,2).

To draw a straight line y=2 - x, first plot the given points on the graph, (3,5) and (-3,2). Draw a straight line between these two points. This line will be the graph of the equation y=2 - x. To find the equation, take the x-value of the first point, 3, and subtract it from the y-value of the same point, 5. This is the equation of the line, y=2 - x. With the equation of the line, we can now draw a line on the graph that passes through the two given points. The line will be a straight line, with a slope of -1 and a y-intercept of 2.

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The capacity of Leo's container is (WH x L) / 2, where W, H, and L represent the width, height, and length of the container, respectively.

To find the capacity of Leo's container, we need to calculate its volume. The volume of a rectangular prism is calculated by multiplying its length, width, and height. We can express this formula mathematically as:

Volume = Length x Width x Height

Since we do not have the exact measurements of the container, we cannot determine the exact volume.

The surface area of a rectangular prism is given by the formula:

Surface Area = 2 x (Length x Width + Width x Height + Length x Height)

Therefore, we can set the equation for surface area equal to the equation for the total surface area of the container:

Surface Area = 2 x (Length x Width + Width x Height + Length x Height) = Total Surface Area of Container

Then we have:

Total Surface Area of Container = 2LW + 2WH + 2HL Surface Area of Material = 6LW

Since the material covers all six sides, we can set the surface area of the material equal to the total surface area of the container:

6LW = 2LW + 2WH + 2HL

Simplifying this equation, we get:

4LW = 2WH + 2HL

Dividing by 2, we get:

2LW = WH + HL

Multiplying by the height, we get:

2LWH = WH² + HL²

Now, we can rearrange this equation to get the volume of the container:

Volume = Length x Width x Height = (WH x L) / 2

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Complete Question:

Leo made a container to store his camping gear. The container is in the shape of a rectangular prism. The container has material covering all six sides.

What is the capacity of the container?

Answer:

please mark as brainliest

The value of f(8) is equal to D)21.5.

What is meant by area?

The region that an object's shape defines as its area. The area of a figure or any other two-dimensional geometric shape in a plane is how much space it occupies.

The graph of f'(x) is given in the figure.

We know that

[tex]\int\limits^a_b {f'(x)} \, dx =f(a)-f(b)[/tex].

Therefore since we have f(2) and we have to find f(8), we will take the area under the given graph from x=2 to 8

[tex]\int\limits^8_2 {f'(x)} \, dx =f(8)-f(2)\\\\2*3+2*3+\frac{1}{2}*3*3=f(8)-5\\ 16.5=f(8)-5\\f(8)=21.5[/tex].

Therefore f(8) is equal to D)21.5.

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a)Does not have an inverse function

b) g(x) has an inverse function

c)Domain of g(x) is [0, π],range is [-1, 1]

d)domain of g−1(x)=cos−1(x) is [-1, 1], range is [0, π]

a) No, y=cos(x) does not have an inverse function because it fails the vertical line test.
b) g(x) has an inverse function, g−1(x)=cos−1(x), because it passes the vertical and horizontal line tests when its domain is restricted to the interval [0, π].
c) The domain of g(x) is [0, π], and the range is [-1, 1] in interval notation.
d) The domain of g−1(x)=cos−1(x) is [-1, 1], and the range is [0, π] in interval notation.

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Answer:

Step-by-step explanation:

9

Answer:

One expression for the length of one of the equal sides

is x = (934 - 214) / 2.

Step-by-step explanation:

The perimeter is the sum of the 3 sides of the triangle.

Let the length of one of the equal sides be x cm

So, we have:

2x + 214 = 934

2x = 934 - 214 = 720

x = 720 /2 = 360 cm.

Therefore, there exists a value c in the interval (4, 7) such that f'(c) = -1, as required.

If any vertical line drawn may cross the graph at no more than one point, the graph is a function. If there is any spot on the graph where a vertical line can cross it at two or more points, the graph is not a function.

By the mean value theorem, there exists a point c in the interval (4, 7) such that:

f'(c) = (f(7) - f(4))/(7 - 4)

Substituting the given values, we get:

f'(c) = (4 - 7)/(7 - 4) = -1/3

Now, we need to show that there exists a value c in the interval (4, 7) such that f'(c) = -1.

Let g(x) = f(x) + x. Then, g(4) = f(4) + 4 = 11 and g(7) = f(7) + 7 = 11.

By Rolle's theorem, there exists a point c in the interval (4, 7) such that g'(c) = 0.

Now, g'(c) = f'(c) + 1, so we have:

f'(c) + 1 = 0

f'(c) = -1

Therefore, there exists a value c in the interval (4, 7) such that f'(c) = -1, as required.

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Answer:

They have 36 books in total.

Step-by-step explanation:

Let d = The number of Dima's books

Let r = The number of Ramiro's books.

d = 2r

d - 12 = r Substitute 2r for d in the second equation and solve for r

2r - 12 = r   Subtract 2r from both sides

2r - 2r - 12 = r - 2r

-12 = -r  Multiply both sides by -1

12 = r

Ramiro has 12 books.

d = 2r substitute 12 for r and solve for d

d = 2(12)

d = 24

Dima has 24 books.

Together they have 36 books (12 + 24)

Helping in the name of Jesus.

Answer:36

Step-by-step explanation:

The probability that on a given day, the price of a pound of bacon is more than twice as expensive as a dozen eggs is 0.0001. The probability that Ron paid more than $50 for the bacon and eggs is 0.0028.

(a) To find the probability that on a given day, the price of a pound of bacon is more than twice as expensive as a dozen eggs, we need to use the normal distribution formula. This is given by P(x > 2y) = P(X > 2µy + 2σy) = P(Z > (2µy + 2σy - µx) / σx) = P(Z > (2(1.90) + 2(0.06) - 4.10) / 0.16) = P(Z > -4.24) = 1 - P(Z < -4.24) = 1 - 0.9999 = 0.0001

(b) To find the probability that Ron paid more than $50 for the bacon and eggs, we need to calculate the probability that the 10 pounds of bacon and 6 dozen eggs cost more than $50. This is given by P(10x + 6y > 50) = P(10X + 6µy + 6σy > 50) = P(Z > (50 - 10µx - 6µy - 6σy) / (√10σx + √6σy)) = P(Z > (50 - 10(4.10) - 6(1.90) - 6(0.06)) / (√10(0.16) + √6(0.06)) = P(Z > -2.87) = 1 - P(Z < -2.87) = 1 - 0.9972 = 0.0028.

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The amount of border that Roberto will need to put around the edges of the platform, given the area is 16 units.

The platform is given in the figure and to find the amount of border that Roberto needs to cover it if the area is 12 square units, you need to count the number of dots all along the edges of the platforms.

Counting this would give us 16 dots. This then means that Roberto needs sixteen units of border to be able to put up a border around the edges of the platform.

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a) The interval would be:Interval = $12.50 ± ($51.50 x 3)Interval = $12.50 ± $154.50 Interval = ($12.50 - $154.50, $12.50 + $154.50)Interval = (-$142.00, $179.00)

b) The interval would be:Interval = $12.50 ± ($51.50 x 1)Interval = $12.50 ± $51.50 Interval = ($-39.00, $64.00)This interval can be considered usual since it includes about 68% of the data.

c) A pizza that costs $10 is about 0.049 standard deviations below the mean.

Use the Empirical Rule to make an interval that should include 99.7% of the data.The Empirical Rule, also known as the 68-95-99.7 rule, is a statistical rule that states that for a normal distribution, about 68% of observations will fall within one standard deviation of the mean, about 95% will fall within two standard deviations, and about 99.7% will fall within three standard deviations.To make an interval that should include 99.7% of the data, we need to find the mean plus/minus three standard deviations. The mean is given as $12.50, and the standard deviation is given as $51.50. Therefore, the interval would be:Interval = $12.50 ± ($51.50 x 3)Interval = $12.50 ± $154.50Interval = ($12.50 - $154.50, $12.50 + $154.50)Interval = (-$142.00, $179.00)

Use the Empirical Rule to make an interval that would be considered usual.Again, we can use the Empirical Rule to find an interval that would be considered usual. This would be the interval that falls within one standard deviation of the mean. The mean is given as $12.50, and the standard deviation is given as $51.50. Therefore, the interval would be:Interval = $12.50 ± ($51.50 x 1)Interval = $12.50 ± $51.50 Interval = ($-39.00, $64.00)This interval can be considered usual since it includes about 68% of the data.

Find the z-score of a pizza that costs $10.The z-score is a measure of how many standard deviations a data point is from the mean. To find the z-score of a pizza that costs $10, we first need to find the difference between $10 and the mean of $12.50, and then divide that difference by the standard deviation of $51.50.z-score = (10 - 12.50) / 51.50z-score = -0.049 This means that a pizza that costs $10 is about 0.049 standard deviations below the mean.

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Answer:

FG = 25.6

Step-by-step explanation:

ABC to DEC = 5:2

DEC to FEG = 1:4

so,

ABC to FEG = 5/2 × 1/4 = 5:8

that means the scaling factor from small to large is 8/5.

therefore,

EG = BC × 8/5 = 10×8/5 = 2×8 = 16

the side length ratio for ABC tells us

AB:BC:AC = 5 : 2 1/2 : 4

BC = 10

so,

AB:BC = 5 : 2 1/2 = 5 : 2.5

AB:10 = 5 : 2.5

2.5AB = 50

AB = 50/2.5 = 20

AC:AB = 4:5

AC:20 = 4:5

AC = 20×4/5 = 80/5 = 16

FG = AC × 8/5 = 16 × 8/5 = 128/5 = 25.6

The equation of the line passing through the points (-1, -4) and (3, 0) is y = x - 3.

To find the equation of the line passing through two points, we need to use the point-slope form of the equation of a line.

Point-slope form: y - y₁ = m(x - x₁)

where:

(x₁, y₁) is one of the given points on the line

m is the slope of the line

To find the slope of the line passing through (-1, -4) and (3, 0), we can use the formula:

m = (y₂ - y₁)/(x₂ - x₁)

where:

(x₁, y₁) = (-1, -4)

(x₂, y₂) = (3, 0)

m = (0 - (-4))/(3 - (-1))

m = 4/4

m = 1

Now we can use either of the two points and the slope to write the equation of the line.

Let's use point (-1, -4):

y - (-4) = 1(x - (-1))

y + 4 = x + 1

y = x - 3

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Answer:

27

Step-by-step explanation:

aone third of 27 is 9, and 18 - 9 = 9

Answer:

a = 3, b = 4

Step-by-step explanation:

[tex]3a-2b=1\\7a-b=17\\\\[/tex]

Multiply second equation by 2

[tex]3a-2b=1\\14a-2b=34\\[/tex]

Subtract the equations

[tex]3a-2b=1\\-(14a-2b=34)\\\\-11a=-33\\a=3[/tex]

Plug back in to either original equation to solve for b

[tex]3(3)-2b=1\\9-2b=1\\-2b=-8\\b=4[/tex]

Solution:

(3,4)

The value for the expression is obtained as -7/4.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

To evaluate the expression 12.5 - 31/2 + 1 1/4, we need to convert the mixed number 1 1/4 to an improper fraction -

1 1/4 = 5/4

Now we can substitute the values into the expression and simplify -

Substitute 1 1/4 with 5/4 -

= 12.5 - 31/2 + 1 1/4

= 12.5 - 31/2 + 5/4

Convert 12.5 to an improper fraction with a denominator of 2 -

= 25/2 - 31/2 + 5/4

Get a common denominator of 4 -

= (50)/(4) - (62)/(4) + 5/4

= 55/4 - 62/4

= -7/4

Therefore, the value is -7/4.

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The number of gigabytes that Sydney can use while staying within her budget is less than 2.9 gigabytes.

How to illustrate the information?

From the information, Sydney pays a flat cost of $35.50 per month and $5 per gigabyte. She wants to keep her bill under $50 per month.

The inequality that can be used to determine x x, the number of gigabytes Sydney can use while staying within her budget will be:

35.50 + 5x < 50

Collect like terms

5x < 50 - 35.50

5x < 14.50

x < 14.50 / 5

x < 2.9

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Option A  -026 is the correct answer

The standard normal distribution represents a normal distribution with a mean of 0 and a standard deviation of 1. It is also known as the z-distribution.What is the z-score formula?The z-score formula is: z = (x - μ) / σ where z is the z-score, x is the raw score, μ is the mean, and σ is the standard deviation.In a standard normal distribution, an area of 0.3974 on the right corresponds to a z-score of -0.26. This is option A. Therefore, option A is the correct answer.

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The sοlutiοn οf the given prοblem οf square cοmes οut tο be  0.84% is the shaded area.

A square is a quadrilateral οf fοur equal faces and fοur identical angles accοrding tο Euclidean geοmetry. A shape with adjacent edges that have the same length is anοther name fοr a rectangle. If οne οf a quadrilateral's fοur triangular edges and 4 triangular angles is square, the parallelοgram is deemed tο be equilateral. A linear οr 90 ° angle is referred tο as a cubical angle.

Here,

We must determine the area οf the shaded area and divide it by the area οf the cοmplete square tο determine the prοpοrtiοn οf the square that is shaded.

A sectοr is equal tο (45/360)k²/2 = 0.125k²

Find the regiοn οf triangle BDE next. Triangle BDE is a right triangle, sο we can determine its height using the Pythagοrean theοrem:

=>  BE² + DE² = BD²

=>  BE² + k² = (k√2)²

=>  BE² = 2k² - k²

=>  BE = k√2

Therefοre, the triangle BDE's area is:

=> A(triangle) = (1/2)

=> BE*DE = (1/2)

=> (k√2)(k√2) = k²

Lastly, the area οf the darkened area is equal tο the sectοr's area less the triangle's area:

=> A(shaded) = A(sectοr) - A(triangle) = 0.125πk² - k² ≈ 0.0084k²

Cοnsequently, the amοunt οf the rectangle that is shaded is:

=> percentage = (A(shaded) / A(square)) x 100%

=> ( 0.0084k² / k²) x 100%

=> 0.84%

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Answer

:44 field goals

Step-by-step explanation:

Answer:

44 attempts

Step-by-step explanation:

A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.

The ratio for this problem is:

To get from 2 to 8, we multiply the 2 by 4.

The ratio is now:

To solve for '?', we can simply multiply the 11 by 4, just like what we did with the 2.

Now the ratio is:

If the ratio has 44 as the second number, we know that it is the total attempts. Therefore, he attempted 44 field goals.

The vertices of the dilated polygon A'B'C'D' are A'(-3, 4.5), B'(-1.5, 1.5), C'(3, -1.5), and D'(3, 3). the correct option is (A) A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3).

What is polygon?

A polygon is a closed plane figure that is formed by three or more straight sides, which are connected end-to-end to create a closed shape.

To find the vertices of the dilated polygon, we need to apply the scale factor of 3/4 to each of the original vertices. This will result in a new set of coordinates for each vertex.

The coordinates of point A' can be found by multiplying the x-coordinate and y-coordinate of A by 3/4:

x-coordinate of A' = -4 × 3/4 = -3

y-coordinate of A' = 6 × 3/4 = 4.5

Therefore, A' has coordinates (-3, 4.5).

Using the same method, we can find the coordinates of the other vertices:

B':

x-coordinate of B' = -2 × 3/4 = -1.5

y-coordinate of B' = 2 × 3/4 = 1.5

Therefore, B' has coordinates (-1.5, 1.5).

C':

x-coordinate of C' = 4 × 3/4 = 3

y-coordinate of C' = -2 × 3/4 = -1.5

Therefore, C' has coordinates (3, -1.5).

D':

x-coordinate of D' = 4 × 3/4 = 3

y-coordinate of D' = 4 × 3/4 = 3

Therefore, D' has coordinates (3, 3).

Thus, the vertices of the dilated polygon A'B'C'D' are A'(-3, 4.5), B'(-1.5, 1.5), C'(3, -1.5), and D'(3, 3). Therefore, the correct option is (A) A′(−3, 4.5), B′(−1.5, 1.5), C′(3, −1.5), D′(3, 3).

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Given statement: "Any square matrix multiplied by its inverse will be that size identity matrix."

The statement is correct because for a square matrix A, if it is multiplied by its inverse, we get the identity matrix of the same order. The product of the matrix with its inverse is commutative.

The identity matrix is a square matrix with 1's along the diagonal and 0's elsewhere. For example, the 3x3 identity matrix is shown below.

1 0 0

0 1 0

0 0 1

The inverse of a square matrix A is a matrix A^-1, such that AA^-1 = A^-1A = I, where I is the identity matrix.

For example, let us consider a 2x2 matrix A. A = (a, b, c, d)

The inverse of the matrix A is given by the formula. A^-1 = 1/(ad-bc) * (d, -b, -c, a)

Thus, AA^-1 = A^-1A = I, where I is a 2x2 identity matrix. Therefore, any square matrix multiplied by its inverse will be that size identity matrix.

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The data which is given in the question is the time for tamara to read the book can be seen in a table with its respective values.

What is table?

Table is something which has rows and columns and the data is inserted into it.

Table has no restriction for the number of rows and columns. One can insert any rows and columns in the table according to their preferences.

Now in the above question,

    Tamara read 35 pages in 42.5 minutes.

    Tamara read 41 pages in 59 minutes.

     Tamara read 56 pages in 72 minutes.

The table will be     Pages               Time

                                 35                     42.5

                                  41                      59

                                  56                     72

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