help me with my geometry study guide the first one only please

3.6 pounds of chicken will be needed. Hope this helped! :)

Answer:

\(y_1 = -2\) and \(y_2 = 4\)

Step-by-step explanation:

\( \sqrt{10y + 24} - 3 = y + 1\)

Move the constant to the right-hand side and change their sign.

\( \sqrt{10y + 24} = y + 1 + 3 \)

combine like terms

\( \sqrt{10y + 24} - 3 = y + 4\)

Square both side to remove square brackets.

10y + 24 - 3 = y²+ 8y + 16

Move the expression to the left-hand side and change its sign.

10y + 24 - y² - 8y - 16 = 0

Combine like terms

10y - 8y + 24 - 16 - y² = 0

2y + 8 - y² = 0

Use commutative property to reorder the terms.

-y² + 2y + 8 = 0

Change the sign of expression.

y² -2y -8 = 0

split -2y

y² + 2y - 4y - 8 = 0

Factor out y from the first pair and -4 from the second equation.

y ( y + 2 ) - 4 ( y + 2 ) = 0

Factor out y+2 from the expression.

( y + 2 ) ( y - 4)

When the products and factors equals 0, at least one factor is 0.

y + 2 = 0

y - 4 = 0

Solve for y

y = -2

y = 4

When we plug the both solution as y we found that both is true solution of this equation.

This equation has two solutions which are -2 and 4.

Answer:

Solution given:

\( \sqrt{10y + 24} - 3 = y + 1\)

keep the constant term in one side

\( \sqrt{10y + 24} =y+1+3\)

solve possible one

\(\sqrt{10y+24}=y+4\)

now

squaring both side

\((\sqrt{10y+24})²=(y+4)²\)

10y+24=y²+8y+16

taking all term on one side

10y+24-y²-8y-16=0

solve like terms

8+2y-y²=0

doing middle term factorisation

8+4y-2y-y²=0

4(2+y)-y(2+y)=0

(2+y)(4-y)=0

either

y=-2

or

y=4

y=-2,4

Answer:

Step 1:  The problem is arranged in a way that allows us to use the elimination method by canceling out the ys since 1y - 1y = 0.  Then, we'll add the like terms including the xs, and the constants (-4 and 10):

    x + y = -4

+

    x - y = 10

-----------------

2x = 6

x = 3

Step 2:  Now, we can plug in 3 for x in any of the two original equations to find y.  Let's try the first equation:

3 + y = -4

y = -7

Optional Step 3:  We can check by plugging in 3 for x and -7 for y in both equations and see if we get -4 and 10

Plugging in solutions for first equation:

3 - 7 = -4

-4 = -4

Plugging in solutions for second equation:

3 - (-7) = 10

3 + 7 = 10

10 = 10

The optimal values of these parameters are:

a. β₁ = 0

b. β₂ = 0

The linear regression y = β1 + β2x + e, assuming that the sum of squared errors (SSE) takes the following form:

SSE = 382 + 681 + 382 + 18β1β2

Derive the partial derivatives of SSE with respect to β1 and β2 and solve the optimal values of these parameters.

Given that SSE = 382 + 681 + 382 + 18β1β2 ∂SSE/∂β1 = 0 ∂SSE/∂β2 = 0

Now, we need to find the partial derivative of SSE with respect to β1.

∂SSE/∂β1 = 0 + 0 + 0 + 18β2 ⇒ 18β2 = 0 ⇒ β2 = 0

Therefore, we obtain the optimal value of β2 as 0.

Now, we need to find the partial derivative of SSE with respect to β2. ∂SSE/∂β2 = 0 + 0 + 0 + 18β1 ⇒ 18β1 = 0 ⇒ β1 = 0

Therefore, we obtain the optimal value of β1 as 0. Hence, the partial derivative of SSE with respect to β1 is 18β2 and the partial derivative of SSE with respect to β2 is 18β1.

Thus, the optimal values of β1 and β2 are 0 and 0, respectively.

Therefore, the answers are: a. β₁ = 0 b. β₂ = 0

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Answer:

13.400

Step-by-step explanation:

Lets start with 416 First go to the 6 and since its over 4 we can automatically know that it makes the 1 in 416 to a 2 and the 2 cannot go up any higher so we make everything else below 4 a zero.

A match of the items have been creating in the space below to fit in with the best decription that it should have as its definition

The list with the matched descriptions is as follows:

When something is bi, this means it has 2 sides to it

Quarterly indicates four

thrice or Tricycle has to do with wheels been three

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When the older brother turns 100, the younger brother would be 50 years old.

Let's assume the older brother's age is X years. According to the given information, the younger brother's age is half that of the older brother, so the younger brother's age would be X/2 years.

We are told that when the older brother turns 100 years old, we need to determine the age of the younger brother at that time.

Since the older brother is X years old when he turns 100, we can set up the following equation:

X = 100

Now we can substitute X/2 for the younger brother's age in terms of X:

X/2 = (100/2) = 50

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y = 5x + 3

-1 = 5(2) + 3

-1 = 13 (wrong)

y = -2x - 4

-1 = -2(2) - 4

-1 = -8 (wrong)

Answer

The equation of the line is

y = (-x/7)

We can cross multiply and write it in the form of

7y = -x

OR

x + 7y = 0

Explanation

The slope and y-intercept form of the equation of a straight line is given as

y = mx + b

where

y = y-coordinate of a point on the line.

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

b = y-intercept of the line.

The relationship between the slopes of two lines that are perpendicular to each other is

m₁m₂ = -1

m₁ = Slope of line 1

m₂ = Slope of line 2

For the given equation, if we compare its equation with y = mx + b,

y = 7x - 3

y = mx + b

m = 7, b = -3

We can now find the slope of the line we want.

m₁m₂ = -1

m₁ = 7

m₂ = ?

m₁m₂ = -1

(7)m₂ = -1

7m₂ = -1

Divide both sides by 7

(7m₂/7) = (-1/7)

m₂ = (-1/7)

Then we can find the equation of the line we want.

For that line,

m = slope = (-1/7)

b = y-intercept (where the line crosses the y-axis) = 0

This is obtained from the point given that the line passes through the origin, (0, 0)

So, we can write y = mx + b

y = (-1/7)x + 0

y = (-x/7)

We can cross multiply and write it in the form of

7y = -x

OR

x + 7y = 0

Hope this Helps!!!

Answer:

Step-by-step explanation:

Answer: WIth the discount: $3.56, you do not have enough money, and are $0.56 short.

Step-by-step explanation:

Find 20% of 4.45

(4.45*0.2)= 0.89

Subtract the 20% from 4.45.

4.45-0.89=3.56

$3.56 is more than the $3 you have.

Subtract the $3 you have from the discounted price.

3.56-3.00=0.56

you are $0.56 short.

a) Since the triangles are congruent, and ΔABC is congruent to ΔDEF, segments AB and DE have the same value. Therefore, you can use algebra to solve for x when using the knowledge that (12 - 4x) is equal to (15 - 3x).

To solve:

12 - 4x = 15 - 3x

12 = 15 + x

-3 = x

Therefore, x is equal to -3.

b) To find the value of AB, plug in the value of x found in part a).

12 - 4x

12 - 4(-3)

12 - (-12)

12 + 12 = 24

Thus, segment AB is equal to 24.

c) As shown in part b), plug in the value of x found in part a) to find the value of segment DE.

15 - 3x

15 - 3(-3)

15 - (-9)

15 + 9 = 24

Thus, segment DE is also equal to 24.

We can confirm the knowledge of the equal side lengths because the triangle are congruent. This means that all the side lengths in the triangle are the same, which is confirmed when algebraically plugging in the value of x to solve for the values of the segments AB and DE.

I hope this helps!

The angle of elevation formed by the signal sent out to the plane and the ground near the tower is approximately 5.71 degrees.

The angle of elevation can be calculated using trigonometry. In this case, we have a right-angled triangle formed by the signal, the tower, and the ground. The height of the airplane (12 km) represents the opposite side of the triangle, while the distance from the tower to the airplane (2 km) represents the adjacent side.

To find the angle of elevation, we use the tangent function, which is defined as the ratio of the opposite side to the adjacent side. Therefore, the tangent of the angle of elevation can be calculated as opposite/adjacent, which is 12 km/2 km = 6.

To determine the angle itself, we can take the inverse tangent (arctan) of the tangent value. So, arctan(6) ≈ 81.87 degrees. However, this angle represents the angle between the signal and the ground, and we are interested in the angle between the signal and the horizontal plane. Therefore, we subtract 90 degrees from 81.87 degrees to get the angle of elevation near the tower.

Angle of elevation = 81.87 degrees - 90 degrees ≈ -8.13 degrees.

However, since the angle of elevation cannot be negative in this context, we take the absolute value of -8.13 degrees, which is approximately 8.13 degrees. Therefore, the angle of elevation formed by the signal sent out to the plane and the ground near the tower is approximately 8.13 degrees.

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The equation of line t in slope intercept form is 5y - 3x = -1

The equation of line s is y=3/5x + 2/5

This is in the slope intercept form

y = mx + c

where m represents the slope of the line

The slope of the line  y=3/5x + 2/5 is 3/5

The slope of two parallel line is same

The slope of line t is 3/5, it passes through the points (2, 1)

The equation of the line is

y - y₁ = m(x - x₁)

y - 1 = 3/5 (x - 2)

5y - 5 = 3x - 6

5y - 3x = -6 + 5

5y = 3x  -1

y = 3/5 x - 1/5

Therefore, the equation of line t in slope intercept form is 5y - 3x = -1

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Answer:

1

Step-by-step explanation:

3.2/0.4=8

8×2=16

16×0.4=6.4

6.4÷0.1=64

Based on the formula of the quadratic function y=-x^2+6x-5, we know that its graph is a downward-facing parabola that opens wide, with a vertex at (3,-14), and an axis of symmetry at x=3.

Based on the formula of the quadratic function y=-x^2+6x-5, we can determine several properties of its graph, including its shape, vertex, and axis of symmetry.

First, the negative coefficient of the x-squared term (-1) tells us that the graph will be a downward-facing parabola. The leading coefficient also tells us whether the parabola is narrow or wide. Since the coefficient is -1, the parabola will be wide.

Next, we can find the vertex using the formula:

Vertex = (-b/2a, f(-b/2a))

where a is the coefficient of the x-squared term, b is the coefficient of the x term, and f(x) is the quadratic function. Plugging in the values for our function, we get:

Vertex = (-b/2a, f(-b/2a))

= (-6/(2*-1), f(6/(2*-1)))

= (3, -14)

So the vertex of the parabola is at the point (3,-14).

Finally, we know that the axis of symmetry is a vertical line passing through the vertex. In this case, it is the line x=3.

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Answer:

The value of PQ is;

Explanation:

Given the figure in the attached image;

We can see from the figure that the triangle RSQ is similar to the triangle ROP.

So their corresponding sides are proportional;

Substituting the given values;

Therefore, the value of PQ is;

The container's volume is about 0.532 liters.

To determine the volume of a container that can hold 18 ounces (oz) of liquid, we need to convert ounces to a unit of volume, such as cubic inches or liters.

Since 1 fluid ounce is equal to approximately 1.80469 cubic inches, we can convert 18 ounces to cubic inches:

18 oz * 1.80469 in³/oz ≈ 32.48442 in³

So, the volume of a container that can hold 18 oz of liquid is approximately 32.484 cubic inches. If you prefer the metric system, we can convert this volume to liters:

32.48442 in³ * 0.0163871 L/in³ ≈ 0.532 liters

Therefore, the container's volume is about 0.532 liters.

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The Complete Question

What is the volume of a container that can hold 18 oz of liquid?

The constraints to represent the incoming students at the college is B. 0 < x ≤ 100 and 0 < y ≤ 400

Inequalities are created through the connection of two expressions. It should be noted that the expressions in an inequality aren't always equal. Inequalities implies that the expressions are not equal. They are denoted by the symbols ≥ < > ≤.

In this situation, the college is currently accepting students that are both in-state and out-of-state. They plan to accept four times as many in-state students as out-of-state, and they only have space to accept 100 out-of-state students.

Let x = the number of out-of-state students and

y = the number in-state students.

The constraints is 0 < x ≤ 100 and 0 < y ≤ 400.The correct option is B.

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we have

13+x^2=62

subtract 13 both sides

x^2=62-13

x^2=49

Applying the square root property

Answer:

Step-by-step explanation:

QWEQEQWEQEQEQEQ

Answer:

1 3/20

Step-by-step explanation:

5 3/4 divided by 5

5 3/4 divided by 5/1

5x4+3=23

23/4 divided by 5/1

Keep Change Flip

23/4 x 1/5

23 x 1=23

4   x 5=20

23/20=1 3/20

Answer:

-1/2

Step-by-step explanation:

2x-y=-8 --> y=2x+8 (slope: 2)

to be perpendicular, the product of two slopes should be -1

thus, the slope of a line perpendicular to this one is -1/2

Answer:

Your friend left the bigger tip.

Step-by-step explanation:

We have to first find how much you tipped the waiter, 15%.

15% of 15.85 is 2.4.  So, you tipped the waiter $2.40 (about)

Your friend leaves a 20% tip, so we have to also find 20% of $14.30

20% of 14.30 is 2.86.  So your friend tipped $2.86 to the waiter.

Your friend left the bigger tip.

The equation of the line of best fit that Frank drew will be y = -(1/3) x + 16. Then the correct option is D.

Suppose the given points are (x₁, y₁) and (x₂, y₂), then the equation of the straight line joining both two points is given by

\(\rm (y - y_1) = \left [ \dfrac{y_2 - y_1}{x_2 - x_1} \right ] (x -x_1)\)

Frank created a scatter plot and drew a line of best fit, as shown.

From the graph, the two points are taken that are (0, 16) and (3, 15).

(x₁, y₁) → (0, 16)

(x₂, y₂) → (3, 15)

Then the equation of line will be

y – 16 = -1/3(x – 0)

       y = -(1/3) x + 16

Then the correct option is D.

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Therefore, the speed of the boat in still water is 30 miles/hour.

Let's denote the speed of the boat in still water as "v" and the speed of the current as "c".

When the boat is traveling downstream (with the current), the effective speed of the boat is increased by the speed of the current. Therefore, the speed of the boat downstream is v + c.

Similarly, when the boat is traveling upstream (against the current), the effective speed of the boat is decreased by the speed of the current. Therefore, the speed of the boat upstream is v - c.

We have the following information:

Downstream speed = v + c = 120 miles / 3 hours = 40 miles/hour

Upstream speed = v - c = 120 miles / 6 hours = 20 miles/hour

We can set up a system of equations using these two equations:

v + c = 40

v - c = 20

By adding the two equations, we can eliminate the variable "c":

2v = 60

Solving for "v":

v = 60 / 2

v = 30

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Answer:

Step-by-step explanation:

The best measure of the center for this data is the __Median___

The value of this measure of center is _42_

If each person receives the same amount, each person at Hugo's party will get 0.5 cups, or 1/2 cup, of fruit sorbet.

To determine how many cups of fruit sorbet each person will get, we need to convert the volume of the sorbet from gallons to cups, and then divide by the number of people who will be served.

Since 1 gallon is equal to 16 cups, we can multiply the number of gallons by 16 to get the total number of cups of sorbet. In this case, 1 gallon x 16 cups/gallon = 16 cups of fruit sorbet.

To find out how many cups of sorbet each person will get, we simply divide the total number of cups by the number of people. In this case, 16 cups ÷ 32 people = 0.5 cups/person.

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