The following system of equations is graphed below.
y=-2x -9
y=2/3x +13/3
Find the solution to the system.
A. x = 1, y = -5
B. x = -5, y = 1
C. x = -5, y = 2
D. x = -4, y = 1

Jane has 6 - 14 - 12 = -20 boxes of beads left.

Jane initially had 6 boxes of beads.

She used 14 of those boxes to make face mask holders and gave 12 boxes to her sister.

To find out how many boxes of beads she has left, we need to subtract the boxes used and given away from the initial number.

First, let's calculate the total number of boxes used and given away:

Total boxes used and given away = Boxes used for face mask holders + Boxes given to sister

Total boxes used and given away = 14 + 12

Total boxes used and given away = 26

Next, we can subtract the total boxes used and given away from the initial number of boxes Jane had:

Boxes left = Initial number of boxes - Total boxes used and given away

Boxes left = 6 - 26

Boxes left = -20

The result is -20, which implies that Jane has a deficit of 20 boxes of beads.

This means she doesn't have any boxes of beads left; she has a shortage of 20 boxes based on the activities she performed.

It's important to note that having a negative value indicates that Jane doesn't have enough boxes to fulfill her activities.

If the result were positive, it would represent the number of boxes remaining.

However, in this case, Jane has used and given away more boxes than she initially had, resulting in a negative value.

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To solve for the value of x, let's simplify the equation by eliminating the parenthesis first applying the distributative property.

The next step is to join similar terms on each side. Let's transfer -5/4x to the other side and -8 to the right side. In doing so, the signs will reverse as well. From positive to negative and vice versa.

The last step is to divide both sides of the equation by 5/4 to solve for x.

Therefore, the value of x is 8.

To check if it is correct, we can substitute the x value in the original equation by 8 and see if both sides are indeed equal.

Indeed both sides are equal therefore, the value of x must be 8.

Answer:

i think the answer is -3/4

Answer:

B I hope

Step-by-step explanation:

The length of the base of a square prism is 3.872 cm and the surface area of a square prism is 184.9 cm ²

Let h is the height length of the prism and a is the length of base edge.

then the volume is a²h and the surface area is 2a²+4ah

(a) The volume of a square prism is 150 cm³ and  10 cm is height length

Let a is the length of base edge.

We know the volume is a²h.

Substitute the values

a²(10) = 150

     a² = 15

      a = √15

      a = 3.872 cm

Since length of base is 3.872 cm.

(b) The height length of the prism is 10 cm and the base edge length is √15 cm.

We know the surface area is 2a²+4ah

Substitute the values

S = 2(√15)² + 4 (3.87 )(10)

  =  2(15) + 40(3.87)

  = 30 + 154.91

  = 184.9 cm ²

Since the surface area of a square prism is  184.9 cm ².

According to the unitary method,

A) The time taken for Peter to finish the job alone is 4 hours, 48 minutes.

B) The time taken for Emily and Peter to finish the job together is 2 hours, 36 minutes.

Unitary method:

In math, unitary method refers the process of finding the value of a single unit, and based on this value.

Given,

Emily, Ashley and Peter can clean a warehouse in 2 hours. If Emily does the job alone, she can finish it in 6 hours. If Ashley does the job alone she can finish it in 8 hours.

Here we need to find the following:

A) The time take for Peter to finish the job alone

B) The time taken for Emily and Peter to finish the job together

Let us consider x be the time taken for Peter to finish the job alone.

So, based on the given question we can write it as,

=> 1/6 + 1/8 + 1/x = 1/2

=> (8 + 6)/48 + 1/x = 1/2

=> 14/48 + 1/x = 1/2

=> 7/24 + 1/x = 1/2

=> 1/x = 1/2 - 7/24

=> 1/x = 12 -7/24

=> 1/x = 5/24

=> x = 24/5

=> x = 4.8

So, the time taken for Peter to finish the job alone is 4 hours, 48 minutes.

Then the time taken for Emily and Peter to finish the job together is calculated as,

=> 5/24 + 1/6

=> 5 + 4/ 24

=> 9/24

=> 3/8

Therefore, the time taken for Emily and Peter to finish the job together 2 hours, 36 minutes.

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Answer:

9/64

Step-by-step explanation:

\(=0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\0.75\times \frac{\left(3.75+-3.5\right)}{1.3}\\=0.75\times \frac{0.25}{1.3}\\=0.75\times 0.1875(\left a.k.a\:\frac{3}{16}\right)\\\frac{\left(3\times 0.1875\right)}{4}\\\mathrm{\left(Clarification:\:The\:\:math\:\:above\:\:is\:\:a\:\:broken\:\:down\:version\:of\:the\:original\:problem.\right)}\\=\frac{0.5625\left(\frac{9}{16}\right) }{4}\\=0.1406\left(\frac{9}{64}\right)\)

Hope this helps!

Answer:

ixtjtxgixgixyixiyxyifyicjgckckhckhcjgckckhckhckhcihciyciyfiyfiyfiyfiyfiyyif

Step-by-step explanation:

ridutd6utsutsursustysysyytshfzyrsyrsyrsyrsutd

The distance between the boat and the diver is D = 276.5 feet

Given data ,

A scuba diver is 356 feet under the water's surface.

And the diver establishes a 39° angle of depression with her boat.

Therefore, using the trigonometric relationships, we can

tan θ = opposite / adjacent

On simplifying , we get

tan 39° = D / 356

Multiply by 356 on both sides , we get

D = 276.5 feet

Hence , the distance is therefore 276.5 ft.

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Answer:

d

Step-by-step explanation:

The number of years must be non-negative.

This eliminates all of the options except for d.

Answer:

Population parameters

Step-by-step explanation:

Population parameters usually find from the average values, ​​in a simple way we can say that finding the average value comes in the Population Parameters.

In the given question, car manufacturing companies provide sample of average.

So, given scenario is a type of "Population parameters".

Answer:

0.

Step-by-step explanation:

The slope of the line is defined as the change of elevation of the line (\(\frac{rise}{run}\)).

In this case, there is no change in the slope as the line continues across (0 , 2), meaning that the slope of the line is 0.

If the slope of the line is 1, then the line will have (rise 1/run 1), meaning that it will have a linear slope. (See attached image).

Vertical lines have infinite slope, and so can also be called undefined as it moves neither left or right, giving it no run.

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Answer:

try D

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

1 because we need to round down

i had to do the answer as a pic cuz my iPad is gonna die.

sorry <:)

Answer:

Step-by-step explanation:

x = - 23

y = - 5

z = - 10

(x - 12)/(y+z)=

(-23 - 12)/(-5-10)=

45/15=

7/3

Answer:

41.5 units

Step-by-step explanation:

Given the data :

Month : J F M A M J J A S O N D

Inflow : 3 4 5 3 4 10 28 17 7 6 3 2

Outflow : 7 8 7 11 6 8 21 12 5 4 5 9

The unit of water in reservoir at the middle of August :

Initial unit = Unit of water at the start of the year = 50

Middle of August :

Inflow = 17 /2 = 8.5

Outflow = 12 /2 = 6

Unit of water at the middle of August :

Initial unit + Inflow - Outflow

Inflow till mid-August = (3+4+5+3+4+10+28+8.5) = 65.5

Outflow till mid-August = (7+8+7+11+6+8+21+6) = 74

50 + 65.5 - 74 = 41.5

Answer:

left

Step-by-step explanation:

if the mouth is eating on the number it's left but if the mouth is eating on the X is going to point to the right

Answer:

x-7/ x+7

^ fraction ^

Step-by-step explanation:

The expression |-4| has a value of 4 when evaluated

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

|-4|

The above expression is an absolute expression

So, the solution is the positive value of the expression in bracket

Evaluate the expressions in the brackets

So, we have the following representation

|-4| = 4

Hence, the expression has a value of 4

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Answer:

r = 3.667

h = 1.5

Step-by-step explanation:

Given:-

- The base radius of the right circular cone, R = 5.5

- The height of the right circular cone, H = 4.5

Solution:-

- We will first define two variables that identifies the volume of a cylinder as follows:

                                r: The radius of the cylinder

                                h: The height of cylinder

- Now we will write out the volume of the cylinder ( V ) as follows:

                                \(V = \pi*r^2h\)

- We see that the volume of the cylinder ( V ) is a function of two variables ( don't know yet ) - ( r,h ). This is called a multi-variable function. However, some multi-variable functions can be reduced to explicit function of single variable.

- To convert a multi-variable function into a single variable function we need a relationship between the two variables ( r and h ).

- Inscribing, a cylinder in the right circular cone. We will denote 5 points.

              Point A: The top vertex of the cone

              Point B: The right end of the circular base ( projected triangle )

              Point C: The center of both cylinder and base of cone.

              Point D: The top-right intersection point of cone and cylinder

              Point E: Denote the height of the cylinder on the axis of symmetry of both cylinder and cone.  

- Now, we will look at a large triangle ( ABC ) and smaller triangle ( ADE ). We see that these two triangles are "similar". Therefore, we can apply the properties of similar triangles as follows:

                              \(\frac{AC}{AE} = \frac{BC}{DE} \\\\\frac{H}{H-h} = \frac{R}{r}\)

- Now we can choose either variable variable to be expressed in terms of the other one. We will express the height of cylinder ( h ) in term of radius of cylinder ( r ) as follows:

                             \(H- h = r\frac{H}{R} \\\\h = \frac{H}{R}*(R-r)\)

- We will use the above derived relationship and substitute into the formula given above:

                            \(V = \pi r^2 [ \frac{H}{R}*(R - r )]\\\\V = \frac{\pi H}{R}.r^2.(R-r)\)

- Now our function of volume ( V ) is a single variable function. To maximize the volume of the cylinder we need to determine the critical points of the function as follows:

                            \(\frac{dV}{dr} = \frac{\pi H}{R}*(2rR-2r^2 - r^2 )\\\\\frac{dV}{dr} = \frac{\pi H}{R}*(2rR-3r^2 ) = 0\\\\(2rR-3r^2 ) = 0\\\\2R -3r = 0\\\\r = \frac{2}{3}*R\)

- We found the limiting value of the function. The cylinder volume maximizes when the radius ( r ) is two-thirds of the radius of the right circular cone.

- We can use the relationship between the ( r ) and ( h ) to determine the limiting value of height of cylinder as follows:

                          \(h = \frac{H}{R} * ( R - \frac{2}{3}R)\\\\h = \frac{H}{3}\)

- The dimension of the inscribed cylinder with maximum volume are as follows:

                         \(r = \frac{2}{3}*5.5 = 3.667\\\\h = \frac{4.5}{3} = 1.5\)

Note: When we solved for the critical value of radius ( r ). We actually had two values: r = 0 , r = 2R/3. Where, r = 0 minimizes the volume and r = 2R/3 maximizes. Since the function is straightforward, we will not test for the nature of critical point ( second derivative test ).

The surface area of a rectangular prism is 48 5/6 mi².

In Mathematics and Geometry, the surface area of a rectangular prism can be calculated and determined by using this mathematical equation or formula:

Surface area of a rectangular prism = 2(LH + LW + WH)

Where:

By substituting the given side lengths into the formula for the surface area of a rectangular prism, we have the following;

Surface area of rectangular prism = 2[6 × 2 1/3 + (1 1/4 × 6) + (1 1/4 × 2 1 /3)]

Surface area of rectangular prism = 2[14 + 15/2 + 35/12]

Surface area of rectangular prism = 48 5/6 mi².

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Answer:

Step-by-step explanation:

You take items out of a square root if you have a pair of numbers or if you know the square root.  

\(\sqrt{48b^{7} }\)=\(\sqrt{4*4*3*bbbbbbb}\)

So I know the \(\sqrt{4}\)=2 so i can take both out so outside the root will be 2*2 and inside the root will be 3

Now for the b's for every pair there are, you can take that out.  There are 3 pairs of b's so b³ is outside and one b is left inside.

Answer:

4b³\(\sqrt{3b}\)

Answer:

The answer is 132 square units

Step-by-step explanation:

Cutting the shape

we have two trapeziums

A=(area of small +Area of big)Trapezium

A=1/2(3+9)8 + 1/2(9+12)8

A=1/2×12×8 + 1/2×21×8

A=12×4 + 4×21

A=48+84

A=132 square units

Answer

x = (2 + 2√5)

OR

x = (2 - 2√5)

Explanation

In order to use the quadratic formula for the general quadratic equation,

ax² + bx + c = 0 is given as

For x² - 4x - 16 = 0,

a = 1

b = -4

c = -16

Hope this Helps!!!

Step-by-step explanation:

If you divide the distance by the elapsed time, the result will be the rate of water loss (evaporation). To convert this evaporation rate in to gallons lost over a specific time period, you will need convert the measure into a volume. WTG GLAD U GOT IT RIGHT..

Answer:

He will pay $1.20 sales tax.

Step-by-step explanation:

Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

ANSWER: y = (1/2)x - 1.

To find the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1), we need to determine the slope of the tangent line and its y-intercept.

First, let's find the derivative of the function y = √(x - 3) using the power rule:

dy/dx = 1/(2√(x - 3))

Now, we can substitute x = 4 into the derivative to find the slope of the tangent line at that point:

m = dy/dx = 1/(2√(4 - 3)) = 1/2

So, the slope of the tangent line is 1/2.

Next, we can use the point-slope form of a line to find the equation of the tangent line. Given the point (4, 1) and the slope m = 1/2, the equation becomes:

y - y1 = m(x - x1)

Substituting the values (x1, y1) = (4, 1):

y - 1 = (1/2)(x - 4)

Simplifying the equation:

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

y = (1/2)x - 1

Therefore, the equation of the tangent line to the curve y = √(x - 3) at the point (4, 1) is y = (1/2)x - 1.

Answer:

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

Step-by-step explanation:

Step 1: Find the derivative of the function

The derivative of a function gives the slope of the tangent line to the curve at any point. To find the derivative of the given function y = sqrt(x - 3), we can use the power rule of differentiation which states that:

d/dx (x^n) = nx^(n-1)

Applying this rule to our function, we get:

dy/dx = d/dx sqrt(x - 3)

To differentiate the square root function, we can use the chain rule of differentiation which states that:

d/dx f(g(x)) = f'(g(x)) * g'(x)

Applying this rule to our function, we have:

g(x) = x - 3

f(g) = sqrt(g)

So,

dy/dx = d/dx sqrt(x - 3) = f'(g(x)) * g'(x) = 1/(2*sqrt(g(x))) * 1

Substituting g(x) = x - 3, we get:

dy/dx = 1/(2*sqrt(x - 3))

So, the derivative of y with respect to x is 1/(2*sqrt(x - 3)).

Step 2: Evaluate the derivative at the given point

To find the slope of the tangent line at the point (4, 1), we need to substitute x = 4 into the derivative expression:

dy/dx = 1/(2*sqrt(4 - 3)) = 1/2

So, the slope of the tangent line at the point (4, 1) is 1/2.

Step 3: Use point-slope form to write the equation of the tangent line

Now that we know the slope of the tangent line at the point (4, 1), we can use point-slope form to write the equation of the tangent line. The point-slope form of a line is given by:

y - y1 = m(x - x1)

where (x1, y1) is the point on the line and m is the slope of the line.

Substituting the values x1 = 4, y1 = 1, and m = 1/2, we get:

y - 1 = (1/2)*(x - 4)

Simplifying this equation, we get:

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

So, the equation of the tangent line to the curve y = sqrt(x - 3) at the point (4, 1) is y = (1/2)x - 1/2.

Hope this helps!