Roberto will put a border around the edges of the platform how much border will he need if the area is 12 square units?

The calculated vertex of the graph represented in the figure is (-3, -3)

Given that we have the graph

The curve on the graph is a quadratic function

As a general rule, the vertex of a graph is the minimum or the maximum point on a graph

From the graph, we have the minimum point to be

Minimum = (-3, -3)

This means that

Vertex = (-3, -3)

Hence, the vertex is (-3, -3)

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By using the graph, the key features of the function include the following:

In Mathematics, the horizontal extent of any graph of a function represents all domain values and they are read and written from smaller to larger numerical values, and from the left of a graph to the right.

By critically observing the graph shown in the image attached above, we can reasonably and logically deduce the following domain and range:

Domain = {-∞, ∞} or {x|x ∈ R}.

Range = {-1, ∞}.

Based on the graph, the x-intercept and y-intercept of the function both occur at the origin (0, 0).

When x = -2, the y-value is given by:

f(-2) = 3.

When x = 2, the y-value is given by:

f(2) = -1.

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Based on the information provided, the probability of both events happening is 0.011 or 1.1% (option A).

The probability can be described as the proportion between the desired outcome happening and the total of possible outcomes. Using this principle, let's calculate the probability:

Probability of Gypsy finishing first: 1 / 10 = 0.1

Probability of Silver Rush finishing second: 1/ 9 = 0.11

Total probability 0.1 x 0.11 = 0.011 or 1.1% (0.011 x 100)

Therefore, the answer that matches the probability is option A.

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The domain of the function is y = -1/2(x-5)^2 + 4, for 3 ≤ x ≤ 9.

To transform the function y=x^2 according to the given specifications, we can use the following steps:

Domain: Finally, the domain of the transformed function is given as [3, 9], which means that the function is only defined for x-values between 3 and 9. Therefore, we need to restrict the domain of the function to this interval. Therefore, the final transformed function is:

Therefore the transformation is y = -1/2(x-5)^2 + 4, for 3 ≤ x ≤ 9.

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Answer[tex]n^{2} -4n+4[/tex]

Step-by-step explanation:

had to keep the minus than add a plus sign

Answer: 592

Step-by-step explanation:

A=2(wl+hl+hw)

A=2(8*10+12*10+12*8)=592

The correct locations for the three missing labels in the diagram are "Analyze the Situation" in the top-left corner, "Identify Options" in the bottom-left corner, and "Make a Decision" in the bottom-right corner. We need to apply the decision-making process to the three missing labels in the diagram.

The first missing label is for the top-left corner of the diagram. The correct location for this label is "Analyze the Situation." This is because the decision-making process begins with an analysis of the situation to understand the problem and identify any potential constraints.

The second missing label is for the bottom-left corner of the diagram. The correct location for this label is "Identify Options." This is because the decision-making process involves identifying all of the available options for solving the problem.

The third missing label is for the bottom-right corner of the diagram. The correct location for this label is "Make a Decision."

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Answer:

3/8

Step-by-step explanation:

1/4+1/8

2/8+1/8

=

3/8

3/8

1+2 to equal 3, which is all the numerators above the least common denimonater 8

Answer:

To find out which expression must be added to 3x - 7 to equal 0, we need to solve the equation:

3x - 7 + a = 0

where "a" is the expression to be added.

To solve for "a", we can isolate "a" on one side of the equation by adding 7 to both sides:

3x - 7 + a + 7 = 0 + 7

Simplifying the left side, we get:

3x + a = 7

Therefore, the expression that must be added to 3x - 7 to equal 0 is:

a = -3x + 7

We can check that this is correct by substituting -3x + 7 for "a" in the original equation:

3x - 7 + (-3x + 7) = 0

Simplifying the left side, we get:

3x - 3x - 7 + 7 = 0

0 = 0

The equation is true, which confirms that the expression -3x + 7 must be added to 3x - 7 to equal 0.

Step-by-step explanation:

Therefore the total cost for 18 months of membership is[tex]$742.50[/tex].The equation to find the cost of initiation and x months of membership is y + 59x = 742.50

The equation to find the cost of initiation and x months of membership is y + 59x = 742.50. Since the cost for one year of membership is known, the cost for initiation can be found by subtracting 59x from both sides of the equation, resulting in y = 742.50 - 59x. To find the total cost for 18 months of membership, we plug x = 18 into the equation, resulting in y + 59(18) = 742.50. This can be simplified to y + 1062 = 742.50, which means that y = -319.50. Therefore, the total cost for 18 months of membership is[tex]$742.50 - $319.50[/tex], which equals [tex]$423.00[/tex]. This calculation can be represented by the equation y + 59x = 742.50, where y is the cost of initiation and x is the number of months of membership. Plugging in the number of months of membership (x = 18) gives us the total cost for 18 months of membership (y + 1062 = 742.50). Simplifying this equation yields y = -319.50, and therefore the total cost for 18 months of membership is[tex]$742.50.[/tex]

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Answer: 32+2.25(8)=50

Step-by-step explanation:

If you have $50 and waste $32 that leaves you with $18.

If each dip cost 2.25 you can have a total of 8 dips.

32+2.25(x)=50

32+2.25(8)=50

Answer and Explanation:

1. corresponding: bottom right graph

         → the angles are in the same place in relation to the parallel lines

2. alternate interior: bottom left graph

         → the interior angles are on opposite sides of the transversal

3. alternate exterior: top left graph

         → the exterior angles are on opposite sides of the transversal

4. none of these: top middle graph

         → there are no parallel lines

Answer: 17.5

Step-by-step explanation:

First find the two numbers (data values) that are in the middle. Thats 15 and 20. When you have two numbers in the middle of a data set you average them. (Buy adding 15 and 20 then dividing by 2) So the answer is 17.5

Answer:

1.)  51.515%  2.) 48.485%

Step-by-step explanation:

In this question we know 66 is 100% of the fraction, so we can start the process of converting a fraction into a percent, by figuring out how to adjust the fraction so that the denominator will be 100. First, divide 100 by the denominator.

100/66 = 1.515

Now we want to multiply denominator and numerator by 100.

34 × 1.515 = 51.515

66 × 1.515 = 100

Therefore, 34/66 as a percentage will be 51.515%

Now we want to convert 32/66. We will do the same for this equation.

100/66 = 1.515

32 × 1.515 = 48.485

66 × 1.515 = 100

Therefore 32/66 as a percentage will be 48.485

Hope this helps : )

The ordered pairs that correspond to input-output pairs of the function y=-7x+3 are  (5,32).

The input-output pairs of the function y=-7x+3 can be determined by plugging in the input value x into the function and solving for y. The formula y=-7x+3 can be used to calculate the output value corresponding to a given input value x. For example, if x=4, then y=-7(4)+3=-28+3=5, so the input-output pair is (4,5). Similarly, if x=5, then y=-7(5)+3=-35+3=32, so the input-output pair is (5,-32). The ordered pairs that correspond to input-output pairs of the function y=-7x+3  and (5,32).

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A $9. 00 album is marked up 6 1/4% and then is offered for 14% off. If the sales tax is 5%. The total amount of tax that must be paid for this album is $0.41.

Let's break this problem down into steps:

Markup price = $9.00 + 6.25% of $9.00

Markup price = $9.00 + $0.56

Markup price = $9.56

Sale price = Markup price - 14% of Markup price

Sale price = $9.56 - 14% of $9.56

Sale price = $9.56 - $1.34

Sale price = $8.22

Tax amount = 5% of the Sale price

Tax amount = 5% of $8.22

Tax amount = $0.41

Therefore, the total amount of tax that must be paid for this album is $0.41.

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The answer of the given question based on the exponential random variable with mean  i.e. [tex]\mu o \leq \bar x + \frac{z \alpha \sigma}{\sqrt{n} }[/tex].

The null hypothesis is  statement or assumption about population parameter that is tested for its validity using statistical methods. It is  statement of no effect, no difference, or no relationship between the variables of interest,

(a) To test the null hypothesis  [tex]H$ o: \mu =\mu o[/tex], we can use a one-sided test with rejection region R =  [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex], is the critical value from the Standard Normal distribution that corresponds to a significance level of α = 0.10 (since we want a 90% confidence interval). If the observed sample mean  falls in the rejection region R, we reject the null hypothesis and conclude that the true mean μ is greater than μ0 with 90% confidence.

To find the confidence interval of the form [∗,[infinity]), we can solve the inequality   [tex]\bar x \geq \mu o + \frac{z \alpha \sigma}{\sqrt{n} }[/tex]  for [tex]\mu[/tex] which gives:

[tex]\mu o \leq \bar x - \frac{z \alpha \sigma}{\sqrt{n} }[/tex]

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The number of sets is 128 by using the multiplication principle.

The multiplication principle states that if there are k events, and if the first event can happen in n_1 ways, the second event can happen in n_2 ways, and so on, then the k events can happen in n_1 × n_2 × ... × n_k ways.

To find the number of sets of four marbles include one of each color other than lavender, A bag contains two red marbles, four green ones, one lavender one, four yellows, and four orange marbles.

There are two red marbles.

There are four green ones.

There are four yellows.

There are four orange marbles.

So, total of 2 + 4 + 1 + 4 + 4 = 15 marbles in the bag.

To find the total number of sets of four marbles including one of each color other than lavender, use the multiplication principle.

In this question, there are 5 events (choosing one of each color).

The first event can happen in 2 ways.

The second event can happen in 4 ways.

The third event can happen in 4 ways.

The fourth event can happen in 4 ways.

Therefore, by the multiplication principle, the total number of sets of four marbles includes one of each color other than lavender

= 2 × 4 × 4 × 4 ⇒ 128 sets.

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Answer:

  4.0 feet

Step-by-step explanation:

You want the diameter of a rubber ball that costs $1, if that cost is $0.02 per square foot.

The surface area of a sphere is given by ...

  A = 4πr²

In terms of diameter, this is ...

  A = 4π(d/2)² = πd²

The cost will be ...

  Cost = (cost/square foot)(area)

  1.00 = 0.02(πd²)

Solving for d, we have ...

  d² = 1.00/(0.02π) ≈ 15.915

  d ≈ √15.915 ≈ 3.989 ≈ 4.0 . . . . feet

The diameter of the ball is about 4.0 feet.

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The minimum value of the function is 9, and the function never stops increasing.

The given function is y=(x−9)²+9.

We need to find the minimum and maximum value of the function. The given function is a quadratic function whose graph is a parabola. Since the coefficient of x² is positive, the graph of the quadratic function will be in the form of an upward parabola whose vertex is at the point (h,k).

The vertex form of the quadratic function is given byy = a(x - h)² + k, where(h,k) is the vertex of the parabola.

a is the coefficient of (x - h)².

In the given function,y = (x-9)² + 9, the vertex of this function is (9,9) and a=1.

Therefore, the minimum value of the function is 9 at x=9, which is the vertex of the parabola.

The function y=(x−9)²+9 is an upward parabola, and hence it never stops increasing, which means that the function has no maximum value.

Thus, the minimum value of the function is 9, and the function never stops increasing.

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Answer:

Step-by-step explanation:

[tex]\frac{3x+9}{12x} \\we \ can \ write \ 3x+9 \ as 3(x+3)\\\frac{3x+9}{12x}=\frac{3(x+3)}{3*4x}=\frac{x+3}{4x}[/tex]

Answer:

[tex]\frac{x+3}{4x}[/tex]

Step-by-step explanation:

[tex]\frac{3(x)+9}{12x}[/tex]

[tex]\frac{3(x+3)}{12x}[/tex]

Answer:

2000 pounds

Step-by-step explanation:

Let's start with the initial amount of gravel in the mound, which is g pounds.

After 300 pounds are added, the total amount of gravel in the mound becomes:

g + 300

Then, two orders of 600 pounds are sold and removed from the mound. So, the total amount of gravel in the mound after these two orders are sold becomes:

g + 300 - 2(600) = g + 300 - 1200 = g - 900

Finally, we know that at the end of the day, the mound has 1400 pounds of gravel. So, we can set up an equation:

g - 900 + 300 = 1400

Simplifying this equation, we get:

g - 600 = 1400

Adding 600 to both sides, we get:

g = 2000

Therefore, the initial amount of gravel in the mound was 2000 pounds.

Answer:

2000 pounds

Step-by-step explanation:

sorry it took a while;)

Answer:

40 and 27

Step-by-step explanation:

Answer:Let's call the two numbers x and y.

From the problem, we know that:

x + y = 67 (equation 1)

and

x - y = 13 (equation 2)

To solve for x and y, we can use the method of elimination. We can add equations 1 and 2 to eliminate y:

(x + y) + (x - y) = 67 + 13

Simplifying this equation, we get:

2x = 80

Dividing both sides by 2, we get:

x = 40

Now we can use equation 1 to solve for y:

x + y = 67

40 + y = 67

Subtracting 40 from both sides, we get:

y = 27

Therefore, the two numbers are 40 and 27.

Step-by-step explanation:

Answer:

50s

Step-by-step explanation:

180cm³= 30s

300cm³=x s

Thus,

180x= 30×300

180x = 9000

x= 50s.

Hope this helps! :)

The reasons for the statements supporting the proof that ∡TV ≅ ∡ XW are given as follows;

A - Given

H - Vertical Angles

F- Angles that inscribe a half circle are congruent and 90°

C - Angle-Angle-Side Triangle Congruence

E - CPCTC

D - Reflexive Property

I - Hypotenuse Leg (H-L) Triangle Congruence

G - CPCTC

B - Arcs of a congruent angles are congruent

CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent". It is a theorem used in geometry to prove that two triangles are congruent.

An inscribed angle is half the measure of its intercepted arc. A half circle is a semicircle, which has an intercepted arc of 180°, so the inscribed angles are 1/2(180°) = 90° and congruent.

The reflexive property is a property of equality that states that any quantity is equal to itself. In other words, a = a. This property is used in many mathematical proofs.


The Hypotenuse-Leg (H-L) Triangle Congruence is a rule used to prove that two right triangles are congruent. If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and the corresponding leg of another triangle, then the two triangles are congruent.


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Accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.

A quadrilateral is a fοur-sided pοlygοn, which is a twο-dimensiοnal geοmetric figure with straight sides. Quadrilaterals can have a variety οf shapes, sizes, and angles, but they all have fοur sides and fοur vertices (cοrners).

Since the quadrilateral PQRS is inscribed in a circle, we knοw that angle PQR is an inscribed angle οf arc PR. By the Inscribed Angle Theοrem, the measure οf an inscribed angle is equal tο half the measure οf its intercepted arc. Therefοre, the measure οf arc PQR is twice the measure οf angle PQR, which is:

2 * 85 = 170 degrees.

Therefοre, accοrding tο the given infοrmatiοn the measure οf arc PQR is 170 degrees.

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The sum of the measures of the interior angles of an 11-sided polygon is 1620 degrees.

The formula to find the sum of the measures of the interior angles of a polygon is:

Sum of interior angles = (n - 2) × 180 degrees

Where n: number of sides of the polygon.

Using this formula, we can find the sum of the measures of the interior angles of a polygon with 11 sides:

Sum of interior angles = (11 - 2) × 180 degrees

Sum of interior angles = 9 × 180 degrees

Sum of interior angles = 1620 degrees

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