f(x) = x2 – 8x+7
Find an equation for axis of symmetry

Answer:

4x²+35x+24

Step-by-step explanation:

FOIL the binomials and simplify

4x^2 + 35x + 24

That's all I know.

Answer:

BD  =  8

m∠BDA  =  90°

∆ABD and ∆BCD are both right triangles, each with two known side lengths.

Step-by-step explanation:

Direct answer from PLATO so change it a bit.

The asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t are the vertical asymptote t = 1, the horizontal asymptote y = 0 (x-axis), and the horizontal asymptote x = 0 (y-axis).

To find the asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t, we need to examine the behavior of the equations as t approaches certain values.

Let's first consider the vertical asymptotes. Vertical asymptotes occur when the denominator of either the x or y equation approaches zero. In this case, the vertical asymptote will occur when the denominator of the x equation, (t-1), approaches zero. Solving for t, we find that t = 1 is the value that makes the denominator zero. Therefore, the vertical asymptote is the line t = 1.

Next, we will determine the horizontal asymptotes. Horizontal asymptotes are defined by the behavior of the x and y equations as t approaches positive or negative infinity. To find the horizontal asymptotes, we need to examine the limits of x and y as t approaches infinity and negative infinity.

As t approaches infinity, the x equation, 1/(t-1), approaches zero since the numerator remains constant while the denominator grows larger. Therefore, the x-coordinate tends to zero as t approaches infinity.

Similarly, as t approaches negative infinity, the x equation approaches zero. Therefore, the x-coordinate tends to zero as t approaches negative infinity.

For the y equation, as t approaches infinity, the y equation, 2/t, approaches zero since the numerator remains constant while the denominator grows larger. Therefore, the y-coordinate tends to zero as t approaches infinity.

As t approaches negative infinity, the y equation approaches zero as well. Therefore, the y-coordinate tends to zero as t approaches negative infinity.

Hence, we have identified that the horizontal asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t are the x-axis (y = 0) and the y-axis (x = 0).

To summarize, the asymptotes of the graph defined by the parametric equations x = 1/(t-1) and y = 2/t are the vertical asymptote t = 1, the horizontal asymptote y = 0 (x-axis), and the horizontal asymptote x = 0 (y-axis). These asymptotes provide valuable information about the behavior of the graph as t approaches certain values, helping us understand the overall shape and characteristics of the parametric curve.

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Answer:

[(2, 8),(3, 7),(4, 6)]

Graph the equation like normal.

Use the procedures explained below to answer the next question.

Step-by-step explanation:

To obtain 3 points, choose any values for x and substitute into the equation for corresponding values of y. To make this easier, I'm going to use function notation instead. But, this works the same using slope-intercept form.

\(f(x)=-x+10\\f(2)=-2+10=8 \rightarrow (2,8)\\f(3)=-3+10=7 \rightarrow (3,7)\\f(4)=-4+10=6\rightarrow(4,6)\)

All I did was substitute three different values of x, to get the corresponding values for y.

So, the three points that are on the line are (2, 8), (3, 7), and (4, 6). Now, you can graph the equation as you normally would.

As shown in the attached screenshot, the three points that we found are correctly on the graphed line.

Use the same procedures to answer the next question.

Answer:

f(x) = 4x4 – 7x2 + x + 25 f(x) = 9x4

Step-by-step explanation:

Because it has to be this one

(a) The smallest positive value of n for which a simple graph on n vertices and 2n edges can exist is 3. An example of such a graph for the smallest n is a triangle, where each vertex is connected to the other two vertices.

In this case, we have 3 vertices and 2n = 2 * 3 = 6 edges, which satisfies the condition.

To determine the smallest positive value of n, we need to consider the conditions for a simple graph:

1. Each vertex must be connected to at least one other vertex.

2. There should be no multiple edges between the same pair of vertices.

3. There should be no self-loops (edges connecting a vertex to itself).

Considering these conditions, we start by trying with the smallest possible n, which is 3. We construct a graph with 3 vertices and connect each vertex to the other two vertices, resulting in a triangle. This graph satisfies the conditions and has 2n = 2 * 3 = 6 edges.

(b) To prove that G is connected, we will use a proof by contradiction.

Assume that G is not connected, meaning it has two or more components. Let's consider two distinct components, C1 and C2.

Since G has at most two components, each component can have at most 10 vertices (20 vertices / 2 components). Let's assume C1 has x vertices and C2 has y vertices, where x + y ≤ 20.

Now, let's consider two vertices u and v, where u belongs to C1 and v belongs to C2. According to the given condition, deg(u) + deg(v) > 19.

Since deg(u) represents the degree of vertex u, it means the number of edges incident to vertex u. Similarly, deg(v) represents the degree of vertex v.

In C1, the maximum possible degree for a vertex is x - 1 (since there are x vertices, each connected to at most x - 1 other vertices in C1). Similarly, in C2, the maximum possible degree for a vertex is y - 1.

Therefore, deg(u) + deg(v) ≤ (x - 1) + (y - 1) = x + y - 2.

But according to the given condition, deg(u) + deg(v) > 19. This contradicts the assumption that G has at most two components.

Hence, our assumption that G is not connected is false. Therefore, G must be connected.

In conclusion, if a simple graph G has 20 vertices, at most two components, and every pair of distinct vertices satisfies the inequality deg(u) + deg(v) > 19, then G is connected.

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Answer:

x= 0 has one solution

Step-by-step explanation:

Here, we want to get the number of solution

Looking at the relation, we can see that what we have is a linear relation

mathematically, a linear relation has a single solution

Thus, x = 0 has one solution

(a) To find the values of z for which the matrix does not have an inverse, we can set up the determinant of the matrix and solve for z when the determinant is equal to zero.

The given matrix is:

|x3  x|

|9   1|

The determinant of a 2x2 matrix can be found using the formula ad - bc. Applying this formula to the given matrix, we have:

Det = (x3)(1) - (9)(x) = x3 - 9x

For the matrix to have an inverse, the determinant must be non-zero. Therefore, we solve the equation x3 - 9x = 0:

x(x2 - 9) = 0

This equation has two solutions: x = 0 and x2 - 9 = 0. Solving x2 - 9 = 0, we find x = ±3.

So, the values of x for which the matrix has no inverse are x = 0 and x = ±3.

(b) (i) To find the size of the acute angle between the vectors (3,0) and (5,5), we can use the dot product formula:

u · v = |u| |v| cos θ

where u and v are the given vectors, |u| and |v| are their magnitudes, and θ is the angle between them.

Calculating the dot product:

(3,0) · (5,5) = 3(5) + 0(5) = 15

The magnitudes of the vectors are:

|u| = sqrt(3^2 + 0^2) = 3

|v| = sqrt(5^2 + 5^2) = 5 sqrt(2)

Substituting these values into the dot product formula:

15 = 3(5 sqrt(2)) cos θ

Simplifying:

cos θ = 15 / (3(5 sqrt(2))) = 1 / (sqrt(2))

To find the acute angle θ, we take the inverse cosine of 1 / (sqrt(2)):

θ = arccos(1 / (sqrt(2)))

(ii) If the vector (-k, 3) is orthogonal to (5,5), it means their dot product is zero:

(-k, 3) · (5,5) = (-k)(5) + 3(5) = -5k + 15 = 0

Solving for k:

-5k = -15

k = 3

So, the value of k is 3.

(c) Let J be the linear transformation from R2 to R2 that reflects points in the horizontal axis and then scales them by a factor of 2. The matrix of J can be found by multiplying the reflection matrix and the scaling matrix.

The reflection matrix in the horizontal axis is:

|1  0|

|0 -1|

The scaling matrix by a factor of 2 is:

|2  0|

|0  2|

Multiplying these two matrices:

J = |1  0| * |2  0| = |2  0|

   |0 -1|   |0  2|   |0 -2|

So, the matrix of J is:

|2  0|

|0 -2|

Therefore, y = 2 and z = -2.

(d) The volume of a parallelepiped can be found by taking the dot product of two adjacent sides and then taking the absolute value of the result.

The adjacent sides of the parallelepiped P are (0,3,0)

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there are 1,320 different ways in which the winners can be drawn in the lottery game.

To determine the total number of different ways in which the three grand prize winners can be drawn, we can use the formula for combinations.

The number of ways to choose r items from a set of n items is given by the formula

nCr = n! / (r! × (n - r)!)

where n! represents the factorial of n, or n × (n-1) × (n-2) × ... × 2 × 1, and r! represents the factorial of r.

For the first prize, there are 12 possible winners, so there are 12 ways to choose the first prize winner.

For the second prize, there are 11 remaining finalists, since the first prize winner cannot win the second prize. So, there are 11 ways to choose the second prize winner.

For the third prize, there are 10 remaining finalists, since the first and second prize winners cannot win the third prize. So, there are 10 ways to choose the third prize winner.

The total number of different ways to choose the three grand prize winners is the product of the number of ways to choose each prize

12 × 11 × 10 = 1,320

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Answer:

-1/4

Step-by-step explanation:

slope= y2-y1/x2-x1

change in y: 3 - 4 = -1

change in x: 5 - 1 = 4

slope (A.K.A. m) = -1/4

Answer:

it's is a repeating decimal

Answer:

8/9 = 0.88888...

This decimal never stops and keeps on repeating, so it is a repeating decimal.

Let me know if this helps!

As a result, the solid's volume in the first octant, which is restricted by the paraboloid z = 4 + 2 x + 2 y, is 9.

We must determine the limits of integration for x, y, and z in order to determine the volume of the solid in the first octant bounded by the paraboloid z = 4 + 2x + 2y + 2 and the plane z = 10.

At z = 10, where the paraboloid and plane overlap, we put the two equations equal and find z:

4 + 2x^2 + 2y^2 = 10

2x^2 + 2y^2 = 6

x^2 + y^2 = 3

This is the equation for a circle in the xy plane with a radius of 3, centred at the origin. We just need to take into account the area of the circle where x and y are both positive as we are only interested in the first octant.

Integrating over the circle in the xy-plane, we may determine the limits of integration for x and y:

∫∫[x^2 + y^2 ≤ 3] dx dy

Switching to polar coordinates, we have:

∫[0,π/2]∫[0,√3] r dr dθ

Integrating with respect to r first gives:

∫[0,π/2] [(1/2)(√3)^2] dθ

= (3/2)π

So the volume of the solid is:

V = ∫∫[4 + 2x^2 + 2y^2 ≤ 10] dV

= (3/2)π(10-4)

= 9π

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Answer: 35 is 70% of 50

Step-by-step explanation:

Steps to solve "35 is 70 percent of what number?"

We have, 70% × x = 35

or,

70

100

× x = 35

Multiplying both sides by 100 and dividing both sides by 70,

we have x = 35 ×

100

70

x = 50

If you are using a calculator, simply enter 35×100÷70, which will give you the answer.

Answer:

50

Step-by-step explanation:

35 + 15 = 50

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

15 is 30% of 50 There fore 50 is the correct answer

I took this exam, its the 5.08 Ratios and rates practice exam right?

Have an amazing Day and good luck (:

The area of the parallelogram is 45 square units.

The area of the right trapezoid is 42.5 square units.

A parallelogram is a convex quadrilateral in which each pair of opposite edges are parallel and of equal length.

Area of parallelogram = base × height

= 9 × 5

= 45 square units

Area of a right trapezoid = 1/2 (a + b)h

= 1/2(10 + 7)5

= 1/2(17)5

= 1/2(85)

= 42.5 square units

Therefore, the area of the parallelogram and right trapezoid is 45 square units and 42.5 square units respectively.

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Answer:

3 grams are in one chicken wing

Step-by-step explanation:

Set up an equation:

Variable x = grams per 1 chicken wing

1000/3000 = 1/x

Cross multiply

1000 × x = 3000 × 1

1000x = 3000

Divide both sides by 1000 to isolate the variable x

x = 3

Answer:

3

Step-by-step explanation:

3000/1000=3

Answer:

True

Step-by-step explanation:

True, because a polygon have all angles that are equal and all lengths are the same length.

If the null hypothesis is rejected, it means there is sufficient evidence to support the claim that the standard deviation is not at most 2.5 years. Conversely, if the null hypothesis is not rejected, it means there is insufficient evidence to support the claim.

In hypothesis testing, the null hypothesis (H₀) represents the default or initial assumption, while the alternative hypothesis (H₁) represents the researcher's claim or the hypothesis they want to establish. In this case, the researcher's claim is that the standard deviation of the life of a certain type of lawn mower is at most 2.5 years. Since this claim does not contain a statement of equality (such as "equal to" or "not equal to"), it represents the alternative hypothesis.

If the null hypothesis is rejected after performing the hypothesis test, it means there is sufficient evidence to support the claim made in the alternative hypothesis. In this scenario, it would indicate that the standard deviation of the life of the lawn mower is indeed greater than 2.5 years.

On the other hand, if the null hypothesis is not rejected, it means there is insufficient evidence to support the claim made in the alternative hypothesis. In this case, it would suggest that the standard deviation of the life of the lawn mower is likely at most 2.5 years, as stated in the null hypothesis.

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79 hours will it take for one person to harvest the entire strawberry patch.

The same property is expressed using a unit conversion but in a distinct unit of measurement. For instance, time can be stated in minutes rather than hours, and distance can be expressed in kilometers, feet, or any other length unit instead of miles.

Finding the strawberry patch's area in square meters and dividing it by the amount that one person can harvest in an hour will give us the total number of hours needed to solve this issue.

The strawberry patch's measurements must first be changed from decameters (dam) to meters.

1 decameter (dam) = 10 meter

Strawberry patch length in meters = 1.7 dam * 10 m/dam = 17 m.

The strawberry patch width in meters = 1.4 dam x 10 m/dam = 14 m.

The strawberry patch's area is therefore:

Area of strawberry patch = length × width = 17 m × 14 m = 238 m²

We must now determine how long it will take one individual to pick 3 m² of strawberries, in hours. We can calculate this by dividing the patch's overall area by the area that a single individual can select in an hour:

= a number of hours needed to harvest the complete patch.

The total harvesting time is  = 79.33 hours nearly equal to 79

Therefore, it would take one person 79 hours to gather the complete strawberry patch.

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Answer:

The answer would be 73%

Step-by-step explanation:

It makes sense because there is a lot of under 7 year olds at the park ;-;

The answer is 73

I took the test :)

and its the only reasonable answer

Answer:

B= 67

Step-by-step explanation:

Being vertically opposite angle

Answer:

300

Step-by-step explanation:

3:120 =1:60 ==300:12000

Answer:

A) y + 1 = -3 ( x - 7 )

Step-by-step explanation:

I used the Desmos website. Hope this helps.

Answer:

A

Step-by-step explanation:

3x + y = 4

y = -3x + 4

y + 1 = -3(x - 7)

Answer:

nope

Step-by-step explanation:

nope

Let ABC be the given triangle. We can construct two triangles PAB and PBC such that they share the same height from P to AB and P to BC, respectively. We can label the side lengths of PAB and PBC as x and y, respectively. The total area of the triangle ABC is the sum of the areas of PAB and PBC:

Area_ABC = Area_PAB + Area_PBC We can write the area of each of the sub-triangles in terms of x and y by using the formula for the area of a triangle: Area_PAB = (1/2)(12)(x) = 6xArea_PBC = (1/2)(15)(y) = (15/2)y Setting the areas equal to each other and solving for y yields: y = (4/5)x Substituting this into the equation for the area of PBC yields:

Area_PBC = (1/2)(15/2)x = (15/4)x The area of ABC can also be written in terms of x by using the formula: Area_ABC = (1/2)(AB)(PQ) = (1/2)(12)(PQ) + (1/2)(15)(PQ) = (9/2)(PQ) Setting the areas equal to each other yields:(9/2)(PQ) = 6x + (15/4)x(9/2)(PQ) = (33/4)x(9/2)(PQ)/(33/4) = x(6/11)PQ = x(6/11)Thus, we can see that the longest possible integer length of the third altitude is $\boxed{66}$.

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The type of diagram used to graphically show the relationship between two numerical variables is called a scatter plot.

A scatter plot is a visual representation of data points plotted on a graph, with one variable represented on the x-axis and the other variable represented on the y-axis.

Each data point on the plot corresponds to a pair of values from the two variables being analyzed. The position of each point on the graph indicates the values of both variables, allowing us to examine the relationship between them.

The main purpose of a scatter plot is to visualize the correlation or relationship between the two variables. The pattern formed by the data points on the plot can indicate the direction, strength, and nature of the relationship.

For example, if the points on the scatter plot tend to form a linear pattern, it suggests a linear relationship between the variables. On the other hand, if the points are scattered randomly with no clear pattern, it indicates a weak or no relationship between the variables.

Scatter plots are commonly used in various fields, including statistics, data analysis, and scientific research. They provide a visual way to explore and interpret relationships between variables, identify outliers, detect trends, and assess the strength and direction of associations.

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Answer: The fourth person will receive \(\dfrac{13}{60}\) of a bar.

Step-by-step explanation:

Total people = 4

Fraction of chocolate received by first person  =  \(\dfrac13\)

Fraction of chocolate received by second person  =  \(\dfrac14\)

Fraction of chocolate received by third person  =  \(\dfrac15\)

Now, Fraction of chocolate received by fourth person  =  \(1-(\dfrac13+\dfrac14+\dfrac15)\)

\(=1-(\dfrac{20+15+12}{60})\\\\=1-(\dfrac{47}{60})\\\\=\dfrac{60-47}{60}\\\\=\dfrac{13}{60}\)

So, the fourth person will receive \(\dfrac{13}{60}\) of a bar.

Answer: 98268

Step-by-step explanation:

Given: In an international company,

Employees in one country = 22,700

If this is 23.1% of the total number of company's employees,

[\(1\%=\dfrac1{100}\) , replace 'of' by '×']

i.e. 23.1% of (total employees) = 22700

\(\Rightarrow\ \dfrac{23.1}{100}\times\text{(total employees)}=22700\\\\\Rightarrow\ \text{Total employees}=\dfrac{22700\times100}{23.1}\\\\\Rightarrow\ \text{Total employees}=98268.4\approx98268\)

Hence, there are 98268 employees in total.

Answer:

\(42.86, or 43\)%

Step-by-step explanation:

3 out of 4 as a percentage is 42.86.