The better definition of Intersection is:
OA system that has at least one solution.
O Where lines cross over each other. The lines have a common point.
OA value we can put in place of a variable (such as x) that makes the equation true.
OA system that has no solutions.

Answer:

We have similar triangles.

7/3.5 = 5/x

2 = 5/x, so x = 2.5

Having the information that segment AC ≅ segment EF, angle B ≅ angle E, and segment BC ≅ segment FE is sufficient to prove that triangles ΔABC and ΔDEF are congruent by the Side-Angle-Side (SAS) criterion.

To prove that triangles ΔABC and ΔDEF are congruent using the Side-Angle-Side (SAS) criterion, we need the following additional information:

The length of segment AC is equal to the length of segment EF: This establishes that one pair of corresponding sides is congruent.

The measure of angle B is equal to the measure of angle E: This provides the congruent angle between the corresponding sides.

The length of segment BC is equal to the length of segment FE: This establishes that the other pair of corresponding sides are congruent.

By having this information, we can apply the SAS congruence criterion. The SAS criterion states that if two triangles have a pair of corresponding sides that are congruent, and the included angles are congruent, then the triangles are congruent.

In this case, having segments AC ≅ EF, angle B ≅ angle E, and segment BC ≅ FE would be sufficient to prove that ΔABC ≅ ΔDEF by SAS.

To learn more about Side-Angle-Side

https://brainly.com/question/30459968

#SPJ8

Answer:

Step-by-step explanation:

The given expression is: 14x^(2n+1) + 7x^(n+3) - 21^(n+2)

Unfortunately, it seems there is a missing exponent for the term "21" in the expression. Please provide the correct exponent for 21, and I'll be happy to help you further simplify the expression.

Step-by-step explanation:

in the formula

y = Ae^rt

y is 675,000

A is 250,000

r is 0.08

to get the value of t

y = Ae^rt

y/A = e^rt

ln(y/A) = rt

[ln(y/A)]/r = t

Answer:

(r q)(-3) = -3

(q r)(-3) = -3

Step-by-step explanation:

let x = 1

q(1) = -1 +2 = 1

r(1) = 1² = 1

(r q)(-3) = ?

(1×1)(-3) = -3

(q r)(-3) = ?

(1×1)(-3) = -3

The mean of the scores to the nearest tenth is 83.7.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

Given the question above, we need to find the mean of the scores to the nearest tenth.

We can find the mean by using the formula below:

[tex]\text{Mean} = \dfrac{\text{Sum of all the observations}}{\text{Total number of observations}}[/tex]

Now,

[tex]\text{Mean} = \dfrac{70(6)+75(3)+80(9)+85(5)+90(7)+95(8)}{6+3+9+5+7+8}[/tex]

[tex]\text{Mean} = \dfrac{420+225+720+425+630+760}{38}[/tex]

[tex]\text{Mean} = \dfrac{3180}{38}[/tex]

[tex]\text{Mean} = 83.7[/tex]

Therefore, the mean of the scores to the nearest tenth is 83.7.

Read more about the mean at:

https://brainly.com/question/32056327

Answer:

The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.

Step-by-step explanation:

The given directrix of the parabola is y = 2, which is a horizontal line.

This means that the parabola is vertical, with a vertical axis of symmetry.

The focus of a parabola is a fixed point located inside the curve. The y-coordinate of the given focus is y = -10. As this is below the directrix, it means that the parabola opens downwards.

The standard form of a vertical parabola is:

[tex]\boxed{(x-h)^2=4p(y-k)}[/tex]

where:

As the focus is (3, -10), then:

[tex](h, k+p)=(3,-10)[/tex]

     [tex]\implies h = 3[/tex]

[tex]\implies k+p=-10[/tex]

As the directrix is y = 2, then:

[tex]k - p=2[/tex]

To find the value of k, sum the equations involved k and p to eliminate p:

[tex]\begin{array}{crcccr}&k &+& p& =& -10\\+&k& -& p& = &2\\\cline{2-6}&2k&&& =& -8\\\cline{2-6}\\\implies &k&&&=&-4\end{array}[/tex]

To find the value of p, substitute the found value of k into one of the equations:

[tex]-4-p=2[/tex]

        [tex]p=-4-2[/tex]

        [tex]p=-6[/tex]

Therefore, the values of h, k and p are:

The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.

The parabola has a vertex at (3, -4), has a p-value of -6 and it opens downwards.

In Mathematics, the standard form of the equation of the directrix lines for any parabola is given by this mathematical equation:

(x - h)² = 4p(y - k).

Where:

Since the directrix is horizontal, the axis of symmetry would be vertical. This ultimately implies that, we would have the following parameters;

directrix is y = 2

Focus, (h, k + p) = (3, -10)

Next, we would determine the value of k as follows;

k + p = -10     .......equation 1

k - p = 2     .......equation 2

By solving the equations simultaneously, we have:

2k = -8

k = -4

For the value of p, we have the following from equation 2:

k - p = 2

-4 - p = 2

p = -4 - 2

p = -6

In conclusion, we can logically deduce that the parabola opens downward because the p-value is negative.

Read more on parabola here: brainly.com/question/27814369

#SPJ1

Answer:

[tex]m = \frac{35 - 15}{4 - 0} = \frac{20}{4} = 5[/tex]

[tex]y = 5x + 15[/tex]

Answer:A

Step-by-step explanation:the graph shows the values that are greater than 2

The midpoint of AB is M(-4,2). If the coordinates of A are (-7,3), and the coordinates of B is (-1, 1).

To find the coordinates of point B, we can use the midpoint formula, which states that the coordinates of the midpoint between two points (A and B) can be found by averaging the corresponding coordinates.

Let's denote the coordinates of point A as (x1, y1) and the coordinates of point B as (x2, y2). The midpoint M is given as (-4, 2).

Using the midpoint formula, we can set up the following equations:

(x1 + x2) / 2 = -4

(y1 + y2) / 2 = 2

Substituting the coordinates of point A (-7, 3), we have:

(-7 + x2) / 2 = -4

(3 + y2) / 2 = 2

Simplifying the equations:

-7 + x2 = -8

3 + y2 = 4

Solving for x2 and y2:

x2 = -8 + 7 = -1

y2 = 4 - 3 = 1

Therefore, the coordinates of point B are (-1, 1).

Know more about coordinates here:

https://brainly.com/question/29765572

#SPJ8

...................................................................

Answer:

Step-by-step explanation:

the answer is 13 remaining papers

Answer:

y > Two-thirds x + 1     /c

(i) R is not reflexive, symmetric, vacuously antisymmetric, and not transitive.

(ii)  It is important that S has at least two different elements because if S had only one element, then the power set P(S) would contain only two sets: the empty set and the set S itself.  

(iii)  If S was empty, there would be no elements in S, and hence the power set P(S) would only contain the empty set. The answers regarding reflexivity, symmetry, antisymmetry, and transitivity would all change, and the relation R would not possess any of these properties. If S had only one element, the power set P(S) would contain two sets: the empty set and the singleton set containing the one element of S. The relation R would be reflexive, symmetric, antisymmetric, and transitive, as it satisfies all these properties by definition.

(i)Let's analyze the properties of relation R on P(S):

Reflexive: A relation R is reflexive if for every element x in the set S, (x, x) belongs to R. In this case, since the intersection of any set with itself is never empty, the relation R is not reflexive.

Symmetric: A relation R is symmetric if for every pair (x, y) in R, (y, x) also belongs to R. In this case, since the intersection of two sets is commutative, if (X, Y) belongs to R, then (Y, X) also belongs to R. Thus, the relation R is symmetric.

Antisymmetric: A relation R is antisymmetric if for every distinct pair (x, y) in R, (y, x) does not belong to R. Since the relation R is defined by the condition X∩Y = φ, there are no distinct pairs (X, Y) that satisfy the condition. Therefore, the relation R is vacuously antisymmetric.

Transitive: A relation R is transitive if for every three sets X, Y, and Z such that (X, Y) belongs to R and (Y, Z) belongs to R, then (X, Z) also belongs to R. In this case, if X∩Y = φ and Y∩Z = φ, it does not imply that X∩Z = φ. Hence, the relation R is not transitive.

(ii) In this scenario, the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S, because the intersection of any two non-empty subsets would never be empty. Thus, the relation R would be trivial and uninteresting.

(iii) In this case, since there are no non-empty subsets in P(S), the relation R would not have any pairs (X, Y) where X and Y are non-empty subsets of S.

In this case, the relation R would have only one possible pair (X, Y) with X and Y being the empty set, and their intersection would indeed be empty.

For more such questions on symmetry

https://brainly.com/question/20168388

#SPJ8

Answer:

37

Step-by-step explanation:

x=-4

=2(5-(-4)2+1

=2(5+4)2+1

=2(9)2+1

=18(2)+1

=36+1

=37

Answer:

[tex](y+1)^2=8(x+3)[/tex]

Step-by-step explanation:

The focus of a parabola is a fixed point located inside the curve. It is equidistant from the vertex and the directrix.

The directrix is a line that is located outside the curve. As the directrix on the given graph is a vertical line, the parabola is horizontal (sideways). The directrix is located to the left of the focus, which means the parabola opens to the right.

The axis of symmetry is perpendicular to the directrix and passes through the focus. So the axis of symmetry in this case is y = -1.

The vertex is the turning point of the parabola. It is located on the axis of symmetry, and is halfway between the focus and the directrix. Therefore, the y-coordinate of the vertex is y = -1. Given the focus is (-1, -1) and the directrix is x = -5, the vertex is (-3, -1).

The standard equation of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

As the vertex is (-3, -1), then h = -3 and k = -1.

Use the formula for the focus to find the value of p:

[tex]\begin{aligned}(h+p, k)&=(-1,-1)\\(-3+p, -1)&=(-1, -1)\\\implies -3+p&=-1\\p&=2\end{aligned}[/tex]

To write an equation for the parabola based on the given focus and directrix, substitute the values of h, k and p into the standard equation :

[tex](y-(-1))^2=4(2)(x-(-3))[/tex]

[tex](y+1)^2=8(x+3)[/tex]

Therefore, the equation of the parabola is:

[tex]\boxed{(y+1)^2=8(x+3)}[/tex]

The equation of the parabola with focus (-1, -1) and directrix x = -5 is (x + 1)² = 16(y + 1).

The equation of a parabola with a focus at (-1, -1) and a directrix of x = -5 can be written in standard form as:

(x - h)² = 4p(y - k)

Where (h, k) represents the vertex of the parabola and p is the distance between the vertex and the focus (or directrix).

In this case, the x-coordinate of the focus (-1, -1) is h = -1, and the y-coordinate is k = -1. The directrix is a vertical line x = -5, which means the parabola opens to the right.

Step 1: Determine the value of p

The distance between the vertex and the directrix is given by the absolute difference of their x-coordinates. In this case, p = |-5 - (-1)| = |-5 + 1| = 4.

Step 2: Write the equation

Substituting the values into the standard form equation, we have:

(x - h)² = 4p(y - k)

(x - (-1))² = 4(4)(y - (-1))

(x + 1)² = 16(y + 1)

Learn more on equation of parabola here;

https://brainly.com/question/4061870

#SPJ1

Answer:

x=4 explanation: I got it right

The correct combination is option a) 1 twenty, 3 tens, and 5 singles, which allows us to make change for $55 without making change for a twenty dollar bill.

The correct answer is a) 1 twenty, 3 tens, 5 singles.

To make change for $55 using exactly nine bills without making change for a twenty dollar bill, we need to avoid using any combination that includes a twenty dollar bill.

Option a) includes 1 twenty, 3 tens, and 5 singles. The total value of these bills is 20 + 3(10) + 5(1) = $55. This combination allows us to make the exact change for $55 without including a twenty dollar bill.

Option b) includes 4 tens, 2 fives, and 5 singles. The total value of these bills is 4(10) + 2(5) + 5(1) = $55. Although this combination also makes the exact change for $55, it includes four tens, which can be exchanged for a twenty dollar bill.

Option c) includes 2 twenties, 1 ten, and 6 singles. The total value of these bills is 2(20) + 10 + 6(1) = $57. This combination exceeds $55 and also includes two twenty dollar bills, making change for a twenty dollar bill.

Option d) includes 2 twenties, 2 fives, and 5 singles. The total value of these bills is 2(20) + 2(5) + 5(1) = $55. However, this combination includes two twenty dollar bills, making change for a twenty dollar bill.

For more such questions on combination

https://brainly.com/question/29595163

#SPJ8

Jerry's error is that he incorrectly assumes that the measure of angle ABC is equal to the sum of the measures of angles A and C. Hence Statement B is answer.

This is not true because angle ABC is an inscribed angle, which means its measure is half the measure of the intercepted arc.

In this case, the intercepted arc is AC. Since angle A measures 135 degrees and angle C measures 119 degrees, the sum of their measures is 254 degrees. However, angle ABC is not equal to 254 degrees.

To find the measure of angle ABC, we need to find the measure of arc AC. Since arcs A and C are equal in measure, we can find the measure of arc AC by subtracting angle A's measure (135 degrees) from the full circle measure (360 degrees).

Therefore, the measure of arc AC is 360 - 135 = 225 degrees. Since angle ABC is an inscribed angle, its measure is half the measure of arc AC, which is 225/2 = 112.5 degrees.

Hence Statement B is answer.

For more similar questions on inscribed angle

brainly.com/question/22962244

#SPJ8

Step-by-step explanation:

Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:

y = -2

Answer:

y=-2

and m=0 must be your answer

Step-by-step explanation:

as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate

so

equation of line is y-y'=m(x-x')

so m=0 m is slope

y'=-2 and x'=4

so by substituting the values

y+2=0

so y=-2

and m=0 is your answer

If 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially.

To determine how many plants to start with initially, we need to perform a series of calculations based on the information provided.

On Monday 23 plants were planted, on Tuesday 28 plants were planted and on Wednesday 29 plants were planted. If on Thursday there were a total of 90 plants, we can add all the plants planted until Thursday and then subtract them from the total to obtain the initial amount.

Adding the plants planted:

23 + 28 + 29 = 80

Then, we subtract this amount from Thursday's total:

90 - 80 = 10

Therefore, we started with 10 plants initially.

In summary, if 23 plants were planted on Monday, 28 plants on Tuesday and 29 plants on Wednesday, and 90 plants were planted on Thursday, we can determine that we started with 10 plants initially. This is obtained by adding the plants planted until Thursday and then subtracting that amount from the total for Thursday.

for more such question on initially visit

https://brainly.com/question/2228446

#SPJ8

Julio bought clothes for $5000 with a 20% down payment, which amounts to $1000. Hence, he ends up paying $4000 for the clothes.

Julio's clothing purchase involved a total cost of $5000. To secure the purchase, he made a down payment of 20% of the total cost. To calculate the down payment, we multiply the total cost by the down payment percentage:

Down payment = 20% * $5000

Down payment = 0.20 * $5000

Down payment = $1000

The down payment amount is $1000. To determine the final amount that Julio ends up paying for the clothes, we need to subtract the down payment from the total cost:

Total cost - Down payment = $5000 - $1000

Total cost - Down payment = $4000

Therefore, Julio ends up paying $4000 for the clothes.

For more such information on: down payment

https://brainly.com/question/1698287

#SPJ8

The question probable may be:

Julio bought clothes for a cost of $5000, for which he left a 20% down payment. How much money does he end up paying for the clothes?

Answer: 2,2

Step-by-step explanation:

trust me

For the data point (2, 5), the residual is 5 - 6 = -1. For the data point (3, 6), the residual is 6 - 8 = -2. For the data point (4, 11), the residual is 11 - 10 = 1. For the data point (5, 14), the residual is 14 - 12 = 2. For the data point (6, 15), the residual is 15 - 14 = 1.

To plot the residuals for the given linear function, we need to calculate the difference between the actual y-values of the data points and the corresponding predicted y-values based on the linear function.

Let's start by calculating the predicted y-values using the linear function y = 2x + 2 for each x-value in the dataset:

For x = 2, the predicted y-value is 2(2) + 2 = 6.

For x = 3, the predicted y-value is 2(3) + 2 = 8.

For x = 4, the predicted y-value is 2(4) + 2 = 10.

For x = 5, the predicted y-value is 2(5) + 2 = 12.

For x = 6, the predicted y-value is 2(6) + 2 = 14.

Now we can calculate the residuals by subtracting the predicted y-values from the actual y-values.

To visualize these residuals, we can create a scatter plot with the x-values on the horizontal axis and the residuals on the vertical axis. Each data point will represent the x-value from the dataset and its corresponding residual. The residuals can be either positive or negative, so we should include both sides of the vertical axis.

By plotting the residuals, we can observe the deviations between the actual y-values and the predicted y-values based on the linear function. This plot helps us assess how well the linear function fits the data and identify any patterns or trends in the residuals.

For more such questions on data point

https://brainly.com/question/23447356

#SPJ8

Answer:

5⁴

Step-by-step explanation:

625= 5×5×5×5

Answer:

Option C is correct.

The kind of growth model is shown in the table is exponential

Step-by-step explanation:

Exponential growth function is in the form of :    ......[1];   where a is the initial value and b> 0.

Consider any two point from the table:

(1 , 5) and ( 2 , 25)

Substitute these in the equation [1] we get;

        ......[2]

     ......[3]

Divide equation [3] by [2] we have;

Simplify:

Now substitute this value in equation [2] we get;

Divide both sides by 5 we get;

Simplify:

1=a or a = 1

Therefore, the table shown the  exponential growth function y=5^x

The total petty cash expenditures would be =$130.84

To calculate the petty cash expenditures, the following is added up as follows;

The cost for stamp = $12.50

The cost for coffee supplies = $25.19

The cost for pizza delivery = $15.50

The cost for white board markers = $20.00

The cost for sympathy greeting card= $5.78

The cost of flowers for Jean's retirement farewell = $39.87

The cost of courier = $12.00

Therefore the total petty cash expenditures would be= 12.50+25.19+15.50+20+5.78+39.87+12= $130.84

Learn more about cost price here:

https://brainly.com/question/30205161

#SPJ1

The equivalent ratio of the corresponding sides and the triangle proportionality theorem indicates that the similar triangles are;

1. ΔAJK ~ ΔSWY according to the SAS similarity postulate

2. ΔLMN ~ ΔLPQ according to the AA similarity postulate

3. ΔPQN ~ ΔLMN

LM = 12, QP = 8

4. ΔLMK~ΔLNJ

NL = 21, ML = 14

Similar triangles are triangles that have the same shape but may have different sizes.

1. The ratio of corresponding sides between the two triangles circumscribing the congruent included angle are;

24/16 = 3/2

18/12 = 3/2

The ratio of each of the two sides in the triangle ΔAJK to the corresponding sides in the triangle ΔSWY are equivalent and the included angle, therefore, the triangles ΔAJK and ΔSWY are similar according to the SAS similarity rule.

2. The ratio of the corresponding sides in each of the triangles are;

MN/LN = 8/10 = 4/5

PQ/LQ = 12/(10 + 5) = 12/15 = 4/5

The triangle proportionality theorem indicates that the side MN and PQ are parallel, therefore, the angles ∠LMN ≅ ∠LPQ and ∠LNM ≅ ∠LQP, which indicates that the triangles ΔLMN and ΔLPQ are similar according to the Angle-Angle AA similarity rule

3. The alternate interior angles theorem indicates;

Angles ∠PQN ≅ ∠LMN and ∠MLN ≅ ∠NPQ, therefore;

ΔPQN ~ ΔLMN by the AA similarity postulate

LM/QP = (x + 3)/(x - 1) = 18/12

12·x + 36 = 18·x - 18

18·x - 12·x = 36 + 18 = 54

6·x = 54

x = 54/6 = 9

LM = 9 + 3 = 12

QP = x - 1

QP = 9 - 1 = 8

4. The similar triangles are; ΔLMK and ΔLNJ

ΔLMK ~ ΔLNJ by AA similarity postulate

ML/NL = (6·x + 2)/(6·x + 2 + (x + 5)) = (6·x + 2)/((7·x + 7)

ML/NL = LK/LJ = (24 - 8)/24

(24 - 8)/24 = (6·x + 2)/((7·x + 7)

16/24 = (6·x + 2)/(7·x + 7)

16 × (7·x + 7) = 24 × (6·x + 2)

112·x + 112 = 144·x + 48

144·x - 112·x = 32·x = 112 - 48 = 64

x = 64/32 = 2

ML = 6 × 2 + 2 = 14

NL = 7 × 2 + 7 = 21

MN = 2 + 5 = 7

Learn more on similar triangles here: https://brainly.com/question/2644832

#SPJ1

Answer:

  (a)  10, $2088.81

  (b)  see attached

  (c)  B. increases at a slower rate

Step-by-step explanation:

Given the cost function g(x) = -1736.7 +1661.4·ln(x) for the average dollar cost of health insurance in year x after 2000, you want the cost in 2010, a graph for the years 2006 to 2015, and a description of the shape of the curve.

The value of x is years after 2000, so for the year 2010, the value of x is ...

  x = 2010 -2000 = 10

Substituting 10 for x in the function will give the cost in 2010. That is ...

  g(10) = -1736.7 +1661.4·ln(10) ≈ 2088.81

The cost in 2010 is about $2088.81.

The second attachment shows a graphing calculator's rendition of the graph. We note it has positive slope everywhere, but does not intersect the lines y=1000 or y=3000. This eliminates choices A, C, and D, leaving choice B for the graph.

The logarithm function has positive and decreasing slope. The function here is a scaled and shifted version of the logarithm function, but it still has positive and decreasing slope. That is, ...

 the average cost increases at a slower rate as time goes on

<95141404393>