Find the midpoint of the segment with the following endpoints.
(4,2) and (1,8)

Answer:

One is 3x+2 while the other is 2x-1

Step-by-step explanation:

It is opposite to one another

the one with 3x+2 is opposite to the non given one and the one withb2x-1 is opposite

The line itself is not included in the solution. So, the line is a broken line and not a continuous line.

What is inequality?

In arithmetic, the relationship between 2 values that don't seem to be equal is outlined by inequalities. difference means that not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”

Given:

The inequality to graph is given as:

y ≤ -1/3x+2

In order to graph it, we first graph the line. So, we replace the inequality sign by equal to sign. This gives,

y = -1/3x+2

Now, let x = 0. So, the value of 'y' is given as:

y = 2

A point on the line is (0, 2)

Now, let y = 0 . So, the value of 'x' is given as:

0 = -1/3x+2

x = 6

Another point on the line is (6, 0).

Now, mark the points on the graph and draw a line passing through these two points.

Now, we consider the inequality .

y ≤ -1/3x+2

As 'y' is less than -1/3x+2 , so the solution region is the region below the line as shown in the graph below.

Also, the line itself is not included in the solution.

Hence, the line is a broken line and not a continuous line.

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The probability that the card will be a spade or a club 50%

Probability in math is referred as  how likely an event is to occur, or how likely it is that a proposition is true.

Here we have given that a card is drawn from a standard deck of 52 playing cards.

And we need to find  the probability that the card will be a spade or a club and we have to express your answer as a fraction or a decimal number rounded to four decimal places.

While we looking into the given question, we have identified the the total number of cards is 52.

And the number of spade cards = 13 and the number of club cards = 13

Therefore, the total number of spade and club cards

=> 13 + 13

=> 26

Therefore, the probability of getting a spade or  a club from a single draw is,

=> 26/52

When we simplified this one, then we get,

=> 0.5

When we convert this into percentage then we get

=> 50%.

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Answer:

y = 60 - 10x

Step-by-step explanation:

Sorry for the delay, I was answering before I had to go, but anyways.

Jackson right now has 60 dollars. He spends 10 dollars per day.

Assuming that the y will be his remaining money, and x will be per day, the equation will be y = 60 - 10x.

The value of the sides are;

FG = 4. 06

EF = 6. 59

<E = 38 degrees

From the information given, we have;

Using the tangent identity;

tan 52 = 5.2/FG

cross multiply the values, we have;

FG = 4. 06

Then,

using the sine identity, we have;

sin 52 = 5.2/EF

cross multiply the values, we get;

EF = 6. 59

To determine the angle E, we have;

sin E = 4.06/6. 59

Divide the values

sin E = 0. 6160

E = 38 degrees

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Answer:

We need to find the value of f(g(10)) when k = 3, where f(x) = 6x - 2 and g(x) = 5x - kx + 15.

First, we need to evaluate g(10) when k = 3:

g(x) = 5x - kx + 15

g(10) = 5(10) - 3(10) + 15

g(10) = 50 - 30 + 15

g(10) = 35

Now that we know g(10) = 35, we can evaluate f(g(10)):

f(x) = 6x - 2

f(g(10)) = 6(35) - 2

f(g(10)) = 208

Therefore, when k = 3, f(g(10)) = 208.

The 1st Quartile germination rate is 92%, the 1st Quartile germination rate represents the threshold below which 25% of the germination rates fall.

To determine this, we need to arrange the germination rates in ascending order and find the value that corresponds to the 25th percentile.

In this case, we have a packet of 160 seeds with 95% germination rate. To find the 1st Quartile germination rate, we need to consider the germination rates of the remaining 5% of seeds that did not germinate.

Since 92% is the claimed germination rate mentioned on the seed packet, we can assume that the 5% of seeds that did not germinate fall below this claimed rate. Therefore, the 1st Quartile germination rate is 92%.

The 1st Quartile, also known as the lower quartile or 25th percentile, divides a dataset into four equal parts. It represents the threshold below which 25% of the data points fall.

In this scenario, we have a packet of 160 seeds with a 95% germination rate. This means that 95% of the seeds successfully germinated. To find the 1st Quartile germination rate, we need to consider the remaining 5% of seeds that did not germinate.

Since the information on the seed packet claims a germination rate of 92%, we can assume that the 5% of seeds that did not germinate fall below this claimed rate.

As a result, the 1st Quartile germination rate is 92%. This indicates that 25% of the seeds in the packet had a germination rate below 92% while the remaining 75% had a germination rate equal to or higher than 92%.

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Answer:

x=-12        x =2

Step-by-step explanation:

-x^2-10x+24=0

Divide by -1

x^2 +10x -24 = 0

Factor

What 2 terms multiply to -24 and add to 10

12 * -2 = -24

12 -2 = 10

(x+12) ( x-2) = 0

Using the zero product property

x+12 =0    x-2 =0

x=-12        x =2

The cylindrical coordinates of (−7, 7, 7) are (√98, -π/4, 7). cylindrical coordinate (−7, 7 3 , 1) is  (14, -π/3, 1).

We must switch from rectangular to cylindrical coordinates in the provided problem. (let r ≥ 0 and 0 ≤ θ ≤ 2π.)

A)(−7, 7, 7)

Given rectangular coordinates(x, y, z) =(−7, 7, 7)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²+(7)²

r = √49+49

r = √98

θ = tan⁻¹ (y/x)

θ =tan⁻¹  (7/-7)

θ =tan⁻¹  (-1)

θ = -π/4

So cylindrical coordinate = (r, θ, z) = (√98, -π/4, 7)

B) (-7,7√3,1)

Given rectangular coordinates(x, y, z) = (-1,1,1)

The cylindrical coordinates are (r, θ, z)

As a result, we determine each value of r and θ  separately.

r = √x²+y²

r = √(-7)²(7√3)²

r = √49+147

r = √196

r = 14

θ = (y/x)

θ = (7√3/-7)

θ = (-√3)

θ = -π/3

So cylindrical coordinate = (r, θ, z) = (14, -π/3, 1)

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The required ratio of trombones to all the brass section members is 3 : 7.

The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.

Here,
The total number of members in the brass section of the jazz band is:

4 trumpets + 3 trombones = 7 members

The ratio of trombones to all the brass section members can be expressed as,

= 3 trombones / 7 brass section members

This ratio cannot be simplified further because the numbers are relatively prime.

Therefore, the ratio of trombones to all the brass section members is 3 : 7.

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Answer:

3 and -2

Step-by-step explanation:

3+(-2) = 1

3*(-2) = -6

Answer:

3  and -2

Step-by-step explanation:

Answer:

104

Step-by-step explanation:

5 to 4 equals 9

divide 234 by 9 and you get 26

26 times 5 is 130

and 26 times 4 is 104

so 130 to 104 adding up gives you 234

and the number of women employees would be 104

Answer:

17 160 inches

Step-by-step explanation:

Area = width x length

so 165 x 104 which is 17 160

Therefore, the area of the rectangle is 17 160 inches

hope this helps, give brainliest?

Answer:

y = 1/6

Step-by-step explanation:

6y - 5 = (2y + 1)

move the parentheses

6y - 5 = 6y - 3

move the terms

6y + 6y = -3 + 5

collect like terms and calculate

12y = 2

divide both sides

answer:

y = 1/6

The proofing that ABCD is a parallelogram can be done through the parallelogram side theorem.

To prove the Parallelogram Side Theorem, which states that in a parallelogram ABCD, the opposite sides are congruent, we need to show that AB = CD and BC = DA.

Given:

ABCD is a parallelogram.

Proof:

To prove AB = CD and BC = DA, we will use the properties of parallelograms.

Opposite sides of a parallelogram are parallel:

In parallelogram ABCD, we know that AB is parallel to CD and AD is parallel to BC.

Corresponding angles of parallel lines are congruent:

Since AB is parallel to CD, we can conclude that angle ABC is congruent to angle CDA (corresponding angles).

Opposite angles of a parallelogram are congruent:

In parallelogram ABCD, we know that angle ABC is congruent to angle CDA (proved in step 2). Similarly, angle BCD is congruent to angle DAB (opposite angles).

Triangle congruence:

By applying the Angle-Side-Angle (ASA) congruence criterion, we can prove that triangles ABC and CDA are congruent.

Angle ABC ≅ Angle CDA (proved in step 2)

Side AB ≅ Side CD (corresponding sides of congruent triangles)

Angle BCA ≅ Angle DAC (proved in step 3)

Corresponding sides of congruent triangles are congruent:

In triangles ABC and CDA (proved in step 4), we have AB ≅ CD (corresponding sides).

Repeating the same logic for the other pair of opposite sides:

By following a similar reasoning, we can prove that BC ≅ DA.

Therefore, we have successfully proved the Parallelogram Side Theorem, which states that in a parallelogram ABCD, the opposite sides AB and CD are congruent, and the opposite sides BC and DA are congruent.

This completes the proof.

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Answer:

5.75

Step-by-step explanation:

hope this helps :)

a.  the unit vector in the direction of steepest ascent at P is (1/sqrt(233))[-8, -13].

b.  A vector that points in the direction of no change in the function at P is [x, y] = [13, -8].

The given function is f(x, y) = 4x^4 - 3x^2y + 5y^2 + 5, and the point is P(-1, 1).

a. Unit vectors that give the direction of steepest ascent and steepest descent at P:

The gradient of the given function is given by:

gradient f(x, y) = [8x^3 - 3xy, -3x^2 + 10y]

Substituting the coordinates of P(-1, 1), we get:

gradient f(-1, 1) = [-8, -13]

To find the unit vector in the direction of steepest ascent at P, we normalize the gradient vector by dividing it by its magnitude:

|gradient f(-1, 1)| = sqrt((-8)^2 + (-13)^2) = sqrt(233)

The unit vector in the direction of the gradient vector is given by:

(1/sqrt(233))[-8, -13]

Therefore, the unit vector in the direction of steepest ascent at P is (1/sqrt(233))[-8, -13].

b. Vector that points in the direction of no change in the function at P:

The direction that gives no change in the function is perpendicular to the gradient vector. Thus, it is a vector that is orthogonal to [-8, -13].

Let the vector that is orthogonal to [-8, -13] be [x, y]. Since the dot product of orthogonal vectors is zero, we have:

[-8, -13] · [x, y] = 0

-8x - 13y = 0

y = -(8/13)x

Therefore, a vector that points in the direction of no change in the function at P is [x, y] = [13, -8].

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The graph at the bottom left shows the new function.

Observe that the initial provided graph corresponds to the equation:

\(y = 2x + 1\)

As the line exhibits a slope of 2/1, equivalent to 2, and the y-intercept is situated at the point (0, 1).

Now, if we were to alter the equation by multiplying the existing slope by 1/2, and simultaneously increasing the y-intercept by 3 units, the resulting function would be:

\(y = x + 4\)

This represents a line with a slope of 1 and a y-intercept located at (0, 4).

Take note that the graph depicted in the lower-left section among the available options accurately illustrates such a function.

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Answer:

Step-by-step explanation:

The figure has 5 sides. Therefore the formula to solve it is (n - 2)*180

(5 - 2)*180 = 3*180 = 540

That is the total of the interior angles so

x + 86 + 140 + 138 + 59 = 540

x + 423 = 540                            Subtract 423 from both sides

x = 540 - 423

x = 117

Answer:b is the answer

Step-by-step explanation:

Answer:

24.52

Step-by-step explanation:

Pythagorean Theorem

a^2 + b^2 = c^2

24^2 + 5^2 = 601

Square root 601 = 24.52

Answer:

49°

Step-by-step explanation:

106 + 135 + 70 + x = 360

311 + x = 360

x = 49°

Answer:

8

Step-by-step explanation:

note that 33 \(\frac{1}{3}\)% = \(\frac{1}{3}\) as an exact fraction, then

66 \(\frac{2}{3}\) = 2 × 33 \(\frac{1}{3}\) = 2 × \(\frac{1}{3}\) = \(\frac{2}{3}\) as an exact fraction

Then

66 \(\frac{2}{3}\) of 12

= \(\frac{2}{3}\) × 12 = 2 × 4 = 8

\(66 \frac{2}{ 3 } \% = > \frac{200}{3} \div 100 = > \frac{200}{300} = > \frac{2}{3} \)

\( = > \frac{2}{3} x = 12\)

\( = > x = \frac{3 \times 12}{2} = 3 \times 6 = 18\)

Answer:

B

Step-by-step explanation:

Answer:

it's asking how do you know this lengths are congruent.

since those lines are congruent I'll come to the conclusion that's it could be b as well

Step-by-step explanation:

b

Answer:

Step-by-step explanation:

Draw a picture.

c and b are Malaya’s distance from the courthouse and bank, respectively.

tan(72°) = c/90

c = 90tan(72°)

tan(35°) = b/54

b = 54tan(35°)

Distance between courthouse and bank = c+b

= 90tan(72°) + 54tan(35°)

= 301.5 ft

The best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day, option C is correct.

On Day 1, the total value of the 30 shares of Metropolis stock is:

30 shares x $17.95 per share = $538.50

And the total value of the 55 shares of Suburbia stock is:

55 shares x $5.63 per share = $309.65

So the total value of both stocks on Day 1 is:

$538.50 + $309.65 = $848.15

On Day 2, the total value of the shares of Metropolis stock is:

30 shares x $18.28 per share = $548.40

And the total value of the shares of Suburbia stock is:

55 shares x $5.88 per share = $323.40

The total value of both stocks on Day 2 is: $871.8

for Day 3, total value of both stocks on Day 3 is $$821.40

Therefore, we can see that the best day to sell both stocks is Day 2, since the total value of both stocks is highest on that day:

$871.80 - $848.15 = $23.65

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The x-intercepts of a quadratic function are the points where the function graph intersects the x-axis. To find the x-intercepts of the given quadratic function, we need to determine the values of x when the y-value (or the function value) is equal to 0.

From the given information, we can see that the quadratic function passes through the points (-2, 0) and (1, 0), which indicates that the function intersects the x-axis at x = -2 and x = 1. Therefore, the quadratic function x-intercepts are (-2, 0) and (1, 0).

The correct answers are (d) (-2, 0) and (1, 0).

Answer:

One half times the difference of twenty and a variable is two thirds

one half times the quantity y minus 20 equals two thirds

one half times the quantity 20 minus y equals two thirds

one half times y minus 20 equals two thirds

one half times 20 minus y equals two thirds

0.5(20 - y) = 2/3

One half times the difference of twenty and a variable is two thirds :
1/2(20 - y) = 2/3
[this one im not too sure, please confirm it cause i don't think it is clear enough]

One half times the quantity y minus 20 equals two thirds :
1/2(y - 20) = 2/3

One half times the quantity 20 minus y equals two thirds :
1/2(20 - y) = 2/3

One half times y minus 20 equals two thirds :
1/2 x y - 20 = 2/3

One half times 20 minus y equals two thirds :
1/2 x 20 - y = 2/3

Answer:

To calculate Alan's profit percentage, we need to first find his total cost and total revenue.

Total cost:

Alan pays £2.25 for 1.2 kg of sweets, which is equivalent to 1200 g of sweets. Therefore, the cost per gram of sweets is:

Cost per gram = £2.25 ÷ 1200 g = £0.001875/g

Alan puts 150 g of sweets in each bag, so the cost of sweets per bag is:

Cost per bag = 150 g × £0.001875/g = £0.28125

To find the total cost, we divide the total weight of sweets by the weight of sweets in each bag and multiply by the cost per bag:

Total cost = (1.2 kg ÷ 150 g) × £0.28125 = £2.25

Total revenue:

Alan sells each bag of sweets for 30p, so the total revenue is:

Total revenue = (1.2 kg ÷ 150 g) × £0.30 = £2.40

Profit:

To find Alan's profit, we subtract the total cost from the total revenue:

Profit = £2.40 - £2.25 = £0.15

Profit percentage:

To calculate the profit percentage, we divide the profit by the total cost and multiply by 100:

Profit percentage = (Profit ÷ Total cost) × 100%

= (£0.15 ÷ £2.25) × 100%

= 6.67%

Therefore, Alan's percentage profit is 6.67%.