Please help with the unfilled spots! :)

The x-intercepts of the quadratic function g(x) = x² - 10x + 24 are given as follows:

(4, 0) and (6, 0).

A function crosses the x-axis when the numeric value of the function is of y = 0, hence these points are called the x-intercepts of the function.

In this problem, the definition of the function is given as follows:

g(x) = x² - 10x + 24.

This function can be simplified as follows:

g(x) = (x - 6)(x - 4).

Applying the inverse of the Factor Theorem, the x-intercepts are given as follows:

Hence the x-intercepts of the function are given by the third option, which is of (4, 0) and (6, 0).

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Answer: C

Step-by-step explanation: trust me

Answer:

Step-by-step explanation:

dees

The equation of the graph in point slope form is y + 2 = -3(x - 1)

The equation of the graph in point slope form can be represented as follows;

y - y₁ = m(x - x₁)

where

using two point let's find the slope

(0, 1)(-1, 4)

Hence,

m = 4 - 1 / -1 - 0

m = 3 / -1

m = -3

Therefore, the slope of the line is - 3.

Therefore, using one coordinates(1, -2) from the graph, the equation of the graph in point slope form is y + 2 = -3(x - 1)

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Answer:get a tutor

Step-by-step explanation:

its free

An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

Given that;

The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,

Let 'T' be the number of times the price is decreased.

So, price;

     p = 38 – 5x

     x = (38 - p) / 5

And as per the given condition attendance;

a = 1000 + 50x

So, the Revenue is;

To develop an equation for revenue (r) as a function of p, the price of tickets;

R = p * a

R= p * (1000 + 50x)

But,  x = (38 - p) / 5

Then,

R = P * (1000 + 50(38 - p)/5)

  = p * (1000 + 380 - 10p)

  = p * (1380 – 10p)

  = 1380p - 10p²  → (I)

To get R(25) from (I);

R(25) = 1380(25) - 10(25)²

         = 34500 - 6250

         = 28250

Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,

and R(25) = 28250.

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Answer:

r ≤ -21.75

Step-by-step explanation:

Forming the equation,

→ r ÷ (-2.5) ≤ 8.7

Then the value of r will be,

→ r ÷ (-2.5) ≤ 8.7

→ r ≤ 8.7 × (-2.5)

→ r ≤ -21.75

Hence, value of r is -21.75.

Answer: $5.14

Step-by-step explanation:

divide $539.70 by 105 to get the answer

so 539.70 divide by 105 is 5.14

step1 get rid of the decimal but you will ad it later so

53970

/   105

=514

step2 move the decimal 2 places to the left.

There are 39% of all the people on the trip are female students on a school trip.

One to fifteen teachers are assigned to every hundred students.

and there are 7:5 more female students than male students.

Let's say there are x teachers. Students multiply by 15 as a result.

Take the ratio of male to female as 7 years for the male and 5 years for the female.

The total student trip is made up of both male and female pupils.

Thus,

15x = 7y + 5y

15x = 12y

5x = 4y

x = 4/5y  ...eq 1

Then, the percentage of the female students.

5y/(x + 5x)×100

5y/16x ×100

Put the value of x from eq 1

625/ 16 = 39%

Thus, there are 39% of all the people on the trip are female students.

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The equation 22+(d-1)0.5 = 30 may be used to determine how many days it will take the plant to reach a height of 30 cm. The value of d is 17, and it stands for the number of days.

There are two definitions for an arithmetic sequence. It is a series where the differences between every two succeeding terms are identical or each term in an arithmetic sequence is formed by adding a fixed number (positive, negative, or zero) to its preceding term.

The following details are available to us:

A 22 cm tall basil plant that is gaining half a centimeter daily was purchased by Matteo.

We now have the arithmetic progression shown below with the common difference, indicated by the letter d:

22, 22.5, 23, 23.5, ...

The formula for calculating the nth term:

When an is the first term, a(n) = a+(n-1)d.

A) 22+(d-1)0.5 = 30

B) The plant still needs to develop 8 cm, as there is a difference of 8 cm between 30 and 22.

C) D's value:

22+(d-1)0.5 = 30

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Formula of parabola for given values is F(x) = 7.5(x^2-15.7x+61.32)

The general equation of a parabola in math is: y = a(x-h)^2 + k ,where (h,k) denotes the vertex. The standard equation of a the parabola is y^2 = 4ax.

We have, horizontal intercepts x=8.4 and x=7.3, passes through point(0, 8.2)

As we parabola is quadratic function,

f(x) = a(x-8.4)(x-7.3)

It is passing through the point (0, 8.2)

8.2 = a(-8.4)(-7.3)

a = 8.2/61.32 =7.5 (approx)

Now, equation of parabola is

F(x) = 7.5(x-8.4)(x-7.3)

f(x) = 7.5(x^2-7.3x-8.4x+61.32)

F(x) = 7.5(x^2-15.7x+61.32)

Thus, required equation of parabola is F(x) = 7.5(x^2-15.7x+61.32).

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A minimum of 3 weighings are required to identify the heavy marble out of 8 marbles.

As all the marbles weigh the same except one which is heavier, therefore firstly 8 marbles are divided into half. 4 marbles are placed in one pan while the other 4 are placed in another pan. In this two-pan balance, the pan which is lower than the other contains a heavier marble.

Now, the pan with heavier marble has 4 marbles which are again divided into half. 2 marbles are placed in each pan. Similarly, the pan with heavier marble goes down as compared to another pan with 2 marbles of the same weight. Now the final weighing is done by placing 1 marble in each pan out of 2 marbles taken from the pan which went down before as compared to another pan.

The pan with heavier marble will move down and thus with 3 weighings, a heavier marble is identified.

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Answer:

$2.34

Step-by-step explanation:

2.75 x 0.85 = $2.3375

Since we are rounding, it will round up to $2.34.

Answer:

Step-by-step explanation:

Cost of 2.75 pounds of potato =.

2.75x0.85

 = $2.3375

The height of utility poles is B. 12 meters.

The height of the utility pole will be calculated by the formula -

tan theta = perpendicular ÷ base, where theta is the angle of elevation, perpendicular is the height of utility pole and base is the distance from the base of pole to the wire.

Keep the values in formula to find the height of utility pole.

tan 59 = perpendicular ÷ 7

Perpendicular = tan 59 × 7

Perpendicular = 1.66 × 7

Performing multiplication on Right Hand Side of the equation

Perpendicular = 11.65 metres

On rounding off, we get 12 metres.

Thus, the height is B. 12 meters.

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The length of the shorter leg is 16 units which was found using the given data.

A quadratic equation is a second-degree algebraic equation in x. In its usual form, the quadratic equation is ax² + bx + c = 0.

Given: The larger leg of a right triangle is twice more than three times the shorter leg, and the triangle's area is 400.

We know that,

Area of triangle = 1/2(larger leg)(shorter leg)

                  400=1/2(larger leg)(shorter leg)   Equation(1)

larger leg = 2 + 3(shorter leg)

We need to substitute this in Equation(1)

400 = 1/2[2+3(shorter leg)](shorter leg)

800 = 2(shorter leg) + 3(shorter leg)²

3(shorter leg)² + 2(shorter leg) - 800 = 0

Solving this quadratic equation,

we get, shorter leg = - 16 or +16

Thus, we found that the length of the shorter leg is 16 units as -16 cannot be the length because it is negative.

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The measures, using the normal distribution, are given as follow:

a) Probability that a wedding costs less than $20,000: 0.257 = 25.70%.

b) Probability that a wedding costs between $20,000 and $32,000: 0.659 = 65.90%.

c) Minimum cost of the most expensive 5% of weddings:  $33,564

Normal Probability Distribution

The z-score of a measure X of a variable that has to mean symbolized by  and standard deviation symbolized by  is given by the rule presented as follows:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

The z-score represents how many standard deviations measure X is above or below the mean of the distribution, depending if the calculated z-score is positive or negative.

Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of measure X in the distribution.

The mean and the standard deviation for the wedding prices are given as follows:

μ = 23858, σ = 5900

a) The probability that a wedding costs less than $20,000 is the p-value of Z when X = 20000, hence:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z = (20000 - 23858)/5900

Z = -0.65

Z = -0.65 has a p-value of 0.257.

The probability that it costs between $20,000 and $32,000 is the p-value of Z when X = 32000 subtracted by the p-value of Z when X = 20000, found above, hence:

[tex]Z=\frac{X-\mu}{\sigma}[/tex]

Z = (32000 - 23858)/5900

Z = 1.38

Z = 1.38 has a p-value of 0.816.

0.916 - 0.257 = 0.659.

The minimum cost for a wedding to be in the most expensive 5% of weddings is the 95th percentile, which is X when Z = 1.645, hence:

1.645 = (X - 23858)/5900

X - 23858 = 1.645 x 5900

X = $33,564.

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Answer:

$6.72

Step-by-step explanation:

1 us liquid pint =2 us cups

3.36*2 cups

Answer:

ii think that the figure will be determined by 13#

Step-by-step explanation:

you have to round up to the nearest meter

Answer:

Step-by-step explanation:

Get the same denominator by multiplying 4/9 by 2/2 and 1/2 by 9/9 to get 8/18-9/18=-1/18

The two negative signs can become an addition to make -1/9+2/5 which can be rewritten as 2/5-1/9. We make them the same denominator and subtract to get 13/45.

Answer:

324 ft

Step-by-step explanation:

[tex]v=\sqrt{2gh}[/tex]

[tex]v^2=(\sqrt{2gh})^2[/tex]

[tex]v^2=2gh[/tex]

[tex]\frac{v^2}{2g}=\frac{2gh}{2g}[/tex]

[tex]\frac{v^2}{2g}=h[/tex]

[tex]\frac{144^2}{2(32)}=h[/tex]

[tex]\frac{20736}{64}=h[/tex]

[tex]324=h[/tex]

The interior angle and the exterior angle of triangle XYZ is 68° and 112° respectively.

A triangle is a plane shape that has three sides.

Recall that, the sum of a interior angle and an exterior angle of a triangle is 180°.

Using the formula,

Where:

From the question,

Given:

Substitute these values into equation 1

Solve for g

Hence, interior angle of X = (5×10)+18 = 50+18 = 68° and exterior angle of X = (8×10)+32 = 80+32 = 112°

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Answer: I belive the answer is A

Step-by-step explanation: i could be wrong

Answer:

A = Ao * (1+ i)^n       amount Ao invested for n yrs at i/yr

14900 = 4500 (1.07)^n

3.311 = (1.07)^n

log 3.311 = n log 1.07 = n* .0294

n = log 3.311 / .0294 = .52 / .0294 = 17.6 yrs

Check:

Money will double about very 70 / 7 = 10 yrs

At 10 yrs around 9000 return

At 20 yrs 18,000 return - result appears reasonable

Answer:

XY = 12.4 cm

Step-by-step explanation:

a² + b² = c²

(4 cm)² + (XY)² = (13 cm)²

16 cm² + XY² = 169 cm²

XY² = 153 cm²

XY = √(153 cm²)

XY = 12.4 cm

The algebra properties associated to each case are listed below:

Case 1: Distributive property

Case 3: Associative property (multiplication)

Case 5: Existence of inverse (addition)

In this question we find three algebraic expressions, in which we need to determine what algebra property is used. The most important properties in real algebra are listed below:

Now we proceed to determine the property associated to corresponding operation:

Case 1

9 · (x + y) = 9 · x + 9 · y → Distributive property

Case 3

[8 · (3 / 2)] · 15 = 8 · [(3 / 2) · 15] → Associative property (multiplication)

Case 5

(6 · x + 1) + (- 6 · x + 1) = 0 → Existence of inverse (addition)

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By using tangent property of circle, it has been proved that [tex]\Delta[/tex] ABC is isosceles

What is tangent to a circle?

At first it is important to know about circle.

Circle is a two dimensional round figure in which every point of the circle maintains a fixed distance from a point known as the center. The fixed distance is called the radius of the circle.

The straight line which touches the circle at any point is known as the tangent to a circle.

Tangent property of circle is used here

[tex]\angle BAY = 72^{\circ}[/tex]

[tex]\angle ABC = 54^{\circ}[/tex]

[tex]\angle ACB = 72^{\circ}[/tex] [Angle in alternate segment are equal]

[tex]\angle BAC = 180 - (54 + 72)\\[/tex] [Sum of three angles of a triangle is 180°

          =   180 - 126

          =   54°

[tex]\Delta ABC[/tex] is isosceles

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The measure of the angle ACB is 87°.

Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.

An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.

When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.

In triangle ADE and triangle ACB, the triangles are similar.

So,

∠AED/ ∠ABC = ∠DAE/∠CAB

∠AED = ∠ABC

11x-2 = 6x + 13

11x - 6x = 13 + 2

5x = 15

x = 15/5

x = 3

So, the measure of angle ABC is

∠ ABC = 6(3)+13

∠ ABC = 18+13

∠ ABC  = 31°

Now, consider triangle ABC, the sum of all angles = 180°

So, 62° + 31° + ∠ACB = 180°

∠ACB + 93° = 180°

∠ACB =  180° - 93°

∠ACB = 87°

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250 bicycles must be manufactured to minimize the cost.

The cost C in dollar of manufacturing x bicycles at a production plant is given by:

C(x) = 3x² - 1500x + 198,500

a. To find number of bicycle that can minimize the cost

differentiate C(x) with respect to x

C'(x) = 6x - 1500

equating C'(x) = 0

6x - 1500 = 0

x = 1500/6

x = 250 , is our stationary point

Differentiate C'(x) = 6x - 1500 again and put x = 250,

C''(x) = 6 (positive)

At x = 250 , cost is minimum

Therefore , 250 bicycles must be manufactured to minimize the cost.

b. C(x) = 3x² - 1500x + 198,500

putting x = 250,

C(x) = 3(250)² - 1500(250) + 198,500
= 187,500 - 375 ,000 + 198,500

= $11,000 is the minimum cost

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Answer:

Step-by-step explanation:

28xy

Answer:

a. 87 b. 9 c. 4

Step-by-step explanation: