2. Find the product (11x2 + 7x - 3)(-5x + 1).
-55x3 - 24x2 + 22x - 3

Answer:

# AB is bisected by CD

# AE = 1/2 AB

# CE + EF = FD

Step-by-step explanation:

* Lets talk about the mid point

- The mid-point of a segment is divided the segment into two

  equal parts

- The figure has line segment AB

- E is the mid-point of AB

∴ E divides the line segment AB into two equal parts

∴ AE = EB

∴ AE = 1/2 AB ⇒ (1)

- Any line passes through the point E will bisects the line segment AB

∴ AB is bisected by CD ⇒ (2)

∵ F is the mid-point of CD

∴ F divides the line segment CD into two equal parts

∴ CF = FD

∵ Point E lies on CF

∴ CE + EF = CF

∵ CF = FD

∴ CE + EF = FD ⇒ (3)

* There are three statements must be true (1) , (2) , (3)

# AB is bisected by CD

# AE = 1/2 AB

# CE + EF = FD

Answer:1,3,5

Step-by-step explanation:

In older series light strings, if a bulb burns out, the string goes dark as the circuit is broken, with each bulb operating at 3 V normally. In modern strings with short-circuiting bulbs, the rest of the lights remain lit and each bulb would then operate at approximately 3.08 V if one burns out.

When strings of holiday lights are wired in series, the entire circuit is affected if one bulb fails. In older versions, if a bulb burns out, it acts like an open switch, causing the entire string of lights to go out as the electrical circuit is broken. Each of the 40 identical bulbs in a string operating on 120 V would have a normal operating voltage of 120 V / 40 = 3 V per bulb.

In newer versions of holiday lights, where bulbs short circuit when they burn out, the string continues to operate even when one bulb fails. However, the total voltage of the string remains the same, so the voltage gets redistributed among the remaining bulbs. If one bulb out of 40 burns out, you then have 39 bulbs through which the 120 V is distributed, giving an operating voltage of 120 V / 39 ≈ 3.08 V per bulb.

Answer:

Tthe distance between the police station and the fire station  is 4 miles

Step-by-step explanation:

Let's call x the distance between the library and the police station

Let's call z the distance between the police station and the fire station

We know that:

[tex]x = 5[/tex] miles

The distance (x) between the library and the police station is 3 miles less than twice the distance (z) between the police station and the fire station

This is:

[tex]x = 2z-3[/tex]

We wish to find the distance z.

Then we equate both equations and solve for the variable z

[tex]5 = 2z -3\\\\2z = 5+3\\\\2z = 8\\\\z =\frac{8}{2}\\\\z = 4\ miles[/tex]

Answer:

c) 4 miles

Step-by-step explanation:

Answer:

The cost of one bucket of popcorn is $2.75

The cost of one drink is $1.25

Step-by-step explanation:

Let

x ----> the cost of one bucket of popcorn

y ----> the cost of one drink

we know that

5x+2y=16.25 -----> equation A

3x+y=9.50

y=9.50-3x ----> equation B

Solve the system of equations by substitution

Substitute equation B in equation A and solve for x

5x+2(9.50-3x)=16.25

5x+19-6x=16.25

6x-5x=19-16.25

x=$2.75

Find the value of y

y=9.50-3x

y=9.50-3(2.75)=$1.25

therefore

The cost of one bucket of popcorn is $2.75

The cost of one drink is $1.25

Answer:

The radius is equal to 5 inches or 12.7 cm

Step-by-step explanation:

Answer:$35.40

Step-by-step explanation:

1. $4.50 multiplied by 4 is $18

2. $2.90 multiplied by 6 is $17.4

3. $18+$17.4=$35.40

Answer:

[tex]\large\boxed{y-4=-\dfrac{8}{7}(x-4)}[/tex]

Step-by-step explanation:

The point-slope equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

We have the slope m = -8/7, and the point (4, 4). Substitute:

[tex]y-4=-\dfrac{8}{7}(x-4)[/tex]

Answer:

34

Step-by-step explanation:

Given that

2x - 7 = 9 ← solve for x

Add 7 to both sides

2x = 16 ( divide both sides by 2 )

x = 8

Substitute x = 8 into 5x - 6

5x - 6 = (5 × 8) - 6 = 40 - 6 = 34

Hello There!

WHAT WE KNOW  25 students in a class and 16 out of the 25 students in the class are girls. There are 9 boys in the class because "25-9=16"

HOW TO SOLVE If we know that 9 out of the 25 students in the class are girls, we can represent it as the fraction [tex]\frac{9}{25}[/tex]. Next, we divide 35 by 9 to get a quotient of 0.36 and then multiply by 100 to get our percent of girls in the class which is 36%

HAVE A GREAT DAY!

To find the percentage amount of girls in the class, we need to first find the amount of girls in the class.

Since 16 of the 25 students are boys, the rest must be girls. Subtract 16 from 25 to find the amount of girls in class.

25-16=9

Now, to find out what percent of 25 9 is, divide 9 by 25.

9/25= .36

The percentage of girls in the class was 36%.

Hope this helps!

Answer:

Q - [R + S] - T = 10m + 5n - 24 ⇒ 1st answer

Step-by-step explanation:

* Lets explain how to solve the problem

- The value of Q = 7m + 3n

- The value of R = 11 - 2m

- The value of S = n + 5

- The value of T = -m - 3n + 8

* To simplify Q - [R + S ] - T substitute the value of each letter in

  the expression

- Lets find R + S

∵ R = 11 - 2m

∵ S = n + 5

∴ R + S = 11 - 2m + n + 5 ⇒ coolect the like term

∴ R + S = 16 - 2m + n

∵ Q = 7m + 3n

∵ T = -m - 3n + 8

- Lets simplify the rest of the expression

- Remember (-)(-) = + and (-)(+) = -

∵ Q - [R + S] - T = (7m + 3n) - (16 - 2m + n) - (-m - 3n + 8)

∴ Q - [R + S] - T = 7m + 3n -16 + 2m - n + m + 3n - 8 ⇒ add like terms

∴ Q - [R + S] - T = (7m + 2m + m) + (3n - n + 3n) + (-16 - 8)

∴ Q - [R + S] - T = 10m + 5n - 24

Answer:

10m + 5n - 24

Step-by-step explanation:

Answer:

0.0466

Step-by-step explanation:

For a random variable X which follows a binomial distribution:

[tex]n = 7\\p = 0.35[/tex]

Thus,

[tex]P(X=5)={7\choose5}(0.35)^5(1-0.35)^{7-5}\\P(X=5)={7\choose5}(0.35)^5(0.65)^{2}\\P(X=5)=0.0466[/tex]

Final answer:

To find out how many pages Kelli will have read by day 53, we need to calculate how many pages she reads each day and add them up.

Explanation:

To find out how many pages Kelli will have read by day 53, we need to calculate how many pages she reads each day and add them up. On the first night, Kelli read 77 pages. Every day after that, she reads 35 pages more than the previous day. So each day, the number of pages she reads is increasing by 35. To find out how many pages she will have read by day 53, we can use the formula:

Total Pages Read = (First Night's Pages) + (35 * (Total Number of Days - 1))

Plugging in the values, we have:

Total Pages Read = 77 + (35 * (53 - 1))

Total Pages Read = 77 + (35 * 52)

Total Pages Read = 77 + 1820

Total Pages Read = 1897

well, Matti's house is a triangular prism, and to get the volume of it, we simply get the area of the triangle upfront and multiply by its length of 15.

[tex]\bf \stackrel{\stackrel{\textit{area of }}{\textit{triangular front}}}{\cfrac{1}{2}(7)(7)}\times \stackrel{\textit{length}}{15}\implies \cfrac{49}{2}\cdot 15\implies 367.5~ft^3[/tex]

Answer:

Option B.

Step-by-step explanation:

Volume of a green house in the backyard which in the shape of triangular prism V = (Area of base)×(Height)

In the figure attached,

Height of the triangular base = 7 ft

Base = 7 ft

Area of the triangle = [tex]\frac{1}{2}(7)(7)[/tex]

Area = [tex]\frac{49}{2}=24.5[/tex] ft²

Therefore, volume of the prism = 24.5 × 15

                                                    = 367.5 ft²

Option B. is the correct option.

Answer: The answer is no solution, since any number plugged into that equation wouldn't work out, because 1/x - 1/x cancels out itself, so therefore there is NO SOLUTION. :)

Step-by-step explanation:

Answer:

Slope tells you about the steepness of a line. It can is the ration of vertical change to horizontal change and you can solve this by using the slope formula:

[tex]m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

a. So in your case, starting from the bottom, the slope is:

[tex]m=\dfrac{8}{13}[/tex]

If you want to use coordinates, you can think of the first point (bottom of the stairs} would be at the point of origin (0,0). The next point would be at the top of the first stair 13 inches wide (horizontal or x) and 8 inches high (vertical or y)

So the coordinates of the two points would be:

(0,0) and (13, 8)

Using the formula we would have:

[tex]m=\dfrac{\triangle y}{\triangle x}=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{8-0}{13-0}=\dfrac{8}{13}[/tex]

b. Looking at the answer above, you can see that the slope with increase if the vertical change is greater, so if you increase the height of the stairs, the stair would be steeper. The opposite is true if you would increase the width.

However, if you proportionally increase the width and the height, then the slope will remain the same.

Attached is how the graph of this would look like.

Answer:

Step-by-step explanation:

In some fashion or another, the two factors are 6 and 8. But how are they put together?

-(x^2 + 2x - 48)

The 8 will be plus. That would make 2x plus. It should factor like this.

-(x + 8)(x - 6)

To check it, we should find the roots and post the graph. The graph will be upside down. That's what the minus outside the brackets  does.

x + 8= 0

x = - 8

=======

x - 6 = 0

x - 6 + 6 = 6

x = 6

I agree. It reflects A G A I N

"Reflect across the x-axis and then reflect across the y-axis" will result in an image that maps onto itself. The correct option is B.

Transformations in mathematics refer to the process of changing the position, size, or shape of a geometric figure in a coordinate plane.

When a figure is reflected across the x-axis, the y-coordinate of each point on the figure is multiplied by -1, while the x-coordinate remains unchanged.

Similarly, when a figure is reflected across the y-axis, the x-coordinate of each point on the figure is multiplied by -1, while the y-coordinate remains unchanged.

When we reflect a figure across the x-axis and then across the y-axis, we essentially multiply the x-coordinate of each point by -1 and then the y-coordinate by -1.

This corresponds to a 180-degree rotation around the origin. Because a 180-degree rotation maps a figure onto itself, this transformation will produce an image that also maps onto itself.

Thus, the correct option is B.

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Answer:

[tex]3[/tex]

Step-by-step explanation:

These [tex]3[/tex] ways are:

Answer:

11

Step-by-step explanation:

At least one means 1  being 4 or 2 of them being 4 this in case.

You could set a table:

1| 1  2  3  4  5   6

2| 1  2  3  4  5   6

3| 1  2  3   4  5   6

4| 1  2  3   4  5   6

5| 1  2  3   4   5  6

6| 1  2  3   4   5  6

There are 11 different ways to get at least one 4.

See this:

(first dice, second dice)

(1,4)

(2,4)

(3,4)

(4,4)

(4,5)

(4,6)

But there is also

(4,1)

(4,2)

(4,3)

(4,4) already counted earlier so don't count this one again

(4,5)

(4,6)

Answer:

x=-1/2

y=-1/2

-1/2-(-1/2)

0

Step-by-step explanation:

Answer:

So starting with:  

1000 ft / 5 min  

we need to convert minutes into seconds, then divide the above value into it to get knots (follow the labels so they cancel out)  

1000 ft / 5 min (1/60 min/sec) (1 kt / 1.68780986 ft/sec)  

1.974946 kt

Step-by-step explanation:

Please mark brainliest and have a great day!

The speed is the distance covered by an object at a particular time. Your speed is 200 feet per minute.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Given that you travel 1000 feet in 5 minutes. Therefore, your speed is,

Speed = 1000 feet / 5 minutes

Speed = 200 feet per minute

Hence, your speed is 200 feet per minute.

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Answer: $50 per year, y = 50x + 1200

Step-by-step explanation:

The rate of change is the slope of the two coordinates (0, 1200) & (3, 1350). Note that 2005 is represented as 0 years since the company started and 2008 represents 3 years since the company started.  

Use the slope formula: [tex]\dfrac{y_2-y_1}{x_2-x_1} = \dfrac{1350-1200}{3-0}=\dfrac{150}{3}=\$50 \text{ per year}[/tex]

To write the equation in slope-intercept form, input a point (x₁, y₁) and the slope (m) into the Point-Slope formula: y - y₁ = m(x - x₁) and solve for y

y - 1200 = 50(x - 0)

y - 1200 = 50x

          y = 50x + 1200 ; where x represents the number of years the

                                      company has been in business.

Among the options, A (h(2) = 16) is the statement that fits within the given range and domain for the function h(x) and could be true.

The statement that is true of the domain

Given:

h(8) = 19

h(-2) = 2

Domain: -3 ≤ x ≤ 11

Range: 1 ≤ h(x) ≤ 25

A. h(2) = 16 - This value doesn't conflict with the range (1 ≤ h(x) ≤ 25) and fits within the given function's range and domain. It's a possible value for h(2) based on the constraints given.

B. h(8) = 21 - This contradicts the information provided (h(8) = 19).

C. f(13) = 18 - This option refers to a value outside the domain specified for h(x).

D. h(-3) = -1 - This value is outside the range provided for h(x) as the range starts from 1.

So, among the options, A (h(2) = 16) is the statement that fits within the given range and domain for the function h(x) and could be true.

Given that a function, h, has a domain of -3≤ x≤ 11 and a range of 1≤ h(x)≤ 25 and that h(8)=19 and h(-2)=2 , select the statement that could be true for h. A h(2)=16 B. h(8)=21 C. f(13)=18 D. h(-3)=-1

Answer:

x + 5 = (x + 5) - 5, which has no solution ⇒ answer C

Step-by-step explanation:

* Lets study the situation in the problem

- Jessica is 5 years older than her sister Jenna

- After five years Jenna's age will be as old as Jessica was five years ago

- Jenna's age now is x

* Lets change all information above to equation

∵ Janna's age now is x

∵ Jessica is 5 years old than Janna

∴ The age of Jessica now is x + 5

- After 5 years Janna's age will be add by 5 years

∵ Her age now is x

∴ Her age after 5 years will be x + 5

- From 5 years ago Jessica's age was her age now mins 5 years

∵ Her age now is x + 5

∴ Her age from 5 years ago is (x + 5) - 5

∵ Janna's age after 5 years = Jessica age from 5 years ago

∴ x + 5 = (x + 5) - 5

- Lets solve the equation to know how many solution

∵ x + 5 = x + 5 - 5 ⇒ add the like terms

∴ x + 5 = x ⇒ subtract x from both sides

∴ 5 = 0

- But 5 ≠ 0, the two sides of the equation not equal each other

∴ There is no solution for this equation

* The equation is x + 5 = (x + 5) - 5, which has no solution

Answer:

C x + 5 =(5 - x) - 5

Step-by-step explanation:

Step-by-step explanation:

7q + 3 or 7q+5 or 7q + 6

solve for q

7q + 3 =

7q + 3 -3 =-3

7q = -3

7q/7 = -3/7

q = -3/7

7q + 3 =

7q + 6 -6 =-6

7q = -6

7q/7 = -6/7

q = -6/7

Answer:

(f+g)(x)= 3x^2 -2x-1

Step-by-step explanation:

f(x) = -4x+3

g(x) = 3x^2+2x-4

(f+g)(x)= -4x+3 +3x^2+2x-4

Combine like terms

(f+g)(x)= 3x^2 -2x-1

Answer:

7

Step-by-step explanation:

4[tex]\frac{2}{3}[/tex] can be written as [tex]\frac{14}{3}[/tex]

number of [tex]\frac{2}{3}[/tex] portions = [tex]\frac{14}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]

= [tex]\frac{14}{3}[/tex] x  [tex]\frac{3}{2}[/tex]

= [tex]\frac{14}{2}[/tex] = 7

Lily can get 7 portions of 2/3 ounces each from the 4 2/3 ounces of saffron she bought at the Union Market.

To calculate the number of 2/3 ounce portions that Lily can get from the 4 2/3 ounces of saffron she bought, we need to divide the total weight of saffron by the weight per portion. We can convert 4 2/3 to an improper fraction, which becomes 14/3. Next, we divide 14/3 by 2/3 to get the number of portions. Dividing fractions involves multiplying the first fraction by the reciprocal of the second. So, 14/3 ÷ 2/3 = 14/3 * 3/2 = (14 * 3) / (3 * 2) = 42/6 = 7 portions.

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Answer:

Option B (-sin 30°)

Step-by-step explanation:

Sine function is one of the trigonometric functions. Sine function is regarded as an odd function, which means that f(-x) = - f(x). Also, sine function is positive in the first two quadrants and negative in the last two quadrants. 210° lies in the third quadrant since 210° is greater than 180°. Therefore, the basic angle or the reference angle of 210° is 210° - 180° = 30°. We already know that sin 30° = 0.5. This means that whenever the angle is between 180° and 360°, the output of the sine function is negative. Therefore, sin 210° = -0.5. Only answer B is the correct option since -sin 30° = -0.5.

For this case we have a function of the form [tex]y = f (x).[/tex]

Where:

[tex]f (x) = 2x ^ 2 + 3x + 5[/tex]

They tell us that the function has a value of 19, and we want to know the values of the input, that is:

[tex]2x ^ 2 + 3x + 5 = 19\\2x ^ 2 + 3x + 5-19 = 0\\2x ^ 2 + 3x-14 = 0[/tex]

We apply the formula of the resolvent:

[tex]a = 2\\b = 3\\c = -14[/tex]

[tex]x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\x = \frac {-3 \pm \sqrt {3 ^ 2-4 (2) (- 14)}} {2 (2)}\\x = \frac {-3 \pm \sqrt {9 + 112}} {4}\\x = \frac {-3 \pm \sqrt {121}} {4}\\x = \frac {-3 \pm11} {4}[/tex]

We have two roots:

[tex]x_ {1} = \frac {-3 + 11} {4} = \frac {8} {4} = 2\\x_ {2} = \frac {-3-11} {4} = \frac {-14} {4} = - \frac {7} {2}[/tex]

Answer:

The inputs of the function [tex]y = 19[/tex]are:

[tex]x_ {1} = 2\\x_ {2} = - \frac {7} {2}[/tex]

Answer:

The area is  522.935 square inches.

Step-by-step explanation:

A trapezoid's area is calculated as follows: h(b1+b2)/2

Plugging numbers in gives 34.3+12.6=46.9

so now all that's left is to multiply 22.3 and 46.9, and divide by 2.

This gives 522.935

Hope this helps!

Answer:

522.935 square inches

Step-by-step explanation:

OPTION 1:

First, the area of the rectangle in the center is 12.6*22.3 (w*l or b*h), or 280.92

Second, the area of the two triangles on the side are right triangles since we made a rectangle in the center, so the area of that is (base2 - base1)*h*1/2, or (34.3-12.6)*22.3*1/2=21.7*22.3*1/2=483.91*1/2=241.955

Therefore, the area is 280.98+241.955 or 522.935 square inches

OPTION 2:

Using the formula to find the area of a trapezoid, you would do ((base1 + base2)/2)*h, or ((12.6+34.3)/2)*22.3 which is 522.935 square inches