prove that angle abc is a right angle with vertices a(-4,3), B(0,-1) and C(2,1)​

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]

The formula for finding the midpoint of a line segment is[tex](\frac{x1+x2}{2}, \frac{y1+y2}{2})[/tex].  Plug in and solve:

[tex](\frac{2-3}{2} , \frac{3-2}{2})[/tex]

(-1/2, 1/2)

(-0.5, 0.5)

Hope this helps!!

The midpoint of the segment is (-0.5, 0.5)

The midpoint of a line segment is a point that lies halfway between 2 points. The midpoint is the same distance from each endpoint.

Given points: (2, 3) and (-3.-2).

The formula for midpoint is

(x1+x2/2, y1+y2/2)

= (2-3/2, 3-2/2)

=(-1/2, 1/2)

= (-0.5, 0.5)

Hence, the midpoints of the segment is  (-0.5, 0.5).

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[tex]\bf (\stackrel{x_1}{-4}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-4}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-4-4}{6-(-4)}\implies \cfrac{-8}{6+4}\implies \cfrac{-8}{10}\implies -\cfrac{4}{5}[/tex]

[tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=-\cfrac{4}{5}[x-(-4)]\implies y-4=-\cfrac{4}{5}(x+4) \\\\\\ y-4=-\cfrac{4}{5}x-\cfrac{16}{5}\implies y=-\cfrac{4}{5}x-\cfrac{16}{5}+4\implies y=-\cfrac{4}{5}x+\cfrac{4}{5}[/tex]

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

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

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

Answer:

(c-3) (4n)

Step-by-step explanation:

5n(c - 3) - n(C - 3) =

Factor out (c-3) from each term

(c-3) (5n-n)

Simplify the 2nd term

(c-3) (4n)

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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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:

5 6 7 is the correct answer

Step-by-step explanation:

The possible lengths of the shortest straw are 5 inches, 6 inches, 7 inches and 8 inches

The lengths of the two straws are given as: 9 inches and 12 inches

Represent the length of the shortest straw with x.

So, we have the following inequality

[tex]x + 9 > 12[/tex]

Subtract 9 from both sides

[tex]x > 3[/tex]

This means the length of the shortest straw is greater than 3 inches

Hence, the possible lengths are 5 inches, 6 inches, 7 inches and 8 inches

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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

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:

The radius is equal to 5 inches or 12.7 cm

Step-by-step explanation:

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:

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:

Answer:

4 times 8 is 32 then 8 times 2 is 16 then add them together

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

48 miles

Step-by-step explanation:

4 times 8 equals 32 plus 8 times 2 equals 16 add them up equals 48

Answer:

x=-1/2

y=-1/2

-1/2-(-1/2)

0

Step-by-step explanation:

Answer:

Is an scalene obtuse triangle

Step-by-step explanation:

step 1

Find the type of triangle by the measure of the interior angles

we know that

If applying the Pythagoras Theorem

[tex]c^{2}=a^{2}+b^{2}[/tex] ----> we have a right triangle

[tex]c^{2} > a^{2}+b^{2}[/tex] ----> we have an obtuse triangle

[tex]c^{2}< a^{2}+b^{2}[/tex] ----> we have an acute triangle

where

c is the greater side

we have

[tex]c=\sqrt{19}\ units[/tex]

[tex]a=2\ units[/tex]

[tex]b=\sqrt{12}\ units[/tex]

substitute

[tex]c^{2}=(\sqrt{19})^{2}=19[/tex]

[tex]a^{2}+b^{2}=(2)^{2}+(\sqrt{12})^{2}=16[/tex]

so

[tex]19 > 16[/tex] -----> [tex]c^{2} > a^{2}+b^{2}[/tex]

we have an obtuse triangle

step 2

Find the type of triangle by the measure of the sides

we have that

The measure of its three sides is different

therefore

Is an scalene triangle

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.

Not enough information (attach the statements).

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: 13.4 meters by 6.1 meters

Step-by-step explanation: Applying the scale to the given measurements gives us: 13.4 meters long and 6.1 meters wide

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:

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:

25

Step-by-step explanation:

Is means equals and of means multiply

16 = 64% * W

Change to decimal form

16 = .64 * W

Divide each side by .64

16/.64 = .64W/.64

25 = W

Answer:

25

Step-by-step explanation:

We can model this question with:

16 = 0.64x

x represents "what number."

0.64x = 16

Divide 0.64 from both sides

0.64x ÷ 0.64 = 16 ÷ 0.64

16 ÷ 0.64 = 25.

Therefore, 16 is 64% of 25.

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:

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:

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.