The steps in writing f(x) = 18x + 3x2 in vertex form are shown, but a value is missing in the last step.



Write the function in standard form.

f(x) = 3x2 + 18x
Factor a out of the first two terms. f(x) = 3(x2 + 6x)
Form a perfect square trinomial.

f(x) = 3(x2 + 6x + 9) – 3(9)

Write the trinomial as a binomial squared. f(x) = 3(x + ______)2 – 27

What is the missing value in the last step?


Answers

Answer 1

Answer:

3

Step-by-step explanation:

f(x) = 18x + 3x^2

f(x) =  3x^2+18x

Factor out a 3

     = 3(x^2 +6x)

Take the coefficient of x, divide by 2 and then square

6/2 = 3 3^2 =9

Remember the 3 out side 3*9 =27 so we are really adding 27

3(x^2+6x+9) -3*9

The number inside the parentheses added to x is b/2  or 6/2

3(x+3)^2 -27

Answer 2

Answer:

[tex]f(x)=3(x+3)^{2}-27[/tex]

Step-by-step explanation:

In the last step is missing the number 3 which is the second term of the binomial squared expression.

Basically, the complete step is

[tex]f(x)=3(x+3)^{2}-27[/tex]

As you can see, the three inside the parenthesis is the missing part in the last step.


Related Questions

Mrs. Bell graded 6.5 students' tests in 0.5 hours. At this rate, how long will i
grade 30 students' papers? State your answer in hours and minutes​

Answers

Answer:

2 hours 18 minutes (to the nearest minute)

Step-by-step explanation:

6.5 / 0.5 hours

--> Multiply the whole equation by 4.61538461538 so that 6.5 becomes 30

= 30 papers in 2.30769230769 hours = 02:18:28

Mrs. Bell will take 2 hrs 18 mins approximately.

What is the unitary method?

The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

Given that 6.5 students' papers can be checked in 0.5 hours

1 student's paper can be checked in 0.5/6.5 hours

30 students' paper can be checked in (0.5 /6.5)*30 hours = 2.307 hours

Therefore, Mrs. Bell will take 2 hrs 18 mins approximately.

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What is the equation of the line perpendicular to 2x – 3y = 13 that passes through the point (–6, 5)?

Answers

Answer:

[tex]y =- \frac{3}{2}x - 4[/tex]

Step-by-step explanation:

Given equation of line is:

2x-3y=13

We will convert the equation of line in point-slope form to find the slope of the line

Let  

m_1  be the slope of the line

So,

2x-3y=13

-3y= -2x+13

Dividing both sides by -3

(-3y)/(-3)=(-2x)/(-3)+13/(-3)

y=(2/3)x-13/3

The co-efficient of x is the slope of the line.

So,

m_1=2/3

Let

m_2  be the slope of second line

As we know that product of slopes of two perpendicular line is -1

m_1 m_2= -1

2/3*m_2= -1  

m_2= -1*3/2

m_2= -3/2

So m2 is the slope of the line perpendicular to given line.

The standard equation of a line is  

y=mx+b

To find the equation of line through (-6,5), put the point and slope in the given form and solve for b

5= -3/2 (-6)+b

5=18/2+b

5=9+b

b=5-9

b= -4  

Putting the values of slope and b, we get

[tex]y =- \frac{3}{2}x - 4[/tex]

Answer: [tex]y=-\frac{3}{2}x-4[/tex]

Step-by-step explanation:

The equation of the line in Slope-intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

To express the given equation of the line in this form, we need to solve for "y":

[tex]2x - 3y = 13\\\\-3y=-2x+13\\\\y=\frac{-2}{-3}x+\frac{13}{-3}\\\\y=\frac{2}{3}x-\frac{13}{3}[/tex]

We can identify that the slope of this line is:

[tex]m=\frac{2}{3}[/tex]

Since the slopes of perpendicular lines are negative reciprocals, then the slope of the other line is:

[tex]m=-\frac{3}{2}[/tex]

Now, we need to substitute the given point  and the slope into  [tex]y=mx+b[/tex] and solve for "b":

[tex]5=-\frac{3}{2}(-6)+b\\\\5=9+b\\\\5-9=b\\\\b=-4[/tex]

Substituting values, we get that the equation of this line is:

[tex]y=-\frac{3}{2}x-4[/tex]

What number belongs to the solution of the inequality
3x>96

Answers

[tex]\text{Hey there!}[/tex]

[tex]\text{3x}>\text{96}[/tex]

[tex]\text{You have to DIVIDE by 3 on BOTH OF YOUR SIDES.}[/tex]

[tex]\dfrac{3\text{x}}{3}>\dfrac{96}{3}[/tex]

[tex]\text{Cancel out: }\dfrac{3\text{x}}{3}\text{ because it equals to 1}[/tex]

[tex]\text{Keep: }\dfrac{96}{3}\text{ because it helps us solve for our answer, to compare}[/tex] [tex]\text{both numbers.}[/tex]

[tex]\text{96}\div3\text{ = 32}[/tex]

[tex]\boxed{\boxed{\bf{Answer:x > 32}}}\checkmark[/tex]

[tex]\text{It's a}[/tex] [tex]\text{(o)(p)(e)(n)(e)(d) circle shaded to the right side of the number line}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

x>32

Step-by-step explanation:

Divide by 3 from both sides of equation.'

3x/3>96/3

Simplify, to find the answer.

96/3=32

x>32 is the correct answer.

I hope this helps you, and have a wonderful day!

What is the distance between (6, 2) and (-3, -2)?

9
3

5

Answers

Answer:

Option A is correct.

Step-by-step explanation:

Distance between two points can be calculated from formula

[tex]d = \sqrt {\left( {x_1 - x_2 } \right)^2 + \left( {y_1 - y_2 } \right)^2 }[/tex]

Here x₁ = 6, y₁ = 2,x₂ = -3 and y₂ = -2

Putting the values in the formula

[tex]d = \sqrt{(-3-(6))^2+(-2-(2))^2}\\d = \sqrt{(-3-6)^2+(-2-2)^2} \\d = \sqrt{(-9)^2+(-4)^2} \\d = \sqrt{81+16}\\d = \sqrt{97}\\d= 9.85[/tex]

So, the distance between points (6, 2) and (-3, -2) is 9.85 or ≈ 9.

So, Option A is correct.

ANSWER

[tex] \sqrt{ 97 }[/tex]

EXPLANATION

The formula for calculating the distance between two points is

[tex]d = \sqrt{ {(x_2-x_1)}^{2} +(y_2-y_1)^{2} } .[/tex]

We use this formula to find the distance between (6,2) and (-3,-2)

We plug in the points to get,

[tex]d = \sqrt{ {( - 3-6)}^{2} +( - 2-2)^{2} } .[/tex]

[tex]d = \sqrt{ {( - 9)}^{2} +( - 4)^{2} } .[/tex]

[tex]d = \sqrt{ 81+16}[/tex]

[tex]d = \sqrt{ 97 }[/tex]

The distance between the two given points is

[tex] \sqrt{ 97 }[/tex]


A student needs at least 80% of all points on the tests in a class to get a B. There are three
100-point tests and a 250-point final. The student's test scores are 72%, 85%, and 78% for
the 100 point tests. What is the least score the student can make on the final and still get a B?

Answers

How many points are there total? (3*100)+250 = 550

So far, he has 72 + 85 + 78, or 235

He needs 0.80 * 550 for a B, or 440 points

 

440 - 235 = 205 points on the final to get a B

Percentage-wise, he needs 205/250, or 0.82

Can someone help me?

Is it possible that cos⁡(A−B) = cos ⁡A−cos ⁡B? Why or why

Answers

Answer:

Distributive Property.

Step-by-step explanation:

Cos(A-B)= Cos A- Cos B

The variables in the parenthesis gets multiplied into the Cos

Cos A - Cos B

Deshawn won 95 pieces of gum playing hoops at the county fair. At school he gave four to every student in his math class. Write an expression for how many pieces of gum deshawn has now

Answers

Answer:

x = 95 - 4y

Step-by-step explanation:

Let the pieces he has now be a variable x and the no. of students in his class be y, So the pieces he gave to everyone become 4y (note that 4 here means he had given four to each) and as he had won 95 pieces at the fair in the starting,

therefore the equation becomes:-

x = 95 - 4y

Final answer:

The expression for how many pieces of gum Deshawn has now is 95 - (4 x number of students in his math class).

Explanation:

To find out how many pieces of gum Deshawn has after giving four to every student in his math class, we need to subtract the number of pieces of gum he gave away from the total number he won at the county fair.

We can represent this situation using the expression: 95 - (4 x number of students in Deshawn's math class).

For example, if there were 20 students in Deshawn's math class, the expression would be: 95 - (4 x 20) = 95 - 80 = 15.

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HELPP ME PLEASE ASPAAAAAAP PLEASEEEEE

Answers

Answer:

4

Step-by-step explanation:

1, 2 and 3 are interior angles

4 is the exterior angle

The students in a class were asked how many siblings they have. The data obtained is represented in the dot plot. The number of students who have no siblings is . The number of students who have three or more siblings is .

Answers

Answer:

0 Siblings: 4 Students

3 or more siblings: 5 students

Step-by-step explanation:

The numbers at the bottom represents how many siblings they have and the dots represent the number of studens so using this we know:

0 Siblings: 4 Students

1 Sibling: 3 Students

2 Siblings: 3 Students

3 Siblings: 1 Student

4 Siblings: 0 Students

5 Siblings: 2 Students

6 Siblings: 1 Student

7 Siblings: 1 Student

3 or more: 1 + 0 + 2 + 1 + 1 = 5

3 or more siblings: 5 students

Answer:

0 Siblings: 4 Students3 or more siblings: 5 students

Step-by-step explanation:

Are the graphs of the lines in the pair parallel? Explain.

y = 2/3x– 17
4x – 6y = –6

Answers

Answer:

Yes, they are parallel.

Step-by-step explanation:

Parallel lines have the same slope. We must find the slopes of the two lines.

When the equation of a line is written in the slope-intercept form,

y = mx + b,

the slope is m.

The first line has equation

[tex] y = \dfrac{2}{3}x - 17 [/tex]

It is already written in the slope-intercept form. Comparing y = 2/3x - 17 with y = mx + b, you see that m = 2/3. The slope of the first line is 2/3.

Now we solve the second equation for y to obtain the slope-intercept form of that equation.

4x - 6y = -6

Subtract 4x from both sides.

-6y = -4x - 6

Divide both sides by -6.

[tex] \dfrac{-6}{-6}y = \dfrac{-4}{-6}x + \dfrac{-6}{-6} [/tex]

[tex] y = \dfrac{2}{3}x + 1 [/tex]

We now compare this form of the second equation with y = mx + b, and we see that m = 2/3.

Both equations have the same slope, 2/3, so the lines are parallel.

Yes they are parallel

What percent is represented by the shaded area? ( sorry if the picture is sideways)​

Answers

Answer:

40%

Step-by-step explanation:

2 out of 5 of the rectangles are shaded. With a ratio of 2/5 this represented as a percent is 40%

Answer:

40%.

Step-by-step explanation:

2 out of 5 rectangles are shaded.

As a percentage that is 2/5 * 100 = 40%.

7. A large wall map is drawn so that 1 inch equals
3 miles. On the map, the distance from Kansas
City to Denver is 192 inches. How far is the
round trip from Kansas City to Denver in
miles?
(A) 192- miles
(B) 577 miles
(C) 385 miles
(D) 1,155 miles
CHAPTI​

Answers

From all the math I’ve done it does not seem that any of them a correct

The correct answer is (D) 1,155 miles (rounded to the nearest whole number).

To find the round trip distance from Kansas City to Denver, we need to calculate the actual distance in miles based on the scale given in the map.

On the map, 1 inch represents 3 miles. The distance from Kansas City to Denver on the map is given as 192 inches. To find the actual distance in miles:

Actual distance = (Distance on the map) × (Scale factor)

Actual distance = 192 inches × 3 miles/inch

Actual distance = 576 miles

Since the round trip distance includes going from Kansas City to Denver and back, we need to double the actual distance:

Round trip distance = 2 × 576 miles

Round trip distance = 1152 miles

So, the correct answer is (D) 1,155 miles (rounded to the nearest whole number).

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∠MPR is an acute angle and PQ is in the interior of ∠MPR. ∠QPR must be
A. Straight
B. Obtuse
C. Right
D.Acute

Answers

Answer:

∠QPR must be an acute angle

Step-by-step explanation:

Given : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

To Find :∠QPR must be?

Solution:

Acute Angle : An angle whose measure is less than 90°

Since ∠MPR is an acute angle

This means ∠MPR is less than 90°

Now PQ is in the interior of ∠MPR

So, referring the attached figure

∠QPR should be less than ∠MPR

So, the measure of ∠QPR should be less than ∠MPR

So,  the measure of ∠QPR is also less than 90°

So, ∠QPR must be an acute angle

So, Option D is correct.

Answer: D. Acute

Step-by-step explanation:

We are given that : ∠MPR is an acute angle and PQ is in the interior of ∠MPR.

Definition :

Acute Angle : An angle having measure is less than 90°

.

Obtuse angle : An angle having measure is greater than 90° but less than 180

°.

Right angle : An angle whose measure exactly 90°

.

Straight angle : An angle whose measure exactly 180°

.

∵∠MPR is an acute angle  ,

Then ∠MPR must be less than 90°

.

Also, PQ is in the interior of ∠MPR

.

⇒∠QPR should be less than ∠MPR

.

⇒ the measure of ∠QPR is also less than 90°

⇒∠QPR must be an acute angle  . [By definition of Acute angle.]

Hence, the correct answer is option D.


What is the equation of the given circle?

Answers

Answer:

A

Step-by-step explanation:

The equation of a circle is:

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius.

Here, the center is (2, 1) and the radius is 1.

(x - 2)² + (y - 1)² = 1²

The equation of the given circle is Option(A)  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

What is equation of circle ?

The standard equation of any circle is given as -

[tex](x-h)^{2} + (y - k)^{2} = r^{2}[/tex]  

where (h,k) is the coordinate of the center of the given circle and r is the length of radius of the circle.  

How to form the equation of the given circle ?

In the diagram given aside, we can see that the circle has its center at (2,1) and also the radius of the circle measures 1 units.

Thus, we have h = 2 , k = 1 and r = 1 in the standard representation.

The equation of the circle is -

⇒ [tex](x-2)^{2} + (y - 1)^{2} = 1^{2}[/tex]

∴  [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex]

Therefore, the equation of the given circle is Option (A) [tex](x-2)^{2} + (y - 1)^{2} = 1[/tex] .

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Helpppppppp plssssssssss

Answers

your correct it is 240

lengthxwidthxheight

8x6x5=240

Volume of prism: l*w*h
L=8
W=6
H=5

8*6*5=240

So, you are correct. The volume of the prism is 240 units cubes.

3x − y − 3z if x = −2, y = 1, and z = −2.

Answers

Answer: -1

Step-by-step explanation:

3x − y − 3z           if x = −2      y = 1     z = −2

Step 1: 3(-2)-1-3(-2)

Step 2: -6-1+6

Step 3: -7+6

Step 4: -1

Please help with this question!
At a fruit stand, apples cost 80 cents for x apples and oranges cost 75 cents for y oranges. Which of the following represents the cost, in dollars, of 5 apples and 6 oranges?

Answers

Answer:

($4.00/x)+($4.50/y)

Step-by-step explanation:

we know that

Apples cost 80 cents for x apples

so

One apple cost $0.80/x

Oranges cost 75 cents for y oranges

so

One orange cost $0.75/y

Find the cost of 5 apples and 6 oranges

Multiply the number of apples by the cost of one apple and multiply the number of oranges by the cost of one orange

so

5($0.80/x)+6($0.75/y)=($4.00/x)+($4.50/y)

Final answer:

The cost of 5 apples at 80 cents each is $4.00 and the cost of 6 oranges at 75 cents each is $4.50. The total cost for 5 apples and 6 oranges is therefore $8.50.

Explanation:

To calculate the cost, in dollars, of 5 apples and 6 oranges at a fruit stand where apples cost 80 cents for x apples and oranges cost 75 cents for y oranges, you can follow these steps:

Determine the cost per apple by dividing 80 cents by x. Since we do not have the value of x, assume x equals 1 for this explanation, making the cost 80 cents per apple.

Multiply the cost per apple by 5 to find the total cost for 5 apples.

Determine the cost per orange by dividing 75 cents by y. Assuming y equals 1 for this explanation, the cost is 75 cents per orange.

Multiply the cost per orange by 6 to find the total cost for 6 oranges.

Add the total cost for apples and oranges to find the combined cost, converting cents to dollars as necessary.

Therefore, the cost for 5 apples is 5 × 0.80 = $4.00, and the cost for 6 oranges is 6 × 0.75 = $4.50. Adding these together, the total cost for 5 apples and 6 oranges is $4.00 + $4.50 = $8.50.

Fraction: 17/60 what is the decimal?
Fraction: 1/60 what is the decimal?
Fraction:5/60 what is the decimal?
Fraction: 4/60 what is the decimal?
Fraction:6/60what is the decimal?
Fraction:12/60 what is the decimal?
Fraction:3/60 what is the decimal?
Fraction:2/60 what is the decimal? I'm sorry if this is alot of work.i only have 12 points I would give more if I had the chance

Answers

Answer:

1. 0.283333333

2. 0.016666667

3. 0.0833333333333333

4.0.0666666666666667

5. 0.1

6. 0.2

7. 0.05

8.0.0333333333333333

Step-by-step explanation:

Simply divide the numerator by the denominator. ex. 17 divided by 60.

Hope this helps :)

Use your calculator. Put in 17 divided by 60 =. It will give you the decimal

I leave my family's vacation cabin at 8 a.m. and start driving home at a nice, safe 45 mph. Two hours later, my husband, who always drives as fast as the law will allow, leaves the cabin and starts driving home 65 mph. When can I expect him to pass me?​

Answers

Answer:

2:30 pm

Step-by-step explanation:

In two hours (from 10am), she is 45 * 2 = 90 miles from vacation cabin.

From then on her average is still 45 mph and her husband's is 65 mph. So, husband catches her 20 miles (65-45=20) in every hour.

The husband has to catch up 90 miles. How long would it take if he is catching up at 20 miles an hour?

90/20 = 4.5 hours

So husband starts at 10am and 4.5 hours form that time is 2.30pm

Which statement about this figure is true?




It has rotational symmetry with an angle of rotation of 30°.


It has no reflectional symmetry.


It has no rotational symmetry.


It has reflectional symmetry with 6 lines of symmetry.

Answers

Answer:

b and d

Step-by-step explanation:

The figure has 12 peaks. A full circle has 360 degrees.

(360 degrees)/12 = 30 degrees.

b. It has rotational symmetry with an angle of rotation of 30 deg.

If you draw a line between each pair of opposite peaks, that line is an axis of reflectional symmetry. Since there are 12 peaks, there are 6 such lines.

d. It has reflectional symmetry with 6 lines of symmetry.

Answer:

It has rotational symmetry with an angle of rotation of 30°.

Step-by-step explanation:

A shape is said to possess rotational symmetry, when it still looks the same after some rotation.

We can see, that the given shape looks the same from every angle and every side.

So, the correct answer is: It has rotational symmetry with an angle of rotation of 30°.

30 degrees because it has 12 angles and [tex]360/12=30[/tex] degrees.

What would y=
4.6
13.9
21.6

Answers

Answer:

13.9 is the right answer :)

Step-by-step explanation:

For this case we have to define trigonometric relations of rectangular triangles, that the tangent of an angle is given by the leg opposite the angle on the leg adjacent to the angle.

Then, according to the figure we have:

[tex]tg (60) = \frac {y} {8}\\y = 8 * tg (60)\\y = 8 * 1.73205081\\y = 13,85640648[/tex]

Rounding the value we have that [tex]y = 13.9[/tex]

ANswer:

Option B

y = –x + 4
x + 2y = –8

Answers

X=16
y= -12


X+2( -x+4)=-8
X-2x+8=-8
-1x=-16
X=16

Y=-16+4
Y=-12

Answer:

(16,-12)

Step-by-step explanation:

To find where these lines intersect, we must first know their slope. If the slope is equal, then the lines don't intersect and they are parallel.

The best formula for knowing slope is slope-intercept form, y=mx+b whereas m is the slope and b is the y-intercept (where the line crosses x=0)

The first equation is already in slope-intersect form so we can substitute the section that is equal to y into the second equation where y is.

x + 2(-x + 4) = -8

x + -2x + 8 = -8

-x + 8 = -8

-x = - 16

x = 16

Now we can use this known variable to find y.

y = -(16) + 4

y = -16 + 4

y = -12

From the top of a 100 foot high pole, an observer measures the angle of depression of a car on the road as 28 degrees. Find, to the nearest hundredth of a foot, the distance from the car to the base of the pole.

Answers

This is a quick sketch of the problem

the answer is about 235.31 ft

you have to use this equation to get the length of the other side, which is roughly 213 ft:

[tex]100 \div \sin(28) [/tex]

then it's just Pythagorean Theorem to get the end result:

[tex] {100}^{2} + {213}^{2} = {c}^{2} [/tex]

Final answer:

To find the distance from the car to the base of the pole, use the tangent function. Plug in the values and solve for the adjacent side.

Explanation:

To find the distance from the car to the base of the pole, we can use trigonometry. Since the observer is looking down at an angle of depression, we can use the tangent function. Tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the height of the pole (100 ft) and the adjacent side is the distance from the car to the base of the pole.

So, using the formula tan(angle) = opposite/adjacent, we can plug in the values and solve for the adjacent side:

tan(28 degrees) = 100 ft/adjacent

adjacent = 100 ft / tan(28 degrees)

Using a calculator, we find that the distance from the car to the base of the pole is approximately 169.38 ft.

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WILL MARK BRAINLIEST
the last two pics are for question two

Answers

Answer:

1. 702 square centimeters

2. m∠YWX = 63°

Step-by-step explanation:

1.

The total surface area is area of all the sides.

There are 2 triangles (slanted side) with base 14 and height 11. Thus area would be  [tex]2(\frac{1}{2}*14*11)=154[/tex]There are 2 triangles (another slanted side) with base 10 and height 12. Thus area would be  [tex]2(\frac{1}{2}*10*12)=120[/tex]There are two rectangles with base 10 and height 6. Thus area would be  [tex]2(10*6)=120[/tex]There are two rectangles with base 14 and height 6. Thus area would be  [tex]2(14*6)=168[/tex]The bottom is a rectangle with area 10 * 14 = 140

Adding all these up  154 + 120 + 120 + 168 + 140 = 702 centimeters square.

2.

Angle WYX is equal to 46° (vertical angles are equal).

Now looking at triangle XWY, we know all three angles will add up to 180°. Given x =71° and Y = 46°, we can figure out W (Angle YWX)

71 + 46 + Angle YWX = 180

Angle YWX = 180 - 71 - 46 = 63°

Second answer choice is correct.

If f(x) = 4x - 12, what is f(2)

Answers

Answer:

D

Step-by-step explanation:

f(2)=4(2)-12

=8-12

=-4

Answer:

D. -4

Step-by-step explanation:

We have the following function:

[tex]f(x)=4x-12[/tex]

and we are asked to find the value of the function [tex]f(x)[/tex] when the variable [tex]x[/tex] is equal to 2:  [tex]f(2)[/tex].

This means that we must substitute the value of [tex]x = 2[/tex] wherever there is an [tex]x[/tex] in the function:

[tex]f(2)=4(2)-12[/tex]

[tex]f(2)=8-12[/tex]

[tex]f(2)=-4[/tex]

The answer is D. -4

The Bishop family celebrated a birthday by dining out at a local restaurant. Their
18 percent tip at the table for the server. What is the total amount that the family v
if necessary.
O
$17.54
$107.20
$114.99
$116.94

Answers

Answer:

$114.99

Step-by-step explanation:

rt4by5by4by5v4fcefrcekjj3ivc24ino3rmf44g4g

gv5y43t4r3wgy54bt3bt 4hnht6bgrvf

sorry if there is random numbers and letters i am glitchy

Answer:

97.45 • 0.18 = 17.54. 97.45 + 17.54 = 114.99. I think this is right.

Step-by-step explanation:

Which system of equations is represented by the graph?
A) y = x
y = -x-10, over x-4

B) y = −x
y = x+10, over x-4

C) y = x
y = -x+10 divided by the quantity x-4

D) y = −x
y = -x+10 divided by the quantity x-4

Answers

Answer:

[tex]\large\boxed{C)\ \left\{\begin{array}{ccc}y=x\\\\y=\dfrac{-x+10}{x-4}\end{array}\right}[/tex]

Step-by-step explanation:

We have the points

(-2 , -2) → x = -2 and y = -2 → x = y

(5, 5) → x = 5 and y = 5 → x = y

The equation of a line is [tex]y=x[/tex]

The hyperbola has the vertical asymptote x = a and the horizontal asymptote y = -1.

Therefore the second equation is:

[tex]y=\dfrac{a}{x-4}-1=\dfrac{a}{x-4}-\dfrac{x-4}{x-4}=\dfrac{a-(x-4)}{x-4}=\dfrac{a-x+4}{x-4}[/tex]

Where a > 0.

The corresponding equation in the solutions to choose is:

[tex]y=\dfrac{-x+10}{x-4}[/tex]

Help. Find the value of x to the nearest tenth

Answers

I will assume that line 4 bisect line x exactly in half. This means that if we solve the last side of the triangle like seen in the pic below we will know what half of line x is

To find the length of the last side of the triangle (let's call this y) you must use Pythagorean theorem

[tex]a^{2} +b^{2}=c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 4

b = y

c = 6

^^^Plug these numbers/variables into the theorem

[tex]4^{2} +y^{2} =6^{2}[/tex]

solve for y

16 + [tex]y^{2}[/tex]  = 36

[tex]y^{2}[/tex] = 20

x = √20

x ≈ 4.472

^^^This is only half of x so if you double it then it will get you the full length of x

4.472 * 2 = 8.944

8.9 (D)

Hope this helped!

~Just a girl in love with Shawn Mendes

What is the distance between –3 and 2 on the number line?

Answers

Answer: 5

Step-by-step explanation: The distance between two numbers can be found by finding the absolute value of the difference of the numbers. Put more simply, subtract -3 - 2 to get -5, which has an absolute value of 5. Or, you can do 2 - -3 to get 5, which has the same absolute value of 5.

The distance between -3 and 2 on the number line is 5 units.

What is the distance?

It is the measurement done between two points on a surface.

Distance=speed*time

How to calculate distance?

If we plot -3 and 2 on the number we find that -3 will be on the left side of 0 and 2 will be on the right side of 0. To reach 2 from -3 we have to first go to-2 then -1, then 0 and then 0 to 1 and 1 to 2.

Hence we have to go to 5 units. That's why the distance between -3 and 2 is 5 units.

Learn more about distance at https://brainly.com/question/2854969

#SPJ2

A radar operator on a ship discovers a large sunken vessel lying fiat on the ocean
floor 200 m directly beneath the ship. The operator measures the angks of
depression of the front and back of the sunken ship to be 56° and 62°. How
long is the sunken ship?

Answers

The length of the sunken ship is 28.56m

To calculate the length of the sunken ship , we have to calculate the distance between the beneath of the ship to the front and to the back.

distance between the beneath of the ship to back of the sunken ship

Tan 62 = 200/x

x = 200/tan 62

x = 106.34m

distance between the beneath of the ship to front of the sunken ship

Tan 56 = 200/y

y = 200/tan 56

y = 134.90m

The length of the sunken ship = 134 .90 - 106.34

= 28.56m

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