If f of x equals the quotient of the quantity x squared minus 36 and the quantity x plus 6 is continuous at x = -6, find f(-6).

Answers

Answer 1

Answer:

f(-6) = -12

Step-by-step explanation:

If you immediately plug in x=-6 and solve it (x^2-36)/x+6, you will not get the right answer.

You need to first expand the perfect square on the numerator (x^2-36) into (x-6)(x+6).

With the perfect square expanded, notice how you have the term (x+6) on both the numerator and denominator. You can cancel out both terms, and you will be left with (x-6).

Now you can plug in x=-6, which will give you -12.


Related Questions

This is for geometry, please help ASAP

Answers

Answer:

Option C,

y² = 18x, since the graph opens right

Answered by GAUTHMATH

A steep mountain is inclined 75 degree to the horizontal and rises 3900 ft above the surrounding plain. A cable car is to be installed by connecting a cable from the top of the mountain to a spot on the plain that is 910 ft from the base of the mountain. Find the shortest length of cable needed.

Answers

Answer: [tex]4004.76\ ft[/tex]

Step-by-step explanation:

Given

inclination is [tex]\theta=75^{\circ}[/tex]

Mountain is [tex]h=3900\ ft[/tex] high

Cable is tied [tex]x=910\ ft[/tex] from the base of the mountain

From the figure, length of the shortest path is [tex]l[/tex]

It is given by using Pythagoras theorem

[tex]\Rightarrow l^2=3900^2+910^2\\\Rightarrow l=\sqrt{(3900)^2+(910)^2}\\\Rightarrow l=4004.76\ ft[/tex]

The width of a rectangle is 9
inches less than the length. The
perimeter is 86 inches

Answers

Answer:

Below.

Step-by-step explanation:

If the length is x then the width is x-9 inches.

Perimeter

= 2L + 2W = 86

2x + 2(x - 9) = 86

4x - 18 = 86

4x = 104

x = 26

So the length is 26 inches and the width is 17 inches.

What’s this topic called

Answers

Answer: MATH

Step-by-step explanation:

Answer:

answer for the question is

x = 1

y = 4

subject is math btw if you are asking about that

Can someone please explain this step by step.

Answers

Answer:

-5 and 2

-3 and 0

-2 and -1

...gives -3

Step-by-step explanation:

Answer:

Step-by-step explanation:

(-5,2), (-2,-1), (-3,0)

all pairs add up to -3

State the slope of the line shown below (help ASAP)
Is it a, b, c or d?

Answers

Answer:

D

Step-by-step explanation:

(the above graph depicts a horizontal line that intersects the y axis at -2)

(so, y = -2)

Answer:

0

Step-by-step explanation:

Horizontal line x axis is 0 while the vertical y axis is undefined.

Find the length of the third side. If necessary, round to the nearest tenth. 5 10 ​

Answers

Answer:

[tex]\boxed {\boxed {\sf 8.7}}[/tex]

Step-by-step explanation:

We are asked to find the length of the third side in a triangle, given the other 2 sides.

Since this is a right triangle (note the small square in the corner of the triangle representing a 90 degree /right angle), we can use the Pythagorean Theorem.

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

In this theorem, a and b are the legs of the triangle and c is the hypotenuse.

We know that the unknown side (we can say it is a) and the side measuring 5 are the legs because they form the right angle. The side measuring 10 is the hypotenuse because it is opposite the right angle.

b= 5 c= 10

Substitute the values into the formula.

[tex]a^2 + (5)^2 = (10)^2[/tex]

Solve the exponents.

(5)²= 5*5 = 25 (10)²= 10*10= 100

[tex]a^2 + 25=100[/tex]

We are solving for a, so we must isolate the variable. 25 is being added to a. The inverse operation of addition is subtraction, so we subtract 25 from both sides.

[tex]a^2 +25-25=100-25[/tex]

[tex]a^2=100-25[/tex]

[tex]a^2 = 75[/tex]

a is being squared. The inverse of a square is the square root, so we take the square root of both sides.

[tex]\sqrt {a^2}= \sqrt{75}[/tex]

[tex]a= \sqrt{75}[/tex]

[tex]a= 8.660254038[/tex]

Round to the nearest tenth. The 6 in the hundredth place tells us to round the 6 up to a 7 in the tenth place.

[tex]a \approx 8.7[/tex]

The length of the third side is approximately 8.7

Perpendicular=P=5Hypontenuse=H=10Base=B=?

Using Pythagorean theorem

[tex]\boxed{\sf B^2=H^2-P^2}[/tex]

Putting values

[tex]\\ \sf \longmapsto B^2=10^2-5^2[/tex]

[tex]\\ \sf \longmapsto B^2=100-25[/tex]

[tex]\\ \sf \longmapsto B^2=75[/tex]

[tex]\\ \sf \longmapsto B=\sqrt{75}[/tex]

[tex]\\ \sf \longmapsto B=\sqrt{25\times 3}[/tex]

[tex]\\ \sf \longmapsto B=5\sqrt{3}[/tex]

[tex]\\ \sf \longmapsto B=5\times 1.732[/tex]

[tex]\\ \sf \longmapsto B=8.66[/tex]

[tex]\\ \sf \longmapsto B\approx 8.7[/tex]

Write an equation of the line that is parallel to the given line and passes through the given point.

9. y= -2x+6 (0,-4)

10. -2x+3y=12 (3,2)


pls help me!!!!!

Answers

Answer:

9.) y=-2x-4

10.)y=2/3x

Step-by-step explanation:

Parallel lines have the same slope, different intercepts

9.) The slope is -2x

To find the parallel line

y-(-4)=-2(x-0)

y+4=-2x

y-4=-2x-4

y=-2x-4

10.) You must first put the equation in slope-intercept form.

-2x+2x+3y=2x+12

3y=2x+12

Divide by 3

3y/3=2x/3+12/3

Simplify

y=2/3x+4

Slope = 2/3x

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

y-2=2/3x-6/3

y-2=2/3x-2

y-2+2=2/3x-2+2

y=2/3x

Jo bought a used car for $6000 and paid a 15% deposit. How much did he still have to pay?

Answers

Answer:

900 is the correct awnser

x^{4} - 5x^(2) + 2x + 3 < 0

Answers

the Answer is irrational number

If the right angle triangle LMN.
L=30°, MN = 4cm and diagonal LM.
Find the LM and LN.​

Answers

LM is 6.9 to 1dm and LM is 8

PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
Evaluate the following expression.
"the quotient of 18 and 2"
A. 1/9
B. 9
C. 16
D. 20

Answers

Answer:

B) 9

Step-by-step explanation:

Quotient means that it’s for DIVISION. The 18 is the dividend, 2 is the divisor, and the quotient is the answer:

Dividend ÷ Divisor = Quotient

18 ÷ 2 = 9

WILL GIVE BRAINLIEST

[tex]\frac{x^2+10x+25}{8x+40}[/tex]

What is an equivalent expression in the lowest terms?

Answers

The top is (x+5)^2 over 8(x+5)

The final answer is (x+5)/8

Hope this helps please brainliest.

In the equation $\frac{1}{j} + \frac{1}{k} = \frac{1}{3}$, both $j$ and $k$ are positive integers. What is the sum of all possible values for $k$?

Answers

Answer:

Hello,

answer 22

Step-by-step explanation:

[tex]\dfrac{1}{j} +\dfrac{1}{k} =\dfrac{1}{3} \\\\\dfrac{k+j}{j*k} =\dfrac{1}{3} \\\\\\3k+3j=j*k\\\\k(3-j)=-3j\\\\k=\dfrac{3j}{j-3} \\\\k=\dfrac{3j-9+9}{j-3} \\\\k=3+\dfrac{9}{j-3} \\\\\\j-3\ must\ be \ a divisor\ of\ 9 ==> 1,3,9\\\\j-3=1 ==> j=4 , k=3+\dfrac{9}{1} =12\\\\j-3=3 ==> j=6 , k=3+\dfrac{9}{3} =6\\\\j-3=9 ==> j=12 , k=3+\dfrac{9}{9} =4\\\\\sum\ k=12+6+4=22\\[/tex]

The sum of all possible values for k is 22.

What is fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

1/j + 1/k= 1/3

Simplifying the fraction

(k+ j)/ kj= 1/3

3k + 3j = kj

k(3- j) = -3j

k = -3j/ (3- j)

k= 3j/ (j-3)

k = 3j + 9 - 9 / (j-3)

k = 3 + 9/ (j-3)

Since (j-3) must be divisor of 9.

j- 3 = 1---> j=4, k= 3 +9 = 12

j- 3 = 3---> j=6, k= 3 +9/3 = 6

j- 3 = 9---> j=12, k= 3 +9/9 = 4

So, The sum is = 12+ 6 + 4 = 22

Learn more about Fraction here:

https://brainly.com/question/10354322

#SPJ6

John and Pablo caught fish that have the lengths, in centimeters, listed below. 45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44 Which box-and-whisker plot correctly represents the data?

Answers

The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.

Answer:

Step-by-step explanation:

Given :

45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44

Using technology, the box and whisker plot generated for the data is attached below.

The 5 - number summary is also given below :

Minimum: 39

Median: 45

First quartile: 42

Third quartile: 47

Interquartile Range: 5

Maximum: 49

Outliers: none

Answer:

Step-by-step explanation:

find the shaded area ..

Answers

Answer:

39°

Step-by-step explanation:

The angle adjacent to 115° in the lower triangle = 180° - 115° = 65°

angle on circle in lower triangle

= 180° - (65 + 76)°  ← angle sum in triangle

= 180° - 141° = 39°

Angles on the circle subtended from the same arc are congruent, then

shaded angle = 39°

HAI HELP ME ASAP PLEASE

Answers

Answer:

Y/X = 2/3 x^2 + 16/3

Y= 2/3 x^3 + 16/3 x

Just replace y with y/X and X with x^2

Priya bought a football for £3.50.
She received £1.50 change.
How much money did she give the shop assistant?
£10.00
£4.00
£5.00
Which one £10.00, £4.00 or £5.00?

Answers

Answer:

$5.00

Step-by-step explanation:

$3.50+$1.50=$5.00

She gave them £5.00
£5 - £1.50 = £3.50

pleaseee answer this question quickly.. I will give brainliest MAKE SURE ITS RIGHT

Answers

Answer:

JKM is acute and MKL is obtuse

Step-by-step explanation:

because an acute triangle's interior angles are always 180° and an obtuse triangle's sum is greater than 90°

Please Help

Select the correct answer.

What is the slope of a line parallel to line r?

A. A line parallel to line r has an undefined slope.
B. 0
C. -1
D. 1

Answers

Answer:

B 0

Step-by-step explanation:

r is a horizontal line

horizontal lines are of the form y= constant

The slope for horizontal lines are 0

Parallel lines have the same slope.

Answer:

B 0

Step-by-step explanation:

the slope of a line is the rise divided by the run, or the Y increase divided by the X increase. the fact that the Y value does not increase makes the slope 0

Find the first three terms of the sequence below. 3n^2+5n−2

Answers

Answer:

-2, 6, 20 ,...

Step-by-step explanation:

3n² +5n -2

if n=0 , then 3*0² +5*0 -2= -2

if n=1, then 3*1² +5*1 -2 = 3+5-2 = 6

if nu 2, then 3*2² +5*2 -2 = 12 +10 -2 = 20

What is an
equation of the line that passes through the points (-3,-1) and (-4,-4)

Answers

Answer:

y= 3x+8

Step-by-step explanation:

not a 100% sure...

sry if its wrong

(try using Math-way, its rly helpful)

Answer:

Step-by-step explanation:

y=mx+b

To find slope: -4+1/-4+3

Slope=3

y=3x+b

Plug in either points ,as an example, i'll plug in (-3,-1)

-1=3(-3)+b

-1=-9+b

8=b

Finished formula: y=3x+8

[tex](a+b)^{2}[/tex]

Answers

Answer:

[tex] ({a + b})^{2} [/tex]

[tex](a + b)(a + b)[/tex]

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

hope this help you

what is value of y if 2x+3y=4​

Answers

Answer:

y=(4-2x)/3

Step-by-step explanation:

3y= 4-2x

y= (4-2x)/3

pls help me with this question and reply answer​

Answers

Step-by-step explanation:

From both the cases we can say that √n is either a natural number or an irrational number. Hence the correct option is (d)Either a natural number or an irrational number. Note: Before solving this type of question we should have proper knowledge of natural numbers, rational numbers and irrational numbers.

Solve by substitution:
y=x-12
8x+8y=-16

Answers

Answer:

[tex](x,y) = ( 5 , - 7)[/tex]

Step-by-step explanation:

we would like to solve the following system of linear equation by substitution:

[tex] \displaystyle \begin{cases} y = x - 12\\ 8x + 8y = - 16\end{cases}[/tex]

notice that, we're already given the value of y therefore simply substitute it to the II equation

[tex]8x + 8(x - 12) = - 16[/tex]

distribute:

[tex]8x + 8x - 96= - 16[/tex]

simplify addition:

[tex]16 x- 96= - 16[/tex]

isolate -96 to left hand side and change its sign:

[tex]16 x= - 16 + 96[/tex]

simplify addition:

[tex]16 x= 80[/tex]

divide both sides by 16 and that yields:

[tex] \boxed{x= 5}[/tex]

now substitute the got value of x to the first equation:

[tex]y = 5- 12[/tex]

simplify subtraction:

[tex]y = - 7[/tex]

hence,

the solution is (x,y)=(5,-7)

G I V E N :

Solve by substitution :

y = x - 12

8x + 8y = -16

S O L U T I O N :

y = x - 12 ------- eq(1)

8x + 8y = -16 ------- eq(2)

Finding x

Putting y = x - 12 in eq(2) we get

8x + 8(x - 12) = -16

8x + 8x - 96 = -16

16x = 96 - 16

16x = 80

x = 80/16

x = 5

Finding y

Putting x = 5 in eq(1) we get

y = x - 12

y = 5 - 12

y = -7

Hence, x is 5 and y is -7

Please solve fast. It's really easy!

Answers

Answer:

j = 10.1

Step-by-step explanation:

The difference between 9.5 and 11.3 is

11.3 - 9.5 = 1.8

This is split into 3 divisions, that is

1.8 ÷ 3 = 0.6

Then

j = 9.5 + 0.6 = 10.1

3. Grace has twice as much money as tad
Together they have $36. How much Money
des Tad have?

Answers

Answer:

Tad has 12 dollars and Grace has 24

Step-by-step explanation:

Grace has twice as much, 24 is double 12. So Tad has 12 dollars.

How to muilti step equation this problem

Answers

-5(x+3)=-4x-15
-5x-15=-4x-15
-5x+4x=-15+15
-1x=0 /-1
x = 0

The ratio of girls to boys in grade 6 was 3:2 at Lincoln middle school last year. There were 60 kids in grade 6. How many in grade 6 were girls

Answers

Answer:

40 girls 20 boys i think / guess

Step-by-step explanation:

Answer:

20/40

Step-by-step explanation:

i hope it help

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