I assume the limit you're asked to copmute is supposed to be
[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5}[/tex]
Rationalize the numerator by multiplying it by its conjugate:
[tex]\dfrac{\sqrt{x+4}-3}{x-5} \times \dfrac{\sqrt{x+4}+3}{\sqrt{x+4}+3} = \dfrac{\left(\sqrt{x+4}\right)^2-3^2}{(x-5) \left(\sqrt{x+4}+3\right)} = \dfrac{x-5}{(x-5) \left(\sqrt{x+4}+3\right)}[/tex]
Since x is approaching 5, we have x ≠ 5 and can cancel the factors of x - 5 to remove the discontinuity.
Then
[tex]\displaystyle \lim_{x\to5} \frac{\sqrt{x+4}-3}{x-5} = \lim_{x\to5} \frac1{\sqrt{x+4}+3} = \frac1{\sqrt9+3} = \boxed{\frac16}[/tex]
because the simplified limand is continuous at x = 5.
Answer:
it is C. 1/6th
Step-by-step explanation:
60. Students were asked to write a trinomial that could not be factored using integers.
Patricia wrote: x2 + 5x - 14
Shelly wrote: x2 - x - 30
Melanie wrote: x2 + 4x - 2
Lisa wrote: x2 + 4x - 5
Which student followed the given directions?
-
-
Melanie write the quadratic equation x^2 + 4x - 2 according to the directions that write a trinomial that could not be factored using integers.
What is a quadratic equation?Any equation of the form [tex]\rm ax^2+bx+c=0[/tex] where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.
Patricia wrote:
[tex]\rm x^2+5x-14=0\\\\\rm x^2 -2x+7x-14=0\\\\\rm (x-2)(x+7)[/tex]
Shelly wrote:
[tex]\rm x^2-x-30=0\\\\\rm x^2-6x+5x-30=0\\\\\rm (x-6)(x+5)=0[/tex]
Melanie wrote:
[tex]\rm x^2+4x-2=0[/tex]
Here is the value of D:
[tex]\rm D = \sqrt{4^2-4(1)(-2)}[/tex]
D = √24
Lisa wrote:
[tex]\rm x^2+4x-5=0\\\\\rm x^2-x+5x-5=0\\\\\rm (x-1)(x+5)[/tex]
Thus, Melanie write the quadratic equation x^2 + 4x - 2 according to the directions that write a trinomial that could not be factored using integers.
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Which statement is true about the equation (x – 4)(x 2) = 16?
The roots of the given quadratic equation are 6 and -4.
The given quadratic equation is:
[tex](x-4)(x+2)=16[/tex]
What is a quadratic equation?Any equation of the form [tex]ax^{2} +bx+c=0[/tex] is called a quadratic equation where [tex]a\neq 0[/tex].
[tex]x^{2} -2x-8=16[/tex]
[tex]x^2-2x-24=0[/tex]
[tex]x^{2} -6x+4x-24=0[/tex]
[tex]x(x-6)+4(x-6)=0[/tex]
[tex](x-6)(x+4)=0[/tex]
[tex]x=6[/tex]
[tex]x=-4[/tex]
Hence, the roots of the given quadratic equation are 6 and -4.
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Answer:
The factored form of the equation is (x + 4)(x – 6) = 0.
(option C)
Anybody knows this?? 3x^2+6x-10 + 3x+5
Answer:
3x2+9x−5
Step-by-step explanation:
You just have to add the like terms
Answer:
3x² + 9x - 5
Step-by-step explanation:
Group like terms:
3x² + 6x - 10 + 3x + 5
3x² + 9x -5
hope this helps :)
What is the range of the function shown in the graph below?
A. x ≥ 0
B. y ≤ 0
C. x ≤ 0
D. y ≥ 0
NO TROLLING OR LINKS OR I WILL REPORT.
Answer:
A
Step-by-step explanation:
Answer:
Correct answer is: B: y ≤ 0
Step-by-step explanation:
Help!! I need to pass this class by the end of this week!!!!
2. You are making wooden picture
frames of different sizes but you
have limited supplies, so you are
restricting the perimeter of each
frame to 4 feet or less and the length
to exactly 1.5 feet. Find the range of
the frame width. Show your work.
The range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.
What is the range of a particular data set?For a set of data, the range is the difference between the maximum and minimum value. It sort of gives an idea of spread of the data.
For this case, we're given that:
Frame is rectangular (assumingly).The perimeter of the frame ≤ 4 feetThe length of the frame = 1.5 feetPerimeter of a rectangle = 2(length + width)
Let 'l' denotes length, and 'w' denotes width, then we get:
[tex]Perimeter \leq 4\\2(l+w) \leq 4\\2(1.5 + w) \leq 4\\\\\text{Dividing both the sides by 2}\\\\1.5 + w \leq 2\\\\\text{Subtracting 1.5 from both the sides so as to get 'w' on one side}\\\\w \leq 0.5[/tex]
Now since the lowest value of width of a frame can be zero only, therefore, we get:
[tex]0 \leq w \leq 0.5[/tex]
Thus, the range of values 'w' can assume is: 0.5 - 0 = 0.5
Thus, the range of the frame width for the considered case is 0.5 (feet), because for this case, it can be at max of 0.5 feet, and at minimum of 0 feet.
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The manager at Green Tee's golf course conducted a study to see how long it takes to complete a round of golf. The manager records the
time it takes randomly selected golfers to finish a round of golf at Green Tee's golf course. The manager conducts the survey on a golf league
day, therefore all the golfers within the sample have previous golf experience. Based on the study, the average time spent to complete a
round of golf was 4 hours.
What inference can be made from the survey?
The Inference that can be made from the survey is: B. On average, it will take 4 hours to complete a round of golf at Green Tee's golf course.
What is survey?Survey can be defined as the process of collecting data or informationso as to reach or draw a conclusion.
The survey analysis shows that it will take an average of 4 hours for an experience golfers to complete or finish a round of golf based on the fact that the golfers all had previous experience.
Therefore on average, it will take 4 hours to complete a round of golf at Green Tee's golf course.
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Rebbeca needs a box with a rectangular base of 36 cm^2 and a volume of 180 cm^3. What would be the height
of the box?
Answer:5cm
Step-by-step explanation: Area =length × breadth
Volume = length ×breadth ×height
180= Area ×height
180 = 36×h
180÷36=h
Ans 5
How could you define area?
[tex] \huge\fbox\green{ANSWER} [/tex]
Area is the amount of space taken up by a 2D shape
Answer:
The area is the extent or measurement of a surface or piece of land. You find out the area by doing the height x the Width.
Hope this helps..
Step-by-step explanation:
A construction team builds a brick wall in 2 weeks. At the end of the
first week, the wall is 3.6 meters high. During the second week, the
team makes the wall 2.25 meters higher. The final height of the wall is
1.3 times the originally planned height.
How tall was the wall originally going to be?
Answer:
no idea sorry
Step-by-step explanation:
.... .. . .... ...... . . . . .. ... .. . .
The potential energy of an object varies jointly with the mass of the object and the height of the object off the ground. a 25-kg object has 980 joules of potential energy when it is 4 meters off the ground. another object has 150 joules of potential energy at 3 meters off the ground. what is the mass of the second object? round to two decimal places. 0.32 kilogram 2.88 kilograms 5.10 kilograms 45.90 kilograms
The mass of the object which is at 3 meters off the ground (earth assumingly), with the potential energy of 150 joules is given by: Option C: 5.10 kg
What is gravitational potential energy?Gravitational potential energy is the energy which a body posses because of its position.
The gravitational potential energy of a body is given as,
[tex]U=mgh[/tex]
Here, (m) is the mass of the body, (g) is the gravitational accelaration and (h) is the height of the body.
Here, for the second object, we have:
Potential energy = 150 joulesDistance from the ground = 3 mg = gravitational acceleration = [tex]9.8 \: \rm m/s^2[/tex]Let its mass be m kg, then:
[tex]U=mgh\\\\150 = m(9.8)(3)\\\\m = 50/9.8 \approx 5.10 \: \rm kg[/tex]
Thus, the mass of the object which is at 3 meters off the ground (earth assumingly), with the potential energy of 150 joules is given by: Option C: 5.10 kg
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PLEASE HELP ME WITH MY MATH WHO EVER GETS IT GETS BRAINLIEST
Answer:
don't use this this is just a guess but I think that it is the lowest possible one so A It coulld be wrong
Step-by-step explanation:
E
Step-by-step explanation:
PLEASE HELP ME ASAP!!!!! I WILL GIVE YOU 30 POINTS!
For each equation, draw a tape diagram and find the unknown value.
Part A:x+9=16
Part B:4⋅x=28
Answer:
Part A=7
Part B=7
Step-by-step explanation:
Part A = 7+9=16
Part B = 4 times 7= 28
What is the area if this parallelogram?
Answer:
32
Step-by-step explanation:
PLEASE HELPPP!!! I will give brainly points
Answer:
should be a. took the test and It was horrible. I remember trying and forgot how to do everything beother
Step-by-step explanation:
no balls
Sunny is a volunteer at the animal shelter. The animal shelter has only dogs and cats. 3
10
of the animals are dogs. There are 8 fewer dogs than cats. How many animals are there in the animal shelter?
Answer: 14 Animals
Step-by-step explanation: Made of 3 dogs and 11 Cats
Dogs( 11-8)
Hello, I reallly neeeeeed your help! This is due in 45 minutes and Im so confused.!!
Answer: just graph it using the x and y coordinate points
Step-by-step explanation:
Answer:
(-4, -2)
Step-by-step explanation:
Rewrite the equations to make y the subject, so that it's easier to calculate the points on each line:
Equation 1
x - y = -2
⇒ x + 2 = y
⇒ y = x + 2
Equation 2
2x - 3y = -2
⇒ 2x + 2 = 3y
⇒ y = (2/3)x + 2/3
Calculate 2 points on each line:
Equation 1 (blue line on attached graph)
Substitute x = 0 and x = -2 into Equation 1 to create 2 points:
x = 0: y = 0 + 2 ⇒ (0, 2)
x = -2: y = -2 + 2 ⇒ (-2, 0)
Plot the points and draw a line through them.
Equation 2 (red line on attached graph)
Substitute x = 2 and x = -1 into Equation 1 to create 2 points:
x = 2: y = (2/3)(2) + 2/3 ⇒ (2, 2)
x = -1: y = (2/3)(-1) + 2/3 ⇒ (-1, 0)
Plot the points and draw a line through them.
Solution
The solution is the point where the two lines intersect.
Therefore, the point of intersection is (-4, -2)
Mitch tried to solve an equation step by step.
7.7 = W - 2
7.7 – 2 = W - 2 + 2 Step 1
5.7 = w
Answer:
Mitch did not make a mistake
Step-by-step explanation:
The -2 and 2 on the right side cancel out and so you are left with 7.7-2=w. Combine like terms and your left with 5.7=w
Melissa and tomas are playing a game with complex numbers. if melissa has a score of 5 – 4i and tomas has a score of 3 2i, what is their total score? 8 – 6i 8 6i 8 – 2i 8 2i
The total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.
What is complex number?A complex number is the combination of real and imaginary number. It can be written as,
[tex]a+bi[/tex]
Here, (a) is a real number and (b) is an imaginary number.
Melissa and Tomas are playing a game with complex numbers. Melissa has a score of 5 – 4i and Tomas has a score of 3 2i. The sum of their score is,
[tex]S=5 -4i +(3+2i)\\S=5+3-4i+2i\\S=8-2i[/tex]
Hence, the total score of Melissa and Tomas who are playing a game with complex numbers is 8-2i.
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Answer:
8-2i
Step-by-step explanation:
c
a flower shop is selling 2 roses for $84.00. What is the cost, in dollars, per rose?
Answer:
42
Step-by-step explanation:
2x = 84
x = roses
x = 84/2
x = 42
Answer:
$42.00
Step-by-step explanation:
You divide 84 by 2 and find the answer 42. Therefore, each rose is 42 dollars.
D = x4 + 5x – x2 + x - 1
E = x4 - 4x3 - 2x2 + 2
D + E?
D - E?
Answer:
D + E = 2x⁴ + x³ – 3x² + x + 1
D - E = 9x³ + x² + x – 3
Step-by-step explanation:
D = x⁴ + 5x³ – x² + x – 1
E = x⁴ – 4x³ – 2x² + 2
D + E : D - E :
x⁴ + 5x³ – x² + x – 1 x⁴ + 5x³ – x² + x – 1
+ –
x⁴ – 4x³ – 2x² + 0 + 2 x⁴ – 4x³ – 2x² + 0 + 2
_________________ _________________
2x⁴ + x³ – 3x² + x + 1 0 + 9x³ + x² + x – 3
WILL GIVE BRAINLIEST, THANKS, AND 5 STARS!
PLEASE HELP ME!
Answer:
-4 and 4
Step-by-step explanation:
Method 1
Apply Difference of Two Squares Formula: [tex]a^2-b^2=(a+b)(a-b)[/tex]
Given [tex]x^2-16=0[/tex]
Rewrite 16 as 4²
Therefore, [tex]a^2=x^2[/tex] and [tex]b^2=4^2[/tex]
[tex]\implies a = \sqrt{x^2}=x[/tex]
[tex]\implies b=\sqrt{4^2} =4[/tex]
[tex]\implies x^2-16^2=(x+4)(x-4)[/tex]
[tex]\implies (x+4)(x-4)=0[/tex]
[tex]\implies (x+4)=0 \implies x=-4[/tex]
[tex]\implies (x-4)=0 \implies x=4[/tex]
Method 2
Given equation:
[tex]x^2-16=0[/tex]
Add 16 to both sides:
[tex]\implies x^2-16+16=0 + 16[/tex]
[tex]\implies x^2=16[/tex]
Square root both sides:
[tex]\implies \sqrt{x^2}=\sqrt{16}[/tex]
[tex]\implies x=\pm4[/tex]
Therefore, x = -4, x = 4
Martha's class is making banners to fly outside of the school. Each banner will be in the shape of a triangle with a base of 12 inches and a height of 20 inches The class needs 12 banners. How much material will they need?
Answer:
1440 square inches of fabric
Step-by-step explanation:
Answer:
1440 square inches of fabric
Step-by-step explanation:
Solve for 1 banner
Area of 1 banner:
12*20/2
12*10
120.
12 banners,
12*120
= 1440 square inches of fabric
(or other types of material)
P: 800
Situation:
r-3.5
How many years will it take for the account to
reach $14,000? Round your answer to the
nearest hundredth.
Enter the correct answer.
Tina wants to save money for school.
Tina invests $800 in an account that
pays an interest rate of 7.5%.
DONE
C.
Answer:
huhh
Step-by-step explanation:
If 10 lemons are required to make 15 cups of lemonade at what rate are lemon being used per cup of lemonade
Answer:
2/3 lemon's per cup.
Step-by-step explanation:
10÷15=2÷3 .
Please give me brainliest.Thank you. :-):-)
Someone help me please
Answer:
Step-by-step explanation:
14,19,16,13,16,14
The median is
.
Question 2
Find the mode(s) of the data.
13
13
14
14
16
16
19
19
There is no mode.
There is no mode.
Answer:
the median is 15, there is no mode.
Step-by-step explanation:
to find the median- put the numbers in order from least to greatest (13,14,14,16,16,19) use a sheet of paper and cross off each number on the ends until you get to the middle. Once you have reached the middle you should have the two numbers 14, 16. Take 14 and 16, add them together and you will get 30. Divide 30 by 2 because there is two numbers for the median. You should end with 15 as your median.
to find the mode- find the number that occurs the most in the set of numbers, in this case all numbers occur the same amount of times, so therefor there is no mode.
happy to help<33.
Question 4 options:
y = -2
x = -2
x = 0
y = -1
Answer:
i think its y=-1
Step-by-step explanation:
hope u get it right
The radius of a circle is 20 centimeters.
What is the circumference, in centimeters, of the circle? Round your answer to
the nearest tenth.
Response:
Answer:
The circumference is 125.7cm
Theo started to solve the quadratic equation (x 2)2 – 9 = –5. he added 9 to both sides and the resulting equation was (x 2)2 = 4. next, he took the square root of each side. which was the resulting equation of that step? x 2 = ±4 x 2 = ±2 x 2 = ±8 x 2 = ±16
The resulting equation of that step is the square root of (x + 2)² is (x + 2).
What is the square root function?A square root function is defined as a one-to-one function that takes a positive number as an input and returns the square root of the given input number.
From there, it was pretty easy for Theo to find the solutions
to the original equation.
If (x + 2) = +2 , then x = 0 .
If (x + 2) = -2 , then x = -4
Hence, the resulting equation of that step is the square root of (x + 2)² is (x + 2).
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