find the solution set of the inequality 52-3x<-14
Answer:
22<x
Step-by-step explanation:
52-3x<-14
66<3x
(we divide both sides to 3)
22<x
Use definition of a derivative to compute the derivative of g(x)= 1/3x^2
If g(x) = 1/(3x²), the by the definition of the derivative, we have
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{g(x+h) - g(x)}h[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{\frac1{3(x+h)^2} - \frac1{3x^2}}h[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{\frac{x^2}{3x^2(x+h)^2} - \frac{(x+h)^2}{3x^2(x+h)^2}}h[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{x^2 - (x+h)^2}{3x^2(x+h)^2h}[/tex]
[tex]\displaystyle g'(x) = \lim_{h\to0} \frac{x^2 - x^2 - 2xh - h^2}{3x^2(x+h)^2h}[/tex]
[tex]\displaystyle g'(x) = - \lim_{h\to0} \frac{2xh + h^2}{3x^2(x+h)^2h}[/tex]
[tex]\displaystyle g'(x) = - \lim_{h\to0} \frac{2x + h}{3x^2(x+h)^2}[/tex]
[tex]\displaystyle g'(x) = - \frac{2x}{3x^4} = \boxed{-\frac2{3x^3}}[/tex]
Please solve this puzzle
Answer:
a = 25 m²
b = 5 m
c = 7.94 m
d = 35.73 m²
Code: H I A B
Step-by-step explanation:
Formulae
Pythagoras’ Theorem: [tex]a^2+b^2=c^2[/tex]
(where a and b are the legs, and c is the hypotenuse, of a right triangle)
Area of a square = x² (where x is the side length)
------------------------------------------------------------------------------------------------------
Assuming that all the quadrilaterals are squares.
Side length of blue square with area 16 m² = √16 = 4 m
Side length of yellow square with area 9 m² = √9 = 3 m
Use Pythagoras' Theorem to find the length of b:
[tex]\implies 4^2+3^2=b^2[/tex]
[tex]\implies b^2=25[/tex]
[tex]\implies b=\sqrt{25}[/tex]
[tex]\implies b=5\: \sf m[/tex]
Now we have found length b, we can find area a:
[tex]\textsf{Area a}=b^2=5^2=25\: \sf m^2[/tex]
Side length of purple square with area 144 m² = √144 = 12 m
Side length of green square with area 81 m² = √81 = 9 m
Use Pythagoras' Theorem to find the length of c:
[tex]\implies 9^2+c^2=12^2[/tex]
[tex]\implies c^2=63[/tex]
[tex]\implies c=\sqrt{63}[/tex]
[tex]\implies c=3\sqrt{7}[/tex]
[tex]\implies c=7.94\: \textsf{(nearest hundredth)}[/tex]
Now we have found length d, we can find area d:
[tex]\textsf{Area d}=\dfrac{1}{2}(9)(7.94)=35.73\: \sf m^2[/tex]
Code: H I A B
Find b
√16+9√255#a
Area
b²5²25m²H
#b
Done already
I#c
√144-81√63c=7.94A
#d
1/2(7.94)(9)35.73m²B
Code is
HIABFor the exact binomial test, we are using the binomial distribution assuming ____________________ to compute the probability of observing the equal number of successes or more extreme number of successes.
Answer:
The proportion defined by the null hypothesis.
Step-by-step explanation:
I am thinking of a number. I multiply it by 8 and subtract 56.
I get the same answer if I multiply by 5 and subtract 8
What is my number?
Answer:
16
Step-by-step explanation:
[tex]8x-56=5x-8\\\\3x-56=-8\\\\3x=48\\\\x=16[/tex]
So, the number is 16
Mario borrows $620 from his parents and agrees to pay them back the same amount each month without interest. After 6 months of payments, he still owes them $320. Write a linear function to model the remaining amount over time that Francisco has to repay. Identify the slope and the y-intercept in terms of the context.
A linear function that models the remaining amount he would have to repay is y =620 - 50x. The slope is -50 and the y-intercept is 620.
What is the linear function?A linear function is a function in which there is only one variable that is raised to the power of one. Linear functions usually have the form: mx + b.
Where:
x = slope b = y -interceptThe first step is to determine the amount that would be repaid each month: (620 - 320) / 6 = $50
The linear function: =620 - 50x.
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a triangle ABC like the one below suppose that a=40, B = 62 and c= 23 (the figure is not drawn to scale) solve the triangle carry your intermediate computations to at least four decimal places , and round your answers to the nearest tenth . if there is more than one solution , use the button labeled "or"
Answer:
Answer:
A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
∴ A =24.7° ; B = 40.6° ; C =114.7°
Step-by-step explanation:
Im not sure if it is right. But hope it helps
Some newer phones provide a screen time summary, which shows the amount of screen time for a user in a given week. A student would like to estimate the mean screen time for all phone users. She asks a random sample of 50 students at her school to share their screen time for the past 24 hours. The mean screen time for the chosen students is 2.73 hours. Which statement is an appropriate interpretation of the results?
A.)All students probably have screen times close to 2.73 hours.
B.)To obtain a better estimate of mean screen time, more students should be surveyed.
C.)Because of undercoverage, 2.73 likely underestimates the mean screen time of all phone users.
D.)2.73 hours is a suitable estimate for mean screen time of all phone users because a random sample was taken.
Answer:
c
Step-by-step explanation:
got it right on edge
Anyone know the value of x for these
Angle C is inscribed in circle O. AB start overline, A, B, end overline is a diameter of circle O. What is the measure of \angle B∠Bangle, B?
The measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.
What is triangle angle sum theorem?According to the triangle angle sum theorem, the sum of all the angle(interior) of a triangle is equal to the 180 degrees.
In the image attached below:
Angle C is inscribed in circle O. AB is a diameter of circle O.The measure of the angle A is,
[tex]m\angle A=71^o[/tex]
The measure of the angle C in a semicircle is,
[tex]m\angle C=90^o[/tex]
The sum of all the angle(interior) of a triangle is equal to the 180 degrees. Thus,
[tex]\angle A+\angle B+\angle C=180\\90+\angle B+71=180\\\angle B=180-90-71\\\angle B=19^o[/tex]
Thus, the measure of ∠angle B when Angle C is inscribed in circle O and AB is a diameter of circle O, is 19 degrees.
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6a+6b Factorise these expressions.
The coordinates of a parallelogram are given segment AB is parallel to the x-axis determine the values for a,b,c,d
Answer:
a=3 d=1 b and c cant be solved
Step-by-step explanation:
because segment AB is parallel to x axis . So the slope of ABco is 0. So the y value is congruent
a=3 d=1
We know AB=CO b+2=8-C
we can only find ad, but we could not get b,c
need help with this one geometry problem asap
Answer:
Step-by-step explanation:
A cosmetologist conducted a survey to see which color hair was most popular among her customers. She surveyed 160 people. The results are shown in this circle chart.
How many more customers chose brown than red?
24 customers
35 customers
40 customers
88 customers
Circle graph titled Hair Color showing colors by percentage. Sectors are labeled Brown, 40 percent. Red, 15 percent. Black, 25 percent. Blonde, 20 percent.
Answer:
40 customers
Step-by-step explanation:
40% brown,
25% black
20% blonde
15% red
100% = 160
(40* 160)/ 100
6400 / 100 = 64
40% = 64 customers
(15 * 160)/100
2400/100 = 24
15% = 24 customers
64 customers - 24 customers =40 customers.
I need help, question is in image.
Answer:
[tex]9 > x > - 4[/tex]
9 is greater than x and -4 is less than x
Answer:
- 4 < x < 9
Step-by-step explanation:
given 9 is greater than x then x is less than 9 and - 4 < x , so
- 4 < x < 9
Helppp meee please so confused
Answer:
1. Blue = 8 votes
2. Green = 4 votes
3. Yellow = 6 votes
4. Red = 2 votes the first 2 votes one
5. Pink = 2 votes the second one that says 2 votes.
Step-by-step explanation:
okay I understand this.
You just use the colors from above and fill them in in order.
Answer:
1.blue has got 8 number of votes
2.yellow has got 4 number of votes
3.green has got 6 number of votes
4.red has got 2 number of votes
and the last one is written there
Explanation:
I hope it helps
Can someone help me with the steps to create the formula? It involves quadratics
The formula of the quadratic function passing through the points (-2,0), (8,0) and (2, -24) is f(x) = x² - 6x - 16
How to create the formula?The points are given as:
(-2,0) , (8,0) and (2, -24)
The points (-2,0) and (8,0) are the zeros of the function.
So, we have:
f(x) = a(x + 2)(x -8)
Substitute (2, -24) in the above equation
-24 = a(2 + 2)(2 -8)
Evaluate the sum and the difference
-24 = a(4)(-6)
Divide both sides by -24
a = 1
Substitute a = 1 in f(x) = a(x + 2)(x -8)
f(x) = (x + 2)(x -8)
Expand
f(x) = x² + 2x - 8x - 16
Evaluate the like terms
f(x) = x² - 6x - 16
Hence, the formula of the quadratic function is f(x) = x² - 6x - 16
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please tell me the answers of. the question please
Answer:
1%
Step-by-step explanation:
Money spent by the stationer :
100 books x 80 rupees8000 rupeesMoney earned (after donation and sales) :
Donated 10 books = 0 rupeesSold rest at 88 rupees per book90 books x 88 rupees7920 rupeesHere, the money spent is more than the money earned. Hence, we have to find the loss percentage.
Loss % = New - Old / OldLoss % = 7920 - 8000 / 8000Loss % = -80/8000Loss % = -1/100
The loss percentage is 1%
Anna is painting the outside of cardboard box for an art project. The box is a rectangular prism that has a lenght of 24 inches, a width of 24 inches, and a height of 30 inches. Fine the Surface area of the cardboard box.
Show how to write 3/4 with the denominator 12
Solve the equation. Determine the solution(s) and any extraneous solution.
√2x = x - 4
I assume you mean the equation
√(2x) = x - 4
Take the square of both sides. Note that √(2x) is a non-negative number, so any solution we find must also satisfy x - 4 ≥ 0, or x ≥ 4.
(√(2x))² = (x - 4)²
2x = x² - 8x + 16
x² - 10x + 16 = 0
(x - 8) (x - 2) = 0
x - 8 = 0 or x - 2 = 0
x = 8 or x = 2
If x = 2, then x ≥ 4 is false. The only solution is then x = 8.
find the perimeter of the figure below, in centimeters
Answer:
73
Step-by-step explanation:
(7.7 * 2) + (9.6 * 6) = 74
can you help me solve this equation? 20 POINTS
Answer:
x = 63
Step-by-step explanation:
In [tex]\odot \:O, [/tex] ML and MN are tangents from external points M at points L and N respectively. OL and ON are radii of the circle.[tex]\implies ML\perp OL,\:\&\: MN \perp ON[/tex] (By tangent theorem)[tex]\implies m\angle MLO = m\angle MNO = 90\degree[/tex][tex]m\angle LON = 117\degree[/tex] (Given)In quadrilateral LMNO, by interior angle sum theorem, we have:[tex] m\angle LON+m\angle MOL +m\angle MON +m\angle LMN= 360\degree[/tex][tex] \implies 117\degree+90\degree +90\degree +x\degree= 360\degree[/tex][tex] \implies 297\degree+x\degree= 360\degree[/tex][tex] \implies x\degree= 360\degree-297\degree[/tex][tex] \implies x\degree= 63\degree[/tex][tex] \implies\red{\boxed{\bold{ x= 63}}}[/tex]Answer:
63°
Step-by-step explanation:
The central angle is 117°The angles at the tangent are 90° each (property of tangents)Applying the Angle Sum of Quadrilaterals,
117° + 2(90°) + x° = 360°180° + x° = 243°x° = 63°One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. What was the afternoon temperature? Show your work.
One morning the temperature in Bangor, Maine was 18 degrees. By afternoon, it had dropped 20 degrees. The afternoon temperature in Bangor, Maine, was -2 degrees.
To find the afternoon temperature, we need to subtract 20 degrees from the morning temperature of 18 degrees.
Afternoon temperature = Morning temperature - Temperature drop
Afternoon temperature = 18 degrees - 20 degrees
To perform the subtraction, we have to handle negative numbers:
Afternoon temperature = 18 degrees - 20 degrees
Afternoon temperature = -2 degrees
So, the afternoon temperature in Bangor, Maine, was -2 degrees.
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Help me please help me
the answer to that is -120
Step-by-step explanation:
-120+74=-46
Answer:
k = -120
Step-by-step explanation:
k + 74 = -46
Subtract 74 from both sides:
k + 74 = -46
- 74 - 74
k = -120
Final answer: k = -120
Hope this helps!
Which of the following is in standard form of quadratic?
A 13-foot ladder is leaning against a building, forming a right triangle.
The height where the ladder touches the building is seven feet more
than the distance from the base of the ladder to the building. At what
height does the ladder touch the building?
The height from the ground at which the ladder touched the building is 12feet.
What is a right-angled triangle?A right-angled triangle is a type of triangle that has three sides and one of its three angles as 90°.
Analysis:
The ladder length, height of the ladder from the ground, and the distance of the foot of the ladder from the foot of the building form a right angle triangle.
let x, be the distance from the foot of the building to the foot of the ladder.
x+7 = height of ladder from building to foot of building.
length of ladder = 13 feet
using Pythagoras, we have
[tex](13)^{2}[/tex] = [tex]x^{2}[/tex] + [tex](x+7)^{2}[/tex]
169 = [tex]x^{2}[/tex] + [tex]x^{2}[/tex] + 7x + 7x + 49
169 = 2[tex]x^{2}[/tex] + 14x + 49
2[tex]x^{2}[/tex] + 14x = 169-49
2[tex]x^{2}[/tex] + 14x = 120
divide through by 2
[tex]x^{2}[/tex] + 7x - 60 = 0
[tex]x^{2}[/tex] +12x -5x - 60 = 0
(x+12) -5(x+12) = 0
(x+12)(x-5) = 0
x = -12 or 5
Since measurement cannot be negative, therefore x = 5
Height the ladder touches the building is x+7 = 5+7 = 12 feet
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please help me with this
Answer:
In the explanation
Step-by-step explanation:
AB = line segment
ABC = angle
AB = line segment
CD = intersecting line
AC = line segment
AB = line segment
EBC = angle
BC = line segment
The radius of a small ornament in the shape of a sphere is 2 inches. what is the approximate volume of the ornament? use 3.14 for pi. round to the nearest tenth of a cubic inch. recall the formula v = four-thirds pi r cubed. inches cubed
Answer: 33 is your answer my love.
Step-by-step explanation: Hope this helps.
Answer:
33 give the guy above me branliest
Step-by-step explanation:
Find the area of a circle with a diameter of 14 meters. Round your answer to the nearest hundredth of a square meter.
To find the area of the circle:
⇒ need to know the formula: [tex]\pi r^{2}[/tex]
r: radius or half of diameter's length ⇒ 7 metersLet's calculate:
[tex]Area = \pi (7)^2=49\pi =153.9380m^3[/tex]
The problem asks us to round to the nearest hundreth:
[tex]Area = 153.94m^3[/tex]
Answer: [tex]153.94m^3[/tex]
Hope that helps!