Answer:
a)
We know that:
a, b > 0
a < b
With this, we want to prove that a^2 < b^2
Well, we start with:
a < b
If we multiply both sides by a, we get:
a*a < b*a
a^2 < b*a
now let's go back to the initial inequality.
a < b
if we now multiply both sides by b, we get:
a*b < b*b
a*b < b^2
Then we have the two inequalities:
a^2 < b*a
a*b < b^2
a*b = b*a
Then we can rewrite this as:
a^2 < b*a < b^2
This means that:
a^2 < b^2
b) Now we know that a.b > 0, and a^2 < b^2
With this, we want to prove that a < b
So let's start with:
a^2 < b^2
only with this, we can know that a*b will be between these two numbers.
Then:
a^2 < a*b < b^2
Now just divide all the sides by a or b.
if we divide all of them by a, we get:
a^2/a < a*b/a < b^2/a
a < b < b^2/a
In the first part, we have a < b, this is what we wanted to get.
Another way can be:
a^2 < b^2
divide both sides by a^2
1 < b^2/a^2
Let's apply the square root in both sides:
√1 < √( b^2/a^2)
1 < b/a
Now we multiply both sides by a:
a < b
y=-1/4(x-10)^2+28 write in standard form
Answer:
[tex]y = -\frac{1}{4}x^{2} + 5x + 3[/tex]
Kari worked twice as many hours as Chris. She also worked ten less than three times as many hours as Mark. Chris and Mark worked the same number of hours.
Answer:
Kari = 20 hours
Chris = 10
Mark = 10
Explanation:
K is Kari's hours
C is Chris's hours
Karis = 2 x C = K
Chris = C
Mark = C
3C - 10 = K
Assume C is 10 (since 10 is 1/3 of the hours mentioned)
2 x 10 = 20 so K worked 20 hours
20 is twice as much as 10 (C's hours)
and it's 30 - 10 (10 less than 3 times as many hours as Mark)
A bag contains 4 yellow balls, 5 red balls, and 6 blue balls.
Part A: What is the probability of picking a yellow ball from the bag?
Part B: what is the probability of picking a blue ball from the bag?
Part C What is the probability of picking a yellow ball and then a blue ball after
replacement? Determine if the two events are independent events.
Answer:
A) The probability of picking a yellow ball from the bag is 26.66%.
B) The probability of picking a blue ball from the bag is 40%.
C) The probability of picking a yellow ball and then a blue ball is 11.42%.
Step-by-step explanation:
Since a bag contains 4 yellow balls, 5 red balls, and 6 blue balls, to determine what is the probability of picking a yellow ball from the bag, what is the probability of picking a blue ball from the bag and what is the probability of picking a yellow ball and then a blue ball after replacement, the following calculations must be performed:
A)
4 + 5 + 6 = 100
4 = X
15 = 100
4 = X
4 x 100/15 = X
400/15 = X
26.66 = X
Therefore, the probability of picking a yellow ball from the bag is 26.66%.
B)
15 = 100
6 = X
6 x 100/15 = X
600/15 = X
40 = X
Therefore, the probability of picking a blue ball from the bag is 40%.
C)
14 = 100
6 = X
6 x 100/14 = X
600/14 = X
42.85 = X
0.2666 x 0.4285 = X
0.1142 = X
Therefore, the probability of picking a yellow ball and then a blue ball is 11.42%.
Find an equation for the inverse for each of the following relations.
4. y = x - 5
Answer:
y = x + 5
Step-by-step explanation:
We need to find the inverse of the given relation . Firstly replace x with y and then solve for y to get the inverse . We have ,
=> y = x - 5
Replacing x and y=> x = y - 5
=> y = x + 5
Hence the Inverse of the relation is y = x + 5 .Olivia's team played 8 games of basketball. During those 8 games her team's score was: 70, 67, 79, 66, 64, 80, 64 and 75. Find the mode and range
Round to the nearest TENTH.
Question 3 options:
Answer:
64 is the mode and
it goes from 64, 64, 66,67, 70, 75, 79, and 80, so the range is 80- 64 which is 16
Step-by-step explanation:
a polygon is shown what is the measure of U
Answer:
120
Step-by-step explanation:
That's a guess, but it's the most logical one.
You are giving a bag of jelly beans. There are 7 red, 8 blue, 4 elbow, and 10 pink. Find the probability of eating 3 red jelly beans in a row
Only answer if you’re sure... will give Brainly thank you :)
Answer:
Step-by-step explanation:
f(x) = x^2 + 3x - x/2
f(x) = x^2 + 2.5x
3x - 1/2x = 6x/2 - 1/2x = 5x/2 = 2.5x
f(6) = 6^2 + 2.5*6
f(6) = 36 + 15
f(6) = 51
The base of a rectangular prism has an area of 6 cm². The height of the
rectangular prism is 5 cm. What is the volume of the prism?
Answer:
30 cm ^3
Step-by-step explanation:
Volume = Length x Width x Height
L and W =6cm^2
H=5cm
Hope this helps!
NO LINKS. Find the measure of the angle or arc indicated. Part 2
9514 1404 393
Answer:
14. C) 136°
15. C) 40°
Step-by-step explanation:
Inscribed angles are half the measure of the arc they intercept. For an inscribed quadrilateral, this means opposite angles are supplementary.
__
14) ∠H +∠W = 180°
34x +55x +2 = 180
89x = 178 . . . . . . . . . subtract 2
x = 2 . . . . . . . . . . . . . divide by 89
arc VX = 2(34x) = 68(2) = 136 . . . degrees
__
15) The sum of angles in the triangle is 180°.
? + 80° + (120°/2) = 180°
? = 40° . . . . . . . . . . subtract 140°
Answer:
Solution given:
14.
34x+55x+2=180°[sum of opposite angle of a cyclic quadrilateral is supplementary]
89x=180°-2
x=178/89
x=2°
now
m arc VX=2× <H[ central angle is twice the inscribed angle standing on a same base]
m arc VX=2(34×2)=136°
Option C.
15.
Solution given:
<B=80°
<C=½ arc AB[central angle is twice the inscribed angle standing on a same base]
<C=½×120°=60°
we have
<A+<B+<C=180°[ sum of interior angle of a triangle is 180 ]
<A=180-80°-60°
<A=40°
option C.
What is the slope of the following table?
Answer:
slope: 5/2
Step-by-step explanation:
Ms. Silvia earns $3 every time she sells a cupcake. If she earns $15, how many cupcakes did she sell?
Answer:
Okay very easy, The answer is: She sold 5 cupcakes.
Step-by-step explanation:
She sold 5 cupcakes
Because if you add 3 till you get to 15 you get 5
what's the answer to the picture below
9514 1404 393
Answer:
B. √900
Step-by-step explanation:
The solutions to the equation are ...
x = ±√900 = ±3√100 = ±10√9 = ±30
Of the offered choices, the only one that matches any of these is ...
√900
Solve for x.
x + 14
5x - 74
x = [?]
Answer:
[tex]\huge \fbox \pink {A}\huge \fbox \green {n}\huge \fbox \blue {s}\huge \fbox \red {w}\huge \fbox \purple {e}\huge \fbox \orange {r}[/tex]
x + 14 = 5x - 74 (corresponding angles are equal to each other)
[tex]x + 14 = 5x - 74 \\ 14 + 74 = 5x - x \\ 88 = 4x \\ \frac{88}{4} = x \\ 22 = x[/tex]
Answer:
22
Step-by-step explanation:
Angles x + 14 and 5x - 74 are adjacent angles.
Adjacent angles are equal.
5x - 74 = x + 14
5x - x = 14 + 74
4x = 88
x = 88 / 4
x = 22
Simplify the expression. - 17b + a +235 + 240
Answer:
a-17b+475
Step-by-step explanation:
Let's simplify step-by-step.
−17b+a+235+240
Combine Like Terms:
=−17b+a+235+240
=(a)+(−17b)+(235+240)
=a+−17b+475
Answer:
=a−17b+475
Click on three points that are solutions to y = 2x + 1.
A. (0,0)
B. (0, 1)
C. (1,0)
D. (1,3)
E. (2,5)
F. (4,8)
Answer:
B, D, E
Step-by-step explanation:
The school that Emily goes to is selling tickets to the annual dance competition.
On the first day of ticket sales the school sold 3 senior citizen tickets and 14 child tickets for a total of $145.
The school took in $178 on the second day by selling 6 senior citizen tickets and 14 child tickets.
Find the price of a senior citizen ticket and the price of a child ticket.
Answer:
price for senior citizen is $11
price for child ticket is $8
Convert 15L 25ml into litres
Answer:
15.025 L
Step-by-step explanation:
25 mL = 25 ml * 1 L/1000 mL = 0.025 L
15 L + 0.025 L = 15.025 L
if you triple the number of times elizabeth has cooked dinner for her family and then add for you get the number of times her sister joy has coached the family's thinner of joy has cut the family's dinner 25 times how many times did has elizabeth cook dinner?
Answer:
Step-by-step explanation:
She has cooked 75 times
Tessellations
How do you distinguish between problems requiring area formulas and problems requiring perimeter formulas?
a. area - space inside a figure perimeter - distance around figure
b. area - distance around figure perimeter - space inside a figure
c. area - twice the width plus twice the length perimeter - length times width
d. area - the sum of all sides perimeter - 2 times the diagonal of the figure
Please select the best answer from the best choices provided
Answer:
A. Area - space inside a figure perimeter - distance around figure
Step-by-step explanation:
I calculated it logically
WHATS THE ANSWER?? answer ASAP NO FILE AT ALL
Answer:
B
Step-by-step explanation:
Answer:
The answer would be B!
Plz Help!! I’m stuck on this.
Answer:
1. (5,7)
2. (8,0)
3. (2,1)
4. (4,22)
5. (-3,78)
6. (2,10)
7. (3,9)
8. (-2,1)
Step-by-step explanation:
Find the area of the parallaogram to the nearest tenth
Answer:
sorry I think yr question is incomplete.
u forget to add picture.
stay safe healthy and happy.A population of 1,500 insects grows exponentially by a factor of 3 every week. Select all equations that represent or approximate the population, p. as a function of time in days.t, since the population was 1,500.
The required equation that represent or approximate the population is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
To represent the population, P, as a function of time in days, t, we need to find an exponential growth equation.
Since the population grows exponentially by a factor of 3 every week, we need to convert the weekly growth to daily growth.
Let's break down the problem step by step:
The population grows by a factor of 3 every week.There are 7 days in a week, so the daily growth factor can be calculated by taking the 7th root of 3. (Growth factor per day = [tex]3^{(1/7)[/tex])The initial population is 1,500.Now, we can represent the population, P, as a function of time, t, using the exponential growth equation:
[tex]\mathrm P(t) = \mathrm{Initial \ Population} \times \mathrm {Growth \ Factor}^t[/tex]
where:
Initial Population (Po) = 1,500 (given)
Growth Factor per day = [tex]3^{(1/7)[/tex]
So, the equation representing the population as a function of time in days is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
Hence the required equation that represent or approximate the population is:
[tex]\mathrm P(t) = 1,500 \times 3^{(1/7)}^t[/tex]
Learn more about exponential growth click;
https://brainly.com/question/1596693
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Which pair of expressions is equivalent using the Associative Property of Multiplication?
A. 4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
B. 4(2a ⋅ 5) = 8a ⋅ 20
C. 4(2a ⋅ 5) = (2a ⋅ 5) ⋅ 4
D. 4(2a ⋅ 5) = 4 ⋅ 2a ⋅ 5
Answer:
4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
Step-by-step explanation:
Let A, B and C be the required expression, according to Associative property;
(A+B)+C = A+(B+C)
This shows that no matter the sum of values in parenthesis, it does not alter the values at both sides.
From the given expression, the expression that is equivalent using the Associative Property of Multiplication is 4(2a ⋅ 5) = (4 ⋅ 2a) ⋅ 5
Note that the product of the values in bracket do not affect the final values
4(2a ⋅ 5) = 4(10a) = 40a
(4 ⋅ 2a) ⋅ 5 = 8a ⋅ 5 = 40a
You can see that both expressions gives the same values
HELP ME PLEASEEEEEEEEEEEE
Answer:
c
Step-by-step explanation:
6x9=54
54/2= 27
Answer:
27 square units
Step-by-step explanation:
Area of a triangle = (1/2)(base)(height)
A = 1/2(6)(9)
A = 1/2(54)
A = 27
What is the volume of the rectangular prism? . choices: (63yd^3) (7yd^3) (22.5yd^3) (189yd^3)
Answer: (7yd^3)
Step-by-step explanation:
Width= [tex]3*\frac{1}{3}[/tex]
Length= [tex]7*\frac{1}{3}[/tex]
Height= [tex]9*\frac{1}{3}[/tex]
Width= 1
Length= 2.33333333333...
Height= 3
1*2.33333333333*3= 6.99999999999
6.99999999999 is round up to 7
So that would be (7yd^3)
Answer:
Step-by-step explanation:
I just did the test. Answer is 7yd
Factor 3x2 + 42x + 147 completely.
A) 3(x + 1)(x + 49)
B) (3x + 21)(x + 7)
C) 3(x + 7)2
D) (3x + 7)2
(no links please and than you! :))
Answer:
Line D represents a proportional relationship.
Step-by-step explanation:
In an easy way to explain what a proportional relationship is, it is basically a line graph that passes through the origin point. When a line graph passes through the origin point (0,0), it is proportional.
Other graphs do not intersect the origin points so they are not proportional.
Answer:
Line D represents a proportional relationship.
Step-by-step explanation:
In an easy way to explain what a proportional relationship is, it is basically a line graph that passes through the origin point. When a line graph passes through the origin point (0,0), it is proportional.
Other graphs do not intersect the origin points so they are not proportional.
Help I’m stuck on this
Answer:
49 is the answer.
Step-by-step explanation:
[tex] - 11 \frac{2}{3} \times - 4 \frac{1}{5} [/tex]
[tex] - \frac{35}{3} \times - \frac{21}{5} [/tex]
[tex] - 7 \times - 7 = 49[/tex]