Step-by-step explanation:
Use this algebra 2 theorem:
If r and q are roots of a polynomial function then
the polynomial function can be expressed as
[tex](x - r)(x - q)[/tex]
Here the roots are
1- root of 6, 1+ root 6, and. 7-i so our. function can be expressed as
[tex](x - (1 - \sqrt{6} ))(x - (1 + \sqrt{6} ))(x - (7 - i))[/tex]
The first two binomials are difference off squares so the we have
[tex] {x}^{2} + x( - 1 + \sqrt{6} ) + x( - 1 - \sqrt{6} ) + ( - 5)[/tex]
[tex] {x}^{2} - 2x - 5[/tex]
The other root is (7-i).
Also note since (7-i) is a root, then (7+I) is also a root.
So
[tex](x - (7 - i)(x - (7 + i)( {x}^{2} - 2x - 5)[/tex]
[tex]( {x}^{2} - 14x + 50)( {x}^{2} - 2x - 5)[/tex]
Simplify and it gives us
[tex] {x}^{4} - 16 {x}^{3} + 73 {x}^{2} - 30x - 250[/tex]
round 68.321 to the nearest tenth
Answer:
When 68.321 rounded to the nearest tenth the result is 68
Which of the following is the solution to 3I x-1 I≥ 12?
A. x≤ -3 or x≥ 5
B. x≤ -3 and x≥ 5
C. x≥ 5
D. x≥ -3 or x≥ 5
The solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
For the given inequality the solution can be found as,
When the value of x is negative,3|x-1| ≥ 12
x-1 ≥ 4
x ≥ 5
When the value of x is positive,3|x-1| ≥ 12
- x + 1 ≥ 4
-x ≥ 3
x ≤ -3
Hence, the solution for the given inequality will be x≤ -3 or x≥ 5. Thus, the correct option is B.
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Help me pls. I need the answer so i can get a good grade and get my math credit
Answer:
D
Step-by-step explanation:
the zero is the value of x where the line crosses the x- axis, that is
zero is x = - 2
Jada is comparing membership costs for two gyms. What is the difference in membership costs after m months if she joins Be strong instead of Zippy Health Club?
Write an expression for each membership cost for m months and subtract them.
Answer: Difference in membership costs after m months = -($24.96m + $34.94)
Step-by-step explanation:
Cost of Zippy health club = $49.95 + $19.95 per month
Cost of Be strong = $24.99 per month and $10 off the first month
Total cost after m months of Zippy health club = $49.95 + $19.95m
Total cost after m months of Be strong = $24.99 (m - 1) + $ 10
Difference in membership costs after m months ={ $24.99m - $24.99 + $10 ]-[$49.95m + $19.95}
=$(24.99 - 49.95) m -$14.99 - $19.95
= -$24.96m - $34.94
=-($24.96m + $34.94)
So Difference in membership costs after m months =-($24.96m + $34.94)
therefore jada have to pay more if she joins Be strong.
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bill $42 , tax 9% , tip 18%
Answer:
Tax 3.78 $ and tip 7.56 $
Step-by-step explanation:
42*0.09 = 3.78
42*0.18 = 7.56
Drag each tile to the correct box.
A certain kind of bacteria multiplies at a rate of 150 percent per hour. When a person’s blood has 45,000,000 of these bacteria, the person will fall sick. Let’s suppose 100 such bacteria entered a person’s blood. How many hours will it take for the person to become sick? Arrange the steps in the right order to show how to find the number of hours it will take for the person to fall sick.
The steps arranged in the right order are:
45,000,000 = [tex]100(1 + 1.5)^{t}[/tex]
45,000,000 = [tex]100(2.5)^{t}[/tex]
450,000 = [tex](2.5)^{t}[/tex]
log 450,000 = log [tex](2.5)^{t}[/tex]
log 450,000 = log t (2.5)
[tex]\frac{log 450,000}{log 2.5} = t[/tex]
5.632 / 0.3979 = t
t = 14.21 hours
What are the correct steps?The equation that can be used to represent the growth rate of the bacteria is an exponential equation. The form of exponential equations is:
FV = P(1 + r)^t
Where:
FV = future value of the bacteria PV = present population r = rate of increase t = number of hours45,000,000 = 100( 2.5)^t
t = log 450,000 / log 2.5
t = 14.21 hours
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Find the value of y.
Answer:
its 0
Step-by-step explanation:
you just gotta do the math correctly to get the answer. x & y are both values with different meanings. but in this case it's 0
Find the slope of the line that goes through (2, 8) and (5, 13).
Answer:
1 (2/3) or 1.66666667
Step-by-step explanation:
The slope of a line is found by using the equation :
y2 - y 1 / x2 - x1
So all we have to do is plug in our values given.
To find which belongs with which variable (such as x2 or y1), we do the following:
We know that the coordinates of a point are represented by (x, y). So we must assign a number to each points number.
(2, 8) will be x1 and y1.
(5, 13) will be x2 and y2
Plug in the values :
13 - 8 = 5
5 - 2 = 3
5 / 3 = 1 (2/3)
So, the slope of the line is 1.66666667 or 1 and (2/3)s
Can someone help me with this?
D option is correct by SSS congruence rule
Solve for x :
[tex] \sf \: \: \: \: \: \: \: \: \: \: \: 29x + x = 30[/tex]
[tex] \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ [/tex]
[tex] \tiny \sf bluh... \: \: so \: \: boring[/tex]
Answer:
x = 1
Step-by-step explanation:
Step 1: Combine like terms.
[tex](29x + x) = (30)[/tex] [tex]30x=30[/tex]Step 2: Divide both sides by 30.
[tex]30x/30=30/30[/tex] [tex]x=1[/tex]Step 3: Check if solution is correct.
[tex]29(1)+(1)=30[/tex] [tex]29+1=30[/tex] [tex]30=30[/tex]Therefore, x = 1.
Solution: X=1
[tex]\searrow[/tex]
Detailed explanation:
Here we need to solve for x. x is our unknown. It's what we should find.
[tex]\searrow[/tex]
Note right up front that we can add the x's. This is a process that is known as "Combining Like Terms". We can combine them by adding, like here.
[tex]\twoheadrightarrow\sf 29x+x=30[/tex]
"x" is the same as 1x.
[tex]\twoheadrightarrow\sf 30x=30[/tex]
We're getting closer to finding the value of the unknown!
Now we know that if we multiply 30 times the unknown, we will get 30.
What will we get if we multiply 1 times the unknown? 1 is what we will obtain upon dividing by 30.
So our unknown, or x, is 1.
Voila! There's our answer!
Cheers! ^-^_____________________________
Hope I helped! Best wishes.
Reach far. Aim high. Dream big.
_____________________________
(d) Two alarm clocks are set to ring at intervals of 42 minutes and 56 minutes respectively. If the alarm clocks ring together at 0830, at what time will they next ring together again?
Answer:
11:18
Step-by-step explanation:
the lowest common multiple [meaning the nearest possible time these clocks will be ringing at the same time] of 42 and 56 is 168
(56 x 3 = 168 ; 42 x 4 = 168)
So, in 168 minutes, the clock will ring together again.
Now, we need to add 168 minutes to 08:30
(168 can be made up of 2 hours and 48 minutes [120 + 48 = 168])
08:30 + 2 hours = 10:30
10:30 + 48 minutes = 11:18
So, at 11:18, these clocks will ring together again
At Total Viewing, the
wholesale price of a 52-inch television is
$1.950. What does it cost to buy the
television if the store's markup is 15%?
Answer:
It would be 2242.5
Step-by-step explanation:
1950X0.15=292.5
292.5+1950=2242.5
Sonam says that the 20th figure in this pattern has 400 small triangles. do you agree? explain your thinking.
Answer:
No. There should be 210 small triangles
Step-by-step explanation:
The number of small triangles in these figures forms a sequence
Fig No Small Triangles
1 1
2 3 (1+2)
3 6 (1+2+3)
So the nth figure should have 1+2+3+.....+(n-1)+ n
1+2+3+.....+(n-1)+ n = [tex]\frac{n (n-1)}{2}[/tex]
So for 20th figure, n = 20 and number of small triangles = 20 x 21 /2 = 420/2 = 210
I just asked a question and this user name venus1234 deleted it for "Violating the Brainly Code" blah blah blah..............Here's the question. Points A and B are on a line with a slope that is . Point C is on the same line. Which could be the ratio of rise to run between points B and C? A. 9/12 B. 8/5 C. 14/17 D. 15/24 please hurry! :) thats all and I apparently "violated the code" I don't understand Isn't this a site for asking questions?
The ratio of rise to run between points B and C is the same as the slope of line AB
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Slope of a line = ratio of rise to run = rise / run
Hence:
The ratio of rise to run between points B and C is the same as the slope of line AB
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Philippa threw some darts. Her minimum score was 5 and
her maximum score was 53. What was the range of her
scores?
Min = 5
Max = 53
Range = ?
[tex]\frac{16x^{2} y^5}{(-4x^-6)( y^8)}[/tex]
simplify
please help me with these or just the first one even ty
Answer:
-3+15-75+375
=12-75+375
=-63+375
=302
n=8
302÷8 = 37
Select all the correct answers.
Which expressions are equal to
Given the data from the question, the expressions that are equal to 10⁵ are
10³ ⋅ 10²10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10To determine the expressions that are equal to 10⁵, we shall evaluate the options given from the question.
How to evaluate (10⁴)¹Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10⁴)¹ = 10⁴
How toevaluate 10³ ⋅ 10²Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
Thus,
10³ ⋅ 10² = 10³⁺²
10³ ⋅ 10² = 10⁵
How to evaluate 1 / 10⁵Recall
1 / Aᵐ = A⁻ᵐ
Thus,
1 / 10⁵ = 10⁻⁵
How to evaluate (10³)²Recall
(Aᵐ)ⁿ = Aᵐⁿ
Thus,
(10³)² = 10⁶
How to evaluate 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10Recall
Aᵐ ⋅ Aⁿ = Aᵐ⁺ⁿ
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10¹⁺¹⁺¹⁺¹⁺¹
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
SUMMARY
(10⁴)¹ = 10⁴
10³ ⋅ 10² = 10⁵
1 / 10⁵ = 10⁻⁵
(10³)² = 10⁶
10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 = 10⁵
From the above illustrations, only 10³ ⋅ 10² and 10 ⋅ 10 ⋅ 10 ⋅ 10 ⋅ 10 are equal to 10⁵
Complete question
See attached photo
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Given parallelogram ABCD and AB || CD, if mAB = -5 then mCD must be:
A)-5
B)
- 1
——
5
C) 5
D) 1
—
5
The slope of CD, which is parallel to AB must be: A. -5.
What is the Slope of Parallel Segments?If two line segments are parallel to each other, their slope value (m) would be equal to each other.
Side AB and CD in the parallelogram are parallel segments, therefore, their slope (m) would be the same.
Slope (m) of AB = -5, therefore, the slope of CD must be: A. -5.
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23 4 Which expression is equivalent to (- 2 1/4)/(- 2/3) ?
The equivalent expression is: .[tex]3\frac{3}{8}[/tex]
What is expression?An expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division)
Given:
(- 2 1/4)/(- 2/3)
=-9/4÷ (-2/3)
= -9/4 * (-3/2)
= 27/8
= [tex]3\frac{3}{8}[/tex]
Hence, the equivalent fraction is [tex]3\frac{3}{8}[/tex].
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Examine the following dot plot.
A dot plot with 1 dot above 5, 1 dot above 10, 1 dot above 20, 2 dots above 30, 5 dots above 40, and 6 dots above 50.
© 2018 StrongMind. Created using GeoGebra.
Which answer correctly describes the shape of the data in the dot plot?
right-skewed
left-skewed
symmetrical
uniform
The data in the plot is Right skewed.
Therefore , Option A is the right answer
What is a Right skewed ?A right skewed distribution means most of the data lies to the right side of the graph's peak.
A dot plot is given and observing the data it can be seen that peak is towards the right side of the graph.
Thus the data in the plot is Right skewed.
Therefore , Option A is the right answer.
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Volume and surface area rectangular prism
13 in 7in 7in
The Volume and Surface Area of Prism is 462 in² and 637 in³.
What is Prism?
Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections.
Surface area of rectangular prism,
= 2( lb +bh +lh)
= 2 ( 13*7 + 7*7+ 13*7)
=2*231
= 462 in²
Now, Volume,
= bhl
= 13*7*7
= 637 in³
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The length of a conference room is one and a half times its width. There is a carpet in the
centre of the room. The length of the carpet is twice its width. This leaves a 3m wide
border around the edges of the carpet. Find the area of the carpet.
The Area of carpet for the given dimension is 72m².
What is Area of rectangle?Area of rectangle is the region occupied by a rectangle within its four sides or boundaries. The area of a rectangle depends on its sides.
Let the width of the room w = x m
and the length, L = 1.5x
Length of carpet + 6 = length of room
2(x-6)+6=1.5x
2x-12+6=1.5x
0.5x=6
x = 6 / 0.5
x = 12
length of room x = 12 m
width of room = 18 m
18-6 by 12-6 = 12 by 6 dimensions of carpet
Area of carpet = 12 X 6=72 m²
Thus, the Area of carpet for the given dimension is 72m².
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find the value of x
a) 5
b) 35
c) 3
d) 7
Answer:
x=3
Step-by-step explanation:
due to its same angle of the graphic. it has to be +6 as well
23-29-35
35=11.×+2
35-2=33
33=11.×
x=3
Lines CD and DE are tangent to circle A, as shown below:
Lines CD and DE are tangent to circle A and intersect at point D. Arc CE measures 110 degrees. Point B lies on circle A.
If arc CE is 110°, what is the measure of ∠CDE?
55°
70°
100°
Using the outside angle theorem, the measure of angle CDE is: 70°.
How to Apply the Angle of Intersecting Tangents Theorem?According to the angle of intersecting tangents theorem, we would have the following equation using the diagram given:
Angle CDE = ½(measure of arc CBE - measure of arc CE)
Given the following:
Measure of arc CE = 110°Measure of arc CBE = 360 - 110 = 250°Plug in the values into the equation
Angle CDE = ½(250 - 110)
Angle CDE = 70°
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Answer: Angle CDE = 70°
Step-by-step explanation:
Yaqub, Angus and Iris share 18 slices of pizza in the ratio
1:3:2.
How many slices of pizza does Iris have?
Answer:
6 Slices
Step-by-step explanation:
Total units = 1 + 3 + 2 = 6 Units
6 Units = 18 Slices of Pizza
Iris shared 2 units.
1 Unit = 18/6 = 3 Slices of Pizza
2 Units = 2 * 3 = 6 Slices of Pizza
PLEASE ANSWER ASAP!!!!!!!!
A Ferris wheel completes 7 revolutions in 14 minutes. The radius of the Ferris wheel is 30 feet.
What is the linear velocity of the Ferris wheel in inches per second?
Enter your answer, rounded to the nearest tenth, in the box.
The linear velocity of the Ferris wheel in inches per second is 18.9 inches/second.
What is the speed of an object?The speed of an object is the ratio of the total distance covered by the object and the total time taken by the object to complete that distance.
Here, the radius of the Ferris wheel is (r) = 30 feet.
The circumference of the wheel is
C= 2πr
C= 2 × π × 30 feet
C= 60π feet
Here, the Ferris wheel completes 7 revolutions.
Therefore, it covers the linear distance of
D= 7 × circumference of the wheel
D= 7 × 60π feet
D= 420π feet
Now, the Ferris wheel took 14 minutes to complete 420π feet.
Therefore, the speed of the wheel is
S= (420π/14) feet/minute
S= 30π feet/minute
S= (30π × 12)/60 inches/second
S= 6π inches/second
S= 18.9 inches/second
Therefore the linear velocity of the object will be 18.9 inches/second
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Jamie is interested in taking dance lessons, but she would have to pay $35 for balet shoes and also pay $20 per hour. write an ssion that represents jamies total cost in terms of h
PLLLEAASSEE HELP ME!!
AND IF YOU DON"T MIND EXPLANING TO ME HOW TO SLOVE THESIS TYPE OF PROBLEMS CAUSE IM SO CONFUSED
Answer:
75 Seconds
Step-by-step explanation:
First divide 90,000 by 16 then square root that answer for 75 and when you plug it in you'll end up with -90,000 + 90,000
If y varies inversely as x, and y = 58 when x = 9, find y when x = 261.
Answer:
y = 2
Step-by-step explanation:
Y varies indirectly with x (as x gets bigger, y gets smaller)
You have to find k, the constant of proportionality.
y = [tex]\frac{k}{x}[/tex]
Plus in the x & y values you are given
58 = [tex]\frac{k}{9}[/tex] Multiply both sides by 9 to solve for k
k= 522
Now plug in the new value of x to solve for y
y = [tex]\frac{522}{261}[/tex]
y = 2
