The value of a in terms of b is given as [tex]a = 8b^3[/tex]
Given the equation solved by Leo expressed as [tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]
We are to solve the equation for the variable "a"
Given;
[tex]b=\frac{1}{2}\sqrt[3]{a-1}[/tex]
Cross multiply
[tex]2b=\sqrt[3]{a-1}[/tex]
Cube both sides of the equation:
[tex](2b)^3=(\sqrt[3]{a-1})^3 \\8b^3=a-1[/tex]
Add 1 to both sides of the equation:
[tex]8b^3+1=a-1+1\\8b^3=a\\Swap\\a=8b^3[/tex]
Hence the value of a in terms of b is given as [tex]a = 8b^3[/tex]
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Write an integer for each situation
1. A deposit of $40
2. A loss of 20 pounds
What is the simplified form of the following expression? Assume x not-equals 0. RootIndex 5 StartRoot StartFraction 10 x Over 3 x cubed EndFraction EndRoot StartFraction RootIndex 5 StartRoot 10 x EndRoot Over 3 x EndFraction StartFraction RootIndex 5 StartRoot 30 EndRoot Over 3 x EndFraction StartFraction RootIndex 5 StartRoot 120 x cubed EndRoot Over 3 x EndFraction StartFraction RootIndex 5 StartRoot 810 x cubed EndRoot Over 3 x EndFraction.
Equivalent expressions are expressions of different forms that have the same value
The equivalent simplified expression of [tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex] is [tex]\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]
The equation is given as:
[tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex]
Multiply the fraction by 810x^2.
So, we have:
[tex]\sqrt[5]{\frac{10x}{3x^3}} =\sqrt[5]{\frac{10x \times 81x^2}{3x^3\times 81x^2}}[/tex]
Evaluate the products
[tex]\sqrt[5]{\frac{10x}{3x^3}} =\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]
Hence, the equivalent simplified expression of [tex]\sqrt[5]{\frac{10x}{3x^3}}[/tex] is [tex]\sqrt[5]{\frac{810x^3}{243x^5}}[/tex]
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Answer:
d
Step-by-step explanation:
Determine the equation of the line for the given information: The graph has y-intercept (0, 6) and contains the point (2, 1). a. y = 2.5 x + 6 b. y = negative 2.5 x + 6 c. y = 6 x + negative 2.5 d. y = 2 x + 6 Please select the best answer from the choices provided A B C D
The equation of the line for the graph that has y-intercept (0, 6) and contains the point (2, 1) is; y = -2.5x + 6
What is the Equation of the Line in Slope Intercept form?The general form of the equation of a Line in Slope Intercept form is;
y = mx + c
where;
m is slope
c is y-intercept
We are told that the graph has the points (0, 6) and (2, 1). Thus, the formula for slope is;
m = (y₂ - y₁)/(x₂ - x₁)
m = (1 - 6)/(2 - 0)
m = -5/2
m = -2.5
Now, since the y-intercept is at (0, 6), then it means that;
c = 6
Thus, the equation of the line is; y = -2.5x + 6
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A cyclist travels 4 miles in 20 minutes and then a further 6 miles in 30 minutes without stopping. Calculate the cyclist's average speed in mph.
Answer:
11 miles per hr because 10 miles took 50 minutes so add 1 mile and it is 1hr. Which is 11 miles per hr
patrick said that the product of any number and 4 is always double the product of that number and 2. Is patrick correct. explain
Patrick is correct, since the two parts of the statement are equal.
From the question,
Patrick said that the product of any number and 4 is always double the product of that number and 2. We are to investigate if Patrick is correct.
First, let the number be x,
From the first part of the statement
The product of any number and 4
That is,
4 × x = 4x
And
The second part of the statement,
double the product of that number and 2
That is,
2(x × 2) = 2(2x)
Now, we will investigate if
4x = 2(2x)
Expand the right hand side of the equation
That is,
4x = 2 × 2x
Then, we get
4x = 4x
Since the two parts of the statement are equal, then Patrick is correct.
Hence, Patrick is correct, since the two parts of the statement are equal.
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which graph best represents the solution set of y< -4x?
D because the line is not "dotted' and it's on the y intercept and not in the x-axis
Angelo has to pack 7 books in boxes he can pack 7 books in each box how many boxes are need to pack all the books
1 box?
I'm confused whether you made a mistake writing the question or of this is what the actual question is like.
Which of the following functions is graphed below
Answer:
Option B: [tex]y=\left \{ {{x^2+6,x<3} \atop {-x+6,x\geq3}} \right.[/tex]
Step-by-step explanation:
We can see that the first part of the piecewise function is a parabola with a y-intercept of (0,6) where the domain is restricted for all values of x less than 3 given the open circle at x=3.
The second part of the piecewise function is a linear function with a negative slope where the domain is restricted for all values of x greater than or equal to 3 given the closed circle at x=3.
Essentially, the piecewise function has a jump discontinuity at x=3 where the first part of the function goes to the second part of the function at one point by "jumping".
Please help on both. I’m not sure of my answrs before I submit. Thank u :)
Answer:
ok so first you got to wait All the faith he had had had had no effect on the outcome of his life. ...
2 One morning I shot an elephant in my pajamas. ...
3 The complex houses married and single soldiers and their families. ...
4 The man the professor the student has studies Rome.
Step-by-step explanation:
What is 7/4+2/3
I can’t find the answer pls help
Answer:
2.41666666667
Step-by-step explanation:
2.41666666667 is the answer because of the additon. Just convert it.
2.41666666667 as a fraction equals 241666666667/100000000000.
Answer:
7/4 + 2/3 = 2 5/12
Step-by-step explanation:
What is 7/4 plus 2/3?
FractionCalculator
It can sometimes be difficult to add fractions, such as 7/4 plus 2/3.
But it's no problem! We have displayed the answer below:
7/4 + 2/3 = 2 5/12
How did we solve the problem above? When we add two fractions, such as 7/4 + 2/3, we make sure that the two denominators are the same and then we simply add the numerators.
In cases where the denominators are not the same, we find the lowest common denominator and adjust the fractions to keep them.
10 A seal pup gains 28% of its birth weight each
day for the first 10 days of its life.
A one-day-old pup weighs 17.92 kg.
How much did it weigh at birth?
Answer:
WEIGHT
550 to 880 pounds
LIFESPAN
25 to 35 years
LENGTH
7.5 to 10 feet
THREATS
Entanglement, harassment, chemical contaminants, oil spills and energy exploration, vessel and vehicle interactions
REGION
New England/Mid-Atlantic
Step-by-step explanation:
Step-by-step explanation:
Hmm so a pup gains 28% weight every day for the next 10 days.. But a day old puppy weight 17.92kg sooo
28%+10every day=10.28
17.92-28%=12.9
17.92x10=179.2
Hmmmm
Well a seal pup weights 8-12kg on birth so ye I was right anweser is 12
What is the slope of this graph?
0.3
-3
los
1
3
3
1
2 3 4 5
Answer:
A
Step-by-step explanation:
Use the formula rise/run. The rise, in this case, was 3 and the run was 1. There for it would be 3/1 which is simplified to 3.
What is the Area of semicircle?
Step-by-step explanation:
Area of Semi Circle
The area of a semicircle is half of the area of the circle. As the area of a circle is πr2. So, the area of a semicircle is 1/2(πr2 ), where r is the radius.
HELP!! I desperately need help!! I would appreciate if you could show work please!!!
Answer:
a) 137.9°
b) 12.2° (please refer to explanation because I didn't know what to round to)
Step-by-step explanation:
1a) A supplementary angle will equal 180°, so you must subtract 42.1 from 180
180-42.1 = 137.9
1b) A complementary angle will equal 90°, so you need to use the expression given and add an x for the other part of 90°
8x-20+x = 90
9x-20=90
9x=110
x=12.2
HELP ME PLEASE
(NO LINKS PLEASE FOR REAL NO LINKS PLEASE)
1. A student and a teacher work together to make toy cars. The student made 2/7 of the total toy cars, 21 less than the teacher. How many toy cars are there?
The total number of cars both the student and the teacher made is 49
let
total cars = x
cars made by student = s
cars made by teacher = t
Total = student + teacher
x = s + t
s = 2/7x
So,
x = 2/7x + t
x - 2/7x = t
t = (7x - 2x) / 7
t = 5/7x
Similarly,
s = t - 21
s = 5/7x - 21
equate both s equation
2/7x = 5/7x - 21
2/7x - 5/7x = -21
(2x - 5x) / 7 = -21
- 3/7x = -21
x = -21 ÷ -3/7
= -21 × - 7/3
= (-21 × -7) / 3
= 147/3
x = 49
Therefore, the total number of cars both the student and the teacher made is 49
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please answer this, click file, thank you
Answer:
the answer is 34°
Step-by-step explanation:
a straight line = 180°
just do 180 - 146 = 34
HELP ME OUT REAL QUICK!
Answer:
Step-by-step explanation:
ab abahha
What is the slope of the line through (6,9)(6,9)left parenthesis, 6, comma, 9, right parenthesis and (7,1)(7,1)
Answer:
-8
Step-by-step explanation:
I don't really have an explenation
Answer:
y = -8x + 57
Step-by-step explanation:
hope this helps! :)
Hello please answer everything carefully :)
Answer:
Line 3
Step-by-step explanation:
Line three should be
2*3*sqrt(5)-3sqrt(5)
Which equation shows a proportional relationship between x and y?
A. y = 3x + 1
B.y= 4x
C.y = -3x - 2
D.y=9
Answer:
A
Step-by-step explanation:
PLZZZZZZZZZ HELP 30 POINTS AND BRAINLIEST
Cotton farmers constantly battle with insects that want to eat their crops. Geneticists created transgenic cotton with leaves that repelled insects, such as caterpillars.
Which statement best describes an unintended negative consequence of creating the transgenic cotton?
The cotton plants grew at increased rates but produced fewer flowers.
The cotton produced more and larger flowers.
The cotton began dying very quickly.
The caterpillars instead ate the cotton flowers and damaged cotton production.
hi have a nice day,❤️
Occurrence of diversity in ecosystem sustains particular characteristic of a biological community and also ensures stability of the community. Transgenic crops may affect insect biodiversity by unintended impacts on non-target arthropod population. For example, transgenic GM cotton specific to target lepidopterous pests can change the cotton pest spectrum and may induce the growth of new harmful pest species having no pest status. The change in species composition may influence IPM approach in cotton crop. The results of authors’ research studies as well as global impact indicate that GM cotton is highly specific to target pests and has no unintended impact on non-target insect population. GM cotton provides significant season-long field control of target pests (Helicoverpa armigera, Earias spp. and Pectinophora gossypiella), with no significant control of Spodoptera species. The decreased insecticide use in GM cotton has a positive impact on beneficial insect populations and can increase the stability of rare species.
Answer:
The caterpillars instead ate the cotton flowers and damaged cotton production.
Explanation:
Bt cotton was developed for cold temperate countries like the US where pests are limited - chiefly the bollworm, against which the Bt toxin works and pest load in fields is not high.
But the problem is with the warmer climates like India, where bollworms flourish. Over time, because of the sheer amount of bollworms in warmer climates like India or Southern United States, these bollworms grown an immunity to the Bt toxin and we are back to square one.
~That's All Folks~
-Siascon
What angle would you use to represent 5 blue cars out of 20 cars in total on a pie chart?
Answer:
check online for more information
Which quadratic equation is equivalent to (x + 2)2 + 5(x + 2) – 6 = 0?
(u + 2)2 + 5(u + 2) – 6 = 0 where u = (x – 2)
u2 + 4 + 5u – 6 = 0 where u = (x – 2)
u2 + 5u – 6 = 0 where u = (x + 2)
u2 + u – 6 = 0 where u = (x + 2)
Answer:
we have
(x+2)^{2} +5(x+2)-6=0(x+2)
2
+5(x+2)−6=0
Let
u=(x+2)u=(x+2)
Substitute in the expression
(u)^{2} +5(u)-6=0(u)
2
+5(u)−6=0
therefore
the answer is
(u)^{2} +5(u)-6=0(u)
2
+5(u)−6=0 is equivalent to (x+2)^{2} +5(x+2)-6=0(x+2)
2
+5(x+2)−6=0
What are the other steps?
Answer:
63 degrees
Step-by-step explanation:
Angle IGH is 40 degrees because it is vertical to angle BGD.
Angle HIG is 77 degrees because it is a linear pair with CIH.
Since 2 of the angles of triangle GHI are 40 and 77 degrees, and the 3 angles add to 180, angle IHG must be 63 degrees
What is the value of x?
A. 24
B. 33
C. 72
D. 75
Answer:
B. x = 33
Step-by-step explanation:
i need help pleasee. i will give brainlest
Answer:
lp
Step-by-step explanation:
y
This weekend, Jerome earned $252.50 in all. What was the dollar amount of the meals that Jerome served?
Answer:
Is that the full question? I can't solve this unless I have the full question. I don't know how many different meals she sold.
please help! i need for this to be done.
Solve.
t+7.45=1334
Enter your answer as either a decimal or a mixed number in simplest form in the box.
t =
Answer:
t = 6.3
Step-by-step explanation:
t + 7.45 = 13 [tex]\frac{3}{4}[/tex] = 13.75 ( subtract 7.45 from both sides )
t = 6.3
1. Which figure comes next in the pattern below?
The figure that comes next in the pattern below is option D.
Option D is the correct answer.
We have,
From the pattern,
The next figure must be a white figure.
Now,
We see that,
The two small figure inside the figure is moving in a clockwise direction.
So,
The next figure in the pattern is option D.
Thus,
The figure that comes next in the pattern below is option D.
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Select the correct answer.
Which expression is equivalent to the difference shown?
5/m - m+8/ m^2-4m
The expression 5/m - (m+8)/(m^2-4m) is equivalent to 4(m-7)/m(m-4) option (C) is correct.
What is polynomial?Polynomial is the combination of variables and constants in a systematic manner with "n" number of power in ascending or descending order.
We have a expression:
[tex]=\rm \frac{5}{m} - \frac{m+8}{m^2-4m}[/tex]
To simplified the above expression take the LCM [tex]\rm m^2-4m[/tex]
[tex]=\rm \frac{5(m-4)-(m+8)}{m^2-4m}[/tex]
[tex]=\rm \frac{5m-20-m-8}{m^2-4m}[/tex]
[tex]=\rm \frac{4m-28}{m^2-4m}[/tex]
[tex]=\rm \frac{4(m-7)}{m(m-4)}[/tex]
Thus, the expression 5/m - (m+8)/(m^2-4m) is equivalent to 4(m-7)/m(m-4) option (C) is correct.
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Answer:
see photo
Step-by-step explanation:
Plato/Edmentum