We need to know about inequality to solve the given problem. The double inequality to represent the possible length of a gymnastics routine is given by 3≤b≤7.
Inequality is a realtion which makes comparison between numbers or other expressions. Double inequality means when two or more inequalities are joined together. Here in this question we know that each gymnastic routine is at least 3 minutes long. We assume that the length of a gymnastic routine is b, then we can say from the given information 3≤b. It is also said that no gymnastic routine is longer than 7 minutes, so maximum length of any gymnastic routine is 7 minutes, we can write it as, b≤7. Joining these two inequalities we get the double inequality which describes the possible length of a gymnastic routine.
3≤b≤7
Therefore using the concept of inequality we found the double inequality for possible length of gymnastic routine which is 3≤b≤7.
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answer for x
−8x=−x−28
Answer:
x = 4
Step-by-step explanation:
-8x = -x - 28
Move the -x on the right side to the left
-8x + x = -28
-7x = -28
Cross out the negatives
7x = 28
Divide by 7
x = 4
Answer:
[tex]x = 4[/tex]
Step-by-step explanation:
[tex]-8x = -x - 28 \text{ / Add 8x}\\-8x + 8x = -x - 28 + 8x\\\to 0 = 7x - 28 \text{ / Add 28}\\0 + 28 = 7x - 28 + 28\\\to 28 = 7x \text{ / Divide by 7}\\\frac{28}7 = \frac{7x}7\\4 = x[/tex]
Choose the correct term to complete each sentence.
When two functions are combined so the range of one becomes the domain of the other, the resulting function is called a (square root function/composite function).
When two functions are combined so the range of one becomes the domain of the other, the resulting function is called a Composite Function .
Composite Function : If f ( x ) is a function with domain x and f ( x ) = y is its range , then g [ f ( x ) ] is a composite function , where f ( x ) is the domain and g [ f ( x ) ] = z is the range of function g [ f ( x ) ] .
Hence , when two functions are combined so the range of one becomes the domain of the other, the resulting function is called a composite function .
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The apparent brightness of stars is measured on a logarithmic scale called magnitude, in which lower numbers mean brighter stars. The relationship between the ratio of apparent brightness of two objects and the difference in their magnitudes is given by the formula
m₂-m₁=-2.5 log b₂ / b₁, where m is the magnitude and b is the apparent brightness.
The star Rigel has a magnitude of 0.12 . How many times brighter is Capella than Rigel?
Capella is 1.09 times brighter than Rigel.
What is logarithmic equation ?In, mathematics a logarithmic equation is inverse of exponential equation. That means, we can easily convert the logarithmic equation into exponential equation and vice versa. The basic form of the logarithm function can be written as .
[tex]log_ax=N[/tex]
where, a is the base of function or equation
x =expression or equation
There are many formulas that are given to us for solving several simple and complex problems based on logarithmic functions and logarithmic equations. Some of them are listed below.
Some important formulas of logarithms are :
log_c a × b = log_c a + log_c b , c is the baselog a/b = log a - log blog a^x = x log alog a^a = 1log (√x) = 1/2 log (x)In the question given here to us,
We use the given formula:
[tex]m_2-m_1= -2.5log\frac{b_2}{b_1} \\[/tex]
Here, m1 = magnitude of Rigel = 0.12
m2 = magnitude of Capella =0
put the values in eq.
[tex]= > m_2-m_1= -2.5log\frac{b_2}{b_1} \\\\= > - 0.12 = -2.5log\frac{b_2}{b_1}\\\\= > 0.04 = log \frac{b_2}{b_1}\\ \\= > \frac{b_2}{b_1} = 10^{0.04} = 1.09 approx[/tex]
Hence, Capella is 1.09 times brighter than Rigel.
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At an amusement park there are 2 rides. the lightning bolt starts at a elevation of 15ft. from the platform and speeds the passengers to an elevation of 327 ft. The highest loop on the twirl mater is 295 ft and the lowest tunnel goes 21 ft underground. which ride ha the greatest elevation and how much is the change in elevation?
a) Lightning bolt : 312 ft
b) Lightning bolt : 327
C) Twirl Master : 274
d) Twirl Master : 316
The ride that has the greatest elevation based on the information is B. Lightning bolt : 327 feet.
How to illustrate the information?The term elevation is typically used to describe locations on the surface of the Earth, whereas altitude or geopotential height is used to describe locations above the surface, such as those of flying airplanes or orbiting satellites, and depth is used to describe locations below the surface.
Elevations show how your house will appear from various perspectives. Regarding these particular angles, there are many elevation kinds. Some varieties include split elevations, rear elevations, side elevations, and front elevations.
From the information, it was stated that the lightning bolt starts at an elevation of 15ft from the platform and speeds the passengers to an elevation of 327 ft.
It should be noted that the information is to simply find the elevation that is the greatest.
Based on the figures given, the appropriate elevation will be 327 feet.
Therefore, the correct option is B.
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Count by 5 from 6 to 51
Answer:
9
Step-by-step explanation:
keep adding
Alicia ran 6 miles in 21 minutes. At this rate, how long will it take her to run 15
miles? Do not round
Answer:
52.5 minutes
Step-by-step explanation:
[tex]21/6=3.5\\3.5*15=52.5[/tex]
Answer: 52 minutes and 30 seconds
Step-by-step explanation:
You are going to do cross multiplication for this. So 6 miles over 21 minutes is equal to 15 miles over x minutes. When we cross multiply this brings us to 315 over 6. Then we divide 315 by 6 getting us 52.5 minutes and .5 of a minute is 30
Here is a list of four fractions. 3/15 2/10 5/20 15/75 One of these fractions is not equivalent to 1/5
Answer:
5/20 is not equivalent to 1/5.
Step-by-step explanation:
We can start by simplifying all of the fractions, by finding numbers we can divide both the numerator and denominator by the same number.
[tex]\frac{3}{15} =\frac{1}{5}[/tex] by dividing by 3.
[tex]\frac{2}{10} =\frac{1}{5}[/tex] by dividing by 2.
[tex]\frac{5}{20} =\frac{1}{4}[/tex] by dividing by 5.
and last but not least
[tex]\frac{15}{75} =\frac{1}{5}[/tex] by dividing by 15.
We can see that 5/20 is the only one that equals to 1/4 when simplified.
Therefore, 5/20 is not equivalent to 1/5.
Hope this helped! Have a great day!
2. Abby, Chantral, Dougie, Kajan, Minh, and
Zara are all in a race and are considered
to be equally fast. What is the probability
that Abby and Chantral will be the first two
finishers?
1414
Based on the Abby, Chantral, Dougie, Kajan, Minh, and Zara being equally fast, the probability that Abby and Chantral will be the first two finishers is 1/15.
How to find the probability?The probability that Abby and Chantral will be the first two finishers can be found by the formula:
= Number of successful outcomes where Abby and Chantral will be the first two finishers / Total number of outcomes
Solving gives:
= (21! - 4!) / 6!
= 48 / 720
= 1 / 15
In conclusion, the probability that Abby and Chantral will finish first is 1/15.
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Solve using the Quadratic Formula. 5 x²+x=3
The correct answer of the question is {-1+√61}/ 10 or {-1-√61}/ 10 .
The given quadratic equation is 5 x²+x=3
First, we have to convert the equation in the form
ax² + bx + c = 0, then apply the quadratic formula i.e.
x = {-b±√(b²- 4ac)}/ 2a .
Now,
5 x²+x=3
⇒ 5 x²+ x - 3 = 0
Here, a = 5, b = 1 and c = -3
Now, applying quadratic formula
{-b±√(b²- 4ac)}/ 2a
= {-1±√(1²- 4 × 5 × -3)}/ (2 × 5)
= {-1±√(1 + 60)}/ 10
= {-1±√61}/ 10
= {-1+√61}/ 10 or {-1-√61}/ 10
Therefore the final answer to the given equation is is {-1+√61}/ 10 or {-1-√61}/ 10 .
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There are 4 white and 8 red roses in a bouquet. Find the ratios.
the ratio of the number of all roses to the number of red roses
Answer: White rose ratio: 4/12 (simplify) Red rose ratio: 8/12 (simplify)
But you ask for total then red rose so 12/8
Step-by-step explanation: 4+8=12 That is total number of roses. You have 4 white rose so 4 out of 12. Have 8 red rose so 8 out of 12
Write each expression in exponential form. -√17
The number -√17, expressed as a value or number exponential is -17¹/².
What are exponentials?An exponential number is a mathematical expression and one of the many mathematical operations of reduction, it involves the successive multiplication of a number, it has the form:
aᵇ
Where:
a is the number that is multiplied by itself known as the baseb is the number of times it is multipliedTo convert a root into a exponential we must know the way in which these are related, and it is by means of the following property:
√a = a¹/²
Now in our case we have -√17 which can be expressed as.
(-1)√17, where 17 = a, then
(-1)17¹/²
-17¹/²
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1
Write an expression that is equivalent to æ+1+
3
70
Regroup the like terms.
=x+1+
4
314
X
2-
2
3
+
1 1
x=x+1+
2 4
+ (-1/3) + (-1/²)
1
- (++)+(+-)
23
x+ ?
2
x.
?
3
E
X
Answer:
on how to do this
I'm no sure
Answer:
I'm no sure
Step-by-step explanation:
Couldn’t fit all answers choices please help
5. Lines and mare perpendicular. A point Q has this
property: rotating Q 180 degrees using center P has the
same effect as reflecting Q over line m.
a. Give two possible locations of Q.
b. Do all points in the plane have this property?
me
Lines and mare perpendicular is The same result is obtained by reflecting Q over the Line M as well as rotating Q 180 degrees using the center P.
As a reminder, perpendicular lines are those that cross at a 90-degree angle. Two non-vertical lines are said to be perpendicular when they are in the same plane and intersect at a right angle.
The axes of the coordinate plane, or the horizontal and vertical lines, are simply perpendicular to one another. Additionally, the slopes of the parallel lines have negative reciprocal slopes.
Since Lines L and M are perpendicular lines, or lines that meet at a right angle (90°), rotating Q 180 degrees using the center P has the same result as reflecting Q across Line M.
Q will therefore be identical to reflecting Q over any of the perpendicular lines when rotated 180 degrees from the center.
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Need help , having trouble with this
Answer:
that would 14 jars LoL in of pop tarts
Gwendolyn draws a hotdog on graph paper using the scale shown below. The hotdog has a length of 999 units in the drawing. What is the length in c, m, , of the actual hotdog?
The length of the actual hotdog is 15 cm
How to determine the length of the actual hotdog?The graph that completes the question is added as an attachment
The length of the hotdog in the figure is given as
Length = 9 units
The scale is given as
Scale: 6 units = 10 cm
So, we have
6 * 9 units = 10 * 9 cm
Divide both sides by 6
So, we have
9 units = 15 cm
Substitute 9 units = 15 cm in Length = 9 units
Length = 15 cm
Hence, the length of the actual hotdog is 15 cm
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2+(889*567)+8402773+29273
Answer:
8936111
Step-by-step explanation:
2+(889*567)+8402773+29273 =
2 + 504063 + 8402773 + 29273 =
8936111
HELPPP ASAPPP!!!!In 5-7 complete sentences, write a real world situation that can be modeled by the equation. 19.25x =17.25x +26.77
A situation in the real world that the equation can simulate. A corporation charges 19.25 per hour, whereas another charges 17.25 per hour plus a one-time fee of 26.77. This is represented by 19.25x =17.25x +26.77. How many hours do they cost the same?
What is a equation?An equation is used to show the relationship between the variables that are illustrated.
In this instance, a situation from the actual world that the equation can simulate.
A corporation charges 19.25 per hour, whereas another charges 17.25 per hour plus a one-time fee of 26.77.
This is represented by 19.25x =17.25x +26.77. How many hours do they cost the same?
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how do you compare 6.51326 and square root of 39
Answer:
6.51326 is greater than √38
Step-by-step explanation:
6.51326 compared with √39
6.51326 compared with 6.244998
means 6.51326 is greater than √38
determine what type of solutions the function f(x)=x^2+9 will have
Type of solutions the function f(x)=[tex]x^2[/tex]+9 will have Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}. Range is [-9,[tex]\infty[/tex]),{y|y≥-9}.
Given function [tex]f(x)=x^{2} +9[/tex]
To determine the function's domain and range.
Domain and range is nothing but the sets of all the x-coordinates and all the y-coordinates of ordered pairs, respectively, are the domain and range of a relation. For instance, if the relation is R ={(1, 2), ( 2, 2), ( 3,3 ), ( 4, 3)}
Domain is the set of all x-coordinates with values of {1, 2, 3, 4}.
The set of all y-coordinates in the range is equal to {2, 3}.
Domain and range for the function is
Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}.
range is [-9,[tex]\infty[/tex]),{y|y≥-9}
Therefore, the function has the domain and range as
Domain is (-[tex]\infty\\[/tex],[tex]\infty[/tex]),{x|x∈R}.
range is [-9,[tex]\infty[/tex]),{y|y≥-9}.
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What is 5,780 divided by 240 as a decimal?
A 24.083324
B 24.08324,083
C 24.08324
D 24.083
Answer:
answer is D
how ?
when doing long division it will give 24.0833333333 so to 3dp is 24.083
Hunter kicked a soccer ball. the ball went 33/2 yards in 3/8 second. at that rate, how far would the ball go in 1 second?
The ball would go 44 yards in 1 seconds
How to calculate the number of yards ?
Hunter kicked a soccer ball
It went 33/2 yards in 3/8 seconds
The distance it will travel in 1 second can be calculated as follows
33/2 = 3/8
x= 1
Cross multiply both sides
3/8x = 33/2
x= 33/2 ÷ 3/8
x= 33/2 × 8/3
x= 44
Hence the ball will move 44 yards in 1 second
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what are the zeros of the function below f(x)= x^2-x-12/x^2+x-12
The function is equal to zero when x = -3 or +4
What are the zeros of a function?We know that a function is a mathematical rule. It is an instruction to perform an operation on a given set of values. In this case, we have the function given as; f(x)= x^2-x-12/x^2+x-12. Recall that the function is equal to zero when the numerator is equal to zero.
Now we have to solve the quadratic equation;
x^2-x-12 =0
x^2 - 4x + 3x - 12 = 0
x(x - 4) + 3(x - 4) = 0
(x - 3) (x - 4) =0
x = -3 or +4
We can now see that the function is equal to zero when x = -3 or +4
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domain of 3 cubed of 1 minus x squared
Please help me with this!!! Will give Brainliest!
Answer:
Step-by-step explanation:
Perimeter = 110 in
Area = 490 in²
You have 4 tests so far and you scored 12, 14, 11, 13. You want to keep your overall average at 12. Write and solve
the equation you would use to find what do you need to score on your fifth test to keep this average.
Answer:
You would need to score a 10.
Set-UpThe equation is going to have a total of 5 values where one is unknown. We will call this unknown x and include it as a value in the equation.
Since we are going to have to find an average, we will need a fraction. We also know we will take five total tests. This will equal 12 as this is the desired average.
To start, create the fraction that will add all five values together and divide that by the number of values.
[tex]\displaystyle \frac{12+14+11+13+x}{5}[/tex]
Then, set this equal to 12.
[tex]\displaystyle \frac{12+14+11+13+x}{5}=12[/tex]
SolveTo solve, we will first combine all like terms.
[tex]\displaystyle \frac{50+x}{5}=12[/tex]
Then, divide the fraction.
[tex]\displaystyle 10+\frac{x}{5}=12[/tex]
Now, move the constants to the right side of the equation. To do this, subtract 10 from 12.
[tex]\displaystyle \frac{x}{5}=2[/tex]
Finally, multiply both sides of the equation by 5 to get rid of the denominator.
[tex]x=10[/tex]
Therefore, on test 5, you must score a 10 to maintain an average of 12.
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The perimeter of a square is 20 centimeters. Find the length of a diagonal. Sketch the figure. Round decimals to the nearest tenth (1 decimal place).
length of a diagonal =
The length of the diagonal is 7.05cm of a square.
The perimeter of the square is 20 cm.
The formula of the perimeter of the square is 4a, where a is the length of the side of the square.
So, 4a = 20
a = 5
Now we have to find the diagonal of the square.
In a square there is two diagonal, each of equal length
Therefore,
diagonal = [tex]\sqrt{2}[/tex]a
= 1.41 × 5
7.05cm
Therefore the diagonal of the square is 7.05cm.
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Two trains going in opposite directions leave at the same time. train b travels 10 mph faster than train a. in 7 hours the trains are 630 miles apart. find the speed of each.
If two trains going in opposite directions leave at the same time and train b travels 10 mph faster than train a and in 7 hours the trains are 630 miles apart, then the speed of the faster and slower train is equal to 50mph and 40mph respectively.
The speed of each train can be determined by using an algebraic
expression.
As one train travels 10 miles per hour faster than the other, consider x to be the speed of the slower train. In this case, the algebraic expression to find the speeds of each train can be given as,
7x + 7(x + 10) = 630
7x + 7x + 70 = 630
14x = 630 - 70
14x = 560
x = 560 ÷ 14
x = 40 mph
Therefore, x + 10 = 40 mph + 10 mph = 50 mph
Hence, the speed of the faster train is 50 mph and the speed of the slower train is 40mph.
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someone plis help me with algebro 3 homeowrrok :((((((
Answer:
Step-by-step explanation:
Company A:
The recursive formula is, aₙ=aₙ₋₁+4,000, where a₁=42,000
Company B:
The recursive formula is, aₙ₊₁=(1+0.09) x aₙ, where a₁= 42,000
I'm sure she should go for company B, in the long run, she would make much more money. This is proven because company a is increasing using an arithmetic sequence; based on this all they're doing is adding 4,000. But company B is increasing at a percentage of 9 after a while that can really amount to a lot.
Hope this helps, if you are still confused don't hesitate to ask :))
Josie's pay [tex]a_n[/tex] from company A in the [tex]n[/tex]-th year is given recursively by
[tex]\begin{cases} a_1 = 42000 \\ a_{n+1} = a_n + 4000 & \text{for } n\ge1 \end{cases}[/tex]
while her pay [tex]b_n[/tex] from company B is
[tex]\begin{cases} b_1 = 42000 \\ b_{n+1} = 1.09 b_n & \text{for } n \ge1 \end{cases}[/tex]
From these recurrences, we have
[tex]a_2 - a_1 = 4000[/tex]
[tex]a_3 - a_2 = 4000[/tex]
[tex]a_4 - a_3 = 4000[/tex]
and so on - this is just confirming that the pay from company A increases at flat rate of $4000 each year.
Similarly,
[tex]b_2 = 1.09 b_1 = 45780 \implies b_2 - b_1 = 3780[/tex]
[tex]b_3 = 1.09 b_2 \approx 49900 \implies b_3 - b_2 \approx 4120[/tex]
[tex]b_4 = 1.09 b_3 \approx 54391 \implies b_4 - b_3 \approx 4491[/tex]
and we see here that [tex]b_n[/tex] increases at a larger rate year. In only 2 years of working at company B, Josie would be making more money, and the amount by which her salary increases each year is also increasing.
Assuming Josie hopes to make more money, invest in her future, etc, she should take the offer from company B.
6x+1=-6(1-x) kinda need as soon as possible
Answer:
No solution
Step-by-step explanation:
The sides of the equation are unbalanced, therefore, the equation has no solution. Here's an example(The problem is not designed to mathematically make sense).
[tex]x + 1 = -y \times z\\(w)x+1-1=-y+(z)x-1\\0 = -b[/tex]
Since the first side which was equal to 0 is unbalanced to the other side, the rule is that [tex]a = \mathrm{false\:if}\:a < 0[/tex], and since this rule applies in such a scenario, the equation ends up having no solutions.
Hope this helps!