The area of a square with a side length √8 represents a rational number, which is equal to 8 square units.
Is the number behind the area of the square a rational number?
Rational numbers are real numbers of the form m / n, where m and n are integers, where n ≠ 0. The rest of real numbers are irrational (i.e. π, √5, ∛7, e) Besides, the area of the square is determined by the following formula:
A = l²
Where l is the side length of the square.
First, substitute the side length of the square in the area formula:
A = (√8)²
Second, use algebraic properties to simplify the expression and find the corresponding result:
A = ([tex]8^{\frac{1}{2} }[/tex])²
A = 8
This number represents a rational number as 8 is equivalent to the rational number 8 / 1.
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Calculate the height (in m) of a cliff if it takes 2.41 s for a rock to hit the ground when it is thrown straight up from the cliff with an initial velocity of 8.14 m/s. (Enter a number.)
How long (in s) would it take to reach the ground if it is thrown straight down with the same speed? (Enter a number.)
The height of the cliff is 7.57m and the time to reach the ground when thrown straight down is 0.814s
What is motion under gravity?Motion under gravity refers to the movement of an object whose vertical motion is affected by the presence of gravity. The force that attracts objects downwards is GRAVITY. In fact, gravity works towards the centre of the Earth.
When an object is moving upward,it is moving against gravity and when it is moving down it is moving with gravity.
from equation of motion
H= ut-1/2gt^2( the object is moving upward)
where h is the height of the cliff and u is the initial velocity and g is acceleration due to gravity
(g=10ms^-2).
therefore h= 8.14×2.41-(1/2×10×2.41)
= 19.62-12.05
h= 7.57m
when the object is thrown Down,
V = u + gt
u will be 0 at top before coming down
V = gt
t= 8.14/10
= 0.814s
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Question 2b answer please
and working out
Answer:
20 mph
Step-by-step explanation:
If it took the car originally 12 minutes to travel the road with an average speed of 60 mph. Than you would just divide the average speed by three because it is taking 3 times the amount of time than it would originally.
36/12=3
60/3=20
20 mph
If f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55, then find the
value of f(-1), to the nearest hundredth.
The value of the exponential function (-1) will be equal to f(-1) = -0.02.
What is an exponential function?The mathematical expression f(x)=exp or e^x denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, though it can be extended to complex numbers or adapted to other mathematical objects.
Given that f(x) is an exponential function where f(-3) = 11 and ƒ(4) = 55. The value of the exponential function will be calculated as,
[tex]y=ax^b[/tex]
[tex]11=a(-3)^b\\55=a(4)^b[/tex]
Calculate the value of constants,
log5 = blog(4 / 3)
b = 0.7 / 0.125
b = 5.6
The value of 'a' will be,
11 = a(-3)⁵°⁶
a = -0.02
The exponential function f(-1) will be calculated as,
f(-1) = -0.02(-1)⁵°⁶
f(-1) = -0.02
Therefore, the value of the exponential function (-1) will be equal to f(-1) = -0.02.
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Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus
The equation of the line in the graph is y = 4x - 9..
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
The line forms a linear equation.
Therefore,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (0, -9)(3, 3) let's find the slope
m = 3 + 9 / 3 - 0
m = 12 / 3
m = 4
Therefore, let's find the y-intercept using (0, -9).
-9 = 4(0) + b
b = -9
Therefore, the equation is y = 4x - 9.
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Bahir is h cm tall. Sienna is 4 cm taller than Bahir.
Write down an expression, in terms of h, for Sienna’s height.
Answer:
.
Step-by-step explanation:
The graph shows Derek’s pay compared to the hours he has worked.
What is Derek’s hourly rate of pay?
Charlie earns $52.25 in 5 hours of work. What is Charlie’s hourly rate of pay?
Who gets paid more per hour? How much more?
Answer:
Charlie gets paid more then Derek. Charlie gets paid per hour $52.25
An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. He believes that the mean income is $28, and the standard deviation is known to be $5.5. How large of a sample would be required in order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42? Round your answer up to the next integer.
In order to estimate the mean per capita income at the 90% level of confidence with an error of at most $0.42. The sample size would be 85
How to find the size of sample when the error of at most $0.42Information form the question
the mean income is $28
the standard deviation is known to be $5.5
the mean per capita income at the 90% level of confidence
an error of at most $0.42
What is the formula for the sample size?This is given as from margin of error:
This is the term refers to the minimum error that is to be allowed
Margin of error, E = Zc * √(SD²/n)
n = sample size
n = SD x (Zc/E)²
SD = standard deviation
Zc = would be the critical value at 90 percent level of confidence = 1.65
plugging in the values
n = 5.5 x (1.65/0.42)²
n = 0.25 x 15.4337
n = 84.8854
n = 85
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PLEASE HELP!!!
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Number of Years at the Company Dianelys' Salary (Dollars)
00 40000\hspace{3px}\color{green}{\checkmark}40000
11 42500\hspace{3px}\color{green}{\checkmark}42500✓42500
22 45000\hspace{3px}\color{green}{\checkmark}45000✓45000
33 47500\hspace{3px}\color{green}{\checkmark}47500✓
1. The table of values for Dianely's salary can be represented for 4 years as follows:
Year Salary
1 $40,000
2 $42,500
3 $45,000
4 $47,500
2. The equation that models Dianely's salary after n years is S = 40,000 + 2,500n.
What is an equation?An equation is a mathematical statement stating that two mathematical expressions are equivalent or equal.
For instance, given the number of years, one can claim that Dianely's salary will be a given amount based on the above equation.
Equations involve variables, numbers, and the use of the equation sign (=) with some mathematical operands.
Initial salary = $40,000
Salary raise per year = $2,500
Disney's salary after n years in equation form, S = 40,000 + 2,500n.
Table of Values for Dianely's Salary:
Year Salary
1 $40,000
2 $42,500 (40,000 + 2,500)
3 $45,000 (42,500 + 2,500)
4 $47,500 (45,000 + 2,500)
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5 pounds=______ounces
Answer:
Step-by-step explanation:
1. Basic systems in fluids: 1 pound equals 16 ounces.
2. Multiply 16 ounces by 5 to become equivalent!
16 ounces*5= 80 ounces!
3. Always double check
80 ounces/16=5 pounds
Answer: 80 ounces
what is 2 +2
4+5
0+9
Answer:
Step-by-step explanation:
2+2=4
4+5=9
0+9=9
Answer:
4, 9 , 9 OR 4 + 9 + 9 = 22
Step-by-step explanation:
bag has 5 red beads 3 Blue, 4 green random probability a single picked bead is blue
Answer:
1/4
Step-by-step explanation:
add all of them to get the sum which is 12. Since he asked for the blue which are 3. You put the 3/total which is 3/12. Then simplify. Which is equal to 1/4
Solve for x.
Please help asap
Find an nth-degree polynomial function with real coefficients satisfying the given conditions.
n=4;
i and 2i are zeros;
f(-1)=20
f(x) = ?
(Type an expression using x as the variable. Simplify your answer.)
The polynomial satisfying the given conditions is given as 2x⁴ + 10x² + 8.
What is a polynomial?The polynomial is an algebraic expression in which no any terms has the power other than a whole number.
The degree of a polynomial is the highest power of one of its terms.
Given that,
The degree of polynomial is n = 4.
The zeros of the polynomial are i and 2i.
And, f(-1) = 20
Since, a polynomial with real coefficients have either real zeros or complex conjugate zeros.
Here, the given zeros of the polynomial are imaginary which implies that the remaining two zeros are the conjugate of the given two zeros.
Thus, the zeros of the given polynomial are i, 2i, -i and -2i.
The general form of a 4th degree polynomial is given as,
ax⁴ + bx³ + cx² + dx + e
Use the factor theorem to get,
ax⁴ + bx³ + cx² + dx + e = K(x - i) (x - (-i)) (x - 2i) (x- (-2i)) (1)
⇒ ax⁴ + bx³ + cx² + dx + e = K(x² + 1) (x² + 4) (2)
Now, f(-1) = 20 which gives,
K((-1)² + 1) ((-1)² + 4) = 20
⇒ k = 2
Substitute K =2 in equation (2) to get,
ax⁴ + bx³ + cx² + dx + e = 2(x² + 1) (x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2(x⁴ + 5x² + 4)
⇒ ax⁴ + bx³ + cx² + dx + e = 2x⁴ + 10x² + 8
Hence, the nth-degree polynomial function with real coefficients satisfying n = 4 and zeros i and 2i is 2x⁴ + 10x² + 8.
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Solve for j.
–3(j − 8) + –6 = –9
Answer:
j = 9
Step-by-step explanation:
Given equation,
→ -3(j - 8) + (-6) = -9
Let's solve for the value of j,
→ -3(j - 8) + (-6) = -9
→ -3j + 24 - 6 = -9
→ -3j + 18 = -9
→ -3j = -9 - 18
→ j = (-27)/(-3)
→ [ j = 9 ]
Hence, the value of j is 9.
Answer:
j = -9
Step-by-step explanation:
[tex] - 3(j - 8) + - 6 = - 9 \\ open \: brackets \\ - 3j + 24 + - 6 = - 9 \\ 3j + 24 = - 9 + 6 \\ 3j + 24 = - 3 \\ 3j = - 3 - 24 \\ 3j = - 27 \\ divide \: by \: 3 \\ j = - 9[/tex]
1. What is the result if you divide -12x8y8 by 3x4y ²?
O A. 4x4yê
O B. 4x²y
O C.-4x²yA
O D. -4x^y6
Please look at photo, it didn’t type correctly.
What is the next fraction in this sequence? Simplify your answer.
9
14
,
4
7
,
1
2
,
3
7
,
Answer:
5/14
Step-by-step explanation:
they subtract 1/14th each time
(You cant simplify)
Suppose that the number of cars manufactured at an automobile plant varies jointly as the number of workers and the time they work. If 160 workers can produce 32 cars in 2 hours, find the number of workers that can produce 66 cars in 3 hours.
If 160 workers can produce 32 cars in 2 hours, The number of workers that can produce 66 cars in 3 hours is 220 .
How to find the number of workers?Using this formula
W = kC/H
160 = k(32 )/2= 17k
k = 160 /16
Hence,
W = (160 /16)C/H
W = (160 /16) (66/3)
W= 220 workers
Therefore we can conclude that 220 workers can produce the cars in 3 hours.
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a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape
ice concentrate is 3 to 1.
a. Find two more ratios of cups of sparkling water to cups of juice concentrate that
would make a mixture that tastes the same as this recipe.
b. Describe another mixture of sparkling water and grape juice that would taste
different than this recipe.
Lesson 3 Practice Problem
Answer:
3:2
Step-by-step explanation:
You need to find two more equivalent ratio of cups of sparkling water to cups of juice concentrate that would make a mixture that tastes the same as this recipe.
Another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate
Ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1
ratio of cups of sparkling water : cups of grape juice concentrate = 3 : 1
Equivalent ratio to 3 : 1 are
6 : 2,
9 : 3,
12 : 4
15 : 5
21 : 7
Non equivalent ratio of 3 : 1 are
3 : 2
4 : 2
5 : 5
6 : 4
Therefore, another mixture of sparkling water and grape juice that would taste different than this recipe is 3 : 2 of cups of sparkling water to cups of juice concentrate
Help quick please this is hard for me
Answer:
525 cm
Step-by-step explanation:
a heptagon has 7 sides and it can be split into 7 different equal triangles and one already has the side so we just find the area of the triangle.
1/2(12)(12.5)
6(12.5)
75
75 is the area of the triangle so now we multiply by 7
75x7=525 cm
Hopes this helps please mark brainliest
Answer: 525 cm squared
Step-by-step explanation:
Find the area of 1 of the Isoceles triangle and then multiply it by 7, because there are 7 Isoceles triangles in the heptagon. Area= 1/2 base x height = 1/2 x 12cm x12.5cm = 75cm squared. Now 75 cm squared x 7 = 525 cm squared
When you flip a biased coin the probability of getting a tail is 0.4.
How many times would you expect to get tails if you flip the coin 160 times
Answer:
64 times
Step-by-step explanation:
Multiply 0.4, the chance of getting tails, which 160, the amount of times you flip the coin, and you get 64. This is reasonable, because the probability of getting heads is 0.6, and if you flip the coin 160 times, you will get heads 96 times. Hope this helped :)
what kind of transformation converts the graph of f(x)= -10(x-2)^2 into the graph of g(x)= -2(x-2)^2
The transformation that converts f(x) to g(x), f(x) is contraction by 5 units
What are transformations?Transformations are mathematical operations which change the shape and orientation of an object or function.
The types of transformations include
Dilation, Reflection, translationcontraction and rotationHow to find what kind of transformation converts f(x) to g(x)?Since we have the graph of f(x) = -10(x - 2)² into the graph of g(x)= -2(x - 2)².
We see that f(x) = -10(x - 2)²
= 5 × -2(x - 2)²
= 5g(x)
Since f(x) = 5g(x)
⇒g(x) = f(x)/5
So, we converts f(x) to g(x), f(x) is contraction by 5 units
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What is the y-intercept of the function f(x) = 2 ^x?
A.27
B.2
C. 6
D. 1
Answer:
D
Step-by-step explanation:
the y- intercept is the value of y on the y- axis where the function crosses.
the function crosses the y - axis when x = 0
substitute x = 0 into f(x)
f(0) = [tex]2^{0}[/tex] = 1
y- intercept is 1
Parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n, what is true for the transformation that took place?
Line m was translated down 4 units.
Line m was translated up 4 units.
Line n was translated up 8 units.
Line l was translated down 8 units.
Line l was translated down 8 units, is true for the transformation that took place.
What is transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.
Given that, parallel lines l, m, and n are shown. If line l is mapped to line m and line m is mapped to line n,
We can see line is the original line is l which is first mapped into line m then into line n, so, we can say line is mapped to n.
Hence, Line l was translated down 8 units, is true for the transformation that took place.
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Solve for d. 3 + d < 3 −d
d < −6
d < 6
d < 0
d < −3
Answer:
d is great than -3
Step-by-step explanation:
because negative numbers are less than whole numbers
HELP WILL GIVE BRAINLYEST!!!!!!! 30 POONTS Which of the following is the fourth vertex needed to create a rectangle with vertices located at (−4, −25), (−4, −12), and (−7, −12)?
(−12, 7)
(−7, −25)
(−7, 12)
(−25, 7)
Answer: I believe the answer is (-7, 12)
Step-by-step explanation:
Answer:
-7,12
Step-by-step explanation:
helppppppppppppppppppppppppp
Answer:
E
Step-by-step explanation:
I am a line & domain is -7
The price of a climbing trip to Mount Kilimanjaro includes an initial fee plus a constant fee per
meter.
The table compares the total distance of a trip (in meters) and the price of the trip (in dollars).
Distance (meters)
80
110
140
How far can you climb for $131?
to be honest ion even know
Answer: 200 Meters
Step-by-step explanation:
Your friend uses the figure to say that all the exterior angles of any isosceles triangle are congruent. Is your friend correct? Explain your reasoning
Answer:
All the exterior angles of any isosceles triangle are congruent - FALSE statementStep-by-step explanation:
We know that the exterior angle of a triangle is the sum of remote interior angles.
If the triangle is equilateral then the sum of any two interior angles is same otherwise, with any isosceles triangle, we get different sums and therefore the friend is wrong.
Answer:
No.
Step-by-step explanation:
An isosceles triangle has two sides of equal length. Therefore, only two of its interior angles are congruent.
The exterior angle of a triangle is equal to the sum of the two opposite interior angles (remote interior angles). Therefore, as not all of the three interior angles of an isosceles triangle are congruent, all the exterior angles will also not be congruent.
perpendicular bisector of the line segment whose endpoints are 7,4) and (−9,−4).
Answer:
y=-2x-2
Step-by-step explanation:
If the endpoints of the line segment are (7,4) and (-9,-4), that means that the slope will be:
[tex]\frac{-4-4}{-9-7}[/tex] = [tex]\frac{-8}{-16}[/tex]=[tex]\frac{1}{2}[/tex]. For the perpendicular bisector to be perpendicular to the line, it must have a perpendicular slope, which will be the negative reciprocal of [tex]\frac{1}{2}[/tex], which is -[tex]2[/tex]. The perpendicular bisector must also go through the midpoint of the segment, which is (-1, 0) because -1 is the average of 7 and -9 and 0 is the average of 4 and -4.
Now we find the equation!
y=mx+b. Plug in -[tex]2[/tex] as the "m", or slope:
y=-[tex]2[/tex]x+b
Now, plug in the point (-1, 0):
0=-[tex]2[/tex]*-1+b
0=[tex]2[/tex]+b
b=-[tex]2[/tex]
So, we have m=-[tex]2[/tex] and b=-[tex]2[/tex] and we can form our equation!
y=-[tex]2[/tex]x-[tex]2[/tex]
Hope this helps!! :D
A house was valued at $254,000. Over several years, the value increased by 16%, giving the house a new value.
Answer:
289560
Step-by-step explanation: