[tex]Use:\\\sqrt[n]{a^m}=a^{\frac{m}{n}}\\\\(a^n)^m=a^{nm}\\\\\left(5^{\frac{3}{4}}\right)^{\frac{2}{3}}=5^{\frac{3}{4}\cdot\frac{2}{3}}=5^{\frac{1}{2}\cdot\frac{1}{1}}=5^{\frac{1}{2}}=\sqrt[2]{5}=\boxed{\sqrt5}[/tex]
A paper company produces 3,320 notebooks in 4 days. How many notebooks can it produce in 12 days?
A.
9,906
B.
1,992
C.
9,960
D.
3,139
Answer:
C. 9960
Step-by-step explanation:
HELP PLEASE! solve for x and y.
Answer:
x=24
y = 8 sqrt(3)
Step-by-step explanation:
Since this is a right triangle, we can use sin and cos
sin 30 = opposite/ hypotenuse
sin 30 = y/ 16 sqrt(3)
Multiply each side by 16 sqrt(3)
16 sqrt(3) * sin 30 = y
16 sqrt(3) * 1/2 = y
8 sqrt(3) = y
cos 30 = adjacent/ hypotenuse
= x/16 sqrt(3)
Multiply each side by 16 sqrt(3)
16 sqrt(3) cos 30 = x
16 sqrt(3) * (sqrt(3)/2) = x
8 * sqrt(3)*sqrt(3)
8 * 3 = x
24 =x
Sylvie has a leather cord that is 30 inches long. She needs 6 inches of leather to make a bracelet. How much leather cord will Sylvie have after she removes 6 inches?
Answer:
30-6=24
Step-by-step explanation:
Subtract the 6 inches from the 30 inches.
The circumstances of Z is 84cm. What is the length of XY (the mirror arc)
Answer:
B
Step-by-step explanation:
arc length = circumference × fraction of circle
= 84 ×[tex]\frac{90}{360}[/tex] = 21 cm
An airplane flies 810 km in 1.5 hours. Find the constant of variation.
[tex]\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{\textit{\underline{d}istance of 810 km in 1.5 \underline{h}ours}}{d=kh} \\\\\\ \textit{we know that } \begin{cases} h=1.5\\ d=810 \end{cases}\implies 810=k(1.5)\implies \cfrac{810}{1.5}=k\implies 540=k[/tex]
Answer : The value of constant of variation is, 540
Step-by-step explanation :
As we know that,
[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]
That means,
d = s × t
Here,
's' is constant of variation.
Given:
d = distance = 810 km
t = time = 1.5 hr
Now put the values in the above expression, we get:
d = s × t
810 km = s × 1.5 hr
[tex]s=\frac{810km}{1.5hr}=540km/hr[/tex]
Thus, the value of constant of variation is, 540
A cheetah can run 224 miles in 3 1/2 hours how many miles per hour can the cheetah run?
Is it possible to trisect any angle using only a compass and a straight edge
Hello from MrBillDoesMath!
Answer:
No. That problem cited is one of 3 great unsolved problems of antiquity. See https://en.wikipedia.org/wiki/Angle_trisection for details.
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
Answer:
NO , an angle is not trisected using only a compass and a straight edge.
Step-by-step explanation:
We are given two tools a compass and a straight edge
We need to tell if an angle is trisected using them or not.
Answer is NO , an angle is not trisected using only a compass and a straight edge.
When we draw a semicircle by point pointer of compass at vertex of angle and then draw a line using points we get when semicircle intersects the arms of the angle. We get angle Bisection.
We again try to bisect we get four equal angles not Three.
So It is impossible to make odd numbers of equal angles from a given angle using a compass and a straight edge.
divisibility rule for 4.
Answer:
Divisable by 4? look at the last two digets If divide by 4, the whole number divides by 4.
4 = 2^2, so if you can divide a number by 2 twice, then the number is divisible by 4.
Write the equation of a line in slope intercept form that is parallel to 2x + 4y = 10 and passes through the point (8, 2).
A) 16x + 8y = 10
B) y = −12x + 6
C) y = −12x+2
D) y=8x + 2
Answer:
y = -1/2 x + 6
Step-by-step explanation:
2x + 4y = 10
4y = -2x + 10
y = -1/2 x + 5/2
Parallel lines, slope is the same = -1/2
passes through the point (8, 2) so
y - 2 = -1/2(x - 8)
y - 2 = -1/2 x + 4
y = -1/2 x + 6
Answer:
y = -1/2x + 6
Step-by-step explanation:
We know that the slope intercept form of a line is [tex]y=mx+c[/tex].
Also, if two lines are parallel, they have the same slope. So re-writing the given equation 2x + 4y = 10 in the slope intercept form to find know its slope.
[tex]2x + 4y = 10\\\\4y=-2x+10\\\\y=\frac{-2}{4} +\frac{10}{4}\\ \\y=\frac{-1}{2} +\frac{10}{4}[/tex]
So the slope of the equation will be [tex]-\frac{1}{2}[/tex].
Finding the y-intercept (c):
[tex]y=mx+c\\\\2=-\frac{1}{2} (8)+c\\\\c=6[/tex]
Therefore, the equation of the line n slope intercept form that is parallel to 2x + 4y = 10 and passes through the point (8, 2) is y = -1/2x + 6.
Find the common denominator by multiplying each fraction by the other fraction's denominator. Choose < or > for the blank.
3/5
[_]
3/8
Amara needs 4545 kilograms of meat to feed her 22 pet dragons each day. Each pet dragon eats the same amount of meat. How many kilograms of meat does Amara need to feed 44 pet dragons each day?
Answer:
9090 kilograms
Step-by-step explanation:
To find the number of kilograms per dragon, we divide the amount of meat by the number of dragons.
4545/22 kilograms per dragon
Now we can multiply by the 44 dragon that she has.
4545/22 * 44 = 9090 kilograms
Answer:
i believe your answer is 9090
Step-by-step explanation:
4545 =22 dragons each day
22 times 2=44
4545 times 2
9090
How many 1 3/4 foot pieces of ribbon can be cut from a piece of ribbon that is 36 feet long?
Answer:
Approximately 20 complete pieces of 1 3/4 foot of ribbon can be obtained.
Step-by-step explanation:
You have a piece of ribbon 36 feet long that should be divided into pieces of 1 [tex]\frac{3}{4}[/tex] feet. In order to know the quantity of pieces of said measurement, the total length of the ribbon (36 feet) must then be divided by the desired measurement of each of the pieces (1 3/4 feet):
[tex]amount of pieces of ribbon=\frac{36}{1 \frac{3}{4} }[/tex]
1 [tex]\frac{3}{4}[/tex] is a mixed number. A mixed number or mixed fraction consists of a whole part (natural number) and a fractional part. All fractions greater than unity can be expressed as a mixed number.
To be able to make the division stated previously, it is convenient to pass the mixed number to an improper fraction (An improper fraction is a fraction in which the numerator is greater than or equal to the denominator). For this you multiply the denominator by the whole number. To the result, you must add the numerator. Then that number is placed over the original denominator. Expressed in general is:
[tex]a \frac{b}{c} =\frac{a*c+b}{c}[/tex]
In this case:
[tex]1 \frac{3}{4} =\frac{4*1+3}{4}=\frac{7}{4}[/tex]
Then the previously stated division is expressed as:
[tex]\frac{36}{\frac{7}{4} }[/tex]
One way to perform this division is to reverse the SECOND FRACTION, that is, change the denominator to the numerator and change the numerator to the denominator. Then, both numbers are multiplied.
[tex]\frac{36}{\frac{7}{4} } =36*\frac{4}{7}[/tex]
Given that 36 can be expressed as 36/1, the multiplication is done "online." That is, the numerator of the first fraction by the numerator of the second and the denominator of the first fraction by the denominator of the second.
[tex]\frac{36}{1} *\frac{4}{7} =\frac{36*4}{1*7} =\frac{144}{7}[/tex]
Now it will be passed from fraction to mixed number. For that, the numerator is divided by the denominator. The quotient of the division becomes the integer of the mixed number. The rest of the division is the numerator of the fraction. The denominator is the same as that of the fraction, being the divisor of the division.
When dividing 144 by 7 the quotient is 20, the remainder is 4 and the divisor is 7. Then the mixed number formed is [tex]20 \frac{4}{7}[/tex]
This indicates that approximately 20 complete pieces of 1 3/4 foot of ribbon can be obtained.
Answer
about 20 complete pieces can be cut
Step-by-step explanation:
Draw an array to show how to arrange 20 chairs into 5 equal rows
What is the range of the relation
(-4,1),(-2,0),(8,-1)
Answer:
Range of the relation is, {1 , 0, -1}
Step-by-step explanation:
Given: Relation R = {(-4, 1), (-2, 0) , (8, -1)}
To find the range of the relation R;
In the set of ordered pairs, the domain is the set of the first number in every pair, and the range is the set of the second number of all the pairs.
Then;
Domain of the relation: {-4, -2, 8}
Range of the relation is; {1 , 0, -1}
therefore, the range of the relation is, {1 , 0, -1}
The range of the given relation is {-1, 0, 1}
Explanation:The range of a relation refers to the set of all possible output values of the relation. In this case, the relation consists of three ordered pairs: (-4, 1), (-2, 0), and (8, -1). To find the range, we need to determine the set of all possible second values (y-values) in the ordered pairs. The range of the relation is {-1, 0, 1}.
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33 points
What did I do wrong for this equasion the answer cannot be a decimal
Thank you in advanced
Answer:
x=-5, y=-2
Step-by-step explanation:
6x+ 28 =y
5x-y=-23
Substitute 6x+28 in for y in the second equation
5 x-(6x+28)=-23
Distribute the negative sign
5x -6x-28 = -23
-x -28 = -23
Add 28 to each side
-x-28+28 = -23+28
-x = 5
Multiply by -1
x = -5
Now we need to solve for y
y = 6x+28
Substitute x=-5
y = 6(-5) + 28
y = -30+28
y = -2
what is the value of the 3 in parenthases [3]45,423,912
Answer:
300,000,000
Step-by-step explanation:
change everything after the 3 to a zero, hope this is the answer you are looking for
Which of the following inequalities matches the graph?
is this right and if it's not could you please tell me the answer
Answer:
3x+ 5 = 6 . Correct.
Step-by-step explanation:
Let x = the number.
The number tripled: 3x
Tripled and increased by : 3x + 5
Equals 6: 3x+ 5 = 6
Correct.
Shelly types 301 words in 3 1/2 minutes what is the rate at which Shelly types in words per minute
Answer:
86 wpm
Step-by-step explanation:
You need to set up a proportion
x words in 1 minute301 words in 3.5 minutesx/1 = 301/3.5x = 301 / 3.5x = 86 words / minuteAnswer:
86 words per minute
Step-by-step explanation:
You would divide 301 by 3 1/2 to find the unit rate. The answer will be 86. So Shelly types 86 words per minute.
Please help!!!!
What does it mean to say that a number is a perfect square? Give one example of a number that is a perfect square and one that is not. Explain your examples.
What dose it mean to say that a number is a perfect square? Give one exampel of a number that is a perfect square and one that is not.
Be sure to include the following:
Define the term perfect square
Provide examples and explain why each is or is not a perfect square
Write a translation rule that maps point (7, –3) onto point (2, 5).
Harriet needs to ship a small vase. The box she will use has a volume of 216 cubic inches. If the side lengths are all the same, what is the length of each side of the box?
Using the numbers 5, 8, and 24, create a problem using no more than four operations (addition, subtraction, multiplication, division, square, square root, cube, cube root) where the solution will be an irrational number. Explain why the result of your operations is an irrational number.
Answer:
a perfect square is when a number is multiplied by itself. For example, 4*4=16.
16 is the perfect square
something like 20 would not be a perfect square because it is 5*4 and they are not the same number.
Step-by-step explanation:
Answer:
The product of a rational number multiplied by itself.
Step-by-step explanation:
9² = 9×9 which equals 81. 81 is the perfect square of 9 which can also be said that 9 is the square root of 81 or √81
chloe made a conjecture that given any two numbers, the greater number can always be arranged into more arrays.
State whether you agree or disagree. Then explain why you think so by giving an example of two numbers that prove or disprove the conjecture.
Solution:
Array means arrangement of numbers in terms of rows and columns.
The conjecture is not True.
So, the conjecture made by chloe that given any two numbers, the greater number can always be arranged into more arrays is not true.
For example ,
1.(2,3)
2→(2×1),(1×2)
3→(3×1),(1×3)
This pair has same number of arrays because both of them are prime.
2. (3,4)
Here, 4>3
3→ (3 × 1),(1×3)
4→(4×1),(1×4),(2×2)
The pair of numbers are Co-prime, one of them is not prime. So Composite number has more number of arrays.
4. (6,11)
6→(1×6),(6×1),(2×3),(3×2)
11→(1×11),(11×1)
The number 6 is smaller, but it has more number of arrays.
5. (6,8)
6→(1×6),(6×1),(2×3),(3×2)
9→(1×9),(9×1),(3×3)
Both the numbers are composite.Smaller number 6 has more arrays.
These examples disprove the Conjecture made by Chloe, which states that given any two numbers, the greater number can always be arranged into more arrays.
If ABE is similar to ACD what is the value of AB
AB corresponds to AC. Both are the left diagonal lines of triangle ABE and triangle ACD. Both AB and AC are also the first two letters of ABE and ACD respectively
BE and CD correspond as well. They are the horizontal sides of the two triangles. BE and CD are the last two letters of ABE and ACD.
Set up the proportion below. Then solve for x
AB/AC = BE/CD
AB/(AB+BC) = BE/CD
x/(x+3) = 2/5
5x = 2(x+3)
5x = 2x+6
5x-2x = 6
3x = 6
x = 2
Answer: AB = 2
note how AB = x = 2, so AC = AB+BC = x+3 = 2+3 = 5. This forms the ratio AB/AC = 2/5 which is identical to the ratio BE/CD = 2/5
To find the value of AB in the similar triangles ABE and ACD, use the ratio of the corresponding sides.
Explanation:Given that ∆ABE is similar to ∆ACD, we can write the ratio of the corresponding sides: AB/AC = AE/AD = BE/CD. Note that corresponding sides of similar triangles are proportional. Therefore, the value of AB can be determined by the ratio AB/AC.
For example, if the length of AC is 10 units and the ratio AB/AC is 3/5, we can find the length of AB by multiplying 10 by 3/5: AB = (3/5) * AC = (3/5) * 10 = 6 units.
So, the value of AB depends on the specific information given about the ratios of the sides of ∆ABE and ∆ACD.
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What is the slip of a line that is parallel to the line -3
Answer:
-3
Step-by-step explanation:
Parallel lines have slopes that are the same.
So if one line has a slope that is -3, any line that is parallel will have the same slope
The entry fee to the fair is $4.00. Each ride requires a ticket that cost $0.50. Heidi spent a total of $12.00. How many ticket did Heidi purchase?
Answer:
16 tickets
Step-by-step explanation:
The entry fee ($4) is to be subtracted from the total that Heidi spent ($12). This leads to $8 left for spending on tickets.
Let the number of tickets Heidi purchased be x. Then:
$8.00 = ($.50/ticket)x.
Dividing both sides by $0.50,we get 16.
Heidi bought 16 ride tickets.
Write the first five terms of the geometri.c sequence in which a1 - 8 and the common ratio is 5/2.
Answer:
8 , 20, 50, 125, 625/2 option D
Step-by-step explanation:
Given that,
first term a₁ = 8
common ratio (r) = [tex]\frac{5}{2}[/tex]
We need to find the five terms of the geometric progression
We know that the nth term formula :
aₙ = a₁rⁿ-¹
where a₁ is first term and r is the common ratio
n is the number of terms
Second term (n=2)
a₂ = 8*[tex](\frac{5}{2} )^{2-1}[/tex] = [tex]\frac{8*5}{2}[/tex] = 20
Third term (n = 3)
a₃ = 8*[tex](\frac{5}{2} )^{3-1} = 8*(\frac{5}{2} )^{2} = (\frac{8*25}{4} ) = 50[/tex]
Forth term (n=4)
a₄ = [tex]8(\frac{5}{2} )^{4-1} = 8*(\frac{5}{2} )^{3} = (\frac{8*125}{8} ) = 125[/tex]
Fifth term (n=5)
a₅ = [tex]8(\frac{5}{2} )^{5-1} = 8*(\frac{5}{2} )^{4} = (\frac{8*625}{16} ) = \frac{625}{2}[/tex]
So, five terms are :
8 , 20, 50, 125, 625/2
Answer:
D right on edg 2020
Step-by-step explanation:
Bailey has an hour to get ready for school he spends 3/6of that time getting dressed she spends 1/4of that time eating breakfast Bailey spend more time getting a dress or eating breakfast
Final answer:
Bailey spends more time getting dressed, which is 1/2 of an hour (30 minutes), whereas she spends 1/4 of an hour (15 minutes) eating breakfast.
Explanation:
The question is asking which activity Bailey spends more time on in the morning: getting dressed or eating breakfast. Since Bailey has an hour to get ready, 3/6 of an hour is spent getting dressed, and 1/4 of an hour is spent eating breakfast.
First, we simplify the fraction for getting dressed, as 3/6 can be reduced to 1/2. Thus Bailey spends 1/2 hour or 30 minutes getting dressed. To find how much time is spent eating breakfast, we calculate 1/4 of an hour, which is 15 minutes.
Comparing the two, we see that Bailey spends more time getting dressed (30 minutes) than eating breakfast (15 minutes).
The functions f(x) = (x + 1)^2 - 2 and g(x) = -(x-2)^2 + 1 have been rewritten using the completing-the-method. Is the vertex for each function a minimum or a maximum? Explain your reasoning for each function.
Answer:
see explanation
Step-by-step explanation:
the equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
• If a > 0 then the vertex is a minimum
• If a < 0 then the vertex is a maximum
f(x) = (x + 1)² - 2 → has a > 0
vertex = (- 1, - 2 ) and is a minimum
g(x) = - (x - 2)² + 1 → has a < 0
vertex = (2, 1 ) and is a maximum
The expression 3/8d+3/4 factored is
The answer would be (3/8) (d+2)
The expression 3/8d + 3/4 is factored by first factoring out the common factor of 3, resulting in the factored form 3*(1/8d + 1/4).
The student's question involves the factoring of a linear algebraic expression. The given expression is 3/8d + 3/4, where 'd' is a variable. To factor this expression, we need to look for common factors in each term. Here, both terms contain a factor of 3, which we can factor out. This results in:
Factor out the common factor of 3: 3*(1/8d + 1/4).Recognize that 1/4 is equivalent to 2/8 in order to have a common denominator.Combine the two terms inside the parentheses: 3*(1/8d + 2/8).Thus, the fully factored expression is 3/8d + 3/4 = 3*(1/8d + 1/4), with the understanding that 1/4 has been converted to 2/8 to have a common denominator.
Match the following items by evaluating the expression for x = -6.
For x = -2 expressions yield 1/4 , -1/2 , 1 , -2 , 4 for x^-2 , x^-1 , x^0 , x^ 1 , x^2 .
Evaluating Expressions for x = -2
When we evaluate expressions containing variables, we substitute the given value for the variable into the expression and simplify. In this case, we're asked to evaluate the following expressions for x = -2:
x^-2
x^-1
x^0
x^1
x^2
1. x^-2
x^-2 represents the reciprocal of the square of x. Substituting x = -2, we get:
x^-2 = 1/(-2)^2 = 1/4
2. x^-1
x^-1 represents the reciprocal of x. Substituting x = -2, we get:
x^-1 = 1/-2 = -1/2
3. x^0
Any non-zero number raised to the power of 0 is 1. Therefore:
x^0 = 1
4. x^1
x^1 represents the value of x itself. Substituting x = -2, we get:
x^1 = -2
5. x^2
x^2 represents the square of x. Substituting x = -2, we get:
x^2 = (-2)^2 = 4
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The question probable may be:
Match the following items by evaluating the expression for
x = -2
. x^-2
x ^-1
x^0
x^1
x^2
Based on the polynomial reminder theorem, what is the value of the function when x= -5
F (x)= x^4 + 12x^3 + 30x^2 - 12x + 70
Answer:
-15
Step-by-step explanation:
Given is a polynomial in x
[tex]F (x)= x^4 + 12x^3 + 30x^2 - 12x + 70[/tex]
We have to find the remainder when the above polynomial is divided by x+5
Remainder theorem says that f(x) gives remainder R when divided by polynomial x-a means f(a) = R
Applying the above theorem we can say that value of the function when x =-5
= Remainder when f is divided by x+5
= F(-5)
Substitute the value of -5 in place of x
= (-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70
= 625-1500+750+60+70
= 5
Hence answer is 5
Answer:
[tex]f(-5)=[/tex] 5
Step-by-step explanation:
According to the polynomial remainder theorem, when a polynomial f(x) is divided by a linear polynomial (x - a), the remainder of that division will be equal to f(a).
Therefore, substituting the value of x as -5 in the given function to find its value:
[tex]f(x)[/tex] = [tex]x^4 + 12x^3 + 30x^2 - 12x + 70[/tex]
[tex]f(-5)[/tex] = [tex](-5)^4 + 12(-5)^3 + 30(-5)^2 - 12(-5) + 70[/tex]
[tex]f(-5)[/tex] = [tex]625+(-1500)+750-(-60)+70[/tex]
[tex]f(-5)[/tex] = [tex]5[/tex]
Therefore, the value of the given function when x = -5 is 5.