Answer:
[tex]a^{\frac{5}{2}} = a^{2}\sqrt{a}[/tex]
Step-by-step explanation:
Given:
Given expression is.
[tex]= a^{\frac{5}{2}}[/tex]
We need to write the given expression in radical form.
Solution:
Rewrite the expression as.
[tex]= a^{\frac{5}{2}}[/tex]
Now we extract power as [tex](a^{m})^{\frac{1}{n} }=a^{\frac{m}{n}}[/tex]
[tex]=(a^{5})^{\frac{1}{2} }[/tex]
Now we write the above expression in radical form and simplify.
[tex]=\sqrt[2]{(a^{5})}[/tex]
[tex]=\sqrt[2]{(a\times a)\times (a\times a)\times a}[/tex]
[tex]=\sqrt[2]{a^{2}\times a^{2}\times a }[/tex]
[tex]= a\times a\times \sqrt[2]{a}[/tex]
[tex]= a^{2}\times \sqrt[2]{a}[/tex]
[tex]a^{\frac{5}{2}} = a^{2}\sqrt{a}[/tex]
Therefore, the radical form of the given expression [tex]a^{\frac{5}{2}} = a^{2}\sqrt{a}[/tex]
if the circumference of one of the world's largest pizzas is 215 feet, what is its radius? Use 3.14 to approximate pi. Round to the nearest tenth.
Answer: 34.2
Step-by-step explanation:
If h(x) = 6 - X, what is the value of (h*h)(10)?
The value of [tex]\bold{ h(h(10))=10}[/tex]
Solution:
Given: [tex]h(x) = 6 - x[/tex]
To find: The value of (h*h)(10)
We know that, [tex](h*h)(x)=h(h(x))[/tex]
which is,
[tex]\Rightarrow h(h(x))=6-(6-x)=x[/tex]
On solving we get,
[tex]\Rightarrow6-6+x=x[/tex]
So, for x = 10 it will be,
[tex]h(h(10))=10[/tex]
Hence, the required value is 10.
The area of a rectangle is 17 1/2 in and it’s shorter side is 3 1/2in.draw a diagram that shows this information. What is the length of the longer side
Answer: 5
Step-by-step explanation:
17 1/2 is equal to 17.5
3 1/2 is equal to 3.5
Since 17.5 is the area, you must divide by 3.5, which equals 5
To find the length of the longer side of a rectangle with an area of 17 1/2 square inches and a shorter side of 3 1/2 inches, divide the area by the width to get the length. The length of the longer side is 5 inches.
Explanation:The question is asking how to find the length of the longer side of a rectangle given that the area of the rectangle is 17 1/2 square inches and one of the shorter sides is 3 1/2 inches. To find the length of the other side, which we will call length, use the formula for the area of a rectangle which is area = length × width. Since the area and width (shorter side) are known, the equation can be set up as follows:
17 1/2 = length × 3 1/2To find the length, divide the area by the width:Length = (17 1/2) / (3 1/2)Convert mixed numbers to improper fractions:Length = (35/2) / (7/2)Multiply by the reciprocal of the divisor:Length = (35/2) × (2/7)Simplify the fractions:Length = 5Therefore, the length of the longer side of the rectangle is 5 inches.
In one city, there are four straight streets that form a square block. The length of each side of the block is 154 m. Find the perimeter of the square defined by this city block.
Final answer:
The perimeter of the square defined by the city block is 616 meters.
Explanation:
In order to find the perimeter of the square block, we need to know the length of each side. The question states that each side of the block is 154 m, so we can use this information to calculate the perimeter. The perimeter of a square is equal to four times the length of one side, so in this case it would be 4 * 154 m = 616 m. Therefore, the perimeter of the square defined by this city block is 616 meters.
Find the distance between the points with the given coordinates (-4, 9) and (1, -3).
Answer: 13
Step-by-step explanation:
The formula for finding distance between two points is given by :
D = [tex]\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}[/tex]
[tex]x_{1}[/tex] = -4
[tex]x_{2}[/tex] = 1
[tex]y_{1}[/tex] = 9
[tex]y_{2}[/tex] = -3
Substituting the values into the formula , we have :
D = [tex]\sqrt{(1 -(-4))^{2} +(-3-9)^{2}}[/tex]
D = [tex]\sqrt{(5)^{2}+(-12)^{2}}[/tex]
D = [tex]\sqrt{25+144}[/tex]
D = [tex]\sqrt{169}[/tex]
D = 13
Therefore : the distance between the points is 13
The volume of a sphere is 288pi cm^3
What is the radius of the sphere?
Answer:
radius = 6 cm
Step-by-step explanation:
The volume (V) of a sphere is calculated as
V = [tex]\frac{4}{3}[/tex] πr³ ← r is the radius
Given V = 288π, then
[tex]\frac{4}{3}[/tex] πr³ = 288π
Multiply both sides by 3 to clear the fraction
4πr³ = 864π ( divide both sides by 4π )
r³ = 216 ( take the cube root of both sides )
r = [tex]\sqrt[3]{216}[/tex] = 6
Thus the radius of the sphere is 6 cm
To find the sphere's radius from its given volume of 288pi cm^3, we use the volume formula V = (4/3) π r³ and solve for r, resulting in a radius of 6 cm.
Explanation:The student is asking for the radius of a sphere given its volume, which is 288pi cm³. To find the radius, we need to use the formula for the volume of a sphere:
V = (4/3) π r³
Where V is the volume and r is the radius. We can solve for r by rearranging the formula:
r = √[3V / (4π)]
In this case, substituting the given volume into the equation:
r = √[3(288π) / (4π)]
r = √[864π / (4π)]
r = √[216]
The radius of the sphere is 6 cm.
Learn more about Volume of a Sphere here:https://brainly.com/question/21623450
#SPJ12
For which equation is y=7 a solution
A)7y= 1
B)y - 26= -19
C)y + 7 = 0
D) y/2 = 7
Which of the following lengths cannot be the lengths of the sides of a triangle?
A. 4,6,9
B. 3,4,2
C. 2,2,3
D. 1, 1, 2
Complete the following equation: a2 = b2 + c2 - ______.
2 bc cos A
2 ca cos B
2 ab cos C
none of the above
Answer:
2 bc cos A
Step-by-step explanation:
Cosine rule
The missing part of the equation is 2bc cos A. This equation is a form of the Law of Cosines from trigonometry, which provides a relationship between the lengths of the sides of a triangle and one of its angles.
Explanation:The equation presented is a variant of the Law of Cosines in trigonometry. To complete the equation accurately, we need to choose the right trigonometric relationship between sides a, b, c, and one of the angles. The correct completion of the equation is 2bc cos A.
The Law of Cosines can be stated in three different ways depending on the specific circumstances:
a² = b² + c² - 2bc cos Ab² = a² + c² - 2ac cos Bc² = a² + b² - 2ab cos CLearn more about Law of Cosines here:https://brainly.com/question/32188599
#SPJ6
in 2014 there were about 126 million women in the United States, and women were about 51.4% of the total population. what was the total population in 2014?
Answer:
Step-by-step explanation
51.4% of the total population is 126 million
let x be the total population
turn ur percent to a decimal
0.514x = 126,000,000
x = 126 / 0.514
x = 245,136,186.77 <==
Answer:
245 millions
Step-by-step explanation:
51.4 > 126million
100 > X
X=100*126/51,4
X=245.1
79 percent of 145 is what?
Round 9.3959 to the nearest hundredth
Answer:
The answer is 9.396
Step-by-step explanation:
Find the value of the y-intercept of the line whose equation is 5x - 3y = -12.
To find the y-intercept, rewrite the equation of the line in slope-intercept form:
Slope-intercept form: y = mx + b (b is the y-intercept)
This is how you get your equation in slope-intercept form:
5x -3y = -12
-3y = -5x - 12
-3y/-3 = (-5x -12)/-3
y = (5/3)x + 4
The answer is 4.
Please let me know if you understand in the comments!
During the summer, a property owner will pay $24.72 plus $1.32 per hcf for Conservation Usage. The bill for Conservation Usage would be between or equal to $31.32 and $52.12. How many hcf can the owner use if she wants her usage to stay in the conservation range? Enter truncated values for answers. Example: Enter 8.93 as 8 and 6.34 as 6.
Answer:
The owner can use between 5 and 20 HCF to stay in the conservation range
Step-by-step explanation:
Let's calculate the number of HCF, this way:
Lower value = (31.32 - 24.72)/1.32 = 6.60/1.32 = 5
Upper value = (52.12 - 24.72)/1.32 = 27.4/1.32 = 20.76 = 20 as truncated value
The owner can use between 5 and 20 HCF to stay in the conservation range
The owner can use between 5 and 20 hcf to stay within the conservation range.
Explanation:To find the range for the number of hcf the owner can use, we need to subtract the base cost from the maximum and minimum bill amounts. The base cost is $24.72, so subtracting this from the maximum bill amount of $52.12 gives us $27.40. Similarly, subtracting the base cost from the minimum bill amount of $31.32 gives us $6.60. In order to determine the maximum and minimum number of hcf, we divide these amounts by the additional cost per hcf, which is $1.32.
The maximum number of hcf would be $27.40 divided by $1.32, which is approximately 20 hcf. The minimum number of hcf would be $6.60 divided by $1.32, which is approximately 5 hcf.
Therefore, the owner can use between 5 and 20 hcf to stay within the conservation range.
Learn more about water usage here:https://brainly.com/question/31621985
#SPJ11
-2°F ___ -6°F
=?
>?
<?
Answer:
-2 °F > -6 °F
Step-by-step explanation:
-2 is to the right of -6 on the number line, so is the greater of the two values. The temperature has to go up from -6 to get to -2. Thus, ...
-2 °F > -6 °F
Average snowfall for Boise
Answer:
20 inches
Step-by-step explanation:
hope this helps you
Please help me with the question. You must solve for x.
Answer:
[tex]x= (3, \frac{3}{10} )[/tex]
Step-by-step explanation:
The figure is composed of two similar triangles; therefore,
[tex]\frac{7x}{19x-4} =\frac{7x+8}{(5x+5)+(19x-4)}[/tex] this says the ratio of the sides is same for the two triangles.
we simplify and a rearrange to get
[tex]7x(24x+1)=(7x+8)(19x-4)[/tex]
which we expand and get
[tex]168x^2+7x=133x^2+124x-32[/tex]
[tex]35x^2-117x+32=0[/tex]
this quadratic equation has solutions
[tex]x=3.04[/tex]
[tex]x=0.30[/tex]
As integers and simplified fractions these are
[tex]x= (3, \frac{3}{10} )[/tex]
Convert the decimal to a fraction.
0.6 repeating
35 POINTS!!!! PLEASE HELP! (2.01)A polygon is shown on the graph: A polygon is shown on a coordinate plane. Vertex A is at 1 comma 5, vertex B is at 0 comma 1, vertex C is at 6 comma 1, and Vertex D is at 5 comma 5. If the polygon is translated 2 units down and 4 units left, what will the coordinates of the new image be? Use prime notation in expressing the new coordinates.
Answer:
A’ is (3,-3)
B’ is (-1,-4)
C’ is (-1,2)
D’ is (3,1)
Step-by-step explanation:
the other person gto one wrong this is what it should be
have a good day hope this helped
I have a pic to show you
what is StartFraction one-half EndFraction x is less than or equal to 18.x ≤ 18
Answer:
[tex]x\leq 36[/tex]
The solution for [tex]x[/tex] is all real numbers less that or equal to 36.
Step-by-step explanation:
Given expression:
[tex]\frac{1}{2}x\leq18[/tex]
To find the solution for [tex]x[/tex]
Solution:
In order to solve for [tex]x[/tex] , we will make sure to isolate the unknown variable [tex]x[/tex] on left side alone by doing math operations on both sides of the inequality.
We have:
[tex]\frac{1}{2}x\leq18[/tex]
Multiplying both sides by 2.
[tex]2.\frac{1}{2}x\leq18\times 2[/tex]
The 2 on left side will cancel each other leaving [tex]x[/tex] alone.
Thus, we have:
[tex]x\leq 36[/tex]
Thus, solution for [tex]x[/tex] is all real numbers less that or equal to 36.
Answer:
D
Step-by-step explanation:
what is x-13+2x+1=180
Answer:
64
Step-by-step explanation:
x-13+2x+1=180
3x-13+1=180
3x-12=180
3x=180+12
3x=192
x=192/3
x=64
Answer:
X=83
Step-by-step explanation:
UH TOO LAZY TO EXPLAIN. lol
What is the exact value of cos (67.5° )?
The exact value of cos(67.5°) is found using half-angle identities in trigonometry, which leads to the solution √(2 - √2)/2.
Explanation:To find the exact value of cos (67.5°), we can use the half-angle identity for cosine which states that cos(θ/2) = ± √ ((1+cosθ)/2). In this case, to find the cosine of 67.5 degrees, we effectively need to calculate the half-angle of 135 degrees.
Thus, cos(67.5°) = cos(135°/2) = √ ((1+cos135°)/2) = √ ((1 - √2/2)/2). This further simplifies to √(2 - √2)/2.
This is because the cosine of 135 degrees equals -√2/2 (as it's in the second quadrant where cosine is negative).
Therefore, the exact value of cos(67.5°) is √(2 - √2)/2.
Learn more about cosine here:https://brainly.com/question/34375338
#SPJ11
What is the simplified expression for 6 (2 (y + x))?
6 y + 12 x
12 y + 12 x
12 y + 8 x
8 y + 8 x
Step-by-step explanation:
6(2(y+x))=6(2x+2y)=12x+12y
Answer:
12y + 12x
Step-by-step explanation:
You're welcome.
Evaluate each expression if d = 12 and e = 1/3 2d-5
Answer:
19
Step-by-step explanation:
Plug it in
Which of the following inequalities could be the result of the first step in solving the inequality
3(x – 4) < 8x + 13 for x?
AX-45 x+13
B x-458x+10
(C3x – 4 5 8x+13
D
3x – 12 5 8x + 13
In the inequality 3(x – 4) < 8x + 13, the first step is to distribute the 3 on the left-hand side. That results in the inequality 3x – 12 < 8x + 13. Therefore, the correct answer from the options given is (D) 3x – 12 < 5 8x + 13.
Explanation:The question is asking for the inequality that could result after the first step when solving the given inequality 3(x – 4) < 8x + 13. The first step involves distributing the multiplication on the left side of the inequality. Therefore, 3 multiplied by x gives 3x and 3 multiplied by -4 gives -12. This leads to the inequality 3x – 12 < 8x + 13.
So, the correct answer from the options given is:
(D) 3x – 12 < 5 8x + 13.
https://brainly.com/question/32625151
#SPJ2
Identify the property and equation that satisfies the following statement: The solution of an equation is x = –2. Addition Property of Equality; x + 6 = 8 Substitution Property of Equality; x + 8 = 6 Division Property of Equality; x + 8 = 6 Subtraction Property of Equality; x + 6 = 8
Answer: identity is subtraction property of equality equation is x + 8 = 6
Substitution Property of Equality; x + 8 = 6
Take the equation x + 8 = 6. subtract 8 from both sides using the subtraction property of equality x + 8 - 8 = 6 - 8 simplify x + 0 = -2 x = -2
The Addition Property of Equality and the equation x + 6 = 8 are the property and equation that satisfy the statement 'The solution of an equation is x = –2'. This is because when you subtract 6 from both sides of the equation, x equals -2.
Explanation:To find the property and equation that fits the statement 'The solution of an equation is x = –2', we need to understand the basic properties of equality and apply those in this context.
Following the statement, it seems that the Addition Property of Equality fits the best here. The Addition Property of Equality states that when we add the same number to both sides of an equation, the equation remains balanced and the solution is the same. Now, if we think of an equation 'x + 6 = 8', and solve it using the Addition Property by subtracting 6 from both sides, we get the solution x = -2.
That means the property that satisfies the statement is Addition Property of Equality and the equation that satisfies the statement is x + 6 = 8.
Learn more about Equality Properties here:
https://brainly.com/question/33955920
#SPJ3
A two-column proof
O uses a visual representation of the logical flow of steps needed to reach a conclusion
o contains a table with a logical series of statements and reasons that reach a conclusion
O contains a set of sentences explaining the steps needed to reach a conclusion,
O uses inductive reasoning to prove a statement.
Answer:
B contains a table with a logical series of statements and reasons that reach a conclusion.
Step-by-step explanation:
A two-column proof
uses a visual representation of the logical flow of steps needed to reach a conclusion.
contains a table with a logical series of statements and reasons that reach a conclusion.
contains a set of sentences explaining the steps needed to reach a conclusion.
uses inductive reasoning to prove a statement.
what is the fraction of 66.7%
Use the formula d=rt to find the average speed of a car if the car traveled 320 miles in 8 hours.
Answer:
320 miles = (8 hours)(r)
r = 40 mph
Jenna and Callie collect stamps. Jenna has 20 less than twice the number of stamps that Callie has. Write an expression that represents the number of stamps that Jenna has.
The expression that represents the number of stamps that Jenna has is 2x - 20
Step-by-step explanation:
Let us revise some algebraic expressions
a is 5 more than b ⇒ a = b + 5a is 3 less than b ⇒ a = b - 3a is twice b ⇒ a = 2 bThe sum of a and b ⇒ a + bThe difference of a and b ⇒ a - bThe quotient of a and b ⇒ a ÷ bThe product of a and b ⇒ a × b∵ Jenna and Callie collect stamps
∵ Jenna has 20 less than twice the number of stamps that Callie has
- Assume that Callie has x stamps, that means to find the number
of stamps of Jenna multiply x by 2 and subtract 20 from the product
∵ Callie has x stamps
∵ Twice means × 2
∴ Jenna has = 2(x) - 20
∴ Jenna has = 2x - 20
The expression that represents the number of stamps that Jenna has is 2x - 20
Learn more:
You can learn more about the expressions in brainly.com/question/1600376
#LearnwithBrainly