The expression [tex]5^{3} \times \sqrt{5}[/tex] written as a single power of 5 is [tex]5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
To write the given expression 5^3 x √5, as a single power of 5,
First, we will write the expression properly.
[tex]5^{3} \times \sqrt{5}[/tex]
Now, to write the above expression as a single power of 5,
First, express [tex]\sqrt{5}[/tex] in index form
By law of indices [tex]\sqrt{x} = x^{\frac{1}{2} }[/tex]
∴ [tex]\sqrt{5} = 5^{\frac{1}{2} }[/tex]
Now, the expression becomes
[tex]5^{3} \times 5^{\frac{1}{2} }[/tex]
Also, by law of indices, [tex]x^{y} \times x^{z} = x^{y+z}[/tex]
∴ [tex]5^{3} \times 5^{\frac{1}{2} } = 5^{3+\frac{1}{2} }[/tex]
[tex]= 5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
Hence, the expression [tex]5^{3} \times \sqrt{5}[/tex] written as a single power of 5 is [tex]5^{3\frac{1}{2} } \ OR \ 5^{\frac{7}{2} }[/tex]
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A parallelogram is transformed according to the rule (x, y) - (x. y). Which is another way to state the
transformation?
O R0 90 degrees
O R0 180 degrees
O R0 270 degrees
O R0 360 degrees
Find the volume of a right circular cone that has a height of 11.4 in and a base with a radius of 5.1 in. Round your answer to the nearest tenth of cubic inch.
Answer:
155.3"^3
Step-by-step explanation:
the volume of a cone: 1/3 [tex]\pi[/tex]r^2 h
the volume of a right circular cone will be
1/3 [tex]\pi[/tex](5.1)^2 * 11.4
310.60 for a full circular cone.
for a right circular cone, we use 90/180 of the volume.
= 155.3
The volume of the cone is 121.8 in³.
A cone is a 3-dimensional shape that consists of a flat circular base and a tip known as the vertex.
Volume of a cone = [tex]\frac{1}{3}[/tex]πr²h
Where:
π = pi = 22/7
r = radius
h = height
Volume = [tex]\frac{1}{3}[/tex] x 22/7 x 5.1² x 11.4 = 121.8 in³
To round off to the nearest tenth, if the hundredth figure is greater or equal to 5, add to the tenth figure, if this is not the case, the tenth figure remains unchanged.
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One week a student exercised 2 hours at school and 2/3 hour at home. If 1/4 of the student's total exercise came from playing basketball, how much time did the student spend playing basketball that week?
Answer:
The student played basketball for 40 minutes.
Step-by-step explanation:
Given that one week a student exercised for 2 hours at school and for 2/3 of an hour at home, it can be stated that the student exercised for 2 hours and 40 minutes (since 60 x 2/3 is equal to 40 ). Thus, in total the boy exercised for 160 minutes (2 x 60 + 40).
Now, since he spent 1/4 of that time playing basketball, the time spent doing this sport is determined through the following calculation:
160/4 = X
40 = X
Thus, the student played basketball for 40 minutes.
Answer: 4/9
Step-by-step explanation:
¿Qué miden el IQR y el MAD?
Step-by-step explanation:
El IQR se utiliza en las empresas como marcador de sus tasas de ingresos. Para una distribución simétrica (donde la mediana es igual a la bisagra media, el promedio de los cuartiles primero y tercero), la mitad del IQR es igual a la desviación absoluta de la mediana (MAD). La mediana es la correspondiente medida de tendencia central.
PERSEVERE When is 4x < 4? Use a drawing to justify your
reasoning.
The expression 4x < 4 is true, when x is less than 1
How to determine when 4x < 4?The inequality expression is given as
4x < 4
Divide both sides of the inequality by 4
So, we have
4x/4 < 4/4
Evaluate the quotient
x < 1
This means that the expression 4x < 4 is true, when x is less than 1
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find the range of 5,11,2,12,4,2
Answer:
10
Step-by-step explanation:
to find the range, subtract the smallest number from the largest number
Answer:
Range: 10
General Formulas and Concepts:
Statistics
Range = Biggest number - smallest numberStep-by-step explanation:
Step 1: Define
5, 11, 2, 12, 4, 2
Step 2: Rearrange
2, 2, 4, 5, 11, 12
Step 3: Identify
Biggest number = 12
Smallest number = 2
Range = 12 - 2 = 10
there are 19 pieces of candy in the candy jar Mrs Breen lost her mind and started eating all these mindlessly she realize she had consumed eight pieces of candy approximately.what percent of candy does she eat??
You have 2/4 of a pizza and you want to share it equally between 2
people. How much of the pizza does each person get?
Answer:
1/4
Step-by-step explanation:
2/4 divided by 2 equals 1/4.
Answer:
HonEy me dont no no anything PERIODT
Step-by-step explanation:
A side of the triangle below has been extended to form an exterior angle of 127. Find the value of x.
Answer:
37
Step-by-step explanation:
180-127=53
180-53-90=37
i need help with this pleaseeeeeeeeeee
Answer:
1820
Step-by-step explanation:
65 pushups x 28 days
what is the estimate of 210 x 733
Answer:
153,930 that is the answer hope it is right
Answer:
about 1,400
Step-by-step explanation:
its about 1,400 because you would round 210 to 200, and 733 to 700.
please give brainliest :))
You will visit the nine states below, with the following rather odd rule: you must cross each border between neighboring states exactly once (so, for example, you must cross the Colorado-Utah border exactly once). Can you do it? If so, does it matter where you start your road trip? What fact about graph theory solves this problem?
ASAP I'LL GIVE BRAINLIEST
Answer:
ITS A THE FIRST ONE
Step-by-step explanation:
What the slope of the different lines please help
Answer:
Purple y=5/2x - 4
Yellow y=1/5x + 0
Red undefined
Green y = -3/2x - 4
Blue Undefined
Step-by-step explanation:
If a Slope is Vertical, the slope is undefined. I used rise/run for the others.
Tom is 8 years older than Jerry. The sum of their age is 80. What is Tom's age?
Answer: Tom is 46 years old and Jerry is 34 years old.
2/9 divided by 4????
Answer:
2/36 or simplfyed is 1/18
Step-by-step explanation:
Answer:
2/9 ÷ 4 = 2/36
Step-by-step explanation:
2/9 & 4
2/9÷4=?
2/9×1/4
=2/36
So 2/36 is equivalent fraction for 2/9 divided by 4
Explain why a graph that fails the vertical-line test does not represent a function. Be sure to use the definition of function in your answer. Need help with this I don't know.
Answer:
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
Step-by-step explanation:
The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value.
I attached an Image you can visualize it clearly
P.S I ain't that good at drawing though :P
The first three terms of an arithmetic series are 6p+2, 4p²-10 and 4p+3 respectively. Find the possible values of p. Calculate the common difference for each value of p.
Answer:
First Case:
[tex]\displaystyle p=\frac{5}{2}\text{ and } d=-2[/tex]
Second Case:
[tex]\displaystyle p=-\frac{5}{4}\text{ and } d=\frac{7}{4}[/tex]
Step-by-step explanation:
We know that the first three terms of an arithmetic series are:
[tex]6p+2, 4p^2-10, \text{ and } 4p+3[/tex]
Since this is an arithmetic sequence, each subsequent term is d more than the previous term, where d is our common difference.
Therefore, we can write the second term as;
[tex]4p^2-10=(6p+2)+d[/tex]
And, likewise, for the third term:
[tex]4p+3=(6p+2)+2d[/tex]
Let's solve for d for each of the equations.
Subtracting in the first equation yields:
[tex]d=4p^2-6p-12[/tex]
And for the second equation:
[tex]2d=-2p+1[/tex]
To avoid fractions, let's multiply the first equation by 2. Hence:
[tex]2d=8p^2-12p-24[/tex]
Therefore:
[tex]8p^2-12p-24=-2p+1[/tex]
Simplifying yields:
[tex]8p^2-10p-25=0[/tex]
Solve for p. We can factor:
[tex]8p^2+10p-20p-25=0[/tex]
Factor:
[tex]2p(4p+5)-5(4p+5)=0[/tex]
Grouping:
[tex](2p-5)(4p+5)=0[/tex]
Zero Product Property:
[tex]\displaystyle p_1=\frac{5}{2} \text{ or } p_2=-\frac{5}{4}[/tex]
Then, we can use the second equation to solve for d. So:
[tex]2d_1=-2p_1+1[/tex]
Substituting:
[tex]\begin{aligned} 2d_1&=-2(\frac{5}{2})+1 \\ 2d_1&=-5+1 \\ 2d_1&=-4 \\ d_1&=-2\end{aligned}[/tex]
So, for the first case, p is 5/2 and d is -2.
Likewise, for the second case:
[tex]\begin{aligned} 2d_2&=-2(-\frac{5}{4})+1 \\ 2d_2&=\frac{5}{2}+1 \\ 2d_2&=\frac{7}{2} \\ d_2&=\frac{7}{4}\end{aligned}[/tex]
So, for the second case, p is -5/4, and d is 7/4.
By using the values, we can determine our series.
For Case 1, we will have:
17, 15, 13.
For Case 2, we will have:
-11/2, -15/4, -2.
What is 3 2/5 compared to 3 1/3
PLEASE answer this correctly bc i will give u brainliest and extra points
The tables show the cost of different numbers of t-shirts ordered at two different stores, Store C and Store D: Store C Number of T-shirts Cost (in $) 2 $12 4 $24 8 $48 Store D Number of T-shirts Cost (in $) 3 $21 6 $42 9 $63 Which of these explains which store has a better buy? Store C, because the ratio of the number to the cost is 6:1 in Store C and 7:1 in Store D. Store C, because the ratio of the number to the cost is 1:6 in Store C and 1:7 in Store D. Store D, because the ratio of the number to the cost is 2:14 in Store C and 3:24 in Store D. Store D, because the ratio of the number to the cost is 14:2 in Store C and 24:3 in Store D.
Answer:
This is late, but the answer was B.
Answer:
The answer is b
Step-by-step explanation:
Suppose that N(x) = x denotes the number of bags sold by a shop, and the selling price per bag is
given by p(x) = 320 – 8x, for 0 ≤ x ≤ 10. Suppose further that the cost of producing x bags is given
by C(x) = 200x. Find (a) (N ∙ p)(x) and (b) (N ∙ p – C)(x). What do these functions represent?
A. (N • p)(x) = -8x² + 320x
B. (N • p - C)(x) = -8x² + 120x .
Function - a function is a relationship or expression involving one or more variables. It has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
given that -
N(x) = x
p(x) = 320 – 8x for 0 ≤ x ≤ 10
C(x) = 200x
(N ∙ p)(x) =?
(N ∙ p – C)(x) =?
For the question A....
(N ∙ p)(x) = N(p(x))
N(p(x)) = N(320 – 8x)
N(p(x)) = x(320 – 8x)
(N ∙ p)(x) = 320x - 8x²
For the question B....
(N ∙ p – C)(x) = N.((p-c)(x))
N.((p-c)(x)) = N.(p(x) - c(x))
N.((p-c)(x)) = x.(320 – 8x) -(200x)
N.((p-c)(x)) = 320x - 8x² - 200x
N.((p-c)(x)) = -8x² - 120x
Thus , the function represent (N • p)(x) = -8x² + 320x and (N • p - C)(x) = -8x² + 120x . These are the relationship between N , P , C.
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In the figure below what is the value of the CD arc?
a) 114°
b) 84°
c) 40°
d) 134°
e) 124°
Answer:
e
Step-by-step explanation:
The secant- secant angle CAD is half the difference of the intercepted arcs, that is
[tex]\frac{1}{2}[/tex] ( CD - BE ) = 20 ( multiply both sides by 2 )
CD - BE = 40 , substitute values
3x + 10 - 2x - 8 = 40
x + 2 = 40 ( subtract 2 from both sides )
x = 38
Thus
arc CD = 3x + 10 = 3(38) + 10 = 114 + 10 = 124° → e
I need this ASAP!!
Please show work as well, TY SO MUCH!!
Answer:
Step-by-step explanation:
19.
a) to find thhe x- intercept we make y=0
x² +4x -5 = 0
(x+5)(x-1) =0
x+5=0 so x=- 5
x-1 =0 so x= 1
b)
y-intercept is at (0, -5)
c)
axis of symmetry is at
x=-b/2a =-4/2*1 = -2
x= -2
d)
vertex is at (-2, -9) because x coordinate is on the axis of symmetry at -2 and
y= x² +4x -5= (-2) ² +4(-2) -5 = 4-8-5 = 4-13 = -9
6th grade math help me please :)
Answer:
katie
Step-by-step explanation:
because 10 is bigger than 8
Derek wants to order some roses online. Florist A charges $4.75 per blue rose plus $40 delivery charge. Florist B charges 5.15 per red pose plus 25$ delivery charge. If Florist B increases the cost per rose to $5.20, for what number of roses is it less expensive to order from Florist A or Florist B?
The number of roses that will be less expensive to order from A is 33
In this question, Florist A charges $4.75 per blue rose plus $40 delivery charge and the Florist B charges 5.15 per red pose plus 25$ delivery charge.
If Florist B increases the cost per rose to $5.20, we need to find the number of roses for which it would be less expensive to order from Florist A or Florist B.
Let the total charge be y and the number of rose be x
Florist A : the equation for the total cost would be,
y = 40 + 4.75x ---------1
Florist B : the equation for the total cost would be,
y = 25 + 5.2x --------2
We solve above equations to find the value of x i .e., to solve for the number of roses.
Equating equation 1 and 2,
40 + 4.75x = 25 + 5.2x
40 - 25 = 5.2x - 4.75x
15 = 0.45x
x = 15/0.45
x = 33.33
x ≈ 33
Therefore, the number of roses that will be less expensive to order from A is 33
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Solve for x
–2x +3 = –x + 12
Answer:
X =-9
Step-by-step explanation:
Answer:
x = -9
Step-by-step explanation:
–2x +3 = –x + 12
+x +x
-x +3 = 12
-3 -3
-x = 9
/-1 /-1
x = -9
12 6 4 18 x=2.5; y=2 O x=6;y=8 X=30, 42 x=7; y=10 x O x=6 x=8; y=6
Answer:
Step-by-step explanation:
Answer:
I have no clue to me have u tryed using a online solver thing
Step-by-step explanation:
18/6 as a whole number?
The answer is 3
Explanation: Divide using long division. The whole number portion will be the number of times the denominator of the original fraction divides evenly into the numerator of the original fraction, and the fraction portion of the mixed number will be the remainder of the original fraction division over the denominator of the original fraction. 3
Answer:
its 3
Step-by-step explanation:
Write the equation of the line in slope-intercept form that passes through (3, 10) and (2, 4)
Answer:
y=6x-8
Step-by-step explanation:
10-4/3-2
m=6/1
y=mx+b
y=6x+b
4=6(2)+b
4=12+b
-8=b
y=6x-8