[tex]\bf (x^9y^6z^{15})^{\frac{1}{3}}\implies \stackrel{\textit{distributing the exponent}}{\left(x^{9\cdot \frac{1}{3}}y^{6\cdot \frac{1}{3}} z^{15\cdot \frac{1}{3}} \right)}\implies x^3y^2z^5[/tex]
what is the value of x?
• 7
• 7√2
• 14
• 14√2
The value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex]. The correct option is [tex]\(14\)[/tex].
In a right triangle with a 45-degree angle, the sides are related by the special angles of 45-45-90 triangles. In such triangles, the sides are in the ratio [tex]\(1:1:\sqrt{2}\)[/tex].
Given that the height is [tex]\(7\sqrt{2}\)[/tex] and the hypotenuse is [tex]\(x\),[/tex] we can identify the relationship as follows:
[tex]\[ \text{Height} : \text{Base} : \text{Hypotenuse} = 1 : 1 : \sqrt{2} \][/tex]
So, the height is [tex]\(7\sqrt{2}\)[/tex], and the base would be [tex]\(7\sqrt{2}\)[/tex]as well, and the hypotenuse [tex](\(x\))[/tex] would be [tex]\(7\sqrt{2} \times \sqrt{2} = 7 \times 2 = 14\)[/tex].
Therefore, the value of [tex]\(x\)[/tex] is [tex]\(14\)[/tex], and the correct option is:
• [tex]\(14\)[/tex]
The correct answer is [tex]\boxed{14}[/tex]. The value of x is [tex]\boxed{14}[/tex].
To determine the value of [tex]\( x \)[/tex], we need to consider the given options and the context of the question, which involves the square root of 2. The options provided are [tex]\( 7 \), \( 7\sqrt{2} \), \( 14 \), and \( 14\sqrt{2} \).[/tex]
Let's analyze the options:
1. [tex]\( 7 \)[/tex] is a straightforward integer.
2. [tex]\( 7\sqrt{2} \) is \( 7 \)[/tex] times the square root of 2, which is an irrational number approximately equal to [tex]\( 1.414 \)[/tex].
3.[tex]\( 14 \) is \( 7 \)[/tex] times [tex]\( 2 \)[/tex], which is a simple integer multiplication.
4. [tex]\( 14\sqrt{2} \) is \( 14 \)[/tex] times the square root of 2.
Given that the question is asking for the value of [tex]\( x \)[/tex] and the options involve multiples of [tex]\( 7 \)[/tex] and [tex]\( 14 \)[/tex], it is reasonable to suspect that the answer might involve the square root of 2, since it is the only mathematical operation present in all the options.
However, without additional context or a mathematical equation to solve for [tex]\( x \)[/tex], we cannot definitively determine which of these options is correct based solely on the information given. In mathematics, problems involving square roots typically require an equation or a geometric representation to provide a clear path to the solution.
Since the question does not provide an equation or additional context, we must rely on the principle that the most straightforward answer is often correct when dealing with multiple-choice questions. In this case, the simplest option that does not involve an irrational number is [tex]\( 14 \)[/tex].
Therefore, without further information, the most logical and simple choice is [tex]\( 14 \)[/tex], as it is a whole number and does not introduce the complexity of an irrational number like [tex]\( \sqrt{2} \)[/tex].
Thus, the final answer is [tex]\boxed{14}[/tex].
HELP! The answer is 3 but I can't seem to get to the answer, instead I keep getting -3.
Answer:
x=3
Step-by-step explanation:
[tex]45-\frac{90}{x} = 15[/tex]
Minus 45 from both sides
[tex]-\frac{90}{x}=-30[/tex]
Multiply both sides x
[tex]-90=-30x[/tex]
Divide both sides by -30
[tex]3=x[/tex]
Answer:
3
Step-by-step explanation:
To eliminate the x on the denominator, multiply all terms by x
45x - 90 = 15x ( subtract 45x from both sides )
- 90 = - 30x ( divide both sides by - 30 )
3 = x ⇒ x = 3
Find the volume of a cylinder with a radius of 6 cm and height 15 cm?
The volume of the cylinder is defined (as usual) as the base area times the height. The base is a circle, so the base area is [tex]\pi r^2[/tex]
So, the volume is
[tex]h\pi r^2 = 15\cdot \pi \cdot 36 = 540\pi[/tex]
Answer:
[tex]
1696.46 {cm}^{3}
[/tex]
Step-by-step explanation:
[tex]V
=
π
{r}^{2}
h
\\ =
π
·
{6}^{2}
·
15
\\
≈
1696.46003
[/tex]
On a map of the United States the line from Portland, Oregon, to Twin Falls, Idaho, is 11 centimeters long. If the scale of the map is 2 centimeters to 100 miles, how far is it from Portland to Twin Falls?
Not sure what to do about Oregon and Idaho but the 2/100 gives you a 50 unit rate 50x11= 550
Answer:
using the information we have we can see that each mile centimeter is 50 miles. 11 x 50 is 550 so that is your answer
550 miles
On a blueprint with a scale of 1 cm = 4 ft, the length of the wall is 9 cm. If the scale of the blueprint were 1 cm = 3 ft, what would the length of the wall be
Final answer:
To find the length of the wall on the new blueprint with a scale of 1 cm = 3 ft, a proportion can be used. The length of the wall on the new blueprint would be 0.75 ft.
Explanation:
To find the length of the wall on the new blueprint with a scale of 1 cm = 3 ft, we can use a proportion.
In the original blueprint with a scale of 1 cm = 4 ft, the length of the wall is 9 cm. Let's let x represent the length of the wall on the new blueprint.
Set up the proportion: 1 cm/4 ft = x cm/3 ft
Cross multiply: 1 * 3 = 4 * x
Solve for x: x = 3/4
Therefore, the length of the wall on the new blueprint would be 3/4 ft or 0.75 ft.
What is the common difference between consecutive terms in the following arithmetic sequence -11, -8, -5, -2, 1
Answer:
The common difference is +3
Step-by-step explanation:
When you add 3 to -11 it becomes -8, add 3 again and you get -5, keep doing this and you'll notice that +3 is the common difference.
Answer:
The common difference is +3
Step-by-step explanation:
If you add "3" since -11 you obtain this arithmetic sequence.
(-11+3) = -8
(-8+3) = -5
(-5+3) = -2
(-2+3) = 1
-11, -8, -5, -2, 1
The scatterplot shows the sales, in dollars, of snow cones in relation to the outside temperature, in degrees Celsius. According to the line of best fit, which is the closest approximation of sales when the outside temperature is 21 °C?
A) $420
B) $450
C) $480
D) $520
B) it is 450 dollars
Answer: C: 480
Step-by-step explanation:
trust me its this answer not the other guys
A function whose graph goes up as it is followed from left to right is called
A graph that goes from left to right is called a direct graph.
Characteristics of a direct graph include:
- passes through origin
- is an increasing line
- is a straight line
- doesn't cut through either of the y or x axis
;)
HELP!
There are 6 seniors on student council . Two of them will be chosen to go to an all district meeting. how many ways are there to choose the students who will go to the meeting?
Answer:
U think the answer is C.
Answer:
Number of ways of selecting two students is 15
Step-by-step explanation:
number of ways of selecting n out of r is given by
[tex]n_{C_{r} } =\frac{n!}{r!(n-r)!}[/tex]
It is given that there are 6 seniors on student council.
2 students are selected for district meeting
So we have [tex]n= 6[/tex] and [tex]r=2[/tex]
number of ways of selecting two students =[tex]6_{C_{2} } [/tex]
=[tex]\frac{6!}{2!(6-2)!}[/tex]
=[tex]\frac{6!}{2!4!}=15[/tex]
So we have number of ways of selecting two students is 15
PLEASE HELP ASAP!!
What is the probability that the first spinner will land on 7 and the second spinner will land on C?
A. 1/3
B. 1/6
C. 1/12
D. 1/4
i believe the answer is c. 1/12
hope this helped! have a good day!
The required probability is 1/12 that the first spinner will land on 7 and the second spinner will land on C.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
The probability that the first spinner will land on 7
P(7) = favorable outcomes / total outcomes
P(7) = 1/4
The probability that the second spinner will land on C
P(C) = 1/3
As per the given question, the required probability will be as:
⇒ P(7) × P(C)
⇒ 1/4 × 1/3
⇒ 1/12
Hence, the correct answer would be an option (C).
Learn more about probability here:
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(Cole) is conducting an experiment in which he will roll a six sided number cube numbered 1 to 6 twice. What’s the probability that the result of the rolls is two sixes
Answer:1/36
Step-by-step explanation:
11 12 13 14 15 16
21 22 23 24 25 26
31 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 61 63 64 65 66 <=only 1 with 2 sixes
You can buy 4 bottles of water from a vending machine for $7. At this rate, how many bottles of water can you buy for $28
Answer:
16
Step-by-step explanation:
Divide 7 by 4, which gives you 1.75 . Multiply 1.75 & 28 and you get 16.
Answer:
16 bottles
Step-by-step explanation:
We can write a ratio, dollars over bottles of water
7 28
-------- = ----------
4 x
Using cross products
7x = 4*28
Divide each side by 7
7x/7 = 4*28/7
x = 4 * 4
x = 16
What is the value of x?
Answer:
x = 71°
Step-by-step explanation:
The triangle is clearly an isosceles triangle.
We know that all interior measures of a triangle must add up to 180°.
So: 180° - 38° = 142°
Because it is an isosceles triangle, the other two missing angles must be equal.
142° ÷ 2 = 71°
Answer:
x=71
Step-by-step explanation:
Because of the side being marked 27, you know that the triangle is an isosceles triangle. That means that the other 2 angles would be congruent. To find the sum of the remaining angles, you need to subtract 38 by 180 degrees. (All of the angles in a triangle add up to 180) 180-38=142. Since we already know that the two remaining angles will be congruent, you take 142 and divide by 2 to get the final answer 71.
Please help me ll give you 40 branily
Answer: Figure 2
Step-by-step explanation: A translation of the blue shaded shape would be figure 2
Harry wanted to know the amount of hours that his classmates spent doing homework on any given
night. He surveyed his classmates and received the following data set.
.5, .5, .75, .75, .75, 1, 1, 1, 1, 1.5, 1.5, 2, 2, 3, 4
What is the interquartile range of the data set that Harry collected?
Answer:
1.25
Step-by-step explanation:
Hopefully that's right. It's a bit hard to see separation
The interquartile range of Harry's collected data set is 1.25 hours.
To calculate the interquartile range (IQR) for the given data set, we must first arrange the data in ascending order, which is already done in this case. The data set is .5, .5, .75, .75, .75, 1, 1, 1, 1, 1.5, 1.5, 2, 2, 3, 4. The next step is to find the medians of the lower and upper halves of the data set to locate the first quartile (Q1) and the third quartile (Q3).
Since the data set has 15 numbers, the median (which is also Q2) would be the 8th value, which is 1.
For Q1, we take the lower half, which consists of the first 7 numbers. The median of this subset is the fourth value: 0.75.
For Q3, we consider the upper half, which consists of the last 7 numbers. The median of this subset is the fourth value: 2.
Now, calculate the IQR by subtracting Q1 from Q3: IQR = Q3 - Q1 = 2 - 0.75 = 1.25.
Therefore, the interquartile range of the data set that Harry collected is 1.25 hours.
Which question is best modeled with a division expression
A; what is the sum of 3 and 8/11
B: what is the quotient of 3 8/11
C: what is the product of 3 and 8/11
D: what is the difference of 3 and 8/11
Answer:
B
Step-by-step explanation:
Quotient is the answer of a division expression.
Could you mark brainliest sorry that if I bother you by asking.
What is the quotient of 3 and 8/11 is best modeled with a division expression
What is quotient?A quotient in mathematics is the amount created by dividing two numbers. In mathematics, the term "quotient" is frequently used to refer to the integer portion of a division, as well as to a fraction or a ratio.
Given
Quotient is the answer of a division expression.
To know more about quotient refer to :
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Which are true about the area of the circle? Check all that apply
Answer:
Step-by-step explanation:
2, 3, 5
Answer:
Answers:2, 3, 5
Step-by-step explanation:
In the metric system, the numbers 10, 100, 1,000, 10,000, and so on serve as
Answer:
prefixes
Step-by-step explanation:
The exact response will depend a lot on what you learned in your manual and the terms used in it, but the metric system is all based on the base of 10, like the numbers system you use every day.
Unlike the US/Imperial system where there's no clear relation between an inch, a yard and a mile for example, in the metric system everything is related by the factor 10 somehow.
The unit multiplier is also used as a prefix to identify measurements. Like for meter...
10 meters = 1 decameter
100 meters = 1 hectometer
1000 meters = 1 kilometer
and so on.
Answer:
what he said
Step-by-step explanation:
There are 10 students in a class. The teacher chooses three students to go to the library. The order in which they are chosen does not matter. How many ways are there to choose the students?
Answer:
I think the answer is C.
Answer:B. 120
Step-by-step explanation:
Describe the trend in the scatter plot.
A:Negative trend
B:positive trend
C:no trend
It is positive . Every time it’s to the right it’s positive when it’s to the left it’s negative and when the points are all over the place it’s no Trend
Answer: Positive trend
Step-by-step explanation: In this scatter plot, notice that we can draw a line of best fit to represent the data. This means that we have a trend. Notice the x-values increase while the y-values increase which means we have a positive correlation between x and y.
Therefore, this scatter plot represents a positive trend.
Image provided.
Ricky is filling an 8-inch by 4-inch by 4 1/2 inch rectangular box with cubes.the cube come in two different sizes, 1 cubic inch and 1/8 cubic inch.he uses some of each size cube and he packs the box so there are no gaps.what is the least smaller subs that Ricky can use
A.)32
B.)64
C.)128
D.)256
To fill the rectangular box with cubes, Ricky can use 144 larger cubes and 0 smaller cubes, resulting in the least number of smaller cubes being 0. The correct answer is option A) 32.
Explanation:To find the least number of smaller cubes that Ricky can use to fill the rectangular box, we first need to calculate the volume of the box. The volume of the box can be found by multiplying its length, width, and height. In this case, the volume is 8 inches x 4 inches x 4.5 inches = 144 cubic inches.
The larger cubes have a volume of 1 cubic inch, while the smaller cubes have a volume of 1/8 cubic inch. To minimize the number of cubes used, we want to use the larger cubes as much as possible.
We can now calculate the number of larger cubes that can fit in the box. 144 cubic inches / 1 cubic inch = 144 cubes.
Next, we need to fill any remaining space with the smaller cubes. The remaining space can be calculated by subtracting the volume occupied by the larger cubes from the total volume of the box. 144 cubic inches - 144 cubic inches = 0 cubic inches.
Since there is no remaining space, we do not need to use any smaller cubes. Therefore, the least number of smaller cubes that Ricky can use is 0.
So, the correct answer is option A) 32.
Solve for t.
19=12gt2
A. t=76g‾‾‾√
B. t=g76‾‾‾√
C. t=(38g)2
D. t=38g‾‾‾√
Step-by-step explanation:
[tex]12gt^2=19\qquad\text{divide both sides by}\ 12g\\\\t^2=\dfrac{19}{12g}\to t=\sqrt{\dfrac{19}{12g}}[/tex]
Answer: >____(38g/g
Step-by-step explanation:
What is the solution to log 5 (x+30)= 3
Answer:
x = 95
Step-by-step explanation:
Using the rule of logarithms
• [tex]log_{b}[/tex] x = n ⇔ x = [tex]b^{n}[/tex]
Given
[tex]log_{5}[/tex](x + 30) = 3, then
x + 30 = 5³ = 125 ( subtract 30 from both sides )
x = 95
please help w precalculus will mark brainliest!
-see attachment-
ANSWER
x=-3, y=6
EXPLANATION
The given equation is
[tex] - 3 + yi = x + 6i[/tex]
We can rewrite this equation as:
[tex]x - yi = - 3 - 6i[/tex]
The two complex number equations are equal therefore their corresponding parts are also equal.
Comparing the real number parts,
[tex]x = - 3[/tex]
Comparing the complex number part,
[tex] - y = - 6[/tex]
y=6.
A mother who is 40 years old has a daughter and a son. The son is twice as old as the daughter. In 15 years the sum of all their ages will be 100 years. How old are the siblings now?
Answer:
the son is 30 and the daughter is 15
Step-by-step explanation:
the mom is 55 in 15 years
100-55=45
45-30=15
15x2=30
Answer:
15 and 5
Step-by-step explanation:
Mother's current age: 40
daughter's age: d
son's age: s
son is 2x as old as daughter: s = 2d
Then, 15 years from now, the sum of their ages will be:
(40 + 15) + (2d + 15) + (d + 15) = 100
or
55 + 15 + 15 + 3d = 100
85 + 3d = 100, or 3d = 15, or d = 5.
Then the son's age is 3(5) = 15 and the daughter's is 5.
2 friends equally share 5 cookies how many cookies does each friend get?
Answer:
They both get 2 and 1/2 of a cookie!
Hope this helped, God bless you!
Final answer:
Two friends sharing 5 cookies equally will each get 2.5 cookies after dividing the total number of cookies by the number of friends.
Explanation:
If two friends equally share 5 cookies, each friend gets 2.5 cookies. Since cookies typically cannot be equally divided by 2 without cutting them into pieces, we assume here that it's possible to split the cookies such that each person gets an equal share. Here's the calculation:
Start with the total number of cookies, which is 5.
Divide that number by 2, because there are 2 friends sharing the cookies.
The answer is 2.5 cookies for each friend.
This question involves simple division and is an example of how to apply fair sharing in a real-world scenario.
Help please and need to show the work!
To find how many small cubes can fit inside a larger cube, you need to find the volume of both.
Once you have the volumes, divide the volume of the larger cube, by the volume of the smaller cube.
Volume = L x W x H
Small cube: Volume = 3/4 x 3/4 x 3/4 = 0.421875 cm^3
Large cube: Volume = 3 x 3 x 2 = 18 cm^3
Number of small cubes that can fit: 18 / 0.421875 = 42.67 Cubes.
Since you can't have a partial cube ( 0.67) round down to a whole number:
That means you can fit 42 cubes.
student government members survey every 15th student who enters the school building and asks whether students favor the school’s new school mascot. the sample statistics show that 57% oppose the new school mascot., 37% favor the school mascot, and 6% have no opinion.
The student's question pertains to a survey on students' opinions about a new school mascot. The survey results showed varying levels of support and opposition, which are crucial for decision-making in educational policy. This demonstrates the real-world application of mathematics in understanding public opinion through statistics.
The student's question deals with a survey conducted by student government members to understand the school community's stance on the new school mascot. This survey follows a systematic sampling method by asking every 15th student entering the school. The outcome showed that 57% oppose, 37% are in favor, and 6% have no opinion regarding the new mascot. Such a poll is useful for making decisions related to public policy and ensuring that actions consider community preferences.
Another key component is understanding the methodology behind this survey. If we consider a similar scenario where 600 students are surveyed with 480 opposing new legislation (as mentioned in one of the examples), we could calculate the percentage opposing the legislation and use this to propose actions or influence decision-making processes regarding school policies.
In the context of educational institutions, conducting polls or surveys is a practical way to involve student bodies in decision-making processes, reflecting a democratic practice in school governance. This kind of statistical analysis forms a crucial part of mathematics in the real world, particularly within the fields of statistics and probability.
If sin(x+y) - sin(x-y) = 2f(x)sin(y), then f(x) equals?????
From the function sin(x+y) - sin(x-y) = 2f(x)sin(y), we can deduce that f(x) = cosx
But sin(x + y) = sinxcosy + cosxsiny.
Also, sin(x - y) = sinxcosy - cosxsiny..
Hence:
sin(x+y) - sin(x-y)
= sinxcosy + cosxsiny - (sinxcosy - cosxsiny)
= sinxcosy - sinxcosy + cosxsiny + cosxsiny
= 2cosxsiny
2cosxsiny = 2f(x)sin(y)
Hence, f(x) = cosx
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what are the roots of this equation?
x²-4x+9=0
a. 1±i√5
b. 2±i√5
c. 2±i√3
d. 1±i√52
Answer:
x = 2 ± (i)√5 (Answer b)
Step-by-step explanation:
x²-4x+9=0 can be solved in a variety of ways; the first two that come to mind that are also appropriate are (1) completing the square and (2) using the quadratic formula.
Completing the square is fast here:
Rewrite x²-4x+9=0 as x²-4x +9=0
Identify the coefficient of the x term: it is -4
Take half of that, obtaining -2
Square this result, obtaining 4
Add 4 to x²-4x +9=0, in the blank space in the middle, and then subtract 4: x²-4x +4 -4 +9=0
Rewrite x²-4x +4 as the square of a binomial:
(x - 2)² - 4 + 9 = 0 → (x - 2)² = -5
Take the square root of both sides: x - 2 = ±√(-5) = ± (i)√5
Then x = 2 ± (i)√5