Given:
[tex]\frac{x^{-1}\left(y^{-8}z^5\right)^3}{x^{-4}y^{-3}z^6}[/tex]Simplify:
[tex]\frac{x^{-1}y^{-24}z^{15}}{x^{-4}y^{-3}z^6}[/tex]And:
[tex]x^{-1-(-4)}y^{-24-(-3)}z^{15-6}=x^3y^{-21}z^9[/tex]Re order:
[tex]\frac{x^3z^9}{y^{21}}[/tex]Answer:
[tex]\frac{x^{3}z^{9}}{y^{21}}[/tex]The scores at the end of a game are shown.List the scores in order from greatest to least.Scores:Vince:-0.5, Allison: 3/8, Mariah:-7/20
To arrange the numbers from greatest to least, let us begin by changing all the numbers to decimals.
Vince's Score: -0.5
Allison's Score: 0.375
By long division, we can convert the fraction to a decimal:
Mariah's Score: -0.35
By long division, we have:
Given that we have calculated the scores in decimal, we can clearly see the bigger and smaller numbers.
The order from biggest to smallest is:
Allison: 3/8, Mariah: -7/20, Vince: -0.5
Solve the following equation.
(√x -7) (√x -2)= -18
Answer:NO SOLUTION
Step-by-step explanation:
Consider parallelogram VWXY below using information given in the figure to find x, m angle zvw and m angle zwv
ANSWERS
• x = 5
,• m∠ZVW = 46°
,• m∠ZWV = 41°
EXPLANATION
The diagonals of a parallelogram bisect each other, so
[tex]11=5x+1[/tex]To find x subtract 1 from both sides of the equation,
[tex]\begin{gathered} 11-1=5x+1-1 \\ 10=5x \end{gathered}[/tex]And divide both sides by 5,
[tex]\begin{gathered} \frac{10}{5}=\frac{5x}{5} \\ 2=x \end{gathered}[/tex]Hence x = 5
By the SAS property, triangle VZW and XZY are congruent:
Therefore, corresponding angles are also congruent. Angle ZXY is the one formed by the blue half-diagonal and the third side of the triangle, therefore its corresponding angle for the other triangle is the one formed also by the blue half-diagonal and the third side of the triangle, which is angle ZVW,
[tex]\angle ZVW\cong\angle\text{ZXY}[/tex][tex]m\angle ZVW=46[/tex]It is a similar situation for angle ZWV. This angle is formed by the light blue half-diagonal and the third side of triangle VZW, so its corresponding angle in triangle XZY is the one also formed by the light blue half-diagonal and the third side of the triangle, which is angle ZYX,
[tex]\angle\text{ZWV}\cong\angle\text{ZYX}[/tex][tex]m\angle ZWV=41[/tex]Find the perimeter of quadrilateral ABCD with vertices A(0,4), B(4,1), C(1, -3), and D(-3,0).25 units100 units5 units20 units
The perimeter is the sum of the length of each side of the quadrilateral. We would find the length of each side by applying the formula for finding the distance between two points which is expressed as
[tex]\text{Distance = }\sqrt[]{(x2-x1)^2+(y2-y1)^2}[/tex]Thus, we have
[tex]\begin{gathered} ForAB,x1=0,y1=4,x2=4,\text{ y2 = 1} \\ \text{Distance = }\sqrt[]{(4-0)^2+(1-4)^2\text{ }}\text{ = }\sqrt[]{16\text{ + 9}} \\ AB\text{ = 5} \\ \text{For BC, x1 = 4, y1 = 1, x2 = 1, y2 = - 3} \\ \text{Distance = }\sqrt[]{(1-4)^2+(-3-1)^2}\text{ = }\sqrt[]{9\text{ + 16}} \\ BC\text{ = 5} \\ \text{For CD, x1 = 1, y1 = - 3, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-1)^2+(0--3)^2}\text{ = }\sqrt[]{16\text{ + 9}} \\ CD\text{ = 5} \\ \text{For AD, x1 = 0, y1 = 4, x2 = - 3, y2 = 0} \\ \text{Distance = }\sqrt[]{(-3-0)^2+(0-4)^2\text{ }}\text{ = }\sqrt[]{9\text{ + 16}} \\ AD\text{ = 5} \end{gathered}[/tex]Perimeter = AB + BC + CD + AD = 5 + 5 + 5 + 5
Perimeter = 20 units
it says use the table to rewrite the expression you wrote for problem 2. rewrite that expression so that both terms are written with the same exponent number 4. says use the distributive property simplify the expression you wrote for problem 3.number 5. says write your expression as the product of a decimal times a power of 10.number 6 says write your solution in scientific notation and number 7. says Evaluate (7.4 x 10^15 -- (9.9 x 10^13number 8 says Evaluate (8.9 x 10^5) + (6.5) x 10^6
7)
Given data:
The given expresson is a=7.7x10^15-(9.9x10^13)
The given expression can be written as,
a=770x10^13-9.9x10^13
=(770-9.9)x10^13
=760.1x10^13.
8)
Given data:
The given expresson is b=8.9x10^5-(6.5)x10^6
The given expression can be written as,
b=8.9x10^5-65x10^5
=(8.9-65)x10^5
=-56.1x10^5
State weather the triangles are similar. If so write a similarity statement and that postulate or theorem you used. The diagram is not drawn to scale.
Given:
To prove the similarity.
Two triangles similarity condition:
If two triangles are similar then the corresponding sides are proportional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex][tex]\begin{gathered} \frac{OK}{ON}=\frac{OJ}{OM}=\frac{KJ}{NM} \\ \frac{3}{3+1}=\frac{30}{30+10} \\ \frac{3}{4}=\frac{30}{40} \\ \frac{3}{4}=\frac{3}{4} \end{gathered}[/tex]From the given values the corresponding sides are proves as propotional.
[tex]\Delta\text{OKJ Similar to }\Delta ONM[/tex]the triangles are similar. find the similarity ratio of the first to the second
To get the similarity ratio between both triangles, write down a ratio between two similiar sides. Let's take the base, for example
[tex]4\colon6[/tex]Simplifying,
[tex]2\colon3[/tex]Thereby, the similarity ratio between both triangles is:
[tex]2\colon3[/tex]Ans: Option B
1v=9. Which equation represents the equation of theparabola with focus (-3,3) and directrix y = 7?A),= (x+3)2 – 5B) y = 5(? – 3)2 +5C) y=-( + 3)2 +5D) y=-2 (2-3)2 +5
SOLUTION
From the focus (-3, 3) and the directrix y = 7 given, note that the vertex is usually between the focus and the directrix.
So, the vertex will have the same x-coordinate as the focus, which is -3, and the y-coordinate of the vertex becomes
[tex]\begin{gathered} \frac{3+7}{2} \\ that\text{ is 3 from the y-coordinate of the focus and 7 from the directrix} \\ y=7 \\ \frac{3+7}{2}=\frac{10}{2}=5 \end{gathered}[/tex]Hence coordinate of the vertex is (-3, 5)
Now, equation of a parabola is given as
[tex]\begin{gathered} (x-h)^2=4p(y-k) \\ where\text{ \lparen h, k\rparen is the coordinate of the vertex and p is the focal length} \\ y=k-p,\text{ so we have } \\ 7=5-p \\ p=5-7=-2 \end{gathered}[/tex]So putting in the values of h, k and p into the equation, we have
[tex]\begin{gathered} (x-h)^{2}=4p(y-k) \\ (x-(-3)^2=4(-2)(y-5) \\ (x+3)^2=-8(y-5) \\ -\frac{1}{8}(x+3)^2=y-5\text{ that is dividing through by -8} \\ making\text{ y the subject, we have } \\ y=-\frac{1}{8}(x+3)^2+5 \end{gathered}[/tex]Hence the answer is
[tex]y=-\frac{1}{8}(x+3)^{2}+5[/tex]The local weather report states that there is 3/5 a chance of rain today, but it is more likely to rain tommorrow than today. What is a possible probability of rain for tommorrow? A.0.4 B. 0.5 I C. 0.6 D. 0.7
D. 0.7
Explanations:Probability is the chance (likelihood) that an event will take place
The probabilty that it will rain today = 3/5 = 0.6
There is more likelihood that it will rain tomorrow that today.
This means that the probabilty that it will rain tomorro is greater than the probability that it will rain today.
Therefore, the probability of rain tomorrow is more than 0.6
Only option D (0.7) is greater than 0.6, and it is the only correct choice
the perimeter of a square box is 12x + 32 drag number to complete an equivalent expression that shows the premier has four times the side length of the box
The perimeter of the box is given as
12x + 32
To write an equivalent expression that shows the premier has four times the side length of the box , we would factorise the expression. It becomes
4(12x/4 + 32/4)
= 4(3x + 8
use the diagram at the right name the following three points ray
From the geometric diagram below
(1) Three diagram
[tex]\text{ Points JQE is a 3 points}[/tex](2) A ray
[tex]RP\text{ is a ray}[/tex](3) Two intersecting lines but not perpendicular
[tex]\text{ line RF and line NI are the two intersecting lines but not perpendicular}[/tex]translate and simplify subtract 18 from -11 .enter only the simplified results
Problem
translate and simplify subtract 18 from -11 .enter only the simplified results
Solution
For this case we can do the following:
-11- 18= -29
Final answer: -29
Use the spinner shown in the figure below to find the probability indicated.Landing on green or a consonant
Based on the spinner, there are a total of 8 possible outcomes.
2 of which are green and 4 are consonants, however, 1 outcome is both consonant and a green (F green).
Therefore, the probability of landing on a green or consonant is:
[tex]\begin{gathered} P(A\text{ or B)}=P(A)+P(B)-P(A\text{ and B)} \\ P(A\text{ or B)}=\frac{2}{8}+\frac{4}{8}-\frac{1}{8} \\ P(A\text{ or B)}=\frac{5}{8} \end{gathered}[/tex]The probability of landing on a green or consonant is 5/8 or 62.5%.
Hello, I need help completing and showing appropriate steps for this problem. Thank you so much!
The first step is to factorise the quadratic expression on the right side of the equation. The expression is
x^2 + 9x + 20
We would find two terms such that their sum or difference is 9x and their product is 20x^2. The terms are 5x and 4x. Replacing 9x with 5x and 4x, it becomes
x^2 + 5x + 4x + 20
By factorising, it becomes
x(x + 5) + 4(x + 5)
Since x + 5 is common, it becomes
(x + 4)(x + 5)
Thus, the original expression becomes
x/(x + 4) + 3/(x + 5) = (x + 2)/(x + 4)(x + 5)
The lowest common multiple of the denominators on both sides of the equations is (x + 4)(x + 5). We would multiply each term in the equation by
(x + 4)(x + 5). It becomes
(x + 4)(x + 5)x/(x + 4) + 3(x + 4)(x + 5)/(x + 5) = (x + 2)(x + 4)(x + 5)/(x + 4)(x + 5)
By cancelling out common terms in the numerator and denominator, we have
x(x + 5) + 3(x + 4) = x + 2
We would expand the parentheses on both sides by multiplying the terms inside with the term outside. It becomes
x^2 + 5x + 3x + 12 = x + 2
By collecting like terms, we have
x^2 + 5x + 3x - x + 12 - 2 = 0
x^2 + 7x + 12 = 0
Again, We would find two terms such that their sum or difference is 7x and their product is 12x^2. The terms are 4x and 3x. Replacing 7x with 4x and 3x, it becomes
x^2 + 4x + 3x + 12 = 0
By factorising, it becomes
x(x + 4) + 3(x + 4) = 0
Since x + 4 is common, it becomes
(x + 3)(x + 4) = 0
x + 3 = 0 or x + 4 = 0
x = - 3 or x = - 4
The solutions are x = - 3 or x = - 4
what is the difference in a probability that the student will spin a factor of 83 times in a row in the probability that a student will spin a number greater than 63 times in a row
The number 8 has factors 1, 2, 4 and 8.
The only numbers in the spin greater than 6 are 7 and 8,
The probability that the student will spin a factor of 8 three times in a row is given by: (4/8)*(4/8)*(4/8) = (1/2)*(1/2)*(1/2) = 1/8
The probability that the student will spin a number greater than 6 three times in a row is given by (2/8)*(2/8)*(2/8) = (1/4)*(1/4)*(1/4) = 1/64
Then, the difference between these two probabilities is given by 1/8 - 1/64 = 7/64
At a sale this week,a suit is being sold for $364. This is a 35% discount from the original price. What is the original price?
Okay, here we have this:
Considering the provided information, we are going to calculate the requested original price, so we obtain the following:
So we have the following formula:
Discount Price=Original Price*(100%-Discount)
Clearing for "Original price":
Discount Price=Original Price*(100%-Discount)
Original Price=Discount Price/(100%-Discount)
Replacing with the given data:
Original Price=Discount Price/(100%-Discount)
Original Price=$364/(100%-35%)
Original Price=$364/(65%)
Original Price=$364/(0.65)
Original Price=$560
Finally we obtain that the original price is $560.
3. What is the domain of the relation described by the set of ordered pairs {(-2, 8), (-1, 1), (0, 0), (3, 5), (4, -2)}?{-2, -1, 0, 4,5){-2, 0, 1, 5, 8}{-2, -1,0,3,4}{-2, -1, 0, 1,5}
The domain is related to x axis coordinates. So, you have to take the x coordinate of each point
-2,-1,0,3,4
Select all sets of triangles that can be provencongruent using Side-Angle-Side(SAS).
SOLUTION
We want to select all triangles from the image that can be proven by the side angle side theorem which states that
If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent.
Now looking at the triangles
We can see that triangles in number 1, 2, 3 follows this theorem.
4 does not because the equal angles are not present
5, the triangles are congruent, but do not follow the SAS theorem
6 follows as we can see the equal sides and angle
7 shows two equal angles only, but we need one equal angles and two equal sides.
Hence the answer is 1, 2, 3 and 6 only
Which is the best estimate for 2 2/3 × 3 1/4
The best estimate of the real number expression; 2 ⅔ × 3 ¼ as given in the task content is; 8 ⅔.
What is the best estimate of the real number expression given?It follows from the task content that the best estimate of the real number expression given is to be determined.
On this note, the mixed numbers must be converted to fractions for ease of computation as follows;
Therefore; 2 ⅔ = 8 / 3.
And, 3 ¼ = 13 / 4.
Therefore, the required evaluation of the expression is;
2 ⅔ × 3 ¼ = 8 / 3 × 13 / 4
= 104/12
= 26 / 3
Hence, the best estimate for the given expression is; 26 / 3 Or 8 ⅔.
Read more on fractions multiplication;
https://brainly.com/question/7335118
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Need help with number five. The question is solve each system
5)
The given equations are
- 4x - 2y + 3z = 7
- 3x + 5y - 3z = 13
- 5x + y - z = 11
From equation 3, we have
y = 11 + 5x + z
We would substitute y = 11 + 5x + z into equations 1 and 2. For equation 1, we have
- 4x - 2(11 + 5x + z) + 3z = 7
- 4x - 22 - 10x - 2z + 3z = 7
- 4x - 10x - 2z + 3z = 7 + 22
- 14x + z = 29
For equation 2, we have
- 3x + 5(11 + 5x + z) - 3z = 13
- 3x + 55 + 25x + 5z - 3z = 13
- 3x + 25x + 5z - 3z = 13 - 55
22x + 2z = - 42
Dividing both sides of the equation by 2, we have
11x + z = - 21
z = - 21 - 11x
Substituting z = - 21 - 11x into - 14x + z = 29, we have
- 14x - 21 - 11x = 29
- 14x - 11x = 29 + 21
- 25x = 50
x = 50/- 25
x = - 2
z = - 21 - 11(- 2) = - 21 + 22
z = 1
Substituting x = - 2 and z = 1 into y = 11 + 5x + z, we have
y = 11 + 5(-2) + 1
y = 11 - 10 + 1
y = 2
The solutions are
x = - 2, y = 2, z = 1
Answer each part. If necessary, round your answers to the nearest hundredth.(a) Abdul runs 3 miles in 17 minutes.How many miles does he run per minute?I miles per minute(b) It takes 37 pounds of seed to completely plant a 4-acre field.How many pounds of seed are needed per acre?pounds per acre
To determine the speed of Abdul, we can divide 3 miles by 17 minutes.
[tex]\frac{3mi}{17\min}=\frac{0.17647mi}{\min}\approx\frac{0.18mi}{\min }[/tex]Therefore, Abdul runs approximately 0.18 miles per minute.
1. How is the orientation of the triangie affected by the translation?
Solution: The orientation is inverted
Explanation:
Given a triangle ABC if we reflect if along a straight line L we get the triangle A'C'B' and now we are going to draw it
Find the equation of this line.(2,2) and (0,-4)
To find the equation;
x₁ = 2 y₁ = 2 x₂ = 0 y₂=-4
we will use the formula;
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x_{}-x_1)[/tex]substituting the values into the above;
[tex]y-2=\frac{-4-2}{0-2}(x-2)[/tex]Then, we will go ahead and evaluate;
[tex]y-2\text{ = }\frac{-6}{-2}(x-2)[/tex][tex]y-2\text{ =3(x-2)}[/tex]y - 2 = 3x - 6
add 2 to both-side of the equation
y = 3x -6+ 2
y = 3x -4
What is the residual of a performance with a revenue of $700 and 70 seats occupied?
its asking for the approximate depth of the river. but I don't know how to determine that
From figure, trngles VWX and VYZ are similar.
So, the ratio of corresponding sides of triangles will be equal. Hence,
[tex]\begin{gathered} \frac{VW}{VY}=\frac{WX}{YZ} \\ \frac{3}{62}=\frac{5}{d} \\ d=\frac{5\times62}{3} \\ =103.3\text{ m} \end{gathered}[/tex]Therefore, the approximate depth of the river is d=103.3 m.
Enter your answer, rounded to the nearest tenth, in the box.
ANSWER:
-11.4
STEP-BY-STEP EXPLANATION:
We have the following function:
[tex]f\mleft(x\mright)=\frac{100}{-10+e^{-0.1x}}[/tex]We calculate the result when x = -2, just like this:
[tex]\begin{gathered} f(-2)=\frac{100}{-10+e^{-0.1\cdot-2}} \\ f(-2)=\frac{100}{-10+e^{0.2}} \\ f(-2)=\frac{100}{-10+1.22} \\ f(-2)=\frac{100}{-8.78} \\ f(-2)=-11.4 \end{gathered}[/tex]When x = -2, the value of the function is equal to -11.4
How much money will he raise based on the two donations?
The neighbor will donate $0.25 for every 40ft run.
The aunt will donate $18 for every mile run.
To determine how much he will raise if he runs 5miles, you have to calculate the amount per donor and then add them:
Neighbor
1 mile is equal to 5280 feet
To determine how many feet correspond to 5 miles, multiply the distance by 5280
[tex]5\cdot5280=26400ft[/tex]Next, calculate how much we will make:
40ft → $0.25
26400ft → $x
[tex]\begin{gathered} \frac{0.25}{40}=\frac{x}{26400} \\ 26400\cdot\frac{0.25}{40}=26400\cdot\frac{x}{26400} \\ 165=x \end{gathered}[/tex]For running 5miles, Dustin will raise $165 from the neighbor.
Aunt
The aunt will donate $18 per mile run, to determine how much she will donate, multiply $18 by 5
[tex]18\cdot5=90[/tex]For running 5 miles, Dustin will raise $90 from the neighbor.
Next, add both amounts:
[tex]165+90=255[/tex]Dustin will raise $255 for running 5 miles.
which function will have the greatest value of x equals 80
In order to solve this, we can replace 80 for x into each one of the three given functions, then we identify what value of y is the greatest, like this:
For the first function:
y = 4x
y = 4×80
y = 320
For the second function:
y = x² - 15x + 88
y = 80² - 15×80 + 88
y= 6400 - 1200 + 88
y = 5288
For the third function:
[tex]\begin{gathered} y=1.1135^{80} \\ y=5435.23 \end{gathered}[/tex]As you can see, at x = 80 the function that has the greatest value is the third one.
b) Use the graph to estimate the
value of x when y = 1
Answer:
Hey bro you're welcome.
Step-by-step explanation:
The ages (in years) of the 6 employees at a particular computer store are the following.31, 41, 35, 22, 38, 31Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.(If necessary, consult a list of formulas.)
The standard deviation of the population = 6.08
Explanations:The given ages of the employers are:
31, 41, 35, 22, 38, 31
Find the mean of the dataset:
[tex]\begin{gathered} \mu\text{ = }\frac{\sum ^{}_{}x_i}{N} \\ \mu\text{ = }\frac{31+41+35+22+38+31}{6} \\ \mu\text{ = }\frac{198}{6} \\ \mu\text{ = }33 \end{gathered}[/tex]Find the summation of the square of each deviation from the mean
[tex]\begin{gathered} \sum ^6_{i\mathop=0}(x_i-\mu)^2=(31-33)^2+(41-33)^2+(35-33)^2+(22-33)^2+(38-33)^2+(31-33)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=(-2)^2+(8)^2+(2)^2+(-11)^2+(5)^2+(-2)^2 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=4+64+4+121+25+4 \\ \sum ^6_{i\mathop{=}0}(x_i-\mu)^2=222 \end{gathered}[/tex]The standard deviation is given by the formula:
[tex]\begin{gathered} \sigma\text{ = }\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N}} \\ \sigma\text{ = }\sqrt[]{\frac{222}{6}} \\ \sigma\text{ = }\sqrt[]{37} \\ \sigma\text{ = }6.08 \end{gathered}[/tex]The standard deviation of the population = 6.08 (rounded to 2 decimal places)