The value of the expression in the options is (a) three raised to the sixth power divided by six raised to the fifteenth power
How to determine the equivalent expression of the expression?The expression is given as
A fraction with six raised to the negative third power in the numerator and the quantity three raised to the negative second power times six squared end quantity in the denominator and the entire fraction is cubed.
Rewrite the expression properly
So, we have
[6^-3/(3^-2 x 6^2)]^3
Apply the law of indices to the expression
So, we have
[6^-3/(3^-2 x 6^2)]^3 = [6^(-3 - 2)/(3^-2)]^3
Evaluate the difference
[6^-3/(3^-2 x 6^2)]^3 = [6^-5/(3^-2)]^3
Apply the change of power rule
[6^-3/(3^-2 x 6^2)]^3 = [3^2/6^5]^3
Evaluate the product of exponents
[6^-3/(3^-2 x 6^2)]^3 = 3^6/6^15
In words, the result is (a) three raised to the sixth power divided by six raised to the fifteenth power
Hence, the value of the expression is (a)
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Consider the equation 3x3 + 14x2 – 14x + 60 = 0. The real solution is –6. What are the nonreal solutions?
HURRY Negative 2 i StartRoot 26 EndRoot, 2 i StartRoot 26 EndRoot.
4 minus 2 i StartRoot 26 EndRoot, 4 + 2 i StartRoot 26 EndRoot.
StartFraction negative 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction negative 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
StartFraction 2 + i StartRoot 26 EndRoot Over 3 EndFraction, StartFraction 2 minus i StartRoot 26 EndRoot Over 3 EndFraction.
The non-real solutions of the polynomial expression are x = (2 + i√26)/3 and x = (2 - i√26)/3
How to determine the non-real solutions?The equation of the polynomial expression is given as:
3x^3 + 14x^2 - 14x + 60 = 0
From the question, we have
Real solution = -6
Rewrite the above equation as
x = -6
Add 6 to both sides of the equation
So, we have
x + 6 = 0
The next step is to divide the polynomial equation 3x^3 + 14x^2 - 14x + 60 = 0 by x + 6 = 0
This is represented as
3x^3 + 14x^2 - 14x + 60/x + 6
Using a graphing calculator, we have
3x^3 + 14x^2 - 14x + 60/x + 6 = 3x^2 - 4x + 10
Next, we determine the solution of the quadratic expression 3x^2 - 4x + 10 using a quadratic formula
So, we have
x = (-b ± √(b² - 4ac))/2a
This gives
x = (4 ± √((-4)² - 4 * 3 * 10))/2 * 3
So, we have
x = (4 ± √-104)/6
This gives
x = (4 ± 2√-26)/6
Divide
x = (2 ± √-26)/3
Rewrite as
x = (2 ± i√26)/3
Split
x = (2 + i√26)/3 and x = (2 - i√26)/3
So, the conclusion is that
Using the polynomial expression, the non-real solutions are x = (2 + i√26)/3 and x = (2 - i√26)/3
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How many terms does the expression 2x + 7 have
The total number of terms in the given expression 2x + 7 is equal to two.
As given in the question,
Expression is given by:
2x + 7
Number of terms in the given expression 2x + 7 are as follow:
7 is the constant term of the given expression 2x + 7
x is the variable which is multiply by two written as 2x in the given expression 2x + 7.
Both the terms 7 and 2x in the given expression are related with the operation addition'+'
Therefore, the total number of terms in the given expression 2x + 7 is equal to two.
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Adam is baking 4 pizzas. Each pizza is a rectangle. It takes Adam 35 minutes to bake the pizzas. He divides each pizza into the equal-size square slices shown.
Adam multiplies to find the total number of square Slices for each pizza.
For each pizza tell the factors Adam multiplies .
For Pizza 1, Adam multiplies 6 by 6 slices
For Pizza 2, he multiplies 6 by 7 slices
For Pizza 3, he multiplies 4 by 7 slices, while
for Pizza 4, he multiplies 4 by 8 slices.
What is multiplication?A product is the outcome of multiplication or an expression that indicates factors to be multiplied in mathematics.
To put it another way, we may deduce that in math, multiplying implies adding equal groups.
The number of items in the group grows as we multiply. A multiplication issue includes the two elements and the product. The factors in the multiplication problem, 4 7 = 28, are the numbers 4 and 7, while the result (product) is the number 28.
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Can someone please help me with this geometry question
Answer:
Step-by-step explanation:
Quadrilateral A B C D is shown. The uppercase right angle, angle A, is 79 degrees.
What are the remaining angle measures if the figure is to be a parallelogram?
m∠B =
°
m∠C =
°
m∠D =
For Quadrilateral A B C D as shown the remaining angle measures if the figure is to be a parallelogram ∠B=∠D=101° ∠C = 79
This is further explained below.
What is a parallelogram?A parallelogram is a basic quadrilateral in Euclidean geometry that has two pairs of sides that are parallel to one another.
The sides that are perpendicular to one another, also known as facing sides, of a parallelogram, have the same length, and the angles that are perpendicular to one another have the same measure.
In most cases, a parallelogram will have two sets of parallel opposing sides. The angles that are diagonal to it are likewise equal.
When angle A is given as 79 degrees and the parallelogram ABCD is used, the remaining angles may be obtained as follows:
Angle A is diametrically opposed to angle C.
[tex]\angle A$ is opposite to $\angle C \\\\\angle A=\angle C \\\\\angle C=79^{\circ}[/tex]
Hence ∠C=79°
Because it is a parallelogram, the two remaining angles are complementary to one another and have the same degree:
[tex]\angle B=\angle D\\\\=0.5\left(360^{\circ}-2 \times 79^{\circ}\right)[/tex]
<B=101
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Please help me, it's due today!
Answer:
I believe it is -123
Step-by-step explanation:
you have to replace all the x's with -4 so you would do the equation -6(-4)^2+8(-4)+5
-6(-4)^2 is -96
-96+8(-4) is -128
-128+5 is -123
A monkey can eat 24 pieces of fruit in 12 hours.
The equation y = 2x can be used to represent
this situation. What is the constant of
proportionality? What does the constant of
proportionality represent in the context of the
problem?
The constant of proportionality for the equation y = 2x is k = 2.
The number of pieces of fruit the monkey can eat is two times the amount of time the monkey takes.
The equation y = 2x can be used to represent a monkey eating 24 pieces of fruit in 12 hours.
The constant of proportionality, which is a fixed value that represents the rate at which two or more ratios rise or decrease, is used to compare them. The result of dividing the denominator by the numerator when a ratio is expressed as a fraction is the constant of proportionality.
When a ratio is expressed as a fraction, the constant of proportionality is found by dividing the denominator by the numerator. The constant of proportionality, k, can be calculated from the equation if x is the ratio's numerator and y is its denominator.
k = y/x
Therefore, the constant of proportionality in this case is:
y = 2x
k = y/x = 2
The constant of proportionality in this case represents that the number of pieces of fruit a monkey eats is two times the amount of time the monkey takes.
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Peyton needs to order some new supplies for the restaurant where she works. The restaurant needs at least 732 forks. There are currently 287 forks. If each set on sale contains 10 forks, write and solve an inequality which can be used to determine x, the number of sets of forks Peyton could buy for the restaurant to have enough forks.
If Peyton needs to order some new supplies for the restaurant where she works. The restaurant needs at least 732 forks. the number of sets of forks Peyton could buy for the restaurant to have enough forks is 44.5.
Number of set of forkLet x represent the number of sets of forks
Formulate the inequality
287 + 10 × x = 732
Hence,
10x = 732 -287
10x = 445
Divide both side by 10x
x = 445/10
x = 44.5
Therefore we can conclude that 44.5 represent the number of the set of forks that could be bought.
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8 Five negative numbers are shown below. -2.5, -1į, -, -3, -30% Which list shows the numbers in order from least to greatest? (8.1B, 8.1F) F -2.5, -12, 3 4 -30%, -310 -13, -2.5, -31 3 G -30%, - 4' 10 Alw H -310, -30%, -2.5, -11, J-310,-2.5, -1 -2.5, -12, J 3 -- -30% 1 4
The given numbers are :
[tex]-2.5,\text{ -1}\frac{1}{2},\text{ }-\frac{3}{4},\text{ -3}\frac{1}{10},\text{ -30\%}[/tex]Simplify each term into decimal form :
- 2.5 = - 2.5
Now simplify the second term : -1 1/2
[tex]\begin{gathered} -1\frac{1}{2}=-\frac{1\times2+1}{2} \\ -1\frac{1}{2}=-\frac{3}{2} \\ -1\frac{1}{2}=-1.5 \end{gathered}[/tex][tex]-\frac{3}{4}=-0.75[/tex][tex]\begin{gathered} -3\frac{1}{10}=-\frac{3\times10+1}{10} \\ -3\frac{1}{10}=-\frac{30+1}{10} \\ -3\frac{1}{10}=-\frac{29}{10} \\ -3\frac{1}{10}=-2.9 \end{gathered}[/tex][tex]\text{ -30 \% = 0.3 \%}[/tex]So, the numbers are :
[tex]-2.5,\text{ -1}\frac{1}{2},\text{ }-\frac{3}{4},\text{ -3}\frac{1}{10},\text{ -30\%}[/tex]Thus, we get :
[tex]\begin{gathered} -2.5=-2.5 \\ -1\frac{1}{2}=-0.5 \\ -\frac{3}{4}=-0.75 \\ -3\frac{1}{10}=-2.9 \\ -30\text{ \%=- 0.3} \end{gathered}[/tex]The greater is the number with the neagtive sign least is the number,
So, the greatest number - 2.9 < - 2.5 < - 0.75 < - 0.5 < -0.3
Arrange of these number from least to greatest :
[tex]\begin{gathered} -2.9<-2.5<-0.75<-0.5<-0.3 \\ \text{ Since : - 1.5=}\frac{3}{2} \\ -0.75\text{ = }-\frac{3}{4} \\ -2.9=-3\frac{1}{10} \\ \text{- 0.3}=\text{ -30 \% } \end{gathered}[/tex]No comapre :
-2.9 < - 2.5 < - 0.75 < - 0.5 < -0.3
[tex]-3.1<-2.5<-0.75<-1.5<-0.3=-3\frac{1}{10}<-2.5<-1\frac{1}{2}<-\frac{3}{4}<-\text{ 30\%}[/tex]Answer : d)
[tex]-3\frac{1}{10}<-2.5<-1\frac{1}{2}<-\frac{3}{4}<-\text{ 30\%}[/tex]
I do not understand this can someone please help?
Answer:
1. x = 18
2. x = 154
Step-by-step explanation:
2 12
------- = -------
3 x
3 × 12 = 36
2 × x = 2x
36 = 2x
÷2 ÷2
---------------
x = 18
----------------------------------------------------------------------------------------------------------
6 84
------- = -------
11 x
6 × x = 6x
84 × 11 = 924
6x = 924
÷6 ÷6
-----------------
x = 154
I hope this helps!
Rachel sketches the graph of quadratic function that never crosses the X axis. which statement is true concering the roots of the function?
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Define a quadratic equation that does not passes through the x-axis
When a quadratic function never crosses the x-axis, then it has no real roots or solutions. Hence, the discriminant must be negative. meaning the solutions are imaginary/complex.
Hence, the answer will be:
The function has two imaginary roots
5 plus twice a number
Where “a number” is the letter x
Answer:
5 + 2x
Since 2 times a number is multiplication we make it 2x
1. Let U = {q, r, s, t, u, v, w, x, y, z} A = {q, s, u, w, y} B = {q, s, y, z} C = {v, w, x, y, z}. List the elements in the set: (Ac ∩ B).
The elements in the set A'∩B is { z } .
Set theory is a branch of mathematical logic that studies sets, which are essentially collections of objects.
Despite the fact that any type of object can be assembled into a set, set theory is a branch of mathematics that primarily deals with issues that are relevant to mathematics as a whole.A straightforward binary link between an object o and a set A serves as the basis of set theory. If o is a component (or member) of A, it is expressed as o A. When describing a set, members are listed with commas to indicate separation, or a property of those components is contained in braces. Since sets are objects, they can be related by the membership relation.Given universal set U = {q, r, s, t, u, v, w, x, y, z}
set A = {q, s, u, w, y}
∴A' = {r, t, v, x, z}
set B = {q, s, y, z}
Now A'∩B = { z }
Hence the elements in the set A'∩B is { z } .
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3430
3. A price increased by 18.2%. How could you write the new amount
as a percentage of the price before the increase?
The new amount as a percentage of the price before the increase is =[tex]\frac{118.2x}{100}[/tex]
What is percentage?The Latin word "per centum," which means "by the hundred," is where the word "percentage" originally came from. With 100 as the denominator, percentages are fractions. To put it another way, it's the relationship between a component and a whole in which the value of the whole is always assumed to be 100.
Let, the odd price be x then
we can write the new amount as a percentage of the price before increasing as
x ×[tex]\frac{(100+18.2)}{100}[/tex]
=[tex]\frac{118.2x}{100}[/tex]
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....................
1220 km apart
rates
320 km/ hr
290 km/hr
___________________________________
x= t* rate
t = time in hours
x = distance in km
__________________
total distance = t1 * 320 Km/h + t2* 290 km/h
because they started at the same time
Total distance = 1220 km = t * 320 Km/h + t* 290 km/h
1220 = (320 + 290 ) t
1220 = 610 t
t = 1200/ 610
t = 2 hours
_______________________--
Answer
2 hours
Calculate the missing value. (Not drawn to scale.)
Answer:5in
Step-by-step explanation:
1. Identify the triangle
you are given a right triangle with the hypotonus missing and are given the side lengths 3 and 4 you know the hypotonus is 5 by the 3,4,5 Pythagorean tripe, if you do not notice this it can be solved with the Pythagorean theorem a^2+b^2=c^2
2. solve (if not done with 3,4,5 triple)
3^2+4^2=c^2
9+16=c^2
25=c^2
5=c | square root both sides to cancel the square
which expression is equivalent to 36+26
We can try to write the expression 36+26 taking a common factor, so:
[tex]\begin{gathered} 36\text{ and 26 are even numbers, so we can take 2 as common factor:} \\ 36+26=2\cdot(18+13) \end{gathered}[/tex]The option B is the correct answer.
I need help with my practice starr
Is valid proportion here
(10 + 5 )/ 18 = 10/d
then find d
d= 18• 10/ (10+5)
d= 180/15 =
d= 12
Then answer is
d = 12 mm
An artist is designing a mural that will be 3 feet wider than it is tall. If the area of the mural is 108 square feet, what will be height of the mural?
나무
7 1
al
117)
10) The level of water in a pail has changed by -7 in. from the original water level.
If the original level was 23 3/8 in., what is the current water level?
What is the measure of angle LJK? Round to the tenths.
Answer:
90 degrees
Step-by-step explanation:
We can take a look at that each these triangles are in truth right triangles, seeing that the two angles of and both have measures of 90 degrees.
Muskco gave 88 people a bonus. If Muskco had given 4 more people bonuses, Muskco would have rewarded 2 over 3of the work force. How large is Muskco's work force
The amount of Muskco's work force that he has in his business is; 138 people
How to solve Algebra Word Problems?We are told that Muskco gave 88 people a bonus. Now, we are further told that if he had given 4 more people bonuses, then it means he would have rewarded two thirds of his workforce.
Thus we can begin too solve this problem to find the size of Muskco's work force by;
Let the total number of his workforce be denoted as x. Then the algebraic equation for this problem would be expressed as;
88 + 4 = (2/3)x
Simplify by adding up the left hand side values to get;
(2/3)x = 92
Use multiplication property of equality to Multiply both sides by 3 to get;
2x = (92 * 3)
2x = 276
Now, use division property of equality to divide both sides by 2 to get;
2x/2 = 276/2
x = 138
Thus, we would conclude from the calculations as seen in the above that the size of Muskco's workforce is 138 people.
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Write an absolute value equation from the solutions -5 and 7.
The membership of a gym from 2000 to 2017 is given by the function:
M(x)= 180x + 125
where M is the number of members and x is the number of years after 2000 (when the gym was
founded). Show your work to receive credit. (6)
a)
What was the membership of the gym in 2007?
The membership of the gym after 7 years is 1385 .
What is a function?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable ). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
A function, according to a technical definition, is a relationship between a set of inputs and a set of potential outputs, where each input is connected to precisely one output.
Given: The function : M(x)= 180x + 125
where x is the number of years so in this case we have to find the value of M when x= 7 years
Thus the given function on substituting the value becomes
M (7)= 180× 7 + 125
= 1385.
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How do you graph: y=75x + 2
Explanation
[tex]y=75x+2[/tex]we have a linear function, to graph a linear function you need 2 points
Step 1
find 2 coordinates of the line
a) when x= 0
then
[tex]\begin{gathered} y=75x+2 \\ y=75(0)+2 \\ y=0+2 \\ y=2 \\ \text{coordinate 1(0,2)} \end{gathered}[/tex]b)when x=2
[tex]\begin{gathered} y=75x+2 \\ y=75(2)+2 \\ y=150+2 \\ y=152 \\ \text{coordinate 2(2,152)} \end{gathered}[/tex]Step 2
now, draw a line that passes through the points
I hope this helps you
Complete the square to solve the equation below.
X²+10x-13 17
O A. x= 4+ √√30; x = 4 - √30
OB. x= -10 + √55; x = -10 - √55
C. x = 5 + √√29; x = 5-√√√29
OD. x= -5+ √55; x = -5- √55
Answer:
D
Step-by-step explanation:
...................
The solutions to the quadratic equation x² + 10x - 13 = 17 are x = -5 + √55 and x = -5 - √55. The correct answer is option D.
The quadratic equation is given as:
x²+10x-13 =17
Move the constant term to the right side of the equation:
x² + 10x - 13 - 17 = 0
x² + 10x - 30 = 0
Take half of the coefficient of the x-term (10) and square it: (10/2)² = 25.
Add the squared value to both sides of the equation:
x² + 10x + 25 - 30 = 25
(x + 5)² - 30 = 25
Simplify the equation:
(x + 5)² = 25 + 30
(x + 5)² = 55
Take the square root of both sides of the equation:
√((x + 5)²) = ±√55
x + 5 = ±√55
Solve for x by subtracting 5 from both sides:
x = -5 ± √55
Therefore, the solutions to the equation x² + 10x - 13 = 17 are:
x = -5 + √55 and x = -5 - √55.
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An electrician has a 16 foot spool of wire and he needs to cut an 11 foot, 4 inch piece from the spool to make a repair. How many inches of wire will he have left on a spoop after he makes the repair
The inches of wire that he will have left on a spoop after he makes the repair is 4 2/3 feet.
How to calculate the fraction?From the information, the electrician has a 16 foot spool of wire and he needs to cut an 11 foot, 4 inch piece from the spool to make a repair.
Therefore, the inches of wire that he will have left will be:
Note that 1 feet = 12 inches
11 foot 4 inches = 11 4/12 = 11 1/3
The amount left will be:
= 16 - 11 1/3
= 4 2/3 feet.
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The equation 32 = 4 x 8 can mean (fill in the bubble beside every true statement):
32 is 4 times as many as 8
O 32 is 4 less than 8
32 is 8 times as many as 4
32 is twice as much as 4 x8
Answer:
A) 32 is 4 times as many as 8
C) 32 is 8 times as many as 4
Step-by-step explanation:
8x4=32
4×8=32
2.
Give an example of two fractions whose product is an integer due to common factors.
An example of two fraction whose product is an integer due to common factors is [tex]\frac{6}{3}[/tex].
What is fraction?Any number of equal parts is represented by a fraction, which also represents a portion of a whole. A fraction, such as one-half, eight-fifths, or three-quarters, indicates how many components of a particular size there are when stated in ordinary English.
What is a common factor?
The largest positive integer that divides each of the integers is known as the greatest common divisor of two or more non-zero integers. The greatest common divisor of two integers x and y is indicated by the display style "gcd"
Given that,
Two fraction whose product is an integer due to common factor.
The fraction is
[tex]\frac{6}{3}[/tex].
Since,
2 x 3 = 6
1 x 3 = 3
Here, 3 is the common factor.
[tex]\frac{6}{3}[/tex] = 2
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Solve for x.
4 + x/3 =9
x =
Answer:
x = 15
Step-by-step explanation:
[tex]4 + \frac{x}{3} = 9[/tex]
[tex] \frac{x}{3} = 5[/tex]
[tex]x = 15[/tex]
Answer:
x = 15
Step-by-step explanation:
Subtract 3 from each side: 12 + x = 27
Subtract 12 from both sides: x =27 − 12
Subtract 12 from 27 to get 15: x = 15