Answer:
Pretty sure its 525.74
can someone help please
1/2
plsss mark brainliestt
Step-by-step explanation:
3/6
1.5/3
5/2.5
1) The measures of the angles of a triangle are in the ratio of 1:3:6. What are the measures of the angles?
1:
3:
6:
Answer:Answered 2 years ago. The total of the sum of the measures of any triangle has been proven to be 180 degrees. If the ratio of angle measure is 1:3:6.
Step-by-step explanation:
Answer:
1: 18 3: 54 6: 108
Step-by-step explanation:
A triangle has 180 degrees.
You need to add up all the ratios 1+3+6
Then divide that by 180----> 180/10=18
Then multiply all the ratios by but answer(18)
1*18=18
3*18=54
6*18=108
Draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure ({N}, {T}, {M})
A cross-sectional effect diagram, also known as an axial force-shear force-bending moment diagram or simply an internal force diagram, is a graphical representation that shows the distribution of internal forces (axial force, shear force, and bending moment) along the length of a structural member, such as a beam or column.
To draw the cross-sectional effect diagrams for the beam whose loading condition is given in the figure, we need to follow these steps:
Step 1: Identify the type of loadingFor this question, the loading conditions are {N}, {T}, {M}. So, the loading types are axial force, shear force, and bending moment.
Step 2: Draw the cross-sectional diagram of the beam. We need to draw the diagram of the cross-section of the beam in the direction of the forces acting on the beam. In this case, it will be a rectangular beam.
Step 3: Draw the effect diagrams After drawing the cross-sectional diagram, we need to draw the effect diagrams for each loading condition.
The effect diagrams are as follows: 1. Axial force diagram (N):In this case, the axial force is positive (+) which means it is a tensile force. 2. Shear force diagram (T):The shear force is negative (-) from x = 0 to x = 1, which means the shear force is acting downward. It is zero at x = 1 and then becomes positive (+) from x = 1 to x = 2, which means the shear force is acting upward. 3. Bending moment diagram (M):The bending moment is zero at x = 0, becomes negative (-) from x = 0 to x = 1, reaches a minimum at x = 1, and then becomes positive (+) from x = 1 to x = 2.
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A grocery store sells a bag of 6 oranges for $4.20. If Ayden spent $2.80 on oranges, how many did he buy?
Answer:
4 bags of oranges
Step-by-step explanation:
First, we need to find out how much each bag of oranges costs so we divide.
$4.20 divided by 6 equals 0.7 which means that each bag of oranges costs $0.70.
Next we need to find out how much Ayden spent on oranges so we divide 0.70 by 2.80
2.80 divided by 0.70 equals 4.
This means that Ayden bought 4 bags of oranges.
Hope this helps!
Answer:
4 oranges
Step-by-step explanation:
First find the unit rate by dividing the price of 6 oranges by the amount of oranges in the bag. So $4.20÷6=0.7. 0.7 is the price of one orange. Since the dollar amount is small I just divided $4.20 by 2 and got $2.10 for three oranges. The question is asking how much he bought for $2.80 so add another .70 which is one more orange therefore he bought 4 oranges for $2.80
What is the sum of the first five prime numbers?
18
26
28
39
find hcf of x³y and x⁴y³
no a and d
Answer:
See solutions below
Step-by-step explanation:
a) Given the expressions
x³y and x⁴y³
Find their factors
x³y = (x * x * x * y)
x⁴y³ = (x * x * x * y) * x * y * y
GCF = x*x*x*y
GCF = x³y
The expressions in parenthesis is the GCF. Hence the GCF of x³y and x⁴y³ is x³y
b) For 48m⁶n⁵p⁴ and 20m⁴n⁵p⁶
48m⁶n⁵p⁴ =12 * (4 * m⁴ * n⁵ * p⁴) * m²
20m⁴n⁵p⁶ = 5 * (4 * m⁴ * n⁵ * p⁴) * p²
GCF is the expression common to both terms
GCF = 4 * m⁴ * n⁵ * p⁴
GCF = 4m⁴n⁵p⁴
Solving systems of equations by graphing
The solution is,
a) Option A
y = 2x + 10
Option B
y = 3x
b) Option A is represented with the red line and Option B is represented by the blue line.
Total Cost is presented on the y-axis and the Number of rides is presented on the x-axis.
The graph is presented below.
From this graph, we can see that the two lines cross at (10, 30)
So, the two options will have the same rides and the same total cost when
x = 10 rides
y = 30 dollars
Explanation:
There are two options to consider,
Let the amount to be paid be y
Let the number of rides be x
Option A
Each ride costs $2
x rides will cost 2x dollars
Activation fee = 10 dollars
Total cost = y
y = 2x + 10
Option B
Each ride costs $3
x rides will cost 3x dollars
Activation fee = 0
Total cost = y
y = 3x
So, we end up with a system of equation for when the number of rides and the total cost for both options become the same
y = 2x + 10
y = 3x
b) We are asked to solve this system of equations by graphing.
To do this, we will first plot the two lines for each equation, then the solution will be where the two lines cross each other.
We will use intercepts to plot the first line
y = 2x + 10
when x = 0,
y = 2x + 10
y = 2(0) + 10
y = 0 + 10
y = 10
First point on this line is (0, 10)
when y = 0
y = 2x + 10
0 =2x + 10
-2x = 10
Divide both sides by -2
(-2x/2) = (10/-2)
x = -5
Second point on the line is (-5, 0)
For the second option
y = 3x
when x = 0
y = 3x
y = 3(0)
y = 0
First point on this line is (0, 0)
when x = 1
y = 3x
y = 3(1) = 3
Second point on the line is (1, 3)
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Which type(s) of symmetry does the following object have?
Select all that apply.
Answer: You are correct. There is only one answer and that is choice B) vertical line of symmetry.
We can draw a vertical line through the center to have one half mirror over this line to get the other half. We can't do the same with a horizontal line or any other kind of line.
We do not have rotational symmetry. Rotating the figure will produce an image different from the original. The angle of rotation is some angle x such that 0 < x < 360.
Answer:
Theres more than one answer so b and a
Step-by-step explanation:
A set of cloth napkins costs $6.67. How much would it cost to buy 10 sets of cloth napkins?
Answer:
$66.70 for 10 sets
Step-by-step explanation:
Multiply the cost of 1 set by the number of sets wanted
$6.67 * 10
66.70 for 10 sets
Answer:
$66.70
Step-by-step explanation:
In order to figure out the cost of 10 sets of napkins, you have to multiply the cost of one set by 10.
American General offers a 9-year annuity with a guaranteed rate of 6.28% compounded annually. How much should you pay for one of these annuities if you want to receive payments of $1500 annually over the 9 year period? How much should a customer pay for this annuity? (Round to the nearest cent)
You should pay approximately $10,117.09 initially to secure the annuity and receive annual payments of $1500 over the 9-year period.
To find the cost of the annuity, we need to calculate the present value of the future payments. The present value represents the current worth of future cash flows, taking into account the interest earned or charged over time. In this case, we'll calculate the present value of the $1500 payments using compound interest.
The formula to calculate the present value of an annuity is:
PV = PMT × [1 - (1 + r)⁻ⁿ] / r
Where:
PV is the present value of the annuity (the amount you should pay initially)
PMT is the payment amount received annually ($1500 in this case)
r is the interest rate per period (6.28% or 0.0628)
n is the total number of periods (9 years)
Let's substitute the values into the formula:
PV = $1500 × [1 - (1 + 0.0628)⁻⁹] / 0.0628
Calculating this expression:
PV = $1500 × [1 - 1.0628⁻⁹] / 0.0628
PV = $1500 × [1 - 0.575255] / 0.0628
PV = $1500 × 0.424745 / 0.0628
PV ≈ $10117.09
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What is the following difference?
2ab2/192an? -5 V81a4 b5
Answer:
C
Step-by-step explanation:
2ab * sqrt[3](192ab^2) - 5 * sqrt[3](81 a^4b^5) =
= 2ab * sqrt[3](4^3 * 3 * a * b^2) - 5 * sqrt[3](3^3 * 3 * a^3 * a * b^3 * b^2)
= 2ab * 4 sqrt[3](3 * a * b^2) - 5 * 3 * a * b * sqrt[3](3 * a * b^2)
= 8ab * sqrt[3](3 * a * b^2) - 15ab * sqrt[3](3 * a * b^2)
= -7ab * sqrt[3](3ab^2)
Answer: C
What are the domain and the range of this function ?
D: _ _ X _ _
R: _ _ Y _ _
Answer:
the answer in interval notation is
domain : [-5,1),
range [-4,7)
x intercept : (-3,0)
y-intercept: (0,5)
Step-by-step explanation:
i hope this helps :)
find the area of this shape. 100pts
Answer:
A = 540 m²
Step-by-step explanation:
consider the shape split into 3 rectangles
the length is divided into 3 congruent sections
single dash = 30 m ÷ 3 = 10 m
the width is divided into 3 congruent sections
double dash = 27 m ÷ 3 = 9 m
then area (A) is the total of the 3 rectangular areas
A of left rectangle = 10 × 9 = 90 m²
A of middle rectangle = 10 × (9 + 9) = 10 × 18 = 180 m²
A of right rectangle = 10 × 27 = 270 m²
total area = 90 + 180 + 270 = 540 m²
5(4x - 1.5)+12=4x - 2
Ignore air resistance. A certain not-so-wily coyote discovers that he just stepped off the edge of a cliff. Four seconds later, he hits the ground in a puff of dust. How high in meters was the cliff?
To determine the height of the cliff, we can use the equations of motion under free fall. In this case, ignoring air resistance, the acceleration due to gravity is approximately 9.8 m/s².
We can use the equation for displacement during free fall:
h = (1/2) * g * t²
where h is the height of the cliff, g is the acceleration due to gravity, and t is the time of fall.
Given that the coyote falls for 4 seconds, we can substitute the values into the equation:
h = (1/2) * 9.8 * (4²)
h = (1/2) * 9.8 * 16
h = 78.4 meters
Therefore, the height of the cliff is approximately 78.4 meters.
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if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The above table represents the contents ( colored marble) of a bag. The probability that selected marble had a color other than white or blue is equals to the 0.766234 ( nearest to milinoth).
We have a bag that contains five different types of marbles. See the above table
number of red marbles in a bag = 16
number of green marbles in a bag = 23
number of blue marbles in a bag = 13
number of pink marbles in a bag = 20
number of white marbles in a bag = 5
So, total number of marbles in a bag= 16 + 23 + 5 + 13 + 20 = 77
Now, a single marble is selected and out of the bag. We have to determine probability that it is a color other than white or blue. Let X , Y and Z be three events defined as the following
X = selected marble is white
Y = selected marble is blue
Z = selected marble is other than blue or white
Probability of seclecting white marble, P(X) = 5/77
Probability of seclecting blue marble, P(Y)
= 13/77
Probability of seclecting blue or white marble, P(Y UX) = P(X) + P(Y) = 5/77 + 13/77 = 18/77
So, probability that selected marble has a color other than white or blue, P(Z) = 1 - P( X UY) = 1 - 18/77
= 59/77 = 0.76623376623
Hence, required probability is 0.766234.
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Complete question :
The above table discribes the contents of a bag that contains red,green, blue,pink and white marbles if you select a single marble out of the bag, what is the probability that it is a color other than white or blue? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
89, 74, 100, 86, 74, 67, 86, 72, 60, 93, 83, 86 what is the median?
Answer:
\( \boxed{ \bold{ \huge{ \boxed{ \sf{84.5}}}}}\)
Step-by-step explanation:
Given data :
89 , 74 , 100 , 86 , 74 , 67 , 86 , 72 , 60 , 93 , 83 , 86
Arranging the data in ascending order, we have,
60 , 67 , 72 , 74 , 74 ,83 , 86 , 86 , 86 , 89 , 93 , 100
Here, n ( total no.of observation ) = 12
Now, finding the position of media :
\( \boxed{ \sf{position \: of \: median = ( \frac{n + 1}{2} ) ^{th} \: item}}\)
⇒\( \sf{ (\frac{12 + 1}{2} ) ^{th} item}\)
⇒\( \sf{( \frac{13}{2} ) ^{th} item}\)
⇒\( \sf{ {6.5}^{th} item}\)
6.5 th item is the average of 6 th and 7 th items.
Again,
\( \sf{median = \frac{ {6}^{th \: item} + {7}^{th} item}{2} }\)
⇒\( \sf{ \frac{83 + 86}{2} }\)
⇒\( \sf{ \frac{169}{2} }\)
⇒\( \sf{84.5}\)
Hope I helped!
Best regards!!
Define the relation O on Z as follows: ᵾm, n € z, m O n <----> ⱻk € z |(m – n) = 2k +1 Which one of the following statements about the relation O is true? a. The relation is reflexive, symmetric, and transitive. b. The relation is not reflexive, not symmetric, and transitive. c. The relation is not reflexive, symmetric, and not transitive. d. The relation is reflexive, not symmetric, and transitive.
The relation O is not reflexive, symmetric, and not transitive is one of the following statements that is true about the relation O. which is option (C).
Given, \(\forall m, n \in Z, m O n \longleftrightarrow \exists k \in Z \mid(m-n)=2 k+1\)
Let's verify for the following relations :
Reflexive relation:
\(\forall a\in Z, a O a \longrightarrow \exists k\in Z \mid (a-a)= 2k+1\)
\(0\neq 2k+1\) for all k \(\in\) Z
Since 2k+1 can never be zero for any k \(\in\) Z, hence we conclude that the relation O is not reflexive.
Symmetric relation:
Suppose a, b \(\in\) Zsuch that a O b i.e. (a-b)=2k+1, where k\(\in\) Z.
Now, we need to check whether b O a is true or not i.e. (b-a)=2j+1 for some j\(\in\) Z
We have,
\((a-b) = 2k+1 \longrightarrow (b-a) = -2k-1 = 2(-k) - 1\)
Let j=-k-1, then we have j\(\in\) Z and 2j+1 = -2k-1
Hence, (b-a) = 2j+1, and we conclude that the relation O is symmetric.
Transitive relation:
Suppose a, b, c\(\in\) Z such that a O b and b O c.
Now, we need to check whether a O c is true or not.
We have,
(a-b)=2k_1+1 and (b-c)=2k_2+1 for some k_1,k_2\(\in\) Z
(a-b)+(b-c) = 2k_1+1 + 2k_2+1
a-c = 2k_1+2k_2+2
Let j=k_1+k_2+1, then we have j\(\in\) Z and a-c=2j
Hence, (a-c) is even and we conclude that the relation O is not transitive.
Therefore, the relation O is not reflexive, symmetric, and not transitive. Hence, option (C) is the correct answer.
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joseph omuederiay = E Homework: Quiz 2 Question 13, 19.1-12 > HW Score: 41.33 points O Points: 0 of 1 In order to determine the economy's real GDP growth rate between two time periods, we should look at ... OA. real national income in each time period, which is equal to nominal national income corrected for price - level changes. OB. nominal national income, because it compares actual output in each time period. OC. only the real national product from the latest time period. OD. potential national income, corrected for price -level changes. OE. real national income in each period, which is equal to nominal national income corrected for quantity changes. ہے joseph omuederiay = E Homework: Quiz 2 Question 13, 19.1-12 > HW Score: 41.33 points O Points: 0 of 1 In order to determine the economy's real GDP growth rate between two time periods, we should look at ... OA. real national income in each time period, which is equal to nominal national income corrected for price - level changes. OB. nominal national income, because it compares actual output in each time period. OC. only the real national product from the latest time period. OD. potential national income, corrected for price -level changes. OE. real national income in each period, which is equal to nominal national income corrected for quantity changes. ہے
In order to determine the economy's real GDP growth rate between two time periods, we should look at real national income in each time period, which is equal to nominal national income corrected for price-level changes.
Therefore, the correct option is A.
What is real national income?Real national income is the total income generated by the economy in a particular time frame. It reflects the total output of the economy during a given period of time adjusted for inflation. It's calculated by adjusting nominal national income for price changes or inflation.
To calculate real national income, economists use a deflator index, which is a price index. It calculates the difference in price level between the base year and the current year for each item produced.
As a result, economists can figure out how much of the change in nominal national income from one year to the next is due to price level changes.
Hence, the answer of the question is A
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triangle ABC ~ triangle XYZ , where AB = 18 cm, BC = 30 cm , and CA = 42 cm . The longest side of triangle XYZ is 25.2 cm. What is the perimeter of triangle XYZ ?
Answer:
The perimeter of triangle XYZ is 54 cm
Step-by-step explanation:
In similar triangles, their corresponding sides are proportional, which means the ratios of the corresponding sides are equalTheir perimeters have the same ratio as their corresponding sides, which means P1 = r × P2, where r is the ratio of similarityTheir areas have the square of the ratio as their corresponding sides, which means A1 = r² × A2∵ Δ ABC is similar to Δ XYZ
∵ The longest side in Δ XYZ is 25.2 cm
→ That means its corresponding side in Δ ABC is the longest side
∵ AB = 18 cm, BC = 30 cm, CA = 42 cm
∴ The longest side in Δ ABC is CA
∴ CA is the corresponding side of the side of length 25.2 cm
∴ The ratio of similarity = \(\frac{25.2}{42}\) = 0.6 ⇒ (r)
∵ The perimeter of Δ ABC = AB + BC + CA
∴ The perimeter of Δ ABC = 18 + 30 + 42
∴ The perimeter of Δ ABC = 90 cm
→ Use the 2nd fact above
∵ P of Δ XYZ = r × P of Δ ABC
∵ r = 0.6 and P of Δ ABC = 90
∴ The perimeter of Δ XYZ = 0.6 × 90
∴ The perimeter of Δ XYZ = 54 cm
a biologist created the following graph to show the relationship between the temperature of water (x), in degrees celsius, and the number of insect larvae (y) in the water: what does the peak of the graph represent? the number of larvae in the water is greatest at 450 degrees celsius. the number of larvae in the water is greatest at 5 degrees celsius. the least number of larvae in the water is 450. the least number of larvae in the water is 5.
The peak of the graph represents option B: the number of larvae in the water is greatest at 5 degrees Celsius.
The peak of a graph represents the highest point of the graph. In this case, it represents the temperature at which the number of insect larvae in the water is greatest. So, if you look at the graph created by the biologist, you can see that the number of larvae in the water is greatest at 5 degrees Celsius.
The graph is a quadratic function graph because it is a parabola and opens downward; as a result, it has a negative leading coefficient, or a negative coefficient of x².
The function's graph demonstrates that,
The parabola's peak, or highest point, is (450).
In other words, if x=5, then the value of y=450.
That is, when the temperature of the water is 5°, then the number of larvae in water is 450. Therefore, at 5 degrees Celsius, the number of larvae in the water is at its peak.
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Complete question is:
A biologist created the following graph to show the relationship between the temperature of water (x), in degrees Celsius, and the number of insect larvae (y) in the water: what does the peak of the graph represent?
the number of larvae in the water is greatest at 450 degrees celsius.
the number of larvae in the water is greatest at 5 degrees celsius.
the least number of larvae in the water is 450.
the least number of larvae in the water is 5.
Determine whether A and B are inverse matrices.
The matrices A and B are not inverse matrices
How to determine if the matrices are inverse matrices?From the question, we have the following parameters that can be used in our computation:
\(A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right]\)
\(B = \left[\begin{array}{cc}1&-1&-1&2\end{array}\right]\)
To determine if the matrices are inverse matrices, we simply calculate the inverse of matrix A and then make the comparison.
The matrix A is given as
\(A = \left[\begin{array}{cc}-2&-3&2&-2\end{array}\right]\)
Calculate the determinant of the matrix A
So, we have the following representation
|A| = -2 * -2 + 3 * 2
Evaluate the sum of products
|A| = 10
The inverse is then calculated as
\(A^{-1} = \frac 1{10} * \left[\begin{array}{cc}-2&3&-2&-2\end{array}\right]\)
Evaluate
\(A^{-1} = \left[\begin{array}{cc}-\frac 1{5}&\frac 3{10}&-\frac 1{5}&-\frac 1{5}\end{array}\right]\)
When compared to matrix B, both matrices are different
Hence, the matrices are not inverse matrices
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Dana invests £5000 for 4 years in a savings account She gets 2% per annum compound interest in the first year, then x% for 3 years, Dana has £5508.23 at the end of 4 years, work out the value of x.
Answer:
£1,330.46
Hope this helps, mate!
Step-by-step explanation:
Hope this helps, mate! :)
PLEASE PLEASE AND ANWER FAST PLEASE!
Answer:
Option A. The student incorrectly used < instead of > for the second inequality. The correct inequality is >.
Step-by-step explanation:
Defintions:Boundary lines that are often used in systems of linear inequalities determine the location of the solutions region in a coordinate plane.
Solid boundary lines are used for the equal sign, "=," and the inequality symbols "≥" and "≤." This implies that the points along the line (endpoints) are included as solutions to the given system. Dashed boundary lines are used for inequality symbols, ">" and "<." Using the dashed lines as the boundary implies that the points along the line (endpoints) are not included as solutions to the given system. Solution:Given the systems of linear inequalities: y ≤ 0.5x + 1 and y = -2x + 1:
In order to determine what is the appropriate inequality symbols for both equations, we must first set the second equation with an equal sign. Then, choose a test point (not in either lines) to determine which half-plane region must be shaded.
Test point: (0, 0)
Substitute the test point into both equations to determine whether it satisfies the given equation:
y ≤ 0.5x + 10 ≤ 0.5(0) + 1
0 ≤ 0 + 1
0 ≤ 1 (True statement).
y = -2x + 20 = -2(0) + 2
0 = 0 + 2
0 = 2 (False statement). Therefore, the half-plane region that doesn't contain the test point must be shaded. Hence, we must use the ">" symbol for this equation, as we're shading "above" where the values for y is greater than the y-intercept, (0, 2).
Therefore, the correct answer is Option A: The student incorrectly used < instead of > for the second inequality. The correct inequality is > (greater than symbol).
In the diagram below, DE ¯¯¯¯¯¯¯∥ BC¯¯¯¯¯. Elena thinks length BC¯¯¯¯¯ is 16.5 units. Lin thinks the length of BC ¯¯¯¯¯¯is 17.1 units. Who do you agree with? Why? (2 points)
Both Elena and Lin are right , in my opinion. According to Elena, length BC is 16.5 units. Lin estimates that BC is 17.1 units long.
Whose are agree this ?The remainder of the query is included in the attachment. The figure shows that ED is parallel to A B and B C is parallel to A B. In light of the Pythagoras theorem,
\($\mathrm{AC}^ 2=\mathrm{AB}^ 2+\mathrm{BC}^ 2$\)
\($\mathrm{BC}^ 2=196-36=160$\)
\($\mathrm{BC}=12.649$\) or \($12.65$\)
Both Elena and Lin are right .A visual that conveys information rather than just representing it. particularly : a diagram demonstrating the relationships and arrangements (as between parts): a dotted line drawing used in science or math .
A diagram is a picture that shows how something works, how it's organised, or how it's related to something else. Even when they go by the names "map," "chart," or "graph," several diagram kinds are still considered to be diagrams. as flowcharts, organisational charts, and mind maps. An illustration that depicts an object's component elements and their relationships to one another is called a diagram.
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help meeeeeeeeeeeeeee!!!!!!!!
Answer:
1) 4/29
2) 3/29
3) 16/29
4) 23/29
5) 22/29
The number of bales of cotton that were grown in selected countries for the year 2008 is as follows: United States - 21,590,000; China - 35,500,000; Brazil - 7,000,000; and India - 21,800,000. Rank the statistics. I WILL GIVE BRAINLIEST PLS!!!
Answer:
1) China
2) India
3) United States
4) Brazil
Step-by-step explanation:
Find the simplified product: 3sqrt9x^4 x 3sqrt3x^8
\(\sqrt[3]{9\text{x}^4} \times\sqrt[3]{3\text{x}^8}\)
To simplify it we multiply all the terms inside the cube root
\(\sqrt[3]{9\text{x}^4} \times\sqrt[3]{3\text{x}^8}\)
\(\sqrt[3]{9\text{x}^4\times{3\text{x}^8}}\)
Now we apply exponential property
\(\text{a}^\text{m}\times\text{a}^\text{m}=\text{a}^\text{mn}\)
\(\text{x}^4\times\text{x}^8=\text{x}^{12}\)
\(\sqrt[3]{9\text{x}^4\times{3\text{x}^8}}\)
\(\sqrt[3]{27\text{x}^{12}}\)
Now we take cube root
\(\sqrt[3]{27}=3\)
\(\sqrt[3]{\text{x}^{12}}=\sqrt[3]{\text{x}^3\times\text{x}^3\times\text{x}^3\times\text{x}^3}=\text{x}^4\)
\(\sqrt[3]{27\text{x}^{12}}\)
Answer:
\(\rightarrow\boxed{\bold{3x^4}}\)
#7Change from standard form to vertex formy= x²-6x+7
So the vector form of the quadratic function y = x² - 6x + 7 is: y = (x - 3)² - 2.
To change from standard form to vertex form, we need to complete the square.
First, we group the x-terms together and factor out any common coefficient of x², giving:
y = x² - 6x + 7
y = 1(x² - 6x) + 7
Next, we need to add and subtract a constant inside the parentheses to complete the square. To determine this constant, we take half of the coefficient of x (-6) and square it:
(-6/2)² = 9
So we add and subtract 9 inside the parentheses:
y = 1(x² - 6x + 9 - 9) + 7
Now we can factor the quadratic expression inside the parentheses as a perfect square:
y = 1[(x - 3)² - 9] + 7
Simplifying and rearranging terms, we get:
y = (x - 3)² - 2
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y is inversely proportional to V1+x.
When x = 8, y = 2.
Find y when x = 15.
Answer:
y = 1.5
Step-by-step explanation:
Given x is inversely proportional to \(\sqrt{1+x}\) , then the equation relating them is
y = \(\frac{k}{\sqrt{1+x} }\) ← k is the constant of proportion
To find k use the condition when x = 8, y = 2
2 = \(\frac{k}{\sqrt{1+8} }\) = \(\frac{k}{\sqrt{9} }\) = \(\frac{k}{3}\) ( multiply both sides by 3 )
6 = k
y = \(\frac{6}{\sqrt{1+x} }\) ← equation of proportion
When x = 15 , then
y = \(\frac{6}{\sqrt{1+15} }\) = \(\frac{6}{\sqrt{16} }\) = \(\frac{6}{4}\) = \(\frac{3}{2}\) = 1.5