Answer:
d
Step-by-step explanation:
Divide
6x2+5x+1
x+2
=6x−7+
15
x+2
Umm.. Could someone answer this question pls...?
Find the value of v if 4(2v-1)=28
Answer:
v = 4
Step-by-step explanation:
4(2v - 1) = 28
4(2v - 1)/4 = 28/4
2v - 1 = 7
2v - 1 + 1 = 7 + 1
2v = 8
2v/2 = 8/2
v = 4
Write an augmented matrix for the following system of equations and give its size.- 8x + 3y = 1 4x - 7y = 4What is the augmented matrix?
SOLUTION:
The equation is;
[tex]\begin{gathered} -8x+3y=1 \\ \text{ }4x-7y=4 \end{gathered}[/tex]Writing in matrix form, we have;
[tex]\begin{bmatrix}{-8} & {3} \\ {4} & {-7}\end{bmatrix}\begin{bmatrix}{x} & {} \\ {y} & {}\end{bmatrix}=\begin{bmatrix}{1} & {} \\ {4} & {}\end{bmatrix}[/tex]The augmented matrix is thus;
[tex]\begin{bmatrix}{-8} & {3} & |{\text{ }1} \\ {4} & {-7} & |{\text{ }4} \\ {} & {} & \end{bmatrix}[/tex]HELP PLEASE!!!!!!!!
To rent a certain meeting room, a college charges a reservation fee of $13 and an additional fee of $4 per hour. The chemistry club wants to spend at most $33 on renting the room. What are the possible numbers of hours the chemistry club could rent the meeting room?
Use t for the number of hours.
Write your answer as an inequality solved for t.
The inequality that represents the possible number of hours the chemistry club could rent the meeting room is 13 + 4t ≤ 33 or t ≤ 5.
The possible numbers of hours the chemistry club could rent the meeting room are 1, 2, 3, 4 and 5 hours.
Given that:-
Reservation fee charged to rent the meeting room by college = $ 13
Additional fee per hour charged by the college = $ 4
The maximum amount the chemistry club want to spend on meeting room = $ 33
Let t be the number of hours.
Hence,
13 + 4t ≤ 33
4t ≤ 33 - 13
4t ≤ 20
t ≤ 5 hours.
Hence, the possible number of hours the meeting room can be booked by chemistry club are 1, 2, 3, 4 and 5 hours.
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Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.
Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.
They set up the situation with the equation below, where x is the number of pairs of pants.
Is there a situation in which they pay the same amount for their purchases?
Which statements are true? Select all that apply.
17.95x + 24 = 18.95x + 18
There are no solutions to the equation.
There is one solution to the equation.
There are infinitely many solutions to the equation.
There is never a situation in which both girls will pay the same amount for their purchase.
The girls will both pay the same if they buy six pairs of pants and one sweater.
The girls will pay the same amount for any number of pants and one sweater.
Considering the definition of an equation and the way to solve it, the girls will both pay the same if they buy six pairs of pants and one sweater.
Definition of equationAn equation is the equality existing between two algebraic expressions connected through the equals sign in which one or more unknown values appear.
The solution of a equation means determining the value that satisfies it. In this way, by changing the unknown to the solution, the equality must be true.
To solve an equation, keep in mind:
When a value that is adding, when passing to the other member of the equation, it will subtract.If a value you are subtracting goes to the other side of the equation by adding.When a value you are dividing goes to another side of the equation, it will multiply whatever is on the other side.If a value is multiplying it passes to the other side of the equation, it will pass by dividing everything on the other side.This caseBeing "x" the number of pairs of pants, you know that:
Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.The equation in this case is:
17.95x + 24 = 18.95x + 18
Solving:
24 -18= 18.95x - 17-95x
6= x
Finally, this means that Kelsey and Jeana pay the same if they buy six pairs of pants and one sweater.
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Please help I’ll mark you as brainliest if correct!!
Answer:
a = 22, b = 6, c = 14, d = 8
Step-by-step explanation:
sum the elements in the leading diagonal , that is
7 + 15 + 23 = 45
then all other rows and columns and the other diagonal total 45
top row
7 + a + 16 = 45
23 + a = 45 ( subtract 23 from both sides )
a = 22
middle row
24 + 15 + b = 45
39 + b = 45 ( subtract 39 from both sides )
b = 6
left column
7 + 24 + c = 45
31 + c = 45 ( subtract 31 from both sides )
c = 14
bottom row
c + d + 23 = 45 , that is
14 + d + 23 = 45
37 + d = 45 ( subtract 37 from both sides )
d = 8
whats the explicit equation for r=3; f ( 1 ) = 1
The geometric sequence has an explicit equation of f(n) = 3^(n - 1)
How to determine the explicit equation of the function?The given parameters are
r = 3
f(1) = 1
The above means that we have the following parameters:
Type of sequence: Geometric sequenceFirst term: f(1) = 1Common ratio: r = 3The explicit equation of the geometric sequence is represented as
f(n) = f(1) * r^(n - 1)
Substitute the known values in the above equation
So, we have the following equation
f(n) = 1 * 3^(n - 1)
Evaluate the products
So, we have the following equation
f(n) = 3^(n - 1)
Hence, the explicit equation of the function is f(n) = 3^(n - 1)
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n(x) = -1 -1/3x + 1 2/3 given x = -2, 0, 5
The solution to the equations are n(-2) = 4/3, n(0) = 2/3 and n(5) = -1
How to solve the equation using the replacement sets?The equation of the function is given as:
n(x) = -1 -1/3x + 1 2/3
The replacement set is given as
x = -2, 0, 5
So, we replace the variables using the elements in the replacement set
When x = -2, we have
n(-2) = -1 -1/3 x -2 + 1 2/3
Evaluate the equation
So, we have the following equation
n(-2) = 4/3
When x = 0, we have
n(0) = -1 -1/3 x 0 + 1 2/3
Evaluate the equation
So, we have the following equation
n(0) = 2/3
When x = 5, we have
n(5) = -1 -1/3 x 5 + 1 2/3
Evaluate the equation
So, we have the following equation
n(5) = -1
Hence, the values of the functions are 4/3, 2/3 and -1
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Write an equation of the line through the points (2,1) and (1,4). Write the equation in slope-intercept form.
The equation of the line through the points (2,1) and (1.4) is
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
The equation of line in slope-intercept form is found as y = -3x + 7.
What is meant by slope-intercept form?The slope-intercept part of a line is a method for writing a line's equation so that the slope and y-intercept are easily recognizable. The slope of the line is its steepness, as well as the y-intercept is where the line intersects the y-axis.For the given question;
The two passing point of the line are;
(x1, y1) = (2,1)
(x2, y2) = (1,4)
Slope = m = (y2 - y1)/(x2 - x1)
Put the values.
m = (4 - 1)/(1 - 2)
m = -3
Then, the equation of the line in slope intercept form is found using two point equation.
y - y1 = m(x - x1)
y - 1 = -3(x - 2)
Simplifying,
y = -3x + 7
-3 is the slope and 7 is the y intercept.
Thus, the equation of line in slope-intercept form is found as y = -3x + 7.
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How did the capture of the forts at Vincennes, Kaskaskia and Cahokia help end the war? A) It helped the Americans control the Ohio Valley. B) It helped the Americans control the Appalachian Mountains. C) It helped the Americans control the Mississippi Delta. D) It helped the Americans control Virginia.
The capture of the forts at Vincennes, Kaskaskia and Cahokia help end the war because it helped the Americans control the Appalachian Mountains.
What was the Siege of Fort Vincennes?It was the War frontier battle that was fought in present-day Vincennes in which the Indiana won by the militia led by George Rogers Clark over a British garrison led by Henry Hamilton.
What was the Siege of Fort Kaskaskia?The battle happened on 1778 where George Rogers Clark & his men reached Kaskaskia, seized it from the British men and bringing the colonies' battle for independence to the western edge of British territory in North America.
What was the Siege of Fort Cahokia?It was one of the battle that happened in the West as the leader of the secret expeditionary forces captured Kaskaskia, Cahokia and Vincennes in 1778 to 1779.
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A z-score less than -2 or greater than 2 is considered unusual in a normal curve. Assuming that the data collected form normal distributions, what would data that is outside the [-2,2] range mean?
The data points from the set of collected that are outside the [-2, 2] range means that the data is an outlier or unusual data
What is a z–score?The z–score also known as standard score is the number of standard deviation a score is differs from the mean or average score
The z–score is given by the formula;
[tex]Z = \frac{x - \mu}{ \sigma} [/tex]
The Z–Score is therefore, the number of standard deviations, a data point, x is far from the mean, [tex] \mu [/tex]
The standard deviation, [tex] \sigma [/tex], is given by the formula;
[tex] \sigma = \sqrt{ \frac{ \sum {( x_{i} - \mu)}^{2} }{N} } [/tex]
As the value of [tex] \sigma [/tex] increases, the variability increases, and the Z–Score decreases, such that a Z–Score of less than -2 or greater than 2 are unusual.
From the z–score calculator, the probability that a data point has a z–score of less than -2 or more than 2 is 0.02275
Such a data point can be taken as an outlier
Therefore, data that is outside the [-2, 2] range is an unusual (outlier) data
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Answer for this question
Answer:
Proofs provided below
Step-by-step explanation:
[tex]\bold {\text{Prove } (a + b)^2 = a^2 + 2ab + b^2}}[/tex]
[tex]\\\\\implies (a + b)^2 = (a+b) \times (a+b)\\\\\implies (a + b)^2 = a \times (a+b) +b \times (a+b)\\\\\implies (a + b)^2 = a \times a + a \times b + b \times a + b \times b\\\\\implies (a + b)^2 = a^2+ab+ba+b^2\\\\\implies (a + b)^2 = a^2+ab+ab+b^2 \;\;\;\;\text{ since ab = ba}\\\\\implies (a+b)^2 = a^2+2ab+b^2\\\\[/tex]
[tex]\bold{\text{Prove } a^2-b^2 \,=\, (a+b)(a-b)\\\\}[/tex]
1. Add and subtract ab to LHS
[tex]\implies a^2-b^2 = a^2-b^2-ab+ab\\\\\implies a^2-b^2 = a^2-ab+ab-b^2\\\\[/tex]
2. Factorize the above expression
[tex]\implies a^2-b^2 = a(a-b)+b(a-b)\\\\\implies a^2-b^2 = (a-b)(a+b) \;\;\;\; \text{since (a-b) is a common factor in RHS }[/tex]
∴ (a² - b²) = (a - b) (a + b)
[tex]\bold{\text{Prove $\dfrac{\sqrt{3}+1}{\sqrt{3}-1}$= $2+\sqrt{\ensuremath{3}}$}}\\[/tex]
[tex]\text{1. Multiply LHS by $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$}\\\\\implies $\dfrac{\sqrt{\text{}3}+1}{\sqrt{3}-1}$ \times $\dfrac{\sqrt{\text{}3}-1}{\sqrt{3}-1}$ \\\\[/tex]
[tex]\implies \dfrac{ (\sqrt{3} + 1)(\sqrt{3}-1) }{(\sqrt{3} - 1)(\sqrt{3}-1) }\\\\[/tex]
Numerator is
[tex](\sqrt{3} + 1)(\sqrt{3}-1) = (\sqrt{3})^2 - 1^2 = 3 - 1 = 2\\\\[/tex]
Denominator is
[tex](\sqrt{3}-1)^2 = (\sqrt{3})^2 - 2\cdot \sqrt{3} \;\cdot 1 + (-1)^2\\\\= 3 - 2 \sqrt{3} + 1\\\\= 4 - 2 \sqrt{3}\\\\[/tex]
So LHS becomes
[tex]\dfrac{2}{4 - 2\sqrt{3}} \\\\[/tex]
Dividing numerator and denominator by 2 yields
[tex]\dfrac{2}{4 - 2\sqrt{3}} = \dfrac {1}{2 - \sqrt{3}}[/tex]
Multiply numerator and denominator by [tex]{2-\sqrt {3}}[/tex]
[tex]$\dfrac{1\cdot(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3)}}$[/tex]
[tex]=$\dfrac{\ensuremath{2}+\sqrt{3}}{2^{2}-(\sqrt{3)^{2}}}=$$\dfrac{\ensuremath{\ensuremath{2}+\sqrt{3}}}{4-3}=\ensuremath{2}+\sqrt{3}$[/tex]
Hence Proved
Find the first 5 terms of the sequence given the nth term.
1. an=2n^2+5n-10
2. an=3n+4/n^2+5
Part 1: The first five terms of the sequence are -1, 16, 69, 266, 1039
Part 2: The first five terms of the sequence are 12, 12, 130/9, 69/4, 126
Part 1:
For finding the first five terms we will substitute values in n from 1,2,3,4 and 5
an = 2n^2 + 5n-10
a1 = 2(1)^2 + 5(1)-10
=4+5-10 = -1
So, the first term is -1
a2 = 2(2)^2+5(2)-10
= 16+10-10 =16
The second term is 16
a3 = 2(3)^2+5(3)-10
=64+15-10
=69
The third term is 69
a4 = 2(4)^2+5(4)-10
=256+20-10
=266
The fourth term is 266
a5 = 2(5)^2+5(5)-10
= 1024+25-10
= 1039
The fifth term is 1039
Part 2:
an = 3n+4/n^2+5
a1 = 3(1)+4/1^2+5
= 3+4+5
= 12
The first term is 12
a2 = 3(2)+4/2^2+5
= 6+1+5
= 12
The second term is 12
a3 = 3(3)+4/3^2+5
= 9+4/9+5
= 81+4+45/9
=130/9
The third term is 130/9
a4 = 3(4)+4/4^2+5
= 12+4/16+5
=17+1/4
=69/4
The fourth term is 69/4
a5 = 3(5)+4/5^2+5
= 15+4/25+5
=20+4/25
=504/4
= 126
The fifth term is 126
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The carnival spinner shown below is divided into equal sections. On every spin, each outcome is equally likely.
If the spinner lands on a number less than 10 on its next spin, what is the probability that it is a multiple of 4?
a. 1/5
b. 2/9
c. 1/4
d. 1/3
Answer:
2/9
Step-by-step explanation:
The possibilities that satisfy the condition are 4 and 8.
This is 2 numbers out of the possible 9, so the probability is 2/9.
Find the value of x.
Is 6c + 5 an odd integer?
Yes, because 6 c+5=2(3 c+2)+1 and 3 c+2 is an integer. Option A
This is further explained below.
What is Integer?Generally, A natural number that is either positive or negative expressed as an integer, or the number zero itself are all examples of integers.
The additive inverses of the positive numbers that they relate to are represented by the negative numbers.
In conclusion, Because 6c+5=2(3c+2)+1 and 3c+2 is an integer, the answer to this question is yes.
is correct, Integer
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CQ
[tex](b) Is\ $6 c+5$ \an \odd \integer?\\\\Yes, because $6 c+5=2(3 c+2)+1$ and $3 c+2$ is \ an \ integer.\\\\Yes, because $6 c+5=2(3 c+2)$ and $3 c+2$ is \ an integer.\\\\No, because $6 c+5=2(3 c+2)+1$ and $3 c+2$ is an integer.\\\\No, because $6 c+5=2(3 c+2)$ and $3 c+2$ is an integer.[/tex]
Solve the equation using the Quadratic Formula. 2x² + 5x = 3
Answer:
x = (1/2)
x = -3
Step-by-step explanation:
Quadratic:
2x² + 5x = 3
-3 -3
----------------------
2x² + 5x - 3 = 0
-b ± √b² - 4(a)(c)
-------------------
2(a)
-5 ± √5² - 4(2)(-3)
---------------------------
2(2)
-5 ± √25 + 24
---------------------------
4
-5 ± √49
----------------
4
-5 ± 7
----------
4
-5 + 7 2 1
---------- = ------- = ------
4 4 2
-5 - 7 -12
---------- = --------- = -3
4 4
----------------------------------------------------------------------------------------------------------
Factored (for fun):
(2x² + 6x) (-1x - 3) = 0
2x(x + 3) -1 (x + 3)
(2x - 1)(x + 3) = 0
2x - 1 = 0, x + 3 = 0
+1 +1 -3 -3
--------------- ------------------
2x = 1 x = -3
÷2 ÷2
-------------
x = (1/2)
I hope this helps!
What type of linear equation is X +1 equals X +1?
The given equation is 1-degree linear equation in one variable.
What is linear equation?
A linear equation is one that may be written as a1x1+a2x2+......+anxn in mathematics, where a1, a2,...., an are the coefficients, which are frequently real integers. The coefficients, which may be any expressions as long as they don't contain any of the variables, can be thought of as the equation's parameters. The coefficients a1 to a must not all be 0 in order for the equation to have any sense. An alternative method for creating a linear equation is to equalize a linear polynomial over a field, from which the coefficients are drawn, to zero. The numbers that, when used to replace the unknowns in such an equation, result in the equality, are the solutions.
x+1 = x+1 is a 1-degree linear equation in one variable (x).
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A dolphin swims at a depth of 13.5 meters below sea level while a seagull flies 10 meters above sea level. How far apart are they? Write and evaluate an expression to answer this question.
I need help i dont understand this
Answer:
oh god what da heck is this math :')
Step-by-step explanation:
f(x) = -4/3 (-x+5)^3 +12
X Y
3 1.333
4 10.667
5 12
6 13.333
8 48
A forest fire leaves behind an area of grass burned in an expanding circular
pattern. If the radius of the circle of burning grass is increasing with time
according to the formula r(t) = 2t + 1, express the area burned as a function of
time.
The function of the area of the forest in terms of time is A(t) = π(2t + 1)²
How to determine the area function?The given parameters are
Radius function, r(t) = 2t + 1
From the question, we understand that:
The pattern is circular
The area of a circle is
A = πr²
Express as a function
A(r) = πr²
Substitute r(t) = 2t + 1
A(t) = π(2t + 1)²
Hence, the area function in terms of time is A(t) = π(2t + 1)²
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Which of the following expressions illustrates how you can use the
associative property of addition to solve 13+6.2+5.8 more simply?
a. 13+5.8+6.2
b. (13+6.2)+5.8
c. 13+(6.2+5.8)
d. (13+6.2)+(13+5.8)
Answer:
c.
Step-by-step explanation:
13+6.2+5.8
= 13+(6.2+5.8)
- the sum in the parentheses is easy to calculate (it = 12).
Divide 8 1/2 by the positive difference between 4 4/5 and 7 7/10
The division of 8 1/2 by the positive difference between 4 4/5 and 7 7/10 is 85/29.
How can we make the division?We can find the difference between 4 4/5 and 7 7/10, but we will need to convert the mixed number into the improper fraction as
Then we have 24/5 and 77/10, then the difference between the values are:(77/10 - 24/5) = 29/10
Then we can proceed to find the division of this number that we got from the difference as ( 29/10)/ 8 1/2
But we can make the 8 1/2 as improper fraction from the mixed fraction it was 17/2
Then the division of the values will be ( 17/2)/ ( 29/10) = 85/29
Therefore the division is 85/29.
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There are 16 boys and 12 girls in the running club. What is the ratio of girls to boys?
3:4
16:12
4:3
12:16
Answer:
4:3
Step-by-step explanation:
it will be 16:12 and when you divide both by 3 it will be 4:3
Maximize:
z= 6x +12y
subject to: 4x + 5y ≤20
8x + y ≤ 20
x≥0, y 20
Answer:
48
Step-by-step explanation:
Given:
[tex]\textsf{Maximize}: \quad z=6x+12y[/tex]
[tex]\begin{aligned}&\textsf{Subject to}: \quad &4x+5y & \leq 20\\&&8x+y &\leq 20\\&&x\geq 0, y&\geq 0\end{aligned}[/tex]
Graph the lines:
[tex]\textsf{Draw the line } \;\;4x+5y=20 \;\;\textsf{and shade under the line}.[/tex]
[tex]\textsf{Draw the line } \;\;8x+y=20 \;\;\textsf{and shade under the line}.[/tex]
[tex]\textsf{Draw the line } \;\;x=0\;\;\textsf{and shade above the line}.[/tex]
[tex]\textsf{Draw the line } \;\;y=0\;\;\textsf{and shade above (to the right of) the line}.[/tex]
Therefore, the feasible region is bounded by the corner points:
A = (0, 0)B = (0, 4)C = (⁵/₂, 0)D = (²⁰/₉, ²⁰/₉)Determine the value of z at the corner points by substituting the x and y values of the points into the equation for z:
[tex]\textsf{Value of $z$ at $A(0,0)$}: \quad 6(0)+12(0)=0[/tex]
[tex]\textsf{Value of $z$ at $B(0,4)$}: \quad 6(0)+12(4)=48[/tex]
[tex]\textsf{Value of $z$ at $C\left(\dfrac{5}{2},0\right)$}: \quad 6\left(\dfrac{5}{2}\right)+12(0)=15[/tex]
[tex]\textsf{Value of $z$ at $D\left(\dfrac{20}{9},\dfrac{20}{9}\right)$}: \quad 6\left(\dfrac{20}{9}\right)+12\left(\dfrac{20}{9}\right)=40[/tex]
Hence, the maximum value of z is 48 at B(0, 4).
[tex] \rm \int_{0}^{1} \sqrt{ \frac{2 - {x}^{2} }{1 - {x}^{2} } } dx \\ [/tex]
Substitute [tex]x=\sin(t)[/tex] and [tex]dx=\cos(t)\,dt[/tex], and recall the definition of the elliptic integral of the second kind,
[tex]\displaystyle E(k) = \int_0^{\pi/2} \sqrt{1 - k^2 \sin^2(\theta)} \, d\theta[/tex]
Then the integral has a value of
[tex]\displaystyle \int_0^1 \sqrt{\frac{2-x^2}{1-x^2}} \, dx = \int_0^{\pi/2} \sqrt{2-\sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \sqrt2 \int_0^{\pi/2} \sqrt{1 - \frac12 \sin^2(t)} \, dt \\\\ ~~~~~~~~~~~~~~~~~~~~~= \boxed{\sqrt2 E\left(\frac1{\sqrt2}\right)}[/tex]
If a new truck is valued at $19,700, what will its value be in 1 year if it depreciates 14.4 % each year?
depreciated value of truck after 1year is $16863.2
WHAT IS PERCENTAGE ?% is a relative number that is used to represent hundredths of any quantity. Since one percent (1%) equals one tenth of something, 100 percent denotes the entire amount, and 200 percent denotes twice the amount mentioned.
CALCULATIONnew truck valued depreciates 14.4% then
if old truck value be 100 % , depreciated value will be 85.6 %
so depreciated value will be = 19700* 85.6 /100
= $16863.2
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If Rebekah can run 6 miles every 60 minutes, how
many miles can she run in 50 minutes?
Answer:
5 miles in 50 minutes
Find the area of the figure. 16cm 9cm
area: cm2
The area of the figure is 144 square centimeters
What are areas?The area of a shape is the amount of space on the shape
For most regular quadrilaterals, you multiply the side lengths to determine the area
How to determine the area of the shape?The given parameters are
Shape = parallelogram
Base = 9 cm
Height = 16 cm
The area of a parallelogram shape is
Area = Base * Height
So, we have
Area = 9 * 16
Evaluate the expression
Area = 144
Hence, the area is 144 square centimeters
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Is any real number exactly 2 more than its cube?
Answer: Yes
Step-by-step explanation: The real number, which most exceeds its cube, is A 21