The simplification of the expression will be; 15t³ + 9t² + 14y
What are equivalent expressions?Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions. To derive equivalent expressions of some expressions, we can either make them look more complex or simple.
Given that the expression as 8t³ + 8y + 7t³ + 6y + 9t²
Now combining like terms;
8t³ + 7t³ + 9t² + 8y + 6y
Simplify;
15t³ + 9t² + 14y
It cannot be solved further because of unlike terms in the expression.
Therefore, the simplification of the expression will be; 15t³ + 9t² + 14y
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1 a) is the above sequence arithmetic? Justify your answer. b) Write the explicit formula for the above sequence. c) Find the 18th term.
First, we count the number of boxes.
We have: 4,8,12,16
(a)Now:
• 8-4=4
,• 12-8=4
,• 16-12=4
Since the difference is the same, the sequence is an arithmetic sequence.
(b)In the sequence
First term, a =4
Common difference, d=4
The nth term of an arithmetic sequence is:
[tex]\begin{gathered} U_n=a+(n-1)d \\ =4+4(n-1) \\ =4+4n-4 \\ =4n \end{gathered}[/tex]The explicit formula for the above sequence, f(n)= 4n.
(c)18th term
f(18)= 4 x 18
=72
The 18th term is 72.
Two lines intersect in the diagram shown below. 127° to What is the value of x? Hide All 37 53 127 D 217 O
x=127º
1) Since those angles x, and 127º share a common vertex we can state that these are Vertical Angles
2) Therefore they are congruent to each other. And we can state:
x = 127º as well.
Find the equation of the line passing through the points (3,-2) and (3, 4).The answer is x = 3. I'm just wondering how my textbook got to this solution.My work:y-y1=m(x-x1). m=y2-y1 / x2-x1. y=mx+bm=4--2 / 3-3 = 6/0 = 0. m=0.y--2=0(x-3) = y=0-2 y=-2 <<<
Given two points. we can find the equation of a line passing through the points
The formula to be used is:
[tex]\frac{y_2-y_1}{x_2-x_!}=\frac{y-y_1}{x-x_!}[/tex]where
[tex]x_1=3,y_!=-2,x_2=3,y_2=4[/tex][tex]\frac{4-(-2)}{3-3}=\frac{y-(-2)}{x-3}[/tex]=>
[tex]\frac{6}{0}=\frac{y+2}{x-3}[/tex]The next step is to cross multiply
[tex]6(x-3)=0(y+2)[/tex]=>
[tex]6(x-3)=0[/tex]Divide both sides by 6 and make x the subject
x=3
Find the first four terms of the sequence given by the following
1) In this question, we need to resort to that Explicit formula, with the first term so that we can find the terms:
[tex]\begin{gathered} a_n=54+8(n-1) \\ a_1=54+8(1-1) \\ a_1=54 \\ \\ a_2=54+8(2-1) \\ a_2=54+8 \\ a_2=62 \\ \\ a_3=54+8(3-1) \\ a_3=54+8(2) \\ a_3=54+16 \\ a_3=70 \\ \\ a_4=54+8(4-1) \\ a_4=54+8(3) \\ a_4=78 \\ \end{gathered}[/tex]2) As we can see, this is an Arithmetic sequence. And the answer is:
[tex]54,62,70,78[/tex]The sign points at the smaller number. True or False. Example 2 < 100 True False
When working with inequalities you have to remember that:
The symbol "<" indicates that the number on the left is smaller than the number on the right, then, for example:
[tex]85<90[/tex]This indicates that 85 is less than 90.
The symbol ">" indicates that the number of the left is greater than the number on the right, for example:
[tex]70>54[/tex]This indicates that 70 is greater than 54.
Now for the given statement:
[tex]2<100[/tex]"The sign points at the smaller number"
The expression indicates that 2 is less than 100, so the statement is true.
Select all the true statements about this graph A. The graph is nonlinearB. The function increases at the same rateC. The rate decreases after x = 2.D. The graph is a functionE. The graph is increasing in two intervals.SELECT ALL ANSWER CHOICES THATS RIGHT
In the graph the points are connected by the straight lines, so graph is linear graph. In nonlinear graph the points are connected by the curve. So option A is incorrect.
The slope of the line changes after x=2. The inclination of line with positive x axis is different before and after x=2. So the function not increases at same rate. Then option B is incorrect.
The rate is given by the slope of line. The inclination of line with positive x axis increase after x=2, so rate increases not decreases. Then option C is incorrect.
The graph of a straight line is function or not a function can be inspected by vertical line test.
If we draw a vertical line, then the vertical line intersect the line only once, so the graph is function. Option D is correct.
The value of y increases with increase in value of x but increase in value of y with x is different for two lines. So graph is increasing in two intervals. Option E is also correct.
Thus option D and E is only true for given graph.
A tank is in the shape of a cylinder of radius 15 cm and height 50 cm.Work out the volume of the tank.
Answer: [tex]11250\pi \\[/tex] cm^3
Step-by-step explanation:
This could be solved with integral calculus or simple arithmetic.
If you need to show the work in calculus, let me know, otherwise, here's the easiest way to reach the answer:
Volume of a solid is equal to the area of its 2D projection multiplied by its height, assuming that it's uniform throughout its entire height. Fortunately, a cylinder is uniform throughout its height.
What is a cylinder's 2D projection? A circle!
Area of a circle = [tex]\pi r^{2}[/tex]
r = 15
Area = 225pi cm^2
Now, we multiply the area of the 2D projection by the height of the cylinder.
225pi * 50 = 11250pi cm^3
How do I add the probabilities? And what is the solution after doing that?
In order to calculate the probability of P(Z<3), let's add all cases where Z<3:
[tex]P(Z<3)=P(Z=0)+P(Z=1)+P(Z=2)[/tex]The minimum value of Z is given when X = 0 and Y = 1, so Z = 1.
The maximum value of Z is given when X = 1 and Y = 2, so Z = 3.
Therefore P(Z = 0) is zero.
Z = 1 can only happen when X = 0 and Y = 1.
Z = 2 can happen when X = 1 and Y = 1 or when X = 0 and Y = 2.
So we can rewrite the expression as follows:
[tex]\begin{gathered} P(Z<3)=0+P(X=0)P(Y=1)+[P(X=1)P(Y=1)+P(X=0)P(Y=2)\rbrack\\ \\ =0+0.5\cdot0.4+0.5\cdot0.4+0.5\cdot0.6\\ \\ =0+0.2+0.2+0.3\\ \\ =0.7 \end{gathered}[/tex]Therefore the correct option is A.
Use the given sets to find A∩B.A={2,4,6,8,10,12}B={7,9,11,13,14,15,16}
Recall that
[tex]A\cap B[/tex]is a set that consists of all the elements that are in both A and B.
From the given sets we get that the elements that are in both A and B are:
[tex]\text{None.}[/tex]Therefore, the intersection of the sets is the empty set.
Answer:
[tex]A\cap B=\emptyset.[/tex]A number cube labelled 1 to 6 is rolled 276 times. Predict how many times a 5 will show.
All the outcomes of the cube are equally probable, therefore, it is expected to have all the outcomes after 6 rolls. To find the amount of times we're supposed to get one of the outcomes, we multiply the amount of rolls by the probability of this outcome.
The theoretical probability is defined as the ratio of the number of favourable outcomes to the number of possible outcomes. We have one number five out of six possible numbers, therefore, the probability of getting a 5 is:
[tex]P(5)=\frac{1}{6}[/tex]Therefore, in 276 rolls we're going to get the following amount of 5's:
[tex]276\times P(5)=\frac{276}{6}=46[/tex]5 will show 46 times.
The functions f(x) and g(x) are shown on the graph.f(x)=x^2What is g(x)?A. g(x)=(x+3)^2B. g(x)=(x-3)^2C. g(x)=(1/3x)^2D. g(x)=3x^2
Given:
[tex]f(x)=x^2[/tex]Let's find g(x).
From the given graph, we can see the graph of g(x) is compressed horizontally from f(x).
Thus, to find g(x) aply the transformation rules for function.
We have:
Horizontal compression of b units ==> f(bx)
Given the point on g(x):
(x, y) ==> (2, 12)
Let's solve for the value of the compressed factor.
We have:
[tex]\begin{gathered} 12=b(2)^2 \\ \\ 12=b4 \\ \\ \text{Divide both sides by 4:} \\ \frac{12}{4}=\frac{b4}{4} \\ \\ 3=b \\ \\ b=3 \end{gathered}[/tex]This means the graph of f(x) was compressed horizontally by a factor of 3 to get g(x).
Thus, to write the function for g(x), we have:
[tex]g(x)=3x^2[/tex]ANSWER:
[tex]D\text{.}g(x)=3x^2[/tex]I am asked to graph f(x) = (- 1/x-2) -1
Answer
[tex]f(x)=-\frac{1}{x-2}-1[/tex]A gumball machine contains 5 blue gumballs and 4 red gumballs. Two gumballs are purchased, one after the other, without replacement.
Find the probability that the second gumball is red.
===================================================
Work Shown:
5 blue + 4 red = 9 total
A = P(1st is red, 2nd is red)
A = P(1st is red)*P(2nd is red, given 1st is red)
A = (4/9)*(3/8)
A = 12/72
B = P(1st is blue, 2nd is red)
B = P(1st is blue)*P(2nd is red, given 1st is blue)
B = (5/9)*(4/8)
B = 20/72
C = P(2nd is red)
C = A+B
C = 12/72 + 20/72
C = 32/72
C = 4/9
The figure below is made up of a triangle and a circle. The ratio of the area of the triangle to the area of the circle is 5:6. If 1/5 of the area of the triangle is shaded, what is the ratio of the shaded area to the area of the figure?
ANSWER
[tex]\begin{equation*} 1:10 \end{equation*}[/tex]EXPLANATION
The ratio of the area of the triangle to the area of the circle is:
[tex]5:6[/tex]Let the area of the triangle be T.
1/5 of the area of the triangle is shaded i.e. 1/5 T
The total area of the figure is the sum of the area of the triangle that is not shaded and the area of the circle.
The area of the triangle that is not shaded is:
[tex]\begin{gathered} T-\frac{1}{5}T \\ \frac{4}{5}T \end{gathered}[/tex]Let the area of the circle be C. The ratio of the area of the triangle to that of the circle is 5/6. This implies that:
[tex]\begin{gathered} \frac{T}{C}=\frac{5}{6} \\ \Rightarrow C=\frac{6T}{5} \end{gathered}[/tex]And so, the area of the figure is in terms of T is:
[tex]\begin{gathered} \frac{4}{5}T+\frac{6}{5}T \\ 2T \end{gathered}[/tex]Therefore, the ratio of the shaded area to the area of the figure is:
[tex]\begin{gathered} \frac{1}{5}T:2T \\ \Rightarrow\frac{1}{5}:2 \\ \Rightarrow1:10 \end{gathered}[/tex]That is the answer.
Madison is in the business of manufacturing phones. She must pay a daily fixed cost of $400 to rent the building and equipment, and also pays a cost of $125 per phone produced for materials and labor. Make a table of values and then write an equation for C,C, in terms of p,p, representing total cost, in dollars, of producing pp phones in a given day.
I need the equation
Here is the completed table:
Number of phones manufactured Total cost of Manufactured phones
0 $400
1 $525
2 $650
3 $775
The equation that represents the total cost is C = $400 + $125p .
What is the total cost?The equation that represents the total cost is a function of the fixed cost and the variable cost. The fixed cost remains constant regardless of the level of output. The variable cost changes with the level of output.
Total cost = fixed cost + total variable cost
Total cost = fixed cost + (variable cost x total output)
C = $400 + ($125 x p)
C = $400 + $125p
Total cost when 0 phones are made = $400 + $125(0) = $400
Total cost when 1 phone are made = $400 + $125(1) = $525
Total cost when 2 phones are made = $400 + $125(2) = $650
Total cost when 3 phones are made = $400 + $125(3) = $775
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A printer takes 5 seconds to print 3 pages. How many pages can it print in 125 seconds? Enter the answer in the box.
Answer: 75
Step-by-step explanation:
So first, we need to divide 125 by 5
125÷5=25
Next we need to multiply 3 by 25.
25×3=75
The printer can print 75 pages in 125 seconds.
I need help with my pre-calculus homework, please show me how to solve them step by step if possible. The image of the problem is attached. These are 2 parts of the same question.
We are given the following triangle:
We need to determine the area of the triangle. To do that we need to determine sides "a" and "b". We will use the sine law to determine the side "b":
[tex]\frac{b}{sin107}=\frac{98}{sin48}[/tex]Now, we multiply both sides by "sin107":
[tex]b=sin(107)\frac{98ft}{sin(48)}[/tex]Solving the operations:
[tex]b=126.11ft[/tex]Now, before determining side "a" we will determine the angle "x" that is opposed to "a". To do that we will use the fact that the sum of the interior angles of a triangle is 180, therefore:
[tex]107+48+x=180[/tex]Adding the values:
[tex]155+x=180[/tex]Now, we subtract 155 from both sides:
[tex]\begin{gathered} x=180-155 \\ x=25 \end{gathered}[/tex]Therefore, the angle opposite to "a" is 25 degrees. Now, we apply the sine law:
[tex]\frac{a}{sin(25)}=\frac{98}{sin(48)}[/tex]Now, we multiply both sides by "sin(25)":
[tex]a=sin(25)\frac{98}{sin(48)}[/tex]Solving the operations:
[tex]a=55.73ft[/tex]Now, we determine the area using the following formula:
[tex]A=\sqrt{s(s-a)(s-b)(s-c)}[/tex]Where:
[tex]s=\frac{a+b+c}{2}[/tex]Now, we determine the value of "s":
[tex]s=\frac{55.73ft+126.11ft+98ft}{2}[/tex]Solving the operation:
[tex]s=139.92ft[/tex]Now, we substitute the value in the formula for the area:
[tex]A=\sqrt{(139.92ft)(139.92ft-55.73ft)(139.92ft-126.11ft)(139.92ft-98ft)}[/tex]Solving the operations:
[tex]A=2611.43ft^2[/tex]Now, since the search party can cover 300 ft^2/h we can use a rule of 3 to determine the number of hours it takes them to cover 2611.43 ft^2:
[tex]\begin{gathered} 300ft^2\rightarrow1h \\ 2611.43ft^2\rightarrow x \end{gathered}[/tex]Now, we cross multiply:
[tex](300ft^2)(x)=(1h)(2611.43ft^2)[/tex]Now, we divide both sides by 300ft^2:
[tex]x=\frac{(1h)(2611.43ft^2)}{(300ft^2)}[/tex]Solving the operations:
[tex]x=8.7h[/tex]Therefore, it takes 8.7 hours to cover the area. Therefore, the search party won't be able to conclude before the sun goes down.
Solve for c.
6>c+8>5
Step-by-step explanation:
Solve the equation using the justification given for each step.
Multiplicative property of equality
[tex]\begin{gathered} Multiply\text{ both sides by 3} \\ (5x+7)3=\frac{3(-15x-1)}{3}+3(\frac{4}{3}) \end{gathered}[/tex]Distributive property of equality
[tex]3(5x+7)=-15x-1+4[/tex]Associative property
[tex]\begin{gathered} 15x+21=-15x-1+4 \\ 15x+21=-15x+3 \end{gathered}[/tex]Subtraction property of equality
[tex]\begin{gathered} 15x+21-21=-15x+3-21 \\ 15x=-15x-18 \end{gathered}[/tex]Addition property of equality
[tex]\begin{gathered} 15x+15x=-15x+15x-18 \\ 30x=-18 \end{gathered}[/tex]Division property of inequality
[tex]\begin{gathered} \text{divide both sides by 30} \\ \frac{-18}{30}=\frac{30x}{30} \\ x=-\frac{18}{30}=-\frac{3}{5} \end{gathered}[/tex]what is the probability that a student will be in both chemistry and math but not Spanish round to three decimal places
Answer :
3/13
Explanation :
The probablity of an event = favourable outcome / total outcomes
Now in our case,
favorable outcome = 60
Total number of outcomes = 5 + 70 + 5 + 85 + 60 + 15 + 3 + 17 = 260
Therefore,
probablity = 60 / 260
= 3 /13
What is the value of 9 − (−4)?
Answer:13
Step-by-step explanation:
Step-by-step explanation:
remember, when 2 signs and/operations come together, for addition/subtraction and multiplication/division it always applies :
+ + = +
- + = -
+ - = -
- - = +
and therefore,
9 - (-4) = 9 + 4 = 13
a minus meeting a minus always results in a plus.
using the given quadratic function f(x)=x^2+2x-15, find the following information"Coordinates of x- intercept(zero) as ordered pairs"
the given expression is
f(x) = x^2 + 2x - 15
we will find x intercept by putting f(x) = 0
x^2 + 2x - 15 = 0
x^2 + 5x - 3x - 15 = 0
x(x +5) -3(x + 5) = 0
(x +5) (x -3) = 0
x = -5 & x = 3
so the ordered pairs are
(-5, 0) and (3, 0)
INT. ALGEBRA: Write an equation that passes through (-10,-30) and is perpendicular to 12y-4x=8
Thank you for your help, and please do show work! I will be looking to give the Brainliest answer to someone!
The equation of the perpendicular line is y = -3x - 60
How to determine the line equation?The equation is given as
12y - 4x = 8
Make y the subject
12y= 4x + 8
y = 1/3x + 2/3
The point is also given as
Point = (-10, -30)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 1/3
This means that the slope of 12y - 4x = 8 is 1/3
So, we have
m = 1/3
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -3
The equation of the perpendicular lines is then calculated as
y = m(x - x₁) +y₁
Where
m = -3
(x₁, y₁) = (-10, -30)
So, we have
y = -3(x + 10) - 30
Evaluate
y = -3x - 30 - 30
y = -3x - 60
Hence, the perpendicular line has an equation of y = -3x - 60
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what is the conjugate of the denominator of the expression 9i/-2+7i
The answer is D.
Simplify. -(-6w + x - 3y)
Answer: 6w - x + 3y
Step-by-step explanation:
since birth hakem has had a savings account that started at $3,000 and had been growing at a rate of 13% per year the amount of money in the account can be modeled by the equation y equals P =(1.13)^ Z where why is the value of the count is the number of years and pee was original deposit amount is it possible for hakem account to grow to $31812 11.42 in hakem lifetime?( try to figure out the bounds of the perameter)
Solution
For this case we have the following formula:
[tex]y=3000(1.13)^x^{}[/tex]And we want to find the value for t in order to have y = 3181211.42 , solving for y we got:
[tex]3181211.42=3000(1.13)^x[/tex]and solving for x we got:
[tex]\ln (\frac{3181211.42}{3000})=x\cdot\ln (1.13)[/tex][tex]x=56.99\approx57[/tex]for this case we need 57 years to reach the amount so then assuming that a person lives about 80 years , then is possible
yes
An air plane can cruise at 640mph. How far can it fly in 3/2 Ths of an hour?
Answer: 960 miles
3/2 of an hour would be 1 hour and 30 min or an hour and a half
640mph (mph = miles per hour)
1/2 of an hour is 30 minutes so its 640 miles in half so 320
now all you gotta do is add it
so 640 + 320 = 960
GWhich inequalities have no solution? Check all of the boxes that apply.XX-3x -3x–4 + x>-2 + xX-2
For every number x, x = x, not x < x. So, the inequality x < x has no solution.
Since -3x = -3x for every real number, the inequality
[tex]-3x\leq-3x[/tex]holds for every real number, that is, every number is a solution.
Consider the inequality
[tex]-4+x>-2+x[/tex]Subtract x on both sides gives -4 > -2, which is not possible.
Hence the inequality - 4 + x > - 2 + x has no solution.
Consider the inequality
[tex]x-2Subtract x on both sides gives -2 < 3, which is true.Every real number is a solution of the inequality. Hence the inequality has solution.
Thus the inequalities with no solution are: x < x and -4+x>-2+x
Picture translating A ABC three units to the left and five units up.What are the coordinates of A'?A(2,-2)
The coordinates of point A are (2, -2)
If the picture is translated 3 units to the left, we need to subtract 3 units to the x coordinate as:
( 2 - 3, -2) = (-1, -2)
Then, if the picture is translated 5 units up, we need to sum 5 units to the y-coordinate as:
( -1 , -2 + 5) = (-1, 3)
So, the coordinates of A' are (-1, 3)
Answer: (-1, 3)
For each quadratic expression below, drag an equivalent expression to its match
1. Given the expression:
[tex]\mleft(x+2\mright)\mleft(x-4\mright)[/tex]You can use the FOIL method to multiply the binomials. Remember that the FOIL method is:
[tex](a+b)\mleft(c+d\mright)=ac+ad+bc+bd[/tex]Then, you get:
[tex]\begin{gathered} =(x)(x)-(x)(4)+(2)(x)-(2)(4) \\ =x^2-4x+2x^{}-8 \end{gathered}[/tex]Adding the like terms, you get:
[tex]=x^2-2x-8[/tex]2. Given:
[tex]x^2-6x+5[/tex]You have to complete the square:
- Identify the coefficient of the x-term". In this case, this is -6.
- Divide -6 by 2 and square the result:
[tex](\frac{-6}{2})^2=(-3)^2=9[/tex]- Now add 9 to the polynomial and also subtract 9 from the polynomial:
[tex]=x^2-6x+(9)+5-(9)[/tex]- Finally, simplifying and completing the square, you get:
[tex]=(x-3)^2-4[/tex]3. Given the expression:
[tex]\mleft(x+3\mright)^2-7[/tex]You can simplify it as follows:
- Apply:
[tex](a+b)^2=a^2+2ab+b^2[/tex]In this case:
[tex]\begin{gathered} a=x \\ b=3 \end{gathered}[/tex]Then:
[tex]\begin{gathered} =\lbrack(x)^2+(2)(x)(3)+(3)^2\rbrack-7 \\ =\lbrack x^2+6x+9\rbrack-7 \end{gathered}[/tex]- Adding the like terms, you get:
[tex]=x^2+6x+2[/tex]4. Given:
[tex]x^2-8x+15[/tex]You need to complete the square by following the procedure used in expression 2.
In this case, the coefficient of the x-term is:
[tex]b=-8[/tex]Then:
[tex](\frac{-8}{2})^2=(-4)^2=16[/tex]By Completing the square, you get:
[tex]\begin{gathered} =x^2-8x+(16)+15-(16) \\ =(x-4)^2-1 \end{gathered}[/tex]Therefore, the answer is: