Answer:
[tex] Quotient = \frac{8 - 2t}{3} [/tex]
Step-by-step explanation:
Quotient, in maths, is what you get when two number or expressions together. That is, dividend over the divisor.
Thus, from what we're given:
dividend is 8 decreased by 2 times t, which can be expressed as [tex] 8 - 2*t = 8 - 2t [/tex].
The divisor is 3.
[tex] Quotient = \frac{8 - 2t}{3} [/tex]
what’s the answer to 4 + 6x + 5 = 7x
Answer: 9
Step-by-step explanation:
4+6x+5=7x
-6x -6x
=
4+5=1x
9=1x
X=9
I dug a hole that was 16 feet deep. My dog came and put 8 feet of dirt back into the hole but then my husband put 5 feet of dirt back into the hole. What integer represents the depth of the hole?
Answer:
3 feet
Step-by-step explanation:
Initial depth = 16 feet
Then:
16 - 8 - 5= 8 - 5 =3 feet depth leftplease help me immediately
The arithmetic mean of 3 numbers is less than 20.The first number is 5 and the second number is 25.Find the possible values for the third no number.
Answer:
The third number can be any number less than 30.
Step-by-step explanation:
If the arithmetic mean of three numbers is less than 20, then their sum must be less than 20 * 3, or 60. We know that two of the numbers are 5 and 25, which add up to 30. In order for the arithmetic mean of the three numbers to be less than 20, the unknown number must be less than (60 - 30), or in order words, less than 30. So the third number can be any number less than 30.
If the zeros of f(x) are x=-1 and x=2, then the zeros of f(x/2) are
A. -1, 2
B. -1/2, 5/2
C. -3/2, 3/2
D. -1/2, 1
E. -2/4
Answer:
E (-2, 4).
Step-by-step explanation:
(x/2 + 1)(x/2 - 2) = 0
x/2 = -1, x/2 = 2
x = -2, 4.
The roots will be 2 times the roots of f(x).
Answer:
[tex]\Large \boxed{\mathrm{E. \ -2, \ 4}}[/tex]
Step-by-step explanation:
The zeros of f(x/2) will double the zeros of f(x).
x = -1 × 2 = -2
x = 2 × 2 = 4
The graph shown here is the graph of which of the following rational
functions?
FOO
- 10
10
A. F(X) = **-5)
(x+2)
O B. F(x) = (x + 2)(x
O C. F(x) = (x + 2)(x-5)
Answer:
Option (B)
Step-by-step explanation:
From the graph attached,
Vertical asymptotes of the function are x = -2, 5
Horizontal asymptote is y = 0
Now we take each option,
Option (A),
F(x) = [tex]\frac{x(x-5)}{(x+2)}[/tex]
No horizontal asymptote
Vertical asymptote : x = -2
Option (B),
F(x) = [tex]\frac{x}{(x+2)(x-5)}[/tex]
Horizontal asymptotes : y = 0
Vertical asymptotes : x = 5, -2
Option (C),
F(x) = [tex]\frac{(x+2)(x-5)}{x}[/tex]
Vertical asymptote : x = 0
No horizontal asymptote.
Therefore, Function given in Option (B) matches the asymptotes given in the graph.
Option (B) represents the graph.
Function given in Option (B) matches the asymptotes given in the graph.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Now, From the graph attached,
Vertical asymptotes of the function are x = -2, 5
And, Horizontal asymptote is y = 0
Hence, we take each option and check as,
For Option (A),
F(x) = x (x - 5) / (x + 2)
Hence, No horizontal asymptote
And, Vertical asymptote : x = -2
Option (B),
F(x) = x / (x + 2) (x - 5)
Hence, Horizontal asymptotes : y = 0
And, Vertical asymptotes : x = 5, -2
Option (C),
F(x) = (x + 2) (x - 5) / x
Hence, Vertical asymptote : x = 0
And, No horizontal asymptote.
Therefore, Function given in Option (B) matches the asymptotes given in the graph.
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Day and Night Kennel charges $20 per day plus a one-time food fee of $15 to board a pet. Bark Time Hotel charges $30 per day plus a one-time food fee of $5. Which system represents this real-world situation?
Answer:
See below.
Step-by-step explanation:
Let x represent the number of days.
Since Day and Night Kennel charges a fee of $20 per day and only a one-time fee of $15:
[tex]y=20x+15[/tex]
Where y represents the total cost, 20x represents the cost for staying x days and 15 is the initial one-time fee.
For Bark Time Hotel, similarly:
[tex]y=30x+5[/tex]
Again, y represents the total cost, 30x represents the cost for staying x days, and 5 is the initial one-time fee.
Thus, the system of equations is:
[tex]y=20x+15\\y=30x+5[/tex]
The system that represents this real-world situation is:
Cost = 20d + 15
Cost = 30d + 5
What is an equation?An equation contains one or more terms with variables connected by an equal sign.
Example:
2x + 4y = 9 is an equation.
2x = 8 is an equation.
We have,
The system that represents this real-world situation is:
Let d be the number of days the pet will be boarded.
For Day and Night Kennel:
Cost = 20d + 15
For Bark Time Hotel:
Cost = 30d + 5
In this system, d represents the number of days the pet will be boarded, the constant 20 represents the daily boarding fee charged by Day and Night Kennel, the constant 30 represents the daily boarding fee charged by Bark Time Hotel, the constant 15 represents the one-time food fee charged by Day and Night Kennel, and the constant 5 represents the one-time food fee charged by Bark Time Hotel.
Thus,
Cost = 20d + 15
Cost = 30d + 5
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At a certain golf course, the cost to rent a golf cart for h hours is given by c = 12h + 25. How much would a customer pay to rent a golf cart for 4 hours? Question 10 options: A) $37 B) $112 C) $73 D) $41
Answer:
c)$73
Step-by-step explanation:
You just have to substitute 4 in for h because h stands for how many hows. They're renting it for 4 hours.
Answer:
c) 73
Step-by-step explanation:
c=12(4 hours) + 25
c=48 + 25
c=73
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A rectangle's length is 3 more than it width, if the perimeter is 26 inches, what is the width of the rectangle.
Answer:
5 is the width i think
Step-by-step explanation:
g) 73 x -0.14 =
h) 57.1 x -0.23 -
i) -4300 x -1.23
j) 3.12 x 8.33
Suppose Neil Armstrong decided to throw a golf ball into the air while he was standing on the
moon and that the height of the golf ball was modeled by the equation below, where s is
measured in feet and t is measured in seconds s(t) = -2.72t2 + 26.9t + 6. Find the best
approximation for the instantaneous rate of change (velocity) of the golf ball at 7 seconds.
Answer:
At 7 seconds the instantaneous rate of change of the function s(t) with time which is the velocity is -11.18 m/s
Step-by-step explanation:
The given information on the height can be written as follows;
s(t) = -2.72·t² + 26.9·t + 6
Where;
s = The height (displacement) of the golf ball
t = The time taken during the motion of the golf ball
The velocity is found by finding the derivative of the displacement s as follows;
v = d(s(t))/dt = d(-2.72·t² + 26.9·t + 6)/dt = 2×(-2.72)×t + 26.9
When t = 7, v = 2×(-2.72)×7 + 26.9 = -11.18 m/s
Therefore the ball is coming down with 11.18 m/s speed at 7 seconds.
What is the perimeter of the rectangular with a length of 2.5 m and breadth of 1.6m
Answer:
Step-by-step explanation:
length of the rectangle = 2.5 m
breadth of the rectangle = 1.6 m
Perimeter of rectangle = 2( l + b )
= 2 × 4.1
= 8.2 m
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Answer: Option A & D are true statements.
Work:
For option A, it states 1 pound = 2.75. Now when we divide 16.50 by 6 we get 2.75, so option A is true.
Option B states 2.75 pounds = 1$. We already know this isn't true seeing as 2.75 pounds would equal 7.56, so option B is false.
Option C reads as 5 pounds equal 15.50. When we multiply 5 by 2.75, we get 13.75, so option C is also untrue.
Option D quotes 12 pounds equals 33. When we multiply 12 by 2.75, it equals 33, so this is a true statement!
Option E says the point 3,9 is on the graph, but its not. So this is not true.
Write the equation for a parabola that has x − intercepts (−2.2, 0) and (−0.6, 0) and y − intercept (0,3.3). URGENT
PLEASE ANSWER
Answer:
[tex]\bold{y=2.5x^2+7x+3.3}[/tex]
Step-by-step explanation:
Given:
Parabola with
x − intercepts (−2.2, 0) and (−0.6, 0)
and
y − intercept (0,3.3)
To find:
Equation of parabola ?
Solution:
We can use factored form to find the equation of the parabola.
[tex]y=a(x-\alpha)(x-\beta)[/tex]
Where [tex]\alpha, \beta[/tex] are the x intercepts.
Let use put
[tex]\alpha = -2.2\\\beta = -0.6[/tex]
[tex]y=a(x-(-2.2))(x-(-0.6))\\\Rightarrow y =a(x+2.2)(x+0.6)[/tex]
Now, let us put y − intercept (0,3.3) in the above equation to find the value of a.
[tex]\Rightarrow 3.3 =a(0+2.2)(0+0.6)\\\Rightarrow 33 =a(22)(0.6)\\\Rightarrow 3 = 2a\times 0.6\\\Rightarrow a = 2.5[/tex]
So, the equation becomes:
[tex]\Rightarrow y =2.5(x+2.2)(x+0.6)\\\Rightarrow \bold{y=2.5x^2+7x+3.3}[/tex]
Sam will take four science tests this quarter. Her scores on three of the tests are shown below. What does Sam need to score on the fourth test to ensure that she will have an average of 90% for all four tests?
Answer:
98%
Step-by-step explanation:
83%+91%+88%+?=90×4
262+?=360
?=360-262
?=98%
Answer:
98% i believe
Step-by-step explanation:
prove sin^6x+cos^6x+3 sin^2x cos^2x=1
Answer:
its a formulae
we know (sinx+cosx)^3= sin^3x +cos^3x+3sinxcosx(sinx+cosx)
(a+b)^3= a^3 +b^3+3ab(a+b)
Step-by-step explanation:
(sin^2x)^3 +cos^2x)^3+3sin^2x cos^2x(sin^2x+cos^2x)
according to formulae
(sin^2x+cos^2x)^3 {as we know sin^2x+cos^2x =1}
so the (1)^3= 1
{proved}
thank u
Answer: see proof below
Step-by-step explanation:
Use the formula for factoring a cubic: (a³ + b³) = (a + b)(a² - ab + b²)
and the formula for a perfect square: a² + 2ab + b² = (a + b)²
and the Pythagorean Identity: cos²x + sin²x = 1
Proof LHS → RHS
Given: sin⁶x + cos⁶x + 3sin²x cos²x
Regroup: (sin²x)³ + (cos²x)³ + 3sin²x cos²x
Factor Cubic: (sin²x + cos²x)(sin⁴x - sin²x cos²x + cos⁴x) + 3sin²x cos²x
Pythagorean Identity: 1(sin⁴x - sin²x cos²x + cos⁴x) + 3sin²x cos²x
Add like terms: sin⁴x + 2sin²x cos²x + cos⁴x
Regroup: (sin²x)² + 2sin²x cos²x + (cos²x)²
Factor Perfect Square: (sin²x + cos²x)²
Pythagorean Identity: (1)²
Simplify: 1
LHS = RHS: 1 = 1 [tex]\checkmark\\[/tex]
At what annual simple interest rate should a loan of Rs.5000 be given to receive the same interest that is received when a loan of Rs.6000 is given at an annual simple interest rate of 8%?(Rs is the money unit of sri lanka.)
Formula :-
[tex]\sf \: S.I \: = \frac{P.R.T}{100} \\ [/tex]
Given that :-
The interest received on Rs 5000 = interest received on Rs 6000 , when rate of interest on Rs 6000 is 8 % .
To Find :-
The rate of interest on rupees 5000 .
Solution :-
→ S.I = P.R.T/100
→ 5000.R. 1 / 100 = 6000 × 8 × 1 / 100
→ 50 R = 60×8
→ 50 R = 480
→ R = 480/ 50
→ Rate of interest = 9.6 %
So rate on Rs 5000 is 9.6 %
Two sides of a triangle measure 9 cm and 23 cm. Which could be the
measure of the third side of the triangle?
Answer:
h²=b²+p²
x²= 9²+23²
x²= 81+529
x²=610
X= √610
Choose the correct expression using the fewest number of bases possible that is equivalent to the current expression. Let x and y be positive integers and x>y. 11x11y=? Question 3 options: 11x+y 11x−y 11xy 11y−x
Answer:
11^(x-y)
Step-by-step explanation:
If there is a same number which is divided by the same number, but with different powers, then we subtracted down value from the upper one.
Example: 17^7/ 17^5
=> 17^(7-5)
=> 17^2
So, the answer to this question is 11^(x-y).
Ifteen bales of hale were loaded into a truck. Some of the bales weight 150 pounds, and some weighed 100 punds. Hpw many bales of 100 pounds and 150 pounds were loaded into the truck, total weight is 1900 pounds
Answer:
There are 7 bales of 100 pounds and 8 bales of 150 pounds hale
Step-by-step explanation:
Let the amount of bale of 100 pounds be x and the bale of hale of 150pounds be y
If fifteen bales of hale were loaded into a truck, then x+y = 15 ... 1
Also if some of the bales weight 150 pounds, and some weighed 100 pounds with total weight of pounds to be 1900 pounds, then mathematically;
150y + 100x = 1900
Dividing through by 100;
1.5y+x = 19 ..... 2
Solving equation 1 and 2 simultaneously;
x+y = 15 ... 1
1.5y+x = 19 .... 2
Subtracting 1 from 2
y-1.5y = 15-19
-0.5y = -4
Divide both sides by 0.5
-0.5y/-0.5 = -4/-0.5
y = 8
Substituting y = 8 into equation 1, we will have;
x+y = 15
x+8 = 15
x = 15-8
x = 7
Hence there are 7 bales of 100 pounds and 8 bales of 150 pounds hale
the distance a jet travels (d) varies directly with the number of hours (t) flown. a jet travels 1,350 miles in three hours write an equation that represents this direct variation
Answer:
The answer is 3,150
Step-by-step explanation:
You multiply 1350 with 7 and divide it by 3 and you get 3,150 as your answer.
s=450t is the equation that represents this direct variation.
What is Distance?The length along a line or line segment between two points on the line or line segment.
Given that the distance a jet travels (d) varies directly with the number of hours (t) flown.
A jet travels 1,350 miles in three hours.
Distance is one thousand three hundred fifty and the time is three hours.
The speed is 1350/3 which is equal to four hundred fifty.
We need to write the equation that represents this direct variation.
s=450t
Hence, s=450t is the equation that represents this direct variation.
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For Every 6 dogs there are 15 cats at the animal shelter. Sam counted 45 cats. so how many dogs are there?
Answer:18
Step-by-step explanation:
Answer:
5
Step-by-step explanation:
that is the answer
Equation of line joining the origin and centroid of a triangle having vertices (1,
-2), (3, 5) and (5, -6).
Step-by-step explanation:
the formulae for finding centroid is (x1+x2+x3/3 , y1+y2+y3/3)
so the coordinates of centroid is (1+3+5/3 , -2+5-6/3)
(3,-1) and other point is the origin (0,0)
we know ,the equation is
x-x1/x1-x2= y-y1/y1-y2
x-3/3-0= y-(-1)/-1-0
x-3/3=y+1/-1
-x+3=3y+3
or -x+3y=0
or x-3y=0(multiplying -1 in both sides)
so the eq is x-3y=0 ans
thank u
The plot below represents the function f(x):
Evaluate f(-1):
f(x) represents x-axis. So, for f(-1), look the point of -1. Then vertically, it reaches the point of -3 which is in the y-axis.
Answer is -3.
draw a ven diagram to show relation between irrational number rational and real number
Answer:
Real numbers include both Rational and Irrational number sets.
Rational and Irrational numbers sets are independent from each other.
See the diagram attached.
40÷{19−1+(6÷4−1)} PEMDAS form
Answer & Step-by-step explanation:
PEMDAS:
Parentheses
Exponents
Multiplication and Division left to right
Addition and Subtraction left to right
We have two forms of grouping in the expression. Do the inner-most one first, still following PEMDAS within the grouping symbol:
Simplify division:
[tex]6/4=1.5\\1.5-1=0.5\\[/tex]
Re-insert:
[tex]40/(19-1+0.5)[/tex]
Simplify subtraction and addition within parentheses:
[tex]19-1+0.5\\18+0.5\\18.5[/tex]
Re-insert:
[tex]40/18.5[/tex]
Simplify division:
[tex]40/18.5=2.162162162162162162.....[/tex]
:Done
Describe how the shape moves to get from its position in each frame to the next.
Answer:
1 to 2.
We can see that the figure starts at the bottom left, and then moves to the bottom right.
So the vertical position remains constant, and the horizontal position changed, this can be a reflection around the vertical axis.
2 to 3.
Now the figure goes from the bottom right and moves to the top right, not only that, in (2) the figure is facing up, and in (3) the figure is facing down, then we have a reflection around the horizontal axis.
3 to 4.
Similar to the first case, this is a reflection over the vertical axis.
4 to 5.
Similar to the second case, this is a reflection over the horizontal axis.
(Something to notice, the movements can be called "Rotations over the ___ axis". I used reflection because it is specific for this type of motion, while rotation can be used to describe really complex types of motion)
20 points! Thanks for the help :)
Answer:
Step-by-step explanation:
a) (-2x³ + x - 5)(x³ - 3x - 4)
= (-2x³) (x³ - 3x - 4) + x(x³ - 3x - 4) - 5(x³ - 3x - 4)
= -2x³*x³ - (-2x³)*3x - (-2x³)*4 + x*x³ - x*3x - x*4 + x³ * (-5) - 3x*(-5) -4*(-5)
= -2x⁶ + 6x⁴ + 8x³ + x⁴ - 3x² -4x - 5x³ + 15x + 20 {add like terms}
= -2x⁶ + 6x⁴ + x⁴ + 8x³ - 5x³ - 3x² - 4x + 15x + 20
= -2x⁶ + 7x⁴ + 3x³ - 3x² + 11x + 20
Hint: When multiplying two terms, multiply the coefficient, and add the powers of the variables {[tex]a^{m}*a^{n}=a^{m+n}[/tex] }
-2x³*x³ = (-2*1) * [tex]x^{3+3}[/tex] = -2x⁶
b) Yes , same because of commutative property of multiplication
Answer:
[tex]-2x^6+7x^4+3x^3-3x^2+11x+20[/tex]
Step-by-step explanation:
a) We can expand [tex](-2x^3 + x - 5) (x^3 - 3x - 4)[/tex], getting [tex]-2x^6+6x^4+8x^3+x^4-3x^2-4x-5x^3+15x+20[/tex]. We can then combine like terms, getting [tex]-2x^6+7x^4+3x^3-3x^2+11x+20[/tex].
b) Yes it is the same, as it doesn't matter the order if you multiply two polynomials. It will always be the same.
The second and third terms of a G.P is 6 times the fourth term. Find the possible values of the common ratio.
Answer:
-1/3 or 1/2.
Step-by-step explanation:
Second term = ar, the third = ar^2 and the fourth = ar^3.
So we have the equation:
ar + ar^2 = 6ar^3
r + r^2 = 6r^3
6r^3 - r^2 - r = 0
r(6r^2 - r - 1) = 0
(3r + 1 )(2r -1) = 0
r = -1/3, 1/2.
I need help finding the weather it is continuity or not
Answer:
it is discontinuety bcz at 1,4 and 6 it is discontinued
Giles is making tacos for dinner and bought some beef and chicken. At the store, he bought twice as much beef as chicken. The chicken costs $1.85 per pound, and the beef costs $3.70 per pound. Before sales tax, Giles spent a total of $12.95 on beef and chicken. The system of equations below represent the pounds of chicken, x, and pounds of beef, y, that Giles purchased. Part A: Use the ray tool to graph the system of equations on the coordinate plane. Part B: Use the point tool to select the approximate pounds of beef Giles purchased.
Answer:
The answer is below
Step-by-step explanation:
Chicken costs $1.85 per pound, and the beef costs $3.70 per pound. Let x represent the pounds of chicken and y represent the pound of beef. If he spent a total of $12.95, therefore:
1.85x + 3.7y = 12.95 (1)
He bought twice as much beef as chicken, therefore:
y = 2x
y - 2x = 0 (2)
Solving eqn 1 and eqn 2 simultaneously. Multiply equation (2) by 3.7 and subtract from equation (1)
9.25x = 12.95
x = 1.4 pounds
Also substitute x = 1.4 in equation 2:
y - 2(1.4) = 0
y = 2(1.4)
y = 2.8 pounds
The graph was plotted using geogra, the y coordinate of the point of intersection of the two lines, is the approximate pounds of beef.
Answer: Part A. First line= (0,0), (1,2). Second line= (0,3.5), (1,3)
Part B. 2.75 pounds
Step-by-step explanation: It's correct.