Answer:
60
Step-by-step explanation:
Mr Jone's home distance is 60 miles away from his appointment place .
Distance = Speed x Time
Distance planned & distance covered is same.
Time covered is 20 minutes more than time planned ; Actual Speed is 15mph lower than planned speed (60 mph) , ie = 45 mph.
Let the planned time be = t , Actual time = t + 20 mints = t + 20 / 60 = t + 1/3 = 4 t / 3
As distance is same : 60 t = 45 ( 4t / 3)
60t = 60t
t = 1 hour
Distance = Speed x Time :
60 x 1 = 45 ( 4/3) = 60 miles
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Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. After how many weeks will Gina have exactly $700 in her account, excluding interest?
Answer:
After 33 weeks.
Step-by-step explanation:
Let w be number of weeks.
We have been given that Gina opened a bank account with $40. She plans to add $20 per week to the account and not make any withdrawals. So the balance after w weeks will be 20w+40.
To figure out number of weeks Gina will have exactly $700 in her account, we will equate the balance after w weeks to 700.
[tex]20w+40=700[/tex]
Let us subtract 40 from both sides of equation.
[tex]20w+40-40=700-40[/tex]
[tex]20w=660[/tex]
Upon Dividing both sides of our equation by 20 we will get,
[tex]\frac{20w}{20}=\frac{660}{20}[/tex]
[tex]w=\frac{660}{20}[/tex]
[tex]w=33[/tex]
Therefore, after 33 weeks Gina will have exactly $700 in her account, excluding interest.
solve f(x)=x²+7x+12/-x²-3x+4
[tex]x^2+7x+12=x^2+4x+3x+12=x(x+4)+3(x+4)=(x+4)(x+3)\\\\-x^2-3x+4=-(x^2+3x-4)=-(x^2+4x-x-4)\\\\=-[x(x+4)-1(x+4)]=-(x+4)(x-1)\\\\f(x)=\dfrac{x^2+7x+12}{-x^2-3x+4}=\dfrac{(x+4)(x+3)}{-(x+4)(x-1)}\\\\\text{The domain:} x\neq-4\ and\ x\neq1\\\\canceled\ (x+4)\\\\f(x)=\dfrac{x+3}{-(x-1)}=-\dfrac{x+3}{x-1}\ for\ x\neq-4\ and\ x=1[/tex]
Can someone please help with these 2 math questions? :)
Answer:
4. 8.8 years
5. 8.6 meters
Step-by-step explanation:
4. The process of solving the equation f(x) = g(x) gives rise to a 4th-degree equation. Those are best solved using some sort of machine solver. A graphing calculator is often a good place to start. If you're going to do that anyway, you may as well start with a graphical solution to the question.
A plot of the two curves finds they intersect at about x = 8.8. (See the first attachment.) This avoids the extraneous solutions introduced by the process of eliminating the radical.
___
5. Analytical solution is simpler here, but the graphing calculator is faster yet. It shows the two rocks are at the same height at 8.6 meters (if they're launched at the same time).
... f(x) = g(x)
... -4.9x^2 +17 = -4.9x^2 +13x
... 17 = 13x . . . . . add 4.9x^2
... 17/13 = x . . . . time when rocks meet
... f(17/13) = -4.9(17/13)^2 +17 = -1416.1/169 +17 ≈ 8.62071
... f(17/13) ≈ 8.6 . . . . height at which rocks meet
A total of 17,100 seats are still available for the next hockey game. If 62% of the tickets are sold, how many seats are in the arena? A. 7,100 seats B. 7,900 seats C. 45,000 seats D. 27,900 seats
Answer:
We have
seats x ( 62 / 100 ) = (seats - 17,100);
seats x 62 = 100 x (seats - 17,100);
seats x 62 = seats x 100 - 1710000;
1,710,000 = seats x 38;
seats = 1,710,000 ÷ 38;
seats = 45,000;
The correct answer is c. 45,000 seats;
Step-by-step explanation:
45, 000 A for plato users
Step-by-step explanation:
Trust me im Master chief
line A and line B are parallel. If line A is 2x + 3y =10, what is the equation for line B if it passes through the point (-6,8)
Let us Represent the Line A in the Standard form : y = mx + c
where : m is the Slope of the Line and c is the y-intercept
Given : Equation of Line A is 2x + 3y = 10
[tex]\bf{\implies y = \frac{-2}{3}x + \frac{10}{3}}[/tex]
Comparing with the Standard form, We can notice that :
Slope of Line A [tex]\bf{= \frac{-2}{3}}[/tex]
We know that : Parallel lines have Same Slope
Given : Line A and Line B are Parallel
⇒ Slope of Line B [tex]\bf{= \frac{-2}{3}}[/tex]
Given : Line B passes through the Point (-6 , 8)
We know that : Equation of a Line passing through a Point (x₀ , y₀) and having Slope 'm' is given by : y - y₀ = m(x - x₀)
Here : x₀ = -6 and y₀ = 8 and Slope(m) [tex]\bf{= \frac{-2}{3}}[/tex]
Equation of Line B is :
[tex]\bf{\implies y - 8 = \frac{-2}{3}(x + 6)}[/tex]
⇒ 3y - 24 = -2x - 12
⇒ 2x + 3y = 12
A graph is translated according to the following rule. Describe the translation.
(x, y) → (x, y – 3)
The graph is translated three units to the right.
The graph is translated three units to the left.
The graph is translated three units down.
The graph is translated three units up.
Answer:
The graph is translated three units down.
Step-by-step explanation:
We know that, a 'Translation' is an transformation where the figure or graph is shifted in any direction.
According to our question (x,y) becomes (x, y-3) , this means that the graph value of 'x' co-ordinate remains same and the value of 'y' co-ordinate is decreased by 3 units.
So, the graph is shifted three units downwards i.e. it is translated three units down.
Brooke has to set up 70 chairs in equal rows for the clas talent show. But, there is not room for more than 20 rows. What are the possible number of rows that Brooke could set up?
Kristy asks Lonnie to think of a number, and 3 to it, multiply the sum by 2, and then subtract 6. Let n stand for Lonnie's starting numbers. Which expression represents Lonnie's final number?
Answer:
2(n + 3) - 6 is the expression that represents the final number.
Step-by-step explanation:
-Given the number Lonnie thinks of at the beginning is 'n'-
1) adding 3 to n
sum = n + 3
2) multiply the sum by 2
sum = 2(n + 3)
3) subtract 6
sum = 2(n + 3) - 6.
Answer: 2(n + 3) - 6
Step-by-step explanation:
Tommy notices that he reads 2/3 page in a minute. At the rate, how long will it take him to read 12 pages
Answer:
18 minutes
Step-by-step explanation:
To do this, you need to divide 12 by the two thirds to find out how many 2/3 there are in 12, giving the amount of minutes it takes:
12 ÷ 2/3 = 18
So it would take him 18 minutes!
Please help ASAP!
What is the value of cosθ given that (−5, −4) is a point on the terminal side of θ ?
A). 5√41/41
B). −4√41/41
C). 4√41/41
D). −5√41/41
Answer:
D
Step-by-step explanation:
The value of the trigonometric expression cos θ, when (-5, -4) is a point on the terminal side of θ is -5√41/41. Hence, option D is the right choice.
What are trigonometric expressions?
Trigonometric expressions are the ratios of the sides of a right triangle, which are always constant despite the increase or decrease in the size of its sides.
These are the trigonometric ratios:
sin θ = perpendicular/hypotenusecos θ = base/hypotenusetan θ = sin θ/cos θ = perpendicular/basecot θ = 1/tan θ = cos θ/sin θ = base/perpendicularsec θ = 1/cos θ = hypotenuse/basecosec θ = 1/sin θ = hypotenuse/perpendicular.How to solve the question?In the question, we are asked to find the value of cos θ, given that (-5, -4) is a point on the terminal side of θ.
This means that we; are in quadrant III. As we know, cos θ is negative in the 3rd quadrant.
The base is the distance of the x-coordinate from the origin, that is, 5 units.
The perpendicular is the distance of the y-coordinate from the origin, that is, 4 units.
By Pythagoras' Theorem,
Hypotenuse² = Base² + Perpendicular²,
or, Hypotenuse² = 5² + 4²,
or, Hypotenuse² = 25 + 16,
or, Hypotenuse = √41.
As we know, cos θ = Base/Hypotenuse = 5/√41 = 5√41/41.
Because of the 3rd quadrant, we will take, cos θ = - 5√41/41.
Thus, the value of the trigonometric expression cos θ, when (-5, -4) is a point on the terminal side of θ is -5√41/41. Hence, option D is the right choice.
Learn more about trigonometric expressions at
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Sara drives 425 miles in 6 hours and 45 minutes. What is her average rate of speed? Round your answer to the nearest whole number.
Answer: 63 miles per hour (mph)
6 hours + 45 minutes = 6 hrs + 0.75 hrs = 6.75 hrs
Divide the distance (425 miles) over the time (6.75 hours) to get the speed. You must convert the time value to a single unit rather than a mixed unit of hours and minutes. So we get 425/6.75 = 62.96926 which rounds to 63
A square lawn is surrounded by a path 2.5 m wide . If the area of the path is 165 m sq, find the area of the lawn
What is the perimeter of a triangle with the given side lengths? s1 = x + 4 cm s2 = 3x + 1 cm s3 = 7x + 3 cm P = x + cm
Answer:
11x+8 cm = Perimeter
Step-by-step explanation:
A triangle has 3 sides. We add up all three sides to get the perimeter.
s1+s2+s3 = Perimeter
(x+4) +( 3x+1) + (7x+3) = Perimeter
Combine like terms
11x+8 = Perimeter
Answer:
P = 11x + 8 cm
Step-by-step explanation:
The perimeter of a triangle is the sum of the lengths of the three sides.
... P = s1 + s2 + s3
... P = (x +4 cm) +(3x +1 cm) +(7x +3 cm) . . . . substitute for s1, s2, s3
... P = x(1 +3 +7) + cm(4 + 1 + 3) . . . . . . collect terms
... P = 11x + 8 cm
The bus comes at 6:55. It takes meg 19 minutes to get to the bus stop. What time would she have to leave at to catch the bus?
Answer:
6 hrs 36 mins
Step-by-step explanation:
Bus at 6:55
Minutes to get to the bus 19.
deduct 19 Minutes from 6:55 = 6 hrs 36 mins
Under a dilation, the point (2, 6) is moved to (6, 18).
What is the scale factor of the dilation?
Divide the new X value by the original x value:
6 / 2 = 3
Then check that with the Y value:
Original Y value = 6, 6 x 3 = 18, which is the new Y value.
This means the scale factor is 3.
Can someone help me with 1-3
Write an explicit formula for the sequence -13, -6, 1, 8, ...
a) an = -13n+7
b) an = -13+(n+7)
c) an = -13+7(n-1)
d) an = -13n+7
Answer:
c) an = -13+7(n-1)
Step-by-step explanation:
We can use the formula for arithmetic sequences
an =a1+d(n-1)
where a1 is the first term in the sequence
d is the common difference
and n is the term number
a1 is -13
d is found by taking the second term and subtracting the first term
d = -6--13
= -6+13
d=7
We are adding 7 each time
Substituting what we know,
an = -13 + 7(n-1)
The answer is:
c) [tex]a_{n}=-13+7(n-1)[/tex]The matrix shows the number of different basketball shots three players made in two minutes. These players want to double these results. Which matrix shows what the players want to do?
Answer:
B
Step-by-step explanation:
Javi [5 1]
Victor [3 2]
Chris [4 2]
A.
[10 1]
[6 2]
[8 2]
B.
[10 2]
[6 4]
[8 4]
C.
[7 3]
[5 4]
[6 4]
D.
[10 1]
[3 2]
[4 2]
Answer:B. [10 2]
[6 4]
[8 4]
Step-by-step explanation:
Javi [5 1]
Victor [3 2]
Chris [4 2]
A.
[10 1]
[6 2]
[8 2]
B.
[10 2]
[6 4]
[8 4]
C.
[7 3]
[5 4]
[6 4]
D.
[10 1]
[3 2]
[4 2]
Explanation:
As a general rule, to double, triple or as the case may be, the result of a matrix, we apply what is known in Maths as scalar multiplication.
Scalar multiplication seeks to multiply the entries in a matrix by a scalar. The resulting matrix is called the scalar product of the original matrix.
For instance:
Let matrix A = [a b] [c d] and k be a scalar.
The matrix kA is called a scalar product of the matrix, A and the constant, k is defined as:
kA = k [a b] [c d]
= [ka kb] [kc kd]
So, for the given question, the best option would be the matrix that depicts a scalar multiple of 2 of the original matrix entry. Option B.
I.e:
Javi = 2[5 1] = [2*5 2*1] = [10 2]
Victor= 2[3 2] = [2*3 2*2] = [6 4]
Chris = 2[4 2] = [2*4 2*2] = [8 4]
heyyy help pls with pciutreeeee
Answer:
12 Fetches
Step-by-step explanation:
this one is easy but you probably overthought it,
since 2 is half of 4 then you would just multiply everything by 2
let's just say that didn't work right, for these types of problems you have to make a proportion so in this case it would be 2 minutes/6 fetches= 4 minutes/ x fetches. then you solve by cross multiplication.
Which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16?
(–4, 6)
(6, –4)
(–4, –6)
(–6, –4)
Answer:
(–6, –4)
Step-by-step explanation:
After converting the two equations from standard form to slope -int form I graphed the two equations on a coordinate plane and found the intersection (in this case solution) of the equation to be (–6, –4)
Answer:
(–6, –4)
Step-by-step explanation:
This pair of linear equations may be solved simultaneously by using the elimination method. This will involve ensuring that the coefficient of one of the unknown variables is the same in both equations.
It may be solved by substitution in that one of the variable is made the subject of the equation and the result is substituted into the second equation.
Using the substitution method, make y the subject in the first equation
y = 5x + 26
substitute into the second equation
2x -7(5x + 26) = 16
-33x - 182 = 16
-33x = 16 + 182
-33x = 198
x = 198/-33
x = -6
since y = 5x + 26
y = 5(-6) + 26
= -30 + 26
= -4
hence (x,y) = (-6,-4)
What is the vertex and axis of symmetry for y=4x^2-12x+9?
Answer:
axis of symmetry x=3/2
vertex (3/2, 0)
Step-by-step explanation:
to find the axis of symmetry we use h = -b/2a
where ax^2 + bx+c
h = -(-12)/2(4)
h= 12/8
h = 3/2
the axis of symmetry is x = 3/2
the x coordinate of the vertex is h x=3/2
to find k, the y coordinate of the vertex, substitute x=3/2 into the equation
y=4x^2-12x+9
y=4(3/2) ^2-12(3/2)+9
= 4 (9/4) - 6*3 +9
= 9-18+9
= 0
the vertex (3/2, 0)
Which equation is a quadratic model for the data set? Hint: Use a graphing calculator or a spreadsheet program.
Data table
Answer:
Equation for the quadratic model for the data set is;
[tex]y = 1.0774x^2-0.9393x+0.6905[/tex]
Step-by-step explanation:
A Quadratic regression is the process of finding the equation of the parabola that best fits the set of data.
An equation is in the form of: [tex]y=ax^2+bx+c[/tex] where a≠0.
You just enter the x-coordinates and y-coordinates in your graphing calculator and
then do a quadratic regression.
The equation of the parabola that best approximates the points is
:
[tex]y = 1.0774x^2-0.9393x+0.6905[/tex]
Now, plot the graph of the above equation as shown below in the figure.
Also you can see that the [tex]R^2[/tex] value for the above data is, 0.994
PLEASE HELP ASAP!!! CORRECT ANSWERS ONLY PLEASE!!
Simplify.
Answer:
(B): (x - 2)/(x + 1)
Step-by-step explanation:
The numerator is x^2 + 5x - 14. That is equal to (x - 2)(x + 7).
The denominator is x^2 + 8x + 7. That is equal to (x + 1)(x + 7).
You can then eliminate (x+7) to get (x - 2)/(x + 1).
Answer: B
Step-by-step explanation:
[tex]\dfrac{x^{2}+5x-14}{x^{2}+8x+7}[/tex]
[tex]=\dfrac{(x+7)(x-2)}{(x+7)(x+1)}[/tex]
[tex]=\dfrac{(x-2)}{(x+1)}[/tex]
Light travels at a speed of 1.17 × 107 miles per minute. Pluto's average distance from the Sun is 3,670,000,000 miles. On average, how long does it take sunlight to reach Pluto? Enter your answer in scientific notation, and, if necessary, round your multiplier to the nearest hundredth.
Speed is the rate of change of distance over time.
It will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.
The given parameters are:
[tex]\mathbf{Speed = 1.17 \times 10^7 miles/mins}[/tex]
[tex]\mathbf{Distance = 3670000000 miles}[/tex]
Speed is calculated as:
[tex]\mathbf{Speed = \frac{Distance}{Time}}[/tex]
Make Time the subject
[tex]\mathbf{Time = \frac{Distance}{Speed}}[/tex]
Substitute values for Speed and Distance
[tex]\mathbf{Time = \frac{3670000000\ miles}{1.17 \times 10^7 miles/mins}}[/tex]
[tex]\mathbf{Time = \frac{3670000000\ mins}{1.17 \times 10^7 }}[/tex]
Rewrite as:
[tex]\mathbf{Time = \frac{3.67\times 10^9\ mins}{1.17 \times 10^7 }}[/tex]
Apply law of indices
[tex]\mathbf{Time = \frac{3.67\times 10^{9 - 7}\ mins}{1.17}}[/tex]
Divide
[tex]\mathbf{Time = 2.20 \times 10^{2}\ mins}[/tex]
Hence, it will take [tex]\mathbf{2.20 \times 10^{2}}[/tex] minutes to get to Pluto.
Read more about speed and rates at:
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Given h(x)=5(x-6)^2+2 what transformations were done compared to the parent function f(x)=x^2?
Answer:
1. Translation 6 units to the right.
2. Stretch by a factor 5.
3. Translation 2 units up.
Step-by-step explanation:
Consider parent function [tex]f(x)=x^2.[/tex]
1. Translate the graph of the function 6 units to the right. Then you get the function [tex]f_1(x)=(x-6)^2.[/tex]
2. Stretch the graph of the function [tex]f_1(x)=(x-6)^2[/tex] by a factor 5 and get the function [tex]f_2(x)=5(x-6)^2.[/tex]
3. Translate the graph of the function [tex]f_2(x)=5(x-6)^2[/tex] 2 units up to fet the function [tex]h(x)=5(x-6)^2+2.[/tex]
Sinea wants to spend money using the same ratios as on her last trip to the car nivel. If she spends $26 on games,how much will she spend on souvenirs? CHART Snacks Games Souvenirs Sinea $5 $8 $12 Ren. $10 $8 $20
Answer:
A. Sinea spends $26 on games, she wants to keep the same ratio, how much does she spend on souvenirs?
A- (snacks- 16.25) (games- 26) (souvenirs- 39)
B. Ren spends $5 on souvenirs, he wants to keep the same ratio, how much does he spend on snacks
B- (snacks- 2.5) (games- 2) (souvenirs- 5)
C. Both spend $40 on snacks, they want to keep their original ratio, who spends more on souvenirs?
C. Ratios
Sinea- (snacks- 40) (game- 64) (souvenirs- 96)
Ren- (snacks- 40) (game- 32) (souvenirs- 80)
Which person would be eligible to run for president of the United States in the Election of 2020?
A) Susan, born in 1988 in Texas, has lived in Georgia for 15 years
B)George, a naturalized citizen, has lived in New York for 20 years
C) Tiffany, born in 1973 in Nebraska, has lived in the U.S. for 45 years
D)John, a legal immigrant, has lived in the U.S. for 14 consecutive years
Answer:
C. Tiffany, born in 1973 in Nebraska, has lived in the U.S. for 45 years
Step-by-step explanation:
its right bro
1. What is the radical form of the expression 4 2/3?
2. What function equation is represented by th graph?
Answer:
1. [tex]\sqrt[3]{4^2}[/tex]
2. Answer A
Step-by-step explanation:
1. A fraction exponent can be represented using a radical. The base number is the number in the radical. The numerator of the fraction is the exponent inside the radical. The denominator is the type of radical.
[tex]4^{\frac{2}{3} }[/tex]
[tex]\sqrt[3]{4^2}[/tex]
2. An exponential always crosses at (0,1) This function crosses at (0.6) meaning it has shifted up 5 units or +5. These means only answer options A and D are possible solutions. Also, since the graph starts high and ends low and leveling out, this means the base is less than 1. Only 3/4 is less than 1. Answer A is the solution.
Please answer quickly, more might be coming soon. 50 Points!
Answer:
2) ∠SDH and ∠SDT are right angles because SD ⊥ HT.
3) [tex]\bar{SH}\cong \bar{ST}[/tex] as it is given in the question.
4) [tex]\bar{SD}\cong \bar{SD}[/tex] is the reflexive property.
5) ΔSHD ≅ ΔSTD by RHS congruency.
Step-by-step explanation:
Given in the question:
[tex]\bar{SH}\cong \bar{ST}\\\bar{SD}\perp \bar{HT}[/tex]
In ΔSHD and ΔSTD
[tex]\bar{SH}\cong \bar{ST}[/tex] (Given)
[tex]\angle SDH\cong \angle SDT=90^o[/tex] (SD ⊥ HT)
[tex]\bar{SD}\cong \bar{SD}[/tex] (Common)
Therefore, [tex]\Delta SHD\cong \Delta STD[/tex] (By RHS rule)
Reflexive property of congruency is defined as the property in which something is equal to itself. Hence, the reflexive property of these two triangles is [tex]\bar{SD}\cong \bar{SD}[/tex]
[15 POINTS] A rectangle has a width w and a length that is two more than its width. what is the perimeter of the rectangle? Write and simplify an expression.
Answer: P = 4w + 4
Step-by-step explanation:
width (w) = w
length (L) = w + 2 (2 more than its width)
Perimeter (P) = 2L + 2w
P = 2L + 2w
= 2(w + 2) + 2(w)
= 2w + 4 + 2w
= 4w + 4