9514 1404 393
Answer:
a) x = ±5
b) x = ±√11 ≈ ±3.317
Step-by-step explanation:
Since we want x for some function value, it is convenient to determine the inverse function.
x = g(y)
x = y^2 -5
x +5 = y^2
y = ±√(x +5)
__
a) x = ±√(20 +5) = ±5
b) x = ±√(6 +5) = ±√11 ≈ ±3.317
Find the surface area of each prism. I'll give brainliest if you get it right.
Answer:
There's only one prism? But the answer is 366.
Step-by-step explanation:
39+39+27+27+117+117= 366
Answer:
368
Step-by-step explanation:
4. Jim and Kirk are playing a card game where they trade chips. At the beginning of the game, Jim has four times as many chips as Kirk does. After Kirk wins the game, Jim gives Kirk 18 of his chips, at which point they now have the same number of chips. How many did Kirk have to begin with?
(a) If j represents the original number of chips Jim had and k represents the original number of chips that Kirk had, then write an equation that models the amount of chips they originally had. Explain your equation.
(b) The equation j k − = + 18 18models the scenario after Kirk wins the game. Explain why.
(c) Determine how many chips both Kirk and Jim started with.
Answer:
(a) [tex]j = 4k[/tex]
(b) [tex]4k - 18 = 18 + k[/tex]
(c) Jim initially had 48; Kirk initially had 12
Step-by-step explanation:
Given
[tex]j = Jim[/tex]
[tex]k=Krik[/tex]
Solving (a): An equation for the amount they originally had.
From the question, we understand that j is 4 times as many as k.
Mathematically, this is:
[tex]j = 4 * k[/tex]
[tex]j = 4k[/tex]
Solving (b): Equation after Kirk wins
Initially Kirk had k.
To get the new expression, we add 18 to k.
This gives: 18 + k
In the same vein, Jim's number of chirps will reduce by 18.
Initially, Jim had j chirps (or 4k chirps)
To get the new expression, we subtract 18 from j.
This gives: j - 18
So, the equation is:
[tex]j - 18 = 18 +k[/tex]
Solving (c): Number of chirps they started with.
In (b), we have:
[tex]j - 18 = 18 +k[/tex]
Substitute 4k for j
[tex]4k - 18 = 18 + k[/tex]
Collect Like Terms
[tex]4k - k = 18 + 18[/tex]
[tex]3k = 36[/tex]
Divide both sides by 3
[tex]k =12[/tex]
Substitute 12 for k in [tex]j = 4k[/tex]
[tex]j = 4 * 12[/tex]
[tex]j = 48[/tex]
The 25 students in Mr. Martinez’s class vote on their favorite farm animal. 40% like pigs. How many students like pigs?
Answer:
10
Step-by-step explanation:
PLEASE HELP ME ITS DUE IN 20 MINUTES ( 30 POINTS )
PRACTISE NOW 11
Ex
15
Mr Lee drove from City P to City Q, which are 600 km apart. During his return journey,
his average speed was increased by 7 km/h and the time taken was 15 minutes less.
() If he drove at an average speed of x km/h on his journey from City P to City Q,
formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.
(ii
) Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to
2 decimal places.
(iii) Find the time taken for the return journey.
Answer:
i. x² + 7x - 16800 = 0 ii. x = 126.16 km/h or -133.16 km/h iii. 5.01 h
Step-by-step explanation:
i. If he drove at an average speed of x km/h on his journey from City P to City Q formulate an equation in x and show that it reduces to x2 + 7x – 16 800 = 0.
For the first journey from City P to City Q, with Mr Lee moving at an average speed of x km/h, he reaches there in time, t and covers the distance, d = 600 km
So, xt = 600 (1)
On his return journey from City Q to CIty P, his average speed increases by 7 km/h, so it is (x + 7)km/h and his time is 15 minutes less than his first journey. 15 min = 15/60 h = 0.25 h, we have that his time for the journey is (t - 0.25) h. Since the distance covered is the same d = 600 km,
We have (x + 7)(t - 0.25) = 600 (2)
Expanding the brackets, we have
xt - 0.25x + 7t - 0.25(7) = 600
xt - 0.25x + 7t - 1.75 = 600
From (1) t = 600/x and xt = 600
Substituting these into the equation, we have
600 - 0.25x + 7(600/x) - 1.75 = 600
simplifying
-0.25x + 4200/x - 1.75 = 600 - 600
-0.25x + 4200/x - 1.75 = 0
multiplying through by x, we have
-0.25x² + 4200 - 1.75x = 0
dividing through by -0.25, we have
-0.25x²/-0.25 + 4200/-0.25 - 1.75x/-0.25 = 0
x² - 16800 + 7x = 0
re-arranging, we have
x² + 7x - 16800 = 0
ii. Solve the equation x² + 7x - 16 800 = 0, giving both your answers correct to 2 decimal places.
Using the quadratic formula, we solve x² + 7x - 16800 = 0 for x
So, [tex]x = \frac{-7 +/-\sqrt{7^{2} - 4 X 1 X -16800} }{2 X 1}\\x = \frac{-7 +/-\sqrt{49 + 67200} }{2} \\x = \frac{-7 +/-\sqrt{67249} }{2} \\x = \frac{-7 +/- 259.32}{2} \\x = \frac{-7 + 259.32}{2} or x = \frac{-7 - 259.32}{2} \\x = 252.32/2 or x= -266.32/2\\x = 126.16 km/hor x = -133.16 km/h[/tex]
So, x = 126.16 km/h or -133.16 km/h
iii. Find the time taken for the return journey
The time taken for the return journey is t' = t + 0.25. Now. t = 600/x
Since x cannot be negative, we use x = 126.16 km/h.
So, t = 600/x = 600/126.16 = 4.76 h
t' = t + 0.25
t' = 4.76 + 0.25
t' = 5.01 h
what is the minimum value of the parabola y = x^2 + 10 ?
What is the slope????
Answer:
-6
Step-by-step explanation:
is that quizzes join lol
Someone please help and please make sure the answer is right :(
Answer:
it's 11
Have a good day!!
Figure ABCD is a rectangle. Find the value of x.
X= [?]
the answer is
x=2
qwertyuioplkjhgfdsazxcvbnmzxcvbnmasdfghjkgfwertyuytrewertyujhgfdsdefgbhgvftcdrxsxdrcftvgyvftcx4f
3rd times the charm. Someone please help me.
50 PTS BRAINLIEST
Use Desmos to graph the following system of equations. Paste a link to your Desmos graph.
y = 2/3x-2
y = 2/3x+5
How many solutions does the graph have?
Answer:
it has 5 hopefully this helps you with work
Answer:
No solutionsStep-by-step explanation:
Given lines:
y = 2/3x-2 y = 2/3x+5These have same slopes of 2/3 and therefore are parallel, so no intersection. There is no solution if lines don't intersect.
The graph is attached as well to show lines are parallel.
PLS HELP I REALLY NEED IT RNNNNNN 20 POINTSSS
Which function matches the mapping shown?
A) f(x) = 2x
B) f(x) = 4x
C) f(x) = x4
D) f(x) = x + 4
Answer:
B.f(x)=4x
Step-by-step explanation:
Multiply x value by 4
solve : 3x - 3 = 2x
if you can show workings that would be great thank you !
Answer:
3
Step-by-step explanation:
3x-3=2x
3x-2x=3
x=3
Answer:
x=3
Step-by-step explanation:
3x - 3 = 2x
-3x -3x
-3 = -x
The x cannot be a negative so you divide both sides by -1 and then the answer becomes x=3
Fill in the missing number in this newspaper report:
Houses cost £100 000 one year ago
They now cost £
This is a 25% increase
How much does it now cost ?
Answer:
£125000
Step-by-step explanation:
Original cost of house = £100 000
Percent increase = 25%
Increase in price = 25% of 100,000
Increase in price = 0.25 * 100,000
Increase in price = 25000
New cost = original cost + Increment
New cost = 100,000 + 25,000
New cost = 125,000
Hence it now cost £125000
A billiard ball is struck by a cue. It travels 100 cm before ricocheting off a rail and traveling another 100 cm into a corner pocket. The angle between the path as the ball approaches the rail and the path after it strikes the rail is 45 degrees. How far is the corner pocket from where the cue initially struck the ball?
Answer:
76.53 cm
Step-by-step explanation:
From the question, the triangle formed has 2 sides and an included angle ;
Angle, θ = C = 45°
We use cosine rule :
Taking the side to find as c
a = 100 ; b = 100
From cosine rule :
c = sqrt(a² + b² - 2abCosC)
c = sqrt(100² + 100² - 2(100*100)Cos45
c = sqrt(10000 + 10000 - 20000 * 0.7071067)
c = sqrt(20000 - 14142.135)
c = sqrt(5857.865)
c = 76.536690
c = 76.53 cm
Suppose the ratio of Lev's age to Mina's age is $1 : 2$ and the ratio of Mina's age to Naomi's age is $3 : 4$. What is the ratio of Lev's age to Naomi's age? Give your answer in simplest form.
Answer:
3:8
Step-by-step explanation:
The ratio of Mina's age to Naomi's age is 3 : 4
Multiplying the above ratio by 2 = 6:8
The ratio of Lev's age to Mina's age is 1 : 2
Multiplying the above ratio by 3
= 3:6
Therefore, ratio of Lev's age to Naomi's age in simplest form.
= 3:8
Answer:
3:8
Step-by-step explanation:
Let L, M, and N stand for the three ages.
The given ratios tell us that
M = 2L
and
N = 4/3M.
Therefore,
N = 4/3 x 2L = 8/3L.
This means that Lev's and Naomi's ages are in the ratio 3:8.
AB = 6cm , AC = 12cm. Calculate the length of CD
Give your answers to 3 significant figures
Answer:
6cm , 12cm
Step-by-step explanation:
Please help me with this
Answer:
True
Step-by-step explanation:
Cuz if u substitute (3,-3/2) it would work
Y = 1/2x - 3
-3/2 = 1/2(3)-3
-3/2 = 1.5 - 3
-3/2 = -1.5
& -3/2 is -1.5 as a decimal lol
does anyone know the answer?????
Answer:
-3x + 7
Step-by-step explanation:
she used the y-intercept as the slope and the slope as the y- intercept.
Answer:
its y= -3x+7
Step-by-step explanation:
she used the x intercept for the y - intercept and the y- intercept for the c-intercept
How do I solve 2/3x-1=-3
Which graph shows a vertical translation of ƒ(x) up 5 units to give a new function g(x)?
I mist that one its not the first one
Step-by-step explanation:
Answer:
The correct answer is the last image...I just got it right on the quiz.
Step-by-step explanation:
The perimeter of a triangle is 19 units. The second side is four units longer than the first side and the third side is three times the length of the first side. What are the lengths of the sides?
Answer:
First: 3 units Second: 7 units Third: 9 units
Step-by-step explanation:
19=x+(x+4)+3x
19=5x+4
15=5x
x=3
first side is 3 units
3+4=7
second side is 7 units
3*3=9
third side is 9 units
An equation is different from an expression because it has...
Answer:
Because it bears an equal sign
Expressions don't have a definite solution to the problem.
WHOEVER ANSWERS FIRST GETS BRAINLIEST!! PLZ EXPLAIN CLEARLY
A standard sheet of paper in the United States is 11 inches long and 8.5 inches wide
Each inch is 2.54 centimeters. How long and wide is a standard sheet of paper in centimeters?
A standard sheet of paper in Europe is 21.0 cm wide and 29.7 cm long. Which has the greater area, the standard sheet of paper in the United States or the standard sheet of paper in Europe?
Answer:
Step-by-step explanation:
1 in = 2.54 cm
Part (a)
Answer: 8.268 in
Part (b)
Answer: 11.693 in
Part (c)
In SI units standard-sized paper is 21.0 cm by 29.7 cm, which is equivalent to 8.268 in by 11.693 in.
Answer: 8.268 in by 11.693 in.
Part (d)
The U.S sized standard paper is 8.0 in by 11.0 in. Therefore the SI (internationally) sized paper is longer.
Part (e)
If the U.S> adopts the SI standard for letter-sized paper, both the width and length of standard paper will have to be increased. Therefore letter-sized paper will occupy a larger area and will be heavier if the thickness and density do not change.
URGENT HELP NEEDED SO PLS HELP
Answer:
1. 18π
2. 39.27cm
3. 4[tex]x^{5}[/tex][tex]z^{8}[/tex]
Izzy's Frozen Treats sells both frozen yogurt and frozen custard by the ounce. Last week, Marco noticed that a 3-ounce cup of frozen yogurt cost less than a 3-ounce cup of frozen custard. Marco has $5 to spend at Izzy's Frozen Treats today. Which can he buy more of, frozen yogurt or frozen custard?
A)frozen yogurt
B)frozen custard
plz show the work i really need help and this is Compare rates: word problems
Answer:
A. Frozen yogurt
Step-by-step explanation:
The frozen yogurt costs less than the frozen custard, even though you get the same amount (3 ounces)
No matter how much money Marco has, he would be able to buy more of the frozen yogurt because it has a cheaper unit rate.
So, the answer is A, frozen yogurt
10×-50
---------- =13
5
Answer:
I think it's -500 = 135
Step-by-step explanation:
multiply 10 and -50 to get -500
POSSIBLE POINTS: 33.33
Tyler can complete his Algebra Il project in 2.5 hours, but if he works with Luke they can finish in 1.5 hours. How long would it take Luke to finish the
project on his own?
4
1
-4
-3
2
3
4
-1-
-2-
-3+
-4-
What is the slope of the line?
what is the common difference of the arithmetic sequence 5,8,11,14?
Answer:
3
Step-by-step explanation:
8-5= 3
11-8= 3
14-11= 3
Answer:
common difference = difference between two consecutive number in a given series
hence,
8-5=3
common difference =3