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Explanation:
Roy spends 1/4 of his money on 3 pens and 6 notebooks. That means 3/4 of it is leftover.
2/3 of 3/4 = (2/3)*(3/4) = 1/2 of his money is spent on buying some unknown number of additional pens. We'll come back to this later.
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In terms of cost,
1 pen = 3 notebooks
which is another way of saying 1 pen is the same price as 3 notebooks.
Multiply both sides by 2 to get
2 pens = 6 notebooks
Therefore, saying "3 pens + 6 notebooks" is the same as "3 pens + 2 pens = 5 pens" when just thinking about costs.
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In short, Roy buying 3 pens and 6 notebooks is the same as him buying 5 pens. He spends 1/4 = 25% of his money on getting these 5 pens.
Multiply those two values by 2 to find that 50% = 1/2 of his money would allow him to get 10 pens.
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Recall that at the end of the first section, we concluded that Roy spent 1/2 of his money on buying those unknown additional number of pens. Then the previous section mentioned that 1/2 of his money gets him 10 pens. Therefore, he must have bought 10 additional pens on top of the original 3 mentioned in the instructions.
Overall, he purchased 3+10 = 13 pens
Answer:
13 pens
Step-by-step explanation:
If a pen costs 3 times the cost of a notebook, then the cost of 3 notebooks will equal the cost of a pen. The 6 notebooks that Roy bought are equivalent in cost to 2 pens, so 1/4 of Roy's money is the cost of 3+2 = 5 pens.
After the first purchase, Roy has (1 -1/4) = 3/4 of his money remaining. If he spends 2/3 of that on more pens, he will have spent ...
(2/3)(3/4) = 2/4
of his money on more pens. We've already seen that 1/4 of his money buys 5 pens, so 2/4 will buy 10 more pens.
Roy bought 3 +10 = 13 pens altogether.
what is the percent change of
30 to 90?
what is what is the percent change of 30 to 90?
Answer:
200% increase
Step-by-step explanation:
How to find the inverse of 3log3(x+3)+1. Its with a base of 3
Let [tex]f^{-1}(x)[/tex] be the inverse of
[tex]f(x) = 3 \log_3 (x + 3) + 1[/tex]
Then by definition of inverse function,
[tex]f\left( f^{-1}(x) \right) = 3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
Solve for the inverse :
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) + 1 = x[/tex]
[tex]3 \log_3 \left(f^{-1}(x) + 3\right) = x - 1[/tex]
[tex]\log_3 \left(f^{-1}(x) + 3\right) = \dfrac{x - 1}3[/tex]
[tex]3^{\log_3 \left(f^{-1}(x) + 3\right)} = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) + 3 = 3^{\frac{x-1}3}[/tex]
[tex]f^{-1}(x) = 3^{\frac{x-1}3} - 3[/tex]
Write the equation in standard form.
y - 10=-2(x-8)
Answer:
2x + y = 26
Step-by-step explanation:
The standard form of a linear equation is A x + By = C.
Simplify -2(x - 8)
Multiply -2 by -8
y - 10 = -2x + 16
2x + y - 10 = 16
Add 10 to both sides.
Add 16 and 10
Answer= 2x + y = 26
The value of x² – 2yx + y² when x = 1, y = 2 is
[tex]x^2 - 2xy +y^2 = (x-y)^2 = (1-2)^2 = (-1)^2 =1[/tex]
SOMEBODY HELP ME NO LINKS PLEASE
pls help me
I m giving brainliest
Step-by-step explanation:
the general line equation format is
y = ax + b
a is the slope or gradient of the line. it is the ratio of "y coordinate change / x coordinate change".
b is the y-intercept, the y value when x = 0. we get this by putting one point into the equation and solve for b.
(i)
A (3, 5)
B (5, 9)
x changes by +2 (from 3 to 5).
y changes by +4 (from 5 to 9).
so, the slope (or gradient) is +4/+2 = 2
(ii)
the semi-finished equation is
y = 2x + b
let's use A to get b :
5 = 2×3 + b = 6 + b
b = -1
and the full equation is
y = 2x - 1
(iii)
for point (4, k) we get
k = 2×4 - 1 = 8 - 1 = 7
The sum of two angles of a triangle is
110°. Calculate the third angle in
degrees.
Answer:
70
Step-by-step explanation:
the sum of all angles is 180°
so 180-110= 70
Find the area of the triangle
Please help me - I don't get how to do this.
Please show your work - I really need to understand this
Answer:
Step-by-step explanation:
1. Pythagorean theorem: a^2+b^2=c^2
Note that the hypotenuse is 11 (for the second right triangle).
Find the length of the dotted line by doing 7^2+b^2=11^2
49+b^2=121, b=[tex]\sqrt{72\\}[/tex].
Now you can the area of the second right triangle: ([tex]\sqrt{72\\}[/tex](7))/2=29.7.
Find the length of the first right triangle:
Note that 9 is the hypotenuse; ([tex]\sqrt{72\\}[/tex])^2+b^2=9^2
=72+b^2=81
b=3.
([tex]\sqrt{72}[/tex])(3))/2=12.7
How do I get the result for 1/8 out of 40?
Answer:
5
Step-by-step explanation:
You divide your number by the denominator and then times it by the numerator
Geologists collected some rock samples. Of the 12,000
grams of ore they collected, about 600 grams contain a
valuable mineral
What is the concentration of the mineral in the
sample?
5%
6%
50%
60%
Answer:
5%
Step-by-step explanation:
600 / 12000 = .05
Answer:
2 %
Step-by-step explanation:
A company claims that their new bottle holds 40% more laundry soap.
If their original container held 53 fluid ounces of soap, how much does the new container hold?
plz show work too plz
Answer:
74.2
Step-by-step explanation:
53 x .4 = 21.2
21.2 + 53 = 74.2
Help me please i really need it
Answer:
Step-by-step explanation:
RSB is a right angle
12. RSB is 90 degrees
13. A right angle is 90 degrees
H is between P and S
14. PS + PH = HS
15. Deductive Reasoning
An eight-person relay team completed a race in 96.8 seconds. On average, what was each runner's time?
Answer:
12.1
Step-by-step explanation:
Answer:
12.1 Seconds
Step-by-step explanation:
96.8/8=12.1
Which of the following statements best describes the location of −(−1) on a number line? (5 points)
Question 6 options:
1)
It is 1 unit to the left of 0.
2)
It is 1 unit to the right of 0.
3)
It is 1 unit to the right of 1.
4)
It is 1 unit to the left of 1.
Answer:
It is 1 unit to the right of 0.
Step-by-step explanation:
If angle 1 is 110°, what would the other angle measures have to be in order for m || n andq || p?
Angle 2 = °
Angle 3 = °
Angle 4 = °
Answer:
8
Step-by-step explanation:
Answer:
ANGLE2=110° ANGLE3=70° ANGLE4=70°
Which graph represents a linear function? (4 points)
A coordinate plane is shown with a curved line that starts in the bottom left area of the graph, passing through the point -1 comma -5, curving to pass through the y-axis at 2.5, then curving up again to pass through the point 1 comma 5
A coordinate plane is shown with a line passing through the x-axis at negative 2 and the y-axis at negative 6.
A coordinate plane is shown with a parabola graphed in an upward U shape. The bottom of the parabola touches the y-axis at -10 and curves upward on both sides
A coordinate plane is shown with a wavy line that sits on the x-axis and moves across the graph in even up and down waves.
Answer:
The second option
Step-by-step explanation:
Linear means a straight line.
Choices 1, 2, and 4 are wrong because they are either a parabola or wavy, and by definition of both of these terms, they are not straight and are therefore not linear.
I need the anwser to this right now please
Answer:
b. 9
Step-by-step explanation:
2+9=11
11+11=22
22+6=28
Find the disFind the distance between the points P and Q shown.
tance between the points P and Q shown below
Step-by-step explanation:
I am sorry but please give detailed question
Dog slept 3 hours . If the dog snored 1/3 of an hour . How many times did he snore
Answer:
it depends how much the god snores within a certain time period
which expression has the same value as tan (-45degrees)?
Answer: B
Step-by-step explanation:
Trust
what is the output of the function when the input is −3
It depends on the function. Please add a picture or type your function.
The curve y= 1/3 x⁴ - 4x² -3x has a gradient of -3 at three points.
Find the coordinates of these points.
Answer:
[tex]\boxed{(0, 0), (\sqrt{6}, -12-3\sqrt{6}), (-\sqrt{6}, -12+3\sqrt{6})}[/tex]
Step-by-step explanation:
Step 1: Take the derivative of the function with respect to x
[tex]\frac{d}{dx} (\frac{1}{3}x^4-4x^2-3x)\\=\frac{d}{dx} (\frac{1}{3}x^4)-\frac{d}{dx}(4x^2)-\frac{d}{dx}(3x)\\=\frac{4}{3}x^3-8x-3[/tex]
Now, you have the gradient of every point given the x value. We want the gradient to be -3, so,
Step 2: Set the derivative of the function equal to -3 and solve for x
[tex]\frac{4}{3}x^3-8x-3=-3\\\frac{4}{3}x^3-8x=0\\4x(\frac{1}{3}x^2-2)=0\\[/tex]
We can see that one solution is x=0.
The other 2 solutions are:
[tex]\frac{1}{3}x^2-2=0\\\frac{1}{3}x^2=2\\x^2=6\\x=\sqrt{6}, x=-\sqrt{6}[/tex]
Now that we found out the x value, we can plug it in back to the equation to find their respective y value:
x=0: y=0
x=sqrt(6): y=-12-3sqrt(6)
x=-sqrt(6): y=-12+3sqrt(6)
Hence we have our answer.
Help please, help please
Answer:
i think the perimeter is 60
Step-by-step explanation:
9²+12² = x²
15 = x
perimeter = 15×4 = 60
Jordan has a part-time job which pays $75 a week. He has already saved $55 toward the purchase of a $400
could use to find the minimum number of weeks Jordan must work to have enough money to buy the iPhone.
Answer:
5 weeks
Step-by-step explanation:
75 w + 55 ≥ 400
75 w ≥ 345
15 w ≥ 69
w ≥ [tex]\frac{23}{5}[/tex] = 4.6 weeks ⇒ the minimum number of weeks Jordan must work is 5 weeks
20 charecters lol pls solve
Answer:
-3x+12
Since we are adding like terms you add everything that has an "x" after it [(3.4x) + (-5.4x) + (-x)] it all that adds up to -3x and the you add the 12 to it. It could also be written 12-3x
68 is 40% of what number?A.17 B.136 C.170D.270
Answer:
C. 170
Step-by-step explanation:
68/4=17
17 is 10% of the unknown number
17 times 10 is 170
Answer:
C. 170Step-by-step explanation:
68 is 40% of what number?
A.17
B.136
C.170
D.270
68 : 40 * 100 = 170
simplify help me to do this
Answer:
204
Step-by-step explanation:
90-5 (9-5 (9- (14-12) 3 ) ÷5
▪︎ First we have to solve the ones in the brackets ___ ( 14-12 ) which is e equal to 2
90-5 (9-5 (9- 2×3 ) ÷5 "the 3 comes inside the bracket coz we solved the previous one"
▪︎then we have to solve ( 9-2×3 ) which is equal to 3 _____ is 3 because if we go in the BODMAS way it will be
( 2×3 =6) , then... (9-6=3)
▪︎at the same time we can subtract 9-5 because we are done with the first bracket ( 9-5=4 )
90-5 (4×3)÷5
▪︎at the same time we can subtract 90-5 as well coz we are done with the first bracket ( 90-5=85)
▪︎then we can multiply (4×3) coz it's in the brackets (4×3=12)
85×12÷5
▪︎so then we hv to multiply 85 by 12 , then the answer is 1020
1020÷5
▪︎then divide (1020÷5=204)
☆90-5 (9-5 (9- (14-12) 3 ) ÷5
=90-5(9-5(9-2×3)÷5
=90-5(4×3)÷5
=85×12÷5
=1020÷5
=204
hope this helps☆☆☆
( sorry fr the long answer )
First the first 4 term for 4n-5
Answer:
-1, 3, 7, 11
Step-by-step explanation:
First, let's find term 1. To find this term, we need to replace n with 1 - what is 4(1) - 5? Well, that's just 4 - 5, or -1. So, our first term is -1. Next, we'll find our second term. To do this, we'll replace n with 2. 4(2) = 8, and then 8 - 5 is equal to 3, so our second term is 3. Let's now find the third term by replacing n with the number 3. 4(3) - 5 is equal to 12 - 5, or 7. So, 7 is our third term. Finally, we'll find the fourth term. 4(4) is equal to 16, and 16 - 5 is equal to 11. So, the fourth and final term is equal to 11.
Hopefully that's helpful! :)
Step-by-step explanation:
Term 1: - 1
Term 2: 3
Term 3: 7
Term 4: 11
The rule is, where you see n, substitute with the position/term requested
First 4 terms are: - 1,3,7, 11
Molly went to play miniature golf on Monday, when it cost $7 to rent the club and ball, plus $1 per game. Sharon went Thursday, paying $2 per game, plus rental fees of $4. By coincidence, they played the same number of games for the same total cost. How much did each one spend?
Answer:
Molly played 4 games
4.A counterexample can be used to show that a conjecture is false. Below are three
conjectures students made after visiting a zoo. Write a counterexample that shows that
conjecture is false.
a. There are always more elephants in a zoo than giraffes.
b. The oldest leatherback sea turtle in captivity is 33 years
old.
c. American bison are never over 6 feet tall.
Counterexamples are simply used to disprove conjectures.
(a) Elephants and Giraffes
This conjecture may or may not be true.
However, it can be disproved by the following counterexample
There are sometimes more elephants in a zoo than giraffes
The word "sometimes" disproves the original conjecture
(b) The oldest leatherback sea turtle
This conjecture is not true.
This is so because the oldest leatherback sea turtle in captivity is actually 400 years old.
So, the conjecture can be disproved by the following counterexample
The oldest leatherback sea turtle in captivity is 400 years old.
(c) American bison
This conjecture may or may not be true.
However, it can be disproved by the following counterexample
American bison are sometimes over 6 feet tall
The word "sometimes" disproves the original conjecture
Read more about conjectures and counterexamples at:
https://brainly.com/question/1619980