Answer:
x = 20
Step-by-step explanation:
[tex]16x+90=2(10x+5)\\\\16x+90=20x+10\\\\90=4x+10\\\\80=4x\\\\20=x[/tex]
Afreen says, "I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6." What could the numbers be? Can you find 3 possible sets of numbers?
Answer:
The 3 ses that we found are:
{4, 5, 6}
{64, 65, 66}
{124, 125, 126}
Step-by-step explanation:
3 consecutive numbers are written as:
n, (n + 1), (n + 2)
We know that the first one is a multiple of 4.
Then n is a multiple of 4:
n = k*4
where k is an integer.
The second one is a multiple of 5, then:
(n + 1) = j*5
where j is an integer.
The last one is a multiple of 6.
(n + 2) = p*6
where p is an integer.
We want to find 3 sets.
The first one is trivial:
n = 4
n + 1 = 5
n + 2 = 6
4 is a multiple of 4
5 is a multiple of 5
6 is a multiple of 6.
Now let's find a set that is not trivial.
First, remember that all the multiples of 5 end with a 0 or a 5,
Then we can look for a value n, that is multiple of 4, and that has a last units digit equal to 4 (then the next one will have a units digit and will be multiple of 5)
For example, 4*6 = 24
24 is a multiple of 4.
The next number is 24 + 1 = 25, which is multiple of 5.
The next number is 25 + 1 = 26, which is not multiple of 6.
So let's try again.
4*11 = 44, is a multiple of 4.
The next number is 44 + 1 = 45
45 is a multiple of 5.
The next number is 45 + 1 = 46, which is not multiple of 6
So we need to try with another set.
4*16 = 64, is a multiple of 4.
The next number is 64 + 1 = 65, which is multiple of 5.
The next number is 66, which is multiple of 6:
6*11 = 66
Then the set:
n = 64
n + 1 = 65
n + 2 = 66
Is a possible set.
Now we can keep trying this, we can see that the next set has the numbers:
n = 4*31 = 124 is a multiple of 4.
The next number, is 124 + 1 = 125, which is a multiple of 5.
The next number is 125 + 1 = 126, which is multiple of 6
6*21 = 126
Then the set:
n = 124
n + 1 = 125
n + 2 = 126
Is another possible set.
The 3 ses that we found are:
{4, 5, 6}
{64, 65, 66}
{124, 125, 126}
Measure the length of AC. Use coordinate algebra to locate a point E on AC such that the ratio of AE to EC is equal to the ratio of AD to DB. Show how you derived your answer. (Hint: Let x and AC − x represent the two line segments that make up AC .)
If AC is 13 unit, then AC = 4.875 (5.875, 1) then the ratio of the segment via which E divides line AC is said to be equal to the ratio of AD and DB.
What is the line segment about?In the image attached, The length of AC = 13.
Take length of AE = x.
Take length of EC = 13 x.
The ratio of AE to EC = 0.6.
The [tex]\frac{AC}{EC}[/tex]
x = 0.6(13 - x)
x = 7.8 - 0.6x
1.6x = 7.8
x = 4.875
Therefore, AC = 4.875
Since E is found on AC so EC = 13 -x = 13 - 4.875 = 8.125
Therefore,
AC = 4.875
EC = 8.125
See full question below
Line AC is 13 units long. Use coordinate algebra to locate a point E on Line AC such that the ratio of AE to EC is equal to the ratio of AD to DB which is 0.6. Show how you derived your answer. (Hine: Let x and AC - x represent the two line segments that make up Line AC
Learn more about Line segments from
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Sage is 7 years older than Jonathan. If Jonathan is x years old, how old was Sage 10 years ago?
Answer:
(x-3) years
Step-by-step explanation:
We are given that
Age of Jonathan= x years
Sage is 7 years older than Jonathan
It means
Age of Sage=(x+7) years
We have to find the age of Sage 10 years ago.
10 Years ago,
Age of Jonathan=(x-10) years
Age of Sage=(x+7-10) years
Age of Sage=(x-3) years
Hence, 10 years ago, age of Sage =(x-3) years
Can someone help me with this math homework please!
Answer:
1.33 & n - 6 = 0.75(t - 8)
Explanation:
Speed can be calculated as miles ÷ minutes
4 ÷ 3 = 1.33 and 8 ÷ 6 = 1.33 as well
Since we know the n and t, we can substitute one into the equation to find the other (substitute t = 8 into all four equations and see do we get n = 6)
You can do this with t = 4 and n = 3 as well
Answer:
you are a great woman removing the sum o saare and pa and pa to the lord and your life to you for drawing the sum o the streets
calculate the surface area of a hockey puck with a height of 1 in. and a diameter of 3 in
Answer:
23.56
Step-by-step explanation:
2([tex]\pi r^{2}[/tex]) + 2[tex]\pi[/tex]rh
2([tex]\pi[/tex] [tex]1.5^{2}[/tex])+ 2[tex]\pi[/tex](1.5)(1)
23.56
23.56 in² is the surface area
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
Given
2(πr²) + 2πrh
2π( 1.5)²+ 2π(1.5)(1)
= 23.56 in²
To know more about surface area refer to:
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A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a 3 and the second card is an eight
Answer:
4 / 663
Step-by-step explanation:
Given that :
Number of cards in a standard deck = 52
Number of 3's in s standard deck = 4 (each suit has one card each)
Number of 8's in a standard deck = 4 (each suit has one card each)
Probability, P = required outcome / Total possible outcomes
Choosing without replacement :
P(top card is a 3) = 4 / 52
P(second draw is 8) = 4 / 51
P(top card is a 3 and second is 8) :.
4/52 * 4/51 = 16 / 2652 = 4 / 663
Calculate the maximum absolute uncertainty for R if:
R = 9A / B
A = 32 +/- 2 seconds
B = 11 +/- 3 seconds
1 second
0.33 seconds
9 seconds
2 seconds
6 seconds
Answer:
1.1 small inches of the day
Step-by-step explanation:
HELP!! pie/3 is the reference angle for:
Answer:
A, C and D.
Step-by-step explanation:
Answer:
yctcuvhino
ubuvyvubigu
The first side of a triangle measures 5 in. less than the second side, the third side is 3 in. more than the first side, and the perimeter is 17 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.
3s - 10 = 17
3s - 7 = 17
2s -7 = 17
2s - 5 = 17
Answer:
3s-10=17
s=9
3×9-10=17
27-10=17
There are 3 pizzas. Each child will get 1/2 of the pizza. How many 1/2's will there be in 3 pizzas?
Answer:
There are 6 halves of the pizza
Step-by-step explanation:
3/0.5=6
can u guys help me with this
Answer:
O
Step-by-step explanation:
We can answer this by using the process of elimination
We want to find the position of 0.5
So let's begin
Looking at the number line...
D and E are both in between negative numbers
0.5 is not a negative number so immediately we can eliminate D and E
So it is between O and M
O is between 0 and 1
.5 is between 0 and 1 so O might be the answer
However let's look at M just to be safe.
M is located between 3 and 4.
Both 3 and 4 are greater than .5 meaning that M cannot represent .5
So we can conclude that O is the best answer
Solve the inequality -10 is greater or equal to -2x
Answer:
-10 and - 2x
The x is unknown number so, we don't know which one if -2x or -10 is greater.
6. Show how to simplify the expression 8x + 3 + 4x - 2 without using algebra tiles. Describe each step of the process.
Answer:
12x+1
Step-by-step explanation:
8x+3+4x-2
8x+4x+3-2
Arranging Like terms
12x+1
Adding Like terms (8x+4x) and Substracting numbers ! ++- = - So we substrate it and in addition we don't change symbols so 3 is greatest number so we write + there !
what is the value of 5 in the number 68.513?
Answer:
00000000.1
Step-by-step explanation:
1+1=2-1%000.1
On a coordinate plane, a curved line with a maximum value of (negative 1, 2) crosses the x-axis at (negative 3, 0) and (1, 0), and crosses the y-axis at (0, 1.5).
What are the x-intercepts of the graphed function?
(–3, 0) and (0, 1.5)
(–3, 0) and (1,0)
(–1, 2) and (1, 0)
(0, 1.5) and (1, 0)
9514 1404 393
Answer:
(–3, 0) and (1,0)
Step-by-step explanation:
The x-intercepts are where the curve crosses the x-axis. Your problem statement tells you ...
"crosses the x-axis at (negative 3, 0) and (1, 0)"
This means the x-intercepts are (-3, 0) and (1, 0).
Answer:
The answer would be B= (–3, 0) and (1,0)
Question 2.
If 0 is an angle in the first quadrant, and cos(θ) = 0.669, determine the value of
cos(π - θ), cos(π + θ), and cos(4π - θ) using Symmetry.
Answer:
1) -0.669
2) -0.669
3) 0.669
Step-by-step explanation:
Since we are subtracting or adding multipled of pi, we will either obtain 0.669 or -0.669 as our answer for each of the three different questions.
Cosine is the x-coordinate in our orderes pairs. If our point ends up on the right side of the y-axis, the cosine will be positive. If our point ends up on left side, it will be negative.
Choose a thetha (I'm going to choose it in degrees) in the first quadrant to help with a visual.
If theta=70:
1) then 180-70=110 which is in second quadrant, so our cosines will be opposite in value.
2) then 180+70=250 which is in third quadrant, so our cosines will be opposite in value.
3) then 4×180-70=720-70=650 =1(360)+290 which ends up in the 4th quadrant which means the consines will have the same value.
write y=4x+3 in mapping notation
Answer:
y=7x
Step-by-step explanation:
because y= 4x+3=7x
4. Three friends are collecting football cards. They have 240 cards between them. Zukile has 60 more cards than Adam, and Siya has twice as many cards as Adam. If Adam has x number of cards, write and solve an equation to find how many cards they each have.
Answer:
Zukile has 105, Adam has 45, Siya has 90
Step-by-step explanation:
Not sure how right this is, but I did: 240=2x+x+(60+x)
Simplify to: 240=60+4x
Simplify to: 180=4x
Simplify to: 45=x
identify each of the following as rational or irrational.
Answer:
Step-by-step explanation:
A rational number can be written as a fraction of two integers.
√23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction.
104.42 is rational because it can be expressed as 10442/100 . We can express it as this because
104.42 * 1 = 104.42 * 100/100 = 10442/100, and multiplying something by 1 keeps it the same
√64 is rational because it is equal to 8, and 8/1 is equal to 8
49.396 with the 6 repeating is rational because we can express 49.39 as
49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with
49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.
For example, 0.6 with the 6 repeating can be represented as 6/9. This is because 0.6 * 10 = 6, and we divide that by 9. Similarly, 0.006 with the 6 repeating can be represented by 0.06/9
We add the two fractions together to get
4939/100 + 0.06/9
multiply both fractions by the other's denominator to even them out and make the numerator of the second fraction an integer
(4939*9)/(100*9) + (0.06*100)/(9*100)
= 44451/900 + 6/900
= 44460/900
Assuming that the last number has only the digits given, that is rational because, similarly to 104.42, it can be multiplied by a power of 10 to result in (integer)/(integer), making it rational. If the dots represent infinite digits, then it is not rational because there are infinite digits that are not repeating, and there is no way to know the last digit, so it is impossible to write a fraction from it
Carlos compro cierta cantidad de panes puso 1/4 de esa cantidad sorbre su bandeja y dejo el resto de panes en la bolsa ¿Cuantos panes dejo Carlos en la bolsa?
Answer:
The quantity of loaves left in the bag is 3/4.
Step-by-step explanation:
Carlos bought a certain amount of loaves, put 1/4 of that amount on his tray and left the rest of the loaves in the bag. How many loaves did Carlos leave in the bag?
Quantity of loaves in tray is 1/4
So, the quantity of loaves in the bag is
[tex]1-\frac{1}{4}=\frac{3}{4}[/tex]
Year 10 girls = 70, year 10 boys = 140, what fraction of year 10 are boys?
Answer:
2/3
Step-by-step explanation:
140/(140+70)
=140/210
simplified
=2/3
I don't think that there is enough info for this problem, but could someone try to help?
Answer:
12
Step-by-step explanation:
Rectangle : Let length = b & width = a
PQ = QR = 6
LR = QR - PL = 6 - a
ΔPQR ~ ΔMLR
In similar triangles, corresponding sides are in same ratio.
[tex]\frac{PQ}{QR}=\frac{ML}{LR}\\\\\frac{6}{6}=\frac{a}{6-b}[/tex]
[tex]1 =\frac{a}{6-b}[/tex]
6 - b = a
6 = a + b
a +b = 6
Perimeter of rectangle = 2*(length +width}
= 2*(a+ b)
= 2 * 6
= 12
Part C
Now try this one. Write a description of the partitioned function using known function types, including transformations.
Answer:
Please find the complete question in the attached file.
Step-by-step explanation:
All three functions are defined as follows:
For function 1:
The module on the absolute value function instance example also is known as this function:
[tex]f(x)=|x| \ \left \{ {{x, \ \ x>0} \atop {-x \ \ <0}} \right.[/tex]
This is [tex]f(x)= x, \ \ x<0[/tex] in the following diagram.
For function 2:
It is an algebraic function of in this function
It also is a quadratic polynomial functional with a [tex]y=x^2, \ \ x>0[/tex] value.
For function 3:
The cubic polynomial equation is evaluated for in this function
The value of the graph is:
[tex]y=-x^3 \ \ \ \ and\\\\\to y= f(x)\\\\\to y= -f(x)\\\\[/tex]
a.) What is the measurement of the missing side (c)?
b.) What is the angle of (x)?
Which theorem is used?
Answer:
E
Step-by-step explanation:
I believe it should be E because it uses parallel lines
Evaluate 6 + 3b if b = 7
Step-by-step explanation:
6+3b=6+3(7)=6+21=27
Very easy
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Which of the following is the solution to 9|x +4|>54 ?
O A. x2-10 or x 2 2
O B. xs-10 and x 2
C. x2
O D. X<-10 or x >2
Answer:
x>2 or x<-10
Step-by-step explanation:
9|x +4|>54
Divide each side by 9
9/9|x +4|>54/9
|x +4|>6
There are two solutions, one positive and one negative
x+4 >6 or x+4 < -6
Subtract 4 from each side
x+4-4 >6-4 or x+4-4 < -6-4
x>2 or x<-10
The graph shows a line and two similar triangles.
On a coordinate plane, a line goes through (0, 0) and (6, 4). A small triangle has a rise of 2 and run of 3. A larger triangle has a rise of 4 and run of 6.
Which expression finds the equation of the line?
StartFraction y Over x EndFraction = three-halves
StartFraction y Over x EndFraction = two-thirds
StartFraction y Over 2 EndFraction = StartFraction 3 Over x EndFraction
StartFraction y Over 3 EndFraction = StartFraction x Over 2 EndFraction
Answer: Choice B) [tex]\frac{y}{x} = \frac{2}{3}[/tex]
This is the same as saying y/x = 2/3
Or I suppose you could say "y over x = two-thirds".
===============================================
Explanation:
Recall that slope is rise over run
slope = rise/run
The rise being the change in y, while the run is the change in x.
So we could informally think of it as slope = y/x
-----------
Since we're told that it "has a rise of 2 and run of 3", this means slope = 2/3.
The slope is both y/x and also 2/3.
Equating the two expressions leads us to y/x = 2/3. This is why choice B is the final answer.
-----------
Side notes:
This trick only works when the line goes through the origin (0,0)To rephrase the last bullet point, the line must have y intercept 0.If you multiplied both sides by x, then you get y = (2/3)xAnswer:
B
Step-by-step explanation:
(-_-)
The distance traveled (in meters) by a frog is modeled by the equation d=0.2t where d is the distance traveled in meters and t is the time in minutes. Find the distance traveled in 25 minutes
Answer:
5 meters traveled in distance.
Step-by-step explanation:
Since we are finding the distance of a frog traveling ? distance in 25 mins, we can substitute t for 25. If we do, 0.2 x 25 = 5, d = 5.
Hope this helps!
The dimensions of a conical funnel are shown below: A conical funnel is shown with the height of the cone as 8 inches and the radius of the base as 3 inches. Nisha closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 15 cubic inches per minute, how long will it take for all the liquid to pass through the nozzle? (Use π = 3.14.) 3.34 minutes 5.02 minutes 13.39 minutes 15.07 minutes
Answer:
B
Step-by-step explanation:
r=3 in
h=8 in
Volume of funnel
[tex]V=\frac{1}{3}\pi r^2h\\=\frac{1}{3} \times 3.14 \times 3^2 \times 8\\=75.36 in.^3\\time ~taken~to~drip out=\frac{75.36}{15}\\\approx 5.02~minutes.[/tex]
Answer:
5.02 is right
Step-by-step explanation:
i hope this helps
