Give to each part of the fraction a variable (a letter)
Numerator: n
Denominator: d
the denominator of a fraction is two more than the numerator:
[tex]d=n+2[/tex][tex]\frac{n}{d}=\frac{n}{n+2}[/tex]both numerator and denominator are increased by ten, the simplified is 9/10:
[tex]\frac{n+10}{n+2+10}=\frac{9}{10}[/tex]Use the equation above to find the value of n:
[tex]\begin{gathered} 10(n+10)=9(n+12) \\ 10n+100=9n+108 \\ 10n-9n=108-100 \\ n=8 \end{gathered}[/tex]As n is equal to 8 find the value of d:
[tex]\begin{gathered} d=n+2 \\ d=8+2 \\ d=10 \end{gathered}[/tex]The original fraction is:
[tex]\frac{8}{10}[/tex]Alexander's hobby is dirt biking. On one occasion last weekend, he accelerated from rest to 10.3m/s in 5.98 seconds. He then maintained this speed for 7.92 seconds. Seeing a coyote cross the trail ahead of him, he abruptly stops in 4.33 seconds. Determine Alexander's average speed for this motion.
Using the equation of motion, it can be determined that Alexander travels at an average speed of 37.73 m/s while operating a bike.
What are motion equations?Equations of motion are equations that explain how a physical system behaves in terms of how its motion changes over time.
The three equations are,
v = u + at v² = u² + 2as s = ut + 1/2at²For the initial 5.98 seconds, initial velocity = 0, acceleration = 10.3 m/s and time taken = 5.98 s
Using first equation of motion,
v = u + at
v = 0 + 10.3(5.98) = 61.594 m/s
He then kept this speed up for 7.92 seconds.
For the last 4.33 seconds, final velocity = 0, initial velocity = 61.594 m/s
Acceleration = (0-61.594)/4.33 = -14.224 m/s
Distance travelled in 5.98 seconds is given as follows:
s = u t + 1/2(at²)
= 0 + 1/2(10.3)(5.98)²
= 184.16 m
Distance travelled in 7.92 seconds = 61.594 × 5.98 = 368.33 m
Distance travelled in 4.33 seconds is given as follows:
s = u t + 1/2(at²)
s = 61.594(4.33) + 1/2(-14.224)(4.33)²
= 133.35 m
Total distance travelled = 184.16 + 368.33 + 135.35 = 687.84 m
Average speed = Total distance/Total time = 687.84/(5.98+7.92+4.33)
= 37.73 m/s
Therefore, average motion speed for Alexander while riding a bike is 37.73 m/s which is calculated by using the equation of motion.
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The angle bisectors of AABC are AV, BV, and CV. They meet at a single point V.
(In other words, V is the incenter of AABC.)
Suppose TV=20, CV=23, mZTCU= 34°, and m SAV=26°.
Find the following measures.
Note that the figure is not drawn to scale.
S
B
U
mZSAU =
mSBV =
SV = [
The measure of the angles is m∠SAU= 24°
What is an incenter in geometry?The incenter is the point at which all of the attitude bisectors meet in the triangle, like within the video. It is not always the middle of the triangle.
In triangle ABC, V is the incenter of the triangle.
Since, m∠SAV = 26°
And m∠SBV = 2(m ∠SAV)
= 2 × 26°
= 52°
Since Property of the incenter of a triangle;
Therefore, DG = EG = GF = 10
Since, m∠A + m∠B + m∠C = 180°
2(18)° + 34° + 2(m∠SAU) = 180°
2(m∠SAU) = 180° - 132°
m∠SAU= 24°
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What is the prime factorization of 7850?
Answer:
the prime factorization of 7850 is 2, 5, 5, 157
two sides of a triangle are 18 ft and 23 ft. Find the range for the measure of the third side.
Using the triangle inequality theorem the range of measures of the third side is 5 < x < 41
How to find the third side of the triangle?The triangle inequality theorem states that any side of a triangle must be shorter than the other two sides added together.
In other words, the triangle inequality theorem describes the relationship between the three sides of a triangle. According to this theorem, for any triangle, the sum of lengths of two sides is always greater than the third side.
Therefore, for a triangle that has the sides a, b and c will follow the principle below:
c < a + b
b < a + c
a < b + c
Therefore, the triangle has two sides as 18 ft and 23 ft. The range of the third side is as follows:
x < 23 + 18; x < 41
18 < 23 + x
23 < x + 18
Therefore, base on the first and third inequality.
x < 41
x > 5
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Why is it important to always label your numeric answers with unit labels? Give at least one example of how labeling a numeric answer with the wrong label would make a big difference in the answer.
It is important to always label your numeric answers with unit labels on order not to confuse others and to understand what it illustrates.
An example is when solving for the area of a shape abd the person writes cm³. This means volume and is incorrect.
What is labeling?A graph labelling is the process of assigning labels, which are often represented by integers, to the edges and/or vertices of a graph in the field of mathematics known as graph theory.
The information you need to obtain the answer must first be considered after you have determined what the challenge is asking for. You draw attention to certain aspects of the issue. After that, you label them so you can keep them organized and avoid becoming confused by them.
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an amusement park is running a special where you pay an entrance fee of $13 and will only charge $1 for the first 5 rides. After 5 rides, the price goes up to $4 per ride.
a. Write a function that represents the total cost of a trip to this amusement park
b. How much money will be spent if you go on 7 rides?
c. How many rides did someone go on who ended up spending $46?
Imagine that it is now 2 p.m. What time will it be when the minute hand has rotated through
1260°?
A. 5:30
B. 4:50
C. 6:00
D. 4:10
when the minute hand rotated through 1260° time will became 5:30 PM
Complete angle:-
A complete angle is a type of angle that measures 360°.A complete angle deals with one full rotation measuring 360°.
In an hour or in 60 minute, minute hand covers a 360° angle.
According to question,
initially it is 2:00PM,that is minute hand at 12 and hour hand at 2
it is given that minute hand has rotated through 1260°
1260° = 3 x 360° + 180°
which means minute hand will have three complete rotation and one half rotation.
when minute hand rotated through 360° angle then hour hand will move from 2 to 3.
And again in second rotation, when minute hand rotated through 360° angle then hour hand will move from 3 to 4.
Again in third rotation, when minute hand rotated through 360° angle then hour hand will move from 4 to 5.
As of now, minute hand have taken three complete rotation and so hour hand reached at 5
Now, when minute hand rotated through 180° (one half rotation),minute hand will reach at 6 from 12.
So, right now the position of hour hand is between 5 and 6 and the position of minute hand at 6.
hence, time will be 5:30 PM
Option A is correct
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Hey I really don’t understand this pls someone help or explain
The value of sin ∠A in the right triangle is 3 / 5
How to find the angle of a right triangle?A right triangle is a triangle that has one of its angles as 90 degrees.
Base on the angles, the side of a right triangle can be named as follows:
opposite sidehypotenuse sideadjacent sideUsing trigonometric ratio, sin ∠A can be found as follows:
sin ∠A = opposite / hypotenuse
Hence,
opposite side = 3
hypotenuse side = 5
Therefore,
sin ∠A = 3 / 5
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complete the table of values x+y=6
Answer:
See below
Step-by-step explanation:
Number of distinct variations:
3
[tex]\left[\begin{array}{ccc}1&5\\2&4\\3&3\end{array}\right][/tex]
The answer to x + y = 6 can pretty much be anything that equals 6 but in addition so for example 3 + 3!
Fill in the blank h(-5) • g(-2) = ________g(x) = x2. h(x) = 3x - 2
The first step to solve this question is to find the values of h(-5) and g(-2)
In order to do that, you need to use the value of x=-5 in the function h(x) and x=-2 in the function g(x).
So we have that:
[tex]\begin{gathered} g(x)=x^2 \\ g(-2)=(-2)^2=4 \\ \\ h(x)=3x-2 \\ h(-5)=3\cdot(-5)-2=-15-2=-17 \end{gathered}[/tex]Now we can calculate the product of h(-5) and g(-2):
[tex]h(-5)\cdot g(-2)=(-17)\cdot4=-68[/tex]So the value to fill the blank is -68.
how do i create a visual for -7+10
Answer:
Let's say you have a table with spots for 10 plates and each plate can hold 1 pie. But 7 plates are missing from the table. You place your pies in each spot anyway. Out of those 10 spots available, only 3 have both pies and plates.
please help meeee!!!
Answer:
195 feet? (I know the answer but I'll leave the rest to you about typing it either cm2 or those stuff.
Step-by-step explanation:
To work this out so, congruent means identical. We already have the answer to EF so 13 x ? But BC = 15 feet. And BC = FG So,
13 x 15 = 195.
Hope this helps
What is the domain of the function f(x) - 50 ? 5 + 720-2 {x: 0 < 20) {0, 1, 2, 3,.20} {a: 2 < 20} {0, 1, 2, 3,....19
The domain of a function f(x) is the set of values of the variable x for which the function is defined (has a defined finite value).
In the case of rational functions like this one, the function becomes undefined when the denominator is 0, so we can write:
[tex]\begin{gathered} 5+\sqrt[]{20-x}=0 \\ \sqrt[]{20-x}=-5\longrightarrow\text{ there is no real value for x that will satisfy this condition} \end{gathered}[/tex]As the square root will only give positive values or zero, there is no value of x that will make the square root be equal to -5. Then, this condition does not give us any discontinuity for f(x).
We have now to consider that the square root of (20-x) will not accept negative arguments in order to be in the realm of real numbers. So then, we have the condition:
[tex]\begin{gathered} 20-x\ge0 \\ 20\ge x \\ x\le20 \end{gathered}[/tex]Then, f(x) will not be defined for x that do not satisfy this condition.
We can conclude that f(x) is defined for all values of x that are equal or less than 20.
Answer: The domain is {x: x<=20}
Then
If (2a) (2b) = 128, what is a + b equal to?
The exponents' best option will be determined by
a + b's value is seven.
Describe exponent.How often a number is multiplied by itself is indicated by the exponent.
For instance
In this case, 2 is multiplied by 4
Now in ( m times)
The base is designated as a, and the power is designated as m.
There are some indexing laws.
[tex]1)a^m \times a^n = a^{m+n}\\2)\frac{a^m}{a^n} = a^{m-n}\\3) (a^m)^n = a^{mn}\\4) (ab)^m = a^mb^m\\5) a^0 = 1\\6) a^{-m} = (\frac{1}{a})^m[/tex]
Here,
[tex](2^a)(2^b) = 128\\[/tex]
[tex]2^{a+b} =2^7[/tex] [According to laws of indices]
[tex]a + b = 7[/tex]
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Complete Question
If [tex](2^a)(2^b) = 128\\[/tex], then a + b is equal to?
Solve the equation.
pls n ty
Answer:
0
Step-by-step explanation:
use a calculator =)
or
[tex]\sqrt[3]{125} = 5\\\sqrt{25} = 5\\ so , 5 - 5 = 0[/tex]
What is the value of x
What is the measure of the smaller angle
What is the measure of the larger angle
Answer:
x=8
larger angle=113
smaller angle=67
Step-by-step explanation:
8x+3=a(Vertically opposite angle)
a+14x+1=180°(Angles between parallel line)
8x+3+14x+1=180°
22x+4=180°
22x=176°
x=8
dennis has sold $40 worth of chocolate bars for a fundraiser. if he sells over 175 worth of chocolate, he’ll win a prize.each bar is 2.50. How many bars does he need to sell in order to wins prize
Answer:
Dennis needs to sell 54 more
Step-by-step explanation:
pls help me answer this
Answer:
hello!
Step-by-step explanation:
firstly lets convert the mixed fraction into a single fraction itself
thats 5/4
if each rope contributes to 5/4 meters then a rope with 8 pieces would be 5/4 x 8 which gives you the answer 10
determine whether the triangle is a right angled angle or not if AC=6cm, AB=15cm and BC=9cm
The given parameters did not satisfied the conditions. Therefore, it is not a right angle triangle.
What is triangle?
In mathematics, the triangle is a closed polygon shape which has three vertex as well as three sides. It consist of three forms depending upon the sides. If all the sides are different then it is scalene otherwise equilateral triangle.
According to the question, the given triangle parameters are as follows:
AC = 6 cm; AB = 15 cm; BC = 9 cm;
Using Pythagoras theorem, the right angle property can be checked:
Let us assume the triangle ABC, with three sides:
AB² + BC² = AC² ⇒ (15)² + (9)² = (6)²
The given parameters did not satisfied the right angle triangle conditions. Therefore, it is not a right angle triangle.
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Answer:
not a triangle
Step-by-step explanation:
You want to know if side lengths AC=6 cm, AB = 15 cm, and BC = 9 cm will define a right triangle.
Triangle inequalityThe triangle inequality requires the sum of the two shortest sides of a triangle exceed the length of the longest side. Here the requirement for the given lengths to form a triangle is ...
6 cm + 9 cm > 15 cm . . . . . . . . false
The given side lengths do not satisfy the triangle inequality, so do not form any kind of triangle.
__
Additional comment
Side lengths of a right triangle will satisfy the Pythagorean theorem, so that would be the test for a right triangle. We used the triangle inequality here, because we noticed the short sides add up to the long side. We need go no further, because these lengths do not even form a triangle.
Jogging at a constant speed, Ahmed
completes
a run of 4 miles in 60 minutes.
Answer: Every 15 minutes he runs a mile. 60 / 4 = 15
I hope this helps or answers the question needed
Find the domain of the relation represented on the mapping diagram:
3-------> -1
6-------> 4
8-------> 4
Explain how to do it please!!
{3, 6, 8} is the domain of the relation R={(3,-1)(6,4)(8,4)}
What is Function?An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
A function has three important parts, domain, codomain and Range.
The domain of the relation R is the set of arguments i.e. first members of each ordered pair and the codomain is the set of which the values i.e. second members of all the ordered pairs.
In the Given relation
R={(3,-1)(6,4)(8,4)}
All the values in x place are domain values.
The domain equals all of the x values which are r on the left in a ordered pair
x= {3, 6, 8}
Hence {3, 6, 8} is the domain of the relation R={(3,-1)(6,4)(8,4)}
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a recipe calls for 2 tsp of vanilla, we are doing a 6 times batch, how many cups of *
vanilla do you need?
Answer:
0.75 cups
Step-by-step explanation:
each batch needs 2 tablespoons your doing 6 batches so 6x2 is 12 and 12 tablespoons is 0.75 cups
Solve for L.
A=LW
L=
f(x)= -8x ; f(-3) times f(5)
Answer: -960... It seems like a really big answer but it's right!
Step-by-step explanation:
what is negative five times negative one third
Answer:
-5 1/3
Step-by-step explanation:
Answer:
5/3
Step-by-step explanation:
A negative times a negative is a positive. So your answer will be positive.
When multiplying a whole number times a fraction, you multiply the whole (big) number times the top number (numerator) and just keep the bottom number (denominator) the same.
5 × 1/3
Is 5×1 on TOP and just keep the 3 on the bottom.
(5×1)/3
5/3
5/3 is the best answer, but if you are being asked for a "mixed number" then 5/3 is the same as 1 2/3.
the value of [tex]\sqrt{6}[/tex] is not -4 because ______.
Answer:
D
Step-by-step explanation:
(-4^2) = 16 not -16
since,
you cant raise a number to an even power and get a negative value
WILL MARK BRAINLIEST Simplify 3√5-2√7+√45-√28.
O 2√12
O 2√2
O 6√5-4√7
O 6√10-4√14
Answer:
The result of [tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + \sqrt{45} - \sqrt{28} [/tex] is [tex]\tt{}6\sqrt{ 5} - 4 \sqrt{7}. [/tex]
Step-by-step explanation:
[tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + \sqrt{45} - \sqrt{28} [/tex]
[tex]\tt{}3 \sqrt{5} - 2 \sqrt{7} + 3\sqrt{5} -2 \sqrt{7}[/tex]
[tex]\tt{}6\sqrt{5} - 4 \sqrt{7}[/tex]
I need help in math can you please help me
That's it, do you have any question about the answer? my ple
Allan has 4 buckets of paint. He spills 3. buckets. Estimate how many buckets of paint Allan has left.
14
12
O
2
bucket
O1 bucket
01- buckets
O2 buckets
angle 1 and angle 2 are supplements with m angle 1 = 10y + 46 and m angle 2 = 6y + 6. Find m angle 2
Answer: 54 Degrees
Step-by-step explanation:
Supplements add up to 180 deg.
Ang. #1 + Ang. #2 = 180 Deg
Angle 1=10y+46
Angle 2= 6y+6
16y+52=180 deg
16y=128
y=8
Since angle #2 is 6y+6, plugin y=8 6(8)+6=54 deg
:)