Answer:
One segment is 8.89 long and the other one is: 11.11 long
Step-by-step explanation:
Recall that the bisector of a triangle divides the opposite side it intersects into two segments that are proportional to the other two sides of the triangle.
In our case the bisector is generated on the angle opposite to the size 20 side (it is the smallest angle in the triangle since it is opposite to the smallest side). This bisector divides the side of length 20 into a segment of length x and a segment of length 20-x.
The proportionality indicated by the bisector theorem gives;
[tex]\frac{20-x}{x} =\frac{30}{24}[/tex]
and we can solve for "x":
[tex]\frac{20-x}{x} =\frac{30}{24}\\24\,(20-x)=30\,x\\480-24\,x=30\,x\\480=54\,x\\x=480/54\\x\approx8.89[/tex]
Then the other segment is: 20 - 8.89 = 11.11
If 10% of a number is 12, what is 5% of half the original number?
Simplify the expression. (7−2)24+34−10 13 35 53 3
Answer:
144
Step-by-step explanation:
Subtract 2 from 7 to get 5.
5×24+34−10=144
Multiply 5 and 24 to get 120.
120+34−10=144
Add 120 and 34 to get 154.
154−10=144
Subtract 10 from 154 to get 144.
The result of the given expression is 144
Expression has different terms separated by mathematical signs
Given the expression
(7−2)24+34−10
Using the PEDMAS rule
Parethesis first to have:
(7−2)24+34−10
= 5(24) + 34 - 10
Followed by multiplication
= 120 + 34 - 10
Then followed by Addition
= 154 - 10
Finally subtraction
154 - 10 = 144
The result of the given expression is 144
Learn more here: https://brainly.com/question/17788156
A large western state consists of 3129 million acres of land. Approximately 55% of this land is federally owned. Find the number of acres that are not federally owned
Answer:
1408.5 acres
Step-by-step explanation:
If 55% of the land is federally owned, then 100 - 55 = 45% of the land is not federally owned.
We need to find how many acres are not federally owned, in other words, we need to find how many acres represent 45% of the total 3129 acres. So, to do this we can apply a rule of three:
3129 acres ---- 100%
x acres ------ 45%
[tex]x=\frac{(3129)(45)}{100} =3129(0.45)= 1408.05[/tex]
Therefore, the total of acres that are not federally owned are 1408.5 acres.
Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50 of the cost. If the original cost of the bike is x dollars, which of the expressions below represent the amount Brandon has to pay?
Answer:
0.85x - $50
Step-by-step explanation:
Given that :
Brandon wants to buy a new bike. The model he likes is on sale for 15% off its original price. His parents agree to pay for $50 of the cost. If the original cost of the bike is x dollars, which of the expressions below represent the amount Brandon has to pay
Discount on price = 15%
Amount parents agreed to pay = $50
Cost of bike = x
Discount on bike = 0.15x
Cost after discount is removed = (x - 0.15x) = 0.85x
Parent pays $50 of cost price, amount Brandon will have to pay equals :
(0.85x - $50)
Answer:
0.85x - $50
Step-by-step explanation:
why isnt 16:14 equivlant to 64:60
Answer:
The scalar used does not exist in the real number system.
Step-by-step explanation:
The ratio 16:14 is not equivalent to the ratio 64:60 because the scalar used does not exist in the real number system.
Note, that the ratio 64:60 can be scaled down by 4 to be the ratio 16:15, which is not the ratio 16:14.
In order to scale 64:60 to 16:14 or vise versa, you'd have to use a number that simply does not exist in the real number system.
Cheers.
Angle A and angle B are supplementary angles. If
angle B is 30° more than four times angle A, find
angle A and angle B.
Answer:
Angle A is 30
Angle B is 150
Step-by-step explanation:
So we have the supplementary angles A and B. In other words:
[tex]A+B=180[/tex]
We are also told that Angle B is 30 more than four times Angle A. In an equation, this is:
[tex]B=30+4A[/tex]
We now have a system of equations. Solve by substitution of B into the first equation:
[tex]A+B=180[/tex]
[tex]A+(30+4A)=180[/tex]
Combine like terms:
[tex]5A+30=180[/tex]
Subtract 30:
[tex]5A=150[/tex]
Divide by 5:
[tex]A=30[/tex]
So, Angle A is 30 degrees.
And since the angles are supplementary, this means that Angle B is 180 minus 30 or 150 degrees.
fiften increased by a number
Answer:
15+n
Step-by-step explanation:
Let the number be 'n'
Fifteen=15
increased by= +
a number= n
Hope this helps ;) ❤❤❤
Answer:
It could be 15+ (any varible)=?
Step-by-step explanation:
8 gal to 9 1/3 gal write ratio in lowest form with whole numbers in numerator and denominator
Answer:
[tex]\bold{\dfrac{6}{7}}[/tex]
Step-by-step explanation:
Given ratio is:
8 gal to [tex]9\frac{1}3[/tex] gal
To find:
Ratio in Lowest form with whole numbers in numerator and denominator.
Solution:
First of all, let us convert [tex]9\frac{1}3[/tex] to simple [tex]\frac{p}{q}[/tex] form:
Formula:
[tex]a\dfrac{b}{c} = \dfrac{a\times c+b}c[/tex]
Using the formula, we get:
[tex]9\dfrac{1}{3} = \dfrac{9\times 3+1}{3} = \dfrac{28}{3}[/tex]
Now, let us have a look at the ratio:
[tex]8 : \dfrac{28}{3}[/tex]
Any ratio, [tex]p:q[/tex] can be written as [tex]\frac{p}{q}[/tex].
Writing given ratio as per above:
[tex]\dfrac{8}{\dfrac{28}{3}}\\\Rightarrow \dfrac{8 \times 3}{28}\\\Rightarrow \dfrac{2\times 3}{7}\\\Rightarrow \bold{\dfrac{6}{7}}[/tex]
Therefore, the answer is
[tex]\bold{\dfrac{6}{7}}[/tex]
On James’s MP3 player, he has 12 sad songs and 40 upbeat songs that he wants to put into playlists. He wants to have the same number of sad songs and upbeat songs in each playlist. What is the maximum number of playlists that he can create?
Answer:
4 playlists
:)
A garden hose faucet is able to fill a gallon conainer in 20 seconds. A homeowner accidentally left his hose on for a full day. How many gallons per day can a hose release?
One day is equivalent to 86400 seconds.
So 86400÷20=4320 gallons
Simplify the expression where possible. (6 3 ) -3
.
Model Problem
Coffee vs. Tea
A café by Lindsay's house sells coffee and tea. They are trying to make the most amount of money
possible. In other words they are trying to maximize profit. They asked me to look at their sales
receipts and figure out what they should do. But they had a few limitations on what could be done.
Constraint #1: The Baristas (the people who makes the coffee) can only reasonably serve 90 cups
per shift. It can be 90 cups of coffee, 90 cups of tea or a mixture of the two.
Constraint #2: Coffee costs $3 per cup and Tea costs $2. In order to stay on track to pay their
bills, the owners would like to sell at least $120 worth of beverages every shift.
Constraint #3: They have a limited supply of coffee and tea that gets delivered every day. If they
don't want to sell out (And annoy customers) they can sell no more than 70 cups of tea per shift.
Constraint #4: Similar to the last constraint, they can only sell 60 cups of coffee per shift before
they sell out.
Question: How much tea and how much coffee should they sell every shift in order to maximize
profits? They make $1.10 on each cup of coffee and $.90 on each cup of tea.
Answer:
coffee is the best answer in my mind
Justo ayer fue el cumpleaños de Mauricio. Si a la edad e Mauricio, le sumo 13, al resultado le resto 10, luego al nuevo resultado lo divido entre 23 y finalmente le sumo 20, obtendré el número 21. ¿EN QUE AÑO nació mauricio?
Answer:
Mauricio nació en el año 2000.
Step-by-step explanation:
Supóngase que el cumpleaños se celebra en el año 2020, si [tex]x[/tex] es la edad actual de Mauricio, entonces la expresión matemática que traduce el enunciado del problema es:
[tex]\frac{(x+13)-10}{23} +20 = 21[/tex]
Ahora, se desarrolla y se simplifica la ecuación:
[tex]\frac{x+3}{23}+20 = 21[/tex]
[tex]\frac{x+3}{23} = 1[/tex]
Se despeja [tex]x[/tex]:
[tex]x +3 = 23[/tex]
[tex]x = 20[/tex]
Mauricio tiene 20 años.
Ahora, el año de nacimiento de Mauricio es la sustracción de la edad de Mauricio del año actual:
[tex]y = 2020-20[/tex]
[tex]y = 2000[/tex]
Mauricio nació en el año 2000.
Which is the mode of this data set?
55, 78, 43, 39, 78, 61, 75, 50, 43, 78
Answer:
78
Step-by-step explanation:
Mode = number that appears most in a set of numbers
The number that appears the most in this set is 78. So, the mode is 78. Hope it helps!
Answer:
Step-by-step explanation:
arrange in ascending order
39,43,43,50,55,61,75,78,78,78
mode=78
In a game experience, the experience of monsters, E, is measured by the formula E= 100M/L, where M=number monsters and L=level of monsters. Solve the formula for L
Answer: The formula solved for L is E/100M = L.
Step-by-step explanation:
So far we have the givens:
E, is measured by the formula E = 100M/L, where M = number monsters and L= level of monsters and solve for L.
Thus, isolate L to solve for it.
E = 100M/L
Divide each side by 100M to get rid of it and to free L.
E/100M = L
Hence your answer!
Answer: 50M/E is correct
Step-by-step explanation: I got it right :D
I’ve noticed here are around 4 ways to solve a Quadratic Equation. Factoring, Completing the square, The quadratic Formula, and graphing. With some equations, it seems that all 4 can be used for solving. But for a lot of equations, sometimes factoring doesn’t work, and you’ll have to use the Quadratic formula. Or maybe the Quadratic Formula is too slow and you need to factor instead etc. Is there an easy or quick way to tell, just by looking at a quadratic equation, which method is best for solving?
Answer:
See explanation
Step-by-step explanation:
Usually, I just find the quadratic formula the easiest to go, but here are some tips to tell if which you should use.
1. First see if you can get integer values for the roots to multiply to c and add to b.
This is the easiest way to solve a quadratic equation, and I always check for whether I can easily find the roots by multiply two numbers for c and adding them for b.
For instance, the Quadratic [tex]x^2 + 5x + 6[/tex]
I can easily see that 2 and 3 are the roots here - as [tex]2\cdot3=6[/tex] and [tex]2+3=5[/tex]. If you can do this and receive integer values, then great! I'd definitely stick with this.
2. See if you can complete the square
If you have a quadratic which is a perfect square, you'll be able to tell if c is a perfect square, and b is twice that number. This will be easiest. Any quadratic equation can be solved by completing the square, but I personally stick to this method only if I can tell it's a perfect square quadratic.
3. Stick to the Quadratic Formula
If all else fails, go with the Quadratic formula. It's not that hard and it gets the job done. I would highly discourage going with graphing, as it takes too much time and it's quite a hassle unless you have a graphing calculator.
I really hope this helped!
Answer:
In my preferred order, ...
use a graphing calculatorfactoruse the quadratic formulaStep-by-step explanation:
My personal favorite is to use a graphing calculator. If it shows the zeros are whole numbers, your solution is at hand. If it shows the zeros are recognizable decimal fractions*, the solution is also at hand. If it shows the zeros are unrecognizable as fractions, they are likely irrational. Then the vertex of the graph gets you most of the way to an exact solution.
If the quadratic's coefficients are not integers, then the quadratic formula is least likely to give difficulty.
Example
The attached is a graph of the quadratic ...
y = 2x^2 -3x -4
We can see from the x-intercepts that the roots are irrational (none are fractions with a denominator that is a factor of 2). The vertex of the graph is (3/4, -5 1/8), so the vertex form of the equation for this graph is ...
y = 2(x -3/4)^2 -(5 1/8)
Solving this for y=0, we find ...
0 = 2(x -3/4)^2 -(5 1/8)
5 1/8 = 2(x -3/4)^2 . . . . . .add the constant (vertex y-value)
(5 1/8)/2 = (x -3/4)^2 . . . . divide by 2 (the leading coefficient)
2 9/16 = (x -3/4)^2
x = 3/4 ± √(41/16) . . . . . . . add the horizontal offset (vertex x-value)
x = (3 ± √41)/4 . . . . . . . . . . simplify
If you see what we've done here, you can write down the answer from the vertex and the leading coefficient:
x = (3/4) ± √((5 1/8)/2) . . . . . vertex (3/4, 5 1/8), leading coefficient 2
__
With a little practice, factoring can be a relatively simple way to find the solution. As a preliminary step, the equation should be divided by any common factor of the coefficients, so they are all relatively prime. It helps immensely to know your times tables thoroughly. I like this method, because it can get a solution with fewer steps than using the quadratic formula.
The product of two binomials is ...
(ax +b)(cx +d) = acx^2 +(ad+bc)x +bd
The product of the leading coefficient (ac) and the constant (bd) is abcd. It has factors of ad and bc, whose sum is the coefficient of the linear term. So, if you can factor the product of the leading and trailing coefficients and find a sum of factors that is the middle coefficient, you're home free. Sometimes the factors jump out at you, and sometimes you need to list a bunch of them before you see what you need.
In our example, we would be looking for factors of 2(-4) = -8 that have a sum of -3.
-8 = (-8)(1) = -4(2) = (-2)(4) = (-1)(8)
These pairs have sums of -7, -2, 2, 7. None of the sums is -3, so factoring by integers is not possible. You can see that it is unnecessary to list the pairs with positive sums in this case.
Once you have the values ad and bc, you can see that 'a' is the greatest common divisor of ac and ad. Then ad/a = d, and ac/a = c. Now you know 3 of the 4 numbers in the binomial factors.
_____
* The Rational Root Theorem can tell you what reasonable fractions might be for your quadratic. You should be familiar with the decimal equivalents of fractions with small integer denominators.
A playground is (4x + 4) feet wide and 6x feet long. Find the area of the playground.
Area of a rectangle= length*width
So:
Area of the playground= (6x)(4x+4)
Use distributive property.
Area of the playground= (6x*4x)+(6x*4)
=24x^2+24x
Answer: 24x^2+24x
what is 5x - 3 = -28
Answer:
X= -5
Step-by-step explanation:
5x -3 = -28
Add 3 to both sides
5x= -25
divide by 5 on both sides to isolate x
x=-5
A store donates 3% of total sales to a charity. Mr. Winn bought 4 jackets at the store. Each jacket had a price of $150. How much money did the store donate to charity because of the jackets Mr. Winn bought?
Answer: The donated $18
Step-by-step explanation:
If each jacket cost $150 then multiply 150 by 4 to find out the total that the store received.
150 * 4 = 600
Now find 3% of 600 to find out how much they donated to the charity.
3% * 600 = $18
(4x5 - 13x2 - 10) - (2x5 - 9x2 + 15)
2x5 - 11x2 + 5
2x5 - 4x2 - 25
2x5 - 4x2 + 5
-27x7
Next QuestionNext
Answer:
2x5-4x2-25
Step-by-step explanation:
First you distribute the negative sign to the second equation which makes each number it's opposite
Which would result in 4x5-13x2-10-2x5+9x2-15
Then you combine like terms and get 2x5-4x2-25
Answer:
-23
Step-by-step explanation:
what is the value when 25 is subtracted from - 25
Answer:
[tex]\Huge \boxed{-50}[/tex]
Step-by-step explanation:
25 is subtracted from -25.
[tex]\Rightarrow -25-25 \\ \\ \\ \Rightarrow -50[/tex]
The value is -50.
A recipe that makes 25 oatmeal cookies calls for 2.5 cups of oats and one cup of sugar. Jerry needs to make 195 cookies for his party. How many cups of oats will he need?
5. Which of the following is a multiple of 8?
A 4
C 20
B 8
D 100
Answer:
8
Step-by-step explanation:
8 can be divisible by 8. Therefore, it would be a multiple of 8.
The first multiple of a number is always that number.
All other options given are not multiples of 8.
Hope this helps.
Given the following equation, solve for r.
Step-by-step explanation:
I try my best I not a math expert
3(x + 5) = 2(4x + 9)
Answer:
x=-3/5
Step-by-step explanation:
3(x + 5) = 2(4x + 9)
First, distribute:
3(x)+3(5)=2(4x)+2(9)
3x+15=8x+18
-5x= 3
x= -3/5
someone tell me the answers tho these please. Part A: Factor 3x2y2 − 2xy2 − 8y2. Show your work. (4 points) Part B: Factor x2 + 10x + 25. Show your work. (3 points) Part C: Factor x2 − 36. Show your work. (3 points)
Step-by-step explanation:
x2 + 10x + 25
x2 + 5x + 5x + 25
x(x + 5) + 5(x + 5)
(x + 5)(x+ 5) are the factors
x2 - 36
Both are squares so
x2 - (4)2
HELP PLEASE! I dont know what to do now! 10 points!
Answer:
It would be losing 300.
Step-by-step explanation:
The opposite of gaining is losing the integer would be -300
Answer:
-300
Step-by-step explanation:
3(2v-9)=5 solve for v
Answer:
v=16/3
Step-by-step explanation:
3(2v-9)=5
Multiply 2v and -9 with 3
6v-27=5
Add 27 to both sides
6v=32
Divide both sides by 6
v=16/3
Find the discriminant then state the number of rational, irrational, or imaginary solutions:
11. 9n^2 -3n+2=0
12. y^2 +6y+4=0
13. 9m^2 +6m+1=0
14. -2a^2 -2a+1=0
15. -9b^2 +8b=8
16. -x^2 -9=6x
17. 4r^2 +6=-4r
18. -3b^2 -8b=-1
Answer:
no
Step-by-step explanation:
5. Will had a summer job at a car wash. He earned $8.50 per hour and was expected to
pay a one-time fee of $15 for his uniform. If he worked 32 hours his first week, about how
much money did he make at the end of his first week? (Can you help explain step by step ?)
Answer:
$257
Step-by-step explanation:
First we multiply the rate by time
8.5*32=$272
then we subtract the uniform fee
272-15=$257
(plz give brianliest ty)
Answer:
8.50x-15
Step-by-step explanation:
Flat rate is 15 so you subtract from income made. 8.50x is how much you make depending on how many hours you work. Thus income-fee= how much you make first week.