solve the given equation state the number and type of roots x^2+x-12=0
Answer:
Step-by-step explanation:
x 1= 3 x 2=−4
Bruce wants to make 50 ml of an alcohol solution with a 12% concentration. He has a 10% alcohol solution and a 15% alcohol solution. The equation 0.10x + 0.15(50 – x) = 0.12(50) can be used to find the amount of 10% alcohol solution Bruce should use.
How much of the 10% alcohol solution should Bruce use
Answer:
30 mL
Step-by-step explanation:
You are being asked to solve the given equation for the value of x.
__
0.10x +0.15(50 -x) = 0.12(50) . . . . given
-0.05x = -0.03(50) . . . . . subtract 0.15(50), combine terms
x = 30 . . . . . . . . . . . divide by -0.05
Bruce should use 30 mL of the 10% alcohol solution.
Solve for an angle in right triangles. Round to the nearest hundredths
Answer:
Use SOH CAH TOA to rember how the trig function fit on the triangle
Step-by-step explanation:
we are given the Hypotenuse and the Opposite or H and O look for the trig function with each of those, SOH is good
Sin Ф = Opp / Hyp, or SOH
now plug in what you are given
Sin Ф = 5 / 8
use inverse trig fuction to find the angle
arcSin ( Sin Ф) = arcSin ( 5/8)
trig functions cancel out
Ф = arcSin(5/8)
I'm using my calculator to find the arcSin(5/8)
Ф=38.6821...°
also make sure you know if your calculator is in degrees or radians.
Ф=38.68° to the nearest hundredth :)
Answer:
∠A = 38.68°
Step-by-step explanation:
The side opposing ∠A and the hypotenuse are given.
Therefore, take the inverse sin function of ∠A.
sin∠A = 5/8∠A = sin⁻¹ (0.625)∠A = 38.6821875∠A = 38.68° (nearest hundredth)Mary spends 2 2/3 hours on math homework everyday. She also spends 3 1/3 hours on art homework. How much time does Mary spend in total working on math and art homework?
It has to be like an actual fraction. All I know is that 24 is the whole number. Use that to solve the problem.
Answer:
6 hours
Step-by-step explanation:
2 2/3 +3 1/3= 5+1=6
Answer:
2 2/3+ 3 1/3 = 6. Multiply 6 by 4 weeks. 24 as your whole number.
Step-by-step explanation:
hope this helps
Enrique estimates that his utilities will cost him $86.00 per month over the courses of the next 3 years. What is his total estimated cost for utilities over the next 3 year period??
Please help thank you !!!
Answer:
$3096
Step-by-step explanation:
There are 12 months in 1 year.
3 × 12 = 36
There are 36 months in 3 years.
$86 × 36 = $3096
Answer:
3096
Step-by-step explanation:
I just completed the quiz.
Please help i have an assignment due TODAY i need to get this done
rules:
NO LINKS! im not getting myself a virus
Answer:
r = 50 degrees.
Step-by-step explanation:
r = 50 degrees ( vertical angles are congruent).
Question #12: A department store has a discount on shoes based on a
percentage of the price. Suppose one pair of shoes is marked down from
$70 to $49. What is the price for a $110 pair of shoes after the discount is
applied?
a
O $89.00
O $77.00
O $73.33
O $33.00
Answer:
$77
Step-by-step explanation:
The answer is $77 because first you need to find how much money was discounted by doing 70-49 to get 21. Then you need to find how much percent 21 is of 70 by doing 21/70, then you would get 0.3 which is 30% since you have to multiply it by 100. This means that there is a 30% discount. Then you would do 0.3*110=33. This means that the 30% discount takes away $33. So 110-33=77. The answer is $77.
please answer correctly don't answer a link thanks. FUNDAMENTAL PRINCIPLE OF COUNTING.
The answer is [tex] {2}^{5} [/tex] or 32.
The best way to represent this is with a binary tree. Each split represents a choice, and each line represents a possible outcome. Choice #1 at the top of the tree has 2 possible outcomes. The second level repeats that process with 2 possible choices and 4 possible outcomes, this repeats for all 5 levels giving us 32 possible outcomes at the bottom.
2)There will be eight outcomes.
Sample space : {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT}
Suppose 3 and 8 are the only individual scores that can be made in a certain game. How many integer total scores are impossible to obtain?
Answer: 3
Step-by-step explanation:
3x8 = 24
24x2= 48!
8x12= 96!
Answers must be divisible by both numbers, and achievable by both inputs.
Hope This Helped
How many different three person relay teams can be chosen from six students?
Regan operates an orange juice stand. On Monday she used 1/3 of a bag of oranges. On
Tuesday she used 2/5 as many oranges as on Monday. How many bags of oranges did Reg
use on Tuesday?
Write your answer as a fraction or as a whole or mixed number.
Please help meee
Answer:
0.825 bags of oranges
Step-by-step explanation:
1/3 is 0.33 and 2/5 is 0.4 so 0.33/0.4 is 0.825
[tex] \displaystyle \rm\int_{0}^1 { ln }^{2k} \left \lgroup \frac{ ln \left \lgroup \dfrac{1 - \sqrt{1 - {x}^{2} } }{x} \right \rgroup }{ ln \left \lgroup \dfrac{1 + \sqrt{1 - {x}^{2} } }{x} \right \rgroup } \right \rgroup \: dx[/tex]
Substitute [tex]x\mapsto\sqrt{1-x^2}[/tex], which transforms the integral to
[tex]\displaystyle \int_0^1 \ln^{2k} \left(\frac{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}\right) \, dx = \int_0^1 \ln^{2k}\left(\frac{\ln\left(\frac{1-x}{\sqrt{1-x^2}}\right)}{\ln\left(\frac{1+x}{\sqrt{1-x^2}}\right)}\right) \frac{x}{\sqrt{1-x^2}} \, dx[/tex]
and factoring [tex]\sqrt{1-x^2}=\sqrt{(1-x)(1+x)}[/tex] reduces this to
[tex]\displaystyle = \int_0^1 \ln^{2k}\left(\frac{\ln\left(\sqrt{\frac{1-x}{1+x}}\right)}{\ln\left(\sqrt{\frac{1+x}{1-x}}\right)}\right) \frac x{\sqrt{1-x^2}} \, dx[/tex]
The inner logarithms differ only by a sign, so that
[tex]\displaystyle = \int_0^1 \ln^{2k}(-1) \frac x{\sqrt{1-x^2}} \, dx[/tex]
Using the principal branch of the complex logarithm, we have
[tex]\ln(-1) = \ln|-1| + i\arg(-1) = i\pi[/tex]
and hence
[tex]\displaystyle \int_0^1 \ln^{2k} \left(\frac{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}{\ln\left(\frac{1-\sqrt{1-x^2}}x\right)}\right) \, dx = (i\pi)^{2k} \underbrace{\int_0^1 \frac x{\sqrt{1-x^2}} \, dx}_{=1} = \boxed{(-\pi^2)^k}[/tex]
where I assume k is an integer.
Set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-
Jordan elimination.
Sylvia invested a total of $27,000. She invested part of the money in a certificate of deposit (CD) that earns 3% simple
interest per year. She invested in a stock that returns the equivalent of 7% simple interest, and she invested in a bond fund
that returns 2%. She invested three times as much in the stock as she did in the CD, and earned a total of $1140 at the
end of 1 yr. How much principal did she put in each investment?
She invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.
DistributionsGiven that Sylvia invested a total of $27,000, and she invested part of the money in a certificate of deposit (CD) that earns 3% simple interest per year, she invested in a stock that returns the equivalent of 7% simple interest, and she invested in a bond fund that returns 2%, and she invested three times as much in the stock as she did in the CD, and earned a total of $1140 at the end of 1 yr, to determine how much principal did she put in each investment, the following calculation must be made:
9000 x 0.07 + 3000 x 0.03 + 15000 x 0.02 = 630 + 90 + 300 = 10209900 x 0.07 + 3300 x 0.03 + 13800 x 0.02 = 693 + 99 + 276 = 106812,000 x 0.07 + 4,000 x 0.03 + 11,000 x 0.02 = 840 + 120 + 220 = 1,18011400 x 0.07 + 3800 x 0.03 + 11800 x 0.02 = 798 + 114 + 236 = 114810800 x 0.07 + 3600 x 0.03 + 12600 x 0.02 = 756 + 108 + 252 = 111611160 x 0.07 + 3720 x 0.03 + 12120 x 0.02 = 781.2 + 111.6 + 242.4 = 1135.211190 x 0.07 + 3730 x 0.03 + 12080 x 0.02 = 783.3 + 111.9 + 241.6 = 1136.811250 x 0.07 + 3750 x 0.03 + 12000 x 0.02 = 787.5 + 112.5 + 240 = 1140Therefore, she invested $11,250 in the stock, $3,750 in the CD and $12,000 in the bond fund.
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Find the length of the arc.
120°
6ft
Answer:
The length of the arc is 8*pi cm. An arc that subtends a central angle of 120 degrees has a length of 120/360 = 1/3 the length of the total circumference of the circle. We know the entire circumference of the circle is 2πr, which in this case is 2π*12 = 24π.
Step-by-step explanation:
sorry I only have the 8
Write a propotion that can be used to convert 50 meters into kilometers. Then solve
Answer:
0.05km
Step-by-step explanation:
There are 1000 meters in a single kilometer. Using some dimensional analysis, we get set up the following expression:
[tex]\frac{50}{1} \frac{meters}{1}\frac{1}{1000} \frac{kilometers}{meters}[/tex]
The meters will cancel leaving the units of kilometers:
[tex]\frac{50}{1000} km=0.05km[/tex]
Consider a triangle...
Answer:
1. Triangle: B = 47.0° , C = 103.05° , c = 2.53 cm
2. Lake: c = 1105.31 ft
Step-by-step explanation:
Law of Sine Formula:[tex]\frac{sin(A)}{A} = \frac{sin(B)}{B} = \frac{sin(C)}{C}[/tex]
Given: A = 30° , a = 1.3 cm , b = 1.9 cm
[tex]\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9} = \frac{sin(C)}{C}[/tex]
Solving for sin(B). Cross Multiply.
[tex]\frac{sin(30)}{1.3} = \frac{sin(B)}{1.9}\\1.3*sin(B)=1.9*sin(30)\\sin(B)=\frac{1.9*sin(30)}{1.3} \\[/tex]
B = sin^-1( [tex]\frac{1.9*sin(30)}{1.3}[/tex] )
B ≈ 46.9509202
B = 47.0°
Solve for C°
A° + B° + C° = 180°
30° + 46.95° + C° = 180°
C° = 180° - 30° - 46.95°
C° = 103.05°
Solve for sin(C)
[tex]\frac{sin(30)}{1.3} = \frac{sin(103.05)}{C}\\[/tex]
Cross Multiply
[tex]C*sin(30)=1.3*sin(103.05)\\C=\frac{1.3*sin(103.05)}{sin(30)}[/tex]
C ≈ 2.532850806
C = 2.53 cm
Law of Cosine Formula: [tex]c^2=a^2+b^2-2*a*b*cos(C)[/tex]
Given: a = 850 ft , b = 960 ft , C=75°
Solve for c.
[tex]c^2=a^2+b^2-2*a*b*cos(C)\\c^2=(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\\\c=\sqrt{(850ft)^2+(960ft)^2-2*(850ft)*(960ft)*cos(75)\\} \\[/tex]
c ≈ 1105.308698
c = 1105.31 ft
5 Four children are measuring their height.
Aisha
1.39 metres
Teddy
1.37 metres
Scott
1.4 metres
Kim
1.43 metres
Order the children from tallest to shortest.
Find the length of the third side . If necessary , round to the nearest tenth .
Answer:
umm 9?
Step-by-step explanation:
Suppose that $3^a = 2$ and $3^b = 5$. If \[3^x = 150,\]then write an expression for $x$ in terms of $a$ and $b$.
Use logarithms to solve for a.
[tex]3^a = 2 \implies \log_3(3^a) = a\log_3(3) = \log_3(2) \implies a = \log_3(2)[/tex]
Similarly, for b and x.
[tex]3^b = 5 \implies b = \log_3(5)[/tex]
[tex]3^x = 150 \implies x = \log_3(150)[/tex]
Factorize 150:
150 = 2 • 3 • 5²
Then we can expand log₃(150) using the product-to-sum and exponent property,
[tex]\log_3(150) = \log_3(2\times3\times5^2) = \log_3(2) + \log_3(3) + \log_3(5^2)[/tex]
[tex]\implies \log_3(15) = \log_3(2) + 1 + 2 \log_3(5) \iff \boxed{x = 1 + a + 2b}[/tex]
The sum of the two numbers is 40. One number is 3 times the other number. Find the 2 numbers
Answer:
10 and 30
Step-by-step explanation:
The sum of 10 and 30 is 40.
30 is three times ten (10 x 3 = 30).
hope this helps!
The answer is 10 and 30
10 times 3 is 30, meaning 10 will be the number times 3 they wanted. 10 + 30 is 40, therefore the answer is 10 and 30
The committee spent $372 on costumes for 20 people each costume cost the same amount of money, how much did each costume cost, in dollars ? PLEASE ANSWER I'LL GIVE 68 POINTS TO THE FIRST ONE THAT MAKES SINCE, AND I'LL MAKE UU BRAINLIEST, also I'm gonna ask 4 questions on my page and whoever answers them all first get 100 points I promise!
Answer:
$18.60
Step-by-step explanation:
The total amount spent is $372, and this can be divided by 20. Each costume would cost $18.60.
If 43,560 square feet equals one acre, how many acres are in one square mile?
Answer: 640
Step-by-step explanation:
How many acres are there in 1 square mile? There are 640 acres in 1 square mile. To convert from square miles to acres, multiply your figure by 640 (or divide by 0.0015625) .
Answer:
640 acres²
Divide the area value by 68
[tex]43,560 / 68 = 640[/tex]
or
[tex]1~mile^2 * 640 = 640[/tex]
you multiply the area value by 640 for each square mile, since there is only one square mile, the answer is 640
A candle's height, in inches, is a function of the number of hours it has been burning. After 4 hours the
candle's height is 10 inches, and after 16 hours the candle's height is 7 inches. The candle is burning at
constant rate.
Construct an equation that can be used to determine the candle's height, y, after x hours.
Enter your equation in the space provided. Enter only your equation.
The linear function that gives the candle's height, y, after x hours, is defined by:
y = -0.25x + 11.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.In this problem, in 12 hours, the height decayed 3 inches, hence the slope is given by:
m = -3/12 = -0.25.
So:
y = -0.25x + b.
After 4 hours, the height was of 10 inches, hence we use this to find b:
10 = -0.25(4) + b
b = 11
Thus the equation is given by:
y = -0.25x + 11.
More can be learned about linear functions at https://brainly.com/question/24808124
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Pleas I need help this is so hard
Answer:
Equation:
C = 1.75x + 5 25
A 22-mile ride costs $43.75.
Step-by-step explanation:
Because there is a flat fee of 5.25, only the first two equations could possibly be correct.
Then check with the examples given. If a 7 mile ride costs 17.50, the second equation cannot possibly be right. 7 miles times over $5 per mile will cost more than $35 not even including the flat fee.
Check:
1.75(7) + 5.25 = 17.50
and
12(1.75) + 5.25 = 26.25
So, the correct equation is
C = 1.75x + 5.25
Next use this equation to find the cost of the 22 mile ride.
1.75(22) + 5.25
= 43.75
jessica spent 20% of her money for snacks. She spent 25% of the remainder for school supplies. She has P30 left. How much money did Jessica start with?
When yara and her sister came home there was 3/4 of a pan of brownies left over yara and her sister ate 2/3 of the 3/4 pan of brownies how much of the entire pan of brownies did yara and her sister eat
Answer:
3/4_2/3 find the LCM= 1/12
The grades on a language midterm at Loyola are roughly symmetric with u = 69 and standard deviation = 4.0. Vanessa Scored 65 on the exam.
Answer:
the question can be understand but the question is not telling what to find
it is comfugen to answe're the question
Find an equation for the graph
Answer:
y=6^x+0.612 - 4
Step-by-step explanation:
x = -4 ---> horizontal asymptote
m = 6 ---> use points (0, -1) and (1, 5)
Parent function of the graph: [tex]y=b^x[/tex]
Our equation: [tex]y=6^x[/tex]
Add alterations:
Reflections = N/AVertical & horizontal shifts = down 4Vertical & horizontal stretches = left approx 0.612Final equation: y=6^x+0.612 - 4
A sweater is marked 30% off the original price. The original price was $37.50. What is the sale price of the sweater before sales tax?
(I will give brainliest if you show your work)!!
Answer:
$26.25
Step-by-step explanation:
To find the discounted price, subtract the discount amount from the original price. The amount of the discount is the product of the discount rate and the original price.
__
discounted price = original price - (original price) × (discount rate)
You can calculate it this way, or you can factor out the original price:
discounted price = (origina price) × (1 - discount rate)
= $37.50 × (1 -0.30) = $37.50 × 0.70 = $26.25
The sale price of the sweater is $26.25.
__
Additional comment
The amount of the discount is ...
$37.50 × 0.30 = $11.25
which makes the discounted price be ...
$37.50 -11.25 = $26.25
The length of a rectangle is five more than double the width. If the perimeter is 100 inches, find the dimensions.
width?
length?