You have th following equation;
[tex]3x^2-5x+1=0[/tex]In order to find the solution to the previous equation, use the quadratic formula:
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]In this case, a = 3, b = -5 and c = 1. By replacing these values into the quadratic formula, you obtain:
[tex]\begin{gathered} x=\frac{-(-5)\pm\sqrt[]{(-5)^2-4(3)(1)}}{2(1)} \\ x=\frac{5\pm\sqrt[]{25-12}}{2}=\frac{5\pm\sqrt[]{13}}{2} \\ x=\frac{5\pm3.60}{2}=2.5\pm1.80 \end{gathered}[/tex]Hence, the solutions are:
x = 2.5 + 1.80 = 4.30
x = 2.5 - 1.80 = 0.70
Write the equation for a circle with the following informationcenter: (5,-3) radius: 7
Step 1: Problem
To determine the equation of a circle with centre (5, -3) and radius 7
Step 2: Substitute the centre value and radius to the equation
[tex]\begin{gathered} \text{Equation of a circle} \\ (x-a)^2+(y-b)^2=r^2 \\ \text{centre (5,-3) , radius =7} \\ a=5,\text{ b=-3, r=7} \\ (x-5)^2+(y-(-3))^2=7^2 \end{gathered}[/tex]Step 3: Simplify the above equation
[tex]\begin{gathered} (x-5)(x-5)\text{ + (y+3)(y+3) = 49} \\ x^2-5x-5x+25+y^2+3y+3y+9=49 \\ x^2-10x+25+y^2+6y+9=49 \\ x^2+y^2-10x+6y=49-25-9 \\ x^2+y^2-10x+6y=15 \\ x^2+y^2-10x+6y-15=0 \end{gathered}[/tex]Hence the equation of the circle is
[tex]x^2+y^2-10x+6y-15=0[/tex]A shellfish absorbed 40% of the heavy metals in the water in and just the concentration of heavy metals is 0.0002 mg/m³ .The shellfish ingests 4 L of water per hour. How many heavy metal does it absorb in 3 months? (Assume there are 30 days in a month there are 1000 L in one cubic meter)
Answer:
Step-by-step explanation:
whats x+7, y equals and how do i find it?
The figure HGD was translated 7 units right; and then it was translated 9 units up. This can be shown as:
(x, y) → (x + 7, y + 9)
Answer = 9
Trying to figure out this for my home work assignment
Given:
Choosing a even number from the numbers between 1 and 10.
The sample space is
[tex]\mleft\lbrace2,3,4,5,6,7,8,9\mright\rbrace[/tex]Let A be the event of choosing a even number.
There are 4 out comes in the experiment.
Point A is shown on the complex plane.What is the standard form of the complex number that point A represents?
Hello there. To solve this question, we have to remember some properties about the representation of a complex number in the complex or Argand-Gauss plane.
Given the complex plane with the point A representing a complex number:
We have to remember that in the complex plane, a complex number z:
[tex]z=a+ib[/tex]has coordinates
[tex](a,\,b)[/tex]And it is more commonly represented by a vector starting at the origin and with the tip on this point.
In this case, we find that the coordinates of the point A are:
[tex]A=(-5,\,3)[/tex]Which means that the complex number is
[tex]-5+3i[/tex]And this is the answer contained in the last option.
Rewrite the polynomial expression using the GCF: 4x^2+8x+24 ?What is the new polynomial expression
GCF of 4,8 and 24
is. = 4
Then new expression is
y = 4• (x^2 + 2x + 6)
How do you decide which rational number operations to use to solve problems
One can decide which rational number operations to use to solve problems based on the context of the information.
What is a rational number?Studying rational numbers is significant because they illustrate how the world is so complex that we will never be able to comprehend it.
A rational number is defined as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. Every integer and 3/7, for example, are rational numbers.
A rational number is defined as the quotient of the fraction p/q of two integers, a numerator p and a non-zero denominator q. Every integer is a rational number since q might be equal to 1.
In this case, the operation include addition, subtraction, division, etc. This will be based on the context.
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24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas Choose the correct letter
Since 24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas
These are 2 equal ratios, then
They will be 2 equal fractions
[tex]\frac{24\text{ miles}}{1\text{ gallon}}=\frac{60\text{ miles}}{2.5\text{ gallons}}[/tex]The correct answer is D
Question 2 A recipe for homemade modeling clay requires 4 parts plain flour to 1 part cornstarch. Indicate whether each set of ingredients below is proportional to the recipe. Proportional Not Proportional 8 cups plain flour and 2 cups cornstarch 20 cups plain flour and 5 cups cornstarch 2 cups plain flour and 1 cup cornstarch Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Frequirements | Platform Status 2021 McGraw-HI Education. All Rights Reserved
The given ratio is 4 parts of plain flour to 1 part of cornstarch.
So, each recipe with the same ratio will be the answer.
As you can observe, the first choice is proportional because the plain flour is 4 times the cornstarch.
The second choice is proportional too because the plain flour is 4 times the cornstarch.
However, the last choice is not proportional because it has a ratio of double, which is not correct.
write three things you used to do but don't do anymore
Answer:
Trusting peoples
Be happy
make friends
A can contains 24 fluid ounces of fruit juice. How many pints of fruit juice does the can contain?A 12 ptB 3 pt C 1 1/2 ptD 1/3 pt
In order to convert from fluid ounce to pint, we need to know that 16 fluid ounces is equivalent to 1 pint.
Then, to find how many pints is 24 fluid ounces, we can use a rule of three:
[tex]\begin{gathered} 16\text{ fluid ounces}\to1\text{ pint} \\ 24\text{ fluid ounces}\to x\text{ pints} \\ \\ \frac{16}{24}=\frac{1}{x} \\ x=\frac{24}{16}=\frac{3}{2}=1\frac{1}{2} \end{gathered}[/tex]So 24 fluid ounces is equivalent to 1 1/2 pints, therefore the correct answer is C.
Sarah needs to lease out a music studio to record her new album. The studio chargesan initial studio-use fee plus an hourly fee for each hour in the studio. The fixed fee touse the studio is $150 and the total cost charged for 2 hours is $300. Write anequation for P, in terms of t, representing the amount of money Sarah would have topay to use the studio for t hours.
Fixed fee is 150
Total cost for 2 hours is 300
If the fixed fee is 150, and Sarah paid 300, then she paid 150 for the fixed fee and anohter 150 for the two hours, that means that each hour is 75
Then we can write the equation:
P = 75t + 150
Answer:
P = 75t + 150
Brody spent $260 on 4 chairs. To find out how much he spent on each chair, he did the following work in long division. 65 4) 260 -24 20 -20 0 Did he do the problem correctly? Why or why not? O A. No, because there is a remainder of o. B. No, because the first digit in the quotient should be 4, not 6. O C. No, because the problem should be 260 14. O D. Yes, he worked the problem correctly.
He spend $260 on 4 chairs:
To know how much he spent on each chair he must:
Divide 260 into 4You first pick the firt digit of the dividend (260) and look if you can divide that digit into the divider (4) as in this case the firt digit 2 cannot be divided into 4 you take the first and secon digit (26) and divide it into 4 (how many times fix 4 in 26), this is equal to 6 times (this is the first digit of the quotient), then you multiply the 6 by 4 (6*4=24)and put the result under the 26 to substract it:
Now you lower the zero (of the 260) next to the result of the previous subtraction:
And divide 20 into 4 (how many times fix 4 in 20) this is equal to 5 times (this is the second digit of the quotient ) then you multiply the 5 by 4 (5/4 =20) and put the result under the 20 to substract it:
The remainder of 0 means the division has not decimal result, the result of 260 into 4 is an interger number (65)
The firt digit of the quotient is 6 because 26 into 4 is 6.
So the division he did is the correct form to find how much cost each chair ($65)For the function f(x)5x – 2, what does the x represent?
The given function is
f(x) = 5x - 2
If we are given a function f(x), the x is called argument of the function.
You just have to pass argument x to get the value of f(x).
Tom Blasting invested $4,500 in an investment paying 10% compounded quarterly for 3 years. Find the interest
Given that Tom invested $4500 in an investment paying 10% compounded quarterly for 3 years.
We have to find the interest for the given time period.
We know that the formula of amount on a principal P, rate r per annum, time t years where interest is compounding quarterly is:
[tex]A=P(1+\frac{r}{4})^{4t}[/tex]Here, P = 4500, r = 0.1 and t = 3. So,
[tex]\begin{gathered} A=4500(1+\frac{0.1}{4})^{4(3)} \\ =4500(1+0.025)^{12} \\ =4500(1.025)^{12} \\ =4500(1.3448) \\ =6051.6 \end{gathered}[/tex]So, the amount we get is $6051.6.
Now, it is known that the interest is the difference between the amount and the principal. So,
[tex]\begin{gathered} \text{ interest}=\text{ amount-principal} \\ =6051.6-4500 \\ =1551.6 \end{gathered}[/tex]Thus, the interest is $1551.6.
which of the following would be an acceptable first step in simplifying the expression?
Solution:
Given:
[tex]\frac{cos\text{ }x}{1-sin\text{ }x}[/tex]The only acceptable first step in simplifying the expression from the options that would not change or alter the values of the expression is by multiplying (1 + sin x) to both the numerator and the denominator.
Therefore, the correct answer is OPTION B.
Which number is irrational? A. 0.656656665... B. 0.78 C. 2.35 D. 꼭
can be expressed as a fraction:
[tex]\frac{39}{50}[/tex]Therefore, it is a rational number
[tex]2.35[/tex]Can be expressed as a fraction:
[tex]\frac{47}{20}[/tex]Therefore, it is a rational number
However:
[tex]0.656656665[/tex]can't be expressed as a fraction, therefore, it is an irrational number
The graph of F(x), shown below, resembles the graph of G(X) = x2, but it hasbeen changed somewhat. Which of the following could be the equation ofF(x)?600 = x2FUO = ?O. A. F(x) = 0.272 - 3B. F(x) = -x2 - 3C. F(x) = 2x2 - 3D. F(X) = 32 - 3
You have G(x) = x².
take into account that G(x) can be considered as an streched of the F(X), moreover, F(x) is a translation of G(x) downward 3 units. If G(x) is an strech of F(x), then, G(x) is multipled by a constant lower than 1.
Then, based on the previous considerations, you have that the form of F(x) is:
F(x) = 0.2x² - 3
Find the exact values of the six trigonometric functions of the real number t
In a unit circle, given the (x,y) coordinate, x corresponds to cosine, and y corresponds to sine.
Then use the trigonometric identity to solve for tangent.
We therefore have the following ratios for sin, cos, and tan.
[tex]\begin{gathered} \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=\frac{\sin t}{\cos t}=\frac{\frac{15}{17}}{-\frac{8}{17}}=-\frac{15}{8} \\ \\ \text{Therefore,} \\ \sin t=\frac{15}{17} \\ \cos t=-\frac{8}{17} \\ \tan t=-\frac{15}{8} \end{gathered}[/tex]Solving for the reciprocal of sin, cos, and tan we have
[tex]\begin{gathered} \csc t=\Big(\sin t\Big)^{-1}=\Big(\frac{15}{17}\Big)^{-1}=\frac{17}{15} \\ \sec t=\Big(\cos t\Big)^{-1}=\Big(-\frac{8}{17}\Big)^{-1}=-\frac{17}{8} \\ \cot t=\Big(\tan t\Big)^{-1}=\Big(-\frac{15}{8}\Big)^{-1}=-\frac{8}{15} \\ \\ \text{Therefore,} \\ \csc t=\frac{17}{15} \\ \sec t=-\frac{17}{8} \\ \cot t=-\frac{8}{15} \end{gathered}[/tex]Select the similarity transformation(s) that make ABCD similar to EFGH.
Answer:
D
F
Explanation:
We would compare the coordinates of the corresponding vertices of rectangles ABCD and EFGH. We would compare vertices A and E. From the information given,
A = (1, - 2)
E = (- 2, 4)
If we apply (x, y)---(- x, - y) to A, it becomes (- 1, - - 2) = (- 1, 2)
If we apply (x, y)---(2x, 2y) to (- 1, 2), it becomes (2 * - 1, 2 * 2) = (- 2, 4)
Thus, the correct similarity transformation(s) that make ABCD similar to EFGH are
D
F
Audrey was attempting to draw a picture that would be the cover of the upcoming movie, Up 2. Thepicture would be of the house being carried by balloons again. She started her drawing with theballoons, which she wanted to make all the same size.She drew a circle for the balloon and found the radius, which was 9cm. How big around will all ofAudrey's balloon drawings be?——Please help me.
Audrey drew a circle for the balloon, this circle has a radius of 9 cm.
To know how big the baloon is you have to determine its circumference.
To calculate the circumference of a circle you have to multiply its diameter by number pi:
[tex]C=d\pi[/tex]The formula is C=dπ
The diameter is twice the circle so the diameter of the baloon is:
[tex]\begin{gathered} d=2r \\ d=2\cdot9 \\ d=18\operatorname{cm} \end{gathered}[/tex]The calculation for the diameter is:
d=2r
d=2*9
d=18cm
So the circumference of a circle with diameter 18cm is:
[tex]\begin{gathered} C=18\pi \\ C\cong56.548\operatorname{cm} \end{gathered}[/tex]For this balloon:
C=18π
C≅56.548xm
(A) A shipment of 10 cameras will likely have 6 defectives. If a person buys 2 cameras, what is the probability of getting 2 defectives?(B) What are the odds in favor of getting a defective camera?
To solve the exercise, you can use the formula of the binomial distribution:
[tex]\begin{gathered} P(x)=\binom{n}{x}p^x(1-p)^{n-x} \\ \text{ Where } \\ n\text{ is the number of trials (or the number being sampled)} \\ x\text{ is the number of successes desired} \\ p\text{ is the number of getting a success in one trial} \end{gathered}[/tex]So, in this case, we have:
[tex]\begin{gathered} n=10 \\ p=\frac{6}{10}=0.6 \end{gathered}[/tex]Because "success" is that there are defective cameras, 6 defective cameras out of 10 in total.
For part A, we have:
[tex]\begin{gathered} x=2 \\ P(x)=\binom{n}{x}p^x(1-p)^{n-x} \\ P(2)=\binom{10}{2}\cdot0.6^2\cdot(1-0.6)^{10-2} \\ P(2)=\binom{10}{2}\cdot0.6^2\cdot(0.4)^8 \\ P(2)=45\cdot0.36\cdot0.00065536 \\ P(2)=0.0106 \end{gathered}[/tex]Therefore, the probability of getting 2 defective cameras is 0.0106.
For part B, we have:
[tex]\begin{gathered} x=1 \\ P(x)=\binom{n}{x}p^x(1-p)^{n-x} \\ P(1)=\binom{10}{1}\cdot0.6^1\cdot(1-0.6)^{10-1} \\ P(1)=\binom{10}{1}\cdot0.6^1\cdot(0.4)^9 \\ P(1)=10\cdot0.6\cdot0.000262144 \\ P(1)=0.0016 \end{gathered}[/tex]Therefore, the probability of getting one defective camera is 0.0016.
You are researching the speed of sound waves in dry air
at 86°F. The linear function d = 0.217t represents the distances d (in miles) sound waves
travel in t seconds.
A. Represent the situation using a table and a graph.
B. Which of the three representations would you use to find how long it takes sound waves to travel 0.1 mile in dry air at 86°F? Explain.
By observing the pace at which this compressed region moves through the medium, we may determine the sound speed.The speed of sound is roughly 343 meters per second or 767 miles per hour in dry air at 20 degrees Celsius.
Calculate speed of sound wave?
The formula for the airborne sound speedThe equation for the speed of sound in air as a function of absolute temperature is given by the simplification of v=RTM:v=√γRTM=√γRTM(273K273K)=√(273K)γRM√T273K≈331m 2) Time required for 1620m to be traveled at that speed: t = d / v 0.217m / 0.1 m/s) = 2.17m/ s from the beginning of the sound wave.Since you were watching the lightning, you might have wanted to know the time.Then, using the speed of light, you can determine how long it was between the lights being generated o.217 meters distant from you and Light travels at a speed of3*108 m/s, hence t = 0.217m / (3*108 m/s) = 0.000669 s.
The answer is o.000669 s, as determined in step 2, even though this time is entirely negligible.
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The science class is taking a trip to the science center. there are 20 students and an unknown number of adult chaperones going. the bus holds at most 35 people.what is the greatest number of adults who can chaperone? I know the answer is 15. however, what they want us to do is create an equation using inequalities (<, >, etc..) That's what I don't know how to do with this problem. I'm trying to explain it to my daughter but I don't know how to do it myself.
We are given that there are 20 students and an unknown number of adult chaperones.
Let x denotes the unknown number of adult chaperones.
The bus holds at most 35 people
We know that 20 students plus x number of adult chaperones should be at most 35
at most 35 means equal or less than 35
So we can write
[tex]20+x\le35[/tex]Now we can easily solve for x
[tex]\begin{gathered} 20+x\le35 \\ x\le35-20 \\ x\le15 \end{gathered}[/tex]Lloyd is standing near a telephone pole. When his head touches the support wire, he is 25 feet from where the wire meets the ground. Lloydis 5 ft tall. Hon tallis the pole?1-8f feetO A 20 ft.B. 15 ftC. 80 ft.D. 17 ft
We will use the pythagorean theorem to figure the answer out.
Applying the Pythagorean Theorem, we have (let unknown side be x):
[tex]\begin{gathered} 6^2+x^2=10^2 \\ 36+x^2=100 \\ x^2=100-36 \\ x^2=64 \\ x=\sqrt[]{64} \\ x=8 \end{gathered}[/tex]Answer 8 feet (B)A car drove 300 miles in four hours. How fast was the car traveling in miles per hour?
Given that,
A car drove 300 miles in four hours.
We can simply put it in this way.
In 4 hours, a total distance covered by the car = 300 miles
In 1 hour, a total distance covered by the car = 300/4 miles = 75 miles.
Hence, the car was traveling at a speed of 75 miles per hour.
Add these fractions using fraction bars after choosing a common denominator Use the fraction bar inactivate to find the difference
The fractions you have to add are 1/3 and -5/6
[tex]\frac{1}{3}+(-\frac{5}{6})[/tex]The denominators are "3" and "6"
The common denominator between both numbers is 6.
6*1=6
3*2=6
Multiply 1/3 by factor 2 so that both fractions will have the same denominator
[tex]\frac{1}{3}\cdot2=\frac{1\cdot2}{3\cdot2}=\frac{2}{6}[/tex]Now you can add both fractions
[tex]\frac{2}{6}+(-\frac{5}{6})=\frac{2}{6}-\frac{5}{6}=\frac{2-5}{6}=-\frac{3}{6}[/tex]The result is not in its most reduced form, to siplify the fraction divide both the numerator and denominator by 3
[tex]-\frac{3}{6}\div3=-\frac{1}{2}[/tex]The result is -1/2, in the number line:
Jacob is constructing a pentagonal tent for his school carnival. The tent has a side length of 5.13 meters. What is the area of the tent? What is the perimeter of the tent? What is the sum of three of the interior angles in the tent once Jacob obtains the value of its area and perimeter?
The tent is pentagonal , this means it has 5 sides. The tent have a side length of 5.13 meters.
The area of the pentagon can be calculated below
[tex]\begin{gathered} \text{area of the tent=}\frac{perimeter\times apothem}{2} \\ \tan \text{ 36=}\frac{2.565}{a} \\ a=\frac{2.565}{\tan \text{ 36}} \\ a=\frac{2.565}{0.726542528} \\ a=3.53041962601 \\ \text{perimeter}=\text{ 5.13}\times5=25.65\text{ meters} \\ \text{area =}\frac{25.65\times3.53041962601}{2} \\ \text{area}=\frac{90.5445}{2} \\ \text{area}=45.27225 \\ \text{area}\approx45.27meter^2 \end{gathered}[/tex]Each interior angle of a pentagon is
[tex]\begin{gathered} \text{ interior angle=}\frac{180\times3}{5}=\frac{540}{5}=108^{\circ} \\ \text{ Sum of thr}ee\text{ interior angles = 108}\times3=\text{ }324\text{ degre}e \end{gathered}[/tex]1 litre=1000cm³. About how many test tubes, each holding 24cm³ of water, can be filled from a
1 litre flask?
Answer: 125/3 or about 41.667
Note that you can't have 2/3 of a test tube, so the expected answer may be 42 test tubes.
Step-by-step explanation:
Write a simple algebra equation using the word problem
24x = 1000
x represents the number of test-tubes, each of which hold 24cm^3 of water.
divide both sides by 24
x = 125/3 or about 41.667
A grocery store sales for $522,000 and a 25% down payment is made a 20 year mortgage at 7% is obtain compute and amortization schedule for the first three months round your answer to two Decimal place if necessary
The value of the mortgage (the real amount to be financed) is A = $391,500.
The annual interest rate is r = 7%. We must convert it to montly decimal rate:
r = 7 / 12 / 100 = 0.005833
Note: The decimals will be kept in our calculator. Only two decimal places will be shown in the results.
The monthly payment is R = $3,034.13 which includes interest and principal.
For the first month, the loan has not been paid upon, so the interest for this period is:
I = $391,500 * 0.005833 = $2,283.75
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,283.75 = $750.38
So the new balance of the loan is:
$391,500 - $750.38 = $390,749.62
Thus, for payment 1:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
Repeating the calcuations for the second payment:
The interest for this period is:
I = $390,749.62 * 0.005833 = $2,279.37
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,279.37 = $754.76
So the new balance of the loan is:
$390,749.62 - $754.76 = 389,994.86
The table is updated as follows:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
For the third month:
The interest for this period is:
I = $389,994.86 * 0.005833 = $2,274.97
From the monthly payment, the portion that goes to pay the principal is:
$3,034.13 - $2,274.97 = $759.16
So the new balance of the loan is:
$389,994.86 - $759.16 = $389,235.70
The final updated table is:
Interest - Payment on Principal - Balance of Loan
$2,283.75 - $750.38 - $390,749.62
$2,279.37 - $754.76 - $389,994.86
$2,274.97 - $759.16 - $389,235.70