Answer:
Sum of the solutions of [tex]x^2+9x+20=0[/tex] is -9.
Product of the solutions of [tex]6x^2+7x=3[/tex] is [tex]-0.50[/tex]
Step-by-step explanation:
1. [tex]x^2+9x+20=0[/tex]
Given:
The expression whose sum of the solution is required is given as:
[tex]x^{2} +9x+20=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the sum of the solutions is given as:
Sum = [tex]\frac{-b}{a}[/tex]
Here, [tex]a=1,b=9,c=20[/tex]
Therefore, the sum of the solutions = [tex]-\frac{9}{1}=-9[/tex]
2. [tex]6x^2+7x=3[/tex]
Rewriting the above equation in a standard quadratic equation, we get:
[tex]6x^2+7x-3=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the product of the solutions is given as:
Product = [tex]\frac{c}{a}[/tex]
Here, [tex]a=6,b=7,c=-3[/tex]
Therefore, the product of the solutions = [tex]\frac{-3}{6}=-0.50[/tex]
How to solve system
X+y=10
X-y=2
Answer:
x=6, y=4. (6, 4).
Step-by-step explanation:
x+y=10
x-y=2
----------
x=y+2
y+2+y=10
2y+2=10
2y=10-2
2y=8
y=8/2=4
x+4=10
x=10-4=6
A rectangle is 15 ft longer than it is wide it’s area is 1000ft2 what are it’s dimensions
The dimension of the rectangle is 25 by 40
Let :
width = x length = x + 15Area of rectangle = x * (x + 15)
1000 = x² + 15x
x² + 15x - 1000 = 0
solving the quadratic equation
x(x - 25) +40(x - 25)
x = 25 or x = -40
The width cannot be negative.
Hence,
width = 25 Length = 25 + 15 = 40Therefore, the dimension of the rectangle is 25 by 40
please solve 3.4-2.8d+2.8d-1.3
Answer:
2.1
Step-by-step explanation:
3.4-2.8d+2.8d-1.3
3.4-1.3=2.1
I am doing a math problem and i need help. Could you please find the missing fraction?
5/2 - ? = 1/3
Answer:
?=13/6
Step-by-step explanation:
5/2-?+?=1/3+?
5/2-1/3=?
?=15/6-2/6=13/6
Answer:
13/6???
Step-by-step explanation:
I turned 5/2 into 15/6 and 1/3 into 2/6. I multiplied both their numerators and denomonators by 3. I then subtracted the two numbers and got 13/6.
The diagram shows a cone and its axis of rotation. Which type of cross section is formed when the cone is intersected by a plane containing the axis of rotation?
Answer:
Right-triangle
Step-by-step explanation:
Take a right triangle for example, then twist it 360 degrees, keeping the longest leg at the center of rotation. It will then form a cone.
Answer:
the answer is an isosceles triangle
Solve this problem on paper using all four steps.
Ted weighs twice as much as Julie. Mike weighs three times as much as Julie. Together, Ted, Mike, and Julie weigh 210 lbs. What is the weight of each person?
Julie weighs pounds, Ted weighs pounds, and Mike weighs pounds.
Answer:
Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.
Step-by-step explanation:
Let the weight of Julie be [tex]x[/tex]
Given:
Ted weighs twice as much as Julie
Weight of Ted = [tex]2x[/tex]
Mike weighs three times as much as Julie.
Weight of Mike = [tex]3x[/tex]
Together, Ted, Mike, and Julie weigh 210 lbs.
[tex]x+2x+3x=210[/tex]
Solving above we get;
[tex]6x=210\\x=\frac{210}{6}=35\ lbs[/tex]
Hence Julie weight is 35 lbs.
Weight of Ted = [tex]2x=2\times 35 = 70 \ lbs[/tex]
Hence Ted weight is 70 lbs.
Weight of Mike = [tex]3x=3\times 35 = 105 \ lbs[/tex]
Hence Mike weight is 105 lbs.
Answer:
Julie weighs 35 lbs, Ted weighs 70 lbs, Mike weighs 105 lbs.
I hope this helps you
Solve for h
A=1/2(ah/bh)
Answer the answer is in the attachment
To solve for h in the given equation A = (1/2)(ah/bh), divide both sides by (a/b) to isolate h, resulting in h = 2A/b.
Solve for h:
Start with the given equation A = (1/2)(ah/bh).
Divide both sides by (a/b) to isolate h.
Therefore, h = 2A/b.
Mr. Westnoticed grapes were priced at $2.99 per pound, and bananas were priced at $0.99 per pound. How much would 3 pounds of grapes and 2 pounds bananas cost altogether?
A.$3.98
B.$9.96
C.$10.95
D.$2.96
#1 Cassie and Anna went out to dinner together. Cassie paid 8 dollars more than
Anna. If Anna paid 40% of the bill, then what was the total price of the bill?
Answer:
$40
Step-by-step explanation:
Let the total bill be "x"
Now,
Anna paid 40% (40/100 = 0.4) of the bill, that means
Cassie paid 100 - 40 = 60% of the bill, that is 60/100 = 0.6
Anna paid 0.4x & Cassie paid 0.6x
Cassie's amount is 8 dollar more, so we can write:
0.6x - 8 = 0.4x
Now, we solve for x:
0.6x - 0.4x = 8
0.2x = 8
x = 8/0.2
x = 40
THe total bill is $40
I am horrible at math plz help
The answer is B I believe, because the parallelogram b is half parallelogram a and is reflected across the y axis, NOT the x.
- 4(5a - 3b) simplified is?
Answer:
-20a+12b
Step-by-step explanation:
Answer:
-20a+12b
Step-by-step explanation:
-4(5a-3b)=-20a+12b
The calculation
add the quotient of 108 and 12 and the quotient of 18 and 2
Answer:
18
Step-by-step explanation:
108/12=9
18/2=9
---------------
9+9=18
The chance that a positive response is obtained from Chicago fro program 1 is %. The chance that a positive response is obtained from Chicago for program 2 is %.
Answer:
The chance that positive response obtained for program 1 is 65.90
And The chance that positive response obtained for program 2 is 87.50
Step-by-step explanation:
Given data as :
The positive response for program of different cities in percentage
Now, The positive response is obtained from Chicago for program 1 is 65.90
The total positive response for program 1 in % = 68.80
So, The chance that positive response obtained = 65.90
Again ,
The positive response is obtained from Chicago for program 2 is 87.50
The total positive response for program 1 in % = 81.70
So, The chance that positive response obtained = 87.50
Hence The chance that positive response obtained for program 1 is 65.90
And The chance that positive response obtained for program 2 is 87.50 answer
Complete the table. In the row with x as the input, write a rule as an algebraic expression for the output. Then complete the last row of the table using the rule.
Input Output
Tickets Cost ($)
2 60
6 180
9 270
x
10
Final answer:
The rule for determining the cost based on the number of tickets is Cost = 30 × Tickets. Using this rule, the cost for 10 tickets is calculated to be 300 dollars.
Explanation:
The question requires us to determine a rule for the output based on the given input of tickets and then use this rule to find the cost for 10 tickets. By examining the input and output values provided, we see a consistent pattern: the cost increases by 30 dollars with each additional ticket. Given this pattern, the rule can be formulated as an algebraic expression: Cost = 30 × Tickets.
Applying this rule to an input of x tickets, the expression becomes Cost = 30 × x. To find the cost for 10 tickets, we replace x with 10: Cost = 30 × 10 = 300 dollars.
What is the measure of the apothem
Answer:
The apothem is also the radius of the incircle of the polygon. For a polygon of n sides, there are n possible apothems, all the same length of course. The word apothem can refer to the line itself, or the length of that line. So you can correctly say 'draw the apothem' and 'the apothem is 4cm'.
Final answer:
To find the apothem in geometry, one must utilize trigonometry, knowing the polygon's side length. In astronomy, calculating distances such as the semi-major axis involves understanding celestial mechanics and requires knowing the aphelion and perihelion distances. The problem content combines concepts from geometry and astronomy to discuss angles and distances.
Explanation:
Calculating the Measure of the Apothem
When attempting to find the measure of the apothem of a geometric figure, you're essentially looking for a segment that connects the center of the figure to the midpoint of one of its sides and is perpendicular to that side. This is especially common in regular polygons. However, this particular problem seems to blend geometry and astronomy, discussing the apparent width of the Moon and comparing it using similar triangles.
To calculate the apothem in a regular polygon, you can use trigonometry if you know the length of one of the sides and the number of sides. On the other hand, if the setting involves celestial bodies like the moon and planets, determining an apothem-like distance would involve understanding the object's orbit, size, and distance from the observer.
To compute the semi-major axis of an elliptical orbit, like that of a planet around a sun, you would use the sum of the aphelion and perihelion, divided by two. For instance, if we know the perihelion (rp) and aphelion (ra), we calculate the semi-major axis (a) as (ra + rp)/2.
Remember, an angle is used in astronomy to measure the apparent separation between celestial objects as seen from Earth. Astronomers use degrees to describe these angles, and knowing the angular size can help in estimating distances in space.
To find the aphelion or semi-major axis of an orbit, certain equations are used that involve these distances. Such calculations are essential for understanding celestial mechanics and the movement of objects in our solar system.
At age 20 a person deposits $370 in a savings account paying 2% interest compounded quaterly.how much money will be in the account 60 years later, when he is 80 years old? Would his savings have tripled in that time?
Final answer:
After 60 years, with an initial deposit of $370 at a 2% interest rate compounded quarterly, the amount in the savings account would be approximately $996.26. This amount does not triple the initial savings, as it is less than $1110.
Explanation:
To calculate the amount of money in the savings account 60 years later with an initial deposit of $370, an interest rate of 2% compounded quarterly, we use the compound interest formula:
A = P(1 + rac{r}[tex]{n})^{nt}[/tex]
Where:
A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for in years.
In this case:
P = $370
r = 0.02 (2% as a decimal)
n = 4 (since the interest is compounded quarterly)
t = 60
So, the equation becomes:
A = 370(1 + rac{0.02}[tex]{4})^{4 imes 60}[/tex]
A = 370[tex](1 + 0.005)^{240}[/tex]
A = 370[tex](1.005)^{240}[/tex]
A = 370(2.69259) = $996.26 (rounded to two decimal places)
So, after 60 years, the amount in the account would be approximately $996.26. To check if the savings have tripled:
370 imes 3 = $1110
Since $996.26 is less than $1110, the savings have not tripled.
Use the ALEKS calculator to write 14/15 as a decimal rounded to the nearest tenth.
Answer:from calculator
0.9333333333
Answer: 3.3
Step-by-step explanation:
49 divided by 15 =3.26
Rounding 3.26 to the nearest tenth gives you 3.3
70th term of the arithmetic sequence -6, 5, 16, is
Answer:753
Step-by-step explanation:
The value of [tex]n^{th}[/tex] term can be calculated by,
[tex]T_{n} = a+(n-1)d\\[/tex]
where,
a = first number of the series
d = constant difference between the numbers
So, according to the question,
a = -6
d = 11
n = 70
hence, by substituting,
[tex]T_{n} = (-6)+(70-1)11\\T_{n} = 753[/tex]
Final answer:
The 70th term of the arithmetic sequence -6, 5, 16 is calculated using the formula for the nth term of an arithmetic sequence, resulting in the 70th term being 753.
Explanation:
The student is asking for the 70th term of the arithmetic sequence -6, 5, 16. In an arithmetic sequence, the difference between consecutive terms is constant. This difference is referred to as the common difference "d". The formula for finding the nth term an of an arithmetic sequence is:
an = a1 + (n - 1)d
Using the provided sequence, we can find the common difference by subtracting the first term from the second term:
d = 5 - (-6) = 11
Now, apply the formula to find the 70th term:
a70 = a1 + (70 - 1) imes d
a70 = -6 + 69 imes 11
a70 = -6 + 759
a70 = 753
Therefore, the 70th term of the given arithmetic sequence is 753.
do the angles 76.2,81.7,and 22.1 make a triangle
The given angles 76.2°, 81.7°, and 22.1° can make a triangle, as the sum of these angles is exactly 180°, aligning with the geometric rule that the sum of the interior angles of a triangle must be 180°.
Explanation:To determine whether the given angles can make a triangle, the law in geometry states that the sum of the measures of the interior angles in a triangle must add up to 180 degrees. To see if the angles 76.2°, 81.7°, and 22.1° can make a triangle, we add them up. The sum is 76.2 + 81.7 + 22.1 = 180 degrees. Thus, yes, these three angles can form a triangle because their sum is exactly 180°.
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Only 6. Please and thanks
Answer:
Part a) [tex]7.536\ m[/tex]
Part b) [tex]\$34.14[/tex]
Step-by-step explanation:
Part 6)
a) How much edging is needed?
we know that
To find out how much edging is needed determine the circumference of the circular garden
The circumference of the circular garden is equal to
[tex]C=\pi D[/tex]
where
D is the diameter
we have
[tex]D=2.4\ m[/tex]
assume
[tex]\pi =3.14[/tex]
substitute
[tex]C=(3.14)(2.4)[/tex]
[tex]C=7.536\ m[/tex]
Part b) we know that
To find out the cost to edge the garden, multiply the length of edging plastic needed by the cost of $4.53 per meter
so
[tex](7.536\ m)(4.53\ \$/m)=\$34.14[/tex]
The memory card on Melchers digital camera can hold about 430 pictures make sure used 18% of the mirror memory card while taking pictures at family reunion about how many pictures did Melcher take out the family room and round to the nearest whole number
Answer:
77
Step-by-step explanation:
0.18*430=77.4
on a scale drawing 4 inches represents 25 miles if a line segment on the drawing is 6 inches long what distance dose this like segment represent
Answer:
37.5 miles
Step-by-step explanation:
4in = 25 miles
1in = 25/4
4 + 2 = 6
6 = 25 +(6.25*2)
6 = 37.5
To find the distance represented by a line segment on a scale drawing, set up a proportion and solve for x.
Explanation:To determine the distance represented by a line segment on the scale drawing, we can set up a proportion using the given information. Since 4 inches represents 25 miles, we set up the proportion 4/25 = 6/x, where x represents the distance represented by the line segment. To find x, we can cross-multiply and solve for x: 4x = 150, and dividing both sides by 4 gives x = 37.5. Therefore, the line segment represents a distance of 37.5 miles.
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kimi is playing hide-and-seek with Tommy and Manuel. Tommy is hiding 12 feet south of Kimi, and Manuel is hiding due east of Tommy. If Kimi is 20 feet from Manuel, how far apart are Tommy and Manuel?
Answer:
Tommy and Manuel are 16 ft apart
Step-by-step explanation:
The locations of all three players are shown in the image below
They form a right triangle where the hypotenuse is 20 ft, and one of the legs is 12 ft. We must find the other leg.
We must use Pythagoras's theorem. Being a and b the legs of a right triangle and c its hypotenuse, then
[tex]c^2=a^2+b^2[/tex]
Knowing c and one of the legs, say b:
[tex]a^2=c^2-b^2[/tex]
Using the values c=20, b=12 we find
[tex]a^2=20^2-12^2=400-144=256[/tex]
[tex]a=\sqrt{256}=16[/tex]
So, Tommy and Manuel are 16 ft apart
A rectangle has a length of 12 meters and a width of 400 centimeters. What is the perimeter ,in cm of the rectangle
Answer:
perimeter =3200cm
Step-by-step explanation:
l=12m=1200cm
w=400cm
perimeter=2(w+l)
=2(1200+400)
=2(1600)
=3200cm
The perimeter of a rectangle in cm that has a length of 12 meters and a width of 400cm is 3200 cm
perimeter of a rectangle = 2(l + w)
where
l = length
w = width
Therefore,
let's convert meters to centimetres
1m = 100 cm
12m = ?
cross multiply
length = 1200 cm
width = 400 cm
perimeter of the rectangle = 2(1200 + 400)
perimeter of the rectangle = 2(1600)
perimeter of the rectangle = 3200 cm
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The residents of a city voted on whether to raise property taxes. The ratio of yes votes to no votes was 3 to 5. If there were 4360 no votes, what was the total
number of votes?
total votes
Answer:
The total number of votes 6976 votes
Explanation:
We are given the ratio of yes to no votes is equal to 3 to 5 and there were total 4360 no votes.
Let no. of yes votes be equal to x
So we can write 3:5 = x:4360
total number of yes votes can be obtained by Solving for x
[tex]x = \frac{(4360\times 3)}{5}[/tex]
= 2616
Now total number of votes =
sum of total number of yes votes and total number of no votes
= 2616 + 4360
= 6976
Hence, 6976 is the total number of votes of the residents
Answer:
The total number of votes 6976 votes
Explanation:
We are given the ratio of yes to no votes is equal to 3 to 5 and there were total 4360 no votes.
Let no. of yes votes be equal to x
So we can write 3:5 = x:4360
total number of yes votes can be obtained by Solving for x
= 2616
Now total number of votes =
sum of total number of yes votes and total number of no votes
= 2616 + 4360
= 6976
Hence, 6976 is the total number of votes of the residents
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Step-by-step explanation:
Given: g(x) = 2x2 + 3x + 10
k(x) = 2x+16
Solve the equation g(x) = 2x(x) algebraically for x, to the nearest tenth. Explain why you
shose the method you used to solve this quadratic equation.
Answer:
x = 3.576 and x = - 3.076
Step-by-step explanation:
Two functions are given to be, g(x) = 2x² + 3x + 10 and k(x) = 2x + 16.
Now, we have to solve the equation g(x) = 2k(x)
⇒ 2x² + 3x + 10 = 4x + 32
⇒2x² - x - 22 = 0
The expression in the left hand side can not be factorized and therefore we have to use Sridhar Acharya formula which gives the solutions of the equation in the form ax² + bx + c = 0 are given by
[tex]x = \frac{-b + \sqrt{b^{2} - 4ac} }{2a}[/tex] and [tex]x = \frac{-b - \sqrt{b^{2} - 4ac} }{2a}[/tex]
Therefore, the solutions of the given equation are
[tex]x = \frac{-(- 1) + \sqrt{(- 1)^{2} - 4 (2)(-22)} }{2(2)} = 3.576[/tex]
and [tex]x = \frac{-(- 1) - \sqrt{(- 1)^{2} - 4 (2)(-22)} }{2(2)} = -3.076[/tex] (Answer)
Final answer:
To solve the equation g(x) = k(x) for x, we simplify it to 2x² + x - 6 = 0 and factor it, resulting in x = 1.5 or x = -2. The method used is factoring due to the simplicity of the equation.
Explanation:
To solve the equation g(x) = k(x) algebraically for x, we set the given functions equal to each other. Given the functions g(x) = 2x² + 3x + 10 and k(x) = 2x + 16, the equation becomes 2x² + 3x + 10 = 2x + 16. To solve for x, we must first simplify the equation by moving all terms to one side and then using the quadratic formula or factoring, if possible.
Step 1: Subtract 2x and 16 from both sides to obtain the quadratic equation 2x² + x - 6 = 0.
Step 2: Factor the quadratic equation if possible. In this case, it factors to (2x - 3)(x + 2) = 0, so the possible solutions for x are x = 1.5 or x = -2.
The chosen method for solving this quadratic equation is factoring because the equation simplifies nicely and the factors are easily observable.
You invest $15,000 in a savings account with an annual interest rate of 2.5% in
which the interest is compounded quarterly. How much money should you expect to
have in the account after 5 years? Show your work to receive full credit!
Answer:
[tex]\$16,990.62[/tex]
Step-by-step explanation:
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
[tex]t=5\ years\\ P=\$15,000\\ r=2.5\%=2.5/100=0.025\\n=4[/tex]
substitute in the formula above
[tex]A=15,000(1+\frac{0.025}{4})^{4*5}[/tex]
[tex]A=15,000(1.00625)^{20}[/tex]
[tex]A=\$16,990.62[/tex]
what is the solution to the system
C= ?
D= ?
Answer:
c=29/20
d=13/5
Step-by-step explanation:
4c+2d=11 A
7d=82-44c 7d+44c=82 B
The first equation multiply by 11
and we get 44c+22d=121 C
C-B=44c+22d-7d-44c=39
15d=39
d=39/15=13/5
so c= 29/20
The cost to take a car across a bay on a ferry is $16.00. The ferry has a capacity of 42cars. The revenue collected is a function of the number of cars, c . R()=16 Use the drop-down menus to complete the statements below about the domain of this function.
The domain of this function is first restricted to all nonnegative integers because the ferry can carry only a whole number number of cars.
The domain is restricted to number less than or equal to 42 because the ferry cannot carry more cars than capacity .
The domain of this function is the set of non-negative integers.
Explanation:The domain of a function represents the set of possible input values for that function. In this case, the function represents the revenue collected by the ferry, which depends on the number of cars. The number of cars, denoted as c, must be a non-negative integer because the ferry cannot transport a fraction of a car. Therefore, the domain of this function is the set of non-negative integers, or {0, 1, 2, 3, ...}.
Which number is a composite number?
17, 29, 37, 31, 47, 27
Answer:
27
Step-by-step explanation:
9x3