The value of c from the given equation is 34.
What is the solution of a quadratic equation?The solutions to the quadratic equation are the values of the unknown variable x, which satisfy the equation. These solutions are called roots or zeros of quadratic equations. The roots of any polynomial are the solutions for the given equation.
The given equation is x²+19x+c=0
Vieta's Theorem is If f(x) = ax² + bx + c is a quadratic equation with roots α and β then,
Sum of roots = α + β = -b/a
(x + a) (x + b) = x² + (a + b) x + ab
a + b = 19
a - b = 15
a = 17
b = 2
c = ab = 34
Therefore, the value of c from the given equation is 34.
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Using Vieta's Theorem, the difference of the roots was used to set up two equations. Solving them simultaneously gave us the individual roots, which were then multiplied to find the required product, c, which is 34.
Explanation:To solve for c in the quadratic equation x^2 + 19x + c = 0 using Vieta's Theorem, we need to find the two roots of the equation and their relationship to the coefficients.
According to Vieta's formulas, for a quadratic equation of the form ax^2 + bx + c = 0, the sum of the roots -b/a and the product of the roots c/a. Since the coefficient a is 1 in our equation (x^2 + 19x + c = 0), the sum of the roots is -19, and the product is c.
We are told the difference of the two roots is 15. Let's denote the larger root as r1 and the smaller one as r2. Thus, r1 - r2 = 15. But we also know that r1 + r2 = -19 (the negative coefficient of x).
We can now set up two equations:
r1 + r2 = -19r1 - r2 = 15By solving these two equations simultaneously, we add them together to eliminate r2:
2r1 = -4
r1 = -2
Substitute r1 back into one of the original equations to find r2:
r1 + r2 = -19
-2 + r2 = -19
r2 = -17
Now, we use the product of the roots to find c:
c = r1 * r2
c = -2 * -17
c = 34
Therefore, the value of c in the quadratic equation is 34.
Janine walks on a circular track whose radius is 60 meters. If she walks a total of 100 meters, which of the following represents the radian angle she rotates about the center of the track?
(1) 5/3
(2) 3/5
(3) 5π/3
(4) 3π/5
Answer: OPTION 1
Step-by-step explanation:
For this exercise you need to remember that, by definition, the Arc length can be calculated with the following formula:
[tex]arc\ length=rC[/tex]
where "C" is the central angle of the arc in radians and "r" is the radius.
Since you need to find the Central angle, you have to solve for "C" from that formula, as following:
[tex]C=\frac{arc\ length}{r}[/tex]
According to the information given in the exercise, you can identify that:
[tex]arc\ length=100\ m\\\\r=60\ m[/tex]
Therefore, the final step is to substitute these values into the formula and evaluate, in order to find the value of "C":
[tex]C=\frac{100\ m}{60\ m} \\\\C=\frac{5}{3}\ rad[/tex]
Nicole sells T-shirts, t, for $8, and sells sweatshirts, s, for $18. She earns $475
in revenue. Which equation below represents this relationship?
Answer:
Step-by-step explanation:
Cost of t, T-shirts = t*8 = 8t
Cost of s, sweatshirts = s*18 = 18s
Equation:
8t + 18s = 475
uuuuLITUNCION
Given the function f(x) = -2x2 + 3 over the closed
interval [-1, 2], what are the extreme values?
Minimum:
Maximum:
Answer:
Step-by-step explanation:
hello :
f(x) = -2x²+3
in : [-1, 2] f'(x) = - 4x
f'(x) = 0 means : -4x=0 so : x=0
f(0) = -2(0)²+3 = 3 (Maximum:) because : a= -2 and a<0
in : [-1, 0] f is crasing
in : [-1, 2] f is decrasing
Answer:
1.-5
2.3
Step-by-step explanation:
just did it
Will mark brainlist
Given. QR I PT and
Prove: APQR – ATSR
Angles
Segments
Triangles Statements Reasons
ZQPR
ZQRP
The mathematics question involves proving two triangles congruent in geometry, likely using congruence criteria such as SSS, SAS, or ASA, with the given information that line QR is parallel to PT.
Explanation:The subject of this question is Mathematics, specifically it involves geometry and the proof of congruent triangles. The statement 'QR I PT' suggests that line QR is parallel to line PT. To prove triangles APQR and ATSR are congruent, one would need to demonstrate that they satisfy the criteria for congruence such as side-side-side (SSS), side-angle-side (SAS), or angle-side-angle (ASA). The angles mentioned, such as ∠QPR and ∠QRP, are likely parts of the required congruence criteria. However, additional information and a specific criteria of congruence need to be applied in a step-by-step explanation.
A jar contains 2 caramels, 7 mints and 16
dark chocolates. What is the probability of
choosing a dark chocolate, eating it, then
choosing a caramel?
Answer:
Answer A: 16/25
Answer B: 2/24
Step-by-step explanation:
There are 16 dark chocolates, so the probability of choosing one is 16/25. the total number of candies is 25, so when one is eaten, the number changes to 24. There are 2 caramels, so the number is 2/24.
The measure of central angle RST is pi radians. What is the area of the shaded sector? 4pi units^2 8pi units^2 16pi units^2 20pi units^2
Answer:
8π units²
Step-by-step explanation:
Area of the circle can be defined as pi 'π' times the radius squared 'r²'
A= πr²
radius given is 4 (see attachment for the figure)
r=4
A = π4²
A= 16π
Now, if you look at the figure, you can see that the shaded area of the circle is 'half' of the whole circle.
We will half the Area which we have found it above in order to determine the area of shaded sector
Therefore,
area of the shaded sector = 16π/2 => 8π units²
Answer:
8[tex]\pi[/tex] [tex]units^{2}[/tex]
Step-by-step explanation:
did it on edge
What method can we use to rewrite Quadratic Equation in standard form to a Quadratic Formula? Go ahead and rewrite ax^2 + bx+c = 0 to quadratic formula. (please help. this is urgent.)
Answer:
SOLUTION: Rewrite the quadratic equation in standard form by completing the square. f(x)=x^2+8x+14 Answer (f(x)= (x, plus or minus ___)^2 plus or minus ____ I have worked this to x, 4 a Algebra -> Quadratic Equations and Parabolas -> SOLUTION: Rewrite the quadratic equation in standard form by completing the square.
Step-by-step explanation:
mathhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Answer:
21
Step-by-step explanation:
2³ = 8
8/2
= 4
3.4(5)
= 17
4 + 17
= 21
Answer:
Your answer is going to be: 21.
Step-by-step explanation:
In this problem, we're going to be using PEMDAS.
[tex]\frac{1}{2} x^{3} +3.4y[/tex]
Now, we have to fill the blanks:
[tex]\frac{1}{2} 2^{3} +3.45[/tex] [tex](5)\\[/tex]
There's no parenthesis (3.45(5) is just another way of multiplying so that doesn't count). So, we move to the exponent part.
[tex]\frac{1}{2} 8+3.4(5)[/tex]
Everything else is just multiplication.
[tex]\frac{8}{2} + 17[/tex] = 4+ 17
Add it all together and your answer is going to be:
21.
P.S. Good luck with the rest of your assignment!!
the midpoint of AB is M (6,3). If the coordinates of A are (7,4) what are the coordinates of B
Answer:
B(5,2)
Step-by-step explanation:
What is the average rate of change for f(x) = -3* + 1 over the interval -2 < x <-1?
A. -1/9. B. -2/9. c. 1/9. d. 2/9
Answer:
B
Step-by-step explanation:
You can check it before choosing the answer.
I think 85% correct.
Solve -4x ≥ -8. Graph the solution.
Answer: x is less then or equal to 2
Step-by-step explanation:
divide -4x and -8 both by -4 to get x is greater then or equal to 2 and flip the sign to less then or equal then because your dividing by a negative number
Four lines are drawn on a coordinate plane to form trapezoid WXYZ.
Which statements are true about the lines? Select three options.
Line WZ has the same slope as line XY.
Line YX has a greater slope than line ZY.
Line XW has a lesser slope than line YZ.
Line ZW has the same y-intercept as line YZ.
Line XY has a lesser y-intercept than line XW.
Answers: Line WZ has the same slope as line XY. Line XW has a lesser slope than line YZ. Line ZW has the same y-intercept as line WZ.
Solve the system of equations by substitution.
x+y=18
y=8x
Answer:
x=2, y=16
Step-by-step explanation:
x+y=18
y=8x
x+8x=18
x=2
y=16
Answer:
2
Step-by-step explanation:
x + y = 18
y = 8x
x + 8x = 18
9x = 18
x = 18÷9
x = 2
) Yoona gives guitar lessons for $70 per session. She gives a 10% discount to students who
come to her studio for the lesson.
The question is about calculating the price of guitar lessons after a 10% discount and the answer explains the steps to calculate the discounted price.
Explanation:The subject of this question is Mathematics and the grade level is High School.
To calculate the amount after the discount, subtract 10% of $70 from $70. 10% of $70 is $7, so the discounted price is $70 - $7 = $63.
Therefore, Yoona gives a 10% discount to students which means the price per session is $63.
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Find the common difference Ce:-34,-29,-24,-19,...
Answer:
d = 5
Step-by-step explanation:
The common difference d is the difference between consecutive terms in the sequence
- 29 - (- 34) = - 29 + 34 = 5
- 24 - (- 29) = - 24 + 29 = 5
- 19 - (- 24) = - 19 + 24 = 4
Thus the common difference is d = 5
The common difference between consecutive terms in the given sequence is 5.
Explanation:The given sequence is {-34, -29, -24, -19, ...}
To find the common difference, we need to look for a pattern between consecutive terms. So, let's observe the differences between consecutive terms:
-29 - (-34) = 5
-24 - (-29) = 5
-19 - (-24) = 5
As we can see, the common difference between consecutive terms is 5.
use the pythagorean theorem to prove whether or not each set of numbers represent the side length of a right triangle in your final answer, include your proof A. 6,12,15 B. 5,,12, and 13
Answer:
a. no, it is not a right triangle
b. yes, it is a right triangle
Step-by-step explanation:
The ratio of dogs to cats at the local pet store is 5:3
If there is 12 cats at the pet store, how many dogs
are at the pet store?
Answer:
20 dogs
Step-by-step explanation:
Answer:
20 Dogs.
Step-by-step explanation:
5:3=x:12
12/3=4
5x4=20
Find the value of x in the triangle
Answer:
x = 28
Step-by-step explanation:
The sum of the angles of a triangle add to 180
85+67+x = 180
Combine like terms
152 +x =180
Subtract 152 from each side
152-152+x = 180-152
x = 28
Answer:
x=28 degrees
Step-by-step explanation:
180-85=95
95-67=28
Using the rule of 72, how long will it take for the principal to double with an annual compound interest rate of 6%?
A. 6
B. 9
C. 12
D. 15
Answer:
C. 12
Step-by-step explanation:
With the rule of 72, you would divide 72 by the periodic interest rate to get the number of years for the principal to double
72 ÷ 6 = 12
Please help, I’m not too smart
Answer:
x = - 4
Step-by-step explanation:
Given
r(x) = - 5x - 1 and r(x) = 19, then equating the right sides gives
- 5x - 1 = 19 ( add 1 to both sides )
- 5x = 20 ( divide both sides by - 5 )
x = - 4
Oil prices are projected to increase by 100% by next june. A quart of oil currently costs $2.45. What is the projected cost of a gallon of oil next june?
Answer:
The projected cost of a gallon of oil by next june is $19.60.
Step-by-step explanation:
Given:
Oil prices are projected to increase by 100% by next june.
A quart of oil currently costs $2.45.
Now, to find the cost of a gallon of oil next june.
So, to get the projected cost of a quart of oil by next june:
Cost of one quart of oil currently = $2.45.
Rate of oil prices projected to increase by = 100%.
[tex]100\%\ of\ \$2.45+\$2.45\\\\=\frac{100}{100}\times 2.45+2.45\\\\=2.45+2.45\\\\=\$4.90.[/tex]
Now, to get the projected cost of a gallon of oil by next june we use conversion factor:
4 quart = 1 gallon.
If, 1 quart oil price = $4.90.
Then, 4 quarts oil price = [tex]\$4.90\times 4[/tex] = [tex]\$19.60.[/tex]
Thus, 1 gallon oil price = $19.60.
Therefore, the projected cost of a gallon of oil by next june is $19.60.
Answer:
19.60
Step-by-step explanation:
The area of a rectangular fountain is x2 + 9x + 20 square feet. A 3-foot walkway is built around the fountain. Find the dimensions of the outside border of the walkway. The dimensions of the outside border of the walkway are
Answer:
(x+11) by (x+10)
Step-by-step explanation:
We know that Area = Length x width
Given: Area = x²+9x+20
Lets sort this out first
Area = x²+5x + 4x + 20
Area = x(x+5) + 4(x+5)
Area = (x+5) (x+4)
Therefore, it is concluded that:
Length 'l' = (x+5) feet
Width 'w' = (x+4) feet
if a 3-foot walkway is built around the fountain, we'll add 3 feet on both sides
Therefore,
Outer Length = (x+5+3+3) = (x+11) feet
Outer Width = (x+4+3+3) = (x+10) feet
Answer:
The fountain is (x+5) by (x+4).
dimensions of the outside border of the walkway are (x+11) by (x+10)
(x + 3)2 + (x + 3) - 2 = 0
Answer:
x=-7/3
Step-by-step explanation:
2(x+3)+(x+3)-2=0
2x+6+x+3-2=0
3x+7=0
3x=-7
x=-7/3
Answer:
Step-by-step explanation:
What is the 30th term of the linear sequence below?
−
5
,
−
7
,
−
9
,
−
11
,
−
13
,
.
.
.
Answer:
63
Step-by-step explanation:
5,7,9,11,13
common factor= adding by 2
2n+3
find the 30th term
2×30+3=63
answer= 63
The 30th term of the linear sequence −5, −7, −9, −11, −13, . . . is -63. This is found using the formula for the nth term of a linear sequence, which is expressed as nth term = first term + (n - 1)*common difference.
Explanation:The 30th term of a linear sequence can be found using the formula: nth term = first term + (n - 1)*common difference. In this sequence, the first term is -5 and the common difference (distance between each term) is -2 (since -7 minus -5 equals -2).
By substituting the appropriate values into the formula, we get: 30th term = -5 + (30 - 1)*(-2) = -5 - 58 = -63. Therefore, the 30th term of the sequence is -63.
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is x greater than, less than, or equal to 50*
Answer:
c
Step-by-step explanation:
because they are opposites
A square's diagonal (hypotenuse) is 28V2. What is the length of each side?
In a square, all four sides are the same length. Imagine a square that has been cut by a diagonal. We have two triangles, each with the same length hypotenuse (diagonal length) and two equal side lengths. To find the length of each side, we can use the Pythagorean theorem.
I used x in place of a and b, as both side lengths are equal.
x^2 + x^2 = (28 [tex]\sqrt{2}[/tex])^2
2x^2 = 1568
x^2 = 784
x = 28
The length of each side is 28 units.
Hope this helps!! :)
Answer:
Once it is a square, the lengths are the same. Considering that
a square's diagonal is [tex]s\sqrt{2}[/tex], thus, each length measures 28.
You may use the pythagorean theorem:
[tex](28\sqrt{2} )^2=s^2+s^2\\28\sqrt{2} =\sqrt{s^2+s^2} \\28\sqrt{2} =s\sqrt{2} \\[/tex]
Which two-dimensional figure results from slicing the sphere with the blue plane?
A square
A circle
A line
A cone
A parabola
Question 2
If it takes 8 meters of fabric to make 5 pairs of curtains, how many meters are required to make 22 pairs?
Answer:
35.2m
Step-by-step explanation:
8 meters of fabric make 5 pairs of curtains so divide 8 by 5 to find that it takes 1.6 meters of fabric to make 1 pairs of curtains
multiply 1.6 by 22 to get 35.2 meters of fabric
Evaluate each expression if a=4, b=6 and c=3
7c+8a-5b
Answer: 38
Step-by-step explanation:
To solve this problem, you are simply going to plug in the values for the numbers into the equation so it would look like this:
7(3)+8(4)-5(6)
Answer:
23
Step-by-step explanation:
7(3)+8(4)-5(6)
21+32-30
53-30
23
The ages of the members of four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
(a) Based on the information above, which team has the youngest members on average?
Team A
Team B
Team C
Team D
(b) Based on the information above, which team's ages have the least variability?
Team A
Team B
Team C
Team D
The answer the statement a and statement b is
a) the answer is team C
b)we can conclude that the answer is team A.
We have given that,
The ages of the members of the four teams are summarized below. Answer the questions about them.
Team A: The mean age is 52 and the range of ages is 27.
Team B: The mean age is 49 and the range of ages is 28.
Team C: The mean age is 48 and the range of ages is 31.
Team D: The mean age is 54 and the range of ages is 33.
We have to determine the a and b
a) The information above, which team has the youngest members on average
from the above observations we can conclude that the answer is team C.
What is the least variability?
A related measure of variability is called the semi-interquartile range. The semi-interquartile range is defined simply as the interquartile range divided by 2.
b) The information above, which team's ages have the least variability
from the above observations, we can conclude that the answer is team A.
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