The nature of the roots of the quadratic equation 3x² -4x- 2 has two distinct real roots.
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
The given quadratic equation is 3x² -4x- 2.
Three times of x square minus four times of x minus two.
Nature of Roots depending upon Discriminant.
If the discriminant is equal to zero (b² – 4ac = 0), a, b, c are real numbers, a≠0, then the roots of the quadratic equation ax² + bx + c = 0, are real and equal.
b=-4, c=-2, a=3
b² – 4ac=16-4(3)(-2)
=16+24=40
b² – 4ac>0
The quadratic function has two distinct real roots.
Hence, the nature of the roots of the quadratic equation 3x² -4x- 2 has two distinct real roots.
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Sally designed a gold bracelet using 8 thin gold circles, arranged each circle has a radius of 2.5 what is the diameter and what is the length '5cm' of the chain
Answer:
Diameter of the circle = 5.0 unit
The length of the chain = 40 units
Step-by-step explanation:
Given
Number of thin gold circles used for making bracelet is equal to 8
Radius of the circle = 2.5 units
Diameter of the circle = 2 * Radius of the circle
Diameter of the circle = 2 * 2.5 = 5.0 unit
The length of the chain = 8 * diameter = 8 * 5 = 40 units
in a triangle two sides of the same length the ratio of each of these sides to the third side is 5:3 if the perimeter of the triangle is 65 in find the length of each side of the triangle.?
Answer:
Step-by-step explanation:
Perimeter of a triangle equals side 1 plus side 2 plus side 2
P = s1 + s2 + s3 side 1 = side 2 = x
x/side 3 = 5 / 3
x = (5/3) side 3
x (3/5) = side 3
perimeter = 65 slove for x
65 = x + x + 3x/5
325 = 5x + 5x + 3x
325 = 13X
25 = x equal side 1 and side 2
side 3 = 25(3/5) = 15
Len has a board 9ft, 3in. If he cuts off 1ft 10in, what is the length of the remaining board?
Answer:
7.5 inches
Step-by-step explanation:
9ft 3in - 1ft 10in = 7.5 inches
hope this helps :)
6(x/2+4)≥9 what is the answer
Answer:
6(x/2 + 4)>9
x/2 + 4 > 9/6
x/2 + 4 > 3/2
x/2 > 3/2 - 4
2*(x/2) > 2*(3/2 - 4)
x > 3 - 8
x > - 5
Step-by-step explanation:
Answer:
X>-5
Step-by-step explanation:
Can i get brainiest please
Which triangle is NLM congruent to ? Please answer correctly !!!!! Will mark Brianliest !!!!!!!!!
Answer:
Triangle YZX
Step-by-step explanation:
I put it in that order because L in triangle NLM is 42 and Z in triangle YZX is also 42.
Best of luck in school!
Can someone help me understand this and how to find it?
Answer:
triangle y= -3, triangle x= 5 M= -1 1/2
Step-by-step explanation:
actually I used the app that my teacher gave me in 7th grade so I'm gonna give it to you Just look up slope calculator and it says OMNI calculator
answer choices: (5,6) (5,2) (3,6) (3,2).
can someone help me pls immediately!!! i’ll mark brainiest if u don’t guess or leave links. pls don’t guess tho actually know it if ur going to say the answer
Answer:
(3,6)
Step-by-step explanation:
If the starting point is the dot then we start from there - (4,4) then we go up 2 units at (4,6) then moving one unit to the left our answer is (3,6).
Which is equivalent to 3/84 ?
VEA *
+/W
78%
1/8*
3
4x
A 1,500-gallon hot tub is at a temperature of 38°C. Then, the hot tub's thermal energy increases. Assume its mass does not change.
Which is a possible new temperature for the hot tub?
ANSWER IS 37
Answer:
40⁰ C
Step-by-step explanation:
As long as the number is higher than 38⁰ C, it is a valid answer. as long as its not anything crazy like 111846284⁰ C. But anything around 40⁰ C would be a valid answer as long as the temperature is higher. mass doesn't matter. They are trying to trick you with the question lol
Find the surface are of a prism
Answer:
c. 424 inches squared
Step-by-step explanation:
Surface Area = 2(Length x Base, Length x Height, Base x Height)
8 in. x 4 in. +
8 in. x 15 in. +
15 in. x 4 in. =
212 in.
212 in. x 2 = 424 in. squared (*REMEMBER TO SQUARE IT!!)
I hope this helped! <3
Solve the following system of equations using SUBSTITUTION method. {x−3y=2 2x−6y=6
Answer:
x=3-3y
Step-by-step explanation:
What is the following product?
(V14 - 13) (V12+17)
O 2.42 +7V7-6-V21
O √14-6+7
O 26+ V21 - /15 - 10
O 2./42 - 21
Answer:
the trid one becasue
Step-by-step explanation:
To get the correct answer, you can count the total number of shaded tenths and the total number of shaded hundredths and then regroup.
There are 9 shaded tenths and 18 shaded hundredths. Regroup 10 hundredths into 1 tenth to get 10 tenths and 8 hundredths. Then regroup the 10 tenths in one whole, giving you 1 whole and 8 hundredths. The product is 1.08.
Another way to get the answer is to count the total number of shaded hundredths. There are 108 hundredths. Regroup 100 of them as one whole, giving you 1 whole and 8 hundredths.
Option A is correct, the product of (√14 - √3) (√12+√7) is 2√42-7√2-6-√21
What is Expression?An expression is combination of variables, numbers and operators.
We need to find the product of (√14 - √3) (√12+√7)
Let us apply distributive property to solve this
√14(√12+√7) - √3(√12+√7)
√14.√12 + √14√7 -√3√12-√3√7
√168 + √98 -√36 -√21
168 can be written as 4 times of forty two.
98 can be written as forty nine times of 2.
So we get
2√42-7√2-6-√21
Hence, Option A is correct, the product of (√14 - √3) (√12+√7) is 2√42-7√2-6-√21
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A tea that is 20% jasmine is blended with a tea that is 15% jasmine. How many pounds of each tea are used to make 5lb of tea that is 18% jasmine?
Answer:
21
Step-by-step explanation:
The amount of each tea are used to make 5lb of tea that is 18% jasmine is 3 lb of first type of tea, and 2 lb of second type of tea.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we can assume that:
x = number of pounds we mix first type of tea (tea with 20% jasmine)y = number of pounds we mix first type of tea (tea with 15% jasmine)Then, as the total weight of the mixture is 5 lb, thus:
[tex]x + y = 5[/tex]
18% jasmine in 5 lb of mixture = 20% jasmine in x lb of first tea + 15% jasmine in y lb of second tea
Comparing in terms of weight, we get:
[tex]\dfrac{5}{100}\times 18 = \dfrac{x}{100} \times 20 + \dfrac{y}{100} \times 15\\\\90 = 20x + 15y\\18 = 4x + 3y[/tex]
Thus, we get a system of two linear equations as;
[tex]x + y = 5\\4x + 3y =18[/tex]
From first equation, getting x in terms of y:
[tex]x = 5 -y[/tex]
Substituting this in second equation, we get:
[tex]4(5-y) + 3y = 18\\20-4y + 3y =18\\y = 2\\[/tex]
Putting this value in expression for x, we get:
[tex]x = 5-y = 5-2 = 3[/tex]
Thus, the amount of each tea are used to make 5lb of tea that is 18% jasmine is 3 lb of first type of tea, and 2 lb of second type of tea.
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Last week, Danny started washing cars to earn some money to pay for a trip to Disney world. He washed four cars on Day 1 and six cars every day after that. Write the function that models the total number of cars, c(d), Danny has washed after d days?
Answer:
c(d) = 4 + 6(d - 1)
Step-by-step explanation:
Let
d = number of days Danny washed cars
Day 1 = 4 cars
Other days after day 1 = 6 cars
Function that models the total number of cars, c(d), Danny has washed after d days?
c(d) = 4 + 6(d - 1)
What is the volume, in cubic inches, of a cylinder with a height of 7 inches and a base radius of 2 inches, to the nearest tenths place?
87.96inches3 is wrong by the way
also any music suggestions
Answer: V=πr2h=π·22·7≈87.96459in³
Step-by-step explanation:
YOU HAVE A JAR OF PENNIES & QUARTERS. YOU WANT TO CHOOSE 25 COINS
THAT ARE WORTH EXACTLY $2.65
Answer:
10 quarters and 15 pennies
please help I am confused
Answer:
y=-2x+11
Step-by-step explanation:
Slope-intercept form is y=mx+b.
Slope is rise/run, which is y2-y1/x2-x1. Using these points, that's (13-5)/(-1-3). This is 8/-4, or -2.
You can plug this into y=mx+b to get y=-2x+b.
To solve for b, you can use one of the original points and plug it back into the formula:
y=-2x+b
5=-2(3)+b
5=-6+b
b=11
So, putting it all together, you get y=-2x+11.
Let m = slope
m = (13 - 5)/(-1 - 3)
m = 8/-4
m = -2
Now use the point-slope formula.
Here is the formula: y - y_1 = m(x - x_1).
y - 5 = -2(x - 3)
y - 5 = -2x + 6
y = -2x + 6 + 5
y = -2x + 11
Done.
Mr. Rosas had $90 to purchase snacks for a school party. He bought 36 bags of chips and 36 bottles of juice. Each bag of chips cost $0.69, and each bottle of juice cost $1.20. How much money did Mr. Rosas have left after these purchases?
Answer:
$21.96
Step-by-step explanation:
Total money with Mr. Rosas = $90
Total cost of chips = 36*0.69 = $24.84
Total cost of juices = 36*1.20= $43.2
Total money spent = $24.84 + $43.2 = $68.04
Money left with Mr. Rosas
= $90 - $68.04
= $21.96
y 20 18 16 14 12 Total Cost ($) 10 000 2 3 1 2 Time (hours) 2. 3 4 6 8 y = IX +
Which equation is equivalent to y=23x−6?
Answer:
d
Step-by-step explanation:
A. 2x + 3y = −6
B. 3x − 2y = 6
C. 3x − 2y = 12
D. 2x − 3y = 18
The degree of the polynomial below .
Answer:
C: 9
Step-by-step explanation:
The highest power in the polynomial is 9.
A ride to the airport costs $13.86 plus
a $3.00 tip. If Michael and Jeff share
the ride, then how much will each person
pay?
Answer:
$33.72
Step-by-step explanation:
$13.86 + $3.00 + $13.86 + $3.00
$33.72
Comert
3T=_b
3 tons is equal to
pounds.
Answer:
i think 3 tons equal 6000 pounds
ACME Institute of Technology changed its semester tuition from $17,500 to $17,900. Find the percent increase in the semester tuition at ACME.
How many credit hours a student have to take for the two tuition cost to be equal round the answer to the nearest 10th of an hour 250+200 H equals 300+180 250+200 H equals 300+180-180-180 H 250+20 = 300 H equals credit hours
Answer:
Total credit hours a student have = 2.5 hours.
Step-by-step explanation:
P.S - The exact question is -
Given - The tuition costs, C, for a local community college are modeled by C(h) = 250 + 200h, where h represents the number of credit hours taken. The local state university has tuition costs, S, modeled by the function S(h) = 300 + 180h.
To find - How many credit hours will a student have to take for the two tuition costs to be equal.
Proof -
If the two tuition cost are equal, then
C(h) = S(h)
⇒250 + 200h = 300 + 180h
⇒200h - 180h = 300 - 250
⇒20h = 50
⇒2h = 5
⇒h = [tex]\frac{5}{2}[/tex]
⇒h = 2.5
∴ we get
Total credit hours a student have = 2.5 hours.
Is rational numbers are asscociative in addition, Subtraction, multiplication and Division?
Answer needed in Yes/No!
Addition and multiplication are associative for rational numbers. Subtraction and division are not associative for rational numbers.
Answer:
Yes
Step-by-step explanation:
how do you find the volume of spheres?
Phoebe owns a business making birdhouses. The profit can be represented by p = 62 – 126 + 250, where p represents profit and b
represents the number of birdhouses she sells. How many birdhouses would she have to sell to make a profit of $263?
What is it? This is science
Answer:
i believe C is correct :)
Answer:
The answer you got was correct.
Step-by-step explanation:
Predation means the preying of one animal on others,or more simplified,the action of attacking or plundering.
Help please!
Find the value of x. Round to the
nearest tenth.
12
Х
25°
x = [?]
Answer:
5.1
Step-by-step explanation: