Given:
The quadratic equation is:
[tex]6x^2-x-2=0[/tex]
To find:
The nature of the solutions by using the discriminant.
Solution:
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then its discriminant is:
[tex]D=b^2-4ac[/tex]
If D<0, then both roots are complex.
If D=0, then both roots are real and equal.
If D>0, then both roots are real and distinct.
We have,
[tex]6x^2-x-2=0[/tex]
Here, [tex]a=6,b=-1,c=-2[/tex]. So, the value of the discriminant is:
[tex]D=(-1)^2-4(6)(-2)[/tex]
[tex]D=1+48[/tex]
[tex]D=49[/tex]
Since [tex]D>0[/tex], then both roots are real and distinct.
Hence, the discriminant of the given quadratic equation is 49 and both roots are real and distinct.
5 is 5% of what number?
Answer:
100
Step-by-step explanation:
Jacub is trying to find the volume of a traffic cone that has the height of 2.4 ft and a diameter of 1.25 ft. He calculated that the
volume is 11.8 ft. What did he do wrong?
CAN SOMEONE HELP ME PLEASE!❤️ i would really appreciate it it’s due today and I’m having trouble understanding this question. 4/15/21
Answer:
he did half the diameter
Step-by-step explanation:
In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°
Answer:
14.2cm
Step-by-step explanation:
Complete question:
In circle O, the length of radius OL is 6 cm and the length of arc LM is 6.3 cm. The measure of angle MON is 75°.
Rounded to the nearest tenth of a centimeter, what is the length of arc LMN?
Find the diagram attached
arc LN= arc LM + arc MN
First we need to get the arc MN
length of an arc = theta/360 * 2πr
length of arc MN = 75/360 * 2(3.14)(6)
length of arc MN = 0.20833*37.68
length of arc MN = 7.85
Hence;
arc LN = 6.3 + 7.85
arc LN = 14.15cm
Hence the length of arc LN is 14.2cm
Help pls thank you!!!!!!!!!!!!!!
Answer:
that would be b
Step-by-step explanation:
i am not positive but i am pretty sure it is b
it's all on the picture please answer
Anyone know how to do this?
Answer:
60.22in^2.
Step-by-step explanation:
First, find the area of the rectangle. 14.1x7=98.7.
Then, we need to find the area of the circle and subtract it from the area of the rectangle.
The area of the circle is pi*r^2. so, pi*3.5^2 is about 38.48. (The radius is half of the diameter, so the radius would be 3.5).
Since there are two halves of the circle, we can just subtract 38.48 from 98.7 so get the area of the shaded region. So, the area of the yellow area is 60.22in^2.
Find rectangle area: 14.1 x 7 = 98.7
Find areas of semicircles: a = 3.14(3.5)^2 = 76.96
Subtract area of semicircles: 98.7 - 76.96 = 21.74
Write the slope-intercept form of the line with the given slope and point.
m = -2; (5, 1)
Answer:
y = -2x + 11
Step-by-step explanation:
If you already have the slope, all you need to do is find the y-intercept.
y = -2x + b
1 = -2(5) + b
1 = -10 + b
11 = b
The equation is y = -2x + 11
A little girl throws her jackstone ball horizontally out of the window with a velocity of 30 m/s. if the window is 3 m above the level ground, how far will the ball travel before it hits the ground?
2 PLEASE HELP! WILL GIVE BRAINLIEST!
Answer:
Area
Step-by-step explanation:
If you are paving the parking lot, you would need every sqaure inch of the parking lot, not only the outside (which is what the perimeter is)
I need helppppppppppppp please
Answer:
I want to say A)
Step-by-step explanation:
Zeke earned 23 extra credit points. Sofia earned e fewer extra credit points than Zeke. Write
an expression that shows how many extra credit points Sofia earned.
Answer:
s = 23 - e
Step-by-step explanation:
In this expression, s is equal to the amount of extra credit Sofia earns. She earns e less points than the 23 points Zeke earns.
So, s (Sofia's points) = 23 (Zeke's points) - e (the difference in points).
The expression is s = 23 - e.
Good luck ^^
What is the area and perimeter of the equilateral triangle? Round your final answer to the nearest tenth of a square unit.
Answer:
In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3s/ 2 * s = √3s2/4. 2 ways to find the area of a triangle using Pythagorean Theorem? 1. Using Pythagorean theorem. The basic formula for triangle area is side a (base) times the height h , divided by 2: area = (a * h) / 2 2.Using trigonometry. Let's start from the trigonometric triangle area formula: area = (1/2) * a * b * sin(γ) , where γ is the angle between sides.
Answer:
In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3s/ 2 * s = √3s2/4. 2 ways to find the area of a triangle using Pythagorean Theorem? 1. Using Pythagorean theorem. The basic formula for triangle area is side a (base) times the height h , divided by 2: area = (a * h) / 2 2.Using trigonometry. Let's start from the trigonometric triangle area formula: area = (1/2) * a * b * sin(γ) , where γ is the angle between sides.
Debby used a garden hose to fill up a 4-gallon bucket in just 1/6 of a minute. At what rate does water flow through the hose?
Answer:
24 gallons
Step-by-step explanation:
When Ben does his math homework, he finishes 10 problems every 7 minutes. At this rate, how long will
it take him to complete 35 problems?lols please help.
Answer:
in 7 minutes he solve 10 problems
he solve one problem in = 7/10= 0.7 minute
he solve 35 problem in = 0.7x35= 24.5 minute
Step-by-step explanation:
hope it helps ❤️
i need help with the last two. I forgot the formula and wondering if you will help me find which one is and isnt a triangle
Answer:
3. D) 26, 7, 31
4. B) 6, 34, 27
Step-by-step explanation:
Both #3 and #4 use the same strategy: the two shorter sides' sum has to be greater than the longer side.
#3:
2 + 8 is 10, which is less than 13. So A wouldn't form a triangle.
12 + 22 is 34, which is the length of the longer side. So B wouldn't form a triangle either.
14 + 18 is 32, which is less than 40. So C wouldn't form a triangle.
7 + 26 is 33, which is greater than 31. So D would form a triangle.
D. 26, 7, and 31 are the only lengths of the ones shown that form a triangle.
#4:
17 + 18 is 35, which is greater than 19. So A would form a triangle.
11 + 22 is 33, which is greater than 25. So C would also form a triangle.
5 + 18 is 23, which is greater than 20. So D would form a triangle.
6 + 27 is 33, which is less than 34. So B wouldn't form a triangle.
B. 6, 34, and 27 are the only lengths of the ones shown that don't form a triangle.
The solid is a right hexagonal pyramid. What is the sum of the number of faces, vertices, and edges of the solid?
o7
o 12
o26
o38
Answer: 26
Step-by-step explanation: assignment on edg
Answer:
26
Step-by-step explanation:
got it right on test
Choose the correct symbol
Answer:
[tex]2,000lb < 1 t[/tex]
Step-by-step explanation:
1 Ton = 2,240 lb
PLEEEEEEASE HELP ME
Janette needs to break down the food container shown below for recycling purposes:
Which of the following will be the resulting net of the food container?
Answer:
Pretty sure the one you pointed an arrow to is correct.
Step-by-step explanation:
It has a circle at the bottom and the top as well as a slip for the body!
The net of the food container is the first diagram in the options.
What is the net of the food container?The net of a shape is the shape of the object when it is laid out flat. The food container has the shape of a cylinder. A cylinder is a three-dimensional object. It is a prism with a circular base.
The net of a cylinder is two circles and a rectangle.
To learn more about a cylinder, check: https://brainly.com/question/9624219
What is the equation for the nth term of geometric sequence 32,48,72
Answer:
[tex]\bold{a_n =32\left(\frac32\right)^{n-1}}[/tex]
Step-by-step explanation:
[tex]a_1=32\\a_2=48\\a_3=72\\\\\dfrac{a_2}{a_1}=\dfrac{48}{32}=\dfrac32\\\\ \dfrac{a_3}{a_2}=\dfrac{72}{48}=\dfrac32\\\\\\\dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac32=r[/tex]
Therefore the formula:
[tex]a_n=a_1\cdot q^{n-1}\\\\a_n =32\left(\frac32\right)^{n-1}[/tex]
whats the measure of angle E ?
Answer:
57degrees
Step-by-step explanation:
The triangle is an isosceles triangle, hence m<D = m<E (base angles are equal)
Taking the sum of the angles and equating to 180
5x-4 + 4x+1 + 4x+1 = 180
5x+4x+4x-4+1+1 = 180
13x - 2 = 180
13x = 180 + 2
13x = 182
x =182/13
x = 14
Get m<E
m<E = 4x+ 1
m<E = 4(14)+ 1
m<E = 56+1
m<E = 57degrees
Hence the measure of m<E is 57degrees
Mr. Tan bought a mobile phone at a discount of 25 %. The original price of mobile phone was of $400. How much did he pay for the mobile phone.?
Answer:
$300
Step-by-step explanation:
$400 is 100% of the price
25% is a quarter of 100%
A quarter of 400 is 100 so the discount was $100
400-100 =300
Solving a word problem involving a sum and another basic relationship using a system of linear equations.
At a basketball game, a vender sold a combined total of 130 sodas and hot dogs. The number of hot dogs sold was 44 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold.
Number of sodas sold:
Number of hot dogs sold:
sodas: 130
hot dogs: 86
there is 130 sodas sold if you subtract 44 from 130 you get how many hotdogs
Need help need help
I really need help with this question
Answer:
where is it at
Step-by-step explanation:
sheeeeeeesh
Every seventh-grade student at Martin Middle School takes one world language class.
One-tenth of the seventh-grade students take French. Eighteen seventh-grade students take French.
Which equation represents s, the total number of seventh-grade students at the middle school?
18 = 0.1 s
18 = StartFraction 10 over s EndFraction
StartFraction s over 0.1 EndFraction = 18
10 s = 18
Option (A) 18 = 0.1s
Step-by-step explanation:
Every seventh-grade student at Martin Middle School takes one world language class.
Now we will form the equation as per statement of the question.
Let total students of seventh-grade = s
" one tenth of seventh grade students take French."
" Students who took French were 18."
So of s = 18
(0.1)s = 18
therefore, Option (A) 18 = 0.1s is the answer.
Answer
a
Step-by-step explanation:
Sierra has plotted two vertices of a rectangle at (3,2) and (8,2). What is the length of the sides of the rectangle
Answer:
5units
Step-by-step explanation:
Given the two vertices of a rectangle at (3,2) and (8,2). We are to calculate the distance between the two points.
Using the formula
D = √(x2-x1)²+(y2-y1)²
D = √(2-2)²+(8-3)²
D = √0+5²
D = √25
D = 5
Hence the length of the side of the rectangle is 5units
One angle of a triangle measures 95° the other two angles are in a ratio of 7:10 what are the measures of those two angles
Answer:
35 degrees and 50 degrees
Step-by-step explanation:
The sum of all the angles in a triangle must be 180 degrees. So 180 - 95 = 85 leftover for the other two angles. Since we have a ratio of 7:10, we can add that up to get 17 total pieces of that 85-degree angle. 85 / 17 = 5, so each piece is 5 degrees. Therefore, the other two angles are 7*5 = 35 degrees and 10*5 = 50 degrees.
Which expression below has a coefficient, a product, and a sum? A. (3 / 3) + (6 – 2) B. (3/n) + (6 + 2) C. 3n(6) + (6 – 2) D. n + (6 – 2)
Answer:
C. 3n(6) + (6 – 2)
Step-by-step explanation:
C. 3n(6) + (6 – 2) has a coefficients, a product and a sum
Coefficients = 3
3 is the coefficients of n
Product means multiplication
3n(6) = product of 3n and 6
Sum means addition(+)
3n(6) + (6 – 2) = the addition of 3n(6) and (6 - 2)
3n(6) + (6 – 2)
= 18n + (4)
= 18n + 4
please please help me
(the number in the photo is 20 and then the letter is x)
(also if you can pls go to my profile and answer the question underneath this one)
Answer:
20°
Step-by-step explanation:
for alternate angles
Answer:
angle x= 20°
I hope it's helps you
Evaluate: |9 - 3k| = 3
Answer:
k=2,4
Step-by-step explanation:
