Answer:
Roots: x = 5; x = 4
Step-by-step explanation:
Given the quadratic equation, x² -9x + 20 = 0
where a = 1, b = -9, and c = 20
Determine the nature and number of solutions based on the discriminant, b² - 4ac:
b² - 4ac = (-9)² - 4(1)(20) = 1
Since b² - 4ac > 0, then it means that the equation will have two real roots.
Use the Quadratic Formula:
[tex]x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}[/tex]
[tex]x = \frac{-(-9) +/- \sqrt{(-9)^{2} - 4(1)(20)} }{2(1)}[/tex]
[tex]x = \frac{9 +/- \sqrt{1}}{2}[/tex]
[tex]x = \frac{9 + 1}{2}; x = \frac{9 - 1}{2}[/tex]
[tex]x = \frac{10}{2}; x = \frac{8}{2}[/tex]
x = 5; x = 4
Therefore, the roots of the quadratic equation are: x = 5; x = 4.
An aquarium is creating a display of a shark that has 100 teeth in each row. The aquarium can buy shark teeth for $10 each. How much will the aquarium spend on shark teeth to create the model?
Answer:10,000
Step-by-step explanation:10x100=1000
How do you calculate 5x5
Answer:
25
Step-by-step explanation:
5 x 5 is just a shorter way of saying 5 + 5 + 5 + 5 +5
Divide the difference between 1,000 and 200 by 4
Answer:
200
Step-by-step explanation:
1,000-200=800
800/4=200
Answer:3200
Step-by-step explanation:
1000 subtracted by 200 =800
multiply 800 by 4 =3200
One number exceeds another by 6 and their sum is 16. Find the two numbers.
Answer:
answer is 11 or 5
Step-by-step explanation:
x+y=16 ------ 1
x-y= 6 ------ 2
______
2x = 22
x =22/2 =11
put the value of x on equation 1
x+y =16
11+y =16
y =16-11 =5
Find the distance between the points.
(-1, 1), (3, -2)
Ariadne jogs at an average speed of 8 km/h. How far does she travel in 1½ hours?
Answer:
12km
Step-by-step explanation:
1 hour = 8 half hour = 4
8+4=12
PLEASE HELP!!!!!
will mark brainliest!!!!!
Step-by-step explanation:
f(0)=0+1=1
f(1)=1+1=2
f(7)=7+1=8
f(8)=8+1=9
f(9)=9+1=10
now you plot these points:
(0,1) (1,2) (7,8) (8,9) (9,10)
and then connect them to get the function
help me please. Thank you if you do.
PLEASE SOME ANSWER QUICKLY!!!!
×2 multiple with 2
D
enjoy me hard work
River Fun Boats rents paddle boats. The euqation C = 0.10t + 4 gives the charge in dollars, C, for renting a paddle boat for t minutes. A customer paid $9.00 for their rental. How lond did the customer use a paddle boat?
Answer:
Step-by-step explanation:
9 = 0.10t + 4
5 = 0.10t
t = 50 minutes
Write an
equation of the line that passes through each pair of points.
(-3,9), (-3,-5)
Answer:
x = -3
Step-by-step explanation:
x is -3 in all values so we just write an equation.
Step-by-step explanation:
slope=(-5-9)/-3+3
= undefined
Use the vertical line test to determine whether the relation is a function. If not, identify two points a vertical line
would pass through.
Answer:
function
Step-by-step explanation:
The verticle line test is basically seeing if it is a function
It is a function when the verticle line touches only one point on the graph at once
For example, if the graph was a circle, and u drew a verticle line through it, it would touch two points on the graph, so it is NOT a function
But for this parabola, if you draw a verticle line at any point, it only touches one point of the graph, so it is a function
A vertical line test is a graphical approach for assessing if a curve in the plane reflects the graph of a function.
The correct option is C, function.
What is a Vertical-line test?The vertical line test is a method used to determine whether a graph represents a function or not. If a vertical line can be drawn on the graph such that it intersects the graph in more than one point, then the graph is not a function.
The graph of the given function, intersect the vertical axis or the y-axis at most one time, therefore, the given graph passes the vertical line test. Thus, it can be concluded that the given graph is a function.
Hence, the correct option is C, function.
Learn more about vertical line test at:
https://brainly.com/question/30343513
#SPJ3
3. What is the hypothesis of the following conditional statement?
Conditional Statement: If two angles form a right angle,
then they are complementary.
Two angles form a right angle.
They are complementary.
If two angles are complementary, then they form a right angle.
The angles are adjacent.
Answer:
A: Two angles form a right angle.
Step-by-step explanation:
took the test
Answer:
Two angles form a right angle.
Step-by-step explanation:
The first part of the statement, the condition that must be met, is the hypothesis.
Anyone help me please?
Each rhombus has four right angles-False
Each square has four right angles-True
please help! I will mark brainliest.
Answer:
2^4 × 3^2
Step-by-step explanation:
Check out the factor tree below.
Write 9.9.9.9
9.9.9 using exponential notation
4n > with the line under it 20. Plot on number line
Answer:
5
Step-by-step explanation:
divide 4 by both numbers
Estimate 636 divided by 25
Answer:
25.44
Step-by-step explanation:
If a=7, then the value of a² - 3a is ______.
a) -7
b) 35
c) -28
d) 28
Answer:
-7
Step-by-step explanation:
Given
a = 7
Since a = 7, then that would mean it the base of the exponent would be replaced to 7 to the second power.
So 7 x 7 = 49 ( multiplied twice itself)
--------------------------------------------
7×2-3×7=14-21 = -7
-----------------------------------------------------
help please acellus sucks kind of
Answer:
126 cm^3
462 cm^3
Step-by-step explanation:
The volume of the triangular prism (green) is the area of the base multiplied by the height.
The base is the front surface which is a triangle with base 6 cm and height 7 cm.
The height of the prism is 6 cm.
V = AH
V = (1/2)bhH
V = (1/2)(6 cm)(7 cm)(6 cm)
V = 126 cm^3
The volume of the green triangular prism is 126 cm^3
The total volume of the composite solid is the sum of the two volumes.
Total Volume = 336 cm^3 + 126 cm^3
Total Volume = 462 cm^3
35 divided by 8693 long division or decimal form thank u
Answer:
0.00402622...
Step-by-step explanation:
Of the 64 students on a field trip to a museum, five-eighths brought their lunch. How many students brought their own lunch?
A. 39
B. 46
C. 40
D. 38
Answer:
C. 40
Step-by-step explanation:
1. To find how many students brought their own lunch, we have to multiply 5/8 by 64.
[tex]\frac{5}{8} * 64[/tex] [tex]\frac{5}{1}* 8[/tex] [tex]40[/tex]Therefore, the answer is C. 40.
Help me Please....................
9514 1404 393
Answer:
1.3363
Step-by-step explanation:
The basic idea here is to find an expression for the direction vector between a point on L1 and a point on L2. Then, solve for the points on L1 and L2 that make that vector perpendicular to both lines L1 and L2. (The dot product of direction vectors is zero.) The distance between the points found is the shortest distance between the lines.
__
Let P be a point on L1. Then the parametric equation for P is ...
P = (6t, 0, -t) . . . . . . origin + t × direction vector
Let Q be a point on L2. The direction vector for L2 is given by the difference between the given points. It is (4-1, 1-(-1), 6-1) = (3, 2, 5). Then the parametric equation for Q is ...
Q = (3s+1, 2s-1, 5s+1) . . . . (1, -1, 1) + s × direction vector
The direction vector for PQ is ...
Q -P = (3s+1-6t, 2s-1, 5s+1+t)
The dot product of this and the two lines' direction vectors will be zero:
(3s+1-6t, 2s-1, 5s+1+t)·(6, 0, -1) = 0 = 13s -37t +5 . . . perpendicular to L1
(3s+1-6t, 2s-1, 5s+1+t)·(3, 2, 5) = 0 = 38s -13t +6 . . . perpendicular to L2
The solution to these equations is ...
s = -157/1237
t = 112/1237
Then (Q-P) becomes (94, -1551, 564)/1237, and its length is ...
|PQ| = √(94² +1551² +564²)/1237 ≈ 1.3363
The distance between the two lines is about 1.3363 units.
Find the distance between the two numbers on the number line, -4 7/12 and -3 1/6.
Answer:
1 1/2
Step-by-step explanation:
50×54+23-44+66 Simplification no spam steps must
Answer:
=2745
Step-by-step explanation:
=2700+23−44+66
=2723−44+66
=2679+66
=2745
Help me with this lol
Answer:
13
Step-by-step explanation:
5+3+5=13
I NEED A 100% ACCURATE ANSWER FOR THIS QUESTION ASAP NO LINKS !!!
Answer:
infinitely many solution
Step-by-step explanation:
Answer:
Any value of x makes the equation true.
All real number
Interval Notation:
(−∞,∞) So it's Infinitely many solutions.
Simplify the linear expression.
- 2x +3(-5x + 1)
Enter your answer in the box.
Answer:
-17x+3
Step-by-step explanation:
Answer:
-17x+3
Step-by-step explanation:
=-2x+3(-5x+1)
=-2x-15x+3
=-17x+3
some people use a rule to see how many hours a child should sleep at night. Subtract the child's age in years from 30, then divide by 2.
Samantha is 14 years old she wakes up every morning at 7 am. Use the rule to work out what time she should go to sleep?
Number 15 Part B
Help me Explain and Solve
Answer:
Fran's would have 18 and Mia's would have 12
Step-by-step explanation:
Use the chart you set up in 15a to substitute the values. You look at the corresponding purple shell value to the value of 6 pink shells.