Answer:
The solutions to the quadratic equations are:
[tex]x=\sqrt{13}+3,\:x=-\sqrt{13}+3[/tex]
Step-by-step explanation:
Given the function
[tex]y\:=\:x^2\:-\:6x\:-\:4[/tex]
substitute y = 0 in the equation to determine the zeros
[tex]0\:=\:x^2\:-\:6x\:-\:4[/tex]
Switch sides
[tex]x^2-6x-4=0[/tex]
Add 4 to both sides
[tex]x^2-6x-4+4=0+4[/tex]
Simplify
[tex]x^2-6x=4[/tex]
Rewrite in the form (x+a)² = b
But, in order to rewrite in the form x²+2ax+a²
Solve for 'a'
2ax = -6x
a = -3
so add a² = (-3)² to both sides
[tex]x^2-6x+\left(-3\right)^2=4+\left(-3\right)^2[/tex]
[tex]x^2-6x+\left(-3\right)^2=13[/tex]
Apply perfect square formula: (a-b)² = a²-2ab+b²
[tex]\left(x-3\right)^2=13[/tex]
[tex]\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=\sqrt{a},\:-\sqrt{a}[/tex]
solve
[tex]x-3=\sqrt{13}[/tex]
Add 3 to both sides
[tex]x-3+3=\sqrt{13}+3[/tex]
Simplify
[tex]x=\sqrt{13}+3[/tex]
now solving
[tex]x-3=-\sqrt{13}[/tex]
Add 3 to both sides
[tex]x-3+3=-\sqrt{13}+3[/tex]
Simplify
[tex]x=-\sqrt{13}+3[/tex]
Thus, the solutions to the quadratic equations are:
[tex]x=\sqrt{13}+3,\:x=-\sqrt{13}+3[/tex]
FinWhat is the perimeter of the triangle in the graph? Round your answer to the nearest tenth if necessary. (1 point) 8.9 8.0 12.9 8.5d the missing y-coordinate that makes the two triangles congruent. Triangle ABC: A(8,4), B(2,6), C(5, 0) Triangle MNO: M(7,4), N(1,2), O(4, y)
Answer:
man did you ever find out the answer bc I'm dying I cannot fail this test-
Answer:
12.9
Step-by-step explanation:
it is common sense
also i just took test
What is the least common denominator of 1/4 and 7/9
Answer: It is 36
Step-by-step explanation:
Are the lines y=4 and x=-3 perpendicular
Answer:
Yes, because y=5 will intersect the y axix (giving a horizontal line) and x =-3 will intersect the x axis (giving a vertical line). They will intersect at angle 90.
Step-by-step explanation:
Please gimme brainliest
Answer:
Yes
Step-by-step explanation:
When you graph y=4 it is a horizontial line going straight forever. You would mark a dot on postive four on the y-axis. For x, do the same thing mark on the negative three on the x-axis. But this one will be vertical.
REMEMBER-
Although the x-axis is horizontial when there is no Y (x,y) it will be vertical. And it is opposite for the Y.
below this text is the question
Answer
The multiplicative rate of change that should be in Hal’s function = 49/50=0.98
=9.8×10⁻¹
Explanation
The investment of $10,000 decreases by 2% every year. So the following year is usually (100 - 2)=98% of the previous year. This is a geometric progression.
In this case the first term = 10000
The second term = 98% × 10000 = 9800.
The common ratio = 9800/10000=49/50
The multiplicative rate of change that should be in Hal’s function = 49/50=0.98.
The equation of the exponential rate would be;
10,000ₓ0.98ⁿ.
where n is the number years.
Answer:
Answer:
1). Option (A)
2). Option (A)
Step-by-step explanation:
1). A worker bee has the mass = 0.00011 kg
In scientific notation we can convert the mass of bee as,
0.00011 =
=
Since 1.1 ≈ 1,
Therefore, 1.1 × 10⁻⁴ ≈ 1 × 10⁻⁴ kg
Option (A) is the answer.
2). An African elephant has a mass = 8139 kg
In scientific notation,
8139 = 8.139 × 10³
Since, 8.139 ≈ 8
Therefore, 8139 kg = 8.139 × 10³ kg
Option (A) is the answer.
Step-by-step explanation:
Hope this helps! ;)
Answer:
The investment of $10,000 decreases by 2% every year. So the following year is usually (100 - 2)=98% of the previous year. This is a geometric progression.
In this case the first term = 10000
The second term = 98% × 10000 = 9800.
The common ratio = 9800/10000=49/50
The multiplicative rate of change that should be in Hal’s function = 49/50=0.98.
The equation of the exponential rate would be;
10,000ₓ0.98ⁿ.
where n is the number years.
Step-by-step explanation:
the Pythagorean theorem
please help answer all the questions
Answer:
Step-by-step explanation:
A.)
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]16^{2} +20^{2}= c^{2}[/tex]
256 + 400 = [tex]c^{2}[/tex]
656 = [tex]c^{2}[/tex]
25.6 = c
__________________________________________________________
B.)
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]25^{2}+ 10^{2} = c^{2}[/tex]
625 + 100 = [tex]c^{2}[/tex]
725 = [tex]c^{2}[/tex]
26.9 = c
__________________________________________________________
C.)
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]12^{2} +10^{2}= c^{2}[/tex]
144 + 100 = [tex]c^{2}[/tex]
244 = [tex]c^{2}[/tex]
15.6 = c
__________________________________________________________
D.)
[tex]a^{2} + b^{2} = c^{2}[/tex]
[tex]26^{2}+ 24^{2} =c^{2}[/tex]
676 + 576 = [tex]c^{2}[/tex]
1,252 = [tex]c^{2}[/tex]
35.4
__________________________________________________________
Sry it takes a lot of time to put in these equations and all that
Hope it helped!
What would you tip for a $22 meal if you wanted to leave 15%?
$18.70
$4.40
$3.30
$25.30
a circle has a center at (-2,7). if a point on the circle has coordinates (3,-1) then which of the following would be the length of the radius of the circle
Answer:
square root of 65 or 8.06
Step-by-step explanation:
(x-2)^2+(y-7)^2+65
hope this helps
The length of radius is 7.81 unit.
What is Distance Formula?The distance between two points P(a, b)a nd Q(c, d) is
D = √(c- a)² + (d- b)²
Given:
Center at (-2,7) if a point on the circle has coordinates (3,-1).
Using Distance Formula
D = √( 3-(-2))² + (1-7)²
D = √ (3 +2)² + (-6)²
D = √5² + 36
D = √25+36
D = √61
D= 7.81 unit
Hence, the length of radius is 7.81 unit.
Learn more about distance formula here:
https://brainly.com/question/28956738
#SPJ2
Consider all four-digit numbers that can be made from the digits 0-9 (assume that numbers cannot start with 0). What is the probability of choosing a random number from this group that is less than or equal to 5000
Answer: 0.44
Step-by-step explanation:
First, let's count the total number of four-digit numbers.
Let's think it as four empty slots:
_ _ _ _
In each slot, we can put a single digit.
In the first slot, we have 9 options {1, 2, 3, 4, 5, 6, 7, 8, 9}
The zero is not an option here, because if there was a 0, this would be a 3 digit number, then the 0 can not be in the first slot.
For the second slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
for the third slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
for the fourth slot we have 10 options {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}
The total number of combinations is equal to the product between the numbers of options for each slot, this means that we have:
Combinations = 9*10*10*10 = 9000
So there are 9000 different 4 digit numbers.
Now we want to find the probability of selecting a number at random that is equal or smaller than 5000.
Let's see the number of 4-digit numbers that are equal or smaller than 5000.
The smallest 4-digit number is 1000.
Then the number of numbers between 1000 and 5000 is:
5000 - 1000 = 4000
This means that there are 4000 4-digit numbers that are equal or smaller than 5000.
Now, the probability of selecting one of them at random is equal to the quotient between the number of 4-digit numbers that meet the condition (4000) and the total number of 4-digits (9000)
Then te probability is:
P = 4000/9000 = 4/9 = 0.44
T
ASAP PLS HELP
Which fraction is equivalent to 2 over negative 6 ? (5 points)
Select one:
a.
negative 2 over 6
b.
2 over 6
c.
negative 2 over negative 6
d.
6 over 2
Part A : At Mountain Park Middle school, there are 250 seventh-grade students who are not in advanced math. Let a represent the number of seventh-grade students who are not in advanced math?
Part B: How many students are NOT in advanced math?
Answer:
hard to explain
Step-by-step explanation:
Answer:I think 80 at bottom like
Step-by-step explanation:
Jake says that there should be a decimal point in the quotient 142.45 ÷ 7.4 = 1,925 after the 2.
Part A
Which equation shows the best estimate for the quotient?
A. 150 ÷ 10 = 15
B. 150 ÷ 5 = 30
C. 140 ÷ 10 = 14
D. 140 ÷ 7 = 20
Part B
.
Answer:
sorry
Step-by-step explanation:
heres more lolllllllllllll
Answer:
Awwww ty <3
You are too nice lollllllllllllll
Step-by-step explanation:
The museum of natural history has an auditorium that can seat 200 people. A class of 45 students is seated in the auditorium for a lecture. What decimal represents the portion of the seats in the auditorium that are empty? Please help FAST!
Answer:
.225
Step-by-step explanation:
45/200
5 actions a good friend would make.
Answer:
1. respect your opinion
2. defend you/stand up for you
3. support your passions and goals
4. keep stuff you tell them to themselves
5. make you feel comfortable and like you can be yourself
Step-by-step explanation:
60
70
50
Find angle x
Answer:
Where is the pictureeeeeeee
Answer:
picture??
Step-by-step explanation:
Which pair shows equivalent expressions? (a) 2(2/5x+2)=2 2/5 x+1 (B) 2(2/5x+2) = 2/5x+4 (C) 2(2/5x+2) =2/5x+2 (D) 2(2/5x+2) =2 2/5x+8
Answer: C) 2(2/5x+2) =2/5x+2 this would be the answer.
Step-by-step explanation:
Which answer shows the proper use of the distributive property?
A. 2(a+b) = 2ab
B. 2(a+b) = 2a + b
C. 2(a+b) =2a+2b
D. 2(a+b) = a+2b
Answer:
c is showing the proper distributive property
Step-by-step explanation:
suris age is 4 less than 3 times her cousins age. suri is 17 years old. which method can be used to find c, her cousins age?
Hannah says that 2.11 is a rational number. Gus says that 2.11 is a repeating decimal.
Who is correct and why? Use the drop-down menus to explain your answer.
Answer:
Yes, hannah is correct.
The lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min. If one such class is randomly selected, find the probability that the class length is between 50.8 and 51 min.
Answer: the probability that the class length is between 50.8 and 51 min is 0.1 ≈ 10%
Step-by-step explanation:
Given data;
lengths of a professor's classes has a continuous uniform distribution between 50.0 min and 52.0 min
hence, height = 1 / ( 52.0 - 50.0) = 1 / 2
now the probability that the class length is between 50.8 and 51 min = ?
P( 50.8 < X < 51 ) = base × height
= ( 51 - 50.8) × 1/2
= 0.2 × 0.5
= 0.1 ≈ 10%
therefore the probability that the class length is between 50.8 and 51 min is 0.1 ≈ 10%
The Molina family went to a concert together. They purchased 4 concert tickets for $25 each, 3T -shirts for $15 each, and a poster for $10.Write an expression for the total cost. Then find the total cost.
Answer:
155
Step-by-step explanation:
( 25 x 4 ) + ( 3 x 15 ) + 10 = 155
Danny charges $45 for 5 hours of swimming lessons, Martin charges $24 for 2 hours of swimming lessons.
Who offers a better deal?
(select) offers the better deal.
Answer:
Danny charges $45 for 5 hours of swimming lessons
Answer: Danny
Step-by-step explanation:
45/5=9 and 24/2=12 Danny charges 4.5 an hour and Martin charges 6 an hour so Danny is better.
Find the measure of angle b (15
Answer:
Angle b is 15 measure the scale
Steph needs to help her parents put a fence around their pool. They want the fence to be square and want each side to measure 6 meters. They already have 10 meters of fencing. How many more meters of fencing should they buy?
Answer:
14 more meters
Step-by-step explanation:
6 times square (4) = 24
24-10 = 14
3x-2y=1x+4y=33 elimination process
Answer:
x = 5 ; y = 7
Step-by-step explanation:
3x - 2y = 1 --------------------(I)
x + 4y = 33 ------------(II)
Multiply equation (II) by (-3) and then add. So, x will be eliminated and we can find the value of y
(I) 3x - 2y = 1
(II)*(-3) -3x -12y = -99 {Now add}
- 14y = -98
y = -98/14
y = 7
Plugin y = 7 in equation (I)
3x - 2*7 = 1
3x - 14 = 1
3x = 1 + 14
3x = 15
x = 15/3
x = 5
List all the factor pairs for 48. make a table to help and add the table.
Answer:
The factor pairs of the number 48 are: 1 x 48, 2 x 24, 3 x 16, 4 x 12, and 6 x 8
Step-by-step explanation:
What is the slope of a line parallel to the line 2x + 3y = 5?
i think its 2/3 but im not sure .
Answer:
D
Step-by-step explanation:
Parallel lines have same slope
Write the equation in slope - intercept form
2x + 3y =5
3y = -2x + 5
Divide the equation by 3
[tex]y = \frac{-2}{3}x +\frac{5}{3}[/tex]
So, slope = (-2/3)
Is 45 a multiple of 4? Explain your answer.
50
Consider the following frequency table representing the scores on a test.
Scores on a Test
Class Frequency
40–43 7
44–47 7
48–51 7
52–55 8
56–59 4
Required:
a. Determine the lower class boundary for the fifth class.
b. Determine the upper class boundary for the second class.
c. Determine the class width of each class.
d. Determine the number of scores between 39.5 and 55.5
Answer:
(a)56
(b)47
(c)3
(d)29
Step-by-step explanation:
From the given frequency
(a) Fifth class is 56-59.
The lower class boundary for the fifth class is 56.
(b) Second class is 44-47.
The upper-class boundary for the second class is 47.
(c) Class width = 47-44 = 3, 47-44 = 3.
(d) Number of scores between 39.5 and 55.5 is
=7 + 7+ 7 + 8 =29