Given:
The quadratic equation is
[tex]x^2+1=2x-3[/tex]
To find:
The expression that correctly sets up the quadratic formula with the given equation.
Solution:
We have,
[tex]x^2+1=2x-3[/tex]
[tex]x^2+1-2x+3=0[/tex]
[tex]x^2-2x+4=0[/tex]
On comparing with [tex]ax^2+bx+c=0[/tex], we get
[tex]a=1,b=-2,c=4[/tex]
The quadratic formula is
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Putting [tex]a=1,b=-2,c=4[/tex], we get
[tex]x=\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex]
Therefore, the required expression is [tex]\dfrac{-(-2)\pm \sqrt{(-2)^2-4(1)(4)}}{2(1)}[/tex].
2 2/3 - 1 1/2 - 4/5
Need answers pls show how you got it
Which exponential function is represented by the values in the table?
Answer:
[tex]\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x[/tex]
Step-by-step explanation:
Exponential Function
The exponential function can be written with the general equation:
[tex]f(x)=A\cdot r^x[/tex]
Where A is the value when x=0 and r>0 is the ratio. If r is greater than 1, the function is increasing, if r is less than 1, the function is decreasing.
The table shows the relation between values of x and values of the function y. Note that as x increases (one by one), y decreases with a ratio of 1/2. Only the last two choices have ratios of r=1/2. We only have to test which one of them has the correct value of y=4 when x=0.
Substituting in the third function:
[tex]\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x[/tex]
[tex]\displaystyle f(0)=4\cdot\left(\frac{1}{2}\right)^0[/tex]
[tex]f(0) = 4[/tex]
This gives the correct value of f(0)=4.
Substituting in the fourth function:
[tex]\displaystyle f(x)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^x[/tex]
[tex]\displaystyle f(0)=\frac{1}{2}\cdot\left(\frac{1}{2}\right)^0[/tex]
[tex]f(0) = \frac{1}{2}[/tex]
This choice is wrong
Correct choice:
[tex]\boxed{\displaystyle f(x)=4\cdot\left(\frac{1}{2}\right)^x}[/tex]
PLS HELP: I am unsure how to calculate this into final numbers.
Cal Amity decided to survey 880 inhabitants of the Kingdom so that he could have a confidence level of 95% and a margin of error of 3%. He found that 72% of his sample answered "yes" to the second survey question, which was, "Have you done anything, or will you do anything, to prepare your kitchen for Gourmando's visit?"
Mr. Amity can infer that, most likely, between _[blank A]_ and _[blank B]_ inhabitants of the Kingdom have done, or will do something, to prepare their kitchen before Gourmando's visit.
Options:
blank A: 3450
blank B: 5000
blank A: 0
blank B: 300
blank A: 3600
blank A: 150
blank B: 3600
blank B: 3750
Complete question :
Cal Amity decided to survey 880 inhabitants of the Kingdom so that he could have a confidence level of 95% and a margin of error of 3%. He found that 72% of his sample answered "yes" to the second survey question, which was, "Have you done anything, or will you do anything, to prepare your kitchen for Gourmando's visit?"
Mr. Amity can infer that, most likely, between _[blank A]_ and _[blank B]_ inhabitants of the Kingdom have done, or will do something, to prepare their kitchen before Gourmando's visit.
If a population is 5000
Answer:
blank A: 3450
blank B: 3750
Step-by-step explanation:
Number of inhabitants surveyed = 880
Population size = 5000
Error margin = 3%
Percentage that answered 'yes' = 72%
The confidence interval :
Mean ± Error margin
Lower Bound = 72% - 3% = 69% = 0.69
Upper bound = 72% + 3% = 75% = 0.75
Since the question want us know the overall inhabitants of the kingdom who fall between this interval :
Blank A = lower boundary = 0.69 * 5000 = 3450
Blank B = upper boundary = 0.75 * 5000 = 3750
Angles that ALWAYS sum to 180°
Answer:
supplementary angles
Step-by-step explanation:
I need help solving these two questions
3x-5x=0
x-5x=-10
Answer:
x=0 and x=5/2
Step-by-step explanation:
Combine like terms.
-2x=0
x=0/-2
x=0
-4x=-10
x=-10/-4
x=5/2
pls answer this asap
Answer:
its c or d
Step-by-step explanation:
Question 10(Multiple Choice Worth 1 points)
(05.02 MC)
The table below shows data from a survey about the amount of time students spend doing homework each week. The students were in either college or high school:
High Low Q1 Q3 IQR Median Mean σ
College 50 6 8.5 17 8.5 12 15.4 11.7
High School 28 3 4.5 15 10.5 11 10.5 5.8
Which of the choices below best describes how to measure the spread of these data?
(Hint: Use the minimum and maximum values to check for outliers.)
Both spreads are best described by the IQR.
Both spreads are best described by the standard deviation.
The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
The college spread is best described by the standard deviation. The high school spread is best described by the IQR.
Answer:
The college spread is best described by the IQR. The high school spread is best described by the standard deviation.
Step-by-step explanation:
The college data has large outliers which skews the data, therefore the IQR is better measure of spread.
The high school data does not appear to be skewed so the standard deviation is fine as a measure of spread.
Gina went to a restaurant for lunch. On her bill the sales tax equals $2.34. If the tax is 8.5%, what was the subtotal (without tax) of her meal?
Answer:
$2.5389
Step-by-step explanation:
Given data
Cost of lunch = $2.34
Tax= 8.5%
Let us compute the cost of the tax
=8.5/100*2.34
=0.085*2.34
= $0.1989
Hence the total is = 0.1989+2.34
=$2.5389
5.25 divided by 3
Thank You.
Answer:
1.75
Step-by-step explanation:
1.75 :) you can check your answer by multiplying by 3!
Brainliest would be appreciated
Which expression is equivalent to 3 the 5th power?
Answer:
The expression equivalent to 3 to the 5th power is 3^5.
The number 3 raised to the 5th power is represented through the expression 3 ^ 5, which means that the number 3 is multiplied by itself 5 times (3x3x3x3x3), which results in the number 243, which is can be corroborated by the following calculations:
3x3 = 9
9x3 = 27
27x3 = 81
81x3 = 243
The solution is: The expression equivalent to 3 to the 5th power is 3^5.
Here, we have,
The number 3 raised to the 5th power is represented through the expression 3 ^ 5,
which means that the number 3 is multiplied by itself 5 times (3x3x3x3x3),
which results in the number 243,
which is can be corroborated by the following calculations:
3x3 = 9
9x3 = 27
27x3 = 81
81x3 = 243
Hence, The solution is: The expression equivalent to 3 to the 5th power is 3^5.
To learn more on Expression click:
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Please Please Help ME!!! its so hard 50 points
Brainiest for correct answer.
Answer:
hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Step-by-step explanation:
Kristy wrote down a decimal number that is greater than 0.76 but less than 0.82. Which number did Kristy write?
Answer:
Step-by-step explanation:
0.79
8, 20, 50, ...
Find the 10th term.
Answer:
[tex]a_{10}=\frac{5^{10}}{2^7} -1[/tex]
Step-by-step explanation:
[tex]a_{n}=a_1 . r^{n}-1[/tex]
Here
[tex]r=\frac{5}{2}[/tex]
[tex]a_1 =8[/tex]
For n=10 (tenth Term)
[tex]a_{10}=8(\frac{5}{2})^{10} -1[/tex]
[tex]a_{10}=\frac{5^{10}}{2^7} -1[/tex]
Math
Skip count by tens and fill in the missing numbers.
550, 660 570, 580, 590,
610,
Answer:
560, 600, 620, 630, 640, 650
Step-by-step explanation:
Just counted from 10, I guess.
Amanda's monthly salary increased from $5,300 to $5,538.50. Mary's salary also increased by the same percentage as Amanda's.
If Mary was earlier getting $6,300, what is her new salary?
Answer:
$6,583.5
Step-by-step explanation:
Amanda's monthly salary increased by 4.5%. You can get the percentage by getting the increased amount in salary and dividing it by the previous salary of Amanda.
$5,538.50 - $5,300 = $238.5$238.5 ÷ $5,300 = 0.045 (4.5%)In order to get the new salary of Mary, you have to multiply the same percentage, 4.5%, to Mary's previous salary, $6,300. This will give you the amount that will be added to her new salary.
$6,300 x 0.045 (4.5%) = $283.5$283.5 + $6,300 = $6,583.5Mary's new salary is $6,583.5
Angel and Jayden were at track practice. The track is 2/5 kilometers around.
Angel ran 1 lap in 2 minutes,
Jayden ran 3 laps in 5 minutes.
a) How many minutes does it take Angel to run
one Kilometer?
b) How many minutes does it take Jayden to run
one Kilometer?
will give brainlist!!
Can you help my sister
Answer:
40
Step-by-step explanation:
The teacher ordered 5 pizzas with 8 slices each which is 5*8=40
11 12 13 14 15
There were 180 people who voted at the town council meeting. Of these people, 60% voted for building a
new basketball court in the park
How many people voted against building the new basketball court? Complete the explanation of how to
find the answer
60% of 180 equals
and 180-
people that are against building the basketball court.
There are
the graphing would be easier to use because it demonstrates the numbers that are in the situation
What is 3 1/4 as a fraction
Answer:
13 / 4
Step-by-step explanation:
Sally runs for 5 miles. She drinks one bottle and 4/5 a bottle of water for every mile. If she runs for 3 more miles, how many bottles of water will she have drunk? Please help!!
Answer:
2.4 or 2 2/5 bottles of water
Help please!
And thank u
Answer:
[tex] \frac{a}{7} + \frac{a}{3} = 10 \\ \frac{(3a + 7a)}{21} = 10 \\ \frac{10a}{21} = 10 \\ a = \frac{(10 \times 21)}{10} \\ \boxed{a = 21}[/tex]
a=21 is the right answer.B.
-2x + 8 = y
3x - y = 22
How do I solve it
answer
x=6, y=-2
explanation
-2x + 8 = y -------equ 1
3x - y = 22 -------equ 2
u can use any of the simultaneous equation method
using elimination method
rearrange first from -------equ 1
-2x+8=y
-y-2x=-8
multiple through by -1
y+2x=8 -------equ 3
rearrange first from -------equ 2
3x-y=22
-y+3=22 ------equ 4
equate 3 and 4, adding them together
y+2x=8 -------equ 3
-y+3=22 ------equ 4
0+5x=30
5x=30
x=6------equ 5
replace 6 for x in any equation
using -------equ 3
y+2x=8
y+2(5)=8
y+10=8
y=8-10
y=-2
Answer:
(x, y)=(6, -4)
Step-by-step explanation:
-2x+8=y
3x-y=22
Substitute the given value of y into the equation 3x-y=22
3x-(-2x=8)=22
Solve the equation for x
x=6
Substitute the given value of x into the equation 3x-y=22
3x6-y=22
Solve the equation for y
y=-4
The possible solution of the system is the ordered pair (x, y)
(x, y)=(6, -4)
Check if the given ordered pair is the solution of the system of equations
-2x6+8=-4
3x6-(-4)=22
Simplify the equalities
-4=-4
22=22
Since all of the equalities are true, the ordered pair is the solution of the system
(x, y)=(6, -4)
A pool is surrounded by a rectangular fence with a
perimeter of 72 yards. If the length of the fence is 3
times the width, what is the length of the fence, in yards?
Answer:
width is 33
Step-by-step explanation:
width (b) =?
length(l)=3
perimeter (p)=?
now,
perimeter = 2(l+b)
or,72= 2(3+ b)
or,72/2= 3+b
or,36= 3+b
or,36-3= b
or,33= b
therefore width is 33
help pls thank you :)))$$:$:
Answer:
C.
Step-by-step explanation:
please mark me brainliest!!
Answer:
The answer is A
Step-by-step explanation:
Denominator *100* is higher
Its PreCal I’ll give brainliest
Answer:
tan²x + tan x - 12 = 0 (1)
suppose: tan x = t
(1)=> t² + t - 12 = 0
a = 1 b = 1 c = -12
⇒ Δ = b² - 4ac = 1 + 48 = 49 > 0 => has 2 solutions
=> t = [tex]\frac{1+\sqrt{49} }{2}=\frac{8}{2}=4[/tex]
or t = [tex]\frac{1-\sqrt{49} }{2}=\frac{-6}{2}= -3[/tex]
because t = tan x => tan x = 4 or tan x = -3
because x ∈ [0;2pi) => with tan x = 4 => x = arctan(4) or x = arctan(4) + pi
with tan x = -3 => x = arctan(-3) + pi
Step-by-step explanation:
help i need help fast
Answer:
Vertical, Horizontal, and Diagonal
Step-by-step explanation:
5 lines of Symmetry.
It has four lines of symmetry and four sides. A regular pentagon has 5 sides and 5 lines of symmetry. The number of lines of symmetry in a regular polygon is equal to the number of sides.
Which of the following has zeros that are not significant?
2.05 m/s
10.0 J
1.30 N
100 kg
Answer:
Your answer would be D. 100 kg
Step-by-step explanation:
I took the test and got it correct
Hope this helps
Good luck!
The required zero that has not significant is 100, 10.0, and 1.30.
Given that,
To determine the number that has zeros that are not significant.
A number system is described as a technique of composing to represent digits. It is the mathematical inscription for describing numbers of a given set by using numbers or other characters in a uniform method. It delivers a special presentation of every digit and describes the arithmetic structure.
Here,
Zeros between non-zero numbers are significant.
So it contains 2.05,
Zeros to the left of the first non-zero digit are not significant.
It contains 100, 10.0. and 1.30
Thus, the required zero that has not significant is 100, 10.0 and 1.30
Learn more about the number system here:
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Need help on this!! And is urgent!!!!
Solve the following, where 0° 0, then find cot
Answer:
Nativism is the political position of preserving status for certain established inhabitants of a nation as compared to claims of newcomers or immigrants. It is characterized by opposition to immigration based on fears that the immigrants will distort or spoil existing cultural values.
Step-by-step explanation:
What is the solution to the system of equations?
2x+3y=26
3x+5y=40
1. X=10, y=2
2. X=10, y=-2
3. X=-10, y=-2
4. X=-10, y=2
Answer:
1. x = 10 , y = 2
Step-by-step explanation:
hope it helps ☺️