Answers
Answer:
x = - [tex]\frac{3}{2}[/tex] , x = [tex]\frac{1}{2}[/tex]
Step-by-step explanation:
4x² + 4x = 3 ← factor out 4 from each term on the left side
4(x² + x) = 3
to complete the square
add/subtract ( half the coefficient of the x- term )² to x² + x
4(x² + 2([tex]\frac{1}{2}[/tex] )x + [tex]\frac{1}{4}[/tex] - [tex]\frac{1}{4}[/tex] ) = 3
4(x + [tex]\frac{1}{2}[/tex] )² - 1 = 3 ( add 1 to both sides )
4(x + [tex]\frac{1}{2}[/tex] )² = 4 ( divide both sides by 4 )
(x + [tex]\frac{1}{2}[/tex] )² = 1 ( take square root of both sides )
x + [tex]\frac{1}{2}[/tex] = ± 1 ( subtract [tex]\frac{1}{2}[/tex] from both sides )
x = - [tex]\frac{1}{2}[/tex] ± 1
then
x = - [tex]\frac{1}{2}[/tex] - 1 = - [tex]\frac{3}{2}[/tex]
x = - [tex]\frac{1}{2}[/tex] + 1 = [tex]\frac{1}{2}[/tex]
Related Questions
Which sequence of transformations shows that Figure A is similar to Figure B?
Rotate Figure A 180º about the origin, then dilate it with the center at the origin and a scale factor of 2.
Rotate Figure A 90º about the origin, then dilate it with the center at the origin and a scale factor of 2.
Reflect Figure A across the y-axis, then dilate it with the center at the origin and a scale factor of 12.
Dilate Figure A with the center at the origin and a scale factor of 2, then translate it to the left 4 units.
Answers
Answer:
That would be the second option: Rotate Figure A 90º about the origin, then dilate it with the center at the origin and a scale factor of 2.
-yOuR nEiGhbOrhOoD cLEaNeR ;)
F(X)=2(X-1)^2-4 in standard form
Answers
Answer:
[tex]f(x)=2x^2-4x-2[/tex]
Step-by-step explanation:
Standard form of a quadratic equation: [tex]y=ax^2+bx+c[/tex]
[tex]\begin{aligned}f(x) & =2(x-1)^2-4\\& =2(x^2-2x+1)-4\\& = 2x^2-4x+2-4\\& = 2x^2-4x-2 \end{aligned}[/tex]
Tumbleweed, commonly found in the western United States, is the dried structure of certain plants that are blown by the wind. Kochia, a type of plant that turns into tumbleweed at the end of the summer, is a problem for farmers because it takes nutrients away from soil that would otherwise go to more beneficial plants. Scientists are concerned that kochia plants are becoming resistant to the most commonly used herbicide, glyphosate. In 2014 , 19. 7% of 61 randomly selected kochia plants were resistant to glyphosate. In 2017 , 38. 5% of 52 randomly selected kochia plants were resistant to glyphosate. Do the data provide convincing statistical evidence, at the level of α=0. 05 that there has been an increase in the proportion of all kochia plants that are resistant to glyphosate
Answers
Using the z-distribution, it is found that the data provides convincing evidence that the proportion has increased.
What are the hypotheses tested?At the null hypotheses, it is tested if the proportion has not increased, that is, the difference of the 2017 proportion and the 2014 proportions is not positive, hence:
[tex]H_0: p_2 - p_1 \leq 0[/tex]
At the alternative hypothesis, it is tested if the proportion has increased, hence:
[tex]H_1: p_2 - p_1 > 0[/tex]
What are the mean and the standard error for the distribution of differences?For each sample, they are given by:
[tex]p_1 = 0.197, s_1 = \sqrt{\frac{0.197(0.803)}{61}} = 0.0509[/tex]
[tex]p_2 = 0.383, s_2 = \sqrt{\frac{0.385(0.615)}{52}} = 0.0675[/tex]
Hence, for the distribution of differences, they are given by:
[tex]\overline{p} = p_2 - p_1 = 0.383 - 0.197 = 0.186[/tex]
[tex]s = \sqrt{s_1^2 + s_2^2} = \sqrt{0.0509^2 + 0.0675^2} = 0.0845[/tex]
What is the test statistic?It is given by:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
In which p = 0 is the value tested at the null hypothesis.
Hence:
[tex]z = \frac{\overline{p} - p}{s}[/tex]
[tex]z = \frac{0.186 - 0}{0.0845}[/tex]
z = 2.2
What is the decision?Considering a right-tailed test, as we are testing if the proportion is higher than a value, the critical value at the 0.05 significance level is [tex]z^{\ast} = 1.645[/tex].
Since the test statistic is greater than the critical value for the left tailed test, the data provides convincing evidence that the proportion has increased.
More can be learned about the z-distribution at https://brainly.com/question/26454209
before getting to school john has a few errands to run john has to walk 5 blocks to the galley and 9 blocks to the library before walking the final 7 blocks to arrive at school if john has already walked 12 blocks how many more blocks must he walked before arriving school
Answers
Answer:
9 blocks
Step-by-step explanation:
The total of what John has already walked and the number more he must walk will be equal to the number he has to walk to get to school.
12 + more = 5 + 9 + 7
more = 9 + 5 + 7 - 12 . . . . . subtract 12 from both sides
more = 9
John must walk 9 blocks more.
_____
We recognize that 5+7 = 12, so that last part of the sum totals zero.
If I were to be walking 8MPH How fast would I be walking per minute? PLEASE HELP. (Hint: Half of 8MPH is 4, so that would be 4 Miles every 30 minutes.)
Answers
Answer:
0.13 miles per minute
Step-by-step explanation:
If you walk 8 miles in an hour, that is 8 miles per 60 minutes. We can divide 8 by 60 to get the miles per minute because there are 60 minutes in an hour. 8/60 = 0.13 (3 is repeating)
The following points lie on a certain line.
х, у
-2, -11
1. -5
4, 1
6, 5
What is the equation of the line?
Oy=-3x + 3
Oy - 2x - 3
Oy - 2X-7
o y = -4x + 2
Answers
[tex]y = 2x - 7[/tex]
should be it
You buy a car from your neighbor at a price of $9,000. You pay $500 down and pay 9.5% on the balance. If you make monthly payments of $200, how many months (to the nearest hundredth of a month) will it take to pay off the loan? (Hint: Solve for N.)
Answers
If the monthly payments mad s $200, the number of months it would take to pay off the loan is 46.54 months.
How many months would it take to pay off the loan?The first step is to determine the total value of the loan.
Total value of the loan = (1 + interest) x amount of the loan
Amount of the loan = 9000 - 500 = $8,500
Total value of the loan = (1.095) x $8500 = $9307.50
Number of months it would take to pay off the loan = total value of the loan / monthly payments
$9307.50 / 200 = 46.54 months
To learn more about loans, please check https://brainly.com/question/25811386
Simplify the expression.
Answers
Answer:
Step-by-step explanation:
Exponent rule:
[tex]\boxed{(a^{m})^{n}=a^{m*n}}[/tex]
[tex](x^{\frac{2}{5}})^{10} = x^{\frac{2}{5}*10} \\\\\\[/tex]
[tex]=x^{2*2}\\\\=x^{4}[/tex]
The quotient of 36 and a whole number increased by 3, is 20 less than four times the number.
Find the number(s).
Answers
Answer: [tex]\frac{12}{19}[/tex]
The quotient of 36 and a whole number increased by 3, is 20 less than four times the number. The solution to the algebraic equation here are 6 and -4.
An algebraic equation or polynomial equation is an equation of the form P=0 where P is a polynomial with coefficients in some field, often the field of the rational numbers.
The algebraic equation becomes =
[tex]\frac{36}{x+3}-20 = 4x\\[/tex]
We simplify the equation to find the value of x.
[tex]=\frac{36}{x+3}+20 = 4x\\\\= \frac{36}{x+3} = 4x -20\\\\= \frac{36}{x+3} = 4(x-5)\\\\=36 = 4(x-5)(x+3)\\\\=9 = (x-5)(x+3)\\\\=x^2-5x+3x -15 = 9\\\\= x^2-2x-24=0\\\\=x^2-6x+4x-24=0\\\\=x(x-6)+4(x-6) =0\\\\=(x+4)(x-6) =0\\\\x = -4,6[/tex]
Learn more about algebraic equation here
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What is the slope of the line that passes through the points (-4, 13) and (6, -17)
Answers
Find the measure of angle A.
(BRAINLIEST :D)
Answers
Answer:
180 - 90 - 60
Step-by-step explanation:
all internal angles of a triangle add up to 180. this means A must be equal to 180 - 90 - 60 = 30
Answer:
30
Step-by-step explanation:
A triangle always = 180 degrees :)
So first we can add :D
60 + 90 + a = 180
150 + a = 180
Now we subtract :)
180 - 150 = 30
The answer is 30!
Have an amazing day!!
Please rate and mark brainliest!!
If an investment has a 5% annual interest rate and it is compounded
monthly, how many years will it take to double in value?
Answers
Answer:
2 years
Step-by-step explanation:
If it is annunal I think it would be 2 years
5 x annual year (year) =2
PLEASE HELP NOW!! NO LINKS PLEASE!
The wholesale price for a bookcase is $189. a certain furniture store marks up the wholesale price by 19%. find the price of the bookcase in the furniture store. round your answer to the nearest cent, as necessary.
Answers
Answer:
it is 35.91, 36 to the nearest cent
Step-by-step explanation:
I don't know how to explain it to u sorry
help me with this math question
Answers
[tex]\text{Given that,} \sin x = \dfrac{\sqrt 5}3,~~ \text{and}~~~ \sin y =\dfrac{\sqrt 2}2\\\\\\~~~~~~~\sin x = \dfrac{\sqrt 5}3\\\\\implies \sin^2 x = \dfrac 59\\\\\implies 1- \cos^2 x = \dfrac 59\\\\\implies \cos^2 x =1- \dfrac59 \\\\\implies \cos^2 x = \dfrac 49\\\\\implies \cos x = \dfrac 23~~~~~~~;[\text{In quadrant I, all ratios are positive.}]\\\\\\\\[/tex]
[tex]~~~~~~\sin y =\dfrac{\sqrt{2}}2\\ \\\implies \sin y = \dfrac 1{\sqrt 2}\\\\\implies \sin^2 y = \dfrac 12\\\\\implies 1-\cos^2 y = \dfrac 12\\\\\implies \cos^2 y = 1-\dfrac 12=\dfrac 12\\\\\implies \cos y = \dfrac 1{\sqrt 2}\\\\\\[/tex]
[tex]\text{Now,}\\\\\cos(x+y) = \cos x \cos y - \sin x \sin y\\\\\\~~~~~~~~~~~~~~=\dfrac 23 \cdot \dfrac 1{\sqrt 2}- \dfrac{\sqrt 5}3 \cdot \dfrac 1{\sqrt 2}\\\\\\~~~~~~~~~~~~~~=\dfrac{2- \sqrt 5}{3\sqrt 2}\\\\\\~~~~~~~~~~~~~~=\dfrac{\sqrt2\left(2 -\sqrt 5 \right)}6[/tex]
*HIGHER POINTS* Solve for m<A
Answers
Answer:
The answer should be about 114.
Step-by-step explanation:
Of you look at the shape of the other angles. B and D seem to be about 90 and the shape of A is just a little bit bigger than ninety. I started by adding 78, 90, and 90 together which gave me 246. Then I subtracted 246 from 360 which gave me 114. I had estimated the answer to be around 110.
Graph 1 on the numberline?
Answers
Answer:
directly before 5/4
Step-by-step explanation:
graph a straight vertical line directly before 5/4
or maybe it's just asking for where the value 1 should is and it's the same.
Answer:
It is the line to the left of 5/4
Step-by-step explanation:
it goes 5/4 then 4/4 or 1 then 3/4, 2/4, 1/4 then 0
4
Required
Mr. Sanchez's class sold fruit pies for $1.73 each and Mr. Kelly's class sold bottles of fruit juice for $1.44 each.
Together, the classes sold 83 items and earned $130.83 for their school. Write and solve a system of equations
that models this prolem. Show all your work!
Answers
The system of equations of the number of bottles in both classes has two distinct equations
Mr. Sanchez's class sold 39 bottles, while Mr. Kelly's class sold 44 bottles
How to solve the system of equations?
The given parameters are:
Mr. Sanchez = $1.73
Mr. Kelly = $1.44
Represent the number of bottles in both classes with x and y,
So, we have the following equations
1.73x + 1.44y = 130.83
x + y = 83
Next, we plot the graphs of the equations
From the graph (see attachment), we have:
(x,y) = (39,44)
Hence, Mr. Sanchez's class sold 39 bottles, while Mr. Kelly's class sold 44 bottles
Read more about system of equations at:
https://brainly.com/question/14323743
Please help with this problem. I don’t understand the answer for this equation. The answer for this equation is 7/2( a+ b) i’m just not understanding where the seven is coming from.
Answers
Answer:
7/2(a+b)
Step-by-step explanation:
To add fractions you need to find the LCM (least common multiplier) and then combine.
least common multiplier of a+b, 2(a+b) : 2(a + b)
Adjust fractions based of LCM
2/2(a + b) + 5/2(a +b)
2+5/2 (a + b) =
7/2 (a + b)
I hope this makes sense! :)
what is the volume of the cylinder when the height is 13m and the radius is 10m
Answers
another question !!!
Answers
Answer:
All are complementary angles
Step-by-step explanation:
See attachment
The function P(x)=x^3−2x^2 is dilated by the function I(x)=P(4x).
Which function rule represents I(x)?
A.) I(x)=4x^3−8x^2
B.) I(x)=64x^3−32x^2
C.) I(x)=4x^3−2x^2
D.) I(x)=64x^3−2x^2
Answers
Answer:
Its C
Step-by-step explanation:
Why? because its C
good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answers
Answer:
Perimeter of rectangle = 14x - 2
Area of rectangle = 10x² + x - 2
Step-by-step explanation:
Finding the perimeter of the rectangle:
⇒ Perimeter of rectangle = 2(L) + 2(B)
⇒ Perimeter of rectangle = 2(2x + 1) + 2(5x - 2)
⇒ Perimeter of rectangle = 4x + 2 + 10x - 4
⇒ Perimeter of rectangle = 14x - 2
Finding the area of the rectangle:
Area of rectangle = LB
⇒ Area of rectangle = (2x + 1)(5x - 2)
⇒ Area of rectangle = 10x² - 4x + 5x - 2
⇒ Area of rectangle = 10x² + x - 2
Answer:
Perimeter = 14x - 2
Area = 10x² + x - 2
Step-by-step explanation:
Formulae
Perimeter = 2W + 2L Area = W x L(where W is the width and L is the length)
Given information
width = 2x + 1length = 5x - 2Perimeter
⇒ Perimeter = 2(2x + 1) + 2(5x - 2)
= 4x + 2 + 10x - 4
= 14x - 2
Area
⇒ Area = (2x + 1)(5x - 2)
= 10x² - 4x + 5x - 2
= 10x² + x - 2
The measure of arc MQL IS degrees
Answers
Answer: 214 degrees
Step-by-step explanation:
pleas help in math!! i need an explanation on how you got he answer too please!!
(no links please!)
Answers
Answer:
a = 70 degrees.
Step-by-step explanation:
Use this circle angle theorem:
The angle subtended by an arc at the center of a circle = 2 times the angle subtended by the arc on the circumference.
So m < a = 1/2 * 140 = 70 degrees.
Does the budgeted amount cover the actual amount for expenses, savings, and emergencies? a) no, it's short $207.00. b) no, it's short $227.00. c) yes, there's a surplus of $207.00. d) yes, there's a surplus of $227.00.
Answers
The expense amount is more than the savings amount. No, it's short $207 then the correct option is A.
What are statistics?Statistics is the study of collection, analysis, interpretation, and presentation of data or to discipline to collect, and summarise the data.
From the table, we have
The amount of the savings will be
Saving amount = $ 20
Then the amount of the expense will be
Expense amount = 150 + 75 + 2 = 227
Then the budgeted amount covers the actual amount for expenses, savings, and emergencies will be
→ savings amount - expense amount
→ 20 - 227
→ $ 207
Thus, the expense amount is more than the savings amount. No, it's short $207.
More about the statistics link is given below.
https://brainly.com/question/10951564
An angle measures 46° less than the measure of its complementary angle. What is the measure of each angle?
Answers
Answer:
68 and 22 degrees
Step-by-step explanation:
Complimentary angles sum to 90
x + (x-46) = 90
2x = 90 + 46
2x = 136
x = 68 and the other is 68 - 46 = 22
i cant figure this problem can you guys help/i cant figure this problem can you guys help?
Answers
Answer:
50.0in²
Step-by-step explanation:
C=2πr
25.12/2π=r
r=3.99(taking π=22/7)
Area=πr²
=22/7×(3.99)²=50.0in²
I need help please!!!!
Answers
Answer:
297 ft squared
Step-by-step explanation:
find the area of the triangle, which is (bh)/2
(22*7)/2=77
find the area of the rectangle (bh)
22*10=220
add
77+220=297
a cylindrical tank has a diameter of 24 dm And a height of 30, dm.how many litters of a water can it hold when full (1 dm³ = 1 L)
Answers
R = 12
To find the area of a circle you must do (R)^2 x Pi (3.14)
Meaning you must do:
12 x 12 = 144 = (R)^2
144 x (3.14) Pi = 452.16
Next we need to find the volume of the tank, by using the area of the circle we can now use the formula Area ((R)^2 xPi (3.14)) x height
We know the height equals 30dm so:
452.16 x 30 = 13,564.8
As it is 1dm^3 to 1L we don’t need to divide anything to equal them as they are the same meaning the answer is
13,564.8 Litres
6 minutes3 minutes3 minutes 5 minutes 1 minute 3 minutes What is the mode
Answers
Answer:
the answer is 3.
Step-by-step explanation:
mode if what numberhappens most often