2x^2 + 8x - 12 = 0..divide by 2
x^2 + 4x - 6 = 0
x^2 + 4x = 6...add 4 to both sides of the equation
x^2 + 4x + 4 = 6 + 4
(x + 2)^2 = 10....<== ur constant is 10
x + 2 = (+-)sqrt 10
x = -2 (+ - ) sqrt 10
x = -2 + sqrt 10
x = -2 - sqrt 10
Date Page The male population of a village is 9840 and the female population is 8965. Find the total population of the village ii) How many more males are there than females
On Monday, Ray had $153.75 in his bank account. On Tuesday, he withdrew $71.00 from his account. After depositing #292.50 on Wednesday, how much money did Ray have in his account
Answer:
$375.25
Step-by-step explanation:
[tex]===========================================[/tex]
Withdrew- taking out money (-)
Deposit- putting in money (+)
[tex]===========================================[/tex]
Ray started off with 153.75. He withdraws (-) 71.
[tex]153.75-71=82.75[/tex]
Then he deposits (+) 292.5.
[tex]82.75+292.5=375.25[/tex]
That's your answer!
I hope this helps ❤
Adam borrowed $5,600 from the bank. The bank charges 4.2% simple interest each year.
Which equation represents the amount of money in dollars, x, Adam will owe in one year, if no payments are made?
x=5,600+5,600(42)(12)
x=5,600+5,600(0.042)(1)
x=5,600+5,600(42)(1)
x=5,600+5,600(0.042)(12)
Answer:
[tex]x = 5600 + 5600 * 0.042 * 1[/tex]
Step-by-step explanation:
Given
[tex]P = 5600[/tex] -- Principal
[tex]R = 4.2\%[/tex] -- Rate
[tex]T = 1[/tex] -- Time
Required
The amount (x) to be paid
This is calculated as:
[tex]x = P + I[/tex]
Where:
[tex]I = PRT[/tex]
So, we have:
[tex]x = 5600 + 5600 * 4.2\% * 1[/tex]
Express percentage as decimal
[tex]x = 5600 + 5600 * 0.042 * 1[/tex]
(c) is correct
Solve by graphing. Round each answer to the nearest tenth.
6x2 = −19x − 15
a: −2, 1.7
b: −1.7, −1.5
c: −1.5, 1.5
d: −1.5, 1.7
9514 1404 393
Answer:
b: -1.7, -1.5
Step-by-step explanation:
The graph is shown below. We have annotated the x-intercepts for the equivalent equation ...
6x^2 +19x +15 = 0
can anyone help with this please !!!!
Answer:
"Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
Step-by-step explanation:
Let be the following system of linear equations:
[tex]4\cdot x + 4\cdot y + z = 24[/tex] (1)
[tex]2\cdot x - 4\cdot y +z = 0[/tex] (2)
[tex]5\cdot x - 4\cdot y - 5\cdot z = 12[/tex] (3)
1) We eliminate [tex]y[/tex] by adding (1) and (2):
[tex](4\cdot x + 2\cdot x) +(4\cdot y - 4\cdot y) + (z + z) = 24 + 0[/tex]
[tex]6\cdot x +2\cdot z = 24[/tex] (4)
2) We eliminate [tex]y[/tex] by adding (1) and (3):
[tex](4\cdot x + 5\cdot x) +(4\cdot y - 4\cdot y) +(z -5\cdot z) = (24 + 12)[/tex]
[tex]9\cdot x -4\cdot z = 36[/tex] (5)
Hence, the correct answer is "Add equations A and B to eliminate [tex]y[/tex]. Add equations A and C to eliminate [tex]y[/tex]".
need help with algebra problem
Answer:
[tex]option \: d \: 4.2 \times {10}^{ - 3} [/tex]
Step-by-step explanation:
Multiplication,
[tex] = 8.4 \times {10}^{ 8 } \times 5 \times {10}^{ - 11} \\ = 8.4 \times 5 \times {10}^{8 + ( - 11)} \\ = 4.2 \times {10}^{8 - 11} \\ = 4.2 \times {10}^{ - 3} [/tex]
Julie and Mona know that that Earth’s average distance from the Sun is approximately 93 million miles and it takes 1 year to complete an orbit of the Sun. A new asteroid has been discovered orbiting the Sun at an average distance of 1,488 million miles. How long will it take for the asteroid, in Earth years, to complete one orbit of the Sun.
Answer:
16 years
Step-by-step explanation:
Given that :
Earth's distance from sun = 93 million miles
Number of years to complete an orbit = 1 year
Average orbiting distance of new asteroid = 1488 million miles
Number of years to complete an orbit = x
93,000,000 Miles = 1
1488000000 miles = x
Cross multiply :
93000000x = 1488000000
x = 1488000000 / 93000000
x = 16 years
Period taken to orbit the sun = 16 years
Answer: 64 Earth years...
We deposit $12000 into an account carning 3 % interest compounded continuously, How many years will it take
for the account to grow to $16800? Round to 2 decimal places,
Answer:
The answer is 13.33 year
Step-by-step explanation:
P = $12000
Rate = 3%
Amount = $16800
so,
I = A-P
= $16800 - $12000
= $4800
So,
T = (I × 100)/P×R
= (4800×100)/P×R
= 480000/($12000×3)
= 480000/36000
= 480/36
= 13.33 year
Consumers Energy states that the average electric bill across the state is $39.09. You want to test the claim that the average bill amount is actually different from $39.09. What are the appropriate hypotheses for this test
The null hypothesis is [tex]\mu = 39.09[/tex]
The symbol [tex]\mu[/tex] is the Greek letter mu
The alternate hypothesis is [tex]\mu \ne 39.09[/tex] telling us we have a two-tailed test here. The "not equal" is directly tied to the keyword "different" given in the instructions. In other words, mu being different from 39.09 directly leads to [tex]\mu \ne 39.09[/tex]
So either mu is 39.09 or it's not 39.09
You can use H0 and H1 to represent the null and alternate hypotheses respectively.
----------------------
Summary:
The two hypotheses are
H0: [tex]\mu = 39.09[/tex]
H1: [tex]\mu \ne 39.09[/tex]
This is a two tailed test.
. A small home business is set up with an investment of Birr 1,000,000 for equipment. The business manufactures a product at a cost of Birr 60 per unit. If the product sells for Birr 140, how many units must be sold before the business breaks even?
Answer:
12,500
Step-by-step explanation:
P = R-E
b.e.p : P=0
R=E
140x = 1000000 + 60 x
80x = 1000000
x=12,500
A little help?? It’s trig
Answer:
12 [tex]\pi[/tex] = 37.699 f/s
Actually, the more interesting question
would have been how fast is the ball going in MPH?
25.7 MPH
Step-by-step explanation:
C = 2[tex]\pi r[/tex]
C = 2 [tex]* \pi * 1.2[/tex]
C = 2.4 [tex]\pi feet[/tex]
C (per second) = (5)(2.4 [tex]\pi feet[/tex])
C(per second) = 12 [tex]\pi[/tex] = 37.699 f/s
Evaluate:
11x - 8(x - y)
Answer:
11x-8x+8y
3x+8y SEEESH IN DEEZ NU TS
Step-by-step explanation:
In a random sample of students at a university, stated that they were nonsmokers. Based on this sample, compute a confidence interval for the proportion of all students at the university who are nonsmokers. Then find the lower limit and upper limit of the confidence interval.
Answer:
(0.8165 ; 0.8819)
Lower boundary = 0.8165
Upper boundary = 0.8819
Step-by-step explanation:
Given :
Sample proportion. Phat = x/ n = 276/ 325 = 0.8492
Confidence interval :
Phat ± margin of error
Margin of Error = Zα/2* [√Phat(1 - Phat) / n]
Phat ± Zα/2* [√Phat(1 - Phat) / n]
The 90% Z critical value is = 1.645
0.8492 ± 1.645*[√0.8492(1 - 0.8492) / 325)
0.8492 ± 1.645*[√0.8492(0.1508) / 325]
0.8492 ± 1.645*√0.0003940288
0.8492 ± 0.0326535
Lower boundary = 0.8492 - 0.0326535 = 0.8165
Upper boundary = 0.8492 + 0.0326535 = 0.8819
Confidence interval = (0.8165 ; 0.8819)
3 coins are flipped.
Answer:
just keep writing down outcome on a sheet of paper then count total
Step-by-step explanation:
SCC U of 1 pt 3 of 1 1.2.11 Assigned Media A rectangle has a width of 49 centimeters and a perimeter of 216 centimeters. V The length is cm.
Answer:
The length is of 59 cm.
Step-by-step explanation:
Perimeter of a rectangle:
The perimeter of a rectangle with width w and length l is given by:
[tex]P = 2(w + l)[/tex]
Width of 49 centimeters and a perimeter of 216 centimeters:
This means that [tex]w = 49, P = 216[/tex]
The length is cm.
We have to solve the equation for l. So
[tex]P = 2(w + l)[/tex]
[tex]216 = 2(49 + l)[/tex]
[tex]216 = 98 + 2l[/tex]
[tex]2l = 118[/tex]
[tex]l = \frac{118}{2}[/tex]
[tex]l = 59[/tex]
The length is of 59 cm.
An adult soccer league requires a ratio of at least 2 women per 7 men on the roster. If 14 men are on the roster, how many women are needed to maintain that ratio?
Answer:
Atleast 4 women
Step-by-step explanation:
Ratio of
Women to men = 2 : 7
Number of women needed to maintain the ratio if there are 14 men on the roster :
The minimum number of women required :
(2 : 7) * number of men in roster
(2 / 7) * 14
2 * 2 = 4 women
Atleast 4 women are required to main the ratio
Which point represents the unit rate?
A
B
C
D
Answer:
Point C represents the unit rate
Step-by-step explanation:
Two vectors and are given by and . If these two vectors are drawn starting at the same point, what is the angle between them
Answer: hello your question is incomplete below is the complete question
The Two vectors; A = 5i + 6j +7k and B = 3i -8j +2k.
answer;
angle = 102°
Step-by-step explanation:
multiplying the vectors
A.B = |A| * |B|* cosθ
hence : Cosθ = (Ai*Bi )+ (Aj*Bj) + ( Ak*Bk/ (√A^2 *√B^2 )
= 15 - 48 + 14 /(√25+26+29) * (√9+64+4)
= -0.206448454
θ = cos^-1 ( -0.206448454) = 101.9° ≈ 102°
The top and bottom ends of a windshield wiper blade are R = 24 in. and r = 14 in., respectively, from the pivot point. While in operation, the wiper sweeps through 135°. Find the area swept by the blade. (Round your answer to the nearest whole number.)
Answer:
Area swept by the blade = 448[tex]in^{2}[/tex]
Step-by-step explanation:
The arc the wiper wipes is for 135 degrees angle.
So, find area of sector with radius 24 inches. And the find area of arc with r=14 inches.
Then subtract the area of sector with 14 inches from area of sector with radius as 24 inches.
So, area of sector with r=24 in =[tex]\frac{135}{360} *\pi *24^{2}[/tex]
Simplify it,
=216[tex]\pi[/tex]
Now, let's find area of sector with radius 14 inches
Area of sector with r=14 in = [tex]\frac{135}{360} *\pi *14^{2}[/tex]
Simplify it
=73.5[tex]\pi[/tex]
So, area swept by the blade = 216[tex]\pi[/tex] -73.5[tex]\pi[/tex]
Simplify it and use pi as 3.14.....
Area of swept =678.584 - 230.907
=447.6769
Round to nearest whole number
So, area swept by the blade = 448[tex]in^{2}[/tex]
(Will mark brainliest!!!) 20 PTS !!
Sixty percent of all children in a school do not have cavities. The probability, rounded to four decimal places, that in a random sample of 9 children selected from this school, at least 6 do not have cavities is:
Answer:
probability[Number of 6 random sample do not have cavities] = 0.8
Step-by-step explanation
Given:
Number of student do not have cavities = 60%
Number of random sample = 9 children
Find:
Probability[Number of 6 random sample do not have cavities]
Computation:
n = 9
p = 60% = 0.6
P(At least 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than 6)
Probability[Number of 6 random sample do not have cavities] = 1 - P(Less than or equal to 6)
Probability[Number of 6 random sample do not have cavities] = 0.8
37. Two numbers are such that their
difference, their sum and their
product are in the ratio 1:7: 24.
Find the product of the
number.
Answer:
8 and 6
Step-by-step explanation:
Two numbers are such that their difference, their sum, and their product are to
each other as 1:7:24. Their product must equal what number?
:
Two numbers a & b
Let x = the multiplier
:
a - b = 1x
a + b = 7x
a * b = 24x
:
Add the 1st two equations
a - b = x
a + b = 7x
2a = 8x
a = 4x
or
x = .25a
:
a * b = 24x
Replace 24x; a = 4x therefore:
a * b = 6a
b = 6
;
Using the 1st equation
a - b = 1x
Replace b with 6 and x with .25a
a - 6 = .25a
a - .25a = 6
.75a = 6
a =
a = 8
:
Find the multiplier
a - b = x
8 - 6 = 2
:
Check this
a - b = 2 (1*2)
a + b = 14; (7*2)
a * b = 48: (24*2)
:
The numbers are 8 and 6; their products = 48
The Cougar Swim Club acquired some Speedo Fastskin bodysuits and decided to test them out. A number of the club's fastest swimmers performed a 50m freestyle swim in a regular spandex bodysuit and in a Speedo Fastskin suit. The table below summarizes their times in seconds.Swimmer Spandex Speedo Fastskin1 31.1 29.12 28.9 30.43 31.4 32.04 34.9 31.75 27.7 28.26 36.7 32.97 33.3 28.68 30.8 26.2Perform a t-test for dependent means to determine if there is a difference between the regular spandex suit and the Fastskin bodysuit in terms of performance.t = _____df = _____Critical value of t = _____ (use alpha = 0.05)Would you reject the null hypothesis?
Answer:
T = 2.215
df = 7
Critical value = 2.364
Fail to reject the null
Step-by-step explanation:
Swimmer __Spandex __Speedo Fastskin__ d
1 __________31.1 _______29.1 __ 2
2_________ 28.9 ______30.4 __ -1.5
3_________ 31.4 ______ 32.0 __ - 0.6
4_________ 34.9 ______31.7 __ 3.2
5 _________27.7 ______28.2 __ - 0.5
6_________ 36.7 _____ 32.9 ___ 3.8
7 _________ 33.3 _____28.6 ___ 4.7
8_________ 30.8 _____26.2 ___ 4.6
The mean difference = Σd / n
2, - 1.5, - 0.6, 3.2, - 0.5, 3.8, 4.7, 4.6
μd = Σd / n = 15.7 / 8 = 1.9625
Sd = standard deviation of difference = 2.5065 (using calculator)
H0 : μd = 0
H1 : μd ≠ 0
The test statistic:
T = μd / (Sd/√n)
T = 1.9625 / (2.5065/√8)
T = 2.2145574
The degree of freedom, df = n - 1 = 8 - 1 = 7
Using a Pvalue calculator :
α = 0.05
Critical value, Tcritical = 2.364 (T distribution table)
Since Test statistic < Critical value
we fail to reject H0 ;
A rectangular prism has a volume of 60cm^3. What could the length, width and
height be? Explain how you know. "Recall, the formula for the volume of a prism
is V=lwh.
Can you guys help
What is the inverse of function f? f(x)=10/9+11
Answer:
Option D is answer.
Step-by-step explanation:
Hey there!
Given;
f(x) = 10/9 X + 11
Let f(X) be "y".
y = (10/9) X + 11
Interchange "X" and "y".
x = (10/9) y + 11
or, 9x = 10y + 99
or, y = (9x-99)/10
Therefore, f'(X) = (9x-99)/10.
Hope it helps!
2/5 e +4 = 9
Help please
Answer:
e=12.5 or e=25/2
Step-by-step explanation:
Let f(x) = (x − 1)2, g(x) = e−2x, and h(x) = 1 + ln(1 − 2x). (a) Find the linearizations of f, g, and h at a = 0. What do you notice? How do you explain what happened?
Answer:
Lf(x) = Lg(x) = Lh(x) = 1 - 2x
value of the functions and their derivative are the same at x = 0
Step-by-step explanation:
Given :
f(x) = (x − 1)^2,
g(x) = e^−2x ,
h(x) = 1 + ln(1 − 2x).
a) Determine Linearization of f, g and h at a = 0
L(x) = f (a) + f'(a) (x-a) ( linearization of f at a )
for f(x) = (x − 1)^2
f'(x ) = 2( x - 1 )
at x = 0
f' = -2
hence the Linearization at a = 0
Lf (x) = f(0) + f'(0) ( x - 0 )
Lf (x) = 1 -2 ( x - 0 ) = 1 - 2x
For g(x) = e^−2x
g'(x) = -2e^-2x
at x = 0
g(0) = 1
g'(0) = -2e^0 = -2
hence linearization at a = 0
Lg(x) = g ( 0 ) + g' (0) (x - 0 )
Lg(x) = 1 - 2x
For h(x) = 1 + ln(1 − 2x).
h'(x) = -2 / ( 1 - 2x )
at x = 0
h(0) = 1
h'(0) = -2
hence linearization at a = 0
Lh(x) = h(0) + h'(0) (x-0)
= 1 - 2x
Observation and reason
The Linearization is the same in every function i.e. Lf(x) = Lg(x) = Lh(x) this is because the value of the functions and their derivative are the same at x = 0
if x can be divide by 7 and 9 without leaving a remainder, it can also divided by which number without leaving a remainder
Answer:
all counting numbers except one
62. A chemist mixes 15 liters of 40 percent acid solution and 25 liters of 20 percent acid solution.
What percent of the mixture is acid?
40% of 15 L = 6 L of acid
20% of 25 L = 5 L of acid
This means the mixture contains a total of 11 L of acid, and with a total volume of 15 L + 25 L = 40 L, that means the mixture is at a concentration of
(11 L acid) / (40 L solution) = 0.275 = 27.5%
Help asap!!!!!!
A.
B.
C.
D.
Answer:
Function has a minimum value
So, f(x)=0 and f(4)=-3
f(x)= - 1/2x^2+4x-11f(4)=-3 and f(x)=-x+4
f(4)=0
OAmalOHopeO
If 3 3/4m of cloth was used for one suit, how many suits can be made with 30m cloth
Answer:
8 suits
Step-by-step explanation:
Divide 30 m by 3 [tex]\frac{3}{4}[/tex] m , or 30 ÷ 3.75 , then
30 ÷ 3.75 = 8
Then 8 suits can be made from 30 m of cloth
