Step-by-step explanation:
[tex]3x^{2} -5x -7 = 0 \\ 3x^{2} -5x = 7 \\ x^{2} -\frac{5}{3}x = \frac{7}{3} \\ x^{2} -\frac{5}{3}x +\frac{25}{36} = \frac{7}{3} +\frac{25}{36} \\ (x -\frac{5}{6})^{2} = \frac{84 +25}{36} \\ (x -\frac{5}{6})^{2} = \frac{109}{36} \\ x -\frac{5}{6} = ±\sqrt{\frac{109}{36}} \\ x -\frac{5}{6} = ±\frac{\sqrt{109}}{6} \\ x = ±\frac{\sqrt{109}}{6} +\frac{5}{6}[/tex]
Equation from the positive root:
[tex]x = \frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{\sqrt{109} +5}{6}[/tex]
Equation from the negative root:
[tex]x = -\frac{\sqrt{109}}{6} +\frac{5}{6} \\ x = \frac{-\sqrt{109} +5}{6}[/tex]
Answer:[tex]x = \frac{\sqrt{109} +5}{6}\\[/tex] and [tex]x = \frac{-\sqrt{109} +5}{6}\\[/tex] satisfy your quadratic equation.
Given : A quadratic equation is given to us . The equation is 3x² - 5x - 7 = 0 .
To Find : The roots of the equation .
Solution : Given quadratic equation is 3x²-5x-7=0. So , let's factorise it to get the zeroes of the equation .
⇒ 3x² -5x - 7 = 0.
Here now , use Quadratic formula , of the quadratic equation in standard form of ax² + bx + c = 0.
[tex]\boxed{\red{\bf x\:\:=\:\:\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}}}[/tex]
On substituting respective values ,
⇒ x = -(-5) ± √ (-5)² - 4×3×(-7) / 2 × 3.
⇒x = 5 ± √ [ 25 + 84 ]/ 6 .
⇒ x = 5 ± √ 109 / 6 .
⇒ x = 5 + √109 / 6 , 5 - √109 / 6.
[tex]\purple{\underbrace{\underline{\boxed{\red{\tt \purple{\longmapsto} x = \dfrac{5+\sqrt{109}}{6}, \dfrac{5-\sqrt{109}}{6}}}}}}[/tex]
Henry ran 3.43 kilometers last week. He ran 6.25 kilometers this week. How many
kilometers did run in all?
Answer:
Henry ran 3.43 kilometers last week. He ran 6.25 kilometers this week. How many
kilometers did run in all?
Step-by-step explanation:
Henry ran 3.43 kilometers last week. He ran 6.25 kilometers this week. How many
kilometers did run in all?
Answer:
9.68 kilometers
Step-by-step explanation:
subtract 8 from the input to get the output
divided the input by 3 to get the output
Answer: that will be 5
Step-by-step explanation:
Answer:
6
Step-by-step explanation:
evaluate the function when x = 5
P(x) = -3 + 4x
Answer:
P(x) = 17
Step-by-step explanation:
P(5) = -3 + 4(5) <- Substitute X
P(5) = -3 + 20 <- Multiply
P(5) = 17 <- Combine Like Terms
Answer:
P(5)=-3+4(5)
P(5)=-3+20
P(5)=17
Pls help me I will give Brainlyest
Mrs. Rodriguez wants to pay her restaurant bill which is $24.00. If Mrs. Rodriguez wants to leave a 20% tip on the
total, how much should she pay?
O $20.35
O $26.40
O $28.80
O $33.60
Answer:
C
Step-by-step explanation:
$28.80
Answer:
c
Step-by-step explanation:
A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior
citizens. Create a function f (x) which models the amount, in dollars, a senior citizen would pay for 2 pounds
of bananas on Wednesday
Answer:
2
Step-by-step explanation:
f(x)= 0.90(0.59*2)
A grocery store sells bananas for $0.59 per pound. On Wednesdays, the store offers a 10% discount to senior citizens. We need to create a function f(x) which models the amount in dollars, a senior citizen would pay for 2 pounds
What is a simple Equation?
A mathematical equation which represents the relationship of two expressions on either side of the sign.
The 10% discount will make it so the senior citizens will pay 90% of the price.
90%=0.90
Also we need to know that 0.59*2 means how much money per pound the bananas cost.
So when you put it together, you should get f(x)=0.90(0.59*2)
The function f (x)=0.90(0.59*2) which models the amount, in dollars, a senior citizen would pay for 2 pounds of bananas on Wednesday
So the required function is f(x)=0.90(0.59*2)
To learn more on simple equations click here:https://brainly.com/question/19459372
#SPJ6
select 3 names for the angle.
Round 1.24236 to the nearest hundredth
Answer:
1.24
Step-by-step explanation:
can someone please help me
Answer:
y = -5/3x -7
Step-by-step explanation:
If lines are parallel they have the same slope m = -5/3. Just need to figure out the new y-intercept going through the point (-9, 8).
y = mx + b
8 = -5/3(-9) + b
8 = 15 + b
b = -7
Now use m and b to form new equation of parallel line.
y = mx + b
y = -5/3x -7
Explain how you would solve -5/8 divided by 2/3 and what the solution is?
Answer:
-15/16
Step-by-step explanation:
-5/8 ÷ 2/3
Copy dot flip
-5/8 * 3/2
Multiply the numerators
-5*3 = -15
Multiply the denominators
8*2 =16
Put the numerator over the denominator
-15/16
fplzz ans my question
factorize p^4+4
Answer:
Step-by-step explanation:
(p²)²+2²
(p²+2)²-2p²2
(p²+2)²-4p²
(p²+2)²-(2p)²
(p²+2-2p)(p²+2+2p)
find the square root of 625
Step-by-step explanation:
square root of 625 is 25
which of the rolling values are solutions to the inequality , ILL MARK BRAINLIST !!!
Answer:
II and III
Step-by-step explanation:
I...
-9 - 5x > -1
-9 - 5(2) > -1
-9 - 10 > -1
-19 > -1
FALSE
II...
-9 - 5x > -1
-9 - 5(-5) > -1
-9 + 25 > -1
16 > -1
TRUE
III...
-9 - 5x > -1
-9 - 5(-10) > -1
-9 + 50 > -1
41 > -1
TRUE
Best of Luck!
Answer:
II. and III.
Step-by-step explanation:
-9 - 5x > -1
I. 2
-9 - 5(2) > -1
-9 - (10) > -1
-19 > -1
- 19 is not more than -1, thus I. is not an option
II. -5
-9 - 5(-5) > -1
-9 + 25 > -1
16 > -1
16 is more than -1, thus II. is an option
III. -10
-9 - 5(-10) > -1
-9 + 50 > -1
41 > -1
41 is more than -1, thus III. is an option
A population has standard deviation o = 17.2.
Part 1 of 2
(a) How large a sample must be drawn so that a 99.8% confidence interval for u will have a margin of error equal to 3.8?
Round the critical value to no less than three decimal places.
Round the sample size up to the nearest integer.
A sample size of
3.8.
is needed to be drawn in order to obtain a 99.8% confidence interval with a margin of error equal to
Answer:
idk
Step-by-step explanation:
Find the value of f(15) if f(x) = 100x – 5x2.
this problem is to replace the variable (here "x" ) with a certain numerical value.
the given function is f(x) followed by the algebraic expression " 100x -5x^2 "
now u r asked to find f(15), mean u have to find the value of the "expression" with the numerical value "15" replacing "x"
so it looks like this:
f(x) = 100x -5x^2
f(15) = 100*15 - 5*(15)^2 [only "x" got replaced by it's numerical value "15"]
now u can calculate it
so
f(15) = 1500 - 5*225 = 1500 - 1125 = 375 (Ans.)
hope u got the basic idea.
feel free to ask if u have further queries.
all the best!
There is 3 questions help asap
HELP ME PLEASE
In the diagram below, which distance represents the distance from point to
KE?
A JL
В. КМ
C. JM
D. JK
The force of gravity on an object varies directly with its mass. The constant of variation due to gravity is 32.2 feet per second squared. Which equation represents F, the force on an object due to gravity according to m, the object’s mass?
A) F = 16.1m
B) F = F equals StartFraction 16.1 Over m squared EndFraction.
C) F = 32.2m
D) F = F equals StartFraction 32.2 Over m squared EndFraction.
Answer:
fart poop ball tingle tingle pop tart and maybe not cause fart part and thg e answer is C
Answer:
Option C is Correct : F = 32.2mExplanation: I got it right on the quiz.
3x^2-4+5= 0 PLEASE HELP ASAP will mark brainliest
Answer:
3x^2+1
Step-by-step explanation:
you cannot add in the 3x^2 and the -4 and 5 but you can add the -4 and the 5
I hope this helps!
Step-by-step explanation:
3x to the power 2 is 9x;
New equation: 9x-4+5 = 0
9x- (4+5) = 0
9x-9=0
x=1
Marco has joined a bowling league, and is trying to raise his average to 140. On his last four games he scored 133, 130, 131, and 136. How much will he need to score on the next game to raise his mean to 140?
help ASAP. Which relation is a function?
Answer:
Answer choice on the top right.
Step-by-step explanation:
A function of points can not share the same x value.
1.3.3- You currently have $50. You plan on spending $2 each day on candy at the
comer store on your way home from school. How long will it take until you are
left with only $18?
Your answer
Answer:
It will take 16 days.
Step-by-step explanation:
50-18=32
32/2=16
32 represents the total amount of money spent before ending up with $18 left. If you spend $2 a day, just divide 32/2 (Total/Rate?). The final answer is 16 days.
To check, divide 50/2 to get 25 (days) and subtract the days we have (16).
25-16=9
9x2=18 or the $18 in the end of the problem.
If any of that was confusing, I'll be happy to answer any questions. It's just a pretty easy question so I am not sure if I did anything how you want or don't want it done.
"An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in Texas. Suppose that the mean income is found to be $20.3 for a random sample of 2333 people. Assume the population standard deviation is known to be $11.3. Construct the 98% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place."
Answer: ($19.8, $20.8)
Step-by-step explanation:
Confidence interval for mean : [tex]\overline{x}\pm z^*\dfrac{\sigma}{\sqrt{n}}[/tex] , where [tex]\overline{x}[/tex] = Sample mean, n= sample size, [tex]\sigma[/tex] = population standard deviation, z* = two tailed critical z-value.
Given: [tex]\overline{x}[/tex] = $20.3
n= 2333
[tex]\sigma[/tex] = $11.3
For 98% confidence, z* = 2.326
Then, the98% confidence interval for population mean will be:
[tex]20.3\pm (2.326)\dfrac{11.3}{\sqrt{2333}}\\\\=20.3\pm (2.326)\dfrac{11.3}{48.3011387}\\\\=20.3\pm (0.544165224825)\\\\\approx 20.3\pm 0.5\\\\=(20.3-0.5,\ 20.3+0.5)\\\\=(19.8,20.8)[/tex]
Hence, the 98% confidence interval for the mean per capita income in thousands of dollars = (19.8, 20.8)
Zenzizenzicube is an obsolete word that represents the square of the square of a cube. In symbols, zenzizenzicube is written as
(((x^3)^2))^2
Required:
a. Use the chain rule twice to find the derivative.
b. Use the properties of exponents to first simplify the expression, and then find the derivative.
Answer:
Step-by-step explanation:
Given the expression (((x^3)^2))^2
a) Differentiating the function with respect to x using chain rule.
Given y = (((x^3)^2))^2
Let u = (x³)²
y = u²; dy/du = 2u
Let p = x³; dp/dx = 3x²
u = p²; du/dp = 2p
Applying the chain rule formula:
dy/dx = dy/du • du/dp • dp/dx
substitute in the formula
dy/dx = 2u•2p•3x²
Since u = (x³)² and p = x³
dy/dx = 2(x³)²(2x³)(3x²)
dy/dx = 12x^6•x^5
dy/dx = 12x¹¹
b) Using property of exponent
y = (((x^3)^2))^2
y = (x^6)²
y = x¹²
dy/dx = 12x^12-1
dy/dx = 12x^11
An ant crept to a hole, which was 210 cm away.
It crept 40 cm per minute, but the wind pushed
it back 5 cm every minute. How many minutes
will it take the ant to reach the hole?
Answer:
6 minutes
Step-by-step explanation:
The ant can crawl 40 cm per minute but is pushed back 5 cm every minute aswell. In total the ant will crawl 35 cm per minute (40 - 5 = 35).
In order to find how long it will take for the ant to reach the hole we divide 210 by 35 (210/35) to get the answer of 6, therefore it takes the ant 6 minutes to reach the hole.
The ratio of boys to girls in homeroom is 2:3. If there are 8 boys, how many girls are there? Do not include units.
Answer:
12 girls =)
Step-by-step explanation:
Make a table labeled girls and boys like this
2|3
4|6
6|9
8|12
Multiply until you get to 8 boys
scientists are studying a population of 20 bugs and tracking the population, y, as it grows over time, t, in weeks. If the population grows by at least 6.1% each week, which system of inequalities represents the scenario?
Answer:
I am pretty sure it is
y >_ 20(0.061)^t
t >_ 0
Step-by-step explanation:
Which values of a, b, and c correctly represent the answer in simplest form?
4 and one-half divided by 1 and one-fourth = a StartFraction b Over c EndFraction
a = 3, b = 6, c = 10
a = 3, b = 3, c = 5
a = 5, b = 3, c = 3
a = 10, b = 6, c = 3
Answer
the answer is a i
thinnk
Step-by-step explanation:
hope this helped!!
The values of the fraction are a = 3, b= 3, c= 5 is the correct answer.
What is a fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts. It is a number expressed as a quotient, in which a numerator is divided by a denominator.
For the given situation,
The fraction is given as [tex]\frac{4\frac{1}{2} }{1\frac{1}{4} }[/tex]
⇒ [tex]\frac{\frac{9}{2} }{\frac{5}{4} }[/tex]
⇒ [tex]\frac{9}{2}[/tex] × [tex]\frac{4}{5}[/tex]
⇒ [tex]\frac{18}{5}[/tex]
⇒ [tex]3\frac{3}{5}[/tex]
Thus from the above value a = 3, b= 3, c= 5.
Hence we can conclude that the values of the fraction are a = 3, b= 3, c= 5 is the correct answer.
Learn more about fractions here
https://brainly.com/question/17205173
#SPJ2
For each of these intervals, list all its elements or explain 2.1 Sets 131 why it is empty. a) [a,a] c) (a, a] e) (a,b), where a > b b) [a,a) d) (a, a) f) [a,b],wherea>b
Answer: b
Step-by-step explanation:
13/20 of a number is what percentage of that number?
Answer:
65%
Step-by-step explanation:
Determine the intercepts of the graph please be sure
Answer:
X= (_7, 0)
Y= (0, 2
Step-by-step explanation:
We meet again