6x²-7x=20 solve the following quadratic equation
Answer:
x = -4/3 and x = 5/2.
Step-by-step explanation:
6x² - 7x = 20
6x² - 7x - 20 = 0
To solve this, we can use the quadratic formula to solve this.
[please ignore the A-hat; that is a bug]
\(\frac{-b±\sqrt{b^2 - 4ac} }{2a}\)
In this case, a = 6, b = -7, and c = -20.
\(\frac{-(-7)±\sqrt{(-7)^2 - 4 * 6 * (-20)} }{2(6)}\)
= \(\frac{7±\sqrt{49 + 80 * 6} }{12}\)
= \(\frac{7±\sqrt{49 + 480} }{12}\)
= \(\frac{7±\sqrt{529} }{12}\)
= \(\frac{7±23 }{12}\)
\(\frac{7 - 23 }{12}\) = \(\frac{-16 }{12}\) = -8 / 6 = -4 / 3
\(\frac{7 + 23 }{12}\) = \(\frac{30}{12}\) = 15 / 6 = 5 / 2
So, x = -4/3 and x = 5/2.
Hope this helps!
Answer:
\(x1 = - \frac{4}{3} \)\(x2 = \frac{5}{2} \)Step-by-step explanation:
\(6 {x}^{2} - 7x = 20\)
Move constant to the left and change its sign
\( {6x}^{2} - 7x - 20 = 0\)
Write -7x as a difference
\(6 {x}^{2} + 8x - 15x - 20 = 0\)
Factor out 2x from the expression
\(2x(3x + 4) - 15x - 20 = 0\)
Factor out -5 from the expression
\(2x(3x + 4) - 5(3x + 4) = 0\)
Factor out 3x + 4 from the expression
\((3x + 4)(2x - 5) = 0\)
When the product of factors equals 0 , at least one factor is 0
\(3x + 4 = 0\)
\(2x - 5 = 0\)
Solve the equation for X1
\(3x + 4 = 0\)
Move constant to right side and change its sign
\( 3x = 0 - 4\)
Calculate the difference
\(3x = - 4\)
Divide both sides of the equation by 3
\( \frac{3x}{3} = \frac{ - 4}{3} \)
Calculate
\(x = - \frac{4}{3} \)
Again,
Solve for x2
\(2x - 5 = 0\)
Move constant to right side and change its sign
\(2x = 0 + 5\)
Calculate the sum
\(2x = 5\)
Divide both sides of the equation by 2
\( \frac{2x}{2} = \frac{5}{2} \)
Calculate
\(x = \frac{5}{2} \)
\(x1 = - \frac{4}{3} \)
\(x2 = \frac{5}{2} \)
Hope this helps...
Best regards!!
A boat can travel 37mph in still water. if it travels 135 miles with the current in the same length of travels 87 miles against the current, what is the speed of the current
If it travels 135 miles with the current in the same length of travels 87 miles against the current, The speed of the current is 8.
How to find the speed?Let speed of water current = x mph
Let speed with the current = x+37 mph
Time = distance/time =135/x+37 hrs
Speed against the current = 37-x mph
Hence,
Time = 87 /37-x
87 /37-x =135 /37+x
87 (37+x)= 135 (37-x)
3219 +87 x=4995 -135x
Combine like terms
87x+135 x= 4995 - 3219
222x = 1776
Divide both side by 222x
x = 1776/222
x = 8
Therefore the speed is 8.
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Colin buys a tv
for £800.
It depreciates at a rate of 4% per year.
How much will it be worth in 3 years?
Give your answer to the nearest penny where appropriate.
The amount of the tv in 3 years which depreciates at a rate of 4% per year is £708 .
Compound interest is interest calculated on the principal and the interest accrued in previous periods. It differs from simple interest where interest is not added to the principal when calculating interest for the next period. In mathematics, compound interest is usually represented by C.I.If the interest is compounded annually, then amount is given by \(A=P(1+\frac{r}{100} )^t\) where " A " = Amount , " R " = annual interest rate , "T" = number of years , " P" is principal amount .
We have given principal amount = £800 , rate = 4% and time = 3 years .
Putting above values in equation (1) , we get
\(A=800(1-\frac{4}{100} )^3\\A= 800(1 -0.04)^3\\A=800(0.96)^3\\A=800\times 0.88\\A= \£707.78\)
Note that the minus sign is due to depreciation .
On rounding off , amount will be £708 .
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Round to the nearest thousands 34,385
need help
Answer:34,000
Step-by-step explanation:
Answer:
its 34,000 because it below 5
Step-by-step explanation:
brainliest please
What is the equation of -8 -3y =25
log9 (8-2x) = log9(-3x+2)
Answer: X=-6
Step-by-step explanation: Since both logarithms have a base of 9, we can simply get rid of them. We could also do 9^(log9(8-2x))=9^(log9(-3x+2)). This would eliminate the logarithms.
Now we are just left with a simple algebraic equation: 8-2x=-3x+2.
We add 3x on both sides to get 8+x=2. We subtract 8 on both sides to get x=-6. There is no need to create a domain for the values of x since this is not an inequality problem.
Which expression is equivalent to square root a^7
Answer is d
Step-by-step explanation:
If you multiply a^6 and a it equals a^7
what is the percent increase from 18 to 26
Find the total surface area of the following cone. Leave your answer in terms of Pi. 4cm 3cm
The triangle formed from the height of the cone and the radius of its base is a special 3,4,5 triangle. The slant height is 5cm.
Recall that the area of a circle = pi*r^2
Substitute 3 in for r
Area = pi * (3)^2 = 9pi
SA = pi*r*l + B
Substitute our values into the equation
SA = pi * 3 * 5 + 9pi
SA = 15pi + 9pi
SA = 24pi cm^2
Find the median weight, in kilograms (kg),
of the weights below:
14 kg, 5 kg, 16 kg,
13 kg,
17 kg,
5 kg
Answer:
See below
Step-by-step explanation:
Median is the number in the middle of a list....if there are two numbers in the middle average them
5 5 13 14 16 17 <=====average of 13 and 14 is 13.5 kg
Kevin bought a used guitar at a garage sale for $150. He fixed it up and sold it for $200. What was the percent increase?
(Need explanation to show my work)
Answer:
33.3
Step-by-step explanation:
You need to divide 200 and 150 to get you 4/3. Then you will have to _____________________________
difference between the place values of 2 is in 4242
Answer:
\(\huge\colorbox{violet}{✏﹏ \: ᴀɴsᴡᴇʀ \: }\)
4242
2 = 200 ( 2 is in hundred's place )
4242
2 = 2 ( one's place )
Difference = ?
\( = 200 - 2 \\ = 198\)
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
\( \huge\blue{ \mid{ \underline{ \overline{ \tt ꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐ }} \mid}}\)
-4.6p-6.3p+3.9=-9.18
Answer:
−4.6p−6.3p+3.9=−9.18
−4.6p+−6.3p+3.9=−9.18
(−4.6p+−6.3p)+(3.9)=−9.18(Combine Like Terms)
−10.9p+3.9=−9.18
−10.9p+3.9=−9.18
Step 2: Subtract 3.9 from both sides.
−10.9p+3.9−3.9=−9.18−3.9
−10.9p=−13.08
Step 3: Divide both sides by -10.9.
−10.9p
−10.9
=
−13.08
−10.9
p=1.2
Answer:
\( \boxed{p = 1.2} \)
Step-by-step explanation:
\(Solve \: for \: p: \\ = > -4.6p - 6.3p+3.9=-9.18 \\ \\ -4.6p-6.3p=-10.9p: \\ = > - 10.9p +3.9=-9.18 \\ \\ Subtract 3.9 \: from \: both \: sides: \\ = >
(3.9-3.9)-10.9p=-3.9-9.18 \\ \\3.9-3.9=0: \\ = > - 10.9p =-3.9-9.18 \\ \\ -3.9-9.18 = -13.08: \\ = > - 10.9p = - 13.08 \\ \\ Divide \: both \: sides \: of \: - 10.9 p = - 13.08 \: by \: - 10.9: \\ = > \frac{ \cancel{ - 10.9}p}{ \cancel{- 10.9}} = \frac{ - 13.08}{ - 10.9} \\ \\ \frac{ - 10.9}{ - 10.9} = 1: \\ = > p = \frac{ \cancel{- }13.08}{ \cancel{- }10.9} \\ \\ \frac{13.08}{10.9} = 1.2: \\ = > p = 1.2\)
the population of a small town can be modeled with the function P(t)=18,751(1,09)^(t). Which statement about this situation is true?
A.The population will decrease by 9%.
B. The population will increase by 9%.
C. The population will increase by 1.09%.
D. The population will decrease by 1.09%.
PLEASE HELP ASAP!!
Thank You!
Statement B is true: The population will increase by 9%.
What are function's different types?Various Functions:
A single function (Injective function) Many – one function. From onto function (Surjective Function) Function is into. polynomial operation.
P(t)=18,751(1.09)t is the population function, where t is the time in years.
The function's growth factor or multiplier, which is bigger than 1, is represented by the expression (1.09t). In other words, the population is growing over time.
Finding the difference between the final and starting values, dividing by the initial value, and then multiplying by 100% will give us the percentage growth in the population.
Let's contrast the population at t=0 and t=1 to see how they differ:
P(0) = 18,751(1.09)^0 = 18,751
P(1) = 18,751(1.09)^1 = 20,436.59
In the last year, the population has grown from 18,751 to 20,436.59.
The population has grown by the following amount:
[(20,436.59 - 18,751)/18,751] × 100% ≈ 9.0%
Thus, the population will grow by 9%, as stated in statement B.
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HELP JIMTHOMPSON5910
13. To ride a roller coaster, you must be 48 inches tall. There are 30.48 centimeters in 1 foot. Approximately how many centimeters is 48 inches? Round to the nearest whole centimeter.
14. A water cooler contains 240 cups of water. One gallon is equal to approximately 3.8 liters. About how many liters of water are in the water cooler? Round to the nearest whole liter.
15. A billboard is 6 meters long. One centimeter is approximately 0.39 inch. About how long is the billboard in inches? Round to the nearest whole inch.
Answer:
13- pretty sure its 122
14- 58
15- i think its 236?
Problem 13
Answer: 122 cm------------------
Explanation:
It's not mentioned, but keep in mind that 1 foot is equivalent to 12 inches. This means that 48 inches is equal to 48/12 = 4 feet. So you must be 4 feet tall, or taller, to be able to ride the roller coaster.
To convert this to centimeters, we multiply by 30.48 to get 4*30.48 = 121.92 cm, which then rounds to 122 cm
==========================================================
Problem 14
Answer: Approximately 57 liters------------------
Explanation:
1 gallon = 16 cups
Note how 240/16 = 15, which means we can multiply both sides of that equation above by 15 and we end up with
15*(1 gallon) = 15*(16 cups)
15 gallons = 240 cups
The water cooler is 15 gallons.
Multiply this by 3.8, since there are about 3.8 liters per gallon, and we end up with the answer of 3.8*15 = 57 liters
This answer is approximate since the 3.8 was approximate.
==========================================================
Problem 15
Answer: Approximately 234 inches------------------
Explanation:
1 meter = 100 cm
6 meters = 600 cm (multiply both sides by 6)
1 cm = 0.39 inches
600*(1 cm) = 600*(0.39 inches)
600 cm = 234 inches
This answer is approximate because the 0.39 was approximate.
20!/1! in binominal distribution
Answer:
The expression 20!/1! is not directly related to the binomial distribution.
The expression 20!/1! represents the number of ways to arrange 20 distinct objects in a specific order, where each object is used exactly once. This is known as a permutation, and the number of permutations of n objects is given by n!.
On the other hand, the binomial distribution is a probability distribution that describes the number of successes in a fixed number of independent trials, where each trial has the same probability of success. The probability of getting k successes in n trials, each with probability p of success, is given by the binomial probability mass function:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where (n choose k) represents the number of ways to choose k items from a set of n items, and is given by the formula:
(n choose k) = n!/k!(n-k)!
So, while the expression 20!/1! is not directly related to the binomial distribution, the binomial distribution does involve calculating combinations (i.e., choosing k items from a set of n items), which are related to permutations.
help can be 50,60,and need to have x
Answer:
30 $ is 50 % of 60$
Step-by-step explanation:
The original price is 60$
The sell price 50% of the initial price
so we state that:
60$⇒ 100%x(the sell price)⇒ 50%x =\(\frac{50*60}{100}\) = 30$Simplify this expression.
-9d – 4p – 6 – 10d + 8
Answer:
-19d + 2
Step-by-step explanation:
-9d - 4p - 6 - 10d + 8
-9d - 10d - 6 + 8
-19d + 2
Jeff is playing a racing game. The game awards him an initial $4,000 of virtual money. In addition, he gets $100 of virtual money for each race he wins. In the end, he calculates average earnings $200 of for each race he won. If x represents the number of races he won, which equation can be used to find the number of wins?
Answer:A
Step-by-step explanation:
Answer:
[4000+200x] /x=100 is your answer
What were the rental rates?
answer/explanation:
d = daily rental chargem = the charge per mileJon rented a car from a company that charged a daily rental fee and a mileage charge. He rented the car for 6 days and drove 300 miles and was charged $285.6d + 300m = 285His friend Amanda later rented the same car for 7 days and drove 260 miles and was charged $310.7d + 260m = 310by solving the system of equations6d + 300m = 2857d + 260m = 310we findd = $35m = $0.25the daily rental charge is $35.the company charge per mile is $0.25.hope this helps
Three blocks are shown: Block A has mass 3 kilograms, length 8 centimeters, height 2 centimeters, and width 1 centimeters. Block B has mass 4 kilograms, length 1 centimeters, height 8 centimeters, and width 2 centimeters. Block C has mass 4 kilograms, length 8 centimeters, height 1 centimeters, and width 2 centimeters. Which statement is correct? (1 point) a Block A has the greatest density. b Block B has the least density. c The density of Block A is equal to the density of Block B. d The density of Block B is equal to the density of Block C.
Answer:
b & c
Step-by-step explanation:
triangle BOX has vertices at B(-8,3), O(5,4), and X(-7,-10). what is the area of triangle BOX? pls answer quick like in a few mins
The area of the triangle is 85 square units
How to find the area of a triangle using vertices?The area of a triangle with vertices (x₁, y₁), (x₂, y₂) and (x₃, y₃) is given by:
A = (1/2) [x₁(y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]
Where:
B: (x₁, y₁) = (-8, 3)
O: (x₂, y₂) = (5, 4)
X: (x₃, y₃) = (-7, -10)
A = (1/2) [x₁ (y₂ – y₃) + x₂(y₃ – y₁ ) + x₃(y₁ – y₂)]
A = (1/2) [-8 (4 – (-10)) + 5(-10 – 3) + (-7)(3 – 4)]
A = (1/2) [-112 - 65 + 7]
A = 85 square units
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Graph for f(x)=6^6 and f(x)=14^x
Graph Transformations
There are many times when you’ll know very well what the graph of a
particular function looks like, and you’ll want to know what the graph of a
very similar function looks like. In this chapter, we’ll discuss some ways to
draw graphs in these circumstances.
Transformations “after” the original function
Suppose you know what the graph of a function f(x) looks like. Suppose
d 2 R is some number that is greater than 0, and you are asked to graph the
function f(x) + d. The graph of the new function is easy to describe: just
take every point in the graph of f(x), and move it up a distance of d. That
is, if (a, b) is a point in the graph of f(x), then (a, b + d) is a point in the
graph of f(x) + d.
As an explanation for what’s written above: If (a, b) is a point in the graph
of f(x), then that means f(a) = b. Hence, f(a) + d = b + d, which is to say
that (a, b + d) is a point in the graph of f(x) + d.
The chart on the next page describes how to use the graph of f(x) to create
the graph of some similar functions. Throughout the chart, d > 0, c > 1, and
(a, b) is a point in the graph of f(x).
Notice that all of the “new functions” in the chart di↵er from f(x) by some
algebraic manipulation that happens after f plays its part as a function. For
example, first you put x into the function, then f(x) is what comes out. The
function has done its job. Only after f has done its job do you add d to get
the new function f(x) + d. 67Because all of the algebraic transformations occur after the function does
its job, all of the changes to points in the second column of the chart occur
in the second coordinate. Thus, all the changes in the graphs occur in the
vertical measurements of the graph.
New How points in graph of f(x) visual e↵ect
function become points of new graph
f(x) + d (a, b) 7! (a, b + d) shift up by d
f(x) Transformations before and after the original function
As long as there is only one type of operation involved “inside the function”
– either multiplication or addition – and only one type of operation involved
“outside of the function” – either multiplication or addition – you can apply
the rules from the two charts on page 68 and 70 to transform the graph of a
function.
Examples.
• Let’s look at the function • The graph of 2g(3x) is obtained from the graph of g(x) by shrinking
the horizontal coordinate by 1
3, and stretching the vertical coordinate by 2.
(You’d get the same answer here if you reversed the order of the transfor-
mations and stretched vertically by 2 before shrinking horizontally by 1
3. The
order isn’t important.)
74
7:—
(x) 4,
7c’
‘I
II
‘I’
-I
I NEED HELPP Solve for PMR please
The angle PMR in the quadrilateral is 32 degrees.
How to find the angle PMR?The angle PMR can be found as follows;
The line AP is an angle bisector of angle RPM. Therefore, the following relationships are formed.
∠RPM ≅ ∠WPM
Hence,
∠RPM ≅ ∠WPM = 58 degrees
Therefore,
∠WPM = 58 degrees
∠PWM = 90 degrees
Let's find ∠PMR as follows
∠PMR = 180 - 90 - 58
∠PMR = 90 - 58
∠PMR = 32 degrees
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Aidan buys a bag of cookies that contains 5 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 8 oatmeal cookies.
What is the probability that Aidan reaches in the bag and randomly selects a peanut butter cookie from the bag, eats it, then reaches back in the bag and randomly selects an oatmeal cookie? Write your answer as a percent. Round to the nearest tenth of a percent.
Answer- 62%
Step-by-step explanation
5+5+8+8= 26 There are 8 peanut butter cookies,so 8/26 is the chance we will get a peanut butter cookie. In percentage form that is 0.307692308 or 30% chance that a peanut butter cookie will be selected. This also means that since there are 8 oatmeal there is a 30% percent chance for those as well.5/26 is 0.192307692, which is almost 20 percent. 30 +30 +20+20 is 100 percent. Now that we know there is a 30 percent for both peanut butter and oatmeal, we would have to have the percent of 8+8/26. 16/26 is 0.615384615. This means that the chance of picking a peanut butter then oatmeal cookie, back-to-back would be around 62%
Hope this helps good luck.
1.1.1 To determine how much grass seeds they will need, the caretaker measure the length and breadth of the area of the sports field. He measured the length to be 162m and the breadth 160m. Calculate the area where the grass will be planted. You may use the formula: Area of rectangle = length x breadth (2)
Answer:
the area where the grass will be planted is 25,920 square meters.
Step-by-step explanation:
To calculate the area where the grass will be planted, we need to multiply the length and breadth of the sports field.
Area = length x breadth
Area = 162m x 160m
Area = 25,920 square meters
Therefore, the area where the grass will be planted is 25,920 square meters.
Chong can paint a car in y hours how long will it take him to paint 25 such cars
Answer:
Y25, considering the fact that y is a unknown variable and y is the amount of time that it takes to paint one car so multiply that by 25 for the 25 other cars he is painting and you will get your answer
You can also write it like this
Y25
(Y)25
Yx25
Y*25
Verónica Ana y Luis pintan una barda y les pagan 300 cuánto dinero debería recibir cada quien
Si Verónica, Ana y Luis están pintando una barda y se les paga un total de 300 unidades monetarias (por ejemplo, dólares, pesos, etc.), para determinar cuánto dinero debería recibir cada uno, necesitamos más información sobre cómo se distribuye el trabajo entre ellos.
Si los tres contribuyen de manera equitativa y realizan la misma cantidad de trabajo, podrían dividir el pago de manera igualitaria. En ese caso, cada uno recibiría 100 unidades monetarias (300 dividido entre 3).
Sin embargo, si uno de ellos realiza más trabajo o tiene una mayor responsabilidad en la tarea, podría ser justo que reciba una porción mayor del pago. En ese caso, la distribución de los 300 unidades monetarias dependerá de un acuerdo previo entre ellos sobre cómo se divide el pago en función de la cantidad o calidad del trabajo realizado.
Es importante tener en cuenta que la asignación exacta de dinero puede variar dependiendo de las circunstancias y el acuerdo al que lleguen Verónica, Ana y Luis.
Use what you know about decomposing fractions to write 11/10 as a mixed number
Answer:
11/10 as a mixed number is 1 and 1/10
Step-by-step explanation:
10 out of 10 is 1 but there is still another tenth that needs to be added so it is 1 and one tenth.
What is an equation with the formula of an Acute Angle?
An equation with the formula of an acute angle is a²+b²>c².
What is an acute angle triangle?Triangles can be categorised based on their sides and angles. According to the measurement of angles, a triangle is categorised as acute. A triangle is referred to as an acute triangle if all of its inner angles are smaller than 90°.
In an acute triangle, the following statement holds good for the length of the sides:
a²+b²>c²
b²+c²>a²
c²+a²>b²
Where a, b and c are the sides of a triangle.
Therefore, an equation with the formula of an acute angle is a²+b²>c².
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