Factor and solve each quadratic equation
Show your work
2t^t+t-3=0
Answers
Answer:
t=1
Step-by-step explanation:
2t+t−3=0
2t+t+−3=0
(2t+t)+(−3)=0(Combine Like Terms)
3t+−3=0
3t−3=0
Step 2: Add 3 to both sides.
3t−3+3=0+3
3t=3
Step 3: Divide both sides by 3.
3t
3
=
3
3
t=1
Related Questions
I pent $4. 80 on grocerie and $1. 20 on vegetable what i the ratio of
Cot of grocerie to cot of vegetable
Answers
The ratio of Cost of grocerie to cost of vegetable 4:1 .
What is the cost?
Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup.
Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.
Given that,
Spent $4.80 on groceries and $1.20 on vegetables.
Total cost = 4.80 + 1.20
Total cost = $6.00
a. Cost of groceries to cost of vegetables;
Ratio = 4.80 / 1.20 = 4 / 1
Learn more about Cost
brainly.com/question/15135554
#SPJ4
Prehistoric cave paintings were discovered in a cave in France. the paint contain 25% of the original Carbon-14. Use the exponential decay model for carbon-14, A=A0e^-0.000121t to estimate the age of the paintings
Answers
Answer:
The age of paintings is - 26,601 years .
Step-by-step explanation:
Lets calculate-
A= \(0.25 A\)o
Therefore ,
\(A= A\)o \(e^-^0^.^0^0^0^1^2^1^t\)
\(ln0.25=-0.000121t\)
\(-3.2188=-0.000121t\)
\(t=\frac{-3.2188}{-0.000121}\)
t= 26,601.65
Therefore , the age of paintings is 26,601 years old.
Liza comes to the swimming pool once every 6 days. Jenny comes once every 4 days and Olga comes once every 10 days. This Monday all of them were in the pool.
How many days after this Monday will all of them meet at the swimming pool again?
Answers
Answer:
60 days
Step-by-step explanation:
L.C.M. of 6,4,10=60
as 6=2×3
4=2×2
10=2×5
L.C.M. =2×3×2×5=60
after 60 days they will again together.
let ss denote the sum of all of the three digit positive integers with three distinct digits. compute the remainder when ss is divided by 10001000.
Answers
The remainder when the sum of all three-digit positive integers with three distinct digits is divided by 10001000 is 549,450
To find the sum of all three-digit positive integers with three distinct digits, we can use the concept of arithmetic progression.
An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant. In this case, the difference between consecutive three-digit positive integers is 1.
To find the sum of an arithmetic progression, we can use the formula: Sum = (first term + last term) * number of terms / 2
In this case, the first term is 100, the last term is 999 (the largest three-digit positive integer with three distinct digits), and the number of terms is the count of numbers between 100 and 999 inclusive.
To find the count of numbers between 100 and 999 inclusive, we subtract the starting number from the ending number and add 1:
(999 - 100) + 1 = 900.
Substituting the values into the formula, we get:
Sum = (100 + 999) * 900 / 2 = 549,450
Now, to find the remainder when the sum is divided by 10001000, we can use the modulo operation.
Remainder = 549,450 % 10001000
= 549,450
Therefore, the remainder when the sum is divided by 10001000 is 549,450.
The remainder is 549,450.
To find the sum of all three-digit positive integers with three distinct digits, we can use the concept of arithmetic progression.
The first term is 100, the last term is 999, and the difference between consecutive terms is 1.
The formula for the sum of an arithmetic progression is
(first term + last term) * number of terms / 2.
In this case, the number of terms is the count of numbers between 100 and 999 inclusive, which is
(999 - 100) + 1 = 900.
Substituting the values into the formula, we get a sum of 549,450. To find the remainder when the sum is divided by 10001000, we can use the modulo operation.
The remainder is 549,450.
The remainder when the sum of all three-digit positive integers with three distinct digits is divided by 10001000 is 549,450.
To Know More about formula visit:
brainly.com/question/20748250
#SPJ11
!!20 POINTS!! An electrician charges a set fee for every house call and then charges an hourly rate depending on how long the job takes. The total cost of the electrician's services can be determined using the equation C=110+55t, where t is the number of hours the electrician spends at the house working. What is the slope of the equation and what is its interpretation in the context of the problem?
Answers
A coffee shop sold 2,880 iced coffees in July. In all, the coffee shop sold
12,000 coffees that month. What percent of the coffees sold were iced?
Answers
Answer:
76%
Step-by-step explanation:
Simply do 12,000-2,880. Answer the to is 9,120. Then just 9,120 / 12,000 and you get 76% :D
Answer 19by-step explanation:
Evaluate the expression using the given value 5a+3 a=6
Answers
Answer- 33
We are told that A=6, there for we can right out our equation fully.
(5 x 6)+3. Our multiplication sentence with go in parentheses ( ) so we know to do that part of our equation first. 5 times 6 is 30. After we multiply we add our outside number(s). 30 plus 3 is 33. Which means the solution to the equation is 33.
5a +3= 33 or (5x6) +3 = 33
Hope this helps! and GOOD LUCK.
What number is 0. 01 less than 16?
Answers
Answer: 15.99
Step-by-step explanation:
16 - 0.01 = 15.99
Another way to think about this is, if you add 0.01 to 15.99, youd get back to 16
Determine whether each matrix has an inverse. If an inverse matrix exists, find it.
[2 3 2 4]
Answers
The inverse of the matrix [2 3; 2 4] is [2 -3/2; -1 1]. If the determinant is non-zero, then the matrix has an inverse. If the determinant is zero, the matrix does not have an inverse.
To determine if a matrix has an inverse, we need to calculate its determinant. Let's find the determinant of the matrix [2 3; 2 4]:
The determinant is calculated as:
(2*4) - (3*2) = 8 - 6
= 2
Since the determinant is non-zero (2 is not equal to 0), the matrix [2 3; 2 4] does have an inverse.
To find the inverse, we can use the formula:
Inverse Matrix = (1/determinant) * adjoint matrix
The adjoint matrix is obtained by swapping the diagonal elements and changing the sign of the off-diagonal elements. In this case, the adjoint matrix is [4 -3; -2 2].
Now, we can calculate the inverse matrix:
Inverse Matrix = (1/2) * [4 -3; -2 2]
= [2 -3/2; -1 1]
To know more about the matrix, visit:
https://brainly.com/question/29995229
#SPJ11
1. Find the length of each leg.
R
Q
30⁰
4
60%
P
Answers
Answer:
QP = 2
QR = 2√3
Step-by-step explanation:
This is a special right triangle with angle measures as follows:
30° - 60° - 90°
And side lengths represented with:
x - x√3 - 2x respectively to angle measures.
The side length that sees angle measure 90, hypotenuse, is given as 4 so the legs would be:
2 and 2√3
On a trip to Washington, D.C., you and your friend are standing next to the Washington Monument. Your friend wants to buy a guide book to find out how tall the Washington Monument is, but will use the money to buy a snack to share instead if you can figure it out. If you know your own height, what two additional measurements must you know to solve the problem?(1 point)
the length of the shadow cast by the Washington Monument and the length of the shadow cast by the Lincoln Memorial
the length of your shadow and the length of your friend’s shadow
the length of your shadow and the length of the shadow cast by the Washington Monument
the length of your friend’s shadow and the length of the shadow cast by the Washington Monument
If a 30-foot tree casts an 18-foot shadow, find the length of the shadow cast by a 24-foot tree. (1 point)
14.4 feet
432 feet
22.5 feet
40 feet
In △ABC, m∠A=42°, m∠B=50°, AB=4, and AC=3. In △XYZ, m∠X=42°, m∠Z=88°, XY=14, and YZ=9.5. Find the measures of BC¯¯¯¯¯¯¯¯ and XZ¯¯¯¯¯¯¯¯. Round to one decimal place.(1 point)
BC=2, XZ=7.1
BC=2, XZ=10.5
BC=2.7, XZ=7.1
BC=2.7, XZ=10.5
Answers
Answer:
1) the length of your shadow and the length of the shadow cast by the Washington Monument
2) 14.4 feet
3) BC=2.7, XZ=10.5
Step-by-step explanation:
just too the quiz
Answer:
1: The length of your shadow and the length of the shadow cast by the Washington Monument
2: 14.4
3: Yes, the triangles are similar.
/\ PSQ~/\RST
4: The solution for the value of x is incorrect because the proportion does use the ratios of corresponding sides
5:
Step-by-step explanation:
a rectangular swimming pool is 15 feet long and x feet wide. What is the perimeter when x=12 feet
Answers
Answer: 54 square feet
Step-by-step explanation:
To find perimeter of a rectangle we must use the formula l+l+w+w=p where l and w represent width and length
Since we know length and width is x=12 just substitute so
15+15+12+12=54 so 54 is the perimeter
Starting from 50 miles away, a car drives toward a speed checkpoint and then passes it. The car
travels at a constant rate of 30 miles per hour.
The distance of the car from the checkpoint is given by d=150-3001
At what times is the car 5 miles from the checkpoint?
Plz show steps
Answers
Answer: the two times such that the car is 5 miles away from the checkpoint are 1.5 hours and 1.83 hours.
Step-by-step explanation:
We know that:
At the beginning, at t = 0h, the car is 50 miles away from the checkpoint (let's define the checkpoint as the position 0mi).
And the speed of the car is 30mi/h.
Then the movement equation for the car will be:
d(t) = 50mi - 30mi/h*t
Then at t = 0h, we will have:
d(t) = 50mi - 30m/h*0h = 50mi
So at the beggining, the distance to the checkpoint is 50 miles, so it is consistent with our case.
Now we want to find the times such that the car is 5 miles away from the checkpoint.
These times are when:
d(t1) = 5mi
d(t2) = -5mi
Then let's solve these two equations:
d(t1) = 5mi = 50mi - 30mi/h*t1
-45mi = -30mi/h*t1
(45/30) h = t1 = 1.5 hours.
And the other time is:
d(t2) = -5mi = 50mi - 30mi/h*t2
-55mi = -30mi/h*t2
(55/30) h = t2 = 1.83 hours.
Then the two times such that the car is 5 miles away from the checkpoint are 1.5 hours and 1.83 hours.
Use the given information to find the equation of the quadratic function. Write the function in standard form f(x) ax² + bx + c.
The zeros of the function are x = 8 and x = -2. Use the fact that f(2)=-72 to find a.
f(x)=
Answers
The equation of the quadratic function is: f(x) = 3x² - 18x - 48
To find the equation of a quadratic function in standard form, we need to use the zeros of the function and one additional point.
Given that the zeros are x = 8 and x = -2, we can write the equation in factored form as:
f(x) = a(x - 8)(x + 2)
To find the value of "a," we can use the fact that f(2) = -72.
Substituting x = 2 into the equation, we have:
-72 = a(2 - 8)(2 + 2)
Simplifying, we get:
-72 = a(-6)(4)
-72 = -24a
Dividing both sides by -24, we find:
3 = a
Now that we know the value of "a," we can rewrite the equation in standard form:
f(x) = 3(x - 8)(x + 2)
So, the equation of the quadratic function is:
f(x) = 3x² - 18x - 48
Learn more about quadratic function :
https://brainly.com/question/28038123
#SPJ11
4) A spinner has 8 congruent sections as shown in the diagram. If the
spinner is spun twice, what is the probability that the first spin will land on
a whistle and the second spin will land on a yo-yo?"
a. 1/2
b. 1/8
c. 2/8
d. 1/32
Answers
plzzzzz guys help emergency plz really I got problem
if you do jpt then I will report
Answers
Answer:
\(let \: their \: points \: of \: intersection \: be \to \: x \\ since : \\ \: \overline{MN} \: intersects \: \overline{QL} \: at \: point \: x : \\ and\\ \overline{QL} \: also \: meets \: \overline{MN} \: at \: point \: x : \\ hence \: \overline{QL}\: and \: \overline{MN} \: bisects \: each \: other.\)
During a 3 hour period, 2,292 people rode the roller coaster at an amusement park. Which proportions can be used to find x, the number of
people who rode the coaster during a 12-hour period, if the rate is the same.
Answers
Answer:
2,292/3 = x/12
Step-by-step explanation:
if you were to solve
2,292/3 finds you how many people per hour
and multiply that by 12 to find how many people for 12 hours.
Step-by-step explanation:
\(\frac{2292}{3} =\frac{x}{12}\)
cross multiply divide.
x=9168
which three points in the figure are collinear?
Answers
Answer:
A, D, and E
Step-by-step explanation:
A, D, and E all fall on the same line, therefore, they are all collinear.
Calculating with a modulus [10 points] Assign to the Latin alphabet (the alphabet used for English) these values for each letter: o for 'a', 1 for 'b', 2 for 'c', ..., 25 for 'z'. 1. Translate the word 'encryption' into a sequence of values as given above (for example, 'hello' would become 7 4 11 11 14) 2. Multiply each of those numbers by 7 3. Take each of those numbers modulo 26, that is, divide each by 26 and write down the remainder 4. Translate those numbers back into letters
Answers
1.The word 'encryption' translated into a sequence of values using the given alphabet-to-number mapping is 4 13 15 20 17 8 14 24 0.
2.Each number in the sequence obtained from step 1 is multiplied by 7, resulting in the sequence 28 91 105 140 119 56 98 168 0.
3. Taking each number in the sequence from step 2 modulo 26, we obtain the remainder after dividing by 26, resulting in the sequence 2 13 1 12 17 4 20 16 0.
4. Translating the numbers from step 3 back into letters using the alphabet-to-number mapping, we obtain the word 'cmalmqet'.
1. To translate the word 'encryption' into a sequence of values, we use the provided mapping where 'a' is assigned the value 0, 'b' is assigned 1, 'c' is assigned 2, and so on until 'z' is assigned 25. Applying this mapping to each letter in the word 'encryption,' we get the following sequence of values: 4 13 15 20 17 8 14 24 0.
2. In this step, we multiply each number from the sequence obtained in step 1 by 7. Therefore, multiplying each value in the sequence 4 13 15 20 17 8 14 24 0 by 7 gives us the following sequence: 28 91 105 140 119 56 98 168 0.
3. To find the remainder after dividing each number in the sequence obtained from step 2 by 26, we perform modulo 26 operation. Dividing each number in the sequence 28 91 105 140 119 56 98 168 0 by 26 gives us the following remainder sequence: 2 13 1 12 17 4 20 16 0.
4. Using the given alphabet-to-number mapping, we assign the letter 'a' to the value 0, 'b' to 1, 'c' to 2, and so on. Translating the numbers 2 13 1 12 17 4 20 16 0 back into letters using this mapping, we get the word 'cmalmqet'.
To learn more about multiplying Click Here: brainly.com/question/23536361
#SPJ11
for each value c determine how many solutions the system has
Answers
Answer:
can we get a picture or something? we cant help unless we have more context
Step-by-step explanation:
If you borrow 700$ for five years at a annual interest rate of 7%, how much will you pay all together
Answers
Answer:
$2,245.
Step-by-step explanation:
Your interest will have grown to $2,245 dollars and you will have earned $1,545.
Hope this helped
how many words can be formed by using the W,X,Y,Z if repetitions is not allowed?
- 30
- 24
- 18
- 12
Answers
Answer:
24
Step-by-step explanation:
What you have here is a permutation, seeing as each element can only be used once.
We have 4 letters initially, so we can choose any 1 as our first letter. We have 4 choices for our first letter
However, once we choose our first letter, we can't use it anymore, so, for our second letter, we can only choose from the remaining 3 letters.
Furthermore, once we choose our second letter, we can only choose our 3rd letter from the remaining two letters we didn't choose yet.
Finally, our last letter will always be the one we didn't choose the last 3 times. So there is only one choice here.
Going off of this, we have four choices for the 1st letter, three choices for the 2nd letter, two choices for the 3rd letter, and one choice for the 4th letter
The way to calculate how many permutations we have without repetition is using factorials
N!
Where N is the number of elements you have.
In this case, it would be 4!
4! is 4 * 3 * 2 * 1
Which equals 24
If you notice, each number in 4! is the number of options we have for each choice. 4, then 3, and so on
Given the following linear optimization problem Maximize 250x + 150y Subject to x + y ≤ 60 3x + y ≤ 90 2x+y>30 x, y 20 (a) Graph the constraints and determine the feasible region. (b) Find the coordinates of each corner point of the feasible region. (c) Determine the optimal solution and optimal objective function value.
Answers
The linear optimization problem is to maximize the objective function 250x + 150y, subject to the constraints x + y ≤ 60, 3x + y ≤ 90, and 2x + y > 30, where x and y are both greater than or equal to 20.
what is the feasible region and the optimal solution for the given linear optimization?The feasible region can be determined by graphing the constraints and finding the overlapping region that satisfies all the conditions. In this case, the feasible region is the area where the lines x + y = 60, 3x + y = 90, and 2x + y = 30 intersect. This region can be visually represented on a graph.
To find the corner points of the feasible region, we need to find the points of intersection of the lines that form the constraints. By solving the systems of equations, we can find that the corner points are (20, 40), (20, 60), and (30, 30).
The optimal solution and the optimal objective function value can be determined by evaluating the objective function at each corner point and selecting the point that yields the maximum value. By substituting the coordinates of the corner points into the objective function, we find that the maximum value is achieved at (20, 60) with an objective function value of 10,500.
Learn more about constraints
brainly.com/question/32387329
#SPJ11
In AOPQ, p = 38 cm, q = 29 cm and 20=39°. Find the length of o, to the nearest
centimeter.
Answers
Answer:
Step-by-The length of o in the triangle AOP can be found using the Law of Cosines. The Law of Cosines states that for a triangle with sides a, b, and c and opposite angle C, the following formula holds:
c^2 = a^2 + b^2 - 2ab cos(C)
In this case, a = 38 cm, b = 29 cm, and C = 39°. The length of o can be found by rearranging the formula and solving for c:
c^2 = 38^2 + 29^2 - 2(38)(29) cos(39°)
c = sqrt(38^2 + 29^2 - 2(38)(29) cos(39°))
Using a calculator, we can find that c ≈ 47.3 cm, to the nearest centimeter, o = 47 cm.step explanation:
f(x) = -4x^2 + 5x
Find f(6)
Answers
Answer:
-114
Step-by-step explanation:
f(6) it means f(x=6) so substituting x=6 in your equation gives us
f(6)= -4*(6)²+5*(6)
= -4*36+30
= -144+30
= -114
A triangular prism is 12 meters long and has a triangular face with a base of 8 meters and a height of 9 meters. What is the volume of the triangular prism?
Answers
The volume of the triangular prism is 216 cubic meters.
To find the volume of a triangular prism, we need to multiply the area of the triangular base by the length of the prism.
Calculate the area of the triangular base.
The base of the triangular face is given as 8 meters, and the height is 9 meters. We can use the formula for the area of a triangle: area = (1/2) * base * height.
Plugging in the values, we get:
Area = (1/2) * 8 meters * 9 meters = 36 square meters.
Multiply the area of the base by the length of the prism.
The length of the prism is given as 12 meters.
Volume = area of base * length of prism = 36 square meters * 12 meters = 432 cubic meters.
Adjust for the shape of the prism.
Since the prism is a triangular prism, we need to divide the volume by 2.
Adjusted Volume = (1/2) * 432 cubic meters = 216 cubic meters.
Therefore, the volume of the triangular prism is 216 cubic meters.
For more such information on volume of triangular prism, visit:
https://brainly.com/question/31637705
#SPJ8
Can you help me please I can't get it
Answers
Answer:
-2x - 6 = 2 - 4x - (x - 1)
-2x - 6 = 2 - 4x - x + 1
-2x - 6 = 3 - 5x
3x = 9
That is the furthest it can be simplified without solving it.
Answer is x=3 if needed.
Please brainliest if this helped.
Please help me this is due tonight
Answers
Answer:
1. The new drummer in the band contributes an appealing rhythm to our songs.
2. One feature of personality is how well someone can control impulse.
3. The adaptation in polar bears' fur sufficiently
4. After learning that the twins were distinct people, I had to process the new information.
5. Early scientists insisted that the earth is round, but others denied it. (? can we mess with the tense and such of the words?)
Step-by-step explanation:
Of the total school population of 800 students, 200 live outside the student limits. What percentage of students live outside the city limits?
Answers
Answer:
1/4 population
Step-by-step explanation:
Answer: 25%
Step-by-step explanation: 200/800=0.25
Move the decimal places of 0.25 two spaces to the right so is 25.
multiply v by w, then add 9 to the result
Answers
\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)
Here we go ~
1. Multiply v and w :
\(\qquad \sf \dashrightarrow \:v \times w = vw\)
2. add 9 to the vw :
\(\qquad \sf \dashrightarrow \: vw + 9\)
Hence the required expression is : vw + 9