The quadratic formula can be used to find the solutions of a quadratic equation. In this case, the equation is 2x² - 3x - 5 = 0. Using the quadratic formula, the two solutions are x = 2 and x = -1.
Explanation:To find the solutions to the equation 2x² - 3x - 5 = 0, we can use the quadratic formula. The formula states that the solutions of any quadratic equation ax² + bx + c = 0 can be calculated using the formula:
x = (-b ± √(b² - 4ac)) / 2a
In this case, a = 2, b = -3, and c = -5. Substituting these values into the formula, we get:
x = (-(-3) ± √((-3)² - 4(2)(-5))) / (2(2))
Simplifying further, we have:
x = (3 ± √(9 + 40)) / 4
x = (3 ± √49) / 4
x = (3 ± 7) / 4
Therefore, the two solutions to the equation 2x² - 3x - 5 = 0 are x = (3 + 7) / 4 = 2 and x = (3 - 7) / 4 = -1.
Learn more about Quadratic formula here:https://brainly.com/question/11540485
#SPJ12
Simplify the expression
- 3/6 - 5/7
can you show me how?
A multivitamin tablet contains 14.5mg of calcium. How much calcium does a bottle of 50 tablets contain? Write your answer in grams.
Answer:
The correct answer is 725mg of calcium.
Step-by-step explanation:
To solve this problem, you can to use the rule of three.
1 tablet → 14.5 mg.50 tablets → x mg.Now, you have to multiply 50 tablets by 14.5 mg, then divide by 1 tablet:
[tex]x = \frac{50 tb * 14.5mg}{1 tb} = 725 mg[/tex] // tb divided by tb is 1
[tex]x = 725 mg[/tex]
how do you evaluate the expression |4/13|
Ryan runs 9 miles in 73 minutes. How many minutes does he take per mile?
find the solution of
2x - 2y = -20 and -2x + 4y = 14
What is the simplified expression for –3cd – d(2c – 4) – 4d?
A:–5cd
B:cd – 8d
C:5cd – 8d
D:–5cd – 8d
Draw one card at random from a standard deck of cards. the sample space s is the collection of the 52 cards. assume that the probability set function assigns 1/52 to each of the 52 outcomes. let a = {x: x is a jack, queen, or king}, b = {x: x is a 9, 10, or jack and x is red}, c = {x: x is a club}, d = {x: x is a diamond, a heart, or a spade}.
We have P(A) = 3/13, P(A ∩ B) = 3/52, P(A ∪ B) = 17/52, P(C ∪ D) = 1, and P(C ∩ D) = 0.
(a) To find P(A), we first determine the number of outcomes in A, which consists of 12 cards (4 jacks, 4 queens, and 4 kings).
Since there are 52 cards in total, P(A) = 12/52 = 3/13.
(b) For P(A ∩ B), we look for the cards that are both in A and B.
There are 3 such cards (jack of hearts, jack of diamonds, and jack of hearts).
So, P(A ∩ B) = 3/52.
(c) To find P(A ∪ B), we combine the outcomes in sets A and B, but we avoid double-counting the jacks.
So, A ∪ B consists of 12 cards from A and 5 cards from B, totaling 17 cards.
Hence, P(A ∪ B) = 17/52.
(d) P(C ∪ D) includes all cards that are clubs, diamonds, hearts, or spades.
Since all cards fall into these categories, P(C ∪ D) = 1.
(e) P(C ∩ D) represents the probability of drawing a card that is both a club and either a diamond, heart, or spade.
Since clubs do not intersect with these suits, P(C ∩ D) = 0.
Complete Question:
Draw one card at random from a standard deck of cards. The sample space S is the collection of the 52 cards. Assume that the probability set function assigns 1/52 to each of the 52 outcomes.
Let
A = {x: x is a jack, queen, or king},
B = {x: x is a 9, 10, or jack and x is red},
C = {x: x is a club},
D = {x: x is a diamond, a heart, or a spade}.
Find (a) P(A), (b) P(A ∩ B), (c) P(A ∪ B), (d) P(C ∪ D), and (e) P(C ∩ D).
If P = Q squared ⋅ O, express O in terms of P and Q.
B. if lucinda has only $18 to spend and the price of kewpie dolls and the price of beanie babies are both $6, how many of each would lucinda buy if she were rational? 0 kewpie dolls and 3 beanie babies 3 kewpie dolls and 0 beanie babies 2 kewpie dolls and 1 beanie baby 1 kewpie doll and 2 beanie babies
Lucinda can rationally choose to buy 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies, as all combinations fit within her $18 budget. The prices for each are $6.
In order to determine how many Kewpie dolls and Beanie Babies Lucinda can buy, we need to explore her budget constraint. Lucinda has $18 to spend, and the prices of both Kewpie dolls and Beanie Babies are $6 each. We can calculate the maximum possible combinations of each that fit within her budget.
If Lucinda buys 0 Kewpie dolls and 3 Beanie Babies, she spends $0 + $18 = $18.If Lucinda buys 3 Kewpie dolls and 0 Beanie Babies, she spends $18 + $0 = $18.If Lucinda buys 2 Kewpie dolls and 1 Beanie Baby, she spends $12 + $6 = $18.If Lucinda buys 1 Kewpie doll and 2 Beanie Babies, she spends $6 + $12 = $18.All these combinations maximize her budget, so any of these options could be rational depending on her preference. Therefore, Lucinda could rationally choose to buy any of the following combinations: 0 Kewpie dolls and 3 Beanie Babies, 3 Kewpie dolls and 0 Beanie Babies, 2 Kewpie dolls and 1 Beanie Baby, or 1 Kewpie doll and 2 Beanie Babies.
I have 7 hundreds blocks, 5 tens blocks, and 8 ones blocks. I use my blocks to model two 3-digit numbers. What could my two numbers be?
The GCF of two different numbers is greater than the LCM of the numbers
The governor of state a earns $50,935 more than the governor of state b. If the total salaries is $287,225. Find the salaries for both
Which statement best describes the function h(t) 210- 15t
the some of two consecutive even integers is 170. find the two integers.
The required value of integers are 84 and 86 respectively.
How to write a linear equation?A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.
Suppose the first even integer be x.
Then, the second even integer is x + 2.
Since the sum is given as 170, the following equation can be formed as,
x + x + 2 = 170
⇒ 2x + 2 = 170
⇒ 2x = 168
⇒ x = 84
Then, the other integer is 84 + 2 = 86.
Hence, the two integers for the given case are 84 and 86 respectively.
To know more about linear equation click on,
https://brainly.com/question/11897796
#SPJ2
A recursive arithmetic sequence is defined ad f(1)=6, f(n+1)=f(n)+5 for n>1. The first four terms of the sequence are shown in the table. Write an explicit formula that represents the sequence using function notation. Find the slope of the line that passes through the points given in the table. The slope is
Answer:
Find the slope of the line that passes through the points given in the table. The slope is
✔ 5
.
Use one of the given points to find the y-intercept. Substitute values for x, y, and m into the equation y = mx + b and solve for b. The y-intercept is
✔ 1
.
Write the formula as a function of n in slope-intercept form. The function is
✔ f(n) = 5n+ 1
for n in the set of natural numbers.
An automotive repair center charges $45 for any part of the first hour of labor, and $25 for any part of each additional hour. Which of the following is a correct cost?
A. C(t) = 95 for 1 < x ≤ 2
B. C(t) = 95 for 2 < x ≤ 3
C. C(t) = 120 for 2 < x ≤ 3
D. C(t) = 120 for 4 < x ≤ 5
An item is regularly priced at $91 . It is now priced at a discount of 15% off the regular price. What is the price now?
To decrease an amount by 7%, what single multiplier should you use?
Write an equation that defines the exponential function with base a > 0.
walt is mixing fruit punch for the party. he combines 1 gallon 2 quarts 3 pints of orange juice , 1 gallon 3 quarts 7 pints of pineapple juice, and 1 gallon 3 quarts 3 pints of ginger ale. what is the total liquid measure of the punch ?
i need help with 1 and 2
Is dividing 4/5 the same as multiplying by 5 then dividing by 4?
Each second for 20 seconds, an elevator descends 6 feet. Find the total change in elevation.
Which set of ordered pairs could be generated by an exponential function?
(0, 0), (1, 1), (2, 8), (3, 27)
(0, 1), (1, 2), (2, 5), (3, 10)
(0, 0), (1, 3), (2, 6), (3, 9)
(0, 1), (1, 3), (2, 9), (3, 27)
Answer:
THE ANSWER IS D
Step-by-step explanation:
THE ANSWER IS D because if you square 3 you get 9, if you cube 3, you get 27
Answer: (0, 1), (1, 3), (2, 9), (3, 27)
Step-by-step explanation:
f(x) = 3x + 10x and g(x) = 4x – 2, find (f – g)(x)
a grading machine can grade 48 tests in 1 minute. How
long will it take the machine to grade 300 tests?
Gretchen lives in Florida, for the current temperature 69°F and rising at a rate of 2°F per hour. She's talking on the phone to her friend in Indiana where the temperature is now 84°F and falling at a rate of 3°F per hour.
A.) If the temperature continue changing at the same rates, how many hours would Gretchen and her friend have to talk before the temperature become equal?
B.) What will the temperature be?
Answer:
A) Gretchen and her friend have to talk 3 hours before the temperature become equal.
B) The temperature after 3 hours will be 75°F.
Step-by-step explanation:
Current temperature in Florida = 69°F
Rate at which temperature is rising = 2°F per hour
Current temperature in Indiana = 84°F
Rate at which temperature is falling= 3°F per hour
A) Suppose in x hours both places have same temperature:
[tex] 69^oF +2F^o\times x=84^oF-3^oF\times x[/tex]
[tex]5x=84^oF-69^oF[/tex]
x = 3 hours
Gretchen and her friend have to talk 3 hours before the temperature become equal.
B) The temperature after 3 hours:
x = 75°F
[tex]69^oF +2F^o\times x=69^oF +2F^o\times 3=75^oF[/tex]
a rectangle has a length of 2 1/5 yards and a width of 4 9/20 what is the perimeter of the rectangle? express your answer in mixed number form and reduce if possible
A principal of $2,000 was invested in a savings account for 4 years. If the interest earned for the period was $240, what was the interest rate?
To find the interest rate, you can use the formula R = I / (PT). In this case, the principal is $2000, the time is 4 years and the interest is $240, resulting in an interest rate of about 3%.
Explanation:The subject of this question falls under Mathematics, specifically, financial mathematics, which deals with concepts like interest. The principle here is the initial amount of money that was deposited or borrowed. In this case, the principal is $2000. The time, in this scenario, is 4 years and the interest earned over this period is $240.
To answer the question, we'll use a formula for simple interest, expressed as I = PRT (where 'I' stands for the interest, 'P' is the principal, 'R' is the rate of interest and 'T' is the time in years). To calculate the interest rate, we rearrange the formula to R = I / (PT). Here, R would equal $240 / ($2000 x 4).
So, the interest rate (R) would be approximately 3%.
Learn more about Interest Rate Calculation here:https://brainly.com/question/32997798
#SPJ2
You own a house cleaning business. It takes you 2hours and 45 minutes to clean a house. You have 3 houses to clean tomorrow, how long would it take you to clean all three houses?