quadratic formula for 2x^2-x-3=0
A distance of 6.5 x 10^-8 is multiplied by 10. The result is written in scientific notation. What is the new exponent
The new exponent of the product is -7
How to determine the new exponentFrom the question, we have the following parameters that can be used in our computation:
6.5 x 10^-8 is multiplied by 10.
This means that
Product = 6.5 x 10^-8 * 10
Evaluate the product
So, we have
Product = 6.5 x 10^-7
From the above, we have
Exponent = -7
Hence, the new exponent is -7
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This is a mathematical sentence written with a greater than, a less than sign, or a NOT equal to sign.
The mathematical sentence written with a greater than, a less than sign, or a not equal sign is know as Inequality.
What is Inequality?Inequalities are mathematical formulas in which neither side is equal. Unlike equations, we compare two values in inequality. In between, the equal sign is substituted by a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
As, the mathematical sentence written with a greater than, a less than sign, or a not equal sign.
The definition of inequality is that two things are NOT equal. One of the items could be less than, greater than, less than or equal to the other things, or greater than or equal to the other things.
So, the statement is Inequality statement.
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Ava's game piece is on 36. She wants to capture a chip that is on 72. Can she do it with these change cards?if so, how? If not,explain why not. -10 +30 -1 +1-2
Final answer:
Ava can capture the chip on square 72 by using the +30 change card once to reach 66, and then the +1 change card six times to reach the final value of 72.
Explanation:
Ava's game piece is on square number 36, and she wants to capture a chip on square number 72. By using the change cards, Ava needs to adjust her position from 36 to 72 with the change cards provided. The change cards are: -10, +30, -1, +1, and -2. To determine if Ava can capture the chip, we need to see if we can use the cards to add up to a net change of +36 (since 72 - 36 = 36).
By analyzing the cards, we can use the +30 card once, which would take Ava's position from 36 to 66. Next, she can use the +1 card six times to go from 66 to 72. Ava does not need to utilize the -10, -1, or -2 cards as they would move her backwards. Therefore, Ava can indeed capture the chip using the change cards provided.
The steps Ava should follow are:
Use the +1 card six times to move from 66 to 72.
A 13-oz iced tea at a certain restaurant has 78 calories. How many calories are there in a 21-oz iced tea?
The calories in a 21-oz iced tea that is originally 78 calories in a 13-oz serving, multiply the calories per ounce by the new serving size for a total of 126 calories.
The 13-oz iced tea contains 78 calories. To find the calories in a 21-oz iced tea:
Calculate the calories per ounce: 78 calories ÷ 13 oz = 6 calories/oz
Multiply the calories per ounce by the 21-oz serving size: 6 calories/oz × 21 oz = 126 calories in a 21-oz iced tea
The perimeter of a rectangle is 36 meters. The length is 2 meters more than three times the width find the length of the rectangle
The length of the rectangle with a perimeter of 36 meters and a length that is 2 meters more than three times the width is 14 meters.
The perimeter of a rectangle is twice the sum of its length and width. According to the question, the perimeter of the rectangle is 36 meters, and the length (L) is 2 meters more than three times the width (W). We can express this relationship as follows: L = 3W + 2.
The formula for the perimeter (P) of a rectangle is P = 2L + 2W.
Using the given perimeter of 36 meters, we can set up the equation as 2(3W + 2) + 2W = 36.
Simplifying this equation, we find that 8W + 4 = 36, and thus W = 4 meters.
Substituting the value of W back into the equation for L gives us L = 3(4) + 2, which means the length of the rectangle is 14 meters.
A certain radioactive isotope has leaked into a small stream. Four
hundred days after the leak, 13% of the original amount of the substance remained. Determine the half-life of this radioactive isotope.
The half-life of this radioactive isotope is 135.897 days and this can be determined by using the formula of half-life.
Given :
A certain radioactive isotope has leaked into a small stream.Four hundred days after the leak, 13% of the original amount of the substance remained.The formula of the half-life is given by:
[tex]\rm A =P \left(\dfrac{1}{2} \right)^{\dfrac{t}{t_{1/2}}}[/tex]
where A is the final concentration, P is the initial concentration, t is the time period, and [tex]\rm t_{1/2}[/tex] is the half-life.
Now, substitute the known values in the above formula.
[tex]\rm 0.13P =P \left(\dfrac{1}{2} \right)^{\dfrac{400}{t_{1/2}}}[/tex]
Simplify the above expression.
[tex]\rm 0.13 = \left(\dfrac{1}{2} \right)^{\dfrac{400}{t_{1/2}}}[/tex]
Take the log on both sides.
[tex]\rm log(0.13) = {\dfrac{400}{t_{1/2}}} \times log\left(\dfrac{1}{2} \right)[/tex]
[tex]\rm t_{1/2} = \dfrac{400\times log(0.5)}{log(0.13)}[/tex]
Simplify the above expression in order to evaluate the [tex]\rm t_{1/2}[/tex].
[tex]\rm t_{1/2} = 135.897\;days[/tex]
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The half-life of a radioactive isotope is calculated by using the decay formula and solving for the known half-life, given that 13% of the original isotope remained after 400 days.
Explanation:To determine the half-life of a radioactive isotope, we first need to understand that half-life is the time required for half of a sample of a radioactive isotope to decay. From the problem, it stated that after 400 days, only 13% of the original isotope remained. The formula for decay is N = N0 * (1/2)^(t/T), where N is the final amount, N0 is the initial amount, t is the time elapsed, and T is the half-life.
Given that N/N0 is 0.13 after 400 days, we can rewrite the decay formula to solve for T. By substituting the values into the equation, i.e., 0.13 = (1/2)^(400/T), we can use the laws of logarithms to solve for T. So then we will get the half-life (T) of the isotope.
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find the least LCM of 28 and 98 to the 2nd power
Find MF if M is the midpoint of CF for the points C(3,7)F(5,5)
At a concession stand, three
hot dogs
and two
hamburgers
cost $7.75
;
two
hot dogs
and three
hamburgers
cost $8.50
.
Find the cost of one hot dog
and the cost of one hamburger
.
To find the individual cost of a hot dog and hamburger from a concession stand, we set up a system of equations from the given information and solve it to get the cost of one hot dog as $1.25 and one hamburger as $2.00.
To find the cost of one hot dog and one hamburger, we set up a system of equations based on the information given:
3 hot dogs + 2 hamburgers = $7.752 hot dogs + 3 hamburgers = $8.50Let's denote the cost of one hot dog as d and the cost of one hamburger as h. We can then rewrite the given information as:
3d + 2h = 7.752d + 3h = 8.50Solving this system of equations, we can multiply the first equation by 2 and the second equation by 3, and subtract them, cancelling out the hamburger terms:
6d + 4h = 15.506d + 9h = 25.50Subtracting the first equation from the second gives:
0d + 5h = 10.00Thus, one hamburger costs $2.00. Plugging this back into the first equation, we get:
3d + 2(2) = 7.75Which simplifies to:
3d + 4 = 7.753d = 3.75d = 1.25Therefore, one hot dog costs $1.25.
Da sofa is on sale for $98.60, which is 29% of the regular price. What is the regular price ?
37.5% of what number is 57?
Answer in factored form 3x^2+21x+36
brent counted 10 red cards, 10 black cards and 20 blue cards. what is the ratio of red cards to other cards
Final answer:
The ratio of red cards to other cards that Brent counted (10 red cards, 10 black cards, 20 blue cards) is 1:3 after summing black and blue cards to find the total number of other cards and simplifying the ratio.
Explanation:
Brent counted 10 red cards, 10 black cards and 20 blue cards. The question is what is the ratio of red cards to other cards. To calculate the ratio, we need to determine the total number of cards that are not red, which would be the black and blue cards combined.
First, we sum the black and blue cards:
10 black cards + 20 blue cards = 30 other cards.
Now, we set up the ratio of red cards to other cards:
10 red cards : 30 other cards, which simplifies to 1 : 3 when both sides of the ratio are divided by 10, the greatest common divisor.
Therefore, the ratio of red cards to other cards is 1:3.
The ratio of boys to girls at a movie is 4 font size decreased by 4 : 7. If there are 21 girls, how many boys are at the movie?
You are a farmer and want to spend under $35,000 on farm equipment. You need a hay bailer that costs $6,250 and several plowing disks cost $2,500 each. Write an inequality that models how many plowing disks could be purchased within your budget. What is the maximum number of plowing disks you can buy?
Which of the following statements concerning the standard normal curve is/are true (if any)?
a) The area under the standard normal curve to the left of -3 is zero.
b) The area under the standard normal curve between any two z-scores is greater than zero.
c) The area under the standard normal curve between two z-scores will be negative if both z-scores are negative.
d) The area under the standard normal curve to the left of any z-score is less than 1.
A. a, b
B. b, d
C. a, c
D. a
One person in a stadium filled with 100,000 people is chosen at random to win a free pair of airline tickets. what is the probability that it will not be you?
Between which two ordered pairs does the graph of f(x) = x2 + x – 9 cross the negative x-axis?
Quadratic formula: x =
(–6, 0) and (–5, 0)
(–4, 0) and (–3, 0)
(–3, 0) and (–2, 0)
(–2, 0) and (–1, 0)
we have that
[tex] f(x) =x^{2} + x - 9 [/tex]
Using a graph tool
see the attached figure
The function represent a vertical parabola that open up
the vertex is a minimum-------> is the point [tex] (-0.5,-9.3) [/tex]
The x-intercepts are the points when the y coordinate is equal to zero
The x-intercepts are the points [tex] (-3.5,0) [/tex] and [tex] (2.5,0) [/tex]
so
the function cross the negative x-axis at point [tex] (-3.5,0) [/tex]
therefore
the answer is
(–4, 0) and (–3, 0)
A person can purchase a particular model of a new car with a choice of ten colors, with or without automatic transmission, with or without four-wheel drive, with or without air conditioning, and with two, three, or four radio-CD speakers. How many different options are there for this model of car?
To find the different options for a car model with multiple customizable features, you multiply the number of choices for each feature. For this model, with 10 colors, 2 options each for transmission, four-wheel drive, and air conditioning, and 3 speaker options, there are 240 different combinations.
Explanation:To calculate the number of different options for this model of a car, we need to consider all the features that can be selected and multiply the number of choices for each feature together. For the color, there are 10 options. For each of the features, such as automatic transmission, four-wheel drive, and air conditioning, there are 2 choices: with or without. Finally, for the radio-CD speakers, there are 3 options: two, three, or four speakers. Multiplying these choices together gives us the total number of different options:
10 (colors) × 2 (transmission) × 2 (four-wheel drive) × 2 (air conditioning) × 3 (radio-CD speakers) = 240 different options.
So, there are 240 different options available for this model of a car.
Final answer:
To find the total number of different options for the car, we multiply the number of choices for each feature resulting in 240 different options.
Explanation:
The student is asking about the number of different option combinations for a specific model of a new car. The car can be customized with ten colors, automatic transmission or not, four-wheel drive or not, air conditioning or not, and can have two, three, or four radio-CD speakers. To determine the total number of different options, we multiply the number of choices for each feature:
10 colors2 options for automatic transmission (with or without)2 options for four-wheel drive (with or without)2 options for air conditioning (with or without)3 options for the number of radio-CD speakers (two, three, or four)Therefore, the total number of different options is calculated as follows:
10 (colors) × 2 (transmission) × 2 (drive) × 2 (air conditioning) × 3 (speakers)
= 240 different options.
lettuce is packaged in four bags to a box. if there are 3.5 boxes of lettuce in a cooler, how many bags of lettuce would there be?
Answer:
There are 14 bags in 3.5 boxes.
Step-by-step explanation:
Given : Lettuce is packaged in four bags to a box. If there are 3.5 boxes of lettuce in a cooler.
To find : How many bags of lettuce would there be?
Solution :
Lettuce is packaged in four bags to a box.
i.e, In 1 box there are 4 bags.
If there are 3.5 boxes of lettuce in a cooler.
In 3.5 boxes number of bags are [tex]4\times 3.5=14[/tex]
Therefore, There are 14 bags in 3.5 boxes.
A ladder is leaning against a building so that the distance from the ground to the top of the ladder is 2 feet less than the length of the ladder. Find the length of the ladder if the distance from the bottom of the ladder to the building is 6 feet.
To find the length of the ladder, we can use the property of right triangles. The length of the ladder is 10 feet.
Explanation:To find the length of the ladder, we can use the property of right triangles. Let's assume the length of the ladder is 'L'.
According to the given information, the distance from the ground to the top of the ladder is 2 feet less than the length of the ladder. So, the height of the triangle formed by the ladder, the building, and the ground is L - 2.
The distance from the bottom of the ladder to the building is given as 6 feet. Using the Pythagorean theorem, we can set up the following equation: (L-2)^2 + 6^2 = L^2
Simplifying the equation, we get L^2 - 4L + 4 + 36 = L^2, which simplifies further to 40 = 4L. Dividing both sides by 4, we get L = 10.
Therefore, the length of the ladder is 10 feet.
One integer is 5 more than another. Their product is 126. Find the integers.
write 26/20 as a percent
Find the point on the hyperbola xy=8 that is closet to the point (3,0)
The point that is closest to the point (3, 0) can be found by finding the
minimum value for the function of the distance between points.
The closest point on the hyperbola x·y = 8 to the point (3, 0) is the point [tex]\underline{(4, \ 2)}[/tex]
Reasons:
The equation of the hyperbola is x·y = 8
The given point = (3, 0)
Therefore;
[tex]y = \dfrac{8}{x}[/tex]
The distance of a point from a line, [tex]d = \mathbf{ \sqrt{\left (y_{2}-y_{1} \right )^{2}+\left (x_{2}-x_{1} \right )^{2}}}[/tex]
Where;
(x₁, y₁) = (3, 0)
(x₂, y₂) = The closest point on the hyperbola
We get;
[tex]d = \sqrt{\left (y-0 \right )^{2}+\left (x-3 \right )^{2}}[/tex]
Which gives;
[tex]d = \sqrt{\left (\dfrac{8}{x} -0 \right )^{2}+\left (x-3 \right )^{2}} = \mathbf{ \sqrt{\left (\dfrac{8}{x}\right )^{2}+\left (x-3 \right )^{2}}}[/tex]
At the minimum distance, using an online app, we have;
[tex]\dfrac{d}{dx}d = \dfrac{d}{dx} \left( \sqrt{\left (\dfrac{8}{x}\right )^{2}+\left (x-3 \right )^{2}} \right) = \dfrac{-64 + x^3 \cdot (x - 3)}{x^2 \cdot \sqrt{x^2 \cdot (x - 3)^2 + 64} } = 0[/tex]
Which gives;
x³·(x - 3) - 64 = 0
Using a graphing calculator, we get;
(x - 4)·(x³ + x² + 4·x + 16) = 0
Therefore;
A solution for the closest or point of minimum distance is x = 4
Which gives;
[tex]y = \dfrac{8}{4} = 2[/tex]
Therefore, the closest point on the hyperbola x·y = 8 to the point (3, 0) is the
point [tex]\underline{(4, \ 2)}[/tex]
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Michelle wants to save $150 for a trip to the Six Flags amusement park. if she saves $12 each week, how many weeks will it take her to save enough money
It will take her 13 weeks to save enough money for a trip to the Six Flags amusement park
Further explanationComparison is an effort to compare two or more objects in terms of shape or size, or number
Proportional Comparisons / Directly proportional are comparisons of two or more numbers where one number increases, the other numbers also increase at the same rate
Can be formulated
[tex]\displaystyle \frac {x1} {y1} = \frac {x2} {y2}[/tex]
so that if:
x = 2
then
[tex]\displaystyle y ={ \frac {y} {x} \times \: 2}[/tex]
While the reversal value comparison / inversely proportional is the comparison of two or more numbers where one number increases, the other number decreases in value
or when one value decreases at the same rate that the other increases
Can be formulated
[tex]\displaystyle \frac {x1} {y2} = \frac {x2} {y1}[/tex]
so that if:
x = 2
then
[tex]\displaystyle y = \frac {x} {y} \times \: 2[/tex]
KnownMichelle wants to save $150
she saves $12 each week
Askedthe number of weeks needed to save money
Answerevery weeks , she save $12 or we can make equation 1:
1 weeks = $12
the amount of money needed to travel to the six flags amusement park
= $150
we can make equation 2
? weeks = $150
Because this includes Proportional Comparisons / Directly proportional,
from two equation above , we can make comparison :
[tex]\displaystyle \frac{1\:weeks}{\$12} =\frac{x\:weeks}{\$150}[/tex]
[tex]\displaystyle x\:weeks=\frac{\$150\times1\:weeks}{\$12}[/tex]
[tex]\large{\boxed{x\:weeks= 12.5}}[/tex]
or we round up to :
[tex]\large{\boxed{\bold{13\:weeks}}}[/tex]
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Keywords: save money,a trip to park, Proportional Comparisons / Directly proportional
Jeremy can type 140 words in 4 minutes and 525 words in 15 minutes. Let x= minutes spent typing and y= words typed. what is the rate of change of y with respect to x
The rate of change of y with respect to x is 35 words per minute.
Explanation:The rate of change of y with respect to x can be found by taking the slope of the line that represents the relationship between x and y. To find the slope, we can use the formula:
slope = change in y / change in x
Using the given information, we can calculate the slope as:
slope = (525 - 140) / (15 - 4) = 385 / 11 = 35
Therefore, the rate of change of y with respect to x is 35 words per minute.
Final answer:
Jeremy's rate of change in typing speed is 35 words per minute, calculated by dividing the change in words typed by the change in time (385 words/11 minutes).
Explanation:
The student is asking about the rate of change of the words typed with respect to time spent typing. To calculate this, we will use the given values: 140 words in 4 minutes and 525 words in 15 minutes. The rate of change, essentially being the slope of the line that represents the relationship between words typed (y) and the time (x), can be calculated by finding the ratio of the change in words to the change in time:
Firstly, calculate the change in words typed (Δy) which is 525 - 140 = 385 words.Then, calculate the change in time (Δx) which is 15 - 4 = 11 minutes.The rate of change (slope) is Δy/Δx which equals 385 words / 11 minutes = 35 words per minute.This means that Jeremy types at an average speed of 35 words per minute.
add 3 feet 6 inches 8 feet 2 inches 4 inches 2 feet 5 inches
Please help ASAP
Find how long it take $600 to double if it is invested at 7% interest compounded monthly.
The Extreme Rock Climbing Club planned a climbing expedition. The total cost was $1400, which was to be divided equally among the members going. Prior to the trip, 3 members decided not to go. If the cost per person increased by $105, how many people went on the expedition?
Answer:
5 people
Step-by-step explanation:
Let
x = number of peopley = cost per personThe total cost was $1400, which was to be divided equally among the members going. Then,
y = 1400 / x [1]
Prior to the trip, 3 members decided not to go. The cost per person increased by $105.
y + 105 = 1400 / (x - 3)
(y + 105) . (x - 3) = 1400 [2]
We replace [1] in [2],
(1400/x + 105) . (x - 3) = 1400
1400 - 4200/x + 105x -315 = 1400
- 4200/x + 105x = 315
(- 4200 + 105x²)/x = 315
- 4200 + 105x² = 315 x
105x² - 315x - 4200 = 0
When we solve this quadratic equation using the quadratic formula, we get x₁ = 8 and x₂ = -5. Only the positive x has sense.
The people that went to the expedition was x - 3 = 8 - 3 = 5.