Answer:
180 meters
Step-by-step explanation:
The function you have here is negative function meaning the function has a concave down parabola (if you graph it on desmos or a graphing calculator you'll see what I'm talking about).
So they gave it to you in factored form and asked you to find the max. The max of this function is at the vertex of the parabola. In order to find the vertex you have distribute or multiply to get the original polynomial.
-5(x-8)(x+4)
-5(x^2+4x-8x-32)
-5(x^2-4x-32)
-5x^2-20x-160
Vertex formula is: -b/2a
b = 20
a = -5
\(\frac{-20}{2(-5)}\)
= 2
The x-coordinate of the vertex is 2.
Plug 2 into the equation
-5(2)^2+20(2)+160
= 180 meters
A child swallowed a substance with an LD50 of 6 mg/kg of body weight. It is crucial that the child's stomach be pumped promptly as the material is highly poisonous.
False
True
Yes, It is crucial that the child's stomach be pumped promptly as the material is highly poisonous.
How to LD50 represents?The LD50 is a Lethal dose and 50 represents 50 percent of the test animal's population, that is it will be lethal to half of the tested animals. The amount of a toxic agent (such as a poison, virus, or radiation) that is powered to wipe 50 percent of a population of animals on which it is tested.
Therefore, It is crucial that the child's stomach be pumped promptly as the material is highly poisonous.
Learn more about LD50 here: https://brainly.com/question/10042271
#SPJ2
Find the area and the perimeter of the figure. Use in terms of pi. (no approximations)
Answer:
See below.
Step-by-step explanation:
So first, we can separate the entire figure into a semi-circle and an isosceles triangle.
AREA:
The area for a semi-circle is \(\frac{1}{2}\pi r^2\).
The diameter is 8cm, so the radius is 4cm.
Area of the semi-circle is:
\(\frac{1}{2}(4)^2\pi=\frac{1}{2}(16\pi)=8\pi cm^2\)
The area for a triangle is \(\frac{1}{2}bh\).
The base is the same as the diameter (8), and we are given the height as 10. Thus:
\(\frac{1}{2} (8)(10)=8(5)=40cm^2\)
The total area is \((8\pi +40 )cm^2\)
PERIMETER:
The perimeter of a semicircle is: \(\pi r + 2r\) (this is derived from dividing the circumference by 2 and then adding on the diameter).
Thus, the perimeter is:
\(4\pi +8\)
However, we ignore the 8 since the 8 is not part of the perimeter.
The perimeter of the triangle is the two slant lengths. We know the base and the height, so we can use the Pythagorean Theorem:
\(a^2+b^2=c^2\)
\(4^2+10^2=c^2\)
\(c^2=116\)
\(c=\sqrt{116}=2\sqrt{29\)
Two of them will be \(4\sqrt{29}\)
Thus, the total perimeter is \(4\pi + 4\sqrt{29}\)
Estimate the annual wages for Hourly rate $7.15
Lets assume someone works 10 hours a day for 5 days a week.
Weekly total:
10 * 7.15 = $71.50 per day
71.5 * 5 = $357.50 per week
There are 52 weeks in a year so we can multiply.
357.50 * 52 = $18,590 per year
This is how you can solve this problem if you are given these details.
Best of Luck!
Solve the proportion x+1/2=21/14 x=
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
x+1/2=21/14
x = ?
Step 02:
\(\frac{x+1}{2}=\frac{21}{14}\)14 (x + 1 ) = 2 * 21
14x + 14 = 42
14x = 42 - 14
x = 28 / 14
x = 2
The answer is:
The value of x is 2
In the same shop(as in question 8) , under the same conditions of discount, find the marked price of the articles whose selling prices are given below.
where is the question??
The unshaded trapezoid is the image of the shaded trapezoid after a series of transformations.
On a coordinate plane, a shaded trapezoid has points (negative 5, 1), (negative 4, 5), (negative 3, 5), (negative 2, 1). An unshaded trapezoid has points (0, 1), (1.5, 9), (4.5, 9), (6, 1).
Answer:
Translation: Shift the trapezoid 5 units to the right.
Dilation: Enlarge the trapezoid vertically by a factor of approximately 3.365.
Reflection: Reflect the trapezoid across the y-axis.
Note: The order of transformations may vary depending on the convention used.
Step-by-step explanation:
To determine the series of transformations that result in the unshaded trapezoid being the image of the shaded trapezoid, we can analyze the changes in the coordinates.
Translation:
The shaded trapezoid is shifted horizontally by 5 units to the right to become the unshaded trapezoid. Therefore, the first transformation is a translation.
Translation vector = (5, 0)
Dilation:
The shaded trapezoid is enlarged in the vertical direction. To determine the dilation factor, we compare the corresponding side lengths.
The length of side AB in the shaded trapezoid is given by the distance formula:
AB = sqrt((-4 - (-5))^2 + (5 - 1)^2) = sqrt(1^2 + 4^2) = sqrt(17)
The length of side A'B' in the unshaded trapezoid is given by the distance formula as well:
A'B' = sqrt((1.5 - 0)^2 + (9 - 1)^2) = sqrt(1.5^2 + 8^2) = sqrt(66.25) = 2.5sqrt(26)
The dilation factor is the ratio of the corresponding side lengths:
Dilation factor = A'B' / AB = (2.5sqrt(26)) / sqrt(17) = 2.5sqrt(26/17) ≈ 3.365
Reflection:
The unshaded trapezoid is a reflection of the shaded trapezoid across the y-axis. This transformation reverses the sign of the x-coordinates.
The ratio of boys to girls in a class is 4:2. There are 30 students in class. How many girls and boys are there?
Answer:
20 boys, 10 girls
Step-by-step explanation:
4 + 2 = 6
4:6 ⋅ 5:5 = 20:30
2:6 ⋅ 5:5 = 10:30
The length of Carl's hair was 9 3/4 inches. After his hair cut, the length was 6 1/2 inches . How many inches did he cut?
Answer: 3 1/4 inches
Step-by-step explanation:
9 3/4 - 6 1/2
I turned 6 1/2 into an easier fraction so it can be easier to subtract. Now the expression is:
9 3/4 - 6 2/4
6 2/4 is equivalent to 6 1/2
I then got 3 1/4
John's son will start college in 10 years. John estimated a today's value of funds to finance college education of his son as $196,000. Assume that after-tax rate of return that John is able to earn from his investment is 8.65 percent compounded annually. He does not have this required amount now. Instead, he is going to invest equal amounts each year at the beginning of the year until his son starts college. Compute the annual beginning of-the-year payment that is necessary to fund the estimation of college costs. (Please use annual compounding, not simplifying average calculations).
John needs to make an annual beginning-of-the-year payment of approximately $369,238.68 to fund the estimated college costs of $196,000 in 10 years, given the after-tax rate of return of 8.65% compounded annually.
To compute the annual beginning-of-the-year payment necessary to fund the estimated college costs, we can use the present value of an annuity formula.
The present value of an annuity formula is given by:
P = A * [(1 - (1 + r)^(-n)) / r],
where P is the present value, A is the annual payment, r is the interest rate per period, and n is the number of periods.
In this case, John wants to accumulate $196,000 in 10 years, and the interest rate he can earn is 8.65% compounded annually. Therefore, we can substitute the given values into the formula and solve for A:
196,000 = A * [(1 - (1 + 0.0865)^(-10)) / 0.0865].
Simplifying the expression inside the brackets:
196,000 = A * (1 - 0.469091).
196,000 = A * 0.530909.
Dividing both sides by 0.530909:
A = 196,000 / 0.530909.
A ≈ 369,238.68.
Learn more about after-tax rate of return here:-
https://brainly.com/question/31825431?referrer=searchResults
#SPJ11
3. a salsa recipe uses green pepper, onion, and tomato in the extended ratio 1:3:9. how many cups of onion are needed to make 117 cups of salsa.
4. the 2 rectangles are similar. which is the correct proportion for corresponding sides.
3.To make 117 cups of salsa, 3 cups of onion are needed, since the ratio is 1:3:9 for green pepper, onion, and tomato.
4.The corresponding sides are in the same proportion, which is 5:6.
3.The extended ratio for a salsa recipe is 1:3:9 for green pepper, onion, and tomato. This means for every 1 cup of green pepper, there should be 3 cups of onion and 9 cups of tomato in the recipe. To figure out how many cups of onion are needed for 117 cups of salsa, we can use the ratio to calculate. Since the ratio for onion is 3, for every 1 cup of green pepper, we would need 3 cups of onion. Since there are 117 cups of salsa, we would need 117 divided by 1, which is 117, multiplied by 3, which equals 351. Then, since we need 3 cups of onion for every 1 cup of green pepper, we would need to divide 351 by 3, which equals 117 cups of onion. Therefore, to make 117 cups of salsa, 3 cups of onion are needed.
4.Two shapes are similar if their corresponding sides are in the same proportion. In this case, there are two rectangles and it is given that the shapes are similar. This means that the corresponding sides of the rectangles are in the same proportion. To find the proportion for the corresponding sides, we need to compare the lengths of each side. The length of the first rectangle is 5 units, while the length of the second rectangle is 6 units. This means that the proportion for the corresponding sides is 5:6. Therefore, the correct proportion for the corresponding sides of the two rectangles is 5:6.
Learn more about ratio here
https://brainly.com/question/13419413
#SPJ1
Find the value of x by finishing solving the system shown below.
Answer:
x = 10
Step-by-step explanation:
Since both equations give y in terms of x, equate the right sides
3x - 28 = - 2x + 22 ( add 2x to both sides )
5x - 28 = 22 ( add 28 to both sides )
5x = 50 ( divide both sides by 5 )
x = 10
3
8)
2 7 .1 .5 .3 .9
3 '8'5'8'4 '10
Prefer it from least to greatest
Answer:
shenf dhd
Step-by-step explanation:
rhrbrutb hnjngb bdjdhdhdgdg jdjdurbervy
Find the value of x so that line m is parallel to line l.
Based on the given parameters, the value of x such that the lines are parallel is 20
What are parallel lines?Parallel lines are lines that extend indefinitely and do not meet
How to determine the value of x?The given parameter is the lines in the figure
From the figure, we have the following angles:
3x + 20 and 2x + 40
The angles are corresponding angles
Corresponding angles are congruent
So, we have
3x + 20 = 2x + 40
Collect the like terms
3x - 2x = 40 - 20
Evaluate the like terms
x = 20
Hence, the value of x such that the lines are parallel is 20
Read more about angles at
https://brainly.com/question/7620723
#SPJ1
ANSWER ASAP PLEASE PICTURE BELOW
can you please explain it more clearly
Step-by-step explanation:
You buy a used car for $10,000. The value of the car decreases by22% each year. Approximately how much is the car worth in 3 years?
Answer:
The value will be $3,400 after 3 years
Step-by-step explanation:
Convert the percentage into the cash decrease each year, multiply that by 3 and then subtract $10,000 by the sum.
.22 x 10,000 = 2,200
2,200 x 3 = 6,600
10,000 - 6,600 = 3,400
It takes your equipment 3 minutes to travel 264 feet. what speed is the equipment traveling?
Answer:
To determine the speed, we can use the formula:
speed = distance / time
where distance is measured in feet and time is measured in minutes.
In this case, the distance is 264 feet and the time is 3 minutes. Plugging these values into the formula, we get:
speed = 264 feet / 3 minutes
simplifying, we get:
speed = 88 feet/minute
Therefore, the equipment is traveling at a speed of 88 feet per minute.
18. A rectangular storage container has a volume of 10 m³. The length of its base is twice the width. Materials for the top and the base cost $10 and $8 per square meter, respectively. Material for the sides costs $6 per square meter. Find the cheapest cost of materials for such a container.
The cheapest cost of materials for a rectangular storage container with a volume of 10 m³, where the length of the base is twice the width, can be determined by minimizing the total cost of materials for all sides.
To find the dimensions of the container, we can express the volume in terms of the length, width, and height. Let's assume the width is x, then the length would be 2x. The height can be calculated by dividing the volume by the product of the length and width, giving us a height of 10 / (2x * x) = 5 / x².
To calculate the cost of materials, we need to determine the areas of each component. The top and bottom surfaces have areas of 2x * x = 2x². The four sides have areas of 2(2x * 5/x²) + 2(5/x²) = 20/x.
The total cost of materials can now be expressed as 2x² * $10 + 20/x * $6 + 2x² * $8. Simplifying this expression, we have a cost function C(x) = 20x + 120/x + 16x².
To find the minimum cost, we can differentiate the cost function with respect to x, set it equal to zero, and solve for x. After finding the critical points, we can determine the minimum value of the cost function by evaluating it at these points.
The solution to this optimization problem shows that the cheapest cost of materials for the storage container is achieved when the width is approximately 1.4 meters, the length is approximately 2.8 meters, and the height is approximately 1.79 meters. The minimum cost of materials is then calculated using the cost function, yielding the final answer.
Learn more about optimization problem here: brainly.com/question/28455205
#SPJ11
What is the proportional relationship represented by this table?
Answer:
the constant of proportionality is 0.2 and it is a proportional relationship
Step-by-step explanation:
2 divided by 10 is 0.2
1 divided by 5 is 0.2
they have the same answer so they are proportional
since they have the answer 0.2 it
is there constant of proportionality
Mrs Wall usually buys 12 pints of milk each week and pays her milkman £3.72. One week she had visitors and ordered an extra 3 pints. How much was her bill?
Answer:
£4.65 is her bill
Step-by-step explanation:
Here, we firstly need to calculate the unit price of a pint
Mathematically, in this case, that will be 3.72/12 = 0.31
ordering 3 extra pints means she would be buying a total 15
The price of this will be;
0.31 * 15 = £4.65
Can someone just help me !
Answer:
\(\sqrt{a} 900\) - 2
Step-by-step explanation:
I won't be answering using words.
1. (3a+2a)(6a²+1-3)
2. (5a)(6a²-2)
3. 6a² × 5a - 2 × 5a
4. 6a × 6a × 5a - 2 × 5a
5. 180a × 5a - 2
6. 900a - 2
7. \(\sqrt{a} 900\) - 2
What is the average rate of change for this quadratic function for the interval from x = 0 to x = 2?
Answer:
8
Step-by-step explanation:
The average rate of change for this quadratic function for the interval from x = 0 to x = 2 is -2
What is a function?A relation is a function if it has only One y-value for each x-value.
The average rate of a function f(x) from x=a to x=b is given as:
= f(b)-f(a)/b-a
Clearly we are asked to find the average rate of change from x=0 to x=2.
i.e. a=0 and b=2
Also, from the graph it could be observed that:
f(0)=1
and f(2)=-3
=f(2)-f(0)/2-0
=-3-1/2
=-4/2
=-2
Hence, the average rate of change for this quadratic function for the interval from x = 0 to x = 2 is -2
To learn more on Functions click:
https://brainly.com/question/30721594
#SPJ7
In a recent poll, 280 people were asked if they liked dogs, and 48% said they did. Find the margin of error of this poll, at the 95% confidence level.
As in the reading, in your calculations:
--Use z = 1.645 for a 90% confidence interval
--Use z = 2 for a 95% confidence interval
--Use z = 2.576 for a 99% confidence interval.
To find the margin of error for the poll at the 95% confidence level, we can use the formula:
Margin of Error = z * sqrt(p * (1 - p) / n)
Given that the sample size is 280 and the proportion of people who liked dogs is 48% (0.48), we need to determine the appropriate value of z for a 95% confidence interval. The value of z for a 95% confidence interval is 2.
Substituting the values into the formula, we have:
Margin of Error = 2 * sqrt(0.48 * (1 - 0.48) / 280)
Calculating this expression, we find:
Margin of Error ≈ 2 * sqrt(0.48 * 0.52 / 280) ≈ 2 * sqrt(0.2496 / 280) ≈ 2 * sqrt(0.000892)
Simplifying further, we get:
Margin of Error ≈ 2 * 0.0299 ≈ 0.0598
Therefore, the margin of error for this poll, at the 95% confidence level, is approximately 0.0598 or 5.98%.
The margin of error represents the maximum expected difference between the estimated proportion in the poll and the true proportion in the entire population. It indicates the level of uncertainty associated with the poll's results and helps determine the range within which the true proportion is likely to fall. In this case, at a 95% confidence level, we can expect the actual proportion of people who like dogs to be within 5.98% of the estimated proportion obtained from the poll.
To learn more about margin of error : brainly.com/question/29419047
#SPJ11
In OG, mLAGC = 90°, AC
=DF and AB = EF Complete each statement.
The completion of the statements, we can deduce that Angles LAGC and DAF are both right angles (90°), segment AC is congruent to segment DF, and segment AB is congruent to segment EF. These relationships are derived from the given conditions and the properties of congruent segments and angles.
The following information:
m∠LAGC = 90° (angle LAGC is a right angle),
AC = DF (segment AC is equal to segment DF), and
AB = EF (segment AB is equal to segment EF).
Now, let's complete each statement:
1. Since m∠LAGC is a right angle (90°), we can conclude that angle DAF is also a right angle. This is because corresponding angles in congruent triangles are congruent. Therefore, m∠DAF = 90°.
2. Since AC = DF, we can say that segment AC is congruent to segment DF. This is an example of the segment addition postulate, which states that if two segments are equal to the same segment, then they are congruent to each other. Therefore, AC ≅ DF.
3. Since AB = EF, we can say that segment AB is congruent to segment EF. Again, this is an example of the segment addition postulate. Therefore, AB ≅ EF.
To summarize:
1. m∠DAF = 90°.
2. AC ≅ DF.
3. AB ≅ EF.
Based on the information given and the completion of the statements, we can deduce that angles LAGC and DAF are both right angles (90°), segment AC is congruent to segment DF, and segment AB is congruent to segment EF. These relationships are derived from the given conditions and the properties of congruent segments and angles.
To know more about Angles .
https://brainly.com/question/28394984
#SPJ8
The population on a certain island increased from 1500 in 2000 to 1577 in 2001 a. Determine the growth rate b. Write a general equation for the popolation p(t) c. Estimate the population in 2010 d. How many years will it take for the population to double?
Therefore, it will take approximately 13.7 years for the population to double.
a. To determine the growth rate, you need to calculate the percentage increase in population. The formula for growth rate is:
Growth Rate = (New Value - Old Value) / Old Value * 100
Using the given values, we have:
Growth Rate = (1577 - 1500) / 1500 * 100
Growth Rate = 77 / 1500 * 100
Growth Rate ≈ 5.13%
b. To write a general equation for the population, you can use the formula:
p(t) = p(0) * (1 + r/100)^t
where p(t) is the population at time t, p(0) is the initial population, r is the growth rate, and t is the number of years.
c. To estimate the population in 2010, we need to find the population at time t = 2010 - 2000 = 10 years. Using the general equation from part b, and substituting the given values:
p(10) = 1500 * (1 + 5.13/100)^10
p(10) ≈ 1500 * (1.0513)^10
p(10) ≈ 1500 * 1.6436
p(10) ≈ 2465.4
Therefore, the estimated population in 2010 is approximately 2465.
d. To find out how many years it will take for the population to double, we need to solve the equation:
2 * p(0) = p(0) * (1 + r/100)^t
Simplifying the equation, we have:
2 = (1 + r/100)^t
Taking the logarithm of both sides, we get:
log(2) = t * log(1 + r/100)
Finally, solving for t, we have:
t = log(2) / log(1 + r/100)
Substituting the growth rate from part a, we have:
t = log(2) / log(1 + 5.13/100)
t ≈ log(2) / log(1.0513)
t ≈ 13.7 years
Therefore, it will take approximately 13.7 years for the population to double.
To know more about population visit :
https://brainly.com/question/19169926
#SPJ11
YOU GET 60 POINTS!! Ronald rents a car from Cheap Rent-a-Car for $25 plus $0.05 per mile. Dixon rents a car from Great Cars for $40 plus $0.03 per mile. How many miles must they both drive for their rental fees to be the same?
Answer:
750 miles
Step-by-step explanation:
25+0.05x=40+0.03x
0.02x=15
x=750
Please help 60 points for a rapid answer-In the figure below which of the following is true in circle E?
Answer:
all 3 options are true : A, B, C
Step-by-step explanation:
warning : it has come to my attention that some testing systems have an incorrect answer stored as right answer for this problem.
they say that A and C are correct.
but I am going to show you that if A and C are correct, then also B must be correct.
therefore, my given answer above is the actual correct answer (no matter what the test systems say).
originally the information about the alignment of the point F in relation to point E was missing.
therefore, I considered both options :
1. F is on the same vertical line as E.
2. F is not on the same vertical line as E.
because of optical reasons (and the - incomplete - expected correct answers of A and C confirm that) I used the 1. assumption for the provided answer :
the vertical line of EF is like a mirror between the left and the right half of the picture.
A is mirrored across the vertical line resulting in B. and vice versa.
the same for C and D.
this leads to the effect that all 3 given congruence relationships are true.
if we consider assumption 2, none of the 3 answer options could be true.
but if the assumptions are true, then all 3 options have to be true.
now, for the "why" :
remember what congruence means :
both shapes, after turning and rotating, can be laid on top of each other, and nothing "sticks out", they are covering each other perfectly.
for that to be possible, both shapes must have the same basic structure (like number of sides and vertices), both shapes must have the same side lengths and also equally sized angles.
so, when EF is a mirror, then each side is an exact copy of the other, just left/right being turned.
therefore, yes absolutely, CAD is congruent with CBD. and ACB is congruent to ADB.
but do you notice something ?
both mentioned triangles on the left side contain the side AC, and both triangles in the right side contain the side BD.
now, if the triangles are congruent, that means that each of the 3 sides must have an equally long corresponding side in the other triangle.
therefore, AC must be equal to BD.
and that means that AC is congruent to BD.
because lines have no other congruent criteria - only the lengths must be identical.
Solve the following system of equations algebraically:
4x - 5y = 18
3x – 2y = 10
Answer:
D
Step-by-step explanation:
Given the 2 equations
4x - 5y = 18 → (1)
3x - 2y = 10 → (2)
Multiplying (1) by 3 and (2) by - 4, then adding will eliminate the x- term
12x - 15y = 54 → (3)
- 12x + 8y = - 40 → (4)
Add (3) and (4) term by term to eliminate x, that is
- 7y = 14 ( divide both sides by - 7 )
y = - 2
Substitute y = - 2 into either of the 2 equations and solve for x
Substituting into (1)
4x - 5(- 2) = 18
4x + 10 = 18 ( subtract 10 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
solution is (2, - 2 ) → D
Examine the system of equations at right. y=-2x + 6 y = -9
a. Solve the system below twice graphically and algebraically. Verify that your solutions from the different methods are the same.
b. What is the relationship between the two lines? How can you tell?
c. Solve the system at right using your method of choice. 2x + 3y = 18 4x - 3y = 6
Answer: -6
Step-by-step explanation: y-intercept: Put x = 0 in the equation y = 2x - 6 and solve for x. The y-intercept is -6
Hope This Helps Dude
Construct a box-and-whisker graph using the following data:
87, 94, 82, 78, 95, 91, 87, 83, 101, 83, 82, 77, 80, 102, 75
data given: {87, 94, 82, 78, 95, 91, 87, 83, 101, 83, 82, 77, 80, 102, 75}
arrange in ascending order:
75, 77, 78, 80, 82, 82, 83, 83, 87, 87, 91, 94, 95, 101, 102
Identify:
Q1 = 80Q2 = 83Q3 = 94IQR = 14Median = 83Plot box-and-whisker graph:
If both pairs of opposite sides of a quadrilateral are congruent, then thequadrilateral is a parallelogram.A. TrueB. False
Answer:
True
Explanation: