how do i find the finite approximation to estimate the area using the lower sum of 4 rectangles for f(x)= 4-x^2 between x=-2 and x=2?
...?
Use the graph to determine and interpret the solution. A 4 cm bean plant grows at a rate of 1/2cm per week. A 5.5 cm flower grows at a rate of 1/4cm per week. If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:
h = 1/2t + 4
h = 1/4t + 5.5
The solution to the system,___?___
, means that the plants will both be ___?___ centimeters tall after__?___weeks.
The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.
Given that
A 4 cm bean plant grows at a rate of 1/2cm per week.
A 5.5 cm flower grows at a rate of 1/4cm per week.
If h is the height of the plant in centimeters and t is the number of weeks, then the system of equations is:
h = 1/2t + 4
h = 1/4t + 5.5
According to the question
The solution of the system of equation is;
h = 1/2t + 4
h = 1/4t + 5.5
Substitute the value of h from equation 1 in equation 2
[tex]\rm h = \dfrac{1}{4}+5.5\\\\\dfrac{1}{2}t +4 = \dfrac{1}{4}t +5.5\\\\\dfrac{1}{2}t-\dfrac{1}{4}t = 5.5-4\\\\\dfrac{2t-t}{4} = 1.5\\\\\dfrac{t}{4} = 1.5\\\\t = 4\times 1.5\\\\t = 6[/tex]
Substitute the value of t in equation 1
[tex]\rm h = \dfrac{1}{2}\times 6+4\\\\h = 3+4\\\\h = 7[/tex]
Hence, The solution of the system is h =7 and t = 6 means that the plants will both be 7 centimeters tall after 6 weeks.
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Which best describes the solution to 4-7?
Answer:
the answer is the second option; because 4+(-7) is an equivalent expression the answer Is -3
The simplified value.
4^0 + 2 ⋅ 3 - 2
1
2
5
8
14
26
Answer: option c.) 5
Step-by-step explanation: you must always follow PEMDAS
so first step would be parentheses but there are none so you move on to exponents. 4^0=1. so now you have 1+2x3-2.
Next step is multiplication. 2x3 is 6 so now you have 1+6-2.
Now we only have addition and subtraction so you move from left to right. 1+6=7
7-2=5
giving you option c. 5
Determine whether the following relation is a function.
{(3,7), (3,8), (3,-2), (3.4),(3,1)}
A) it is a function because the ordered pairs all have the same x-value.
B) it is not a function because there are multiple y-values paired with a single x-value.
C) it is a function because none of the ordered pairs have the same y-value.
D) it is not a function because none of the ordered pairs have the same y-value.
The relation is not a function it is not a function because there are multiple y-values paired with a single x-value. Option B.
Is the relation a function?A relation is a function only if every input is mapped into a single output.
Here we have the relation {(3,7), (3,8), (3,-2), (3.4),(3,1)}
Remember that the first number of each pair is the input, so we can see that all the inputs are the same one
So the input x = 3 is mapped into different outputs, thus, this is not a function.
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The correct option is B) it is not a function because there are multiple y-values paired with a single x-value.
To determine if a relation is a function, one must check if each x-value is associated with exactly one y-value. In other words, for every x, there should be one and only one y. This is known as the vertical line test in the context of graphs.
Let's examine the given set of ordered pairs: {(3,7), (3,8), (3,-2), (3,4), (3,1)}.
We can see that the x-value of 3 is repeated with different y-values: 7, 8, -2, 4, and 1.
This means that the x-value of 3 is associated with multiple y-values, which violates the definition of a function.
Therefore, the relation is not a function because it fails to satisfy the condition that each x-value must correspond to exactly one y-value.
The presence of multiple y-values for a single x-value is the key indicator that the relation is not a function.
The equation 9(u – 2) + 1.5u = 8.25 models the total miles Michael traveled one afternoon while sledding, where u equals the number of hours walking up a hill and (u – 2) equals the number of hours sledding down the hill. Which is the value of u?
Answer:
2.5
Step-by-step explanation:
Given: The equation [tex]9(u - 2) + 1.5u = 8.25[/tex]models the total miles Michael traveled one afternoon while sledding.
To Find: Which is the value of u?
Solution:
[tex]9(u - 2) + 1.5u = 8.25[/tex]
[tex]9u - 18+ 1.5u = 8.25[/tex]
[tex]10.5u = 8.25+18[/tex]
[tex]10.5u =26.25[/tex]
[tex]u =\frac{26.25}{10.5}[/tex]
[tex]u =2.5[/tex]
Hence the value of u is 2.5
HELP ME ASAP!! Some red white and blue candies were placed in a bowl. Some contain nuts, and some do not. Suppose one of the candies were chosen randomly from all the candies in the bowl. According to the table below, if the candy is blue, what is the probability that is does not contain any nuts?
Red with nuts=10. Red without nuts=10. White with nuts=20. White without nuts=10. Blue with nuts=20. Blue without nuts=30.
A. 20%
B. 40%
C. 60%
D. 10%
Answer:
Option C: 60%
Step-by-step explanation:
The number of blue candies with nuts = 20
The number of blue candies without nuts = 30
The total number of blue candies = 20 + 30 = 50
As the chosen candy is blue, the probability that is does not contain any nuts will be = (The number of blue candies without nuts)/(Total number of blue candies)
So, the probability = 30/50 = 0.6 *100% = 60%
Answer: 20%
Step-by-step explanation:
general admission to the americanmuseum of natural history is $19. if a group of 125 students visits the museum how much will the group's tickets cost
mrs. fletcher bought 5 coins for $32 each later she sold all the coins for $300 how much more did mrs. fletcher receive for each coin that she paid
Answer:
She received $60 for each coin.Step-by-step explanation:
Mrs. Fletcher bought 5 coins for $32.Then, she sold them for $300.We need to divide to know how much Mrs. Fletcher received for the coins
[tex]\frac{\$300}{5}=\$60[/tex]
She received $60 for each coin.
Now, each coin had a cost of
[tex]\frac{\$32}{5}= \$6.40[/tex]
So, he earned a profit of
[tex]\$60 - \$6.40=\$53.60[/tex]
Solve for x. -3(x-5)-2x=-10
Which of the following is not equivalent to the formula for the circumference of a circle, C = 2pir ?
A) C over r equals 2 times pi
B) C over pi equals 2 times r
C) C over the quantity of r times pi equals 2
D) Cr = 2pi
Answer:
the answer is d. Cr= 2 pi
Step-by-step explanation:
The correct answer that is not equivalent to the formula for the circumference of a circle is: Cr = 2pi. (Option D).
How to get the Circumference of a Circle?To prove the options, it is important to test the formulas given:
In option A, C over r equals 2 times pi:
C/r = 2 * pi
This equation is equivalent to the formula for the circumference of a circle, C = 2 * pi * r, as you can simply multiply both sides by 'r' to get the standard formula.
In Option B, C over pi equals 2 times r:
C/pi = 2 * r
This equation is equivalent to the formula for the circumference of a circle as pi can be multiplied on both sides
In Option C, C over the quantity of r times pi equals 2:
C / (r * pi) = 2
This equation is equivalent to the formula for the circumference of a circle since you can multiply both sides by (r * pi) to get C = 2 * (r * pi).
In option D, This equation is not equivalent to the formula for the circumference of a circle. It is missing the division by 'r' on the right side of the equation.
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How much less would a 25 year old male pay for a $50,000 policy of 20 y life insurance @ $5.84 per $1000, than a straight life policy @ $15.66 per $1000?
A 25-year-old male would pay $491 less for a $50,000 policy of 20-year life insurance at $5.84 per $1,000, than for a straight life policy at $15.66 per $1,000. This is calculated by first determining the total cost of each policy and then finding the difference between the two.
Explanation:To calculate the cost difference between the 20-year life policy and the straight life policy, we first need to calculate the cost of each policy. The cost of the policies is given per $1,000, and the policies provided are worth a total of $50,000.
The 20-year life policy costs $5.84 per $1,000. Therefore, we calculate 50 (as $50,000 divided by $1,000 gives 50) multiplied by $5.84, which equals to $292. The straight life policy costs $15.66 per $1,000. Therefore, we calculate 50 multiplied by $15.66, which equals to $783.
To find out how much less a 25-year-old male would pay for the 20-year policy than the straight life policy, we subtract the cost of the 20-year policy from the cost of the straight life policy: $783 - $292 = $491.
So, a 25-year-old male would pay $491 less for a $50,000 20-year policy than a straight life policy.
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solve
3x + 2y + 5x - y
Answer: 8x+y
Step-by-step explanation:
you always combine your like terms, a trick is to put a line infront of your equation signs making it look like 3x/+2y/+5x/-y. This makes it easier to see if your terms are positive or negative. Now you have 5x+3x and 2y-y giving you 8x+y because its still positive.
What are the common factors of 30 and 300?
how do i find this answer....
215.4% of 55= 118.47...
I have a TEAS test tomorrow and i cant figure out how to find this answer! ...?

Which points are solutions to the linear inequality y < 0.5x + 2? Check all that apply.
(–3, –2)
(–2, 1)
(–1, –2)
(–1, 2)
(1, –2)
(1, 2)
Answer:
Points (-3,-2), (-1,-2), (1,-2) and (1,2) are solutions to the given inequality.
Step-by-step explanation:
We are given the following inequality in the question:
[tex]y < 0.5x + 2[/tex]
We have to check which points give the solution to the given inequality.
1) (-3,-2)
Putting the values in the given inequality:
[tex]-2 < 0.5\times (-3) + 2\\-2 < 0.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
2) (-2,1)
Putting the values in the given inequality:
[tex]1 < 0.5\times (-2) + 2\\1 < 1\\\text{which is not true}[/tex]
The above point is not a solution to the given inequality.
3) (-1,-2)
Putting the values in the given inequality:
[tex]-2 < 0.5\times (-1) + 2\\-2 < 1.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
4) (-1,2)
Putting the values in the given inequality:
[tex]2< 0.5\times (-1) + 2\\2 < 1.5\\\text{which is not true}[/tex]
The above point is not a solution to the given inequality.
5) (1,-2)
Putting the values in the given inequality:
[tex]-2 < 0.5\times (1) + 2\\-2 < 2.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
6) (1,2)
Putting the values in the given inequality:
[tex]2 < 0.5\times (1) + 2\\2 < 2.5\\\text{which is true}[/tex]
The above point is a solution to the given inequality.
Points (-3,-2), (-1,-2), (1,-2) and (1,2) are solutions to the given inequality.
Constructing a box. From a rectangular piece of cardboard having dimensions 20 inches x 30 inches, an open box is to be made by cutting out identical squares of area x^2 from each corner and turning up the sides.
(a) Show that the volume of the box is given by the function V(x)=x(20-2x)(30-2x).
(b) Find all positive values of x such that V(x)>0. ...?
height=x length=20-2(what u cut out)=20-2x width=30-2(what u cut out)=30-2x so v(x)=l*w*h=x(20-2x)(30-2x) b) (0,10)
If parallelogram ABCD was reflected over the y-axis, reflected over the x-axis,and rotated 180°, where would point A' lie?
[Hint: Place your coordinates in the blank with no parantheses and a space after the comma in the form: x, y.] (5 points)
Point A is (-4,1) .Point A is reflected along y axis so y will remain same and x coordinate will have opposite sign .The reflected point A' ---(4,1) .The point is now reflected along x axis so its x ordinate will remain same and y will be at an equal distance from x axis The new reflected point is A" (4,-1) .The point is now rotated 180 degrees the x and y coordinate changes sign so the rotated final point is A"'( -4,1).
A dolphins heart beats 688 times in 6 minutes
What is the negative reciprocal of 3/4 or three over 4
Final answer:
The negative reciprocal of 3/4 is -4/3. This is found by inverting the fraction to get 4/3 and then applying the negative sign.
Explanation:
The negative reciprocal of a number refers to the value that, when multiplied by the original number, results in -1. For the fraction 3/4 (three over four), taking the reciprocal involves flipping the numerator and the denominator, which gives us 4/3. Making this reciprocal negative results in -4/3. The concept of reciprocals relates to the broader mathematical principles of multiplication and division, where negative exponents indicate the inverse of the corresponding positive exponent. For example, x to the power of -1 is equal to 1 divided by x to the power of 1, which demonstrates how negative exponents introduce division into the operation.
Find an equation of the tangent line to the curve
y = 8x sin x at the point (π/2, 4π).
y'=8(sinx)+8xcosx
8(sinπ)+8π(cosπ)
0+(-8π)
In a group of 10 batteries, 3 are dead. You choose 2 batteries at random.
Create a probability model for the number of good batteries.
The probability model for the number of good batteries when selecting 2 out of 10 with 3 dead is calculated as combinations of selecting good and dead batteries for each scenario. The probabilities are always divided by the total ways of drawing 2 from 10.
Explanation:This question is a typical problem related to probability. Firstly, we need to identify the number of ways we can draw 2 batteries randomly from this given set. We know there are 10 batteries in total with 3 dead ones. That leaves us with 7 good batteries.
Assuming 'X' is the number of good batteries we could select when drawing two batteries at random, 'X' could be 0, 1, or 2. Here are the three possible cases:
Both batteries are good (X = 2): The number of ways to select 2 batteries from 7 is combination of 7 by 2, denoted as C(7, 2). One battery is good and one is not (X = 1): The number of ways for this case can be calculated as the combination of picking 1 good battery from 7 and 1 dead battery from 3, denoted as C(7, 1)*C(3, 1). None of the batteries are good (X = 0): The number of ways for this case can be calculated as the combination of picking 2 dead batteries from 3, denoted as C(3, 2).To find out the probability of each scenario, we would have to divide by the total number of ways of drawing 2 batteries from 10, which equals to C(10, 2).
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A line tangent to a circle is ________ to a radius of the circle at the point of tangency.
congruent
perpendicular
parallel
similar
Answer:
Perpendicular... I had the same question and I got a 100%! Hope this helps!
What is the average rate of change of the function below on the interval from x = 0 to x = 2?
f(x)=250(0.5)x
A. -93.75
B. 62.5
C. 0
D. -0.25
Bob gets paid an annual salary of $30,000 and earns 5% commission on all sales he makes. If Bob wants to make $6,000 this month, how much in sales does he need to have?
Answer: Correct answer is 70,000 just took the test
A once thriving company in Teaneck had its monthly profits, in thousands of dollars, modeled by the equation?
f(t) = t^2 + 9/ 1t^2 + 2
where t is in months after June 1st, 2002.
Estimate the company's profits on June 1st, 2002.
Estimate the company's profits many years into the future
Answer:
1) 4.5% 2)1%
Step-by-step explanation:
Given equation The monthly profits: [tex]f(t) = \frac{t^2 + 9}{t^2 + 2}[/tex]
where t is in months after june 1st,2002
To find : The company's profits on June 1st, 2002
which means t=0
⇒ [tex]f(0) = \frac{0^2 + 9}{0^2 + 2}[/tex]
⇒ [tex]f(0) = \frac{9}{2}[/tex]
⇒ [tex]f(0) = 4.5[/tex]
The company's profits on June 1st, 2002 = 4.5%
To find :The company's profits many years into the future
we take limit tends to infinity
[tex]\lim_{n \to \infty}( \frac{t^2 + 9}{t^2 + 2})[/tex]
[tex]\lim_{n \to \infty}( \frac{2t}{2t})=1[/tex]
The company's profits many years into the future = 1%
Juanita is cutting a piece of construction paper in the shape of a parallelogram. Two opposite sides of the parallelogram have lengths (5n − 6) cm and (3n − 2) cm. The third side measures (2n + 3) cm. What are the lengths of two adjacent sides of the parallelogram?
A)2 cm and 2 cm
B)4 cm and 7 cm
C)7 cm and 9 cm
D)13 cm and 19 cm
Solve for u
3(2u+5)=33
Simplify your answer as much as possible.
Turn 357 centimeters into meters
A triangular tent flap measures 3 1/2 ft along the base and has a height of 4 1/2 ft. How much canvas is needed to make the flap