The coordinates of the point on the directed line segment from (-7, 9) to (3, -1) that partitions the segment into a ratio of 2 to 3 are (-3, 5).
To find the coordinates of the point that divides the directed line segment from (-7, 9) to (3, -1) into a ratio of 2 to 3, we can use the section formula.
Let's label the coordinates of the desired point as (x, y). According to the section formula, the x-coordinate of the point is given by:
x = (2 * 3 + 3 * (-7)) / (2 + 3) = (6 - 21) / 5 = -15 / 5 = -3
Similarly, the y-coordinate of the point is given by:
y = (2 * (-1) + 3 * 9) / (2 + 3) = (-2 + 27) / 5 = 25 / 5 = 5
Therefore, the coordinates of the point that divides the line segment in a ratio of 2 to 3 are (-3, 5).
To understand this conceptually, consider the line segment as a distance from the starting point (-7, 9) to the ending point (3, -1). The ratio of 2 to 3 means that the desired point is two-thirds of the way from the starting point and one-third of the way from the ending point. By calculating the x and y coordinates using the section formula, we find that the desired point is located at (-3, 5).
For more such questions on segment
https://brainly.com/question/280216
#SPJ8
Vinay buys some fruits. He buys 7 fruits more than the place value of 2 in the number 37,523. Find out the number of fruits that vinay buys and write the same in number names.
Vinay buys "two thousand seven" fruits.
To find the number of fruits that Vinay buys, we need to determine the place value of 2 in the number 37,523 and add 7 to it.
In the number 37,523, the digit 2 is in the thousands place.
The place value of 2 in the thousands place is 2,000.
Adding 7 to the place value of 2, we get:
2,000 + 7 = 2,007.
Therefore, Vinay buys 2,007 fruits.
In number names, we can write 2,007 as "two thousand seven."
So, Vinay buys "two thousand seven" fruits.
For similar question on buys.
https://brainly.com/question/30228885
#SPJ8
The points A, B and C have position vectors a, b, c, referred to an origin O. i. Given that the point X lies on AB produced so that AB : BX = 2 : 1, find x, the position vector of X, in terms of a and b. ii. If Y lies on BC, between B and C so that BY : Y C = 1 : 3, find y, the position vector of Y, in terms of a and b iii. Given that Z is the midpoint of AC, Calculate the ratio XY : Y Z.
i. The position vector of X is 2b - a.
ii. The position vector of Y is (3b + c)/4.
iii. The ratio XY : Y Z is [tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex]. Simplifying this expression will give us the final ratio.
i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.
ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.
iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =[tex]|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|[/tex].
For more such questions on vector
https://brainly.com/question/15519257
#SPJ8
JLK is similar to PQR find the value of X
Answer:
30
Step-by-step explanation:
22/33=20/x
cross multiply
22x=33x20
22x=660
x=660/22
x=30
⦁ The construction of copying is started below. The next step is to set the width of the compass to the length of . How does this step ensure that the new angle will be congruent to the original angle?
Answer:
i believe by creating radii of equal lengths.
Step-by-step explanation:
it gives a path to create an angle congruent to angle APB. The angle APB would have the same radii (BP and AP) and the same width as the congruent angle that would be created.
Wish you good luck.
1. The annual sale volumes of three products X, Y, Z whose sale prices per unit are GHS 3.50, GHS 2.75, GHS 1.50 respectively, in two different markets I and II are shown below: Product Market X Y Z I 6000 9000 1300 II 12000 6000 17000 Find the total revenue in each market with the help of matrices.
Answer:
Step-by-step explanation:
To find the total revenue in each market, we can calculate the product of the sale volumes and sale prices per unit using matrices.
Let's represent the sale volumes as a matrix V and the sale prices per unit as a matrix P:
V = [6000 9000 1300]
[12000 6000 17000]
P = [3.50]
[2.75]
[1.50]
To calculate the total revenue in each market, we need to perform matrix multiplication between V and P, considering the appropriate dimensions. The resulting matrix will give us the total revenue for each product in each market.
Total revenue = V * P
Calculating the matrix multiplication:
[6000 9000 1300] [3.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[12000 6000 17000] [2.75] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
Performing the calculation:
[60003.50 + 90002.75 + 13001.50] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[120003.50 + 60002.75 + 170001.50] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
Simplifying the calculation:
[21000 + 24750 + 1950] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[42000 + 16500 + 25500] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
[47650] = [Total revenue for product X in Market I Total revenue for product Y in Market I Total revenue for product Z in Market I]
[84000] [Total revenue for product X in Market II Total revenue for product Y in Market II Total revenue for product Z in Market II]
Therefore, the total revenue in Market I is GHS 47,650 and the total revenue in Market II is GHS 84,000.
Complete the item by performing the proper operations of evaluation. (8y)2, (y=5)
Answer:
Step-by-step explanation:
To evaluate the expression (8y)², where y = 5, we substitute the value of y into the expression and perform the operations.
First, substitute y = 5:
(8y)² = (8 * 5)²
Next, perform the operation inside the parentheses:
(8 * 5)² = 40²
Now, calculate the square of 40:
40² = 1600
Therefore, when y = 5, (8y)² is equal to 1600.
So i'm doing this Equation and it told me to use the values below, bit I'm so confused on how to do it can some of y'all help me out?
Part A: solve the equation---
5+x-12=2x-7
x-7=2x-7
x-7+7=2x-7+7
x=2x
x-2x=2x-2x
-x=0
--- ---
-1 -1
x=0
--
-1
x=0
Part B: use the values
x= -0.5, 0, 1
Answer:
when substituting x = -0.5, 0, and 1 into the equation, we get the results -8, -7, and -5, respectively.
Step-by-step explanation:
Part A:
To solve the equation 5 + x - 12 = 2x - 7, follow these steps:
Combine like terms on each side of the equation:
-7 + 5 + x - 12 = 2x - 7
-14 + x = 2x - 7
Simplify the equation by moving all terms containing x to one side:
x - 2x = -7 + 14
-x = 7
To isolate x, multiply both sides of the equation by -1:
(-1)(-x) = (-1)(7)
x = -7
Therefore, the solution to the equation is x = -7.
Part B:
Now let's substitute the given values of x and evaluate the equation:
For x = -0.5:
5 + (-0.5) - 12 = 2(-0.5) - 7
4.5 = -1 - 7
4.5 = -8
For x = 0:
5 + 0 - 12 = 2(0) - 7
-7 = -7
For x = 1:
5 + 1 - 12 = 2(1) - 7
-6 = -5
. Calculez P(5) sachant que P(x) = x3 − 5x2 − 2x + 7.
Answer:
P(5) = - 3
Step-by-step explanation:
to evaluate P(5) substitute x = 5 into P(x)
P(5) = (5)³ - 5(5)² - 2(5) + 7
= 125 - 5(25) - 10 + 7
= 125 - 125 - 3
= 0 - 3
= - 3
Seafloor rocks from a secret area above the Arctic Circle will recently analyzed by the globe. The company had a contract with spacegov.bids to test the rocks for nickel. Zieglow found that setting samples from the first location were composed of an average of 8.43% nickel. Six samples from the second location yielded an average of 7.81% nickel. What was the overall average nickel content of the rock samples
Answer:
The overall average nickel content of the rock samples is approximately 7.97%.
Step-by-step explanation:
To find the overall average nickel content of the rock samples, we need to take into account the number of samples from each location. Since we know the average nickel content of each set of samples, we can use a weighted average formula:
overall average nickel content = (total nickel content from first location + total nickel content from second location) / (total weight of samples from both locations)
To calculate the total nickel content from each location, we need to multiply the average nickel content by the number of samples:
total nickel content from first location = 8.43% x 1 sample = 8.43%
total nickel content from second location = 7.81% x 6 samples = 46.86%
To calculate the total weight of the samples from both locations, we need to add up the number of samples:
total weight of samples from both locations = 1 + 6 = 7
Now we can substitute these values into the formula and calculate the overall average nickel content:
overall average nickel content = (8.43% + 46.86%) / 7 ≈ 7.97%
Therefore, the overall average nickel content of the rock samples is approximately 7.97%.
Question 5 of 8
Which choice is the solution set of the inequality below?
OA. x< 4.1
OB. X<-4.1
OC. X> 4.1
O D. x≤ 4.1
OE. -4.1
OF. x<-4.1 or x> 4.1
x < 4.1, as it represents the solution set for the given inequality. A.
The solution set of the inequality x < 4.1 can be determined by examining the given answer choices:
OA. x < 4.1:
This choice represents all values of x that are strictly less than 4.1.
It is a valid solution set for the given inequality.
OB. x < -4.1:
This choice represents all values of x that are strictly less than -4.1.
It is not a valid solution set for the given inequality.
OC. x > 4.1:
This choice represents all values of x that are strictly greater than 4.1.
It is not a valid solution set for the given inequality.
OD. x ≤ 4.1:
This choice represents all values of x that are less than or equal to 4.1.
It is not a valid solution set for the given inequality because the inequality is strict (x < 4.1), not inclusive.
OE. -4.1 < x < 4.1:
This choice represents all values of x that are strictly between -4.1 and 4.1.
It is not a valid solution set for the given inequality because it does not include the possibility of x being less than -4.1 or greater than 4.1.
OF. x < -4.1 or x > 4.1:
This choice represents two separate solution sets: one for x < -4.1 and another for x > 4.1.
It is not a valid solution set for the given inequality because it combines two separate possibilities.
For similar questions on inequality
https://brainly.com/question/27679119
#SPJ8
Suppose a finite population has 6 items and 2 items are selected at random without replacement,then all possible samples will be:
Select one:
a. 15
b. 2
c. 36
d. 6
e. 12
Note: Answer D is NOT the correct answer. Please find the correct answer. Any answer without justification will be rejected automatically.
When 2 items are selected without replacement from a population of 6 items, there are 15 possible samples that can be formed. Option A.
To determine the number of possible samples when 2 items are selected at random without replacement from a population of 6 items, we can use the concept of combinations.
The number of combinations of selecting k items from a set of n items is given by the formula C(n, k) = n! / (k! * (n-k)!), where n! represents the factorial of n.
In this case, we have a population of 6 items and we want to select 2 items. Therefore, the number of possible samples can be calculated as:
C(6, 2) = 6! / (2! * (6-2)!) = 6! / (2! * 4!) = (6 * 5 * 4!) / (2! * 4!) = (6 * 5) / (2 * 1) = 15. Option A is correct.
For more such question on samples. visit :
https://brainly.com/question/13219833
#SPJ8
Solve the system of equations using the substitution or elimination method.
y = 4x - 7
4x + 2y = -2
.
Show your work
Correct x and y
The solution to the system of equations is x = 1 and y = -3.
To solve the system of equations using the substitution or elimination method, let's start with the substitution method.
Given equations:
y = 4x - 7
4x + 2y = -2
We'll solve equation 1) for y and substitute it into equation 2):
Substituting y from equation 1) into equation 2):
4x + 2(4x - 7) = -2
4x + 8x - 14 = -2
12x - 14 = -2
Now, we'll solve this equation for x:
12x = -2 + 14
12x = 12
x = 12/12
x = 1
Now that we have the value of x, we can substitute it back into equation 1) to find y:
y = 4(1) - 7
y = 4 - 7
y = -3
Therefore, the solution to the system of equations is x = 1 and y = -3.
for such more question on system of equations
https://brainly.com/question/4262258
#SPJ8
20 Points N Brainly Promised
The coterminal of 4π/3 angle measure are 10π/3 and -2π/3
How do you find angles that are coterminal with an angle measure of 4π/3?We add or subtract integer multiples of 2π.
So, 4π/3 + 2π = 10π/3 is one coterminal angle, and
4π/3 - 2π = -2π/3 is another coterminal angle.
To convert 125.67° to degree, minute, and second measure:
125.67° = 125° + 0.67°
Since there are 60 minutes in 1 degree, we can multiply 0.67 by 60 to get the minutes:
0.67° × 60 = 40.2'
Since there are 60 seconds in 1 minute, we can multiply 0.2 by 60 to get the seconds:
0.2' × 60 = 12"
So, 125.67° is equivalent to 125° 40.2' 12".
To find the degree measure equivalent to 10π/13 rounded to the nearest hundredth of a degree, we can divide 10π/13 by π and then multiply by 180° to convert from radians to degrees:
(10π/13) / π * 180° ≈ 138.46° (rounded to the nearest hundredth).
Learn more about coterminal angles at: https://brainly.com/question/23093580
#SPJ1
4. In triangle PQR, Q = 90°, cos R = 0.6 and PQ = 8 cm. Find PR and RQ. (May draw the own diagram by above info provided)
Answer:
PR = 10
RQ = 6
Step-by-step explanation:
We have cos R = 0.6
also, cos R = adjacent/ hypotenuse
= RQ/PR
⇒ RQ/PR = 0.6
⇒ RQ = 0.6 PR -eq(1)
By pythagoras theorem,
PQ² + RQ² = PR²
given PQ = 8 and sub the value of RQ from eq(1):
8² + (0.6 PR)² = PR²
⇒ 64 + 0.36PR² = PR²
⇒ (1-0.36)PR² = 64
⇒ 0.64 PR² = 64
⇒ PR² = 64/0.64
⇒ PR² = 100
⇒ PR = 10
sub PR in eq(1):
RQ = 0.6*10
⇒ RQ = 6
Is x=-4, x=1 parallel lines?
Step-by-step explanation:
Use the following models to show the equivalence of the fractions 35 and 610 a) Set modelUse the following models to show the equivalence of the fractions 35 and 610 a) Set model
Answer:
Step-by-step explanation:
no
they would be on different sides on the y axis
What else would need to be congruent to show that ABC=AXYZ by SAS?
A
B
OA. ZB=LY
B. BC = YZ
OC. C= LZ
OD. AC = XZ
с
X
Z
Given:
AB XY
BC=YZ
What is needed to be congruent to show that ABC=AXYZ is AC ≅ XZ. option D
How to determine the statementGiven that in ΔABC and ΔXYZ, ∠X ≅ ∠A and ∠Z ≅ ∠C.
We are to select the correct condition that we will need to show that the triangles ABC and XYZ are congruent to each other by ASA rule..
ASA Congruence Theorem: Two triangles are said to be congruent if two angles and the side lying between them of one triangle are congruent to the corresponding two angles and the side between them of the second triangle.
In ΔABC, side between ∠A and ∠C is AC,
in ΔXYZ, side between ∠X and ∠Z is XZ.
Therefore, for the triangles to be congruent by ASA rule, we must have AC ≅ XZ.
Learn more about triangles at: https://brainly.com/question/14285697
#SPJ1
Team A and Team B together won 50% more games than Team C did. Team A won 50% as many games as Team B did. The three teams won 60 games in all. How many games did each team win?
GEOMETRY 50POINTS
What is the angle of elevation to the kite? TYSM
Answer:
10.4°
Step-by-step explanation:
the angle of elevation is the angle from the horizontal , upward from one point on the horizontal to another point, not on the horizontal
in this case the angle of elevation is represented by ∠ A
using the sine ratio in the right triangle
sin A = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{36}{200}[/tex] , then
∠ A = [tex]sin^{-1}[/tex] ( [tex]\frac{36}{200}[/tex] ) ≈ 10.4° ( to the nearest tenth )
the angle of elevation to the kite is approximately 10.4°
Copy the axes below.
a) By completing the tables of values to help
you, plot the lines y = 2x + 1 and
y = 10x on your axes.
b) Use your diagram to find the solution to the
simultaneous equations y = 2x + 1 and
y = 10 - x.
y = 2x+1
x012
Y
y = 10-x
x012
Y
Y
-3 -2 -1
10
2987
65
6
-5
4
3
NW
21
1
-14
--2
73
1 2 3 4 5 6 7 8 9 10 x
The solution to the simultaneous equations is x = 3 and y = 7
Finding the solution to the simultaneous equationsFrom the question, we have the following parameters that can be used in our computation:
y = 2x + 1
y = 10 - x
Subtract the equations
So, we have
3x - 9 = 0
This gives
3x = 9
So, we have
x = 3
Next, we have
y = 10 - x
y = 10 - 3
Evaluate
y = 7
Hence, the solution is x = 3 and y = 7
Read more about equations at
https://brainly.com/question/32583193
#SPJ1
please answer ASAP I will brainlist
(a) The average cost in 2011 is $2247.64.
(b) A graph of the function g for the period 2006 to 2015 is: C. graph C.
(c) Assuming that the graph remains accurate, its shape suggest that: A. the average cost increases at a slower rate as time goes on.
How to estimate the average cost in 2011?Based on the information provided, we can logically deduce that the average annual cost (in dollars) for health insurance in this country can be approximately represented by the following function:
g(x) = -1736.7 + 1661.6Inx
where:
x = 6 corresponds to the year 2006.
For the year 2011, the average cost (in dollars) is given by;
x = (2011 - 2006) + 6
x = 5 + 6
x = 11 years.
Next, we would substitute 11 for x in the function:
g(11) = -1736.7 + 1661.6In(11)
g(11) = $2247.64
Part b.
In order to plot the graph of this function, we would make use of an online graphing tool. Additionally, the years would be plotted on the x-axis while the average annual cost would be plotted on the x-axis of the cartesian coordinate as shown below.
Part c.
Assuming the graph remains accurate, the shape of the graph suggest that the average cost of health insurance increases at a slower rate as time goes on.
Read more on exponential functions here: brainly.com/question/28246301
#SPJ1
21. In each of these problems, determine a suitable form for Y (t) if the method of undetermined coefficients is to be used. Do not evaluate the constants.
a. y"" - 2y" + y' = t³ + 2e^t
b. y''' - y' = te^-t + 2cost
c. y^4 - 2y'' + y = e^t + sin(t)
d. y^4 + 4y" = sin 2t + te^t + 4
e. y^4 - y''' - y" + y' = t² + 4 + tsin(t)
f. y^4 + 2y''' + 2y" = 3e^t + 2te^-t + e^-t sin(t)
Answer:
a. Y(t) = At³ + Be^t + Ct² + Dt + E
b. Y(t) = At + B + Ce^t + Dsin(t) + Ecos(t)
c. Y(t) = Aet + Bte^t + Csin(t) + Dcos(t)
d. Y(t) = At³ + Bt² + Ct + D + Ecos(2t) + Fsin(2t)
e. Y(t) = At² + Bt + C + Dsin(t) + Ecos(t) + Fsin(t) + Gcos(t)
f. Y(t) = Aet + Bte^-t + Ccos(t) + Dsin(t) + E + Ft + G
A basket of cucumbers contains 10 cucumbers that were grown using conventional methods and 22 cucumbers that were grown using organic methods. If a customer randomly selects 5 cucumbers, what is the probability they select two conventional cucumbers and 3 organic cucumbers?
The overnight temperature drops from 11°C to -2°C. B how many degrees has the temperature dropped?
Answer: I'm pretty sure it's 13.
Step-by-step explanation: Hope this helped!!
What are the coordinates of the image of point (−1, 5) after a counterclockwise rotation of 90° about the origin?
Responses
(1, 5)
(5, 1)
(−5, −1)
(-5, -1)
Answer: (5, -1)
Step-by-step explanation:
To rotate a point counterclockwise by 90° about the origin, we swap the x and y coordinates and negate the new x-coordinate. For the point (-1, 5), we swap the x and y coordinates to get (5, -1). The x-coordinate becomes positive, and the y-coordinate becomes negative. Therefore, the coordinates of the image of the point (-1, 5) after a counterclockwise rotation of 90° about the origin are (5, -1).
I think you put down the same answer choice twice and instead meant to say (5, -1) instead of (-5, -1) twice.
A jewelry company makes copper heart pendants. Each heart uses 0.75in® of copper and there is o.323 pound of copper per cubic inch. If copper costs $3.68 per pound, what is the total cost for 24 copper hearts?
The total cost for 24 copper hearts would be $21.41.
To calculate the total cost for 24 copper hearts, we need to determine the total amount of copper used and then multiply it by the cost of copper per pound.
First, let's find out the total amount of copper used for 24 copper hearts. Each heart uses 0.75 square inches of copper, so for 24 hearts, the total amount of copper used would be:
0.75 square inches/heart [tex]\times 24[/tex]hearts = 18 square inches.
Next, we need to convert the square inches into cubic inches. Since we don't have information about the thickness of the hearts, we'll assume they are flat hearts with a thickness of 1 inch. Therefore, the volume of copper used for the 24 hearts would be:
18 square inches [tex]\times 1[/tex] inch = 18 cubic inches.
Now, we can calculate the total weight of copper used. Given that there is 0.323 pounds of copper per cubic inch, the total weight of copper for the 24 hearts would be:
18 cubic inches [tex]\times 0.323[/tex] pounds/cubic inch = 5.814 pounds.
Finally, we multiply the total weight of copper by the cost of copper per pound to find the total cost:
5.814 pounds [tex]\times[/tex] $3.68/pound = $21.41.
For more such questions on total cost
https://brainly.com/question/5168855
#SPJ8
Use the definition of inverses to determine whether f and g are inverses.
Are the given functions inverse: A. No.
What is an inverse function?In Mathematics and Geometry, an inverse function is a type of function that is obtained by reversing the mathematical operation in a given function (f(x)).
In order to determine whether f(x) and g(x) are inverses, we would determine the corresponding composite function of f(x) and g(x) in simplified form as follows;
(fog)(x) = -5[-1/5(x) - 9] + 9
(fog)(x) = x + 45 + 9
(fog)(x) = x + 54
(gof)(x) = -1/5(-5x + 9) - 9
(gof)(x) = x - 9/5 - 9
(gof)(x) = x - 54/5
Since (fog)(x) and (gof)(x) are not equal to x, we can conclude that f(x) and g(x) are not inverses of each other.
Read more on inverse function here: brainly.com/question/14033685
#SPJ1
I need help please!!
Answer:
(r q)(-3) = -3
(q r)(-3) = -3
Step-by-step explanation:
let x = 1
q(1) = -1 +2 = 1
r(1) = 1² = 1
(r q)(-3) = ?
(1×1)(-3) = -3
(q r)(-3) = ?
(1×1)(-3) = -3
A jar of kosher dill spears is filled to the brim with a vinegar based pickling liquid and then
sealed. The base of the cylindrical jar has an area of 45 cm² and the height of the jar is
13 cm. When the pickles are opened, all the pickle juice is drained into a measuring cup,
amounting to 160 cm³ of pickle juice. Find the total volume of the dill spears.
The total volume of the dill spears is approximately 1013 cm³.
To find the total volume of the dill spears, we can use the formula for the volume of a cylinder, which is given by V = πr²h,
where V is the volume, r is the radius of the base, and h is the height of the cylinder.
First, let's find the radius of the base.
Since the area of the base is given as 45 cm², we can use the formula for the area of a circle,
A = πr², to solve for the radius.
Rearranging the formula, we have r = √(A/π).
Given that the area of the base is 45 cm², we can substitute this value into the formula to find the radius:
r = √(45/π) ≈ 3 cm (rounded to the nearest centimeter)
Now that we have the radius and the height of the jar, we can calculate the volume of the jar using the formula V = πr²h:
V = π(3²)(13) ≈ 1173 cm³ (rounded to the nearest cubic centimeter)
However, we need to subtract the volume of the pickle juice that was drained from the jar.
We are given that the amount of pickle juice is 160 cm³, so the total volume of the dill spears is:
Total volume = Volume of jar - Volume of pickle juice = 1173 cm³ - 160 cm³ = 1013 cm³
For similar question on total volume.
https://brainly.com/question/16721932
#SPJ8
The sum of negative twenty-nine and twenty-eight is negative seven more than a number. What is the number?
Answer:
8
Step-by-step explanation:
let x be the number,
according to the question,
-29 + 28 = -7 + x
1 + 7 = x
thus, x = 8
Suppose that an object is thrown upward from ground level with an initial velocity of 160ft/sec. Its height after t seconds is a function h given by h(t)=-16t^2 +160t.
a) Find an equivalent expression for h(t) by factoring out a common factor with a negative coefficient.
b) Check your factoring by evaluating both expressions for h(t) at t=1.
The factored expression is
a) The factored expression for h(t) is -16t(t - 10), obtained by factoring out a common factor of -16 and a common factor of t from the original expression -16t^2 + 160t.
b) Both the original expression -16t^2 + 160t and the factored expression -16t(t - 10) yield the same result of 144 when evaluated at t = 1, confirming the correctness of the factoring.
a) To factor out a common factor with a negative coefficient from the expression h(t) = [tex]-16t^2 + 160t[/tex], we can rewrite it as:
h(t) = [tex]-16(t^2 - 10t)[/tex]
Now, let's focus on factoring the quadratic expression inside the parentheses. We can factor out a common factor of t:
h(t) = -16t(t - 10)
Therefore, the factored expression for h(t) is -16t(t - 10).
b) To check the factoring by evaluating both expressions for h(t) at t = 1, we substitute t = 1 into the original expression and the factored expression and compare the results.
Using the original expression:
h(1) = [tex]-16(1)^2 + 160(1)[/tex]
h(1) = -16 + 160
h(1) = 144
Using the factored expression:
h(1) = -16(1)(1 - 10)
h(1) = -16(1)(-9)
h(1) = 144
Both expressions yield the same result of 144 when evaluated at t = 1. Therefore, the factoring is correct.
For more such information on: factored expression
https://brainly.com/question/29877882
#SPJ8