The rate at which the length of a side is decreasing when the area of the triangle is 100 cm² is equal to -0.227 centimeters per minute.
What is rate of change?Rate of change is a type of function that describes the average rate at which a quantity either decreases or increases with respect to another quantity.
How to calculate the area of an equilateral triangle?Mathematically, the area of an equilateral triangle can be calculated by using this formula;
A = (√3/4)s²
Where:
A represents the area of an equilateral triangle.s represents the side length of an equilateral triangle.Next, we would determine the side length of a square by making s the subject of formula as follows:
s = (√4A)/√3
s = (√4 × 100)/√3
Side length, s = 15.20
Note: The rate of change (dA/dt) is negative because it is decreasing.
By applying chain rule of differentiation, the rate of change (dA/dt) in area of this equilateral triangle with respect to time is given by:
dA/dt = (√3/4)(2s)ds/dt
dA/dt = (√3/4) × (2 × 15.20) × -3
dA/dt = -0.227 centimeters per minute.
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A witch's brew calls for I 1/4 cups of
pond water. Wendy the witch has
access to a small frog pond
with 7 1/2 cups of water in it.
How many times can she
make her special brew?
The witch can make her special brew 6 times with the amount of water present in the small frog pond.
Given that:-
Total amount of water present in the small frog pond = 7 and 1/2 cups = 15/2 cups
Amount of water the witch needs to make her special brew = 1 and 1/4 cups = 5/4 cups
We have to find the number of times Wendy the witch can make her special brew with the amount of water present in the small frog pond.
We know that,
Number of times the witch can make the brew = Total amount of water/Water needed for brew
Hence, by simple division, we can write,
Number of times the witch can make the brew = (15/2) ÷ (5/4) = (15/2)*(4/5) = 6 times.
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Kayla wants to have new doors installed in herhome. A door company charges a one-time fee of$125 plus $ per window installed. Write anexpression that represents the total cost to installnew windows in terms of the number of windows(w) installed.
Kayla wants to have new doors installed.
The door company charges $125 as a one time fee.
They also charge $50 per window installed.
If the number of new windows installed is w, then it means that to install w new windows, they will charge an additional:
w * 50 = $50w
This will be in addition to the one time fee.
Let T be the total cost of installation.
Therefore, the total cost for installing w new windows (in dollars) is:
T = 125 + 50w
Liz is collecting aluminum cans for a school fundraiser. So far, she has collected 16 cans, which is 20% of her goal. How many cans must she collect to reach her goal?Parts A & B
Given the word problem, we can deduce the following information:
1. Liz collected 16 cans, which is 20% of her goal.
To determine the number of cans that Liz needs to collect to reach her goal, we use below equation:
[tex]0.20x=16[/tex]where:
x= total number of cans that Liz needs to collect
So,
[tex]\begin{gathered} 0.20x=16 \\ \text{Simplify} \\ x=\frac{16}{0.20} \\ x=80 \end{gathered}[/tex]Hence, the total number of cans is 80.
A.
To complete the double number line, we must determine first the other percent values. It the goal is 100%, we must subtract 20% from 100% and divide it by 4 to get the remaining percent values. So,
[tex]\frac{100-20}{4}=20[/tex]So the other percent values are:
0%
20%
20%+20%=40%
40%+20%=60%
60%+20%=80%
80%+20%=100%
To determine the amount of cans for each percent value,the process is shown below:
[tex]80(\frac{40}{100})=32[/tex][tex]\begin{gathered} 80(.6)=48 \\ \end{gathered}[/tex][tex]80(.8)=64[/tex][tex]80(\frac{100}{100})=80[/tex]Therefore, the answer for double number line is:
Cans : 0 16 32 48 64 80
Percent : 0% 20% 40% 60% 80% 100%
B.
Based on the information gathered from A, for every 16 cans Liz collects, she adds 20% toward her goal. She will have 32 cans if she reaches 40% of her goal. Liz must collect 80 cans to reach her goal.
which point lies on the wall with point slope equation y+5=2(x+8)
The slope intercept form of equation is given as
(y - y1) = m(x - x1)
Where m = slope
From the equation: y + 5 = 2(x + 8)
Equate y + 5 = 0 and x + 8 = 0
y + 5 = 0
y = 0- 5
y = -5
For x + 8 = 0
x + 8 = 0
x = 0 - 8
x = -8
Hence, the point is (-8, -5)
The answer is (-8, -5)
consider the polynomial function p given by p(x)=7x³-2x²+3x+10. Evaluate the function at x = -3.
Answer: -206
Step-by-step explanation:
[tex]p(-3)=7(-3)^3 -2(-3)^2 +3(-3)+10=-206[/tex]
Where are the minimum and maximum values for f(x)A. min: x =2¹ 2Reset Selectionmax:z = = 0, π, 2πOB. min:z = π max:x = 0, 2OC. min:z = 0, 2π max:x = πOD. min:z = ,,max:x = 0, 3, 4,2=- 3 cos z - 2 on the interval [0, 2π]?2P
Given:
The function f(x) = 3cos(x) - 2.
Required:
What are the minimum and maximum value of function?
Explanation:
To check maximum and minimum value of function.
First derivate the original function.
After putting first derivative equal to zero, critical points can be found.
Then, do second deritvative to check points of maxima and minima.
The critical points at which second derivative greater than zero. Point will be of minima.
The critical points at which second derivative less than zero. Point will be of maxima.
So,
[tex]\begin{gathered} f(x)=3cos(x)-2 \\ \text{ First derivative} \\ f^{\prime}(x)=-3sinx \\ \text{ Put }f^{\prime}(x)=0 \\ sinx=0 \\ x=0,\pi,2\pi \end{gathered}[/tex]Now, do second derivative test for maximum and minimum points
[tex]\begin{gathered} f^{\prime}^{\prime}(x)=-3cosx \\ \text{ At }x=0 \\ f^{\prime}^{\prime}(0)=-3\times1=-3<0 \\ \text{ At }x=\pi \\ f^{\prime}^{\prime}(\pi)=-3\times cos(\pi)=-3\times-1=3>0 \\ At\text{ }x=2\pi \\ f^{\prime}^{\prime}(2\pi)=-3\times1=-3<0 \\ \end{gathered}[/tex]Answer:
[tex]\text{ The points }0,2\pi\text{ are points of maxima and }\pi\text{ giving minima.}[/tex]
which graph show the solution set for -1.1×+6.4>-1.3
Problem
-1.1x + 6.4 > - 1.3
Concept
Solve for x by collecting like terms.
Which describes a line passing through (3,3) that is perpendicular to the line described by y=3/5x+2 ?
Given:
Point (3,3)
The equation of the line,
[tex]y=\frac{3}{5}x+2[/tex]To find the equation of the line that passes through (3,3) and is perpendicular to the line:
The perpendicular slope is,
[tex]m=-\frac{5}{3}[/tex]Using the point-slope formula,
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y-3=-\frac{5}{3}(x-3) \\ y=-\frac{5}{3}x+5+3 \\ y=-\frac{5}{3}x+8 \end{gathered}[/tex]Hence, the equation of the line is,
[tex]y=-\frac{5}{3}x+8[/tex]Let us find the intercepts.
When x=0, we get y=8
So, the y-intercept is (0,8).
When y=0, we get
[tex]\begin{gathered} -\frac{5}{3}x+8=0 \\ \frac{5}{3}x=8 \\ x=\frac{24}{5} \\ x=4.8 \end{gathered}[/tex]So, the x-intercept is (4.8,0).
Hence, the correct option which satisfies the equation of the line is D (last option).
Help me please I've watched like five videos and still don't get it!
14)
Given data:
The given triangle.
As all the sides of the triangle are equal, it means all the angles are equal. The expression for the angle sum property of the triiangle is,
[tex]\begin{gathered} x+x+x=180^{\circ} \\ 3x=180^{\circ} \\ x=60^{\circ} \end{gathered}[/tex]In the given triangle each angle is 60 degree, so it is an acute angle triangle.
Thus, the given triangle is an acute angle triangle, so first option is correct.
15)
The all sides and all angles of the triangle are equal.
Thus, the given triange is an equilateral triangle, so third option is correct.
Find the missing length of the triangle. 22 cm 17.6 cm The missing length is centimeters.
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Answer: ∠ABD = 19°
Step-by-step explanation:
The angle formed by ABC is a complementary angle. This means the sum of both angles adds up to 90 degrees.
Since angle DBC is 71 degrees, 90 - 71 equals ∠ABD
90 - 71 = 19
Therefore ∠ABD = 19°
Answer:
m∠ABD = 19°
Step-by-step explanation:
Hello!
Recall that all angles of a rectangle are 90° in measure.
Angle B is 90°, and is made up of angles ABD and DBC.
We know the measure of angle DBC, it's given as 71°. We can find the measure of ABD by subtracting 71° from 90°.
Find ABDABC = ABD + DBC90 = ABD + 7119 = ABDSo the measure of angle ABD is 19°.
In order for the parallelogram to be a rhombus, x equals?
In this case, we'll have to carry out several steps to find the solution.
Step 01:
data:
parallelogram diagram
Step 02:
geometry:
solve for x:
(5x + 25)° = (12x + 11)°
5x + 25 = 12x + 11
25 - 11 = 12x - 5x
14 = 7x
14 / 7 = x
2 = x
The answer is:
x = 2
Downhill RacerA snowboardertravels 105 metersin 7 seconds.A skier travels for4 seconds andcovers 72 metersHow far will a skier travel in 2minutes? Explain how you figured it out.
To be able to determine the distance that the skier travels, let's first determine its constant rate (speed).
A skier travels for 4 seconds and covers 72 meters.
Constant Rate (Speed):
[tex]\text{ }\frac{\text{ Distance Traveled}}{\text{ Time}}\text{ = }\frac{\text{ 72 meters}}{\text{ 4 seconds}}\text{ = }18\text{ meters/second}[/tex]Determining the distance covered in 2 minutes:
Step 1: Convert the time in minutes into seconds.
[tex]\text{ 2 (minutes) x }\frac{\text{ 60 seconds}}{\text{ 1 (minute)}}\text{ = 2 x 60 seconds = 120 seconds}[/tex]Step 2: Multiply the time by the constant rate (speed) of the skier.
[tex]\text{ Distance Traveled = 120 (seconds) x }18\text{ }\frac{\text{ meters}}{\text{ (second)}}[/tex][tex]\text{ = 120 x 18 meters}[/tex][tex]\text{ Distance Traveled = 2,160 meters}[/tex]Therefore, in 2 minutes, the skier travels 2,160 meters.
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year. When will the sharks be equal in length? Let x = time in years Let y = length of the sea creatures
In 20 years the length of shark will be equal.
what is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
A certain Greenland shark is 37 cm long at birth and grows 0.75 cm / year.
. A certain spiny dogfish shark is 22 cm long at birth and grows 1.5 cm/year.
Let x = time in years Let y = length of the sea creatures
So, the equation can be written as
For Green land shark: y= 37+ 0.75x
For Spiny Dogfish: y= 22 + 1.5x
When both equation are equal
37+ 0. 75x = 22 + 1.5x
37- 22 = 1.5x - 0.75x
15 = 0.75x
x= 15/0.75
x= 20
and, y= 22 + 1.5(20)= 52
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The table shows the volume of water released by a dam over a certain period of time. Graph a line representing the data in the table, and find the slope and y-intercept of the line from the graph. Then enter the equation for the graph in slope-intercept form.
Okay, here we have this:
Considering the provided information. we are going to calculate the slope, and y-intercept of the line, so we obtain the following:
First we will calculate the slope using the following formula:
m=(y2-y1)/(x2-x1)
m=(80000-40000)/(10-5)
m=40000/5
m=8000
y-intercept:
y=mx+b
40000=(8000)5+b
40000=40000+b
b=0
Finally we obtain that the equation of the line is: y=8000x.
Let's graph the equation:
If the function rule is to add 6, and an output value is 6, what is the input value?options:01-612
Given,
If the function rule is to add 6, and an output value is 6.
To find: What is the input value?
Solution:
When we add 0 to any number, we got the same number.
So adding 0 with 6 we get the same number 6.
[tex]6+0=6[/tex]Thus, the answer 0 is the correct option.
In a certain fraction, the denominator is 3 less than the numerator. If 1 is added to both the numerator and denominator, the resulting fraction is equal to 10/7 Find the original fraction.
The original fraction has a denominator that is 3 less than the numerator. If we define the numerator as x, then the denominator is x-3, and the fraction can be written as x/(x-3).
If 1 is added both to the numerator and denominator, the resulting fraction is equal to 10/7.
Then, we can write:
[tex]\begin{gathered} \frac{x+1}{(x-3)+1}=\frac{10}{7} \\ \frac{x+1}{x-2}=\frac{10}{7} \\ 7(x+1)=10(x-2) \\ 7x+7=10x-20 \\ 7x-10x=-20-7 \\ -3x=-27 \\ x=\frac{-27}{-3} \\ x=9 \end{gathered}[/tex]With the value of x, we can replace it in the fraction and know the value of it:
[tex]\frac{x}{x-3}=\frac{9}{9-3}=\frac{9}{6}=\frac{3}{2}[/tex]Answer: The fraction is 9/6, that can be simplified to 3/2 or 1.5.
the variables x and y are related proportionaly. when x=4,y=10 find y when x =18when x=18,y=_____
For variables to be related proportionally, the relationship must have a constant of proportionality. In our case we will represent the constant of proportionality as k. Therefore,
[tex]\begin{gathered} y=kx \\ \text{where} \\ k=\text{constant of proportionality} \\ 10=4k \\ k=\frac{10}{4} \\ k=\frac{5}{2} \end{gathered}[/tex]Now lets find y when x = 18
[tex]\begin{gathered} y=kx \\ y=\frac{5}{2}\times18 \\ y=\frac{90}{2} \\ y=45 \end{gathered}[/tex]A graph has age (weeks) on the x-axis, and height (inches) on the y-axis. Points are grouped closely together. One point is outside of the cluster. Which statement is true? There is no relationship between the height of the plant and its age. Although the outlier is an extreme value, it should be included in the interpretation. By excluding the outlier, a better description can be given for the data set
Answer:
Step-by-step explanation:
The answer is C
Answer:All three 1. to compare groups, not individuals2. to lessen the influence of outliers3. to clearly see trends
Explanation:edge 2022
Solve this system of linear equations. Separatethe x- and y-values with a comma.7x - by = -414x + 5y = 43
Answer
x = 2, and y = 3
Explanation:
given the following linear equation
7x - 6y = -4------------- equation 1
14x + 5y = 43 ---------- equation 2
This equation can be solve simultaneously by using elimination method
Step 1 : eliminate x
To eliminate x, multiply equation 1 by 2 qnd equation 2 by 1
7x * 2 - 6y * 2 = -4 * 2
14x * 1 + 5y * 1 = 43 * 1
14x - 12y = -8 ----------------- equation 3
14x + 5y = 43------------------ equation 4
Substract equation 4 from3
(14x - 14x) - 12 - 5y = -8 - 43
0 - 17y = -51
-17y = -51
Divide both sides by -17
-17y/-17 = -51/-17
y = 51/17
y = 3
To find x, put the value of y into equation 1
7x - 6y = -4
7x - 6(3) = -4
7x - 18 = -4
Collect the like terms
7x = -4 + 18
7x = 14
Divide both sides by 7
7x/7 = 14/7
x = 2
Therefore, x = 2 and y = 3
This question has two parts. First, answer Part A. Then, answer Part B. Part A Conjecture: A quadrilateral with one pair of sides both congruent and parallel is a parallelogram. Which of the following shows the marked diagram of the situation?restate the conjecture as a specific statement using the diagram you chose from part AIn quadrilateral ABCD, AB is congruent to___ and ____ is parallel to CD. show that ABCD is a ____
We have the following:
We can know when they are congruent, since being congruent they are equal sides.
By notation we know that " ' " means that they are the same, therefore
[tex]AB=DC[/tex]And the parallel lines are:
[tex]BA\parallel CD[/tex]Therefore, the answer is B.
In quadrilateral ABCD, AB is congruent to CD and AB is parallel to CD. show that ABCD is a parallelogram
Bella competed in the 5,000 m race at the Olympics she finished in the race 14.2 minutes after the race Bella wrote the equation c equals 18.1 m to model the relationship between the number of calories she burned c and the number of minutes she ran m.how many calories did Bella burn in the first 10 minutes of the 5,000 meter race.
Answer
She burnt 181 calories in that first 10 minutes of the 5,000 meter race.
Explanation
Bella wrote the equation that relates her calories burnt (c) to number of minutes (m) she has run as
c = 18.1m
The question then asks us to find how much calories she burnt in the first 10 minutes of the 5,000 meter race.
That is, find c when m = 10 minutes
Recall,
c = 18.1m
c = 18.1 (10)
c = 181 calories.
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what is the answer help pls
Answer:
1 ½ feet
Step-by-step explanation:
The shortest lizard is ½ a feet
The longest lizard is 2 feet
To find the difference in length:
2-½ = 1½ feet
If the scale factor is 4, what is the measurement of x?24 m4 m20 m16 m
Let:
[tex]\begin{gathered} 6k=x \\ \end{gathered}[/tex]where:
k = scale factor
If the scale factor is 4, then:
[tex]\begin{gathered} 6(4)=x \\ 24=x \\ x=24 \end{gathered}[/tex]Draw the image of the figure under thegiven transformation.8. reflection across the y-axis
Whne the coordinates are reflected over y -axis, then the coordinates are (x,y) = (-x,y)
.
The coodinates of A(3,0) and after reflection A'(-3,0)
The coordinates B(1,4) and after reflection B'(-1,0)
The coordinates C(5,3) and after reflection C'(-5,3)
Plot the image on the graph
A string that is 10 1/2 feet long is cut into 3 equal pieces. How long is each piece?
Answer:
3½
Step-by-step explanation:
10½=21/2
since it is cut into 3 pieces we can as well said it is divided into 3
21/2 divide 3
21/2 / 3/1
21/2 ×1/3
=7/2
=3½
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Answer:
The answer is 3.5
Step-by-step explanation:
Why?
Because since we know we have to divide the measurement of the string with the amount of pieces which will be
= 10 1/2 divided by 3
How long is each piece= 3.5
So that means each piece is 3.5
Hope this answers your question!
6+[(-9)+(-1)] what does this equal
-4
Explanation:
6+[(-9)+(-1)]
Open the bracket:
6 + (-9) + (-1)
Note: Multiplication of opposite signs give a negative number.
6 - 9 - 1
= 6 - 10
= -4
in the diagram the figures are simular, what is x?triangle with 30cm and 13cmtriangle with 24cm and x
If the figures are similar, the proportion between the corresponding sides is the same.
The side of 30 cm corresponds to the side of 24 cm, and the side of 13 cm corresponds to the side of x cm.
So if the proportion is the same, we have that:
[tex]\begin{gathered} \frac{30}{24}=\frac{13}{x} \\ 30\cdot x=24\cdot13 \\ x=\frac{24\cdot13}{30}=\frac{4\cdot13}{5}=\frac{52}{5}=10.4 \end{gathered}[/tex]So the value of x is 10.4 cm, therefore the answer is b.
4) Math Club members want to advertise their fundraiser each week in the school paper. They knowthat a front-page ad is more effective than an ad inside the paper. They have a $30 advertisingbudget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertiseat least 20 times. a) Write and graph a system of inequalities to model the number of advertisements the club canpurchase to stay under budget. Be sure to label all parts of your graph.b) State one solution that would work. How much money will remain in the club's budget?
Problem:
Math Club members want to advertise their fundraiser each week in the school paper. They know that a front-page ad is more effective than an ad inside the paper. They have a $30 advertising budget. It cost $2 for each front-page ad and $1 for each inside page ad. The club wants to advertise at least 20 times.
a) Write and graph a system of inequalities to model the number of advertisements the club can purchase to stay under budget. Be sure to label all parts of your graph.
Solution:
Let us denote the number of front-page ads by x, and the number of inside ads by y:
x = number front-page ads
y= number of inside ads
Now, because they have a $30 advertising budget and It cost $2 for each front-page ad and $1 for each inside page ad, the first inequality that we have is:
[tex]2x+\text{ y }\leq30[/tex]If we represent the graph of the equality (line) 2x+y = 30, we have:
On the other hand, because the club wants to advertise at least 20 times, the second inequality that we have is:
[tex]x+y\ge20[/tex]If we represent the graph of the equality (line) x+y = 20, we have:
Now, the intersection point of the above lines, that is 2x+y = 30 and x+y = 20 is found as follows:
we have
y = 30 - 2x
and
y = 20-x
then
30-2x = 20-x
and
30-20 = 2x-x
that is
10 = x
when x = 10 then y = 20-x = 20-10 = 10
Figure 1 and Figure Il are similar figures. Figure I Figure II R S А B F C w T E D V U Which proportion must be true?
From the diagram,
CD is corresponding to WR
VW is corresponding to BC
RS is corresponding to DE
ST is corresponding to EF
TU is corresponding to FA
Final answer
[tex]\frac{ST}{EF}\text{ = }\frac{WR}{CD}[/tex]