Given:
A rectangle has a length of 9 inches and a width of 5 inches whose sides are changing. The length is increasing by 3 in/sec and the width is shrinking at 9 in/sec.
To find:
The rate of change of the perimeter.
Solution:
It is known that the perimeter of the rectangle is twice the sum of length and width.
[tex]P=2(l+w)[/tex]DIfferentiate the perimeter with respect to t:
[tex]\frac{dP}{dt}=2(\frac{dl}{dt}+\frac{dw}{dt})[/tex]From the given information:
[tex]\begin{gathered} \frac{dP}{dt}=2(3-9) \\ =2(-6) \\ =-12 \end{gathered}[/tex]Thus, the perimeter of the rectangle is decreasing at the rate of 12 inches per second.
choose which group of sets the following number belongs to. Be sure to account for ALL sets. 2/7
A. Real numbers, rational numbers
Explanations:Note:
Real numbers are numbers that can be found on the number line. They include all rational and irrational numbers
Natural numbers are counting numbers. They include 0 and all whole numbers (1, 2, 3, ....)
Rational numbers are numbers that can be expressed as fractions of two integers. eg 2/3, 5/4, etc
Irrational numbers are numbers that cannot be expressed a s fractions of two integers. eg √7, π, etc
2/7 is a real number because it can be found on the number line, and is continuous
Also, 2/7 is a rational number because it is expressed as a fraction of two integers (2 and 7)
Directions: Identify the slope and y-intercept of the line on the graph. Then, write the equation of the line in slope-intercept form.
To find out the slope, we need two points
so
looking at the graph
we take
(-4,5) and (0,-3)
m=(-3-5)/(0+4)
m=-8/4
m=-2the y-intercept (value of y when the value of x is zero) is the point (0,-3)
the equation of the line in slope-intercept form is
y=mx+b
where
m is the slope
b is the y-coordinate of the y-intercept
so
m=-2
b=-3
substitute
y=-2x-37, -28, 112, -448, ..... as a formula
n = number
We can see that the value of each number is multiplied by 4 at each point in time
And the initial value is 7
[tex]a_n=7(4)^{n-1}[/tex]you are 5 feet and 4 inches tall and cast a shadow 6 feet long. At the same time , a nearby tree cast a shadow 40 feet 6 inches long. Find the heigh of the tree.
The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet.
What are the ratio and proportion?The ratio is the division of the two numbers.
For example, a/b, where a will be the numerator and b will be the denominator.
As per the given question,
The height of a person is 5 feet and 4 inches.
Since 1 feet = 12 inches so 4 inches = 1/3 feet
Therefore,height of a person = 5 + 1/3 = 16/3 feet
Its shadow length = 6 feet
The ratio of the height to shadow length = (16/3)/6
Now, the shadow of the tree = 40 feet and 6 inches so 40.5 feet
Let's say its length was x feet.
Then x/40.5 = (16/3)/6
x = 36 feet
Hence "The height of the tree is such that it cast a shadow 40 feet 6 inches long and maintains the given ratio will be 36 feet".
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Find the measure of the indicated angle to the nearest degreeQuestion 15
Question 15.
Given:
Length of side opposite the indicated angle = 12 units
Length of side adjacent the hypotenuse = 24 units
Let's find the measure of the indicated angle.
Here, we have a right triangle.
To find the measure of the indicated angle, apply the trigonometric ratio formula for sine:
[tex]sin\theta=\frac{opposite\text{ side}}{hypotenuse}[/tex]Where:
θ is the indicated angle.
Thus, we have:
[tex]\begin{gathered} sin\theta=\frac{12}{24} \\ \\ sin\theta=\frac{1}{2} \end{gathered}[/tex]Take the sine inverse of both sides:
[tex]\begin{gathered} \theta=sin^{-1}(\frac{1}{2}) \\ \\ \theta=30^o \end{gathered}[/tex]Therefore, the measure of the indicated angle us 30 degrees.
• ANSWER:
30°
Consider the following equation of a parabola.y? + 4y = 8r + 4Step 1 of 3: Find the focus of the parabola.
Given the equation:
[tex]y^2+4y=8x+4[/tex]Let's find the focus of the parabola.
To find the focus of the parabola, let's first rewrite the equation in vertex form:
[tex]y=a(x-h)^2+k[/tex]We have:
[tex]undefined[/tex]If a line passes thru the points (5,5) and (9,3) the slope of this line is
The initial point is (5,5)
the final point is (9, 3)
The formula for determining slope is expressed as
slope = (y2 - y1)/(x2 - x1)
y2 and y1 are the final and initial y values
x2 and x1 are the final and initial x values
From the information given,
x1 = 5, y1 = 5
x2 = 9, y2 = 3
Slope = (3 - 5)/(9 - 5) = - 2/4
Slope = - 1/2
6. Point A (-16,8) is one of the verticesof a rectangle. After a dilation of 1/2, arotation of 90 degrees clockwise, and areflection over the x-axis, what are thecoordinates of A"'?
Given the coordinate: A(-16, 8), let's perform the following:
First step:
A dilation with a scale factor of 1/2.
Here, we are to multiply the coordinates by 1/2.
A(-16, 8) ==> A'(-16*½, 8*½) = A'(-8, 4)
Second step:
Perform a rotation of 90 degrees clockwise.
(x, y) will change to (y, -x)
A'(-8, 4) ==> A''(4, 8)
Third step:
A reflection over the x axis.
To perform a reflection over the x axis, (x, y) becomes (x, -y)
A''(4, -8) ==> A'''(4, -8)
Therefore, the coordinates of A''' are:
A'''(4, -8)
use the data below make a frequency table take a picture of you frequency table and attach it to your answer marathon time
A frequency table is a table that shows how many times each number appears.
Looking at this set of numbers, we can see that each number appears only one time.
So we can create the following frequency table:
[tex]\begin{gathered} \text{value | frequency} \\ 135\text{ | 1} \\ 211\text{ | 1} \\ 220\text{ | 1} \\ 180\text{ | 1} \\ 175\text{ | 1} \\ 161\text{ | 1} \\ 246\text{ | 1} \\ 201\text{ | 1} \\ 192\text{ | 1} \\ 167\text{ | 1} \\ 235\text{ | 1} \\ 208\text{ | 1} \end{gathered}[/tex]The length of a rectangle is given by a number, x (metres). The width is two metres longer than the length. The area of the rectangle is 120 m^2
metersGiven:
a.) The length of a rectangle is given by a number, x (meters).
b.) The width is two meters longer than the length.
c.) The area of the rectangle is 120 m^2.
Let's first recall the formula for getting the area of the triangle.
Area = L x W
Where,
L = Length
W = Width
The width is two meters longer than the length. Therefore, we can say that:
W = L + 2
Let's now determine the measure of the dimension of the rectangle:
Let,
x = length of the rectangle
We get,
[tex]\begin{gathered} \text{ A = L x W} \\ 120\text{ = L x (L + 2)} \\ 120=L^2\text{ + 2L} \\ L^2\text{ + 2L - 120 = 0} \\ (L\text{ - 10)(L + 12) = 0} \end{gathered}[/tex]Based on the relationships given, the Length of the rectangle has two possible measures.
L - 10 = 0
L = 10 m
L + 12 = 0
L = -12 m
Since a length must never be a negative value, the length of the rectangle must be 10 m.
For the width, we get:
W = L + 2 = 10 + 2 = 12 m
Summary:
Length = 10 m
Width = 12 m
Identify the algebraic expression for the following word phrase: 5 less than twice a number y.
Answer:
5-2y because 5 less is 5- and 2 twice a number is y number is y and twice mean 2
▸ Charice created a painting with an area of 63 square inches and a length of 7 inches. They create a second painting with an area of 81 square inches. It has the same width as the first painting. What is the length of the second painting?
The length of the second painting is 9 inches.
Given,
The area of the first painting = 63 square inches
Length of the first painting = 7 inches
The area of the second painting = 81 square inches
Width of the first painting = Width of the second painting = x
We have to find the length of the second painting:
Here,
We can consider the painting as a rectangle.
Area of rectangle = length × width
Now,
First painting:
Area = length × width
63 = 7 × x
x = 63/7 = 9
That is, the width of the first painting is 9 inches.
The width of the second painting also 9 inches.
Now,
Second painting:
Area = length × width
81 = length × 9
length = 81/9 = 9
Therefore, the length of the second painting is 9 inches.
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What is 175% of 48? Show work.
Let 175% of 48 be y.
This implies that
[tex]\frac{175}{100}\times48=y[/tex]To evaluate y,
[tex]\begin{gathered} \frac{175}{100}\times48=y \\ \Rightarrow\frac{175\times48}{100}=y \\ \frac{8400}{100}=y \\ \Rightarrow y=84 \end{gathered}[/tex]Hence, 175% of 48 is 84.
please determine 8/12 - 3/8 =
8/12 -3/8=16/24-9/24=7/24
You should make like numbers then subtract
If you need to simplify at the end
A ladder is 12 ft tall, and the base is 4 ft from the house. How high up thehouse does the ladder reach? Round to the nearest tenth of a foot.
ok
t = 12
b = 4
h = ?
[tex]\begin{gathered} \text{ 12}^2=4^2+h^2 \\ \text{ h}^2\text{ = 144 - 16} \\ \text{ h}^2\text{ = 128} \\ \text{ h = }\sqrt[]{128} \\ h\text{ = 11.3 ft} \end{gathered}[/tex]height = 11.3 ft
[tex] - \frac{5}{6} e - \frac{2}{3} e = - 24[/tex]cual es la respuesta
Resolvamos esta ecuación para la variable "e":
[tex]\begin{gathered} -\frac{5}{6}e-\frac{2}{3}e=-24 \\ \frac{5}{6}e+\frac{2}{3}e=24 \\ \frac{5}{6}e+\frac{4}{6}e=24 \\ \frac{(5+4)e}{6}=24 \\ \frac{9e}{6}=24 \\ 9e=24\cdot6 \\ 9e=144 \\ e=\frac{144}{9} \\ e=16 \end{gathered}[/tex]Entonces, el valor de "e" es 16.
DATA ANALYSIS AND STATISTICS Outcomes and event probability A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The 8 outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: An odd number on each of the last two rolls Event B: An even number on the last roll Event C: An even number on the last roll or the second roll (or both) Explanation Check 000 0 0 OOE EEE O Outcomes OEO 0 0 EOO EEO EOE OEE 0 0 Probability 0 0 0 00 음 0/5 X Nikida V Españe
Event A:
The event A occurs when an odd number is rolled in the second roll and in the third roll. We can see in the table that the outcomes that correspond with this event are:
OOO
EOO
Now to calculate the probability, we need to divide the number of favorable outcomes by the number of total outcomes. There are 8 possible outcomes, and the favorable outcomes for event A are 2. Thus:
[tex]P(A)=\frac{2}{8}=\frac{1}{4}[/tex]Event B:
In event B we want the last roll to be even. Then, the outcomes corresponding to this event are:
OOE
EEE
EOE
OEE
The number of favorable outcomes is 4, the total outcome is 4:
[tex]P(B)=\frac{4}{8}=\frac{1}{2}[/tex]Event C:
Here, we are looking for outcomes with an even number in the second or last roll (or both). Thus the outcomes that satisfy this are:
OOE
EEE
OEO
EEO
EOE
OEE
The number of favorable outcomes is 6, and the number of total outcomes is 8:
[tex]P(C)=\frac{6}{8}=\frac{3}{4}[/tex]The garden that Julian is enclosing with chicken wire is in the shape of a parallelogram, Plan The measure of angle A is two thirds less than twice the measure of angle L. Find the measure of each angle of the garden enclosure.
Solution
We can do the following:
1) The condition given is:
m L -2/3
2) We have the other properties in a parallelogram:
m
m
And we also know that:
3) m L + m
2 m 2(2m 4 m6 mm
m
m< P = 1078/9
m < N= 542/9
I List two types of angle pairs: 14) 15)
Let's recall that a type of angle pairs are complementary angles. They're complementary if the sum of their degree measurements equals 90 degrees or the right angle.
Example:
[tex]\angle ABZ\text{ and }\angle ZBC\text{ are complementary angles }[/tex]Let's recall that a second type of angle pairs are suplementary angles. In this case, the angles add up to 180 degrees.
Example:
[tex]\angle ABF\text{ and }\angle FBC\text{ are suplementary angles}[/tex]question given below slove the following equations for r4al x and y .
S={(-24,7/3)}
1) When we're dealing with Complex Numbers we can rewrite this expression:
[tex](3+4i)^2-2(x-yi)=x+yi[/tex]Considering that their real and their imaginary parts can be taken as equal, so:
[tex]\begin{gathered} (3+4i)^2-2(x-yi)=x+yi \\ (3+4i)^2-2(x-iy) \\ 9+24i+16i^2+2x+2yi \\ \end{gathered}[/tex]2) Rewrite that into the Standard form for complex numbers y= ax +bi combining like terms:
[tex]\begin{gathered} 9+24i-16+2x+2yi \\ (-7-2x)+i(24+2y)\text{ = x+ iy} \\ \end{gathered}[/tex]Finally writing those two expressions as a System of equations we have:
[tex]\begin{gathered} \begin{cases}-7-2x=\text{ x} \\ 24+2y=y\end{cases} \\ -7-2x=x\Rightarrow-7=2x+x\Rightarrow3x=7\Rightarrow\frac{3x}{3}=\frac{7}{3} \\ 24+2y=y\Rightarrow24=-2y+y\Rightarrow-y=24\Rightarrow y=-24 \\ S=\mleft\lbrace(\frac{7}{3},-24)\mright\rbrace \end{gathered}[/tex]3) Hence, the answer is S={(-24,7/3)}
In which month was the average temperature closest to 0°C ?
A truck carries 4 chairs and tables. The table weighs 35 pounds. The total weight of the chairs and tables is 63 pounds. How much does each chair weigh?
The weight of each chair is 7 pounds.
What is basic arithmetic?Specific numbers and their computations employing a variety of fundamental arithmetic operations are at the center of arithmetic mathematics. Algebra, on the other hand, deals with the limitations and guidelines that apply to all other types of numbers, including whole numbers, integers, fractions, functions, and so on. Arithmetic math serves as the foundation for algebra, which always adheres to its definition. A large range of subjects fall within the broad definition of mathematics, which encompasses a very broad range of topics. Beginning with the fundamentals like addition, subtraction, and division of numbers, they then move on to more complicated topics like exponents, variations, sequence, progression, and more. This part does touch on some of the mathematical formulas and mathematical sequence. Four essential mathematical operations—addition, subtraction, multiplication, and division—are covered in basic arithmetic.
Total weight = 63 pounds
Weight of the table = 35 pounds
Weight if 4 chairs = 63 - 35
= 28 pounds
Weight of one chair = 28/4
= 7 pounds
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A person invests $9000 at 3% interest compound annually for 4 years and then invests the balance (the $9000 plus the interest earned) in an account at 7% interest for 8 years. find the final value of the investment.
Answer:
$17,404.5
Explanation:
To calculate the balance after t years, we can use the following equation:
[tex]A=P(1+r)^t[/tex]Where P is the initial investment and r is the rate.
So, we can calculate the balance after 4 years, replacing t by 4, r by 3%, and P by $9000. Therefore the balance is:
[tex]\begin{gathered} A=9000(1+0.03)^4 \\ A=9000(1.126)_{} \\ A=10129.579 \end{gathered}[/tex]Now, we can use this quantity to calculate the final value of the investment. So, replacing P by 10129.579, r by 7%, and t by 8 years, we get:
[tex]\begin{gathered} A=10129.579(1+0.07)^8 \\ A=10129.579(1.718) \\ A=17404.503 \end{gathered}[/tex]Therefore, the final value of the investment is $17,404.5
How do you Graph g(x)=x^5-2x^4 ?
Any line can be graphed using two points. Select two x x values, and plug them into the equation to find the corresponding y y values.
For each ordered pair, determine whether it is a solution to the system of equations. 7x - 4y=8 -2x+3y=7 Is it a solution? (x, y) Yes No (0, -2) a (-9,-6) (4,5) (7.7)
7x - 4y = 8 (eq. 1)
-2x + 3y = 7 (eq. 2)
Isolating y from equation 1:
-4y = 8 - 7x
y = 8/(-4) - 7/(-4)x
y = -2 + 7/4x
Isolating y from equation 2:
3y = 7 + 2x
y = 7/3 + 2/3x
Given that the slopes of the equations are different, then there is a solution, which can be found as follows,
[tex]\begin{gathered} -2+\frac{7}{4}x=\frac{7}{3}+\frac{2}{3}x \\ \frac{7}{4}x-\frac{2}{3}x=\frac{7}{3}+2 \\ \frac{^{}_{}7\cdot3-2\cdot4}{4\cdot3}x=\frac{7+3\cdot2}{3} \\ \frac{13}{12}x=\frac{13}{3} \\ x=\frac{13}{3}\cdot\frac{12}{13} \\ x=4 \end{gathered}[/tex]Replacing x = 4 into one of the equations, we get:
[tex]\begin{gathered} y=-2+\frac{7}{4}x \\ y=-2+\frac{7}{4}\cdot4 \\ y=-2+7 \\ y=5 \end{gathered}[/tex]The solution is (4,5)
To check if an ordered pair is a solution, we have to replace the x-coordinate and the y-coordinate of the pair into the equation, as follows:
(0, -2)
7(0) - 4(-2) = 8
8 = 8
-2(0) + 3(-2) = 7
-6 ≠ 7
Given that the second equation is not satisfied, then (0, -2) is not a solution
(-9, -6)
7(-9) - 4(-6) = 8
-81 + 24 ≠ 8
-2(-9) + 3(-6) = 7
18 - 18 ≠ 7
Given that the equations are not satisfied, then (-9, -6) is not a solution
(7,7)
7(7) - 4(7) = 8
49 - 28 ≠ 8
-2(7) + 3(7) = 7
-14 + 21 = 7
Given that the first equation is not satisfied, then (7, 7) is not a solution
Point Q is shown on the number line. Which Value is best represented by point Q? 15 6
According to the given graph, the point Q is between 5 and 5.50.
Therefore, the number that best describes point Q is
[tex]\sqrt[]{29.5}\approx5.4[/tex]Since it's between 5 and 5.50 too.
What is the output value for the following function if the input value is 5?y = 4x - 34223172
Answer:
17
Explanation:
Given the function:
[tex]y=4x-3[/tex]When the input value, x = 5
[tex]\begin{gathered} y=4x-3 \\ =4(5)-3 \\ =20-3 \\ =17 \end{gathered}[/tex]The output value if the input value is 5 is 17.
The measure of the smallest angle in a right triangle is 45° 45 ° less than the measure of the next larger angle. Find the measures of all three angles.
Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.
How to measure the three angles?The smallest angle in a right triangle has a measure that is 45° smaller than the next largest angle.As a result, the other two angles' measurements must sum up to 90. The only solution to this would be for both of the remaining angles to be 45 degrees if the lowest angle is 45 degrees less than the next largest angle. The correct angle would be the next biggest angle.Angle A or B must be 90 degrees since it is a right triangle. Given that C is more than 60 and that there are 180 degrees in a triangle, the other angle must be less than 30 degrees.To learn more about Right triangle refer to:
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16. Four solids labelled A, B, C, and D are shown below. o A B D a. Which of the solids has a curved face? 1mk b. Which solid has 5 faces? 1mk c. Which solid has 12 edges? Imk
a. A solid has curved surface area.
b. C solid has 5 faces.
c. D solid has 12 edges.
the rotation are is a 60° rotation about O,the center of the regular hexagon State the image of B for the following rotation
You have the following rotation:
[tex]R^2\circ R^{-2}[/tex]The result of the previous rotation, by taking into account the rules for the exponents for the transformations is:
[tex]R^2\circ R^{-2}=R^0[/tex]The rotation R⁰ means a rotation of 0 degrees of a specific point.
Then, the given rotation appiled to point B does not move the point B from its place. The transformation makes B to go to B
answer: B