The property of a rhombus regarding the two diagonals states that they bisect each other at right angles.
Hence, option D is the correct answer.
How can you use the Power of a Quotient, Quotient of Powers, Zero Exponent Laws Identity Exponent and to evaluate numerical expressions with whole-number exponents?
Exponents and powers are terms that occasionally get used interchangeably, which can be confusing.
Mathematics uses expressions called powers, where n is the exponent and x is the base. When a number or variable is multiplied repeatedly, it is referred to as a power. The exponent of power tells us how many times to multiply the base by itself.
You can interpret the term as "x to the power." The exponent (n) is written smaller and at the head of the line using superscript, whereas the base (x) is printed in full size (if you are typing it on a computer). For instance, it is written as x squared or x to the second power, which in reality means that the value of x is multiplied by an amount equal to the exponent's value.
If the base is a number: In this situation, all you have to do to discover the solution is multiply the base by itself as many times as the exponent's value.
If the base is a variable, you must first replace the variable with a value before continuing.
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The school record for the greatest number of jumping jacks in a row is 84 in 4 minutes. If the record for jumping jacks made is a constant ratio, how many jumping jacks did the record holder make in 1 minute?
The amount of jumping packs in 1 minute is 21
How to determine the amount of jumping packs in 1 minute?From the question, the given parameters are:
Number of jumping packs in a row = 84 packs
Number of minutes = 4 minutes
The amount of jumping packs in 1 minute is the quotient of the number of jumping packs in a row and the number of minutes
This is represented as
Jumping packs in 1 minute = Number of jumping packs in a row /Number of minutes
Substitute the known values in the above equation
Jumping packs in 1 minute = 84/4
Evaluate
Jumping packs in 1 minute = 21
Hence, the jumping packs in 1 minute is 21
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The record holder makes 21 jumping jacks in 1 minute which is the ratio of the number of jumping jacks performed in a row to the total number of minutes.
What is the ratio?A ratio is a relationship between two amounts that is represented by the division of one by the other.
The ratio of the total number of jumping jacks performed in a row to the total number of minutes determines how many jumping jacks should be performed in a minute.
No. of jumping packs in a row = 84 packs
No. of minutes = 4 minutes
So jumping packs in 1 minute = 84/4
Apply the division operation to get
Jumping packs in 1 minute = 21
Therefore, 21 jumping jacks should be performed in 1 minute.
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Write an equation for the line graphed below.
Answer:
y=-4/3x
Step-by-step explanation:
There is no b because it starts at the origin.
Answer:
-4/3x is the correct answer as provided by IceJadeKitsune
I am merely providing an explanation in case you are curious
Step-by-step explanation:
The equation for a line in slope-intercept form is
y = mx + b
where m is the slope and b the y-intercept
The slope of a line, m can be determined by what is called the rise/run ratio
The process is as follows
Take any two convenient points on the line and note their coordinatesLet's label the points as (x1, y1) and (x2, y2)The rise is the difference in the y values = y2 - y1 (The run is the difference in the x values = x2 - x1Divide this rise over run and you get the slope, mTo get b, find where the line crossed the y-axis and the value of b will be the value of y at that point.From the graph choose points origin (0, 0) which is one point where the line crosses the y axis
From the graph we see that another distinct point where the line passes is at x = -3, y = 4 or the point(-3, 4)
Having got these two points we calculate
rise = 4 - 0 = 4
run = -3 - 0 = -3
Slope m = -4/3
Slope is negative because as y increases, x decreases
So the equation is y = -4/3x + b
Looking at the graph, we see that b = 0 since the graph passes through the origin as correctly stated by IceJadeKitsune
Therefore the equation of the line is [tex]\boxed{\bold{y = -\dfrac{4}{3}x}}[/tex]
What are the six trigonometric ratios, and how are some of them related to each other(which are reciprocals of which)?
Consider the following right triangle:
In this triangle
x = adjacent side to the angle theta.
y = opposite side to the angle theta.
h= hypotenuse.
Now, by definition, we have the following trigonometric ratios:
[tex]\cos(\theta)=\frac{adjacent\text{ side to the angle }\theta}{hypotenuse}\text{ =}\frac{x}{h}[/tex][tex]\sin(\theta)=\frac{opposite\text{ side to the angle }\theta}{hypotenuse}=\frac{y}{h}[/tex][tex]tan(\theta)=\frac{opposite\text{ side to the angle }\theta}{adjacent\text{ side to the angle }\theta}=\text{ }\frac{y}{x}=\frac{y\text{ /h}}{x\text{ /h}}\text{ =}\frac{\sin(\theta)}{\cos(\theta)}[/tex]and according to the above trigonometric ratio, we get:
[tex]cotan(\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]On the other hand, we get the following reciprocals:
[tex]csc(\theta)=\frac{1}{\sin(\theta)}[/tex]and
[tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex]we can conclude that the correct answer is:
Answer:The six trigonometric ratios:
[tex]\cos(\theta)=\frac{adjacent\text{ side to the angle }\theta}{hypotenuse}\text{ }[/tex][tex]\sin(\theta)=\frac{opposite\text{ side to the angle }\theta}{hypotenuse}[/tex][tex]tan(\theta)=\frac{opposite\text{ side to the angle }\theta}{adjacent\text{ side to the angle }\theta}=\text{ }\frac{\sin(\theta)}{\cos(\theta)}[/tex][tex]csc(\theta)=\frac{1}{\sin(\theta)}[/tex][tex]sec(\theta)=\frac{1}{cos(\theta)}[/tex][tex]cotan(\theta)=\frac{\cos(\theta)}{\sin(\theta)}[/tex]1. What would the slope of a line that is parallel to the line in the graph be?
(4,3)
X
keeping in mind that parallel lines have exactly the same slope, let's check for the slope of the line above, since a parallel line will have the same slope anyway
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{1}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{1}-\underset{x_1}{4}}} \implies \cfrac{ -4 }{ -3 } \implies {\Large \begin{array}{llll} \cfrac{ 4 }{ 3 } \end{array}}[/tex]
let f(x) =(4x"3+20)"2 and g(x) =4x"3+20.given that f(x)=(h°g)(x), find h(x)
Here, we want to find the function h(x)
From the question, we can see that the function f(x) is a composite function that was obtained by fitting g(x) into h(x)
What can we notice about g(x) and f(x)?
What we can see is that f(x) is the square of g(x)
Thus, what this mean is that h(x) = x^2
I got -52.7 degrees but I want to make sure. thank you
The given vector is
[tex]m=\langle16,-21\rangle[/tex]The formula to find the direction angle is
[tex]\theta=\tan ^{-1}|\frac{y}{x}|[/tex]Replacing each coordinate, we have
[tex]\theta=\tan ^{-1}|\frac{-21}{16}|=52.7[/tex]Therefore, the direction angle is 52.7°, approximately.A storage bin has the shape of a cylinder with a conical top. What is the volume of the storage bin if its radius is r=5.4 ft, the height of the cylindrical portion is h=7.7 ft, and the overall height is H=16.7 ft?
The Volume of a Compound Solid
The figure consists of a cylinder and a cone, both with the same radius of r=5.4 ft. The height of the cylinder is h=7.7 ft and the total height (of cone and cylinder) is H = 16.7 ft. This means the height of the cone is hc = 16.7 - 7.7 = 9 ft.
The volume of a cylinder of height h and radius r is:
[tex]V_{\text{cyl}}=\pi\cdot r^2\cdot h[/tex]The volume of a cone of height hc and radius r is:
[tex]V_{\text{cone}}=\frac{\pi\cdot r^2\cdot h_c}{3}[/tex]Calculate the volume of the cylinder:
[tex]\begin{gathered} V_{\text{cyl}}=\pi\cdot(5.4ft)^2\cdot7.7ft \\ V_{\text{cyl}}=705.388ft^3 \end{gathered}[/tex]Calculate the volume of the cone:
[tex]V_{\text{cone}}=\frac{\pi\cdot(5.4ft)^2\cdot9}{3}=274.827ft^3[/tex]Now we add both volumes:
V = 705.388 + 274.827 = 980.215 cubic feet
Rounding to the nearest tenth:
V = 980.2 cubic feet
What is a polygon with 10 sides called?dodecagonoctagontarragondecagon
Final Grade An instructor gives four 1-hour exams and one final exam, which counts as three 1-hour exams. Find a student's grade if she received 66, 81, 99 and 86 on the 1-hour exams and 85 on the final exam. Round your answer to one decimal place if necessary.
Answer:
83.9
Explanation:
The final exam counts as three 1-hour exams. Therefore, the student's scores written in terms of 1-hour exams will be:
• One-Hour Exam: 66, 81, 99 and 86
,• Final Exam: (85 x 3)
We take the average to find the student's grade:
[tex]\begin{gathered} \text{Final Grade}=\frac{66(1)+81(1)+99(1)+86(1)+85(3)}{1+1+1+1+3} \\ =\frac{332+255}{7} \\ =\frac{587}{7} \\ =83.857 \\ \approx83.9 \end{gathered}[/tex]The student's grade will be 83.9 correct to one decimal place.
12 is 58% of what number?
Also can you explain how to solve these problems?
Answer:
20.68976
Step-by-step explanation:
Convert the percentage into decimal :
58% = 0.58
0.58 × x = 12
Divide both sides by 0.58 :
x = 12÷0.58
x = 20.689655...
x = 20.68976
So the method to these types of question is to make the question into an equation by converting the percentage into a decimal, rearrange to make the unknown number the subject and solve .
Hope you understood and have a good day
Donny the Dot Dude is saving for a llama. He puts$3,000 in a savings account that earns 12% simpleannual interest. How many years it will it take forhim to have the $4,440 he needs ifhe makes no additional depositsor withdrawals?A) 4 yearsSOB) 5 yearsC) 6 yearseboD) 2 yearsх
The simple interest formula is:
A = P(1 + rt)
where A is the final amount, P is the princiapal, r is the annual interest rate (as a decimal), and t is time in years.
Substituting with A = $4,440, P = $3,000, and r = 0.12 (= 12/100), we get:
[tex]\begin{gathered} 4440=3000\cdot(1+0.12\cdot t) \\ \frac{4440}{3000}=1+0.12\cdot t \\ 1.48-1=0.12\cdot t \\ \frac{0.48}{0.12}=t \\ 4\text{ years = t} \end{gathered}[/tex]I believe you start with 2.4 million has initial start value? Not sure cause it worded weirdly and English not very good
2,466,000
Here, we want to know what is to be used as the initial value
The general exponential equation should be in the form;
[tex]P=I(1+R)^n[/tex]where P is the population at a certain year
I is the initial population which is 2,466,000 in this case
R is the rate of increase
n is the number of years
x + 3 = -7 Solve the inequality
The given inequality is expressed as
[tex]\begin{gathered} x\text{ + 3 }\leq\text{ - 7} \\ x\text{ }\leq\text{ - 7 - 3} \\ x\text{ }\leq\text{ - 10} \end{gathered}[/tex]7. Solve for value of tan A 8. Solve for Cos Q
7. Tan A = opposite/adjecent
Therefore Tan A = 24/7
• Option number (2) is correct .
8. Cos Q = adjacent/hypotaneus
where hypotaneus side : r^2 = x^2+y^2
r^2 = 12^2 +5^2= 169
r =√169 = 13
Now Cos Q = 12/13
• Option 4 is correct .
Enter the value of b when the expression 1/2x + b is equivalent to 1/4(2x+3)
Answer:
b = 3/4
Step-by-step explanation:
[tex]\frac{1}{2}x + b=\frac{1}{4} (2x+3)[/tex]
Distribute.
[tex]\frac{1}{2}x + b=\frac{1}{2} x+\frac{3}{4}[/tex]
Subtract 1/2x from both sides to isolate the b.
[tex]b=\frac{1}{2} x+\frac{3}{4}-\frac{1}{2}x[/tex]
1/2x and -1/2x cancel each other out.
[tex]b=\frac{3}{4}[/tex]
So b = 3/4
someone help please
Answer:
Angle 3 = 95° (vertically opposite angles)
Angle 2 and 4 = 180 - 95
= 85° (adjacent angles on straight line)
Angle 5 = 180 - 144
= 36° (adjacent angles on straight line)
Angle 6 = 180 - angle 3 - angle 5
= 180 - 95 - 36
= 49° (sum of angles in triangle=180)
Angle 1 = 180 - 90 - angle 6
= 180 - 90 - 49
= 41° (sum of angles in triangle=180)
Angle 7 = 180 - 38 - angle 5
= 180 - 38 - 36
= 106° (sum of angles in triangle=180)
What does the dashers part of the figure represent
The figure represents : Line
What is a Line?
A line is an object in geometry that is indefinitely long and has neither breadth nor depth nor curvature. Since lines can exist in two, three, or higher dimensional environments, they are one-dimensional things. The term "line" can also be used to describe a line segment in daily life that contains two locations that serve as its ends.
from the figure we have to find that whether its a line, line segment, vertex or ray
Line: A line is a perfectly straight, one-dimensional shape that extends infinitely in both directions and has no thickness. Sometimes a line is referred to as a straight line or, more formally, a right line.
Line segment: In other words, a line segment is a section or element of a line with two endpoints. A line segment, in contrast to a line, has a known length. A line segment's length can be calculated using either metric measurements like millimeters or centimeters or conventional measures like feet or inches.
Ray: A ray is a vector from a point to another point when seen as a vector. A ray is typically viewed in geometry as a half-infinite line, or half-line, with one of the two points and assumed to be at infinity.
Vertex: A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.
The figure represents a Line
Hence, The dashers part of the figure represent a Line
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Help me asp please!!
ILL GIVE BRAINLIEST!!!!
Answer:
1 = yes
2 = no
3 = no
4 = yes
5 = yes
6 = no
7 = no
8 = no
find the height of a square pyramid with V of 60 cm3 and base side length S of 6cm
Using Volume formula, the height of the square pyramid is 5 cm.
What is volume of a square pyramid?If the side of the square base of the pyramid is b and height of the pyramid be h
Volume of the square pyramid , V is given by the below formula.
V = 1/3(b²h)
Given
Volume of the square pyramid, V = 60 cm³
base side is given , b = 6 cm
let Height of the square pyramid be h
⇒ V = 1/3(b²h)
⇒ 3V = b²h
⇒3V/b² = h
⇒ 3(60)/ 6² = h
⇒ h = 180/36 = 5
Therefore, the height of the given square pyramid id 5 cm.
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v=LMH for L
thankssssss .
A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 67°C, it is cooling at a rate of 1°C per minute.
Let y = T − Ts, where T(t) is the temperature of the coffee in degrees Celsius at time t and Ts is the temperature of the surroundings in degrees Celsius. Find the values of A (in °C) and k for y(t) = Aekt.
Find: A and k
After how many minutes is the temperature of the coffee 67°C? (Round your answer to two decimal places.)
Answer:
The temperature of coffee will reach 67 °C
The rate of temperature change is most directly related to the difference between the body temperature and room temperature.
[tex]\frac{dT}{dt} =-k(T-T1)[/tex]
This equation's solution using the initial condition
T(0) = T0
T(t) = Tr + (T0 - Tr)
At the moment, the cooling rate
k × (T(t) - Tr)
We can write that according to the text
T1 = Tr + (T0 - Tr)
Solving the system of equations generates the unknown time:
t = [tex]\frac{69-20}{1} (ln\frac{95-20}{69-20})[/tex]
t = 21 min.
Hence the coffee will reach the temperature 67°C in 21 minutes.
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Ana has two plants. From Monday to Tuesday, plant A grew 5 cm more than plant B. If the sum of the length of the two plants on Tuesday is 41 cm, how long is each plant on Tuesday?
Write a system of equations using A and B as the variables
The first equation is the sum of the lengths of the plants
[tex]A+B=41[/tex]The second equation is the relation of growth that plant A grew 5cm more than plant B
[tex]A=B+5[/tex]Insert the second equation into the first one to solve for B
[tex]\begin{gathered} A+B=41 \\ (B+5)+B=41 \end{gathered}[/tex]Solve the equation for B
[tex]\begin{gathered} 2B+5=41 \\ 2B=41-5 \\ 2B=36 \\ B=\frac{36}{2} \\ B=18 \end{gathered}[/tex]Use the value of B in the second equation to find the value of A
[tex]\begin{gathered} A=B+5 \\ A=18+5 \\ A=23 \end{gathered}[/tex]Plant A is 23 cm long on Tuesday and plant B is 18 cm long on Tuesday.
A poster is 3 feet wide and 12 feet long. What are the dimensions if the poster is enlarged by a factor of 5/2?
To be able to get the enlarged dimensions, we will multiply the dimension of the poster by the given scale factor 5/2.
We get,
[tex]\text{Width = 3 ft. x }\frac{5}{2}\text{ = }\frac{15}{2}\text{ ft. or 7.5 ft.}[/tex][tex]\text{Length = 12 ft. x }\frac{5}{2}\text{ = }\frac{60}{2}\text{ ft. or 30 ft.}[/tex]Therefore, the enlarged dimension of the poster will be 7.5 ft. x 30 ft.
Middle School Debate Club 30% members are in 6th grade. If there are 12 6th graders in The Debate Club, how many total members are there ?
We know that 30% of the members are in 6th grade, and add up to 12 members.
Lets X be the total members.
Then 0.3*X are in 6th grade, and this is equivalent to 12 members.
NOTE: 0.3 is the decimal form of 30%.
We can write:
[tex]\begin{gathered} 0.3\cdot X=12 \\ X=\frac{12}{0.3} \\ X=40 \end{gathered}[/tex]Answer: there are 40 members in the Debate Club.
PLEASE HELP!!!!!
Answer two questions about Equations AAA and BBB:
A. 4x+2=6-x
B. 5x+2=6
1) How can we get Equation BBB from Equation AAA?
Choose 1 answer:
(Choice A)
Add/subtract a quantity to/from only one side
(Choice B)
Add/subtract the same quantity to/from both sides
(Choice C)
Multiply/divide only one side by a non-zero constant
(Choice D)
Multiply/divide both sides by the same non-zero constant
Based on the previous answer, are the equations equivalent? In other words, do they have the same solution?
Choose 1 answer:
(Choice A)
Yes
(Choice B)
No
We can get equation B from equation A by Adding the same quantity to both sides. The equations are equivalent and have the same solution.
The equations are:
A : 4x+2 = 6-x
B : 5x+2 = 6
(1) We can get equation B from equation A by adding x to both sides of the equation.
We can verify this.
Add x to both sides of the equation A,
⇒ 4x+2 +x = 6-x+x
⇒ 5x+2 = 6
This is equation B.
So Add the same quantity to both sides of equation A to get equation B.
(2) We just added a same quantity on both sides of equation A. This will not change the equations. So equation A and equation B are equivalent. Also they have same solution.
Equation A: 4x+2=6-x
⇒ 4x+x = 6-2
⇒ 5x = 4
⇒ x = 4/5
Equation B: 5x+2 = 6
⇒ 5x = 6-2
⇒ 5x = 4
⇒ x = 4/5
So both have same solution.
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which transformations had to occur for the blue triangle to become the purple triangle? [note: all rotations are about origin]
Let:
A = (-4,3)
B = (-1,3)
C = (-1,1)
after a 90 clockwise rotation:
A = (-4,3)--------->(y,-x)------->(3,4)
B = (-1,3)----------->(y,-x)------>(3,1)
C = (-1,1)------------>(y,-x)------>(1,1)
After a translation 3 units down and 2 units left:
(3,4)------>(x-2,y-3)------->(1,1)
(3,1)------>(x-2,y-3)------->(1,-2)
(1,1)------>(x-2,y-3)------->(-1,-2)
---------------------------
Therefore, the answer is D
How long ago, to the nearest year, was the artifact made?
Let's use the following formula:
[tex]A=A_0(0.5)^{\frac{t}{h}}[/tex]where:
Ao= Initial amount
t = time
h = half-life
[tex]\begin{gathered} A=0.2A_0 \\ so\colon \\ 0.2A_0=A_0(0.5)^{\frac{t}{5730}} \end{gathered}[/tex]solve for t:
[tex]\begin{gathered} 0.2=0.5^{\frac{t}{5730}} \\ \ln (0.2)=\frac{t}{5730}\ln (0.5) \\ t=5730\cdot\frac{\ln (0.2)}{\ln (0.5)} \\ t\approx13305 \end{gathered}[/tex]Find the present value given the following:Amount needed: $9,350Time in years: 3Interest: 5%Compounded: semiannually
Solution:
Amount needed (P): $9,350
Time in years (n): 3
Interest (r): 5%
Compounded: semiannually
To find the Amount (A).
we have the formula A, we get,
[tex]A=P(1+\frac{\frac{r}{2}}{100})^{2n}[/tex][tex]=9350(1+\frac{2.5}{100})^{2(3)}[/tex][tex]=9350(\frac{102.5}{100})^6[/tex][tex]=9350(1.025)^6[/tex][tex]=9350(1.15969)[/tex][tex]A=10,843.13[/tex]The present value is $10,843.133