1. The pairs of measurements that could have the dimensions of Rectangle B include:
A. 6cm by 1.5cm
D. 18cm by 4.5cm
E. 80cm by 20cm
2. Rectangle A is a scaled copy of rectangle B as the scale factor is 3:2.
Rectangle C isn't a scales factor of rectangle B since they have different ratio.
How to illustrate the information?1. It should be noted that from the information, Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A.
Therefore, it should be noted that the ratio will be:
= 12 / 3
= 4 / 1
= 4:1
Therefore, the values that will give same ratio will be:
6cm by 1.5cm = 6/1.5 = 4:1
18cm by 4.5cm = 18/4.5 = 4:1
80cm by 20cm = 80/20 = 4:1
In conclusion, the correct options are A, D, and E.
2. Rectangle A is 12 long and 8 wide. The ratio will be:
= 12/8 = 3/2 = 3:2.
Rectangle B is 15 long and 10 wide. The ratio will be:
= 15/10 = 3/2 = 3:2
Rectangle C is 30 long and 15 wide. The ratio will be:
= 30/15 = 2:1
Therefore, rectangle A and B have same scale.
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Rectangle A measures 12 cm by 3 cm. Rectangle B is a scaled copy of Rectangle A. Select all pairs of measurements that could have the dimensions of Rectangle B.
A. 6cm by 1.5cm
B. 10cm by 2cm
C. 13cm by 4cm
D. 18cm by 4.5cm
E. 80cm by 20cm
Tell if each pair of triangles are either 1. Similar By SSS similarity 2.Similar by AA similarity3.Similar by SAS similarity 4.not similar Pls label the triangle also so it’s easy to tell which one you are talk about thank you
We have the following:
1. Similar By SSS similarity
4/2= 2
7.3.5 = 2
6/3 = 2
2. Similar by AA similarity, same angles, 90°, 70° and 50°
3. Similar by SAS similarity
, same angles and related sides.::
4/2 = 2
6/3 = 2
4. Similar by SAS similarity, same angles and related sides:
12/6 = 2
8/4 = 2
Write the sentence as an inequality.
A number r is no less than -1.5 and fewer than 9.5
Inequality:
Answer:
-1.5 ≤ r < 9.5
Step-by-step explanation:
All you have to do is just insert the numbers
we use ≤ as it says in the question "no less"
Which of the following linear equations represents the data chart?
Answer:
y = -x + 7
Step-by-step explanation:
let's use the first numbers as an example.
x=1 and y=6
now to get this we need to find the difference between the two numbers and we can do this by simply doing - 1 + 7 = 5
therefore making the answer y = -x + 7
Julie is solving the equation 3x² + 5x + 15 = 0 and notices that the discriminant b^2 - 4ac has a value of -155. This
tells her that the equation has
A one real roots.
B one imaginary root.
C two real roots.
D two imaginary roots
Answer: i think b
Step-by-step explanation:
my aunt's food budget is R 3500 . She save 1/5 of her budget. How much money did she save?
The money she saved is 700.
What are fractions?Simply put, a fraction shows us how many pieces of a whole we have. The slash that is printed between the two numbers indicates that the numbers are a fraction. We have two numbers: the numerator at the top and the denominator at the bottom. The number is represented mathematically as a quotient, where the numerator and denominator are split.Given:
Aunt's food budget = 3500
Fraction of the budget she saved = 1/5
So, the total money she saved = 1/5 of the food budget
= 1/5 × 3500
= 700
Therefore, the money she saved is 700.
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Choose the best answer
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:-\dfrac{1}{\sqrt{3-2x}} [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
We newd to find the derivative of given function :
[tex]\qquad \tt \rightarrow \: y = \sqrt{3 - 2x} [/tex]
[tex]\qquad \tt \rightarrow \: y = (3 - 2x) {}^{ \frac{1}{2} } [/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{d}{dx} (3 - 2x) {}^{ \frac{1}{2} } [/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{2} \sdot(3 - 2x) {}^{ - \frac{1}{2} } \sdot( - 2)[/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{1}{ \cancel2} \sdot\frac{1}{(3 - 2x) {}^{ \frac{1}{2} } }\sdot( - \cancel2)[/tex]
[tex]\qquad \displaystyle \tt \rightarrow \: \frac{dy}{dx} = \frac{ - 1}{ \sqrt{ (3 - 2x) {}^{ }} }[/tex]
Correct option : B
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
The number f of miles a helicopter is from its destination x minutes after takeoff is given by f(x)=60−1.5x. The number f of miles a commercial jet is from its destination x minutes after takeoff is shown in the graph below.
The distance of each flight is 60 miles and the time taken is 40 minutes.
Distance is the total path covered by an object or species in a particular time period.
At x = 0 minutes after takeoff,
f(x)=60−1.5x (given)
= 60-1.5*0 (at 0 minutes)
= 60 miles (distance between the helicopter and destination)
So, the distance of the flight is 60 miles.
When the helicopter reaches the destination, distance left is 0 miles
Thus, f(x) = 0 in x minutes.
Putting the above data in the equation, we get
0 = 60 - 1.5x
1.5x = 60 (bringing unlike terms on different sides)
x = 60/1.5
x = 40 minutes
Therefore, the distance of each flight is 60 miles and the time taken is 40 minutes.
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What are the coordinates of the vertices of the image triangle after a 90 clockwise rotation about the origin? :
A'(1, 3) B'(-3, 4) C'(-2,-3)
A'(3, 1) B'(4,-3) C'(-3,-2)
A'(3,-1) B'(4, 3) C'(-3, 2)
A'(1,-3) B'(-3,-4) C'(-2, 3)
A'(-3, 1) B'(-4,-3) C'(3,-2)
Before carrying out rotation transformation, the coordinates of the vertices of the pre-image are;
A (3, -6)
B(1, 2)
C (7, -1).
What is the effect of clockwise rotation transformation?We are given the coordinates of the transformed image as:
A'(6, 3),
B'(–2, 1),
C'(1, 7).
We need to find the coordinates of the pre-image A, B and C.
The rule for rotation of 90° about the origin is (x,y) ---> (-y,x).
But we need to find the coordinates of the vertices of the pre-image.
So, we need to apply rule (-y,x) ---->(x,y).
Applying the 90 degrees clockwise rotation rule,
A'(6, 3) -----> A (3, -6)
B'(–2, 1) -----> B(1, 2)
C'(1,7) -----> C (7, -1).
Therefore, coordinates of the vertices of the pre-image are
A (3, -6)
B(1, 2)
C (7, -1).
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Complete question is;
After a rotation of 90° about the origin, the coordinates of the vertices of the image of a triangle are A'(6, 3), B'(–2, 1), and C'(1, 7). What are the coordinates of the vertices of the pre-image?
During a sleepover, Carissa played karaoke with her friends. Her song was 6 minutes long. She had already sung for 4 minutes. Which equation could be used to see how much longer she will have to sing?
x + 2 = 6
x + 4 = 10
x + 4 = 6
x − 4 = 6
Brett has a box of colored pencils. He uses 78 pencils and has 120 pencils left in the box. Write an equation showing how many pencils are in the box before he starts drawing.
78 + p = 120
p − 78 = 120
120 + p = 78
p = 120 − 78
Answer:
for the first one it is x + 4 = 6
for the second one it is 78 + p = 120
Step-by-step explanation:
i hoped this helped!!!
Answer:
x+4=6
Step-by-step explanation:
x represents the missing number 4 represents the time she had already sang and 6 is the total
One boat sails 30 miles west and 22 miles north. Another boat sails 55 miles west and 40 miles north. Which boat traveled in the direction closest to due north?
The boat that sailed in the direction closest to due north is the both that has lesser angle to the vertical ,which is the boat that that sailed 30 miles west and 22 miles north.
How to find the boat that traveled in the direction closest to due northGiven data
One boat sails 30 miles west and 22 miles north
Another boat sails 55 miles west and 40 miles north
Say boat A sail 30 miles west and 22 miles north while boat B sails 55 miles west and 40 miles north
Boat A
let the angle boat A made with the vertical be a. This is given as
tan a = 30 / 22
a = arc tan ( 30 / 22 )
a = 53.746 degrees
Boat B
let the angle boat B made with the vertical be b. This is given as
tan b = 55 / 40
b = arc tan ( 55 / 40 )
b = 53.973 degrees
Comparing angle a and angle b shows that angle a is lesser hence boat A is the boat that sailed in the direction closest to the north
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Kingston Federal Bank supervises all banks in Jamaica. One Jamaican dollar is equal to 0.0071 US dollars. If Usain Bolt made a $ 3,000 deposit with Kingston Federal Bank with a 5% growth rate, how much money would Usain Bolt have after two years? (dont use advanced math please)
Principal = $3000
Rate = 5%
time = 2
Amount after 2 years =
[tex]\begin{gathered} =p(1+r)^t \\ =\text{ 3000( 1 + }\frac{5}{100})^2 \end{gathered}[/tex][tex]\begin{gathered} =3000(1+0.05)^2 \\ =\text{ 3000( 1.05)2} \\ =\text{ 3000 }\times\text{ 1.05 }\times\text{ 1.05} \end{gathered}[/tex]= $3307.5
Option D is the correct answer
Round all answers to 4 decimal places.
a. A bag contains 4 white marbles, 10 blue marbles, and 3 red marbles. If a marble is drawn from
the bag, replaced, and another marble is drawn, what is the probability of drawing first a white
marble and then a red marble?
b. A bag contains 10 green marbles, 3 red marbles, and 4 blue marbles. If two different marbles
are drawn from the bag, what is the probability of drawing first a green marble and then a blue
marble?
The probabilities are (a) 0.4228, and (b) 0.8382
Define probability?
Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. The greater the likelihood of an occurrence, the more probable it will occur. Tossing a fair (unbiased) coin is a basic example. Because the coin is fair, the two possibilities ("heads" and "tails") are equally likely; the chance of "heads" equals the probability of "tails," and because no other outcomes are possible, the probability of either "heads" or "tails" is 1/2.
(a) probability of drawing first a white marble and then a red marble
= 4/(4+10+3) x 3(3+10+3) = 4/17 + 3/16 = 0.4228
(b) probability of drawing first a green marble and then a blue marble
= 10/(10+3+4) x 4(9+3+4) = 10/17 + 4/16 = 0.8382
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If an object is shot upward with an initial velocity, vo, in feet per second (ft/s), the velocity, v, in ft/s is given by the
formula
v = vo -32t, where t is time in seconds. Find the initial velocity of an object if the velocity after 4 seconds is 41 ft/s.
-
I need help with this practice problem I will send an additional pic that goes along with this, it’s a graph, use the graph to answer
It is given that,
[tex]\begin{gathered} a^-=\langle-3,-5\rangle \\ b^-=\langle1,4\rangle \end{gathered}[/tex]By using parallelogram method,
[tex]a^-+b^-=\langle-2,-1\rangle[/tex]The graph is as shown below:
Correct each of the following errors by circling the error, describing what is wrong, entering what should be there instead, and entering the correct answer.-the equation is in the photo
As given by the question
There are given that expression:
[tex]4a^2\times3a^5[/tex]Now,
First, multiply the numbers:
[tex]4a^2\times3a^5=(4\times3)a^{2+5}[/tex]In the given solution of the question, there are perform addition, so this is the first error.
Now,
[tex](4\times3)a^{2+5}=12a^7[/tex]Hence, the correct answer is :
[tex]12a^7[/tex]I’m begging help me out with this, please
For given function f(x)=8/(x+2) , g(x)=4x² +2 then evaluation of the composition of function (fog)(-1) =1.
As given in the question,
Given function:
f(x) = 8 / (x+2)
g(x) = 4x² +2
Evaluation of the composition of function f(x) and g(x) we get,
(fog)(x)
= f(g(x))
Substitute g(x) = 4x² + 2
= f(4x² +2)
= 8/(4x² +2+2)
= 8/(4x²+4)
= 2/(x²+1)
Substitute x =-1 in the above function
(fog)(-1) = 2/ ((-1)² +1)
= 2/ 2
=1
Therefore, for given function f(x) = 8/ (x+2) , g(x) = 4x² +2 then evaluation of the composition of function (fog)(-1) =1.
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help plssssss I really need help genuinly
The store manager put 7 belts in sale. The belts were originally $16. The manager marked down the price of the belts by 40% how much money did the store receive for selling all 7 belts
Original price: $16
Discount: 40%
First, multiply the original price by the percentage discount in decimal form (divided by 100)
16 x 40/100 = 16 x 0.4 = $6.4 ( discount amount)
Subtract the discount amount to the original price
16-6.4 = $9.6 new price
multiply by 7 :
9.6 x 7 = $67.2
The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table
When the ratio of the number of miles run to the number of miles biked is equivalent for each row in the table, the value for A is C. 2 3/4.
How to illustrate the information?It should be noted that based on the information, the table has been given and the appropriate figures have been put into it.
The constant rate will be:
7 / 3 1/2 = 2
Now we can then write the relationship and this is illustrated as:
B = 2R
where B is the distance biked
R = the distance that's run.
We want to find the missing value of A. This is illustrated as:
5 1/2 = 2 × A
2A = 5 1/2
A = 2 3/4
Therefore, based on the information given, the correct option is C.
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The ratio of the number of miles run to the number of miles biked is equivalent for each row in the table.
Complete the table for A
A 2 1/4
B 2 2/4
C 2 3/4
D 3 3/4
What is the horizontal shift of y = cos(0 – ³7) + 3?4A. noneOB.-37OC. 3rD. 3Reset Selection
The horizontal shift will be the term that is subtracting the angle, in this case: -3pi/4= B .
A submarine was situated 800800 feet below sea level.
If it ascends 275275 feet, what is its new position relative to the sea level?
If a submarine was situated 800 feet below sea level. If it ascends 275 feet, its new position relative to the sea level is: -525 feet.
New position relative to the sea levelGiven :
Initial position of the submarine = 800ft below sea level
Ascending =275ft.
Hence, the New position relative to the sea level is calculated as:
New position relative to the sea level = (-800+ 275)
New position relative to the sea level = - 525 feet
Therefore the new position is: -525 feet.
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Gavin has a smart phone data plan that costs $20 per month that includes 6
GB of data, but will charge an extra $10 per GB over the included amount.
How much would Gavin have to pay in a month where he used 2 GB over the
limit? How much would Gavin have to pay in a month where he used went
over by x GB?
Total cost when over by 2 GB:
Total cost when over by x GB:
Total cost is given by the function $(20 + 10x)
What is a function?
A function in mathematics from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is referred to as the function's domain, and the set Y is referred to as the function's codomain. Al-Biruni and Sharaf al-Din al-Tusi, two Persian mathematicians, are responsible for the earliest known treatment of the concept of function. Initially, functions represented the idealised relationship between two varying quantities. A planet's position, for instance, depends on time. In the past, the idea was developed with the infinitesimal calculus at the end of the 17th century, and the functions that were taken into consideration until the 19th century were differentiable (that is, they had a high degree of regularity).
Total cost is given by the function $(20 + 10x)
Total cost when over by 2 GB = $(20 + 10x2) = $(20+20) = $40
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Based on the information below, what are the values of x and y of the solution to the system of equations used to
create the information?
38
141-14 |Ax|- 2141-
26
x = -5, y = 2
x = -0.2, y = 0.5
x=0.5, y = -0.2
x = 2, y = -5
38
8 26
The values of x and y of the solution to the system of equations are 2 and -5, respectively.
We are given three matrices. The matrices are A, Ax, and Ay.
The determinant of the matrix A is [(4*-2)-(-6*8)] = 40.
The determinant of the matrix Ax is [(38*-2)-(-6*26)] = 80.
The determinant of the matrix Ay is [(4*26)-(38*8)] = -200.
We need to find the values of x and y of the solution to the system of equations.
The value of x is |Ax|/|A| = 80/40 = 2.
Hence, the value of "x" is 2.
The value of y is |Ay|/|A| = -200/40 = -5.
Hence, the value of "y" is -5.
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Whats the solution to this formula?Tan^-1 ( 7 / 420) =
Okay, here we have this:
Considering the provided expression, we are going to solve it, so we obtain the following:
[tex]\begin{gathered} tan^{-1}(\frac{7}{420}) \\ =arctan(\frac{7}{420}) \\ =arctan(\frac{1}{60}) \\ =0.95° \end{gathered}[/tex]Finally we obtain that the expression is equal to 0.95°.
Which set of ordered pairs does not represent a function?O {(2,9), (2,-5),(-6,3), (4, -7)}O {(-7,5), (3,9), (0, 1), (6,5)}O {(0,7), (-5,3), (-9, -1), (1,7)}o {(-1,-8), (2,8), (0,6), (-6, -1)}Submit Answer
{(2,9), (2,-5),(-6,3), (4, -7)} this pair doesn't represent a function
A mathematical function is a relationship that is established between two sets, through which each element of the first set is assigned a single element of the second set or none at all. The initial set or starting set is also called the domain; the final set or arrival set is called the rank.
Since in this set two elements of the range are associated with the same element of the domain [(2,9) and (2,-5)], we can conclude that it is not a function
Scatter Graphs
The best description of a scatter graph does the following:
“tells the story” of the graph from left to right giving specific values and dates for the first data point, the last data point, any relevant high points and low points
explains the overall trend seen on the graph
includes at least one relevant calculation (absolute change, percent change, ratio, etc) to better describe the data, the trends, or changes in the data
ends with some meaningful conclusion or “take away”
uses terminology correctly
1. Write a thorough description of this scatter graph using the guidelines above. [3 pts]
A specific type of graphic or mathematical diagram known as a "scatter plot" employs Cartesian coordinates to display values for typically two variables for a group of data.
A scatter graph, scatter chart, scattergram, or scatter diagram are other names for it.
If the points are color-, shape-, or size-coded, a second variable can be displayed. Each point's location on the horizontal axis is determined by the value of one variable, while its location on the vertical axis is determined by the value of the other. The data is shown as a series of dots.A scatter plot can be used when both continuous variables are independent of one another or when one continuous variable is in the researcher's control and the other one depends on it.The scatter graph can be represented by the line of best fit which is calculated by taking the average of all the x -coordinates and the y-coordinates.
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Conscider this absolute value function.f(x) = (x – 5)How can function fbe written as a piecewise function?
f(x) = lx – 5l
x-5, if x-5 ≥ 0, x ≥5
-(x-5) = -x + 5 if x-5<0, x < 5
Pls answer also
Indicate which property is illustrated in Step 2.
Distributive property is illustrated in Step 2.
What is a distributive property ?The distributive law, which states that in elementary algebra, equality is always true, is generalized by the distributive principle of binary operations.A, B, and C are the operands in the formula for the distributive property, which is written as a (b + c) = (a b) + (a c). Here, each phrase included in a bracket multiplies the number outside of it, and the results are added.According to the associative property, any three terms in an expression can be combined together to solve it. The arrangement of the numbers will never alter the outcome of their computation. For addition and multiplication, the associative property holds true.To learn more about : Distributive law
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Calculate the cone: 1) volume; 2) the area of the lateral surface; 3) the total surface area;for AB = 14, SO = 24.
Given:
AB = 14
SO = 24
To find:
a) the volume
b) the area of the lateral surface
c) the total surface area
a) To find the volume of the cone, we will use the formula:
[tex]Volume\text{ of a cone = }\frac{1}{3}πr²h[/tex]r = radius
diameter = AB = 14
diameter = 2(radius)
radius = diameter/2 = 14/2
radius = 7
height = SO = 24
let π= 3.14
[tex]\begin{gathered} Volume\text{ of the cone = }\frac{1}{3}\times3.14\times7^2\times24 \\ Volume\text{ of the cone = 1230.88 unit}^3 \end{gathered}[/tex]b) To get the lateral surface, we will apply the formula:
[tex]\begin{gathered} lateral\text{ surface of the cone = \pi rl} \\ where\text{ l = }\sqrt{h^2+r^2} \end{gathered}[/tex][tex]\begin{gathered} Lateral\text{ surface of the cone = 3.14 }\times7\times\sqrt{7^2+24^2} \\ \\ Lateral\text{ surface area of the cone = 549.5 units}^2 \end{gathered}[/tex]c) The total surface area formula:
[tex]\begin{gathered} Total\text{ surface area of cone = Area of base + lateral surface area} \\ \\ Total\text{ surface area = \pi r}^2\text{ + \pi rl} \\ \\ Total\text{ surface area = \lparen3.14 }\times\text{ 7}^2)\text{ + 549.5} \end{gathered}[/tex][tex]Total\text{ surface area of cone = 703.36 unit}^2[/tex]Suppose that the relation S is defined as follows.
s={(3, 0), (1, 2), (4, -1), (3, 9)}
Give the domain and range of S.
Write your answers using set notation.
The most appropriate choice for relation, domain and range will be given by-
Domain of S = {3, 1, 4}
Range of S = {0 , 2, -1, 9}
What is relation, domain and range?
A relation over set A and B is the subset of the cartesian product A x B.
Domain of a relation is the set of values for which the relation is defined.
Range is the set of solution obtained on putting the values of domain.
The relation S is defined as follows
S = {(3, 0), (1, 2), (4, -1), (3, 9)}
Now the set of values for which the relation is defined is the domain of the relation
For each ordered pair, the first number gives the values to be put in S. So the first number of every ordered pair is the domain.
So domain of S = {3, 1, 4}
Now, the second number gives the solution after putting the numbers in S.
So the second number of every ordered pair represents the range.
So, range of S = {0 , 2, -1, 9}
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