The areas of two similar squares are 16m and 49m.
What is the scale factor of their side lengths?
Answers
Answer:
The scale factor of their side lengths is 4:7.
Step-by-step explanation:
Let the side length of two squares are p and q.
The area of a square is
[tex]A=a^2[/tex]
Using this formula, we get the area of both squares.
[tex]A_1=p^2[/tex]
[tex]A_2=q^2[/tex]
It is given that the areas of two similar squares are 16m and 49m.
[tex]\frac{p^2}{q^2}=\frac{16}{49}[/tex]
[tex](\frac{p}{q})^2=\frac{16}{49}[/tex]
Taking square root both the sides.
[tex]\frac{p}{q}=\sqrt{\frac{16}{49}}[/tex]
[tex]\frac{p}{q}=\frac{4}{7}[/tex]
Therefore the scale factor of their side lengths is 4:7.
To find the scale factor of the side lengths, we can take the square root of the ratio of the areas. In this case, the scale factor is √7/2.
To find the scale factor of the side lengths of the squares, we can take the square root of the ratio of their areas. In this case, the ratio of their areas is 49m:16m, which simplifies to 7:4. Taking the square root of this ratio gives us the scale factor of their side lengths. So, the scale factor is √(7/4) = √7/√4 = √7/2. Therefore, the scale factor of the side lengths is √7/2.
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Related Questions
Two cars are 400 miles apart when they start moving towards each other. The speed of the first car is 30 mph. The second car moves 20mph faster than the first car. After how many our will the cars meet
Answers
Answer:
5 hr.
Step-by-step explanation:
this is because one car is moving at 30 miles an hour and the other at 30+20 miles an hour = 50mph. so after 1 hour one car would have gone 30 miles and the other 50 = 80 altogether not 400 yet. After 2 hours one car would have gone 60 miles and the other 100 = 160 not 400 yet. ECT... After five hours one car has gone 150 mile (30mph*5hr = 150miles) and the other 250miles (59mph*50hr = 250miles) = 400, since 150+250=400. Therefore it would take 5hr for the cars to meet. and crash ._.
Final answer:
The two cars traveling towards each other, one at 30 mph and the other at 50 mph, will meet after 5 hours, since their combined speed is 80 mph and they are 400 miles apart.
Explanation:
To solve the problem of when two cars moving towards each other will meet, we can use the concept of relative speed. The first car travels at 30 mph, and the second car travels at the faster speed of 50 mph (since it is 20 mph faster than the first car). The combined speed at which the two cars are moving towards each other is the sum of their individual speeds.
The formula for time is:
Time = Distance / Speed
Given that the two cars are 400 miles apart, and the combined speed is 30 mph + 50 mph = 80 mph, the time it takes for the two cars to meet is:
Time = 400 miles / 80 mph = 5 hours
Therefore, the cars will meet after 5 hours of travel.
Write an equation of a line wit the given slope and y intercept
Answers
Answer:
Step-by-step explanation:
the standard equation of a line is in the form y=mx+b where m is the slope and b is the y intercept so if m = 1/4 and b = -3/4 you can just replace those spots giving you y=1/4x+-3/4
please help i will give brainliest!
Which statement is best represented by the inequality p>48?
1.The basketball team scored less than 48 points.
2.The basketball team scored 48 fewer points than last year’s team.
3.The basketball team scored greater than 48 points.
4.The basketball team scored exactly 48 points.
Answers
Answer:
2.
Step-by-step explanation:
The reason I say this one is because that equation say p is greater than 48 that is why,
Answer: Option number 3!
Find the volume of the cone with the given dimensions: d = 26 cm, h = 10 cm
Answers
Answer:
¹⁶⁹⁰/₃π cm³ ≈ 1769.76 cm³
Step-by-step explanation:
Equation of a volume of a cone: V = ¹/₃ * πr²h
1. Find r (radius): r = d/2 = 26/2 = 13 cm
2. Plug in everything into equation: V = ¹/₃ * π(13)² * 10
3. Square: V = ¹/₃ * π * 169 * 10
4. Multiply: V = ¹⁶⁹⁰/₃π cm³ ≈ 1769.76 cm³
if it has a diameter of 26 cm, then its radius is half that, or 13.
[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=13\\ h=10 \end{cases}\implies V=\cfrac{\pi (13)^2(10)}{3} \\\\\\ V=\cfrac{1690\pi }{3}\implies V\approx 1769.76[/tex]
solve for x (x+3)/6 > (x-1)/2
Answers
Answer:
x< [tex]x<−32 or x>−43[/tex]
Step-by-step explanation:
Identify the property used in this equation:
3 + [7 + (–4)] = (3 + 7) + (– 4)
Answers
Answer:
Associativity property of Addition
Step-by-step explanation:
The associate property defines that grouping of more than two numbers and performing the basic arithmetic operations of addition and multiplication does not affect the final result. Note that grouping means placing the parenthesis.
The property used in this equation is the associative property of addition.
What is the associative property of addition?Associative property states that changing the order in which addends are grouped has no effect on the sum.
(a + b) + c = a + (b + c)
The equation given in the question is:
3 + [7 + (–4)] = [3 + 7] + (– 4)
The associative property states that (a + b) + c = a + (b + c)
Both equations are matching.
Hence, the equation given in the question clearly follows the associative law of addition.
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Someone please help me!
Answers
Answer:
ΔAGB ≅ ΔCGBStep-by-step explanation:
Look at the picture
a graphic designer chose a base font size and represented it as 1 on the scale. he then listed some consecutive scale sizes. two consecutive sizes were 5.832 and 10.4976.
what scale size came before 5.832 ?
Answers
Answer:
3.24
Step-by-step explanation:
You would use the two fonts given to find the scale factor.
So the scale factor would be 10.4976/5.832 = 1.8
So if the scale factor is 1.8 we can use that to find the font size just before that. To do this you would divide the font size by the scale factor.
So
5.832/1.8 = 3.24
The font size just before 5832 is 3.24.
Hope this helps, if there is an error in my work please correct me.
a box has a length of 12 inches and a width of 10 inches . If the volume of the box is 960 cubic inches. What is it's height?
Answers
length* width
12*10= 120
Volume /120
960/120=8
height is 8 inches
Rasheed bought five funnel cakes and three milkshakes for a total of 47.25 (more below, please help!!)
Answers
Answer:
The cost of a funnel cake is $6.75 and the cost of a milkshake is $4.50
Step-by-step explanation:
Let
x-----> the cost of a funnel cake
y----> the cost of a milkshake
we know that
5x+3y=47.25 -----> equation A
2x+6y=40.50 ----> equation B
Solve the system of equations by graphing
Remember that the solution of the system of equations is the intersection point both graphs
The solution is the point (6.75,4.50)
see the attached figure
therefore
The cost of a funnel cake is $6.75
The cost of a milkshake is $4.50
The probability of a certain spinner landing on yellow is 2/3. If you spin this spinner 45 times how many times would you expect the spinner to land on yellow? Explain how you determined your answer.
Answers
Answer:
45*2/3 is 90/3 which is 30 times
Step-by-step explanation:
Bryson and his cousins plan to all chip in to get their grandmother a $250
Christmas present. They can afford to put it on layaway with a 5% down
payment and pay $30 a month after that. If payments are due at the
beginning of each month, when should Bryson and his cousins make their
first monthly payment?
O A. July 1
O B. April 1
O C. June 1
O D. May 1
Answers
Answer: May 1st
Step-by-step explanation:
They have pay initially the down payment of 5% and the first month's installment.
You should start on May 1, because if you want to get it for her for Christmas.
Option D is correct.
What is monthly payment and down payment?The monthly payment is the amount paid per month to pay off the loan in the time period of the loan.
Down payment is the initial deposit made by the buyer to the seller when purchasing an expensive item, such as residential property or a car.
According to the question
Bryson and his cousins plan to all chip in to get their grandmother a $250 Christmas present.
They make a down payment of 5% and pay $30 a month after that.
If the payments are due at the beginning of each month, then they have to pay the first month's installment with their down payment.
That means they have pay initially the down payment of 5% and the first month's installment.
Total price = $250
Down payment = $250 x 5% = $12.5
Remaining amount = 250 - 12.5 = 237.5
= [tex]\frac{237.5}{30} =7.91[/tex] ≈ 8 months
You should start on May 1, because if you want to get it for her for Christmas.
May to December is 8 months.
Option D is correct.
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In the figure below what is the value of x
Answers
Answer:
It would be 32. my G
Answer:
D
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the two opposite interior angles.
100° is an exterior angle while 68° and x° are the opposite interior angles, thus
x + 68 = 100 ( subtract 68 from both sides )
x = 32° → D
A counterexample for the expression sinx+cosx=1 is 45 degrees T or F
Answers
True
Step-by-step explanation:A counterexample is a special type of example that is an exception to a general rule, law, proposition or statement. Hence if we prove that [tex]sin(45^{\circ})+cos(45^{\circ})\neq 1[/tex] then this is a counterexample for the expression [tex]sin(x)+cos(x)=1[/tex]. Thus:
[tex]sin(x)+cos(x)=1 \\ \\ Substituting \ x=45^{\circ} \ we \ have: \\ \\ sin(45^{\circ})+cos(45^{\circ})=1 \\ \\\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}=1 \\ \\ Rewriting:\\ \\2\frac{\sqrt{2}}{2}=1 \\ \\ \therefore \sqrt{2}=1 \ FALSE![/tex]
So we observe that the equation is not fulfilled because [tex]\sqrt{2}\neq 1[/tex]. In conclusion:
A counterexample for the expression sin(x)+cos(x)=1 is 45° is true!
A company dyes two sizes of rugs. A small rug requires 8 hours for dyeing and a medium-size rug requires 12 hours for dyeing. The dyers have to make at least 22 rugs, and they must do it in less than 240 hours. Let x equal small rugs and y equal medium rugs. Which of the following inequalities can be paired with x + y ≥ 22 to create a system that represents this situation?
8x + 12y > 240
12x + 8y > 240
8x + 12y < 240
12x + 8y < 240
Answers
Answer:
8x + 12y < 240
Step-by-step explanation:
If x equals the number of small rugs and y equals the number of medium rugs dyed, we would need to multiply both variables by the number of hours taken to dye each sized rug. It takes 8 hours to dye a small rug (8x), and 12 hours to dye a medium rug (12y).
Then, to find the total number of hours they dye them in, add the terms together.
8x + 12y
The company must dye the rugs in less than 240 hours, so we will use a 'less than' (inequality) sign (it cannot be 240, or any more than 240).
8x + 12y < 240
Answer:
c
Step-by-step explanation:
CAN SOMEONE HELP ME SOLVE THIS
Answers
Answer:
60
Step-by-step explanation:
Answer:
x = 60°
Step-by-step explanation:
The sum of the 3 angles in a triangle = 180°, thus
x + x + x = 180
3x = 180 ( divide both sides by 3 )
x = 60
The triangle is equilateral
During the school fundraiser, lsaac sold tubs of cookies dough for $15 each. He made $165. Write an equation that could be used to find the number of tubs that Dominic sold.
Answers
165\15= number of tubs
165 divided by 15 equals the amount of the tubs that he sold.
(I assume the two different name things, isaac&dominic, is a mistake since there isnt any information for Dominic)
If the endpoints of have the coordinates A(9, 8) and B(-1, -2), what is the midpoint of AB?
A.
(5, 3)
B.
(4, 5)
C.
(5, 5)
D.
(4, 3)
Answers
For this case we have that by definition, the formula of the midpoint is given by:
[tex]MP = (\frac {x_ {1} + x_ {2}} {2}, \frac {y_ {1} + y_ {2}} {2})[/tex]
We have the points are:
[tex](x_ {1}, y_ {1}) :( 9,8)\\(x_ {2}, y_ {2}): (- 1, -2)\\MP = (\frac {9 + (- 1)} {2}, \frac {8 + (- 2)} {2})\\MP = (\frac {9-1} {2}, \frac {8-2} {2})\\MP = (\frac {8} {2}, \frac {6} {2})\\MP = (4,3)[/tex]
Answer:
Option D
Answer:
option D is right on plato
Step-by-step explanation:
7. Jackie has one red pencil, one yellow pencil, one blue pencil,
one green pencil, one orange pencil, and one purple pencil. She
also has one red pen, one blue pen, and one black pen. If Jackie
randomly selects one pencil and one pen, what is the probability
that she will select a purple pencil and a black pen in that order?
Answers
Answer:
I believe it is 1/6 for the pencil and 1/3 for the pen. Altogether, 2/9.
Step-by-step explanation:
There is 1 purple pencil out of 6 and 1 black pen out of 3.
Using probability of independent events, it is found that there is a [tex]\frac{1}{15}[/tex] probability that she will select a purple pencil and a black pen in that order.
A probability is the number of desired outcomes divided by the number of total outcomes.
If two events, A and B, are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question:
The pencil and the pen are independent.One of the five pencils are purple, thus [tex]P(A) = \frac{1}{5}[/tex].One of the three pens are black, thus [tex]P(B) = \frac{1}{3}[/tex].The probability is:
[tex]P(A \cap B) = P(A)P(B) = \frac{1}{5} \times \frac{1}{3} = \frac{1}{15}[/tex]
[tex]\frac{1}{15}[/tex] probability that she will select a purple pencil and a black pen in that order.
A similar problem is given at https://brainly.com/question/23855473
The area of the figure is___ square units.
Answers
(21•8)-(8•3/2)-(8•6/2)=
168-12-24= 168-36=132
The big rectangle-small triangle on the left-triangle on the right
On monday ,248 students went on a trip to the zoo.All 4 buses were filled and 8 students had to travel in in cars. How many students were in each bus?
Answers
Answer:
60 students were in each bus.
Step-by-step explanation:
248-8=240
240 students rode on busses.
240/4= 60
60 students per bus.
248-8= 240 (taking away 8 because 8 of the students are not taking the bus)
240/4=60 (dividing the number we got by 4 because there are 4 busses)
i hope i helped :)
Graph the line Y=2/3x-1
Answers
Since this is a linear question in y=mx+b form, and where m is the slope of the line and b is the y-intercept....
The slope in this problem is 2/3
And y intercept is -1
So you would graph the point -1 on y axis then go up 2/3 since it’s positive( go up 2 over 3)
What are the zeros of the function f(x)=x^3+x^2-6x
PLEASE HELP ASAP!!
Answers
Answer:
A
Step-by-step explanation:
Given
x³ +x ² - 6x ( to find the zeros equate to zero ), that is
x³ + x² - 6x = 0 ← factor out x from each term
x(x² + x - 6) = 0
To factorise the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, hence
x(x + 3)(x - 2) = 0
Equate each factor to zero and solve for x
x = 0
x + 3 = 0 ⇒ x = - 3
x - 2 = 0 ⇒ x = 2
The zeros are x = - 3, x = 0, x = 2 → A
Which graph represents a reflection of f(x) = 2(0.4)x across the y-axis?
Answers
Answer:
The graph in the attached figure
Step-by-step explanation:
we know that
In a reflection across the y-axis the y-coordinate remains the same, but the x-coordinate is transformed into its opposite
we have
[tex]f(x)=2(0.4)^{x}[/tex]
The reflection of f(x) across the y-axis is equal to the function g(x)
[tex]g(x)=2(0.4)^{-x}[/tex]
The graph in the attached figure
The graph which best represents a reflection of f(x) across the y-axis is; f(x) = 2(0.4)^-x.
[tex]f(x) = 2(0.4)^{-x}[/tex]
What is the reflection of the graph of the function?A reflection of a point over the y -axis is given by a rule in accordance with mathematical convention. The rule in discuss for a reflection over the y -axis is (x,y)→(−x,y).
Hence, the reflection of the graph is given by the function; f(x) = 2(0.4)^-x.
[tex]f(x) = 2(0.4)^{-x}[/tex]
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35 POINTS
I have a rectangular prism with the dimensions of:
9cm 4cm 12cm
SA=2(4x9+12x9+12x4)=384
V=9x4x12=432
Question: I need a figure (figures - triangular prism, cube, pyramid, cone, cylinder, sphere) to have dimesions that will have less surface area but the same volume as the rectangular prism.
Answers
Answer:
500.874
Step-by-step explanation:
an electric motor makes 3000 revolution per minutes how many degrees does it rotate in a second
Answers
Answer: 18,000deg
Step-by-step explanation:
(3000rev/min)*(1min/60s)*(360deg/1rev)=18,000deg
Answer:
18,000
Step-by-step explanation:
We know that the electric motor makes 3000 revolutions in a minute/60 sec.
In one second, the motor makes 3000/60 revolutions.
In one second, the motor makes 50 revolutions.
∴ 1 revolution = 360 degrees
50 revolutions = 360 × 50 degrees
50 revolutions = 18,000 degrees
Regina is in charge of purchasing notepads to give away at an upcoming trade show. She knows that 65 boxes of notepads will contain a total of 1,625 pads. How many notepads will she receive if she purchases 48 boxes?
1,608
1,200
1,560
1,450
2,200
Answers
The answer is 1,200.
Hope this helps!
Answer:
Option B. 1,200.
Step-by-step explanation:
Regina is in charge of purchasing notepads to give away at an upcoming trade show.
she knows that 65 boxes of notepads will contain a total of 1,625 pads.
We calculate this by unitary method. first we calculate the amount of pads in one box.
∵ 65 boxes contains = 1,625 pads
∴ in one box = 1,625 ÷ 65 = 25 pads
She purchases 48 boxes, so she will receive = 25 × 48 = 1,200 pads
She would receive 1200 pads if she purchases 48 boxes.
A cylindrical-shaped water tank has a diameter of 4 feet and is 12 feet tall. Which is closest to the volume of this tank?
Answers
Answer:
The volume for a cylinder is [tex]\pi[/tex][tex]r^{2} h[/tex].
The diameter is half of the radius, so the r=2.
So pi x 2^2 x 12, this equals around 150.8 cubic feet.
I don't know what are your choice so just pick one that is closest to 150.8
Which of the following represents the factored form of f(x) = x3 − 81x? f(x) = x(x − 9)2 f(x) = (x + 9)(x − 9) f(x) = x(x + 9)(x − 9) f(x) = x(x2 − 9)
Answers
Answer:
f(x) = x(x + 9)(x − 9)
Step-by-step explanation:
Answer: f(x) = x(x+9)(x-9)
Step-by-step explanation:
Joan is 5 years older than Ellen, and 3 years ago the sum of their ages was 17 years. In how many years will Joan be 21 years old?
Answers
Answer:
7
Step-by-step explanation:
If J is Joan's current age and E is Ellen's current age, then:
J = E + 5
(J - 3) + (E - 3) = 17
Solve the first equation for E:
E = J - 5
Substitute into the second:
(J - 3) + (J - 5 - 3) = 17
J - 3 + J - 8 = 17
2J - 11 = 17
2J = 28
J = 14
Joan is 14, so in 7 years, she will be 21.