Given:
Ratio of the side lengths of two similar rectangular prisms is [tex]\dfrac{3}{5}[/tex].
To find:
The ratio of their areas.
Solution:
If two figures are similar then their areas are proportional to the squares of their corresponding sides.
[tex]\dfrac{A_1}{A_2}=\dfrac{s_1^2}{s_2^2}[/tex]
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{s_1}{s_2}\right)^2[/tex] ...(i)
Where, [tex]A_1,A_2[/tex] are areas and [tex]s_1,s_2[/tex] are corresponding sides.
It is given that ratio of the side lengths of two similar rectangular prisms is [tex]\dfrac{3}{5}[/tex]. It means, [tex]\dfrac{s_1}{s_2}=\dfrac{3}{5}[/tex].
Using (i), we get
[tex]\dfrac{A_1}{A_2}=\left(\dfrac{3}{5}\right)^2[/tex]
[tex]\dfrac{A_1}{A_2}=\dfrac{3^2}{5^2}[/tex]
[tex]\dfrac{A_1}{A_2}=\dfrac{9}{25}[/tex]
Therefore, the ratio of their areas is [tex]\dfrac{9}{25}[/tex]. It is also written as 9:25.
Which best describes the relationship between the line that passes through the points (-6, -1) and (-11, 1) and the line
that passes through the points (-3, -8) and (-5, -13)?
A. perpendicular
B. parallel
C. neither perpendicular nor parallel
D. same line
Answer: A. perpendicular
Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.
Use the data in the table to complete the sentence. x y –2 7 –1 6 0 5 1 4 The function has an average rate of change of __________.
Answer: To find the average rate of change, evaluate the function at the given points.
Evaluate the difference of the function at the given points.
Divide the difference of the function at the given points with the difference of the given points.
Step-by-step explanation:
The Average of rate is -1.
Everytime it goes up by one the y goes down by 1 so it would be -1.
The average rate of change of the function in the table given is: -1.
What is Average Rate of Chnge of a Function?Average rate of change of a function = change in y / change in x = rise/run.
Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):
Average rate of change of the function = (7 - 5)/(-2 - 0)
Average rate of change of the function = 2/-2
Average rate of change of the function = -1.
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A pyramid with a triangular base has a volume of 50cm³. If the base and the height of the triangular base are 5cm and 8cm respectively, find the height of the pyramid ?
Answer:
h = 7.5 cm
Step-by-step explanation:
Firstly, we find the area of the triangular base
Mathematically, we have the area of a triangle as;
A = 1/2 * b * h
A = 1/2 * 5 * 8 = 20 cm^2
Mathematically, we have the formula as;
V= 1/3 * A * h
A is base area and h is height
50 = 1/3 * 20 * h
20h = 3 * 50
20h = 150
h = 150/20
h = 7.5 cm
what two numbers add up to 55 and multiply to -375
Answer:
-6.13406 and 61.13406
Step-by-step explanation:
x + y = 55
x × y = -375
y = 55 - x
x × (55 - x) = -375
55x -x² = -375
x² - 55x - 375 = 0
solution of a quadratic equation :
x = (-b ± sqrt(b² - 4ac))/(2a)
a=1
b=-55
c=-375
x = (55 ± sqrt(55² + 4×375))/2 = (55 ± sqrt(4525))/2 =
= (55 ± sqrt(25 × 181))/2 = (5×11 ± 5×sqrt(181))/2 =
= 5/2 × (11 ± sqrt(181)) =
= 61.13406... or -6.13406...
y = 55 - 5/2×(11 ± sqrt(181)) = 55/2 ± 5/2×sqrt(181) =
= -6.13406... or 61.13406...
please answer this 2 question
Answer:
Step-by-step explanation:
AP 1 : 12, 15 , 18 , 21, 24, 27, 30 , 33 , 36, 39,.....
AP 2 : 17 , 21 , 25 , 29, 33, 37 , 41, 45,.....
AP formed with the common terms: 21, 33, 45 , ......
a = 21 , d = 33-21 = 12 ; n = 100
Sum = [tex]\frac{n}{2}(2a +(n-1)d)[/tex]
[tex]=\frac{100}{2}[2*21+99*12]\\\\=50 * [42+1188]\\\\=50*1230\\\\= 61500[/tex]
Find two consecutive positive intergers such that the square of the smaller interger is nineteen more than five times the larger interger.
Answer:
8 and 9
Step-by-step explanation:
Let the two consecutive integers be x - 1 and x
Smaller = x-1
Largere = x
If the square of the smaller integer is nineteen more than five times the larger integer, then;
(x-1)² = 19 + 5x
Expand
x²-2x+1= 19+5x
x²-2x-5x+1-19 -0
x²-7x-18 =0
Factorize
x²-9x+2x-18 =0
x(x-9)+2(x-9) = 0
(x+2) = 0 and x - 9 = 0
x = -2 and 9
SInce x cannot be negative;
x = 9
Smaller number = 9-1
Smaller number = 8
Hence the two consecutive integers are 8 and 9
[tex]128^3+272^3 /128^2-128*272+272^2[/tex]
wait do you want it step by step or just the answer?
the answer is 400
А
3
-2
-1
0
2
3
B.
-1
The distance AB rounded to the
nearest tenth = [?]
Hint: d= (x2 - 1)+ (y2 - yı)2
A piece of ribbon is cut into two pieces in the ratio 3:7. The length of the shorter piece is 45cm. Calculate the length in cm of the longer piece of ribbon.
Answer:
105 cm
Step-by-step explanation:
3/7 = 45/x
cross-multiply:
3x = 315
x = 105
Find all values of x that satisfy the equation below. (x + 1)² - 25/9
= 0
Answer:
x = 8/3, 2/3
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightEquality Properties
Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of EqualityAlgebra I
Multiple RootsStep-by-step explanation:
Step 1: Define
Identify
(x + 1)² - 25/9 = 0
Step 2: Solve for x
[Addition Property of Equality] Add 25/9 on both sides: (x + 1)² = 25/9[Equality Property] Square root both sides: x + 1 = ±5/3[Subtraction Property] Subtract 1 on both sides: x = ±5/3 - 1Evaluate Addition/Subtraction: x = 8/3, 2/3Step-by-step explanation:
Hey there!
Given equation is:
(x+1)² - 25/9 = 0
Then;
(x+1)² - (5/3)² = 0 ( since 5² = 25 and 3² = 9)
or, {(x+1)+5/3} { (x+1)-5/3} = 0. { use a² - b² = (a+b)(a-b) formula}
[tex]( \frac{3x + 3 + 5}{3} )( \frac{3x + 3 - 5}{3} ) = 0[/tex]
[tex]( \frac{3x + 8}{3} )( \frac{3x - 2}{3}) = 0[/tex]
Now;
Either;
( \frac{3x + 8}{3}= 0
or, X = 8/3
Or,
( \frac{3x -2}{3} = 0
x = 2/3
Therefore, X = 8/3 or 2/3.
Hope it helps!
solve algebraically for z : 360000 + 102 = 200000 + 104z NEED ANSWER ASAP PLEASE HELP
Answer:
z = 1539.44230769
Step-by-step explanation:
360000 + 102 = 360102
360102 - 200000 = 160102
160102/104z = 1539.44230769
z = 1539.44230769
hey !! solve it
[tex] \sqrt{44 \times 11} [/tex]
Step-by-step explanation:
✓44×11
=✓2²×11²
=22
!!!!????!!!!!!
Answer:
22
Step-by-step explanation:
First, multiply 11 and 44
11 × 44 = 484
[tex]\sqrt{484}[/tex] = 22
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Have a great summer :)
a fruit seller had thought to sell 120kg of fruit at 150 dollars / kg but sold it 5% less. find out how much dollars the seller lost
What is the value of the rational expression
2x+1
when x = 5?
Step-by-step explanation:
2x+1
x = 5
2(5)+1
=10+1=11
Answer:
2(5)+1
10+1
11
Hope This Helps!!!
61/2×(8/9÷13/18)+(3/4) of 31/5
Answer:
[tex]\frac{10969}{260}[/tex]
Step-by-step explanation:
Find C. See the image below
Answer:
55 degrees
Step-by-step explanation:
First, we can use Thales' Theorem to determine that because AC is along the circle's diameter, angle B (the angle opposite to that side) is a right angle.
Next, we know that an inscribed angle with its vertex on the circle, formed by two intersecting chords (A in this case) is equal to 1/2 of its intercepted arc, so angle A = 70/2=35
We can then use the fact that a triangle adds up to 180 degrees here to get
35+90+C=180
C=55 degrees
In a regular polygon each interior angle is 120 greater than each exterior angle. Calculate the number of sides of the polygon.
Answer:
12 sides.
Step-by-step explanation:
the sum of every pair of interior and exterior angle is always 180 degrees.
x = exterior angle.
the interior angle is then x+120.
so then exterior and interior angle together must be 180.
x + x + 120 = 180
2x + 120 = 180
2x = 60
x = 30 degrees
how many sides ?
the sum of all exterior angles must be 360 degrees.
all exterior angles are the same (because all the interior angles must be the same due to "regular polygon").
so, how many times does 30 fit into 360 ?
360/30 = 36/3 = 12
it has 12 corners and also sides.
Which relationship has a zero slope?
Answer:
b has zero slop mark me as a brilliant
Given 15=3(2x+4)−3
Prove x=1
Complete the proof. Provide reasons for 1-6 below. Make sure to number your answers.
The value of x in the expression 15 = 3(2x + 4) - 3 is 1.
What is expression?A number, a variable, or a combination of numbers and variables and operation symbols is called expression.
According to the given question.
We have an expression
[tex]15 = 3(2x+ 4) -3[/tex]
Solve the above expression for x.
Step 1: open the parentheses
[tex]15 = 3(2x + 4) -3[/tex]
⇒ [tex]15 = 6x + 12 -3[/tex]
Step 2: simplify the above expression.
[tex]15 = 6x + 9[/tex]
Step 3: subtract 9 to the both the sides
[tex]15 - 9 = 6x + 9 -9[/tex]
⇒[tex]6 = 6x[/tex]
Step 4: Divide both the sides by 4
⇒ [tex]\frac{6}{6} =\frac{6x}{6}[/tex]
⇒ [tex]x = 1[/tex]
Hence, we proved that x = 1 for the above expression.
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Please please help me
Answer:
may be the answer is 1000.not sure.
Answer:
answer is c 1600
hope it helps
A general formula for a parabola is y2=4px.
What is the value of p in the equation y2=−4x?
P=−4
P=−1
P=1
P=4
Answer:
P = -1
Step-by-step explanation:
-1 x 4 = -4
The solution is : p= -1, is the value of p in the equation y^2=−4x.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
Explanation:
We have been given parabola along positive side of x-axis with equation
y² = 4px
and, y² = -4x
after equating the values of y² we will get
4px =-4x
Divide each term by x on both left hand side and right hand side we will get
4p= -4
Now, divide each term by 4 on both left hand side and right hand side we will get the final result p=-1
Hence, The solution is : p= -1, is the value of p in the equation y^2=−4x.
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There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1 /9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.
Answer: 7 red marbles.
Step-by-step explanation:
Since we are given the information that there are only red marbles and blue marbles in the bag and that the probability of randomly choosing a red marble is 1 /9 while there are 63 marbles in total.
Then the number of red marbles will be:
= 1/9 × 63
= 7
There are 7 red marbles
The number if blue marbles will be:
= 63 - 7
= 56 blue marbles
Help please!
Brainliest + 20 points
Answer:
im not sure but pls gimme brainlyist bc im a dum dum
Step-by-step explanation:
If there are twice as many bicycles as scooters and there are 945 vehicles in total. How many bicycles and scooters are there in Greenville?
Answer:
Bicycles = 315
Scooters = 630, basic mathematics. The most effective method for these questions is substitution. But I might have intermingled them so double check
APB is parallel to CTRD. PQRT is a quadrilateral. work out the size of the angle marked x you must show your working
Answer: X would be 84 degrees.
Step-by-step explanation: APB is a straight angle, which adds up to 180 degrees. TPQ is 90 degrees, and QPB is 32 degrees, so 180-90-32=58. APT is 58 degrees. APT and PTR are alternate interior angles, therefore they have the same angle measure. So PTR is also 58 degrees. A quadrilateral adds up to 360 degrees, so add up the three known angles in the quadrilateral, 58+90+128, which gives you 276 degrees. 360-276=84 degrees, therefore X would be 84 degrees.
Two large parallel metal plates carry opposite charges. They are separated by 85mm. The work done by the field is 6x10-3J and its field exerts on a particle with charge +8µC. Calculate the surface charge density on each plate.
Answer:
The surface charge density is [tex]7.8\times10^{-8} C/m^2[/tex].
Step-by-step explanation:
separation, d = 85 mm
Work, W = 6 x 10^-3 J
charge , Q = 8µC
The potential difference is given by
W = q V
[tex]V=\frac{6\times 10^{-3}}{8\times 10^{-6}}=750 V[/tex]
Let the charge on he capacitor is q.
[tex]q = CV\\\\q = \frac{\varepsilon oA}{d}\times V\\\\\frac{q}{A} = \frac{8.85\times 10^{-12}\times750}{0.085} =7.8\times10^{-8} C/m^2[/tex]
During a sale, a store offered 35% discount on a particular couch that was originally priced at $390. After the sale, the discount price of the camera was increased by 35%. What was the price of the couch after this increase? Round to the nearest cent.
Answer:
$342.23
Step-by-step explanation:
35/100 x $390 = $136.50
Price of couch after 35% discount
= $390 - $136.50
= $253.50
35/100 x $253.50 = $88.725
Price of couch after the 35% increase
= $253.50 + $88.725
= $342.225
= $342.23 (round off to nearest cents)
(HELP FAST TIMED)Which polynomial is prime x^3+3x^3+2x+6
Answer:
the third one
Step-by-step explanation:
A polynomial with integer coefficients that cannot be factored into polynomials of lower degree.
the third one is the answer
I NEED HELP PLZ it is very much appreciated
Answer:
C
Step-by-step explanation:
average, average, average
if there is one dot to the right that is far away and 3 dots to the left that are close to the like, estimated distance of the right dot would be 3 and the total distance sum of each dot to the left is 3, so the line would be between the 1 right dot and 3 left dots
Answer:
D
Step-by-step explanation:
D has three dots near to the line
Which statement is necessarily true if is an altitude to the hypotenuse of right ? A. ≅ B. C. D. ∠BAC ≅ ∠BDC
Answer:
Step-by-step explanation: