Answer:
second option : the side length was multiplied by 5.
Step-by-step explanation:
a = side length of the original square
A² = a×a
(a+5)×(a+5) = a² + 10a + 25
and that should be equal to a²×25
a² + 10a + 25 = 25a² ?
10a + 25 = 24a²
no, that is not true for all a
a×5 × a×5 = a²×25 = 25A²
this is the correct solution, as it is true for all a.
For the area to be 25a², the side length was increased by 5.
How to calculate the area of a squareLet a be the side length of the original square, hence:
A = a²
Increasing the length by 5 will give:
(a+5)×(a+5) = a² + 10a + 25
Factorizing the result
a² + 10a + 25 = (a+5)²
a² + 10a + 25 = 25a²
This shows that for the area to be 25a², the side length was increased by 5.
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(Trigonometry) Find the values of x and y. Round your answers to the nearest tenth.
Answer:
[tex]x = 38.1[/tex]
[tex]y = 23.4[/tex]
Step-by-step explanation:
The given triangle is a right triangle. This is indicated by the box around one of the angles, signifying that the angle measure is (9) degrees. By its definition, a right triangle is a triangle with a (90) degree angle, thus the given triangle is a right triangle. In this situation, one can use right-angle trigonometry to find the value of the unknown side. In essence, right triangle trigonometry provides one with a series of ratios to describe the relationship between the sides and angles of the right trinagle. These ratios are the following,
[tex]sin(\theta)=\frac{opposite}{hypotenuse}\\\\cos(\theta)=\frac{adjacent}{hypotenuse}\\\\tan(\theta)=\frac{opposite}{adjacent}[/tex]
Keep in mind that the way a side is named is relative to the angle it is being described from. Thus, the (opposite) and (adjacent) sides acquire different names based on the angle relative to them. However, the (hypotenuse) is the hypotenuse no matter the angle, as the hypotenuse is the side opposite the right angle.
Solve for (y) first. One is given the angle measure and the measure of the side opposite the angle measure. One is asked to find the measure of the side adjacent to the angle. Use the ratio of tangent (tan) to achieve this.
[tex]tan(\theta)=\frac{opposite}{adajcent}\\[/tex]
Substitute,
[tex]tan(52)=\frac{30}{y}[/tex]
Inverse operations,
[tex]y=\frac{30}{tan(52)}[/tex]
Simplify,
[tex]y = 23.4386[/tex]
Now solve for the hypotenuse (x). One could use the Pythagorean theorem to do this, but since this is trigonometry, one might as well use the trigonometric ratios. One is given an angle, as well as the side opposite the angle, one is asked to find the hypotenuse. To do this, one can use the trigonometric ratio of sine (sin).
[tex]sin(\theta)=\frac{opposite}{hypotenuse}[/tex]
Substitute,
[tex]sin(52)=\frac{30}{x}[/tex]
Inverse operations,
[tex]x=\frac{30}{sin(52)}[/tex]
Simplify,
[tex]x = 38.0705[/tex]
Choose the number sentence that illustrates the distributive property of multiplication over addition.
a.) 3 × (4 + 6) = (3 × 4) + (3 × 6)
b.) 3 × (4 + 6) = (3 + 4) × (3 + 6)
c.) 3 × (4 + 6) = (3 × 4) + 6
Answer:
A. LHS,
3×(4+6)
3×10
30
NOW,
RHS,
(3×4)+(3×6)
12+18
30
Therefore, A is ans
HELP! Which of the following statements would prove line l is parallel to line m?
Answer:
Non of these.
Step-by-step explanation:
Because each of the options before have ≈ instead of =, however, to prove 2 lines are parallel, some angles must be equal. Corresponding angles and alternate angles should be equal. exactly equal.When factored completely, which is a factor of 6x^3-12x^2-48x?
Answer: C
Step-by-step explanation:
The solution is Option A.
The value of the equation is 6x³ - 12x² - 48x is A = 6x ( x + 2 ) ( x - 4 )
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as A
Now , the value of A is
A = 6x³ - 12x² - 48x be equation (1)
On simplifying the equation , we get
Taking 6x as the common factor , we get
A = 6x ( x² - 2x - 8 )
On simplifying the equation , we get
A = 6x ( x + 2 ) ( x - 4 )
Therefore , the value of A is 6x ( x + 2 ) ( x - 4 )
Hence , the equation is 6x ( x + 2 ) ( x - 4 )
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The point-slope form of the equation of the line that passes through (-9,-2) and (1,3) is y-3=1/2(x-1) what is the slope-intercept form of the equation for this line
Answer:
y = (1/2)x + 2 1/2
Step-by-step explanation:
y - 3 = (1/2)(x - 1)
Distribute the 1/2
y - 3 = (1/2)x - 1/2
Add 3 to both sides
y = (1/2)x + 2 1/2
michelle has three textbooks each way 5/8 pounds what is the total weight of her textbook
Answer:
1 and 7/8 pounds
Step-by-step explanation:
There are 3 textbooks that each weigh 5/8 of a pound
3*5/8=15/8
1 and 7/8
5 people are going to a dinner party. Each person at the party will eat 23 pounds of turkey. If you can only buy whole pounds of turkey, how many pounds should you buy?
if the angle of elevation of the sun is 40 degrees, and is decreasing 1/3 radians/hour how fast is the shadow of a 35m tall pole lengthening?
[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr}[/tex]
Step-by-step explanation:
Let y = height of the pole = 35 m (constant)
x = length of the shadow
They are related as
[tex] \tan \theta = \frac{y}{x} [/tex]
or
[tex]x = \frac{y}{ \tan\theta } = y \cot \theta[/tex]
Taking the time derivative of the above expression and keeping in mind that y is constant, we get
[tex] \frac{dx}{dt} = y( - \csc^{2} \theta) \frac{d \theta}{dt} [/tex]
Before we plug in the numbers, let's convert the degree unit into radians:
[tex]40° \times ( \frac{\pi \: rad}{180°}) = \frac{2\pi}{9} \: radians[/tex]
Since the angle is decreasing, then d(theta)/dt is negative. Therefore, the rate at which the shadow is lengthening is
[tex] \frac{dx}{dt} = (35 \: m)( - \csc^{2} \frac{2\pi}{9} )( - \frac{1}{3} \frac{rad}{hr} )[/tex]
or
[tex] \frac{dx}{dt} = 28.2 \: \frac{m}{hr} [/tex]
Two positive numbers have a difference of 21. The larger number is five more than twice the smaller. Find the two numbers.
what does the scale 1:500 000 mean
A scale of 1:5000000 means that:
This is mainly used in map or shadow etc. things.
For example in map it is given that the scale is 1mm:5000000mm, then it means that 1mm on the map is equal to 5000000mm in real life. So, you can be asked what does 5mm on map means in real life. So, you have to solve like this:
5 × 5000000 = real life size
25000000mm = real life size
In shadow like question, it can be asked that if 5000000 m of building casts a shadow of 1 m, then how much will be the shadow of a 10000000 m building. So, you have to solve it like this:
(10000000/5000000) × 1 = shadow size
=> 2 × 1 = shadow size
=> 2m = shadow size
You can tell me the specific questions so that I can help.
The scale 1:500 000 means 1 unit on a map represents 500000 in real life
What are scales?Scales are used to represent big or small measurements on a map or graph
How to interpret the scale?The scale is given as:
1:500 000
The above means that:
1 unit on a map represents 500000 in real life
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Leon verified that the side lengths 21, 28, 35 form a Pythagorean triple using this procedure. Step 1: Find the greatest common factor of the given lengths: 7 Step 2: Divide the given lengths by the greatest common factor: 3, 4, 5 Step 3: Verify that the lengths found in step 2 form a Pythagorean triple: 3 squared + 4 squared = 9 + 16 = 25 = 5 squared Leon states that 21, 28, 35 is a Pythagorean triple because the lengths found in step 2 form a Pythagorean triple. Which explains whether or not Leon is correct? Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple. Yes, any set of lengths with a common factor is a Pythagorean triple. No, the lengths of Pythagorean triples cannot have any common factors. No, the given side lengths can form a Pythagorean triple even if the lengths found in step 2 do not.
Answer:
Yes, multiplying every length of a Pythagorean triple by the same whole number results in a Pythagorean triple
Step-by-step explanation:
The given side lengths are;
21, 28, and 35
From the given side lengths, the greatest common factor = 7
Therefore, we have;
3 × 7, 4 × 7, and 5 × 7
A Pythagorean triple is formed by three numbers, 'a', 'b', and, 'c', which are both positive and integers, that are related as follows;
c² = a² + b²
Therefore, for the three numbers, we get;
3, 4, and 5 is a Pythagorean triple
5² = 3² + 4²
Multiplying both sides by 7² gives;
(5)² × (7)² = (3)² × (7)² + (4)² × (7)²
By the laws of indices, (a·b)ⁿ = aⁿ × bⁿ
Therefore;
(5 × 7)² = (3 × 7)² + (4 × 7)²
Therefore, multiplying every length of the Pythagorean triple by the same whole number results in a Pythagorean triple.
(The relationship can also be shown using similar triangles, as multiplying the side lengths of a triangle by the same whole number, gives a similar triangle, having the same relationship between its sides)
1. Suly watched a film that was 90 minutes long. 1/6 of the way through the film, the
doorbell rang. The pizza man had arrived with the order.
How many minutes of the film had she watched before the pizza man arrived?
(3 marks)
a.
Answer:
15 minutes
Step-by-step explanation:
Suly watched a film that was 90 minutes long. Then, she stopped at the [tex]\frac{1}{6}[/tex]mark. This means that we have to find [tex]\frac{1}{6}[/tex] of 90 minutes to find the amount of time Suly watched before the pizza man arrived. So therefore, the answer is 15 minutes.
Have a nice day. : )
Answer:
15 minutes
Step-by-step explanation:
Given:
The film Suly is watching is 90 minutes longSuly watched 1/6 of the film before the pizza man arrivedSteps:
90/6=15The following expressions are factorizations of 60. Which is the prime factorization?
Answer:
d
Step-by-step explanation:
press 60 on your casio calculator then the equal sign then shift and then 3rd row this button ".,,," which means factorise
39.76÷7.94
use compatible numbers and estimate
Answer:
5
Step-by-step explanation:
As for estimation, you may round 39.76 to the whole number, resulting in 40.
7.94 to 8
40 / 8 = 5
5 is your answer for the result of estimation
Which one of the following represents exponential growth?
A: y = (48000)(.05)^x
B: y = (48000)(.95)^x
C: y = 2400(.05)^x
D: y = (48000)(1.05)^x
between which 2 square roots does 7 lie
6,7
23,30
32,43
45,60
Answer:
32, 43
Step-by-step explanation:
Your welcome! :)
Answer:
The answer is 45,60.
Step-by-step explanation:
We can use a square chart to answer this question.
I will zoom in to the particular ones we need.
[tex] {6}^{2} = 36[/tex]
[tex]{7}^{2} = 49[/tex]
[tex] {8}^{2} = 64[/tex]
7 is the square root of 49.
45 lies in between 36 and 49 so its square root is more than 6 but less than 7. It is around 6.708 to the nearest thousandth.
Meanwhile, 60 lies in between 49 and 64 so its square root is more than 7 but less than 8. It is around 7.746 to the nearest thousandth.
Hence, we can say that 7 lies in between the square root of 45 and the square root of 60.
A regular polygon of (2A+ 1) sides has 140°
as the size of each
interior angle. Find A
Answer:
Ext angles = 40 degs 360/40 = 9 sides
Step-by-step explanation:
data distribution lol
Answer:
The range of the value of numbers is 8
Step-by-step explanation:
Mathematically, the range refers to the difference between the biggest and the smallest number
From the diagram, the biggest number is 13and the smallest is 5
The difference between this two is the range
we have this as 13 -5 = 8
PLEASE PLEASE I RLY NEED HELP ...... ....... . .. . . . . . . . . .... . . . Pick three Enlightenment thinkers and explain how they inspired America’s founders.
Answer:
Enlightenment philosophers John Locke, Charles Montesquieu, and Jean-Jacques Rousseau all developed theories of government in which some or even all the people would govern. These thinkers had a profound effect on the American and French revolutions and the democratic governments that they produced.
I am guessing your in the same situation as me sweeping across the internet for help in our summer school history classes well I found this hope it helps
Subtract the given polynomials using the vertical format.
===========================================
Explanation:
The negative out front of the parenthesis will swap the sign of each term. That means -3c^3 becomes +3c^3, or simply 3c^3. The other terms in the parenthesis are handled the same way.
After distributing the negative through, we add straight down.
The 7c^3+3c^3 becomes 10c^3
Then we have -5c^2+(-2c^2) become -7c^2
Finally, 2c+2c simplifies to 4c
Answer:
10C³-7C²+4C
7c³-(-3c³) -5c²-(+2c²) +2c-(-2c)
QUESTION 2
Simplify the following
a5×a7
Answer:
[tex]a^{12}[/tex]
Step-by-step explanation:
Identity Used : [tex]a^x \times a^y = a^{x+ y}[/tex]
[tex]a^5 \times a^7 = a^{5 + 7} = a^{12}[/tex]
quadrilateral BANK is a parallelogram. if AB= 10cm and AN= 6cm, what is the length of NK?
guys patulong, thanks!
Answer:
The length of NK is 10 cm.
Answer:
10 cm
Step-by-step explanation:
In parallelogram, opposite sides are parallel and equal.
AB and NK are opposite sides
So, NK = AB = 10cm
Solve the following system by graphing and identify the point of intersection -2x - y=-12 2x-3y=4
Answer:
{x,y} ={10,-8}
Step-by-step explanation:
hope it help please mark me as brinnelist
help me solve this with explanation
Answer:
x = 19
<6 = 109
<7 = 109
Step-by-step explanation:
Angles 6 and 7 are vertical angles so they are equal
7x -24 = 5x+14
Subtract 5x from each side
7x-5x -24 = 5x-5x+14
2x-24 = 14
Add 24 to each side
2x-24 +24 = 14+24
2x = 38
Divide by 2
2x/2 = 38/2
x = 19
<6 = 7x -24 = 7*19 -24 = 109
<7 = 5(19)+14 = 109
A school has 833 students. Of those students, 463 play a sport (A), 52 are in the band (B), and 21 do both(AB). (C) represents neither.
Answer:
Im sorry but it is kind of confusing
Step-by-step explanation:
What is the solution to the system of equations
Step-by-step explanation:
[tex]5x + 3y = 13 \\ 7x + 8y = - 16 \\ 5x = 13 - 3y \\ x = \frac{13 - 3y}{5} \\ 7( \frac{13 - 3y}{5} ) + 8y = - 16 \\ 18.2 - 4.2y + 8y = - 16 \\ 3.8y = - 34.2 \\ y = - 9 \\[/tex]
[tex] x = \frac{13 - 3( - 9)}{5} = \frac{13 + 27}{5} = \frac{40}{5} = 8 \\ x = 8 \\ y = - 9[/tex]
Can someone help please ?!
Step-by-step explanation:
53 is the correct answer
83 in scientific notation
Answer:
8.3 x 10^1
hope this helps
have a good day :)
Step-by-step explanation:
Simplify each of the following by rationalizing the denominator.
please do answer my doubt
Answer:
(47+21√5)/2
Step-by-step explanation:
Given the expression
7+3√5/7-3√5
= 7+3√5/7-3√5 * (7+3√5)/(7+3√5)
= 49+21√5+21√5+9(5)/[7(7)-9(5)]
= 49+42√5+45/49-45
= 94+42√5/4
= 2(47+21√5)/4
=(47+21√5)/2
Hence the required expression is (47+21√5)/2
Evaluate the following expression at x = -5
-2x-3
Answer:
7.
Step-by-step explanation:
-5 x -2 = 10 (2 negatives being multiplies = positive)
Then, 10 - 3 = 7.
