The common multiple of 5y²- 45 and y + 3 is (y + 3).
What is meant by common multiple?For any two or more expressions, if any one of their factors is common in all of them, then that factor is said to be the common multiple of those expressions.
Calculation:The given expressions are 5y²- 45 and y + 3
On factorizing them, we get
5y²- 45 = 5(y² - 9)
⇒ 5(y² - 3²)
From he binomial formula a² - b² = (a + b)(a - b), we can write
5y²- 45 = 5(y + 3)(y - 3)
Now, the second expression has no further simplification. The expression is itself a factor for it.
So, we can write their factors as
5y²- 45 = 5 × (y + 3) × (y - 3)
y - 3 = 1 × (y - 3)
From this, (y - 3) is the only factor that is a common factor for both the expression.
So, (y - 3) is the common multiple for the given expressions.
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Mr. Jackson has just finished building his treehouse and still needs to buy a ladder to be attached to the ledge of the treehouse and anchored at a point on the ground, as modeled below. Mr. Jackson is standing 1.3 meters from the stilt supporting the treehouse. This is the point on the ground where he has decided to anchor the ladder. The angle of elevation from his eye level to the bottom of the treehouse is 56 degrees. Mr. Jackson's eye level is 1.5 meters above the ground. Determine and state the minimum length of a ladder, to the nearest tenth of a meter, that Mr. Jackson will need to buy for his treehouse. (do not round until the very end)
Answer:
The length of the ladder Mr. Jackson will need to buy for his treehouse is approximately 3.7 meters
Step-by-step explanation:
The parameters given in the question are;
The horizontal distance from the point Mr. Jackson has decided to anchor the ladder to the the stilt supporting the tree house = 1.3 meters
The angle of elevation from Mr. Jackson's eye level to the bottom of the treehouse = 56°
The height of Mr. Jackson's eye level from the ground = 1.5 meters
From the question, we can draw the geometry of the ladder attached to the treehouse using Microsoft Visio as shown in the attached diagram
From the diagram, by trigonometric ratios, we have;
tan(56°) = a/1.3
∴ a = 1.3 × tan(56°) ≈ 1.927
By Pythagoras' theorem, we have;
The length of the ladder = √((a + b)² + 1.3²)
From the drawing, b = 1.5 m
Therefore, we have
The length of the ladder = √((1.927 + 1.5)² + 1.3²) ≈ 3.6653
The length of the ladder without rounding = √((1.3 × tan(56°) + 1.5)² + 1.3²) = 3.66559488352
∴ The length of the ladder given to the nearest tenth of a meter ≈ 3.7 m
The length of the ladder Mr. Jackson will need to buy for his treehouse ≈ 3.7 m.
Help just do number 7 please
Inches more: 19.1
Days more: 39
Step by step: 47.71 - 28.61 = 19.1
Step by step 2: 124 - 85 = 39
Answer:
asheville go 19.1 more inches of rain than wichita.
it rained 39 more days in asheville than Wichita.
Step-by-step explanation:
47.71 inches - 28.61 inches = 19.1 inches
124 days - 85 days = 39 days
Hope this helps❤
Jean can pack 5 cartons in 15 minutes. Which expression can be used to show the number of cartons Jean can pack in x hours? Group of answer choices
Answer: 20x
Step-by-step explanation:
First we should note that 60 minutes = 1 hour. Therefore, 15 minutes = 15/60 = 1/4 hour
Since Jean can pack 5 cartons in 1/4 hours, the number of carton that he can pack in one hour will be:
= 5 ÷ 1/4
= 5 × 4
= 20 cartons.
Therefore, to get the number of cartons that Jean can pack in x hours, we will multiply 20 by x. This will be:
= 20 × x
= 20x
Which expression is equivalent to the series shown?
125
Σ
n=17
45n
Answer: it’s b on edg
Step-by-step explanation:
Answer:
C
Step-by-step explanation:
Can y’all please help me
Answer:
its 3
Step-by-step explanation:
how many solutions will this quadratic equation x^2+8x+16 has?
Answer:
one solution
Step-by-step explanation:
to find out how many solutions a quadratic equation (with the equation ax²+bx+c) will have, we need to find the discriminant, which is b²-4ac
first, we can label the coefficients as a, b, and c
a=1 (1 is in front of x²)
b=8
c=16
now substitute into the formula
D=(8)²-4(1*16)
D=64-64
D=0
the discriminant is 0
when the discriminant is 0, that means the quadratic equation only has one solution.
Hope this helps!
//5. Use substitution to solve the system of equations
3x - y = 4
2x - 3y = 9
Solution: (
)
Answer: (3,5)
Step-by-step explanation:
y=3x-4
2x-3y=-9
2x-3(3x-4)=-9
2x-9x+12=-9
7x=21
x=3
y=3(3)-4
y=5
1/2 plus 1/8 equals.
Answer:
5/8
Step-by-step explanation:
hiii
What’s the answer????
Answer:
X = 9
Step-by-step explanation:
The area is approximately ___ square units.
Use 3.14 for π.
Answer:
A = 914 units
Step-by-step explanation:
The figure consists of a rectangle and a circle.
The sides of rectangle are 30 units and 20 units
The diameter of circle is 20 unit
Radius = 10 units
Required area = area of rectangle + area of circle
[tex]=l\times b+\pi r^2\\\\=30\times 20+3.14\times 10^2\\\\=914\ units[/tex]
So, the area of the figure is equal to 914 units.
HELP ASAP
Find the percent change to the nearest whole percent.
From 45 feet to 95 feet . A. 53% decrease
B. 53% increase
C. 111% decrease
D. 111% increases
use the substitution method to solve
3x + 2y=12
y=2x -1
Answer:
1. y=2
2. y= - 2
Step-by-step explanation:
Thats my answer hope it helps
Answer:
the solution is : (2 , 3)
Step-by-step explanation:
hello : here is an solution
3x + 2y=12.....(*)
y=2x -1.....(**)
put the value for y in (*) :
3x + 2(2x-1)=12
3x+4x-2 = 12
7x =14
so : x =2
but : y=2x -1
y =2(2)-1 = 3
the solution is : (2 , 3)
What is the probability the spinner will land on pink or an even number?
Answer:
Step-by-step explanation:
he probability of the spinner landing on an even number is 1/6.
What is the y-intercept to (-2,1) (3,-6)
Answer:
(0,-9/5)
Step-by-step explanation:
You can use the equation y=mx+b to solve
First you have to find the slope (m)
You can do this by using the equation y2-y1=x2-x1
(-6-1)/(3--1)= -7/5
m=-7/5
You then use the slope to find out b or the "y-intercept"
I am using the point (-2,1) to substitute
(1)=-7/5(-2)+b
-9/5=b
y=-7/5x-9/5
Check (3,-6):
(-6)=-7/5(3)-9/5
-6=-21/5- 9/5
-6=-6 true
6x+
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6x−
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6x+
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6x−
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6x+
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=- 10x
6x−
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= x
6x+
?
= 0
6x−
?
= 6
6x+
?
= 10
6x−
?
= 4x - 10
Step-by-step explanation:
6x+
?
= 10x
6x−
?
= 2x
6x+
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= 2x
6x−
?= 10x
6x+
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=- 10x
6x−
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6x+
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= 0
6x−
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= 6
6x+
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= 10
6x−
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= 4x - 10
6x+
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= 10x
6x−
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= 2x
6x+
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= 2x
6x−
?= 10x
6x+
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=- 10x
6x−
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= x
6x+
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= 0
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= 6
6x+
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= 10
6x−
?
= 4x - 10
A circular region with a 6 mile radius has a population density of 50 people per square mile. Find the number of people that live in the region
Answer:
population = 5652 people
Step-by-step explanation:
area = πr² = (3.14)(6²) = 113.04 mi²
at 50 people/mi², then 113.04 x 50 = 5652 people
I dont know if i did this right i wanted to know if someone could check for me
Answer:
I think 5 is wrong but 1 and 4 are right
GUYSSS PLS IM RUNNING OUT OF TIME ANY HELPPPP
Answer:
Welp, good luck the answer is c
Step-by-step explanation:
What is the perimeter of woods in feet
Answer:
what are the side lengths/ measurements of the forest?
Step-by-step explanation:
ill edit the answer once i get more info
2. A quadrilateral is inscribed in a circle. Find the measure of each missing angle as labeled below. Show your work and/or explain how you got your answer. Don't forget to label your answers CDE=
Answer:
おリム。羅語尾。、、利徒歩と
ラトソオコテユタソヨ保とソトコトThe野母
FINDING THE AREA OF A NONRIGHT TRIANGLE USING THE BOX METHOD.
Answer:
Step-by-step explanation:
thank you so much. thank you.
If p is true and ~q is false then p -> ~q is ___ false.
Sometimes
Always
Never
PLEASE HELP ME
The conditional of q by p is "If p then q" or "p implies q" and is denoted by p q. It is false when p is true and q is false; otherwise it is true.
How do I do this problem?
Answer: calculate x e it says and it = 6
Step-by-step explanation: hope this helps pls give me brainly
A full tub of water weighs 3 1/8 pounds. If the tub is filled up only 1/7 full how much would it weigh?
Answer:
[tex]\frac{25}{56}[/tex] pounds
Step-by-step explanation:
By using unitary method,
∵ 1 full tub of water weighs = [tex]3\frac{1}{8}[/tex] pounds
∴ [tex]\frac{1}{7}[/tex] of a water tub will weigh = [tex]3\frac{1}{8}\times \frac{1}{7}[/tex]
= [tex]\frac{(24+1)}{8}\times \frac{1}{7}[/tex]
= [tex]\frac{25}{56}[/tex] pounds
Therefore, water filled in [tex]\frac{1}{7}[/tex]th part of the tub will weigh [tex]\frac{25}{56}[/tex] pounds.
The weight of the tub if filled up to 1/7 full is 25/56 pounds
How to find product of fractionGiven:
Full weight of tub = 31/8 poundsIf filled halfway:
= 1/7 × 3 1/8
= 1/7 × 25/8
= (1 × 25) / (7 × 8)
= 25/56 pounds
Therefore, the weight of the tub if filled to 1/7 of the capacity is 25/56 pounds
Learn more about fraction:
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Which is the most accurate away to estimate 48% of 21?
A: 1/2 x 22
B: 1/4 x 22
C: 1/2 x 20
D: 1/4 x 20
Describe a real-world object that would be measured using square units and another that would be measured using cubic units. Explain.
Answer:
Volume or amount to f water in a jug
The size of a plot of land.
Step-by-step explanation:
The volume of capacity which a certain container can hold such as ; The amount water which can be filled into a cylindrical jug will be measured in cubic units as it requires the multiplication of 3 measured sides of the container ; for a cylinder, radius is squared and multiplied by height. (radius * radius * height).
The size or area of rectangular garden is measured using in square units as it only takes into consideration 2 of the measured parts of a shape.
What is the area of the figure? Please help, will give brainliest
Answer:
4
Step-by-step explanation:
A pet supply company makes a 5-gallon aquarium with a 10 inch by 10 inch base and a height of 14 inches. A museum wants to special-order a 135-gallon aquarium with the same shape. Find the new dimensions (length, width and height) of the new aquarium. Show or explain your work.
Liz flips a coin 50 times. The coin lands heads up 15 times and tails up 35 times. Complete each
statement.
The theoretical probability of the coin landing heads up is %.
Type an integer or a decimal.
Answer:
Theoretical Probability: 30%
Integer/decimal: 0.30
Step-by-step explanation:
Give me the answers for these and i’ll paypal you 5$
Answer:
Its 27
Step-by-step explanation:
Trust me i am Albert Einstein and I dont need Paypal Money.