Answer:
x={-5,-6}
Step-by-step explanation:
x²+11x+30=0
x²+5x+6x+30=0 (as 5*6=30 and 5+6=11)
x(x+5)+6(x+5)=0
(x+5)(x+6)=0
so
x+5=0
x+6=0
therefore
x=-5
x=-6
Answer:
x = - 6, x = - 5
Step-by-step explanation:
Given
x² + 11x + 30 = 0
Consider the factors of the constant term (+ 30) which sum to give the coefficient of the x- term (+ 11)
The factors are + 6 and + 5 , since
6 × 5 = 30 and 6 + 5 = 11, then
x² + 11x + 30 = 0
(x + 6)(x + 5) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 6 = 0 ⇒ x = - 6
x + 5 = 0 ⇒ x = - 5
1) What are the solutions of (x/3) > -1?
is this asking if I need multiple solutions?
Yes...
x/3 > -1
what values of x make x/3 > -1
hint... your answer will look like like x > (number)
The length of a rectangle is represented by 4a+3b and its width is represented by 3a-2b. Enter the polynomial for the perimeter of the rectangle. What is the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number?
Answer:
a) The polynomial for the perimeter of the rectangle is = 14a - 2b
b) 150
Step-by-step explanation:
a) The formula for the area of a rectangle is given as:
P = 2L + 2W
From the question:
The length of a rectangle = 4a+3b
The width of a rectangle = 3a-2b.
The Perimeter of the rectangle is
Perimeter = 2(4a + 3b) + 2(3a - 2b)
Perimeter = 8a + 6b + 6a - 4b
Perimeter = 8a + 6a + 6b - 4b
Perimeter = 14a - 2b
Hence:
The polynomial for the perimeter of the rectangle is = 14a - 2b
b) What is the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number?
Non-zero whole number are single digit number such as: 1, 2, 3, 4, 5, 6, 7, 8, 9
The perimeter of the rectangle is = 14a - 2b
We are asked to find the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number.
In order to solve this, we would used the highest non zero whole number which is 9
Hence,
For a = 12 , b = 9
14 × 12 - 2(9)
= 168 - 18
= 150
Hence, the minimum perimeter of the rectangle if a=12 and b is a non-zero whole number is 150
Factor the greatest common factor out of the expression.
5m + 15m² + 5m
SHIRE
Answer:
5m
Step-by-step explanation:
The expression is 5m(1 + 3m + 1) = 5m(3m + 2), which cannot be simpolified further.
using the slope formula, find the slope of the line through the given points (8,0) and (2,-4)
Answer:
m=2/3
Step-by-step explanation:
the equation for slope (m) is (y2-y1)/(x2-x1)
here are the given points: (8,0) and (2,-4)
label the points
x1=8
y1=0
x2=2
y2=-4
substitute into the equation
m=(-4-0)/(2-8)
m=-4/-6
m=2/3
the slope is 2/3
Determine the value of each variable in the figure below. Keep answers in simplest radical form.
Step-by-step explanation:
cos60° = Adjacent/Hypotenuse = a/42.
=> a = 42cos60° = 21.
sin60° = Opposite/Hypotenuse d/42.
=> d = 42sin60° = 42(√3/2) = 21√3.
tan30° = Opposite/Adjacent = d/b.
=> b = d / tan30° = (21√3) / (1/√3) = 63.
sin30° = Opposite/Hypotenuse = d/c.
=> c = d / sin30° = (21√3) / (1/2) = 42√3.
If you earn about $1,623 per week, what would be your yearly salary?
Answer:
$592,395
Step-by-step explanation:
Because $1,623 x 365= $592,395 in a year
Some liquid will be poured from a 16 ounce container until it is filled to the percent of the the larger container (87.5%).How many ounces of liquid must be poured from to reach the full 16 ounce container?
Answer:
16 ounces
Step-by-step explanation:
First we are told that a container has a capacity of 16 ounces of liquid and therefore 16 ounces of liquid can fill that one container
The 16 ounces liquid from the 16 ounce container is fully emptied in a larger container and fills 87.5% of the larger container therefore the larger container is:
100/87.5×16 ounces= 18.285 ounces in liquid capacity
Therefore to fill the smaller 16 ounce container, the larger container would have to pour 16 ounces of liquid into the smaller container, and would would still have 18.285-16=2.285 ounces if it(the larger container) were filled to the brim(100%)
Simplify
4x + 2y + x2 - x + 3 - x2 - 5
A. 3x2 + 5y - 8
B. 2x2 - 3x + 2y - 2
C. -5x + 2y - 2
D. 4x2 - 2y + 5x + 8 help help help pls help
Answer:
b
Step-by-step explanation:
u just have to think about it
Solve the following for x
Answer:
x = 9
Step-by-step explanation:
50+80+(6x-4)=180 (ANGLE SUM PROPERTY)
130 +(6x-4)=180
6x-4=180-130
6x-4=50
6x=50+4
x=54/6
x = 9
Which product will result in a sum or difference of cubes?
O (x + 7)(x2 – 7x + 14)
O (X + 8)(x2 + 8x + 64)
O (x – 9)(x? mox +81)
O (X – 10)(x2 – 10x + 100)
Answer:
(x – 9)(x² + 9x+81)
Step-by-step explanation:
The sum of cubes of a and b is given by:
a³ + b³ = (a + b)(a² - ab + b²)
While the difference of cubes is given as:
a³ - b³ = (a - b)(a² + ab + b²)
1) (x + 7)(x² – 7x + 14) = x³ -7x² + 14x + 7x² - 49x + 98
= x³ -35x + 98
2) (X + 8)(x² + 8x + 64) = x³ + 8x² + 64x + 8x² + 64x + 512
= x³ + 16x² + 128x + 8³
3) (x – 9)(x² + 9x+81) = x³ + 9x² + 81x - 9x² - 81x - 729
= x³ - 9³
4) (X – 10)(x² – 10x + 100) = x³ - 10x² + 100x - 10x² + 100x - 1000
= x³ - 20x² + 200x - 10³
What is the area of the shaded region in the figure below? Use 3.14 for pie
Answer:
200.96 = area of Shaded portions.
Step-by-step explanation:
Area of the 2 stars.
I don't know if you can see this or not, but the 4 quarter circles surrounding the star is found by subtracting a full small square surrounding the star
Area of 1 star = 4 * (1/4) pi * r^2
Area of 1 star = 3.14 * 4^2
Area of 1 star = 50.24
Area of both stars = 100.48
Area of the 4 semicircles at each end
The 2 semicircles at one end figure = 1 circle
The two circles gives the total area of the 4 semicircles.
Area 1 circle = pr * r^2
Area 1 circle = 3.14 * (8/2)^2
Area 1 circle = 50.24
There are 2 such circles = 100.48
Total area of both results
Total Area = 100.48 + 100.48
Total Area = 200.96
The rectangular diagram shows the design for a food court at the zoo. What is the length of the walk way?
Answer:
Step-by-step explanation:
we have a triangle, one leg is 40, one leg is 30
c^2=40^2+30^2
c^2=1600+900=2500
c=[tex]\sqrt{2500}[/tex]=50
pls help with this math question
Answer:
its x>-249
Step-by-step explanation:
this should be the answer cause x is 0 on the line and the 249 is negative so its much less than 0
What is the value of n?
07
O 11
O 14
15
07
Step-by-step explanation:
just want the answer right. thats the answer. not the answer btw just need points for my question cmon dude you know how it is. struggling really bad rn
The value of n in the given triangle is 11.
What is incenter of a triangle?The incenter is one of the triangle's points of concurrency formed by the intersection of the triangle's 3 angle bisectors.
Given that, triangle DEF, where A is the incenter of the triangle, we need to find the value of n,
Since we know that, incenter is a point in triangle where all the angle bisector meets, therefore,
3n-6 = 27
3n = 33
n = 11
Hence, the value of n in the given triangle is 11.
Learn more about incenter of the triangle, click;
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help for this question pls :)
Step-by-step explanation:
tan(A/2)
tan(A/2)=sinA/1+cos A
tan(A/2)= 5/13÷1+12/13
tanA/2=1/5
Answer:
tan([tex]\frac{A}{2}[/tex] ) = ± [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Using the trigonometric identity
tan ([tex]\frac{A}{2}[/tex] ) = ± [tex]\sqrt{\frac{1-cosA}{1+cosA} }[/tex]
Given
tanA = [tex]\frac{5}{12}[/tex] = [tex]\frac{opposite}{adjacent}[/tex]
This is a right triangle 5- 12- 13 ( with hypotenuse 13 ), then
cosA = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{12}{13}[/tex] , then
tan ([tex]\frac{A}{2}[/tex] )
= ± [tex]\sqrt{\frac{1-\frac{12}{13} }{1+\frac{12}{13} } }[/tex]
= ± [tex]\sqrt{\frac{\frac{1}{13} }{\frac{25}{13} } }[/tex]
= ± [tex]\sqrt{\frac{1}{25} }[/tex]
= ± [tex]\frac{1}{5}[/tex]
Is Noah's work correct? Explain. Yes, Noah's calculations are correct. No, Noah did not simplify correctly. No, Noah used the diameter instead of the radius in the calculations. No, Noah did not use the correct formula for volume of a sphere.
Answer:
No, Noah used the diameter instead of the radius in the calculations.
V = 91.13π
Step-by-step explanation:
Noah is working on a geometry problem that involves finding the volume of a sphere with a diameter of 9 units. His work is shown below.
V = πr3
V = π(9)3
V = π(729)
V = 972π cubic units
Is Noah’s work correct
Volume of a sphere, V = πr³
radius, r = diameter / 2
Diameter = 9 units
r = 9 / 2
= 4.5 units
Volume of a sphere, V = πr³
= π × 4.5³
= π × 91.125
= 91.125π
Approximately 91.13π
V = 91.13π
No, Noah used the diameter instead of the radius in the calculations.
Answer:
no, he used radius instead of diameter
Step-by-step explanation:
A skateboarder is shown below.
we
z
At which point is the skateboarder's potential energy the greatest?
Point X
Point Y
Point W
Point Z
Answer:
answer is w
Step-by-step explanation:
apples cost $0.75 per pound and bananas cost $1.05 per pound
a baker bought a total of 12 pounds of apples and bananas for $10.20.
the systems of equation models the situation, where A is the number of pounds of apples and B is the number of pounds of bananas how many pounds of each did the baker buy?
Answer:
The baker bought 8 apples and 4 bananas
Step-by-step explanation:
System of Equations
Let's call:
a = pounds of apples
b = pounds of bananas
The baker bought a total of 12 pounds of apples and bananas, thus:
a + b = 12 [1]
Apple cost $0.75 per pound and each pound of bananas cost $1.05 per pound. Thus the total cost is 0.75a + 1.05b. We know he spent a total of $10.20, thus
0.75a + 1.05b = 10.20 [2]
Solving [1] for a:
a = 12 - b [3]
Substituting in [2]:
0.75(12 - b) + 1.05b = 10.20
Operating
9 - 0.75b + 1.05b = 10.20
Simplifying:
0.30b = 10.20 - 9 = 1.20
Dividing by 0.30:
b = 1.20/0.30
b = 4
From [3]:
a = 12 - 4 = 8
a = 8
The baker bought 8 apples and 4 bananas
I NEED HELP PLZ I WILL GIVE THANKS AND BRAINLIST
Answer:
No it is not a solution
Step-by-step explanation:
Key skills needed - One variable equations
1) We look at the equation, y = 4x+ 1, and see the scholar's work.
2) The scholar did everything correctly, and at the end got 9 = 13.
3) This statement is FALSE, so it would be the 2nd option (No it is not a solution)
Hope this helps and have a nice day!! :D
What Percent of 18 is 24?
Answer:
133.3333..% of 133 1/3 %
Step-by-step explanation:
100% of 18 is 18.
24-18 = 6.
6 is 33.33333...% of 18.
Therefore 24 is 133.3333..% of 18
or
24/18 = 4/3 = 1.333... = 133.33333...%
The percent 133.3% of 18 is 24.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
let x Percent of 18 is 24.
So, x% of 18 = 24
x/100 (18)= 24
18x = 2400
x= 2400/18
x= 133.33%
Hence, 133.33% of 24 is 18.
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The present age of father is thrice as old as the age of daughter 5 years ago. If 5 years hence ,the age of father will be twice the age of his daughter. Find their present ages
Answer:
Hence the daughter's present age is 15 years
The fathers present age is 35 years
Step-by-step explanation:
Let the present age of daughter be x
Let the present age of father be y
5 years ago;
Daughter's age = x - 5
Fathers age = y - 5
If the present age of father is thrice as old as the age of daughter 5 years ago, then;
y - 5 = 3(x-5)
y - 5 = 3x-15
y = 3x - 10 .... 1
In 5 years time;
Daughters age = x + 5
Fathers age = y + 5
If the age of father will be twice the age of his daughter in 5 years time then;
y+5 = 2(x+5)
y+5 = 2x + 10
y = 2x + 5 .....2
Equate 1 and 2;
3x - 10 = 2x + 5
3x - 2x = 5 + 10
x = 15
Since y = 2x + 5
y = 2(15) + 5
y = 35
Hence the daughter's present age is 15 years
The fathers present age is 35 years
Connor's family took a road trip to Niagara Falls. Connor slept through the last 15% of the trip. If Connor fell asleep after they had travel 663 miles what was the total length of the trip.
Answer:
The length of the trip is 780 miles
Step-by-step explanation:
Given
[tex]Sleep = 15\%[/tex]
[tex]Distance\ Travelled = 663[/tex]
Required
Determine the length of the trip
If Connor slept for 15% of the trip, then Connor was awake for 85%
This is calculated as:
[tex]Sleep + Awake = 100\%[/tex]
[tex]15\% + Awake = 100\%[/tex]
[tex]Awake = 100\% - 15\%[/tex]
[tex]Awake = 85\%[/tex]
Represent the required distance with D.
So the expression for when she was awake is:
[tex]85\% * D = 663[/tex]
Make D the subject
[tex]D = \frac{663}{85\%}[/tex]
Convert % to decimal
[tex]D = \frac{663}{0.85}[/tex]
[tex]D = 780[/tex]
Hence, the length of the trip is 780 miles
Fill in the blank to create a true equation:
-27 + _ = 0
7 + _ = 0
-3 + _ = +1
-7 + _ = -1
Answer:
27
-7
4
6
Step-by-step explanation:
Mental math.........
Answer: I do not know
Step-by-step explanation:
I dropped out of 2nd grade
3x-15=3
what is x in this equation?
Answer: The answer is 6
Step-by-step explanation: 3x-15=3 Add 15 to both side
3x=18 Divide 3 to both side
3= 3
x=6 The answer
Nicholas has 6 ounces of dish soap in an old, nearly empty bottle. He also has 22 ounces of dish soap in a new, unopened bottle. Which expression tells you how much dish soap Nicholas has in all? A. 6+22 B.6x22
9-7w=8w+8
what is w??
Answer:
w=1/15
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
9−7w=8w+8
9+−7w=8w+8
−7w+9=8w+8
Step 2: Subtract 8w from both sides.
−7w+9−8w=8w+8−8w
−15w+9=8
Step 3: Subtract 9 from both sides.
−15w+9−9=8−9
−15w=−1
Step 4: Divide both sides by -15.
−15w/−15 = −1/−15
w = 1/15
Solve the given system by substitution.
Answer:
p = 2; q = 2
Step-by-step explanation:
Simplify the expression below using the distributive property
Answer:
40+15i
Step-by-step explanation:
I don't know why you are doing this when you clearly know the answer. Have a good day.
A model village is built to scale.
It has a scale of 1 : 19.
A road has a real-life length of 1.14 km.
What is the length of the road in the model village in m?
Answer:
The length of the road in the model is 60 m.
Step-by-step explanation:
Given: scale = 1:19
real-life length of the road = 1.14 km
= 1140 m
Let the length of the road in the model be represented by d. A scale is a representative fraction that can be used to either increase or decrease the length of an object.
Scale = [tex]\frac{length on drawing}{actual length}[/tex]
The actual length is the real-life length given as 1140 m.
So that,
[tex]\frac{1}{19}[/tex] = [tex]\frac{d}{1140}[/tex]
19d = 1140
⇒ d = [tex]\frac{1140}{19}[/tex]
= 60
Therefore, the length of the road in the model is 60 m.
Four more than six times a number is 18.
Answer:
2.3 repeating
Step-by-step explanation:
thats what i got