Answer:
The integers are
5 and 7
Step-by-step explanation:
Let
x ---> the first consecutive odd integer
x+2 ---> the second consecutive odd integer
we know that
The algebraic expression that represent this situation is
[tex]x(x+2)=x+30[/tex]
solve for x
[tex]x^2+2x=x+30\\x^2+2x-x-30=0\\x^2+x-30=0[/tex]
Solve the quadratic equation
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b\pm\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^{2} +x-30=0[/tex]
so
[tex]a=1\\b=1\\c=-30[/tex]
substitute in the formula
[tex]x=\frac{-1\pm\sqrt{1^{2}-4(1)(-30)}} {2(1)}[/tex]
[tex]x=\frac{-1\pm\sqrt{121}} {2}[/tex]
[tex]x=\frac{-1\pm11} {2}[/tex]
[tex]x=\frac{-1+11} {2}=5[/tex]
[tex]x=\frac{-1-11} {2}=-6[/tex] ---> is not a odd integer
For x=5
The numbers are
[tex]x=5\\x+2=7[/tex]
so
5 and 7
which unit rate is the lowest price per ounce 30 ounces or 40 ounces
Answer:
30 ounces is the lowest price
Step-by-step explanation:
30<40
A square has a perimeter of 80 yd. What is the lenght of each side?
Answer: each side is 20 yds.
Step-by-step explanation:
The formula to find the perimeter of a square is 4 × side so therefore if we divide 80 by 4 we get 20 and 20 *4 is 80.
2/3 of a 16 ounce bag how much is needed
Answer:
10 2/3
Step-by-step explanation:
Multiply 16 by 2/3
2/3 *16
32/3
Change the improper faction to a mixed number
10 2/3 of an ounce
Answer:
10.666 Ounces
Step-by-step explanation:
16 Ounces ÷ 3 = 5.333 Ounces
5.333 Ounces × 2 = 10.666 Ounces
What is the simplest form of 6 radical 8 plus 8 radical 2
Answer:
20[tex]\sqrt{2}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplify
[tex]\sqrt{8}[/tex] = [tex]\sqrt{4(2)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]
Thus
6[tex]\sqrt{8}[/tex] + 8[tex]\sqrt{2}[/tex]
= 6(2[tex]\sqrt{2}[/tex] ) + 8[tex]\sqrt{2}[/tex]
= 12[tex]\sqrt{2}[/tex] + 8[tex]\sqrt{2}[/tex]
= 20[tex]\sqrt{2}[/tex]
If x = 3 units, y = 6 units, and h = 4 units, find the area of the rhombus shown above using decomposition.
Whats the Area?
Answer:
= 12 square units
Step-by-step explanation:
Please look at the photo attached below, I think it is fit with your question
To find the area, substitute the values given in the question into the formula given below.
Area = base • height
= x • h
= 3 units • 4 units
= 12 square units
Answer:
the answer is 24
Step-by-step explanation:
because if you are in study island it says 24
At the hairdresser, Jenny had 27 centimeters cut
off her hair. How many decimeters of hair did
Jenny have cut off?
Answer: The answer is 270 decimeters
Step-by-step explanation:
There are 10 decimeters in a centimeter.
27 times 10 is 270.
So the answer is 270 decimeters.
Some please help me
There are two ways to solve this problem from the given situation. I'll type out both to help give you a better understanding of this problem.
Method 1: Straightforward, yet complicated
The shaded trapezoid has two base lengths of 25 mm and 50 mm, with a height of 35 mm.
The formula for the area of a trapezoid is the following:
[tex]A=\dfrac{a+b}{2}*h[/tex]
Where a and b are the base lengths and h is the height. Substitute the dimensions of the trapezoid and the formula changes to:
[tex]= \dfrac{25+50}{2}*35[/tex]
Simplifying the equation give us:
[tex]=\dfrac{2625}{2}[/tex]
[tex]=1312.5[/tex]
The trapezoid has an area of 1312.5 mm²
Method 2: Abstract, yet simple
The parallelogram is made up from 2 congruent trapezoids, and one of them is shaded. Thus, we just need to find the area of the parallelogram and divide it by 2 to get the area of a single trapezoid, which will give us the area of the shaded region.
The area formula of a parallelogram is simple, base times height.
The base is 25+50, or 75 mm. The height is 35 mm.
Multiplying these two values gives us 2625 mm². Dividing this by 2 gives us 1312.5 mm². That's the area of a single trapezoid (half the parallelogram), which should also be the area of the shaded region.
This is the same answer we got from method 1.
Conclusion:
The answer is 1312.5 mm²
Both methods give the same answer, which means they each make sure that the other is correct. Let me know if you need any clarifications, thanks!
~ Padoru
Plss help!!! This is just super confusing. : /
Answer:
x^2 +23x +49
Step-by-step explanation:
You know the area of a rectangle is given by the product of its length and width.
The area of the shaded region is the area of the larger rectangle with the area of the square white space subtracted.
The area of the larger rectangle is ...
large area = (length)(width) = (x+10)(2x+5)
Multiplying this out, we find the large area to be ...
large area = 2x^2 +5x +20x +50
large area = 2x^2 +25x +50
The area of the square can be found the same way:
square area = (x +1)(x +1) = x^2 +2x +1
__
Then the shaded area is the difference of these:
shaded area = (large area) - (square area)
shaded area = (2x^2 +25x +50) - (x^2 +2x +1)
shaded area = 2x^2 +25x +50 -x^2 -2x -1 . . . . . . eliminate parentheses
shaded area = x^2 +23x +49 . . . . collect terms
6. Write the following multiplications as exponential abbreviations.
a. 5x5
b. 7 x 7 x 7 x 7
c. 2 x 2 x 2
d. 9 x 9 x 9 x 9 9
a. 5²
b. 7⁴
c. 2³
d. 9⁵
Explanation:
An exponent is the number of times a number is multiplied by itself.
a. 5x5 = 5² ( five is multiplied two times)
b. 7 x 7 x 7 x 7 = 7⁴ ( seven is multiplied four times)
c. 2 x 2 x 2 = 2³ ( two is multiplied three times)
d. 9 x 9 x 9 x 9 x 9 = 9⁵ ( nine is multiplied five times)
Final answer:
Exponential abbreviations express repeated multiplication of the same number as a base raised to a power. For example, 5x5 becomes 5², and 7x7x7x7 becomes 7⁴. This notation simplifies multiplication into a more compact and manageable form.
Explanation:
Writing Multiplications as Exponential Abbreviations
To write the given multiplications as exponential abbreviations, we look for repeated factors and express them as a base number raised to the power of how many times it occurs. Here's how to do it:
a. 5x5 is 5 multiplied by itself 1 more time, so it is written as 5².b. 7 x 7 x 7 x 7 is 7 multiplied by itself 3 more times, so it is written as 7⁴ (7 to the fourth power).c. 2 x 2 x 2 is 2 multiplied by itself 2 more times, so it is written as 2³.d. 9 x 9 x 9 x 9 x 9 is 9 multiplied by itself 4 more times, so it is written as 9⁵ (9 to the fifth power).This process simplifies multiplication by using exponents to indicate the number of times a base is used as a factor.
If h(x) = -2x+3 and g(x)= n2 -1, what if h(g(4)) ?
What are the best approximations of the solutions to this system?
(-1.2,-2.0) and (1.9,2.2) are the best approximations of the solutions to this system.
Option B
Step-by-step explanation:
Here, we have a graph of two functions from which we need to find the approximate value of common solutions. Let's find this:
First look at where we have intersection points, In first quadrant & in third quadrant.
At first quadrant:
Draw perpendicular lines from x-axis & y-axis from this point . After doing this we can clearly see that the perpendicular lines cut x-axis at x=1.9 and y-axis at y=2.2. So, one point is (1.9,2.2)
At Third quadrant:
Draw perpendicular lines from x-axis & y-axis from this point. After doing this we can clearly see that the perpendicular lines cut x-axis at x=-1.2 and y-axis at y= -2.0. So, other point is (-1.2,-2.0).
the estimated population of egypt in 2011 is about 81 million. this is a 1.8% growth rate over the previous year. assuming this continues what would be the population be in 2005?
Population of Egypt in 2005 is 72.64 million.
Step-by-step explanation:
We have ,The estimated population of Egypt in 2011 is about 81 million. this is a 1.8% growth rate over the previous year. According to question , population in year 2010 = population in year 2011 - 1.8% of population in year 2011 i.e.
population in year 2010 = [tex]81 - \frac{81(1.8)}{100}[/tex] = 79.52 million
Similarly, population in year 2009 = [tex]79.52 - \frac{79.52(1.8)}{100}[/tex] = 78.10 million
population in year 2008 = [tex]78.10 - \frac{78.10(1.8)}{100}[/tex] = 76.70 million
population in year 2007 = [tex]76.70 - \frac{76.70(1.8)}{100}[/tex] = 75.32 million
population in year 2006 = [tex]75.32 - \frac{75.32(1.8)}{100}[/tex] = 73.97 million
population in year 2005 = [tex]73.97 - \frac{73.97(1.8)}{100}[/tex] = 72.64 million
Therefore, population of Egypt in 2005 is 72.64 million.
Final answer:
To find Egypt's population in 2005 given a 1.8% annual growth rate and a 2011 population of 81 million, we rearrange the exponential growth formula and calculate backward, resulting in an estimated population of approximately 74.8 million in 2005.
Explanation:
The question involves calculating the population of Egypt in 2005, given its estimated population of 81 million in 2011 and an annual growth rate of 1.8%.
To find the population in 2005, we use the formula for exponential growth: P = [tex]P_oe^{rt[/tex],
where P is the future population, P₀ is the initial population, r is the growth rate, t is the time in years, and e is the base of the natural logarithm.
However, in this scenario, since we are calculating backward and we know the future population,
we rearrange the formula to find the initial population: P₀ = [tex]\frac{P}{e^{rt}}[/tex]
Using a growth rate of 1.8% (or 0.018 as a decimal) over 6 years (from 2005 to 2011), the formula becomes:
P₀ = [tex]\frac{81 \text{ million}}{e^{0.018*6}}[/tex]
After calculation, we find that the population of Egypt in 2005 would be approximately 74.8 million.
The volume of a container varies jointly with the square of its radius, r, and its height, h. The
container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic
centimeters. What is the volume of a container with a radius of 4 centimeters and a height of 4
centimeters?
Solution:
The volume of a container varies jointly with the square of its radius, r, and its height, h
Therefore,
[tex]v \propto r^2h\\\\v = k \times r^2h ----------- eqn\ 1[/tex]
The container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic centimeters
Substitute v = 377 and h = 10 and r = 6 in eqn 1
[tex]377 = k \times 6^2 \times 10\\\\377 = 360 \times k\\\\k = \frac{377}{360}\\\\k = 1.047 \approx 1.05[/tex]
What is the volume of a container with a radius of 4 centimeters and a height of 4 centimeters?
Substitute k = 1.05 and r = 4 and h = 4 in eqn 1
[tex]v = 1.05 \times 4^2 \times 4\\\\v = 1.05 \times 16 \times 4\\\\v = 67.2[/tex]
Thus volume of a container with a radius of 4 centimeters and a height of 4 centimeters is 67.2 cubic centimeter
The volume of the container with a radius of 4 cm and a height of 4 cm is 201.088 cm³.
Explanation:To find the volume of a cylinder, we can use the formula:
V = πr²h
Given that the container has a height of 10 cm, a radius of 6 cm, and a volume of 377 cm³, we can substitute these values into the formula:
V = 3.142 × (6 cm)² × 10 cm
After evaluating the expression, we find that the volume of the container is 1130.152 cm³.
To find the volume of the container with a radius of 4 cm and a height of 4 cm, we can substitute these values into the formula:
V = 3.142 × (4 cm)² × 4 cm
After evaluating the expression, we find that the volume of the container is 201.088 cm³.
The volume of a baseball is about
13.39 cubic inches. What is the diameter? Round to the nearest tenth.
A full explanation would be appreciated.
Answer: 2.9 inches
Step-by-step explanation:
[tex]Volume_{sphere}=\dfrac{4}{3}\pi r^3\\\\\\Given: V=13.39\\\\\\13.39=\dfrac{4}{3}\pi r^3\\\\\\\dfrac{3}{4\pi}(13.39)=r^3\\\\\\\sqrt[3]{\dfrac{3}{4\pi}(13.39)} = r\\\\\\\large\boxed{2.9=r}[/tex]
. Given a bag of 80 marbles with 45 red marbles, 20 blue marbles, 10 green marbles and 5 yellow marbles. How many marbles are blue or green? *
Answer:
30 are blue or green. If you want a fraction, it's 3/8
Step-by-step explanation:
It already states 20 are blue and 10 are green
20 + 10 = 30
and it's out of 80 marbles, so 30/80 which simplified (both divided by 10) is 3/8
Answer:
30 marbles are either blue or green
Step-by-step explanation:
To get the solution add the blue and green marbles up
20+10 = 30
30 marbles are either blue or green
How many apples is 5 plus 5
Answer:
10 apples
5+5 is 10
there are 10 apples. since 5 plus 5 is ten.
Using the following diagram, tick the correct angles which are congruent to the angles given in the first column.
(20 points)
Answer:
Step-by-step explanation:
Angle 1 = 1, 3, 5, 7
Angle 3 = 1, 3, 5, 7
Angle 4 = 2, 4, 6, 8
Pretty much just look at the congruent symbols and you can figure it out.
You have 10 marbles in a bag: 3 blue, 2 green, 4 yellow, and 1 purple. If you close your eyes and choose a marble at random, what is the simple probability that you will choose a blue marble?
Answer:
3/10
Step-by-step explanation:there are 10 marbles all together three blue ones
Answer:
[tex]\frac{3}{10}[/tex]
Step-by-step explanation:
You have 3 possibilities to get a blue marble out of 10
Can I get some help please?
Answer:yes because 34-12=22
Step-by-step explanation:
48 is what percent of 642
Answer: 7.48
Step-by-step explanation:
Let the missing percent be x.
The question implies: 48 = x% of 642
Which means x/100 × 642 = 48
Multiply the numerators = x × 642 = 642x
Multiply the denominators= 100 x 1 = 100
Therefore, 642x /100 = 48
Then, cross multiply:
642x = 100 x 48
642x = 4800
Divide both sides by 642 to get the value of x
x = 4800/642
x = 7.48.
What is the lowest common denominator of x+9/2x and 14/x-5?
Step-by-step explanation:
Denominators of both the fractions are 2x and (x - 5)
Therefore,
Lowest common denominator
[tex]= 2x \times (x - 5) \\
= 2 {x}^{2} - 10x[/tex]
What does 1+3x-7x equal to
Answer:
1 - 4x
Step-by-step explanation:
Combine like terms.
To simplify the expression, we can combine like terms.
= 1 + 3x - 7x
= 1 + (3x - 7x)
= 1 + (-4x)
= 1 - 4x
Note that this is not required but its something that should done, which is turn the equation into standard form.
= -4x + 1
Best of Luck!
3/5 times what equals 2 2/3
Answer:
13 1/3 or 40/3
Step-by-step explanation:
to find the answer you will divide 2 2/3 and 3/5
2 2/3 divided by 3/5
as my Math Teacher says you should do KFC or Keep Flip Change
the equation now is 2 2/3 times 5/3
now you should write 2 2/3 as a improper fraction
2 2/3= 8/3
8/3 times 5/3= 40/3 or 13 1/3
Answer:
13 1/3
Step-by-step explanation:
i think that is it
Help please! Will give Brainliest as always.
Answer:
984 square centimeters
984 cm^2
Step-by-step explanation:
Base: 10 × 24 = 240
Rectangle Sides: 13 × 24 = 312 (×2 = 624)
Triangle Sides: 12 × 10 = 120 (÷2 ×2 = 120)
Add: 240 + 624 + 120 = 984
Hannah's necklace is 10 1/5 inches long. Erin's necklace is 2 2/3 times as long as Hannah's. Abot how long is erins necklace
Erin's Necklace is 47.6 inch long.
Step-by-step explanation:
Hannah 's necklace is 10 1/5 inches long which means = (50+1)/5 = 51/5
Erin's necklace is 2 2/3 times = (6+8)/3 = 14/3 longer than Hannah's
Solving for this :
Erin's necklace = [tex]14/3 *51/5[/tex]
⇒ [tex]714/15[/tex]
⇒ 47.6 Inch
Erin's Necklace is 47.6 inch long.
For the triangle shown, three possible lengths of x, y, and z are given. Find the measurements for the other two sides in
each case
Please answer
Answer:
what are the numbers if there are more than one number then add all numbers up
Step-by-step explanation: for example
one side of cube :5
another side: 4
another side: 8
another side: 3
add all number up 5+4+8+3=20
PLEASE PLEASE HURRY! THANK YOU SO MUCH!!
This equation can be used to find h the number of hours it will take flo and bryan to mow the lawn
h/3+h/6=1
The answer is c. 2
1. List all needed information from the problem
2. Restate the question in your own words, what is it asking you to find (not just x)?
3. What formulas and/or operations do you need to solve this problem?
4. Explain what your variables and values are (if necessary)
5. Work out the problems, using numbers and operations and explaining (in words) all steps (include the words "why" and "because", properties) (substituting the answer in is not working out the problem)
6. Write your final answer in a sentence, restating the question.
7. Why does your answer make sense? This is a good step to show how you checked your work.
Answer:
1. The information from the problem illustrates the number of hours flo and bryan works jointly to mow the lawn.
2. The question demonstrates the numbers of hours worked by the two individuals i.e. flo and bryan to mow the lawn. Find the numbers of hours worked i.e h=? by flo and bryan to mow the lawn.
3. H/3+h/6=1
Take LCM i.e. (2H+H)/6=1
Now add H and and move the 6 on the other side and multiply, that becomes
3H=6
Now take 3 on the other side and divide by 6, which becomes the answer i.e. H=2.
4. Variables are H and values are the hours worked.
5. The problem in this question , why the number of hours are missing which we have to find and gives it a sense that how many hours needed to mow a lawn.
6. The time takes for both of them to mow lawn is 2 hours, which is flo works more than bryan to mow a lawn.
7. If you want to check that your anser is correct put the answer in the equation, if both sides come same then the answer is correct, for instance in the same quwstion where answer is H=2. Now put H in the equation i.e.
H/3+H/6=1
2/3+2/6=1
4+2/6=1
6/6=1
1=1
Hence proved. Enjoy :)
12.
The perimeter of a garden is 82 feet. The length
is 5 more than twice the width. What is the width
of the garden?
A.29feet
C.24 feet
B. 25 feet and 2/3
D. 12 feet
Answer:
D. 12 feet
Step-by-step explanation:
Perimeter of a rectangle = 2(L+W)
Where L is length and W is the width.
Given
perimeter = 82 feet
Length is 5 more than 2w
That’s L = 5 + 2w
Now substitute 5 + 2w for L in the formula above
We have
82 = 2 ( 5 + 2w + w)
Simplify the bracket
82 = 2(5 + 3w)
Distribute 2 into (5 + 3w)
82 = 2 x 5 + 2 x 3w
82 = 10 + 6w
Subtract 10 from both sides
82 - 10 = 10 - 10 + 6w
72 = 6w
Divide both sides by 6
72/6 = 6w/6
12 = w
W = 12 feet
The width of the garden is 12 feet.
Explanation:To find the width of the garden, we can set up an equation using the given information. Let's say the width of the garden is 'w' feet. According to the problem, the length is 5 more than twice the width, so the length would be '2w + 5' feet. The perimeter of a rectangle is equal to twice the sum of its length and width. So, in this case, the perimeter would bec
[tex]2(w + 2w + 5) = 82[/tex]feet. Simplifying this equation, we get 6w + 10 = 82. Solving for 'w', we subtract 10 from both sides and divide by 6, giving us w = 12 feet. Therefore, the width of the garden is 12 feet.
Learn more about Perimeter and dimensions here:https://brainly.com/question/33156479
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Consider P(x) = x4(x − 2)3(x + 1)2. For each zero, determine if the graph crosses the x-axis. How do you know?
Answer:
-1 — does not cross0 — does not cross2 — crossesStep-by-step explanation:
P(x) = x^4(x -2)^3(x +1)^2 has zeros at ...
-1 — multiplicity 2 (does not cross)0 — multiplicity 4 (does not cross)2 — multiplicity 3 (crosses)The zeros that have even multiplicity are points where the graph does NOT cross the x-axis. This is true because an even power of a number does not change sign when the sign of the number changes.
What is the Premeter of 4' square
Answer:
16'.
Step-by-step explanation:
A square has 4 equal sides so it is 4 * 4' = 16'.