Answer:
[tex]\boxed{\sf x = -4 \pm 2\sqrt{6} }[/tex]
Explanation:
3x² + 24x - 24 = 0
factor the coefficient
3(x² + 8x) -24 = 0
Halve the second term and square it
3(x + 4)² -24 -3(4)² = 0
simplify the answer
3(x + 4)² -72 = 0
add 72 on both sides
3(x + 4)² = 72
divide both sides by 3
(x + 4)² = 24
square root both sides
x + 4 = ±√24
subtract both sides by 4
x = -4 ± 2√6
Answer:
[tex]x=-4\pm2\sqrt{6}[/tex]
Step-by-step explanation:
Completing the square for quadratic in the form [tex]ax^2+bx+c=0[/tex]
Given equation:
[tex]3x^2+24x-24=0[/tex]
Factor out 3:
[tex]\implies 3(x^2+8x-8)=0[/tex]
Divide both sides by 3:
[tex]\implies x^2+8x-8=0[/tex]
Add 8 to both sides:
[tex]\implies x^2+8x=8[/tex]
[tex]\textsf{Add }\: \left(\dfrac{b}{2}\right)^2\: \textsf{ to both sides}:[/tex]
[tex]\implies x^2+8x+\left(\dfrac{8}{2}\right)^2=8+\left(\dfrac{8}{2}\right)^2[/tex]
[tex]\implies x^2+8x+16=8+16[/tex]
[tex]\implies x^2+8x+16=24[/tex]
Factor the left side:
[tex]\implies (x+4)^2=24[/tex]
Square root both sides:
[tex]\implies x+4=\pm2\sqrt{6}[/tex]
Subtract 4 from both sides:
[tex]\implies x=-4\pm2\sqrt{6}[/tex]
If y varies directly as x and x=3 when y=12, find x when y=3
Answer:
Answer:
y = 4x
Step-by-step explanation:
Given that x and y vary directly then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition x = 3 when y = 12
k = = = 4
y = 4x ← equation of variation
Cacular m<) ABC
Ayuda
Answer:
m∡ABC=140º
Step-by-step explanation:
Dr. shepherd is studying a bacterial colony with a population of 29,600 bacteria. the colony is
growing 5% per hour. how many bacteria will the colony contain in 12 hours?
if necessary, round your answer to the nearest whole number
bacteria
Answer:
53,157
Step-by-step explanation:
The population growth of a bacterial colony can be modeled by an exponential function of the form ...
p(t) = a·b^t
where a is the initial population and b is the growth factor. The growth factor is ...
b = 1 +r
where r is the growth rate.
__
In this problem we have ...
a = 29,600
b = 1 +5% = 1.05
t = 12
So, the population after 12 hours is
p(12) = 29600×1.05^12 ≈ 53,157
The colony will contain 53,157 bacteria in 12 hours.
please help me find unknown size of angles
Which of the following is a true statement?
6/16 > 7/24
3/5 <5/16
6/16 > 4/10
4/8 < 5/16
The fractional expression 18/48 is greater than 14/48 or 6/16 is greater than 7/24. Then the correct option is A.
What is inequality?Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.
The expressions are 6/16 and 7/24.
Then the LCM of the 16 and 24 will be 48.
Then the expressions will be 18/48 and 14/48.
The fractional expression 18/48 is greater than 14/48 or 6/16 is greater than 7/24.
Thus, the correct option is A.
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HELP!!! Simplify the expression.
3√25t²
Answer:
15t
Step-by-step explanation:
if you do the sqrt of 25 you get five than multiply that by 3 to get 15 then do the sqrt of t to get t
Hope this helps! ;-)
treatment definition
Answer: Heyaa!
If you mean medicine treatment the definition is...
The management and care of a patient to combat disease or disorder.If you mean just basic treatment the definition is...
The manner in which someone behaves toward or deals with someone or something.Hopefully this helps you:
- Matthew
. What is the area of this polygon?
10 m
9 m
8 m
15 m
Answer:10 squared plus 9 squared equals 15 squared
Step-by-step explanation:
take the square root of your answer
Which lists contain only rational numbers? Select all that apply.
-6, -7, -9, -11,61
5, 12, 18, 24, 30
6 4 11 6 13
3' 7'99' 13' 37
0.865, 0.4444, -6.37, -11.11
7.3, 4.15, -6.26, 9.1
(1) the fear of genetically modified foods is not based in facts. (2) the food and drug administration holds genetically modified foods to the same standard as traditional foods, which means that these new products are equally as safe as products that are already on grocery shelves. (3) in addition, common fruits, including nectarines and seedless grapes, are a result of genetic breeding. what would be the best way of revising the second sentence for a presentation?
In order to revise the second sentence for a presentation, the best thing to do would be to break it up into two sentences.
How can we revise the second sentence?The second sentence is quite long and so would not be the best fit for a presentation.
We can solve this by breaking it into two sentences such as:
The Food and Drug Administration holds genetically modified foods to the same standard as traditional foods. This means that these new products are equally as safe as products that are already on grocery shelves.This makes the presentation more readable and ensures that the information is better passed on.
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Answer:
B - Breaking into two sentences
Step-by-step explanation:
Edge 2023
Mr. reeves planted 5 beans and 12 tomato plants in his garden. What is the ratio of bean plants to tomato plants ?
Answer:
5/12 = 0.416666.... also in percentage 29,41 % of the plant are beans and 70.59 % are tomato plants.
Felix’s Feed Mill sells chicken feed for $8.00 per bag. This price is no longer high enough to create a profit. Felix decides to raise the price. He is considering four different plans.
Plan A: Raise the price by $0.10 each week until the price reaches $12.00.
Plan B: Raise the price by 10 percent each week until the price reaches $12.00.
Plan C: Raise the price by the same amount each week for 8 weeks, so that in the eighth week the price is $12.00.
Plan D: Raise the price by $0.25 each week until the price reaches $12.00.
Which plan will result in the price of the feed reaching $12.00 fastest?
plan A
plan B
plan C
plan D
Answer:
B
Step-by-step explanation:
essentially the plan that increases the price the most per week reaches the goal of $12 fastest.
plan A is $0.10 per week.
plan B it is not clear, if it means 10% of the original price every week, or every week 10% of the price of the previous week. I assume the first and simplest.
that means 10% of $8 = $0.80 per week.
plan C : the same amount every week until reaching $12. we need to increase in total by $4 (from $8 to $12). to reach these $4 in 8 weeks, we need to increase the price every week by 4/8 = $0.50.
plan D : $0.25 per week.
so, the plan with the highest increase every week and therefore the fastest one reaching $12 is plan B.
You need new shoes for work which cost $70. You earn $400 net income each week, but have expenses totaling $380 each week. If you set aside the difference between your weekly income and expenses, how many weeks will it take you to save enough to buy the shoes?
Amount earned per week=400-380=$20
Price of one shoe=70$
Total weeks
70/203.5Minimum 4 weeks
Answer:
4 weeks
Step-by-step explanation:
Given:
$400 = weekly net income$380 = weekly expensesTherefore,
Weekly surplus = weekly net income - weekly expenses
= $400 - $380
= $20
Given:
Cost of new shoes = $70Weekly surplus = $20Number of weeks = cost of new shoes ÷ weekly surplus
= $70 ÷ $20
= 3.5
= 4 weeks (rounded to nearest week)
Therefore, it will take 4 weeks to save enough to buy the shoes.
A class of 28 students has 13 boys and 15 girls. what is the ratio of boys to girls in the class?
Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. Which statement must be true?
The pool must have been empty for the entire interval.
The pool must have been the same depth at the start of the interval as it was at the end of the interval.
The pool must have been deeper at the end of the interval than it was at the start of the interval.
The pool must have been more shallow at the end of the interval than it was at the start of the interval.
The correct answer is option B which is the pool must have been the same depth at the start of the interval as it was at the end of the interval.
What is the rate of change?The rate of change is defined as the changes that occur in any data with respect to time like changing of level of water respect to time. Changing of the position of any object with respect to time that is speed.
Here in the question, it is given that Lionel computed the average rate of change in the depth of a pool over a two-week interval to be zero. The meaning of this statement is that the level of the water in the pool is the same as that of the level two weeks ago.
Therefore the correct answer is option B which is the pool must have been the same depth at the start of the interval as it was at the end of the interval.
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Lucia paints a certain room in 5 hours, and Marie paints the same room in 8 hours. How long does it take them to paint the room if they work together? Round to the nearest tenth.
Answer:
3.1 hrs painting together
Step-by-step explanation:
Lucia rate = 1 room/ 5 hr
Marie rate = 1 room/8hr
now combine the rates
1 room / ( 1/5 + 1/8) = 3.077 hrs
What is 4(5x^{2} )+16=400
Step-by-step explanation:
4(5x²) + 16 = 400
5x² + 4 = 100
5x² = 96
x² = 19.5
x = ±sqrt(19.5) = ±4.415880433...
solve the system using substitution. show all work. {4x + 5y = 7 {y = 3x - 10
Answer:
x = 3, y = -1.
Step-by-step explanation:
4x + 5y = 7
y = 3x - 10
Substitute for y = 3x - 10 in the first equation:
4x + 5(3x - 10) = 7
4x + 15x - 50 = 7
19x = 7 + 50 = 57
x = 57/19 = 3.
Now plug x = 3 in the second equation
y = 3(3) - 10
y = 9 -10
y = -1.
PLEASE HELP ME! I WILL MARK THE BRAINLEIST
Answer:
Part B:3/6 should be your answer answer:)!
Part C:The side length is 4 feet 6 inches, it is a rational number because both numbers can be showed as a fraction.
Step-by-step explanation:
6 cookies cost $3.60. What is the cost of 20 cookies?
Answer:
20 cookies - $ 12
Step-by-step explanation:
6 cookies - $3.60
20 cookies - X
X = (20 · 3,60) : 6
X = $ 12
Answer:
$12
Step-by-step explanation:
let the cost of 20 cookies= y
ok!!!
since 6 cookies ---------------$3.60
20 cookies will cost--------- y
making y subject
y= 3.60×20/6
y= 72/6=$12
therefore, 6 cookies will cost $ 12
A broken scale shows a false weight that is always higher than the actual weight by
the same number of grams. When a mobile phone is put on the scale, it shows 202
grams. When an headphone is put on the scale, it shows 221 grams. When the mobile
phone and the headphone are put on the scale together, it shows 415 grams. What is
the actual weight of the mobile phone in grams?
The actual weight of the mobile in grams is 194 grams.
What is Equation?In algebra, an equation can be defined as a mathematical statement consisting of an equal symbol between two algebraic expressions that have the same value.
As broken scale shows a false weight that is always higher than the actual weight by the same number of grams.
When a mobile phone is put on the scale, the real weight will be 'x'
but it shows,
x+a= 202
When an headphone is put on the scale, the real weight will be 'y'
but it shows,
y+a=221
When the mobile phone and the headphone are put on the scale together, the weight is
x+y+a= 415
So,
x+221=415 [Since y+a= 221 grams]
x= 194 grams
The actual weight of the mobile phone in grams is 194 grams.
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Somebody please help I’ve been stuck on this question for 2 hours
The volume of the cylinder when its radius is tripled is 405π unit³.
What is the volume of the cylinder when its radius is tripled?The volume of the cylinder when its radius is tripled is calculated by applying the formula for volume of a cylinder as follows;
V = πr²h
where;
r is the radius of the cylinderh is the height of the cylinderV is the volume of the cylinderV₁/r₁² = V₂/r₂²
where;
V₁ is the initial volume = 45π unit³
r₁ = 3 units
when the radius is tripled, r₂ = 3r₁
V₁/r₁² = V₂/r₂²
V₂ = (V₁/r₁²) x r₂²
V₂ = (V₁/r₁²) x (3r₁)²
V₂ = 9V₁
V₂ = 9 x 45π unit³
V₂ = 405π unit³
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How many edges does this shape have?
Answer:
8 Edges.
Imagine a cardboard box. The top has four edges and the bottom of it has another four.
Answer:
8
Step-by-step explanation:
count top edges then multiply by 2
The bases of Triangle A and Triangle B are equal. The ratio of the height of
Triangle A to the height of Triangle B is 4 : 5. If the height of Triangle A is
16 cm and its base is 12 cm, what is the area of Triangle B?
Answer:
A = 120 cm²
Step-by-step explanation:
The 4 part of the ratio relates to the height of triangle A , then
16 ÷ 4 = 4 cm ← value of 1 part of the ratio, then
5 parts = 5 × 4 cm = 20 cm
The area (A) of triangle B is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
Here b = 12 and h = 20 , then
A = [tex]\frac{1}{2}[/tex] × 12 × 20 = 6 × 20 = 120 cm²
What is the perimeter of ΔWXY?
11.57 cm
12.22 cm
12.46 cm
14.50 cm
The perimeter of the triangle ΔWXY is P = 14.50 cm
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ΔXYZ
Now , the measure of sides of the inscribed triangle ΔQRS is
QR = 2.93 cm
RS = 2.04 cm
QS = 2.28 cm
where the points Q , R and S are the midpoints of the sides of the triangle ΔXYZ
So , the measure of sides of the triangle are twice the lengths of the sides of triangle ΔQRS
And , the perimeter P = 2 ( 2.93 + 2.04 + 2.28 )
On simplifying , we get
P = 2 ( 7.25 )
P = 14.50 cm
Hence , the perimeter is P = 14.50 cm
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The complete question is attached below :
What is the perimeter of ΔWXY?
a) 11.57 cm
b) 12.22 cm
c) 12.46 cm
d) 14.50 cm
volume of hemisphere whos area is 12.5 ft squared
Answer:
radius r = 1.41047396 m
base circumference C = 8.86226925 m
volume V = 5.87697483 m^3
curved surface area A = 12.5 m^2
base surface area B = 6.25 m^2
total surface area K = 18.75 m^2
In Terms of Pi πbase circumference C = 2.82094792 π m
volume V = 1.87069919 π m3
curved surface area A = 3.97887358 π m^2
base surface area B = 1.98943679 π m^2
total surface area K = 5.96831037 π m
Step-by-step explanation:
r = radiusC = base circumferenceV = volumeA = curved surface areaB = base surface areaK = total surface areaπ = pi = 3.1415926535898√ = square rootHemisphere Formulas in terms of radius r:Volume of a hemisphere:V = (2/3)πr^3
Circumference of the base of a hemisphere:C = 2πr
Curved surface area of a hemisphere (1 side, external only):A = 2πr^2
Calculate the base surface area of a hemisphere (a circle):B = πr^2
Total surface area of a hemisphere:K = (2πr^2) + (πr^2) = 3πr^2
Answer:
Approximately 6.4 ft³
Step-by-step explanation:
A *hemisphere* is half of a sphere. As far as surface area goes, we not only need to account for the curved area, but also the area of the circular disc at the bottom. The area of the curved region is going to be half the area of the whole sphere. Since a sphere with radius r has a surface area of 4πr², the curved part of the hemisphere must have half that, or 2πr². Add in the area of the circular disc, πr², and we have a total area of 3πr². Setting this equal to the given area of 12.5 ft², we can solve for r:
[tex]3\pi r^2=12.5\\r^2=12.5/3\pi\\\\r=\sqrt{12.5/3\pi}[/tex]
Now, using the formula for the volume of a sphere, [tex]V=(4/3)\pi r^3[/tex], we can substitute our new value for r and solve:
[tex]V=(4/3)\pi r^3\\=(4/3)\pi(\sqrt{12.5/3\pi})^3\\\approx 6.4[/tex]
Mr. Plati's class has 3 1/2 quarts of paint. They use 2/3 of the paint for the mural.
How many quarts of paint did the class use for the mural?
Answer:
2.32
Step-by-step explanation:
What is the surface area of this rectangular pyramid?
5 mm
4 mm
4 mm
___ square millimeters
PLEASE HELP WILL MARK BRAINLIEST WITH 100 POINTS
What is the best way to describe the center of the data represented in this line plot?
Select from the drop-down menus to correctly complete the statement.
The
median
mean
is
1 inch
1.5 inch
1.8 inch
2 inches
Line plot titled Daily Rainfall. The number line is labeled Number of inches. There are 3 dots above 0, 3 dots above 1, 1 dot above 2, 1 dot above 3, 1 dot above 4, and 1 dot above 6.
.
Answer:
Mean = 1.8 in
Step-by-step explanation:
MedianThe Median is the middle value when all data values are placed in order of size.
Ordered data values: 0, 0, 0, 1, 1, 1, 2, 3, 4, 6
As there is an even number of data values, the middle value is the mean of the middle two data values. Therefore, the Median = 1 in
MeanThe Mean is the sum of all data values divided by the total number of data values.
[tex]\implies \textsf{Mean}=\dfrac{0+0+0+1+1+1+2+3+4+6}{10}=1.8[/tex]
Therefore, the Mean = 1.8 in
ConclusionThe Median is a better measure of central tendency when the data includes outliers (data values that are far away from the majority), as it is not affected by those outliers. As there does not appear to be any outliers in this data set, the mean can be used to best describe the center of the data.
Therefore, the Mean = 1.8 in
will mark brainliest to whoever gets it right
Answer:
x = 74 degrees
Answer:
74 degrees
Step-by-step explanation:
Remember that CO interior angles equal to 180 degrees so what you need to simply do is do 180 minus 106 degrees giving you 74 degrees as your answer