By factor decomposition and algebra properties, the number √180 is equal to 6√5.
How to determine the most simple form of a square root by factor decomposition and algebra properties
In this problem we find an imperfect square root, that is, a square root whose root is an integer. However, we can simplify the expression by means of algebra properties and by redefining the number inside the root operator as a product of integers. Now we proceed to show the complete steps of the procedure:
First, decompose the number inside the root operator by factor decomposition:
√180 = √(2² · 3² · 5)
Second, simplify the resulting expression by algebra properties concerning roots:
√180 = √2² × √3² × √5
√180 = 2 × 3 × √5
√180 = 6√5
Therefore, the number √180 is equivalent by algebra properties and factor decomposition to 6√5.
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Find the solution of the differential equation that satisfies the given initial condition. (dP)/(dt) = sqrt(Pt) P(1) = 2
The solution of the differential equation (dP)/(dt) = sqrt(P(t)) with initial condition P(1) = 2 is P(t) = 0.74 exp(t)
To find the solution of a differential equation, take the integral of both sides, then apply the initial condition.
In the given problem:
dP/dt = sqrt (P(t))
dP/P(t) = dt
Take integral of both sides.
Recall that:
∫ 1/x dx = ln x + C
∫ dt = t + C
Hence,
1/P dP = dt
∫ 1/P dP = ∫ dt
ln P = t + C , with C = constant
P(t) = C . exp(t)
Apply the initial condition:
P(1) = 2
C . exp(1) = 2
C = 2/exp(1) = 0.74
Hence, the solution is:
P(t) = 0.74 exp(t)
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Double knon facts to find each product 5x8
Answer:2304 is the answer
Step-by-step explanation:
Answer:
40
Step-by-step explanation:
Hi, I am wondering how to do this math problem step-by-step.
[ -4 - ( -26)] + 19 ÷ 24 + (7^2 – 35)
Thank you! :)
Answer: Step 1: Start by evaluating the expressions inside the parentheses first.
For the first set of parentheses: -4 - (-26) = -4 + 26 = 22
For the second set of parentheses: 7^2 - 35 = 49 - 35 = 14
Step 2: Next, substitute the values from step 1 into the original expression and perform the arithmetic in the order of operations:
BODMAS rule
Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)
[22] + 19 ÷ 24 + 14
Step 3: Perform the division: 19 ÷ 24 = 0.7916666666666667
Step 4: Perform the addition: 22 + 0.7916666666666667 + 14 = 36.791666666666664
So the final answer is 36.791666666666664
Step-by-step explanation:
How do you solve the surface area this a parallelogram answer B I will give you 10 points
Answer:
c
Step-by-step explanation:
1 1 _x² - 7x+10
Solve +
2 2x
4x
-
Which proportion is equivalent to the original
equation?
O
x+2_x²-7x+10
4x
2x
x-1_x²-7x+10
4x
2x
x+1_x²²-7x+10
4x
2x
by rewriting the equation as a proportion.
DONE
The value of x from the system of equation will be 1 and 8 and the proportion equivalent is x² - 9x + 8 =0.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
Given the expression 1/2+1/2x=x² - 7x+10/4x
Multiply the first term by 2x/2x and second term by 2/2 to have:
2x/4x + 2/4x = (x² - 7x+10)/4x
Multiply through by 4x to have:
2x+2=x² - 7x+10
Collect the like terms and factorize
x² - 7x+10-2x-2=0
x²-9x+8=0
Now factorize the given equation
x²-8x-x+8=0
x(x-8)-1(x-8)
(x-1)(x-8)=0
x=1 and x=8
Hence, the value of x from the system of equation will be 1 and 8 and the proportion equivalent is x² - 9x + 8 =0.
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An object is moving at a speed of 5 feet every 6 weeks express this speed in centimeters per day
The movement of the object in centimeter per day is solved to be
3.63 cm per dayHow to find the centimeter per day equivalent of the movement of the objectThe given problem is solved by conversion of units
feet to centimeters
1 feet = 30.48 cm
5 feet = ?
cross multiplying
? = 5 * 30.48
? = 152.4 cm
week to days
7 days = 1 week
? = 6 weeks
cross multiplying
? = 6 * 7
? = 42 days
speed in centimeters per day
= 152.4 cm / 42 days
= 3.63 cm per day
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can you please help me
Answer: yes
Step-by-step explanation:
Jackie has a box of mixed spring flower bulbs containing 10 daffodils, 12 hyacinths, and 8 tulips. Jackie reaches into the box, randomly chooses a bulb, plants it, then chooses another, and plants it. What is the probability that Jackie plants a tulip followed by a hyacinth?
The required probability of Jackie planting a tulip followed by a hyacinth is 0.1684.
What is probability?Probability is defined as the possibility of an event being equal to the ratio of the number of favorable outcomes and the total number of outcomes.
To determine the probability that Jackie plants a tulip followed by a hyacinth, we can use the formula for conditional probability:
P(tulip and hyacinth) = P(tulip) × P(hyacinth | tulip).
First, we'll find the probability of Jackie choosing a tulip on the first pick: P(tulip) = 8/30 (there are 8 tulips out of 30 total bulbs in the box).
Next, we'll find the probability of Jackie choosing a hyacinth on the second pick, given that she chose a tulip on the first pick:
P(hyacinth | tulip) = 12/29 (there are 12 hyacinths remaining out of 29 total bulbs remaining in the box).
Finally, we'll multiply these two probabilities together to find the overall probability:
P(tulip and hyacinth) = 8/30 × 12/29 = 16/95 = 0.1684.
So the required probability is 0.1684.
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The number of muffins that a baker makes each day is 40% of the total number of muffins she makes
Answer:
A) 90 muffins were baked Monday
B) 24 blue berry muffins were made Tuesday.
Step-by-step explanation:
A
40% for what number is 36
.4x = 36 Divide both sides by .4
x = 90
B
40% of 60 is what number?
.4 x 60 = 24
The average height of the International Space Station is 400km above the Earth. An astronaut on board the International Space Station sights along a tangent line to Earth, viewing Houston Space Center. If the diameter of the Earth is approximately 12,800 km, how far is the astronaut from the Space Center.
The astronaut is located at a distance of 2297.83 km from the Space Center
How to determine how far is the astronaut from the Space Center.From the question, we have the following parameters that can be used in our computation:
Average height (h) = 400 km above the earth
Diameter (d) of the earth = 12,800 km
Because the astronaut on board the International Space Station sights along a tangent line to Earth,
The distance (x) between the astronaut and the Space Center can be calculated using the following secant theorem
x² = h * (h + d)
Substitute the known values in the above equation, so, we have the following representation
x² = 400 * (400 + 12800)
Evaluate the products
x² = 5280000
Take the square root of both sides
x = 2297.83
Hence, the distance is 2297.83 km
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Solve for x: 4(x + 2) = 3(x − 2)
Answer:
[tex]\huge\boxed{\sf x = -14}[/tex]
Step-by-step explanation:
Given equation:4(x + 2) = 3(x - 2)
Distribute4x + 8 = 3x - 6
Subtract 3x from both sides4x - 3x + 8 = -6
x + 8 = -6
Subtract 8 from both sidesx = -6 - 8
x = -14[tex]\rule[225]{225}{2}[/tex]
Need help plss answer
Answer:
x ≤ 1
Step-by-step explanation:
In the graph shown, the blue arrow is facing to the left, so we know that the inequality is some kind of less-than inequality (x < number).
We can also see that the blue arrow starts at a filled-in circle, so we know that the inequality will use the less-than-or-equal-to relator (≤).
Finally, the filled-in dot is at 1, so we can construct the equation:
x ≤ 1
Note that you could replace x with any other variable or even a blank space, since it isn't specified by the number line.
solve for the quadratic equation graphically using two different approaches when necessary guve your solutions to the nearest hundredth 16x^2-400=0 a.x=-1.1 or x=-1 b.x=1.12 or x=-0.82 c.x=5 or x=-5 d.x=1 or x=-1
The solution to the quadratic equation is x=5 and x = -5. Hence option C is the correct option.
What is a quadratic equation?
A quadratic equation is any equation in algebra that can be rearranged in a standard form where x represents an unknown value and a, b, and c represent known numbers, with a ≠ 0.
Given equation is
16x²-400=0
To solve the quadratic equation, equate the left side expression with y and graph it. The x-intercepts are the solution of the equation.
The equation becomes y = 16x²-400
Draw the graph.
The x-intercepts are x=5 and x = -5.
Divide the given equation by 16:
x²-25=0
To solve the quadratic equation, equate the left side expression with y and graph it. The x-intercepts are the solution of the equation.
The equation becomes y = x²-25
Draw the graph.
The x-intercepts are x=5 and x = -5.
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Which of the following are solutions of the inequality 12> 6z
Answer:
-2
-1
0
1
only this digit could satisfy your given function
In △ABC, m∠A = α, m∠B = β, m∠C = γ. AB = c, AC = b, BC = a. Solve the triangle if a=45.0, b=26 and α= 64 degrees
The lengths of the sides of the triangle and the measures of the interior angles of the triangle found using the law of sines;
AB ≈ 49.4, AC = 26, BC = 26
m∠A = 64°, m∠B ≈ 31.3°, m∠C ≈ 84.7°
What is the law of sines?The law of sines states that the ratio of the length of a side of a triangle to the opposite angle to the specified side, is the same for the three sides and angles of a triangle.
The length of AB = c
The length of side BC = a = 45.0
The length of AC = b = 26
The measure of angle α = 64°
According to the law of sine, we get;
a/(sin(α) = b/sin(β) = c/sin(γ)Plugging in the known values, we get;
45.0/(sin(65°) = 26/sin(β) = c/sin(γ)
sin(β) = 26 × sin(64°)/45.0
β = arcsin(26 × sin(64°)/45.0) ≈ 31.3°
m∠B = β ≈ 31.3°
According to the angle sum property of a triangle, we get;
α + β + γ = 180°
γ = 180° - (α + β)
Therefore; γ ≈ 180° - (64 + 31.3)° = 84.7°
m∠C = Angle γ ≈ 84.7°
45.0/(sin(65°) = c/sin(84.7°)
c = sin(84.7°) × 45.0/(sin(65°) ≈ 49.4
AB = c ≈ 49.4
The measure of the sides and angles of the triangle are;
AB ≈ 49.4, AC = 26, BC = 45.0m∠A = 64°, m∠B ≈ 31.3°, m∠C ≈ 84.7°Learn more about the law of sines here:
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Triangle ABC is similar to triangle EDF. Find the length of BC.
Answer:
17.5
Step-by-step explanation:
Angle EDF added up equals to 37.5
12+8=20
37.5-20=17.5, so the answer is 17.5, hope this helps :)
Answer:
BC = 5
Step-by-step explanation:
since the triangles are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{BC}{DF}[/tex] = [tex]\frac{AC}{EF}[/tex] ( substitute values )
[tex]\frac{BC}{7.5}[/tex] = [tex]\frac{8}{12}[/tex] ( cross- multiply )
12 BC = 60 ( divide both sides by 12 )
BC = 5
Ian's bird feeder holds 1 1/2 cups of birdseed. Ian is filling the bird feeder with a scoop that holds 3/4 of a cup. How many scoops of birdseed will Ian put into the feeder
The required scoops of birdseed Ian will put in the feeder are 2.
What is the Ratio?The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.
Here,
Ian's bird feeder holds 1 1/2 cups of birdseed.
Ian is filling the bird feeder with a scoop that holds 3/4 of a cup.
So, the ratio of the cup to scoop gives the number of cups,
Number of scoops = 1 1/2 / [3/4]
= 3/2 × 4/3
= 2 scoops
Thus, the required scoops of birdseed Ian will put in the feeder are 2.
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Can you help me with this please?
The values of x in the figures are (13) 40⁰ (14) 130⁰ (15) 112⁰ (16) 23⁰ (17) 22⁰ (18) 120⁰
How to determine the values of x?You should be knowledgeable with various types of angles for better understanding of the solutions
The solutions appear as follows
13) 43+57=100
=180-100=80 angle on a straight line
this means that 80/2= 40⁰
(14) 108-(80+50)
=180-130=50
x=180-50 = 130
(15) 180-44 angle on a straight line
= 136/2 68
68+44=112
(16) x=122-90 two opposite interior angles equals one exterior
x= 23⁰
(17) 103-x+2x=6x-7 (two opposite interior equals one exterior angle)
x-6x=-7-103
-5x=-110
Making x the subject of the relation we have
x= 110/5 = 22
(18) 60+60 = 120 angles of an equilateral triangle
x=120
In conclusion the various values of x are 40,130,112,23,22,120 respectively
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Mr. Argo went to dinner with a friend at Outfront Steakhouse. His dinner cost $40, and he left a 20% tip. What was his total cost?
Answer = $
Help please.
Answer: 48$
Step-by-step explanation:
20% of 40$ is 8$ so its 48$
Answer:
what the other guy said, 48$
Step-by-step explanation:
Question 5 PLEASEEE
Answer:
C) f(x) = 2x - 3
Step-by-step explanation:
When you multiply the x value by 2 and divide it by three, you get the number that is in the right column.
14. The domain of the function f(x) = 13x-x² is given as {-2, -1, 0, 1, 2}. What is the range? Show your
work.
The range of the function is {-30, -14, 0, 12, 22}
How to determine the range of the function?From the question, we have the following parameters that can be used in our computation:
f(x) = 13x - x²
Then, we have the domain to be
{-2, -1, 0, 1, 2}
Substitute {-2, -1, 0, 1, 2} for x in f(x) = 13x - x²
So, we have
f(-2) = 13(-2) - (-2)² = -30
f(-1) = 13(-1) - (-1)² = -14
f(0) = 13(0) - (0)² = 0
f(1) = 13(1) - (1)² = 12
f(2) = 13(2) - (2)² = 22
Hence, the range is {-30, -14, 0, 12, 22}
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in fig ps is median bisecting ∠P find ∠qps
Considering the figure where PS is median bisecting ∠P. ∠QPS is calculated to be 45 degree
What do we mean by bisection of angle?A ray that divides an angle into two equal pieces is known as an angle bisector or the bisector of an angle.
In the given figure, PQ = PR hence ∠Q = ∠R isosceles triangle
∠Q + ∠R + ∠P = 180
45 + 45 + ∠P = 180
90 + ∠P = 180
∠P = 180 - 90
∠P = 90
PS is the angle bisector that divides ∠P which is angle 90 degrees, into two equal parts which are ∠QPS and ∠RPS, so that ∠QPS = ∠RPS
∠QPS + ∠RPS = 90 (adjacent angles)
∠QPS + ∠QPS = 90 (angle bisection)
2∠QPS = 90
∠QPS = 45
hence ∠QPS = 45 degrees
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Graduation is 4 years away and you want to have $500 available for a trip. If your bank is offering a 4-year CD (certificate of deposit) paying 2.8% simple interest, how much do you need to put in this CD to have the money for your trip?
can someone please explain I am so lost with this
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$ 500\\ P=\textit{original amount deposited}\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ t=years\dotfill &4 \end{cases} \\\\\\ 500 = P[1+(0.028)(4)] \implies 500=1.112P\implies \cfrac{500}{1.112}=P\implies 449.64\approx P[/tex]
determine the value of d that complete the square of x^2+dx+64
Answer:
d = 16
Step-by-step explanation:
x² + dx + 64
since x² and 64 are perfect squares, this is of the form
(x + 8)²
= (x + 8)(x + 8) ← expand using FOIL
= x² + 8x + 8x + 64
= x² + 16x + 64 ← in the form x² + dx + 64
with d = 16
Solve.
12. x + 6 / 2 = 12
Answer:
The answer is 18
Step-by-step explanation:
(x + 6) ÷ 2 = 12
Multiply both sides by 2 we get,
2 × (x + 6) ÷ 2 = 12 × 2
x + 6 = 24
Subtract 6 from both sides we get,
x + 6 - 6 = 24 - 6
x = 18
Thus, The value of x is 18
Answer:
x = 18
Step-by-step explanation:
Now we have to,
→ find the required value of x.
The equation is,
→ (x + 6)/2 = 12
Then the value of x will be,
→ (x + 6)/2 = 12
→ x + 6 = 12 × 2
→ x + 6 = 24
→ x = 24 - 6
→ [ x = 18 ]
Hence, the value of x is 18.
William opens a savings account with $300, and
automatically deposits $100 monthly. He hopes to save up
a minimum of $1,500 to buy himself an electric bike.
Write an inequality to represent the context.
Answer:
300 + 12x ≥ 1500
where x represents the number of months William needs to save.
what is the domain of (x+3)^2/25 - (y-1)^2/4=1
The domain of the function is all values of x such that x ≥ 2.
What is Function?A function is a relation from a set A to a set B where the elements in set A only maps to one and only one image in set B. No elements in set A has more than one image in set B.
Domain is the set of inputs which are the values of x.
The given expression is,
(x+3)^2/25 - (y-1)^2/4 = 1
(x+3)^2/25 - 1 = (y-1)^2/4
[tex](\frac{x+3}{5})^2 - 1=(\frac{y-1}{2})^2[/tex]
[tex]\sqrt{ (\frac{x+3}{5})^2 -1 }=\frac{y-1}{2}[/tex]
[tex]2\sqrt{ (\frac{x+3}{5})^2 -1 }+1=y[/tex]
The value of y is defined only when the value inside the root is non negative.
So [tex](\frac{x+3}{5})^2[/tex] ≥ 1
[tex]\frac{x+3}{5}[/tex] ≥ 1
x + 3 ≥ 5
x ≥ 2
Hence for all x ≥ 2, the function is defined.
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Given: AABC with median segments AX, BY, and CZ
Prove: Medians meet at point O.
B
Z
X
It is given that AABC has median segments AX, BY, and CZ. Because
, then AZ = ZB=AY = CY = 1, and
BX CX = The ratios of AZ to ZB is 1, of AY to CY is 1, and of BX to CX is 1 by substitution. Therefore, AAOC, ABOC, and
AAOB are similar to each other. Then the medians meet at point O.
What is the reasoning for the second step?
O A.
OB.
O c.
OD.
medians intersect at one point
medians intersect at multiple points
medians divide each side of the triangle in half
medians divide each side of the triangle into two parts
The reasoning for the the ratios of AZ to ZB is 1, of AY to CY is 1, and of BX to CX is 1 is because of option C. Medians divide each side of the triangle in half.
What are Medians of a Triangle?Median is the line segment joining from a vertex of a triangle to the mid point of the opposite side to that vertex.
There are three medians for a triangle.
Median is a line segment from the vertex to the exact mid point of the opposite side.
So each median from a vertex make the opposite side into two equal parts. So each side has been divided into half and thus the ratio of the length of a side in terms of the mid point is same.
Hence the reasoning for the second step is due to that medians divide each side of the triangle in half.
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A cell phone company charges $42 per month of service. The cost of a new cell phone, plus 8
months of service is $415.99. write and equation in slope-intercept form for a cell phone charges after x month.
Answer:
122387478565275582528
A student answered 46 problems on a test correctly and received a grade 92%. How many problems were on the test, if all the problems were worth the same number of points?
Please I need help and I will mark Brainlist
Based on the ratio, if all the problems on the test were worth the same number of points and the student correctly answered 46 with a grade of 92%, there were 50 questions.
What is a ratio?The ratio refers to the relative value of a number, weight, or expression to another.
Ratios are expressed as the quotient of one value to another number.
Similarly, proportions are ratios equated to one another.
In this situation, we can equate the correct answers to the ratio of the grade obtained as follows:
If 46 problems answered correctly received a grade of 92%, the number of questions on the test would be 50 (46/92%).
Check: 46/50 x 100 = 92%
Thus, we can conclude that there were 50 questions for which the student answered 46 correctly to receive a 92% grade.
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