[tex]\dfrac{2x^3+4x^2 -x+8}{x^2 +3x+2}\\\\\\=\dfrac{2x^3+6x^2+4x-2x^2-6x-4+x+12}{}\\\\=\dfrac{2x(x^2 +3x+2)-2(x^2 +3x+2)+x+12}{x^2 +3x+2}\\\\\\=\dfrac{2x(x^2+3x+2)}{x^2 +3x +2 }- \dfrac{2(x^2 +3x +2)}{x^2 +3x +2 } + \dfrac{x+12}{x^2 +3x+2}\\\\\\=2x-2 + \dfrac{x+2}{x^2 +3x +2}\\\\\\=2x-2 + \dfrac{x+12}{x^2 +2x +x +2}\\\\\\=2x-2 + \dfrac{x+12}{x(x+2) + x+2}\\\\\\=2x-2 + \dfrac{x+12}{(x+1)(x+2)}\\[/tex]
Your friend Dave has an obsession with hats! The only problem - it's an expensive habit but Dave doesn't seem to think so. You want to help show him exactly how much he is spending on hats. Each hat Dave buys costs \ (\$281). Write an expression to represent the total amount Dave spends on hats (\(h\)).
Answer:
281x
Step-by-step explanation:
each hat (x) cost 281. x times cost is total
What is the answer to (2 * 6)^3/2?
Answer:
864
Step-by-step explanation:
First, you multiply 2 and 6, so it's 12, and multiply it by 144, so it's 1728, and divide it by 2. Therefore, it's 864!
5x- 4y +2z when x= 8,y =3 and z =3
34
Step-by-step explanation:
=5x-4y+2z
=5×8-4×3+2×3
=40-12+6
=46-12
=34
Which expression is equivalent to
4^sqrt 6 / 3^sqrt2
Answer:
[tex]\dfrac{\sqrt[12]{55296} }{2}[/tex]
Step-by-step explanation:
Given expression:
[tex]\dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]
[tex]\textsf{Apply exponent rule} \quad \sqrt[n]{a}=a^{\frac{1}{n}}:[/tex]
[tex]\implies \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}=\dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}}[/tex]
Multiply the numerator and denominator by [tex]2^{\frac{2}{3}}[/tex] :
[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}[/tex]
[tex]\textsf{Apply exponent rule to the denominator} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \dfrac{6^{\frac{1}{4}}}{2^{\frac{1}{3}}} \times \dfrac{2^{\frac{2}{3}}}{2^{\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2^{\frac{1}{3}+\frac{2}{3}}}=\dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}[/tex]
Rewrite 1/4 as 3/12 and 2/3 as 8/12 :
[tex]\implies \dfrac{6^{\frac{1}{4}} \cdot 2^{\frac{2}{3}}}{2}=\dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^c \cdot b^c=(a \cdot b)^c:[/tex]
[tex]\implies \dfrac{6^{\frac{3}{12}} \cdot 2^{\frac{8}{12}}}{2}=\dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}[/tex]
Simplify the operation in the parentheses:
[tex]\implies \dfrac{(6^3 \cdot 2^{8})^\frac{1}{12}}{2}=\dfrac{(216\cdot 256)^\frac{1}{12}}{2}=\dfrac{(55296)^\frac{1}{12}}{2}[/tex]
[tex]\textsf{Finally, apply exponent rule} \quad a^{\frac{1}{n}}=\sqrt[n]{a}:[/tex]
[tex]\implies \dfrac{(55296)^\frac{1}{12}}{2}=\dfrac{\sqrt[12]{55296} }{2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[4]{6}}{\sqrt[3]{2}}[/tex]
^b√a=a^1/b[tex]\\ \rm\Rrightarrow \dfrac{6^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]
6=2×3[tex]\\ \rm\Rrightarrow \dfrac{2^{\dfrac{1}{4}}3^{\dfrac{1}{4}}}{2^{\dfrac{1}{3}}}[/tex]
a^m÷a^n=a^m-n[tex]\\ \rm\Rrightarrow 2^{\dfrac{1}{4}-\dfrac{1}{3}}3^{\dfrac{1}{4}}[/tex]
[tex]\\ \rm\Rrightarrow 2^{\dfrac{-1}{12}}3^{\dfrac{1}{4}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{1}{4}}}{2^{\dfrac{1}{12}}}[/tex]
Equalise exponential denominators[tex]\\ \rm\Rrightarrow \dfrac{3^{\dfrac{3}{12}}}{2^{\dfrac{1}{12}}}[/tex]
[tex]\\ \rm\Rrightarrow \left(\dfrac{3^3}{2}\right)^{\dfrac{1}{12}}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3}{2}}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{3^3\times 2^82^3}{22^82^3}}[/tex]
[tex]\\ \rm\Rrightarrow \sqrt[12]{\dfrac{27(256)(8)}{2^12}}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{6912(8)}}{2}[/tex]
[tex]\\ \rm\Rrightarrow \dfrac{\sqrt[12]{55296}}{2}[/tex]
In a survey of 439 teenagers in the US, 14% said that they worked during their summer vacation. a) What is the Margin of Error for this sample proportion
Answer:
[tex]0.0166[/tex]
Step-by-step explanation:
Let the sample proportion be [tex]\hat{p}=0.14[/tex] and the sample size be [tex]n=439[/tex]:
[tex]\displaystyle \text{Margin of Error}=\sqrt{\frac{\hat{p}(1-\hat{p})}{n}}\\\\\text{Margin of Error}=\sqrt{\frac{0.14(1-0.14)}{439}}\\\\\text{Margin of Error}=\pm0.0166[/tex]
Exponential form of 5670
Answer:
The exponent form of 5670 is 5.67 × 103.
Step-by-step explanation:
you can also use this
it's pretty easy
https://calculator.name/decimal-to-scientific-notation/5670
Translate the shape A four squares right and two squares up.
What are the coordinates of the vertices of the image?
will award brainliest to correct answer
Answer:
(5, 6)
Step-by-step explanation:
The original coordinate is (1, 1) (3, 1) (1, 4)
Translate four squares : (5, 1) (7, 1) (5, 4)
Translate two squares up: (5, 3) (7, 3) (5, 6)
The vertices of the image is (5, 6)
5. janelle got invited to a shopping spree with a friend and is supposed
to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,
she has noticed that it takes about two hours for her to travel to the mall.
she has also noticed that it takes her 30 minutes
to get ready before leaving her apartment. she concludes that she
needs to start getting ready at 0:30 p.m. this is an example of what?
inductive reasoning or deductive reasoning?
The given example is inductive reasoning.
What is inductive reasoning?The method of arriving at a conclusion based on a series of observations is known as inductive reasoning. It is not a valid method of proof in and of itself.
We have the information that. Janelle got invited to a shopping spree with a friend and is supposed to meet her at the mall at 4:00 p.m. when she has gone to the mall in the past,
she has noticed that it takes about two hours for her to travel to the mall. she has also noticed that it takes her 30 minutes to get ready before leaving her apartment. she concludes that she needs to start getting ready at 0:30 p.m.
The given information is giving us the series of the data like we are having a sequence of the timing at what time what she did so we have a series of observations here.
Therefore the given example is inductive reasoning.
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Type the correct answer in the box. use numerals instead of words. the test to determine the presence of a certain virus in a pigeon is 97% accurate for a pigeon that has the virus and 99% accurate for a pigeon that does not have the virus. in a given population, 1.5% of the pigeons are infected. do not round your answer. the probability that a randomly selected pigeon gets an incorrect result is .
The probability that a randomly selected pigeon gets an incorrect result is; 0.0103
How to find the Probability?
We are told that;
1.5% pigeons are infected.
Inaccuracy of the test = 1 - 97% = 3%
1.5% of the pigeons are infected. Thus;
1 - 1.5% = 98.5% pigeons are un-infected.
Inaccuracy of test is 1 - 99% = 1% .
Thus;
0.03 and 0.01 are the probability of an error being made in infected and un-infected respectively.
Meanwhile, probability of infected and un-infected are 0.015 and 0.985 respectively.
Thus, the probability of a randomly chosen person gets an incorrect result = (0.03*0.015) + (0.985*0.01) = 0.0103
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A fish tank is three-fourths full.
One-third of the water leaks out.
How full is the fish tank now?
Answer: [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
We will subtract the amount of water that leaked out from the amount of water originally in the fish tank.
[tex]\displaystyle \frac{3}{4} - \frac{1}{3} =\frac{3*3}{4*3} -\frac{1*4}{3*4} =\frac{9}{12} -\frac{4}{12}=\frac{5}{12}[/tex]
The fish tank is [tex]\frac{5}{12}[/tex] of the way full.
The temperature was 73 degrees at noon. The temperature then changed because -2 degrees F each hour for 4 consecutive hours. What was the resulting temperature?
Step-by-step explanation:
73° starting temperature.
every hour -2° for 4 hours.
that means -2×4 = -8° during 4 hours.
so, the resulting temperature is
73 - 8 = 65°
A monument in the shape of a square pyramid was built in a park.
The four lateral faces of the pyramid will be painted. The cost and coverage information for regular paint and metallic paint are shown in the table. Both paint types will be used on the monument.
PAINT TYPE COST(dollars per gallon) GALLONS(sq ft per gallon)
regular $35 200
metallic $100 80
The regular paint will require 2 coats, and the metallic paint will require 1 coat. Both paint types are sold only by the gallon. Based on the table, what is the least amount of money that should be budgeted to paint the monument?
The least amount of money that should be budgeted to paint the monument is $1692.
Least amount of money that should be budgetedFirst step
Using Pythagorean theorem to find the surface area
Since POR is a right triangle
Hence:
PO=20
BR=12
OR=12
PR=√20²+12²
PR=400+144
PR=544
Area of PBC=1/2×24×√544
Area of PBC=12√544
Lateral surface area=4×12√544
Lateral surface area=48√544
Lateral surface area=1119.54²ft
Second step
Since regular paint is 2 coats 200 sq. ft per gallon
Hence:
Number of gallons=1119.54×2/200
Number of gallons= 11.2 gallons
11.2×35= 392
1119.54/80=13 gallons
13×100 =1300
Last step
Least amount=392+1300
Least amount= $1692
Therefore the least amount of money that should be budgeted to paint the monument is $1692.
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Simplify the following radical expression.
√20
OA. 2√5
OB. 5√2
OC. 4√5
D. 10√5
OO
The solution of the given radical expression√20 using factorization is [tex]2 \sqrt{5}[/tex]. Therefore, the correct option for the radical expression√20 is option A, i.e [tex]2 \sqrt{5}[/tex].
A collection of constants, variables or numbers connected using one or more arithmetic operator is called an expression.
Example = 4y, 3x+4.
An expression containing the values in the form of square root, cube root is called a radical expression.
The breaking of a number into its own factors, so that they multiply to give the same number again, is called factorization.
Given expression, √20
The solution of the expression can be obtained by the factors of 20.
[tex]\sqrt{20} = \sqrt{2\times2\times5}[/tex]
[tex]\sqrt{20}[/tex] = [tex]2 \sqrt{5}[/tex]
Here, 2 and 5 are factors of 20.
Thus, the value of the radical expression [tex]\sqrt{20}[/tex] is [tex]2 \sqrt{5}[/tex].
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Which is the equation of a hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0)? y squared over 40 minus x squared over 10 equals 1 y squared over 10 minus x squared over 15 equals 1 x squared over 10 minus y squared over 40 equals 1 x squared over 10 minus y squared over 15 equals 1
The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
How to determine the equation of the hyperbola?The given parameters are:
Directrices at x = ±2 Foci at (5, 0) and (−5, 0)The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
[tex]\frac{(x - k)^2}{a^2} + \frac{(y - h)^2}{b^2} = 1[/tex]
So, we have:
[tex]\frac{(x - 0)^2}{10} + \frac{(y - 0)^2}{15} = 1[/tex]
Evaluate
[tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
Hence, the equation of the hyperbola is [tex]\frac{x^2}{10} + \frac{y^2}{15} = 1[/tex]
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can anyone help? i dont fully understand this
Answer:
It would be about 1/4
Step-by-step explanation:
The area of a circle is 18.31cm2.
find the length of the radius rounded to 2 dp.
Answer:
Step-by-step explanation:
Over what interval is the function in this graph constant?
W
OA. -3≤x≤2
OB. -4sxs-2
OC. -2≤x≤3
OD. -5≤x≤5
The function in this graph is constant in the range of -4 ≤x≤-2 , Option B is the correct answer.
What is a function ?A function is a mathematical statement which identifies relation between independent and dependent variable.
A graph is given
The graph will be considered constant when the y value is constant for any value of x
The value of y is constant in the range of
-4 ≤x≤-2
Therefore Option B is the correct answer.
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If the sales price is 55.50, and the discount is 75%, what is the original price
Answer:
£74
Step-by-step explanation:
£55.50 = 75%
Find 1% of discounted price by dividing both sides by 75 :
£0.74 = 1%
Using 1%, multiply by 100% to find original price :
£74 = 100%
Check our answer :
£74 × 0.75 (75%) = £55.50 ✅
Hope this helped and brainliest please
Answer:
the original price is 416.25. because you take the 55.50 and times ... percent of discount is 75%, sale price is 55.50
Step-by-step explanation:
Omar deposited $700 in his checking account but also wrote checks for $124.21 and $211.94. Assuming his original balance was $622.43, how much does he have in his account now?
show work
Answer:
$986.28
Step-by-step explanation:
$124.21 + $211.94 = $336.15
700 - 336.15 = 363.85
622.43 + 363.85 = 986.28
Find the circumference of the circle. Use 3.14, Round to the nearest hundredth. the diameter is 20 ft
Answer:
62.8ft
Step-by-step explanation:
20/2=10 so 10*2=20 so 20*3.14=62.8
62.8
Answer:
314
Step-by-step explanation:
20/2 = 10
10 * 10 = 100
3.14 * 100 = 314
Solve for x. Round to the nearest tenth, if necessary.
HELP ASAP PLEASE
Answer:
Step-by-step explanation:
If you invest $18000 at an interest rate of 6.7%, compound quarterly, find the time needed for your investments to be worth $23,000
It will take approximately 5.5 years for the investment to be worth $23,000
Compound interestFrom the question, we are to determine when the investments will worth $23,000
Using the compound interest formula,
[tex]A = P (1+\frac{r}{n})^{nt}[/tex]
Where A is the amount
P is the principal
r is rate
n is the number of times it is compounded
and t is the time in years
From the given information,
A = $23000
P =$18000
r = 6.7%
n = 4
t = ?
Putting the parameters into the formula, we get
[tex]23000 = 18000(1+\frac{6.7}{100 \times 4})^{4t}[/tex]
[tex]\frac{23000}{18000} = (1.01675)^{4t}[/tex]
[tex]1.4375= (1.01675)^{4t}[/tex]
[tex]1.4375 = (1.0687)^{t}[/tex]
t = 5.46
t ≅ 5.5 years
Hence, it will take approximately 5.5 years for the investment to be worth $23,000
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a) What type of triangle is triangle ABC? Isosceles b) Give reasons for your answer.
I know it’s an isosceles triangle I just need help explaining :p
Answer:
It is isosceles by the base angles theorem. It states that when the base angles are equal, the triangle is isosceles.
Step-by-step explanation:
unknown measure : 50°
Help me out please asap
a boat sails due south from a port at a steady speed of 9 km/h.
the wind blows the boat due west at a speed of 3 km/h. how far is the boat from the port after 1 h?
give your answer to 1 decimal place.
The distance travelled by boat after 1 hour will be 10km.
What is speed?Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance.
The distance will be calculated as:-
a²+b²=c²
9² + 3 ²= c ²
81+9 = c²
100 = c²
c = 10 km / hour
The distance travelled after one hour will be calculated as:-
Distance = Speed x Time
Distance = 10 x 1 = 10 Km
Therefore the distance travelled by boat after 1 hour will be 10km.
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Which graph shows a function where f(2)= 4?
From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.
Equation of quadratic graphA quadratic graph is in form of a parabola opened upward or downward.
According to the question, we are to select a graph that has a coordinate (2, 4) on its curve.
To determine thus, we will locate the value of 2 on the x-axis and value of 4 on the y-intercept and trace whether the intersecting point is on the curve.
From the curve given we can see that the graph that shows a function where f(2)= 4 is Graph A.
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Pythagorean theorem. How do I solve this?
Answer:
By using the pythsgorean theorem! simple
Answer:[tex]\sqrt{155}[/tex]
Step-by-step explanation:
Oh god pythagorean triples got thrown out the window for this one. This will be a bit ugly.
First, we find the other side length of the rectangle using the pythagorean theorem.
Then, we use that side length in ANOTHER pythagorean theorem to get our answer.
Well, we know that the side length is [tex]\sqrt{5^{2}+9^{2} }[/tex]
We'll use whatever that number is, let's call it x for now, in our other expression:
[tex]\sqrt{x^{2}+7^{2}}[/tex]
So we can do this in one clean equation by substituting our first equation as x in the second one.
Or do them separately. Your choice.
Anyways, try to solve this one now that you know what to do. If you need more help then message.
Three teams, A, B and C, play in a competition.
games won by A: games won by B = 3:1
games won by B: games won by C = 4:3
Team B has won 10 games.
In total, how many games have the three teams won?
Answer:
47.5 games
Step-by-step explanation:
Finding A :
⇒ Games by A : Games by B = 3 : 1
⇒ Games by A : 10 = 3 : 1
⇒ Games by A = 30
==============================================================
Finding C :
⇒ Games by B / Games by C × Games by A / Games by B = 3 × 4/3
⇒ Games by A / Games by C = 4
⇒ Games by C = 30/4
⇒ Games by C = 7.5
==============================================================
Total games won :
⇒ Games by A + Games by B + Games by C
⇒ 30 + 10 + 7.5
⇒ 47.5 games
I really need help on this please anyone help
What Is the measure of angle A
sin A = 4/12 = 1/3
sin inv 1/3 = 19.47⁰
Answer:
option 4, 19.47°
Step-by-step explanation:
From angle A, the given side length are opposite and hypotenuse
SOH CAH TOA is
sinx = opposite / hypotenuse
cosx = adjacent / hypotenuse
tanx = opposite / adjacent
visual representation below
the given length fits the characteristic to use sin
sinA = opposite / hypotenuse
opposite = 4hypotenuse = 12sinA = 4 / 12
common facto is 4 it becomes sinA = 1 / 3
Apply trig inverse property,
x = arcsin(1/3)
x = 19.47122°
Geometry, Angles questions
Answer:
X= 82⁰
z= 82⁰
Step-by-step explanation:
for X:
we can use co-interior angles sum up to make 180 so,
x+ 98= 180
x= 180-90= 82⁰
for z, we can use either angles on a straight line or corresponding angles
using angles on a straight line,98 + z= 180
z= 180-98= 82⁰
using corresponding anglescorresponding angles are always equal and can be found in the F shape diagram when lines are parallel
therefore X and z are corresponding angles and since we found x= 82⁰ then z= 82⁰
PQRS is a rhombus. Find QR.
Will give points!!
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
As we know, all sides of a Rhombus are equal to each other ~ so we can conclude that :
[tex]\qquad \sf \dashrightarrow \:4x - 16 = 2x + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:4x - 2x = 6 + 16[/tex]
[tex]\qquad \sf \dashrightarrow \:2x = 22[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 22 \div 2[/tex]
[tex]\qquad \sf \dashrightarrow \:x = 11[/tex]
Now, plug in the value of x in any equation to get the side length of rhombus ~
[tex]\qquad \sf \dashrightarrow \:2x + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:2(11) + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:22 + 6[/tex]
[tex]\qquad \sf \dashrightarrow \:28 \: \: units[/tex]
Side PS = Side QR = 28 units