Solve the following equation using the methods learned in this section.
3a2 = 54
Answers
The answer is a = 3√2. The explanation and steps of how I got the answer is in the image below.
Related Questions
Which side lengths form a right triangle?
Answers
Answer:
B. 5, 12, 13
Step-by-step explanation:
√5²+12²=13 - yes
√4²+7²= 8.06- no
√20²+22²=29.73 - no
In converting 750 ounces to pounds, what unit (omit the number) would you
place in the denominator of your ratio? Use the plural form in your answer.
Remember that there are 16 ounces in 1 pound.
Answers
Answer:
I would use the pounds.
Step-by-step explanation:
The reasoning behind using the pound is, if you are using fractions per say to get a side by side ration when you are doing 16 ounces to 1 pound you would want to have a unit rate.
750 ounces 16 ounces
------------------- -----------------
x pounds 1 pound
Do you see how much easier it is to convert from ounces to pounds when you have a unit rate? Now once you see how many times you had to multiply 16 to get 750 you can easily multiply that number by 1!
Write the equation of the line that passes through the points (8,-2)(8,−2) and (5,5)(5,5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answers
Answer:
The the equation of the line through the points (8, -2) and (5, 5) in slope-intercept form is
[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]
Step-by-step explanation:
Let's start by calculation the slope of the line by finding the slope of the segment that joins the two given points (8, -2) and (5, 5):
[tex]slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{5-(-2)}{5-8}\\slope=\frac{7}{-3} \\slope=-\frac{7}{3}[/tex]
Now we use this slope in the general slope-intercept form of a line;
[tex]y=mx+b\\y=-\frac{7}{3} x+b[/tex]
and then we calculate the value of the intercept "b" by using one of the given points through which the line must pass (for example (5,5) ), and solving for b:
[tex]y=-\frac{7}{3} x+b\\5=-\frac{7}{3} (5)+b\\5=-\frac{35}{3} +b\\b=5+\frac{35}{3}\\b=\frac{50}{3}[/tex]
The the equation of the line is
[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]
An observer (O) spots a plane (P) taking off from a local airport and flying at a 33° angle horizontal to her line of sight and located directly above a tower (T). The observer also notices a bird (B) circling directly above her. If the distance from the plane(P) to the tower (T) is 7,000 feet, how far is the bird (B) from the plane (P)? Round to the nearest whole number.
Answers
Answer:
the distance of the Bird (B) from the plane (P) is = 10779 ft
Step-by-step explanation:
From the given information:
a diagrammatic representation is attached below for better understanding and solution to the question.
From the diagram;
Let the Bird (B) be represent as A
The plane (P) be represented by B
The observer be represented by O
and the tower T be represented by C
we will see that:
[tex]\overline {AB} \ \| \ \overline {OC}[/tex]
Also;
[tex]\angle ABO = \angle BOC = 33^0[/tex]
AO = BC = 7000
Let consider the trigonometry of triangle BAO
tan θ = opposite/adjacent
tan 33° = 7000/x
0.6494 = 7000/x
x = 7000/0.6494
x = 10779.18
x = 10779 ft ( to the nearest whole number)
Thus; the distance of the Bird (B) from the plane (P) is = 10779 ft
Answer: 10,779 feet
Step-by-step explanation: I just took the test and got it right
2.
What is the next term of the arithmetic sequence 6, 10, 14, 18, ...?
Answers
Answer:
22
Step-by-step explanation:
In this sequence, the next number is found by adding 4.
Answer:
22
Step-by-step explanation:
10 - 6 = 4
so, all next numbers have to be added by 4
3/16 + 1/8 + 1/4 =?
Simple math let’s see who answers it right !
Answers
Answer:
9/16
Step-by-step explanation:
3/16 + 2/16 + 4/16 = 9/16
Answer:
9/16
Step-by-step explanation:
To solve this, you first need to give all the fractions a common denominator. In this case all the denominators can be mutiplied to 16, so that will be our common denominator. So now that all of the denomitors are the same,(3/16+2/16+4/16) we can start solving the problem. First, 3/16+2/16=5/16. Then do, 5/16+4/16=9/16.
Perform the following operation and express the answer in scientific notation. 9x10^2/3x10^12
Answers
Answer:
3 multiplied by 10^-10
In the diagram, the measure of angle 2 is 126°, the measure of angle 4 is (7x)°, and the measure of angle 5 is (4x + 4)°. A transversal intersects 2 lines to form 8 angles. Clockwise from the top left, the angles are 1, 2, 3, 4; 5, 6, 7, 8. What is the measure of angle 7, to the nearest degree? 35° 54° 76° 104°
Answers
Answer:
The correct option is C
C) 76°
Step-by-step explanation:
The question is incomplete because the figure is not given. I have attached the figure of the same question below. Consult it for better understanding.
We can see in the figure that <2 and <4 are opposite angles, therefore these are equal.
<2 = <4
126 = 7x
x = 18
Similarly we can also see that <5 and <7 are also opposite angles, therefore they are equal too.
<7 = <5
<7 = 4x+4
Substitute x=18
<7 = 4(18) + 4
<7 = 76°
Answer:
option c
Step-by-step explanation:
hope this helps :)
please help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
2000 ft x 2= 4000 ft
So the answer is 4000 ft
Can someone help me find what the highlighted part came from?
Answers
Answer:
[tex]\cos(\frac25\pi) = \frac14(\sqrt5-1) \approx 0.3090[/tex]
[tex]\sin(\frac25\pi) = \sqrt{\frac58 + \frac{\sqrt5}{8}} \approx 0.9511[/tex]
[tex]\cos(2\pi) = 1[/tex]
The value of [tex]\frac{2\pi }{5}[/tex] radians corresponds to an angle of 180/5 = 72 degrees.
How many 3-digit even numbers are there that begin with either 5 or 6?
Answers
Answer:
100 numbers
Step-by-step explanation:
There are 100 numbers with 5 as the hundreds digit. (500-599)
There are 100 numbers with 6 as the hundreds digit. (600-699)
There are 50 even numbers with 5 as the hundreds digit.
(500, 502, 504, ... , 598)
There are 50 even numbers with 6 as the hundreds digit.
(600, 602, 604, ... , 698)
50+50=100 numbers
Arrange the following numbers in increasing order: \begin{align*} A &= \frac{2^{1/2}}{4^{1/6}}\\ B &= \sqrt[12]{128}\vphantom{dfrac{2}{2}}\\ C &= \left( \frac{1}{8^{1/5}} \right)^2\\ D &= \sqrt{\frac{4^{-1}}{2^{-1} \cdot 8^{-1}}}\\ E &= \sqrt[3]{2^{1/2} \cdot 4^{-1/4}}.\vphantom{dfrac{2}{2}} \end{align*}Enter the letters, separated by commas. For example, if you think that $D < A < E < C < B$, then enter "D,A,E,C,B", without the quotation marks.
Answers
Answer:
The order is "D, B, A, E, C".
Step-by-step explanation:
The numbers are as follows:
[tex]A=\frac{2^{1/2}}{4^{1/6}}\\\\B = \sqrt[12]{128}\\\\C=(\frac{1}{8^{1/5}})^{2}\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}[/tex]
Simplify the value of A, B, C, D and E as follows:
[tex]A=\frac{2^{1/2}}{4^{1/6}}=\frac{2^{1/2}}{2^{2/6}}=\frac{2^{1/2}}{2^{1/3}}=2^{1/2-1/3}=2^{1/6}=1.1225\\\\B = \sqrt[12]{128}=(128)^{1/12}=(2^{7})^{1/12}=2^{7/12}=1.4983\\\\C=(\frac{1}{8^{1/5}})^{2}=(\frac{1}{(2^{3})^{1/5}})^{2}=(\frac{1}{2^{3/5}})^{2}=\frac{1}{2^{3/5\times2}}=\frac{1}{2^{6/5}}=2^{-6/5}=0.4353\\\\D = \sqrt{\frac{4^{-1}}{2^{-1}\cdot 8^{-1}}}=\sqrt{\frac{2^{-2}}{2^{-1}\cdot 2^{-3}}}=\sqrt{2^{-2+1+3}}=2\\\\E = \sqrt[3]{2^{1/2}}\cdot 4^{-1/4}= (2^{1/2})^{1/3}\cdot 2^{-2/4}=2^{-1/3}=0.7937[/tex]
Arrange the following numbers in increasing order as follows:
D > B > A > E > C
Thus, the order is "D, B, A, E, C".
Answer:
C, E, A, B, D
Step-by-step explanation:
I had this question and this was the correct answer
Find the domain for the rational function:
Answers
Answer:
3rd Option
Step-by-step explanation:
Since the denominator cannot equal 0, x ≠ 5. Therefore, our domain stops and starts again at 5. So our answer is 3rd option.
a store bought a vacuum cleaner for $120. the overhead is 5% of the cost. the store wants to make a profit of 10% over the cost plus overhead. find the selling price of the cleaner.
Answers
Answer:
The selling price of the cleaner is:
$138.6Step-by-step explanation:
First, we have the base of the value that is $120, now we know that the overhead is 5%, so we must calculate this value in dollars, the 5% of $120 is:
$120 * 5% = $6This value you must add to the base ($120), so the cost with the overhead is $126. How the store wants to make a profit of 10%, you must calculate this 10% of the total cost obtained ($126):
$126 * 10% = $12.6And you must add this value to obtain the final price in the store:
$126 + $12.6 = $138.6if a(x) = 2x - 4 and b(x) = x + 2, which of the following expressions produces a quadratic function?
(ab))
O (a - b)^)
O (a + b)(x)
Answers
Answer:
[tex](ab)(x)[/tex]
Step-by-step explanation:
Data provided in the question
a(x) = 2x - 4
b(x) = x + 2
Now we go through each options
First option
[tex](ab)(x)=(2x-4)(x+2)[/tex]
[tex]=2(x-2)(x+2)[/tex]
[tex]=2(x^2-4)[/tex]
[tex]=2x^2-8[/tex]
Second option
[tex]\dfrac{a}{b}(x)=\dfrac{2x-4}{x+2}[/tex]
Third option
[tex](a-b)(x)=(2x-4)-(x+2)[/tex]
[tex]=2x-4-x-2[/tex]
= x - 6
Fourth option
[tex](a+b)(x)=(2x-4)+(x+2)[/tex]
[tex]=2x-4+x+2[/tex]
= 3x - 2
As we can see from the above options only option A is correct i.e it only produced a quadric function
SIMPLIFY THIS −4(w+1)=−24 ASAP
Answers
Answer:
5
Step-by-step explanation:
Answer:
W=5
Step-by-step explanation:
First we distribute the -4 in
-4w - 4 =-24
Now we isolate the -4w by adding 4 to both sides
-4w=-20
Now divide
w=5
Have a good day!
Origami is the Japanese art of paper folding. The diagram below represents an unfolded paper kabuto, a samurai warriors helmet. From the kabuto below, which of the following are pairs of congruent angles? Check all that apply.
Answers
Answer:
A,C,&D
Step-by-step explanation:any funny bur cute romance anime recommendations?
What is the slope of the trend line drawn into the scatterplot? On a graph, a line goes through points (2, 27) and (13, 36). StartFraction 15 Over 163 EndFraction StartFraction 11 Over 109 EndFraction StartFraction 109 Over 11 EndFraction StartFraction 163 Over 15 EndFraction
Answers
Answer:
15/163
Step-by-step explanation: I dont have one
Answer:
i think its D
Step-by-step explanation:
Given the function f(x)=-3x^2+4x+6 find f(2) and f(3)
Answers
Answer:
f(2)= 2, f(3)= -9
Step-by-step explanation:
To find f(2) o f(3), you simply plug the respective number into the function, substituting it for x:
f(2)= -3(2)^2 + 4(2) + 6
f(2)= -12 + 8 + 6
f(2)= 2
f(3)= -3(3)^2 + 4(3) + 6
f(3)= -27 + 12 + 6
f(3)= -9
I NEED HELP ASAP!!!!This table shows how many male and female students attended two different movies. What is the probability that a randomly chosen person from this group an action movie?
Answers
Answer:
0.43 is the answer
Step-by-step explanation:
you need to take the total of action movie and divide it by the grand total.
204/478 ≈ 0.43
The probability that a randomly chosen person from this group an action movie is 0.43.
What is probability?Probability refers to the idea that an event may or may not happen. The scenario described here is a mutually exclusive event. We must recall that in cases of a mutually exclusive event, we add probabilities.
Hence;
Probability of a male watching an action movie = 105/479
Probability of a female watching an action movie = 99/479
probability that a randomly chosen person from this group an action movie = 105/479 + 99/479 = 0.43
Learn mor about probability: https://brainly.com/question/14227610
27. Solve the equation.
Answers
Answer: r=-56
Step-by-step explanation:
multiply 7 on both sides
[tex]\frac{7r}{7}=7\left(-8\right)[/tex]
7*-8=-56
7 and 7 is eliminated
so x=-56
Answer:
r= -56
Step-by-step explanation:
The equation given is:
[tex]\frac{r}{7}= -8[/tex]
We want to solve for r. In order to do this, we must get r by itself.
Currently, r is being divided by 7. We want to perform the inverse, which is multiplication. Therefore, we should multiply both sides of the equation by 7.
[tex]7*\frac{r}{7}= -8 * 7[/tex]
[tex]r=-8*7[/tex]
[tex]r= -56[/tex]
Let's check our solution. Substitute -56 back in for r and solve.
[tex]\frac{r}{7}= -8[/tex]
[tex]\frac{-56}{7}= -8[/tex]
[tex]-8=-8[/tex]
Both sides of the equation are the same, so we know our answer is correct.
When you need to convert from one system of measurement to another, you should convert to the
A. metric system.
B. system that will have the highest number.
C. system that will have the smallest number
D. system used on the medication label.
Answers
To convert from one unit to another within the metric system usually means moving a decimal point. If you can remember what the prefixes mean, you can convert within the metric system relatively easily by simply multiplying or dividing the number by the value of the prefix.
Demario says that the point (1, 5) on the graph below means that one hat costs $5.00. Is Demario correct? yes or no
Answers
Answer:
I think that Demario is correct.
I think he is correct because the point is (1,5) and it says 5 in dollars.
Explanation: Because according to the graph (1,5) meet each other there so it’s correct
Which graph represents a phase shift of pi/2 units right for the graph of
y = COS X?
A. y = csc x
B. y = sin x
C. y = cos(x+pi/2)
D. y = sec x
Answers
Answer:
B. y = sin x
Step-by-step explanation:
In how many ways can 13 people be divided into four groups with 3, 6, 2 and 2 people respectively?
Answers
Answer:
Total combination = 180,180
Step-by-step explanation:
It is a combination based problem.
So,
Total people = 13
Group = 3,6,2,2
So,
For 6 people
13C6= 1,716
For 3 people
7C3 = 35
For 2 group of 2 people
(4C2)/2 = 3
Total combination = 1,716 × 35 × 3
Total combination = 180,180
Let PQRS be a square piece of paper. P is folded onto R and then Q is folded onto S. The area of the resulting figure is 9 square inches. Find the perimeter of square PQRS.
Answers
Answer:
24 inches
Step-by-step explanation:
After folding the piece of paper, the result will be 1/4 the size of the original square. If you multiply the are of the triangle by 4, you will find that the area of the original square is 36 square inches. The square root of 36 is 6, which shows us that the length of each side of the square is 6. To get the perimeter, multiply 6 by 4 to get 24 inches.
For all values of x
(2)
f(x) = (x + 2)2 and g(x) = 3(x - 1)
a) Find gf(x), giving your answer in the form a(x2 + bx + c)
where a, b and care integers.
(x² +
x +
b) Find g '(12)
(2)
Answers
Answer:
A.) gf(x) = 3x^2 + 12x + 9
B.) g'(x) = 2
Step-by-step explanation:
A.) The two given functions are:
f(x) = (x + 2)^2 and g(x) = 3(x - 1)
Open the bracket of the two functions
f(x) = (x + 2)^2
f(x) = x^2 + 2x + 2x + 4
f(x) = x^2 + 4x + 4
and
g(x) = 3(x - 1)
g(x) = 3x - 3
To find gf(x), substitute f(x) for x in g(x)
gf(x) = 3( x^2 + 4x + 4 ) - 3
gf(x) = 3x^2 + 12x + 12 - 3
gf(x) = 3x^2 + 12x + 9
Where
a = 3, b = 12, c = 9
B.) To find g '(12), you must first find the inverse function of g(x) that is g'(x)
To find g'(x), let g(x) be equal to y. Then, interchange y and x for each other and make y the subject of formula
Y = 3x + 3
X = 3y + 3
Make y the subject of formula
3y = x - 3
Y = x/3 - 3/3
Y = x/3 - 1
Therefore, g'(x) = x/3 - 1
For g'(12), substitute 12 for x in g' (x)
g'(x) = 12/4 - 1
g'(x) = 3 - 1
g'(x) = 2.
Please help I will mark brainliest if you explain WHY the answer is that in simple terms. A thanks and brainliest!
Answers
Answer:
The answer will be 7L/100km.
Step-by-step explanation:
The fuel consumption rate is already given for the first 100 km. So, the next 500 km will be 100km to 600km. You have to find the slope of the line during this travel. If you observe, the fuel lowers from 40 litres to 5 litres in this 500km journey. That means, 35 litres were used for 500km. Divide both with 5. That gives 7litres per 100km.
Hey there! :)
Answer:
x = 7L/100km.
Step-by-step explanation:
Solve this problem by using the slope formula:
[tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Use the points (100, 40) and (600, 5) and plug these into the formula:
[tex]m = \frac{5-40}{600-100}[/tex]
Simplify:
[tex]m=\frac{-35}{500}[/tex]
Since this is describing the rate of consumption, we can simply write the slope as:
[tex]m = \frac{35}{500}[/tex]
The question is asking for the rate of consumption over 100 km, therefore:
[tex]\frac{35}{500} = \frac{x}{100}[/tex]
Cross multiply:
3500 = 500x
Divide both sides by 500:
3500/500 = 500x/500
x = 7L/100km.
Graph the image of the figure after a dilation with a scale factor of 1/3 centered at(1, - 2).
Answers
Answer:
point (4, 7) will go to (2, 1)
point (-8, 4) will go to (-2, 0)
point (-8, -2) will go to (-2, -2)
Step-by-step explanation:
Answer:
point (4, 7) will go to (2, 1)
point (-8, 4) will go to (-2, 0)
point (-8, -2) will go to (-2, -2)
What is the slope of the line that contains the points (-1, 2) and (4, 3)? A. 5 B. 1/5 C. -1/5 D. -5
Answers
Answer:
1/5
Step-by-step explanation:
We can find the slope of a line using two points by
m = (y2-y1)/ (x2-x1)
= (3-2)/(4 - -1)
(3-2) /( 4+1)
1/5
Answer:
B. 1/5
Step-by-step explanation:
The slope can be found through two points.
m = rise/run
m = (y2 - y1)/(x2 - x1)
m = (3 - 2)/(4 - (- 1))
m = 1/(4+1)
m = 1/5
Th slope of the line going through the points (-1, 2) and (4, 3) is 1/5.