Answers
Answer
The power on 2 is either -3.5 in decimal form or (-7/2) in fraction form.
Explanation
To do this, we have to first note that
[tex]\begin{gathered} \sqrt[]{2}=2^{\frac{1}{2}} \\ \text{And} \\ 16=2^4 \end{gathered}[/tex]So, we can then simplify the given expression
[tex]\begin{gathered} \frac{\sqrt[]{2}}{16}=\frac{2^{\frac{1}{2}}}{2^4}=2^{\frac{1}{2}-4} \\ =2^{0.5-4} \\ =2^{-3.5} \\ OR \\ =2^{\frac{-7}{2}} \end{gathered}[/tex]Hope this Helps!!!
Related Questions
Converting between scientific notation and standard form in a real-world situation
Answers
Answer:
[tex]\begin{gathered} a)9.54\times10^6\text{square miles} \\ b)0.0061\sec onds_{} \end{gathered}[/tex]Explanations:
a) The scientific notation is generally expressed as;
[tex]A\times10^n[/tex]A is any real numbers between 1 and 10
n is an integer
Given that the total surface area of North America is 9,540,000 square miles. This is expressed in scientific form as;
[tex]9,540,000=9.54\times10^6mi^2[/tex]From the scientific notation, A = 9.54 and n = 6
b) Given the scientific notation as shown:
[tex]6.1\times10^{-3}\text{seconds}[/tex]Writing in standard form means writing in the normal way we write numbers/decimals. Hence;
[tex]6.1\times10^{-3}=0.0061\text{seconds}[/tex]QUESTION 241 POINTFor a rectangular solid with length 14 feet, height 17 feet, and width 6 feet, find the a. volume and b. surface area.Provide your answer below:volume =cubic feet, surface areasquare feetFEE
Answers
The volume and surface area of a rectangular prism are given by the formulas below
[tex]\begin{gathered} V=l*b*h \\ A=2(lb+bh+hl) \\ l\rightarrow\text{ length} \\ w\rightarrow width \\ h\rightarrow\text{ height} \end{gathered}[/tex]In our case,
[tex]\begin{gathered} l=14,w=6,h=17 \\ \Rightarrow V=14*6*17=1428 \\ and \\ A=2(14*6+6*17+17*14)=848 \end{gathered}[/tex]Thus, the answers are: Surface area=848ft^2, and Volume=1428ft^3
Riley rented folding chairs and tables for an event.• She rented a total of 56 chairs and tables.• She paid $2.25 per chair and $8.50 per table and paid a total of $176.00.Write a system of equations to model this situation.Enter your equations in the space provided. Enter only your equations.+-Х.Iyx rr fr)而
Answers
Total rented= 56 chairs and tables
Chair= $2.25 (let's consider chairs as x)
Table = $8.50 (let's consider tables as y)
Total paid= $176.00
If she rented 56 chairs and tables, then the equation for that would be:
[tex]\begin{gathered} 56=\text{ x + y } \\ 56\text{ -x= y} \end{gathered}[/tex]Then the system of equations to model this situation is:
[tex]176.00=\text{ 2.25x + 8.50\lparen56-x\rparen}[/tex]I am going to have to send you a photo of the problem during the session because it is to large to crop here.
Answers
Direct variations have an special characteristic: they can be represented on a plane by a line paassing through the origin (0,0).
The equation of a line has the following shape:
[tex]y=mx+b[/tex]Where x is the slope, and b is the y intercept.
For direct variations, the line passes through the origin; then, the y intercept is 0, therefore b=0.
For direct variations, we can have an associated line with the following shape:
[tex]y=mx[/tex]We can find the value for m knowing 2 points of the line and calculating the slope. One point is (-1,-4); and the other is the origin (0,0).
Now we can calculate the slope by dividing y distance of the points by the x distance of the points:
[tex]m=\frac{0-(-4)}{0-(-1)}=\frac{0+4}{0+1}=\frac{4}{1}=4[/tex]We have calculated the slope to be 4, then the equation representing the direct variation is:
[tex]y=4x[/tex]Any pair of points x,y that satisfy the equation will an element of the direct variation.
Now, we can try each:
With 8,0:
[tex]\begin{gathered} 0=4\cdot8 \\ 0=16 \end{gathered}[/tex]8,0 does not satisfy, therefore it is not an element of the direct variation.
2,8:
[tex]\begin{gathered} 8=4\cdot2 \\ 8=8 \end{gathered}[/tex]2,8 is element of the dierct variation
-2,0:
[tex]\begin{gathered} 0=4\cdot(-2) \\ 0=-8 \end{gathered}[/tex]-2,0 is not part
4,-1:
[tex]\begin{gathered} -1=4\cdot4 \\ -1=16 \end{gathered}[/tex]4,-1 is not part
8,-1:
[tex]\begin{gathered} -1=4\cdot8 \\ -1=32 \end{gathered}[/tex]8,-1 is not part
-2,-8:
[tex]\begin{gathered} -8=4\cdot(-2) \\ -8=-8 \end{gathered}[/tex]-2,-8 is part.
Finally, we can say points (-4,-1), (2,8) and (-2,-8) are part of the direct variation.
converting to slope intercept formmatch each equation to an equivalent equation written in slope intercept form.
Answers
Statement Problem: Match each equation to an equivalent equation written in slope-intercept form.
Solution:
A slope intercept form equation is written as;
[tex]y=mx+b[/tex](a)
[tex]2y-6=x[/tex]Add 6 to both sides of the equation;
[tex]\begin{gathered} 2y-6+6=x+6 \\ 2y=x+6 \end{gathered}[/tex]Divide each term by 2;
[tex]\begin{gathered} \frac{2y}{2}=\frac{x}{2}+\frac{6}{2} \\ y=(\frac{1}{2})x+3 \end{gathered}[/tex](b)
[tex]undefined[/tex]Write the standard form of the equation and the general form of the equation of the circlewith radius r and center (h.k). Then graph the circle.r= 10; (h,k) = (8,6)The standard form of the equation of this circle isThe general form of the equation of this circle is(Simplify your answer.)Graph the circle.-20 -18Click toenlargegraph
Answers
To solve this problem, we will first find the standard form of the circle equation. Given a circle of radius r and center (h,k), the standard form of the circle equation would be
[tex](x-h)^2+(y-k)^2=r^2[/tex]In our case, we have h=8 , k=6 and r=10. So the equation for the given circle would be
[tex](x-8)^2+(y-6)^2=10^2=100[/tex]The general form of the circle equation can be obtained from expanding the squares on the left side of the equality sign. Recall that
[tex](a-b)^2=a^2-2a\cdot b+b^2[/tex]So, applying this to the standard equation we get
[tex](x-8)^2=x^2-16x+64[/tex][tex](y-6)^2=y^2-12y+36[/tex]So our equation becomes
[tex]x^2-16x+64+y^2-12y+36=100[/tex]Operating on the left side, we have
[tex]x^2-16x+y^2-12y+100=100[/tex]By subtracting 100 on both sides, we get
[tex]x^2-16x+y^2-12y=0[/tex]which the general form of the equation of the given circle.
Using a graphing tool, we have that the circle's graph would be
Express your answer as a polynomial in standard form.f(x) = x^2 + 6x +7g(x) = x + 2Find: g(f(x)
Answers
1) Firstly, let's find the composite function g(f(x)) plugging into the x variable in g(x) the function f(x):
[tex]\begin{gathered} g(f(x))=(x^2+6x+7)+2 \\ g(f(x))=x^{2}+6x+9 \end{gathered}[/tex]2) To write that as the standard form, let's replace g(f(x)) with "y" and write the polynomial orderly to the greatest coefficient to the least one.
[tex]y=x^2+6x+9[/tex]A cone with radius 6 feet and height 15 feet is shown.6ftEnter the volume, in cubic feet, of the cone. Round youranswer to the nearest hundredth.
Answers
EXPLANATION:
Given;
We are given a cone with the following dimensions;
[tex]\begin{gathered} Dimensions: \\ Radius=6ft \\ Height=15ft \end{gathered}[/tex]Required;
We are required to calculate the volume of the cone with the given dimensions.
Step-by-step solution;
To solve this problem, we would take note of the formula of the volume of a cone;
[tex]\begin{gathered} Volume\text{ }of\text{ }a\text{ }cone: \\ Vol=\frac{\pi r^2h}{3} \end{gathered}[/tex]We can now substitute and we'll have;
[tex]Vol=\frac{3.14\times6^2\times15}{3}[/tex][tex]Vol=3.14\times36\times5[/tex][tex]Vol=565.2[/tex]Therefore, the volume of the cone is,
ANSWER:
[tex]Volume=565.2ft^3[/tex]Find the value of b if it is known that the graph of y=-3x+b goes through the point_
M(-2, 4)
Answers
Answer:
b = -2
Step-by-step explanation:
y = mx + b; (-2, 4)
y = -3x + b (x₁, y₁)
m = -3
y - y₁ = m(x - x₁)
y - 4 = -3(x -( -2))
y - 4 = -3(x + 2)
y - 4 = -3x - 6
+4 +4
------------------------
y = -3x - 2
I hope this helps!
I did in paper and this is the answer
I am an even number.
I have three digits and they are all the same.
If you multiply me by 4, all of the digits in the product are 8.
What number am l?
Answers
Answer:
Step-by-step explanation:
The number is 2.
222x4=888
Hence, the number am I is [tex]888[/tex].
What is the even number?
A number that is divisible by [tex]2[/tex] and generates a remainder of [tex]0[/tex] is called an even number.
Here given that,
I am an even number. I have three digits and they are all the same.
If you multiply me by [tex]4[/tex], all of the digits in the product are [tex]8[/tex].
The number is [tex]2[/tex] sp ot would be
[tex]222[/tex]x[tex]4=888[/tex]
Hence, the number am I is [tex]888[/tex].
To kknow more about the even number
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through: (-5,4) perpendicular to x=5
Answers
First let's calculate the slope of the straight line
For slopes that are perpendicular to each other we can use the following formula
[tex]m1m2=-1[/tex]Where
m1 = original slope
m2 = perpendicular slope
[tex]\begin{gathered} m2=-\frac{1}{m1} \\ m2=-\frac{1}{5} \end{gathered}[/tex]Now for the intersection
[tex]\begin{gathered} b=y-mx \\ b=4-(\frac{-1}{5})\cdot(-5) \\ b=4-1 \\ b=3 \end{gathered}[/tex]The equation of the line that passes through the point (-5,4) with a slope of -1/5 is
[tex]y=-\frac{1}{5}x+3[/tex]The picture below shows a pole and its shadow:
What is the height of the pole?
121 centimeters
220 centimeters
225 centimeters
231 centimeters
Answers
The height of the pole according to the attached image and parameters given is; 220 cm.
What is the height of the pole as required in the task content?It follows from the task content that the height of the pole is to be determined from the parameters given.
From observation, the triangle formed by the situation is a right triangle.
Hence, the height of the pole can be determined by Pythagoras theorem; where, c² = a² + b².
Therefore, we have;
221² = 21² + p²
p² = 48,841 - 21²
p² = 48,400
p = √48,400
p = 220.
On this note, the height of the pole is; 220 cm.
Read more on Pythagoras theorem;
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your card gives you a bonus of 0.4%. what is your actual bonus if you charge $3,397.75 on your credit card?
Answers
Answer:
$13.591
Explanation:
To know your actual bonus, we need to find what is 0.4% of $3,397.75 as follows
[tex]3,397.75\times\frac{0.4}{100}=13.591[/tex]Therefore, your actual bonus is $13.591
Problem: A school has a student to teacher ratio of25:5. If there are 155 teachers at the school, howmany students are there?Mike's AnswerCarlos's Answer25 .5 1551552555x = 3875x=77525x = 775x=31There are 31 students at the school.There are 775 students at the scheel.Who is correct? Mike or Carlos? Explain the error thatwas made.
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
ratio = 25:5 (students:teachers)
teachers = 155
students = ?
Step 02:
[tex]\begin{gathered} \text{students = 155 teachers }\cdot\text{ }\frac{25\text{ students }}{5\text{ teachers}} \\ \text{students = }775\text{ } \end{gathered}[/tex]Carlos is correct.
[tex]\frac{25}{5}=\frac{x}{155}[/tex]The answer is:
There are 775 students.
Carlos is correct.
Mike set the variables to find in the wrong way.
Evaluate: sin-¹(1)
A) 0
B) pi/3
C)pi/2
Answers
Answer:
The correct answer is C. Pi/2
Step-by-step explanation:
I got it wrong on edgen, and it told me the correct answer was C.
please help me with this problem this question asks for the angle measure and if the lines are tangent
Answers
step 1
we have that
44=(1/2)[180-arc} ------> by exterior angle
solve for arc
88=180-arc
arc=180-88
arc=92 degrees
give me a minute to draw a figure with letters to better understand the problem
we have that
x+?=180 degrees -------> by form a linear pair (supplemenatry angles)
x=arc=92 degrees ------> by central angle
so
?=180-92
?=88 degrees
therefore
the missing angle is 88 degreesBraden owns a painting that is valued at $27,400. If the value of the artwork increases by 5% every year, how much will it be worth in 3 years?If necessary, round your answer to the nearest cent.
Answers
We know that the painting increase its value by 5% each year.
So, if P(1) is the value the next year and P(0) is the actual value ($27,400) we can write:
[tex]P(1)_{}=P(0)+0.05P(0)=1.05\cdot P(0)[/tex]In the same way, the following year, it will increase another 5% over its value:
[tex]P(2)=1.05P(1)=1.05(1.05\cdot P(0))=1.05^2\cdot P(0)=1.05^2\cdot27,400[/tex]We can generalize this as:
[tex]P(n)=27,400\cdot1.05^n[/tex]For n=3 (3 years) we will have a value of:
[tex]P(3)=27,400\cdot1.05^3\approx27,400\cdot1.1576\approx31,718.93[/tex]Answer: the value of the painting in 3 years is expected to be $31,718.93.
Please help 100 points
Answers
Answer:
y = - 6x² - 12x + 2======================
GivenVertex of parabola = (- 1,8),Point on the graph = (0, 2).To findThe equation of the parabola in standard form.SolutionWe can represent the quadratic equation in vertex or standard forms.
Vertex form:
y = a(x - h)² + k, where (h, k) is the vertex, a- coefficientStandard form:
y = ax² + bx + c, where a and b are coefficients and c- constantUse the vertex form with given coordinates of the vertex:
y = a(x - (-1))² + 8 ⇒y = a(x + 1)² + 8Use the other point to find the value of a:
2 = a(0 + 1)² + 82 = a + 8a = - 6The equation is:
y = - 6(x + 1)² + 8Convert it to standard form:
y = - 6x² - 12x - 6 + 8y = - 6x² - 12x + 2Answer:
[tex]y=-6x^2-12x+2[/tex]
Step-by-step explanation:
Vertex form of a quadratic equation:
[tex]y=a(x-h)^2+k[/tex]
where (h, k) is the vertex.
Given:
Vertex = (-1, 8)Point on the curve = (0, 2)Substitute the given values into the vertex formula and solve for a:
[tex]\implies 2=a(0-(-1))^2+8[/tex]
[tex]\implies 2=a(1)^2+8[/tex]
[tex]\implies 2=a+8[/tex]
[tex]\implies a=-6[/tex]
Substitute the vertex and the found value of a into the vertex formula, then expand to standard form:
[tex]\implies y=-6(x-(-1))^2+8[/tex]
[tex]\implies y=-6(x+1)^2+8[/tex]
[tex]\implies y=-6(x^2+2x+1)+8[/tex]
[tex]\implies y=-6x^2-12x-6+8[/tex]
[tex]\implies y=-6x^2-12x+2[/tex]
Therefore, the quadratic function in standard form whose graph has the given characteristics is:
[tex]y=\boxed{-6x^2-12x+2}[/tex]
Exercise 1: What's In2.Mark’s temperature goes 1.5°C higher from the normal body temperature. What is Marks temperature now?A. 38.5°CB. 37.5°CC. 36.5°CD. 36.5C
Answers
The normal body temperature of a human is 37°C.
If Mark's temperature goes 1.5°C higher than that temperature, his new temperature will be:
[tex]\Rightarrow37+1.5=38.5°C[/tex]OPTION A is the correct option.
How do I understand Standard Form of a Line? I don't know how to do it.
Answers
There are several forms in which one can write the equation of a line. Have in mind that TWO variables should be included in the equation. These two variables are: x and y.
If you type the equation in a form that looks like:
A x + B y = C
where the A, B, and C are actual numbers (like for example: 3 x - 2 y = 5)
This is the standard form of a line. to recognize it notice that bith variables x an y appear in separate terms on the LEFT of the equal sign., and a pure number (no variables) appears on the right of the equal sign.
Another form of writing the equation of a line is in the so called "solpe-intercept" form. This form looks like:
y = m x + b
Notice that in this case the variable ÿ" appears isolated on the left , and on the right of the equal sign you get a term with the variable x, and another constant (pure number) term (b). Like for example in the case of:
y = 3 x
im doing math and im wondering when do i switch the inequality?
Answers
Question:
Solve the following inequality:
[tex]12x+6<17[/tex]Solution:
Consider the following inequality
[tex]12x+6<17[/tex]solving for 12x, we get:
[tex]12x<17-6[/tex]this is equivalent to:
[tex]12x<11[/tex]solving for x, we get:
[tex]x<\frac{11}{12}[/tex]so that, the correct answer is:
[tex]x<\frac{11}{12}[/tex]- A chemist mixes 2,362 milliliters of a solution. The solution must be divided equally among 8 beakers. How much solution should be poured into each beaker?
Answers
Answer:
295.25mm
Explanation:
If the chemist mixes 2362mm of a solution and needs to divide it equally into 8 breakers, to determine how much solution should be poured into each breaker, we have to divide 2362mm divide 8;
[tex]\frac{2362}{8}=295.25\operatorname{mm}[/tex]In the diagram below, BS and ER intersect as show. Determine the measure of
Answers
What's the volume of a cube with a side length of 3 inches?
Answers
ANSWER
27 in³
EXPLANATION
The volume of a cube is the cube of its side length, L,
[tex]V=L^3[/tex]So, if a cube has a side length of 3 inches, then its volume is,
[tex]V=3^3in^3=27\text{ }in^3[/tex]Hence, the volume of a cube with a side length of 3 inches is 27 cubic inches.
The length that a hanging spring stretches varies directly with the weight placed at the end of the spring. If a weight of 8lb stretches a certain spring 9in., how far will the spring stretch if the weight is increased to 37lb? (Leave the variation constant in fraction form. Round off your final answer to the nearest in.)
Answers
ANSWER
L = 42in
EXPLANATION
Can you help me please and thank you very much
Answers
Answer:
∠ FAE = 120°
Step-by-step explanation:
4x and 2x are a linear pair and sum to 180° , that is
4x + 2x = 180
6x = 180 ( divide both sides by 6 )
x = 30
then
∠ FAE = 4x = 4 × 30 = 120°
2. Mr. Cole took a walk with his wife. They walked 4.4 miles in 1.4 hours. What was their average speed inmiles per hour?
Answers
Mr. Cole took a walk with his wife.
They walked 4.4 miles in 1.4 hours.
So we have
Distance = 4.4 miles
Time = 1.4 hours
We are asked to find the average speed in miles per hour.
The average speed is given by
[tex]S=\frac{D}{t}[/tex]Where D is the distance and t is the time.
[tex]S=\frac{4.4}{1.4}=3.142[/tex]Therefore, their average speed is 3.142 miles per hour.
[tex] \frac{x - 2}{x + 3} + \frac{10x}{x {}^{2 } - 9}[/tex]simplify the sum. state any restrictions on the variables.
Answers
We have
[tex]\frac{x-2}{x+3}+\frac{10x}{x{}^2-9}[/tex]first, we need to factorize the next term
[tex]x^2-9=(x+3)(x-3)[/tex]so we have
[tex]\frac{x-2}{x+3}+\frac{10x}{(x+3)(x-3)}[/tex]Remember in order to sum a fraction the denominator must be the same
[tex]\frac{(x-2)(x-3)+10x}{(x+3)(x-3)}[/tex]then we solve the multiplications (x-2)(x-3)
[tex]\frac{x^2-3x-2x+6+10x}{(x+3)(x-3)}=\frac{x^2+5x+6}{(x+3)(x-3)}[/tex]then we can factorize the numerator
[tex]x^2+5x+6=(x+3)(x+2)[/tex]so the simplification will be
[tex]\frac{x^2+5x+6}{(x+3)(x-3)}=\frac{(x+3)(x+2)}{(x+3)(x-3)}=\frac{(x+2)}{(x-3)}[/tex]the final result is
[tex]\frac{(x+2)}{(x-3)}[/tex]If the image of point J under a 180* rotation about the origin is (7, -3), what are the coordinates of point J?
Answers
Answer:
4,3 is the right answer
Step-by-step explanation:
A creative writing class compiled a list of their favorite superheroes. They listed each superhero's superpower and personality flaw. Fly Read minds Forgetful 6 11 Lazy 5 7 What is the probability that a randomly selected superhero is forgetful and can fly? Simplify any fractions.
Answers
The probability is given the following formula:
Probability = Favorable / total outcomes
In this case, there number of students that selected a forgetfull sperheroe that can fly is 6, the total number of outcomes is 6 + 11 + 5 + 7 = 29, then we get:
Probability = 6 / 29
Then, the probability of selecting a forgetful superheroe that can fly is 6/29