Answers
The given value is,
[tex]\sqrt[]{-24}[/tex]We can write this as,
[tex]\sqrt[]{-24}=\sqrt[]{24\times-1}[/tex]As we know, 24 = 4 x 6 and,
[tex]\sqrt[]{-1}=i[/tex]the above expression can again be rewritten as,
[tex]\sqrt[]{-24\times-1}=\sqrt[]{4\times6}\times i=2i\sqrt[]{6}[/tex]Thus, the last option is correct.
Related Questions
write an equation to find the area of each figure. Then determine the area of the composite figure. When pi is used, the area will be an approximation.
Answers
ANSWER:
The area of the composite figure is 34 m^2
STEP-BY-STEP EXPLANATION:
To calculate the area of the complete figure, you have to separate the figure in two ways, just like this:
Figure A is a square and we calculate the area like this:
[tex]\begin{gathered} A_A=l^2 \\ A_A=4^2=16 \end{gathered}[/tex]Figure B is a trapezoid and we calculate the area like this:
[tex]\begin{gathered} A_B=\frac{b_1+b_2_{}}{2}\cdot h \\ A_B=\frac{4+8}{2}\cdot3 \\ A_B=18 \end{gathered}[/tex]Now the total area is the sum of both parts:
[tex]\begin{gathered} A_T=A_A+A_B \\ A_T=16+18 \\ A_T=34 \end{gathered}[/tex]Jim was playing a game in which he gained and lost points. First, helost four points. Next, he lost nine points. Write the total change to hisscore as an integer.
Answers
Let the total game played be x
The first game he played he lost 4 points
Mathematically,
Total game = lost game + gained game
x = 4 + gained game
gained game = x - 4
next game he lost 9 points again
out of the total x game he had already lost 4 and now losing 9 points
The remaining game after losing 4 will be x-4
x - 4 = lost game
the new lost game is 9 points
x - 4 = 9
isolating x
you have x = 9+4
x = 13
A triangle has sides with lengths of 12 yard, 13 yards, and 15 yards. Which numbers are representing the legs of a triangle?
Answers
ANSWER
None of these sides represent the legs.
EXPLANATION
The legs of a triangle are the sides that form the right angle in a right triangle. The legs are always the shortest sides, while the hypotenuse is the longest side.
In this case, the hypotenuse would be 15 yards, while the legs would be 12 yards and 13 yards. For this to be a right triangle, the Pythagorean Theorem must be satisfied,
[tex]\begin{gathered} 12^2+13^2=15^2 \\ 144+169=15^2 \\ 313=225\to false \end{gathered}[/tex]These side lengths do not satisfy the Pythagorean Theorem and, therefore, this is not a right triangle. If it is not a right triangle, then it does not have legs. Hence, none of these represent the legs.
n were to share the juice equally, how much would each child get?
Answers
Please let me know what is the amount of juice to be shared equally among n people.
Please share an image of the problem so I can see the values in question.
What is the amount of juice to be shared?
Whatever that value is, you divide it by the number of children present.
Another problem seems to be show which number is smaller and which one is larger between the following:
[tex]1\text{ }\frac{2}{3}\text{ and 3}[/tex]So, we proceed to write the mixed number as an improper fraction:
[tex]1\text{ }\frac{2}{3}=1+\frac{2}{3}=\frac{3}{3}+\frac{2}{3}=\text{ }\frac{5}{3}[/tex]and on the other hand, the number 3 can be written as 9/3 (nine thirds)
Therefore, since the mixed number is 5/3 and 3 is 9/3, we see clearly that 5/3 is smaller than 9/3 : One shows 5 of the "thirds" while the other one involves 9 of the "thirds".
Now it seems that you want to add the mixed number plus the 3. so, since they already are expressed with the same DENOMINATOR, we can easily add them:
[tex]1\frac{2}{3}+3=\frac{5}{3}+\frac{9}{3}=\frac{14}{3}=4\text{ }\frac{2}{3}[/tex]identify the form of line of the following equation 4x+5y=6
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To make the graph of the equation, we need to solve for y
[tex]\begin{gathered} 4x+5y=6 \\ 5y=-4x+6 \\ y=-\frac{4}{5}x+\frac{6}{5} \end{gathered}[/tex]Then, the slope of the line is -4/5, this means that the line decreases 4 units when we move 5 units to the right. Also, the y-intercept, that is, the point where the line crosses the y axis, is 6/5
Janie is performing a construction. Her work is shown below.If she connects points D and H, she will create
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Looking at the diagram, If she connects points D and H, she will create angle HDG.
We can see that angle HDG is equal to angle ABC. Therefore,
angle HDG is guaranteed to be congruent to anngle ABC
can you help me with the 4th question which is marked b
Answers
we are given the following equation:
[tex]3x+2y=12[/tex]The slope-intercept form is the following:
[tex]y=mx+b[/tex]Therefore, we need to solve for "y" in the equation. To do that we will subtract "3x" to both sides:
[tex]\begin{gathered} 3x-3x+2y=12-3x \\ 2y=12-3x \end{gathered}[/tex]Now we will divide both sides by "2":
[tex]y=\frac{12-3x}{2}[/tex]Now we will separate the numerator:
[tex]y=\frac{12}{2}-\frac{3}{2}x[/tex]simplifying:
[tex]y=6-\frac{3}{2}x[/tex]And thus we get the slope-intercept form.
Using the slope formula, find the slope of the line through the given points.(-3,-7) and (8,-7)
Answers
the slope of the line is 0
ExplanationThe slope of a line is a measure of its steepness of a line , The vertical change between two points is called the rise, and the horizontal change is called the run. The slope equals the rise divided by the run:
[tex]\begin{gathered} slope=\frac{rise}{run}=\frac{change\text{ in y}}{change\text{ in x}}=\frac{y_2-y_1}{x_2-x_1} \\ where \\ P1(x_1,y_1\text{ \rparen and P2\lparen x}_2,y_2)\text{ are 2 points from the line} \end{gathered}[/tex]so
Step 1
given
[tex]\begin{gathered} P1=(-3,-7) \\ P2=(8,-7) \end{gathered}[/tex]replace in the formula
[tex]\begin{gathered} slope=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ slope=\frac{-7-(-7)}{8-(-3)}=\frac{-7+7}{11}=\frac{0}{11}=0 \end{gathered}[/tex]hence, the slope of the line is 0
I hope this helps you
Given the parent graph f(x)=e^x, which of the following functions has a graph that has been translated 3 to the left and reflected over the x-axis?following functions given to pick from are g(x)=−e^x+3g of x is equal to negative e raised to the x plus 3 powerg(x)=e^−(x+3)g of x is equal to e raised to the negative open paren x plus 3 close paren powerg(x)=e^3−xg of x is equal to e raised to the 3 minus x powerg(x)=−e^3−x
Answers
Given the parent function:
[tex]f(x)=e^x[/tex]Let's determine the function that has a graph which has been translated 3 units to the left and reflected over the x-axis.
To find the function, apply the transformation rules for functions.
• After a translation 3 units to the left, we have:
[tex]g(x)=e^{x+3}[/tex]• Followed by a reflection over the x-axis:
[tex]g(x)=-e^{x+3}[/tex]Therefore, the function that has a graph which has been translated 3 units to the left and reflected over the x-axis is:
[tex]g(x)=-e^{x+3}[/tex]3^9/3^6= answer in exponential form
Answers
To express this fraction in exponential form we have to remember the following property:
[tex]\frac{a^m^{}}{a^n}=a^{m-n}[/tex]Applying it to our problem we have:
[tex]\begin{gathered} \frac{3^9}{3^6}=3^{9-6} \\ =3^3 \end{gathered}[/tex]So the exponential form of our fraction is
[tex]3^3[/tex]Which Platonic solid has twenty faces that are equilateral triangles?A. HexahedronB. OctahedronC. IcosahedronD. Dodecahedron
Answers
STEP - BY - STEP EXPLANATION
What to find?
The platonic solid that has twenty faces that are equilateral triangles.
Given:
Platonic solid.
Let's check each option.
A hexahedron is a polyhedron with 6 faces.
So this is not an option.
An octahedron is a polyhedron with 8 faces.
This option is also ruled out.
A Dodecahedron is a polyhedron with 12 faces.
This is also not an option.
An Icosahedron is a polyhedron whose faces are 20 equilateral triangles.
Hence Icosahedron is the correct option.
ANSWER
C. Icosahedron
Ms. Wong wrote a test. Part A had true/false questions, each worth 7 points. Part B had multiple choice questions, each worth 3 points. She made the number of points for Part A equal the number of points for Part B. It was the least number of points for which this was possible.
Answer the following questions.
How many points was each part worth?
How many questions did Part A have?
How many questions did Part B have?
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Considering the least common multiple of 7 and 3, it is found that:
Each part was worth 21 points.Part A had 3 questions.Part B had 7 questions;How to obtain the measures?The amount of points of each question in each part are given as follows:
Part A: 7 points.Part B: 3 points.Both parts have the same number of points, and this amount was the least number of points for which this was possible, hence this amount is the least common multiple of 7 and 3.
Both 3 and 7 are prime numbers, hence the least common multiple of 3 and 7 is given by their multiplication, as follows:
7 x 3 = 21.
Hence each part of the test was worth 21 points.
The number of questions of each part is given by the division of 21 and the worth of each question, hence:
Part A: 21/7 = 3 questions.Part B: 21/3 = 7 questions.More can be learned about the least common multiple at https://brainly.com/question/10749076
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Which of the following expressions is equivalent to -5(-2x - 3)? If you get stuck, use boxes like the ones we used tohelp organize our class work.(А) 3х - 3B 10x - 3C 10x + 15D10x - 15
Answers
We want to find the expression equivalent to -5(-2x - 3), we would have to expand the expression;
[tex]\begin{gathered} -5(-2x-3) \\ -5(-2x)-5(-3) \\ =10x+15 \end{gathered}[/tex]Therefore, the answer is 10x+15, Option C
Choose the correct answer(s) below. Select all that apply.N A. ZHDEB. ZGFDC. ZHDFD. ZBDCE. ZGDFF. There are no angles adjacent and congruent to ZBDG
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OK
These angles are
HDE and GFD
Letter A
Letter B
Letter C
multiply and simplify (5x−4√5)(5x+4√5)
Answers
Answer::
[tex]25x^2-80[/tex]Explanation:
Given the product:
[tex]\left(5x−4\sqrt{5}\right)\left(5x+4\sqrt{5}\right)[/tex]First, expand the brackets:
[tex]\begin{gathered} =5x\left(5x+4\sqrt{5}\right)−4\sqrt{5}\left(5x+4\sqrt{5}\right) \\ =(5x)^2+20x\sqrt{5}-20x\sqrt{5}-(4\sqrt{5})^2 \\ =(5x)^2-(4\sqrt{5})^2 \end{gathered}[/tex]We then simplify:
[tex]\begin{gathered} =5^2x^2-4^2\sqrt{5}^2 \\ =25x^2-16(5) \\ =25x^2-80 \end{gathered}[/tex]The simplified form of the product is:
[tex]25x^2-80[/tex]Please do this fast and quick I need to sleep
Answers
Given:
distance from sea level to top of hill = initial heeight = 73.5 meters
velocity = 9.8 m/s
[tex]\begin{gathered} For\text{ vertical movement:} \\ Final\text{ height = acceleration\lparen t}^2)\text{ + velocity\lparen t\rparen+ initial height} \\ Since\text{ it is reaching sea level, final height = 0} \\ acceleration\text{ = -9.8 m/s}^2 \\ \\ 0\text{ = -}\frac{1}{2}(9.8)t^2\text{ + 9.8t + 73.5m} \end{gathered}[/tex][tex]\begin{gathered} 0\text{ = -4.9t}^2\text{ + 9.8t + 73.5} \\ 4.9t^2\text{ - 9.8t - 73.5 = 0 \lparen quadratic equation\rparen} \\ \\ \text{Using formula method to find the value of t:} \\ t\text{ = }\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ t\text{ = }\frac{-(-9.8)\pm\sqrt{(-9.8)^2-4(4.9)(-73.5)}}{2(4.9)} \\ \text{ t = }\frac{-(-9.8)\pm\sqrt{1536.64}}{9.8} \\ t\text{ = }\frac{9.8\pm39.2}{9.8} \end{gathered}[/tex][tex]\begin{gathered} t\text{ = }\frac{9.8+39.2}{9.8}\text{ ot }\frac{9.8\text{ - 39.2}}{9.8} \\ \\ t\text{ = 5 or -3} \end{gathered}[/tex]Since we can't have t to be negative, t = 5
The cannonball will reach the sea level at 5 seconds
32. What is the rate of change of y with the respect to x for 24x - 4y = 50
Answers
The equation for the graph is given as
[tex]24x-4y=50[/tex]Let us rearrange the equation into its Slope-Intercept form given as
[tex]y=mx+c[/tex]Where
m = rate of change
c = y-intercept
Therefore, we will have
[tex]-4y=-24x+50[/tex]Divide all terms by -4 to make y a standalone variable:
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{-24x}{-4}+\frac{50}{(-4)} \\ y=6x-\frac{25}{2} \end{gathered}[/tex]Comparing with the Slope-Intercept equation, the rate of change is given as 6.
Read the proof. Statement Reason 1. given Given: AE1 EC; BD 1 DC 1. AEI EC;BD IDC Prove: AAEC - ABDC A 2. ZAEC is a rt. 2; ZBDC 2. definition of is a rt. 2 perpendicular 3. ZAEC • ZBDC 3. all right angles are congruent 4. ? 4. reflexive property 5. AAEC - ABDC 5. AA similarity theorem. What is the missing statement in step 4? B D O ZACE = ZBCD O ZEAB DBC O ZEAC LEAC O ZCBD ZDBC
Answers
Answer:
(a) ∠ACE≅∠BCD
Step-by-step explanation:
You want to know the missing statement in the proof that goes with reason "Reflexive Property."
ProofYou are proving two triangles are similar by showing two corresponding angles are congruent. Corresponding angles in the two triangles are ...
EAC and DBCAEC and BDCACE and BCDThe proof already shows AEC is congruent to BDC in statement 3.
Reflexive propertyThe reflexive property says an angle is congruent to itself. Looking at the list of corresponding angles, the only angle that corresponds to itself is angle C, which can be named ∠ACE or ∠BCD.
The appropriate choice is ...
∠ACE≅∠BCD . . . . Reflexive property
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The missing statement in step 4 should be:ZACE = ZBCD
This statement is missing from the proof and should be included to establish the congruence between the angles in the two triangles.Let's go through the proof step by step and explain each statement and reason.
Given:
AE = EC; BD = DC
AEI = EC; BD = DC
Reason: Given
ZAEC is a right angle; ZBDC is a right angle
Reason: Definition of a right angle. This statement indicates that angle ZAEC and angle ZBDC are both right angles.
ZAEC ≅ ZBDC
Reason: All right angles are congruent. This statement asserts that angle ZAEC and angle ZBDC are congruent (have the same measure) because they are both right angles.
[Missing Statement]
Reason: Reflexive property. This statement is missing in the proof and should be included. The reflexive property states that any angle is congruent to itself. In this case, it implies that angle ZAEC is congruent to angle ZAEC.
AAEC ≅ ABDC
Reason: AA similarity theorem. This statement indicates that triangle AAEC is congruent to triangle ABDC. The AA similarity theorem states that if two pairs of corresponding angles in two triangles are congruent, then the triangles are similar.
So, to complete the proof, the missing statement in step 4 should be:
ZACE = ZBCD
Reason: Reflexive property. This statement establishes that angle ZACE is congruent to angle ZBCD, based on the reflexive property.
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How many square feet of outdoor carpet are needed for this hole
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The area of a rectangle is:
[tex]Ar=l\cdot h[/tex]Where:
Ar = area of the rectangle
l = lenght
w = width
And the area of a triangle is:
[tex]At=\frac{1}{2}\cdot b\cdot h[/tex]Where:
At = area of the triangle
b = base
h = height
To solve this problem divide the figure into triangles and rectangles, according to the figure below.
And the square feed (A) needed will be:
A = A1 - A2 + A3 + A4 + A5
Step 01: Calculate A1.
Figure 1 is a rectangle with sides 5 and 6 ft.
[tex]\begin{gathered} A1=5\cdot6 \\ A1=30ft^2 \end{gathered}[/tex]Step 02: Calculate A2.
Figure2 is a rectangle with sides 2 and 3 ft.
[tex]\begin{gathered} A2=2\cdot6 \\ A2=6ft^2 \end{gathered}[/tex]Step 03: Calculate A3.
Figure 3 is a triangle with base 4 (12 - 6 - 2 = 4) and height 3 ft.
[tex]\begin{gathered} A3=\frac{4\cdot3}{2} \\ A3=\frac{12}{2} \\ A3=6ft^2 \end{gathered}[/tex]Step 04: Calculate A4.
Figure 4 is a rectangle with sides 4 (12 - 6 - 2 = 4) and 2 (5 - 3 = 2) ft.
[tex]\begin{gathered} A4=4\cdot2 \\ A4=8ft^2 \end{gathered}[/tex]Step 05: Calculate A5.
Figure 5 is a rectangle with sides 2 and 5 ft.
[tex]\begin{gathered} A4=2\cdot5 \\ A4=10ft^2 \end{gathered}[/tex]Step 06: Find the area of the figure.
A = A1 - A2 + A3 + A4 + A5.
[tex]\begin{gathered} A=30-6+6+8+10 \\ A=48ft^2 \end{gathered}[/tex]Answer: 48 ft² is needed for this hole.
Please help me on my hw I need help on #2
Answers
Given:
The number is,
[tex]5.232323\ldots\text{.}[/tex]To express the given number into fraction . it means in the form,
[tex]\frac{a}{b}[/tex]We can express the given number into geometric series as,
[tex]\begin{gathered} 5.232323\ldots=5+\frac{23}{100}+\frac{23}{10000}+\frac{23}{100000}+\text{.}\ldots\ldots \\ =5+\frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots\ldots\text{.}\mathrm{}(1) \\ \frac{23}{100}+23(\frac{1}{100})^2+23(\frac{1}{100})^3+\text{.}\ldots=-23+\sum ^{\infty}_{n\mathop=1}23(\frac{1}{100})^{n-1} \\ =-23+\frac{23}{1-\frac{1}{100}} \\ =-23+\frac{23(100)}{99} \\ =-23+\frac{2300}{99} \\ =\frac{-2277+2300}{99} \\ =\frac{23}{99} \end{gathered}[/tex]Now, equation (1) becomes,
[tex]5+\frac{23}{99}=\frac{518}{99}[/tex]Answer:
[tex]\frac{518}{99}[/tex]jamial walked 210 miles he has walked 70%of the way how many more miles does he have left
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Given that: jamial walked 210 miles he has walked 70%of the way
So 70% of the total walked he covered
[tex]210\times\frac{70}{100}=147\text{ miles}[/tex]He covered 147 miles
The remaining distance he have to be cover :
[tex]210-147=63\text{ miles}[/tex]Write logaa=4x in exponential form and find x to evaluate logaa for any a>0, a≠1.
Answers
Given:
[tex]\log _aa=4x[/tex]To find the exponential form of the above, all we need to do is to raise the base a to the power of 4x.
That is;
[tex]a^{4x}=a[/tex]To find the value of x, we need to raise the power of the right - hand side so that we can equate the exponent
That is;
[tex]a^{4x}=a^1[/tex]4x = 1
Divide both-side by 4
[tex]x=\frac{1}{4}[/tex][tex]\text{Log}_aa=4(\frac{1}{4})[/tex][tex]\text{Log}_aa=1[/tex]
the function g is a transformation of f. The grab below shows us as a solid blue line and g as a dotted red line. what is the formula of gA) g(x) =(x/2+1)²-3B) g(x) =(2x+1)²-3C) g(x) =(x/2-1)²-3D) g(x) =(x/2+1)²+3
Answers
First we notice that the vertex of the parabola is shift one unit to the left and three units down. To begin we need to remember the following rules:
Suppose c>0. To obtain the graph of
y=f(x)+c, shift the graph of f(x) a distance c units upwards.
y=f(x)-c, shift the graph of f(x) a distance c units downward.
y=f(x-c), shift the graph of f(x) a distance c units to the right.
y=f(x+c), shift the graph of f(x) a distance c units to the left.
Once we have this rules and knowing that the vertex move like we mentioned before we have that the new function should be of the form:
[tex]f(x+1)-3[/tex]From the graph we also notice that the function g is stretch by a factor of two, remembering the rule for stretching graphs:
If c>1 then the function y=f(x/c), stretch the graph of f(x) horizontally by a factor of c.
With this we conclude that the function g has to be of the form:
[tex]f(\frac{x}{2}+1)-3[/tex]Finally, we notice that the function f is:
[tex]f(x)=x^2[/tex]Threfore,
[tex]g(x)=(\frac{x}{2}+1)^2-3[/tex]then the answer is A.
HAve a nice day !
2. Consider the linear expression.
3.2a - 1 - 4 1/3a + 7 - a
(a) What are the like terms in the expression?
(b) Simplify the linear expression.
Please type ALL the steps down.
Answers
a. The like terms are: 3.2a, -4⅓a, and -a; and -1 and 7.
b. The linear expression is simplified as: -2.1a + 6.
How to Simplify a Linear Expression?To simplify a linear expression, the like terms in the expression are combined together. Like terms in a linear expression are terms that have the same variables or variables with the same powers. Constant terms are also like terms. These like terms are combined together to simplify any given expression.
a. Given the linear expression, 3.2a - 1 - 4⅓a + 7 - a, the following are the like terms that exist in the expression:
3.2a, -4⅓a, and -a are like terms because they have the same variable.
-1 and 7 are like terms, because they are constants.
b. To simplify the linear expression, 3.2a - 1 - 4⅓a + 7 - a, combine the like terms together:
3.2a - 4⅓a - a - 1 + 7
3.2a - 4.3a - a - 1 + 7
-2.1a + 6
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A- what is R(300) interpret this result B- what is the revenue from the sale of 2,000 hats write in functional notation3 part question
Answers
Okay, here we have this:
Considering the provided information, and the given function we are going to calculate R(300) and then we will interpret the result, so we obtain the following:
[tex]\begin{gathered} R(x)=17x \\ R(300)=17\cdot300 \\ R(300)=5100 \end{gathered}[/tex]Considering that x corresponds to the number of hats sold, then it means that if 300 hats are sold, the total revenue will be equal to $5100.
can somebody please help me with my homework math by the way
Answers
Here, we want to subtract the mixed fraction from the whole number
To do this, we need to express the mixed fraction as an improper fraction
To do this, we will multiply the numerator by the whole number and add the numerator
We have this as;
[tex]5\frac{3}{4}\text{ = }\frac{(5\times4)+3}{4}\text{ = }\frac{20+3}{4}\text{ = }\frac{23}{4}[/tex]We can now perform the subtraction as follows;
[tex]17-\frac{23}{4}\text{ = }\frac{4(17)-23}{4}\text{ = }\frac{68-23}{4}\text{ = }\frac{45}{4}[/tex]To properly write the answer, we have to express 45/4 as a mixed fraction
What we have to do here is to divide 45 by 4, then place the quotient at the front, then, the remainder as the numerator
We have this as;
[tex]\frac{45}{4}\text{ = 11}\frac{1}{4}[/tex]Each person in a group of students was identified by year and asked when he or she preferredtaking classes: in the morning, afternoon, or evening, The results are shown in the table. Findthe probability that the student preferred afternoon classes given he or she is a junior. Roundto the nearest thousandth. When Do You Prefer to Take Classes?
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Junior
Morning 17
Afternoon 20
Evening 3
Step 02:
Junior
probability afternoon = junior afternoon / total junior afternoon
total junior afternoon = 17 + 20 + 3 = 40
probability afternoon = 20 / (17 + 20 + 3) = 0.5
The answer is:
probability afternoon = 0.5
Find 3 ratios that are equivalent to the given ratio 6:13
Answers
In order to find equivalent ratios, we can multiply the numerator and denominator by the same value.
For example, let's multiply by 2, by 3 and by 4:
[tex]\begin{gathered} 6:13\\ \\ =6\cdot2:13\cdot2\\ \\ =12:26\\ \\ \\ \\ 6:13\\ \\ =6\cdot3:13\cdot3\\ \\ =18:39\\ \\ \\ \\ 6:13\\ \\ =6\cdot4:13\cdot4\\ \\ =24:52 \end{gathered}[/tex]Therefore the equivalent ratios are 12:26, 18:39 and 24:52..
special right triangle find the value of the variables answer must be in simplest radical form
Answers
Here, we have a special right triangle.
Let's solve for the variables, x and y.
Given:
common side = x
Hypotenuse of the larger triangle = 8
Let's find x using trigonometric ratio.
We have:
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse} \\ \\ \sin 30=\frac{x}{8} \\ \\ x=8\sin 30 \\ \\ x=8(0.5) \\ \\ x=4 \end{gathered}[/tex]To solve for y, we have:
[tex]\begin{gathered} \tan \theta=\frac{opposite}{adjacent} \\ \\ \tan 60=\frac{x}{y} \\ \\ \tan 60=\frac{4}{y} \\ \\ \text{Multiply both sid}es\text{ by y:} \\ y\tan 60=\frac{4}{y}\ast y \\ \\ y\tan 60=4 \\ \\ \text{Divide both sides by tan60} \\ \\ \frac{y\tan 60}{\tan 60}=\frac{4}{\tan60} \\ \\ \\ y=\frac{4}{\tan 60} \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}} \\ \\ \end{gathered}[/tex]Multiply both numerator and denominator by √3:
[tex]\begin{gathered} y=\frac{4}{\sqrt[]{3}}\ast\frac{\sqrt[]{3}}{\sqrt[]{3}} \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]ANSWER:
[tex]\begin{gathered} x=4 \\ \\ y=\frac{4\sqrt[]{3}}{3} \end{gathered}[/tex]The cubic function f(x) = z3 - 6x2 + 11x - 6 has a root at z = 3. a What are the other roots of the function?O r = 3, x = 2O r =-3, x = -2O x = -1, x = -2O x = 1, r = 2
Answers
Given the function f(x) as follows:
[tex]f\mleft(x\mright)=x^3-6x^2+11x-6[/tex]The function has a root at x = 3
We will use the synthetic division to find the other roots:
We will divide the coefficients by 3
As follows:
So, the given function will be written as follows:
[tex]f(x)=(x-3)(x^2-3x+2)[/tex]Factor the term of the quadratic function
[tex]f(x)=(x-3)(x-2)(x-1)[/tex]So, there are three zeros x = 1, 2, 3
So, the answer will be option 4) x = 1, x = 2