Given that there are 6 workshops about chemistry and 7 workshops about biology.
So the total number of workshops available are,
[tex]\begin{gathered} =6+7 \\ =13 \end{gathered}[/tex]The number of ways of selecting 'r' objects from 'n' distinct objects is given by,
[tex]^nC_r=\frac{n!}{r!\cdot(n-r)!}[/tex]The total number of ways of selecting 4 workshops having no workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 0 chemistry)}=^7C_4 \\ n(\text{ 0 chemistry)}=\frac{7!}{4!\cdot(7-4)!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5\cdot4!}{4!\cdot3!} \\ n(\text{ 0 chemistry)}=\frac{7\cdot6\cdot5}{3\cdot2\cdot1} \\ n(\text{ 0 chemistry)}=35 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 1 workshop about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 1 chemistry)}=^7C_3\cdot^6C_1 \\ n(\text{ 1 chemistry)}=\frac{7!}{3!\cdot(7-3)!}\cdot\frac{6!}{1!\cdot(6-1)!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4\cdot3!}{3!\cdot4!}\cdot\frac{6\cdot5!}{1!\cdot5!} \\ n(\text{ 1 chemistry)}=\frac{7\cdot6\cdot5\cdot4}{4\cdot3\cdot2\cdot1}\cdot6 \\ n(\text{ 1 chemistry)}=210 \end{gathered}[/tex]The total number of ways of selecting 4 workshops having exactly 2 workshops about chemistry is calculated as,
[tex]\begin{gathered} n(\text{ 2 chemistry)}=^7C_2\cdot^6C_2 \\ n(\text{ 2 chemistry)}=\frac{7!}{2!\cdot(7-2)!}\cdot\frac{6!}{2!\cdot(6-2)!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6\cdot5!}{2!\cdot5!}\cdot\frac{6\cdot5\cdot4!}{2!\cdot4!} \\ n(\text{ 2 chemistry)}=\frac{7\cdot6}{2\cdot1}\cdot\frac{6\cdot5}{2\cdot1} \\ n(\text{ 2 chemistry)}=315 \end{gathered}[/tex]Consider that the number of ways to select 4 workshops if 2 or fewer must be about chemistry, will be equal to the sum of the individual cases when the number of chemistry workshops in the selection are either 0 or 1 or 2.
This can be calculated as follows,
[tex]\begin{gathered} \text{ Total}=n(\text{ 0 chemistry)}+n(\text{ 1 chemistry)}+n(\text{ 2 chemistry)} \\ \text{Total}=35+210+315 \\ \text{Total}=560 \end{gathered}[/tex]Thus, the total number of ways is 560.
Which of these standard form equations is equivalent to (x + 1)(x - 2)(x + 4)(3x + 7)?
The standard form equation that is equivalent to the expression is x⁴ + 16x³ + 3x² - 66x - 56
How to determine the standard form equation that is equivalent?From the question, we have the following expression that can be used in our computation:
(x + 1)(x - 2)(x + 4)(3x + 7)
The above equation is a product of linear factors
This means that the result of the equation is a polynomial with a degree of the number of factors in the expression
So, we have
(x + 1)(x - 2)(x + 4)(3x + 7)
Open the first two brackets
This gives
(x² + x - 2x - 2)(x + 4)(3x + 7)
Evaluate the like terms
So, we have
(x² - x - 2)(x + 4)(3x + 7)
Open the first two brackets
This gives
(x³ + 4x² - x² - 4x - 2x - 8)(3x + 7)
Evaluate the like terms
So, we have
(x³ + 3x² - 6x - 8)(3x + 7)
Open the remaining brackets
This gives
(x⁴ + 7x³ + 9x³ + 21x² - 18x² - 42x - 24x - 56)
Evaluate the like terms
So, we have
(x⁴ + 16x³ + 3x² - 66x - 56)
Remove the bracket
x⁴ + 16x³ + 3x² - 66x - 56
The expression cannot be further simplified
Hence, the result is x⁴ + 16x³ + 3x² - 66x - 56
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It takes approximately 4.65 quarts of milk to make a pound of cheese. Express this amount as a mixed number in simplest form.
The mixed number in simplest form would be 4 and 13/20.
How to convert decimals into mixed fractions?Separate the whole part from the number at the decimal point.The number behind the decimal point becomes the numerator of the fraction.Find the place value of the decimal part. This is the denominator of the fraction.Write the whole part of the number followed by the numerator over the denominator of the fraction.If possible, simplify the fractional part using common factors.Convert 3.4 to a mixed number
The whole part of the number is 3.
The numerator of the fraction is 4.
The place value of the decimal part is tenths, so the denominator of the fraction is 10.
The mixed number is 3*4/10
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"Solve for all values of x on the given intervals. Write all answer in radians." I am stuck on number 4
Answer:
[tex]x=\frac{2\pi}{3}+2\pi n,x=\frac{4\pi}{3}+2\pi n[/tex]Explanation:
Given the equation:
[tex]\sin x\tan x=-2-\cot x\sin x[/tex]Add 2+cot(x)sin(x) to both sides of the equation.
[tex]\begin{gathered} \sin x\tan x+2+\cot x\sin x=-2-\cot x\sin x+2+\cot x\sin x \\ \sin x\tan x+2+\cot x\sin x=0 \end{gathered}[/tex]Next, express in terms of sin and cos:
[tex]\begin{gathered} \sin x\frac{\sin x}{\cos x}+2+\frac{\cos x\sin x}{\sin x}=0 \\ \frac{\sin^2x}{\cos x}+2+\cos x=0 \\ \frac{\sin^2x+2\cos x+\cos^2x}{\cos(x)}=0 \\ \implies\sin^2x+2\cos x+\cos^2x=0 \end{gathered}[/tex]Apply the Pythagorean Identity: cos²x+sinx=1
[tex]2\cos x+1=0[/tex]Subtract 1 from both sides:
[tex]\begin{gathered} 2\cos x+1-1=0-1 \\ 2\cos x=-1 \end{gathered}[/tex]Divide both sides by 2:
[tex]\cos x=-\frac{1}{2}[/tex]Take the arccos in the interval (-∞, ):
[tex]\begin{gathered} x=\arccos(-0.5) \\ x=\frac{2\pi}{3}+2\pi n,x=\frac{4\pi}{3}+2\pi n \end{gathered}[/tex]The values of x in the given interval are:
[tex]x=\frac{2\pi}{3}+2\pi n,x=\frac{4\pi}{3}+2\pi n[/tex]At a bowling alley, the cost of shoe rental is $2.55 and the cost per game is $3.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)? f (n) = (2.55 + 3.75)n, n > 0 f (n) = 2.55 + 3.75n, n > 0 f (n) = 2.55 + 3.75 + f (n − 1), f (0) = 2.55 f (n) = 3.75 + f (n − 1), f (0) = 2.55
To find the recursive function we need to take into account that shoe rental doesn't depend on the number of games you play. You rent a pair of shoes and you pay for it just once, but the cost per game does depend on the number of games (n), then the total cost of shoe rental and n games will be:
[tex]\begin{gathered} f(n)=\cos t\text{ of shoe rental + cost per game x number of games} \\ f(n)=2.55+3.75n,n>0 \end{gathered}[/tex]Find the equation of the line through the followingpair of points: (2, -10) and (4, -7).
Lets find the slope first:
Slope (m) is change in y's by change in x's
Change in y: -7 - - 10 = -7 + 10 = 3
Change in x: 4 - 2 = 2
Slope = 3/2 (this is m)
So, the equation is:
[tex]\begin{gathered} y=mx+b \\ y=\frac{3}{2}x+b \end{gathered}[/tex]b is the y-intercept.
We can get it by plugging in any point. Let's put (2, -10). So we have:
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ -10=\frac{3}{2}(2)+b \\ -10=3+b \\ b=-10-3 \\ b=-13 \end{gathered}[/tex]Final equation is:
[tex]\begin{gathered} y=\frac{3}{2}x+b \\ y=\frac{3}{2}x-13 \end{gathered}[/tex]Joseph deposited $60 in an account earning 10% interest compounded annually.To the nearest cent, how much will he have in 2 years?Use the formula B=p(1+r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Solution:
Using;
[tex]\begin{gathered} B=p(1+r)^t \\ \\ \text{ Where }p=60,r=10\text{ \%}=0.1,t=2 \end{gathered}[/tex][tex]\begin{gathered} B=60(1+0.1)^2 \\ \\ B=72.6 \end{gathered}[/tex]ANSWER: $72.6
y (-3 - 8x) how can i expand this expression with a variable?
Statement Problem: Expand the expression;
[tex]y(-3-8x)[/tex]Solution:
We would multiply the variable with each of the term.
[tex]\begin{gathered} y(-3-8x) \\ (y\times-3)+(y\times-8x) \\ -3y-8xy \end{gathered}[/tex]Need to write the formula and then make a graph for the following problem. Number of tablespoons T = the number of teaspoons X divided by3
Given:
The number of tablespoon is T.
The number of teaspoon is X.
The objective is to write formula and make a graph for the statement, Number of tablespoons T = the number of teaspoons X divided by 3.
Explanation:
The equation can be written as,
[tex]T=\frac{X}{3}[/tex]To plot the graph:
Consider 3 values of X -3, 0, 3.
Substitute the values of X in the obtained equation to find the value of T.
At X = -3,
[tex]\begin{gathered} T=\frac{-3}{3} \\ T=-1 \end{gathered}[/tex]Thus, the coordinate is (-3,-1).
At X = 0,
[tex]\begin{gathered} T=\frac{0}{3} \\ T=0 \end{gathered}[/tex]Thus, the coordinate is (0,0).
At X = 3,
[tex]\begin{gathered} T=\frac{3}{3} \\ T=1 \end{gathered}[/tex]Thus, the coordinate is (3,1).
On plotting the coordinates in the graph,
Hence, the required equation is T = (X/3) and the graph of the equation is obtained.
Write the number 0.2 in the form a over b using integers
We can express 0.2 in the form:
[tex]\frac{2}{10}[/tex]Find the slope of the function 8x - 2y = 10.
Solve the equation in terms of y, so that it is in the slope-intercept form
[tex]\begin{gathered} 8x-2y=10 \\ -2y=10-8x \\ \frac{-2y}{-2}=\frac{10-8x}{-2} \\ y=-5+4x \\ y=4x-5 \end{gathered}[/tex]Since it is already in the slope-intercept form y = mx + b, where m is the slope. We find that m = 4.
Therefore, the slope of the function is equal to 4.
Which phrase represents the algebraic expression below? 8 + 9x O A. the sum of nine and the quotient of a number x and eight O B. the product of eight and nine less than a number x O C. the product of nine, a number x, and eight OD. the sum of eight and the product of nine and a number x 11
Given data:
The given expression is 8+9x.
The given expression can be read as sum of 8 and product of nine times the number.
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$.Find the rental cost for each movie and each video game.
Given
One month Chris rented 8 movies and 4 video games for a total of 49$.The next month he rented 3 movies and 2 video games for a total of 21$. Find the rental cost for each movie and each video game.
Solution
Step 1
Let m represent the movies
And let v represent the video
Therefore,
[tex]\begin{gathered} 8m+4v=\text{ \$49}\ldots Equation\text{ 1} \\ 3m+2v=\text{ \$ 21 }\ldots Equation\text{ 2} \end{gathered}[/tex]Step 2
Find the degree and leading coefficient for the given polynomial.−5x^2 − 8x^5 + x − 40degree leading coefficient
The given polynomial is
- 5x^2 - 8x^5 + x - 40
It can be rewritten as
- 8x^5 - 5x^2 + x - 40
The degree of the polynomial is the highest exponent of the variable in the polynomial. The highest exponent of x is 5. Thus,
degree = 5
The leading coefficient is the coefficient of the term with the highest variable. The coefficient of x^5 is - 8. Thus,
Leading coefficient = - 8
[tex]4112 \div 5 = 822 remainder 2[/tex]drag each expression to a box to show whether it is a correct way to check the answer to this equation
given that
4112/5 = 822 remainder 2
to get the correct way and incorrect way.
so
For,
822 x 5 = 4110
For,
822 x 2 + 5 = 1649
For,
822 x 5 + 2 = 4112
therefore,
The correct way to check The incorrect way to way to check
822 x 5 + 2 822 x 5
822 x 2 + 5
How many solutions does the equation −5a + 5a + 9 = 8 have? (5 points)NoneOneTwoInfinitely many
ANSWER:
1st option: none
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]−5a\:+\:5a\:+\:9\:=\:8\:[/tex]We solve for a:
[tex]\begin{gathered} −5a\:+\:5a\:+\:9\:=\:8\: \\ \\ 0+9=8 \\ \\ 9=8\rightarrow\text{ false} \end{gathered}[/tex]Therefore, the equation has no solution, the correct answer is 1st option: none
PLEASE HELP ANSWER THESE 3 VERY IMPORTANT QUESTIONS!!!
1. The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 98° is added to the data, how does the mean change?
2. The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 48° is added to the data, how does the median change?
3. The average high temperatures in degrees for a city are listed.
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
If a value of 80.8° is added to the data, how does the range change?
If a value of 98° is added to the data, then the mean change is 1.35, if a value of 48° is added to the data, then the median change from the 6th number to the 7th number but the value still same, if a value of 80.8° is added to the data then the range still same.
In the given question we have to find the change in mean, median and range after the addition of another value.
(1) The list of average high temperatures in degrees for a city is
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
So the mean is find as the sum of value divided by the total number of values.
As we see that the total number of values are 12.
Now the sum of values
∑x=58+61+71+77+91+100+105+102+95+82+66+57
∑x=965
Mean = ∑x/n
Mean = 965/12
Mean = 80.42
If a value of 98° is added to the data, then the sum of values will be
∑x'=58+61+71+77+91+100+105+102+95+82+66+57+98
∑x'=1063
The total number of values = 13
So the
Mean'=∑x'/n'
Mean'=1063/13
Mean'=81.77
Now the change in mean=Mean'−Mean
change in mean=81.77−80.42
change in mean=1.35
(2) The list of average high temperatures in degrees for a city is
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
So the median is find after arranging the values in ascending order.
57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
Total number=12
Meadian=n/2 th number
Meadian=12/2 th number
Meadian=6 th number
Meadian= 77
If a value of 48° is added to the data.
So the ascending order of the number is
48, 57, 58, 61, 66, 71, 77, 82, 91, 95, 100, 102, 105
Total number=13
Meadian=(n+1)/2 th number
Meadian=13+1/2 th number
Meadian=14/2 th number
Meadian=7 th number
Meadian=77
Now the range changes from the 6th number to the 7th number but the value still same.
(3) The list of average high temperatures in degrees for a city is
58, 61, 71, 77, 91, 100, 105, 102, 95, 82, 66, 57
So the range is find after subtracting the greatest number to the smallest number.
So the range=Greatest Number−Largest Number
range=105−57
range=48
If a value of 80.8° is added to the data then the range still same because the added value is between the largest and smallest number.
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You spin the spinner twice.678What is the probability of landing on an odd number and then landing on a 6?Simplify your answer and write it as a fraction or whole number.
We are asked to determine the probability of landing on an odd number and then landing on a 6.
To do that we will use the product rule of probabilities:
[tex]P(AandB)=P(A)P(B)[/tex]Where:
[tex]\begin{gathered} A=\text{ landing on an odd number} \\ B=\text{ landing on a 6} \end{gathered}[/tex]To determine the value of the probability of A we need to have into account that there is only 1 odd number (7) out of 3 possible numbers, therefore, the probability is:
[tex]P(A)=\frac{1}{3}[/tex]Now, to determine the value of the probability of "B" we need to have into account that there is only one number 6 out of 3 numbers therefore, we have:
[tex]P(B)=\frac{1}{3}[/tex]Now, we substitute the values:
[tex]P(AandB)=(\frac{1}{3})(\frac{1}{3})[/tex]Now, we solve the operations:
[tex]P(AandB)=\frac{1}{9}[/tex]Therefore, the probability is 1/9
Very confused on question 5 need help as soon as possible
To solve this, we can use the remainder theorem.
The theorem says:
Given a polynomial P(x), the remainder of
[tex]\frac{P(x)}{x-a}[/tex]Is equal to P(a)
This means, that we are looking for a value of x such as P(a) = 0
We need to find the roots of the polynomial. We can do this, by trying values of x.
Let's use:
x = 0, 1, 2, 3
[tex]x^3+3x^2-16x-48[/tex]Then:
[tex]\begin{gathered} x=0\Rightarrow0^3+3\cdot0^2-16\cdot0-48=-48 \\ x=1\Rightarrow1^3+3\cdot1^2-16\cdot1-48=1+3-16-48=-60 \\ x=2\Rightarrow2^3+3\cdot2^2-16\cdot2-48=8+12-32-48=-60 \\ x=3\Rightarrow3^3+3\cdot3^2-16\cdot3-48=27+27-48-48=-42 \end{gathered}[/tex]Let's try negative values,
x = -1, -2, -3
[tex]\begin{gathered} x=-1\Rightarrow(-1)^3+3(-1)^2-16(-1)-48=-1+3+16-48=-30 \\ x=-2\Rightarrow(-2)^3+3(-2)^2-16(-2)-48=-8+12+32-48=-12 \\ x=-3\Rightarrow(-3)^3+3(-3)^2-16(-3)-48=-27+27+48-48=0 \end{gathered}[/tex]We have found that the polynomial evaluated in x = -3 is equal to zero, which means:
[tex]\frac{x^3+3x^2-16x-48}{x+3}[/tex]has remainder zero.
The answer is (x + 3)
[tex](x + 4)x + 5)[/tex]write the equivalente expression
given that (x+4) (x+5) and they are asking for equivalent form.
at first both terms are in multiplication form,so multiply x with (x+5) so we get that
[tex](x+4)(x+5)=x^2+5x+4x+20=x^2+9x+20[/tex]21. What is the probability of getting an odd number? a.1/3b.2/3c.1/4d.1/5
The probability of getting an odd number from 1-10 is 1/5.
Given, we have numbers from1-10
The odd numbers ranging from 1-10 are 5
Hence we know the probability formula = Number of favourable outcomes/ totall number of outcomes.
Probability of getting an odd number = 1/5
Hence we get the answer as 1/5.
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what are the points that are on the graph of the line 2x + 4y = 20
Answer:
The points are 10 on the x-axis, and 5 on the y-axis
Explanation:
Given the line:
2x + 4y = 20
The values that satisfy this equation are x = 10, y = 5
The points are 10 on the x-axis, and 5 on the y-axis
Look at the graph of the line below:
The line intersects the x-axis at point 10, and the y-axis at point 5
Is AABC - ADEF? Explain your reasoning. B E 6 units US Enter your altswer and explanation. 1 polie
SAS Similarity Theorem
If two sides of one triangle are proportional to two sides of another triangle and the included angle in both are congruent, then the triangles are similar by the SAS theorem.
We need to check if the conditions are met in the triangles given in the question.
First, let's test the proportionality of the sides.
In triangle ABC, side AB has a measure of 9 units
In triangle DEF, side DE has a measure of 6 units.
The proportion is 9/6 = 1.5. This is the scale factor.
Now check the other given sides.
In triangle ABC, side CA has a measure of 6 units
In triangle DEF, side FD has a measure of 4 units.
Proportion is 6/4 = 1.5
Given the scale factor is identical for both triangles, the first condition is met.
Now we can see the included angles BAC and EDF are congruent because they have the same measure of 40°.
Since both conditions are met, we conclude the triangles are similar by the SAS theorem
I just don't know how to indicate values on ration equations
Solving the equation we have:
[tex]\begin{gathered} \frac{x+3}{x-3}=\frac{12}{3} \\ \frac{x+3}{x-3}=4\text{ (Simplifying the fraction)} \\ x+3=4(x-3)\text{ (Multiplying x-3 on both sides of the equation)} \\ x+3=4x-12\text{ (Distributing)} \\ x+3+12=4x\text{ (Adding 12 to both sides of the equation)} \\ 3+12=4x-x\text{ (Subtracting x from both sides of the equation)} \\ 15=3x\text{ (Adding)} \\ \frac{15}{3}=x\text{ (Dividing by 3 on both sides of the equation)} \\ 5=x\text{ } \end{gathered}[/tex]The solution is x=5 and it is valid as the result of replacing it in the denominator is not zero. ( 5 - 3 ≠ 0)
A batting average of 0.250 in baseball means a player, on average gets 25 hits in 100 times at bat. How many hits would he expect to get in 360 times at bat
From the given information:
Batting average of the player = 0.25.
This means that, on average, the player gets 25 hits in 100 times at-bat.
Therefore:
The number of hits which he would expect to get in 360 times at-bat
= Batting Average X Number of Times at-bat
[tex]\begin{gathered} =0.25\text{ x 360} \\ =90 \end{gathered}[/tex]The baseball player would expect to get 90 hits in 360 times at-bat.
Another approach is to use ratio.
[tex]\frac{25\text{ Hits}}{100\text{ times at bat}}=\frac{x\text{ Hits}}{360\text{ times at bat}}[/tex]Cross multiply
[tex]\begin{gathered} 100x=25\text{ }\times\text{ 360} \\ 100x=9000 \end{gathered}[/tex]Divide both sides by 100 to solve for x
[tex]x=90[/tex]Therefore, the baseball player would expect to get 90 hits in 360 times at-bat.
A ball is thrown upward and outward from a height of 6 feet. The height of the ball, f(x), in feet, can be modeled byf(x)=−0.6x2+2.7x+6where x is the ball's horizontal distance, in feet, from where it was thrown. Use this model to solve parts (a) through (c).a. What is the maximum height of the ball and how far from where it was thrown does this occur?The maximum height is 1010 feet, which occurs 22 feet from the point of release.
We need to find the vertex of the parabola
Vertex (h,k) is given by the following formula:
[tex]\begin{gathered} (h,k) \\ h=-\frac{b}{2a} \\ k=f(h) \end{gathered}[/tex]Where, a and b are coefficients of the quadratic equation
[tex]f(x)=ax^2+bx+c[/tex]in this example:
[tex]f(x)=-0.6x^2+2.7x+6[/tex]Therefore,
a = 0.6
b = 2.7
Now, we know that, we can find vertex (h,k)
[tex]h=-\frac{2.7}{2\cdot(-0.6)}=2.25[/tex]now, let's determine k
[tex]\begin{gathered} k=f(h)=f(2.25)=-0.6\cdot(2.25)^2+2.7\cdot(2.25)+6 \\ k=9.0375 \end{gathered}[/tex]So, the vertex of the parabola is the point (2.25 , 9.0375)
This means that the maximum height of the ball is k = 9.0375 ft and it occurs h = 2.25 ft from where it was thrown
15. Find the missing sides/angles.i=94jk=42k
From the figure given,
[tex]\begin{gathered} j=\text{opposite}=\text{?} \\ k=adjacent=\text{?} \\ hypotenuse=94 \\ \theta=42^0 \end{gathered}[/tex]Let us solve for 'j'
To solve for j, we will employ the method of Sine of angles.
[tex]\begin{gathered} \text{ Sine of angles=}\frac{opposite}{\text{hypotenuse}} \\ \sin \theta=\frac{j}{hypotenuse} \end{gathered}[/tex][tex]\begin{gathered} \sin 42^0=\frac{j}{94} \\ \text{cross multiply} \\ j=94\sin 42^0 \\ j=94\times0.6691 \\ j=62.8954\approx62.9units(nearest\text{ tenth)} \end{gathered}[/tex]Let us solve for k
To solve for k, we will employ the method of Cosine of angles.
[tex]\begin{gathered} \text{ Cosine of angles=}\frac{k}{\text{hypotenuse}} \\ \cos \theta=\frac{k}{hypotenuse} \\ \cos 42^0=\frac{k}{94} \\ \text{cross multiply} \\ k=94\cos 42^0 \\ k=94\times0.7431 \\ k=69.8514\approx69.9units(nearest\text{ tenth)} \end{gathered}[/tex]Hence, the value of j=62.9units,
k=69.9units.
a. angle addition postulate with angles forming a straight line angle.b. triangle sum theorem c. linear pair postulate
A. angle addition postulate with angles forming a straight line angle
1) Examining that table, we can see that step 4 is a consequence of the third step, the triangle sum theorem.
2) Then in step 4, we have the following reason to state that the sum of those angles is 180º: Then as we can see below:
We have a Linear Pair between the angles ∠ABD, ∠DBE, and ∠CBE since those angles combined add up to 180º (a straight angle) in red.
3). Hence, the answer is A
What is the least common denominator for the following rational equation?x/x+2 + 1/x+4 = x-1/x^2-2x-24
Least Common Denominator (LCD)
We are required to find the LCD for the expression:
[tex]\frac{x}{x+2}+\frac{1}{x+4}=\frac{x-1}{x^2-2x-24}[/tex]We need to have every denominator as the product of the simplest possible expressions.
Since x+2 and x+4 are already factored, we need to factor the expression:
[tex]x^2-2x-24=(x-6)(x+4)[/tex]Now we have the following prime factors:
x+2, x+4, x-6 and x+4
The LCD is the product of all the prime factors:
LCD = (x+2)(x+4)(x-6)
In the diagram below, ALMK - APMN. Based on the relationship between the triangles, which of the following proportions is true? KA d.
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional
In this problem
triangle LMK and triangle PMN are similar
that means
LM/PM=MK/MN=LK/PN
therefore
answer is
option a6- 5 and 1/2 pls help
First, express the mixed number as a fraction:
[tex]5\frac{1}{2}=\frac{\lbrack(5\times2)+1\rbrack}{2}=\frac{11}{2}[/tex][tex]6-\frac{11}{2}[/tex]multiply 6 by (2/2)
[tex]6\times\frac{2}{1}-\frac{11}{2}=\frac{12}{2}-\frac{11}{2}=\frac{1}{2}[/tex]