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I just don't know how to indicate values on ration equations
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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 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.
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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
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.
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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
15. Find the missing sides/angles.i=94jk=42k
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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.
It takes approximately 4.65 quarts of milk to make a pound of cheese. Express this amount as a mixed number in simplest form.
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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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what are the points that are on the graph of the line 2x + 4y = 20
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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
[tex](x + 4)x + 5)[/tex]write the equivalente expression
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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]a. angle addition postulate with angles forming a straight line angle.b. triangle sum theorem c. linear pair postulate
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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
Find the equation of the line through the followingpair of points: (2, -10) and (4, -7).
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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]Write the number 0.2 in the form a over b using integers
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We can express 0.2 in the form:
[tex]\frac{2}{10}[/tex]Very confused on question 5 need help as soon as possible
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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)
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
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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.
"Solve for all values of x on the given intervals. Write all answer in radians." I am stuck on number 4
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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]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?
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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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[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
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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
If x varies directly as y, and x=-30 when y=-6, find x when y=-4.
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Let us now introduce a constant 'k' inorder to get the relationship between x and y,
[tex]\begin{gathered} x\propto ky \\ x=ky \end{gathered}[/tex]Let us substitute x = -30 and y = -6 inorder to get the relationship,
[tex]\begin{gathered} -30=k\times-6 \\ -30=-6k \\ \text{divide both sides by -6} \\ \frac{-30}{-6}=\frac{-6k}{-6} \end{gathered}[/tex][tex]\begin{gathered} k=5 \\ \text{The relationshiop betw}een\text{ x and y is,} \\ x=5y \end{gathered}[/tex]Let us now solve for x when y = -4,
[tex]\begin{gathered} x=5y \\ x=5\times-4 \\ x=-20 \end{gathered}[/tex]Hence, x is -20.
The circumference of a circle is 56.52 what is the diameter
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SOLUTION
We have been given the circumfeence of the circle as 56.52 and we are told to find the diameter
Circumference of a circle C is found as
[tex]\begin{gathered} C\text{ }=\pi d \\ \text{Where }\pi\text{ = 3.14 and d is the diameter. So from } \\ C\text{ }=\pi d \\ 56.52\text{ }=3.14d \\ d\text{ = }\frac{56.52}{3.14} \\ \\ d\text{ = 18} \end{gathered}[/tex]Therefore, the diameter is 18
Find the degree and leading coefficient for the given polynomial.−5x^2 − 8x^5 + x − 40degree leading coefficient
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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
6- 5 and 1/2 pls help
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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]How many solutions does the equation −5a + 5a + 9 = 8 have? (5 points)NoneOneTwoInfinitely many
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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
What is the least common denominator for the following rational equation?x/x+2 + 1/x+4 = x-1/x^2-2x-24
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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)
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
Answers
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.
Answers
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
Which of these standard form equations is equivalent to (x + 1)(x - 2)(x + 4)(3x + 7)?
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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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I kinda started it but I don’t know how to find the answer
Answers
Solution
[tex]\begin{gathered} x^2+2x-16=0 \\ \\ \text{ using quadratic formula} \\ \\ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} \\ a=1,b=2,c=-16 \\ \\ \Rightarrow x=\frac{-2\pm\sqrt{2^2-4(1)(-16)}}{2(1)} \\ \\ \Rightarrow x=\frac{-2\pm\sqrt{4+64}}{2} \\ \\ \Rightarrow x=-1-\sqrt{17} \\ \\ \Rightarrow x=-1+\sqrt{17} \\ \\ \text{ since }x>0 \\ \\ \text{ Therefore the value of }x=-1+\sqrt{17} \end{gathered}[/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
Answers
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]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.
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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
Find the slope of the function 8x - 2y = 10.
Answers
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.
Graph the line y = 3/2x + 7y=3/2 x + 2
Answers
Given:
The equation of line is,
[tex]y=\frac{3}{2}x+2[/tex]Find the points on line.
[tex]\begin{gathered} y=\frac{3}{2}x+2 \\ \text{For x=2} \\ y=\frac{3}{2}\times2+2=5 \\ \text{For x}=-2 \\ y=\frac{3}{2}\times(-2)+2=-1 \\ \text{For x=0} \\ y=\frac{3}{2}(0)+2=2 \\ \text{ For x=4} \\ y=\frac{3}{2}(4)+2=8 \end{gathered}[/tex]So, the points are ( 2,5),(-2,-1),(0,2),(4,8).
The graph of the equation of line is,
21. What is the probability of getting an odd number? a.1/3b.2/3c.1/4d.1/5
Answers
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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