a. Distance travelled
Given that he rides at a constant speed and after riding for 5 hours, he had travelled 46.5 miles. Per review, the distance travelled is dependent on time hence distance or miles covered is the dependent variable
A triangle can be formed by drawing line segments on a map of Texas connecting the cities of Dallas, Houston, and San Antonio (see figure).
If the actual distance from San Antonio to Houston is approximately 192 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate
a. the actual distance from Dallas to Houston.
b. the actual distance from Dallas to San Antonio.
a. The actual distance from Dallas to Houston is 0.058 mi. b. The actual distance from Dallas to San Antonio is 0.064 mi
What is the scale factor?The ratio between comparable measurements of an item and a representation of that thing is known as a scale factor in arithmetic.
Given that the actual distance from San Antonio to Houston is approximately 192 miles.
The scale factor from the map to the real world is;
(actual)/( map) = (192mi)/(3 in) = 64 mi/in
Then the actual distance from Dallas to Houston will be;
(3.75 in)(64 mi/in) = 0.058 mi
And from Dallas to San Antonio, the distance will be;
(4.125 in)(64 mi/in) = 0.064 mi
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Your lunch in the hospital cafeteria cost $6.50. How much will you spend each week if you average spending $6.50 per meal every day for your five day work week?
The apartment you want has a monthly rent of $585. What does your gross monthly income range need to be for you to be able to rent this apartment? Maximum spent on rent should be 25% - 35% of your gross monthly income
The gross monthly income range to be for you to be able to rent this apartment is $1671 - $2340.
How to calculate the value?Let the monthly income be x.
Therefore, 25% of x = 585
0.25x = 585
Divide
x = 585/0.25
x = $2340
The maximum income is $2340.
The minimum income will be:
35% of x = 585
0.35x = 585
Divide.
x = 585 / 0.35
x = $1671
In this case, the minimum value is $1671 and the maximum value is $2340. This illustrates the concept for finding the range.
The range is $1671 - $2340.
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What number would you add to both sides of x2 + 7x = 4 to complete the square?2²0 72이를즐이
To complete the square, we want a number such that:
[tex]\begin{gathered} 2\sqrt{a}=7 \\ a=(\frac{7}{2})^2 \end{gathered}[/tex]because in this way we can writte the square as follows:
[tex]\begin{gathered} x^2+7x+(\frac{7}{2})^2=4+(\frac{7}{2})^2 \\ (x+\frac{7}{2})^2=4+(\frac{7}{2})^2 \end{gathered}[/tex]Hence the answer is the last option:
[tex](\frac{7}{2})^2[/tex]Composition of Functions and Inverses:Question 7Which expression represents f(f(x)) if f(x) = x2 – 1? A. 2x ^2-2 B. X^4-2x^2+1C. XD. X^4-2x^2
To solve the question, we will follow the steps below:
[tex]f(x)=x^2-1[/tex]To find f(f(x)), we will simply replace x by x² - 1 in the function x² - 1
That is:
f((fx)) = (x²-1)² - 1
Then we open the parenthesis
f(f(x)) = (x² - 1)(x² -1) - 1
=x²(x²-1)-1(x²-1) - 1
= x⁴ - x² - x² + 1 - 1
= x⁴ - 2x²
So the correct option is option D. which is x⁴ - 2x²
What type of chart did we use to build a tornado chart?
Bar chart
For 20 charterers
9y-(2y-3)=5(y-2)+2
Should equal ‘no solution’
[tex]9y - 2y + 3 = 5y - 10 + 2 \\ 7y + 3 = 5y - 8 \\ 7y - 5y = - 8 - 3 \\ 2y = - 11 \\ \frac{2y}{2} = \frac{ - 11}{2} \\ y = \frac{ - 11}{2} [/tex]
ATTACHED IS THE SOLUTION OF Y
BE AWARE THERE IS A SOLUTION FOR THE PROBLEM.
I just need to make sure 1-9 are correct so if you could confirm please.9 b)
Given:
[tex]2x^2+3x+9=0[/tex]To find:
The roots.
Explanation:
Here,
[tex]\begin{gathered} a=2 \\ b=3 \\ c=9 \end{gathered}[/tex]Using the quadratic formula,
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]On substitution we get,
[tex]\begin{gathered} x=\frac{-3\pm\sqrt{(3)^2-4(2)(9)}}{2(2)} \\ =\frac{-3\pm\sqrt{9-72}}{4} \\ =\frac{-3\pm\sqrt{-63}}{4} \\ =\frac{-3\pm3i\sqrt{7}}{4} \end{gathered}[/tex]Therefore, the solutions are,
[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]Final answer:
The solutions are,
[tex]x=\frac{-3+3\imaginaryI\sqrt{7}}{4},x=\frac{-3-3\imaginaryI\sqrt{7}}{4}[/tex]
Ward is planning to install a new counter top in kitchen, as shown in the figure. Determine the area of the countertop.
Over the interval [0,2pi), what are the solutions to cos(2x)=cos(x)? Check all that apply.
Answer:
x = 0 and 2pi/3
Explanation
Given the expression
cos(2x)=cos(x)
In trigonometry expression;
cos2x = 2xos^2x - 1
Substituting into the equation given;
cos(2x)=cos(x)
2xos^2x - 1 = cos x
Rearrange
2xos^2x - 1 - cosx - 1 = 0
Let P = cosx
2P^2 - P - 1 = 0
Factorize
2P^2 - 2P+P-1 = 0
2P(P-1)+1(P-1) = 0
2P+1 = 0 and P-1 = 0
P = -1/2 and 1
Recall that P = cosx
-1/2 = cosx
x = cos^-1(-1/2)
x = 120 degrees = 2pi/3
If P = 1
cosx = 1
x = cos^-1(1)
x = 0
Hence the value of x that satisfies the equation is 0 ad 2pi/3
Explain how knowing the linear factor establishes that f(10) multiple of 12.
f(10) is a multiple of 12 because f(x) has a linear factor of x+2 and x+2 = 12, when x = 10
f(10) multiple of 12 is given as:
The first-degree equations that make up a polynomial's linear factors serve as the foundation stone for higher-order and more complicated polynomials. The formula for a linear factor is ax + b, and it cannot be factored further. When paired with other linear factors, each linear factor represents a separate line, resulting in several sorts of functions with progressively more intricate graphical representations.
f(10) = (10+2)(100+20+2)
= (12)(122)
= 1220+244
= 1464
Hence, f(10) is a multiple of 12
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Find the simple interest on $50,000 for 2 years at 7%
Answer:
$7,000
Explanation:
To find the simple interest on any principal, we use the formula:
[tex]Simple\: Interest=\frac{Principal\times Rate\times Time}{100}[/tex]From the given question:
• Principal = $50,000
,• Rate= 7%
,• Time = 2 years
Therefore:
[tex]\begin{gathered} \text{Interest}=\frac{50,000\times7\times2}{100} \\ =\$7,000 \end{gathered}[/tex]The simple interest is $7,000.
help meeeeeee pleaseee !!!!
The linear function that passes through the points (-3, 18) and (2, -7) is defined by the rule:
y = -5*x + 3
How to find the linear function?We can find a general linear function in the slope-intercept form as:
y = m*x + k
Where m is the slope and k is the intercept of the y-axis.
If we know that the line passes through the points (a, b) and (c, d) then the slope of the function is:
m = (d - b)/(c - a)
In this case the line passes through the points (-3, 18) and (2, -7), then the slope is:
m = (-7 - 18)/(2 + 3) = -5
So the line is something like:
y = -5*x + k
To find the value of k, we can use one of the two given points, I will use (2, -7), so we get:
-7 = -5*2 + k
-7 = -10 + k
-7 + 10 = k
3 = k
So the linear function is:
y = -5*x + 3
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A square has an area of 144 ft^2 what is the length of each side
Answer: 12 feet
This is because [tex]12^2 = 12*12 = 144[/tex]
Squaring a number means you multiply it with itself.
The square root goes in reverse to have [tex]\sqrt{144} = 12[/tex]
Answer:
Each side is 12 ft long.
Step-by-step explanation:
So, you have a square, which means all of the sides are going to be the same length. So, you need something times itself that equals 144. Or, you need the square root of 144 (Because when something is squared, it is multiplied by itself). And the square root of 144 is 12.
A square napkin has sides of length 8 inches. To the nearest inch, what is the length of the diagonal of the (1
napkin?
O8 inches
09 inches
O11 inches
O16 inches
The length of the diagonal of the napkin is 11 inches.
Here, we are given that a square napkin has a side of length 8 inches.
All the sides of a square are equal and the measure of angle formed by any two adjacent sides is also equal and 90°.
Thus, by using Pythagoras theorem, we can form the following equation-
[tex]side^{2} + side^{2} = diagonal^{2}[/tex]
Let the diagonal of the square be d. Then, we have-
[tex]8^{2} +8^{2} =d^{2}[/tex]
64 + 64 = [tex]d^{2}[/tex]
128 = [tex]d^{2}[/tex]
[tex]d^{2}[/tex] = 128
d = [tex]\sqrt{128}[/tex]
d = [tex]8\sqrt{2}[/tex]
the value of [tex]\sqrt{2}[/tex] is approximately 1.41. Thus,
d = 8 × 1.41
= 11.28
Thus, the length of the diagonal of the napkin to the nearest inch comes out to be 11.
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The value of a baseball player's rookie card began to increase once the player retired. When he retired in 1997 his card was worth $6.36. The value has increased by $1.93 each year since then. Express the relationship relating the value of the card y in dollars and the number of years x the player has been in retirement with an equation. Is the relationship between x and y proportional? What was the value of the card in 2007
?
Part a: The relationship between x and y can be represented as y = 6.36 + 1.93x
Part b: The relationship between x and y is proportional
Part c: The value of the card in 2007 will be $25.66
Worth of the card in 1997 = $6.36
Increase in value each year = $1.93
Let x be the number of years the player has been in retirement and y be the value of the cards in dollars
Formulating the equations we get the following:
Value of the card = Worth of the card in 1997 + Increase in value each year*Number of years the player has been in retirement
Part a:
y = 6.36 + 1.93x
Part b:
The relationship between x and y is proportional as the increase in the value each year leads to an increase in the worth of the card
Part c:
Value of the card in 2007:
The number of years the player has been retired will be 10 years in this case
Formulating the equation we get the following:
y = 6.36 + 1.93(10)
= 25.66
So, the value will be $25.66
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Find the slope of the line that passes through each of the following sets of points (0, 0) and (1, 4)
Answer:
slope would be 4/1
Step-by-step explanation:
its rise over run, so up 4 and out 1
have a good day!
write the following in the form a+bi (2+5) - (-6 +bi)
The complex expression (2+5) - (-6 +bi) in the form a + bi is 13 - bi
How to evaluate the expression?The expression is given as
(2+5) - (-6 +bi)
The above expression is a complex expression
So, we have the following expression
(2+5) - (-6 +bi)
Remove the brackets in the above expression
So, we have the following expression
(2+5) - (-6 +bi) = 2 + 5 + 6 - bi
Evaluate the like terms in the above equation
So, we have the following expression
(2+5) - (-6 +bi) = 13 - bi
Hence, the solution to the complex expression is 13 - bi
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Which two values of x are roots of the polynomial below?
4x² - 6x+1
A. x = -6-√52/16
B. x = 6+ √20/8
C. x = 6-√20/8
D. x = -8-√28/6
E. x = -8+ √28/6
F. x = -6 + √52/16
Roots are x = - 6 + √20/8 and x = - 6 - √20/8 of polynomial.
What in mathematics is a polynomial?
Sums of terms with the form kxn, where k is any number and n is a positive integer, make up polynomials. For instance, the polynomial 3x+2x-5. a description of polynomials. In this video, basic terms such terms, degrees, standard form, monomial, binomial, and trinomial are covered.4x² - 6x+1 = 0
x = -b ± √b² - 4ac/2a
x = - (6) ± √(-6)² - 4 * 4 * 1/2 * 4
x = -( 6) ± √36 - 16/8
x = - 6 ± √20/8
So, roots are x = - 6 + √20/8 and x = - 6 - √20/8
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Write the equation of the line with a slopeof -3 that passes through (-5,20)
The equation of the line which passes through point (-5,20), with a slope of -3 is y = -3x + 5.
How yo determine the equation of line from a point and slope?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
Given the data in the question;
Slope m = -3Point ( -5,20 )
x = -5y = 20First, we find the y-intercept 'b', by plug the slope m ( -3 ) and point ( -5,20 ) into the equation of line formula and solving for b.
y = mx + b
20 = (-3)(-5) + b
20 = 15 + b
b = 20 - 15
b = 5
Now that both the slope m and y-intercept b is known, plug these into y = mx + b to determine the equation of the line.
y = (-3)x + 5
y = -3x + 5
Therefore, the linear equation of the line is y = -3x + 5.
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Translate the sentence into an equation. Use the variable w for the unknown number.Two times the sum of a number and 7 equals 6.
we have that
Two times the sum of a number and 7 -----> 2(w+7)
Two times the sum of a number and 7 equals 6 ----> 2(w+7)=6
the answer is
2(w+7)=6result step by step of this simple but yet hard for me exercise
Answer:
The anser is
Step-by-step explanation:
DO IT YOURSELF BRO GO LEARN AND STOP USING BRAINLY PU_$$y
The drama club is selling tickets to its play. An adult ticket costs $15 and a student ticket costs $11. The auditorium will seat 300 ticket-holders. The drama club wants to collect at least $3630 from ticket sales.
a. Write and graph a system of four inequalities that describe how many of each type of ticket the club must sell to meet its goal.
b. List three different combinations of tickets sold that satisfy the inequalities.
The system of inequalities is x + y ≤ 300, 11x + 15y ≥ 3630, x ≥ 0 and y ≥ 0 while the three points are (70, 200), (150, 140) and (140, 150)
How to graph the systemFrom the question, we have the following parameters that can be used to determine system of inequalities
An adult ticket = $15Student ticket = $11. Auditorium capacity = 300 ticket-holdersAmount from sales = at least $3630 from ticket sales.Represent the adult with y and the students with x
So, we have the following representations
x + y ≤ 300 ---- the ticket holders cannot exceed the capacity
11x + 15y ≥ 3630 --- the total sales cannot be less than $3630
x ≥ 0 -- the number of students cannot be negative
y ≥ 0 -- the number of students cannot be negative
Write out the inequalities
x + y ≤ 300
11x + 15y ≥ 3630
x ≥ 0
y ≥ 0
Next, we represent the inequalities on a graph
See attachment for the graph of the inequalities
The combinations from the graphTo get the combination, we make use of the coordinate points that are in the shaded region of the graph
Using the above as a guide, we have
(70, 200), (150, 140) and (140, 150)
There are other points too
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given AC=XZ and AB=XY prove BC=YZ
Keandre wants to buy a new pair of shoes that costs $220. In order to earn money for this, Keandre babysits his neighbor for $10 an hour. He also has saved up his monthly allowance which totals $50. What is the minimum number of hours he should babysit in order to be able to afford the shoes?
Answer:
Step-by-step explanation:
$220=$10x+$50
x= hours
subtract $50 from both sides making sure to cancel the right side
$220-$50=$10x
$170=$10x
Divide both sides by $10 to leaving x by itself on the right side
$170/$10=x
17hrs=x
The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.
What is an expression?
Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Cost of new pair of shoes = $220
In order to earn money for this, Keandre babysits his neighbor for $10 an hour.
And, He also has saved up his monthly allowance which totals $50.
Now,
Let number of minimum hours = x hour
So, We can formulate;
⇒ $10x + $50 = $220
Solve for x as;
⇒ $10x + $50 = $220
Subtract 50 both side, we get;
⇒ $10x + $50 - $50 = $220 - $50
⇒ $10x = $170
Divide by 10 both side, we get;
⇒x = 17
Thus, The minimum number of hours is 17 hours to babysit in order to be able to afford the shoes.
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Find the expected value of the winningsfrom a game that has the followingpayout probability distribution:Payout ($) 1 2 5 8 10Probability 0.35 0.2 0.1 0.2 0.15Expected Value = [?]Round to the nearest hundredth.
On the frequency table, you can see the payouts of the lottery and the corresponding probabilities for every payout. To determine the expected payout, you have to multiply each possible price by its corresponding probability and add the results, following the formula:
[tex]E(X)=\sum ^{10}_{n\mathop=1}x_i\cdot P(x_i)[/tex][tex]\begin{gathered} E(X)=(1\cdot0.35)+(2\cdot0.20)+(5\cdot0.10)+(8\cdot0.20)+(10\cdot0.15) \\ E(X)=0.35+0.4+0.5+1.6+1.5 \\ E(X)=4.35 \end{gathered}[/tex]The expected payout for the lottery is $4.35
a line goes through the point (5, -7) and has slope m = -3. write the equation that represents the line.
We are given the following information
Slope of the line = m = -3
The line passes through the point (5, -7)
Recall that the equation of a line in the point-slope form is given by
[tex](y-y_1)=m(x_{}-x_1)[/tex]Where m is the slope and (x₁, y₁) is a point on the line.
Let us substitute the given values into the above equation
[tex]\begin{gathered} (y-(-7)_{})=-3(x_{}-5_{}) \\ (y+7)=-3(x_{}-5_{}) \\ y+7=-3x+15 \\ y=-3x+15-7 \\ y=-3x+8 \end{gathered}[/tex]Therefore, the equation of the line in slope-intercept form is
[tex]y=-3x+8[/tex]which three ordered pairs represents an input value of the function with the corresponding output value? select three answer.A.(-1,0)B.(0,1)C.(2,1)D.(2,4)E.(3,8)F.(4,2)
In order to determine the ordered pairs, look if the given points are on the curve.
Based on the graph, you can identify that the points are:
B. (0,1)
D. (2,4)
E. (3,8)
A coin has 2 sides: heads (H) and tails (T). A bag has 3 balls: 1 red (R), 1 green (G), and 1 blue (B). You toss a coin and randomly pick a ball. What is the sample space?
The space sample is the total quantity of possible results
for each toss there are 3 possible results
so the total results are 2x 3 = 6
The only option with 6 elements is B
so the answer is B.
The sum of two whole numbers is 63. The difference between the numbers is less than 10. Find as many solutions
Answer:
hmmph..
(32, 31)
(33,30)
(34, 29)
(35, 28)
(36,27)
(37, 26)
Step-by-step explanation:
That all I got....