The required slope m is 3 and the y-intercept is - 5.
What is a y-intercept?On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.
· The y-coordinate of a point where a line, curve, or surface intersects the y-axis.
Given : The line y = 3x - 5
This is of the form y = mx + c which is the equation of the line.
On comparing these two equations
Thus the slope is 3 .
And y intercept is :
y = 3x - 5 and when x = 0
y =- 5.
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solve the equation of 3/4 - 1/5
Which function has the greatest average rate of change over the given interval?
Answer: C(x) > a(x) , meaning c(X) has the greatest average rate of change over the given interval.
Explanations :
• The greatest average rate of change = slope
,• given by formula :
[tex]m\text{ = }\frac{y_2-y_1}{x_2-x_1}[/tex](a) For a(x),[tex]\begin{gathered} minitial\text{ = }\frac{-2+3\text{ }}{0+1\text{ }} \\ \text{ = 1/1} \\ \text{ = 1 } \end{gathered}[/tex][tex]\begin{gathered} m\text{ final = }\frac{13-6}{3-2} \\ \text{ = }7\text{ } \end{gathered}[/tex]• The average rate of change over the given interval = 7-1 = 6
(b) for b(x) , we have [tex]\begin{gathered} M\text{ initial = }\frac{3-1}{0+1} \\ \text{ = 2} \end{gathered}[/tex]and
[tex]\begin{gathered} m\text{ final = }\frac{9-7\text{ }}{3-2\text{ }} \\ \text{ = 2} \end{gathered}[/tex]• We can see that b(x) has constant average rate of change at 2 , therefore this will not be considered for this purpose of the exercise.
(c) for C(x) , we have [tex]\begin{gathered} M\text{ initial = }\frac{-1+2}{0+1} \\ \text{ = 1 } \end{gathered}[/tex]
and
[tex]\begin{gathered} m\text{ final = }\frac{13-5\text{ }}{3-2} \\ \text{ = }8\text{ } \end{gathered}[/tex]• The average rate of change over the given interval =, 8 -1 = 7
in conclusion , C(x) = 7 , whereas a(x) = 6 ,
Therfore C(x) > a(x)
The quadratic function G parentheses X parentheses is shown in the table below for the integer values on the interval negative one less than or equal to X less than or equal to four, two just
Since (2,1) is the turning point, let's write the function in its vertex form:
[tex]\begin{gathered} y=a(x-h)^2+k \\ so\colon \\ y=a(x-2)^2+1 \end{gathered}[/tex]Let's use one of the points:
[tex]\begin{gathered} (3,2) \\ 2=a(3-2)^2+1 \\ 2=a(1)^2+1 \\ so\colon \\ a=2-1 \\ a=1 \end{gathered}[/tex][tex]y=(x-2)^2+1[/tex]Therefore:
[tex]\begin{gathered} x=0 \\ y=(0-2)^2+1 \\ y=5 \end{gathered}[/tex]Find the indicated probability. Round to three decimal places.A machine has 6 identical components which function independently. The probability that a component will fail is 0.3. Themachine will stop working if more than two components fail. Find the probability that the machine will be working.
Answer: 74.43%
Let us first list down the probabilities of the machine working.
First is the probability that none of the components will fail. We can write this probability as:
[tex]P(0)=(1-0.3)^6[/tex]Next, the probability that one of the components will fail. This will give us:
[tex]P(1)=C^1_6(1-0.3)^5(0.3)[/tex]Then, the probability that 2 of the components will fail.
[tex]P(2)=C^2_6(1-0.3)^4(0.3)^2[/tex]Adding all of these probabilities and we will have:
[tex]P=(1-0.3)^6+C^1_6(1-0.3)^5(0.3)+C^2_6(1-0.3)^4(0.3)^2[/tex][tex]P=(0.7)^6+(6)(0.7)^5(0.3)+(15)(0.7)^4(0.3)^2[/tex][tex]P=0.74431\times100=74.43\%[/tex]Therefore, the probability that the machine will be working would be 74.43%.
Hi, I was absent today in class and I really need help with question 8 I will be much appreciated if you show work and the step so I can be more understanding thank you!
Question 8
We are to solve
[tex]x^{2.8}=31[/tex]This can be simplified to
[tex]\begin{gathered} x^{\frac{28}{10}}=31 \\ x^{\frac{14}{5}}=31 \end{gathered}[/tex]Raising both sides of the equation to a power of 5 we have
[tex]\begin{gathered} x^{\frac{14}{5}\times5}=31^5 \\ x^{14}=31^5 \\ x^{14}=28629151 \end{gathered}[/tex]By raising both sides of the equation to power of 1/14, we get
[tex]\begin{gathered} x^{14\times\frac{1}{14}}=28629151^{\frac{1}{14}} \\ x=\sqrt[14]{28629151} \end{gathered}[/tex]Simplifying this we get
[tex]x=3.40901[/tex]tommie works at a local store on the weekends. He earns $11.50 per hourr. tommie will get a 10% raise after working 4 weeks. How much will he make per hour after his raise?\
EXPLAIN YOUR ANSWER PLEASE asap!!!=)
Tommie will make $12.65 per hour after his raise.
We will perform addition of value equal to mentioned percentage. So, representing this as equation -
Amount of money earned after raise = 11.5 + 10%×11.5
Converting percentage to whole number
Amount of money earned after raise = 11.5 + (10/100×11.5)
Performing multiplication and division on Right Hand Side of the equation
Amount of money earned after raise = 11.5 + 1.15
Performing addition on Right Hand Side of the equation
Amount of money earned after his raise = $12.65
Therefore, after increase in 10% raise, Tommie will earn total $12.65.
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Graph the following inequalities.4x + y ≥ 0I need TWO COORDINATES
We need to graph the following inequality:
[tex]4x+y\ge0[/tex]First, let's apply the same operations on both sides of the inequality to isolate the variable y on the left side of the inequality. We obtain:
[tex]\begin{gathered} 4x+y-4x\ge0-4x \\ \\ y\ge-4x \end{gathered}[/tex]Now, notice that:
[tex]y=-4x[/tex]represents a line containing all points with coordinates (x,y) such that y=-4x.
The solution to the inequality includes those points, and also the points for which y is greater than -4x.
Thus, the solution to this inequality consists of all the points on that line (solid line) and the whole region above that line:
Notice that, to graph the solid line, we can choose two points on the line, and then join them. We can use the points:
[tex]\begin{gathered} x=0\Rightarrow y=0\text{ point }(0,0) \\ \\ x=1\Rightarrow y=-4\text{ point }(1,-4) \end{gathered}[/tex]Solve the inequality.x² + 3x - 28 < 0
We need to solve the inequality:
[tex]x^{2}+3x-28<0[/tex]We can start by sketching the graph of the parabola:
[tex]x^{2}+3x-28=0[/tex]Then, we need to find the points of the parabola below the x-axis.
The zeros of that parabola are given by:
[tex]\begin{gathered} x=\frac{-3\pm\sqrt[]{3^{2}-4(1)(-28)}}{2(1)} \\ \\ x=\frac{-3\pm\sqrt[]{9+112}}{2} \\ \\ x=\frac{-3\pm\sqrt[]{121}}{2} \\ \\ x=\frac{-3\pm11}{2} \\ \\ x_1=-7 \\ \\ x_2=4 \end{gathered}[/tex]And since the coefficient of x² is positive, the parabola opens upwards. So, its graph looks like this:
Thus, the points on the parabola below the x-axis are those for which:
[tex]-7Therefore, in interval notation, the solution to the inequality is:[tex](-7,4)[/tex](x,2) is a solution to 7x-5>y
No, becuase not all the posible values of x make the inequality true.
For example, if x = 0
7(0) - 5 > 2
0 - 5 > 2
- 5 > 2 This is not true.
Red Brass is an alloy made by combining copper with zinc in a ratio of 16 to 3. How much zinc should be combined with 40 kg of copper to make red brass?
To make red brass alloy ratio of copper : zinc is 16 :3 ,then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.
As given,
Ratio given to make red brass alloy using copper and zinc is:
Copper :Zinc=16 :3
Given quantity of copper to make red brass alloy=40 kg
Let y kg be the quantity required to make red brass alloy using 40 kg copper
Using ratio and proportion we get,
40 :y=16 :3
⇒y ×16=40×3
⇒y=120/16
⇒y=7.5 kg
Therefore, to make red brass alloy ratio of copper : zinc is 16 :3 , then zinc should be combined for making red brass alloy of 40kg copper is 7.5kg.
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Assume that a 24-month CD purchased for $4000 pays an APY of 4.25% (and of course interest is compounded). How much do you have at maturity?
At the CD's maturity in 2 years' time, the future value that you can collect is $4,347.22.
What is the future value?The future value (FV) of CD is the present value compounded at an interest rate of 4.25% for 2 years in the future.
We can compute the future value using the FV formula or an online finance calculator as below.
N (# of periods) = 2 years (24 months)
I/Y (Interest per year) = 4.25%
PV (Present Value) = $4,000
PMT (Periodic Payment) = $0
Results:
FV = $4,347.22 ($4,000 + $347.22)
Total Interest = $347.22
Thus, the 24-month CD purchased for $4000 will yield a future value of $4,347.22 at maturity.
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HELPPPPPPPPPP URGENT
Which of the following methods would NOT be used to prove that two triangles are congruent?
A. Prove that the hypotenuse and one leg of one triangle are congruent to the hypotenuse and one leg of the other triangle.
B. Prove that two sides and an included angle of one triangle are congruent to two sides and an included angle of the other triangle.
C. Prove all three sets of corresponding angles congruent.
D. Prove all three sets of corresponding sides congruent.
The methods which can be used to prove that the two triangles are congruent are:
Prove all three sets of corresponding angles are congruent.
Prove all three sets of corresponding sides are congruent.
Option C and Option D are the correct answer.
What are corresponding angles?Corresponding angles are angles that occur on the same side of the transversal line and are equal in size.
We have,
To prove that two triangles are congruent, we need to show that the corresponding sides and corresponding angles are congruent.
So,
Prove all three sets of corresponding angles are congruent.
Prove all three sets of corresponding sides are congruent.
These two methods can be used to prove that the two triangles are congruent.
Thus,
The methods which can be used to prove that the two triangles are congruent are:
Prove all three sets of corresponding angles are congruent.
Prove all three sets of corresponding sides are congruent.
Option C and Option D are the correct answer.
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The two points on the graph are given by the linear function f use the two points to find the equation that represents the linear function f. What is f(6)?
The function f(6) has a value of 1./3
How to determine the value of the linear equation?The graph that completes the question is added as an attachment
From the graph, we have the following points
(x, y) = (4, 1) and (1, 2)
We start by calculating the slope of the points using the following slope equation
Slope = (y₂ - y₁)/(x₂ - x₁)
Where x and y are defined above
So, we have
Slope = (2 - 1)/(1 - 4)
Evaluate
Slope = -1/3
At f(6), we have
x = 6
So, the point can be represented as (6, y)
Using the slope formula again, we have
Slope = (y₂ - y₁)/(x₂ - x₁)
Where
(x, y) = (4, 1) and (6, y)
This gives
Slope = (y - 1)/(6 - 4)
Evaluate
Slope = (y - 1)/2
So, we have
(y - 1)/2 = -1/3
Evaluate
y = -2/3 + 1
Evaluate
y = 1/3
Hence, the value of f(6) is 1/3
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Rewrite the expression with a rational exponent as a radical expression.
The expression with a rational exponent as a radical expression is [tex]\sqrt[9]{3}[/tex]. Therefore, option B is the correct answer.
The given expression is [tex](3^{\frac{2}{3} } )^{\frac{1}{6} }[/tex].
What is a rational exponent?Rational exponents are exponents of numbers that are expressed as rational numbers, that is, in [tex]a^\frac{p}{q}[/tex], a is the base and p/q is the rational exponent where q ≠ 0.
Now, the given expression can be solved as follows:
Using power law [tex](a^m)^n=a^{m\times n}[/tex], we get
[tex](3^{\frac{2}{3} } )^{\frac{1}{6} }=3^{\frac{2}{3}\times \frac{1}{6}}[/tex]
[tex]=3^{\frac{1}{9} }[/tex]
The equivalent expression to [tex]=3^{\frac{1}{9} }[/tex] is [tex]\sqrt[9]{3}[/tex].
The expression with a rational exponent as a radical expression is [tex]\sqrt[9]{3}[/tex]. Therefore, option B is the correct answer.
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the table shows the workout results for for joggers complete the table to order the joggers from the slowest to the fastest rate
For Wesley:
distance = 7.7miles, time = 3.5h
[tex]\text{Rate (Wesley) = }\frac{7.7}{3.5}=2.2\text{ miles / hour}[/tex]For Xavier:
distance = 3.5 miles, time = 1.25h
[tex]\text{ Rate (}Xavier)\text{ = }\frac{3.5}{1.25}=2.8\text{ miles / hour}[/tex]For Yvette:
distance = 4.224 miles, time = 1.76h
[tex]\text{ Rate (}Yvette)\text{ = }\frac{4.224}{1.76}=2.4\text{ miles / hour}[/tex]For Zubin:
distance = 5.175 miles, time = 2.25h
[tex]\text{Rate (Zubin) = }\frac{5.175}{2.25}=2.3\text{ miles / hour}[/tex]Therefore, the complete table is as given below
On a particular production line the likelihood that a light bulb is defection is 5%. Ten light bulbs are randomly selected. What is the probability that at most 3 of the light bulbs will be defective
The probability that at most 3 of light bulbs will be defective will be 0.998.
Probability may be defined as an expression which may be used to determine the possibility of occurring of any event. The probability of happening an event surely is 1 and probability of not happening an event is zero. Since, 5 percent of bulbs are defective then
5% = 0.05 Now,
Non defective bulbs = 1 - 0.05 = 0.95
n = number of light bulbs = 7
We can calculate this using binomial distribution.
p(x) = ⁿCₓ × (pˣ)(1-p) ^n-x
Our question says at most 3 is defective, so it will be
(⁷C₀ × 0.05⁰ × 0.95⁷) + (⁷C₁ × 0.05¹ × 0.95⁶) + (⁷C₂ × 0.05² × 0.95⁵) + (⁷C₃ × 0.05³ × 0.95⁴)
= 0.698 + 0.257 + 0.040 + 0.003
= 0.998 which is the required probability.
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Which algebraic expression shows the average function points of helium, hydrogen and neon if h represents the function point of hydrogen and represents the neon point
The answer is the option C. (h + j + k)/3
Because to find the average of 3 quantities, you have to add them all and then divide the result by 3
Given sin 60degrees √ 3/2 find cos 60°
cos 60°
Step-by-step explanation:
if I understand you correctly, then you got
sin(60°) = sqrt(3/2)
and now we have to find cos(60°) based on that.
but : sin(60°) = sqrt(3/4) = sqrt(3)/2
I will continue with that.
one major observation with the trigonometric functions in a norm circle (radius = 1) is that sine and cosine are the legs of a right-angled triangle.
the radius at the angle is the Hypotenuse.
and so, Pythagoras applies
c² = a² + b²
c is the Hypotenuse, a and b are the legs.
so,
radius² = sin²(x) + cos²(x)
and because radius = 1
1² = 1 = sin²(x) + cos²(x)
in our case
1 = sin²(60) + cos²(60)
1 = (sqrt(3)/2)² + cos²(60) = 3/4 + cos²(60)
cos²(60) = 1 - 3/4 = 1/4
cos(60) = sqrt(1/4) = 1/2
vera wants to prove that any rectangle is also a parallelogram
We are given a rectangle ABCD
Recall that a rectangle is a quadrilateral in which all angles are right angles (90°)
Each pair of interior angles are supplementary. The two right angles add to a straight angle which means that the opposite sides of a rectangle are parallel.
In quadrilateral ABCD, if m∠A = m∠B = m∠C = m∠D = 90° then AB || DC and AD || BC
Hence, a rectangle is also a parallelogram.
Option B is the correct answer.
Ryan, Darius, and Mason each have $15.75. They each spend the same amount (d), in dollars, at the school fair. The total amount of money they still have can be expressed as 3(15.75 - d). Which expression is equivalent to the total amount, in dollars, they still have?
Which is correct for this function pls help
The graph represents a linear function with negative slope.
How does different type of graph and their equations look like?
1. Linear graph: It is of the form y= mx+ c
First-order variables are present in linear functions, and the graph's placement is determined by two constants. These operations graph into a line in every case. The slope of the line is determined by the constant m. The slope of the line will slope up if it is positive and down if it is negative.
2. Quadratic graph: y= ax^2+ bx+ c
These type of graphs have an U shaped curve and their slope can also be obtained by drawing a tangent.
3. Square root graph : F(x)=x is the parent function of all functions with the formula f(x)=a+b. Keep in mind that f(x)=x has an x0 domain and a y0 range. By translating the graph of f(x)=x to a units to the right and then b units up, the graph of f(x)=root x-a+b can be derived.
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All eleven letters from the word MISSISSIPPI are written on individual slips of paper and placed in a hat. If you reach into the hat and randomly choose one slip of paper, what are the odds against the paper having the letter P written on it?
Given:
There are 11 letters in the word 'MISSISSIPPI'
The number of P's are 2.
The probability that the randomly chosen slip of paper have the letter P written on it is,
[tex]\begin{gathered} P=\frac{Number\text{ of letter P}}{\text{Total letters}} \\ P=\frac{2}{11} \end{gathered}[/tex]The probability that the randomly chosen slip of paperdoes not have the letter P written on it is,
[tex]\begin{gathered} P^{\prime}=1-\frac{2}{11} \\ P^{\prime}=\frac{9}{11} \end{gathered}[/tex]The odd against event is calculated as,
[tex]\begin{gathered} Odd\text{ against=}\frac{P(not\text{ E)}}{P(E)} \\ Odd\text{ against}=\frac{P^{\prime}}{P}=\frac{\frac{9}{11}}{\frac{2}{11}}=\frac{9}{2} \end{gathered}[/tex]Answer: The odds against the paper having the letter P written on it is 9/2 (9:2)
Evaluate the expression when c =-2.5 and d= 8.9.4d-c
To solve the exercise, replace in the expression the given values of c and d and then operate:
[tex]\begin{gathered} c=-2.5 \\ d=8.9 \\ 4(8.9)-(-2.5)=35.6+2.5=38.1 \end{gathered}[/tex]Therefore, the value of the evaluated expression is 38.1
The scatter plot shows the price of gas per gallon. Based on the trend line, which is closet to the expected price of 11 gallons of gas?A. $34B. $36C. $38D. $40
see the attached figure below to better understand the problem
Please give me a minute
The price is about $38
therefore
The answer is option C
Use the diagram to answer the question that follows
What is the image of c under the translation described by the translation rule (x,y) (x+11, y-8)
○ D
○ B
○ E
○ A
The image of C under the translation described by this translation rule (x, y) → (x + 11, y - 8) is: (4, -6)
What is a translation?In Geometry, the translation of a geometric figure to the right simply means adding a digit (11) to the value on the x-coordinate (x-axis) of the pre-image while translating a geometric figure down simply means subtracting a digit (8) from the value on the y-coordinate (y-axis) of the pre-image.
Note: Each point on this graph represents 2 units.
Next, we would translate the image of C 11 units to right and 8 units down. Therefore, this transformation can be modeled by this translation rule:
(x, y) → (x + 11, y - 8)
Point at C = (-7, 2) → Point at C' = (-7 + 11, 2 - 8) = (4, -6)
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Help my hw is due by 12:00 am for final grade!!
Length has 5 cubes
width has 3 cubes
height has 7 cubes
Volume = length x width x height
5/2 * 3/2 * 7/2 = 105/8 = 13.125 ft^2
if you need to install carpet in a room that is 80ft x 50ft how many 10ft x 50ft rolls of carpet do you need to cover the room
Given:
The dimensions of the room are,
[tex]\begin{gathered} l=80ft \\ b=50ft \end{gathered}[/tex]The dimensions of the carpet are,
[tex]\begin{gathered} l_1=10ft \\ b_1=50ft \end{gathered}[/tex]To find:
The number of rolls of carpet.
Explanation:
The number of rolls of carpet is calculated by,
[tex]\begin{gathered} \frac{Area\text{ of the room}}{Area\text{ of a carpet rool}}=\frac{l\times b}{l_1\times b_1} \\ =\frac{80\times50}{10\times50} \\ =8rolls\text{ of carpet} \end{gathered}[/tex]Therefore, the number of rolls of carpet is 8.
Final answer:
The number of rolls of carpet is 8.
A profit of $1.45 was earned on each bag of oranges sold. (See 13 bags.) Find the profit if all the bags were sold.
Solution:
If a profit of $1.45 was earned on each bag of oranges sold, then the profit, if all 13 bags were sold, would be:
13 x $1.45 = $18.85
so that, the correct answer is:
$18.85
Through Viking Brokerage, Erin purchased $23,510 worth of stock and paid
her broker a 1% broker fee. She sold when the stock price increased to
$27,300, and used a discount broker who charged $21 per trade. Compute
her net proceeds.
The most appropriate choice for stocks and net proceeds will be given by-
Net proceeds of Erin = $3533.9
What is stock and net proceeds?
Stock
Stock is a part of share set up by the company so that people can buy.
Net proceeds
After deducting all expenses, amount recieved by the seller after selling of stocks is called net proceeds.
Worth of stocks purchased by Erin = $23510
Percentage paid to her broker = 1%
Amount paid to broker = [tex]\frac{1}{100}\times 23510[/tex]
= $235.1
Now price of stocks increased to $27300
Net profit = $(27300 - 23510)
= $3790
Net proceeds = $(3790 - 235.1 - 21)
=$3533.9
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I need questions 10 , 13 , 15 , and 16 solved with steps and graph
10. |x - 4| - 4 = 1/2x
⇒ Multiplying by 2,
2 |x - 4| - 8 = x
So, x - 4 = (x + 8)/2
= -(x + 8)/2
When,
x - 4 = (x + 8)/2
2x - 8 = x + 8 (Multiplying by 2)
2x - x = 8 + 8 (Adding 8 and subtracting x to both sides)
x = 16
When,
x - 4 = - (x + 8)/2
2x - 8 = -x - 8 (Multiplying by 2)
2x + x = -8 + 8 (Adding 8 and x to both sides)
3x = 0
x = 0
Hence, the solution is x = 16 and x = 0.
13. (3/4)x = 2x - 10
⇒ Subtract 2x from both sides.
-5x/4 = -10
Multiply both sides by 4/(-5).
(-5x/4)×4/(-5) = -10 × 4/(-5).
x = 8 is the solution of the equation.
15. x² - 7x - 8 > 0
⇒ Solve the quadratic equation by splitting the middle term,
x² - 8x + x - 8 > 0
x(x - 8) + 1(x -8) > 0
(x + 1)(x- 8) > 0
-1 and 8 are the critical points of the inequality.
x < -1 and x > 8 are the solutions of the inequality which are represented by the shaded red region in the graph.
16. x - 5 > - 2x + 4
⇒ Adding 2x to both sides.
3x - 5 > 4
Adding 5 to both sides.
3x > 9
Divide both sides by 3.
x > 3 is the required solution represented by blue shade region in the graph.
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