Given:
Linear equation in x and y:
An equation of the form y = mx + c or ax + by +c =0 is a linear equation as the degree of both variables x and y is one.
(a) 2x = 5 + y:
The equation can be written as:
[tex]y=2x-5\text{ or 2x-y-5=0}[/tex]This is of the form of ax+by+c=0 so it is linear.
Here, a=2, b= 1, c= - 5
(b) y = 5x + 3:
[tex]y=5x+3\text{ or 5x-y+3=0}[/tex]This is already in the form of ax + by+ c=0 so it also linear.
Here, a= 5 , b = - 1, c= 3
Helen mean receives a travel allowance of $180 each week from her company from time away from home. If this allowance is taxable and she has 24% income tax rate, what amount will she have to pay in taxes for this employee benefit? (Round your final answer to two decimal places)
The tax rate she needs to pay is 24% of the $180.
Then first, we convert the 24% to decimal, by dividing by 100:
[tex]\frac{24}{100}=0.24[/tex]Now we multiply the total amount by the percentage in decimal:
[tex]0.24\cdot180=43.2[/tex]The amount she will have to pay in taxes is $43.20
You randomly choose one of the chips without replacing the first chip you choose a second chip. Which question is different find both answers.
The probability of event A and event B is the product of the probability of A snd the probability of B given that A has happened. It is written as
P(A and B) = P(A) x P(BIA)
Considering the first option,
We know that
probability = number of favourable outcomes/total number of outcomes
The total number of outcomes is 6
The probability of choosing a 1, P(A) = 1/6
There are 2 blue chips and since the 1 that was chosen was not replaced, the total number of outcomes would be 5. Thus, the probability of choosing a blue chip given that a 1 has been chosen, P(BIA) is 2/5
Thus, the probability of of choosing a 1 and then a blue chip is
1/6 x 2/5 = 1/15
Considering the second option,
The probability of choosing a 1, P(A) = 1/6
there are 3 even numbers. The probability of choosing an even number given that a green chip has been chosen, P(BIA) = 3/5
Thus, the probability of choosing a 1 and then an even number is
1/6 x 3/5 = 1/10
Considering the third option,
The probability of choosing a green chip, P(A) = 1/6
there are 3 chips that are not red after the green chip has been chosen. The probability of choosing a chip that is not red given that a green chip has been chosen, P(BIA) = 3/5
Thus, the probability of choosing green chip and then an even number is
1/6 x 3/5 = 1/10
Considering the fourth option,
The probability of choosing a number less than 2 is , P(A) = 1/6
there are 3 chips that are even numbers. The probability of choosing a chip that is an even number given that a number less than 2 has has been chosen, P(BIA) = 3/5
Thus, the probability of choosing a number less than 2 and then an even number is
1/6 x 3/5 = 1/10
Thus, the only different option is the first one
An experiment consists of drawing two coins out of a jar one at a time without replacement. The jar contains 1 penny, 1 nickel, 1 dimand 1 quarter.Which of the following tree diagrams represents
Explanation
By observation, the possible selections are
Answer: Option Y
What is the probability of drawing four cards from a standard deck and them all being aces?
We start by saying that the deck has 52 cards, in which they have 4 aces (one for each suit).
We are also taking about drawing cards wthout replacement.
Then, for the first draw, we have 4 in 52 chances of drawing an ace.
For the second draw, as one ace is taken out of the deck of cards, there is a chance of 4-1=3 out of 52-1=51 of drawing an ace.
This can be generalized for the 4 draws as:
[tex]P=\frac{4}{52}\cdot\frac{3}{51}\cdot\frac{2}{50}\cdot\frac{1}{49}=\frac{24}{6,497,400}=3.7\cdot10^{-6}[/tex]where P is the probability of drawing 4 aces in 4 draws.
There is a probability of 3.7 * 10^(-6) = 0.0000037 = 0.00037% of drawing 4 cards from a standard deck and all 4 being aces.
What is the constant of variation, k, of the direct variation, y = kx, through (5, 8)?k = – k equals negative (8 Over 5).k = – k equals negative (5 Over 8 ).k = k equals (5 Over 8).k = k equals (8 Over 5 ).I dont understand how to solve this.
Hello! If we rewrite this expression y = kx, we will see that k will have a variation according to y and x values, look:
Now, notice that the exercise has given a point to us: (5, 8).
Remember that (5, 8) = (x, y), so, let's replace it in the formula:
Right answer:
k = k equals (8 Over 5 ).
Find each product in simplest form you may leave your answers as an improper fraction
Given expression:
[tex]\frac{1}{8}\text{ }\times\text{ }\frac{1}{5}[/tex]Taking the product of the fractions implies multiplying the numerator and denominator:
[tex]\begin{gathered} =\text{ }\frac{1\text{ }\times\text{ 1}}{8\text{ }\times\text{ 5}} \\ =\text{ }\frac{1}{40} \end{gathered}[/tex]Hence, the product of the fractions is 1/40
How many ways can the 4 flowers be chosen?Jeanine Baker makes floral arrangements. She has 16 different cut flowers and plans touse 4 of them. How many different selections of the 4 flowers are possible?vaTO#.voMore(1,1)Clear AllHelp Me Solve ThisView an ExampleGet More Help
Given:
Jeanine Baker makes floral arrangements. She has 16 different cut flowers and plans to use 4 of them
We will find a number of ways to select of the 4 flowers
As the arrangement is not necessary
We will use the combinations
So, the number of ways =
[tex]16C4=\frac{16!}{(16-4)!\cdot4!}=1820[/tex]So, the answer will be 1820 possible ways to select 4 flowers
I need help with this question I appreciate the help
when
y = 2
x = 10
Therefore,
[tex]\begin{gathered} y=kx \\ k=\frac{y}{x} \\ k=\frac{2}{10}=\frac{1}{5}=0.2 \end{gathered}[/tex]C = 0.2 g
1) use the equation below to answer part A-Cy=3x-1Part A : What is the slopeA) 3B)3xC)(-1,0)D)(0,-1)Part B : what is the y-intercept? A) (0,-1)B)3xC)(-1,0)D)3Part C: graph y=3x-1
We are given the following equation
[tex]y=3x-1[/tex]Part A: What is the slope?
The standard equation of a line in slope-intercept form is given by
[tex]y=mx+b[/tex]Where m is the slope and b is the y-intercept.
Comparing the given equation with the standard form, we see that the slope is 3.
m = 3
Option (A) is correct.
Part B: What is the y-intercept?
Comparing the given equation with the standard form, we see that the y-intercept is -1.
b = -1
The y-intercept is the value when the line cuts the y-axis, so the corresponding x-value is 0.
So the point is
(0, -1)
Option (A) is correct
Part C: graph y = 3x - 1
The above equation can be graphed by taking some coordinates (substitute x-values into the function and get the y-values from the function.
When x = -1
y = 3x - 1 = 3(-1) - 1 = -3 - 1 = -4
(-1, -4)
When x = 1
y = 3x - 1 = 3(1) - 1 = 3 - 1 = 2
(1, 2)
When x = 2
y = 3x - 1 = 3(2) - 1 = 6 - 1 = 5
(2, 5)
Let us sketch these points to form a line.
The above is a rough graph for the given equation y = 3x - 1
Solve the system of equations by the substitution method. 7x- y=58 5x+6y=28
ANSWER
The solution is (8, -2)
EXPLANATION
The substitution method consists in solving one of the equation for one of the variables - it will be as a function of the other variable, then substitute that variable by this expression into the other equation. There we'll have an equation for one of the variables, we solve that and the substitute the value into the expression we found first.
For this problem let's solve the first equation for y:
[tex]7x-y=58[/tex]We can just add y to both sides of the equation and then subtract 58 from both sides:
[tex]\begin{gathered} 7x-y+y=58+y \\ 7x=58+y \end{gathered}[/tex][tex]7x-58=y[/tex]Now we substitute y by this expression into the second equation:
[tex]5x+6(7x-58)=28[/tex]And solve for x. First apply the distributive property to the second term:
[tex]\begin{gathered} 5x+6\cdot7x-6\cdot58=28 \\ 5x+42x-348=28 \end{gathered}[/tex]Add like terms - this means adding the coefficients of x:
[tex]\begin{gathered} (5+42)x-348=28 \\ 47x-348=28 \end{gathered}[/tex]Then add 348 to both sides of the equation:
[tex]\begin{gathered} 47x-348+348=28+348 \\ 47x=376 \end{gathered}[/tex]Finally, divide both sides by 47:
[tex]\begin{gathered} \frac{47x}{47}=\frac{376}{47} \\ x=8 \end{gathered}[/tex]Now, to find y we just have to substitute x = 8 into the expression we found for y as a function of x:
[tex]y=7x-58[/tex][tex]y=7\cdot8-58=56-58=-2[/tex]So the solution to the equation is x = 8 and y = -2, which is the point (8, -2)
G is the midpoint for FH what is the length of FG
Since G is the midpoint of FH,
[tex]\begin{gathered} FG=GH \\ \Rightarrow11x-7=3x+9 \\ \Rightarrow11x-3x=9+7=16 \\ \Rightarrow8x=16 \\ \Rightarrow x=2 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} FG=11x-7=11\cdot2-7=22-7=15 \\ \Rightarrow FG=15 \end{gathered}[/tex]The answer is 15, option a.
what is a perpendicular line?
Answer:
it is a line that forms a 90° angle with another
Simplify each expression by using the Distributive Property and combine like terms to simplify the expression.Algebra 1-a+11b-7-2a-b
Explanation:
The initial expression is:
-a + 11b - 7 - 2a - b
The terms -a and -2a are like terms. In the same way, 11b and -b are like terms.
So, using the distributive property, we get:
-a + 11b - 7 - 2a - b
-a - 2a + 11b - b - 7
(-1 - 2)a + (11 - 1)b - 7
-3a + 10b - 7
Therefore, the simplified expression is: -3a + 10b - 7.
Answer: -3a + 10b - 7
Convert to radians. (Round to 3 decimal places.)36.45° =___radians
Given:
[tex]36.45\degree[/tex]Required:
To convert the given degree into radian.
Explanation:
To convert the value of the angle in degree, to its equivalent radians, we need to multiply the given value with π/180.
Therefore,
[tex]\begin{gathered} =36.45\times\frac{\pi}{180} \\ \\ =0.6362radians \end{gathered}[/tex]Final Answer:
[tex]36.45\degree=0.6362radians.[/tex]Solve the proportion 10/23=4/x x=
we have
10/23=4/x
multiply in cross
10*x=23*4
10x=92
x=92/10
x=9.2The average person blinks about 15000 times a day. The average blink lasts one tenth of a second.How many seconds of one day does the average person spend blinking? (Sleeping does not count!)a. 150,000b. 25c. 15,000d. 1,500
So, the average person blinks 15,000 times a day. Each blink lasts one tenth, that is, 0.1 seconds.
So:
15,000*0.1 = 1,500 seconds.
Letter D
The slope of the line below is -1/7. - Write a point-slope equation of the line using the coordinates of the labeled point. 10+ (3,3) - 10 110 - 10+ A. y+3 =-;(x +3) y-3--}(x-3) O C. y+3+7(x+3) O D. y-3 - (x-3)
Point slope formula:
y-y1 = m (x-x1)
Where:
m= slope
(x1,y1) = point of the line
Replacing with the point given (3.3) and slope =-1/7
y+3 = -1/7 (x+3)
Number one please How many planes can be drawn through any three non collinear points?
Solution:
Given:
Collinear points are the points that lie on the same straight line or in a single line.
Hence, from the image given, the points that lie on the same straight line are; F, E, G
Therefore, option D is the correct answer.
What is the average rate of change from point A to point B in the graph below? A(1/3) B(3/7) C(3) D(6)
Step 1: Define the formula
The formula for finding the average rate of change is :
[tex]\text{Average rate of change = }\frac{y_2-y_1}{x_2-x_1}[/tex]Step 2: Identify the coordinates of the points on the line
A(-3, -1), B(6, 2)
Step 3: Apply the formula
[tex]\begin{gathered} \text{Average rate of change = }\frac{2-(-1)}{6-(-3)} \\ =\text{ }\frac{2\text{ + 1}}{6\text{ + 3}} \\ =\text{ }\frac{3}{9} \\ =\text{ }\frac{1}{3} \end{gathered}[/tex]Hence, the average rate of change is 1/3
Answer: Option A
Determine if the table is linear or exponential. Tables 2 , 3 and 4 are the same
Exponential and linear relations differ in the way the y-values change when the x-values increase by a constant amount, that is, in a linear relationship, the y-values have equal differences and in an exponential relationship, the y-values have equal ratios.
In our first table, when the x-values increase one unit, the y-values decreses 2 units. Similarly, when the x-values increase 2 units, the y-values decrease 4 units and so on:
. Therefore, the first table shows a linear behavior.
On the other hand, table 2,3 and 4 are the same. In those cases, when the x-values increase one unit the, the y-values have a ratio of 2. Similarly, when the x-values increase 2 units the corresponding ratio for the y-values in 4 and so on.
This means that tables 2, 3 and 4 denote an exponential relationship.
what's the total cost with tax? price $17.95 tax 6%
Answer:
$19.03
Explanation:
Given the price to be $17.95 and a 6% tax, to determine the tax amount we have to find 6% of $17.95;
[tex]\frac{6}{100}\ast17.95=0.06\ast17.95=1.077[/tex]So the tax is $1.08. Let's go ahead and find the total cost by adding the tax to the price;
[tex]1.08+17.95=19.03[/tex]Therefore, the total cost is $19.03.
evaluate the expression which expression is half as large as the expression 345+23
To find the corresponding expression, solve the sum of the given expression and then divide it by 2.
[tex]\frac{345+23}{2}[/tex]It’s Election Day for the honor society. If a president and Vice President are elected, how many different combinations can be made among eleven people?
11 people
11 posibilities for president
10 possibilities for Vice president
11 x 10 = 110
Answer: 110 different combinations
make k the subject of the formula m= √k+1/4
Answer:
∴ [tex]k = m^{2} - \frac{1}{4}[/tex]
Step-by-step explanation:
[tex]m=\sqrt{k} + \sqrt {(\frac{1}{4})}[/tex]
[tex]m^{2} = k+\frac{1}{4}[/tex]
[tex]k+\frac{1}{4} =m^{2}[/tex]
∴ [tex]k = m^{2} - \frac{1}{4}[/tex]
Solve the equation for the indicated variable. (Leave ± in the answer as needed)
The given expression is:
[tex]h=td^2[/tex]Therefore,
[tex]td^2=h[/tex]Dividing both sides of the equation by t:
[tex]\frac{td^2}{t}=\frac{h}{t}[/tex]Hence,
[tex]d^2=\frac{h}{t}[/tex]Thus,
[tex]d=\sqrt{\frac{h}{t}}=\frac{\sqrt{h}}{\sqrt{t}}[/tex]To rationalize the equation by √t:
[tex]\begin{gathered} d=\frac{\sqrt{h}}{\sqrt{t}}\times\frac{\sqrt{t}}{\sqrt{t}}=\frac{\sqrt{ht}}{t} \\ d=\frac{\sqrt{ht}}{t} \end{gathered}[/tex]d =
What is the solution for the equation 6 (3x - 2) = -4(5x - 3) + 8?
Okay, here we have this:
Considering the provided equation, we are going to solve it, so we obtain the following:
6 (3x - 2) = -4(5x - 3) + 8
18x - 12 = -20x + 12 + 8
18x - 12 = -20x +20
18x+20x=+20+12
38x=32
x=32/38
x=16/19
Finally we obtain that the solution for the equation is 16/19.
Find the slope and y-intercept of the line in the graph. ly 6 5 (0, 3) 3 2 1 1 ( 25) -8 The slope is m and the y-intercept is b =
Slope m is -4; y-intercept b is 3
Here, we want to find the slope and y-intercept of the given plot
The y-intercept is the y-value of the point at which the graph crosses the y-axis
Thus, as we can see, the value is 3
To find the slope, we use the slope equation and supply the points
The equation is as follows;
[tex]\begin{gathered} m\text{ = }\frac{y_2-y_1}{x_2-x_1} \\ \\ (x_1,y_1)\text{ = (0,3)} \\ (x_2,y_2)\text{ = (2,-5)} \\ \\ m\text{ = }\frac{-5-3}{2-0}=\text{ }\frac{-8}{2}=\text{ -4} \end{gathered}[/tex]Find the image of (4, 5) under S0.5 withcenter at (1, 6)
We have a pre-image that is the point (4, 5).
We applied a dilation with scale 0.5 and center at (1, 6).
As the center is not the center of coordinates, we applied a change of coordinates to make (1, 6) the center of coordinates.
Then, the point (4, 5) becomes:
[tex](4,5)\longrightarrow(4-1,5-6)=(3,-1)[/tex]We apply the dilation to the point and get:
[tex](3,-1)\longrightarrow(0.5\cdot3,0.5\cdot(-1))=(1.5,-0.5)[/tex]Now, we go back to the original coordinates:
[tex](1.5,-0.5)\longrightarrow(1.5+1,-0.5+6)=(2.5,5.5)[/tex]We can verify the transformation in a graph:
The graph makes sense, as the image point is half the distance from the center of dilation that the pre-image point.
Express the product shown as a fraction in simplest form: -2/5 . 2/5
Answer:
7/25
Step-by-step explanation:
2/5 x 7/10 =14/50 divide by 2/2 = 7/25
I'm not understanding what they're wanting me to do here?? Can someone pls help?
From the given figure,
[tex]\begin{gathered} In\text{ }\Delta ABD,\text{ BD }\perp\text{ AC} \\ \end{gathered}[/tex]By using right angled triangle theorem,
According to right angled triangle theorem, perpendicular drawn on the hypotenuse is equal to the square root of the product of parts in which hypotenuse is divided.
[tex]\begin{gathered} x\text{ = }\sqrt[]{10\text{ }\times\text{ 4}} \\ x\text{ = }\sqrt[]{40} \\ x\text{ = 2}\sqrt[]{10} \end{gathered}[/tex]By using Pythagoras theorem,
[tex]\begin{gathered} AB^2=AD^2+DB^2 \\ z^2=10^2+x^2\text{ } \\ z^2=10^2\text{ + (2}\sqrt[]{10})^2 \\ \end{gathered}[/tex]Further,
[tex]\begin{gathered} z^2=\text{ 100 + 40} \\ z^2\text{ = 140} \\ z\text{ = 2}\sqrt[]{35\text{ }}\text{ } \end{gathered}[/tex]Also,
[tex]In\text{ }\Delta ABC,[/tex]By using Pythagoras theorem,
According to Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the remaining sides.
[tex]\begin{gathered} AC^2=AB^2+BC^2 \\ 14^2=z^2+y^2_{_{_{}\text{ }_{}}} \\ z^2=14^2-y^2_{_{_{}}}\text{ } \end{gathered}[/tex]Further,
[tex]\begin{gathered} y^2=14^2-z^2 \\ y^2\text{ = 196 - (2}\sqrt[]{35})^2 \\ y^2\text{ = 196 - 140} \\ \end{gathered}[/tex]Therefore ,
[tex]\begin{gathered} y^2\text{ = 56} \\ y\text{ = 2}\sqrt[]{14} \end{gathered}[/tex]Thus the required values of x , y and z are
[tex]\begin{gathered} x\text{ = 2}\sqrt[]{10}\text{ units} \\ y\text{ = 2}\sqrt[]{14}\text{ units} \\ z\text{ = 2}\sqrt[]{35\text{ }}\text{ units} \end{gathered}[/tex]