Use the properties of equalities to solve the given equation:
[tex]y+2.4=15.6[/tex]Substract 2.4 from both sides of the equation:
[tex]\begin{gathered} y+2.4-2.4=15.6-2.4 \\ \Rightarrow y=13.2 \end{gathered}[/tex]Therefore, the solution to the equation is:
[tex]y=13.2[/tex]A person tosses a coin twice. Find the set representing the event E that the first toss is tails.
Solution:
Given that;
A person tosses a coin twice.
The tree diagram representing when a coin is tossed twice is shown below
From the tree diagram above;
The set representing the event E that the first toss is tails is
[tex]TH,TT[/tex]Hence, the answer is
[tex]\lbrace TT,TH\rbrace[/tex]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.
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
Mortgages (47-49)Eli is buying a townhouse that costs $276,650. He has $28,000 in savings and earns $4,475 a month. Eli would liketo spend no more than 30% of his income on his mortgage payment. Which loan option would give Eli the lowestmonthly payment? Show your work.A. 30 year FHA, 3.5% down and a fixed rate of 6.5%B. 30 year fixed, 5% down at a fixed rate of 6.25%C. 30 year fixed, 6.5% down and a fixed rate of 5.75%D. 30 year fixed, 10% down at a fixed rate of 5%
Cost C = $276,650
Initial quote = $28000
If Eli spends 30% of 4,475 = $1342.5 monthly
Then now calculate
3.5% down of $276,650 = $9682.75
Substract $28000- $9682.75 = 18317.25
Now find ,fixed rates
For 6.5% , interest is.
She have to pay a quote of (276,650- 9682.75)/12•30
. = $741.57
For 5% down of $276,650 = 13832.5
Eli have now $28000- $13832.5 = 14167.5
She have to pay a quote of (276,650- 13832)/30•12 = $262818/360
. = $730
Interest fixed rate 6.25%
Then find 730• ( 1+ 6.25/100)^ 30 = 4500 in 30 years
Now option C)
6.5% down = $276,650x 6.5/100 = $17982.25
Eli have now $28000 - 17982.25 = 10017.75
She have to pay a quote of (276,650 - 17982)/30•12
. = $718.52
Then find 718.52•( 1+ 5.75/100)^30 = 3844.6. in 30 years
Option D)
10% down = $276,650x10/100 = $27,665
Eli have now $28000- 27,665 = $335
She have to pay a quote of (276,650 - 27665)/30•12 =
. = $691.625
Then find now 691.625•(1+ 5/100)^30 = $2989.16 in 30 years
So ,in conclusion we have to choose the minor value of quote. In this case is
ANSWER IS
OPTION D) $2989,16
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.
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.
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
The 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
is √100 a whole number, irrational number, rational number, or an integer?
The given number is
[tex]\sqrt[]{100}[/tex]The square root of 100 is 10.
So, this is a whole, integer, and rational number.Remember that whole and integers are also rational because they are a subset of rational numbers set.
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.
In the statement 'If it is sunny Thursday, we will go to a ball game', the phrase 'we will go to a ball game' is thehypothesis.conclusion.converse.conditional statement.
Answer:
(B) Conclusion.
Explanation:
Given the statement:
If it is sunny Thursday, we will go to a ball game
The phrase: 'we will go to a ball game' is the conclusion.
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)
what is a perpendicular line?
Answer:
it is a line that forms a 90° angle with another
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
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]
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)
Three friends go on a road trip from Phoenix, AZ toLas Vegas, NV, a distance of 286 miles. The car theyare driving gets 33 miles per gallon. If the price ofgasoline averages $3.86/gallon, how much willeach student have to pay for the trip
First, let's find how many gallons are needed:
[tex]\begin{gathered} \frac{286miles}{33\text{ }\frac{miles}{gallon}} \\ 8.7gallons \end{gathered}[/tex]If the price of one gallon is $3.86, then they will have to pay:
[tex]\begin{gathered} 3.86*8.7 \\ 33.58 \end{gathered}[/tex]The price they will have to pay is $33.58.
Dividing the price by 3 (each student):
[tex]\begin{gathered} \frac{33.58}{3} \\ 11.2 \end{gathered}[/tex]Answer: Each student will have to pay $11.20.
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
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]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
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
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]A race car travels 2 9/16 miles per minute. How far will it travel in 1 1/4 ?
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
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
Find three consecutive odd Integers such that the sum of the largest and twice the smallest is 25.x represents the smallest integer, then which equation could be used to solve the problem?
ANSWER
7, 9, 11
EXPLANATION
We want to find three consecutive odd numbers.
Let the smallest number be x.
Then, the next odd number is (x + 2).
The last odd number is (x + 4).
The sum of the largest odd number and twice the smallest number is 25:
(x + 4) + 2x = 25
=> x + 4 + 2x = 25
3x + 4 = 25
3x = 25 - 4
3x = 21
x = 21 / 3
x = 7
Therefore, the three consecutive numbers are:
7
(7 + 2) = 9
(7 + 4) = 11
They are 7, 9, 11
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.
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