To solve this problem, we will use the two pair of points to find the slope of the equation of each line. Then, by comparing these slopes, we can determine either if they are perpendicular or parallel.
Slope calculations
To calcula the slopes, given the pairs of points, we are going to use the following formula: Given points (a,b) and (c,d) the slope of the line that passes through them is given by the formula
[tex]m=\frac{d\text{ - b}}{c\text{ -a}}=\frac{b\text{ - d}}{a\text{ -c}}[/tex]Let us calculate first the slope of the line that passes through the points (7,5) and (-14,-9). In this case, we have a=7,b=5,c=-14 and d=-9. So we get
[tex]m=\frac{5\text{ - (-9)}}{7\text{ - (-14)}}=\frac{14}{21}=\frac{2\cdot7}{3\cdot7}=\frac{2}{3}[/tex]Now, let us calculate the slope of the line that passes through the points (0,1) and (4,-5). In this case, we have a=0,b=1,c=4 and d=-5. So we get
[tex]m=\frac{1\text{ -(-5)}}{0\text{ - 4}}=\frac{6}{\text{ -4}}=\text{ -}\frac{3\cdot2}{2\cdot2}=\text{ -}\frac{3}{2}[/tex]Slope comparison
Now, we compare the slopes to determine if the lines are perpendicular or parallel. Recall that two lines are parallel if they have the same slope and they are perpendicular if the product of their slopes is -1. From our calculations, we can see that the slopes are not equal. Let us confirm that they are perpendicular. To do so, we multiply both slopes. So we get
[tex]\frac{2}{3}\cdot(\text{ -}\frac{3}{2})=\text{ -1}[/tex]Since their product is -1, this confirms that both lines are perpendicular.
If f(x) is an exponential function where f(4) = 7 and f(5.5) = 53, then find thevalue of f(5), to the nearest hundredth.
Given:
f(x) is an exponential function.
f(4) = 7.
f(5.5) = 53.
Since f(x) is an exponential function, f(x) can be expressed as,
[tex]f(x)=ab^x[/tex]Here, a and b are constants.
Hence, we can write
[tex]\begin{gathered} f(4)=ab^4----(1) \\ f(5.5)=ab^{5.5}\text{ ------(2)} \end{gathered}[/tex]Divide equation (2) by (1).
[tex]\frac{f(5.5)}{f(4)}=\frac{ab^{5.5}}{ab^4}[/tex]Substitute f(4) = 7 and f(5.5) = 53 in the above equation.
[tex]\begin{gathered} \frac{53}{7}=\frac{b^{5.5}^{}}{b^4} \\ \frac{53}{7}=b^{5.5-4} \\ \frac{53}{7}=b^{1.5} \\ \frac{53}{7}=b^{\frac{3}{2}} \\ b=(\frac{53}{7})^{\frac{2}{3}} \\ b=3.855 \end{gathered}[/tex]Now, the value of a can be obtained as,
[tex]\begin{gathered} f(4)=ab^4 \\ 7=a(\frac{53}{7})^{\frac{2}{3}} \\ a=\frac{7}{(\frac{53}{7})^{\frac{2}{3}}} \\ =1.815 \end{gathered}[/tex]what is 338.8882 rounded to the nearest thousandth
Answer:
338.8882 rounded to the nearest thousandth is 338.888
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2: A game is played by tossing a single coin onto a square table. The square is 25 inches o each side, and the coin has a radius of 10 inches (it's old fashioned). If the coin lands entirely on the table (nothing hanging off the edge), the player wins a prize. What fraction of the table can the center point of the coin land on so that the player wins a prize?
Find the area of the square table:
[tex]\text{Area of the square = }L^2=25^2=625in^2[/tex]Find the area of the coin (area of a circle):
[tex]\text{Area of coin= }\pi r^2=\pi10^2=314.16in^2[/tex]To find the fraction of the table the center point of the coin lands, we have:
[tex]\frac{Area\text{ of coin}}{\text{Area of table}}[/tex][tex]=\frac{314.16}{625}\text{ = }0.50[/tex]Since we are to leave the answer in fraction, we have:
[tex]\frac{5}{10}=\text{ }\frac{1}{2}[/tex]Which equation represents a line that is perpendicular to the line represented by
y=2/3x+1?
1) 3x+2y=12
2) 3x-2y=12
3) y=3/2x+2
4) y= -2/3x+4
Answer: (1)
Step-by-step explanation:
Perpendicular lines have slopes that are negative reciprocals. So, since the slope of the given line is 2/3, the slope of the line we want to find is -3/2.
Rearranging equations 1 and 2 into slope intercept form,
[tex]3x+2y=12 \implies 2y=-3x+12 \implies y=-\frac{3}{2}x+6\\\\3x-2y=12 \implies 2y-3x=-12 \implies 2y=3x-12 \implies y=\frac{3}{2}x-6[/tex]
From this, we see that equation 1 is the answer.
What is slope-intercept form of m=-7,b=4
On 25 March 1965, Martin Luther King led thousands of nonviolent demonstrators on a 5-day, 54-mile march from Selma, Alabama to the steps of the capitol in Montgomery, Alabama.
A court order restricted the number of marchers to 300 when passing over a stretch of two-lane highway. However, on the final day of the march, when the road reached four lanes the number of demonstrators swelled to 25,000.
What was the percentage of increase?
The percentage increase is 88%.
What is percent increase?The difference between the final value and the starting value, stated as a percentage, is known as a percentage increase. The initial value and the enhanced (new) value are required in order to calculate the percentage.
Percentage Increase = [(Final Value - Initial Value)/Initial Value] × 100
Given:
Initially, number of marchers = 300
Finally, number of marchers = 25000
Change in amount = 25000- 300 = 22000
Now, the percent increase
=22000 / 25000 x 100
= 22/25 x 100
=22 x 4
= 88
Hence, the percentage increase is 88%.
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72 km/h converted into m/s
Answer: 20 meters per second
Step-by-step explanation:
Write rules for the composition of translations.
Answer: gurl you think i know
Step-by-step explanation:
please do complete and be quick
1. cube root - a number whose cube equals the original number.
2.irrational number -a number that cannot be written in the form a/b, where a and b are integers and b≠ 0
3.Product of powers property- To multiply two powers with the same base, keep the common base and add the exponents.
4.perfect cube- the cube of an integer.
5.perfect square- a number that is the square of an integer.
6.Power of powers property-To multiply two powers with the same exponent and different bases, multiply the bases and keep the exponent.
7.Powers of products property- when you have an exponent raised to a power ,keep the base and multiply the exponents.
8. scientific notation -a way to express a number as the product of two factors, one greater than or equal to 1 and less than 10 and the other a power of 10
9. square root - a number when multiplied by itself equals the original number
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Move numbers to the blanks to rewrite each square root. [tex] \sqrt{ - 4} = [/tex][tex] \sqrt{ - 5 = } [/tex]answers:[tex]2i[/tex][tex] - 2[/tex][tex]4i[/tex][tex] \sqrt{5i} [/tex][tex] - \sqrt{5} [/tex][tex]i \sqrt{5} [/tex]
We have 2 expressions:
[tex]\begin{gathered} a)\text{ }\sqrt[]{-4} \\ b)\sqrt[]{-5} \end{gathered}[/tex]Case a.
We can rewrite our square root as
[tex]\sqrt[]{-4}=\sqrt[]{-1\times4}=\sqrt[]{-1}\times\sqrt[]{4}[/tex]but by definition
[tex]\sqrt[]{-1}=i[/tex]which is the imaginary number. So, our square root is equal to
[tex]\sqrt[]{-4}=\sqrt[]{4}i[/tex]which corresponds to option 3.
Case b.
Similarly,
[tex]\sqrt[]{-5}=\sqrt[]{-1}\times\sqrt[]{5}[/tex]and the answer is
[tex]\sqrt[]{-5}=i\sqrt[]{5}[/tex]which corresponds to option 6
ATTACHMENTS OBJECTIVES A banana is 7 inches long. How many slices of banana can be cut from the 7-inch piece if each piece is 1/2 long? inch sation to solve and check your solution. Submission VIEW GRADE DETAILS M 9
As the banana is 7 inches long and each piece is 1/2 inches you divide 7 into 1/2 to find how many slices of banana can be cut:
Division of fractions:
[tex]\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a\cdot d}{b\cdot c}[/tex]Yo have: 7/1 divided into 1/2:
[tex]\frac{\frac{7}{1}}{\frac{1}{2}}=\frac{7\cdot2}{1\cdot1}=14[/tex]Then, in a banana of 7inches you can cut 14 slices of 1/2inchPLEASE HELP
What is the value of x?
Answer: x = 50
Step-by-step explanation:
The two angles are opposite each other, meaning that they are equivalent.
So, we can set them equal to each other and then solve for x.
2(x + 10) = 3x - 30
2x + 20 = 3x -30
x = 50
Answer:
x = 50
Step-by-step explanation:
Since the two angles are opposite each other, you know that they are equal.
Set both equations equal to each other to isolate x:
2(x + 10) = 3x - 30
Distribute 2 on the left side
2x + 20 = 3x - 30
Subtract 2x from both sides
20 = x - 30
Add 30 to both sides
50 = x
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of ___, a second point by going up 3 and over ___, and then draw a line through the points.
To draw a graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of y = 7, a second point by going up 3 and over y = 10, and then draw a line through the points.
How to know if a point lies in the graph of a function?
All the points (and only those points) which lie on the graph of the function satisfy its equation. Thus, if a point lies on the graph of a function, then it must also satisfy the function.
Given that:
y = 3/4x + 7
At x = 0
y = 7.
Going over by 3 then,
7 + 3 = 10.
So, now y = 10
10 = 3/4x +7
3/4x = 10-7
3/4x = 3
x = 4.
Now,
To draw a graph of 3/4x + 7, a person can draw c point x of 0 and y of 7, a second point by going over 3 and up 4.
Thus, for drawing the graph for y = 3/4x + 7, a person can draw a point at x of 0 and y of 7, a second point by going over 3 and up 10 and then draw a line through the points.
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answers please
im failing
Answer:
y = -5, x = 5
Step-by-step explanation:
le brain
Deborah bought a yard of ribbon for $14.76. How much did Deborah pay per inch? (1 yard = 3 feet.)
$0.41
$0.49
$1.23
$4.92
Answer:
$0.41 per inch
Step-by-step explanation:
Deborah bought a yard of ribbon for $14.76. How much did Deborah pay per inch? (1 yard = 3 feet.)
$0.41
$0.49
$1.23
$4.92
paid $14.76 for 1 yard or 3 feet. Solve for per foot:
$14.76 / 3 = $4.92 per foot
There are 12 inches per feet. Solve per inch:
$4.92 / 12 = $0.41 per inch
6) Paul bought and sold a computer
He wrote his business activity as
follows:
cost price of computer = $1064
5 marked price of computer = $1399
Anscount on marked price
(if paid in cash)
Calculate.
5%
The selling price, if paid
Cash.
"1) The profit or loss as a percent.
of the cost price
The profit percentage of the computer sold by Paul is 31.5%
What is profit?It should be noted that profit simply means the gain that's derivd from selling a particular product.
In this case, the cost price of computer is $1064 and the marked price of computer is $1399.
The profit percentage will be:
= Profit / Cost price × 100
= (1399 - 1064) / 1064 × 100
= 335/1064 × 100
= 31.5%
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Justin earns a base salary of $1500 per month at
the jewelry shop. He also earns a 3% commission
on all sales. If Just sold $82,975 worth of jewelry
last month, how much would he make for the
month including his base salary and commission?
8)
He make $84475 for the month including his base salary and commission.
Define commission.The percentage or fixed payment attached to a specific volume of sales is known as the commission rate. For illustration, a fee can be $30 for each sale or 6% of sales. The payment that is either a fixed amount or a percentage of a sale is the commission rate. When they make a sale, people in commission-based professions like insurance brokers, real estate agents, and automobile salespeople get compensated. A business pays its employees according to the revenue they bring in through a commission structure. An employee receives a commission when they conduct business or provide a service, according to the definition of commission.
Given,
Salary = $1500
Commission = 3%
Sales = $82975
= 1500 + 82975 + [tex]\frac{3}{100}[/tex]
= 84475.03
84475(approximately)
He make $84475 for the month including his base salary and commission.
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1260/27 as a mixed number
what the average for 68,68,84,73,100,91
Answer:
81
Step-by-step explanation:
mean average= sum of values / amount of values
484/6=80.66666666
pls help i give brainliest
Answer: Please check attached image
Kali just started a new sales floor job to save for college. She earns 15.75 plus a flat fee of 50 . She wants to earn between 200 and 400 . The following inequality represents her earning potential
200 ≤ 15.75x + 50 ≤ 400 Solve the inequality PLEASE HELP ASAP
!!
Solving the inequality the range of x becomes 9.523 ≤ x ≤ 22.222.
The given inequality which needs to be solved is 200 ≤ 15.75x + 50 ≤ 400.
If 50 is subtracted from each part or side of the inequality we get,
200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 -50 which will be equal to,
150 ≤ 15.75x ≤ 350, now to solve this inequality divide the given inequality with the coefficient of x which is 15.75 to get the range of x.
Hence the inequality becomes 150÷15.75 ≤ 15.75x÷15.75 ≤ 350÷15.75. solving this equation the value of x becomes 9.523 ≤ x ≤ 22.222.
So the range of inequality that represents Kalis earning potential ranges from (9.523,22.222) for the given question.
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What are the intersection points of the parabola given by the equation y=x^2 - 9 and the line given by the equation y = x - 3?
Since we want the points where both the parabola and the line have in common (i.e., they intersect), then we have the following:
[tex]\begin{gathered} y=x^2-9 \\ y=x-3 \\ \Rightarrow x^2-9=x-3 \end{gathered}[/tex]Now we solve for x to find the first two values of the points that we are looking for:
[tex]\begin{gathered} x^2-9=x-3 \\ \Rightarrow x^2-9-x+3=0 \\ \Rightarrow x^2-x-6=0 \\ \Rightarrow(x-3)\cdot(x+2)=0 \\ x_1=3 \\ x_2=-2_{} \end{gathered}[/tex]Now we use these values of x to find other pair of values for y:
[tex]\begin{gathered} y=x-3 \\ x_1=3 \\ \Rightarrow y_1=3-3=0 \\ \Rightarrow(x_1,y_1)=(3,0) \\ x_2=-2 \\ \Rightarrow y_2=-2-3=-5 \\ \Rightarrow(x_2,y_2)=(-2,-5) \end{gathered}[/tex]Therefore, the intersection points are (3,0) and (-2,-5)
find the perimeter of ABC with vertices A(-4,4), B(5,-6) and C(7,-9)
Answer:
The answer is maybe about around 26
Step-by-step explanation:
Please correct me if I am wrong, but I hope this helped.
two debt payments, the first for $800 due today and the second for $600 due in nine months with interest at 10.5% compound monthly, are to be settled by a payment of $800 six months from now and a final payment in 24 months. Determine the size of the final payment if money is now worth 9.5% compounded quarterly.
Given:
First payment = $800 due today
Second payment = $600 in 9 months
Interest rate = 10.5% compounded monthly
The interest is to be settled in a payment of $800 in 6 months and a final payment in 24 months.
Let's determine the final payment if the money is now worth 9.5% compounded quarterly.
Apply the compound interest formula:
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]Let x represent the initial amount of debt.
Thus, we have the equation:
[tex]\begin{gathered} (x-800)(1+\frac{0.105}{12})^{12\ast\frac{9}{12}}=600 \\ \\ (x-800)(1.00875)^9=600 \\ \\ (x-800)(1.08156)=600 \\ \\ x-800=\frac{600}{1.08156} \\ \\ x=1340.44 \end{gathered}[/tex]For the amount due in six months, we have:
[tex]\begin{gathered} A=1340.44(1+\frac{0.095}{4})^{4\ast\frac{6}{12}}_{} \\ \\ A=1340.44(1.02375)^2 \\ \\ A=1404.87 \end{gathered}[/tex]Hence, the amount which is due after 6 months will be:
$1404.87 - $800 = $604.87
Now, let's find the payment due in 24 months.
Number of months remaining = 24 - 6 = 18 months.
Hence, we have:
[tex]\begin{gathered} A=604.87(1+\frac{0.095}{4})^{4\ast\frac{18}{12}} \\ \\ A=604.87(1.02375)^6 \\ \\ A=696.35 \end{gathered}[/tex]Therefore, the final payment if the money is now worth 9.5% compounded quarterly is $696.35
ANSWER:
$696.35
Rectangle ABCD is graphed in the coordinate plane. The following are the vertices of the
rectangle: A(-8,-6), B(-3,-6), C(-3,-4), and D(-8,-4).
Given these coordinates, what is the length of side AB of this rectangle?
The length of side AB of this rectangle is = 5 units
what is rectangle ?
A shape with four straight sides and four angles of 90 degrees ( right angle ) . two of the sides are longer than the other two . a rectangle with four sides of equal length is square .
we could use distance formula to find the length
A (-8,-6) ; B (3 , -6 )
distance =(( X2 - X1 )^2 +( Y2 - Y1 ) ^2 ) ^1/2
AB = (( -3+8)^2+(-6-[-6]^2)^1/2
AB= 5^2
AB = 5 units .
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Is z(x) = 1 + 6x^2 + 4x a quadratic function? I don't believe it's linear or constant, just wanted to make sure.
Given function is
[tex]z(x)=1+6x^2+4x[/tex]In the given function, the maximum power of x is 2 and it is of the form
[tex]ax^2+bx+c[/tex]Therefore, it is a quadratic function.
Classify the system as independent, dependent, or inconsistent.y=2x-1y=-2x+5
To classify the equations, we will need to define some terms:
Inconsistent equations: Inconsistent equations is defined as two or more equations that are impossible to solve based on using one set of values for the variables.
inconsistent equations of linear equations are equations that have no solutions in common.
An example of a set of inconsistent equations is x+2=4 and x+2=6.
Independent equation: The equations 3x + 2y = 6 and 3x + 2y = 12 are independent because any constant times one of them fails to produce the other one.
Dependent system: Equations in a dependent system can be derived from one another; they describe the same line
We can now proceed to classify the equations.
[tex]\begin{gathered} y=2x-1 \\ \text{and} \\ y=-2x+5 \end{gathered}[/tex]Equating the two equations
[tex]2x-1=-2x+5[/tex]simplifying further
[tex]\begin{gathered} 2x+2x=1+5 \\ 4x=6 \end{gathered}[/tex][tex]\begin{gathered} x=\frac{6}{4}=\frac{3}{2} \\ x=\frac{3}{2} \end{gathered}[/tex]Since it has a solution (x=3/2), and also if we multiply each equation by a constant, we will have an uncommon equation.
Thus, we can classify the system as Independent
3. Which of the following is true about the graph of y = -x] – 2? (A) The graph is increasing when x > -2. (B) The graph is decreasing when x > -2. (C) The graph is increasing when x < 0 (D) The graph is increasing when x > 0.
First let's draw the graph
Now, we can see that the graph is increasing when x<0! thus the answer is (C)
9. Assessment Practice Diego wants to
find 8+ 9. 2.NSO.2.1
Which doubles fact can help him?
A 5+5=10
B6+6=12
C7+7= 14
D 8+8=16
They can use counters or their fingers, but they can also use doubles facts. If they know 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
What is meant by addition?One of the four fundamental mathematical operations, along with addition, subtraction, multiplication, and division, is addition.
The sum of 5 + 6.
They can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, 5 + 6 = 11.
Estimating other doubles-plus-one facts together, such as 3 + 4, 7 + 8, and 9 + 8.
Repeat the doubles facts so they can use them to solve equations.
They can also use doubles-minus-one facts to enable them solve equations.
Write down 9 + 10 and have your children find the sum.
If they know that 10 + 10 = 20, they know that the sum of 9 + 10 will be one less. Therefore, 9 + 10 = 19.
solving different number sentences together.
Therefore, they can utilize counters or their fingers, but they can even utilize doubles facts. If they understand 5 + 5 = 10, they know that the sum of 5 + 6 will be one more.
Therefore, the correct answer is option A) 5 + 5 = 10.
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Write the missing power of 10 in each equation a. 0.06 x ____=6 b. ___X 0.3 = 300
a) the expression can be writen as:
[tex]0.06\times10^2=6[/tex]because we move two units to the right the period.
b) the expression can be written as:
[tex]0.3\times10^3=300[/tex]because we move the period 3 units to the right