Write the equation of a line given the following information:26) The line has a slope =and passes through (8.-1)27) TH
Answers
Answer:
The equation of the line is;
[tex]y=-\frac{3}{4}x+5[/tex]Explanation:
Given that the line has a slope of;
[tex]m=-\frac{3}{4}[/tex]And passes through the point;
[tex](8,-1)[/tex]Applying the point-slope equation of straight line;
[tex]y-y_1=m(x-x_1)[/tex]substituting the given values and solving;
[tex]\begin{gathered} y-(-1)=-\frac{3}{4}(x-8) \\ y+1=-\frac{3}{4}x-\frac{3}{4}(-8) \\ y+1=-\frac{3}{4}x+6 \\ y=-\frac{3}{4}x+6-1 \\ y=-\frac{3}{4}x+5 \end{gathered}[/tex]Therefore, the equation of the line is;
[tex]y=-\frac{3}{4}x+5[/tex]Related Questions
Solven - 8 + n = 1 -4n
Answers
We will solve as follows:
[tex]n-8+n=1-4n\Rightarrow2n+4n=1+8[/tex][tex]\Rightarrow6n=9\Rightarrow n=\frac{3}{2}[/tex]oan, omb, apb and mpn are straight lines and an = 3oa. m is the midpoint of ob. oa = a ов = b ap = kab where k is a scalar quantity. express ab and mn in terms of a and b. express mp in terms of a, b and k. finally, find the value of k.
Answers
The values of the vectors obtained from the vector diagram are;
[tex]\overrightarrow{AB} = - a + b[/tex]
[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]
[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
K = 2.5
What is a vector in geometry?A vector can be expressed as a line segment that has a direction.
The given parameters are;
The straight lines are; OAN, OMB, APB, and MPN
AN = 3•OA
The midpoint of OB = M
The vectors
[tex] \overrightarrow{OA} = a[/tex]
[tex] \overrightarrow{OB} = b[/tex]
[tex]\overrightarrow{AP} = K \cdot \overrightarrow{AB} [/tex]
From the question diagram, we have;
[tex]\overrightarrow{AB} = - a + b[/tex]
[tex]\overrightarrow{AP} = K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MN} = ( -2\cdot a + 0.5 \cdot b)[/tex]
[tex]\overrightarrow{AN} [/tex] = 2•a
[tex]\overrightarrow{NP} = \overrightarrow{AP} - \overrightarrow{AN} [/tex]
[tex]\overrightarrow{NP} = -2\cdot a + K \cdot ( - a + b)[/tex]
[tex] \overrightarrow{MB} = 0.5 \cdot b[/tex]
[tex]\overrightarrow{PB} = -a + b - K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MP} =0.5 \cdot b - -a + b - K \cdot ( - a + b) = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
[tex]\overrightarrow{MP} = ( -0.5\cdot b + a+ K \cdot ( - a + b)[/tex]
Given that we can write;
[tex]x \cdot \overrightarrow{NP} = \overrightarrow{NM}[/tex]
x × (-2•a + k•(-a + b)) = -3•a + 0.5•b
-2•x•a - k•x•a + x•k•b = -3•a + 0.5•b
Which gives;
-2•x - k•x = -3...(1), and x•k = 0.5...(2)
From (2), x = 0.5÷k
From (1), -2×(0.5÷k) - k×(0.5÷k) = 3
-k - 0.5 = -3
-k = -3 + 0.5 = -2.5
k = 2.5
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The sum of an integer and 6 times the next consecutive odd integer is 61. Find the
value of the lesser integer.
Answers
If the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7
Consider the first odd integer as x
Then the next consecutive odd integer = x+2
The 6 times the second integer= 6(x+2)
= 6x+12
Sum of an integer and 6 times the next consecutive odd integer is 61
Then the equation will be
x + 6x+12 = 61
Add the like terms in the equation
(1+6)x + 12 = 61
7x +12 = 61
Move 12 to the right hand side of the equation
7x = 61-12
7x = 49
x = 49/7
x = 7
The second number is
x+2 = 7+2
= 9
Hence, if the sum of an integer and 6 times the next consecutive integer is 61, the the value of lesser integer is 7
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Select the correct answer.
What is the range of the function shown on the graph above?
A. -9 [tex]\leq[/tex] y [tex]\leq[/tex] 8
B. -7[tex]\leq[/tex] y [tex]\leq[/tex] -2
C.-8[tex]\leq[/tex] y [tex]\leq[/tex] 8
D.-2 [tex]\leq[/tex] y [tex]\leq[/tex] -7
Answers
Answer:
A
Step-by-step explanation:
The range is the y values. The y value is as low as -10 and as high as 8.
The perimeter of a rectangle is 82 cm the length is 1 cm more than three times the width find the length and the width of the rectangle
Answers
The length will then be L = 18(41/19) = 738/19 cm.
As a check, the area should be A = LW = (738/19)(41/19) = 30258 cm2
sorry if this isn't much help but i had a similar problem once and i used the same steps for your question
At 6:00 A.M. the temperature was 5°F below zero. At noon the temperature was 2°F above zero. At 6:00 P.M. the temperature was 7°F above zero. Which equation shows the change in temperature from 6:00 A.M. to 6:00 P.M.?
A. |5 – 7| = |–2| = 2°F
B. |2 – 7| = |–5| = 5°F
C. |–5 – 2| = |–7| = 7°F
D. |–5 – 7| = |–12| = 12°F
Answers
Based on the temperature at 6:00 am and the temperature at 6:00pm, the change in temperature can be shown by the formula D. |–5 – 7| = |–12| = 12°F.
How to find the change in temperature?To find the change in temperature, you need to subtract the temperature at 6: 00 pm from the temperature at 6: 00 am.
The change in temperature is therefore:
= | temperature at 6 am - temperature at 6pm |
= | -5 - 7 |
= | - 12 °F|
The absolute value of - 12 °F is 12 °F which was therefore the change in temperature.
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the population of a city will quadruple in 15 years. if its current population is 6,000, using the given rate of change, what will its approximate population be 7 years from now
Answers
Answer:
11200
Step-by-step explanation:
The area of a square is 144 square meters. What is the length (in meters) of one side of the square?
Answers
Answer:
12 m
Step-by-step explanation:
area = (side)²
(side)² = area
√(side)² = √(area)
side = √(area)
side = √(144 m²)
side = 12 m
Hey , I have a quick question about a Homework in math I got confused on how to solve the listed to formula [tex] \frac{x - 3}{2} - 4 \ \textless \ \frac{x}{3} [/tex]
Answers
Solution
- The question would like us to solve the following
[tex]\frac{x-3}{2}-4<\frac{x}{3}[/tex]- The solution is outlined below:
[tex]\begin{gathered} \frac{x-3}{2}-4<\frac{x}{3} \\ \\ Collect\text{ like terms:} \\ Add\text{ 4 to both sides and Subtract }\frac{x}{3}\text{ from both sides} \\ \\ \frac{x-3}{2}-\frac{x}{3}<4 \\ \\ We\text{ need the LCM of 2 and 3. } \\ The\text{ LCM is }2\times3=6 \\ \\ Thus,\text{ multiply both sides by 6 in order to remove the denominator} \\ 2\frac{}{} \end{gathered}[/tex][tex]\begin{gathered} 6\left(\frac{x-3}{2}\right?-6\left(\frac{x}{3}\right?<4\times6 \\ \\ 3\left(x-3\right)-2x<24 \\ Expand\text{ the bracket} \\ 3x-9-2x<24 \\ x-9<24 \\ Add\text{ 9 to both sides} \\ x<33 \end{gathered}[/tex]Final Answer
The answer is x < 33
Add −1 3/10+2/5 using the number line.
Select the location on the number line to plot the sum.
Answers
The location on the number line to plot the sum of the given number is shown in the image attached below.
What is a number line?In Mathematics, a number line simply means a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.
This ultimately implies that, a number line primarily increases in numerical value towards the right and decreases in numerical value towards the left.
Note: Each interval on this number line represents 1/10.
Next, we would add the given numbers together as follows:
Number = −1 3/10 + 2/5
Number = −13/10 + 2/5
Number = (-13 + 4)/10
Number = -9/10 or -0.9.
Therefore, the sum would be located between -4/5 and -1.
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Need help with #6 don’t know how to find truth values.
Answers
The statement p is: Saturn is a planet.
The statement q is: Hong Kong is a city.
Now the first part of our composite proposition is:
[tex]p\lor\sim q[/tex]This means that we have to negate the statement q, this would be: Hong Kong is not a city.
Now we make the disjunction between the statement p and the negation of q, then we have:
[tex]p\lor\sim q\text{ means: Saturn is a planet or Hong Kong is not a city}[/tex]The second part of our composite porposition is:
[tex]\sim p\wedge q[/tex]This means that we have to negate the statement p, then we have: Saturn is not a planet. Then we make the conjunction between the negation of p and q, then we have:
[tex]\sim p\wedge q\text{ means: Saturn is not a planet and Hong Kong is a city}[/tex]Finally we make the disjunction between the statements discussed so far, hence the statament
[tex](p\lor\sim q)\lor(\sim p\wedge q)[/tex]means:
Saturs is a planet or Hon kong is not a city OR Saturn is not a planet and Hong Kong is not a city.
Now, to determine the truth value of the composite proposition we have to remember that a disjunction is TRUE if one of the statements that make it is true and that the conjunction is TRUE only if both stataments that make it are true.
The first statement is: Saturn is a planet or Hong kong is not a city. Since this is a disjunction and the statement Saturn is a planet is TRUE, then the proposition is true.
The second statement is: Saturn is not a planet and Hong Kong is not a city. Since this is a conjunction and the statement Saturs is not a planet is FALSE, the the second statement is FALSE.
Now since the composite statemtent is made of a TRUE and a FALSE statement and it is a disjunction we conclude that the truth value of the statement given is TRUE.
Every rational number is positive.
A. True
B. False
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Answer:
Step-by-step explanation: it is true because when the numerator and denominator both are positive integers both are negative integers it is a positive rational number.
Question 1
A triangle has sides of length 2 cm, 8 cm and 9 cm.
Calculate the value of the largest angle in this triangle.
Answers
Answer: You have to use a calculator
Step-by-step explanation:
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I need help with this practice I attempted this and got 13.96? Make sure your answer is rounded to the nearest hundredth
Answers
Law of Cosines
Given two side lengths a and b of a triangle and the angle included by them θ, the length of the third side can be calculated as:
[tex]c^2=a^2+b^2-2ab\cos \theta[/tex]We have a = 14, b = 9, θ = 71°. Substituting:
[tex]\begin{gathered} c^2=14^2+9^2-2\cdot14\cdot9\cos 71^o \\ c^2=196+81-252\cdot0.325568 \\ c^2=194.956825 \\ c=\sqrt[]{194.956825} \\ c=13.96 \end{gathered}[/tex]The length of CD is 13.96
24. The temperature in ° F on 20 days during the month of June
was as follows:
70° F, 76° F,
74° F, 74° F,
76° F,
78° F,
74° F,
76° F,
70° F, 70° F, 72° F,
78° F, 76° F,
74° F,
74° F, 78° F, 80° F,
80° F, 76° F
78° F
What is the mode of temperature for the month of June?
Answers
determine the equation of line from the graph
Answers
Answer:
y = 2x
Step-by-step explanation:
The slope is 2. Find a point on the line, to go back to the line, go up two and one to the right. You will be back on the line. This pattern repeats over and over and again.
given l || m || n, find the value of x
Answers
Answer:
x = 10
Step-by-step explanation:
(5x + 3) and 53 are corresponding angles and are congruent , then
5x + 3 = 53 ( subtract 3 from both sides )
5x = 50 ( divide both sides by 5 )
x = 10
The value of 'x' is highlighted in the box
Find the measures of the complementary angles that satisfy each case. The measure of the first angle is 40% less than the measure of the second.
Answers
The measure of the angles are 56.25° and 33.75°.
How to calculate the angles?The value in a complementary angle is equal to 90°.
Let the first angle = x
The second angle will be: 1 - (40% × x) = 1 - 0.4x = 0.6x
Therefore, they'll be added together as follows:
x + 0.6x = 90°
1.6x = 90°
Divide
x = 90/1.6
x = 56.25
The second angle will be:
= 0.6x
Since x = 56.25, this will be used in the illustration below.
= 0.6x
= 0.6 × 56.25
x = 33.75
Therefore, the second angle is 33.75.
This illustrates the concept of complimentary angles.
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Triangle ABC is congruent to triangle XYZ. In AABC, AB = 12 cm and AC = 14 cm. In AXYZ, YZ = 10 cm and XZ = 14
!
cm.
Answers
The perimeter of triangle ABC that is congruent to triangle XYZ is: 36 cm.
What are Congruent Triangles?Triangles that are congruent to each other have corresponding side lengths that have the same lengths that are equal to each other.
What is the Perimeter of a Triangle?The sum of all the three sides of a triangle is equal to the perimeter of the triangle.
Since triangle ABC is congruent to triangle XYZ, their corresponding side lengths will also be congruent to each other. That is, they will have the same lengths.
Therefore:
Side AB = side XY = 12 cm [corresponding congruent sides]
Side AC = side XZ = 14 cm [corresponding congruent sides]
Side BC = side YZ = 10 cm [corresponding congruent sides]
Find the perimeter of triangle ABC by adding all three triangles together.
Perimeter of triangle ABC = side AB + side AC + side BC
Perimeter of triangle ABC = 12 + 14 + 10
Perimeter of triangle ABC = 36 cm
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FInd the probability that a student walks to school
Answers
The probability that a student walks to school is 7/15
How to determine the probability of walking to school?The tree diagram represents the given parameter
From the tree diagram, we have the following parameters
P(Rain) = 2/5
P(Rain and walk) = 1/6
P(No rain) = 3/5
P(No rain and walk) = 2/3
The probability of walking to school is then calculated as
P = P(Rain) x P(Rain and walk) + P(No rain) x P(No rain and walk)
Substitute the known values in the above equation
So, we have
P = 2/5 x1/6 + 3/5 x 2/3
Evaluate the products
P = 1/15 + 6/15
Evaluate the sum
P = 7/15
Hence, the probability is 7/15
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I need help with number 16 can I please get help?
Answers
We will break apart the figure into triangles, rectangles, squares etc. We will then find area of each individual figure and sum it.
We can break apart the figure as shown below:
The graphs of the fuctions f and g are shown below, find all values of x for which f(x) < g(x). 30 points!!!
Answers
Answer: [tex]-10 < x < 0, x > 12[/tex]
Step-by-step explanation:
[tex]f(x) < g(x)[/tex] when the graph of [tex]f(x)[/tex] is below the graph of [tex]g(x)[/tex].
WILL GIVE BRAINLOST TO BEST QUSTION
The cost of a ride in a taxi is $4 for the first half-mile plus a constant amount per half-mile after that. The sequence below shows the pattern of numbers that appear on the driver's screen.
2.50, 2.75, 3, 3.25, 3.50,...
Which of the following is the Recursive Function that can be used to determine f(x), the cost in dollars, for a ride in the tax of, x. half miles?
Answers
Answer:
I don't know men iam grade 7 student
it is known that a certain kind of algae in the dead sea can double in population every 4 days. suppose that the population of algae grows exponentially, beginning now with a population of 3,000,000. (a) how long it will take for the population to quadruple in size? days (b) how long it will take for the population to triple in size? days
Answers
Since the algae grow exponentially with doubling time of 4 days, then the population will be quadruple in size in 8 days and will be triple in size in 6.34 days.
The easiest way is to consider the situation as a geometric sequence. If the population doubles its size in 4 days, then it will be quadruple in:
2 x 4 days = 8 days.
In general, we can use the growth formula:
P(t) = Po . 2^(t/Td)
Where:
P(t) = population at time t
Po = initial population
Td = doubling time
Parameters given:
Td = 4 days
P(t) = 3Po
Plug those parameters into the formula:
3 Po = Po . 2^(t/4)
3 = 2^(t/4)
log 3 = (t/4) log 2
t = 4 . log 3 / log 2 = 6.34 days.
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2) m angle2=x+88 50° 2 A) -8 C) 8 B) -7 D) 7
Answers
A
1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle
2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.
We can finally write
x+88 +50 +50 = 180
x +188 =180 subtract 188 from both sides
x= 180-188
x= -8
3) So x=-8 is the answer.
DS
6) You and five friends went out to a movie. You all
shared a large tub of popcorn that cost $16.50,
and you ordered individual boxes of candy that
cost $3,72 per person. You and your friends decide
to split the bill evenly. How much did each of you
pay?
Answers
Answer:
You would each pay $6.42
Have a good one!
help me please help :)
Answers
Step-by-step explanation:
12/4 = x/8
1st: cross multiply
96 = 4x
2nd: divide both sides by 4
96/4 = 4x/4
therefore x = 24
juan went out to eat dnner,and the meal cost $60.00.If juan recived a 18% discount,what was the total value of the discount
Answers
Multiply by the decimal form of the percentage,
60 * 0.18 = 1.08
So the discount is for $1.08 off,
60 - 1.08 = 58.92
Giving a total of $58.92 after the discount is applied
Please help thank you
Answers
The value of the unknown angle in the triangle is as follows;
m∠S = 40 degreesHow to find the angle of a triangle?The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words, an exterior angle of a triangle is equal to the sum of the two opposite interior angles.
The external angle is ∠JRS.
Therefore, m∠S can be found as follows:
∠JRS = m∠S + m∠T
Hence,
m∠S = 3x + 4
m∠T = 8x + 4
∠JRS = 140°
Hence,
140 = 3x + 4 + 8x + 4
140 = 3x + 8x + 4 + 4
140 = 11x + 8
140 - 8 = 11x
132 = 11x
x = 132 / 11
x = 12
Therefore,
m∠S = 3(12) + 4 = 40 degrees.
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Hello I am not sure for what to do for the end of the equation.
Answers
ANSWER
25
EXPLANATION
We are given that p and q intersect to form <1 and <2 that are adjacent.
Let us represent that with a diagram:
We have that <1 and <2 are supplementary.
This means that they add up to 180 degrees.
So:
<1 + <2 = 180
4x - 3 + 3x + 8 = 180
Collect like terms:
4x + 3x + 5 = 180
7x = 180 - 5
7x = 175
x = 175 / 7
x = 25
That s the value of x for which <1 and <2 are supplementary.