The equation of the line in function notation is y.=-2x + 5
Equation of alineThe standard equation of a line is expressed as y = mx + b
where
m is the slope
b is the y-intercept
Given the equation
2y=x-4
y = 1/2x - 2
The slope perpendicular will be -2
Substitute into y-y₁ = m(x-x₁)
y-(-7) = -2(x-6)
y+7 = -2x +12
y = -2x + 5
Hence the equation of the line in function notation is y.=-2x + 5
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the length of a rectangle is four less than twice it’s width. If the width is 6 inches what is the length of the rectangle ?
Answer:
The question states four less than twice its width so we first find twice the width. The width is 6 and twice that is 12. Note that it says four less than, so four less than 12 is 8. so the length of the triangle is 8.
Step-by-step explanation:
Hope it helps! =D
Simplify 9 – 3(4x – 18) + 6x
The expression is simplified to 7(-x + 9)
What are algebraic expressions?
Algebraic expressions are expressions composed of variables, terms, factors, constants and coefficients.
They are also made up of mathematical or arithmetic operations
Given the expression;
9 – 3(4x – 18) + 6x
expand the bracket
9 - 12x + 54 + 6x
collect like terms, we have;
-12x + 5x + 54 + 9
Add or subtract like terms
-7x + 63
Factor out 7
7(-x + 9)
Thus, the expression is simplified to 7(-x + 9)
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(8x-4)+(4x-90)
also simplify
Answer:
12x-94
---------------------
Hope this helps!
Have a great day and God bless! :)
evaluate the polynomial function at x=-2 using direct and synthetic substitution f(x)=3x⁵-x³+6x²-x+1
Answer:
-61
by both methods
Step-by-step explanation:
Let's first see what the terms direct substitution and synthetic substitution mean.
Direct Substitution
In direct substitution, to find the value of a polynomial f(x) at any point x = k. we simply substitute the value of k into the polynomial function and solve for f(k)
Synthetic Substitution
In synthetic substitution we make use of the Remainder Theorem..
The Remainder Theorem states that when we divide a polynomial [tex]f(x)[/tex] by [tex]x-c[/tex], the remainder [tex]R[/tex] equals [tex]f(c)[/tex]
Solving using direct substitution
The given polynomial is
[tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex]
and we are asked to evaluate this function at [tex]x = - 2[/tex]
Using Direct Substitution,
[tex]f(-2) = =3\left(-2\right)^5-\left(-2\right)^3+6\left(-2\right)^2-\left(-2\right)+1\\\\=3\left(-32\right)-\left(-8\right)+6\left(-2\right)^2-\left(-2\right)+1\\\\=- -96 + 8 + 6(4) + 2 + 1\\=-96 + 8 + 24 + 2 + 1\\\\= -61\\\\[/tex]
Using direct substitution we get [tex]\bold{f(-2)= -61}[/tex]
Using Synthetic Substitution
Since the remainder when [tex]f(x)[/tex] is divided by [tex]x - c[/tex] is [tex]f(c)[/tex] , we will divide the polynomial [tex]f(x) = 3x^5 - x^3 + 6x^2 - x + 1[/tex] by [tex]x -(-2) = x + 2[/tex] and find out the remainder which will give f(-2)
This is the technique used in synthetic division
Step 1. Write only the coefficients of [tex]x[/tex] in the dividend inside an upside-down division symbol. Write -2 as the divisor on the left of this row
[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 2
Carry down the leading coefficient as is to below the division symbol
[tex]\begin{matrix}\texttt{\:\:-2|\:\:\:3\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\ \;\;\;\;\;\;\;\texttt{\:\:\:\:|\underline{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\;\;\;\;\;\;\;\;\;\;\;\;\;}}\\ \texttt{\:\:\:\:\;\;\;\;3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 3
Multiply the above carry-down value by -2 and carry that result to the next column:
[tex]3\left(-2\right)=-6[/tex]
[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 4
Add down the column
[tex]\begin{matrix}\texttt{\:\:\:\:\:\:-2|\:\:\:3\:\:\:\:\:\:\:0\:\:-1\:\:\:6\:\:-1\:\:\:1}\\\texttt{\:\:|\ensuremath{\underline{\;\;\;\;\;\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}\\\texttt{\:3\:\:\:\:\:\:\:\:-6\:\:\:\:\:\:\:\:\:\:\:\:}\end{matrix}[/tex]
Step 5
Multiply the above carry-down value by -2 and carry that result to the next column:
(-6)(-2) = 12
2 | 3 0 -1 6 -1 1
| -6 12
-------------------------------------------------
3 -6
Step 6
Add down the column
-1 + 12 = 11
2 | 3 0 -1 6 -1 1
| -6 12
-------------------------------------------------
3 -6 11
Repeat this process for the other two coefficients
The final result is
2 | 3 0 -1 6 -1 1
| -6 12 -22 32 -62
-------------------------------------------------
3 -6 11 -16 31 -61
The last carry-down value s the remainder and the value of f(-2) = - 61
HELP!!
What is the volume of this solid?
A. 39
B. 108
C. 27
D. 63
Answer: B
Step-by-step explanation:
4 times 3 times 3 times 3 times 3=108
Answer:
A. 39
Step-by-step explanation:
Given:
Length of a pyramid (lpy ) = 4 cm
Width of a pyramid (wpy ) = 3 cm
Height of a pyramid (hpy ) = 3 cm
It is given that the rectangular pyramid fits exactly on top of the prism, the length and width of the prism are the same for the base of the pyramid.
So, Length of a prism (lpr) =3 cm, width of a prism (wpr) = 3cm and height of a prism (hpr) = 3 cm
Volume of Prism (Vpr) = lpr × wpr × hpr
⇒ Vpr = 3 cm × 3 cm × 3 cm
⇒ Vpr = 27 cm³ ....(eq 1)
Volume of Rectangular Pyramid Vpy
= (lpy × wpy × hpy ) / 3
⇒ Vpy = (4 × 3 × 3) ÷ 3
⇒ Vpy = 12 cm³ ....(eq 2)
From 1 and 2, Volume of composite space,
Volume of composite space = Volume of prism + Volume of Pyramid
⇒ V = 27 cm³ + 12 cm³ = 39 cm³
⇒ V = 39cm³
The points L, M, N and O all lie on the same line segment, in that order, such that the ratio of LM:MN:NOLM:MN:NO is equal to 5:1:2.5:1:2. If LO=48,LO=48, find NO.NO.
The length of the line segment NO is 12 units
How to determine the length of NO?The ratios of the line segments are given as:
LM : MN : NO = 5 : 1 : 2
The length of LO is given as:
LO = 48
The above means that
NO = (NO Ratio)/(Total Ratio) * LO
So, we have
NO = 2/(5 + 1 + 2) * 48
Evaluate the product
NO = 12
Hence, the length of NO is 12 units
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help, i’ll give you brain list sh or wtv if it’s correct. !!
the combinations that work are "A" and "B" as they both equal to 80
The Shah family's pancake recipe uses 2 teaspoons of baking powder for every
1
3
of a teaspoon of salt. How much baking powder would they need if they used 1 teaspoon of salt?
The baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.
How to illustrate the information?It should be noted that from the information given, the Shah family's pancake recipe uses 2 teaspoons of baking powder for every 1/3 of a teaspoon of salt.
Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated thus:
= Pancake recipe ÷ Teaspoon
= 2 ÷ 1/3
= 2 × 3
= 6
Therefore, the baking powder that they would need if they used 1 teaspoon of salt will be illustrated will be 6 baking Powder.
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1
T
school 1 H
school 2
2
✓
✓
468 10 12 14 16 18
hours in the weight room
The two box plots summarize the number of hours
spent in the weight room for all the players on the
football team for two different high schools. Determine
whether the following statements are true or false.
d) School 1 had the player that spent the most time
in the weight room.
M
True
O
False
Sep 16
3:00
true!!!
school 1 spent 13 hours in the weight room whereas school 2 spent 11 hours in the weight room
What is the greatest common factor of 27 and 36?
Answer:
9!
Step-by-step explanation:
Answer: 9
Step-by-step explanation:So you look at whatever can be multiplied to get 27 or 36. When you do that 9 is your biggest number
5. [0/1 Points]
Find a mathematical model that represents the statement. (Determine the constant of proportionality.)
y varies inversely as x. (y 6 when x = 28.)
DETAILS
Submit Answer
PREVIOUS ANSWERS
x
Check which variable(s) should be in your answer.
Need Help? Read It
LARPCALCLIMSHS 1.10.051.
How do you regular divide
Answer:
These are dividend, divisor, quotient and remainder.
Step-by-step explanation:
Determine the first digit or set of digits your divisor will go into at least once.
Determine the maximum number of times your divisor will go into the said digit or digits.
Place the answer over the corresponding digit. For multiple digits, place it over the last digit.
Multiply the answer from above by your dividend.
Place the result under your dividend starting from the left most digit.
Subtract the result from your dividend. Only subtract the digits that line up. For instance, if you have a five digit dividend, but the result is only two digits, only subtract using the first two digits of your dividend.
Bring down the next digit of your dividend beside the result.
Repeat the process using the new set of digits. Each time, bring down the next digit of your dividend.
697x82=________x________=________
The answer is most probably to round the the numbers to nearest 10 digits and multiply
697x82 = 56,154
700 x 80 = 56000
What is rounded numbers?A rounded number is less precise but roughly equal to the original number in value.
To the closest hundred, 341 is equivalent to 300. This is due to the fact that 341 is more similar in value to 300 than to 400. Because $1.89 is closer to $2.00 than to $1.00, when rounded off to the nearest dollar, it becomes $2.00.
The standard rounding rule is as follows:
Round up if the number you are rounding is followed by a 5, 6, 7, 8, or 9. For instance, 38 rounded up to the nearest ten is 40.Round down if the number you are rounding is followed by a 0, 1, 2, 3, or 4. Example: 30 when 33 is rounded to the nearest ten.Learn more about rounded number
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Full questionRound to nearest 10 digits and multiply
697x82=________x________=________
find the equivalent fractionsss with large denominatorsss
Answer: 24/54
Step-by-step explanation:
[tex]\displaystyle\\\frac{4}{9}=\\\\ \frac{4}{9}*1=\\\\ \frac{4}{9}*\frac{6}{6} =\\\\\frac{4*6}{9*6} =\\\\\frac{24}{54}[/tex]
need help i dont know how to solv
Answer:
It's learn proper English. I'll rewrite your statement. I need help, I do not understand how to solve this. Thank you!
can someone answer 2 1/2 x 1 3/5 =
A kite of area 252 m² has one diagonal of length 9 m. Find the length of the other diagonal
Answer:
The other diagonal of the kite is 56 meters
Step-by-step explanation:
To find the length of the other diagonal you find to know the formula for finding the area of a kite which is A = (p×q)/2. It is given that the area is 252m² and one diagonal is 9m.
Place your given numbers in the formula for the area of the kite. With your numbers given the formula is 252 = (9q)/2 or alternatively 252 = (9p)/2Multiply both sides by 2 the reason being is that we are trying to islolate the unknown variable (weather it is p or q) so we are doing the inverse operation. So you will have 252 × 2 = (9p)/2×2 or (9q)/2×2. At the end of this step it is 504 = 9q or 504 = 9pDivide by 9 on both sides remember that the point is to islolate the variable. 504/9 = 9q/9 or 504/9 = 9p/9. The final answer is that your unknown diagonal (whether it was q or p) is 56 mconnie walks from her home to the bicycle repair shop at 6mk/h and then bikes home at 20km/h. if her total traveling time is 39 minutes, how far is her home from the bicylce repair shop
Her home is 3km far from the bicycle repair shop;
Her avg speed = 2*6*20/(6+20) = 60/13 km/h
d = r*t = (60/13)*(39/60)
d = 3 km;
What is Avg Speed?
In normal use and in kinematics, the speed (normally known as v) of an object is the significance of the change of its position over time or the value of the change of its role consistent with unit of time; it is for this reason a scalar amount.
The common speed of an item in an c programming language of time is the distance travelled by using the item divided by the length of the c program languageperiod
the instant pace is the restriction of the common speed because the length of the time c program languageperiod methods 0. velocity isn't similar to pace.
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Factorise x^2+4x+3=0
Write the equation of a line that passes through point (16,7) with slope 5/4 in point slope form
Answer: y = 5x/4 - 13
Step-by-step explanation:
y=mx+b
7=5/4 *16+b
7=5*16/4 +b
7=80/4+b
7=20+b
b=-13
y = 5x/4 - 13
Two friends are planning for a gathering. The food budget is modeled by one half times the absolute value of the quantity x minus 110 end quantity equals 6 comma where x is the amount spent on food. What are the least and greatest amounts that the two friends could spend on food?
A. $98, $122
B. $104, $116
C. $107, $113
D. $110, $122
The least and the greatest amounts are $98 and $112
How to determine the least and the greatest amounts?The food budget is modeled by 0.5|x - 110| = 6
So, we have:
0.5|x - 110| = 6
Divide both sides by 0.5
|x - 110| = 12
Remove the absolute bracket
x - 110 = 12 and x - 110 = -12
Add 110 to both sides
x = 112 and x = 98
Hence, the least and the greatest amounts are $98 and $112
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write a function g whose graph is a reflection in the x axis of the graph of f(x)=|x|-5
please help
A function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 is g(x) = 5 - |x|
The question asks to find a function g, that is, g(x)
The graph of g(x) is a reflection in the x axis of the graph of f(x) = |x| - 5
Reflection of a function in the x-axis gives us
y = g(x) = - f(x)
=> g(x) = - ( |x| - 5 )
=> g(x) = - |x| + 5
=> g(x) = 5 - |x|
Therefore, using the concept of reflection of a function in x axis of the graph of the given function, we get a function g whose graph is a reflection in the x axis of the graph of f(x) = |x| - 5 as g(x) = 5 - |x|
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Find the equation of the linear function represented below in the slope intercept form.
to get the equation of any straight line, we simply need two points off of it, let's use those two points off the table in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{18})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-22}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-22}-\stackrel{y1}{18}}}{\underset{run} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-40}{6 +4} \implies \cfrac{ -40 }{ 10 }\implies -4[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{18}=\stackrel{m}{-4}(x-\stackrel{x_1}{(-4)})\implies y-18=-4(x+4) \\\\\\ y-18=-4x-16\implies y=-4x+2[/tex]
How do I remember my timetables easily? Any advice?
Answer:
Study a Times Tables map each day if you can soon you will get the hang of it
14. Equation Editor Ryan downloaded a video
game to his computer. The size of the file
was 2.4 x 10 (5 th power) kilobytes. After the game was
installed, he downloaded a patch file for the
game that was 48,000 kilobytes in size.
(Lesson 6)
A. What is the size of the game in standard
form?
B. how many times larger was the game than the patch file
Part a: The size of the game in standard form is 240000 kilobytes
Part b: The game was 5 times larger than the patch file
Part A:
Size of the game downloaded by Ryan on his computer = 2.4 * 10^5
Size of the patch file for the game = 48000 kilobytes
Therefore, converting the size of the game into the standard form:
Size of the game = 2.4 * 10^5
= 2.4 * 100000
= 240000 kilobytes
Therefore, the size of the game is 240000 kilobytes in standard form
Part B:
Size of the game = 240000 kilobytes
Size of the patch file = 48000 kilobytes
Computing the size of the game with respect to the patch file we get:
=240000/48000
= 5
Hence, the game was 5 times larger than the patch file
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A snack recipe calls for 1 1/4 cups of dip and 1/5 cup of chips. charlie wants to make the same recipe using 1 cup of chips. how many cups of dip will charlie need?
Using the concept of ratio the number of cups of chips Charlie needs can be found out.
What is ratio?A ratio in mathematics shows how many times one number is contained in another. The ratio symbol is represented by a colon (:).A ratio is still valid if all of the quantities are multiplied by the same number. By dividing each quantity by the sum of all the numbers' common factors, ratios can be lowered (much like fractions are). The simplest version of a fraction is one in which the ratio's numbers are the smallest feasible integers.
Amount of dip required by the recipe be 'a' =[tex]1\frac{1}{4}[/tex] cups=[tex]\frac{5}{4}[/tex]cups
Amount of chips required by the recipe be 'b'= [tex]\frac{1}{5}[/tex]cups
Amount of chips to be used be 'c'= 1 cup
Number of cups of chips Charlie needs
=[tex]\frac{c*a}{b}[/tex]
=[tex]\frac{1*\frac{5}{4} }{\frac{1}{5} }[/tex]
=[tex]\frac{5*5}{4}[/tex]
=[tex]\frac{25}{4}[/tex] cups
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Mooberry Creamery uses 2 cups of ice cream in each milkshake. How many milkshakes can they make with 1 gallon of ice cream?
ANSWER
8 milkshakes
Step-by-step explanation
16 cups in a gallon. 2 cups per milkshake. 8 milkshakes are the answer
Answer:
8 milkshakes
Step-by-step explanation:
16 cups in a gallon. 2 cups per milkshake.
16/2=8
The triangles are congruent by SSS and HL.
Triangles R S T and V W X are shown. Triangle R S T can be rotated about point S and then shifted down and to the left to form triangle V W X.
Which transformation(s) can be used to map △RST onto
△VWX?
Using translation concepts, the transformations that are used to map △RST onto △VWX are:
Rotation, then a translation.
What is the missing information?The two triangles are given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
Looking at the image, we have that:
The orientation of the triangle changed, hence it underwent a rotation.After the function underwent the rotation, it was moved up and right, then it underwent a translation.More can be learned about translation concepts at https://brainly.com/question/4521517
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estimate the slope of the tangent line at p by averaging the slopes of the two adjacent secant lines corresponding to the two points closest to p.
The secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.Point P: (15, 1257)
(a) The secant lines' slopes PQ.
The points are as follows:
Q = {(5, 3410), ( 10, 2210), (20, 550), (25, 145), (30, 0)}The slope (m) is calculated using:
Therefore, the secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.The slope (m) is calculated as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So far, we have:
The slope of the secant line for Q = (5,3410) is:
[tex]\begin{aligned}m_1 &=\frac{1275-3410}{15-5} \\m_1 &=\frac{-2135}{10} \\m_1 &=-213.5\end{aligned}[/tex]
The slope of the secant line for Q = (10, 2210) is:
[tex]\begin{aligned}&m_2=\frac{1275-2210}{15-10} \\&m_2=\frac{-935}{5} \\&m_2=-187\end{aligned}[/tex]
The slope of the secant line for Q = (20, 550) is:
[tex]\begin{aligned}&m_3=\frac{1275-550}{15-20} \\&m_3=\frac{725}{-5} \\&m_3=-145\end{aligned}[/tex]
The slope of the secant line for Q = (25, 145) is:
[tex]\begin{aligned}&m_4=\frac{1275-140}{15-25} \\&m_4=\frac{1135}{-10} \\&m_4=-113.5\end{aligned}[/tex]
The slope of the secant line for Q = (30, 0) is:
[tex]\begin{aligned}&m_5=\frac{1275-0}{15-30} \\&m_5=\frac{1275}{-15} \\&m_5=-85\end{aligned}[/tex]
(b) The average slope of the tangent.
The secant lines that are closest to tangent P are:
Q = {( 10, 2210), (20, 550)}This is because point P (15, 1275) is located between the two previous points.
The slopes of secant lines at Q = {( 10, 2210), (20, 550)} are:
[tex]\begin{aligned}&m_2=-187 \\&m_3=-145\end{aligned}[/tex]
The average slope (m) is as follows:
[tex]\begin{aligned}&m=\frac{m_2+m_3}{2} \\&m=\frac{-187-145}{2} \\&m=\frac{-332}{2} \\&m=-166\end{aligned}[/tex]
Hence, the average slope is -166.
Therefore, the secant line connects two points on a graph's curve:
Secant lines PQ have slopes of -213.5, -187, -145, -113.5, and -85.The tangent line's average slope is -166.Know more about slopes here:
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The complete question is given below:
a tank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallon) after t minutes.a) If P is the point (15,1275) on the graph of V, find the slopes of hte secant lines PQ when Q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85B) estimate the slope of hte tangent line at P by averaging the slopes of two adjacent secant lines. (Round your answer to one decimal places).
Answer both questions please [ brainliest ]
-
1. The measure of an angle is 84°. The measure of its complementary angle is ___
degrees.
2. The measure of an angle is 29°. The measure of its supplementary angle is ___ degrees.