The quadratic equation that opens down and has vertex at (2,-8) is y = (-|a|)*(x - 2)² + (-8).
The graph of a quadratic function has the shape of a parabola. Although a parabola's "width" or "steepness" and direction of opening can differ, they all have the same basic "U" shape. If the leading coefficient is larger than zero, the parabola opens upward; if it is less than zero, it opens downward.
The quadratic equation's vertex form is y = a*(x - h)2 + k.
Given that (2,-8) or (h, k) is the vertex point (2,-8)
Since the graph starts out downward, a will have a negative value.
Since |a| is the magnitude of a, the quadratic equation will then be written as y = (-|a|)*(x - 2)2 + (-8).
Consequently, y = (-|a|)*(x - 2)2 + is a quadratic equation that opens downward and has a vertex at (2,-8). (-8).
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a figure is made of 2 rectangular prisms...
what is the volume?
The volume of the figure that is composed of two rectangular prisms is: 146 cubic in.
What is the Volume of a Rectangular Prism?The volume of a rectangular prism = (length)(width)(height).
The figure can be decomposed into two rectangular prisms. Find the volume of each of the prisms.
Volume of rectangular prism 1:
Length of the prism = 8 in.
Width of the prism = 7 in.
Height of the prism = 1 in.
Volume of rectangular prism 1 = (8)(7)(1) = 56 in.³
Volume of rectangular prism 2:
Length of the prism = 10 in.
Width of the prism = 9 in.
Height of the prism = 1 in.
Volume of rectangular prism 1 = (10)(9)(1) = 90 in.³
Volume of the figure = 90 + 56 = 146 cubic in.
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How do i solve this.
A) none of these
B) only mean because if we replace 32 by 16 sum will decrease and so mean will decrease
C) both mean and median because when we remove some value os starting total sum will decrease and hence mean decrease
median will change because after remove some values total number will decrease and hence value will change
d)Negative skewed
What is central of tendency ?Measures of central tendency are the values that characterize a data set by indicating the data's central location. Mean, Median, and Mode are the three primary metrics for determining central tendency.Mean is the product of the sum of all observations and the total number of observations.
An ordered set's median is its middle or centre value.
The most frequent value in a data set is called the mode.
Given that :32, 38, 42, 42, 43, 44, 46, 46, 47, 47, 49, 49, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53
32, 38, 42, 42, 43, 44, 46, 46, 47, 47, 49, 49, 51, 51, 51, 51, 52, 53, 53, 53, 53, 53
mean = [tex]\frac{sum of observation}{number of observation}[/tex]
mean = [tex]\frac{1046}{22}[/tex]
= 47.54
How to calculate median ?The median is calculated by sorting the scores into numerical order, dividing the total by two, rounding the result up to get the median position, or using an even number of scores, averaging the median position's value with the following position's value.
here n = 22 which is even
median =[tex]\frac{\frac{n}{2}term +(\frac{n}{2}+1 )term }{2}[/tex]
[tex]\frac{\frac{22}{2}term +(\frac{22}{2}+1 )term }{2}\\ = \frac{11 term + 12 term}{2}[/tex]
= 49
How to calculate mode ?Organize the numbers in a set in whatever order—from lowest to highest or highest to lowest—and then tally the frequency with which each number appears in the group. The mode is the one that shows up most frequently.
mode = 53 as it is repeated more times.
A) none of these
B) only mean because if we replace 32 by 16 sum will decrease and so mean will decrease
C) both mean and median because when we remove some value os starting total sum will decrease and hence mean decrease
median will change because after remove some values total number will decrease and hence value will change
d)Negative skewed
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Question
Simplify: (8c³ + c²d) - (9cd²-5d³) + (-3c²d-8cd²).
Answer: [tex]5d^3 -17cd^2 -2c^2 d+8c^3[/tex]
Step-by-step explanation:
Expanding the parentheses,
[tex]8c^3 +c^2 d-9cd^2 +5d^3 -3cd^2 d-8cd^2[/tex]
Combining like terms yields [tex]5d^3 -17cd^2 -2c^2 d+8c^3[/tex].
Write the equation of the line that passes through the points (0,3) and (2,-1). Put your answer in point-slope form, using fractional form for m and b.
The equation of the line will be y = -2x + 3.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
Given that the equation of the line that passes through the points (0,3) and (2,-1).
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
First calculate the slope of the line:-
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Slope = ( -1 - 3 ) / ( 2 - 0 )
Slope = -2
The y-intercept will be:-
y = mx + c
3 = 0 + c
c = 3
Equation of the line:-
y = mx + c
y = -2x + 3
Therefore, the equation of the line will be y = -2x + 3.
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Bài 1.5 Tính hạng của các ma trận:
1.
1 2 1 −1 0
2 −1 1 3 4
2 −1 2 1 −2
2 −3 1 2 −2
−4 1 −3 1 8
,
2.
25 31 17 43
75 94 53 132
75 94 54 134
25 32 20 48
Answer:
1 is the awnsewer
Step-by-step explanation:
1
The speed limit on a road is 30 miles per hour. Drivers on this road typically vary their speed around the
limit by as much as 3 miles per hour. What is the range of typical speeds on this road?
The range of typical speeds (in miles per hour) is
Answer:
Between 30 and 33 mph or, simply
Range: [30,33]
Step-by-step explanation:
A Range is all possible values of a certain variable or piece of information commonly notated by a minimum and maximum. In this example, our variable is the speed traveled by drivers in a road. We are provided a minimum of 30 mph as this is the speed limit, and told that drivers may speed up to a maximum of 3 mph faster ( or 33 mph).
Therefore, our minimum would be 30, maximum would be 33, and Range would be [30, 33].
Brackets are used here because both our minimum and maximum values are included in the range.
HOPE THIS HELPS!!
Find each of the numbers below.
Simplify your answers as much as possible.
The opposite of 0:
The opposite of 7:0
The opposite of the opposite of 6:
The opposite of 0 is 0, the opposite of 7 is -7 and the opposite of 6 is -6.
If we consider a number x, then the opposite of the number x will be equal to -x. In a number line the opposite of a number lying on the positive side always lies on the negative side of number line. Also, the opposite of a number -x is the x that is the number itself. It is given in the question that we need to find opposite of 0, 7 and 6.
Let x = 0, opposite of x is -x.
=> -x = -0
=> -x = 0
Now, let x = 7, opposite of x is -x
=> -x = -7
Now, let x = 6, opposite of x is -x
=>-x = -6
Thus, the opposite of the numbers 0, 7 and 6 are 0, -7 and -6 respectively.
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what is the slope of the line through (5,4),(-2,-8)
Please do it step by step and asap
Your uncle wants to buy a monthly garage parking pass that costs $49.75.
He has five $10 bills, one $5 bill, five $1 bills, and 3 quarters. Use the table
to show three different ways your uncle could pay for the pass and the
change that he receives.
Answer:
See below
Step-by-step explanation:
Answer
Denomination
10 5 1 0.75 Change
5 0 0 0 0.25
4 1 4 0.75
These are the only 2 ways I see of paying the parking pass. The tens can't drop down to 3 because the rest will never add up to 19.95
what is the large cardinal project
The Large Cardinal Project is a field of set theory.
Set theory deals with basic projects. Giant Numbers card attributes are a subset of Infinite Numbers card numbers. The most active set theorists believe that the most important fundamental axioms studied today are compatible with ZFC. Steele and Leber used a giant map to prove the left finite algebraic pyramid theorem (a(bc) = (ab)(ac)). The idea is to introduce the great cardinals to thinkers from the very beginning. It was a little bit good. By definition, a great cardinal is a hypothesis. This aims to show how to establish some basic facts about big numbers by generalizing the combinatorial features of natural numbers to sets of seconds. It is an investigation of important fundamental positions and the axioms of set theory. Numeric Tables and Sequences Overview Aggregates, classes, and numeric tags are not allowed. Some properties of natural numbers Uncountable generalizations.
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the digits 3,4,5,6,7 and 8 are randomly arranged to form a three-digit number. (Digits are not repeated.) Find the probability that the number is even and greater than 800.
The probability of getting an even number greater than 800 is 0.08
Total outcomes possible when a three-digit number is formed without repetition:
Using the digits 3,4,5,6,7 and 8:
The first digit can be filled in using any of the 6 options
The second digit can be filled using the remaining 5 options
The third digit can be filled in using the remaining 4 options
So, total outcomes possible = 6*5*4 = 120 possibilities
Now, finding even number greater than 800:
The first digit can only be filled by 8 for a number to be greater than 800 which means there is only one option for the first digit
The second digit can be filled using any of the remaining options except 8 which means there are 5 options
The last digit can be filled using 4 and 6 because these are the only even numbers which mean 2 options
Total possible outcomes = 1*5*2 = 10 possibilities
The probability that the number is even and greater than 800:
= 10/120 = 0.08
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Subtract these equations.
INFORMATION:
We have the next subtraction
And we must solve it
STEP BY STEP EXPLANATION:
To solve a subtraction of two expressions, we must multiply the second expression by -1 and then add up the first expression and the result of the multiplication.
1. Multiply the second expression by -1
[tex]\begin{gathered} -1(3x+2y=3) \\ -3x-2y=-3 \end{gathered}[/tex]2. Add up the first expression and the result of the multiplication. We must add similar terms
[tex]\begin{gathered} 3x+4y=17 \\ -3x-2y=-3 \\ -------- \\ 0x+2y=14 \\ →2y=14 \end{gathered}[/tex]Finally, the result of the subtraction is 2y = 14
ANSWER:
aA. 2y = 14
Given the function f(x) in red, write the equation for the transformed function g(x)in green
your class mate was asked to square (2x - 3) , he answered 4x² - 9 . is his answer correct?
His answer is incorrect
The correct answer is:
[tex]4x^2-12x+9[/tex]This is the square of (2x - 3)
Explanation:Given (2x - 3)
The square of this is:
[tex]\begin{gathered} (2x-3)^2 \\ =4x^2-12x+9 \end{gathered}[/tex]His answer of 4x² - 9 is incorrect.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer:
600
Step-by-step explanation:
[tex]R(1)=400 \\ \\ R(2)=1000 \\ \\ R(2)-R(1)=600[/tex]
Find the missing angel.Round to the nearest tenth previous answer previous answer 30.2
From the diagram
[tex]\begin{gathered} \theta\text{ = 32} \\ \text{Opp = X} \\ \text{Adj = }5m \\ By\text{ using Pythagoras Theorem we have.} \\ \text{Tan}\theta\text{ = }\frac{Opp}{\text{Adj}} \\ \text{Tan 32 =}\frac{X}{5} \\ X\text{ = Tan 32 }\times5 \\ X\text{ = }3.124m \end{gathered}[/tex]Final answer = 3.124m
Select the relation that is a function
Which side of EFGH corresponds with CD
nswer
The side of EFGH that corresponds with CD is GH.
xplanation
One of the key points for two figures to be similar is that the angles are the same.
Since parallelograms have opposite angles equal, and adjacent angles sum up to give 180 degrees. We know that ABC
Angle = 180 - 523 = 127
And this makes the similarity makes the order of similarity here to be
BCD = EFGH
o,
dD = GH
Hope this Helps!!!
Dixon and his little sister Ariadne stand next to each other on the playground on a sunny afternoon. Their mother measures their shadows. Ariadne's shadow is feet long and Dixon's shadow is feet long. If Ariadne is feet tall, how tall is Dixon?
Using the similar triangle principle, the height of Dixon in feet is 6 feet.
How to find the side of similar triangle?Ariadne's shadow is 15 feet long and Dixon's shadow is 18 feet long.
Ariadne is 5 feet tall.
The height of Dixon can be found using similar triangle principle.
Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles.
Therefore, using the similar triangle theory,
Let
x = height of Dixon
Hence,
shadow length of Ariadne / Ariadne height = Dixon shadow length / Dixon height
shadow length of Ariadne = 15 ft
Ariadne height = 5 feet
Dixon shadow length = 18 feet
15 / 5 = 18 / x
cross multiply
15 × x = 18 × 5
15x = 90
divide both sides by 15
15x / 15 = 90 / 15
x = 6 ft
Therefore, Dixon height is 6 feet.
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Need help for my son I will give branliest
The value of a = -10, b = -0.2, c = 0.25
What is an equation?
An equation is a formula that is used to express the equality of two expressions with the help of = sign. In other words, it is an mathematic statement that made two expressions equal. There are different type of equation and we are here dealing with linear equation.
Given equation are,
a) 1/5a = -2
cross multiplying.
a = -2(5)
a = -10
b) 8+b = 7.8
Subtracting,
b = 7.8 - 8
b = 0.2
c) -0,5 = -2c
Dividing,
c = -0.5/-2
c = 0.25
Hence the solution of each equation, is solved above.
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Jacob ran 10 miles in 80 minutes at that rate how far would he run in 21/2 hours? (*hint - 1 hour = 60 minutes)
If Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours
Number of miles that Jacob will run in 80 minutes = 10 miles
Number of miles that Jacob will run in 1 minutes = Number of miles that Jacob will run in 80 minutes/ 80
= 10/80
= 0.125 miles
We know,
1 hour = 60 minutes
[tex]2\frac{1}{2}[/tex] hours = 2.5×60
= 150 minutes
Number of of miles that Jacob will run in 150 minutes = Number of miles that Jacob will run in 1 minutes × 150
= 0.125×150
= 18.75 miles
Hence, if Jacob ran 10 miles in 80 minutes at that he will run the distance of 18.75 miles in [tex]2\frac{1}{2}[/tex] hours .
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Please help with question!!
Given:
[tex]\ln x+\ln (x+14)=3[/tex]Use the formula:
[tex]\ln ab=\ln a+\ln b[/tex][tex]\begin{gathered} \ln x+\ln (x+14)=3 \\ \ln x(x+14)=3 \\ x(x+14)=e^3 \\ x^2+14x=20.085 \end{gathered}[/tex]solve the equation :
[tex]\begin{gathered} x^2+14x=20.085 \\ x^2+14x-20.085=0 \\ x=\frac{-14\pm\sqrt[]{14^2-4(1)(-20.085)}}{2} \\ x=\frac{-14\pm\sqrt[]{276.34}}{2} \\ x=\frac{-14\pm16.623}{2} \\ x=-7\pm8.312 \\ x=-7+8.312;x=-7-8.312 \\ x=1.312;x=-15.312 \end{gathered}[/tex]Answer:
[tex]\textsf{Exact form}: \quad x=-7 +\sqrt{49+e^3}[/tex]
[tex]\textsf{Decimal form}: \quad x=1.312\; \sf (3\:d.p.)[/tex]
Step-by-step explanation:
Given equation:
[tex]\ln x + \ln (x+14)=3[/tex]
[tex]\textsf{Apply the product law} \quad \ln x + \ln y=\ln xy:[/tex]
[tex]\implies \ln (x(x+14))=3[/tex]
[tex]\implies \ln (x^2+14x)=3[/tex]
[tex]\textsf{Apply the log law} \quad e^{\ln x}=x:[/tex]
[tex]\implies e^{\ln (x^2+14x)}=e^3[/tex]
[tex]\implies x^2+14x=e^3[/tex]
Subtract e³ from both sides to form a quadratic equation:
[tex]\implies x^2+14x-e^3=e^3-e^3[/tex]
[tex]\implies x^2+14x-e^3=0[/tex]
Quadratic Formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]
Therefore:
a = 1b = 14c = -e³Substitute these values into the quadratic formula and solve for x:
[tex]\implies x=\dfrac{-14 \pm \sqrt{14^2-4(1)(-e^3)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{196+4e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4(49+e^3)} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm \sqrt{4}\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=\dfrac{-14 \pm 2\sqrt{49+e^3} }{2}[/tex]
[tex]\implies x=-7 \pm \sqrt{49+e^3}[/tex]
Solutions:
[tex]x=-7 +\sqrt{49+e^3}, \quad x=-7 -\sqrt{49+e^3}[/tex]
Decimal form:
[tex]x= 1.312, \quad x=-15.312[/tex]
As logs of negative numbers cannot be taken, the only solution is:
[tex]x=-7 +\sqrt{49+e^3}\\\\x=1.312\;\sf (3\;d.p.)[/tex]
What in the world how do you solve this?
Answer:
B
Step-by-step explanation:
using the rule of radicals
• [tex]\sqrt[n]{x}[/tex] ÷ [tex]\sqrt[n]{y}[/tex] = [tex]\sqrt[n]{\frac{x}{y} }[/tex], then
32[tex]\sqrt[8]{18y}[/tex] ÷ 8[tex]\sqrt[8]{3y}[/tex]
= [tex]\frac{32}{8}[/tex] ×[tex]\sqrt[8]{\frac{18y}{3y} }[/tex] ( cancel 18y and 3y by 3y )
= 4 × [tex]\sqrt[8]{6}[/tex]
= 4[tex]\sqrt[8]{6}[/tex]
Match each slope and y-intercept with the appropriate linear equation.
m = 3, b=4
m = 5, b = -2
m = 4, b=3
m = -2, b=5
Intro
↑
↑
y = 4x +3
y = 3x + 4
y = 5x-2
y = -2x + 5
Done
Answer:
Slope-intercept form: y = mx + b
(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)
y = 1.5x - 7 m = 1.5 b = -7
(y = (1.5)x + (-7) ----> y = 1.5x - 7)
y = -1.5x - 4 m = -1.5 b = -4
y = -3x + 4 m = -3 b = 4
y = 3x m = 3 b = 0
y = 7 m = 0 b = 7
(y = (0)x + 7 ---> y = 7)
Step-by-step explanation:
Please help solve equation
EXPLANATION
The first equation is a line with the following slope-intercept form:
[tex]4x+4y=-8[/tex]Subtracting -4x to both sides:
[tex]4y=-4x-8[/tex]Dividing both sides by 4:
[tex]y=-\frac{4}{4}x-\frac{8}{4}[/tex]Simplifying:
[tex]y=-x-2[/tex]The slope is -1 and the y-intercept is -2
Applying the same reasoning to the second equation we get:
[tex]y=-x+3[/tex]3
Now, we can write and graph both linear equation
Two numbers have a difference of 1,200 and a total of 6,484
What are the two numbers
3842 and 2642 are the two numbers.
What is linear equations?
Linear equations are a subset of first order equations. One homogeneous variable of degree one constitutes a linear equation in one variable (i.e., only one variable). A linear equation could contain multiple variables. When a linear equation comprises two variables, for instance, linear equations in two variables are utilized. A mathematical statement known as an equation contains an algebraic expression and the equal symbol (=). It is the equation for a straight line. The equation is shown to be valid when values are substituted for the unknown values in the solutions of linear equations. When there is just one variable, there is just one answer.
How to Solve?
Solving a linear equation involves determining the answer to a linear equation with one, two, three, or more variables. The answer to a linear equation is the value or values of the variable(s) that are part of the equation. There are six main ways to resolve linear equations. For the purpose of solving linear equations, these methods include the Graphical Method, Elimination Method, Substitution Method, Cross Multiplication Method, Matrix Method, and Determinants Method.
Let the greater of the two numbers be "x" and the smaller one be "y".
Given, x - y = 1200 --(i) & x + y = 6484 --(ii)
Adding (i) and (ii), we get, 2x = 7684 ⇒ x = 3842
Subtracting (i) from (ii), we get, 2y = 5284 ⇒ y = 2642
Thus, the greater number of the two numbers is 3842 and the smaller number is 2641.
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Directions: Watch the directions video for how to complete sample work. You must
answer all questions completely, and show all of your work in order to receive credit.
1. ERROR ANALYSIS
Your friend is trying to find the maximum value of P = -x + 6y subject to the
following four constraints.
(y ≤-2x + 4
y≤ x+1
x≥0
y20
The maximum value of P = 11.
Given: P = -x + 6y
In this question we have to first solve the given system of equations.
Ignore the greater or lesser than sign that is:
y = -2x+ 4 -------- 1
And y = x + 1 --------- 2
On solving these two equations we get;
0= -3x + 3
⇒ -3x = -3
⇒ x= 1
Substituting the value of x in equation 2 we get
y = x+ 1
= 1 + 1 = 2
Thus y = 2 and x = 1
So on putting these values in P = -x + 6y we get
P = - 1 + 6× 2
P = - 1 + 12 = 11
Therefore P= 11.
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In a quadrilateral, one angle measures 175.A second angle measures 29, while a third angle measures 54. What is the measure of the remaining angle?
Given:
In a quadrilatral three angle are
[tex]Suppose\text{ }\angle A=175\text{ }\angle B\text{ =29 }\angle C=54[/tex]Required:
Remaining angle i.e.
[tex]\angle D[/tex]Explanation:
In a quadrilatral ABCD
[tex]\begin{gathered} \angle A+\angle B+\angle C+\angle D=360 \\ 175+29+54+\angle D=360 \\ \angle D=360-258 \\ \angle D=102 \end{gathered}[/tex]Final Answer
Remaining Angle= 102
Answer:
102
Step-by-step explanation:
If you add all of the angles (175+29+54) it gives you 258. As you may already know, a quadrilateral's angles have to all equal 360 combined. When you subtract 360-258, you get 102. Hope this helped! :)
2 digit by 2 digit multiplacation 97x57
Answer:
11,280
Step-by-step explanation:
so first you write the equation 97*57. then you multiply them, ( 7*7=49; 5*7= 35, now 9*7= 63; 5*9= 45) and the answer is 11,280
I might be wrong in my calculations because the calculator says the answer is 5,529 so yeah the answer is either 11,280 or 5,529.
Hope this helps
_% of $20 = $10
PLEASE HELP ME ITS IMPORTANT
Answer:
DONT WORRY ITS FIFTY PERCENT