Answer:
W=12cm
L=36cm
Step-by-step explanation:
We are told L=3W
and P=96
so 96=2⋅W+2⋅3⋅W
8W=96
so W=968=12cm
and L=3⋅12=36cm
hope this helps :)
Here are 2 polygons. Select all sequences of translations, rotations, and reflections below that would take polygon Pto polygon Q
The required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.
What is translation?Translation means the displacement of a figure or a shape from one place to another. In translation a figure can move upward, downward, vertical and horizontal.
Some of the Translation are,
A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure.
Rotation means the circular movement of an object around a centre. It is possible to rotate different shapes by an angle around the centre point.
Translation means the displacement of a figure or a shape from one place to another. In translation, a figure can move upward, downward, right, left or anywhere in the coordinate system.
Thus, the required sequences are The first pair is rotated and translated, the second pair is reflected and translated, and the third pair is reflected and translated.
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The complete question image is attached.
Find the equation of the axis of symmetry of the following parabola algebraically.
y=-x^2+12x-38
the independent variable is the one that's squared, namely the "x", that means that the parabola is a vertically opening parabola, so its axis of symmetry will simply be the equation of the vertical line that passes through the vertex, hmmm what's its vertex anyway?
[tex]\textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{-1}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{-38} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right)[/tex]
[tex]\left(-\cfrac{ 12}{2(-1)}~~~~ ,~~~~ -38-\cfrac{ (12)^2}{4(-1)}\right) \implies \left( - \cfrac{ 12 }{ -2 }~~,~~-38 - \cfrac{ 144 }{ -4 } \right) \\\\\\ (6~~,~~-38+36)\implies (\stackrel{x}{6}~~,~~-2)~\hfill \stackrel{\textit{axis of symmetry}}{x=6}[/tex]
Check the picture below.
You invested $10,000 in two accounts paying 2% and 5% annual interest, respectively. If the total interest earned for the year
was $290, how much was invested at each rate?
***
At 2 % annual interest, the amount invested was $ 7,000 and at 5 % annual interest, the amount invested was $ 3,000.
Total amount invested = $ 10, 000
interest earned = $ 290
Let amount invested for 2 % annual interest = x
Let amount invested for 5 % annual interest = 10,000 - x
so, we get that:
2 % x + 5 % (10,000 - x) = 290
0.02 x + 500 - 0.05 x = 290
500 - 0.03 x = 290
0.03 x = 500 - 290
0.03 x = 210
3 x = 21000
x = 21000 / 3
x = 7,000
10,000 - x = 3,000
Therefore, at 2 % annual interest, the amount invested was $ 7,000 and at 5 % annual interest, the amount invested was $ 3,000.
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what is 3-4y=19 for math 8
Answer:
y= -4
Step-by-step explanation:
3-4y=19
-3 -3
-4y=16/-4
y=-4
Write an equation of the line through each pair of points in slope-intercept form.
(2,-1) and (2,6)
The equation x = 2
is the slope-intercept form of the line passing through the points (2,-1) and (2,6)
It is given that, the line is passing through two points (2, -1) and (2, 6)
The formula to find the equation of a line in two point form is
(y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)
where m = [tex]\frac{y2 - y1}{x2 - x1 }[/tex] is the slope of the line
Slope is the measurement of the level of steepness of the line
We need to find the Two- Point form of the line
Using the above formula we get, where
x1 = 2 , x2 = 2, y1 = -1, y2 = 6
m = [tex]\frac{(6-(-1))}{(2-2)}[/tex]= [tex]\frac{7}{0}[/tex]
The equation of the line = (y-y1) = [tex]\frac{y2 - y1}{x2 - x1}[/tex](x-x1)
[y - (-1)] = [tex]\frac{7}{0}[/tex] (x - 2)
0. [y - (-1)] = 7(x-2)
7x - 14 = 0
x = 2
Hence, x =2 is the slope-intercept form of the line passing through the points (2,-1) and (2,6)
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The rectangle on the right is a scaled copy of the rectangle on the left. Identify the
scale factor. Express your answer as a whole number or fraction in simplest form.
Answer: Scale factor = 5/4 and this is a fraction number.
Step-by-step explanation:
Given Data,
find the question in the attachment.
Scale factor = (Dimensions of image) / (corresponding dimensions of preimage)
Let us assume,
Dimensions of image = B
corresponding dimensions of preimage = A
So,
we can write,
Length of rectangle B = 45/2
Length of rectangle A =18
Then,
Scale factor = B/A
= (45/2) / (18)
= 22.5 / 18
= 5/4
= 1.25
Therefore, image rectangle A is dilated with by a scale factor of 1.25
1.25 as a fraction is expressed as 5/4In order to express 1.25 as a fraction, we will first try to remove the decimal.
As 1.25 has 2 numbers after the decimal point, we will divide it by 100 in order to remove the decimal.
Hence, we get: 1.25 = 125/100
Now, dividing both sides by a common factor of 25, we will get:
125/100 = 5/4
Thus, 1.25 a as a fraction is 5/4.
Therefore,
Scale factor = 5/4 and this is a fraction number.
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Mark and Heather Starr are celebrating their 25th anniversary by having a reception at a local reception hall. They have budgeted $4,500 for their reception. If the reception hall charges a $60 cleanup fee plus $36 per person, find the greatest number of people that they may invite and still stay within their budget.
Answer:
123 people
Step-by-step explanation:
60 + 36x ≤ 4500 x is the number of people
36x ≤ 4440 Subtract 60 from both sides of the equation
x ≤ 123.333... Divide both sides by 36.
We cannot have a portion of a person, so we would round down to the next person which would be 123.
Mars has volume 1.31 × 1021
m3
whereas
Pluto has volume 4.93 x 1019
m3
How many times bigger is Mars than Pluto?
Main Answer:
Mars is bigger than Pluto by 27 times.
Explanation:
Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.It is also termed as the capacity of the object.Given: Volume of Mars = [tex]1.31[/tex] × [tex]10^{21} m^{3}[/tex]
Volume of Pluto = [tex]4.93[/tex] × [tex]10^{19} m^{3}[/tex]
To find: Determine how many times bigger is Mars than Pluto.
No. of times bigger = [tex]\frac{Volume of Mars}{Volume of Pluto}[/tex]
= [tex]\frac{1.31 * 10^{21} m^{3} }{4.93 * 10^{19}m^{3} }[/tex]
= [tex]\frac{131}{493} * 10^{2}[/tex]
=0.2657 × 100
= 26.57
=27
Final Answer:
Therefore, 27 times bigger is Mars than Pluto.
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# SPJ 9
Solve the system by graphing.
2x+y = -2
3x-y = -8
Use the graphing tool to graph the system.
Click to
enlarge
graph
Answer:
Step-by-step explanation:
x= -2
y=2
What is -1 = 4 + x/3? Solve and justify each step.
Answer: x=-15
Step-by-step explanation:
-1 = 4 + x/3
-1-4=4-4+x/3
-5=x/3
-5*3=x*3/3
-15=x*1
x=-15
[tex]-1=4+\frac{x}{3}\\ \\-1(-4)=4+\frac{x}{3}-4\ \ \ \ \ \ \ \ \ \ justify:subtract\ by\ 4\ on\ both\ sides\\\\(3)-5=x/3(3)\ \ \ \ \ \ \ \ \ justify:\ multiply\ by\ 3\ on both sides\\\boxed{x=-15}[/tex]
Name the property of real numbers illustrated by each equation.
97(7)=100(7)-3(7)
The property of real numbers illustrated by the equation is commutative property of multiplication.
The basic properties of real numbers are used to determine the sequence of simplifying mathematical expressions.
Commutative property of multiplication states that change order of factors does not change the product. i.e. a*b=b*a.
In the given equation, to determine if the property is applicable, we need to rewrite the equation:
97(7)=100(7)-3(7)
Taking the common factor out on the right side:
97(7)=7(100-3)
Simplifying,
97(7)=7(97)
Both sides of the equation will give the same answer of 679.
Hence, in this form it is evident that commutative property of multiplication is illustrated by the equation 97(7)=100(7)-3(7)
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Geeta's average of four subject is 80.She needs on her fifth subject to raise her average to 84 is
Answer:
a score of 100 is required
Step-by-step explanation:
the average is calculated as
average = [tex]\frac{sum}{count}[/tex]
given her average for 4 subjects is 80 , then
[tex]\frac{sum}{4}[/tex] = 80 ( multiply both sides by 4 to clear the fraction )
sum = 320
let x be the score required to raise average to 84 , then
[tex]\frac{320+x}{5}[/tex] = 84 ( multiply both sides by 5 )
320 + x = 420 ( subtract 320 from both sides )
x = 100
she requires to score 100 in her fifth subject
Answer: she needs score 100 in the fifth subject.
Step-by-step explanation:
Let a subject is nₓ
Hence,
[tex]\displaystyle\\\frac{n_1+n_2+n_3+n_4}{4} =80\\[/tex]
Multiply both parts of the equation by 4:
[tex]n_1+n_2+n_3+n_4=(80)(4)\\n_1+n_2+n_3+n_4=320[/tex]
[tex]\displaystyle\\\frac{n_1+n_2+n_3+n_4+n_5}{5}=84[/tex]
Multiply both parts of the equation by 5:
[tex]n_1+n_2+n_3+n_4+n_5=(84)(5)\\(n_1+n_2+n_3+n_4)+n_5=420\\320+n_5=420\\320+n_5-320=420-320\\n_5=100[/tex]
70 points!! Please help me check if my answers are correct. Best answer will get brainliest :)
Answer: All answers are correct
Step-by-step explanation: ur really smart congrats
based on the information in the table, what is Maria’s net worth
Answer
i.d.k anformation in the table and i.d.k maria's worth
Step-by-step explanation:
Write an equation for each vertical translation of y=f(x) .
4 units up.
The equation for the vertical translation of y=f(x). 4 units up is y=f(x)+4.
Using equations of the form y=f(x), you may be able to modify the graph in various ways. For example, you can move the chart up, down, left, or right, flip it around the x or y-axis, or stretch or shrink it vertically or horizontally. Understanding these transformations makes it easy to graph different functions. Start with a "basic model" and apply a series of modifications/transformations to change it to the desired function.
A point on the graph of y=f(x) has the shape (x,f(x)).
The points on the graph of y=f(x)+4 are of the form (x,f(x)+4).
So, the graph for y=f(x) +4 is the same as the graph for y=f(x) shifted up by 4 units.
The new equation is:
y=f(x)+4
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What is the value of x?
Answer:
im pretty sure it's
Step-by-step explanation:
all the angles added should be 180, so you subtract 62 and 94 from 180 to get 24.
What is the numerical equation?
The quotient of a number cubed and three plus the number
Use x for number of
meters and y for number of kilometers.
meters
1,000
3,500
500
75
1
kilometers
1
The number of kilometers are 1,3.5,0.5,0.075,0.001.
Meters are 1000,3500,500,75,1.
The number of meters is x.
The number of kilometers is y.
kilometer = 1/1000×meter
y = 1/1000×x
The units of length and distance are meters and kilometers, respectively. The kilometer, or 1,000 meters, serves as the unit of distance measurement in the metric system. Therefore, one meter is equivalent to a thousandth of a kilometer.
A meter is denoted by the letter m, whereas a kilometer is denoted by the letter km. The default unit of length measurement in the metric system. Between the length of a ruler and the spacing between objects in a room, meters are used to measure everything.
Therefore the number of kilometers are 1,3.5,0.5,0.075,0.001.
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⁻AD and ⁻CG are diameters of ®B . Identify each arc as a major arc, minor arc, or semicircle. Then find its measure.
m ACD
The measure of m (arc ACD) is 180°
Here,
AD and CG are diameter of circle B.
We have to find the measure of m ACD.
What is Diameter of a circle?
A line that passes through the center and meets the circumference at opposite ends is called diameter of a circle.
Now,
Since, AD is a diameter.
Therefore, ACD is a semicircle.
The measure of a semicircle is 180.
So, The measure of m (arc ACD) is 180°.
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Rex and Samir participated in a walkathon. Rex walked for 1 2/3 hours, and Samir walked for 3 1/3 hours. complete the comparison. Samir walked _____ times ad many hours as Rex walked.
Answer:
2 times as much
Step-by-step explanation:
1 hour 2/3 = 60 + (2/3) 40 mins = 100 minutes
3 hours 1/3 = (60 ×3 ) + 20 mins = 200 mins
200 is twice as much as 100
Answer:
2
Step-by-step explanation:
just did it on khan acadmey.
What is the slope of the line 5y+3 = (2/5)x ?
The slope of the line 5y + 3 = (2/5)x is 2 .
The equation of a straight line can be written as follows,
y = mx + c equation 1
m in the above equation represents slope of the line and c represents the intercept.
The given equation is 5y + 3 = (2/5)x .
To get the slope of this given equation we need to convert the given equation in the format of equation of a straight line i.e., equation1.
So, now we will rearrange the given equation as,
5y + 3 = (2/5)x
⇒ 5y = (2/5)x - 3
Now on dividing this equation by 5 on both sides, we will get
⇒ y = 2x + (-3/5) equation 2
On equating equation 1 and equation 2, we will get
Slope of the line = m = 2
Intercept = c = (-3/5)
The slope of the line 5y + 3 = (2/5)x is 2 .
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dentify each segment BD as a(n) altitude, median, or perpendicular bisector.
A triangle's altitude is the perpendicular segment from the triangle's vertex to the opposite side (or the line containing the opposite side).
BD is an altitude here because is it perpendicular to AC.
What is meant by altitude of a triangle?A triangle's altitude is the perpendicular segment from the triangle's vertex to the opposite side (or the line containing the opposite side).
An altitude of a triangle is a line segment through a vertex that is perpendicular to a line containing the base in geometry. The extended base of the altitude is the line that contains the opposite side. The intersection of the extended base and the altitude is known as the altitude's foot.
A triangle's altitude is the perpendicular drawn from the triangle's vertex to the opposite side. The altitude, also known as the triangle's height, forms a right-angle triangle with the base.
BD is an altitude here because is it perpendicular to AC.
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Write an equation in point-slope form of the line having the given slope that contains the given point.
m: 0,(-2,6)
The equation in point-slope form of the line having the slope m=0 that contains the points (-2,6) is y-6=0(x+2)
Given,
The slope m= 0
The points =(-2,6)
We know the point-slope form,
[tex]y-y_{1}=m(x-x_{1} )[/tex]
Substitute the values in the equation
y-6=0(x-(-2))
y-6=0(x+2)
Hence, the equation in point-slope form of the line having the slope m=0 that contains the points (-2,6) is y-6=0(x+2)
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[ Brainliest + 20 points]
The smallest angle by which a regular 60-sided figure can be rotated to look exactly like the original figure is ___ degrees.
Answer:
first to get a 60 sided figure we know there if 360 degrees in a full rotation so let's simply divide it by 60
360÷60= 60 degrees
Evaluate 81^2/3 then find the square root
Answer:
Below in bold.
Step-by-step explanation:
81^2/3
= 81^2 = 6561
6561^1/3
= ∛(6561)
= 18.72
√18.72
= 4.33 to nearest hundredth.
Ayuda doy muchos puntos muchos
Answer:
$138
Step-by-step explanation:
%15 -> .15
120×.15=18
$120 + $18 = $138
Tommy owes his parents $200. He pays them a $50 payment in July. The next month he has to borrow another $100. How much does he owe his parents altogether?
Answer:
$300
Step-by-step explanation:
subtract $200 by $50= $150, then $150 to $100.
-16=16x2 how many solutions does this equation have?
There are a two solutions of the given quadratic equation.
According to the statement
We have to find that the number of solutions of the equation.
So, For this purpose, we know that the
Quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power
From the given information:
The given equation is a:
-16=16x^2
It becomes
16x^2 = -16
Then solve it with the help of the rearrange the terms
x^2 = -16/16
x^2 = -1
x = (-1)^1/2
x = +i , -i
There is a two solutions of the quadratic equation.
So, There are a two solutions of the given quadratic equation.
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The formula I = √W/R gives the electric current I in amperes that flows through an appliance, where W is the power in watts and R is the resistance in ohms. Which set of numbers best describes the value of I for the given values of W and R ? W=50, R=200
The equation be I = √W/R
Where I is the current.
W stands for electrical power.
R stands for resistance in ohms then the value of I = 0.5.
What is meant by electrical power?A circuit's ability to transport electrical energy is referred to as its electric power. One joule per second, or one watt, is the SI unit of power. Similar to other SI units, watts have standard suffixes that refer to thousands, millions, and billions of watts as kilowatts, megawatts, and gigawatts, respectively.
Let the equation be I = √W/R
Where, I is the current.
W stands for electrical power.
R stands for resistance in ohms.
Simply enter the values of W and R into the equation, i.e.,
When W = 50, R = 200, to solve for the value of I for each set.
I = √50/ 200
The square root of I = √0.25
W = 50, R = 200, I = 0.5.
I = √50/ 200
The square root of I = √0.25
I = 0.5
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Carolyn needs to figure out the missing properties used to simplify the expression below
The properties used in the the simplification of the expression is:
step 1: Inverse multiplication property
step 2: Commutative property
step 3: Associative property
step 4: Commutative property
step 5: Identity property
Given the expression is:
1 ÷ 2/3 × (₋5) × 3 ÷ (₋1/4)
step 1: 1 × 3/2 × (₋5) × 3 × (₋4)
Inverse multiplication property is applied.
The reciprocal of a particular integer is referred to as the multiplicative inverse. It is employed to make mathematical expressions simpler. The word "inverse" denotes an opposing or opposed action, arrangement, position, or direction. A number becomes 1 when it is multiplied by its multiplicative inverse.
step 2: 1 × (₋4) × 3/2 × (₋5) × 3
Commutative property is applied.
Mathematical addition and multiplication operations are covered under the commutative property. In other words, adding or multiplying two integers does not change the outcome if the order or location of the numbers is changed.
step 3: 1 × [(₋4) × 3/2] × (₋5) × 3
Associative property is applied.
According to the associative feature of multiplication, the outcome of a multiplication problem is unaffected by the arrangement of the numbers in the problem's constituent parts.
step 4: 1 ×[-6] × (₋5) × 3
commutative property is applied.
step 5: (-6) × (₋5) × 3
Identity property is applied.
Multiplying 1 by any number yields the number itself, according to the Multiplicative Identity Property, commonly known as the Identity Property of Multiplication. This is because any time a number is multiplied by 1, it retains its identity and does not change.
Hence we have applied the above mentioned properties of multiplication.
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