Answer:
x = 4, y = -3
Step-by-step explanation:
{2x - y = 11
{x + 3y = -5
You can use the substitution method by solving for x in the second equation:
x + 3y = -5
Subtract 3y from both sides:
x = -3y - 5
Now, substitute this value for x into the first equation:
2x - y = 11
2(-3y - 5) - y = 11
Distribute:
-6y - 10 - y = 11
Add 10 to both sides:
-6y - y = 21
Combine like terms:
-7y = 21
Divide both sides by -7:
y = -3
Next, substitute this value for x into the second equation:
x + 3y = -5
x + 3(-3) = -5
Multiply:
x - 9 = -5
Add 9 to both sides:
x = 4
Answer:
(7, 3)
Step-by-step explanation:
2x - y =11 2x-y =11
-2(x+3y)= (-5)-2 -2x-6y= 10
Then you will cross out the x, and add.
-7y =21 divide 7
y=-21/7 or y=3
Then you plug in the y where the y is and solve
2x-(3) = 11
2x = 14
x=7
Town B is 250 km from town A on a bearing of 080°.
Town C is 250 km from town B on a bearing of 220°.
What is the bearing from town A to town C?
Answer:
330 degrees
Step-by-step explanation:
Answer: 300deg
Step-by-step explanation:
Solve for v. 3v + 5v = 72 please simplify as much as possible! v = _ ?
Answer:
v is 9
Step-by-step explanation:
it is 9 because if you simplify it is 8v=72 or 9
Answer:
v = 9
Step-by-step explanation:
3v + 5v = 72
combine like terms
8v = 72
Divide by 8
8v/8 = 72/8
v =9
Someone pls help . Thank you sm !!
Answer:
28 = -3k + 728 - 7 = -3k
21 = -3k
21/-3 = k
k = -7
1/5 x - 17 = 3x/5 = 3 + 17
x/5 = 20
x = 5*20
x = 100
82 = 7/10 G + 1282 - 12 = 7G/10
70 = 7G/10
70*10 = 7G
700 = 7G
700/7 = G
G = 100
Find The Answer PLS..
Answer:
Slope = 1
Greatest value is positive infinite
Smallest value is negative infinite
Step-by-step explanation:
Function
Y=mx+c
Y=x
Which equation represents an ellipse with foci at (3, 2) and (-9, 2)
that passes through the point (-3, 10)?
Answer:
D, since it horizontal ellipse, a is greater than b
An ellipse has two foci. The correct option is D.
What is the equation of ellipse if its major and minor axis and centre are given?Suppose that the major axis is of the length 2a units and that the minor axis is of 2b units, and let the ellipse is centred on (h,k) with a major ellipse parallel to the x-axis, then the equation of that ellipse would be:
[tex]\dfrac{(x-h)^2}{a^2} + \dfrac{(y-k)^2}{b^2} =1[/tex]
Coordinates of its foci would be: (h±c, k) where c² = a² - b²
If its major axis is parallel to the y-axis, then,
coordinates of its foci would be: (h, k±c) where c² = a² - b² and its equation would be:
[tex]\dfrac{(x-h)^2}{b^2} + \dfrac{(y-k)^2}{a^2} =1[/tex]
Given the foci at (3, 2) and (-9, 2) that pass through the point (-3, 10), therefore, the equation of the ellipse will be,
[tex]\dfrac{\left(x+3\right)^{2}}{100}+\dfrac{\left(y-2\right)^{2}}{64}=1[/tex]
Hence, the correct option is D.
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The following frequency table shows the number of hours each of the staff members at Eroy's Electronics slept Thanksgiving night. Find the mean number of hours of sleep.
Answer:
Mean
=Sigma (Number of sleep ×Number of employees) / Sigma Number of employees
= (3×1) + (4×0) + (5×0)+ (6×2)+(7×1)+(8×1) / 1+0+0+2+1+1
= 3+0+0+12+7+8/ 1+0+0+2+1+1
= 30 / 5
= 6
So the mean of number of hour sleep is 6 hours.
I hope this helps
if u have question let me know in comments ^_^
Answer:
Step-by-step explanation:
Mean
=Sigma (Number of sleep ×Number of employees) / Sigma Number of employees
= (3×1) + (4×0) + (5×0)+ (6×2)+(7×1)+(8×1) / 1+0+0+2+1+1
= 3+0+0+12+7+8/ 1+0+0+2+1+1
= 30 / 5
= 6
So the mean of number of hour sleep is 6 hours.
I hope this helps
Please help me i will give brainly!
for vegetable oil, it's increasing by 120, for cornstarch by 30
PLEASE HELP ASAP WILL GIVE BRAINLY!!!!!!Some of the steps in the derivation of the quadratic formula are shown:
Step 3: –c + StartFraction b squared Over 4 a EndFraction = a(x squared + StartFraction b Over a EndFraction x + StartFraction b squared Over 4 a squared EndFraction)
Step 4a: –c + StartFraction b squared Over 4 a EndFraction = a(x + StartFraction b Over 2 a EndFraction) squared
Step 4b: negative StartFraction 4 a c Over 4 a EndFraction + StartFraction b squared Over 4 a EndFraction = a(x + StartFraction b Over 2 a EndFraction) squared
Which best explains or justifies Step 4b?
factoring a polynomial
multiplication property of equality
converting to a common denominator
addition property of equality
.
Answer:
i think it is the third one but dont know just an educational geuss
Step-by-step explanation:
The given steps from the derivation of the quadratic formula are:
Step 3: [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]
Step 4a: [tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 4b: [tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
The property "converting to a common denominator" justifies step 4b. So, option C: "converting to a common denominator" is correct.
What is the quadratic formula?The quadratic formula is as follows:
x = [-b ± (√b²+4ac)]/2a
This formula is derived from the quadratic equation [tex]ax^2+bx+c=0[/tex].
What are the steps to derive the quadratic formula?The standard quadratic equation is [tex]ax^2+bx+c=0[/tex]
Step 1: [tex]ax^2+bx=-c[/tex]
Step 2: Taking 'a' as common
[tex]a(x^2+\frac{b}{a}x)=-c[/tex]
Step 3: Adding [tex]\frac{b^2}{4a}[/tex] on both sides
[tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x)+\frac{b^2}{4a}[/tex]
⇒ [tex]-c+\frac{b^2}{4a}=a(x^2+\frac{b}{a}x+\frac{b^2}{4a^2})[/tex]
Step 4a: Factoring the polynomial
[tex]-c+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 4b: Converting to a common denominator
[tex]\frac{-4ac}{4a}+\frac{b^2}{4a}=a(x+\frac{b}{2a})^2[/tex]
⇒ [tex]\frac{(-4ac+b^2)}{4a}=a(x+\frac{b}{2a})^2[/tex]
Step 5: Applying square root (on one side there is a square, so, on the other side it gets ±)
⇒ [tex]\frac{(-4ac+b^2)}{4a^2}=(x+\frac{b}{2a})^2[/tex]
⇒ ±[tex]\sqrt{\frac{(-4ac+b^2)}{4a^2}} =(x+\frac{b}{2a})[/tex]
⇒ [tex]x+\frac{b}{2a}[/tex] = ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
step 6: Subtacting [tex]\frac{b}{2a}[/tex] from both the sides
⇒ [tex]x=-\frac{b}{2a}[/tex] ± [tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
⇒ x = [-b ± (√b²+4ac)]/2a
Thus, step 4b best explains or justifies the property "Converting to a common denominator".
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Find an equation of the line with the slope m= 3 that passes through the point (2,2). Write the equation in the form Ax+By = C.
Answer:
[tex]y = 3x-4[/tex]
Step-by-step explanation:
We know that if we were to write an equation with the slope of 3, it would be [tex]y=kx[/tex], where k is the constant (in this case 3.)
So right now, we have [tex]y=3x[/tex].
However, this will not pass through the point (2,2). To do this, we need to add a y-intercept in which (2,2) will be crossed through.
If we have a y-intercept of -4, the points will be:
(0, -4)
(1, -1)
(2, 2)
So our final equation is [tex]y = 3x-4[/tex].
Hope this helped!
Answer: 3x-1y=4 in Ax+By=C form
Step-by-step explanation:
the intercept form is y=3x-4
subracting 3x from both sides would get -3x+y=-4
distributing -(-3x+y=-4) would get 3x-y=4.
Please help me on this question.
Answer:
a(n)= 120(1/2)^(n-1)
Step-by-step explanation:
60*x=120, x=60/120=1/2 so the sequence goes by a ratio of 1/2
a(n)=b(c)^n-1 and c=1/2. b= a(1)=120 so the formula is a(n)= 120(1/2)^(n-1)
Answer:120(1/2)^(n-1)
Step-by-step explanation:
60*x=120, x=60/120=1/2 so the sequence goes by a ratio of 1/2
a(n)=b(c)^n-1 and c=1/2. b= a(1)=120 so the formula is a(n)= 120(1/2)^(n-1)
Find the value of x.
Answer:
D. 15
Step-by-step explanation:
Both equations need the same end result because this is a square:
3x - 15 = 45 - x =
3x - 3x = 45 - x - 3x
0 = 45 - 4x
4x = 60
4x/4 = 60/4 =
X = 15
Check:
3(15) - 15 = 45 - 15
45 - 15 = 45 - 15
30 = 30
h(x+1)=x^2-4 evaluate function by substuting x+1
Answer:
h(x + 1) = (x+3)(x-1)
Step-by-step explanation:
Simply plug the value of x+1 into the equation for x.
h(x) = x^2 - 4
h(x + 1) = (x + 1)^2 - 4
h(x + 1) = x^2 + 2x + 1 - 4
h(x + 1) = x^2 + 2x - 3
h(x + 1) = (x+3)(x-1)
Cheers.
Answer:
h(t)= t² - 2t -3
Step-by-step explanation:
h(x+1)= x²-4 is the given function
We can write it x²-4 as:
(x+2)(x-2)= (x+1+1)(x+1 - 3)Substituting x+1 with t. Then function is:
h(t)= (t+1)(t-3)= t² - 2t -3or
h(t)= t² - 2t -3Find the lateral area of the following cone.
Leave your answer in terms of pi
Answer:
The lateral surface area of cone is A = π×r×l where r represents radius and l is slant height.
The formula to find slant height is l = √(h²+r²) where h represents height.
The lateral surface area of the cone is 65[tex]\pi[/tex] square cm.
Given,
The height is 12 cm and the radius is 5 cm.
We are to find the lateral surface area of a cone.
What is the lateral surface area of a cone?The lateral surface area of a cone:
A = [tex]\pi[/tex] x r x l
where r = radius and l = slant height.
The slant height:
l = √(h²+r²) where h =height.
We have,
h = 12 cm and r = 5 cm
l =√(h²+r²)
l = √(12^2 + 5^2)
l = √(144 + 25)
l = √169
l = 13 cm
Now,
l = 13 cm and r = 5 cm
A = [tex]\pi[/tex] x r x l
A = [tex]\pi[/tex] x 13 x 5 = 65[tex]\pi[/tex] square cm
Thus lateral surface area of the cone is 65[tex]\pi[/tex] square cm.
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A package of 8-count AA batteries costs $6.32. A package of 20-count AA batteries costs $16.00. Which statement about the unit prices is true?
Answer:
A
Step-by-step explanation:
The first option is correct.
The 8 count pack of AA batteries has a lower unit price of $0.79 per battery.
What is unitary method?The method in which first we find the value of one unit and then the value of the required number of units is known as the Unitary Method.
According to the given question.
Cost of a package with 8 AA batteries = $6.32
⇒ Cost of 1 AA battery of this package = [tex]\frac{6.32}{8}[/tex] = $0.79
And, cost of another package with 20 AA batteries = $16.00
⇒ Cost of 1 AA battery of another package = [tex]\frac{16}{20}[/tex] = $0.8
Hence, the 8 count pack of AA batteries has a lower unit price of $0.79 per battery.
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(PLSS HALP) What is the area of triangle PQR on the grid? (5 square units) (6 square units) (10 square units) (12 square units)
I Will Give Brainliest
Answer:
6
Step-by-step explanation:
it might be six but can you show me what the chart looks like?
Name five fractions whose values are between 1/8 and 1/5
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
The fraction numbers are given below.
1/8 and 1/5
Convert the fraction number into decimal numbers. Then we have
0.125 and 0.20
The five fractions whose values are between 1/8 and 1/5 will be given as,
0.13, 0.14, 0.15, 0.16, 0.18
13/100, 14/100, 15/100, 16/100, 18/100
13/100, 7/50, 3/20, 4/25, 9/50
The five fractions whose values are between 1/8 and 1/5 will be 13/100, 7/50, 3/20, 4/25, and 9/50.
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A shop sells “Gello” pens and “Inko” pens. A “Gello” pen costs £5 and an “Inko” pen costs £7. One day the shop sold 17 pens and recieved £109. How many of each type of pen were solved? Form a pair of simultaneous equations to solve this question.
Answer:
5 Gello Pens and 12 Inko Pens.
12 Inko Pens adds up to 84.
5 Gello Pens adds up to 25.
84 + 25 = 109.
I hoped this helped :)
Describe the transformations that will map triangle A to triangle B and illustrate the similarity between the two triangles.
A) reflect triangle a across the y-axis and then translate triangle a 5 units down. B) reflect triangle A across the x-axis and then reflect triangle a across the y-axis.
C) translate triangle a 4 units down and then rotate triangle A 180° counterclockwise about the origin.
D) reflect triangle a across the x-axis and then rotate triangle A 90° counterclockwise about the origin
The triangle is shifted 4 units downwards and then is rotated about the origin.
What is image rotation?A rotation is a type of transformation which is a turn.A figure can be turned clockwise or counterclockwise on the coordinate plane.In both transformations the size 3 shape of the figure stays exactly the same.Given are triangles A and B.
Transformation 1 : The triangle is shifted 4 units downwards.
Transformation 2 : The figure is rotated about the origin.
Therefore, the triangle is shifted 4 units downwards and then is rotated about the origin.
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i dont get it plz help
Answer:
440 in²
Step-by-step explanation:
Answer:
(D) 440 in²
Step-by-step explanation:
We can find the surface area of this complex shape by breaking it down into two smaller shapes:
The base (with side lengths of 10, 10 and 2) and the top (with side lengths of 5, 5, and 8.)
Let's first find the surface area of the base.
The sides of the bass are [tex]10\cdot2 = 20[/tex] in², since there are 4 of these sides, the total side area here is [tex]20\cdot4 = 80[/tex] in².
The bottom of this prism has side lengths of 10 and 10, so [tex]10\cdot10=100[/tex].
There are two of these sides.
[tex]100\cdot2=200[/tex].
Let's add up the side lengths and the base lengths.
[tex]200+80=280[/tex]
We aren't done yet - if we see, the top part is taking away some of that surface area. To find how much it is taking away, we need to find the area of that side.
Note that the side on the base is the exact same as the top, who's side lengths are 5 and 5. So [tex]5\cdot5=25[/tex] in² are being taken away from the base, making it [tex]280-25 = 255[/tex]
Now let's find the surface area of the top.
The side, with lengths of 5 and 8, have a surface area of [tex]5\cdot8=40[/tex] in². Since there are 4 of these sides:
[tex]40\cdot4=160[/tex] in².
Now, the top of the box has side lengths of 5 and 5, so the surface area of that is [tex]5\cdot5 =25[/tex] in².
We don't want to find the area of the bottom of the top prism because that cuts into the base and technically is empty space = no surface area.
Let's add the top and the sides of the top box: [tex]160+25=185[/tex] in².
Finally, let's add the base and the top box surface areas together:
[tex]185 + 255 = 440[/tex]
So the total surface area of this design is 440 in².
Hope this helped (oh my god this took so long to write)
help me please real quick
Answer:
D) [tex]360 m^{3}[/tex]
Step-by-step explanation:
Let's review the formula for finding the volume of a cube or rectangular prism.
[tex]V = (l)(h)(w)[/tex] - Basically saying "Volume = length × height × width".
In this case, you can consider 9 meters as the length, 5 meters as the height, and 8 meters as the width (but it doesn't really matter which dimensions are which since you are just multiplying them all together).
Now, let's multiply our dimensions together.
[tex]9 * 5 * 8 = 360[/tex]
That's your answer! Make sure to not forget your units (in this case, meters) cubed.
Hope that helps and maybe earns a brainliest!
Have a splendid day! <3
Determine what type of model best fits the given situation: A model rocket fired straight up from the ground, where h is the height of the rocket and t is the time in seconds. A. none of these B. quadratic C. linear D. exponential
The type of model best fits the given situation is a quadratic equation
Quadratic equationQuadratic equations are equation that has a leading degree of 2.
From the given question, the motion of the rocket from the launch point to the landing point will be parabolic in nature and since the graph of a quadratic function is a parabola, hence the type of model best fits the given situation is a quadratic equation
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PLEASE HELP WILL MARK BRAINLY
Answer:
460256
Step-by-step explanation:
35900 books equal to 7.8% of all copies sold
Total number of books:
7.8% = 35900100% = ?35900*100/7.8 ≈ 460256Answer is 460256 in whole numbers
**TIMED** I REALLY NEED HELP
Answer:
24 students
Step-by-step explanation:
(20 + 23 + 25 + 28)/4
= 94/4
= 24
hope it helps!
Machine A can fill 1 box of nails in 6 minutes. Machine B can fill 1 box of nails in 9 minutes. They started to work at the same time and they stopped also at the same time. In all they filled 100 boxes. How many were filled by machine A?
A-
1 box --- 6 minutes
y boxes --- 1 minute
y = 1/6
B-
1 box --- 9 minutes
t boxes --- 1 minute
t = 1/9
So...
r - used time
r(1/9 + 1/6)=100
r=(100.18)/5
r= 360 minutes
1/6 . 360 = 60 boxes
answer: 60 boxes
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.
Machine A's rate of work is 1 box of nails every 6 minutes.
Machine B's rate of work is 1 box of nails every 9 minutes.
Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.
So, the equation representing the total work is:
x (boxes filled by A) + y (boxes filled by B) = 100
Now, let's use their rates of work to form two more equations:
Rate of work of A = 1 box every 6 minutes
Rate of work of B = 1 box every 9 minutes
Since work = rate × time, we can write two equations:
x (boxes filled by A) = (1/6) * t (time in minutes)
y (boxes filled by B) = (1/9) * t (time in minutes)
Since they both worked for the same time, we can set the time for both machines as equal:
t = t
Now, we have a system of equations:
x + y = 100
x/6 = y/9
t = t
Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:
x + (x/6)*3 = 100
x + (x/2) = 100
Multiply both sides by 2 to eliminate the fraction:
2x + x = 200
3x = 200
x = 200/3
Now, let's find the value of y using the second equation:
y = (x/6)*3
y = (200/3)/6 * 3
y = 200/3
So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.
Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.
Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
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Factor this expression.
3x2 - 6x
Answer:
3x(x - 2)
Step-by-step explanation:
Both terms have a GCF (greatest common factor) of 3x so factoring that out, we get 3x(x - 2).
Answer:
3x ( x - 2 )
Step-by-step explanation:
First we hv to find wat is common in both of them.....
As we can see " 3x " is common in both of them
so....
If we take 3x from both the terms.... It will become....
3x square = 3x ( x )
-6x - 3x ( -2 )
Therefore the expression will become....
3 x square - 6x
= 3x ( x - 2 )
Hope this helps...
HAVE A GOOD DAY !!! ( no the biscuit ) (lol)
Pls mark my ans as brainliest If u mark my ans as brainliest u will get 3 extra pointsPlease help me! There is graph an I out them as pictures!
2. Evaluate the polynomial two ways: by substituting in the given
value of x, and by using long division.
Find P(-3)for P(x)= 4x2 +10x - 8.
Answer:
P(-3) = -2
Step-by-step explanation:
Substitution
P(-3) = 4(-3)^2 +10(-3) -8 = 36 -30 -8
P(-3) = -2
__
Long Division
See the working below. The remainder is -2, so ...
P(-3) = -2
What is the volume of the right triangular prism shown?
Answer:
C. 567yd^3
Step-by-step explanation:
To find the volume of the right triangular prism, it is: 1/2a c h.
In this case, 1/2✖️9✖️6✖️21=567yd^3
So this means that option C is the correct answer.
Hope this helps!
Have a nice day:)
Answer:
567 cu. yard
Step-by-step explanation:
will make it simple and short.
Vol = area of a triangle x length
Vol = (1/2 * 6 * 9 ) * 21
Vol = 567 cu. yard
PLZZ HELPP!! Water is poured from a 1.5 L water bottle into an empty glass until both the glass and the bottle are 3/4 full. What is the volume of the glass?
Answer:
0.5 L
Step-by-step explanation:
volume of bottle: 1.5 L
amount of water = 1.5 L
volume of glass: x
3/4 full is the same as 0.75 full
vol of water in bottle + vol of water in glass = total vol of water
0.75(bottle) + 0.75(glass) = 1.5
0.75(1.5) + 0.75x = 1.5
0.75x = 0.375
x = 0.5
A basketball is shot into the air. Its height is represented by the polynomial equation
h(t) = -16+ + 35t + 5, where h is the height of the basketball at t seconds. What's
the height of the basketball at 1.5 seconds?
18.8 feet
21.5 feet
16.7 feet
1
20.2 feet
Answer:
21.5
Step-by-step explanation:
h(t) = -16t^2 + 35t + 5,
Let t = 1.5
h(1.5) = -16 (1.5)^2 + 35(1.5) + 5
=-16 *2.25 +52.5+5
= -36+57.5
= 21.5