The solutions of the given equations are given by equating the
variables to gives;
First part; 4.00 secondsSecond part; (0, -6) and (1, -5)Third part; (4, 11) and (0, 7)Fourth part: y = x² + 3·x + 2; x + y = 2How can the (common) solution be found?First part;
The given functions are;
y = -3·x² + 24·x + 3, and y = -4·x² + 25·x + 15
When the balloons collided, we have;
The height are equal, which gives;
y = y
-3·x² + 24·x + 3 = -4·x² + 25·x + 15
-3·x² + 24·x + 3 - (-4·x² + 25·x + 15) = x² - x - 12 = 0
Which gives;
x² - x - 12 = (x - 4) × (x + 3) = 0
x = 4, and x = -3
The time at which the balloon collide at the highest point is therefore;
At the time, x = 4.00 secondsSecond part;
The given system of equations are;
x - y = 6
y = x² - 6
y = x - 6
Which gives;
x - 6 = x² - 6
x = x²
Which gives;
x = 0 or x = 1
Similarly, we have;
x = y + 6
Which gives;
y = (y + 6)² - 6
y² + 11·y + 30 = 0
(y + 5)·(y + 6) = 0
Which gives;
y = -5, or y = -6
When y = -5, we have; x = -5 + 6 = 1
The solution are therefore;
(0, -6) and (1, -5)Third part;
The equations are; y = x + 7 and y = x² - 3·x + 7
At the solution, the u-values are equal, which gives;
y = y
x + 7 = x² - 3·x + 7
x² - 3·x + 7 - (x + 7) = 0
x² - 4·x = 0
x·(x - 4) = 0
x = 4, or x = 0
When x = 4, y = 4 + 7 = 11
When x = 0, y = 0 + 7 = 7
The solutions are located at points;
(4, 11) and (0, 7)Fourth part;
Given that the point of intersection of the line and the quadratic function
is the point (2, 0), we have;
On the linear function, when y = 0, x = 2
The possible linear function functions is therefore;
x + y = 2
From the quadratic function that accompanies the above linear function, we have;
y = x² + 3·x + 2
When x = 0, y = 0² + 3×0 + 2 = 2
Therefore;
The correct option is; y = x² + 3·x + 2, and x + y = 2Learn more about the solutions of equations here:
https://brainly.com/question/24400554
what shape are these
Answer:
Those are quadrilaterals
Answer: Square Rhombus
Step-by-step explanation:
expand and simplify x(x-4)(x-1)
Answer:
x^3 - 5x^2 +4x
Step-by-step explanation:
x(x-4)(x-1)
(x^2-4x)(x-1)
x^3-x^2-4x^2+4x
simplify
x^3-5x^2+4x
Answer:
Expand:
This is in its expanded form.
Simplify:
First do the x and the (x-4)
distribute the x
(x^2-4x)
Then FOIL or draw you grid and multiply out.
x^2 times x = x^3
x^2 times -1 = -x^2
-4x times x = -4x^2
-4x times -1 = 4x
Combine like terms.
x^3 + (-4x^2 -x^2) + 4x
Answer : x^3 - 5x^2 + 4x
In the data set (0,-1);(-2,4);(-4,-8);(-1,5);(2,1);(3,-2);(-1,2)},which point is a possible outlier?
If the rise is 6 and the run is 2, what is the slope?
4
3
8
-3
Answer:
3
Step-by-step explanation:
[tex]\frac{rise}{run} =\frac{6}{2}=3[/tex]
Hope this helps!
The slope is [tex]\frac{rise}{run} =\frac{6}{2} =3[/tex]
Thus the slope is 3.
Write the phrase as an expression. Then evaluate the expression when x=2 . 8 more than a number x An expression is . The value of the expression is .
answer this please
prove triangle are congruent if the two column proof
Answer:
Step-by-step explanation:
Order from greatest to least -8 -4.75 -0.9 -.25
Answer:
-.25,-0.9,-4.75,-8
Step-by-step explanation:
sorry if im wrong
Answer:
1. -0.25
2. -0.9
3. -4.75
4. -8
Step-by-step explanation:
I need helpppppppppppppppp
Answer:
b 60 -4x 50 +2x=2,800 is 50 +. 2x
Providing Brainliest when I can <3
Answer:
2) Difference of two squares
3) Perfect square trinomial
Step-by-step explanation:
Hope it helps you in your learning process.
A cylinder has a height of 11 meters and a volume of approximately 1243 cubic feet. What is the height of a cone with the same volume and radius as the cylinder?
Answer:
Step-by-step explanation:
Comment
There is a short cut to this and we might just as well use it. Start by writing the general formulas for the volume of a cylinder and the volume of the cone
Equation
V_cylinder = pi * r^2 * h
V_Cone = (1/3) pi * r^2 * h1
Solution
The volumes are equal, so the right sides must be equal as well
pi * r^2 * h = (1/3)*pi * r^2 * h1 Divide both sides by pi
r^2 * h = (1/3) * r^2 * h1 Divide both sides by r^2
h = (1/3) * h1 Multiply both sides by 3
3*h = h1 h = 11 (given)
3*11 = h1
33 = h1
Answer: the cone's height = 33 meters.
104 term in sequence -4,-1,2,5
ARITHMETIC SEQUENCE
an = a1 + (n-1)d
.
The formula above is used to get the nth term of an arithmetic sequence, but we can also use it to know the number of terms (n).
.
Given:
a1 = 4
d = a2 - a1 = 1 - 4 = -3
an = -29
n = ?
.
Solution:
an = a1 + (n-1)d
-29 = 4 + (n-1)-3
-29 = 4 + (-3n + 3)
-29 = -3n + 7
-29 - 7 = -3n
-36 = -3n
-36/-3 = -3n/-3
12 = n
.
Therefore, -29 is the 12th term of the arithmetic sequence 4, 1, -2, -5, ...
104(th) term in sequence -4, -1, 2, 5 would be 305.
What is function?A function is a relation between a dependent and independent variable.
Mathematically, we can write → y = f(x) = ax + b.
Given is to find 104(th) term in sequence -4, -1, 2, 5.
The sequence given is a arithmetic progression. We can write the function for nth term as -
a{n} = a + (n - 1)d
a{104) = - 4 + 103 x 3
a{104} = - 4 + 309
a{104} = 305
Therefore, 104(th) term in sequence -4, -1, 2, 5 would be 305.
To solve more questions on arithmetic progression, visit the link-
brainly.com/question/29014197
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A store has 32 boxes of candles. Each box contains 24 candles. What is the total number of candles?
Answer:
The total amount of candles is 768.
Step-by-step explanation:
Why? If there are 32 boxes of candles and 24 candles are in each box you would have to multiply 32x24 which is = to 768 candles in each box.
2x+5y=0
3x-4y=23
solve the following simultaneous equation
Answer:
[tex]x = 5[/tex], [tex]y = -2[/tex]
Step-by-step explanation:
[tex]2x + 5y = 0[/tex]
[tex]3x - 4y = 23[/tex]
By using substitution:
[tex]2x + 5y = 0[/tex]
[tex]2x = -5y[/tex]
[tex]x = -\frac{5}{2}y[/tex]
[tex]3x - 4y = 23[/tex]
[tex]3 (-\frac{5}{2} y) - 4y = 23[/tex]
[tex]-\frac{23}{2} y = 23[/tex]
[tex]y = -2[/tex]
[tex]x = -\frac{5}{2} y[/tex]
[tex]x = -\frac{5}{2} (-2)[/tex]
[tex]x = 5[/tex]
(3 4.1. A book is bought for R 50 and sold for R80.What is the percentage profit? unntmont?
Answer:60%
R80-R50=R30
R30/R50*100%=60%
Step-by-step explanation:
If continuous random variable X is normally distributed, with µ = 8.7 and σ = 3.9, what is P(X > 14)?
12.30%
87.70%
91.31%
8.69%
Answer:
I believe it is number 3.
Solve 3x - 6 > 8 using inverse operations
Answer:
x > 14/3
Step-by-step explanation:
3x > 8 + 6
3x > 14
x > 14/3
Answer:
x > 14/3
Step-by-step explanation:
[tex]3x-6 > 8\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:x > \frac{14}{3}\:\\ \:\mathrm{Decimal:}&\:x > 4.66666\dots \\ \:\mathrm{Interval\:Notation:}&\:\left(\frac{14}{3},\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Add\:}6\mathrm{\:to\:both\:sides}[/tex]
[tex]3x-6+6 > 8+6[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]3x > 14[/tex]
[tex]\mathrm{Divide\:both\:sides\:by\:}3[/tex]
[tex]\frac{3x}{3} > \frac{14}{3}[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]x > \frac{14}{3}[/tex]
[RevyBreeze]
Please help me ASAP!!!!!!
Answer:
The last one
Step-by-step explanation:
A positive multipled by a negative equals to negative
If a 16-ounce can of soda has 45 calories per 8 ounces, how many calories are in the can?
Answer: 90
Step-by-step explanation:
if its 45 for 8 ounces 8+8=16 so just do 8 times 2 to get 16 ounces and do 45 times 2 to get 90.
Find the measures of the numbered angles in rhombus ABCD .
look for all four measures numbered in the photo
Answer:
<1=54, <2=36, <3=90, <4=36
Step-by-step explanation:
in the rhombus shown, there are 4 congruent right triangles because the disgonals of a rhombus are perpendicular and the sides of a rhombus are congruent. We already know that the larger acute angles are all 54 degrees and we can use triangle sum to find that the smaller acute angles are all 36 degrees. Obviously the right angles are 90 degrees, so we can look at the picture and find the marked angles.
What is 10,274 - 100,000
Answer:
_89,726
Step-by-step explanation:
This would be a negative answer in less you mean 100,000 - 10,274.
This would be negative because 10,000 per say can't subtract 100,000 in less it goes on the negative side.
But if you meant 100,0000-10,274 it is the same answer just with no nefative sign
Hope this heos have a great day
The percentage of sales tax is 6%. What is the sales tax on a skateboard that costs $98?
Answer:
$5.88
Step-by-step explanation:
Step 1: Multiply 6 by 98.
6 × 98588Step 2: Divide 588 by 100.
588 ÷ 1005.88Therefore, the sales tax price is $5.88.
Answer:
I believe it would be $5.88
Find 20% of 75:please help
Answer:
hi its 15
Step-by-step explanation:
20% as a decimal is 0.20
0.20 x 75 is 15
give brainliest? (click the crown at the top)
In the figure, j∥k and m∠1 = 63°.
What is the m∠4?
Enter your answer in the box.
°
Line t diagonally crossing parallel lines j and k (reading from top to bottom). Angles formed by t crossing j are labeled one through four, starting at top right and going counterclockwise, where angle one is acute. Angles formed by t crossing k are labeled five through eight, starting at top right and going counterclockwise.
Answer: 117
Step-by-step explanation:
Answer: 117
Step-by-step explanation: K12 Quiz, The answer above is correct.
Which expressions are equivalent
express the product of 2x^2+7x-10 and x+5 in standard form
Answer:
2x³+17x²+25x-50
Step-by-step explanation:
Standard Form: All your numbers and variables in order of the highest exponent.
(2x²+7x-10)(x+5)
We want to distribute x and 5 to every single value.
2x³+7x²-10x+10x²+35x-50
Simplify.
2x³+17x²+25x-50
This is standard form because the highest values are on the left (x³ is larger than x²).
Find the length of AB
Answer:
D
Step-by-step explanation:
calculate AB using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A (4, 2 ) and (x₂, y₂ ) = B (9, 10 )
AB = [tex]\sqrt{(9-4)^2+(10-2)^2}[/tex]
= [tex]\sqrt{5^2+8^2}[/tex]
= [tex]\sqrt{25+64}[/tex]
= [tex]\sqrt{89}[/tex]
≈ 9.4 units ( to 1 dec. place )
Answer:
[tex]D:\:about\:9.4\:units[/tex]
Step-by-step explanation:
[tex]d=\sqrt{(x_{2}-x_{1})^2 +(y_{2}-y_{1})^2 }[/tex]
[tex]AB =[/tex] [tex]\sqrt{(9-4)^2+(10-2)^2}[/tex]
[tex]=\sqrt{5^2+8^2}[/tex]
[tex]=\sqrt{25+64}[/tex]
[tex]=\sqrt{89}[/tex]
[tex]9.4\:\:units\:[/tex]
Find the length of the second leg of the triangle round to the nearest hundredth
Answer:
[tex]\displaystyle \frac{3\sqrt{230}}{5}[/tex]
Step-by-step explanation:
Use the Pythagorean Theorem:
[tex]\displaystyle a^2 + b^2 = c^2 \\ \\ 9,7^2 + b^2 = 13,3^2; \sqrt{82,8} = \sqrt{b^2} \\ \\ \frac{3\sqrt{230}}{5}\:[or\:9,0994505329...] = b[/tex]
So, you have this:
[tex]\displaystyle 9,1 ≈ b[/tex]
I am joyous to assist you at any time.
50 pointsss tysm nnnnnn
Answer:
1 batch of sky blue paint:
blue paint = 2 cupswhite paint = 1 gallonClare can make 2 batches of sky blue paint by multiplying the components by 2:
2 batches of sky blue paint:
blue paint = 2 × 2 = 4 cupswhite paint = 1 × 2 = 2 gallonsSo she will need 4 cups of blue paint and 2 gallons of white paint to make 2 batches of sky blue paint.
To make a mixture that is a darker shade of blue, increase the proportion of blue paint and reduce the proportion of white paint.
To make a mixture that is a lighter shade of blue, increase the proportion of white paint and reduce the proportion of blue paint.
Which expression is equivalent to 5x+10y-15?
5(x-2y-3)
5(x+5y-10)
5(x+2y-3)
5(x+2y-15)
Answer:Third optionoption
Step-by-step explanation:
Please help me plsssss