Answer:
2m²
Step-by-step explanation:
Apply the prime factorization method: 2³m², 2 · 5m⁴
Find the greatest common divisor: 2m²
Answer: 2m²
If 5x+ 3 = 10x– 17, what is the value of x?
A. 1
B. 2
C. 3
D. 4
E. 5
Answer:
D
Step-by-step explanation:
First, we will move the variable to the left-hand side and change its sign: 5x + 3 - 10x = -17
Next, we need to collect like terms: -5x = -20
Finally, we will divide both sides of the equation by -5 to give us the answer of x = 4.
Mikala initially launches a toy rocket from a height of 3 feet above the ground. After 2 seconds, the rocket reaches its highest point of 11 ft and then returns to
the ground
.
• Create a model that can be used to determine the height of the toy rocket at a given time. Define your variables and show your work or explain how your
equation models the situation.
• Use the model to determine at what time the toy rocket will land on the ground. Show your work or explain your answer.
Enter your answers and explanations in the box.
[tex]y = -2x^2 + 8x + 3[/tex]
Using the model above, it is found that it lands on the ground after 4.35 seconds.The equation of a quadratic function of vertex (h,k) is given by:
[tex]y = a(x - h)^2 + k[/tex]
The vertex is the maximum point, which is (2,11), hence [tex]h = 2, k = 11[/tex]. Then:
[tex]y = a(x - 2)^2 + 11[/tex]
The initial height is of 3 feet, then when [tex]x = 0, y = 3[/tex], and this is used to find a.
[tex]y = a(x - 2)^2 + 11[/tex]
[tex]3 = 4a + 11[/tex]
[tex]4a = -8[/tex]
[tex]a = -\frac{8}{4}[/tex]
[tex]a = -2[/tex]
Then:
[tex]y = -2(x - 2)^2 + 11[/tex]
In standard format, the model is:
[tex]y = -2x^2 + 8x - 8 + 11[/tex]
[tex]y = -2x^2 + 8x + 3[/tex]
It hits the ground when [tex]y = 0[/tex], so:
[tex]-2x^2 + 8x + 3 = 0[/tex]
[tex]2x^2 - 8x - 3 = 0[/tex]
Which has coefficients [tex]a = 2, b = -8, c = -3[/tex]. So
[tex]\Delta = b^2 - 4ac = (-8)^2 - 4(2)(-3) = 88[/tex]
[tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{8 + sqrt{88}}{4} = 4.35[/tex]
[tex]x_1 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{8 - sqrt{88}}{4} = -0.35[/tex]
Time is positive, so it lands on the ground after 4.35 seconds.
A similar problem is given at https://brainly.com/question/17987697
A farmer rotates wheat, corn, and soybean crops on her farm the farmer produces 293 bushels of produce and sells them for a total of $1,557
The average amount earned based on the information given is $5.31 per product.
Number of farm products = 293
Total amount earned = $1557
Therefore, the average amount will be gotten by dividing the total amount by the number of farm products and this will be:
= $1557/293
= $5.31
In conclusion, the average will be $5.31.
Read related link on:
https://brainly.com/question/25276097
THIS ABOUT TO BE OVERDUE PLS HELP ME
Renee bakes cake pops. Each of her cake pops weigh 334
3
3
4
ounces. She needs to ship a dozen cake pops and will need to tell the shipping company the weight of the pops. What weight should she tell the shipping company for a dozen cake pops?
Answer:
Fraction 3 out of 3 /4
Step-by-step explanation:
Simplify 14 to the fifteenth power over 14 to the fifth power.
Answer:
4^10
subtract 15-5 and leave the 14 be
Answer:
14 to the tenth power
Step-by-step explanation:
fifteen - fifth = ten. When you are working on exponential problems like this, remember to add or subtract the powers.
X^5-2x^4-24x^3=0. solve by factoring
Answer:
1. x=6
2. x = -4
3. x³ = 0
Step-by-step explanation:
Step 1: Equation at the end of step 1
((x⁵) - ( 2 · (x⁴)))-(2³· 3x³) = 0
Step 2:
Equation at the end of step 2:
((x⁵)-2x⁴)-(2³ · 3x³) = 0
Step 3: X
Step 4: Pulling out like terms
Pull out like factors :
x⁵ - 2x⁴ -24x³ = x³· (x² - 2x -24)
Trying to factor by splitting the middle term
Factoring x² -2x - 24
The first term is, x² ts coefficient is 1 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is -24
Step-1 : Multiply the coefficient of the first term by the constant 1 • -24 = -24
Step-2 : Find two factors of -24 whose sum equals the coefficient of the middle term, which is -2 .
-24 + 1 = -23
-12 + 2 = -10
-8 + 3 = -5
-6 + 4 = -2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and 4
x2 - 6x + 4x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
4 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x-6)
Which is the desired factorization
Equation at the end of step
4
:
x3 • (x + 4) • (x - 6) = 0
STEP
5
:
Theory - Roots of a product
5.1 A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
Solving a Single Variable Equation:
5.2 Solve : x3 = 0
Solution is x3 = 0
Solving a Single Variable Equation:
5.3 Solve : x+4 = 0
Subtract 4 from both sides of the equation :
x = -4
Solving a Single Variable Equation:
5.4 Solve : x-6 = 0
Add 6 to both sides of the equation :
x = 6
Supplement : Solving Quadratic Equation Directly
Solving x2-2x-24 = 0 directly
Earlier we factored this polynomial by splitting the middle term. let us now solve the equation by Completing The Square and by using the Quadratic Formula
Parabola, Finding the Vertex:
6.1 Find the Vertex of y = x2-2x-24
Parabolas have a highest or a lowest point called the Vertex . Our parabola opens up and accordingly has a lowest point (AKA absolute minimum) . We know this even before plotting "y" because the coefficient of the first term, 1 , is positive (greater than zero).
Each parabola has a vertical line of symmetry that passes through its vertex. Because of this symmetry, the line of symmetry would, for example, pass through the midpoint of the two x -intercepts (roots or solutions) of the parabola. That is, if the parabola has indeed two real solutions.
Parabolas can model many real life situations, such as the height above ground, of an object thrown upward, after some period of time. The vertex of the parabola can provide us with information, such as the maximum height that object, thrown upwards, can reach. For this reason we want to be able to find the coordinates of the vertex.
For any parabola,Ax2+Bx+C,the x -coordinate of the vertex is given by -B/(2A) . In our case the x coordinate is 1.0000
Plugging into the parabola formula 1.0000 for x we can calculate the y -coordinate :
y = 1.0 * 1.00 * 1.00 - 2.0 * 1.00 - 24.0
or y = -25.000
Parabola, Graphing Vertex and X-Intercepts :
Root plot for : y = x2-2x-24
Axis of Symmetry (dashed) {x}={ 1.00}
Vertex at {x,y} = { 1.00,-25.00}
x -Intercepts (Roots) :
Root 1 at {x,y} = {-4.00, 0.00}
Root 2 at {x,y} = { 6.00, 0.00}
Solve Quadratic Equation by Completing The Square
6.2 Solving x2-2x-24 = 0 by Completing The Square .
Add 24 to both side of the equation :
x2-2x = 24
Now the clever bit: Take the coefficient of x , which is 2 , divide by two, giving 1 , and finally square it giving 1
Add 1 to both sides of the equation :
On the right hand side we have :
24 + 1 or, (24/1)+(1/1)
The common denominator of the two fractions is 1 Adding (24/1)+(1/1) gives 25/1
So adding to both sides we finally get :
x2-2x+1 = 25
Adding 1 has completed the left hand side into a perfect square :
x2-2x+1 =
(x-1) • (x-1) =
(x-1)2
Things which are equal to the same thing are also equal to one another. Since
x2-2x+1 = 25 and
x2-2x+1 = (x-1)2
then, according to the law of transitivity,
(x-1)2 = 25
We'll refer to this Equation as Eq. #6.2.1
The Square Root Principle says that When two things are equal, their square roots are equal.
Note that the square root of
(x-1)2 is
(x-1)2/2 =
(x-1)1 =
x-1
Now, applying the Square Root Principle to Eq. #6.2.1 we get:
x-1 = √ 25
Add 1 to both sides to obtain:
x = 1 + √ 25
Three solutions were found :
x = 6
x = -4
x3 = 0
What is the missing angle
55°
Step-by-step explanation:
110+15+x =180
x = 180 - 125
x = 55°
Answer:
Step-by-step explanation:
Factor completely: 8x^2-4x-4
Answer:
4(2x+1)(x−1)
Step-by-step explanation:
8x2−4x−4
8x2−4x−4
=4(2x+1)(x−1)
Match the pairs of equivalent expressions.
i would say y + 2/5y is the equivalent expression of 7/5y and y - 2/5y is the quivalent expression of 3/5y but im not sure
Someone plz help me :(
D.
I am so sorry if it is wrong
NEED SOME HELP HERE answer
Answer:
C, move (translate) 5 units left
Step-by-step explanation:
Sliding or moving is called translating, and MATH is to the right of M'A'T'H' (prime), so translate 5 units left.
Which of the following is a polynomial?
A.
(x - 2)
(x4 +3)
B. X2 - 1
C. A + x 4 + 16
D. 1/x +2
Answer:
A, B, C
Step-by-step explanation:
Assuming the choices are:
A. [tex](x-2)(x^{4}+3)[/tex]
B. [tex]x^{2} -1[/tex]
C. A+[tex]x^{4} +16[/tex]
D. [tex]\frac{1}{x} +2[/tex]
Put simply, a polynomial in this case will be a function that has at least one variable raised to a power greater than 1.
Choice A already has a variable raised to a power greater than 1 ([tex]x^{4}[/tex]), so no additional manipulation is needed.
Choice B also has a term that is already raised to a power greater than 1 ([tex]x^{2}[/tex]). It is the same for choice C ([tex]x^{4}[/tex]).
Choice D does not have an obvious variable raised to a power greater than 1. When the equation is manipulated it becomes [tex]x^{-1} +2[/tex]. Since -1 is less than 1, choice D is not a polynomial.
Answer:
Option D
Step-by-step explanation:
[tex]\\ \sf\longmapsto \dfrac{1}{x}+2[/tex]
Simplify
[tex]\\ \sf\longmapsto x^{-1}+2[/tex]
Degree is less than 1 .It's not a polynomial
127% of 1958?
there's nothing else for the question so I'm just typing out this lol
What is the image of the point (-9,-1) after a rotation of 270 counterclockwise about the origin?
Answer:
uhh I'm pretty sure it's (9,1) went from quadrant 3 to 2 which is all positives
How Do i get the correct answer for this?
Simple way :-
If a function has co-ordinates (x,y) then it's inverse has co-ordinates (y,x)
Now
(0,4)->(4,0)(1,6)->(6,1)(2,8)->(8,2)(3,10)->(10,3)Somebody please help !
Answer:
Translation
Step-by-step explanation:
Answer:
7 for your x axis and -3 for Y
So your are going from G to H, thats important.
You go to the right seven times and down (hence -3) three times
oliver sewed a quilt 3 2/3 feet long and 2 1/4 feet wide. what is the area of her quilt?
Answer:
8.25 feet
Step-by-step explanation:
3 2/3 times 2 1/4 equals 8.25
Evaluate the function when x= -3,0 and 1. Show work H(x) = 2.5x + 7
Answer:
H(-3)= -0.5
H(0)= 7
H(1)= 9.5
Step-by-step explanation:
For H(-3)
Substitute all of the x into -3
H(-3)=2.5(-3)+7
2.5 times -3 is -7.5
-7.5+7 is -0.5
So the answer for H(-3) is -0.3
For H(0)
Substitute all of the x into 0
H(0)=2.5(0)+7
2.5 times 0 is 0
0+7 is 7
So the answer for H(0) is 7
For H(1)
Substitute all of the x into 1
2.5(1)+7
2.5 times 1 is 2.5
2.5+7 is 9.5
So the answer for H(1) is 9.5
Hope this helps!
I need help pleaseeeee
No links
Answer:
320
Step-by-step explanation:
2 times 64 plus 4 times 48 equals 320
Which number has the greater value, 7*10^-9 or 6*10^-4
Answer:
6*10^-4 has a greater value.
Step-by-step explanation:
7*10^-9= 0.000000007
6*10^-4= 0.0006
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 23 feet up. The ladder makes an angle of 75^{\circ}
∘
with the ground. Find the length of the ladder. Round your answer to the nearest hundredth of a foot if necessary.
The length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.
The ladder forms a right triangle as it lies against the wall as shown in the image below.
Thus:
x = length of the ladder (hypothenuse)
Reference angle [tex](\theta) = 75^{\circ}[/tex]
25 ft = Opposite
Apply SOH:
Thus,
[tex]sin(\theta) = \frac{Opposite}{Hypotenuse}[/tex]
Plug in the values[tex]sin(75) = \frac{25}{x}\\\\x = \frac{25}{sin(75)} \\\\\mathbf{x = 25.88}[/tex]
Therefore, the length of the ladder that makes an angle of 75 degrees and lies against the wall of a house that's 23 feet tall is approximately 25.88 feet.
Learn more here:
https://brainly.com/question/23973168
Answer:
x=32.09 feet long
Step-by-step explanation:
Marci and Levi add 113.5 + 22.41
If the whole numbers are added, the sum would be
Answer:
113 + 22 = 135
113.5 + 22.41 = 135.91
The answer would be 135.91
Step-by-step explanation:
Given the linear equation r=-2.5 t and t can only be a negative number, what quandrant will the r coordinate be located?
Answer:
quadrant 4 i think
Step-by-step explanation:
Answer:
Actually the correct answer is 2
Step-by-step explanation:
please help with number 3 & 4 PLEASE !! will mark BRAINLIEST
Answer:
3 is -15/2 and 4 is -3/2
Step-by-step explanation:
If im not mistaken these are the awansers
A bowling ball and a balloon might have the same _____ , but a different _____ .
Mass, volume
Weight, density
Volume, mass
Density, weight
Answer:
Volume, Mass
Step-by-step explanation:
Mass is how much stuff something is made of. Volume is how much space an object takes up. 1.
The PTA makes a $5.00 profit on each school sweatshirt they sell. If they made a
profit of $2,170.00, how many sweatshirts did they sell?
Answer:
434 sweatshirts were sold
Step-by-step explanation:
$2,170/$5 = 434
Can someone help me plz!!
Answer:
RMT or TMR
Step-by-step explanation:
The angle between the sides is just the angle at which they meet. Since MR and TM meet at M, the resulting angle must include M as well as the ends of the angle, T and R.
PLSSS HLEPP ME OUTT ITS URGENTTTT
Answer:
you got the answer right there
Step-by-step explanation:
Answer:
-14/25
Step-by-step explanation:
7x +2 / 2 - 5x = -2 / 5
First you can cross multiply (shown in the picture):
Next, expand the brackets:
5(7x + 2) = -2(2 - 5x) → 35x + 10 = -4 + 10x
Now, simplify:
35x + 10 = -4 + 10x → 35x - 10x = -4 - 10 → 25x = -14 → x = -14/25
Hope this helps!
How to solve this problem?
Answer:
x° = 35°
Step-by-step explanation:
at 125° to get the opposite angle
180° - 125° = 55°
then,
x° + 90° + 55° = 180°
x° = 180° - 145°
x° = 35°