The product of prime factors of 900 in index form is [tex]2^{2} *3^{2} *5^{2}[/tex] and the ascending order of prime factors is 2, 3 and 5.
According to the question,
We have the following number:
900
This number needs to prime factorized. So, first it can be divided by 2 (450), again 450 can be divided by 2 (225), it can be divided by 3 (75), it can again be divided by 3 (25), this can be divided by 5 (5) and it will be finally divided by 5.
So, we have the following product for the prime factors of 900:
2*2*3*3*5*5
In index form, it will be written as follows:
[tex]2^{2} *3^{2} *5^{2}[/tex]
Now, we know that in ascending order, numbers are arranged from smallest to largest.
So, we have the following order:
2, 3 and 5
Hence, the product of prime factors of 900 in index form is [tex]2^{2} *3^{2} *5^{2}[/tex] and the ascending order of prime factors is 2, 3 and 5.
To know more about product of prime factors here
https://brainly.com/question/21173911
#SPJ9
A parabola can be drawn given a focus of (−3,−3) and a directrix of x=5. Write the equation of the parabola in any form.
Equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
As given in the question,
Focus of the parabola is equal to (-3, -3)
Directrix of the parabola is given by x = 5
Let (x, y) be the point on the parabola.
Distance between the (-3,-3) and (x, y) = Distance between (x, y) and x=5
⇒√(x +3)² + (y +3)² = | x -5|
⇒(x² +6x +9) +(y² + 6y +9) = (x-5)²
⇒x² +6x +y² +6y +18 = x² -10x +25
⇒y² +6y -7 = -16x
⇒x = (-1/16) (y² +6y -7) represents the equation of the parabola.
Therefore, equation of the parabola with focus (-3,-3) and a directrix x=5 is given by x = (-1/16)(y² +6y -7).
Learn more about parabola here
brainly.com/question/4074088
#SPJ1
3x+y-4z=-22
2x+3y+4z=32
x-y+2z=16
Answer: x=-1, y=2, z=-3
Step-by-step explanation:
[1] 2x + 3y - 4z = 16
[2] -x + 2y - z = 8
[3] 2x - y - 2z = 2
Solve by Substitution :
Solve equation [3] for the variable y
[3] y = 2x - 2z - 2
Plug this in for variable y in equation [1]
2x + 3•(2x-2z-2) - 4z = 16
8x - 10z = 22
Plug this in for variable y in equation [2]
-x + 2•(2x-2z-2) - z = 8
3x - 5z = 12
Solve equation [2] for the variable x
3x = 5z + 12
x = 5z/3 + 4
Plug this in for variable x in equation [1]
8•(5z/3+4) - 10z = 22
10z/3 = -10
10z = -30
Solve equation for the variable z
10z = - 30
z = - 3
By now we know this much :
x = 5z/3+4
y = 2x-2z-2
z = -3
Use the z value to solve for x
x = (5/3)(-3)+4 = -1
Use the x and z values to solve for y
y = 2(-1)-2(-3)-2 = 2
please solve the problem
The value of x in the remote angles of the triangle is 22.
How to find external angle of a triangle?The exterior angle theorem states that the measure of an exterior angle of a triangle is greater than either of the measures of the remote interior angles.
In other words the sum of the remote interior angle is equals to the external angle.
Therefore,
110 = 3x + 2x
110 = 5x
divide both sides by 5
110 / 5 = 5x / 5
x = 22
Therefore, using exterior angle theorem, the value of x is 22.
learn more on angle here: https://brainly.com/question/25950519
#SPJ1
A new gaming chair costs $239.87. You have already saved $118.37 and earn $40.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
40.5w + 118.37 = 239.87; w = 3
40.5w − 118.37 = 239.87; w = 9
40.5w − 239.87 = 118.37; w = 9
40.5 + 118.37w = 239.87; w = 3
Answer:
40.5w + 118.37= 239.87; w=3
Step-by-step explanation:
You already saved 118.37.
239.87
118.37
111.50
40x3=120. So you'll need 3 more weeks to buy a gaming chair. And you also get 8.50 dollars extra in profit.
Answer:
40.5w + 118.37= 239.87; w=3
Step-by-step explanation:
you have a deck and you take one card at random and guess what the card is. what is the probability you guess right?
There are 52 cards in the deck and so the probability of guessing the card right is 1/52.
What is probability?Probability is simply the likelihood of something occurring. When we are uncertain about the result of an event, we might discuss the probabilities of several outcomes—how likely they are. Statistics is the study of occurrences guided by probability. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula.
Here,
We can find this probability by seeing that
=1/4×1/13
=1/52
Because there are 52 cards in the deck, the probability of correctly predicting the card is 1/52.
To know more about probability,
https://brainly.com/question/11234923
#SPJ4
Select the correct answer. Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18, which equation represents this situation, and how old is Tina? A. The equation that represents this situation is t − 3 = 18. Tina is 21. B. The equation that represents this situation is t + 3 = 18. Tina is 15. C. The equation that represents this situation is 3 − t = 18. Tina is 21. D. The equation that represents this situation is -3 − t = 18. Tina is 15.
The equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Cole’s age is 3 years less than his sister Tina’s age, t. If Cole is 18.
The equation will be written as,
C = T - 3
18 = T-3
T = 18 + 3
T = 21 years
Therefore, the equation that represents this situation is t − 3 = 18. Tina is 21. The correct option is A.
To know more about an expression follow
https://brainly.com/question/11980704
#SPJ1
Terry sees this offer.
Refurbished phone
35% OFF
Now only £78
How much was the phone before the discounted price?
Answer: The phone was £120 before the discount.
First, complete the story below so that it can be represented by the equation 5000-50x=4800-30x
Pool A started with 5000 liters of water, and 50 liters per minute are being (Drained out or Pumped back in)
Pool B started with 4800 liters of water, and 30 liters per minute are being (Drained out or Pumped back in)
The amount of water after x minutes is more in which pool? Pool A or Pool B?
The amount of water after x minutes is equal in both pools.
What is a Linear equation in one variable?
A univariate linear equation is an equation of the form ax + b = 0, where a and b are two integers, x is a variable, and there is only one solution.
For example, 2x+3=8 is a linear equation in one variable.
The given equation is 5000 - 50x = 4800 - 30x.
solving for 'x',
5000 - 50x = 4800 - 30x
5000 - 4800 = 50x - 30x
200 = 20x
x = 200/20
x = 10
The amount of water after 10 minutes in Pool A will be = 5000 - 50(10)
= 5000 - 500
= 450 liters
The amount of water after 10 minutes in Pool B will be = 4800 - 30(10)
= 4800 - 300
= 450 liters.
Hence, the amount of water will be the same in both pools.
To learn more about the linear equations in one variable, visit:
https://brainly.com/question/10839449
#SPJ13
What is the vertex of f(x)= 3x^2+12x-8? A (2, 28) B (-2, -20) C (4,88) D (-4,-8)
Answer:
B (-2,-20)
Step-by-Step Explanation:
f(x)=3x^2 + 12x - 8
a=3 b=12
x=-12/2*3
x=-2
f(x)=3(-2)^2 + 12x - 8 , x=-2
f(-2) = -20
solution (-2,-20)
Shipping Company A charges $14 plus $2.25 a pound to ship overnight
packages. Shipping Company B charges $20 plus $1.50 a pound to ship
an overnight package. For what weight is the charge the same for the two
companies?
For 8 pounds of weight, the charges be the same for both the companies.
Given, that To ship an overnight package
Shipping Company A charges $14 plus $2.25 per pound
Shipping Company B charges $20 plus $1.50 per pound
Let, the weight be w
And the cost of shipment by company A & B be A(w) & B(w) respectively.
According to the question,
A(w) = 14 + 2.25w
B(w) = 20 + 1.50w
Now, when charges be the same
A(w) = B(w)
14 + 2.25w = 20 + 1.50w
On subtracting 1.50w on both the sides, we get
14 + 2.25w - 1.50w = 20 + 1.50w - 1.50w
14 + 0.75w = 20
Now on subtracting 14 on both the sides, we get
14 + 0.75w - 14 = 20 - 14
0.75w = 6
On dividing both the sides by 0.75, we get
0.75w/0.75 = 6/0.75
w = 8
Hence, weight = 8 pounds.
For 8 pounds of weight, the charges be the same for both the companies.
Learn more about Linear Equations in One variable here https://brainly.com/question/85774
#SPJ9
discuss three strengths of the linear regression. identify a peer-reviewed study that uses linear regression in its analysis. explain why linear regression was used and discuss one challenge in interpreting the results. include the permalink with your citation.
Linear Regression analysis has three key applications:
(1) evaluating predictor strength, (2) anticipating an effect, and as well (3) trend forecasting.
Define the term linear regression?Linear regression is a fundamental and widely used method of predictive analysis. The overall goal of regression is to investigate two things:
How well does a set of predictor factors predict an outcome (dependent) variable? Which variables, in particular, are significantly predictive of both the outcome variable, and how do they influence it?Regression analysis has three key applications:
evaluating predictor strength,anticipating an effect, trend forecasting.The formula y = c + b*x defines the simplest form of the regression equation with one dependent so one independent variable,
where,
y = approximately dependent variable score, c = constant, b = regression coefficient, and x = independent variable score.To know more about the linear regression, here
https://brainly.com/question/25987747
#SPJ4
What is the value of the expression a(b/c)+ a=3
B=4 C=2
help pls!!! I WILL BRAINIEST!!!!
The average daily profit of an electronics store is $27,235. The company estimates that 15% is lost each day to returns, with a margin of error of ±3%. What is the maximum the company can expect for returned items?
The maximum the company can expect for returned items is $4190.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Given, The average daily profit of an electronics store is $27,235.
The company estimates that 15% is lost each day to returns.
∴ The amount of return is (15/100)×27135.
= 0.15×27125.
= $4068.
Now this has an error of ± 3%, therefore the maximum the company can expect for returned items is {(100 + 3)/100}×100
= 1.03×4068.
= $4190.
Learn more about percentages here :
https://brainly.com/question/24159063
#SPJ1
A 145-ft tower is located on the side of a mountain that is inclined 32° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed. (Round your answer to the nearest foot.)
By apply the law of cosine, the shortest length of wire needed is 180 feet.
How to determine the shortest length of wire needed?In order to determine the shortest length of wire needed, we would apply the law of cosine because a mental image of the scenario described produces a right-angled triangle.
In Trigonometry, law of cosine (cos) is given by this mathematical expression:
C² = A² + D² - 2(A)(D)cosD
Note: Angle D = 90° + 32° = 122°
Substituting the given parameters into the formula, we have;
C² = 55² + 145² - 2(55)(145)cos122°
C² = 3,025 + 21,025 - 2(7,975)(-0.5299)
C² = 24,050 - (-8,451.905)
C² = 24,050 + 8,451.905
C² = 32,501.905
C = √32,501.905
C = 180.28 ≈ 180 feet.
Read more on law of cosine here: https://brainly.com/question/13756263
#SPJ1
1. Find the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10).
Hint: Use quadratic regression to find the standard form.
The standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
Define Parabola
A symmetrical open plane curve created when a cone and a plane that runs perpendicular to its side collide. Ideally, a projectile travelling under the pull of gravity will travel along a curve similar to this one.For parabolas that open either up or down, the standard form equation is y = ax² + bx + cThe equation of parabola in standard form is y = ax² + bx + c
We have given the points,
(1, 0), (2, -3), and (3,-10)
Let's put each point in parabola equation and form three equation as,
Equation for point (1, 0)
0 = a * (1)² + b * 1 + c
a + b + c = 0 --------------------eq(i)
Now, equation for point(2, -3)
-3 = a * (2)² + b * 2 + c
4a + 2b + c = -3 --------------------eq(ii)
And, equation for point (3, -10)
-10 = a * (3)² + b * 3 + c
9a + 3b + c = -10 ---------------------eq(iii)
Now, we have three equation let's put them together
a + b + c = 0 --------------------eq(i)
4a + 2b + c = -3 --------------------eq(ii)
9a + 3b + c = -10 ---------------------eq(iii)
Now, form equation which is of two variable.
For that, we take first two equation and subtract eq(ii) from eq(i)
4a+2b+c = -3
a + b + c = 0
- - - -
------------------------
3a + b = -3 ---------------eq(a)
Now, subtract eq(iii) from eq(ii)
9a + 3b + c = -10
4a + 2b + c = -3
- - - -
------------------------
5a + b = -7 ------------------eq(b)
Now, we get eq(a) and eq(b) consist of two variable.
3a + b = -3 ---------------eq(a)
5a + b = -7 ----------------eq(b)
Now, solve this equation simultaneously and find the value of a and b.
3a + b = -3
5a + b = -7
- - -
----------------
-2a = 4
a = -2
put a = -2 in eq(a) to find b
3a + b = -3
⇒3 * -2 + b = -3
⇒-6 + b = -3
⇒b = 3
We get the values of a and b. And, left with value of c for that just put the a and b value in eq(i) and find c
a + b + c = 0
-2 + 3 + c = 0
c = -1
Now, we get all the necessary values for equation.
Next, just put a, b and c values in parabola equation.
y = ax² + bx + c
y = -2x² + 3x - 1
Hence, the standard form of a parabola passing through (1, 0), (2, -3), and (3,-10) is y = -2x² + 3x - 1
To read more about Parabola
https://brainly.com/question/28094027
#SPJ1
help is needed please and thank you
The required value of g(-4) = 1 in the given function is represented in the shown graph.
What is a graph?A graph can be defined as a visual representation or a diagram that represents data or values.
The function is given in the represented graph of g(x)
We have to determine the value of g(-4) of the given function in the graph
According to the given graph, we can see that the value of the domain of the given function g(x) when the value of variable x is -4 when the value of the variable y is 1. this means the value of g(-4) = 1.
Therefore, the required value of g(-4) = 1 in the given function is represented in the shown graph.
Learn more about the graphs here:
brainly.com/question/16608196
#SPJ1
Find the solution(s) of the system of equations:
y = x2 + 6x + 9
y = 2x + 6
Answer:
(-1,4) (-3,0)
picture below (im assuming you meant x^2.)
if you meant x2, please look at the second image
FIRST PHOTO = y=x^2 + 6x + 9 & y=2x+6
SECOND PHOTO = y=x2 + 6x + 9 & y=2x+6
Estimate √700 to one decimal place.
Answer:26.5
Step-by-step explanation:
105 grams as percentage of 2kg
Pls help and answer all questions I will give brainly for whoever answers are correct!.
Answer:
x=-5/2
Step-by-step explanation:
x=-5/2
Answer:
12x+4=20x+24
Add negative 4 to both sides
6x+9=4x-3
Add -9 to both sides
-5x/4=4 Multiply both sides by 04
-4(5x-7)=-18 Distribute -4 on the left side
Step-by-step explanation:
12x+4=20x+24
Add negative 4 to both sides
6x+9=4x-3
Add -9 to both sides
-5x/4=4 Multiply both sides by 04
-4(5x-7)=-18 Distribute -4 on the left side
can somone help will mark u brainliest
22. A train travels 3 hours at 20km per
hour. How long will it take another
train to travel the same distance at
10km per hour?
(a) 6²/³ hours
(b) 6¹/2hours
(c) 6 hours
(d) 3 hours
(e) 2 hours
What I
The train takes 6 hours to travel the same distance.
From the question, we have
A train with 20km per hour takes 3 hours to travel the distance .
Another train with 10km per hour takes = (3*20)/10 hours
=6 hours
Multiplication:
Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.
To learn more about multiplication visit: https://brainly.com/question/5992872
#SPJ9
HLP ME PLSSSS ITS DUE IN 5 MNS
Answer:
It's either 1:3 or 1:3
Step-by-step explanation:
A scale factor is times, calculate and, a reinduced PEMDAS
Is this correct just need to make sure
Yes, it is correct. (a) congruent by SSS
(b) congruent by SAS
(c) congruent by ASA
(a) Given in figure,
MN = OP
∠MNO = ∠NOP
ON = ON (Common)
Hence, ΔMNO ≅ ΔNOP by SAS.
(b) Given in figure,
UV = XY
∠UVW = ∠XYZ
UW = XZ
Hence, ΔUVW ≅ ΔXYZ by SAS.
(C) Given in figure,
∠ABC = ∠EDF
BC = DE
∠ACB = ∠DEF
Hence, ΔABC ≅ ΔDEF by ASA.
Therefore, all are congruent.
To learn more about congruent here:
https://brainly.com/question/12413243
#SPJ1
these researchers said the differences were statistically significant. explain what that means in context.
A statistically significant finding indicates that it is unlikely to just be explained purely by chance or random influences.
Define the term statistically significant?The notion that a set given observed data is not the result of random but can instead be linked to a specific cause is referred to as statistical significance.
A high level of statistical significance signifies that the observed link is unlikely to be coincidental.The calculation for statistical significance is prone to some inaccuracy.When researchers do not utilize precise wording when describing their findings, statistical significance could be misconstrued.Depending on the research, many sorts of significance tests are being used.Statistical significance indicates that a result is unlikely to be attributed purely by chance and random causes.
Thus, in other words, if there is no genuine effect in a research study, a statistically significant conclusion has an extremely low likelihood of occuring.
To know more about the statistically significant, here
https://brainly.com/question/15848236
#SPJ4
Which point is collinear with points A and B?
As stated in the preceding statement the point R is collinear with points A and B.
What is a collinear?An axis is a term used to describe a line upon whatever points are located, particularly if that line is connected to a triangle or other geometric shape. Since two factors determine a line, two points become trivially collinear.
How are collinear points discovered?Two lines may coincide if they have a same point and have the same slope. To put it another way, if A, B, as well as C are three points there in XY plane, they will all lie on a line, or three points will be collinear, but only if AB's slope and BC's slope are both equal.
then
m A B = m BC ( = m AC ).
The point is collinear with points A and B.
Therefore, the correct answer is option (d) R.
To know more about collinear points visit:
https://brainly.com/question/1593959
#SPJ1
cual es el interes que genera $600, colocados al 8% anual durante 1 año 4 meses?
The simple interest on the loan of $600 at rate of 8% over a time period of 16 months is $664 and the interest generated is $64
Simple InterestThe formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.
Simple interest formula is given as:
S.I = P(1 + rt)
S.I = Simple InterestP = principalr = rate t = timeSubstituting the values into the formula
S.I = 600(1 + 0.08 * 16)
S.I = 664
The interest generated is $64
Learn more on simple interest here;
https://brainly.com/question/3575751
#SPJ1
Translation: What is the interest generated by $600, placed at 8% per year for 1 year 4 months?
Find all possible values of x for which these two triangles are simliar.
Please help quickly!!!
The possible value of x which the two triangles are similar is x=60°.
What do you mean by triangle?
A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.
Method:
Given that two angles of the triangle are specified, the triangles can be
similar for only one value of x.
According to the given data in the question,
The two triangles are similar when we have;
x + 10° = 2x - 50°
Which gives;
2x - x = 50° + 10° = 60°
x = 60°
Checking gives;
x + 10° = 2·x - 50° = 70°
Two angles of the first triangle are 70° and 60°
Then, the third angle of the first triangle is (180° - (70° + 60°)) = 50°
The three angles of the first triangle are therefore; 70°, 60° and 50°.
Two angles of the second triangle are 70° and 70°.
The third angle of the second triangle is (180° - (70° + 70°)) = 40°
The three angles of the second triangle are therefore; 70°, 70° and 40°
Therefore, the two triangles are similar by AAA similarity.
The two triangles are similar when, x = 60°
When x = 50°, we have;
x + 10° gives;
50° + 10° = 60°
∴ ∠(x + 10°) = 60°
The two angles of the first triangle are; 60° and 50°
The third angle on the second triangle is 180° - (60° + 50°) = 70°
On the second triangle, we have;
2·x - 50° gives;
2 × 50° - 50° = 50°
∴∠(2·x - 50°) = 50°
Therefore, the two angles of the second triangle are 70° and 50°
The third angle on the second triangle is 180° - (70° + 50°) = 60°
Therefore, the two triangles are not similar when x = 50°
Similarly, the two triangles are not similar when x + 10° = 50°
Hence, the possible value of x which the two triangles are similar is x = 60°.
To learn more about triangle visit to the given link:
https://brainly.com/question/2773823?referrer=searchResults
#SPJ1
Can someone at least explain this to me I’m very confused.
For given line segments RS = TR
In this question, we have been given two line segments QS and TU intersected at point R.
Also, we have been given QS = TU, QR = RU
We need to prove, RS = TR
We can observe that,
QS = QR + RS
and UT = UR + RT
QS = TU ................(Given)
QR + RS = UR + RT
QR + RS = QR + RT .............(Given QR = RU )
QR + RS - QR = QR + RT - QR .............(subtraction property of equality)
RS = TR
Hence proved.
Therefore, for given line segments RS = TR
Learn more about line segments here:
https://brainly.com/question/18019618
#SPJ1
(xy)7 (exponent 7)
—————————
(x²y³)²
please solve quickly!!
i have 2 answers i think it is ,, is it x3y or x6y6?
Answer: (X^3)*y
:) Hope this helps, I spent a lot of time on it!
