Write the prime factorization of the number.
1: 42
2: 50
3: 66
Answers
50: 2 x 5 x 5 or 2 x 5^2
66: 2 x 3 x 11
Related Questions
you have a set of points with a y:x constant ratio of 3:7. what is the equation of the line passing through these points?
Answers
The equation of the line passing through these points i.e (7,3 ) and (14,6) is
y = (3/7) x or 3x - 7y = 0 ,
Which is linear equation of two variables.
A linear equation is an algebraic equation of the form y = mx + b , with only one constant and one first-order (linear) term, m is the slope and b is the y-intercept.
We have given that,
the ratio of y and x is y : x = 3 : 7
So the ratio of x and y can be expressed as ,
x : y = 7 : 3 ( reverse order)
So let's consider two points as
(x₁, y₁)=(7 , 3) and (x₂, y₂) = (14 , 6)
The equation of the line passing through these points will be,
( y - y₁ )/ (y₂ - y₁) = (x - x₁)/(x₂ - x₁)
=> (y - 3)/(6-3) = (x - 7)/(14 - 7)
=> (y - 3)/3 = (x - 7)/7
=> 7(y - 3) = 3( x - 7)
=> 7y - 21 = 3x - 21
=> 7y = 3x
=> y = (3/7) x
Hence, y = (3/7) x is required equation of line.
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1) Fill in the blank with True or False.
Answers
Answer:w
Step-by-step explanation:
Create a system of linear and exponential functions that pass through the point 1,12
Answers
The system of linear and exponential functions passing through (1,12) is given as follows:
Linear: y = 2x + 10.Exponential: y = 6(2)^x.What is the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
For the function to pass through point (1,12), we have that when x = 1, y = 12, hence one example of a linear function is given as follows:
y = 2x + 10.
What is the exponential function?An exponential function is defined as follows:
y = a(b)^x.
When x = 1, y = 12, hence one example is given as follows:
y = 6(2)^x.
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Can somebody help me solve this problem .
Answers
Answer:
b = 40
Step-by-step explanation:
You want your discriminant to be zero because then you have exactly one solution.
Solve b²-4ac = 0
=>
b² - 4·400 = 0
b = ±√1600
so b=±40
but f(-20) also has to be 0
so b=40 remains as the solution
Answer:
b = 40
Step-by-step explanation:
If x = - 20 is a zero of f(x) then f(- 20) = 0 , that is
(- 20)² - 20b + 400 = 0
400 - 20b + 400 = 0
800 - 20b = 0 ( subtract 800 from both sides )
- 20b = - 800 ( divide both sides by - 20 )
b = 40
what is the mx of a slope of -1 and a y-intercept of 4
Answers
y=-1x+4
---
hope it helps
sorry I had no idea how to explain
Choose the number sentence whose product is 5.85. A. 1.7 x 3.5 B. 26 x 2.25 C. 4.5 x 2.3 D. 1.3 x 4.5
Answers
Answer:
b
Step-by-step explanation:
Answer:
The actual right answer is D
Step-by-step explanation:
1.3 x 4.5 = 5.85
answer = D
find the length of the curve. r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4
Answers
To find the length of the curve given by r(t) = cos(7t) i + sin(7t) j + 7 ln(cos(t)) k, 0 ≤ t ≤ π/4, we need to use the formula for arc length:
L = ∫[a,b] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
In this case, we have:
dx/dt = -7 sin(7t)
dy/dt = 7 cos(7t)
dz/dt = -7 sin(t) / cos(t)
So,
[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 sin^2(7t) + 49 cos^2(7t) + 49 sin^2(t) / cos^2(t)
= 49 [sin^2(7t) + cos^2(7t) + sin^2(t) / cos^2(t)]
= 49 [1 + sin^2(t) / cos^2(t)]
Now, using the identity sin^2(t) + cos^2(t) = 1, we can rewrite this as:
[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 = 49 cos^2(t)
Therefore, the length of the curve is:
L = ∫[0,π/4] √[dx/dt]^2 + [dy/dt]^2 + [dz/dt]^2 dt
= ∫[0,π/4] 7 cos(t) dt
= 7 [sin(t)]|[0,π/4]
= 7 sin(π/4) - 7 sin(0)
= 7 (√2/2)
= 7√2/2
So the length of the curve is 7√2/2.
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A bakery is filling an order for 180 cupcakes. Jeff has baked and
decorated 75% of the cupcakes. How many cupcakes has been baked
and decorated?
Answers
Answer:
135 cupcakes
Step-by-step explanation:
What is the cross product of 1/4 = 5/20?
Answers
THhe cross product is found by multiplying the numerator (top number) of one fraction by the denominator (bottom number) of the other fraction.
1/4 = 5/20
1 x 20 = 20
4 x 5 = 20
The cross product is 20
Answer:
20
Step-by-step explanation:
1 x 20 = 20
4 x 5 = 20
Hope that helps!
how to find the x component of this vector
12.1 meters 48.4 degrees
Answers
The magnitude of the x-component of this vector is 9.05m.
The angle of inclination of the vector is calculated as;
θ = 90 ⁰ - 48.4 ⁰
θ = 41.6 ⁰
The magnitude of the x-component of the vector is calculated as;
Vx = 12.1 m x cos ( 41.6 )
Vx = 9.05 m
A vector can be represented by an ordered set of numbers, called components, that indicate the magnitude and direction of the vector in a particular coordinate system. The components of a vector can be added or subtracted using vector addition and subtraction, and multiplied by a scalar (a real number) using scalar multiplication.
Vectors can be visualized as arrows in a two- or three-dimensional space, where the length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector. Vectors can also be represented as matrices, which can be used to perform various operations on vectors, such as dot product and cross product.
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Complete Question:-
What are the ordered pairs of thesolutions for this system of equations? f(x) = x^2 – 2x + 3; f(x) = -6x
Answers
First you subtract the two equations
x^2-2x+3-6x
You simplify that and get
x^2+4x+3 = 0
Now we solve using the quadratic formula.
We get x = -1 and x = -3.
Now we find the y values by plugging the x values into the equation.
f(x) is the same as y.
y = (-1)^2 - 2(-1) + 3
y = 1+2+3
y = 6
Now for the other x value.
y = (-3)^2 - 2(-3) + 3
y = 9+9
y = 18
So the two ordered pairs are (-1,6) and (-3,18)
solve for slop / y- intercept and the equation
Answers
Answer:
Slope: 1/2
Y-intercept: -1
Equation: y = 1/2x - 1
slope: 1/2
equation: y = 1/2x -1
Explanation: y=mx+b
b is -1 and mx is 1/2 hope this helps!
Given 4 and one tenth times negative 4 times 5 over 12, determine the product. negative 16 and 5 over 120 16 and 5 over 60 negative 6 and five sixths 6 and five sixths
Answers
The value of the expression \(4\frac{1}{10}\times-4\times\frac{5}{12}\) is \(-6\frac{5}{6}\).
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
The given, expression is \(4\frac{1}{10}\times-4\times\frac{5}{12}\).
= (41/10) × (- 4) × (5/12).
= (41×-4×5)/(10×12).
= (-820/120).
= - 82/12.
= - 41/6.
= \(-6\frac{5}{6}\).
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numa prova de múltipla escolha com 30 questões, o aluno ganha 3 pontos por cada questão que acerta, mas perde 2 pontos por cada questão que erra. Marcelo resolveu todas as questões dessa prova e conseguiu 50 pontos. Quantas questões ele acertou?
Answers
Answer:
Marcelo acertou 22 questões.
Step-by-step explanation:
Vamos representar
Questões que acerta = a
Questões que erra = b
a + b = 30 .......... Equação 1
a = 30 - b
o aluno ganha 3 pontos por cada questão que realizar, mas perde 2 pontos por cada questão que ocorrerá.
Matematicamente:
3 × a - 2 × b = 50
3a - 2b = 50 pontos ............. Equação 2
Substitua 30 - b por a na Equação 2
3 (30 - b) - 2b = 50
90 - 3b - 2b = 50
90 - 5b = 50
Colete termos semelhantes
90 - 50 = 5b
5b = 40
b = 40/5
b = 8
Questões que erra = b
Marcelo, portanto, perdeu 8 questões.
Dizem-nos que ele respondeu todas as 30 questões. Portanto, se ele perdeu 8 questões, o número de questões acertadas é representado pela Equação 1
a + b = 30 .......... Equação 1
a + 8 = 30
a = 30 - 8
a = 22 questões.
Portanto, ele acertou 22 questões.
2⎜x - 7/2⎟ + 3 > 4
Pls
Answers
Answer: x<3 or x>4
Step-by-step explanation: 2|x-7/2|+3+-3>4+-3 2|x-7/2|/2>1/2 x+|−7/2|+7/2>1/2+7/2 x>4 or x+|−7/2|+7/2<−1/2+7/2 x<3
Consider the system of linear equations: x1 +2 x2 +x3=3, 2 x1 +3 x2 + x3 =3 and 3 x1 +5 x2 +2 x3=1. The system has
Answers
The solution of the system is (x1,x2,x3) = (−1/7,8/7,−3/7).Therefore, the Thus, the solution of the system is (x1,x2,x3) = (−1/7,8/7,−3/7).Therefore, the system has a solution. has a solution.
Consider the system of linear equations:
x1 +2 x2 +x3=3
2 x1 +3 x2 + x3 =3
3 x1 +5 x2 +2 x3=1
The system has a solution.
It can be found as follows.
x1 +2 x2 +x3=3
2 x1 +3 x2 + x3 =3
Subtracting Eq. (1) from Eq. (2),
we get:
x1 + x2 =1 ….(3)
3 x1 +5 x2 +2 x3=1
Putting x2 = 1−x1 in Eq. (3) and Eq. (1), we get:
x1 + 3 x3 =1 ….(4)
2 x1 + x3 =1 ….(5)
Solving Eq. (4) and (5), we get:
x1=1−2x3 and x3=−3x1+1
Substituting the value of x3 in x1 = 1 − 2x3, we get
x1 = −1/7.
Thus, the solution of the system is (x1,x2,x3) = (−1/7,8/7,−3/7).Therefore, the system has a solution.
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A person walks 1 km, turns around, and runs back to where he started. Compare the energy used and the power during the two segments. A. The energy used and the power are the same for both. B. The energy used while walking is greater, the power while running is greater. C. The energy used while running is greater, the power while running is greater. D. The energy used is the same for both segments, the power while running is greater.
Answers
D. The energy used is the same for both segments, the power while running is greater.
Walking and running both require energy, but the distance covered and the time taken are different. In this case, the person covers the same distance of 1 km in both segments.
Therefore, the energy used is the same for both. However, since running involves covering the same distance in less time, the power while running is greater. Power is the rate at which energy is used, and since running takes less time, the power output is higher.
D. The energy used is the same for both segments, the power while running is greater.
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Need help , can’t find this one
Answers
Since it is the inverse g(2) = -3
And f(-3) = 2
Given the function g(x)=2x and the domain {0, 2, 4), what is the range? {0, 1, 2} {2, 4, 8) {1, 2, 3) {0, 4, 8}
Answers
According to the question we get the following outputs For x = 0, g(0) = 0 , For x = 2, g(2) = 4 , For x = 4, g(4) = 8. the range of the function g(x) = 2x, with the given domain {0, 2, 4}, is {0, 4, 8}.
The range of the function g(x) = 2x, with the given domain {0, 2, 4}, can be determined by evaluating the function for each value in the domain.
For x = 0: g(0) = 2(0) = 0
For x = 2: g(2) = 2(2) = 4
For x = 4: g(4) = 2(4) = 8
Therefore, the range of the function is {0, 4, 8}.
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last year, 20 percent of all teenagers purchased a new iphone. this year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iphone. to test whether the percentage has decreased, the p-value is:
Answers
The p-value is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
The p-value can be calculated by using a one-proportion z-test. The null hypothesis would be that the percentage has stayed the same from last year, and the alternative hypothesis is that the percentage has decreased.
The formula for the z-score is (x-p)/√(p(1-p)/n), where x is the observed proportion (39/260), p is the expected proportion (0.20), and n is the sample size (260). The p-value is then calculated using the z-score and the cumulative distribution function.
Therefore p-value, in this case, is 0.063, which indicates that there is not strong evidence to reject the null hypothesis that the percentage has stayed the same.
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What is the x-intercept of the following graph
Answers
Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job. How much total money would Taub have after 7 weeks of saving? Also, write an expression that represents the amount of money Taub would have saved in w weeks.
Total savings after 7 weeks:
Total savings after w weeks:
Answers
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
What is Equation Modelling?Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is a phrase : Taub is saving up to buy a new bicycle. She already has $70 and can save an additional $10 per week using money from her after school job.
Taub will have a total of -
70 + 7 x 10 = $140
The expression that represents the amount of money Taub would have saved in [w] weeks is -
y = 70 + 10w
Therefore -
Total savings after 7 weeks : $140
Total savings after w weeks : $(70 + 10w)
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During the first two weeks of summer vacation, Antonia earned \$ 100 per week. During the next six weeks, she earned \$ 150 per week, What was her average weekly pay?
A \$ 50
B \$ 112.50
C \$ 125
D \$ 135
E \$ 137.50
Answers
Antonia earned a total of $1100 over eight weeks. To find the average weekly pay, we divide $1100 by 8, resulting in $137.50. Therefore, the correct answer is E.
To find the average weekly pay, we need to calculate the total earnings and divide it by the number of weeks.
During the first two weeks, Antonia earned $100 per week, so her total earnings for the first two weeks is 2 * $100 = $200.
During the next six weeks, she earned $150 per week, so her total earnings for the next six weeks is 6 * $150 = $900.
The total earnings for the eight weeks is $200 + $900 = $1100. To find the average weekly pay, we divide the total earnings by the number of weeks: $1100 / 8 = $137.50.
Therefore, the average weekly pay is $137.50. The correct answer is option E.
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the ratio is 5 to 4 so whats the rate
Answers
Answer:
= 1.25 units per unit
Step-by-step explanation:
Plz name me brainliest I would greatly appreciate it Thank You
On a coordinate plane, a v-shaped line crosses the x-axis at (negative 2, 0), the y-axis at (0, negative 2), and the x-axis at (2, 0). What is the domain of the function on the graph?
Answers
Answer:
b
Step-by-step explanation:
i did the test and I got the answer right here after being corrected so yah.
Answer:
All real numbers
Step-by-step explanation:
Determine the solutions of the equation: the absolute value quantity two thirds times x plus 2 end quantity minus 8 equals 0 x = −9 and x = 9 x = −15 and x = 4 x = −15 and x = 9 x = −15 and x = 15
Answers
The solution for the absolute value equation is x = 10 and x = -14
In this question,
Two thirds times the absolute value of the quantity x plus 2 end quantity minus 8 equals 0. The equation for this statement is 2/3 lx + 2l -8 =0.
The solution for the equation is
\(\frac{2}{3}\) lx + 2l -8 =0
\(\frac{2}{3}\) lx + 2l = 8
Multiply by 3/2 on both sides,
\(\frac{2}{3}\) lx + 2l = 8
\(\frac{2}{3}\) ×\(\frac{3}{2}\)lx + 2l =8×\(\frac{3}{2}\)
=> x +2 = 12
Case 1: Take as positive value
=> x + 2 = 12
=> x = 12 - 2
=> x = 10
Case 2: Take as negative value
=> -(x +2) = 12
=> -x - 2 = 12
=> -x = 12 + 2
=> -x = 14
=> x = -14
Hence, we can conclude that the solution for the absolute value equation is x = 10 and x = -14 is the correct answer
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URGENT PLEASE HELP ASAP WILL GIVE BRAINLIEST!!!!!!!!!!!
Answers
Slope is 0.75 or 3/4 I believe!
if you were informed that it takes one year for the earth to revolve around the sun, and that the square of that period was proportional to the cube of the earth's average distance from the sun, what law would fit that description?
Answers
Answer:kepler's 3rd law
Step-by-step explanation:
Pls help this is due soon!!!
Answers
i need help does anyone know this question
Answers
Answer:
The third answer is correct.
Step-by-step explanation:
You are going to translate the smaller quadrilateral (4 sided figure) to the larger quadrilateral. Then you need the scale factor from the smaller figure to the larger.
Side EF times the scale factor will give you side AB. Let's call the scale factor s then our equation would be:
EF x s = AB To find s divide both sides by EF
\(\frac{EF(s)}{EF}\) = \(\frac{AB}{EF}\)
s = \(\frac{AB}{EF}\) This is our scale factor.
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