Answer: Her brother is 5 years old.
Step-by-step explanation:
s = 2b
4b + 3b = 35
7b = 35
First, I used s to represent Sarah's age. We are told that she is twice her brother, I used b to represent her brother's age. The sum of twice her age is 4 times her brother's age (2b + 2b) and 3 times her brother's age is 3b.
Is a dilation with a scale factor greater than 1 is a reduction?
When the scale factor is greater than one, then the dilation is not a reduction.
What is a dilation?
Dilation is a process of changing a thing. It is a process of transformation that to make the objects smaller or larger, with the use of specific scale factor.
The new figure that is the result of dilation is known as the image. Initial figure is referred to as the pre-image.
What is a center of dilation?
Center of dilation is the resizing that happens from a point. The objects/figures are expanded or contracted from the center of dilation.
Scale factor is a figure by which the size of any geometrical figure can be resized, with respect to its original size. The scale factor is multiplied to get image.
Figure size increased, when the scale factor is greater than 1.
Thus, the dilation will be a expansion, when the scale factor is a greater than one.
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PLS HELP ME ASAP I WILL MARK THE BRAINLIEST!!!
Answer:B!!!!
Step-by-step explanation:
HOPE THIS HELPED
The sum of three integers is greater than 9. Show that one of the integers must be greater than 3.
The sum of three integers is greater than 9. Assuming all integers same can show that one of the integers must be greater than 3.
Define integer.The three elements that make up an integer are zero, the natural numbers, and their additive inverse. It can be shown on a number line, but without the fractional portion. Z stands for it.
Given,
Sum of three integers is greater than 9.
Let all the integer be same, then
x + x + x > 9
3x > 9
x > 3
Let take that the three integers are consecutive, then
x+ x + 1 + x +2> 9
3x + 3>9
3x > 6
x> 2
So, the integer must be 3, 4 and 5
Here we can see that one integer must be greater than 3.
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Which translation are performed on f(x) = ln(x) to graph g(x) = –ln(x + 3) – 3?
a. to the left 3?
b. to the right 3?
c. up 3
d. down 3
please right answers only.
The translations performed are
a. to the left 3d. down 3How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
f(x) = ln(x)
g(x) = -ln(x + 1) - 3
First, we have the transformation to be:
From f(x) = ln(x) to f(x) = -ln(x)
This means a reflection across the x-axis
Next, we have
From f(x) = -ln(x) to f(x) = -ln(x + 3)
This means the function is translated left by 3 units
Next, we have:
From f(x) = -ln(x + 3) to f(x) = -ln(x + 3) - 3
This means the function is translated down by 3 units
Hence, the translation is 3 units left and 3 units down
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g find the surface area of that part of the plane 6x+10y+z=9 that lies inside the elliptic cylinder x249+y29=1
The surface area of that part of the plane 6x+10y+z=9 that lies inside the elliptic cylinder [tex]x^{2}/49 + y^{2}/9 =1\\[/tex] is 21 [tex]\pi[/tex] [tex]\sqrt{137\\[/tex].
Given:
6x + 10y + z = 9 ..... (1)
[tex]x^{2}/49 + y^{2}/9 =1\\[/tex] ..... (2)
Equation (1) can also be written as:
z = 9 - 6x - 10y ...... (3)
The surface area is given by the equation:
SA = ∫∫[tex]\sqrt{((df/dx)^2) + (df/dy)^2 + 1} )dA[/tex]
[tex]\sqrt{df}/dx = -6[/tex]
[tex]\sqrt{df}/dy = -10[/tex]
Now, substitute the known values in equation (4).
SA = ∫∫[tex]\sqrt{(-6)^2 + (-10)^2 + 1} dA[/tex]
SA =[tex]\sqrt{137}[/tex] ∫∫dA
Now the area enclosed by an ellipse is given by:
[tex]x^{2}/49 + y^{2}/9 =1\\x^{2}/a^2 + y^2/b^2=1\\[/tex]
By comparing the above equation:
a = 7
b = 3
The area is given by:
SA = [tex]\sqrt{137}[/tex] [tex]\pi[/tex] (7 x 3)
SA = 21 [tex]\pi[/tex] [tex]\sqrt{137\\[/tex]
The surface area of an elliptic cylinder is 21 [tex]\pi[/tex] [tex]\sqrt{137\\[/tex].
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Cameron's car used 15 gallons to travel 675 miles. At what rate does the car use gas, in miles per gallon?
45 is the rate does the car use gas, in miles per gallon.
How to calculate gas miles per gallon?Cameron's car used 15 gallons to travel 675 miles.
Simply dividing the distance driven by the quantity of petrol your car required to fill up is the simplest approach to figure out how much gas you'll need. That is the sum of the miles traveled and the gas consumed.
The car travels 675 miles, which we divide by the 15 gallons in a full tank of gas to determine miles per gallon of fuel.
Rounding to the nearest tenths place, 675/115 equals 45.
45 is the rate does the car use gas, in miles per gallon
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What does the slope of the line of best fit represent
The slope of the line of best fits will be $0.15 per minute. Then the correct option is A.
What is the slope?The slope is the ratio of rising or falling and running. The difference between the ordinate is called rise or fall and the difference between the abscissa is called run.
The slope of the line is given as,
m = (y₂ - y₁) / (x₂ - x₁)
Take two points from the table which are (300, 90) and (100, 60). Then the slope of the line is given as,
m = (90 - 60) / (300 - 100)
m = 30 / 200
m = $0.15 per minute
The slope of the line of best fits will be $0.15 per minute. Then the correct option is A.
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one leg of a right triangle is 1 centimeter shorter than the other leg and the hypotenuse is 2 centimeters longer than hte longer leg. what are lenghts of sides of triangle
3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
Given that,
In a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
We have to find how much longer is the longer leg.
We know that,
Let the one side of the triangle be x
The other side we get x-1 and x+2
From Pythagoras theorem,
x²+(x-1)²=(x+2)²
x²+x²-2x+1=x²+4x+4
2x²-2x+1-x²-4x-4=0
x²-6x-3=0
To find the value of x we have a formula that is
x=-b±√(b²-4ac)/2a
Here, a=1, b=-6 c=-3
x=6±√(-6²-4(1)(-3))/2(1)
x=6±√36+12/2
x=6±√48/2
x=6±4√3/2
x=3±2√3
Therefore, 3±2√3 much longer is the longer leg when in a right triangle, the hypotenuse is 2 cm longer than the longer leg, while one of the legs is 1 cm shorter than the other.
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Seven out of every twenty soda bottles produced have caps indicating that the purchaser has won a prize. Which equation represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced? (Let w represent the number of bottles with winning caps, and let t represent the total number of bottles produced.)
a) w = 7/20t
b) w = 7/13t
c) 7w = 20t
d) 7w = 13t
Equation which represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced is 7w=20t
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Seven out of every twenty soda bottles produced have caps indicating that the purchaser has won a prize.
We need to find the equation which represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced.
Let w represent the number of bottles with winning caps, and
let t represent the total number of bottles produced.
t=7/20w
7w=20t.
Hence, 7w=20t is the equation represents the relationship between the number of soda bottles with winning caps and the total number of soda bottles produced.
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15. Zoey i playing volleyball with her friend. She hit the 0. 2 kg ball traight up for 4m Auming all energy i conerved, what wa the ball' velocity when it left Zoey' hand? Show all work
The ball' velocity when it left Zoey' hand is 8.85 m/s
What is the principle of conservation of energy?
The word "conservation" in physics describes anything that doesn't change. This indicates that a conserved quantity is represented by a variable in an equation that is constant over time. Its value is the same whether an event occurs before or after it.
In physics, there are a lot of conserved quantities. For making forecasts in what would otherwise be exceedingly complex situations, they are frequently remarkably useful. There are three fundamental quantities in mechanics that are conserved. They are power, forward motion, and angular momentum.
According to question
Mass of the ball = 0.2 kg
Maximum height of the ball = 4 m
Gravity = 9.8 m/s²
Therefore:
Using conservation of energy, we know that P.E. top = K.E. bottom. This tells us that the potential energy at the top is all converted to kinetic energy at the bottom. We can substitute the equations for potential energy and kinetic energy
Initial kinetic energy + Initial potential energy = Final kinetic energy + Final potential energy
1/2mv² + 0 = mgh + 0
½(0.2)v² = (0.2)(9.8)4
v² = 78.4
v = 8.854377…
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Which absolute value functions will be narrower than the parent function, f(x) = |x|? check all that apply.
The absolute value function which will be narrower than the parent function is:
f(x) = 2.9|x|
Given parent function is f(x)=|x|
Now we have to find which function from given choices will be narrower than the parent function.
Notice that adding or subtracting some number from the parenth function only shifts the graph up, down, left of right side.
But that will not make function narrorwer or broader.
So f(x) = |x – 2| and f(x) = |x| + 3, can't be the answer.
Multiplying by some positive real number which is more than 1, makes function narrower.
Only f(x) = 2.9|x| from remaining choices fits that case.
Hence f(x) = 2.9|x| is the final answer.
f(x) = 1.2|x + 8| will also make the function narrower but will shift the parent function too.
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Using the Distributive Property, Solve the Problem below:
-2.5(4x - 4) = -6
(After using the Distributive Property, Solve for x)
The solution to the equation -2.5(4x - 4) = -6 is x = 1.6
How to apply the Distributive Property?From the question, we have the following parameters that can be used in our computation:
-2.5(4x - 4) = -6
Open the bracket using the Distributive Property
So, we have the following representation
-10x + 10 = -6
Subtract 10 from both sides of the equation
-10x = -16
Divide both sides by -10
x = 1.6
Hence, the solution is x = 1.6
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If you have the bags in your inventory for more than three months, you plan to mark down the selling price by 25 percent. What will the markdown price be?
State the vector in component form for an object flying at 235 mph at a bearing of N55°W.
The vector in component form for an object flying at 235 mph at a bearing of N55°W is given as follows:
(-134.79, 192.5).
How to define the vector?The vector is composed by two components, the x-component and the y-component, as follows:
<x,y>.
The components are defined as follows:
x = vcos(θ).y = vsin(θ).In which the variables are defined as follows:
v is the velocity.θ is the angle.In the context of this problem, the values of these parameters are given as follows:
v = 235, θ = 55º.
The positions are given as follows:
West -> x negative.North -> y positive.Hence the components of the vector are given as follows:
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Lin runs 5 laps around the track in 6 minutes how many minutes per lap
Answer:
72 seconds I think I am sorry if it is wrong
Why is it called a square 1?
Square 1 is so named because of the shape of the puzzle: it is a cube with four sides, each with nine squares, creating a square shape
The puzzle is also sometimes referred to as a "magic cube" because it can be rearranged into different shapes and configurations.Square 1 is a 3-dimensional puzzle that consists of nine squares on each side of a cube. The puzzle is made up of four layers of nine colored squares that can be rotated around the center axis. This creates a square-like shape, hence the name “Square 1”. The object of the game is to arrange the nine squares on each side so that all of the colors match up. This requires the player to manipulate and rotate the pieces in order to achieve the desired outcome.
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The measurement of angle A is 89°. Classify angle A as an acute, right, or obtuse angle.
Answer:
Acute angle
Step-by-step explanation:
Any angle less than 90° is acute.
Answer:
Acute.
Step-by-step explanation:
90 degree angle = Right Angle
Greater than 90 degrees = Obtuse Angle
Less than 90 degrees = Acute Angle
how many positive perfect squares less than 10^610 6 are multiples of 2424? how many positive perfect squares less than 10^610 6 are multiples of 2424?
Total 83 numbers that are positive perfect squares less than [tex]10^6[/tex] are multiples of 24.
What is perfect Square?
A perfect square is a number that can be written as the second exponent of an integer or as the product of an integer by itself.
For instance, the number 25 is a perfect square since it is the product of the integer 5 multiplied by itself, 5*5 = 25.
21 cannot be expressed as the product of two identical integers, so it is not a perfect square number.
Prime Factorization of 24 is 2^3*3.
There must be at least 3 factors of number 2 and 1 factor of number 3 in each square.
its square root must have 2 factors of number 2 and 1 factor of number 3.
This means each square should be in the from [tex](12*c)^2[/tex]. where 12 is a positive numbers less than [tex]\sqrt{10^6}[/tex] = 1000.
So total numbers of positive perfect squares.
= 1000/12 = 83.
Total 83 numbers that are positive perfect squares less than [tex]10^6[/tex] are multiples of 24.
Given question is incomplete Complete Question here
How many perfect squares less than 10^6 are multiples of 24.
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Write an explicit formula for an,
the nth term of the sequence 6, 16, 26, ....
Answer:
6 plus 10
Step-by-step explanation:
6 beginning number plus 10 repeatedly
The equation y = 6200x represents the number of miles, y, that the satellite Space
Explorer flies in a hours. Find the rate of change.
If equation y = 6200x represents the number of miles, y, that the satellite Space Explorer flies in a hours then 6200 is the rate of change.
What is Equation?
Two or more expressions with an Equal sign is called as Equation.
The given equation is y = 6200x
y equal to six thousand two hundred times of x.
y = 6200x represents the number of miles, y, that the satellite Space
Explorer flies in a hours.
We need to find the rate of change.
Rate of change means how quickly something changes over time.
Differentiate the equation with respect to x
dy/dx=6200
Hence, the rate of change is 6200.
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Use the following graph to answer the question.
The graph represents the movement of a car over the span of 8 seconds. What is the average acceleration of the car from 2-4 seconds?
A. 0 m/s^2
B. 5 m/s
C. 5 m/s^2
D. 1.25 m/s^2
Answer:
Step-by-step explanation:
I think it's B or C because if you look closely u see that the line goes up then straight on 4. Go for an educational guess.
x^2=17x-60
in standard form
The standard form of the quadratic equation is x² -17x + 60 =0
What is a quadratic equation?
A quadratic equation is a second-order polynomial equation with a single variable such as x, where ax²+bx+c=0. with a ≠ 0 . Given that it is a second-order polynomial equation, the algebraic fundamental theorem ensures that it has at least one solution. Real or complicated solutions are both possible.
Standard form of a quadratic equation:
ax² + bx + c=0
Given:
x² = 17x - 60
move right side terms to the left
x² -17x + 60 =0
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find a in degrees a=13 b=9 c=7
Answer: in image
Step-by-step explanation: j
In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?
Option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B
According to the information given in the question,
A true proportion of 0.325 represents that the two simulations will be conducted for sampling proportions from a population
Simulation A -
Sample size - 100
Trials - 1500
Simulation B -
Sample size - 50
Trials - 2000
Now due to the relation of simulation A and simulation B, they are closely equal-
The total sample size of simulation A= 1500 x 100
= 150000
The total sample size of simulation B = 2000 x 50
= 100000
From the above calculations of simulations A and B, we can see that while comparing the,
Sample Size = Simulation A > Simulation B
Variability = Simulation B < Simulation B
Therefore, option c) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B is correct.
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In a recent survey, the proportion of adults who indicated mystery as their favorite type of book was 0.325. Two simulations will be conducted for the sampling distribution of a sample proportion from a population with a true proportion of 0.325. Simulation A will consist of 1,500 trials with a sample size of 100. Simulation B will consist of 2,000 trials with a sample size of 50. Which of the following describes the center and variability of simulation A and simulation B?
A) The centers will roughly be equal, and the variabilities will roughly be equal.
B) The centers will roughly be equal, and the variability of simulation A will be greater than the variability of simulation B.
C) The centers will roughly be equal, and the variability of simulation A will be less than the variability of simulation B.
D) The center of simulation A will be greater than the center of simulation B, and the variability of simulation A will roughly be equal to the variability of simulation B.
E) The center of simulation A will be less than the center of simulation B, and the variability of simulation A will be greater than the variability of simulation B.
[tex]\sqrt{-240\\[/tex]
The required simplified solution of the given expression is 4√15i.
A simplified solution of the given expression √-240 is to be determined.
What is simplification?The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
here,
The square root of the negative value induces the property of the complex number. (a complex number is a number that contains both the real and imaginary parts of the number)
Simplifying,
√-240= √4×4×-15
= 4 √-15
= 4√15i {∵ √-1 = i}
Thus, 4√15i is the required simplified solution to the provided expression.
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The question seems to be incomplete,
The complete question could be as,
Simplify the complex number √-240 ?
How old is my brother 3x9-18
Answer: 9
Step-by-step explanation:
3x9=27
27-18=9
Answer:
Step-by-step explanation:
dw
Use point-slope form to write the equation of a line that passes
through the point (-9, 14) with slope -1/2
Answer:
y - 14 = -0.5(x + 9)
padma works at an electronics store. in addition to her salary, she receives 2 percent of the sales dollars she brings in each month. this extra 2 percent is called a
Answer:
Step-by-step explanation:
A Commission
The extra 2% of the sales dollars that Padma receives each month is called a commission.
What is the commission?The commission is a payment made to an employee in addition to their regular salary or wages, based on the number of sales or business they bring in. Another popular definition of commission is the amount of money earned by an employee when they sell something: He receives a 1% commission on each sale in addition to his pay.
As per the question, Padma receives a commission of 2% of the sales dollars she brings in each month. The commission is a common form of compensation in sales and customer service jobs, where employees are often paid a base salary plus a commission based on their sales or performance.
Thus, the required fill-in-the-blank will be "commission".
Hence, the extra 2 percent of the sales dollars that Padma receives each month is called a commission.
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The graph of a quadratic function has roots at -3 and -7 and a vertex at (-5,4). What is the
equation of the function in vertex form?
A y=-(x + 5)² - 4
B. y = −(x+5)² +4
C. y=(x + 5)² – 4
D. y = (x + 5)² + 4
The equation of the function in vertex form is y = -(x + 5)² + 4
What is quadratic equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .
Given that the quadratic function has roots at -3 and -7 and a vertex at (-5,4).
We need to find the equation of the function in vertex form
equation of the function in vertex form.
As per the information given in the question,
The given roots of the function are -3 and -7,
y = a (x + 3) (x + 7)
y = a (x² + 10x + 21)
y = a (x² + 10x + 25 − 4)
y = a (x² + 10x + 25) − 4a
y = a (x + 5)² − 4a
The vertex is (-5, 4),
So, a = -1.
y = -(x + 5)² + 4
Hence, y = -(x + 5)² + 4 is the equation of the function in vertex form
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no matter what type of population value (or combination of population values) is being estimated using a confidence interval, what items should you be watching for in order to best assess the results?
1. The actual differences that researchers imply causality come from randomized experiments.
2. That the sample selected represents the population.
3. Confidence level clearly stated.
Population values, also called parameters, are calculated from all values in the entire population.
A representative sample is a subset of the population that attempts to accurately reflect the characteristics of the larger group. For example, in a classroom of her 30 students, 15 boys and 15 girls, you can create a representative sample of her 6 students, 3 boys and 3 girls.
Probable sampling is defined as a sampling technique in which the researcher selects samples based on the researcher's subjective judgment rather than at random. This is a less rigorous method. This sampling method relies heavily on the researcher's expertise. This is done through observation and is often used by researchers for qualitative research.
A confidence interval (CI) is the range of estimated values for an unknown parameter. Confidence intervals are computed at the specified confidence level. A 95% confidence level is the most common, but other levels such as 90% and 99% are sometimes used. The confidence level represents the proportion of corresponding CIs over time that contain the true value of the parameter. For example, 95% of all intervals computed at the 95% level must contain the true value of the parameter.
Factors that affect the width of the CI include confidence level, sample size, and intra-sample variation. All other things being equal, the larger the sample, the narrower the confidence interval. Similarly, the greater the sample variability, the wider the confidence interval, and the higher the confidence level, the wider the confidence interval should be.
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