Answer:
Scale factor is 2
Step-by-step explanation:
A rectangle has an area of 16ft²
That is
Length₁ x Breadth₁ = 16 ft²
Every dimension is multiplied by a scale factor, let the scale factor be s.
New dimensions are
Length₂ = s x Length₁
Breadth₂ = s x Breadth₁
New area is given by
Area = Length₂ x Breadth₂ = s x Length₁ x s x Breadth₁
Area = s² x Length₁ x Breadth₁
64 = s² x 16
s² = 4
s = 2
So scale factor is 2
3x^2+5x-2=0 solve quadratic equation by factoring
Factor the common factor out of 8x3 12x.
a. 4x(2x2 3)
b. x(x2 3)
c. 4x2(2x3 3)
d. 4x(6x2 3)
Answer:
A. [tex]4x(2x^2+3)[/tex].
Step-by-step explanation:
We have been given an expression [tex]8x^3+12x[/tex]. We are asked to factor our given expression.
We can see that both terms of our given expression share a common factor that is 4x.
Upon factoring out 4x from our given expression, we will get:
[tex]4x(2x^2+3)[/tex]
Therefore, the factored form of our given expression would be [tex]4x(2x^2+3)[/tex] and option A is he correct choice.
Suppose that $14,000 is invested in a savings account paying 5.2% interest per year.
(a) Write the formula for the amount A in the account after t years if interest is compounded monthly.
What is the value of 6x2 – 4x when x = 5?
Final answer:
To calculate 6x^2 – 4x when x = 5, you square 5 to get 25, multiply by 6 to get 150, then subtract 4 times 5 which is 20, resulting in a final value of 130.
Explanation:
To find the value of the expression 6x^2 – 4x when x = 5, you need to substitute 5 for x in the expression and perform the arithmetic. First, calculate the value of 6x^2 by squaring x (which is 5) and multiplying by 6:
6 * 5^2 = 6 * 25 = 150.
Next, calculate the value of 4x when x is 5:
4 * 5 = 20.
Now subtract the result of 4x from the result of 6x^2:
150 - 20 = 130.
So, the value of the expression when x = 5 is 130.
Indicate the method you would use to prove the two 's . If no method applies, enter "none".SSS
SAS
ASA
None
Answer:
C) ASA
Step-by-step explanation:
Let's name the first triangle ABC and the second triangle DEF.
Statement Reason
∠A ≅∠D Given
AB ≅DE Given
∠B ≅ ∠E Given
In two triangles, if the two angles and the included side of the two triangles are congruent, then the triangles are congruent by the property ASA (Angle-Side-Angle) using corresponding parts of congruent triangles are congruent.
According to the given triangles, the two triangles are congruent by the property of ASA.
explain how you can compare two different mixed numbers that have the same whole number part ?
When writing linear equations, how do you determine which form of a line to use?
In the equation 6x – 2 = –4x + 2, Spencer claims that the first step is to add 4x to both sides. Jeremiah claims that the first step is to subtract 6x from both sides. Who is correct? Explain
Sample Response: Both are correct. As long as inverse operations and the properties of equality are used properly, both methods will generate the same solution. They both isolate the variable on one side of the equation.
Answer:
Spencer and Jeremiah both are correct
Step-by-step explanation:
We have given an equation 6x-2 = -4x+2
In this case spencer and jeremiah both are correct whether we first subtract 6x from both sides or we add 4x to both sides will not lead to any incorrection we will get the same result after simplification from both the methods
If we subtract 6x from both sides we will get 6x-6x-2= -4x-6x+2 after simplification we will get -2 = -10x+2
After further simplification we will get x=4/10=2/5
And if we add 4x on both sides we will get 6x+4x-2= -4x+4x+2 after simplification we will get 10x -2 =2 which eventually gives the result
x=4/10=2/5
Therefore, Both are correct
Find the arc length of the curve y = ln (cos x) for 0 < x < pi/4
Suppose you take an 80 question mc test with 5 choices if 60% is passing, what are your chances of passing
Find the equation of a line that satisfies the given conditions; x-intercept = 2, and y-intercept = -8
The equation of a line with an x-intercept of 2 and a y-intercept of -8 is y = 4x - 8, which follows from applying the slope-intercept form and calculating the slope based on the intercepts.
To find the equation of a line with an x-intercept of 2 and a y-intercept of -8, we use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept.
We can determine the slope by recognizing that the line crosses the x-axis at (2,0) and the y-axis at (0,-8).
The slope m is the rise over the run, which in this case is (-8 - 0) / (0 - 2) = 4.
Therefore, the equation of the line is y = 4x - 8.
This equation satisfies the given conditions, as plugging in x = 0 gives the y-intercept of -8 and setting y to 0, and solving for x yields the x-intercept of 2.
PLEASE HELP!!!
The grams of sugar per serving for three brands of cereal are 4g,8g, and 16g. The probability of choosing a cereal with 4 grams of sugar is 1/4. The probability of choosing a cereal with 8 grams of sugar is 5/8. The probability of choosing a cereal with 16 grams of sugar is 1/8.
What is the expected value of the number of grams of the sugar in cereal?
A 6
B 7
C 8
D 9
Answer: The expected value of the number of gram of the sugar in the cereal is 8 grams.
Step-by-step explanation:
When we multiply each of the possible outcomes by the likelihood each outcome will occur and find out the sum of the all values, we get the expected value of an experiment.
Here, the probability of the different brands 4g, 8g and 16g are 1/4, 5/8 and 1/8 respectively.
Thus, by the above definition,
The expected value of the number of grams of the sugar in the cereal = 4 g × its probability + 8 g × its possibility + 16 gram × Its possibility,
[tex]=4\times \frac{1}{4}+8\times \frac{5}{8}+16\times \frac{1}{8}[/tex]
[tex]=1+5 +2 = 8[/tex]
Thus, The expected value of the number of gram of the sugar in the cereal is 8 grams.
The expected value of the number of grams of sugar in cereal is 8 grams and this can be determined by using the given data.
Given :
The grams of sugar per serving for three brands of cereal are 4g, 8g, and 16g.The probability of choosing a cereal with 4 grams of sugar is 1/4. The probability of choosing a cereal with 8 grams of sugar is 5/8. The probability of choosing a cereal with 16 grams of sugar is 1/8.The following steps can be used in order to determine the expected value of the number of grams of the sugar in cereal:
Step 1 - The probability concept can be used in order to determine the expected value of the number of grams of sugar in the cereal.
Step 2 - According to the given data, the probability of choosing a cereal with 4 grams of sugar is 1/4, the probability of choosing a cereal with 8 grams of sugar is 5/8, and the probability of choosing a cereal with 16 grams of sugar is 1/8.
Step 3 - So, the expected value of the number of grams of the sugar in cereal is:
[tex]\rm Total \;number \;of\; grams\; of\; sugar=4\times \dfrac{1}{4}+8\times \dfrac{5}{8}+16\times \dfrac{1}{8}[/tex]
Step 4 - Simplify the above expression.
Total number of grams of sugar = 8 grams
Therefore, the correct option is C).
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a bowling ball weighs 48 N. With what net force must it be pushed to accelerate it at 3.0 m/s2
Final answer:
The net force required to accelerate a bowling ball weighing 48 N at 3.0 m/s² is 14.7 N, which we round to 15 N using two significant figures.
Explanation:
To find the net force required to accelerate the bowling ball at 3.0 m/s², we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). First, we need to determine the mass of the bowling ball. Since the weight of the bowling ball is given as 48 N and weight can be calculated by multiplying mass with the acceleration due to gravity (weight = mass × gravity), we can find the mass (m = weight / gravity). Assuming the acceleration due to gravity is 9.8 m/s², the mass of the bowling ball would be approximately 4.9 kg (48 N / 9.8 m/s²). Next, we apply Newton's second law to find the net force required for the 3.0 m/s² acceleration by multiplying the mass by the desired acceleration (F = ma).
The calculation is as follows:
F = ma = 4.9 kg × 3.0 m/s² = 14.7 N
Therefore, a net force of 14.7 N must be applied to the bowling ball to achieve the acceleration of 3.0 m/s². We typically round this to two significant figures, giving a final answer of 15 N.
Which is the graph of f(x)=(x-1)(x+4)
The quadratic function is described by the standard equation [tex]\boxed{ \ f(x) = ax^2 + bx + c \ }.[/tex]
We have the quadratic function [tex]\boxed{ \ f(x) = (x - 1)(x + 4) \ }.[/tex]
Let us configure it to obtain a standard equation.
[tex]\boxed{f(x) = (x - 1)(x + 4)}[/tex]
[tex]\boxed{f(x) = x^2 + 4x - x - 4}[/tex]
Hence, we get [tex]\boxed{\boxed{ \ f(x) = x^2 + 3x - 4 \ }}.[/tex]
We identify the coefficients a, b, and c. For this equation, [tex]\boxed{ \ a = 1, b = 3, and \ c = -4 \ }[/tex]The parabola opens upward because a > 0, resulting in a vertex that is a minimum.The y-intercept of the quadratic function f(x) = x² + 3x - 4 is (0, c), i.e., the point [tex]\boxed{ \ (0, -4) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - 1)(x + 4) \ }[/tex] we get the x-intercepts at [tex]\boxed{ \ (-4, 0) \ and \ (1, 0) \ }[/tex]The axis of symmetry is [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex], i.e., [tex]\boxed{ \ x = h = -\frac{3}{2(1)} \rightarrow h = -\frac{3}{2} \ }[/tex]The minimum value is [tex]\boxed{ \ k = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Finding the minimum value is as follows:
[tex]\boxed{ \ k = f (- \frac{3}{2}) = (- \frac{3}{2})^2 + 3(- \frac{3}{2}) - 4 = -\frac{25}{4} = -6\frac{1}{4} \ }, or[/tex][tex]\boxed{ \ k = \frac{3^2 - 4(1)(-4)}{-4(1)} = -\frac{25}{4} = -6\frac{1}{4} \ }[/tex]Notes:
The graph of a quadratic function is called a parabola.When a > 0, the parabola opens upward, resulting in a vertex that is a minimum.When a < 0, the parabola opens downward, resulting in a vertex that is a maximum.The value c is the y-intercept of the graph, because a y-intercept is a point on the graph where x is zero. In other words, the graph passes through the point [tex]\boxed{ \ (0, c) \ }.[/tex]From [tex]\boxed{ \ f (x) = (x - x_1)(x - x_2) \ }[/tex] we get x-intercepts at [tex]\boxed{ \ (x_1, 0) \ and \ (x_2, 0) \ }.[/tex] An x-intercept represents a point on the graph where y is zero.The axis of symmetry represent the line that passes through the vertex of parabola with equation [tex]\boxed{ \ x = h = -\frac{b}{2a} \ }[/tex]The vertex is [tex]\boxed{ \ (h, k) \ },[/tex] where [tex]\boxed{ \ k = f(h) \ }[/tex] or [tex]\boxed{ \ k = \frac{b^2 - 4ac}{-4a} \ }[/tex]Learn moreA line that is not parallel to either the x-axis or the y-axis https://brainly.com/question/4691222 Finding the y-intercept of the quadratic function f(x) = (x – 6)(x – 2) https://brainly.com/question/1332667The midpoint https://brainly.com/question/3269852Keywords: which is the graph of f(x) = (x - 1)(x + 4), the x-intercept, quadratic function, a standard equation, the y-intercept, the axis of symmetry, the vertex, parabola, upward, downward
The graph of f(x) = (x-1)(x+4) is an upward-opening parabola with roots at x = 1 and x = -4. It should be plotted carefully, labeling and scaling the axes to show maximum and minimum values, and ensuring it passes through the roots with the proper shape.
Explanation:The graph of the function f(x) = (x-1)(x+4) can be determined by finding the roots and the shape of the curve. The roots of the function can be found when f(x) = 0, which occurs at x = 1 and x = -4. Therefore, these are the points at which the graph will intersect the x-axis. Since it's a quadratic function, its graph will be a parabola.
Additionally, because the coefficient of x² is positive, the parabola opens upwards. To graph this function accurately, one needs to plot the roots and then sketch the parabola, ensuring that it intersects these points and opens upwards. The vertex of the parabola can also be found by averaging the roots, which gives us the x-value of the vertex as (-4 + 1)/2 = -1.5, with the corresponding y-value obtained by evaluating f(x) at x = -1.5.
The resulting graph would start above the x-axis for x < -4, pass through the x-axis at x = -4, reach a vertex at x = -1.5, pass through the x-axis again at x = 1, and continue upwards for x > 1.
The graph should be accurately scaled and labeled with the function f(x) and the variable x, and include the maximum and minimum values on the axes based on the calculated points and the behavior of the quadratic function.
PLEASE HELP
What is the area of the polygon below?
A. 225 square units
B. 140 square units
C. 115 square units
D. 170 square units
d(n)=3(−2)^ n−1
What is the 4th term in the sequence?
Answer: -24
Step-by-step explanation:
3(-2)^(4-1)=3*-8=-24
what is the slope of the line 3x-4y=7
Find the greatest common monomial factor : 4a^5b^2 and ab
For a car traveling at a speed of 50 miles per hour, the relationship between the distance traveled, d, and the time traveled, t, is described by the function d = 50t. Which statement is true?
Answer:
The distance traveled is based on the time traveled.
Step-by-step explanation:
I did this question.
The inverse of the given function is t(d) = d/50. The time taken to travel 180 miles is 3.6 hours.
What is speed?Speed is measured as distance moved over time. The formula for speed is speed = distance ÷ time. To work out what the units are for speed, you need to know the units for distance and time. In this example, distance is in metres (m) and time is in seconds (s), so the units will be in metres per second (m/s).
Speed = Distance/ Time.
Here, we have,
It is given that a car travels at a constant speed of 50 miles per hour. A function for distance traveled is also given as d(t)=50t.
It is required to find the inverse of the function by expressing the time travel in terms of distance traveled and also find t(180).
To find the inverse, express time traveled in terms of distance traveled using normal algebraic methods and then substitute 180 for t and explain its results.
Step 1 of 2
The given function is d(t)=50t.
Consider d(t) as d and t as t(d) and rewrite the equation.
The rewritten function is d=50 t(d)
Divide by 50 on both sides of the equation.
d/ 50 =50 t(d)/50
t(d) = d/50
Step 2 of 2
Substitute 180 for $t$ in the simplified expression and interpret the results.
t(d) = 180/50
= 3.6
The time taken to travel 180 miles is 3.6 hours.
Hence, The inverse of the given function is t(d) = d/50. The time taken to travel 180 miles is 3.6 hours.
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Which of the expressions are NOT polynomials? Check all that apply.
A. x^2-(square root of x)-3
B. 4 - 3x + 5x^6
C. 5x^1/2 + 4x^2
D. 14x^7
E. x^2-x-12/x+3
F. 8x^10 + 2x^5 ...?
Answer:
A, C, E are not polynomials
Step-by-step explanation:
Identify the expressions that are not polynomials
A. x^2-(square root of x)-3
Polynomial cannot have a square root. so it is not polynomial
B. 4 - 3x + 5x^6
C. 5x^1/2 + 4x^2
A polynomial does not have fractional exponent
D. 14x^7
E. x^2-x-12/x+3
Polynomial cannot have x in the denominator
F. 8x^10 + 2x^5
Two numbers add to 436 and the first is 34 bigger than the second. what are the two numbers?
What is 86.69 rounded to the nearest dollar?
Sams dog weighs 72 pounds. the vet suggests that for the dogs health tis weight should decrease by 12.5 percent. according to the vet what is a healthy weight for the dog?
The standard form of the equation of a parabola is x = y2 + 10y + 22. What is the vertex form of the equation?
Answer:
The vertex form of the parabola is [tex]x=(y+5)^2-3[/tex]
C is the correct option.
Step-by-step explanation:
The standard form of the parabola is [tex]x=y^2+10y+22[/tex]
We can write this equation in vertex form by using the completing square method.
For the expression [tex]y^2+10y[/tex], the value of b is 10.
Hence, add and subtract [tex](\frac{10}{2})^2=25[/tex] to the right side of the equation.
Thus, the equation becomes
[tex]x=y^2+10y+25-25+22[/tex]
Now, the expression [tex]y^2+10y+25=(y+5)^2[/tex]
Hence, we have
[tex]x=(y+5)^2-25+22[/tex]
We can simplify further as
[tex]x=(y+5)^2-3[/tex]
Hence, the vertex form of the parabola is [tex]x=(y+5)^2-3[/tex]
C is the correct option.
Rewrite the radicand as two factors, one of which is a perfect cube.
Answer:
[tex]\sqrt[3]{373248}=\sqrt[3]{18^{3}*64}\\[/tex]
Step-by-step explanation:
A Perfect Cube is an integer number multiple of three that can be expressed as a product of prime factors raised to 3rd power. We have many Perfect Cubes, such as:
15³=3³x5³, and 15 ∈ ={1,3,6,9,12,15,18,..} so 15 is a perfect cube
18³=2³x3³x3³ and 18 ∈ ={1,3,6,9,12,15,18,..} so 18 is a perfect cube.
Finally, for instance, we can rewrite the number 373248 as
cubic root of 18³ times 64. 18 is a perfect cube 64 is not a perfect cube for 64 =[tex]2^{6}[/tex]
Jane sells 8 times as many Volvos as Melissa. If the difference in their sales is 35, how many cars did Jane sell?
Melissa sold 5 Volvos. Given that Jane sold eight times as many Volvos as Melissa, Jane sold 40 Volvos.
Explanation:In order to solve this problem, we can use a simple equation. Let's denote the number of Volvos Melissa sold as 'x'. Since Jane sells 8 times as many Volvos as Melissa, the number of Volvos Jane sold can be denoted as '8x'. We know from the problem that the difference between the number of cars Jane and Melissa sold is 35, so we can write the equation like this: 8x - x = 35.
By simplifying the equation, we get 7x = 35. Therefore, to find the value of 'x', we divide 35 by 7, which gives us 'x' equals to 5.
But 'x' is the number of Volvos Melissa sold. To find out the number of cars Jane sold, we multiply 'x' by 8. Which gives us 5 multiplied by 8 equals to 40 cars.
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Convert 2.4 kg into cg. Please show your work.
Fiona wrote the linear equation y = 2/5 X -5. When Henry wrote his equation they discovered that his equation had all the same Solutions as fionas. which equation could have been Henry's.
A. X- 5/4y =25/4
B. X-5/2y=25/4
C. X-5/4y =25/4
D. X- 5/2y=25/2
To determine which equation could have been Henry's, we need to compare it to Fiona's equation. Option C, x - (5/4)y = 25/4, has the same solutions as Fiona's equation and could have been Henry's equation.
Explanation:To determine which equation could have been Henry's, we need to compare it to Fiona's equation, y = (2/5)x - 5. Henry's equation should have the same solutions as Fiona's, which means it should have the same slope and y-intercept.
Comparing the options:
A. x - (5/4)y = 25/4: This equation does not have the same slope as Fiona's. B. x - (5/2)y = 25/4: This equation has the same slope but a different y-intercept from Fiona's.C. x - (5/4)y = 25/4: This equation has the same slope and y-intercept as Fiona's.D. x - (5/2)y = 25/2: This equation does not have the same slope as Fiona's.Only option C, x - (5/4)y = 25/4, has the same solutions as Fiona's equation. Therefore, it could have been Henry's equation.
A population of rabbits doubles evey 4 months. if the population starts out with 8 rabbits how many rabbits will there be in 1 year
A scout troop is collecting aluminium cans for charity. Their goal is to collect at least the number of cans they collected last year, 5,489, in 6 months. Approximately how many cans does the scout troop need to collect every month to meet their goal?