For the parent function of y = x as sketched by Ana the transformation to get the equation y = 2(x + 7 ) is
translate to the left 7 units
vertical stretch by a factor of 2
What is transformation?A point, line, or geometric figure can be transformed in one of four ways, each of which affects the shape and/or location of the object.
Pre-Image refers to the object's initial shape, and Image, after transformation, refers to the object's ultimate shape and location.
The type of transformation involved here is translation and vertical stretch
form the parent function, y = x
translation of seven unites to the left results to y = x + 7
vertical stretch of 2 units results to y = 2(x + 7)
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Please help me solve this
Answer:
Step-by-step explanation:
This number is much larger than 1. You need to start at the decimal and move left (that's how scientific notation works for numbers larger than 1.)
So the answer is 1.0054 * 10 ^7
The person doing this started at the 1 and moved right until he/she hit the decimal. Wrong direction.
Which functions are a specific type of piecewise-defined functions?Quadratic functionsAbsolute value functionsCubic functionsLinear functions
Solution
The answer is
Absolute Value Function
How do you calculate F G and G of f?
You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
What is function ?
A function is a kind of rule that, for one input, it gives you one output. Image source: by Alex Federspiel. An example of this would be y=x2. If you put in anything for x, you get one output for y. We would say that y is a function of x since x is the input value.
Have given ,
Two functions , f(x) and g(x)
The composition of two functions g and f is the new function we get by performing f first, and then performing g. For example, if we let f be the function given by f(x) = x2 and let g be the function given by g(x) = x + 3, then the composition of g with f is called gf and is worked out as gf(x) = g(f(x)) .
So , You will be calculate the function F(G) = f(g(x)) and G(F) = g(f(x)).
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Faizah is paid $11 per hour for her work at a factory. She works 9 hours a day and 24 days a month. She saves $594 a month. Express the amount she saves as a percentage of her income.
Answer:
The amount she saves is 25% of her income
Step-by-step explanation:
She is paid $11 per hour
She works 9 hours per day
and for 24 days per month
So, she works 9(24) hours per month
= 216 hours per month
Now, she is paid $11 hourly, so for 216 hours,
she will have 11(216) = $2376
Total income = $2376 per month
Saving = $594 per month
As a percentage, we divide the savings by the total income,
savings/(total income) = 594/2376 = 1/4 = 0.25
Hence we get 25%
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
The additional information required to prove that ΔXYZ and ΔFEG are congruent is ∠Z ≅ ∠G and XZ ≅ FG or ∠Z ≅ ∠G and XY ≅ FE. So option 1 and 5 are correct.
Here in the figure it is given that ∠F and ∠X are congruent. To prove the triangle is congruent we have to prove that either two sides including the angles are congruent or another angle and included side is congruent.
When ∠Z ≅ ∠G and XZ ≅ FG, two angles and included sides are congruent, so triangles are congruent.
∠Z ≅ ∠G and ∠Y ≅ ∠E , we can not apply ASA, since three angles are mentioned
XZ ≅ FG and ZY ≅ GE , Two sides are given, ASA cannot be applied, we need two angles
XY ≅ EF and ZY ≅ FG, is not possible.
∠Z ≅ ∠G and XY ≅ FE, one corresponding side and two angles are equal, so ΔXYZ ≅ ΔFEG according to ASA.
So, the correct answer is option 1 and option 5.
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The complete question is as follows and image is given below
What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.
∠Z ≅ ∠G and XZ ≅ FG
∠Z ≅ ∠G and ∠Y ≅ ∠E
XZ ≅ FG and ZY ≅ GE
XY ≅ EF and ZY ≅ FG
∠Z ≅ ∠G and XY ≅ FE
Answer:
1 and 5 are correct
Step-by-step explanation:
someone pls help me with this question
Answer:
volume=0.000064\(m^{3}\)
mass=0.5888kg
Step-by-step explanation:
Jazmin cuts two pieces of construction paper, the first piece is 44 cm and try other is 33cm. She wants to cut the paper into strips that are equal . How wide should Jazmin cut each strip?
Answer:
11 cm
Step-by-step explanation:
Obtain the lowest common multiple of the first piece and the second piece :
Multiples of :
44 : 1, 2, 4, 11, 22, 44
33 : 1, 3, 11, 33
From the multiples above :
The lowest multiple common in both 44 and 33 is 11.
Hence, Jazmin can cut each strip to a width of 11 cm
637,982 + 2,819 i need it
Answer: 640801
Step-by-step explanation: Simply add both together, 637,982 plus 2819.
Answer:
637, 982 + 2,819 = 640,801
Solve the equation. Check your answers. |x-3|=9
To solve the equation |x-3|=9, we consider two cases: (x-3) = 9 and -(x-3) = 9. In the first case, we find that x = 12. In the second case, x = -6. To check our answers, we substitute them back into the original equation, and they satisfy the equation. Therefore, the solutions to the equation are x = 12 and x = -6.
To solve the equation |x-3|=9, we need to consider two cases:
Case 1: (x-3) = 9
In this case, we add 3 to both sides to isolate x:
x = 9 + 3 = 12
Case 2: -(x-3) = 9
Here, we start by multiplying both sides by -1 to get rid of the negative sign:
x - 3 = -9
Then, we add 3 to both sides:
x = -9 + 3 = -6
So, the two solutions to the equation |x-3|=9 are x = 12 and x = -6.
The equation |x-3|=9 means that the absolute value of (x-3) is equal to 9. The absolute value of a number is its distance from zero on a number line, so it is always non-negative.
In Case 1, we consider the scenario where the expression (x-3) inside the absolute value bars is positive. By setting (x-3) equal to 9, we find one solution: x = 12.
In Case 2, we consider the scenario where (x-3) is negative. By negating the expression and setting it equal to 9, we find the other solution: x = -6.
To check our answers, we substitute x = 12 and x = -6 back into the original equation. For both cases, we find that |x-3| is indeed equal to 9. Therefore, our solutions are correct.
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There is a line through the origin that divides the region bounded by the parabola y=5x−3x^2 and the x-axis into two regions with equal area. What is the slope of that line?
The slope of the line that divides the region bounded by the parabola \(y=5x-3x^2\)and the x-axis into two regions with equal area is 5.
To find the slope of the line that divides the region into two equal areas, we need to determine the point of intersection between the parabola and the x-axis. Since the line passes through the origin, its equation will be y = mx, where m represents the slope.
Setting the equation of the parabola equal to zero, we find the x-values where the parabola intersects the x-axis. By solving the equation\(5x - 3x^2 = 0\), we get x = 0 and x = 5/3.
To divide the region into two equal areas, the line must pass through the midpoint between these x-values, which is x = 5/6. Plugging this value into the equation of the line, we have y = (5/6)m.
Since the areas on both sides of the line need to be equal, we can set up an equation using definite integrals. By integrating the equation of the parabola from 0 to 5/6 and setting it equal to the integral of the line from 0 to 5/6, we can solve for m. After performing the integration, we find that m = 5.
Therefore, the slope of the line that divides the region into two equal areas is 5.
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The random variable X has the following probability density function
fx(x)=kx^6e^-0.02x ,x> 0, k is a constant.
Calculate E[X^2].
A 50
B300
с2,500
D10,000
E140,000
The value of E[X^2] is approximately 3.81228668939e-14. The correct option is E: 140,000.
Step 1: Find the value of the constant k.
To do this, we integrate the probability density function over its entire range and set it equal to 1:
∫(kx^6e^(-0.02x)) dx = 1
Using integration by parts, we can simplify the integral as follows:
Let u = x^6 and dv = k e^(-0.02x) dx.
Then, du = 6x^5 dx and v = (-50/k) e^(-0.02x).
Applying the integration by parts formula, we have:
∫(kx^6e^(-0.02x)) dx = (-50/k) x^6 e^(-0.02x) - ∫((-50/k) e^(-0.02x) * 6x^5) dx
= (-50/k) x^6 e^(-0.02x) + (300/k) ∫(x^5 e^(-0.02x)) dx
Step 2: Solve the integral for ∫(x^5 e^(-0.02x)) dx.
This integral can be evaluated using integration by parts multiple times or by using other techniques like substitution. For brevity, I'll provide the final result:
∫(x^5 e^(-0.02x)) dx = -6250 e^(-0.02x) (x^5 + 10x^4 + 40x^3 + 80x^2 + 80x + 32) / (0.04^6)
Step 3: Calculate E[X^2].
Now that we have the integral expression for ∫(kx^6e^(-0.02x)) dx, we can calculate E[X^2] by evaluating the integral:
E[X^2] = ∫(x^2 * kx^6e^(-0.02x)) dx
= k ∫(x^8 e^(-0.02x)) dx
Using the same techniques as before, we integrate the expression and obtain a result that is quite lengthy. For simplicity, I'll provide the final result:
E[X^2] = 8192000000 / (k * 0.0004^9) - 400000000 / (k * 0.0004^8) + 25000000 / (k * 0.0004^7)
Step 4: Calculate the value of k.
To find the value of k, we use the fact that the probability density function must integrate to 1. Therefore:
∫(kx^6e^(-0.02x)) dx = 1
By evaluating the integral, we obtain the following equation:
(50/k) - 300 / (k * 0.0004^6) = 1
Simplifying the equation and solving for k, we find k ≈ 0.0004.
Step 5: Calculate the numerical value of E[X^2].
Substituting the value of k into the expression for E[X^2], we have:
E[X^2] = 8192000000 / (0.0004^10) - 400000000 / (0.0004^9) + 25000000 / (0.0004^8)
First, let's calculate the values of the denominators:
0.0004^10 = 1.048576e+28
0.0004^9 = 2.62144e+24
0.0004^8 = 6.5536e+20
E[X^2] = 8192000000 / 1.048576e+28 - 400000000 / 2.62144e+24 + 25000000 / 6.5536e+20
To perform the division, we can rewrite the expression using scientific notation:
E[X^2] = 7.80517578125e-20 - 1.52587890625e-16 + 3.81228668942e-14
Calculating each term separately:
E[X^2] ≈ -1.52587882837e-16 + 3.81228668942e-14
Adding the terms together:
E[X^2] ≈ 3.81228668939e-14
The correct option for E[X^2] is E: 140,000.
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The daily marginal revenue function associated with selling x widgets is given by R"(x) = -21x2 + 16x + 15 where R'(x) is measured in dollars per unit per day and x denotes the number of widgets produced and sold. (a) Determine the revenue function, R(x), associated with producing and selling x widgets. R(x) = (b) Determine the demand function relating unit price, p(x), to the quantity demanded, X. P(x)
The demand function relating unit price, p(x), to the quantity demanded, x, is: P(x) = -7x^2 + 8x + 15
(a) To determine the revenue function, we need to integrate the marginal revenue function R"(x).
R'(x) = -21x^2 + 16x + 15
Integrating R'(x) gives us the revenue function:
R(x) = -7x^3 + 8x^2 + 15x + C
where C is the constant of integration. Since we want to find the revenue associated with producing and selling x widgets, we can set C = 0.
Therefore, the revenue function associated with producing and selling x widgets is:
R(x) = -7x^3 + 8x^2 + 15x
(b) To determine the demand function, we need to use the inverse demand method.
First, we need to solve for the unit price, p(x), in terms of the quantity demanded, x. We know that revenue, R(x), is equal to the product of the unit price, p(x), and the quantity demanded, x:
R(x) = p(x) * x
Substituting the revenue function we found in part (a), we get:
-7x^3 + 8x^2 + 15x = p(x) * x
Solving for p(x), we get:
p(x) = (-7x^2 + 8x + 15)
Therefore, the demand function relating unit price, p(x), to the quantity demanded, x, is:
P(x) = -7x^2 + 8x + 15
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To study the sleeping habits of all band members in his school, Christopher collects data from all the band members in his class. Which type of sampling is used
The type of sampling used in this scenario is A Systematic sampling.
Systematic sampling involves selecting every kth element from a population list after randomly selecting a starting point. In this case, Christopher collects data from all the band members in his class, indicating that he is sampling systematically from a known list of band members.
This method ensures that every band member in the class has an equal chance of being selected, and it simplifies the process by following a predetermined systematic approach rather than relying on random selection or stratification.
Therefore, the type of sampling used in this scenario is A Systematic sampling.
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Complete question is below
To study the sleeping habits of all band members in his school, Christopher collects data from all the band members in his class. Which type of sampling is used? Select the correct answer below:
A Systematic sampling
B Stratified sampling
C Cluster sampling
D Convenience sampling
The amount of motor oil used during the month by the local stock car racing team is g(t) hundred gallons, where t is the number of months past March of a given year.
(a) Write a sentence of interpretation for
g(4) = 13.10.
The answer is "The local inventory car racing team used 1310 gallons of engine oil in July".
The function consists of 3: input, output, as well as the relationship between the two.The interpretation of a mathematical formalism is to derive important data from a line chart or given symbolic image.Therefore, the amount of oil that the regional sports car racing team is using during the month is G(t), which is 100 gallons, wherein T is the number of months that very last March.Given:
\(\to \bold{g(4) = 13.10}\)
If \(\bold{g(4)=13.10}\) means that \(\bold{1310 }\) gallons of motor oil was used by the local stock car racing squad in July.So, the final answer is "The local inventory car racing team used 1310 gallons of engine oil in July".Learn more:
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Which equation represents a quadratic relation?
a) y = 4x^2
b) y = 4x
c) y = 4x + 4
d) y = x^3
Answer:
a) y = 4x^2
Step-by-step explanation:
Because in a) y = 4x^2 the degree of equation is 2.
the Marked price of watch is rupees 12000 discount of 15% is allowed and 10% VAT is added on it find the selling price of a watch with VAT
Step-by-step explanation:
selling price after 15%discount
=12000-(15/100)*12000
=12000-1800
=10200
after 10% VAT
S.P=110% of 10200
=(110/100)*10200
=11220
Suppose a deep sea diver dives from the surface to 85 feet below the surface. He then dives down
14 more feet. The diver's depth is represented by the sum - 85+ (-14). Find and interpret the sum to
describe the diver's present depth.
Find the sum.
- 85+ (-14) =
What is the diver's present depth?
O-99 feet below the surface
- 71 feet below the surface
O 71 feet below the surface
O 99 feet below the surface
Answer:
Pretty sure it'd be -99 feet below the Surface.
Step-by-step explanation:
If we call 85 the ground level since he stopped and will then dive down another 14,
85 - another 14 =
-99 Feet below the surface?
A certain basketball player practices shooting free throws over and over again. The shots are independent, with probability p of success.
a) In n shots, what is the expected number of streaks of 7 consecutive successful shots? (Note that, for example, 9 in a row counts as 3 streaks.)
b) Now suppose that the player keeps shooting until making 7 shots in a row for the first time. Let X be the number of shots taken. Sow the E(X) <= 7/p^7.
The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p7, where n is the number of shots and p is the probability of success.The probability of making 7 consecutive successful shots in exactly k shots is given by Pk = (1-p)k-7 * p7. The expected value of X is given by E(X) = [k=7,] k. We can use the formula for the sum of an infinite geometric series to simplify the expression and evaluate the numerator of the expression. Thus, E(X) 7 / p7.
a) In n shots, the expected number of streaks of 7 consecutive successful shots is given by the formula below:The expected number of streaks of 7 consecutive successful shots in n shots = (n - 6) * p^7, where n is the number of shots and p is the probability of success. In other words, for each block of 7 shots, we have a probability of p^7 of making 7 consecutive successful shots, and there are (n-6) blocks of 7 shots in n shots. Therefore, the expected number of streaks of 7 consecutive successful shots is the product of these two values.
b) We know that X is the number of shots taken until the player makes 7 consecutive successful shots for the first time. Therefore, X is a random variable that follows the geometric distribution with parameter p. The probability of making 7 consecutive successful shots in exactly k shots is given by:Pk = (1-p)^{k-7} * p^7Therefore, the expected value of X is given by:E(X) = Σ[k=7,∞] k * PkWe can use the formula for the sum of an infinite geometric series to simplify this expression:
\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (1 - (1-p)^7)\) We can also use the formula for the sum of a geometric series to simplify the denominator:
\(E(X) = Σ[k=1,∞] k * (1-p)^{k-1} * p^7 / (p^7 + Σ[j=1,6] (1-p)^j * p^7)\)
\(E(X) = (p^7 * Σ[k=1,∞] k * (1-p)^{k-1}) / (p^7 * (1 + Σ[j=1,6] (1-p)^j))\)
\(E(X) = (1 / p^7) * (Σ[k=1,∞] k * (1-p)^{k-1}) / (1 + Σ[j=1,6] (1-p)^j)\)
We can use the formula for the derivative of a geometric series to evaluate the numerator of this expression:
\(Σ[k=1,∞] k * (1-p)^{k-1} = d/dp\)
Σ[k=1,∞] (1-p)^k
= d/dp (1-p) / (1 - (1-p))²
= 1 / p^2
Therefore, \(E(X) = (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^2) ≤ (1 / p^7) * (1 / (1 + Σ[j=1,6] (1-p)^j)) * (1 / p^7) = 1 / p^{14} ≤ 7 / p^7\)
Thus, \(E(X) ≤ 7 / p^7.\)
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The table shows the number of practice problems completed in 30 minutes in three samples of 10 randomly selected math students.
Which statement is most accurate based on the data?
O A. A prediction based on the data is not completely reliable, because the means are too close together.
B. A prediction based on the data is reliable, because each sample has 10 data points. O
C. A prediction based on the data is reliable, because the means of the samples are close together.
D. A prediction based on the data is not completely reliable, because the means of samples 1 and 2 are greater than 16 and the mean of sample 3 is less than 16.
Answer: C. a prediction based on the data is reliable, because the means of the samples are close together.
Step-by-step explanation:
Solve the system of equations.
4 x - 4 y = 10
3 x + 2 y = 5
Is the point (5, –9) a solution in the equation y < -x -3
Answer:
yes, because if you input 5 for x it would be -8
and if u input -9 for y it is right as -8 is closer to 0 than -9
PLEASE ILL DO ANYTHING I ALREADY OFFERED AS MUCH POINTS AS POSSIBLE
Answer:
A, B, D, E
Step-by-step explanation:
Given expression:
(0.06) · (0.154)When multiplying decimals, multiply as if there are no decimal points:
\(\implies 6 \times 154 = 924\)
Count the number of digits after the decimal in each factor:
0.06 → 2 digits0.154 → 3 digitsTherefore, there is a total of 5 digits.
Put the same number of total digits after the decimal point in the product:
\(\implies (0.06) \cdot (0.154)=0.00924\)
-----------------------------------------------------------------------------------------------
Answer option A
\(\boxed{6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}}\)
When dividing by multiples of 10 (e.g. 10, 100, 1000 etc.), move the decimal point to the left the same number of places as the number of zeros.
Therefore:
6 ÷ 100 = 0.06154 ÷ 1000 = 0.154\(\implies 6 \cdot \dfrac{1}{100} \cdot 154 \cdot \dfrac{1}{1000}=(0.06) \cdot (0.154)\)
Therefore, this is a valid answer option.
Answer option B
\(\boxed{6 \cdot 154 \cdot \dfrac{1}{100000}}\)
Multiply the numbers 6 and 154:
\(\implies 6 \times 154 = 924\)
Divide by 100,000 by moving the decimal point to the left 5 places (since 100,000 has 5 zeros).
\(\implies 6 \cdot 154 \cdot \dfrac{1}{100000}=0.00924\)
Therefore, this is a valid answer option.
Answer option C
\(\boxed{6 \cdot (0.1) \cdot 154 \cdot (0.01)}\)
Again, employ the technique of multiplying decimals by first multiplying the numbers 6 and 154:
\(\implies 6 \cdot 154 = 924\)
Count the number of digits after the decimal in each factor:
0.1 → 1 digit0.01 → 2 digitsTherefore, there is a total of 3 digits.
Put the same number of digits after the decimal point in the product:
\(\implies 0.924\)
Therefore, as (0.06) · (0.154) = 0.00924, this answer option does not equal the given expression.
Answer option D
\(\boxed{6 \cdot 154 \cdot (0.00001)}\)
Again, employing the technique of multiplying decimals.
As there are a total of 5 digits after the decimals:
\(\implies 6 \cdot 154 \cdot (0.00001)=0.00924\)
Therefore, this is a valid answer option.
Answer option E
\(\boxed{0.00924}\)
As we have already calculated, (0.06) · (0.154) = 0.00924.
Therefore, this is a valid answer option.
You have a frame that holds three pictures. You pulled out your favorite five photos. How many sets of three are there? Make a list of all the possible combinations using the numbers 1 - 5 to represent the photos. (I NEED FULL EXPLAINATION)
Answer:
10
Step-by-step explanation:
nCr = 5!/(3! × (5 - 3)!)
= 10
123/ 124/ 125/ 134/ 135/ 145/ 234/ 235/ 245/ 345
The formula for combinations is generally n! / (r! (n -- r)!), where n is the total number of possibilities to start and r is the number of selections made. In our example, we have 52 cards; therefore, n = 52.
Answer: get 2 more frames
Step-by-step explanation:
the procedure for identifying or indicating the value of cases on a variable
Specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.
What is a Variable?
A variable is a quantity that can change in the context of a mathematical problem or experiment. We usually use one letter to represent a variable. The letters x, y, and z are common general symbols used for variables.
The procedure for identifying or indicating the value of cases on a variable is commonly known as data coding or data labeling. It involves assigning specific numerical or categorical values to represent different categories or levels of a variable.
Here is the general procedure for encoding variables:
Define the variable: Start by clearly defining the variable you want to code. Understand its nature (eg nominal, ordinal, interval or ratio) and the categories or levels it covers.
Determine the encoding scheme: Decide on the encoding scheme you will use to represent the variable. For nominal variables (categories without their own order), you can assign numbers or labels to each category. For ordinal variables (categories with a meaningful order), you can assign numbers or labels that reflect the order. For interval or ratio variables, the numerical values themselves can indicate the value of the variable.
Assign Codes: Assign specific codes or labels to represent each category or level of the variable. These codes can be numbers, letters, or any other symbol you choose. Make sure the codes are unique and do not overlap.
Apply Coding: Apply assigned codes to matching cases or observations in your dataset. Depending on the software or tool you are using, there are different ways to do this. You can manually enter codes, use syntax or programming commands, or use data transformation functions.
Verify your coding: Double-check your coding to ensure accuracy. Review a sample of the coded cases to ensure they match the intended coding scheme. This step is essential to avoid errors and inconsistencies in your data.
It is important to note that specific procedures and techniques for coding variables may vary depending on the context, research area, or data analysis software used.
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6.051x10^5 in standard form
Answer:
605100
Step-by-step explanation:
= 6.051 × 105
(scientific notation)
= 6.051e5
(scientific e notation)
= 605.1 × 103
(engineering notation)
(thousand; prefix kilo- (k))
= 605100
(real number)
MARKING BRAINLIEST!
Two numerical patterns are shown below:
Pattern A: 6, 12, 18, 24, 30
Pattern B: 12, 24, 36, 48, 60
Select the statement that describes the numerical patterns.
A. The rule for Pattern B is "multiply by 2."
B. The rule for Pattern A is "multiply by 2."
C. Each term in Pattern B is one half the corresponding term in Pattern A.
D. Each term in Pattern A is one half the corresponding term in Pattern B.
Answer:
D
Step-by-step explanation:
A cube has a surface area of 126 feet. What is the area of one face?
Answer:
21 square feet
Step-by-step explanation:
A cube has 6 faces, therefore 126/6 = 21 sq/ft the area of 1 face
The area of one face of a cube is 21 feet.
What is the surface area of cube?Surface area of cube is the sum of areas of all the faces of cube, that covers it.
The formula for surface area is equal to six times of square of length of the sides of cube.
A cube has a surface area of 126 feet.
The area of one face is given by;
\(\rm Area \ of \ one \ face=\dfrac{Surface \ area}{Total \ number \ of \ faces}\\\\ Area \ of \ one \ face=\dfrac{126}{6}\\\\ Area \ of \ one \ face=21\)
Hence, the area of one face of a cube is 21 feet.
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f(5)= 2(5)+ 4
Thanks
Answer: I HOPE IT HELPS OR WATCH VIDOES ABOUT IT
Step-by-step explanation:
Two unique points define a line. Other geometric figures also may pass through those two points (you will learn those later).
There are several forms of the equation of a line:
Standard form Ax + By = C
Slope-intercept form y = mx + b
Point-slope form y – y1 = m(x – x1)
Two-point form y – y1 = [ (y2 – y1)/(x2 – x1) ](x – x1)
O.K., you picked the two-point form, right?
The points are P1: (5,5) and P2: (7,-4)
y - 5 = [ ((-4) - 5)/(7 - 5) ] (x - 5) (put in x and y values of points)
y - 5 = [ -9 / 2 ](x - 5) (simplify)
y - 5 = -9/2x + 45/2 (distribute -9/2)
y = f(x) = -9/2x + 55/2 (add 5 to both sided)
Check (very important):
Is (5,5) on the line? 5 = (-9/2)(5) + 55/2 ?
5 = -45/2 + 55/2 ?
5 = 10/2 yes.
Is (7,-4) on the line? -4 = (-9/2)(7) + 55/2 ?
-4 = -63/2 + 55/2 ?
-4 = -8/2 ? yes.
There are 45 students in a speech contest. Yesterday, 2/3 of them gave their speeches. Today, 4/5 of the remaining students gave their speeches. How many students still haven't given their speeches
What the correct answer now
Answer:
14.3
Step-by-step explanation:
first find length of VW
10/sin 119 = VW/ sin 26
VW = 5
angle V = 180 - 119 - 26 = 35
then area = 1/2 ab sin C
1/2 (10)(5) sin 35 = 14.33941.....