As tan45 is equal to 1:
\(12\tan 45=12\)PLS HELP!! BRAINLIEST WILL BE REWARDED!!!
Answer: y = 5 when x=3
Step-by-step explanation:
The table already provides the results of the function for several values of x. By golly, x = 3 is among them, and it reports y, at that value of x, is 5,
A researcher tests the hypothesis that people who live in Florida spend less money on clothes than people who live in Pennsylvania because the weather is nicer. One hundred people who live in Florida and one hundred people who live in Pennsylvania are randomly selected and asked how much money they spend on clothes per year. In this study, what is the independent variable
The independent variable in this study is the place of residence, specifically whether the participants live in Florida or Pennsylvania.
The researcher is interested in examining the relationship between the location of residence and the amount of money spent on clothes. By selecting participants from both Florida and Pennsylvania, the researcher can compare the spending habits of individuals from these two locations and determine if there is a significant difference. Thus, the independent variable is the categorical variable that defines the groups being compared, which in this case is the place of residence.
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Where would I put the dot according to the directions?
Answer:
u would go 3 to the right three and down three from the origin
Step-by-step explanation:
Choose all sequences of transformations that produce the same image of a given figure.
a reflection across the y-axis followed by a clockwise rotation 90° about the origin
a reflection across the y-axis followed by a counter-clockwise rotation 90° about the origin
a clockwise rotation 90° about the origin followed by a reflection across the x-axis
a counter-clockwise rotation 90° about the origin followed by a reflection across the y-axis
a reflection across the x-axis followed by a counter-clockwise rotation 90° about the origin
Answer:
a b
Step-by-step explanation:
Answer:
All of these transformations are equivalent to reflection across the line y=x:
A. a reflection across the y-axis followed by a clockwise rotation 90° about the origin
C. a clockwise rotation 90° about the origin followed by a reflection across the x-axis
D. a counter-clockwise rotation 90° about the origin followed by a reflection across the y-axis
E. a reflection across the x-axis followed by a counter-clockwise rotation 90° about the origin
Step-by-step explanation:
EDGE
Answer the following questions based on this word problem:
The Beck family is planning on renting a car for their vacation. The two rental car companies have
different pricing plans.
Company A is $0.10 per mile and $25 a day.
Company B is $0.05 per mile and $40 a day.
Let x represent the number of miles and y represents the cost. They are only renting the van for 1 day.
Answer:
Step-by-step explanation:
A: $0.1(x) + 25(y) = x + 25
B: $0.05(x) + $40(y) = x + 40
Because they didn't give a certain amount of miles traveled, we have to go with we do know.
**this is probably wrong.
Find a polar equation of the form r = f(theta) for the curve represented by the Cartesian equation x = 3.
*NOTE*: Since theta is not a symbol on your keyboard, use t  in place of theta in your answer.Â
r =Â
the polar equation of the form r = f(t) for the curve represented by the Cartesian equation x = 3.sec(t)
To find a polar equation for the given Cartesian equation x = 3, we need to convert it into polar form. We know that x = rcos(t) and substituting x = 3, we get 3 = rcos(t). Solving for r, we get r = 3/cos(t) which simplifies to r = 3sec(t). The polar coordinate system uses an angle t (or theta) and a distance r to describe a point in the plane. To convert a Cartesian equation to polar form, we need to express x and y in terms of r and t. In this case, we are given x = 3. We know that x = rcos(t), so we substitute x = 3 into this equation and get 3 = rcos(t). Solving for r, we get r = 3/cos(t). This can be simplified to r = 3sec(t), which is our polar equation of the form r = f(t).
In this equation, sec(t) is the reciprocal of cos(t), which means that the value of r will get larger as cos(t) gets smaller (i.e. as t approaches 90 degrees or pi/2 radians). This makes sense since the Cartesian equation x = 3 represents a vertical line passing through the point (3,0) on the x-axis. As we move up the line (in the positive y direction), the distance from the origin increases and the angle t approaches 90 degrees. Therefore, the value of r should get larger as t approaches 90 degrees, which is exactly what our polar equation shows.
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Find the area of the part of the plane z=ax+by+c that projects onto a region in the xy-plane with area A.
The area of the part of the plane z = ax + by + c that projects onto a region in the xy-plane with area A is \(\sqrt{1+a^2+b^2} A\).
What is the formula for calculating the area of the part of a plane surface?The formula for calculating the surface area of the required part of the plane when projected onto a region in the xy-plane is
\(\int\int_D\sqrt{1+(\frac{\partial z}{\partial y})^2+(\frac{\partial z}{\partial x})^2 } dA\)
Where D is the projection of the surface on the xy-plane with area A.
Calculation:The given plane is z = ax + by + c
Calculating the partial differentiation of z w.r.t x and y:
\(\frac{\partial z}{\partial x}=\frac{\partial}{\partial x}(ax + by + c)\)
= a
Similarly,
\(\frac{\partial z}{\partial y}=\frac{\partial}{\partial y}(ax + by + c)\)
= b
Then, calculating the surface area,
A(S) = \(\int\int_D\sqrt{1+(\frac{\partial z}{\partial y})^2+(\frac{\partial z}{\partial x})^2 } dA\)
= \(\int\int_D\sqrt{1+(b)^2+(a)^2 } dA\)
= \(\sqrt{1+a^2+b^2}\int\int_DdA\)
Since the area of the xy-plane is A, the integration over dA becomes A.
Thus,
Surface area = \(\sqrt{1+a^2+b^2}A\)
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HELP ASAP
WORTH 10 POINTS
Answer:
0.15 InchesStep-by-step explanation:Ok so here AVERAGE HEIGHT OF BLUEBIRD = 4 1/4 INCHES WHICH IS 4.25 and the AVERAGE HEIGHT OF REDBIRD WHICH IS 4.4 Now we substract 4.4-4.25= 0.15What is the missing reason in Step 7? Triangle angle sum theorem quadrilateral angle sum theorem definition of complementary consecutive ∠s in a ▱ are supplementary
Answer:
Hello your question is incomplete attached below is the complete question
Given: wxyz is a parallelogram, zx ≅ wy prove: wxyz is a rectangle what is the missing reason in step 7? a. triangle angle sum theorem. b. quadrilateral angle sum theorem. c. definition of complementary. d. consecutive ∠s in a ▱ are supplementary. 1. wxyz is a ▱; zx ≅ wy 1. given 2. zy ≅ wx 2. opp. sides of ▱ are ≅ 3. yx ≅ yx 3. reflexive 4. △zyx ≅ △wxy 4. sss ≅ thm. 5. ∠zyx ≅ ∠wxy 5. cpctc 6. m∠zyx ≅ m∠wxy 6. def. of ≅ 7. m∠zyx + m∠wxy = 180° 7. ? 8. m∠zyx + m∠zyx = 180° 8. substitution 9. 2(m∠zyx) = 180° 9. simplification 10. m∠zyx = 90° 10. div. prop. of equality 11. wxyz is a rectangle 11. rectangle ∠ thm.
answer: consecutive angles of any parallelogram are supplementary
Step-by-step explanation:
The missing reason in step 7 is : consecutive angles of any parallelogram are supplementary i.e. m∠ZYX + m∠WXY = 180°
Reason : ZY || WX also XY is the transversal line hence ∠wyx and ∠wxy are the consecutive angles on lines ZY and WX therefore m∠ZYX + m∠WXY = 180° ( sum of consecutive angles )
Answer:
D. consecutive ∠s in a ▱ are supplementary
Step-by-step explanation:
edge2021
WHOEVER DOES MOST ASAP GETS AN EXTRA 50 POINTS
The figures converted from fraction to decimal to percent (Questions 9-14) are given as follows:
Percent Decimal Fraction
9) 316.2%. 3.162 3 4861/30000
10) 6.94%. 0.0694 347/5000.
11) 15.27%. 0.1527 1527/10000
12) 217 2761/3367% 2.178 1089/500
13) 723 12/21% 7.236 1809/250
14) 87% 0.87 87/100
9) Given the compound fraction: 3 4861/30000
To convert 3 4861/30000 to a decimal, we first need to convert the mixed number to an improper fraction:
3 4861/30000 = (30000*3 + 4861)/30000
= 94861/30000
To convert this fraction to a decimal, we divide the numerator by the denominator:
94861/30000 ≈ 3.162
To convert 3 4861/30000 to a percentage, we multiply the decimal by 100:
3.162 x 100 ≈ 316.2%
So, 3 4861/30000 as a percentage is approximately 316.2%
10) Given the decimal 0.0694
To convert 0.0694 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:
0.0694 = 694/10000
We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:
694/10000 = (3472)/(50002) = 347/5000
So, 0.0694 as a fraction is 347/5000.
To convert 0.0694 to a percentage, we multiply the decimal by 100:
0.0694 x 100 = 6.94%
So, 0.0694 as a percentage is 6.94%.
11) Given the decimal - 0.1527
To convert 0.1527 to a percentage, we multiply the decimal by 100:
0.1527 x 100 = 15.27%
So, 0.1527 as a percentage is 15.27%.
To convert 0.1527 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:
0.1527 = 1527/10000
12) Given the compound percentage - 217 2761/3367%
To convert 217 2761/3367% to a decimal, we first need to convert the mixed number to an improper fraction:
217 2761/3367% = (3367*217 + 2761)/3367% = 733400/3367%
743032/3367% = 217.82001782%
217.82001782% = 2.1782001782
220.680724681% \(\approx\) 2.178
Thus, in fraction:
2.178 = 2.178/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000
= 2.178/1 x 1000/1000
= 2178/1000
= 1089/500
13) Given the compound fraction - 723 12/21%
To convert 723 12/21% to a decimal, we first need to convert the mixed number to an improper fraction:
723 12/21% = (21*723 + 12)/21% = (15195/21)%
(15315/21)% = 7.23571428571
15315/21% \(\approx\) 7.236
Converting 7.236 to fraction:
7.236 = 7.236/1
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 10³ = 1000
= 7.236/1 x 1000/1000
= 7236/1000: Divide numerator and denominator by 4
= (7236÷ 4)/(1000÷4)
= 1809/250
14) Given 0.87:
To convert 0.87 to a percentage, we multiply the decimal by 100:
0.87 x 100 = 87%
So, 0.87 as a percentage is 87%.
To convert 0.87 to a fraction, we can write it as the numerator over a power of 10, where the power of 10 has the same number of digits as the number of decimal places in the original number:
0.87 = 87/100
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Exit
From the information in the graph, what is the mean number of books the girls read?
A. 3
B. 4
C. 5
D. 6
Answer:
C
Step-by-step explanation:
\( \frac{10 + 5 + 3 + 2 +5 }{5} = \frac{25}{5} = 5\)
WILL MARK AS BRAINLEIST!!!!
I have more questions on my account of anyone can help me out!!
The question is in the picture!
We need to integrate the function
y = 2x - x² with respect to x, from x = 0 to x = 2.
The graph of the function intersects the x-axis at x = 0 and x = 2.
So,
Area of region R = ∫[0,2] (2x - x²) dx
= [x² - (1/3)x³] from 0 to 2
= [2² - (1/3)(2)³] - [0² - (1/3)(0)³]
= 4/3
Now, let's find the equation of the line y = cx. Since the line passes through the origin (0,0), we have y = cx.
To find the value of c that divides the region R into two equal subregions, we need to find the value of x where the
area under the curve y = 2x - x² is equal to the area under the line y = cx.
∫[0,a] (2x - x²) dx = ∫[0,a] cx dx
[2x²/2 - x³/3] from 0 to a = [c/2 x²] from 0 to a
2a²/2 - a³/3 = c/2 a²
We multiply both sides by 6, we get:
12a² - 2a³ = 3ac
2a² - (1/3)a³ = (1/2)ac
2a - (1/3)a² = (1/2)c
c = (4a - (2/3)a²)/2
We know that the area under the line is equal to the area under the curve up to the point of intersection, we have:
∫[0,a] (2x - x²) dx = ∫[0,a] (cx) dx - ∫[a,2] (2x - x²) dx
2a²/2 - a³/3 = c/2 a² - 2a² + (8/3)a³ - 4a + (4/3)a²
10a³/3 - 7a² + 4a = 0
a = 0, 1.4105, -0.6172
The only value of a that is within the range 0 to 2 is a = 1.4105. Substituting this value into the equation for c, we get:
c = (4a - (2/3)a²)/2 = 1.636
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tally the data into a frequency distribution using 100 as a class interval and 0 as a starting point
The data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0.
To create a frequency distribution, we group the data into intervals or classes and count the number of data points falling within each interval. The class interval represents the range of values covered by each class, and the starting point determines the first interval.
Here is an example of how the data can be tallied into a frequency distribution using a class interval of 100 and a starting point of 0:
```
Class Interval Frequency
0 - 99 12
100 - 199 18
200 - 299 24
300 - 399 15
400 - 499 10
500 - 599 8
600 - 699 5
700 - 799 3
800 - 899 2
900 - 999 1
```
In this frequency distribution, the data is divided into classes based on the class interval of 100. The first class, from 0 to 99, has a frequency of 12, indicating that there are 12 data points falling within that range. The process is repeated for each subsequent class interval, resulting in a frequency distribution table.
By organizing the data into a frequency distribution, we gain insights into the distribution and patterns within the dataset. It provides a summarized view of the data, allowing us to identify the most common or frequent values and analyze the overall distribution.
In summary, the data has been tallied into a frequency distribution using a class interval of 100 and a starting point of 0. The frequency distribution table presents the number of data points falling within each class interval, enabling a better understanding of the distribution of the data.
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Someone pleaseee help I’m struggling
Step-by-step explanation:
(0,5) and (-2,-3)
y=mx+b
find m
\( \frac{y1 - y2}{x1 - x2} \\ = \frac{5 - ( - 3)}{0 - ( - 2)} \\ = \frac{8}{2} \\ = 4 \\ \)
m=4
Substitute (0,5) or (-2,-3)
For easy processing substitute : (0,5)
y=4x+b
5=b
y=4x+5 is the answer
Brainliest please~
If A is m by n and B is n by m, explain why
Do an example with m < n and an example with m > n. Why does your second example automatically have det(AB) = 0?
For my examples, I took
My main problem is with the aforementioned A and B, how do I do? How do I work with a matrix of matrices?
when multiplying two matrices A and B with m>n, the product AB will always result in a square matrix with linearly dependent rows or columns, causing its determinant to be 0.
To explain why the product of matrices A and B has det(AB)=0 when m>n, let's first understand the basics of matrix multiplication and determinants.
Matrix multiplication: If A is an m by n matrix and B is an n by m matrix, then their product AB is an m by m square matrix. To calculate the product, the number of columns in A (n) must be equal to the number of rows in B (n).
Determinants: The determinant is a scalar value that can be computed for any square matrix (i.e., the number of rows and columns are equal). The determinant is used to understand certain properties of the matrix, such as invertibility. If the determinant is 0, the matrix is singular and not invertible.
Example 1 (m < n): Let A be a 2x3 matrix and B be a 3x2 matrix. Their product AB is a 2x2 square matrix. The determinant can be calculated for AB, but not for A or B, as they are not square matrices.
Example 2 (m > n): Let A be a 3x2 matrix and B be a 2x3 matrix. Their product AB is a 3x3 square matrix. Since m > n in this case, the resulting product matrix will have linearly dependent rows or columns, which implies that its determinant will be 0.
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Which sequence is an example of an arithmetic sequence?
Question 9 options:
5, 10, 20, 40, 80, …
5, 10, 15, 20, 25, …
–3, –6, –18, –54, …
20, 10, 5, 2.5, …
Answer: the second sequence.
25- 20= 20-15=15-10=10-5.
From this we can see that the common difference is 5
Step-by-step explanation:
the base of a solid is the region bounded by the ellipse $$. find the volume of the solid given that cross sections perpendicular to the $$-axis are:
The volume of the solid is 16.75 unit³ in the given line x+2y=8 intercseting the x-axis, the y-axis.
What is volumes of Solids?
We shall encounter several solids and their corresponding volumes when discussing the concept of the volume of combination of solids. As is common knowledge, the surface areas and volumes of all three-dimensional shapes depend on their dimensions. As we can see in reality, numerous shapes are created by fusing a variety of shapes. For instance, the combination of a cone and cylinder shapes creates a tent. Similar to how a cone and a hemisphere combine to form an ice cream cone. As a result, the volume of the solids combined will equal the total of the volumes of the individual solids.
The line x+2y=8.
y = (8-x)/2
Volume will be V = π/2 ∫(r²) dr
So we have 1/3 π * r² * h
Here h = 8, r=2.
So V = 1/3 π * r² * h = 1/3 π * 2² * 8
V = 16.75 unit³
Hence ,the volume of the solid is 16.75 unit³
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a line passes through both points (-2, 2) and (8, 9). what is the angle between the line and the x axis?
Step-by-step explanation:
To find the angle between a line and the x-axis, we need to calculate the slope of the line first. The slope of a line passing through two points (x₁, y₁) and (x₂, y₂) is given by the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Using the points (-2, 2) and (8, 9), we can substitute the values into the formula:
m = (9 - 2) / (8 - (-2))
= 7 / 10
= 0.7
The slope of the line is 0.7. The angle between the line and the x-axis can be found using the inverse tangent (arctan) function. The tangent of an angle is equal to the slope of the line, so we can write:
tan(θ) = 0.7
Taking the inverse tangent of both sides, we find:
θ = arctan(0.7)
Using a calculator, we can evaluate this to be approximately:
θ ≈ 35.87 degrees
Therefore, the angle between the line and the x-axis is approximately 35.87 degrees.
we want to test the hypothesis: the fraction of people with severe depression is higher in country a than in country b. we have chosen the statistic of interest to be (fraction of depressed people in country a divided by fraction in country b). we call this ratio r. what is the null hypothesis?
The null hypothesis is R = 0
In this question we have been given a hypothesis that the fraction of people with severe depression is higher in country a than in country b.
We need to test the hypothesis.
Suppose that we have chosen the statistic of interest to be PAPB.
Let the ratio R be the fraction of depressed people in country a divided by fraction in country b
We need to find the null hypothesis.
We know that the null hypothesis as statement says that there is no relationship between two measured variables/phenommena.
In this case, for null hypothesis the ratio must be zero.
Therefore, for given situation the null hypothesis is R = 0
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The complete question is:
We want to test the hypothesis: the fraction of people with severe depression is higher in country A than in country B.
We have chosen the statistic of interest to be PAPB (fraction of depressed people in country A divided by fraction in country B). We call this ratio R.
What is the null hypothesis?
Group of answer choices
1 R=0
2 R=1
Mrs.McDowell is making a big batch of cookies for her son's birthday. The price of the chocolate bags is 2 bags for 4.00$. Use the table to determine the number of bags of chocolate chips r that Mrs.McDowell bought of the cost was $12.
Answer:
if you have. questions let me know
Answer:
Step-by-step explanation:
Tbh i don’t know I’m stuck in the same question
Natasha bought a tennis racket that was marked down in price by 20%. If the racket was originally priced at $125, how much did Natasha pay?
HINT: First find the discount amount. Then, subtract the discount amount from the original price. When doing multiplication, be sure to change your percent to a decimal. PLEASEEE HELPPPPPPP
1Points
A
Natasha paid $25.
B
Natasha paid $45.
C
Natasha paid $100.
D
Natasha paid $80.
Answer: c
Step-by-step explanation: Natasha paid 100$
Correlational research is concerned with Group of answer choices differences between conditions. examining relationships among variables. describing the preferences of some group of people. controlling treatment conditions for appropriate comparison.
Correlational research is concerned with examining relationships among variables. It focuses on understanding the associations or connections between different variables and how they relate to each other.
This type of research aims to explore the extent and direction of the relationship between variables without manipulating them.
In correlational research, researchers measure two or more variables and analyze their statistical relationship using techniques such as correlation analysis. The goal is to determine whether there is a positive or negative association between the variables, or if they are unrelated.
Correlational research does not involve establishing causation or determining differences between conditions, but rather focuses on understanding the patterns and strength of relationships between variables in order to identify potential associations or predict outcomes.
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Find the values of a and b that make the following piecewise defined function both continuous and differentiable everywhere. f(x) = 3x + 4, X<-3
2x2 + ax + b. X>-3
The values of a and b that make the piecewise defined function f(x) = 3x + 4, for x < -3, and f(x) = 2x^2 + ax + b, for x > -3, both continuous and differentiable everywhere are a = 6 and b = 9.
To ensure that the piecewise defined function is continuous at the point where x = -3, we need the left-hand limit and right-hand limit to be equal. The left-hand limit is given by the expression 3x + 4 as x approaches -3, which evaluates to 3(-3) + 4 = -5.
On the right-hand side of the function, when x > -3, we have the expression 2x^2 + ax + b. To find the value of a, we need the derivative of this expression to be continuous at x = -3. Taking the derivative, we get 4x + a. Evaluating it at x = -3, we have 4(-3) + a = -12 + a. To make this expression continuous, a must be equal to 6.
Next, we find the value of b by considering the right-hand limit of the piecewise function as x approaches -3. Substituting x = -3 into the expression 2x^2 + ax + b, we get 2(-3)^2 + 6(-3) + b = 18 - 18 + b = b. To make the function continuous, b must equal 9.
Therefore, the values of a and b that make the piecewise defined function both continuous and differentiable everywhere are a = 6 and b = 9.
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8x+9y=-28
-4x=y
solve the system by subsitution
Answer:
x= 1
y = -4
Step-by-step explanation:
8x + 9y = -28
-4x = y
8x + 9(-4x) = -28
8x - 36x = -28
-28x = - 28
x = 1
y = -4(1) = -4
Answer:
2
Step-by-step explanation:
8 + 9 = 17
17y = 28
28 / 17 = 1.64
test the hypothesis that the mean weight of the two sheets is equal (μ1−μ2)against the alternative that it is not (and assume equal variances). find the t-stat to 3 decimal places.
To test the hypothesis that the mean weight of two sheets is equal (μ1 - μ2) against the alternative that it is not, and assuming equal variances, we can use a two-sample t-test. The t-statistic can be calculated using the following formula:
t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2))
where:
x1 and x2 are the sample means of the two sheets,
s_p is the pooled standard deviation,
n1 and n2 are the sample sizes.
The pooled standard deviation (s_p) can be calculated using the following formula:
s_p = sqrt(((n1 - 1) * s1^2 + (n2 - 1) * s2^2) / (n1 + n2 - 2))
where:
s1 and s2 are the sample standard deviations.
To calculate the t-statistic, we need the sample means, sample standard deviations, and sample sizes.
Once you provide the specific values for these variables, I can assist you in calculating the t-statistic to 3 decimal places.
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To test the hypothesis that the mean weight of the two sheets is equal (μ1 - μ2) against the alternative that it is not, we can use a paired t-test assuming equal variances. The paired t-test is used when we have paired data or measurements on the same subjects or objects.
The t-statistic for a paired t-test is calculated as follows:
t = (X1 - X2) / (s / √n)
where X1 and X2 are the sample means of the two samples, s is the pooled standard deviation, and n is the number of pairs.
Please provide the sample means, standard deviation, and sample size for each sheet so that we can calculate the t-statistic to 3 decimal places.
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help maths equation class 8
Step-by-step explanation:
question 2
let the number be x
2 ( x + 5 ) = 5x - 14
2x + 10 = 5x - 14
2x - 5x = -14 - 10
-3x = -24
dividing both sides by -3
x = 8
to verify, 8 + 5 is 13 times 2 which 26..
so 5 times 8 is 40 minus 14 is 26
how to solve 3-4y=19
step by step
y=-4
________
3(-3)-4y=19(-3)
-4y=16
-4y(÷-4)=16(÷-4)
y=-4
Translate sentence into an equation.
Thirteen is 7 more than one-fifth of a number
Answer:
\(13=7+\frac{1}{5}x\)
Step-by-step explanation:
The answer would be 30
The compression ratio in a certain engine is 9.8 to 1 . If the expanded volume of a cylinder is 49cu in., what is the compressed volume?
The compressed volume of the cylinder is approximately 5 cubic inches.
To find the compressed volume of the cylinder, we can use the compression ratio provided. The compression ratio is defined as the ratio of the volume of the cylinder before compression (expanded volume) to the volume of the cylinder after compression (compressed volume).
Let's denote the compressed volume as Vc and the expanded volume as Ve.
The compression ratio is given as 9.8 to 1, which means Ve is 9.8 times greater than Vc.
We are given that the expanded volume (Ve) is 49 cubic inches. Let's set up the equation:
Ve/Vc = 9.8/1
Substituting the values:
49/Vc = 9.8/1
Now, we can solve for Vc by cross-multiplication:
9.8 * Vc = 1 * 49
9.8 * Vc = 49
Dividing both sides by 9.8:
Vc = 49/9.8
Vc ≈ 5
Therefore, the compressed volume of the cylinder is approximately 5 cubic inches.
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Find an equation for the line tangent to the graph of the given function at the indicated point. 8 3) f(x): () = at at (4,2) X 1 4) f(x)=x2-x at (4, 12)
(a) tangent line to the graph of f(x) = x^3 at the point (4,2).
(b) equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12).
(a) To find the equation of the tangent line to the graph of f(x) = x^3 at the point (4,2), we need to find the slope of the tangent line at that point. We can do this by taking the derivative of f(x) with respect to x and evaluating it at x = 4. The derivative of f(x) = x^3 is f'(x) = 3x^2. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Once we have the slope, we can use the point-slope form of a linear equation to write the equation of the tangent line.
(b) Similarly, to find the equation of the tangent line to the graph of f(x) = x^2 - x at the point (4,12), we differentiate f(x) to find the derivative f'(x). The derivative of f(x) = x^2 - x is f'(x) = 2x - 1. Evaluating f'(x) at x = 4 gives us the slope of the tangent line. Using the point-slope form, we can write the equation of the tangent line.
In both cases, the equations of the tangent lines will be in the form y = mx + b, where m is the slope and b is the y-intercept.
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