Answer:
17
Step-by-step explanation:
You need to use the formula for Arithmetic Sequences.
[tex]a_{n}=a_{1}+(n-1)d[/tex]
You need to plug in the value for [tex]a_{1}[/tex] which is just the first value in your sequence. As well as [tex]n[/tex] which is the term your looking for, in this case it's 48. Lastly [tex]d[/tex] which is the amount that the pattern is increasing or decreasing by. If the sequence is increasing then the [tex]d[/tex] is positive but if the sequence is decreasing then the [tex]d\\[/tex] is negative.
What is the slope of the line represented by the given table?
X -14 0 7 14 21
y -6 2 6 10 14
Graph the line with slope -1 passing through the point (4, -5).
Answer:
y=x-1
Is the line equation.
Step-by-step explanation:
As we know that general equation of line is given by
y=mx + c
M is the slope and C is is Y intercept
Know m = 1 and point (x,y) as (5,4)
So plug in the values and solve for c
4=1*(5)+c
c=-1
So, equation of the line is
y=x-1
#19 i
Solve the system of linear equations by elimination.
1.5x - 9y = -21
-1.5x - 3y = 9
The solution is:
Answer:
to solve a system of linear equations by elimination, we need to eliminate one of the variables, for example, we could add the two equations together to eliminate the variable y. However, we need to make sure that the coefficients of the two equations are the same before we can add them together. We can do this by multiplying the first equation by -1.5 and the second equation by 1.5. This gives us the following system of equations:
-2.25x - 13.5y = -31.5
2.25x - 4.5y = 13.5
We can now add these two equations together to eliminate the variable y, which gives us the following equation:
0 = -18
This equation is not possible, so the system of equations does not have a solution.
Answer:
Math can help you get your answer it has a linear equation by option
Step-by-step explanation:
Answer!!!!!!!!!!!!!!!
Using the AAS rule.
ST ≅ UT (given)
∠SRT≅∠UVT (given)
∠RTS ≅ ∠UVT (opposite angles)
∠RST ≅ ∠VUT (AAS rule)
Proved.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have,
AAS rule:
When two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.
From the figure we have,
ST ≅ UT (given)
∠SRT≅∠UVT (given)
∠RTS ≅ ∠UVT (opposite angles)
∠RST ≅ ∠VUT (AAS rule)
Thus,
∠RST is congurent to ∠VUT using the AAS rule.
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In the diagram below of triangle BCD, E is the midpoint of BD and F is the midpoint of CD. If EF = 43-4x, and BC = 32-2x, what is the measure of EF?
The measure of the length EF of the triangle is; 21
How to solve similar triangles?We are given the the triangle BCD and we are told that;
E is the midpoint of BD.
F is the midpoint of CD
Now, since we have those midpoints, it means that by the concept of similar triangles, that;
DF/DC = EF/BC
Since F is the midpoint of DC, then it means that;
2DF = DC
We are given;
EF = 43 - 4x, and BC = 32 - 2x
Thus, we now have;
DF/(2DF) = (43 - 4x)/(32 - 2x)
1/2 = (43 - 4x)/(32 - 2x)
Cross multiply to get;
32 - 2x = 43 - 4x
4x - 2x = 43 - 32
2x = 11
x = 11/2
x = 5.5
Thus;
EF = 43 - 4(5.5)
EF = 43 - 22
EF = 21
Thus, we conclude that the side length EF is 21.
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The general form of a hyperbola is 6x2−5y2+12x+50y−149=0.
What is the standard form of this hyperbola?
Enter your answer by filling in the boxes.
The quadratic equation (x + 1)² / 46.667 - (y - 5)² / 56 = 1 represents the hyperbola in standard form.
How to derive the standard form of the equation of a hyperbola
In this question we find the equation of a hyperbola in general form, that is, a quadratic equation of the form A · x² + B · y² + C · x + D · y + E = 0, and we need to obtain the standard form of the hyperbola:
(x - h)² / a² - (y - k)² / b² = 1
Where:
(h, k) - Coordinates of the center.a, b - Length of the semiaxes.We can switch from general form into standard form by completing the square, an application of algebra properties:
6 · x² - 5 · y² + 12 · x + 50 · y - 149 = 0
(6 · x² + 12 · x) - (5 · y² - 50 · y) = 149
6 · (x² + 2 · x) - 5 · (y² - 10 · y) = 149
6 · (x² + 2 · x + 1) - 5 · (y² - 10 · y + 25) = 149 + 6 + 125
6 · (x + 1)² - 5 · (y - 5)² = 280
(x + 1)² / 46.667 - (y - 5)² / 56 = 1
The equation of the hyperbola in standard form is (x + 1)² / 46.667 - (y - 5)² / 56 = 1.
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Cashews cost $63.00 per 5 pound bag. How much would a 2 pound bag of cashews cost?
WHAT IS 81x1???????????????????????????????????
Answer:
81
Step-by-step explanation:
81 * 1 = 81
If the 81x1 is = 81 * 1 then it should be 81.
If its not I will redo my answer.
Answer:
81 x 1 is 81
81
x 1
81
If a triangle has lengths of 11tf and 24ft, check all the possible lengths for the third side
All the possible lengths for the third side lie between 13 to 35 feet.
What is a triangle Inequality Theorem?
In Euclidean geometry, the theorem is that the sum of any two sides of a triangle is greater than or equal to the third side; in symbols, a + b ≥ c. In essence, the theorem states that the shortest distance between two points is a straight line.
The Triangle Inequality theorem states that the sum of any 2 sides of a triangle must be greater than the measure of the third side.
So, a difference of two sides <x< sum of two sides, will give you the possible length of a triangle.
Therefore, 24 − 11 < x < 24 + 11
13 < x < 35 is the possible length of the third side of a triangle.
13 < x < 35 satisfies the triangle inequality theorem.
Hence, all the possible lengths for the third side lie between 13 to 35 feet.
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A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each small box of paper weighs 45 pounds and each large box of paper weighs 75 pounds. There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds. Write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped. Define the variables that you use to write the system.
The system of equation is 45x+75y=1455.
The number of small boxes is 14 and large boxes is 11.
In the given question,
The paper will be shipped in small boxes and large boxes.
Each small box of paper weights 45 pounds.
Each large box of paper weights 75 pounds.
There were 3 more small boxes shipped than large boxes and the total weight of all boxes was 1455 pounds.
We have to write a system of equations that could be used to determine the number of small boxes shipped and the number of large boxes shipped.
We also have to define the variables that we use to write the system.
Let x be the number of small boxes.
Let y be the number of large boxes.
There were 3 more small boxes shipped than large boxes.
So x = y+3
Weight of x number of small boxes = 45x
Weight of y number of small boxes = 75y
Total weight of boxes = 1455
So; 45x+75y=1455
Now putting the value of x to this system of equation
45(y+3)+75y=1455
45y+135+75y=1455
120y+135=1455
Subtract 135 on both side, we get
120y=1320
Divide by 120 on both side, we get;
y=11
Now putting the value of y in x=y+3
x = 14
Hence, the number of small boxes is 14 and large boxes is 11.
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Answer!!!!!!!!!!!!!!
By ASA, the two triangles are congruent. They share 2 angles and the line in between them.
Use the number line to plot –3, 1, and 3. Which statements are true? Select all that apply. –3 > 1 –3 = 3 1 < 3 –3 < 1
when me I would say the 1st one but who knows lol
they figure that the waterfall is at point (3'6). The overlook is at point (0.1). the campsite is at point (3-5). The lake is at point (-4,1). And the parking lot is at point (0.5). Which of these pairs of locations are closest to one another
Answer:
Step-by-step explanation:
I'm sorry, but I'm not sure what you're asking. It's not clear to me what you mean by "point (3'6)" or "(3-5)." Could you please provide more information or clarify your question
1. Which of the following identifies the a, b, c, and d of the absolute value function g(x) = −|2x| + 5?
The parameters of the absolute value function g(x) = -|2x| + 5 are given as follows:
a = -1.b = 2.c = 0.d = 5.How to obtain the parameters of the absolute value function?The standard definition of the absolute value function is given as follows:
f(x) = a|bx + c| + d.
The meaning of each parameter is given as follows:
a is the coefficient of vertical stretch/compression.b is the coefficient of horizontal stretch/compression.c is the coefficient of horizontal shift.d is the coefficient of vertical shift.In this problem, the function is defined as follows:
g(x) = −|2x| + 5.
Compared with the standard absolute value function, the values of these parameters are given as follows:
a = -1, b = 2, c = 0, d = 5.
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Is Ax + By = C slope, slope-intercept, point-slope, or standard form?
Answer:
Ax + By = C is standard form.
Step-by-step explanation:
It is standard form because slope intercept is y = mx + b and point slope is y-y₁=m(x-x₁)
Hope this helps
Answer:
Standard form.
Step-by-step explanation:
y=mx + b is the slope-intercept form.
Find value of x and show work please
Answer:
D) 4, H) 14
Step-by-step explanation:
D) both angles form a linear pair so 101-5x + 2x+70 = 180
Simplify
171-3x = 180
-3x = 9
x = -3
H) 11x-23 = 41 + 90 because they are opposite angles
Simplify
11x = 154
x = 14
What’s
: -4 (2x + 4) = 5
Please explain step by step to get picked brainliest!
Answer:
[tex]x=-\frac{21}{8}[/tex]
Step-by-step explanation:
[tex]-4(2x+4)=5 \\ \\ 2x+4=-\frac{5}{4} \\ \\ 2x=-\frac{21}{4} \\ \\ x=-\frac{21}{8}[/tex]
Makayla is a botanist studying production of coconuts by two different groups of her coconut palms. She notices that Group 1 trees produce 25 percent more coconuts than Group 2. based on Makayla's observation, if Group 1 produced 150 coconuts, how many coconuts did group 2 produce?
If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.
What is proportion?Proportion refers to the two ratios equated to each other.
Proportion shows how much quantity or value is contained in another.
We depict proportions using fractional values, such as fractions, decimals, and percentages.
The number of coconuts produced by Group 1 trees = 150
The percentage by which Group 1 trees produce more than Group 2 = 25%
Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)
Let Group 2's production = 100% = 150/125 x 100
= 120 coconuts
Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.
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3. There are five different tables in the class and five students. Each table can be occupied by only onestudent. Their
studying year consists of 200 days. As a small prank on their teacher students would like to sit in a new way every
day, so there are no two days during their studying year such that all students are occupying the same tables.
They would like to see whether this is possible. How many ways are there for them to sit in the class?
There are 3,125 different places to sit if they don't mind sharing s desk sometimes and there are 120 different places to sit, if they all sit on separate tables.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
Given that there are five different tables in the class and five students
Each table can be occupied by only one student
There are 200 days of studying years.
As a small prank on their teacher students would like to sit in a new way every day, so there are no two days during their studying year such that all students are occupying the same tables.
5×4×3×2×1 = 120
There are 120 different places to sit, if they all sit on separate tables.
5×5×5×5×5 = 3,125
There are 3,125 different places to sit if they don't mind sharing s desk sometimes.
Hence, there are 120 different places to sit, if they all sit on separate tables and there are 3,125 different places to sit if they don't mind sharing s desk sometimes.
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XYZ has coordinates X(-7, 8), Y(2, 5), Z(0,7). What are the coordinates of the image r(90,0) XYZ
The new coordinates are X'(8, 7), Y'(5, -2), Z'(7, 0).
How to determine the image of the rotation?The coordinates of the triangle are given as
X(-7, 8), Y(2, 5), Z(0,7).
The rotation is given as r(90,0) XYZ
This means that
We have (x, y) ⇒ (y, -x)
Substitute X(-7, 8), Y(2, 5), Z(0,7) in (x, y) ⇒ (y, -x)
So, we have
X'(8, 7), Y'(5, -2), Z'(7, 0).
Hence, the coordinates of the image are X'(8, 7), Y'(5, -2), Z'(7, 0).
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NO LINKS!! Please help me with the Domain and Range and Functions Part 1bb
Domain - the set of possible x-coordinates of a function.
Range - the set of possible y-coordinates of a function.
Question 21Domain is:
x ∈ [- 4, 2], both ends included as part of the graph or closed circle..Range is:
y ∈ (-6, 6], the lowest point is excluded as open circle, the highest value is included as closed circle..This is not a function as it fails the vertical line test.
Question 22Domain is:
x ∈ [- 6, 2], both ends included as part of the graph.Range is:
y ∈ [-7, 7], both ends included as part of the graph.This is not a function as it fails the vertical line test.
Question 23Domain is:
x ∈ [ -2, 0], both ends included as closed circle or part of the graph.Range is:
y ∈ (-7, 5], the -7 is excluded as open circle, the 5 is included as closed circle.This is not a function as it fails the vertical line test.
Question 24Domain is:
x ∈ [- 6, 6), One end is included and the other end is excluded.Range is:
y ∈ [-7, 1], both ends included as closed circle or part of the graph.This is a function as it passes the vertical line test.
Help plsssssssssssss
Answer: thanks for the ponts
Step-by-step explanation: ahhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
A door is 2 feet off the ground and a contractor needs to develop a wheelchair ramp to go on it. Ramps have to be in a ratio of 1:12 slope. How far away from the house would the ramp have to start. Explain
The slope of the ramp is the ratio of the y and x coordinates thus it will be 24 feet.
What is the slope?A slope is a tangent or angle at a point or a slope is the intensity of inclination of any geometrical lines.
Slope = Tanx where x will be the angle from the positive x-axis at that point.
The situation is making a right-angle triangle as shown below.
The slope of the wheelchair = 2 feet / x
2/x = 1/12
x = 2 x 12 = 24 feet
Hence "The ramp will be 24 feet long since the slope is determined by the ratio of the y and x variables".
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what is the additive inverse of -17-25
Answer: 42
Step-by-step explanation: ik additive inverse
Use polynomial identities to multiply (4 + 2x3 )(4 − 2x3 ).
The product of the polynomials (4 + 2x³)(4 − 2x³) is 16 - 4x⁶
How to determine the product of the polynomialsFrom the question, we have the following parameters that can be used in our computation:
Polynomial products: (4 + 2x3 )(4 − 2x3 )
Rewrite the above product properly
So, we have the following representation
Polynomial products = (4 + 2x³)(4 − 2x³)
Using the difference of two squares identity
We have the following representation
Polynomial products = (4)² - (2x³)²
Evaluate the exponents
Polynomial products = 16 - 4x⁶
Hence, the product is 16 - 4x⁶
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The cost C, in dollars, for a health club membership depends on the number m of whole months you join. This situation is represented by the function rule c = 49 + 20m
is in continuous or discrete and what would the graph look like
The graph of the function C = 49 + 20m is a discrete function and is represented by vertical lines for whole numbered values of 'm'.
What is an equation?An equation is written in the form of variables and constants separated by the operation of multiplication and division,
An equation states that terms in different forms on both sides of the equality sign are equal.
Multiplication and division do not separate the terms of an equation.
Given, That no. of months is a whole month and hence it is discrete as it can not take decimal values.
The graph of the equation C = 49 + 20m would have vertical lines at each whole value of 'm'.
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The table shows Adam's age and shoe size. Generate a linear regression equation for the data. Then, use the equation to predict Adam's shoe size when he is 14-years-old.
The linear regression equation for the data is given as follows:
y = 0.55x + 0.3.
The prediction of Adam's shoe size when he is 14-years-old is given by the following option:
A. 8.
How to obtain the equation for the regression line?The equation for the line of fit is obtained inserting the points of the data-set into a linear regression calculator.
From the table, the points are given as follows:
(6,3), (8, 4.5), (10,5), (12, 7.5).
Inserting these points into a calculator, the regression equation predicting the shoe size at an age of x is given as follows:
y = 0.55x + 0.3.
Then the estimate for the shoe size at an age of 14 is found when x = 14, hence:
y = 0.55(14) + 0.3 = 8.
Meaning that option A is correct.
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(Please answer both I will give brainlest)
Find the indicated side x. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume b-10 and c-22. Round your answer to one decimal place.)
X=
(Refer to picture )
7.
Find the indicated angle. (Use either the Law of Sines or the Law of Cosines, as appropriate. Assume a-10, b-6, and c-12. Round your answer to one decimal place.)
0-
To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:
x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)
x^2 = 100 + 36 - 120
x^2 = 16
x = sqrt(16) = 4
Therefore, the length of the side x is 4.
To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:
a/sin(A) = b/sin(B) = c/sin(C)
In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:
10/sin(0) = 12/sin(C)
sin(C) = 0
Therefore, the measure of the angle C is 0 degrees.
this is original answer
To find the side x, we can use the Law of Cosines, which states that in any triangle, the square of the length of any side is equal to the sum of the squares of the lengths of the other two sides minus twice the product of those two sides and the cosine of the angle between them. In symbols, if a, b, and c are the lengths of the sides of a triangle, and C is the measure of the angle opposite the side of length c, then we have the equation:
c^2 = a^2 + b^2 - 2ab * cos(C)
In our case, we are given the lengths of two sides (a = 10 and b = 6) and the measure of the angle opposite the unknown side (C = 0 degrees), so we can plug those values into the equation to solve for c:
x^2 = 10^2 + 6^2 - 2 * 10 * 6 * cos(0)
x^2 = 100 + 36 - 120
x^2 = 16
x = sqrt(16) = 4
Therefore, the length of the side x is 4.
To find the indicated angle, we can use the Law of Sines, which states that in any triangle, the ratio of the length of a side to the sine of the angle opposite that side is constant. In symbols, if a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the measures of the angles opposite those sides, then we have the equations:
a/sin(A) = b/sin(B) = c/sin(C)
In our case, we are given the lengths of two sides (a = 10 and c = 12) and the measure of the angle opposite one of those sides (A = 0 degrees), so we can use those values to solve for the measure of the angle opposite the other side:
10/sin(0) = 12/sin(C)
sin(C) = 0
Therefore, the measure of the angle C is 0 degrees.
x (4.4) (1.4)
x=5
Help me solve this question please
Solve x(4.4)(1.4) given that x = 5
Plug x into equation
5(4.4)(1.4)
Distribute 5 into 4.4
22(1.4)
Distribute 22 into 1.4
30.8
Hope this helps :)
If you need any more explanation, feel free to ask. If this really helps, consider marking brainliest.
- Jeron
If A = {x|x is an odd integer), B = {2, 3, 4, 5), list the elements of the set AUB.
Choose the correct answer below.
O A. {x x is an even integer or x = 2 or x = 4}
O B. {x|x is an even integer or x = 3 or x = 5}
OC. {x|x is an odd integer or x = 3 or x = 5}
OD. {xx is an odd integer or x = 2 or x = 4}
Answer:
D) {x: | x is an odd integer or x = 2 or x = 4}-----------------------------
Given two sets:
A = {x: | x is an odd integer}, B = {2, 3, 4, 5}Both sets include 3 and 5 so the combination is all the elements of the A and two unique elements of the B:
A∪B = {x: | x is an odd integer or x = 2 or x = 4}The matching choice is D.