Answer:
Equation of a line is y = mx + c
where m is the gradient
c is the y intercept
a.)y = 4x - 1
Comparing with y = mx + c
The gradient = 4
y intercept = - 1
b.)[tex]y = \frac{1}{3} x + 3[/tex]
Comparing with y = mx + c
The gradient is 1/3
The y intercept is 3
Hope this helps you
Answer:
4 and -1
1/3 and 3
Step-by-step explanation:
for y=4x-1
y intercepts where x=0 so f(0)=4*0-1=-1
y intecepts = - 1
the gradient is y2-y1/x2-x1 where y2=f(x2)=4x2-1 and y1=f(x1)=4x1-1
the gradient is 4x2-1-4x1+1/x2-x1=4 ( the coeficient of x)
for y=1/3x+3
the gradient is 1/3
y intercepts is f(0)=3
Use the following data set to find the sample statistics for the following data set. 1. (N) or (n) 2. (x-bar) or (μ) 3. (σ) or (s) Thanks!
Answer:
(1) N or n = 20
(2) [tex]\bar X \text{ or } \mu[/tex] = 43.4
(3) σ = 9.78 and s = 10.04.
Step-by-step explanation:
We are given with the following data set below;
{51, 48, 42, 43, 48, 48, 46, 15, 29, 45, 47, 55, 46, 35, 47, 48, 54, 26, 53, 42}
(1) As we can see in the above data that there are 20 data values in our data set which means that the value of N or n (numner of observations) is 20.
(2) The formula for calculating Mean of the data, i.e. [tex]\bar X \text{ or } \mu[/tex] is given by;
Mean = [tex]\frac{\sum X}{n}[/tex]
= [tex]\frac{51 +48+ 42+ 43+48+48+ 46+ 15+ 29+ 45+ 47+ 55+ 46+ 35+ 47+ 48+ 54+ 26+ 53+ 42}{20}[/tex]
= [tex]\frac{868}{20}[/tex] = 43.4
So, the value of [tex]\bar X \text{ or } \mu[/tex] is 43.4.
(3) The formula for calculating population standard deviation ([tex]\sigma[/tex]) is given by;
Standard deviation, [tex]\sigma[/tex] = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{N} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20} }[/tex]
= 9.78
Similarly, the formula for calculating sample standard deviation (s) is given by;
Sample Standard deviation, s = [tex]\sqrt{\frac{\sum (X - \bar X)^{2} }{n-1} }[/tex]
= [tex]\sqrt{\frac{(51-43.4)^{2}+(48-43.4)^{2}+.......+(42-43.4)^{2} }{20-1} }[/tex]
= 10.04
Write an equation of the line passing through the point (7,3) that is parallel to the line 4x-7y=9
Answer:
y = -7/4x + 61/4
Step-by-step explanation:
Step 1: Write equation in slope-intercept form
-7y = 9 - 4x
y = 4/7x - 9/7
Step 2: Find slope of perpendicular line
Take the negative reciprocal of the 1st equation
m = -7/4
Step 3: Write out known variables
y = -7/4x + b
Step 4: Find b
3 = -7/4(7) + b
3 = -49/4 + b
b = 61/4
Step 4: Rewrite equation
y = -7/4x + 61/4
Question 4 Select Prism from the list of shapes. Set the number of lateral faces to five, and explore the cross sections of a pentagonal prism. Move the intersecting plane, and vary the angle between the intersecting plane and the vertical axis to identify the shapes of different types of cross sections. Part A Note all the types of cross sections you observe. In the table, describe the shape of the cross section formed when a particular plane passes through the prism.
Answer:
Step-by-step explanation:
Answer:
Plato
Step-by-step explanation:
rectangle
pentagon
pentagon
pentagon, hexagon ,heptagon
pentagon, quadrilateral, or triangle
Simplify as a ratio: 100:199:47
Answer:
Find GCF of all values in the given ratio
GCF(100, 199, 47) = 1
When GCF value is equal to 1, the given ratio can not be simplified.
Step-by-step explanation:
It cant be simplified
Answer:
100:199:47
Step-by-step explanation:
The ratio cannot be simplified.
The numbers 199 and 47 are prime numbers, and only have the factors of 1 and themselves.
and distance of the last ramp is ______ feet (round to the nearest foot)
Answer:
The distance of the last ramp is 10 feet.
Step-by-step explanation:
From the options and the question, I assume that the height of the ramp is 6 feet. Pythagorean theorem states:
a² + b² = c²
where c is the hypotenuse, and a and b are the legs of the triangle. In this case:
6² + 8² = x²
√100 = x
10 ft = x
-b -b +5 pls show work and solve
Answer:
Step-by-step explanation:
-b -b +5
= -2b + 5
the ratio of the surface area of two similar solids is equal to the square root of the ratios between their corresponding edge lengths. True or False
Answer:
False
Step-by-step explanation:
Just trust me on this
Answer:
The correct answer is False
Step-by-step explanation:
Struggling!!! Math help plss!!!
Answer:
Step-by-step explanation:
Does this table represent a function? why or why not?
Answer:
I think it's A but I could be wrong
Answer: B
Step-by-step explanation:
A graph or table is a function if it passes the vertical line test. That means, each x and only 1 y. One x cannot have more than 1 y because, that means it does not pass the veritcal line test. In the vertical line test, the vertival line only passes through 1 point, not 2. Since we know that this graph does not pass the vertical in test, we can eliminate C and D. We can eliminate A because 2 y-values can be the same as lone as there have different x. B fits the description of what we see on the table. Therefore, the answer is B.
solve:
|3x+ 2| > 14
show work
Answer:
x < -16/3 or x > 4
Step-by-step explanation:
This is split into two inequalities: 3x + 2 > 14 and -(3x + 2) > 14.
3x + 2 > 14
3x > 12
x > 4
-(3x + 2) > 14
3x + 2 < -14
3x < -16
x < -16/3
Answer:
[tex]x > 4[/tex]
Step-by-step explanation:
Move the constant to the right-hand and change its sign:
[tex]3x > 14 - 2[/tex]
Subtract the number:
[tex]3x > 12[/tex]
Divide both sides of the inequality by 3:
[tex]3 \div 12 = 4[/tex]
Therefore, the answer will be x > 4.
Which are correct representations of the inequality -3(2x - 5) <5(2 - x)? Select two options.
Answer:
The third and fourth options.
Step-by-step explanation:
You simplify the inequality first...
-6x + 15 < 10 - 5x
-x < -5
x > 5
The first option is incorrect since it is less than.
The second option is basically -5x < 15; x > -3; that's incorrect.
The third option is basically -x < -5; x > 5; that is correct!
The fourth option is correct since it shows more than 5.
The fifth option is incorrect because it shows less than -5.
Hope this helps!
Answer: The answer is C and E
Step-by-step explanation:
Hope this helps;)
Which set of ordered pairs below is a function?
I.{(3,3),(6,1),(2,3)} .................. II.{(4,7),(2,8),(4,2)} .............. III.{(9,6),(3,1),(7,3)}
(((((((A I only )))))))) ((((( B II only ))))))) ((((((( C III only)))))) (((D I and III))))
Answer:
C
Step-by-step explanation:
Which description is paired with its correct expression? seven less than the quotient of two and a number squared, increased by six; 7 minus StartFraction 2 Over n squared EndFraction + 6 nine times the difference of a number cubed and three; 9 (n cubed minus 3) eight more than the quotient of a number squared and four, decreased by seven; 8 + StartFraction 4 Over n squared EndFraction minus 7 twice the difference of a number cubed and eight; 2 n cubed minus 8
Answer:
the second description and and expression is correct
Step-by-step explanation:
the first one is wrong because it says 7 minus while it should be minus 7
nine times the difference of a number cubed and three; 9(n³-3)
Paired data in statistics, often referred to the ordered pairs, refers to 2 variables in the individuals of the population that are linked together in the order to determine correlation between them.
Given :
7 less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
9 times the difference of a number cubed and three; 9(n³-3)
8 more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
twice the difference of a number cubed and eight; 2 n³- 8
To Find: Which description is paired with its correct expression
Solution:
7 less than the quotient of two and a number squared increased by six
7 - (2/n²) + 6
Correct Expression is -7 + (2/n²) + 6
nine times the difference of a number cubed and three; 9(n³-3)
Expression is Correct
8 more than the quotient of a number squared and four, decreased by seven; 8 + (4 /n²) - 7
Correct Expression is 8 + (n²/4) - 7
twice the difference of a number cubed and eight; 2 n³- 8
The correct expression is 2( n³- 8)
Hence the correct answer is :
nine times the difference of a number cubed and three; 9(n³-3)
Statistics is a mathematical body of the science that pertains by the collection or analysis, or interpretation and explanation, or presentation of data, and as a branch of mathematics. Some consider statistics to be the distinct mathematical science rather than a branch of mathematics.
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Solve for x in the diagram.
Answer:
x = 15
Step-by-step explanation:
Using Pythagorean Theorem
=> [tex]c^2 = a^2+b^2[/tex]
Where c= x, a = 12, b = 9
=> [tex]x^2 = (12)^2+(9)^2[/tex]
=> [tex]x^2 = 144+81[/tex]
=> [tex]x^2 = 225[/tex]
Taking sqrt on both sides
=> x = 15
A cube has an edge length of 13 feet. What is its volume, in cubic feet?
Answer:
V =2197 ft^3
Step-by-step explanation:
The volume of a cube is given by
V = s^3 where s is the length of a side
V = 13^3
V =2197 ft^3
Answer:
Volume = 2197ft³
I only need help step by step solution for question#40 and #44
the link is not working :(
Every day you collect 3 pennies and keep them in a jar. So the first day you have 3, the second day you have 6, the third day you have 9, etc. How many do you have on the 13th day?
Answer: 39 Pennies
Step-by-step explanation: You can think about this question as a multiplication problem. When you look at the pattern of the the other days you notice that they are all mulitples of 3. So when you want to find the number of pennies on the 13th day. You can do 3*13 = 39.
hi:) I need help with part 9(ii) ? Thanks :)!
Answer:
see explanation
Step-by-step explanation:
Given
2BD = 7BT , then
2(d - b ) = 7(t - b) ← distribute both sides
2d - 2b = 7t - 7b ( add 7b to both sides )
2d + 5b = 7t, thus
2[tex]\left[\begin{array}{ccc}10.5\\10\\\end{array}\right][/tex] + 5[tex]\left[\begin{array}{ccc}0\\3\\\end{array}\right][/tex] = 7t
[tex]\left[\begin{array}{ccc}21\\20\\\end{array}\right][/tex] + [tex]\left[\begin{array}{ccc}0\\15\\\end{array}\right][/tex] = 7t
[tex]\left[\begin{array}{ccc}21\\35\\\end{array}\right][/tex] = 7t , thus
t = [tex]\frac{1}{7}[/tex][tex]\left[\begin{array}{ccc}21\\35\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}3\\5\\\end{array}\right][/tex]
Hence T = (3, 5 )
Answer:
Please see the attached pictures for the full solution.
We reject x= -3 since x has to be between x=0 and x=10.5 since T lies on line BD.
We reject y= 1 since the y value has to be between 3 and 10 for T to lie on line BD.
Useful formula:
gradient=(y1-y2)/(x1-x2)
Further explanation:
1st picture, from line 12 to 13: cross multiply
line 14: expand
line 15: bring 9 over (or +9 on both sides)
line 16: ÷3 throughout
last picture: we have to show '(reject)' because whenever we introduce a square root, there must be a '±' sign.
How is the graph of y = 2 (3)^x+1 -4 translated from the graph of y = 2(3)^x
Answer:
f(x - n) - shift the graph n units right
f(x + n) - shift the graph n units left
f(x) - n - shift the graph n units down
f(x) + n - shift the graph n units up ----------------------------------------------------------------------------
Answer: shift the graph of y = 2(3)ˣ one unit right and four units up.
On which number line do the points represent negative seven and one over two and +1? Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of 0.
Answer:
A number line is used in the mathematical positioning of real numbers that include the numbers from positive infinity to negative infinity. This includes rational, irrational, fractions, and whole numbers. In this case, we are given with an expression that we have to reduce to lowest terms: negative seven and one over two and +1. The first one is equal to -7.5 while the other one is equal to +1. Positive numbers lie on the right side of zero (center of the line) while negative numbers lie on the left on the other hand. -7.5 lies between -8 and -7 while +1 lies exactly between 0 and 2. Both of which are positive numbers
I hope that is what your asking...
Answer:
On which number line do the points represent negative seven and one over two and +1? The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed in between the 6th and 7th tick marks to the left of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed in between the 7th and 8th tick marks to the left of 0. A point labeled T is placed on the 1st tick mark to the right of 0 Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed in between the 7th and 8th tick marks to the right of 0. The Number line from negative 10 to positive 10 in increments of 1 is shown. Only the whole numbers are labeled. A point labeled R is placed on the 1st tick mark to the left of 0. A point labeled T is placed between the 6th and 7th tick marks to the right of
Step-by-step explanation:
Mr. Maddox asked four students to create a number line to help find the sum of the fractions. Negative StartFraction 7 over 10 EndFraction + StartFraction 4 over 10 EndFraction Which number line would be best to find this sum?
Answer:
First choice
Step-by-step explanation:
Sum of fractions:
-7/10 + 4/10= - 3/10
the interval required on the line from the left of - 7/10 to the right of -3/10
Which number line would be best to find this sum?
-8/10 to 0
yes, this is good as covers the interval from -7/10 to - 3/10
-3/10 to 3/10
no, it doesn't include the left half of required section
4/10 to 11/10
no, it doesn't include the required interval
0 to 15/10
no, it doesn't include the required interval
Answer:
A
Step-by-step explanation:
What is the surface area of a can that has radius of 9 ft. and height of 3 ft.? SA = __________ ft.2. Use 3.14 for pi. A. 678.2 B. 458.6 C. 354.3 D. 292.0
Answer:
678.2
Step-by-step explanation:
To find the surface area you need to use the expression [tex]2\pi rh + 2\pi r^2[/tex]
When you substitute the numbers in you get 678.24
The surface are of the can that has radius of 9 ft. and height of 3 ft is 678.2 ft².
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The surface area of the can is the sum of the area of the bases of the can and the lateral surface area of the can. Therefore, the total surface area of the can is,
The surface area of can = 2(Area of base) + Lateral surface area of can
= 2(πr²) + 2πrh
= 2[π×(9 ft)²] + (2 × π × 9ft × 3ft)
= 508.8 ft² + 169.4 ft²
= 678.2 ft²
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What is the equation of the parabola?
A. y=-1/8x^2+5
B. y=1/8x^2+5
C. y=1/8x^2-5
D. y=-1/8x^2-5
Answer:
The answer is option B.
y = 1/8x² + 5
Hope this helps you
Miracle Maid Service charges a $30 house visit fee plus $5 per room to clean a house. What is the independent variable? A) The price per room B) The number of rooms C) The house visit fee D) The Miracle Maid Service
Answer:
B
Step-by-step explanation:
The independent variable is the variable who's variation doesn't depend on the other. Therefore the answer is B because the amount of rooms doesn't depend on the charge, the charge depends of the amount of rooms.
Use the drawing tool(s) to form the correct answer on the provided graph.
Graph the inverse of the line provided on the graph.
Answer: Slope 1/4 therefore slope of new line would be -1/4
Step-by-step explanation:
The points of the inverse of the line provided on the graph are as under:
x=2,y=5
x=0,y=-5
x=1,y=0
What is the inverse of a line?
It means interchanging the values of x with the values of y and form a line which is known a inverse of a line.
How to graph the inverse of a line?firstly point out the points from the graph given in the question as in the graph1 below
now by interchanging the values we get the values of inverse of the line as in the graph 2
By plotting these points on the graph we get the inverse of the line which is in the graph 3
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Find the volume of a pyramid with a square base, where the side length of the base is
15.3 m and the height of the pyramid is 19.6 m. Round your answer to the nearest
tenth of a cubic meter.
Answer:
1529.4 m^3
Step-by-step explanation:
We will use the formula V = 1/3*h*B for the volume of the pyramid, where V is volume, h is height, and B is are of the base.
First, since we know h and are looking for V, we need B. To find this, since it has a square base, we multiply b, the base length, by itself. 15.3m * 15.3m = 234.09m^2.
Next, we plug into the formula.
V = 1/3*19.6m*234.09m^2
And simplify:
V= 1/3 * 4,588.164m^3
V= 15.29.3879....
Last, round to the tenth
1529.4 m^3
Answer: 1529.4
Step-by-step explanation:
Determine the slope of the following equation: 2y -4x = 9
Which expression shows the simplified form of (8 r Superscript negative 5 Baseline) Superscript negative 3? 8 r Superscript 15 StartFraction 8 Over r Superscript 15 Baseline EndFraction 512 r Superscript 15 StartFraction r Superscript 15 Baseline Over 512 EndFraction
Answer:
[tex]\frac{r^{15}}{512}[/tex]
Step-by-step explanation:
Given
[tex](8r^{-5})^{-3}[/tex]
Required
Simplify
This can be simplified using the following law of indices;
[tex](ab)^n = a^{n}b^{n}[/tex]
The equation becomes
[tex](8^{-3})(r^{-5})^{-3}[/tex]
Express [tex]8^{-3}[/tex] as a fraction
[tex](\frac{1}{8^{3}})(r^{-5})^{-3}[/tex]
Simplify [tex]8^3[/tex]
[tex](\frac{1}{8*8*8})(r^{-5})^{-3}[/tex]
[tex](\frac{1}{512})(r^{-5})^{-3}[/tex]
The expression can further be simplified using the following law of indices;
[tex](a^m)^n = a^{mn}[/tex]
[tex](\frac{1}{512})(r^{-5})^{-3}[/tex] becomes
[tex](\frac{1}{512})(r^{-5*-3})[/tex]
[tex](\frac{1}{512})(r^{15})[/tex]
[tex]\frac{r^{15}}{512}[/tex]
Hence, the solution to [tex](8r^{-5})^{-3}[/tex] is [tex]\frac{r^{15}}{512}[/tex]
Answer:
D
Step-by-step explanation:
PLEASE HELP GUYS ILL REWARD BRAINLIEST
Answer:
Step-by-step explanation:
(2,6)
Answer:
The solution of the two equations is where both lines intersect
From the graph they intersect at point
(6,2)
So the solution is x = 6 y = 2
Hope this helps you
What are the first three terms of the Arithmetic Sequence an=11-3(n-1)?
a. 1, 2, 3
b. 0, 8, 16
c. 8, 5, 2
d. 11, 8, 5
Answer:
11,8,5
Step-by-step explanation:
an=11-3(n-1)
Let n=1
a1 = 11 - 3(1-1)
= 11 -0
=11
Let n=2
a2 = 11-3(2-1)
= 11 -3(1)
= 8
Let n=3
a3 = 11-3(3-1)
= 11 -3(2)
= 11 -6
=5
Answer:
The answer is 11,8,5
Step-by-step explanation:
that's the correct answer