Answer:
Part A: The function [tex]f(x)[/tex] has greater slope than function [tex]g(x)[/tex]
Part B: [tex]g(x)[/tex] has a greater y-intercept than [tex]f(x)[/tex].
Step-by-step explanation:
Part A:
For finding the slope of [tex]f(x)[/tex], first we need to pick any two order pairs from the given table in form of [tex](x_{1}, y_{1})[/tex] and [tex](x_{2}, y_{2})[/tex] and then use the formula of slope: [tex]m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Lets choose two points as [tex](-1, -15)[/tex] and [tex](0, -10)[/tex]
So, [tex]m= \frac{-10-(-15)}{0-(-1)}= \frac{-10+15}{0+1}= 5[/tex]
Thus, the slope of the function [tex]f(x)[/tex] is 5.
Another function is: [tex]g(x)=2x+8[/tex]
The function [tex]g(x)[/tex] is given in standard slope intercept form [tex]y= mx+b[/tex]. So, we will get [tex]m=2[/tex]
Thus, the slope of the function [tex]g(x)[/tex] is 2.
So, the function [tex]f(x)[/tex] has greater slope than function [tex]g(x)[/tex]
Part B:
For function [tex]f(x)[/tex], there is one ordered pair as [tex](0, -10)[/tex]. This point is lying on the y-axis. So, the y-intercept of [tex]f(x)[/tex] is -10.
Now, in [tex]y= mx+b[/tex] form, [tex]'b'[/tex] is represented as the y-intercept. So, for function [tex]g(x)=2x+8[/tex], the value of [tex]'b'[/tex] will be 8.
Thus, the y-intercept of [tex]g(x)[/tex] is 8.
As [tex]8>-10[/tex],
So, [tex]g(x)[/tex] has a greater y-intercept than [tex]f(x)[/tex].
For a particular species of wolf, 55% are female, 20% hunt in medium-sized packs, and 15% are both female and hunt in medium-sized packs. The proportion of wolves that are neither female nor hunt in medium-sized packs is
Thus, the proportion of female wolves that do not hunt in medium sized packs is 4/10 or 0.4. When expressed as percent, this is 40%.
What is the probability of drawing 1 red marble out of a bag containing 4 red marbles 3 green marbles 2 blue marbles and 1 purple marbles?
4/10 Probability
-Hiadamcom
Answer:
2/5
Step-by-step explanation:
4 ÷ 10= 2/5
(4 ÷10 is for 4/10 which is red marbles to the total marbles)
The probability of the compliment is 3/5(for edge students)
Which pair of complex numbers has a real-number product? (1 + 2i)(8i) (1 + 2i)(2 – 5i) (1 + 2i)(1 – 2i) (1 + 2i)(4i)
Answer:
(1+2i)(1-2i)
Step-by-step explanation:
Answer:
(1+2i)(1-2i)
Step-by-step explanation:
Following are the pairs of the complex number:
(1+2i)(8i),
(1 + 2i)(2 – 5i)
(1+2i)(1-2i) and (1+2i)(4i)
We have to check which pair out of these is a real number product, which means which pair do not contain terms consisting of "i".
A. [tex](1+2i)(8i)= 8i+16i^{2}[/tex]
=[tex]8i-16[/tex]
B. [tex](1+2i)(2-5i)=2-i-10i^{2}[/tex]
=[tex]12-i[/tex]
C. [tex](1+2i)(1-2i)=1^{2}-4i^{2}[/tex]
=[tex]5[/tex]
D. [tex](1+2i)(4i)=4i+8i^{2}[/tex]
=[tex]4i-8[/tex]
Since, A,B,D contains the term "i" which means they are not real valued, therefore option C that is (1+2i)(1-2i) has a real number product.
What is the measure of angle 1?
SOLUTION: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures. Question 345899: The measure of angle 1 is five less than four times the measure of angle 2. If angle 1 are two form a linear pair, what are their measures.
Statistical questions will have A. only one correct answers., B.a variety of answers., C. fewer than three answers., D. no answer.
the answer is B. hope i helped!
Numbers 38 and 40 pls and thanks
38a) $10.50 To get this answer, you need to multiply $1.50 by 7
38b) $25.50 To get this answer, you need to subtract $10.50 from $36
40) The answer would be $13.7694 and it could be rounded to $13.77. To get this answer .you need to multiply $12.99 by 1.06 since it has a 6% sales tax.
I need help with this Algebra question, if someone could explain how to solve this I'd appreciate it.
See the attached picture:
Given equation: 3 + x/2 = 10
1st step subtract 3 from each side:
x/2 = 7
2nd step multiply both sides by 2:
x = 14
Step 1)
3 + x/2 = 10 ..............This is given
Step 2)
x/2 = 7 ....................... Multiplication property of equality.
This step is wrong. This step is called "Subtraction property of equality". This means you have to subtract 3 from both sides
3 + x/2 - 3 = 10 - 3
Simplifying
x/ 2 = 7
Step 3)
x = 14 ....This is called "Multiplication property of equality" because you multiply both sides by 2.
Hope that helps.
Algebra Word Problem, 9th Grade, Station 2, please help!
ANSWER
ANSWER TO QUESTION 1.
If you give [tex]x[/tex] surfing lessons, then you will earn $ [tex]25x[/tex]
If you are charged $200 for using the place, then your profit will reduce by $200.
The profit function is given by
[tex]P(x)=25x-200[/tex] dollars.
The y-intercept is [tex]-200[/tex]. It is negative because it is a cost which is a liability. So it does not add to your profit.
ANSWER TO QUESTION 2.
The slope is [tex]25[/tex]. It is positive because as the number of hours increases, the profit earned also increases. In other words there is a direct relation between the number of hours worked and the profit earned.
ANSWER TO QUESTION 3.
The slope intercept form is when an equation is written in the form;
[tex]y=mx+c[/tex],
where [tex]m[/tex] is the slope and [tex]c[/tex] is the y-intercept. The profit function in slope intercept form is
[tex]P(x)=25x-200[/tex]
ANSWER TO QUESTION 4.
If you break even, then the difference between the revenue and cost is zero. So we equate the profit function to zero.
[tex]25x-200=0[/tex]
[tex]25x=200[/tex]
[tex]x=8[/tex]
Therefore you need to give 8 different lessons to break even.
ANSWER TO QUESTION 5.
If you give 20 lessons, the [tex]x=20[/tex]. We need to substitute
[tex]x=20[/tex] in to the profit function to calculate the profit made after 20 lessons.
[tex]P(20)=25(20)-200[/tex]
[tex]P(20)=500-200[/tex]
[tex]P(20)=300[/tex].
ANSWER TO QUESTION 6.
If the new price is $75, then the new profit function becomes
[tex]P(x)=75x-200[/tex]
ANSWER TO QUESTION 7.
To find the number of lessons that lets you break even, we equate the new profit function to zero.
[tex]75x-200=0[/tex]
We solve for x by adding 200 to both sides of the equation.
[tex]\Rightarrow 75x=200[/tex]
We now divide through by 75
[tex]\Rightarrow x=\frac{200}{75}[/tex]
[tex]\Rightarrow x=2\frac{2}{3}[/tex]
Therefore you would have to 2\frac{2}{3} lessons to break even. That is approximately 3 lessons.
ANSWER TO QUESTION 8.
If you give 20 lessons and we want to find the profit you made with this new profit function, then we have to plug in [tex]x=20[/tex] in to [tex]P(x)=75x-200[/tex].
That is,
[tex]P(20)=75(20)-200[/tex]
[tex]P(20)=1500-200[/tex]
[tex]P(20)=1300[/tex] dollars
Refer to your math writing journal file named "Lines and Angles." What real-world examples did you describe for the three ways in which two lines may be related?
Answer:
Railway lines are example of parallel linesThe floor and the walls of a room are example of perpendicular linesTwo roads crossing at a signal can be termed as example of intersecting linesStep-by-step explanation:
The lines can be related in following three ways
Lines can be parallelLines can be perpendicularLines can be intersecting at an angle other than 90.Now three real life examples of above three scenarios are described below:
Railway lines are example of parallel linesThe floor and the walls of a room are example of perpendicular linesTwo roads crossing at a signal can be termed as example of intersecting linesAnswer:
1. KI
2. HI and DF
3. 8
4. 4 and 7
Step-by-step explanation:
PQ=RQ?
Someone who is smart in math help me.
Answer:
a=43
Step-by-step explanation:
90+47=137 180-137=43
What is the slope of a line perpendicular to the line in the graph?
A. −3/2
B. −2/3
C. 3/2
D. 2/3
The slope of a line from the given graph is -2/3. Therefore, option B is the correct answer.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
From the given graph,
Slope (m) = Rise/Run
= -1/1.5
Multiply both numerator and denominator by 2, we get
= -2/3
Therefore, option B is the correct answer.
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the number of units in the perimeter of a square is less than or equal to the number of square units in the area of the square which side length of a square provides a counterexample?
Answer:
2
Step-by-step explanation:2+2
The side lengths of a square in which the perimeter of a square is greater than its area is 1 unit, 2 units, and 3 units.
What is a square?A square is a 2D figure of which all sides are equal.
We know that the perimeter of a square is the sum of the lengths of all the sides and the area of a square is (side)².
Assuming a square has a side length of 4 units.
Therefore the perimeter of the square is 4×side = 4×4 = 16 units.
Now the area of the square will be (4)² = 16 sq units.
Now assuming the side length of the square is 2 units.
The area of the square is (2)² = 4 units and the perimeter is (2×4) = 8 units.
∴ The side length which provides a counter-example is 2 units.
Basically, we have to determine the numbers that when multiplied by 4 are greater than it's square such numbers are 1, 2, 3.
learn more about squares here :
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what is the GCF of 45 and 70
GCF of 45 and 70 is 5
Literal Equations Answer 5 and Ill mark brainliest!
3.- 5x-6=y
First you leave the variable alone along with 5 and you pass to the other side number 6 with the opposite sign
5x=y+6
then as 5 is multiplying you pass it dividing
y+6 x= 5
4.-2x-3y=8
First you leave the variable with 3 alone and you pass the 2x to the other side subtracting
-3y=8-2x
Then as -3 is multiplying you pass it dividing
y= 8-2x/-3
12.-7x-y=14
First you leave the variable with the 7 alone and you pass the -y to the other side adding
7x=14+y
then as 7 is multiplying you pass it dividing
x=14+y/7
18.-12x-4y=20
First you leave the variable y with the -4 alone and you pass the 12x to the other side subtracting
-4y=20-12x
Then as -4 is multiplying you pass it dividing
y= 20-12x/-4
20.- R-C/N=P
First you leave the R and the C alone and as N is dividing you pass it multiplying
R-C=PxN
Then as C is subtracting you pass it adding
R= (PxN)+C
I haven't done these types of problems in forever, so I did a few of the easier ones before I went onto a few of the harder ones. Sorry if 20 is incorrect, I wasn't too sure.
URGENT! PLEASE HELP NOW!
Jasmine is 23 years old. Three years less, 20, half is 10. If I am correct, George is 10.
The table shows the five most populated countries in the world. How many times as many people live in China then in the United States? Round to the nearest 10th if necessary.
The answer is about 4 times as many people live in China then in the United States
There are 4.4 times more people living in china than united states as the definition of ratio says "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other".
What is ratio?The indicated quotient of two mathematical expressions is referred to as a ratio. A/B stands for an ordered pair of numbers where B does not equal 0. A proportion is an equation that sets two ratios at the same value. For instance, you could write the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.
Here,
To find that how many times as many people live in China then in the United States, we need to divide the population of china by the population of united states.
let x be the value of how many times as many people live in China then in the United States,
so, the population of china=1.325 billions
the population of united states=0.304 billions
x=1.325/0.304
x=4.356
x≈4.4 times
As stated in the definition of ratio, "the quantitative relation between two amounts showing the number of times one value contains or is contained within the other," there are 4.4 times as many people living in China as there are in the United States.
To know more about ratio,
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in order to obtain energy animals must do what?
A. consume food
B. produce food
C. make new cells
D. get sunlight
Answer:
A. consume food
Step-by-step explanation:
The food they eat has energy. One eaten the energy the food had is passed along to the animal.
write the number three hundred sixty five ten thousandths in standard form
0.0365 is the standard form for this
6 and 2/3 in simplest form
The different forms you can convert 6 2/3 to would be 20/3 and 6.6 but I'd have to say 20/3 would be the simplest form to convert it to. Hope this helps <3
20/3 thats the exact form
[tex] {x}^{2 }+3x + 2 = (x + 2) \times (answer)[/tex]
x² + 3x + 2 = (x + 2)(x + 1)
consider the factors of the constant term ( + 2 ) which sum to give the coefficient of the x- term ( + 3)
These are + 2 and + 1
x² + 3x + 2 = (x + 2 )(x + 1)
I need help with these 3
First of all remeber that "a number" means we don't know the number or it could be many but not all numbers, so it is represented by x.
5. 1/2x + 6 > 20
6. 12 + 3x < -11 (They asked for the opposite of 11, the opposite of a positive number is always the negative of that number, and the opposite of a negative number is the positive of that number).
7. 2x - 8 < 5
Answers:
5) 1/2n + 6 > 20
6) 12 + 3n < -11
7) 2x - 8 < 5
Hope this helps :-)
PLEASE!!! HELP?!? Find two consecutive even integers such that the smaller added to two times the larger gives a sum of 28. The numbers are?
A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function m(x), where x is the length of the radius of the circle in feet. The homeowner estimates that he will pay $1.50 per square foot of mulch. This cost is represented by the function g(m), where m is the area requiring mulch. Which expression represents the cost of the mulch based on the radius of the circle?
If we draw the diagonals of the octagonal gazebo, the 4 diagonals divide the octagon into 8 triangles.
Note that each triangle is an isosceles triangle whose equal sides are x, the radius of the circle.
The top angle of each triangle is obtained by dividing the full angle by 8.
So, each top angle = [tex]\frac{360}{8}[/tex]
= 45°
Now, in fig., consider one of the triangles Δ OAB. Draw an altitude OC from O to the opposite side AB.
This altitude OC bisects the top angle 45°.
Therefore, ∠ AOC = 22.5°.
Now, in Δ AOC,
[tex]sin 22.5=\frac{AC}{OA}[/tex]
[tex]=\frac{AC}{x}[/tex]
So, AC = x sin 22.5°
Note that, AB = 2 AC.
Therefore, AB = 2x sin 22.5°.
Also, [tex]cos 22.5=\frac{OC}{OA}[/tex]
[tex]=\frac{OC}{x}[/tex]
So, OC = x cos 22.5°.
Area of Δ AOB = [tex]\frac{1}{2}(AB)(OC)[/tex]
= [tex]\frac{1}{2}[/tex] × (2x sin 22.5°) × (x cos 22.5°)
= [tex]\frac{1}{2} x^{2}[/tex] (2 sin 22.5° cos 22.5°)
= [tex]\frac{1}{2} x^{2}[/tex] sin 45°
= [tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex]
Area of the octagonal gazebo = 8 × one triangular area
= 8 × ([tex]x^{2}[/tex] / [tex]2\sqrt{2}[/tex])
[tex]=2\sqrt{2} x^{2}[/tex]
[tex]=2.828x^{2}[/tex]
Area required for mulch = circular area - area of the gazebo
[tex]=3.14x^{2} -2.828x^{2}[/tex]
[tex]=0.312x^{2}[/tex]
Now, cost per unit area = $1.50.
Hence, total cost g(m) = area × cost per unit area
Total cost g(m) = [tex]0.312x^{2}[/tex] × 1.5
[tex]=0.468x^{2}[/tex]
Hence, total cost g(m) = [tex]0.468x^{2}[/tex].
Answer:
1.50(piexsqared-2root2xsqared) or on edge A
Step-by-step explanation:
i just did it
Solve for x. x+23=−16 Enter your simplified answer in the box.
Answer:
x=-39
Step-by-step explanation:
subtract 23 from both sides
-16 - 23= -39
therefore x=-39
Which graph passes the vertical line test?
There are no graphs shown, but the vertical line test is something you can use to find out if a function works. If you make a vertical line anywhere on one of the graphs, it should only pass through one point. For example, a regular straight line almost always passes the vertical line test. If it's a sideways parabola, it will not.
find the perimeter....
The perimeter is adding all the outside edges together:
4 + 1 +4 +1 + 3 + 1 = 14 cm.
Judy planted vegetables on a piece of land. The land is in the right-angled triangular shape. Given the longest side of the land is y metre. The other two sides of the land are 2x metre and (2x+6) metre respectively. He fenced the land with 72 metres of barbed wire. Find the length, in metre , of each side of the land.
We know that the perimeter is 72 meters, so we have
[tex] y+2x+(2x+6)=72 \iff y+4x+6=72 \iff y=-4x+66 [/tex]
Now we can use the pythagorean theorem: the sum of the squares of the legs is the square of the hypotenuse:
[tex] (2x)^2+(2x+6)^2 = y^2 \iff (2x)^2+(2x+6)^2 = (-4x+66)^2 [/tex]
Expand the squares to get
[tex] 8 x^2 + 24 x + 36 = 16 x^2 - 528 x + 4356 [/tex]
Bring everything to the right hand side to get
[tex] 8 x^2 - 552 x + 4320 = 0 [/tex]
Divide both sides by 8:
[tex] x^2 - 69x + 540 = 0 [/tex]
This equation has solutions [tex] x=9,\ x=60 [/tex]
This solutions would yield the following side lengths:
[tex] x=9\implies\begin{cases} 2x = 18\\2x+6=24\\-4x+66=30\end{cases}[/tex]
[tex] x=60\implies\begin{cases} 2x = 120\\2x+6=126\\-4x+66=-174\end{cases}[/tex]
Since we can't have negative side lengths, we can only accept the solution x=9.
In fact, you can check that 18,24,30 is a pythagorean triplet, i.e.
[tex] 18^2+24^2=30^2 [/tex]
If y = 7x, what happens to x when y is increased by 5 times its original value?
A) x decreases 5 times its original value
B) x increases to 11/5 its original value
C) x also increases 5 times its original value
D) x decrease to 4/5 of its original value
Answer:
C) x also increases 5 times its original value
35/5=7
70/10=7
Step-by-step explanation:
What’s the answer to number one ? Solve please !!
Originally Dan has X amount of base ball cards.
So the equation would be
(x+6)/2=29
multiply both sides by 2
x+6=58
subtract 6
x=52
Check your work: 52+6=58/2=29
Help me please.......
Area of the horizontal rectangle.
A = L *W
L = 8cm
W = 3 cm
Area = 8 * 3 = 24 cm^2
Area of the Vertical Rectangle
The vertical rectangle has the same dimensions
L = 8 cm
W = 3 cm
Area = L * W
Area = 8 * 3
Area = 24 cm^2
Combined Area
Area = 24 + 24
Area = 48 cm^2 <<< Answer
Hey there!!
In order to solve for the area, let's divide this figure into two rectangles.
Area of a rectangle = Length × Breadth
First rectangle at the top - Length = 8 and width = 3
Hence, the area would be = 24cm²
The second triangle measures : Length = 3 and the width = 5
Area = 3 × 5
... 15cm²
Total area = 24cm² + 15cm²
... 24 + 15 cm²
... 39cm²
Hope my answer helps!!