To solve the exercise, first we are going to find the slope of the function f(x). Since we have a graph of the function, we can see two points through which the line passes:
[tex]\begin{gathered} (x_1,y_1)=(0,2) \\ (x_2,y_2)=(1,-1) \end{gathered}[/tex]Now we can use this formula to find the slope:
[tex]\begin{gathered} m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \text{ Where m is the slope and} \\ (x_1,y_1)\text{ and }(x_2,y_2)\text{ are two points through which the line passes} \end{gathered}[/tex][tex]\begin{gathered} m_{f(x)}=\frac{-1-2}{1-0} \\ m_{f(x)}=\frac{-3}{1} \\ m_{f(x)}=-3 \end{gathered}[/tex]Then, the slope of the function f(x) is -3.
On the other hand, the function g(x) also describes a line and is written in slope-intercept form, that is:
[tex]\begin{gathered} y=mx+b\Rightarrow\text{ slope-intercept form} \\ \text{ Where m is the slope and} \\ b\text{ is the y-intercept of the line} \end{gathered}[/tex]Then, you can see that the slope of the function g(x) is -3, because
[tex]\begin{gathered} g(x)=-3x-6 \\ m_{g(x)}=-3 \\ \text{and} \\ b=-6 \end{gathered}[/tex]Therefore, the slope of f(x) is the same as the slope of g(x) and the correct answer is option A.
Find the greatest possible percent error in calculating the volume of the prism.
Answer:
23%
Step-by-step explanation:
Volume of a rectangular prism:
A rectangular prism has three dimensions, which are the base b, the height h and the width w.
The volume is:
V = b*w*h
In this question:
The base is 12 inches, so b = 12.
The width is 5 inches, so w = 5.
The height is 7 inches, so h = 7.
The volume is:
V = 12*5*7 = 420 cubic inches.
With error:
They are rounded to the nearest inch, so:
The base can go from 12 - 0.5 = 11.5 to 12 + 0.5 = 12.5 inches.
The width can go from 5 - 0.5 = 4.5 to 5 + 0.5 = 5.5 inches
The height can go from 7 - 0.5 = 6.5 to 7 + 0.5 = 7.5 inches.
Volume with the smallest values:
We have that b = 11.5, w = 4.5, h = 6.5. So
V = 11.5*4.5*6.5 = 336.375
Error of 420 - 336.375 = 83.625
As a percent, the error is of (83.625/420)*100 = 19.9%
Volume with the higher values:
We have that b = 12.5, w = 5.5, h = 7.5. So
V = 12.5*5.5*7.5 = 515.625
515.625 - 420 = 95.625
As a percent, the error is of (95.625/420)*100 = 22.7% = 23%
15 lb of beans are distributed equally into 10 bags that give out of at the food bank how many pounds of beans are in each bag until your answer in simplest form
Determine the pounds of beans in each bag.
[tex]\begin{gathered} \frac{15}{10}=\frac{3\cdot5}{2\cdot5} \\ =\frac{3}{2} \\ =1\frac{1}{2} \end{gathered}[/tex]So answer is 1 1/2.
at one point during the summer, Marsha has read 500 pages of her summer reading assignment, and Jan has read read 460 pages. marsha reads reads 20 pages per week for the reminder of the summer, how many weeks,w,will it take before the girls have read the same number of pages?
Answer:
500 + 20w = 460 + 30w
Explanation:
We will calculate an equation for the number of pages read by each girl.
Marsha has read 500 pages and she reads 20 pages per week. It means that after w weeks, she will read 20 times w plus the 500 initial pages, so:
M = 20w + 500
In the same way, Jan has read 460 pages and she reads 30 pages per week. So, the equation that model the number of pages that she reads after w weeks is:
J = 30w + 460
Now, we need to find w such that M and J would be equal, so, we will formulate the following equation:
M = J
20w + 500 = 30w + 460
500 + 20w = 460 + 30w
Therefore, the answer is:
500 + 20w = 460 + 30w
which is rational?3 2/3 + 3
Use the distance formula to determine if angle ABC is congruent to angle DEF.Select Yes or No for each statement.
Dorsain, this is the solution for option A:
Option A:
Step 1: Let's calculate the distance from A to B, as follows:
d = √0² - -5² + 0² - -7²
d = √5² + 7²
d = √25 + 49
d = √74
d = 8.6 units
Step 2: Let's calculate the distance from B to C, this way:
d = √4² - 0² + -7² - 0²
d = √4² - 7²
d = √16 + 49
d = √65
d = 8.06 units
Step 3: Let's calculate the distance from A to C, as follows:
d = √(4 - -5)² + (-7 - -7)²
d = √9² + 0²
d = √81
d = 9 units
Step 4: Let's calculate the distance from D to E, this way:
d = √(-1 - -6)² + (1 - -6)²
d = √5² + 7²
d = √25 + 49
d = √ 74
d = 8.6 units
Step 5: Let's calculate the distance from E to F, as follows:
d = √(5 - -1)² + (-8 -1) ²
d = √6² + -9²
d = √36 + 81
d = √117
d = 10.81 units
Step 6: Let's calculate the distance from D to F, this way:
d = √(5 - -6)² + (-8 - -6)²
d = √11² + -2²
d = √121 + 4
d = √125
d = 11.18 units
Step 7: We can conclude that only sides AB and DE are congruent, (8.6 units) but the other two sides of triangles ABC and DEF aren't congruent. Therefore, these two triangles are not congruent.
Now you can continue, following steps 1 to 7 to evaluate options B and C.
MINI Statistics in 2021 900Carissa Brooks & 10Homework: 2.52016 (18 completeNW Score:Score: DaX 25.49Aceasta es am 38,000 miles and advisor 2, 250 mes. Assume the lens of the res have a belspetsin)the tears are my cheese 3700 ms 31.000 ms. meore that corresponds to amanten
In order to find the z-score for the value 34000, we can use the formula:
[tex]Z=\frac{x-\mu}{\sigma}[/tex]Where μ is the mean and σ is the standard deviation.
So using x = 34000, μ = 38000 and σ = 2250, we have:
[tex]Z=\frac{34000-38000}{2250}=-\frac{4000}{2250}=1.78[/tex]So the z-score for the value 34000 is 1.78.
Isabelle is making a scrapbook. Each page of the scrapbook is a square with a length of 11in. If each page holds three pictures that each have an area of 15in2, what is the remaining area on each page in square inches that can be used for decoration?
Given:
A page of the scrapbook is a square with a length of 11 in
Each page holds three pictures that each have an area of 15in²
To find the remaining area, we will find the area of the page and the total area of the pictures, then subtract the area of the pictures from the area of the page
The area of the page = 11 x 11 = 121 in²
Total area of the pictures = 3 x 15 = 45 in²
So, the remaining area = 121 - 45 = 76 in²
Which best explains the transformation of TUV to form T'U'V
the figure T'U'V' is reflected on the x-axis, therefore is transformed by (x, - y)
answer: the first one
Based on the triangles shown below, which statements are true? Select All that apply.
Answer:
All the options except the third choice are correct.
Explanation:
In the given figure:
[tex]\angle\text{GER}\cong\angle\text{TEA (Vertical Angles)}[/tex]Since angles G and T are congruent:
• Triangles GER and TEA are similar triangles.
Therefore, the following holds:
[tex]\begin{gathered} \triangle\text{GRE}\sim\triangle\text{TAE} \\ \triangle E\text{GR}\sim\triangle E\text{TA} \\ \frac{GR}{TA}=\frac{RE}{AE} \end{gathered}[/tex]Similarly:
[tex]\begin{gathered} \frac{EG}{ET}=\frac{GR}{TA} \\ ET=10,EG=5,TA=12,RG=\text{?} \\ \frac{5}{10}=\frac{RG}{12} \\ \frac{1}{2}=\frac{RG}{12} \\ 2RG=12 \\ RG=\frac{12}{2} \\ RG=6 \\ \text{Therefore if }ET=10,EG=5,and\; TA=12,then\; RG=6 \end{gathered}[/tex]Finally, angles R and A are congruent.
[tex]\begin{gathered} m\angle R=m\angle A \\ 80\degree=(x+20)\degree \\ x=80\degree-20\degree \\ x=60\degree \end{gathered}[/tex]The correct choices are:
[tex]\begin{gathered} \triangle\text{GRE}\sim\triangle\text{TAE} \\ \triangle E\text{GR}\sim\triangle E\text{TA} \\ \frac{GR}{TA}=\frac{RE}{AE} \\ I\text{f }ET=10,EG=5,and\; TA=12,then\; RG=6 \\ \text{If }m\angle R=80\degree\text{ and }m\angle A=(x+20)\degree,then\; x=60\text{ } \end{gathered}[/tex]Only the third choice is Incorrect.
Can you please help me
length of arc PQ = 3.14 meters (option B)
Explanation:[tex]\begin{gathered} \text{Length of an arc in radians = r}\theta \\ \end{gathered}[/tex]The angle given is in degrees:
[tex]\text{length of an arc using angle in degr}ees\text{ = }\theta/360\times2\pi r[/tex][tex]\begin{gathered} \theta\text{ = 60}\degree \\ PR\text{ = radius =3m } \\ \text{let }\pi\text{ = 3.14} \\ \text{length of arc PQ = }\frac{60}{360}\times2\times3.14\times3 \end{gathered}[/tex][tex]\begin{gathered} \text{length of arc PQ = }\frac{1}{6}\times3.14\times6\text{ = 3.14} \\ \text{length of arc PQ = 3.14 meters ( option B)} \end{gathered}[/tex]Eduardo has 45 yards of rupe light.Exactly how many more yards does he need to finish the car's ceiling?ItemLength of Rope Light (yds)Front spoilerRear spoilerCeilingDONENaimmisDashboardWhat is the fraction
(Combining Equations)-2x + 7y = -5 -2x - 4y = 6
-2x + 7y = -5 --------------------------(1)
-2x - 4y = 6 ------------------------------(2)
subtract equation (2) from equation (1)
11y = -11
Divide both-side of the equation by 11
y = -1
substitute y=-1 into equation(1) and then solve for x
-2x + 7(-1) = -5
-2x - 7 = -5
add 7 to both-side of the equation
-2x = -5+7
-2x = 2
Divide both-side of the equation by -2
x= -1
please help me the blue line is what I have to find
Weare given to complete a blank in the equation:
2 m - 3 - _____ + 17 = 14
So, we start by combining all the terms we can combine (the pure numerical terms that don't have the variable "m")
2 m - 3 + 17 - ______ = 14
2 m + 14 - _______ = 14
Now we subtract 14 from both sides of the equal sign:
2 m - ____ = 0
which means that the blank should be exactly "2m" such that subtracted from 2m gives a perfect zero.
Answer: complete the blank with "2 m"
In the following exercise a formula is given, along with the values of all but one of the variables in the formula. Find the value of the variable that is not given S = 2LW+2WH + 2LH; S = 108, L= 3, W= 4
Answer:
H = 6
Explanation:
We are given the values of S, L, and W, and so we put them into the formula to get
[tex]108=2(3)(4)+2(4)H+2(3)H[/tex]We simplify the above to get
[tex]108=24+8H+6H[/tex]Subtracting 24 from both sides gives
[tex]108-24=24-24+8H+6H[/tex][tex]84=8H+6H[/tex]Adding the like terms on the right-hand sides gives
[tex]84=14H[/tex]Finally, dividing both sides by 14 gives
[tex]\frac{84}{14}=\frac{14H}{14}[/tex]which gives
[tex]H=6[/tex]which is our answer!
The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 6.2% per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay). Round your answer to the nearest hundredth.
Solution
for this case we have the following equation:
[tex]A=A_oe^{kt}_{}[/tex]the constant would be:
k= -0.062
Then we can do this:
[tex]\frac{1}{2}A_o=A_oe^{-0.062t}[/tex]solving for t we have:
[tex]\ln (\frac{1}{2})=-0.062t[/tex][tex]t=-\frac{\ln (0.5)}{-0.062}=11.179\text{days}[/tex]Rounded to the nearest hundredth would be:
11.18 days
which of the following is the correct way to simplify
We need to apply the law of exponents. In this case we need to
Keep the base and add the exponents,
that is the third option.
which rational number is the opposite of 1.7? Select all that apply. -1 7/10-1.71 7/10
Answer:
The opposite of 1.7 are;
[tex]\begin{gathered} -1.7 \\ \text{and} \\ -1\frac{7}{10} \end{gathered}[/tex]Explanation:
We want to find the rational number that is opposite of 1.7.
The opposite of 1.7 is;
[tex]-(1.7)=-1.7[/tex]The opposite of 1.7 can be written as;
[tex]-1.7=-1\frac{7}{10}[/tex]The opposite of 1.7 are;
[tex]\begin{gathered} -1.7 \\ \text{and} \\ -1\frac{7}{10} \end{gathered}[/tex]Jefferson works part time and earns 1,520in four weeks how much does he earn each weet
To determine how much he earns each week we need to divide the amount given by 4, that is we need to kae the division:
[tex]1520\div4[/tex]The long division is shown below:
To make the long division we notice that we can't divide the first number (one) by four, then we need to put down the five to get a 15, this number can be divided by four. Fifteen can be divided by four, the number four fits 3 times in fifteen, then we have a three as the first nonzero number. three by 4 is 12. We subtract 12 from 15 to get 3 and the we downed the following two. This procedure is repeated until we have a number that gives zero as a remainder. This is shown in the picture above.
From it we conclude that Jefferson earns $380 each week
Can I find a tutor to help me bro ?
Solution
Given the quadratic equation:
x² + 2x + 7 = 21
x² + 2x + 7 - 21 = 0
x² + 2x - 14 = 0
a = 1, b = 2, c = - 14
(1) The number of solutions of a given quadratic equation is determine by the discriminant.
From the given values;
(2)² - 4(1 x -14) = 4 + 56 = 60
60 > 0 ( 2 solutions)
1 positive solution and 1 negative solution
Thus, number of positive solutions to this equation is one
(2) The greatest solution or positive solution to the equation is calculated as;
2. g(x) = (x-3)^3 identity the parent function, shape (you can draw it), and domain and range of parent function
Step 1
Domain: The domain is the set of values for x, in the function x can take any values, so the set is all the real numbers
Range:The range is the set of values for y, y can take any values, so the set is all the real numbers
[tex]\begin{gathered} \text{Domain(-}\infty,\infty) \\ \text{Range(-}\infty,\infty) \end{gathered}[/tex]1) Find the angle in degrees without using a calculator: a) arcsin( √3/2)
Then, since arcsin is a function:
[tex]\begin{gathered} R\rightarrow\mleft\lbrace-1;\text{ 1}\mright\rbrace \\ We\text{ take only value }\theta=\frac{\pi}{3},\text{ without the periodic values.} \\ \text{That means,} \\ \arcsin (\frac{\sqrt[]{3}}{2})=60\text{ degrees= }\frac{\pi}{3} \end{gathered}[/tex]Given the venn diagram below, what is the correct notation!A. G∩(M∪F)′B. (M∩F)′C. none of theseD. (M∪F)′
Sets
The image shows a Venn diagram of two sets M and F inside of a containing set G.
We must recall the following notations:
U = Union of sets. Everything inside of any of the sets.
∩ = Intersection between two sets. The common part of both sets.
' = Negation. Everything outside of a set or a set operation.
It's required to express in set notation the grayed part of the diagram. Note it's inside of G and outside of both M and F.
As stated above, the notation to express the union of sets is U and it's precisely the white region of the diagram. So M U F is the white part.
But we want the outside of that white part, so we use (M U F)'.
That is outside of the union, but it includes everything (the entire universe). So we must intercept that with G to take only the grayed part, so the answer is:
A. G∩(M∪F)′
Answer:
Step-by-step explanation:
The image shows a Venn diagram of two sets M and F inside of a containing set G.
We must recall the following notations:
U = Union of sets. Everything inside of any of the sets.
∩ = Intersection between two sets. The common part of both sets.
' = Negation. Everything outside of a set or a set operation.
It's required to express in set notation the grayed part of the diagram. Note it's inside of G and outside of both M and F.
As stated above, the notation to express the union of sets is U and it's precisely the white region of the diagram. So M U F is the white part.
But we want the outside of that white part, so we use (M U F)'.
That is outside of the union, but it includes everything (the entire universe). So we must intercept that with G to take only the grayed part, so the answer is:
A. G∩(M∪F)′
where does the x-intercept in to the y-intercept
x-intercept -3
y-intercept 6
What is the hcf of 13 and 31?
Answer: 1
Step-by-step explanation:
The factors of 13 are: 1, 13
The factors of 31 are: 1, 31
So the hcf is 1
A bouncy ball is dropped such that the height of its first bounce is 6.25 feet and each successive bounce is 74% of the previous bounces height. What would be the height of the sixth bounce the ball
EXPLANATION
The heigth of the first bounce is 6.25 feet
Each successive bounce is 74% of the previous bounces height
For the first bounce, the ball hit a height of 6.25 feet
The first successive bounce = 74% of the previous bounce
The previous bounce = 6.25 feets
Hence, 74% x 6.25 = Next successive bounce
The next successive bounce = 74/100 x 6.25
The next succesive bounce = 0.74 x 6.25
= 4.625 feets
For the next successive bounce
The previous successive bounce = 4.625 feets
The next successive bounce = 74% x 4.625
The next successive bounce = 0.74 x 4.625
The second successive bounce = 3.4225 feets
For third successive
Which one of the following graphs represents the solution of the inequality 2x + 1 ≥ 3?A.-3-2-1 0 123B.++-3-2-1 0123-3-2-1 0 123-3-2-1 0 1 2 3OC.OD.
The inequality given is:
[tex]2x+1\ge3[/tex]Let's solve for x:
[tex]\begin{gathered} 2x\ge3-1 \\ . \\ x\ge\frac{2}{2} \\ . \\ x\ge1 \end{gathered}[/tex]The solution set of this inequality is the set of all numbers bigger or equal than 1.
Thus, the correct answer is option A, where we can see that the values start at 1 and goes to positive infinity.
Write an inequality, in slope-intercept form, for the graph below. If necessary,use "<=" for < or ">" for >(4,2)(-4,0)
EXPLANATION
We can write an inequality in slope-intercept form by using the two given points, (x_1,y_1)= (-4,0) and (x_2,y_2)=(4,2), as shown as follows:
[tex]\text{Slope}=\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]Replacing terms:
[tex]\text{Slope}=\frac{(2-0)}{(4-(-4))}[/tex]Subtracting terms:
[tex]\text{Slope}=\frac{2}{8}=\frac{1}{4}[/tex]Now, we need to find the y-intercept.
As we can see in the dashed line, the y-intercept is at point (x,y)=(0,1).
Hence, the equation of the dashed line is as follows:
y = (1/4)x + 1
But as the solution represents all the points that are below this line, the inequality should be as following:
y < (1/4)x + 1
Sorry if it's a little blurryAlso this worksheet is about simplify
Write four different equation with -3 as solution.
5x + 20 = 5 subtract 20 both sides
5x = 5 - 20
5x = -15 divide by 5 both sides
x = -15/5
x = -3
3x - 6 = -3x - 24 add 3x both sides
3x + 3x - 6 = - 24
6x - 6 = -24 add 6 both sides
6x = -24 + 6
6x = -18 divide by 6 both sides
x = -18/6
x = -3
1/3 x + 10 = 9 subtract 10 both sides
1/3 x = 9 -10
1/3 x = - 1 multiply by 3 both sides
x = -1(3)
x = -3
x + 23 = 20 subtract 23 both sides
x = 20 - 23
x = -3
In all previous procedures you constructed the equation by taking into account that x=-3, that is the key to determine the expressions left side and right side. For example in the last procedure for x + 23 = 20, you know that -3 plus 20 is equal to 20.
5) Each table represents a proportional relationship. (From Unit 2 Lesson 2) a) Fill in the missing parts of the table. b) Draw a circle around the constant of proportionality. a х у a b т n 2 10 12 3 15 20 10 3 735 5 10 18 1 1 1
Given:
The table represents a proportional relationship.
a) To find the missing values of table,
For first table,
[tex]\begin{gathered} \frac{10}{2}=\frac{15}{x} \\ 10x=15\times2 \\ 10x=30 \\ x=\frac{30}{10}=3 \\ \frac{15}{3}=\frac{y}{7} \\ 15\times7=3y \\ 3y=105 \\ y=\frac{105}{3}=35 \\ \frac{35}{7}=\frac{y}{1} \\ 35=7y \\ y=\frac{35}{7}=5 \end{gathered}[/tex]For second table,
[tex]\frac{3}{12}=\frac{b}{20}=\frac{10}{a}=\frac{b}{1}[/tex][tex]\begin{gathered} \frac{3}{12}=\frac{b}{20} \\ 3\times20=12y \\ b=\frac{60}{12}=5 \\ \frac{5}{20}=\frac{10}{a} \\ 5a=10\times20 \\ a=\frac{200}{5}=40 \\ \frac{10}{40}=\frac{b}{1} \\ 40b=10 \\ b=\frac{10}{40}=\frac{1}{4} \end{gathered}[/tex]For third table,
[tex]\begin{gathered} \frac{3}{5}=\frac{n}{10}=\frac{18}{m}=\frac{n}{1} \\ \frac{3}{5}=\frac{n}{10} \\ 30=5n \\ n=\frac{30}{5}=6 \\ \frac{3}{5}=\frac{18}{m} \\ 3m=90 \\ m=30 \\ \frac{3}{5}=\frac{n}{1} \\ 5n=3 \\ n=\frac{3}{5} \end{gathered}[/tex]b) To draw the circle around the constant of proportionality.
For first table the constant of proportionality is 5.
For second table the constant of proportionality is 1/4.
For third table the constant of proportionality is 3/5 .
shelton earns an hourly wage at a grocery store. the following expression represents Sheltons take home pay after taxes, social security, and his health care plan deducted. let x represent the number of hours shelton worked. 10.25x-0.21(10.25x) part A: which term represents sheltons total pay before deduction. part B:which term represents sheltons deductions. part C:how much is sheltons hourly wage. part D:what percentage is decuted from sheltons pay for taxes , social security , and health care plan. part E: shelton wants to save 1675 for a new laptop. if shelton saves 25% of his take hime pay,how many hours will be need to work to meet his savings goal
The expression that represents Shelton's take-home pay after all deductions is:
[tex]10.25x-0.21\mleft(10.25x\mright)[/tex](a)Shelton's total pay before deduction = $10.25x
(b) Shelton's deductions = $0.21(10.25x)
(c)Since x represents the number of hours Shelton worked, his hourly wage will be: $10.25
(d)Since 0.21 of his total pay is deducted, the percentage that is deducted from Shelton's pay is 21%.
(e)If Shelton saves 25% of his take-home pay, this will be:
[tex]0.25(10.25x-0.21\mleft(10.25x\mright))[/tex]If he wants to save $1,675, we then have:
[tex]0.25(10.25x-0.21\mleft(10.25x\mright))=1675[/tex]We are required to solve for x.
[tex]\begin{gathered} 0.25(10.25x-2.1525x)=1675 \\ 0.25(10.25x-2.1525x)=1675 \\ 0.25\times8.0975x=1675 \\ 2.024375x=1675 \\ x=\frac{1675}{2.024375} \\ x=827.4\approx827\text{ hours} \end{gathered}[/tex]Shelton will work for 827 hours to meet his goal.