For natural numbers, a multiplication can be seen as a repetitive addition. In this case, 3 times 5 is the same as addign 5+5+5. Then:
[tex]3\times5=5+5+5=15[/tex]f(x) = 4x - 3g(x) = x^3 + 2xFind (f-g)(4)
Given:
Two functions are given as below
[tex]\begin{gathered} f(x)=4x-3 \\ g(x)=x^3+2x \end{gathered}[/tex]Find:
we have to find the value of (f - g)(4).
Explanation:
we will find the value of (f - g)(4) as following
[tex]\begin{gathered} (f-g)(x)=f(x)-g(x)=4x-3-(x^3+2x)=2x-x^3-3 \\ (f-g)(4)=2(4)-(4)^3-3=8-64-3=-59 \\ (f-g)(4)=-59 \end{gathered}[/tex]Therefore, the value of (f - g)(4) = -59
Parts of a CircleFor this assignment, you will draw and label the parts of a circle. Follow the directions below to construct your circle. When you are finished, you may scan your drawing and upload it. If you do not have a scanner, you may take a picture with a digital camera or cell phone and then embed the image into a Word document.Draw circle A.Draw radius AB.Draw diameter CD.Draw chord EF.Draw central angle GAH.
It's important to consider that a radius is a segment from the center of the circle to the circumference, diameter is a segment that crosses the center of the circle and divides the circle into two equal parts, a chord is a segment that goes from one point on the circumference to another without intersecting the center of the circle, at last, a central angle is an angle formed by two radii and it has the center as the vertex.
First, let's draw circle A.
Second, let's draw radius AB.
Third, let's draw diameter CD.
Fourth, let's draw chord EF.
At last, let's draw angle GAH.
Go5. Given functions f(x) = 9x – 2, g(x) = 5 – 3x/2, and h(x) = 4x – 7/4(a) Find g(-8).(b) Find the value of x that makes g(x) = -7.(c) Find the value of x that makes f(x) = g(x).(d) Find the value of x that makes f(x) = h(x)(e) Find the x-intercept of h(x).
Answer
a) g(-8) = 17
b) When g(x) = -7, x = 8
c) When f(x) = g(x), x = (2/3)
d) When f(x) = h(x), x = (1/20)
e) x-intercept of h(x) = (7/16)
Explanation
f(x) = 9x - 2
g(x) = 5 - 3x/2
h(x) = 4x - 7/4
(a) Find g(-8).
g(x) = 5 - 3x/2
g(-8) means the value of g(x) when x = -8
g(-8) = 5 - [3×-8/2]
= 5 - (-12)
= 5 + 12
= 17
(b) Find the value of x that makes g(x) = -7.
g(x) = 5 - 3x/2
When g(x) = -7,
5 - 3x/2 = -7
5 - (3x/2) - 5 = -7 - 5
-(3x/2) = -12
[tex]\begin{gathered} \frac{-3x}{2}=-12 \\ \text{Cross multiply} \\ -3x\text{ = 2}\times-12 \\ -3x\text{ = -24} \\ \text{divide both sides by -3} \\ \frac{-3x}{-3}=\frac{-24}{-3} \\ x\text{ = 8} \end{gathered}[/tex](c) Find the value of x that makes f(x) = g(x).
f(x) = 9x - 2
g(x) = 5 - 3x/2
When f(x) = g(x)
9x - 2 = 5 - (3x/2)
9x + (3x/2) = 5 + 2
(21x/2) = 7
[tex]\begin{gathered} \frac{21x}{2}=7 \\ \text{Cross multiply} \\ 21x\text{ = 2}\times7 \\ 21x=14 \\ \text{Divide both sides by 21} \\ \frac{21x}{21}=\frac{14}{21} \\ x=\frac{14}{21}=\frac{2}{3} \end{gathered}[/tex](d) Find the value of x that makes f(x) = h(x)
f(x) = 9x - 2
h(x) = 4x - 7/4
When f(x) = h(x)
9x - 2 = 4x - (7/4)
9x - 4x = 2 - (7/4)
5x = (1/4)
[tex]\begin{gathered} 5x=\frac{1}{4} \\ \text{Divide both sides by 5} \\ \frac{5x}{5}=\frac{1}{4\times5} \\ x\text{ =}\frac{1}{20} \end{gathered}[/tex](e) Find the x-intercept of h(x).
h(x) = 4x - 7/4
The x-intercept is the value of x when h(x) = 0
When h(x) = 0
4x - (7/4) = 0
4x = (7/4)
[tex]\begin{gathered} 4x=\frac{7}{4} \\ \text{Divide both sides by 4} \\ \frac{4x}{4}=\frac{7}{4\times4} \\ x=\frac{7}{16} \end{gathered}[/tex]Hope this Helps!!!
Answer correctly and I will give Brainly
Answer:
y= 5/6x+4
Step-by-step explanation:
you go up 5
over 6
so 5/6
then its already on positive 4 so its +4
Slope-intercept form is the form of a line where y equals the product of the slope and the input plus the y-intercept, or:
y = mx + b
[tex]m = \frac{y_2 - y_1}{x_2-x_1}\\m = \frac{9 - 4}{6-0}\\m = \frac{5}{6}[/tex]
b = 4
The final equation of the line is:
y = 5/6x + 4
Consider 4 consecutive odd integers. What is the sum of the 2nd and the 4th numbers if the first number is n?1. 2n+82.4n+123. n+64. 3n+6
4 consecutive odd integers
the next consecutive odd number is only 2 more than the first number so: n+2
n = first number
n + 2 = second number
n + 4 = third number
n + 6 = fourth number
the sum of the 2nd and the 4th numbers is:
n + 2 + n + 6 = n + n + 2 + 6 = 2n +8
2n + 8
Hence, option 1 is the correct answer
Part of the proceeds from a garage sale was $305 worth of $5 bills if there were ) more bills than $20 bills find the number of each denomination
We are asked how many $20 bills and $5 bills can make up $305. To do that we will first divide 305 and 20, like this:
Now, we need to find a number that when multiplied by 20 is the closest to 305, that number is 15, since:
[tex](15)(20)=300[/tex]Therefore:
Now, subtract 300 from 305 and we get:
Which expressions simplify to a rational answer?Select each correct answer. 3√⋅2√52⋅−√2√9√⋅16−−√11−−√⋅5√
Among the given options, [tex]5\sqrt{2}.\sqrt{2}[/tex] and [tex]\sqrt{9}.\sqrt{16}[/tex] gives us a rational number.
The given options are -
1. [tex]\sqrt{3}. \sqrt{2}[/tex]
2. [tex]5\sqrt{2}.\sqrt{2}[/tex]
3. [tex]\sqrt{9}.\sqrt{16}[/tex]
4. [tex]\sqrt{11} .\sqrt{5}[/tex]
Now, Considering the 1st option, that is, [tex]\sqrt{3}. \sqrt{2}[/tex]
3 and 2, both are nonperfect squares,
[tex]\sqrt{3}. \sqrt{2} =\sqrt{6}[/tex] which is an irrational number.
Now, Considering the 2nd option, that is, [tex]5\sqrt{2}.\sqrt{2}[/tex]
[tex]5\sqrt{2}.\sqrt{2} = 5*2 = 10[/tex] which is a rational number.
Now, Considering the 3rd option, that is, [tex]\sqrt{9}.\sqrt{16}[/tex]
9 and 16, both are perfect squares,
So, [tex]\sqrt{9}.\sqrt{16} = 3*4 = 12[/tex] which is a rational number.
Considering the 4th option, that is,
3 and 2, both are nonperfect squares, [tex]\sqrt{11} .\sqrt{5}[/tex]
[tex]\sqrt{11} .\sqrt{5} = \sqrt{55}[/tex] which is an irrational number.
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-9(10-6r) help please
Given the expression :
[tex]-9\mleft(10-6r\mright)[/tex]using the distributive property to simplify the expression :
[tex]\begin{gathered} -9\mleft(10-6r\mright) \\ =-9\cdot10-9\cdot-6r \\ =-90+54r \end{gathered}[/tex]So, the result will be = -90 + 54r
Ron made a scale drawing of a hotel the scale of the drawing was 7 inches and 5 feet the actual length of a room in the hotel is 20 ft how long is the room in inches
Given data:
The given lengthof room is R=20 ft.
Th
Helppppppppppp test helppppp for today plssss help 6 and 7
7)
The triangles ABC and JGH are similar figures.
For two figures to be simmilar, the coresponding angles must be congruent and the corresponding sides must be proportional.
For these triangles:
The corresponding sides of the simimilar figures are proportional, you can express this as:
[tex]\frac{JH}{AC}=\frac{JG}{AB}=\frac{GH}{BC}[/tex]This expression indicates that the proportion between the corresponding sides is the same for all three pairs of sides. Using this information, we can determine the value of side GH
The proportion between the corresponding sides of the triangles is:
[tex]\frac{JH}{AC}=\frac{5.8}{11.6}=\frac{1}{2}[/tex]Now calculate GH as:
[tex]\begin{gathered} \frac{GH}{BC}=\frac{1}{2} \\ \frac{x}{6}=\frac{1}{2} \\ x=(\frac{1}{2})\cdot6 \\ x=3 \end{gathered}[/tex]Now the corresponding angles of the similar figures must be congruent, i.e. have the same measure so that:
[tex]\begin{gathered} \angle A=\angle J=31º \\ \angle C=\angle H=59º \end{gathered}[/tex]So a and y are
x=3
y=59º
Which value is equivalent to -7?A. -(-7)B. |-71C. 171D.-|-71
Check Option A.
[tex]-(-7)=+7[/tex]Not equivalent to -7.
Check Option B.to -7.
[tex]|-7|=7[/tex]Not equivalent to -7.
Check Option C.
[tex]|7|=7[/tex]Not equivalent to 7.
Check Option D.
[tex]-|-7|=-7[/tex]Therefore, Option D is right.
James received 60 texts yesterday. Of those texts 3/5 were from his friend Chris. Of the texts from Chris 1/3 referenced football. How many texts did James receive about football?
Out of the 60 texts that James recieved,
[tex]60\cdot\frac{3}{5}\cdot\frac{1}{3}=12[/tex]12 were about football.
The mean mark of 10 boys is 58.If the mean mark of 7 of them is 61, what is the mean mark of the remaining 3 boys
As for the 10 boys altogether,
[tex]\begin{gathered} \operatorname{mean}=58 \\ \text{and} \\ \operatorname{mean}=\frac{1}{10}\sum ^{10}_{i=1}\text{mark}_i \end{gathered}[/tex]Thus,
[tex]\Rightarrow580=\sum ^{10}_{i=1}\text{mark}_i[/tex]On the other hand, as for seven of the boys
[tex]\begin{gathered} \operatorname{mean}=61=\frac{1}{7}\sum ^7_{j=1}\text{mark}_j \\ \Rightarrow427=\sum ^7_{j=1}\text{mark}_j \end{gathered}[/tex]Thus, regarding the remaining three boys,
[tex]\Rightarrow\sum ^3_{k=1}mark_k=580-427=153[/tex]Finally, the mean of those remaining three kids is
[tex]\begin{gathered} \text{MEAN}=\frac{1}{3}\sum ^3_{k=1}mark_k=\frac{1}{3}\cdot153=51 \\ \Rightarrow\text{MEAN}=51 \end{gathered}[/tex]Thus, the mean mark of the remaining 3 boys is 51
multiply or divide as indicated. be sure to reduce all answers to lowest terms. ( the numerator and denominator of the answer should not have any factors in common)
we have the expression
[tex]\frac{3a^2+3a}{a^2-36}\cdot\frac{a^2-6a}{12a}[/tex]Simplify
we have that
a^2-36=(a+6)(a-6)
3a^2+3a=3a(a+1)
a^2-6a=a(a-6)
substitute in the given expression
[tex]\frac{3a(a+1)}{(a+6)(a-6)}\cdot\frac{a(a-6)}{12a}[/tex]Simplify
[tex]\frac{(a+1)}{(a+6)}\cdot\frac{a}{4}[/tex]therefore
the answer is
[tex]\frac{(a^2+a)}{(4a+24)}[/tex]Rebecca was comparing various sizes of canned applesauce. A 16-oz can of one brand costs $7.78 and a 12-oz can of the same brand costs $6.85. Find the savings to thenearest cent on buying 96 ounces of applesauce in 16-oz. cans compared to 12-oz. cans.$6.98$7.87$8.12$9.06None of these choices are correct.
To do the comparison, we need to calculate the cost of buying 96 ounces using both options.
For 16-oz can
The number of cans required to get 96 ounces will be
[tex]\begin{gathered} \frac{96}{16} \\ =6\text{ cans} \end{gathered}[/tex]The cost will be
[tex]\begin{gathered} 6\times7.78 \\ =46.68 \end{gathered}[/tex]The cost of 96 ounces of applesauce in 16-oz cans is $46.68.
For 12-oz can
The number of cans required to get 96 ounces will be
[tex]\begin{gathered} \frac{96}{12} \\ =8\text{ cans} \end{gathered}[/tex]The cost will be
[tex]\begin{gathered} 8\times6.85 \\ =54.80 \end{gathered}[/tex]The cost of 96 ounces of applesauce in 16-oz cans is $54.80.
The savings on buying in 16-oz cans will be
[tex]\begin{gathered} 54.80-46.68 \\ =8.12 \end{gathered}[/tex]The savings will be $8.12.
E:Given f(x) = log x and g(x) = -x + 1,which is the graph of (fog)(x)?-2-2COMPLETEThe domain of (fog)(x) isDONEX>0x < 0X > 1x <1
Given data:
The first function is f(x) = log x .
The second function is g(x) = -x + 1.
The expression for (fog)(x) is,
[tex]\begin{gathered} \mleft(fog\mright)\mleft(x\mright)=f(g(x)) \\ =f(-x+1) \\ =\log (-x+1) \end{gathered}[/tex]The domain of the above function is x<1.
Out of 200 people eating at a diner, 70% ordered sandwiches. How many people ordered sandwiches? Select one: 130 people
if 70% of 200 people ordered sandwiches then the number of people who ordered sandwiches
= 70% * 200
= 70/100 * 200
= 140 People
The 3rd option
Which of the following correctly shows the next two terms after -40 in the pattern?-10, 20, -40,...А.80, 160B-2.5,5С60, -80D80, -160
In the pattern -10,20,-40 every next term is obtained by multiplication of -2.
So terms next to -40 is,
[tex]-40\cdot(-2)=80[/tex]Term next to 80 is,
[tex]80\cdot(-2)=-160[/tex]Thus next two terms od -40 are 80 and -160.
Option D is correct option.
What rule describes a dilation with a scale factor of 1/2 and the center of dilation at orgin.
Explanation:
When we dilate a point by a scale factor "a" and the center of the dilation is the origin, the original point (x,y) changes as follows:
[tex](x,y)\rightarrow(ax,by)[/tex]Each coordinate value is multiplied by the scale factor.
In this case, the scale factor is 1/2:
[tex]a=\frac{1}{2}[/tex]Therefore, the transformation rule is:
[tex](x,y)\rightarrow(\frac{1}{2}x,\frac{1}{2}y)[/tex]This rule is shown in option C.
Answer:
C.
[tex](x,y)\operatorname{\rightarrow}(\frac{1}{2}x,\frac{1}{2}y)[/tex]Which equation represents a line which is parallel to y=0?A. x=1B. y=x+3C. y=xD. y=6
ANSWER
D. y = 6
EXPLANATION
Parallel lines have the same slope.
In this problem, the given line is y = 0, which is a horizontal line at y = 0. Because it is a horizontal line, its slope is 0. From the options, we have to find which line has a slope of 0.
• Option A: x = 1 is a vertical line passing through x = 1. Its slope is undefined → ,not parallel,.
,• Option B: the slope of this line is 1 → ,not parallel.
,• Option C: the slope of this line is also 1 → ,not parallel.
,• Option D:, y = 6 is also a horizontal line, so its slope is 0 → ,this line is parallel ,to the given line.
Find mZCEF if mZCEF= 2x + 30,mZDEC = x + 102, and mZDEF = 132°DEFA) 30°C) 410B) 29°D) 320
1) Gathering the data
m∠CEF=2x +30
m∠DEC=x+102
m∠DEF=132
2) From the picture we infer that
m∠DEF = m∠CEF+m∠DEC
132 = m∠CEF +x +102
132-x-102=m∠CEF
m∠CEF=30
is 53 prime or composite numberhow can I find the numbers for 58
Answer:
Factors of 58: 1,2,29 and 58
58 It is a composite number.
Step-by-step explanation:
The factors of 58 are the numbers that divide 58 leaving 0 as the remainder.
For example, 58/29=2, the remainder of 0.
Factors of 58: 1,2,29 and 58
58 It is a composite number.
Determine the slope of the line represented by the equation: y=3/10x+6
The slope intercept form is given by the equation
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given:
[tex]y=\frac{3}{10}x+6[/tex]Based on the given, it is already in the slope intercept form, and by inspection, we can determine the slope of the line is equal to 3/10.
find the slopes of the line that goes thru the following points
Given:
Find-: Slope of the line.
Sol:
The slope of line is:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Where,
[tex]\begin{gathered} (x_1,y_1)\text{ = First point} \\ \\ (x_2,y_2)=\text{ Second point} \end{gathered}[/tex]Choose any point:
[tex]\begin{gathered} (x_1,y_1)=(-1,-4) \\ \\ (x_2,y_2)=(0,-1) \end{gathered}[/tex]So, the slope of the line is:
[tex]\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ \\ m=\frac{-1-(-4)}{0-(-1)} \\ \\ m=\frac{-1+4}{0+1} \\ \\ m=\frac{3}{1} \\ \\ m=3 \end{gathered}[/tex]Slope of line is 3.
Find the length of the arc in terms of pi. AB=
We will determine the arc length as follows:
*First: We transform the angle to radians:
[tex]\alpha=144\cdot\frac{\pi}{180}\Rightarrow\alpha=\frac{4}{5}\pi[/tex]*Second: We will determine the arc length:
[tex]s=(10)(\frac{4}{5}\pi)\Rightarrow s=8\pi[/tex]So, the arc length from A to B is 8*pi.
. Noah may choose between two accounts in which to invest $4000. Account A offers 2.2% annual interest
compounded monthly. Account B offers continuous compound interest. Noah plans to leave his investment
untouched (no further deposits and no withdrawals) for 15 years.
(a) Which account will yield the greater balance at the end of 15 years?
(b) How much more money does Noah earn by choosing this more profitable account?
Answer:
Using the compound amount formula, account B will yield the greater balance at the end of 15 years and Noah earn $4 more money by choosing this more profitable account.
In the given question,
Noah may choose between two accounts in which to invest $4000.
Principal Amount(P) = $4000
Account A offers 2.2% annual interest compounded monthly.
Rate(r) = 2.2% = 0.022
In a year have twelve month so n=12
Account B offers continuous compound interest.
Noah plans to leave his investment untouched for 15 years.
Time(t) = 15
Formula for amount after t years = P(1+ r/n)^nt
Amount after 15 years = 4000(1+ 0.022/12)^12*15
Simplifying
Amount after 15 years = 4000(1+0.00183)^180
Amount after 15 years = 4000(1.00183)^180
Amount after 15 years = 4000*1.39
Amount after 15 years = $5560
Account B offers compounded continuously.
So formula used = Pe^(rt)
Amount after 15 years = 4000*e^(0.022*15)
Amount after 15 years = 4000*e^(0.33)
Amount after 15 years = 4000*1.391
Amount after 15 years = $5564
(a) We have to find which account will yield the greater balance at the end of 15 years.
As we can see in Account A amount after 15 years is $5550 and in Account B amount after 15 years is $5564.
So account B will yield the greater balance at the end of 15 years.
(b) We have to find how much more money does Noah earn by choosing this more profitable account.
Noah earn money more by profitable account=Account B amount-Account A amount
Noah earn money more by profitable account=$5564-$5560
Noah earn money more by profitable account=$4
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These data are the number of on campus burglaries reported in a given year for nine western Pennsylvania universities.15 11 4 15 9 7 12 5 15For the data find the mean median mid range in the mall round to one decimal place if necessary.
Recall how to find the mean, the median, the midrange and the mode of a data set.
To find the mean, add all the values and divide the result over the amount of values:
[tex]\frac{15+11+4+15+9+7+12+5+15}{9}=\frac{93}{9}=10.333...\approx10.3[/tex]To find the median, list the data from smallest to largest and identify the number that is placed at the middle of the list. If the number of data points is even, the median is the average of the two middle data points in the list:
[tex]4,5,7,9,11,12,15,15,15[/tex]In this case, the median is 11 because there are 4 numbers before it and 4 numbers after it.
To find the midrange, calculate the mean between the minimum and maximum numbers of the data set:
[tex]\frac{4+15}{2}=9.5[/tex]The mode is the value that appears most frequently in the data set. In this case, the number 15 appears three times and the rest just 1. Then, the mode is 15.
Therefore, the answers are:
Mean: 10.3
Median: 11
Midrange: 9.5
Mode: 15
During World War I, mortars were fired from trenches 3 feet below ground level. The mortars had a velocity of150 ft/sec. Determine how long it will take for the mortar shell to strike its target.• What is the initial height of the rocket? -3 ft.• What is the maximum height of the rocket? 348.56 ft• How long does it take the rocket to reach the maximum height ? 4.68750 sec.• How long does it take the rocket to hit the ground (ground level)? 9.35 sec.• How long does it take the rocket to hit a one hundred feet tall building that is in it's downward path?[ Select]• What is the equation that represents the path of the rocket? Select]
the radius of a circle is 1 what is the length of an arc that subtends an angle of 10pi/9 radians
To convert from radians to degrees, you have to know that 180 degrees is equal to one pi
[tex]\frac{10\text{ pi}}{9}\text{ = }\frac{10X180^{\circ}}{9}=200^{\circ}[/tex]Angle 360 -200 = 160
[tex]\begin{gathered} lengthofarc=\frac{\emptyset}{360}X\frac{2\pi\text{ r}}{1} \\ =\text{ }\frac{160}{360}X\frac{2\pi\text{ X 1 }}{1} \end{gathered}[/tex]length of arc =2.7925
The length of the arc is approximately 2.8
Will give brainliest if someone answers this problem correctly
The equation of the line in fully simplified slope intercept form is y = -5x + 8.
From the graph:
Take any two points:
suppose (1,3) and (2,-2)
slope m = y2 - y1 / x2 - x1
= -2 - 3 / 2 - 1
= -5/1
= -5
substitute m and (1,3) in y = mx + c
3 = -5*1 + c
3 = -5 + c
c = 3+5
c = 8
y = mx+c
y = -5x + 8.
Therefore the equation of the line in fully simplified slope intercept form is y = -5x + 8.
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