The slope-intercept form is y = mx + b
Where m is the slope and b is constant represents y-intercept
given the points (-2, 6) and (4,-3)
So, the slope is = m
[tex]m=\frac{6-(-3)}{-2-4}=\frac{9}{-6}=-\frac{3}{2}=-1.5[/tex]So, y = -1.5 x + b
To find b substitute with one of the given points
So,
When x = -2 , y = 6
So,
6 = -1.5 * -2 + b
6 = 3 + b
b = 6 - 3 = 3
So, y = -1.5 x + 3
So, the equation of the line is y = -1.5 x + 3
Find mzi. 1 5 H 9 J Write your answer as an integer or as a decimal rounded to the nearest tenth.
Given
[tex]\begin{gathered} IH=5 \\ IJ=9 \end{gathered}[/tex]We can find the measure of I below.
Explanation
[tex]\begin{gathered} CosI=\frac{Adjacent\text{ }side}{Hypotenuse\text{ side}}=\frac{IH}{IJ}=\frac{5}{9} \\ I=Cos^{-1}\frac{5}{9} \\ I=Cos^{-1}0.98176 \\ I=56.3^{\circ\:} \end{gathered}[/tex]Answer:
[tex]I=56.3^0[/tex]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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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
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
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.
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.
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.
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]
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.
A work shift for an employee at restaurant count of 8 hours what fraction of the employees work shift is represented by 2 hours
Let:
T = Total number of hours = 8
n = Number of hours = 2
Therefore, the fraction is:
[tex]\frac{2}{8}=\frac{1}{4}[/tex]Answer:
[tex]\frac{1}{4}[/tex]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.
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.
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
Write the equation for the given parent function and listed transformations, please.x^2, right 1, reflect across the x-axis, vertical shrink by 1/3
given the function
[tex]f(x)=x^2[/tex]right 1
[tex]f(x-1)=(x-1)^2[/tex]reflect accros x axis
[tex]-f(x-1)=-(x-1)^2[/tex]vertical shrink by 1/3
since it says a shrink
vertical compressions a<1
[tex]-\frac{1}{3}f(x-1)=-\frac{1}{3}(x-1)^2[/tex]then the equation is
[tex]-\frac{1}{3}\left(x-1\right)^{2}[/tex]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
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
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.
. 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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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.
The graph shown is the solution set for which of the following
Given the graph of an inequality, you can identify that the boundary has the form of a "V". Therefore, you can identify that it is an Absolute Value Inequality.
By definition, an Absolute Value Equation written in Vertex Form is:
[tex]y=a|x-h|+k[/tex]Where "h" is the x-coordinate of the Vertex, and "k" is the y-coordinate of the Vertex. If "a" is negative, the graph opens down and if it is positive, the graph opens up.
In this case, the graph opens up, and you can identify in the graph that the Vertex is:
[tex]\mleft(-1,0\mright)[/tex]You can also identify that the boundary is formed by solid lines and the shaded region is below the boundary. This indicates that the inequality has this form:
[tex]\begin{gathered} y\leq a|x-(-1)| \\ \\ y\leq a|x+1| \end{gathered}[/tex]Notice that this inequality is given in the Answer choices:
[tex]y\le\mleft|x+1\mright|[/tex]In order to check it, let's choose two points on the shaded region:
[tex]\mleft(-2,-1\mright),(2,-2)[/tex]Substitute the coordinates into the inequality and evaluate. If they satisfy the inequality, then the are solutions to it:
- For the first point:
[tex]\begin{gathered} -1\le|-2+1| \\ \\ -1\le1\text{ (True)} \end{gathered}[/tex]- For the second point:
[tex]\begin{gathered} -2\le|2+1| \\ \\ -2\le3\text{ (True)} \end{gathered}[/tex]Hence, the answer is: Second option.
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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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:
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
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.
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
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.
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]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
-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
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.