Step-by-step explanation:
When using the equation of a line, one calculates the value of
y
in terms of
x
, say
y
=
m
x
+
c
, then
m
is the slope of the line and
c
is its intercept on
y
-axis.
As
3
x
−
9
y
=
15
can be written as
3
x
−
15
=
9
y
or
y
=
3
9
x
−
15
9
or
y
=
1
3
x
−
5
3
Hence slope of
3
x
−
9
y
=
15
is
1
3
Product of slopes of two perpendicular lines is
−
1
Hence, the slope of the line that is perpendicular to the line
3
x
−
9
y
=
15
is
−
1
1
3
=
−
1
×
3
1
=
−
3
graph{(3x-9y-15)(3x+y+5)=0 [-10, 10, -7.04, 2.96]}
How do you solve this?
Answer:
The highest possible value of b would be 750.
Step-by-step explanation:
If you graph the two equations, you'll get two crossing lines, and because y is supposed to be either equal to or less, the answer is going to be at the shaded area at the bottom.
Equate the two equations to solve them with algebra.
-15x+3000=5x
add 15x to both sides
3000=20x
divide by twenty, you get
150=x
Plug that in to both equations, you'll get y=750, which is the highest possible value of b, (aka y cuz it's on the y axis).
In solving the formula A = (1/2)bh, in solving for h, you could first multiply both side by 1/2. True or False?
Answer:
False.
Step-by-step explanation:
If you multiply both sides by 1/2, you will get 1/4 at the right side.
So the correct way, to solve h, you have to divide both sides by 1/2.
2 and 2/5 ÷ (− 1/4 ) = ?
Answer:
-9.6
Step-by-step explanation:
[tex]2\frac{2}{5} =2.40\\-\frac{1}{4} =-0.25[/tex]
If change them into decimals it looks like that.
Then all you have to do is use standard calculator to find the answer.
[tex]\frac{2.40 }{-0.25} =-9.6[/tex]
Answer:9 and 3/8
Step-by-step explanation:
you have to make 2 and 2/5 into an improper fraction then make the -1/4 into a -4/1 then multiply across to make 48/5 then you have to reduce down to 8 and 8/5. but that cant happen so you reduce again and get 9 and 3/8.
Im needing an answer for this please!
Answer:
x=46 degrees
Step-by-step explanation:
first find the size of the other angles(let call z and y)
the sum of a straight angle is 180:
180=130+z
z=180-130=50
y=180-96=84
sum of angles of triangle =180
x+y+z=180
50+84+x=180
x=180-134=46 degrees
Answer:
46°
Step-by-step explanation:
Angle of a line = 180°
To find the other side of 130°
The other side = 180° - 130° = 50°
To find the other side of 96°
The other side = 180° - 96° = 84°
To find x°
Total angle of a triangle = 180°
180° = x° + 50° + 84°
x° = 180° - 134°
x° = 46°
Romain knows the following information about the 323232 classes he took in high school: He studied for but did not pass 333 classes. He passed 272727 classes in total. He studied for 262626 classes in total. Can you help Romain organize the results into a two-way frequency table?
Answer:
Classes studied for, Classes he did not study for Total
Classes Passed, 23 4 27
Classes Failed, 3 2 5
Total, 26, 6 32
Please find attached the two way frequency table formatted on Excel spreadsheet
Step-by-step explanation:
The given information are;
The total number of classes Romain took in high school = 32
The number of classes he studied for but did not pass = 3
The total number of classes Romain passed = 27
The number of classes Romain studied for = 26
Therefore;
The number of classes Romain studied for and passed = 26 - 3 = 23
The total number of classes Romain failed = 32 - 27 = 5
The total number of classes Romain passed but did not study for = 27 - (26 - 3) = 4
The number of classes Romain did not study for and failed = 5 - 3 = 2
The total number of classes Romain did not study for = 4 + 2 = 6
Jose rented a truck for one day. There was a base fee of $18.99, and there was an additional charge of 91 cents for each mile driven. Jose had to pay $218.28 when he returned the truck. For how many miles did he drive the truck?
Answer:
219
Step-by-step explanation:
do total minus base fee which is
218.28-18.99=199.29
and than
199.29(which is money paid on miles) divided by 91. which is 219
Complete the sequences below :
• please explain the formula in simple words.
a) 18035, 18070 , 18105, ........... , .............. .
b) 3800, 4100, 4400, ............, ............ .
c) 17200, 18300, 19400, .............. , ............ .
Answer:
a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n
b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n
c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n
Step-by-step explanation:
They are all arithmetic progressions (AP) with a common difference, i.e. all differences of one term from the subsequent term are identical.
The general formula is
T(n) = T(0)+n*D
where
n = the term number
T(n) = nth term (considering the first term to be the zeroth term.
D = common difference
a) T(0) = 18035, D = 35, so formula is T(n) = 18035 + 35n
b) T(0) = 3800, D = 300, so formula is T(n) = 3800 + 300n
c) T(0) = 17200, D = 1100, so formula is T(n) = 17200 + 1100n
2 concentric circles have radii 2cm and 3cm respectively, calculate the ratio of their areas
Answer:For the first circle the radius is 2cm and for the second circle the radius is 3cm,by taking the ratio of their areas:
πr^2:πR^2
π cancels out and we are left with only r^2:R^2
r=2cm and R=3cm
Therefore r^2:R^2=2^2:3^2
=4:9
The answer is 4:9
Step-by-step explanation:
Kini and Duke are each working during the summer to earn money in addition to their weekly allowance, and they are saving all of their money. Kini earns $9 an hour at her job, and her allowance is $8 per week. Duke earns $7.50 an hour, and his allowance is $17 per week. How many hours do Kini and Duke need to work in order to save the same amount of money in one week?
Answer:
6 hours
Step-by-step explanation:
Denote the working time T
=> The amount of money that Kini can save after 1 working week:
A1 = 8 + 9T
=> The amount of money that Duke can save after 1 working week:
A2 = 17 + 7.5T
If Kini and Duke save the same amount of money after 1 working week, then:
A1 = A2
=> 8 + 9T = 17 + 7.5T
=> 9T - 7.5T = 17 - 8
=> 1.5T = 9
=> T = 6
=> By working 6 hours in the 1st week, Kini and Duke will save the same amount of money.
Determine the nature of the roots: 2x^(2) +8x +3=0 a. two distinct real solutions c. cannot be determined b. no real solutions d. a unique real solution
Answer:
a
Step-by-step explanation:
Given a quadratic equation in standard form ax² + bx + c = 0 (a ≠ 0 )
Then the discriminant b² - 4ac determines the nature of the roots.
• If b² - 4ac > 0 then 2 real and distinct roots
• If b² - 4ac = 0 then 2 real and equal roots
• If b² - 4ac < 0 then no real roots
Given
2x² + 8x + 3 = 0 ← in standard form
with a = 2, b = 8, c = 3 , then
b² - 4ac = 8² - (4 × 2 × 3) = 64 - 24 = 40
Since b² - 4ac > 0 then 2 real and distinct roots → a
Answer:
a
Step-by-step explanation:
PLEASEEEEANSWERWhich of the following linear equations represents the data chart below? y = 3x + 5 y = x − 5 y = 3x + 11 None of these choices are correcT
Answer:
y=3x+5
Step-by-step explanation:
can someone help me please
Answer:
Compare algebraic relationships in a situation.
Let [tex]m=x^{2}+3[/tex]
Which equation is equivalent to [tex](x^{2}+3)^{2} +7x^{2} +21=-10[/tex]
A.) [tex]m^{2}-7m+10=0[/tex]
B.) [tex]m^{2}-7m+31=0[/tex]
C.) [tex]m^{2}+7m+10=0[/tex]
D.) [tex]m^{2}+7m+31=0[/tex]
Answer:
[tex]{m}^{2} +7m + 28 = 0[/tex]
Step-by-step explanation:
Given that,
[tex]m = {x}^{2} + 3[/tex]
We know that,
[tex] {x}^{2} = m- 3[/tex]
Now look at the sum
[tex]( {x}^{2} + 3) ^{2} + 7 {x}^{2} + 21 = - 10 \\ [/tex]
[tex]( {x}^{2} + 3) ^{2} + 7 {x}^{2} + 21 = - 10 \\ {m}^{2} + 7 \times m- 3 + 21 = - 10 \\ {m}^{2} +7m + 18= - 10 \\ {m}^{2} + 7m + 18+ 10 = 0 \\ {m}^{2} + 7m + 28 = 0[/tex]
A store owner gathered data for several days about the methods customers used to pay for their purchases. The scatter plot shows the data she gathered and the line of best fit. The equation of the line of best fit is y = 0.755x + 11.339. Based on the line of best fit, approximately how many customers are predicted to use a card to pay on a day when 90 customers pay by cash? A.) 68 B.) 79 C.) 92 D.) 104
Answer:
b.79
Step-by-step explanation:
if you look at the graph it shows its right below 80
The 79 customers are predicted to use a card to pay on a day when 90 customers pay by cash option (B) is correct.
What is the line of best fit?A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.
[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}\\\\\\\\\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]
We have a line of best fits:
y = 0.755x + 11.339
Plug x = 90
y =0.755(90) + 11.339
y = 67.95 + 11.339
y = 79.28 ≈ 79
Thus, the 79 customers are predicted to use a card to pay on a day when 90 customers pay by cash option (B) is correct.
Learn more about the line of best fit here:
brainly.com/question/14279419
#SPJ2
Solve the system of equations -8y+9x = -5; 8y+7x = -75
Answer:
x = -5
y = -5
Step-by-step explanation:
-8y+9x = -5; 8y+7x = -75
Add the two equations together to eliminate y
-8y+9x = -5
8y+7x = -75
----------------------
0y + 16x = -80
Divide each side by 16
16x/16 = -80/16
x = -5
Now find y
8y+7x = -75
8y+7(-5) = -75
8y-35 = -75
Add 35 to each side
8y = -40
Divide by 8
8y/8 = -40/8
y = -5
Answer:
[tex]\boxed{x=-5}\\ \boxed{y=-5}[/tex]
Step-by-step explanation:
-8y + 9x = -5
8y + 7x = -75
Add the equations (eliminating the y-variable).
16x = -80
Divide both sides by 16.
[tex]\frac{16x}{16}[/tex] = [tex]\frac{-80}{16}[/tex]
x = -5
Plug x as -5 in the first equation to find y.
-8y + 9(-5) = -5
-8y +-45 = -5
Add 40 to both sides.
-8y = 40
Divide both sides by -8.
[tex]\frac{-8y}{-8}[/tex] = [tex]\frac{40}{-8}[/tex]
y = -5
a two-digit number becomes 5/6 of the reversed number obtained when the digits are interchanged. The difference between the digits is 1. find the number
plz plz help me i wnt answer with full process pls help me plz plz pls.
==============================================
Work Shown:
T = tens digit
U = units digit (aka ones digit)
A number like 27 is really 20+7 = 2*10 + 7*1 = 10*2 + 1*7. We have 2 in the tens digit and 7 in the units digit. So 27 can be written in the form 10T + U where T = 2 and U = 7. Reversing the digits gives 72, so T = 7 and U = 2 now. Clearly the difference between the digits 7 and 2 is not 1, so 27 or 72 is not the answer (as it's just an example).
-----------------------
Let T be larger than U. This doesn't work if T = U.
Because T is larger, saying "The difference between the digits is 1" means T - U = 1. We can isolate T to get T = U+1. We'll use this later.
-----------------------
If T > U, then the original number 10T+U reverses to the new number 10U+T and it becomes smaller. We are told that it becomes 5/6 of what it used to be.
So,
new number = (5/6)*(old number)
10U + T = (5/6)(10T + U)
6(10U + T) = 5(10T + U)
60U + 6T = 50T + 5U
60U + 6(U+1) = 50(U+1) + 5U ... plug in T = U+1
60U + 6U + 6 = 50U + 50 + 5U
66U + 6 = 55U + 50
66U - 55U = 50-6
11U = 44
U = 44/11
U = 4 is the units digit of the original number
T = U+1
T = 4+1
T = 5 is the tens digit of the original number
The original number is therefore 10T + U = 10*5+4 = 54.
We see the difference in their digits is T-U = 5-4 = 1
The reverse of 54 is 45. The number 45 is 5/6 of 54
45 = (5/6)*54
8/15 simplify the quotient to get ?
Answer:
0.5333333333 or 0.53 when simplified.
Step-by-step explanation:
8/15 is simply 8÷15
15 into 8 is not possible so you annex a zero and write a decimal point.The 8 now becomes 80. We now say 80÷15,the answer is 5 because 15x5=75.The remainder is five.We annex another zero and it becomes 50,50÷15=3
I hope this helps.
i don't get division at all i did but i moved a lot of places and i forget things
Answer:
What is the question
Step-by-step explanation:
Complete the sentence by selecting the correct word from each drop-down menu. The middle value of a data set that is ordered from least to greatest is called the ____ . This value is a measure of ____. The options for the first ____ are mean/median/range The options for the second ____ are center/range/variation
Answer: The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.
Step-by-step explanation:
There are three measures of the center: 1) Mean 2) Median 3) Mode
Mean : Average value of the data
Mode = The most repeated value.
Median is the middlemost value in a well-ordered data.
It measures the center of the data.
Hence, the completed statement would be:
The middle value of a data set that is ordered from least to greatest is called the median. This value is a measure of center.
Answer:
First ____ is median
Second ____ is center
Step-by-step explanation:
The median is the middle value of a set of numbers, and is found in the center.
simplify (5 √2 - 1) ^2
Workers in an office of 40 staff were asked their favourite type of take-away. Pizza 9 Curry 6 Fish & chips 11 Kebab 10 Other 4 How many degrees represent 1 person?
Answer:
Hey there!
In total, there are 360 degrees. If there are 40 staff members, then each member has 360/40=9 degrees.
Hope this helps :)
Answer:
9 degrees
Step-by-step explanation:
There are 360 degrees in a circle
There are 40 people
360 / 40 = 9
Each person gets 9 degrees
A store has been selling a certain TV for $210. If the store raised the price by 5% (of the original
price), what would be the new price?
Answer:
Step-by-step explanation:
Selling price = $210
percentage increase = 5 %
Increased amount = 5% of 210
= 0.05 * 210
= $ 10.5
New selling price = 210 + 10.5 = $ 220.50
Which number is the odd one out?
Answer:
8677
Notice that all the numbers in the sequence are divisible by 3 except 8677.
The sum of the digits must be divisible by 3.
8+6+7+7= 2+8 =10
10 isn't divisible by 3.
Two numbers are in the ratio of 3 to 4. If the minor is 27, find the sum of both.
Answer:
Step-by-step explanation:
First we must find the missing number, for that we apply a simple rule of three:
3. 4
27 ------ x
x = 27 (4) / 3 = 36
Now we just do the sum:
27 + 36 = 63
Answer:
Sum = 63
[tex]\boxed{ x = 36}[/tex]
Step-by-step explanation:
3 : 4
It says that the 1st part (3) is 27
27 : x (We've to find the major)
Creating a proportion:
=> 3 : 4 = 27 : x
Product of Means = Product of Extremes
=> 3 * x = 27 * 4
=> 3x = 108
Dividing both sides by 3
=> x = 36
The sum of both is 27+36 = 63
To reach a window, you need a ladder to go up 16 feet on the side of your house. You
set the bottom of the ladder 4 feet from your house. Which choice is closest to the
shortest ladder you can use to reach the window?
possible solutions:
1. 20 feet 2. 4.5 feet
3. 272 feet 4. 16.5 feet
Answer:
4. 16.5
Step-by-step explanation:
You solve for the hypotenuse
a^2+b^2=c^2
16^2+4^2=c^2
256+16= the square root of 272
16.5
Find the area of a circle with a radius of 8. Either enter an exact answer in terms of π or use 3.14 for π and enter your answer as a decimal.
Answer:
64π units²
Step-by-step explanation:
The area (A) of a circle is calculated as
A = πr² ( r is the radius )
= π × 8²
= 64π units²
Please answer this correct answer now fast
Answer:
WX = 8 mm
Step-by-step explanation:
To be able to solve for WX, we need to first find the size of angle [tex]\angle z[/tex].
We use the law of sines in the blue triangle to do such:
[tex]\frac{sin(z)}{11} =\frac{sin(133)}{20} \\sin(z)=\frac{11\,sin(133)}{20} \\sin(z)=0.4022[/tex]
Now we can use this value in the larger right angle triangle where WX is the opposite side to angle [tex]\angle z[/tex], and the 20 mm side is the hypotenuse:
[tex]sin(z)=\frac{opposite}{hypotenuse} \\sin(z)=\frac{WX}{20}\\0.4022=\frac{WX}{20}\\WX=20\,(0.4022)\\WX=8.044\,\,mm[/tex]
which rounded to the nearest integer gives
WX = 8 mm
What is the volume of the pyramid in cubic inches?
9in.
6 in.
8 in.
Answer: C) 144
Step-by-step explanation:
The area of a pyramid can be found via lwh/3
(9*8*6)/3 = area
72*6/3 = area
432/3 = area
144 = area
Hope it helps <3
I WILL MARK BRAINLIEST!!!!!! A direct variation function includes the ordered pair (4, 5). If y varies directly with x, and y is 14 when x is 2, what is the value of x when y is 35?
Answer: x=5
Step-by-step explanation:
[tex]\frac{2}{14} =\frac{x}{35}[/tex]
[tex]\frac{x}{35}=\frac{2}{14}[/tex]
simplify
[tex]\frac{x}{35}=\frac{1}{7}[/tex]
multiply 35 on both sides
[tex]\frac{35x}{35}=\frac{1\cdot \:35}{7}[/tex]
[tex]\frac{1}{7} \cdot 35=5[/tex]
x=5
What is the least number of colors you need to correct color in the sections of these pictures so that no two touching sections are the same color?
You would assume that in this figure, the number of colored sections with which are not colored with respect to a " touching " colored section, would be half of the total colored sections. However that is not the case, the sections are not alternating as they still meet at a common point. After all, it notes no two touching sections, not adjacent sections. Their is no equation to calculate this requirement with respect to the total number of sections.
Let's say that we take one triangle as the starting. This triangle will be the start of a chain of other triangles that have no two touching sections, specifically 7 triangles. If a square were to be this starting shape, there are 5 shapes that have no touching sections, 3 being a square, the other two triangles. This is presumably a lower value as a square occupies two times as much space, but it also depends on the positioning. Therefore, the least number of colored sections you can color in the sections meeting the given requirement, is 5 sections for this first figure.
Respectively the solution for this second figure is 5 sections as well.