Answer:
a) a1=15 first term
b) d=-8 common difference
Step-by-step explanation:
1)a1+d=7
2)a1+a2+a3+a4=12
a1+a1+d+a1+2d+a1+3d=12
4a1+6d=12
2a1+3d=6
We have the system of equations where a1+d=7 and 2a1+3d=6
3a1+3d=21
2a1+3d=6
Subtract the second equation from the first one
a1=15
d=-8
First term = 15
Common difference = -8
Let the first term be a and common difference be d.
Therefore,
a+d = 7 - eq. 1
a+(a+d)+(a+2d)+(a+3d) = 12 - eq. 2
4a + 6d = 12
4a + 4d + 2d = 12
Dividing both sides by 2,
2a + 2d + d = 6
2 (a+d) + d = 6
Substituting value of (a+d) in the above equation,
2*7 + d = 6
d = 6 - 14
d = -8
Substuting value of d in eq. 1
a+d = 7
a + (-8) = 7
a = 7 + 8
a = 15
To learn more about arithematic proggresions:
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Can someone help me with this
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Answer:
A: y = 17x
Step-by-step explanation:
Answer:
21 is A
22 is B
Step-by-step explanation:
51 / 3 = 17, which is the cost of 1 hour. That means, in order to find the charge (y), you need to multiply the # of hours (x) by 17. Equation A represents this correctly.
Now that we know this, for question 22, if someone rented a machine for 3.5 hours, to find the charge, multiply 3.5 by 17. This gives you 59.50.
Find the slope of the line graphed below
Answer:
-4/3
Step-by-step explanation:
To find the slope you do rise over run. The line goes down by four and to the right by three between the two points so the slope is -4/3/
Whats 1+1 Generally have no idea im in 12th grade need this answer for my upcoming test thanks
Find k such that 16x2 – 8 /3x+k=0 has a repeated real solution.
Answer:
k = [tex]\frac{1}{9}[/tex]
Step-by-step explanation:
Using the discriminant
Δ = b² - 4ac
For a repeated real solution then
b² - 4ac = 0
Given
16x² - [tex]\frac{8}{3}[/tex] x + k = 0
with a = 16, b = - [tex]\frac{8}{3}[/tex] , c = k
(- [tex]\frac{8}{3}[/tex] )² - ( 4 × 16 × k) = 0
[tex]\frac{64}{9}[/tex] - 64k = 0 ( subtract [tex]\frac{64}{9}[/tex] from both sides )
- 64k = - [tex]\frac{64}{9}[/tex] ( divide both sides by - 64 )
k = [tex]\frac{1}{9}[/tex]
The number of sweets s that each friend gets is the
number of sweets in a box n divided by the number of
friends f the sweets are shared between. Enter a formula
for the number of sweets each friend gets and enter the
number of sweets each friend gets if there are 54 sweets
and 6 friends.
Answer: 9 sweets/friend
Step-by-step explanation:
s = Number of sweets per friend
n = Number of sweets in a box = 54
f = Number of friends = 6
formula for the number of sweets each friend gets is as follows:
n/f = s
Therefore substituting in formula for n=54 and f=6
54/6 = 9 sweets per friend
Add or Subtract: show your work 30 POINTS
Step-by-step explanation:
hopefully it is clear and understandable
:)
Which best describes the relationship between the line that passes through the points (–9, –7) and (–12, –2) and the line that passes through the points (1, 9) and (6, 6)?
9514 1404 393
Answer:
The lines are neither parallel nor perpendicular. They intersect in the 2nd quadrant.
Step-by-step explanation:
You have provided no descriptions, so we have shown the lines to let you draw your own conclusion regarding the description that best fits.
Multiply -7/-6 x 7 x 1/3 write in simplest form
Step-by-step explanation:
Multiply -7/-6 x 7 x 1/3 write in simplest form
Use the equation v=s+19 to find the value of v when s=2.
V=
Answer:
21
Step-by-step explanation:
s=2
so, v=2+19
19+2=21
please i need to know
Answer:
the answer is 28
Step-by-step explanation:
PEMDAS:
(8-2) = 6
6^2= 36
36/2= 18
18+10= 28
Answer:
D. 28
PEMDAS:
Parenthesis, exponents, multiplication, division, addition, subtraction
10 + (8 - 2)^2 / 2
1. Parenthesis comes first so we're left with
10 + (6)^2 / 2
2. Then we do the exponents
10 + 36 / 2
3. Then it's division
10 + 18
4. Finally we add
28
determine the area and perimeter
Answer:
is there a specific equation to use?
Step-by-step explanation:
The difference of 23 and 6 multiplied by 2
Answer:
23-6=17
17x2=34
Step-by-step explanation:
Please don't report this! I'm sorry if its wrong
If you were able to earn interest at 3% and you started with N100, how much would you have after 3 years?
the answer
Answer: 109.27
Explanation:
N=3 I=3% pv=100 pmt =0 cpt fv
$109.27
if you do not add anything to the $100 and strictly rely on interest.
8/6-5/4=
Please help quick
Answer:
1/12
Step-by-step explanation:
Point A and Point B are placed on a number line. Point A is located at -20 and point B is 5 less than point A. Which statement about point B is true?
a. It is located at -25 and is to the right of point A on the number line.
b. It is located at -15 and is to right of point A on the number line
c, It is located at -25 and is to the left of point A on the number line.
Answer:
so, choose c.
Step-by-step explanation:
[tex] - 20 - 5 = - 25[/tex]
{Please see the figure on the picture}
What is the equation of a line perpendicular to y = -3x + 4 that passes through the point (-1, 6)?
Answer:
Equation is 3y = x + 19
Step-by-step explanation:
General equation:
[tex]y = mx + c[/tex]
For slope, m:
[tex]m_{1} \times m_{2} = - 1[/tex]
but m1 is -3:
[tex] - 3m_{2} = - 1 \\ m_{2} = \frac{1}{3} [/tex]
For y-intercept, c:
[tex]y = mx + c \\ 6 = ( - 1 \times \frac{1}{3} ) + c \\ \\ c = 6 + \frac{1}{3} \\ \\ c = \frac{19}{3} [/tex]
equation:
[tex]{ \sf{y = \frac{1}{3}x + \frac{19}{3} }} \\ \\ 3y = x + 19[/tex]
Find AC someone help please. If you can please include steps
Answer:
AC = 15
Step-by-step explanation:
AC is the entire line split into two segments; AB and BC
We are given that AB = 8 and BC = 2x + 25 so we can combine these two and set them equal to AC ( = x + 24)
x + 24 = 8 + 2x + 25
Combine like terms and isolate x
x + 24 = 2x + 33
-9 = x
Now plug in -9 for x in the equation for line AC
(-9) + 24 = 15
Shane has nine notes in his wallet, three are $50 and the rest are $20 notes. Write the ratio of $50 notes to $20 dollar notes.
Answer:
50x20=1000
Step-by-step explanation:
Use the distributive property to simplify each expression 10(9-1)
Answer:
see below
Step-by-step explanation:
10(9-1)
Distribute
10 * 9 - 10 *1
90 - 10
80
Answer: 80
Step-by-step explanation:
10(9-1) = 90 - 10 = 80
I need help explaining, this homeschool work so hard!!
Answer:
61
Step-by-step explanation:
(7 + 5) + 4 * 13 - 2
~Simplify using PEMDAS
12 + 4 * 13 - 2
12 + 52 - 3
64 - 3
61
Best of Luck~
I’m crying rn I need helppp (number 4 ignore the rest) -1/2 to be left alone like without the x and what happened to the 5/2??
Step-by-step explanation:
The parallel line will have an equation of the form
[tex]y = -\dfrac{1}{2}x + b[/tex]
We solve for b by plugging in the values of the point (3, -4):
[tex]-4 = -\dfrac{1}{2}(3) + b[/tex]
[tex]\Rightarrow -8 = -3 + 2b[/tex]
Solving for b, we get
[tex]b = -\dfrac{5}{2}[/tex]
Therefore, the equation of the line parallel to 2x + 4y = 10 is
[tex]y = -\dfrac{1}{2}x -\dfrac{5}{2}[/tex]
In standard form we can write
[tex]x + 2y = -5[/tex] or [tex]2x + 4y = -10[/tex]
Prove: 3 log3 81= 4 log4 64
Step-by-step explanation:
3log3 3^4=4log4 4^33*4 log3 3=4*3 log4 412 log3 3= 12 log4 412*1=12*1 (loga a=1)12=12Answer:
h
Step-by-step explanation:
Draw a scaled copy of this polygon that has a perimeter of 30 units. What is the scale factor? Explain how you know. Help please
Answer:
Step-by-step explanation:
The given figure has a perimeter of 10 lines, each 1 unit long.
If the perimeter is 30 for the new figure, then the scale factor is 3, because 30 is 3 * 10
2. A boy scored the given marks in various class-tests during a term, (each test being marked out of 20): 15, 17, 16, 16, 10, 12, 14, 16, 19, 12, 16. (a) What is his modal marks?
Answer:
16 is the number occurring most often in the list.
Step-by-step explanation:
Show work and Evaluate 3/4 + 2/5
Answer:
23/20
Step-by-step explanation:
Find the common denominator of the 2 fractions (It's 20):
3/4 + 2/5
Multiply both numerator and denominator by 5 for the first fraction and multiply by 4 for the second fraction:
15/20 + 8/20
Add the fractions together:
23/20
Name and define the two areas of statistics.
Answer:The two major areas of statistics are known as descriptive statistics, which describes the properties of sample and population data, and inferential statistics, which uses those properties to test hypotheses and draw conclusions.
write 1000 as a product using 10 as a factor
Answer:
-
Step-by-step explanation:
Answer:
The answer is right here for you!
Here it is:10x100
Round 57.5958961796 to the nearest hundredth.
Decmial: 0.77 thanks!
Answer:
The digit in the tenths place is 10 times as much as the value of the digit in the hundredths place.
Step-by-step Explanation:
0.07 multiplied by 10 gives you 0.7
a store owner has 7.11 lbs of candy. If she puts the candy into 9 jars
Answer:
7.11 / 9 = 0.79
Step-by-step explanation: