let the n'th term be called x, and the value of the term y,
then there is a function y=a*x + b
that will give us all term we want.
this formula is also used for straight lines.
we just need a and b. we already got two data points. we can just plug the known x/y pairs into the formula
10.5 = a*12 + b
13.5 = a*18 + b
now lets manipulate these lines.
multiply the first line by 3 and the second line by 2
31.5 = a*36 + 3b
27 = a*36 + 2b
subtract the second line from the first line
4.5 = b
yey, we now know b, let's plus b into either line from above, I'll go with the first one, looks easier.
10.5 = a*12 + 4.5
6 = a*12
0.5 = a
now y=a*x + b can be filled with a and b
y = 0.5 * x + 4.5
for x=1 (the first term) it's f(1)=5
each step is 0.5, hence the common difference.
2and way:(13.5-10.5)/(18-12)
= 3 / 6
= 0.5
we got the comment difference by looking at the full difference over 6 steps and divined by these 6 steps.
from step 12 to step one it's 11 steps down
10.5 - 0.5*11
= 10.5 - 5.5
= 5
okay I admit... 2and way to do it might be faster and more intuitive... :DA cylindrical vase has a volume of 192.5 cubic centimeters. The height of this vase is 5 centimeters. The formula for the volume of the cylinder is πr^2h where r is the radius and h is the height of the vase. Find the radius of this vase.(Given that π ≈ 22 / 7 )
Answer:
3.5 cm
Step-by-step explanation:
v = πr²h
r = radius
π = 22/7
h = height
192.5 = 22/7 x 5 x r²
divide both sides of the equation by (7/22 x 1/5)
192.5 x 7/22 x 1/5 = r²
r² = 12.25
find the square root of both sides
r = 3.5cm
Help anyone can help me do this question,I will mark brainlest.
Circumference of a circle = 2πr
So,
[tex]circumference = 2\pi \: r \\ = > circumference = 2 \times \frac{22}{7} \times \frac{63 \: cm}{2} \\ = > circumference = 2 \times \frac{11}{7} \times 63 \: cm \\ = > circumference = 2 \times 11 \times 9 \: cm \\ = > circumference = 198 \: cm[/tex]
Answer: Therefore, the circumference of circle is 198 cm.
Step-by-step explanation:
diameter = 63 cm
radius = 63/2 = 31.5 cm
circumference = ?
circumference or perimeter of circle = 2*pi*r
= 2*(22/7)*31.5
= (44/7)*31.5
= 198 cm
Grandfather Giovanni's hens lay 180 eggs per day, which are placed in containers of 6 each. How many containers will you need per day?
Answer:
6
Step-by-step explanation:
HELPPPPPPPPPPPPPPPPPP. PLEASEEEEEE
Answers:
LCD needed to combine the variables: 15
LCD needed to combine the constants: 21
==============================================
Explanation:
If two numbers m and n do not have any common factors (other than 1), then the LCM is m*n. We simply multiply the values.
So for example, the LCM of 2 and 3 is 2*3 = 6.
For the variable terms, the denominators are 5 and 3. So the LCM is 5*3 = 15, and this is the LCD of those variable fractions.
Similarly, the LCD of the constant terms is 21 because 7*3 = 21.
--------
Again, for all of these examples, the two values had no factors other than 1 in common. If you were dealing with something like the LCM of 8 and 12, then the LCM would not be 8*12 = 96. But we can fix things by dividing that by 4 to get 96/4 = 24 which is the true LCM here.
So the more generalized formula would be (m*n)/(GCF of m and n)
This formula works for the previous section because the GCF was 1.
If 5k = -25, then 5k - 1 = -25 - 1
Segment proof
If the base linear function is F(x) =-3x and 5 is added to the equation, then what best describes what happened to the base equation? 
A.nothing happened stayed the same
B. The base equation shifts up five units
C. The base equation shifts to the left five units
D. The base equation shifts down five units
E. The base equation shifts to the right to five units
Answer:
E the base equation shifts to the right to five unit from the midpoint
Which point should Julio use to determine the amount of pizza sauce he needs to bring?
A
B
C
D
On a coordinate plane, a graph titled Pizza Recipe has Pizzas on the x-axis and Cups of Pizza Sauce on the y-axis. Point A is (3, 2), point B is (4, 2.6), point C is (4.5, 3), point D is (6, 4).
Answer:
The question is incomplete, but after a small search I've found that the complete question is something like:
To celebrate something, a teacher will make pizzas for the class.
There are 30 students in his class and each pizza serves 8
Julio will bring the pizza sauce. Which point should Julio use to determine the amount of pizza sauce he needs to bring?
In a graph, the vertical axis is represented with the variable y, which is defined as the dependent variable, while the horizontal axis represents the variable x, which is the independent variable.
The notation for a point in that graph is (x, y)
Here, we know that the x-axis represents the number of pizzas, and the y-axis represents the number of cups of pizza sauce needed for the x pizzas.
So, for example, the point (3, 2) means that:
for x = 3 pizzas, you need y = 2 cups of pizza sauce.
So, now let's find the number of pizzas that will feed the whole class.
There are 30 students, Each pizza serves for 8.
Then the number of pizzas needed is:
30/8 = 3.75 pizzas.
But we can round it to 4 pizzas because making a 0.75 of a pizza does not make a lot of sense.
Then we could use point B, which is (4, 2.6)
This means that, for 4 pizzas, they need 2.6 cups of pizza sauce.
So Julio should bring 2.6 cups of pizza sauce.
Which point should Julio use to determine the amount of pizza sauce he needs to bring?
(B 4,26)
Can someone please explain how to do this?(Picture above) I'll give brainliest!
Answer:
f(1)=4
f(-3)=4
f(5)=-2
f(0)=2
f(-1)=0
f(3)=2
Step-by-step explanation:
Pose f(x) as your x value. Now apply to the graph
I also need to show calculations for each side length plz help
Answer:
WO [tex]\sqrt{13}\ \ \ \frac{3}{2}[/tex]
OR [tex]\sqrt{13}\ \ \ - \frac{3}{2}[/tex]
RM [tex]\sqrt{13}\ \ \ \frac{3}{2}[/tex]
MW [tex]\sqrt{13}\ \ \ - \frac{3}{2}[/tex]
Step-by-step explanation:
One has to find the slope, and the distance between the successive points on the plane. Use the slope and distance formula to achieve this.
Slope formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Distance formula:
[tex]\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}[/tex]
Remember, the general format for the coordinates of a point on a Cartesian coordinate plane is the following:
[tex](x,y)[/tex]
1. WO
Coordinates of point (W): (3, -5)
Coordinates of point (O): (6, -3)
Find the slope:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\frac{(-5)-(-3)}{(3)-(6)}=\frac{-5+3}{3-6}=\frac{-2}{-3}=\frac{2}{3}[/tex]
Find the distance:
[tex]\sqrt{((-5)-(-3))^2+((3)-(6))^2}[/tex]
[tex]\sqrt{(-2)^2+(-3)^2}\\=\sqrt{4+9}\\=\sqrt{13}\\[/tex]
2. OR
Coordinates of point (O): (6, -3)
Coordinates of point (R): (4, 0)
Find the slope:
[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-3)}{(4)-(6)}=\frac{3}{-2}=-\frac{3}{2}[/tex]
Find the distance:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{((0)-(-3))^2+((4)-(6))^2}=\sqrt{(3)^2+(2)^2}=\sqrt{9+4}=\sqrt{13}[/tex]
3. RM
Coordinates of point (R): (4, 0)
Coordinates of point (M): (1, -2)
Find the slope:
[tex]\frac{y_2-y_1}{x_2-x_1}\\=\frac{(0)-(-2)}{(4)-(1)}=\frac{2}{3}[/tex]
Find the distance:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\sqrt{((-2)-(0))^2+((1)-(4))^2}=\sqrt{(-2)^2+(-3)^2}=\sqrt{4+9}=\sqrt{13}[/tex]
4. MW
Coordinates of point (M): (1, -2)
Coordinates of point (W): (3, -5)
Find the slope:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]=\frac{(-5)-(-2)}{(3)-(1)}=\frac{-3}{2}=-\frac{3}{2}[/tex]
Find the distance:
[tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]=\sqrt{((3)-(1))^2+((-5)-(-2))^2}=\sqrt{(2)^2+(3)^2}=\sqrt{4+9}=\sqrt{13}[/tex]
Plz help plz plzplz plz help
Answer:
the answer is C.7.2. good luck
Answer:
7.3
Step-by-step explanation:
Which number sentence is not true?
A. |-4.5| = 4.5
B. |0| < |-45|
C. |45| > 0
D. |4.5| > |-45|
Answer:
D
Step-by-step explanation:
The absolute value of a number is the actual distance of the number from zero. So, it is always a positive number. No negative value.
A) I -4.5I = 4.5 TRUE
B) I 0I < I -45I TRUE
Reason: 0 < 45
C) I 45 I > 0 TRUE
D) I4.5 I > I - 45 I FALSE
Reason: 4.5is not greater than 45
Answer:
D
Step-by-step explanation:
What is the 100th term of the arithmetic sequence below?
4, 11, 18, 25
Answer:
a₁₀₀ = 697
Step-by-step explanation:
The nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 4 and d = a₂ - a₁ = 11 - 4 = 7 , then
a₁₀₀ = 4 + (99 × 7) = 4 + 693 = 697
The value of -9(square root) is not-3 because
O A. (3)2 = -9
O B. (-9)2 = -3
O c. 329
D. 92 + -3
Answer:
A) [tex](-3)^{2} \neq -9[/tex]
Step-by-step explanation:
Answer:
A) is correct
Step-by-step explanation:
(-3)**2 = 9, not equal -9
The issue is negative numbers can only be imaginary numbers. The sq root of -9 would be 3i, where i is defined as the sq root of -1.
**25 POINTS**
Which of the following lists of ordered pairs is a function?
Answer: A
Step-by-step explanation: A function is when every domain (x value) corresponds to one range (y value) so that it passes the vertical line test
Find the length of U and V. Show work. Giving out brainliest answer.
Answer:
u =√6
v =√5
Step-by-step explanation:
u = √(1²+2²+1²) =√(1+4+1) = √6
v = √(1²+2²) =√(1+4) = √5
help me fast plzzzzzz
Answer:
has been saving is the correct answer I believe
Answer:
"has been saving" is the right answer.
Which of the following are interior angles in the figure below?
O
A. 21, 22, and 26
B. 25 and 26
C. 23 only
D. 21, 22, and 23
Answer:
(A), 21, 22,and 26
Step-by-step explanation:
gakzbzkxvuxnsslvzixvdkdbdjxvshhzvskdvxy dgsjzvsks ysjdbdudvsk jdkdbdb
(5.9)(1.102)
What’s does that mean
Answer:
brackets stand for multiplication therefore this means multiply 5.9 by 1.102..
I hope this helps and sorry if it's wrong
value of x in 2x-7=35 is
Answer:
x=21
Step-by-step explanation:
2x - 7 = 35
+7 +7
-----------------
2x = 42
----- -----
2 2
x = 21
The answer is 21, hope this helps.
Answer:
x = 21
Step-by-step explanation:
2x - 7 = 35
We need to isolate x. First, we add 7 to both sides.
2x - 7 + 7 = 35 + 7
2x = 42
Now we divide both sides by 2.
2x/2 = 42/2
x = 21
Answer: x = 21
Evaluate [10/y + 13] -3, when y=5
Answer:
(10/y+13)-3
(10/5+13)-3
(2+13)-3
15-3
12
I hope this will help you
The length of a rectangle is 7 inches longer than it is wide. If the area is 60 square inches, what are the
dimensions of the rectangle?
Answer: 5 by 12
Step-by-step explanation:
Let's call the dimensions of the rectangle w and w+7
The area is 60, so we can do 60=w(w+7)
60=w^2+7w
w^2+7w-60=0 factor the quadratic equation
(w-5)(w+12)=0
w-5=0, w=5
w+12=0, w=-12
Since the length of a rectangle cannot be negative, w=5
the dimensions of the rectangle are 5 and 12
PLEASE HELP!!! Find the value of x.
A. 11
B. 5
C. 25
D. 31
Answer:
C
Step-by-step explanation:
Consider trapezoid ABCD with
A is the midpoint of ED
C is the midpoint of BF
=> AC is the median of trapezoid EBFD
=>(EB+DF) / 2 = AC
=>(13+x) / 2 = 19
=> 13+x = 38
=> x= 25
The value of x is 5.
According to the Triangle Proportionality Theorem, if a line is parallel to one side of a triangle and intersects the other two sides, it divides those two sides proportionally. In mathematical terms, we can express this as:
(a/b) = c
Where the values of a = 13, b = 19
Now, we can substitute the given values into the proportionality equation:
(13/19) = c
Next, we can cross-multiply the equation:
c = 0.68
Then the value of x is calculated by adding 4.32 on it then we get the value of x as
=> x = 0.68 + 4.32
=> x = 5
Hence the correct option is (b).
To know more about triangle here
https://brainly.com/question/8587906
#SPJ2
Two numbers have a product of −24 and a difference of 11. What are the two numbers?
Answer:
-8 and 3, or -3 and 8
Step-by-step explanation:
xy = -24
x - y = 11
x = y + 11
y(y + 11) = -24
y^2 + 11x + 24 = 0
(y + 8)(y + 3) = 0
y = -8 or y = -3
x = 3 or x = 8
the numbers are -8 and 3, or -3 and 8
Look at the figure. How can you prove ∆ABD and ∆ACD are congruent?
A.It is not possible to determine if the triangles are congruent.
B. ∆ABD ≅ ∆ACD by the SSS Postulate.
C. ∆ABD ≅ ∆ACD by the SAS Postulate.
Answer:
Options (C)
Step-by-step explanation:
For the congruence of the triangles ΔADB and ΔADC,
Statements Reasons
1). AB ≅ AC 1). Given
2). AD ≅ AD 2). Reflexive property
3). ∠BAD ≅ ∠CAD 3). Given
4). ΔABD ≅ ΔCAD 4). SAS postulate
Therefore, Options (C) will be the correct option.
To join the tennis club, there is a $10.20
initial fee and a $3.90 yearly fee. What
would be the value of the slope in this
situation?
Use this space to write down notes or work through problems
Your teacher will see what you wrate.
Answer:
10.20
Step-by-step explanation:
Let
y = Total fee
Initial fee = $10.20
Yearly fee = $3.90
Number of years = x
The equation:
y = 3.90x + 10.20
Recall,
y = mx + c
Where,
x = slope
c = y - intercept
Therefore,
The y - intercept from y = 3.90x + 10.20 is 10.20
Find the value of x.
PLEASE HELP ASAP!!!!!!
Answer:
does it want the degree????
could someone help me with this ASAP? thanks !
A. [tex]6x^2[/tex]+-5x+14x+-35
[tex]6x^2[/tex]+9x-35
B. [tex]5x^4+-3x^3+10x^3+-6x^2[/tex]
[tex]5x^4+7x^3-6x^2[/tex]
C. [tex]25x^2+-20x+20x+-16[/tex]
[tex]25x^2-16[/tex]
D. [tex]x^4+-4x^2+-7x^2+28[/tex]
[tex]x^4-11x^2+28[/tex]
[tex]====================================[/tex]
Step-by-step explanation:
A. (3x*2x)+(3x*-5)+(7*2x)+(7*-5)
Multiply and simplify.
[tex]6x^2[/tex]+9x-35
B. ([tex]x^2*5x^2[/tex])+([tex]x^2*[/tex]-3x)+(2x[tex]*5x^2[/tex])+(2x[tex]*-3x[/tex])
Multiply and simplify.
[tex]5x^4+7x^3-6x^2[/tex]
C. [tex](5x*5x)+(5x*-4)+(4*5x)+(4*-4)[/tex]
Multiply and simplify.
[tex]25x^2-16[/tex]
D. [tex](x^2*x^2)+(x^2*-4)+(-7*x^2)+(-7*-4)[/tex]
Multiply and simplify.
[tex]x^4-11x^2+28[/tex]
I hope this helps!
But you should really do this yourself.
Find the measure of the indicated angle to the nearest degree
[tex]\boxed{\sf tan\theta=\dfrac{p}{b}}[/tex]
[tex]\\ \sf\longmapsto tan\theta=\dfrac{13}{20}[/tex]
[tex]\\ \sf\longmapsto tan\theta=0.6[/tex]
[tex]\\ \sf\longmapsto tan\theta\approx\dfrac{1}{\sqrt{3}}[/tex]
[tex]\\ \sf\longmapsto tan\theta\approx tan60[/tex]
[tex]\\ \sf\longmapsto \theta\approx 60°[/tex]
help xx ndjskcksicksksmnsjzjsjdjsjcjn
B. 4562
Hope this helps(:
!!!!!!!
Answer:
4.562...
Step-by-step explanation:
A rational number can be written in the form a/b where a and b are integer
-54 is an integer ( -54/1)
5/9 is in the form a/b where a is 5 and b is 9
2.13 is in the form a/b where a is 213 and b is 100
4.562... is a non repeating and non terminating decimal, which is irrational
When investing money in a bank account, in which situation will you have the most money in your account at the end of three years?
Compounded semiannually
Compounded yearly
Compounded quarterly
Compounded monthly
Answer:
continuously is the most, and what is actually done at the banks...
as for your answer:
Compounded monthly
Step-by-step explanation:
When investing money in a bank account, you will have the most money in your account at the end of three years when compounded monthly.
What is compound interest?Compound interest is the interest you earn on interest.
[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]
Where,
A = final amount
P = initial principal balance
r = interest rate
n = number of times interest applied per time period
t = number of time periods elapsed
To check in which situation we will earn the most money in end of three years, we calculate the final amount in each situation keeping other variables constant.
Let
P = 5000
r = 5%
t = 3 years
When compounded annually,
[tex]A = 5000(1 + 0.05)^{3} = 5788.125[/tex]
When compounded semiannually,
[tex]A = 5000(1 + 0.025)^{6} = 5798.467[/tex]
When compounded quarterly,
[tex]A = 5000(1 + 0.0125)^{12} = 5803.772[/tex]
When compounded monthly,
[tex]A = 5000(1 + 0.0125)^{12} = 5807.361[/tex]
Thus, it can be said that you have the most money in your account at the end of three years when compounded monthly.
Learn more about compound interest here
https://brainly.com/question/14295570
#SPJ2
