Find the two missing terms of the sequence and determine if the sequence is arithmetic, geometric, or neither.
3, 1, -1, -3, __, __
Answer:
[tex]-5,-7[/tex]
It is Arithmetic.
Step-by-step explanation:
1) A sequence is geometric when it goes from a term to the next term by multiplying by the same number, which is called "Common ratio" ([tex]r[/tex]).
2) A sequence is arithmetic when it goes from a term to the next term by adding or subtracting a common value. This value is called "Common difference" and it is denoted with [tex]d[/tex].
Then, given the following sequence:
[tex]3, 1, -1, -3[/tex]
- Let's find out if it is geometric by dividing each term by its previous one. Then:
[tex]\frac{-3}{-1}=3\\\\\frac{-1}{1}=-1[/tex]
Since there is no Common ratio, it is not a Geometic sequence.
- Now let's see if it is arithmetic by subtracting each term by its previous one:
[tex]-3-(-1)=-2\\\\-1-1=-2\\\\1-3=-2[/tex]
You can idenfity that it has a Common difference:
[tex]d=-2[/tex]
Therefore, it is an Arithmetic sequence.
The next to terms are:
[tex]-3-2=-5\\\\-5-2=-7[/tex]
only need help on these last problems on this photo please help! i’m desperate for help!
Answer:
[tex]x=85\\ \\y=100\\ \\z=100[/tex]
Step-by-step explanation:
Angles with measures of [tex]95^{\circ}[/tex] and [tex]x^{\circ}[/tex] are supplementary angles, thus, they add up to [tex]180^{\circ}:[/tex]
[tex]x+95=180\\ \\x=180-95\\ \\x=85[/tex]
Angles with measures of [tex]80^{\circ}[/tex] and [tex]y^{\circ}[/tex] are supplementary angles, thus, they add up to [tex]180^{\circ}:[/tex]
[tex]y+80=180\\ \\y=180-80\\ \\y=100[/tex]
Find the measures of two remaining interior angles of the pentagon:
[tex]1. \ 180^{\circ}-62^{\circ}=118^{\circ}\\ \\2.\ 180^{\circ}-53^{\circ}=127^{\circ}[/tex]
The sum of the measures of all interior angles in the pentagon is
[tex](5-2)\cdot 180^{\circ}=540^{\circ},[/tex]
then
[tex]95^{\circ}+118^{\circ}+100^{\circ}+z^{\circ}+127^{\circ}=540^{\circ}\\ \\440^{\circ}+z^{\circ}=540^{\circ}\\ \\z^{\circ}=100^{\circ}[/tex]
Cookies are sold singly or in packages of 13 or 39. With this packaging, how many ways can you buy 78 cookies?
To buy 78 cookies using packages of 13 or 39, you can either buy 2 packages of 39 or 5 packages of 13 and 1 additional cookie.
Explanation:To find the number of ways you can buy 78 cookies using packages of 13 or 39, we need to consider the different combinations of packages.
Let's start with the largest package size, 39. If you buy 2 packages of 39, that's a total of 78 cookies. So one option is to buy 2 packages of 39.
Now let's consider the smaller package size, 13. If you buy 5 packages of 13, that's a total of 65 cookies. To reach a total of 78 cookies, you can buy 5 packages of 13 and 1 additional cookie.
Therefore, the total number of ways you can buy 78 cookies is 2 (using only packages of 39) or 1 (using 5 packages of 13 and 1 additional cookie).
Solve for x
(1/x) -2/3 = (4x)
The value of x is [tex]x=\frac{-1+\sqrt{37}}{12}[/tex] and [tex]x=\frac{-1-\sqrt{37}}{12}[/tex]
Step-by-step explanation:
The equation is [tex]\frac{1}{x}-\frac{2}{3}=4 x[/tex]
Subtracting by [tex]4x[/tex] on both sides,
[tex]\frac{1}{x}-\frac{2}{3}-4 x=0[/tex]
Taking LCM,
[tex]\frac{3-12 x^{2}-2 x}{3 x}=0[/tex]
Multiplying by 3x on both sides,
[tex]-12 x^{2}-2 x+3=0[/tex]
Dividing by (-) on both sides,
[tex]12 x^{2}+2 x-3=0[/tex]
Using quadratic formula, we can solve for x.
[tex]\begin{aligned}x &=\frac{-2 \pm \sqrt{2^{2}-4 \cdot 12 \cdot(-3)}}{2 \cdot 12} \\&=\frac{-2 \pm \sqrt{4+144}}{2 \cdot 144} \\&=\frac{-2 \pm \sqrt{148}}{24} \\&=\frac{-2 \pm 2 \sqrt{37}}{24}\end{aligned}[/tex]
Taking out common term 2, we get,
[tex]\begin{array}{l}{x=\frac{-2(1 \pm \sqrt{37})}{24}} \\{x=\frac{-1 \pm \sqrt{37}}{12}}\end{array}[/tex]
Thus, the value of x is [tex]x=\frac{-1+\sqrt{37}}{12}[/tex] and [tex]x=\frac{-1-\sqrt{37}}{12}[/tex]
Asap
The surface area of the prism is ______ square units. All measurements in the image below are in units. (Input whole number only.) A triangular prism is shown with 2 right triangular sides having legs 8 and 6 and hypotenuse 10. The length of the prism is 8.5
Answer:
The surface area of the prism is 252 square units
Step-by-step explanation:
we know that
The surface area of the prism is equal to
[tex]SA=2B+PL[/tex]
where
B is the area of the base of the prism
P is the perimeter of the base
L is the length or the height of the prism
step 1
Find the area of the triangular base B
The area of triangular base B is
[tex]B=\frac{1}{2}(8)(6)=24\ units^2[/tex]
The perimeter of the triangular base P is
[tex]P=8+6+10=24\ units[/tex]
we have
[tex]L=8.5\ units[/tex]
substitute the values in the formula
[tex]SA=2(24)+24(8.5)=252\ units^2[/tex]
You are choosing between two health clubs. Club A offers membership for a fee of $16 plus a monthly fee of $13. Club B offers membership for a fee of $22 plus a monthly fee of $11. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
Answer:
After 3 months the total cost of each health club will be the same, and the total cost for each one will be US$ 55
Step-by-step explanation:
1. Let's review the information provided to us to answer the question correctly:
Club A = Membership fee of $ 16 + Monthly fee of $13
Club B = Membership fee of $ 22 + Monthly fee of $11
2. After how many months will the total cost of each health club be the same? What will be the total cost for each club?
For answering the question, we will use the variable x to be the number of months of membership of the two clubs, this way:
Club A = Club B
16 + 13x = 22 + 11x
13x - 11x = 22 - 16
2x = 6
x = 6/2 = 3
Substituting and proving x = 3:
16 + 13x = 22 + 11x
16 + 13 * 3 = 22 + 11 * 3
16 + 39 = 22 + 33
55 = 55
After 3 months the total cost of each health club will be the same, and the total cost for each one will be US$ 55
What is the slope of a line parallel to a line with slope 2/3
Answer:
2/3
Step-by-step explanation:
parallel lines have the same slope
given that a line has a slope of 2/3
a line that is parallel to this line would also have a slope of 2/3
Would -x times 5x equal -5x² or -5x?
Answer:
-5x^2
Step-by-step explanation:
-x times 5x = -5x^2, because there is a X being multiplied with an X.
Answer:
-5x^2
Step-by-step explanation:
Multiplying a negative variable by the same variable would equal that variable as a negative and also squared
HELPP ITS DUE TOMORROW
x° = 10°
Solution:
In the given figure the angle L represents 90°.
The center ray splits 90° into two angles.
(3x + 6)° + (5x + 4)° = 90°
⇒ 3x° + 6° + 5x° + 4° = 90°
Combine like terms together.
⇒ 3x° + 5x°+ 6° + 4° = 90°
⇒ 8x°+ 10° = 90°
Subtract 10° on both sides of the equation.
⇒ 8x°+ 10° – 10° = 90° – 10°
⇒ 8x° = 90° – 10°
⇒ 8x° = 80°
Divide by 8 on both sides of the equation.
⇒ x° = 10°
Hence, the value of x° = 10°.
Solve 5(x - 1) + 3 = 13
Answer:
Step-by-step explanation:
5(x - 1) + 3 = 13....distribute thru the parenthesis
5x - 5 + 3 = 13
5x - 2 = 13....add 2 to both sides
5x = 13 + 2
5x = 15 ....divide both sides by 5
x = 15/5
x = 3 <====
please help me!! i know u saw this so help me
Answer:
I think 8
Step-by-step explanation:
9/2 and 5/8
here 8 is the LCM.
so, 9/2 × 4/4
5/8 × 1/1
which gives: 36/8 and 5/8
Answer:
It is 2
Step-by-step explanation:
Nothing can go into 2 and 8/4 is 2.
Help me on this please thank you
Answer:
A. ∠ABC ≅ ∠DBE
Step-by-step explanation:
The whole proof is not shown, but in order to show the triangles similar, one would need to (a) show the sides are proportional, and (b) show the included angle is the same. The portion of the proof that is shown is on the way to showing side lengths are proportional. The missing part for showing triangle similarity is the congruence statement for angle B, as shown above.
__
Once the triangles are shown to be similar, additional work is needed to show DE║AC. At least one pair of corresponding "base" angles must be shown congruent, too.
Tara wants to order tickets online so that she and three of her friends can go to the movies together. The cost of the tickets is $16.00 per person. There is also a $3.50 one-time service fee for ordering tickets online. Write an expression in terms of n that represents the cost for ordering n tickets online. What is the expression? Use your expression to find the total cost for ordering 4 tickets online.
Answer:
16×4= 64
64.00+3.50
(16×4)+(64.00+14.00)
Step-by-step explanation:
First you have to find how much the tickets will cost per person then add 14.00 because of the one time person but there is four so time 3.50×4
Answer fast I think is b
Answer:
b
Step-by-step explanation:
yes it b because it goes origion and it not a zero pair
1. What are the term(s), coefficient(s), and
constant(s) described by the phrase, "the cost of
6 pizzas, c being the cost of each pizza, and a
delivery charge of $5?"
A. Term: 6c, coefficient: 6, constant: 5
B. Term: 6c and 5, coefficient: 6, constant: 5
C. Term: 6c and 5, coefficient: 5, constant: 6
D. Term: 11c, coefficient: 11, constant: none
Answer:
Step-by-step explanation:
6c + 5
term : 6c and 5....coefficient : 6......constant : 5
a coefficient is the number multiplied by the variable (the letter)....a constant is just a number with no variables (letters)
The term described by the phrase 'the cost of 6 pizzas, c being the cost of each pizza, and a delivery charge of $5' is 6c. The coefficient is 6 and the constant is 5.
Explanation:The term described by the phrase 'the cost of 6 pizzas, c being the cost of each pizza, and a delivery charge of $5' is 6c. The coefficient is 6 because it is the number multiplying the variable c. The constant is 5 because it is a fixed value that does not involve any variables.
So the correct answer is option A: Term: 6c, coefficient: 6, constant: 5.
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Find the circumference of the figure given below
At Elmwood Middle School there are 4 teachers for every 68 students. There are 425 students enrolled at the school. How many teachers are needed?
The number of teachers required for the 425 students that enrolled at the school is 25.
What are ratio and proportion?A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.
At Elmwood Middle School there are 4 teachers for every 68 students.
There are 425 students enrolled at the school.
Let the number of teachers be x required for the 425 students will be
[tex]\rm \dfrac{x}{4} = \dfrac{425}{68}\\\\x \ = \dfrac{425*4}{68}\\\\x \ = 25[/tex]
The number of teachers required for the 425 students that enrolled at the school is 25.
More about the ratio and the proportion link is given below.
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Approximately 25 teachers are needed at Elmwood Middle School. So the correct option is c) 25.
To find out how many teachers are needed at Elmwood Middle School, we can set up a proportion using the given ratio of teachers to students.
Given:
- There are 4 teachers for every 68 students.
Let's set up the proportion:
[tex]\[\frac{\text{Number of teachers}}{\text{Number of students}} = \frac{4}{68}\][/tex]
We know there are 425 students enrolled at the school, so let's find out how many teachers are needed:
[tex]\[\text{Number of teachers} = \frac{4}{68} \times 425\][/tex]
[tex]\[\text{Number of teachers} = \frac{4 \times 425}{68}\][/tex]
[tex]\[\text{Number of teachers} = \frac{1700}{68}\][/tex]
[tex]\[\text{Number of teachers} \approx 25\][/tex]
So, approximately 25 teachers are needed at Elmwood Middle School.
Therefore, the answer is option C. 25.
The complete question is:
At Elmwood Middle School there are 4 teachers for every 68 students. There are 425 students enrolled at the school. How many teachers are needed? A. 17 B. 21 C. 25 D. 28
A prize was awarded to 56 women and 1490 men.
a. What fraction of the prize winners were women?
b. What fraction were men?
Simplify.
Could a square with whole number side lengths have the same perimeter as the dog pen? The same area
Answer:
Yes
Step-by-step explanation:
I think because you didn't finish explaining the question, go check.
I can't understand what you are trying to ask.
A square with a whole number side length would have the same perimeter or area as the dog pen, assuming that the pen is rectangular.
If a square with a side length of s has the same perimeter as the dog pen, then we can write:
4s = 2(l + w) 2s = l + w
Since s is a whole number, l + w must be an even number. This means that both l and w must have the same parity (they must both be even or both be odd) for the equation to be true. However, if both l and w are even, then the ratio of l:w will not be a whole number, which means that a square with the same area as the dog pen cannot exist with whole number side lengths.
If a square with a side length of s has the same area as the dog pen, then we can write:
[tex]s^2[/tex]= lw
Since s is a whole number, we can express it as the product of two whole numbers:
s = ab
Substituting this into the equation for the area, we get:
[tex]a^2 b^2[/tex] = lw
This means that l and w must have at least two factors each that are perfect squares. However, if we assume that the dog pen is rectangular, then its dimensions cannot both have two factors that are perfect squares, which means that a square with the same area cannot exist with whole number side lengths.
For such more questions on length
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Note: The complete question is - Could a square with a whole number side length have the same perimeter as the dog pen? Could a square with a whole number side length have the same area as the dog pen?
subtracting linear expressions (6x+2)-(9x+3)
Answer:
-3x - 1
Step-by-step explanation:
(6x + 2)-(9x + 3)
We Begin by opening the brackets.
6x + 2 -9x - 3
Please note the change in the signs.
6x - 9x + 2 - 3
-3x - 1
A circle has a radius of 3.6cm.
What is it’s diameter?
Answer:
7.2cm
Step-by-step explanation:
Answer: 7.2 cm
Explanation: It's important to understand that the radius is equal to half of the diameter so to find the diameter of a circle with a radius of 3.6 cm, we simply multiply 3.6 cm by 2 and we will get the diameter or the distance across a circle.
To multiply a decimal times a whole number such as 3.6 x 2, first line up the numbers and begin multiplying as if we were multiplying 2 whole numbers.
6 x 2 is 12 so we bring down the 2 and carry the 1.
2 x 3 is 6 and if we add 1 we get 7.
So we have 7.2 cm which is our diameter
11:
Larry is buying tickets to the state fair for a group of people.
The admission price for kids (k) is $3 and for adults (a) it's $5 .
Larry has just purchased a total of 10 tickets. He paid a total of $45 for all the tickets.
Write an equation that represents the total cost based on the combination of kids and adult tickets purchased.
Answer:
3k+5a=45
Step-by-step explanation:
It says write an equation. It doesn't specify that you have to solve. That means you can use variables like (k) and (a).
That allows for more flexibility and the equation 3k+5a=45.
3k means that 3 dollars per ticket times (k) tickets equals the total price for kid's tickets
5a means that 5 dollars per ticket times (a) tickets equals the total price for adult's tickets
The equation to represent the cost based on the combination of kids' and adult tickets purchased by Larry is 3k + 5a = 45, where k represents the kids' tickets and a represents the adult tickets.
Explanation:The problem can be translated into a simple algebraic equation where the number of kids' tickets (k) and the number of adult tickets (a) are the variables. Given the cost per ticket for each category (kids at $3 and adults at $5), we can define a equation where 3k + 5a = 45. This equation represents the cost distribution of the ten tickets that Larry purchased for the state fair, 3 multiplied by the number of kids' tickets plus 5 multiplied by the number of adult tickets.
Therefore, if Larry knows how many of each ticket he bought, he can insert the values for k and a into the equation to see if it equals to 45, the total amount of money he spent.
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Whats the square root of 49
Answer:
The square root of 49 is 7. 7*7=49
Hope this helps,
:)
Answer:
The square root of 49 is 7
Step-by-step explanation:
7 multiplied by 7 equals 49, that is how you are sure.
- MoonQue
How can you use equivalent fractions to know that 43/200 is between 1/5 and 1/4
The fraction 43/200 is evidently between 1/5 and 1/4 from equivalent fractions.
A fraction which is equivalent to 1/5 with denominator, 200 is; 40/200.A fraction which is equivalent to 1/4 with denominator, 200 is; 50/200.Im essence, since 43 lies between, 40 and 50;
The fraction 43/200 in turn lies between fractions 1/5 and 1/4.
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tabitha wants to find the total cost of a new tablet computer that has a origanall cost of $360 from a store having a 20% sales tax
ANSWER: $432
STEP-BY-STEP EXPLANATION:
The cost of the tablet is $360
Then Tabitha has to pay 20% sales tax.
The tax is the prices times 20% plus the original price
360 ( 1+ 0.2)
360 (1.2)
=432
Is the equation 2x-6+2x+9 an a identity
Answer:
7
Step-by-step explanation:
Find the inverse of y=7x-10. Is the inverse a function?
Answer:
(x+7)/7 =y
Step-by-step explanation:
The first step is to switch the variables
x=7y-10
Add the 10 to both sides
x=7y-10
+10 +10
x+10=7y
Divide both sides by 7
(x+7)/7 =y
Answer:
the inverse function is (x + 10)/7
Step-by-step explanation:
y=7x-10
7x = y + 10
x = (y + 10)/7
therefore the inverse of the given function is (y + 10)/7
Graph the equation y = -6x + 12
Answer:
The three points for the line y = -6x + 12 ...Red color line
point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)
point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)
point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)
The Graph is attached below.
Step-by-step explanation:
Given:
[tex]y = -6x +12[/tex] ........... equation of a line
Let the points be point A, point B, and point C
To Find:
point A( x₁ , y₁) ≡ ?
point B( x₂ , y₂) ≡ ?
point C(x₃ , y₃ ) ≡ ?
Solution:
For Drawing a graph we require minimum two points but we will have here three points.
For point A( x₁ , y₁)
Put x = 0 in the given equation we get
y = 0 + 12
y = 12
∴ point A( x₁ , y₁) ≡ ( 0 , 12)
For point B( x₂ , y₂)
Put y= 0 in the given equation we get
0 = -6x + 12
6x = 12
[tex]x=\dfrac{12}{6}=2[/tex]
∴ point B( x₂ , y₂) ≡ (2 , 0)
For point C(x₃ , y₃ )
Put x = 1 in the given equation we get
y = -6 × 1 + 12
y = 6
∴ point C(x₃ , y₃ )≡ (1 , 6)
Therefore,
The three points for the line -2y = -x + 8 are
point A( x₁ , y₁) ≡ ( 0 , 12) (blue color point on the graph)
point B( x₂ , y₂) ≡ (2 , 0) (green color point on the graph)
point C(x₃ , y₃ ) ≡ (1 , 6) (purple color point on the graph)
The Graph is attached below..
2. After the orchestra completed its program
orchestra completed its program, there was a party to allow the patrons to mingle with the
icians, Kayla's Catering provided the food, drinks and service for the party. There were two
red seven guests. Kayla charges $27.00 per guest for food and $10.00 per quest for drinks. To
That she adds $4.98 per quest for service. What was Kayla's total bill for catering the party?
After the orchestra completed its program, there was a party to allow the patrons to mingle with the musicians. Kayla’s Catering provided the food, drinks, and service for the party. There were two hundred seven guests. Kayla charges $27.00 per guest for food and $10.00 per guest for drinks. To that she adds $4.98 per guest for service. What was Kayla's total bill for catering the party?
Answer:The total bill for catering the party is $ 8689.86
Solution:Kayla’s Catering provided the food, drinks, and service for the party
Total number of guests = 207
Charge for food for 1 guest = $ 27
Charge for drink for 1 guest = $ 10
Charge for service for 1 guest = $ 4.98
To find: Kayla total bill for cater
Total bill = Total number of guests(Charge for food for 1 guest + Charge for drink for 1 guest + Charge for service for 1 guest)
[tex]Total\ bill = 207(27+10+4.98)\\\\Total\ bill = 207(37 + 4.98)\\\\Total\ bill = 207 \times 41.98\\\\Total\ bill = 8689.86[/tex]
Thus total bill for catering the party is $ 8689.86
Parabolas y=3x2 and y=−3x2+k intersect at points M and N that are in the first and the second quadrants respectively. Find k if length of the segment MN is 6.
Answer:
[tex]k=54[/tex]
Step-by-step explanation:
Find the coordinates of points M and N in terms of k. Solve the system of two equations:
[tex]\left\{\begin{array}{l}y=3x^2\\ \\y=-3x^2+k\end{array}\right.\Rightarrow \left\{\begin{array}{l}y=3x^2\\ \\y=-y+k\end{array}\right.\\ \\2y=k\\ \\y=\dfrac{k}{2}\\ \\\dfrac{k}{2}=3x^2\\ \\x^2=\dfrac{k}{6}\\ \\x=\pm\sqrt{\dfrac{k}{6}}[/tex]
Two points have the coordinates [tex]M\left(\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex] and [tex]N\left(-\sqrt{\dfrac{k}{6}},\dfrac{k}{2}\right)[/tex]
Find the distance between M and N:
[tex]MN=\sqrt{\left(\sqrt{\dfrac{k}{6}}-\left(-\sqrt{\dfrac{k}{6}}\right)\right)^2+\left(\dfrac{k}{2}-\dfrac{k}{2}\right)^2}=\sqrt{4\dfrac{k}{6}}=\sqrt{\dfrac{2k}{3}}[/tex]
Since MN = 6, you have
[tex]\sqrt{\dfrac{2k}{3}}=6\\ \\\dfrac{2k}{3}=36\\ \\2k=108\\ \\k=54[/tex]