Answer:
18 terms
Step-by-step explanation:
The first given sequence has first term a1=2 and common difference d=5. Its explicit formula is ...
an = 2 +5(n -1) = 5n -3
We want the n-th term of this sequence to be the same as the n-th term of the sequence defined by ...
an = 4n +15
We can find n that makes this true by setting the 'an' values equal:
an = an
5n -3 = 4n +15
n = 18 . . . . . . . . . . add 3-4n
The number of terms in each sequence is 18.
_____
Additional comment
The last term in each sequence is 87.
65 cm of 5.6 m
find the percentage
Answer:
8.61%
Step-by-step explanation:
5.6/65*100
The café's menu lists 3 choices: Egg &Chips -£3.00 Sausage & Chips - £3.60 Sausage & Mash - £2.70 How much would it charge for Egg & Mash?
The price of the given menu items can be used to find the price of Egg &
Mash to be £2.1.
Response:
The price for Egg & Mash is £2.1
Which method can be used to find the price for Egg & Mash?Let x represent the cost of Egg, let y represent the cost of Chips, let
z, represent the cost of Sausages, and a the cost of Mash we have the
following system of linear equations;
x + y = 3...(1)
z + y = 3.6...(2)
z + a = 2.7...(3)
x + a = Required
Solution:
Subtracting equation (1) from (2) gives;
z + y - (x + y) = 3.6 - 3 = 0.6
z - x = 0.6
Therefore;
z is £0.6 more expensive than x
x = z - 0.6
By plugging in the value of x = z - 0.6, gives;
x + a = z - 0.6 + a = z + a - 0.6
z + a = 2.7, which gives;
x + a = z + a - 0.6 = 2.7 - 0.6 = 2.1
Egg and Mash = x + a = £2.1Learn more about system of simultaneous equation here:
https://brainly.com/question/1346297
270 students went on a field trip. 6 buses were each filled with s students. How many students were on each bus?
Answer:
45
Step-by-step explanation:
Find three consecutive integers whose sum is 0.
0, -3 ,+3
hope it helped u! ^^
Let n=first number. So this means that the second number is n+2 and the third is n+4. Since the sum of the three numbers is 0, this means that
n+n+2+n+4=0
A tractor-trailer travels 205. 296 miles in 3. 12 hours. What is the speed at which the tractor-trailer is traveling? A. 62. 05 miles per hour B. 63. 2 miles per hour C. 64. 05 miles per hour D. 65. 8 miles per hour E. 66. 5 miles per hour.
Answer:
65.8 mph
Step-by-step explanation:
What I did was I divided 205.296 by 3.12 and I got 65.8.
Show all your work and the answer in the space below.
Answer:
m= 12
Step-by-step explanation:
[tex]\frac{3m+4}{8} = 5[/tex]
First multiply both sides by 8 to cancel out the 8 on the left side
[tex]3m + 4 = 80[/tex]
Isolate the m so subtract 4 from both sides.
[tex]3m = 36[/tex]
Divide both sides by 3.
[tex]m = 12\\[/tex]
Please answer this (who ever answers correctly gets brainlest)
Answer:
18480 ft
Step-by-step explanation:
Note that 1 mile = 5280 feet. We can use this information to set up a unit converter:
[tex]3.5mi(\frac{5280ft}{1mi})[/tex]
Miles cancels out on the bottom giving us...
[tex]3.5*5280ft=18480ft[/tex]
The points (-12, 6) and (-4, r) lie on a line with slope - 1/2
Find the missing coordinate r.
Answer:
r = 2
Step-by-step explanation:
Slope formula: [tex]m=\frac{y_2-y_1}{x_2-x_1}\\[/tex]
Substitute the known values for their respective variables and solve for the missing coordinate, r.
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\ -\frac{1}{2}=\frac{6-r}{-12-(-4)}\\\\-\frac{1}{2}=\frac{6-r}{-8}\\\\ -8(-\frac{1}{2})=(\frac{6-r}{-8})-8\\\\ 4=6-r\\\\4-6=6-r-6\\\\-2=-r\\\\\frac{-2}{-1}=\frac{-r}{-1}\\\\ 2=r[/tex]
(4x+7) ° is congruent to [5(x-4)] °
What is the value of x?
Answer:
x=17
Step-by-step explanation:
1) 4x +7 = 5(x-4) Congruent angles
2) 4x + 7 = 5x -10 Distributive Property
3) Simplify
4x + 7 = 5x - 10
-4x -4x
7 = x - 10
+10 +10
x = 17
Which of these is the algebraic expression for the verbal expression "twelve times the difference of a number and four?"
Answer:
12* y-4
Step-by-step explanation:
The first is twelve. then the asterisk is next. y is for the "number" Lastly, subtract 4.
(-2,3)
find tan cos sin
[tex]\huge \underline\frak \red{Answer}[/tex]
Given thing are
cos Θ = 2/3
we know that Cos Θ = Adjacent Side / Hypotenuse, so we get
Adjacent Side = 2
Hypotenuse = 3
Hypotenuse : BC = 3
Adjacent Side : AB = 2 (Adjacent to ∠ Θ)
Opposite Side : AC = ? (Opposite to ∠ Θ)
To find the Opposite Side - AC , we use Pythagoras theorem ((Hypotenuse)2 = (Leg 1)² + (Leg 2)²)
AC = √ BC² - AB²
AC = √ 32 - 22
AC = √ 9 - 4
AC = √5
Now we will try to simplify square root of 5. As no pairs can be made the final value will be
__
AC = √ 5
So Sin, Cos and Tan will be as follows -
Sin Θ = Opposite Side / Hypotenuse
__
Sin Θ = √5/3
Tan Θ = Opposite Side / Adjacent Side
__
Tan Θ = √5/2
Cos Θ = Adjacent Side / Hypotenuse
Cos Θ = 2/3
Can anyone please help me with this? I’d appreciate it a lot!
Answer:
(−2, −3)
Step-by-step explanation:
Let's solve your system by substitution.
x−9y=25;6x−5y=3
Step: Solvex−9y=25for x:
x−9y=25
x−9y+9y=25+9y(Add 9y to both sides)
x=9y+25
Step: Substitute9y+25forxin6x−5y=3:
6x−5y=3
6(9y+25)−5y=3
49y+150=3(Simplify both sides of the equation)
49y+150+−150=3+−150(Add -150 to both sides)
49y=−147
49y
49
=
−147
49
(Divide both sides by 49)
y=−3
Step: Substitute−3foryinx=9y+25:
x=9y+25
x=(9)(−3)+25
x=−2(Simplify both sides of the equation)
Therefore answer:
x=−2 and y=−3 which is (-2, -3)
Hope it helps!
What is the value of n?
Enter your answer in the box.
(NEED ANSWER ASAP. PLEASE DON'T ANSWER ANYTHING IRRELEVANT OR I'LL REPORT U. PROVIDE AN EXPLANATION AS WELL IF POSSIBLE. THANK U FOR UR HELP)
Answer:
5
Step-by-step explanation:
Well, there's a formula: to find the measure of any section, you should multiple every section to its ending after the crossing, and then make a proportion.
So, 9(n+7) = 18(n+1)
9n+63 = 18n+18
-9n+45=0
-9n=-45
n=-45/-9
n=5
Tony wants to buy 2.3 pounds of dried berries and 2.6 pounds of trail mix. How much will he spend?
if the radius of a circle is increased by 50 perent what will be the percent increase in the circumfrence
Answer:
50%
Step-by-step explanation:
The equation for circumference is:
[tex]C=2\pi r[/tex]
In this case, the radius and the circumference are directly proportional meaning that if the radius increases by 50%, the circumference will also increase by 50%.
Let's use some examples to prove this:
Radius : 2
Increase by 50% : 2*50%=2*(50/100)=2(1/2)=1 --> 1+2 = 3
[tex]C=2\pi r=2\pi 3=6\rightarrow 50 \ percent\ increase\ from\ 4\\C=2\pi r=2\pi 2=4[/tex]
Radius : 4
Increase by 50% : 4*50%=4*(50/100)=4(1/2)=2 --> 2+4 = 6
[tex]C=2\pi r=2\pi 6=12\pi\rightarrow50\ percent\ increase\ from\ 8\\C=2\pi r=2\pi 4=8\pi[/tex]
In both cases, when we increased the radius by 50%, the circumference also increased by 50%, proving our previous statement correct.
Therefore, when the radius of a circle is increased by 50%, the circumference will also increase by 50%
If Ben invests $4500 at 4% interest per year, how much additional money must he invest at 5 1 2 % annual interest to ensure that the interest he receives each year is 4 1 2 % of the total amount invested?
You have Pennies and nickles that are equal to $8.80. You have twice the number of nickles than Pennies. Write an equation for this problem. How many nickles do you have and how many Pennies do you have?
Answer:
Step-by-step explanation:
Let's set up the variables as nickel=n and penny=p, for how many coins he has of each type. What we know is that Calvin had $8.80 total and that he has twice as many nickels as pennies. So, one equation for his total money and another for how many separate coins: 8.80 = 0.01p + 0.05n 2p=n
is x =4 a solution of the equation
13=2x + 4?
A.yes
B.no
No, it is not. If you plug 4 into the equation in the place of x, you get 13=2(4)+4
13=8+4
13=12
It equals 12, not 13.
Answer:
No
Step-by-step explanation:
Because If You Do 2 x 4 you get 8 and 8 + 4 = 12 and not 13 so the answer is 4.5 because 4.5 x 2 = 9 and 9 + 4 = 13
HELP ME PLEASE HURRY THIS IS DUE IN 30 MINS
Answer:
F(x)= (x-5)(x+3)
Step-by-step explanation:
we have two roots/ X-intercepts meaning we can assume that it is a quadratic function
8 1/3 divided by x=2 1/3 divided by 8.1
Answer:
[tex]\large\boxed{\tt x \approx 28.9 \overline{285714}.}[/tex]
Step-by-step explanation:
[tex]\textsf{We are asked to solve for x in the given equation.}[/tex]
[tex]\large\underline{\textsf{What are Equations?}}[/tex]
[tex]\textsf{Equations are statements that determine 2 or more expressions are equal.}[/tex]
[tex]\underline{\textsf{This means that;}}[/tex]
[tex]\tt \frac{8 \frac{1}{3} }{x} \ is \ equal \ to \ \frac{2 \frac{1}{3} }{8.1}[/tex]
[tex]\textsf{For equations, rather \underline{proportions} such as these, we should \underline{Cross Multiply}.}[/tex]
[tex]\large\underline{\textsf{What are Proportions?}}[/tex]
[tex]\textsf{Proportions are comparisons to the size, and how large/small a value is.}[/tex]
[tex]\large\underline{\textsf{What is the Cross Multiplying?}}[/tex]
[tex]\textsf{Cross multiplying is indeed as simple as it sounds, basically multiply the oppsite}[/tex]
[tex]\textsf{known value by another known value, then divide the product by last known}[/tex]
[tex]\textsf{number. This sounds like a lot, but I'll give an example.}[/tex]
[tex]\underline{\textsf{Example;}}[/tex]
[tex]\tt \frac{1}{3} = \frac{2}{x}[/tex]
[tex]\textsf{We are asked to find x in the given proportion. We should use the cross}[/tex]
[tex]\textsf{multiplication method. Note that we should multiply the known values that are}[/tex]
[tex]\textsf{on opposite sides, and leave the known value with x as its opposite value alone}[/tex]
[tex]\textsf{until we have our product.}[/tex]
[tex]\tt \frac{1}{\small\boxed{\tt 3}} = \frac{\small\boxed{\tt 2}}{x}[/tex]
[tex]\textsf{3 and 2 are opposite from each other, hence we'll multiply them.}[/tex]
[tex]\tt \frac{1}{\small\boxed{\tt 3}} = \frac{\small\boxed{\tt 2}}{x} \rightarrow \frac{6}{1} = x[/tex]
[tex]\textsf{We'll divide by the last remaining known value, 1, then that should be the value}[/tex]
[tex]\textsf{of x.}[/tex]
[tex]\tt x = 6[/tex]
[tex]\large\underline{\textsf{Solving;}}[/tex]
[tex]\textsf{Use the Cross Multiplication Method.}[/tex]
[tex]\tt \frac{8 \frac{1}{3} }{x} = \frac{2 \frac{1}{3} }{8.1}[/tex]
[tex]\tt 8 \frac{1}{3} \ \textsf{and} \ \tt 8.1 \ \textsf{are opposite from each other, which means we will multiply those}[/tex]
[tex]\textsf{values together.}[/tex]
[tex]\tt \frac{ \small\boxed{\tt 8 \frac{1}{3}} }{x} = \frac{2 \frac{1}{3} }{\small\boxed{\tt 8.1}} \rightarrow 67.5.[/tex]
[tex]\textsf{Our product is 67.5, which means we are ready to divide 67.5 by 2} \tt \frac{1}{3} .[/tex]
[tex]\tt x = \frac{67.5}{2 \frac{1}{3} }[/tex]
[tex]\textsf{This quotient is going to be irrational, hence I will round to 7 digits.}[/tex]
[tex]\large\boxed{\tt x \approx 28.9 \overline{285714}.}[/tex]
si el cartón de huevos es la unidad, y son 30 huevos, responde:
¿cuántos huevos hay en un medio cartón?
Answer:
quince
Step-by-step explanation:
si el cartón de huevos es la unidad, y son 30 huevos,
responde:
¿cuántos huevos hay en un medio cartón?
translation:
if the egg carton is the unit, and it is 30 eggs,
answer:
how many eggs are in a half carton?
30 divided by 2
30
----- = 15
2
Solve for x
2x-3x(3+2)=10
Answer:
Step-by-step explanation:
2x - 3x(3+2) = 10
Distribute the -3x to the numbers inside the parenthesis:
2x - 9x -6 = 10
Simplify:
-7x = 16
Isolated the x:
x = 16/-7
Please help me in this question!
Step-by-step explanation:
The second part fir y
Explained in pic
Estimate to compare. Select < or >. Round each number to the nearest whole number to estimate each sum.
2.73 + 5.28 ? 3.12 + 1.72
estimate estimate
-------------- --------------
Whyy, do vou think, banks and other financial institutions offer cash loans to people that did not apply for it?
Answer:
because there are in need of it
Step-by-step explanation:
yes
3/14/7/10
[tex] \frac{ \frac{ \frac{3}{14} }{7} }{10} [/tex]
simplify
Answer:
= 3/14 × 10/7
= 15/14
hope it helps!
Answer:
= 3/14 × 10/7
= 15/14
Step-by-step explanation:
branliest pls
Solve 5p(2p - 3)(p + 7) = 0.
p=___, p=____, p=_____
Answer:
5p(2p-3)(p+7)=0
10p-15 p +7 =0
10p+p=0+15-7
11p =8
11p=8
p=8/11
Answer:
p=0, p=1.5, p=-7
Step-by-step explanation:
Assuming we need the equation to equal zero we do this.
5p(2p-3)(p+7)
5p = 0 (2p-3) = 0 (p+7)= 0 Separate each part
5(0) = 0 2(1.5)-3 = 0. (-7)+7 = 0 Replace P so the outcome is 0
p=0, p=1.5, p=-7 Solution
Solve for x using the given information. Explain your steps.
6x + ( 3x - 9) = 90°( being complementary angles )
6x+3x -9 = 90°
9x = 90° + 9
x = 99 / 9
x = 11
PLEASE HELP me out with this
A list of all possible outcomes of an experiment is called:.
Answer:
sample space
Step-by-step explanation: