Answer:
common difference is 0.5
first term is 5
Step-by-step explanation:
use the formula for the nth term of an ap Tn=a+(n-1)d
T12=10.5
T18=13.5
therefore come up with two equations
T12=a+(12-1)d
10.5=a+11d(1st equation)
T18=a+(18-1)d
13.5=a+17d(2nd equation)
then solve both as a simultaneous equation
a+11d=10.5
a+17d=13.5
-6d/-6=-3/-6
d=0.5
use one of the equations to find the first term
a+11(0.5)=10.5
a+5.5=10.5
a=10.5-5.5
a=5
I hope this helps
please mark as brainliest
Without using logarithm tables, find value of x in the equation:
log x³+ log5x =5log2-log⅖
Answer:
[tex]x =2[/tex]
Step-by-step explanation:
Given
[tex]\log x\³+ \log5x =5\log2-\log\frac{2}{5}[/tex]
Required
Find x
We have:
[tex]\log x\³+ \log5x =5\log2-\log\frac{2}{5}[/tex]
Apply exponent rule
[tex]\log x\³+ \log5x =\log2^5-\log\frac{2}{5}[/tex]
[tex]\log x\³+ \log5x =\log32 -\log\frac{2}{5}[/tex]
Apply product and quotient rules of logarithm
[tex]\log (x\³* 5x) =\log(32 \div \frac{2}{5})[/tex]
[tex]\log (5x^4) =\log(80)[/tex]
Cancel log on both sides
[tex]5x^4 = 80[/tex]
Divide by 5
[tex]x^4 = 16[/tex]
Take 4th roots of both sides
[tex]x =2[/tex]
If [ -2 5 7 6] and |B| = -|A|, which matrix is matrix B?
|A| and |B| denote the determinants of the matrices A and B.
We have
[tex]|A| = \begin{vmatrix}-2&5\\7&6\end{vmatrix} = (-2)\times6-7\times5 = -12 - 35 = -47[/tex]
Then B is a matrix such that |B| = -|A| = +47.
The only choice satisfying this is C, since
[tex]\begin{vmatrix}12&1\\13&5\end{vmatrix} = 12\times5-13\times1 = 60 - 13 = 47[/tex]
The receipt shows the prices of goods that Mr. Baker bought at the store.
The state Mr. Baker lives in has a sales tax rate of 7% on all purchases.
How much money does Mr. Baker pay in sales tax and what is the total amount he must pay for his purchases?
Answer:
The answer is $82.46 sales tax
$1,260.46 Total
Step-by-step explanation:
Since the price before the Sales tax is $1,178.00 and if you add the 7% Sales tax the total is $1,260.46 and the price of the Sales tax is $82.46
What rate of interest compounded annually is required to triple an investment in years? WORTH 50 points!!
At a rate of interest of 3.86% compounded annually investment will be tripled.
that is how i was taut, sorry if is wrong
Will Give Brainliest!
Solve for r.
Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions.
35r - 21 < -35r + 19
Answer:
r < 4/7
Step-by-step explanation:
35r - 21 < -35r + 19
35r + 35r < 19 + 21
70r < 40
r < 4/7
Answer:
r < 4/7
Step-by-step explanation:
There are 3200 students at Lake High School and 310 of these students are sophomores. If 38 of the sophomores are in favor of the school forming a crew team and 34 of the remaining students (not sophomores) are also in favor of forming a crew team, how many students are opposed to this idea?
Answer: 3128 students
Step-by-step explanation:
Total no of students in the school : 3200
No of sophomores in favor of the school forming a crew team : 38
No of the remaining students in favor of forming a crew team : 34
Total students in favor of forming a crew team = 38+34= 72
No of students against it : Total students - Students in favor
= 3200-72 = 3128 students
What is the range of the function?
Answer:
all real numbers greater than or equal to 11
PLEASE HELP ASAP, will give brainliest!!!!
Answer:
3.398
Step-by-step explanation:
log(2500)=log(25)+log(100)=2+2*0.699=3.398
HELPPP PLEASE:((((( I NEED TO TURN THIS IN TOMORROW
5 a + 3 b + 2 a b + 4 a -7 b
Answer:
5a+4a=9a
3b-7b=-4b
2ab
=9a-4b+2ab or 2ab+9a-4a
Step-by-step explanation:
Calculate liked terms
Hasib earns 30 cents for every carrot he sells.
He earns an extra $3 for every 30 carrots he
sells. How many carrots must he sell in order to
earn $555?
Answer:
He must sell 1390 carrots
Step-by-step explanation:
30x + 300x/30 = 55500
40x = 55500
x = 1387.5
1387.5
multiply 30 by .3 to get $9 for 30 carrots
Then add $3 to this amount to get $12 dollars.
Divide 555 by 12 to get 46 R3.
Multiply 46 by 30 because its 46 bundles of 30 carrots
Then divide the 3 dollars by .3 for each carrot to get 10 carrots
1380+10 = 1390
Hasib must sell 1390 carrots in order to earn $555.
What is a system of equations?A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.
Given information; Hasib earns 30 cents for every carrot he sells. He earns an extra $3 for every 30 carrots he sells.
So, the equation form;
30x + 300x/30 = 55500
40x = 55500
x = 1387.5
Now, multiply 30 by .3 to get $9 for 30 carrots
Then add $3 + 9 = $12 dollars.
Now, Divide 555/ 12 = 46 R3.
46 x 30 = 1380 because its 46 bundles of 30 carrots
For each carrot to get 10 carrots
1380 + 10 = 1390
Therefore, Hasib must sell 1390 carrots in order to earn $555.
Learn more about equations here;
https://brainly.com/question/10413253
#SPJ2
Instructions: Find the value of the trigonometric ratio. Make sure to
simplify the fraction if needed.
С
32
40
B
24
A
Tan C =
Answer:
tanC will be given by the opposite over the adjacent
tanC=24/32
simplified to 6/8
I hope this helps
Match each figure with the number of edges it has.
6
12
8
9
5
10
rectangular prism
rectangular pyramid
triangular pyramid
triangular prism
Answer:
Rectangular prism- 12 edges
Rectangular pyramid- 8 edges
Triangular pyramid- 6 edges
Triangular prism- 9 edges
I hope this helps!
Help anyone can help me do this question,I will mark brainlest.
Answer:
22 mm
Step-by-step explanation:
through: (-4,-1) and ( -1,2) ?
(A) y=-x+3.
(B)y=4x+3
(X) y=5x+3
(E)y=x+3
(D)y=3x+1
Answer:
(E) [tex]y=x+3[/tex]
Step-by-step explanation:
Hi there!
Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis).
1) Determine the slope (m)
[tex]m=\displaystyle \frac{y_2-y_1}{x_2-x_1}[/tex] where two points that fall on the line are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (-4,-1) and ( -1,2):
[tex]m=\displaystyle \frac{2-(-1)}{(-1)-(-4)}\\\\m=\displaystyle \frac{2+1}{-1+4}\\\\m=\displaystyle \frac{3}{3}\\\\m=1[/tex]
Therefore, the slope of the line is 1. Plug this into [tex]y=mx+b[/tex]:
[tex]y=1x+b\\y=x+b[/tex]
2) Determine the y-intercept (b)
[tex]y=x+b[/tex]
Plug in one of the given points and solve for b:
[tex]2=-1+b\\2+1=b\\3=b[/tex]
Therefore, the y-intercept of the line is 3. Plug this back into the original equation:
[tex]y=x+3[/tex]
I hope this helps!
Target has batteries on sale. Keylen purchased 8 batteries for $5.92. What is the unit price?
Publix has navel oranges on sale for $1.89 per pound. Zander purchases 2.7 pounds of oranges. What is the total cost that he will pay for the oranges?
Answer:
the batteries are 74 cents and oranges are 5.10
Step-by-step explanation:
for the first one just divide 5.92 by 8 to get the unit price
and for the second multiply 2.7 by 1.89
(-2 1/2) to the second power
Answer:
6.25
Step-by-step explanation:
[tex](-2\frac{1}{2})^2\\\\(-\frac{5}{2} )^2\\\\(\frac{5}{2})^2\\\\\frac{5^2}{2^2}\\\\\frac{25}{4}\\\\\boxed{6\frac{1}{4}}\text{ or } 6.25[/tex]
Hope this helps.
who can help me PLEASE
Instruction find the measure of the missing angles in the kite
Both the angles will be 105°
Just add up the given angles, subtract the result by 360, and divide by 2.
help me u guys i really neeed help.
Answer:
Q, quadrant 4
Step-by-step explanation:
Answer:
The letter is Q
And the quadrant is (x,-y) i.e quadrant no. 4
Step-by-step explanation:
please answer this question!
Answer:
<A = 51
Step-by-step explanation:
Since AB = AC ( shown by the lines on the sides) we know that this is an isosceles triangle
Since the sides are the same, the base angles are the same
<A = <C
<C = 51 so <A = 51
This is my last problem guys please help me
Answer:
Step-by-step explanation:
a) 9.5 feet above the ground
b) max height at of 34.5 feet 5 feet horizontal distance
c) 10.87 feet away
If f(x)=16x-30 and g(x)=14x-6 for which value of x does (f-g)(x)=0
Answer:
12
Step-by-step explanation:
f(x)=16x-30
g(x)=14x-6
f(x) - g(x) = 16x-30 - (14x-6)
= 16x - 30 - 14x +6
= 2x -24
Set this equal to zero
2x-24 = 0
Add 24 to each side
2x-24 +24 = 0+24
2x = 24
Divide by 2
2x/2 =24/2
x = 12
x=12
Answer:
Solution given:
f(x)=16x-30 and g(x)=14x-6
(f-g)(x)=0
or
f(x)-g(x)=0
16x-30-14x+6=0
2x-24=0
2x=24
x=24/2
x=12
2 cm = 7.5 m in the drawing the mall is 8.6 cm tall how tall is the actual mall
Step-by-step explanation:
here's the answer to your question
HURRY PLEASE
1 To join the school swim team, swimmers must be able to swim at least 500 yards without stopping. Let n represent the number of yards a swimmer can swim without stopping. Write an inequality describing which values of n will result in a swimmer making the team.
Answer:
n = ≥500
Step-by-step explanation:
They must be able to swim 500 yards or more.
Review the table of values for function f(x).
Which number is the value of f^-1(-2)?
O -8
O -7
O 1/8
O 1
Answer:
1/8
Step-by-step explanation:
f^-1 part makes it into a fraction
10x2y+40x2−2xy3−8xy2 factories this expression
Answer:
2(10y + 40 -11xy)
Step-by-step explanation:
First, multiply the expression
20y +80 -6xy - 16xy
Then collect like terms
20y + 80- 22xy
And then lastly factories the expression
2( 10y + 40- 11xy )
Could someone please answer this question for me
Answer:
Yes
Step-by-step explanation:
It's a right angled triangle as 14^2+48^2=50^2.
√3 is a polynomial of degree ________.
Step-by-step explanation:
Therefore, the degree of polynomial √3 is zero.
[tex]\sf\huge\underline\color{pink}{༄Answer:}[/tex]
[tex]\tt{\sqrt{3}}[/tex] is a polynomial of degree 0
[tex]\sf\huge\underline\color{pinl}{༄Note:}[/tex]
The expression is constant, which means it can be rewritten with a factor of x^0. The degree is the largest exponent on the variable.[tex]\color{pink}{==========================}[/tex]
-#CarryOnLearning
-༄⁂✰Park Hana Moon
10) It takes 1 'A cups of sugar and 3 cups of flour to make Sarah's cookies. What is the ratio of sugar to cookies?
Answer:
Step-by-step explanation:
Hello!
1-3
Uma maneira de realizar a operação 9972 - 9 de forma rápida e correta é calculando 1 000 * 994, que é igual a 994 000. A igualdade que justifica esse fato está expressa em:
a) (a + b)² = a² + b² + 2ab
//
b) a² - b² = (a + b)(a - b)
//
c) a² - b² = (a - b)²
//
d) (a - b)² = a² - 2ab + b²
//
e) a² - b² = 1 000(a + b)
Answer:
a)
Step-by-step explanation:
