Answer:
x=17
Step-by-step explanation:
57-x-x=23
57-2x=23
2x=23-57
2x=34
divide both sides wth 2x to make the eqaution equal
x=17
In an arithmetic sequence, the sum of the 3rd and 8th term is 1. Given that the sum of the first seven terms is 35, determine the first term and the common difference.
Answer:
first term: a₁ = 14 the common difference: d = -3Step-by-step explanation:
The sum of the 3rd and 8th term is:
[tex]a_3+a_8=1\\\\a_1+2d+a_1+7d=1\\\\\underline{2a_1+9d=1}[/tex]
The sum of the first seven terms is 35:
[tex]S_7=35\\\\\dfrac{a_1+a_7}2\cdot7=35\\{}\qquad\quad^{\div7\qquad\div7}\\ \dfrac{a_1+a_1+d}2=5\\{}\qquad\qquad^{\cdot2\qquad\cdot2}\\2a_1+6d=10\\{}\qquad\ ^{\div2\qquad\div2}\\a_1+3d=5\\{}\quad\ ^{-3d\quad\ -3d}\\a_1=5-3d[/tex]
[tex]2a_1+9d=1\\\\2(5-3d)+9d=1\\\\10-6d+9d=1\\{}\qquad\qquad^{-10\quad-10}\\{}\qquad3d=-9\\{}\qquad^{\div3\qquad\div3}\\{}\qquad d=-3\\\\\\a_1=5-3(-3)=5+9=14[/tex]
If a + b ≤ 8 and a = 2, then b ≤ 5.Which of the following would be a counterexample?
Answer:
The correct counterexample is [tex]b \leq 6[/tex].
Step-by-step explanation:
We proceed to demonstrate the validity of given implication by direct demonstration and use of our knowledge in algebra:
1) [tex]a + b \leq 8[/tex] Given.
2) [tex]a = 2[/tex] Given.
3) [tex]2+b \leq 8[/tex] 2) in 1)
4) [tex]2 + b +(-2) \leq 8 +(-2)[/tex] Compatibility with addition.
5) [tex]b+[2+(-2)]\leq 6[/tex] Commutative and associative properties/Definition of subtraction
6) [tex]b \leq 6[/tex] Existence of additive inverse/Modulative property/Result.
This contradicts what implies the given proposition. The correct counterexample is [tex]b \leq 6[/tex].
Nakisa spent 328 on a total of CDs and DvDs. If Cds coat 12.00 and DVDs coat 16.00 each, how many CDs did Nakisa buy?
Answer:
[tex]c=\frac{82}{3}-\frac{4}{3}d[/tex]
Step-by-step explanation:
1) Set up an equation
Let c be the number of CDs Nakisa bought.
Let d be the number of DVDs Nakisa bought.
[tex]328=12c+16d[/tex]
Explanation: Each CD costs $12 and each DVD costs $16. Nakisa spent $328 altogether, which means $12c+$16d is equal to $328.
The question is asking for the number of CDs that Nakisa bought, so our goal is to isolate c in the equation above.
2) Isolate c
[tex]328=12c+16d[/tex]
Subtract both sides by 16d
[tex]328-16d=12c+16d-16d\\328-16d=12c[/tex]
Divide both sides by 12
[tex]\frac{328-16d}{12}=\frac{12c}{12} \\\frac{82}{3}-\frac{4}{3}d=c[/tex]
[tex]c=\frac{82}{3}-\frac{4}{3}d[/tex]
I hope this helps!
John drove 504 miles in 8 hours. At the same rate, how many miles would he drive in 13 hours?
The distance travelled by John in 13 hours is 819 miles.
What are arithmetic operations?The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.
The total distance covered in 8 hours is 504 miles.
Then in one hour, distance covered is given as below,
⇒ Number of miles ÷ Number of hours
⇒ 504 ÷ 8 = 63
Then, the distance covered in 13 hours is given as,
⇒ Unit distance in 1 hour × Number of hours
⇒ 63 × 13 = 819
Hence, the miles travelled in 1 hour is given as 819 miles.
To know more about arithmetic operation click on,
https://brainly.com/question/25834626
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Let’s see how good are you with numbers what’s the answer to both of these?
Answer:
A. 22,075.06
B. 17,422.44
Answer:
A. $22,074.94
B. $12,422.44
Step-by-step explanation:
28,485.34 25,405.56
- 6,410.28 - 7, 983.12
= 22,074.94 = 12,422.44
whats 811 divide by 25
Answer:
the answer would be 32.44
Step-by-step explanation:
Can someone answer this question and make sure they show working out. Will reward brainliest to the best answer.
Answer:
8a²+8a+12b = 8a²+8a+12b
Step-by-step explanation:
first, expand the brackets
4a + 4a + 12a² + 8b + 4b - 4a²
then, collect like terms
8a + 8a² + 12b
then, rearrange
8a² + 8a + 12b
Write an equation of the parabola shown.
a. x=3/28y²
b. x=7/12y²
Also please explain how you got the answer :)
Answer:
(B). x=7/12y²
Step-by-step explanation:
Determine an equation that has the solutions x = -4 and x = 3.
Work backward to find the equation:same equation1
We now have an equation answer:
( x=7/12y² )
look at each expression. is it equivalent to "the quotient of 10 plus x and y minus 3"?
Answer:
B
Step-by-step explanation:
B
The numerator is 10 + x.
The denominator is y - 3.
I need help pls anyone
Answer: they are different because h=50 means that h and 50 are equal meaning that h is 50. H>50 means that h is not 50 but could be anything greater than 50
Step-by-step explanation:
Step-by-step explanation:
i think the difference between h=50 and h>50 is that if h=50 then h is 50 but if h>50 then h is larger than 50
F(x)=(X+1)(x+3)(x-4)
Answer:
y=x3−13x−12
Step-by-step explanation:
Simplify the expression (7a5b6)4 .
Answer:
28a20b24
Step-by-step explanation:
(7a5b6)4
= (7a*4)(5b*4)(6*4)
= 28a20b24
Los puntos A (5, 3) y B (-3, -3) representan los extremos de un trozo de madera que será usado por un carpintero para elaborar un mueble, al cual se le agregará una muesca en la tercera parte de su longitud (r = 1/3), tomando como referencia el punto A calcula la coordenada exacta donde ubicará esa muesca, mostrando tus operaciones y selecciona la opción correcta. A) (1.5,3) b) (0.75,3) c) (3,0.75) d) (3,1.5)
Answer:
Las coordenadas del punto son P([tex]2.\overline 3[/tex], 1)
Step-by-step explanation:
Las coordenadas de los extremos de la pieza de madera son A (5, 3) y B (-3, -3)
El punto, P, en el que se agregará la muesca = 1/3 de la longitud de AB
Por tanto, las coordenadas del punto, tomando A como punto de referencia, se dan como sigue;
P (5 + (-3 - 5) × 1/3, 3 + (-3 - 3) × 1/3) = P([tex]2.\overline 3[/tex], 1)
Las coordenadas del punto son P([tex]2.\overline 3[/tex], 1).
An elk tree is 3 1/2 times as talk as an apple tree. The apple tree is 10 2/3 feet tall. How tall is the elm tree?
Answer:
37 1/3
Step-by-step explanation:
10 2/3 * 3.5=37 1/3
Answer:
the answer is 16/7/76
Step-by-step explanation:
ucjss
The work W required to move a particle from a far distance to within radius r of another particle varies jointly as the product of the two particles' charges q1 and q2 and inversely as the radius r. Write a formula that models this proportion. (Use k as the constant of variation.)
Answer:
W = kq1q2 / r
Step-by-step explanation:
W varies jointly as the product of q1 and q2 and inversely as radius r
Product of q1 and q2 = q1q2
W = (k*q1"q2) / r
W = kq1q2 / r
Where,
W = work
q1 = particle 1
q2 = particle 2
r = radius
k = constant of proportionality
The answer is W = kq1q2 / r
Using proportions, it is found that the formula is:
[tex]W = k\frac{q_1q_2}{r}[/tex]
Work varies jointly as the charges, thus, the charges are in the numerator.Inversely as the radius, thus, the radius is in the denominator.There is a constant of proportionality k, which multiplies the fraction;Then, the formula is:
[tex]W = k\frac{q_1q_2}{r}[/tex]
A similar problem is given at https://brainly.com/question/18131403
How can you solve kx-4=90 for x
Answer:
x = 94/k
Step-by-step explanation:
kx-4=90
Add 4 to each side
kx-4+4=90+4
kx = 94
Divide each side by k
kx/k = 94/k
x = 94/k
For the function, f(x) = −x2, find f(-3)
I need you guys help simplifying these questions!!
1. 6n+5(10n−7)
2. 3−10(4p−1)
3. −4(8k+5)−5(9k+4)
Answer:
Hello thanks for the question, if my answqers are correcrt pls mark brain liest
1. 56 n − 35
2. − 40 p + 13
3. − 77 k − 40
Step-by-step explanation:
A rectangular swimming pool measures 50 meters in length and 25 meters in width. What are the length and width of your scaled drawing with a scale of 1 centimeter represents 5 meters?
Answer:
10 cm by 5cm
Step-by-step explanation:
We know that for every 5 meters, there will be 1 centimeter. The pool is 50 meters by 25 meters. So to find this in terms of centimters, divide by 5 to get 10 cm by 5 cm.
Use the diagram of the pyramid to answer the question. Which is the surface area of the pyramid?
5 student in class want to have extra homework. If 20% of the student want extra
homework, how many total students are in the class?
PLS HELP IMMEDIATELY I WILL GIVE BRAINLY
ANSWER THIS CORRECTLY AND GET 100 PTS AND BRAINLIEST
Answer:
4y+6x2-6+y is not equivalent3y+6x2+6 is equivalent, but not fully simplified5y-6x2-5+1 is not equivalent5y-8x2-6+14x2 is equivalent and simplified fully3y+6x2-5-1 is equivalent and simplified fully5y+6x2-6 is not equivalent4y-8x2-5+14x2+y-1 is equivalent, but not fully simplifiedHope I helped!! :)Answer:
nmnm
Step-by-step explanation:
nmnmnm
5x-3=x-12 solve for x
Answer:
x=3
Step-by-step explanation:
Please help I don’t understand this. I suck at this. (Worth 15 points)
Answer:
0.00068
Step-by-step explanation:
By "hm" I think you mean hectometer, and 6.8 cm converted to hectometer is 0.00068. Hope this helped!
Answer:
6.8 cm is equal to 0.00068 hm
Step-by-step explanation:
Hope this helps!
PLZ HELP ME I WILL CALL YOU BRILLIANT Austin is comparing the prices of two car rental companies. Company A charges $24 per day and an additional $25 as service charges. Company B charges $22 per day and an additional $40 as service charges.
Part A: Write an equation to represent each company's total charges for renting a car for a certain number of days. For both equations (one for Company A and one for Company B), define the variable used.
Part B: Which company would charge less for renting a car for 4 days? Justify your answer.
Part C: How much money is saved by using the services of Company A instead of Company B to rent a car for 6 days?
Answer
Step-by-step explanation:
Its A
HI um yeaaaa so do u still need help and um this is taylor megan is at school and aaahhhhh umm yea so................... bye bye
5555555999933333888822228448845657483921234567
JUST HELP. HATE MATH! SKSJSJD
Answer:
56.5
Step-by-step explanation:
its just division
Answer:
226/4 = 56.5
---
[tex]4 \sqrt{226[/tex]
--
simplify 2 x 5^2.
A- 49
B- 20
C- 100
D- 50
solve this equation step by step x+3*2=12-2*2
Answer:
Step-by-step explanation:
x+3*2=12-2*2
x+6=12-4
x+6=8
-6 -6
x=2
Use the function f(x) = 4x – 3 to determine g(x) if
g(x) = f(x) + 5
Answer:
g(x) = 4x + 2
Step-by-step explanation:
g(x) = f(x) + 5 = 4x - 3 + 5 = 4x + 2
7 + 9 – (–3) – 1 + 2
Answer: 20
Step-by-step explanation:
Hope helps
Answer:
7 + 9 - (-3) - 1 + 2
16 - (-3) - 3
19 - 3
16
