The solution for equation is at (-2, 0).
What is linear equation?
When an algebraic equation is graphed, it always results in a straight line since each term in a linear equation has an exponent of 1. For this reason, it is referred to as a "linear equation."
Both linear equations with one variable and those with two variables exist.
Given equations,
y = x + 2
y = x² + 5x + 6
substitute value of y in second equation
x + 2 = x² + 5x + 6
x² + 4x + 4 = 0
x² + 2x + 2x +4 = 0
x(x +2) + 2(x + 2) = 0
(x + 2)(x + 2) = 0
x = -2
and y = x + 2
y = -2 + 2 = 0
Hence, the solution of equation is at x = -2 and y = 0.
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Simplify the following expression
Answer: 0.25 or 1/4
Step-by-step explanation:
1/2*2 = 1/2^2 = 1/4
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!
Answer:
(x+4)
Step-by-step explanation:
Since area is width times length, you can just factor the area to get the width and length
You factor to get (x+4)(x+7)
Since (x+7) is the length, (x+4) must be the width
Answer:
(x + 4) m
Step-by-step explanation:
[tex]Area \: of \: rectangle = length \times width \\ \\ width = \frac{Area \: of \: rectangle}{length} \\ \\ = \frac{ {x}^{2} + 11x + 28 }{x + 7} \\ \\ = \frac{ {x}^{2} + 7x + 4x + 28}{x + 7} \\ \\ = \frac{ x({x} + 7) + 4(x + 7)}{x + 7} \\ \\ = \frac{ ({x} + 7) (x + 4)}{x + 7} \\ \\ = (x + 4) \: m \\ \\ \red{ \boxed{\bold {\therefore \: width \: = (x + 4) \: m}}} [/tex]
You have 1200 feet of fencing and you want to make two fenced in enclosures by splitting one enclosure in
half. What are the largest dimensions of this enclosure that you could build?
Let x = length and y = width
You would have 2 lengths, so 2x and 3 widths, so 3y
Those need to equal total length of fence:
2x + 3y = 1200
The 3 widths would equal total fence minus the 2 lengths:
3Y = 1200-2x
Solve for y: y = 400 -2/3x
Area = length x width = xy. Replace y :
Area = x(400-2/3x) = 400x-2/3x^2
Differentiate:
400-4x/3 =0
4x/3 = 400
4x = 1200
X = 300
Y = 400-2/3(300) = 200
The dimension would be 300 ft x 200 ft
TICKETS Three kinds of tickets are available for a concert: orchestra seating, mezzanine seating, and balcony seating. The orchestra tickets cost $2 more than the mezzanine tickets, while the mezzanine tickets cost $1 more than the balcony tickets. Twice the cost of an orchestra ticket is $1 less than 3 times the cost of a balcony ticket. Determine the price of each kind of ticket.
Answer: an orchestra seating ticket cost $10
A mezzanine seating ticket cost $8
A balcony seating ticket cost $7
Step-by-step explanation:
Let x represent the price of an orchestra seating ticket.
Let y represent the price of a mezzanine seating ticket.
Let z represent the price of a balcony seating ticket.
The orchestra tickets cost $2 more than the mezzanine tickets. It means that
x = y + 2- - - - - - - 1
The mezzanine tickets cost $1 more than the balcony tickets. It means that
y = z + 1 - - - - - - -2
Twice the cost of an orchestra ticket is $1 less than 3 times the cost of a balcony ticket. It means that
2x = 3z - 1- - - - - - - - -3
Substituting equation 2 into equation 1, it becomes
x = z + 1 + 2
x = z + 3 - - - - - - - - - -4
Substituting equation 4 into equation 3, it becomes
2(z + 3) = 3z - 1
2z + 6 = 3z - 1
3z - 2z = 6 + 1
z = 7
x = z + 3 = 7 + 3
x = 10
y = z + 1 = 7 + 1
y = 8
Gracie has 1/2 of a cantaloupe that she wants to divide. How many 's 1/8 of a cantaloupe are there in 1/2 of a cantaloupe?
Answer:
4/8
Step-by-step explanation:
Dividing a whole cantaloupe into eighths will give you 8/8 or 1. When it is cut in half then divided there is one half of 8/8 or there are 4/8 in one half. This is true because 1/2 and 4/8 are equal terms.
Hope this helps!
what is the surface area of a cone in terms of pi with a diameter of 14cm and a slant height of 20cm
Answer:
476 Pi cm^2
Step-by-step explanation:
The surface area of a cone is given by the formula:
● Sa = Pi× r^2 + Pi×r×l
r is the radius and l is the slant heigth.
■■■■■■■■■■■■■■■■■■■■■■■■■■
We are given that:
● r = 14 cm
● l = 20 cm
Let's calculate Sa
● Sa = Pi×14^2 + Pi × 14 × 20
● Sa = 476 Pi cm^2
Sidney is eating lunch at a salad bar where you create your own salad. An 8-ounce salad costs $2.49. Each additional ounce of salad costs $0.25. How much does Sidney's salad cost if it weighs 1 pound, 8 ounces?
Answer:
6.49
Step-by-step explanation:
2.49 + 0.25(16)
2.49+4
6.49
Answer:
$6.49
Step-by-step explanation:
1 lb = 16 oz
His salad weighs 1 lb, 8 ounces which is the same as 16 ounces plus 8 ounces.
8 ounces cost $2.49
His salad weighs 16 ounces more than 8 ounces, so in addition to the $2.49, he needs to pay $0.25 per ounce for 16 extra ounces.
16 * 0.25 = $4.00
Total cost = $2.49 + $4.00 = $6.49
Given the equation,D=m/v if D=6/7 and =m+3 then m=.
Answer:
[tex]m=18[/tex]
Step-by-step explanation:
The equation given is [tex]D=\frac{m}{v}[/tex]
and also we have that [tex]D=\frac{6}{7}[/tex], thus:
[tex]\frac{6}{7}=\frac{m}{v}[/tex]
------------
I think the question is missing which variable is defined as [tex]=m+3[/tex], so I will solve for [tex]v=m+3[/tex] since is the only other variable in the equation.
substituting [tex]v=m+3[/tex] into [tex]\frac{6}{7}=\frac{m}{v}[/tex]:
[tex]\frac{6}{7}=\frac{m}{m+3}[/tex]
and we solve for m:
[tex](m+3)(6)=7m\\6m+18=7m\\18=7m-6m\\18=m[/tex]
m is equal to 18.
The diameter of a circle is __________.
A. The distance around the circle
B. The distance from the center point to any edge of the circle
C. The distance across the circle that cuts it in half.
D. The same as its circumference
Answer:
The answer is C
Step-by-step explanation:
Answer: The answer is C
9 sec2 A - 9 tan2 A=
hcglnlkl gzfog dufkbicfhpffkgdhjdk
Tell whether each outcome is impossible, unlikely, as
likely as not, likely, or certain. Then write the probability
in simplest form.
1.choosing a red crayon from a box of 24 different colored
crayons, including 8 red crayons
Answer: likely, pls mark me as brainliest if it helped u
Step-by-step explanation:
What is equivalent to log2(7)
A.7^2
B.2^7
C.7log(2)
D.log(7)/log(2)
E. Log(2)/log(7)
Answer:
D
Step-by-step explanation:
Using the changing base formula, log base 2 raised to 7 can be written as log7/log2
The correct answer is D. log(7) / log(2).
To find the equivalent of log2(7), you can use the change of base formula for logarithms.
The change of base formula states that log base a of b is equal to log base c of b divided by log base c of a.
In this case, we want to find the equivalent of log2(7), so we can use the change of base formula with base 10 as follows:
log2(7) = log(7) / log(2)
Therefore, the correct answer is D. log(7) / log(2).
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urgent！！！！pleasehelp
Answer:
y + 2 = -2(x - 3)^2
Step-by-step explanation:
We can see immediately that the vertex is at (3, -2).
The vertex form of the equation of a parabola is
y - k = a(x - h)^2.
If the parabola opened upward, the equation would be y + 2 = 2(x - 3)^2. But seeing that this particular parabola opens downward, the equation is
y + 2 = -2(x - 3)^2.
Check: Does the point (2, -4) satisfy this equation?
-4 + 2 = -2(2 - 3)^2 becomes -2 = -2(-1)^2, which is true.
Scientific notation
9.78 × 10^5 - 732,000
It has to be either 2.46 × 10^5 or 2.46 × 10^3
Answer:
[tex]2.46\times 10^5[/tex]
Step-by-step explanation:
[tex]9.78 \times 10^5 - 732,000\\= 9.78 \times 10^5 - 7.32 000\times 10^5\\= 9.78 \times 10^5 - 7.32\times 10^5\\= 2.46\times 10^5[/tex]
City
Atlanta
Positive Response to Program 1 Positive Response to Program 2
77.8%
82.1%
Boston
86.4%
86.6%
65.9%
Chicago
Dallas
87.5%
73.8%
80.9%
69.796
79.4%
78.4%
88.1%
Houston
Los Angeles
Miami
Newark
82.596
82.6%
81.496
83.3%
Total
68.89
81.7%
The probabilities of a positive response to two government programs from citizens in eight cities are given in the table. What is the chance of
a positive response for program 1, given that the individual is from Houston?
ОА
68.896
OB.
69.796
OC.
79.496
OD
insufficient data
Answer:
The correct option is (B) 69.7%.
Step-by-step explanation:
The table provided represents the probabilities of a positive response to two government programs from citizens in eight cities.
The probabilities mentioned in the table are conditional probabilities, i.e. the probability of a positive response for program 1, given that the individual is from city x.
The probability a positive response for program 1 from an individual from Houston is 69.7%.
Then the conditional probability of a positive response for program 1, given that the individual is from Houston is 69.7%.
Thus, the correct option is (B).
You start driving north for 48 miles turn right and drive east for another 14miles at the end of driving what is your striaght line distance from your starting point
Answer: 48 miles
Because north is straight from the starting point and you traveled 48 miles north so 48
Answer:
50 miles
Step-by-step explanation:
If you draw the shape
you'll roughly get the above mentioned one..
so it's a right angle triangle now
using Pythagoras relationship
48^2+14^2=x^2
2304+196=x^2
2500=x^2
x= 50
straight line distance aka displacement is 50 miles
pls help ASAP for brainliest answer
Answer:
324cm^3
Step-by-step explanation:
The formula for calculating volume of a triangular prism is 1/2× bhl (b : base, h : height, l : length)
1/2 × 6 × 9 × 12 = 324cm^3
g(r)=-(r+11)(r+14)
what are the zeros & what is the vertex
Answer:
The roots (r) or the Zeros ( other name ) = -11 and -14
Step-by-step explanation:
Post in comments if u need step by step and Ill give to u :)
.the difference of thirteen and six, multiplied by a number
This is the expression your question creates 13-6•x
Answer:
This can be written as (13-6)n. Hope this helps!
Step-by-step explanation:
Count the possible combinations of 2 numbers chosen from the list 99 98 97 96 95 94 93 92 91
Simplify (3v5+8v3−10v2)−(−12v5+4v3+14v2) . Write answer in standard form.
Answer:
15v^5+4v^3-24v^2
Step-by-step explanation:
Distribute the Negative Sign:
=3v5+8v3−10v2+−1(−12v5+4v3+14v2)
=3v5+8v3+−10v2+−1(−12v5)+−1(4v3)+−1(14v2)
=3v5+8v3+−10v2+12v5+−4v3+−14v2
Combine Like Terms:
=3v5+8v3+−10v2+12v5+−4v3+−14v2
=(3v5+12v5)+(8v3+−4v3)+(−10v2+−14v2)
=15v5+4v3+−24v2
Answer:
=15v5+4v3−24v2
Hope this helps! :)
You want the volume of the box to be 9 cubic inches.
Find the rational solution(s) of the equation. Then use polynomial long division to find the other solution(s).
What are the possible side lengths of the box?
Answer: x^3
Step-by-step explanation: it has no cube so its 3^x or x^3
Please answer correctly !!!!!! Will mark brainliest !!!!!!!!!!!!
Answer:
There were 12 babies and 4 adults
There are group of 20 friends. Every one is a supporter of either Chennai Super Kings or Kolkata Knight Riders or both. If 15 of them support Chennai Super Kings and 10 of them support Kolkata Knight Riders, (i) the number of people who supports both Chennai Super Kings and Kolkata Knight Riders is ____. (ii) the number of people who support only Chennai Super Kings is ____. (iii) the number of people who support only Kolkata Knight Riders is ____.
Answer:
CSK = Chennai Super Kings
KKR = Kolkata Knight Riders
A cube has width of 9 cm. What is the volume of the cube?
Answer:
V = 729 cm³
Step-by-step explanation:
side length a = 9 cm
face diagonal f = 12.727922061358 cm
solid diagonal d = 15.58845726812 cm
surface area S = 486 cm²
volume V = 729 cm³
Formula: V=a³
Patrick made a cake for his mother's birthday. He started making the
cake batter at 9:00 A.M. It took 1 hour and 15 minutes to make the
batter. Then, the cake baked in the oven for 1 hour.
What time did the cake come out of the oven?
Show your work
Answer: 11:15 AM
Step-by-step explanation:
9:00 plus an hour and 15 minutes (75 minutes) makes it 10:15. Then bake for an hour (60 minutes), makes it 11:15
Answer:
what she saisddddddddddd
Step-by-step explanation:
What is the period of the sinusoidal fynction below?
f(x) = 2 cos(3x – 360) + 3
Answer:
Here you go! I have a graph for your answer!
Step-by-step explanation:
The Xmin is -10
The Xmax is 10
The Ymin is -10
Ans the Ymax is 10
The bottom part of this block is a rectangular prism. The top part is a square pyramid. You want to cover the block entirely with paper. How much paper do you need?
Answer:
Total paper required = 165 cm²
Step-by-step explanation:
Paper required to cover the entire block = (Surface area of the prism at the base - area of the top of the prism) + Lateral surface area of the pyramid
Surface area of the rectangular prism = 2(lb + bh + hl)
(here l, b, h are the length, width and height respectively)
= 2(5×5 + 5×4 + 4×5)
= 2(25 + 20 + 20)
= 2×65
= 130 cm²
Area of the top of the prism = (side)²
= 5²
= 25 cm²
Lateral area of the square pyramid = 4 × Area of one lateral side
= 4 × [tex][\frac{1}{2}(\text{Base})(\text{Height})][/tex]
= 4 × [tex][\frac{1}{2}(5)(6)][/tex]
= 60 cm²
Total paper required = (130 - 25) + 60
= 105 + 60
= 165 cm²
May I get Help With this Task 1,2,3,4,5
Answer:
1. We'll be looking at g(x) and from the table when x = 3,000 Angela owes 44,600 dollars.
2. f(3) = 2000
g(2000) = 45,000
3. g(3,500) = 44,400 and f(6) = 3,500 so the answer is 44,400 - 3,500 = 40,900.
4. From the table when f(x) = 2,500, x = 4.
5. From the table when g(x) = 44,200, x = 4,000.
Answer:
1. when f(x) = $ 3000 the loan still 44,600
2. f(3) means her saving in 3rd month. so f(3) is 2000 then g(2000) is 45000
3. g(3500) - f(6) = 44400 - 3500 = 40,900
4. based on table f(x), x is 4
5. based on table g(x) (the right one), x is 4000
The sum of two integers is two times their difference. Which of the following algebraic equations demonstrates this? A) (x + y) = 2(x - y) B) (x + y) = (x - y) + 2 C) (x + y) = (x - y) - 2 D) 2(x + y) = 2(x - y) E) 2(x + y) = (x - y)
Answer:
It is A)
Step-by-step explanation:
