Simplifying
3x2 + 5x + -7x + 3 + -5x2 + 2 = 0
Reorder the terms:
3 + 2 + 5x + -7x + 3x2 + -5x2 = 0
Combine like terms: 3 + 2 = 5
5 + 5x + -7x + 3x2 + -5x2 = 0
Combine like terms: 5x + -7x = -2x
5 + -2x + 3x2 + -5x2 = 0
Combine like terms: 3x2 + -5x2 = -2x2
5 + -2x + -2x2 = 0
Solving
5 + -2x + -2x2 = 0
Solving for variable 'x'.
Begin completing the square. Divide all terms by
-2 the coefficient of the squared term:
Divide each side by '-2'.
-2.5 + x + x2 = 0
Move the constant term to the right:
Add '2.5' to each side of the equation.
-2.5 + x + 2.5 + x2 = 0 + 2.5
Reorder the terms:
-2.5 + 2.5 + x + x2 = 0 + 2.5
Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x + x2 = 0 + 2.5
x + x2 = 0 + 2.5
Combine like terms: 0 + 2.5 = 2.5
x + x2 = 2.5
The x term is x. Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.
Add '0.25' to each side of the equation.
+ 0.25 + x2 = 2.5 + 0.25
Combine like terms: + 0.25 = 1.25
1.25 + x2 = 2.5 + 0.25
Combine like terms: 2.5 + 0.25 = 2.75
1.25 + x2 = 2.75
Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 2.75
Calculate the square root of the right side: 1.658312395
Break this problem into two subproblems by setting
(x + 0.5) equal to 1.658312395 and -1.658312395.
Subproblem 1
x + 0.5 = 1.658312395
Simplifying
x + 0.5 = 1.658312395
Reorder the terms:
0.5 + x = 1.658312395
Solving
0.5 + x = 1.658312395
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.658312395 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.658312395 + -0.5
x = 1.658312395 + -0.5
Combine like terms: 1.658312395 + -0.5 = 1.158312395
x = 1.158312395
Simplifying
x = 1.158312395
Subproblem 2
x + 0.5 = -1.658312395
Simplifying
x + 0.5 = -1.658312395
Reorder the terms:
0.5 + x = -1.658312395
Solving
0.5 + x = -1.658312395
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.658312395 + -0.5
Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.658312395 + -0.5
x = -1.658312395 + -0.5
Combine like terms: -1.658312395 + -0.5 = -2.158312395
x = -2.158312395
Simplifying
x = -2.158312395
Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.158312395, -2.158312395}
Is the answer is b, also what is the perimeter of the rectangular!
yes B is the correct answer, the perimeter would be 16
Answer:
B and 16
Step-by-step explanation:
It's B because all the other answers would make a rectangular shape. You can find the plots on the lie by figuring out what coordinate each number is. For example, (3,1) the 3 is the x coordinate and 1 is the y coordinate. To find the perimeter you count the the boxes between the dots. 1 side is 4 and since it's the other sides are 4 you add it up to get 16 units squared.
In 18 years time Halley will be five times as old as she was two years ago. Write this information in the form of an equation involving Halley's present age, a years How old is Halley now?
To solve any questions relating to ages, I find it easier to make a table, like in the picture below.
See picture for answer and clear diagram.
-----------------------------------------------------------------
Notes/Explanations + answer in written form
Let's say that Halley's age now is: x
That means that her age in 18 years is: x + 18
It also means that her age 2 years ago is: x - 2
In the question, we are told that when Halley is 18 years older that her current age, she will be 5 times the age she was when she was 2 years younger than her current age
That means:
Halley's current age + 18 years = 5 times (Halley's current age - 2 years)
So we get this equation (which we solve to get the answer) :
x + 18 = 5 * (x -2) ( expand the brackets)
x + 18 = 5x - 10 (subtract x from both sides)
18 = 4x - 10 (add 10 to both sides)
28 = 4x (now divide both sides by 4)
7 = x
Therefore, Halley's current age is 7 years
Madison currently has a balance of 5503.51 ina an account earning simple interest. 19 years ago she opend up an account with an intial deposit of 3196. What is the interest rate on the account o
Answer:
The simple interest is 3.80% per year.
Step-by-step explanation:
We are presented with a simple interest problem and the following information has been availed;
Accumulated amount = 5503.51
Time = 19 years
Principal = 3196
The first step is to determine the total interest earned over the entire time period;
Interest = Amount - Principal
= 5503.51 - 3196
= 2307.51
The simple interest formula states the total interest earned is equal to the product of the principal, the interest rate and the time;
[tex]I=\frac{P*R*T}{100}[/tex]
Making R the subject of the formula yields;
[tex]R=\frac{100*I}{P*T}[/tex]
Substituting the values we have and simplifying;
[tex]R=\frac{100*2307.51}{3196*19}=3.80[/tex]
The simple interest is thus 3.80% per year.
Tell whether the System has one solution infinite solution many solutions or no solutions 5x-3y=10 10x+6y=20
ANSWER
The system has one solution.
EXPLANATION
The given system is
1st: 5x-3y=10
2nd: 10x+6y=20
Make y the subject in the first equation to get:
[tex]y = \frac{5}{3} x + \frac{10}{3} [/tex]
Solve for y in the second equationquation to get;
[tex]y = - \frac{5}{3} x + \frac{10}{3} [/tex]
The slope of the two equations are not the same.
The two lines will intersect at exactly one point.
.The system has one solution.
Answer:
One solution
Step-by-step explanation:
We are given the following system of equations and we are to tell if the system has one solution, infinite solution, many solutions or no solutions:
[tex]5x-3y=10[/tex] --- (1)
[tex]10x+6y=20[/tex] --- (2)
If we take the common out from (2), we get:
[tex]2(5x+3y) = 20 [/tex]
[tex]5x+3y = 10 [/tex] --- (3)
So adding the two equations (1) and (3) gives 10x=20 ⇒ x=2.
Therefore, this system of equations has one solution.
choose the correct expression to represent the piecewise-defined function?
Answer:
-3 5 2
Step-by-step explanation:
trust
Match the expression 7x^2-5x+9
A. Cubic trinomial
B. Constant monomial
C. Quadratic trinomial
D. Not a polynomial
it it c becauee I had already learned this
Find the range of the sample data set.
16,465 17,342 19,835 15,147 15,898 18,324
Lowest number is 15,147 the highest number is 19,835 simple subtract the lowest from the highest you get 4688
Answer:
The answer is 4,688
Hope this helped : )
Step-by-step explanation:
the range is the difference between the largest and smallest numbers in a set of data.
So, for this set of data. To find the range you subtract 19,835 - 15,147 = 4,688
Kathy designed a square patio. She made the sides of the patio 15 feet. What is the area of the patio?
Answer:
225 feet.
Step-by-step explanation:
15 X 15
WORTH 98 POINTS
The number of horses occupying stalls at the county fairgrounds can be modeled by the following function, where x represents the number of days since the first of June.
h(x)=-3x^2+30+225
Rewrite this function in the form that reveals when there are no horses occupying stalls at the fairgrounds
Answer:
The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.
Step-by-step explanation:
I assume an x is missing, and the function is h(x) = -3x^2 + 30x + 225
You want to know the number of days in which the function value is zero.
-3x^2 + 30x + 225 = 0
Divide both sides by -3.
x^2 - 10x - 75 = 0
(x - 15)(x + 5) = 0
x - 15 = 0 or x + 5 = 0
x = 15 or x = -5
We discard the negative solution.
Answer: The equation is -3x^2 + 30x + 225 = 0, and the number of days is 15.
Answer:
h(x) = -3 (x + 5) (x - 15)
Step-by-step explanation:
h(x) = -3x^2 + 30 + 225
= -3(x^2 - 10x - 75)
= -3(x + 5)(x - 15)
x = -5 x = 15
Help me please and explain, thanks
Answer:
15 degrees
Step-by-step explanation:
3.5 times 10 = 35
50-35=15
Answer:
29 Degrees Fahrenheit
Step-by-step explanation:
So at 4,000 ft. high, it's 50 Degrees Fahrenheit, that means we don't need the first 4,000 because 50 is our starting point. 10,000 - 4,000 = 6,000.
Every 1,000 ft. is down another 3.5 Degrees Fahrenheit, and so first we divide 6,000 by 1,000 to have 6.
Then we multiply 3.5 with 6 to get 21 Degrees Fahrenheit.
50 - 21 = 29 Degrees Fahrenheit.
A fair die with sides 1, 2, 3, 4, 5, and 6 is rolled. Find the probability of showing a number less than 5. Enter your answer in decimal form, rounded to two decimal places.
Answer:
0.25
Step-by-step explanation:
there are 4 numbers that are less than 5.
1,2,3,4 make a fraction 1/4
which equals 0.25
sorry if this wasn't a good explanation..
Answer:
4/6 = 0.67
Step-by-step explanation:
what's 20 percent of 376,900
376900x.2= 75380.......
To find 20 percent of 376,900, multiply it by 0.2, which equals 75,380.
Explanation:To find 20 percent of 376,900, you can multiply 376,900 by 0.2.
20 percent, written as a decimal, is 0.2.
Multiplying 376,900 by 0.2 gives you 75,380.
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What is the approximate surface area of a cylinder with a height of 12 meters and a base radius of 2 meters? Use 3.14 for π
The approximate surface area of a cylinder with a height of 12 meters and a base radius of 2 meters is 175.84 square meters, using 3.14 for pi.
Explanation:The question asks for the approximate surface area of a cylinder with specific dimensions, using 3.14 for π. The surface area of a cylinder can be calculated through the formula for surface area which includes the areas of the two bases and the side surface. The area of one base is πr², which is the area of a circle. For our cylinder, with a base radius (r) of 2 meters, the area of one base is 3.14 × (2 m)² = 12.56 m². Since the cylinder has two bases, you double this area. The side surface is a rectangle when rolled out, and its area is the perimeter of the base circle (circumference) times the height (h) of the cylinder. The circumference (C) of the base is 2πr, so for our cylinder C = 2 × 3.14 × 2 m = 12.56 m. The side surface area is therefore C × h = 12.56 m × 12 m = 150.72 m². Add the areas of the two bases and the side surface to find the total surface area: 2 × base area + side surface area = 2 × 12.56 m² + 150.72 m² = 175.84 m².
GEOMETRY FIND THE VALUE OF Y Please Help ASAP!!
Answer:
32 degrees
god bless all
plz pray for my dead great grandfather
Find p(A|A^c)
A.1
B.0
C.1/2
D. Unknown
If [tex]A^C[/tex] has occurred, then [tex]A[/tex] cannot occur, so the probability is 0.
This follow directly from the definition of conditional probability:
[tex]P(A\mid A^C)=\dfrac{P(A\cap A^C)}{P(A^C)}[/tex]
but [tex]A[/tex] and [tex]A^C[/tex] are disjoint, so the probability of their intersection is 0.
Answer:
B.
Step-by-step explanation:
By visual inspection, determine the best fitting regression model for the data below
Answer:
A) Quadratic
Step-by-step explanation: It has the U shape of a parabola which a quadratic equation has.
Answer:
The correct option is A.
Step-by-step explanation:
In a scatter plot the best fit curve in known as regression curve. Types of regression curves are
1. Linear regression line : If the best fit of a data is a straight line, then it is known as linear regression line.
2. Quadratic regression : If the best fit of a data is a U-shape curve, then it is known as quadratic regression.
3. Exponential regression : If the best fit of a data is an exponential curve, then it is known as exponential regression.
From the given graph it is clear that scatter data forms a U-shaped curve. Since the best fit of a data is a U-shape curve, therefore the quadratic regression model is best for the data.
Thus, option A is correct.
Mrs Rivas wants to install carpet in her basement and family room. Her basement is 62/square yards and her family room is 18/square yards if carpet costs $13/per square yard ,how much will it cost to carpe these two rooms?
It will cost $1040 in the two rooms
For this case we have that the total cost will be given by:
[tex]C {t} = C {b} + C_ {f}[/tex]
Where:
[tex]C_ {b}:[/tex] Cost of installing carpet in the basement
[tex]C_ {f}:[/tex] Cost of installing carpet in the family room
So:
[tex]C_ {b} = 62 \ yard ^ 2 * 13 \frac {dollars} {yard ^ 2}\\C_ {b} = 806 \ dollars[/tex]
Also:
[tex]C_ {f} = 18 \ yard ^ 2 * 13 \frac {dollars} {yard ^ 2}\\C_ {f} = 234 \ dollars[/tex]
Thus, the total cost will be:
[tex]C_ {t} = 806 + 234\\C_ {t} = 1040[/tex]
ANswer:
The total cost will be 1040 dollars
Gigi makes a scale drawing of a patio. The drawing below shows the two scales use she used to plan two patios of different sizes. Which shows the correct dimensions of the rectangle in both scales?
Answer:
Scale 1 35 ft by 25 ft and Scale 2 56 ft by 40 ft
Step-by-step explanation:
step 1
Find the actual dimensions of a patio with the scale 1
The scale 1 is equal to
1 cm/5 ft
Length=7 cm=7*5=35 ft
Width=5 cm=5*5=25 ft
therefore
The dimensions are 35 ft by 25 ft
step 2
Find the actual dimensions of a patio with the scale 2
The scale 2 is equal to
1 cm/8 ft
Length=7 cm=7*8=56 ft
Width=5 cm=5*8=40 ft
therefore
The dimensions are 56 ft by 40 ft
Answer:
C
Step-by-step explanation:
If Scale 1 is 1 cm:5 ft, multiply 5 and 7 by 5 to get the correct dimensions. 7×5=35 and 5×5=25. If Scale 2 is 1 cm: 8 ft, multiply 5 and 7 by 8 to get the correct dimensions. 7×8=56 and 5×8=40. The answer is: Scale 1: 35 ft by 25 ft; Scale 2: 56 ft by 40 ft.
Hope this helps!
What is the solution to the equation
[tex] \frac{1}{40} \times = \frac{1}{8} [/tex]
x = 320
x = 5
x = 48
x = 32
Solution:
Given Expression is 1/40* x = 1/8
Step : Define x in the Equation:
Step : Divide the Equation by 8
Step : Do cross multiplication
Step : Arrange it in particular form
____________________________
☞ 1/40x = 1/8
☞ x/40 = 1/8
☞ x = ⅛ × 40
☞ x = 5
.
Therefore, Answer is 5.
x = 5
1/40 of x is the same x divided by 40, so let’s put that into the equation to get x/40 = 1/8.
Now, multiply both sides of the equation by 40 to cancel out the division by 40.
x = 1/8 * 40
x = 40/8
Now, just simplify.
x = 5
What’s the difference between ratio and proportion? Do they go under the same category?
Answer:
Step-by-step explanation:
Ratio is a relationship between two numbers indicating how many times the first number contains the the second.
Proportion is a part or share or number considered in comparative relation to whole.
So Ratio and Proportion wouldn't go under the same category.
I hope this would help you!!
e
| 2.
Solve this system of two linear equations using the
linear combination method.
2x - 5y = 18
y-x=-10
Answer:
[tex]x=\frac{32}{3}, y=\frac{2}{3}[/tex]
Step-by-step explanation:
We can multiply the second equation by 2 to eliminate.
[tex]2(y-x)=2(-10) \\ \\ 2y-2x=-20[/tex]
Let's eliminate.
[tex]2x-5y=18 \\ -2x+2y=-20 \\ -3y=-2 \\ y=\frac{2}{3}[/tex]
Now we can substitute back into the equation to find the value of [tex]x[/tex].
[tex]\frac{2}{3}-x=-10 \\ \\ \frac{2}{3}-x=-\frac{30}{3} \\ \\ -x=-\frac{32}{3} \\ \\ x=\frac{32}{3}[/tex]
Find the measure of angle 2
I would say 45 degrees
The whole square is 360 degrees because each corner is a 90 degree angle
Which means each triangle section would be 90 degrees but angle 2 is cut in half, so half of 90 is 45
Hope this helps :)
Which step is part of a proof showing the opposite sides of parallelogram ABCD are congruent?
A) show that AC is congruent to BD
B) show that AD is congruent to AB
C) show that angles A and D are supplementary
D) show that triangle ADB is congruent to triangle CBD
I think it’s D. Because A) and B) are not true and im pretty sure that C) is also false
Answer:
its d
Step-by-step explanation:
Suppose h(t)= -0.2t^2+2t models the height, in feet, of a ball that is kicked into the air where t is given as time in seconds.
After how many seconds does the ball reach its maximum height?
What is the maximum height of the ball?
After how many seconds does the ball reach the ground?
Answer:
Step-by-step explanation:
Height: h(t)= -0.2t^2+2t = 2t(-0.1t + 1)
-0.2t^2+2t is a quadratic expression with a = -0.2 and b = 2.
The ball reaches its max height at t = -b/(2a).
Here, t = -2 / (2·[-0.2] ), or t = 2/0.4 = 5 (sec)
The ball reaches its max height at at 5 sec.
The max ht. of the ball is h(5) = -0.2(5 sec)^2 + 2(5 sec) = (-5 + 10) sec, or 5 ft.
To determine after how many sec the ball reaches the ground, we set h(t) = 0 and solve for t:
h(t)= -0.2t^2+2t = 0 = 2t(-0.1t + 1). Thus, t = 0 sec or t = 10 sec
The ball reaches the ground again after 10 sec.
Use the drop down menus to complete the statements
Answer:
what are on the tabs
Step-by-step explanation:
The ordered pair given in the first row of the table can be written using Function notation as (x, f(x)), which is (3, -2).
f(3) is -2.
f(x) = -5 when x is 4.
Now, let's complete the statements:
f(3) is -2.
This statement tells us that when the input value (x) is 3, the function f(x) evaluates to -2. In the table, you can see that when x = 3, f(x) is indeed -2.
f(x) = -5 when x is 4.
This statement indicates that when the input value (x) is 4, the function f(x) takes on the value of -5. In the table, you can see that when x = 4, f(x) is -5.
In summary, these statements highlight specific values of the function f(x) for particular input values (x) based on the table of values provided. The function notation f(3) = -2 indicates that when x = 3, the function returns -2, and the statement f(x) = -5 when x is 4 tells us that when x = 4, the function evaluates to -5, as observed in the table.
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plss help will give brainliest and thx and 5star
Answer:
12. Heptagon
13. 14 cm
14. 50°
Step-by-step explanation:
12.
A polygon containing
3 sides is a triangle
4 sides is Quadrilateral
5 Sides is a Pentagon
6 sides is a Hexagon
7 sides is a Heptagon
Our polygon contains seven sides, it is hence a Heptagon
13. RST = ?
S is the mid point of RT
Hence RS = ST
ST = 7 given
Hence RS = 7
RT = RST = RS + ST
= 7 + 7
= 14 cms
14.
∠RSQ = ∠QST = 25°
∠RST=∠RSQ + ∠QST = 25°+ 25° = 50°
Miss Clark’s farm has chickens and pigs. There are a total of 26 animal feet and 8 animal heads on her farm. If 20 feet belong to the pigs and 6 feet belong to the chickens, the ratio of the number of pigs to the number of chickens is
Answer:
5 : 3
Step-by-step explanation:
Given in the question that,
total number of animal feet = 26
number of pig's feet = 20
number of chicken's feet = 6
As we know that pig have four legs and chicken have 2 legs so,
number of pigs in the farm = 20/4 = 5
number of chickens in the farm = 6/2 = 3
Questions says that there are 8 heads so we can confirm our calculations as
5 + 3 = 8The ratio of the number of pigs to the number of chickens is
5 : 3
Which of the following statements is true?
15+0=0
15-0=0
15 divided 0=0
0 divided 15=0
0 divided 15=0 is your answer
0 divided by 15 is 0.
Anything multiplied or divided by 0 is 0!
Find the value of term a14 in the sequence.
6, 5, 4, 3, 2, . . .
Answer:
[tex]a_{14}=-7[/tex]
Step-by-step explanation:
The given sequence is:
6, 5, 4, 3, 2, . . .
The first term of the sequence is:
[tex]a_1=6[/tex]
The common difference is
d=5-6=-1
The nth term of the sequence:
[tex]a_n=a_1+d(n-1)[/tex]
[tex]a_n=6-1(n-1)[/tex]
[tex]a_n=6-n+1[/tex]
[tex]a_n=7-n[/tex]
When n=14
[tex]a_{14}=7-14=-7[/tex]
The quadratic function h(t)=-16.1t^2+150 models a balls height in feet over time in seconds after it is dropped from a 15 story building
someone please answer
Answer:
A
Step-by-step explanation:
I did the same test