Answer:
Given
Step-by-step explanation:
4x+2+6=0
4x+2=-6
4x= -6-2
4x= -8
x = -8/4
= -2
Answer:
x = -2
Step-by-step explanation:
[4x + 2] + 6 =0
Combine like terms
4x+ 8 =0
Subtract 8 from each side
4x+8-8 = 0-8
4x = -8
Divide each side by 4
4x/4 = -8/4
x = -2
A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following. 1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute. 2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses. Which statement is correct? Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses. Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes. Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute. Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
Answer:
Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Step-by-step explanation:
Let's rule out the options given one by one.
Option 1: Mark’s method is wrong, because it is impossible to deliver mail to 1.2 houses in a minute. The carrier can only deliver to a whole number of houses.
This is not true, because 1.2 is a rate, it just means that the carrier can finish 1 house in a minute, and also have time to get started delivering to the second house. The total number of houses has to be a whole number, but the rate doesn't.
Option 2: Mark’s method is wrong, because it is impossible to deliver mail for 7.5 minutes. The carrier can only deliver mail for a whole number of minutes.
This option is also incorrect. Delivering mail for 7.5 minutes just means 7 minutes and 30 seconds, which is definitely possible.
Option 3: Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
This option is correct. 1.2 is the rate of which the carrier delivers mail.
Option 4: Mark’s method is correct, because it is possible to deliver mail for 7.5 minutes; 7.5 represents the unit rate of 7.5 minutes per house.
This option is also incorrect. Although it is possible to deliver mail for 7.5 minutes, it is not the unit rate, it is the total amount of time it would take.
Answer:
Mark’s method is correct, because even though it is impossible to deliver mail to 1.2 houses in a minute, 1.2 represents the unit rate of houses per minute.
Step-by-step explanation:
the perimeter of a pickleball court is 128 feet. The width is represented by x and the length is represented by 2x + 4. What are the actual dimensions of the pickleball court (length and width)?
Answer:
x=62.
Step-by-step explanation:
2x +4=128
2x=128-4
2x=124
x= 62
What numbers are not square or even?
Answer:
Search Results
Featured snippet from the web
Odd and even square numbers
As all even square numbers are divisible by 4, the even numbers of the form 4n + 2 are not square numbers. As all odd square numbers are of the form 4n + 1, the odd numbers of the form 4n + 3 are not square numbers.
Step-by-step explanation:
given that a*b=2a-3b,then 2*(-3)=
Answer:
13
Step-by-step explanation:
Given: a*b=2a-3b
To find: 2*(-3)
Solution:
Numbers that are used for counting are known as natural numbers. Number along with the digit 0 are known as whole numbers.
In the question, [tex]*[/tex] is used to define relation between a and b as [tex]a*b=2a-3b[/tex]
To find 2*(-3), use the given condition: a*b=2a-3b
Put [tex]a=2,b=-3[/tex]
[tex]2*(-3)=2(2)-3(-3)=4+9=13[/tex]
Given that a*b = 2a-3b,then 2*(-3)= 13
The given binary operation is:
a*b = 2a - 3b
Applying this binary operation to 2*(-3), we are going to substitute a = 2 and b = -3 into the binary operation a*b = 2a - 3b
If a = 2 and b = -3:
2*(-3) = 2(2) - 3(-3)
2*(-3) = 4 + 9
2*(-3) = 13
Therefore, given that a*b = 2a-3b,then 2*(-3)= 13
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Please help me answer.
Answer:
Slope-intercept: y=3/4x+1
Sorry idk how to do general form
Step-by-step explanation:
Slope-intercept form is y=mx+b, m being the slope, b being the y-intercept.
The slope of this graph is 3/4, and the y-intercept is 1.
Answer:
Slope-intercept form: [tex]y=\frac{3}{4}x+1[/tex]
General form: [tex]-3/4x+y-1[/tex]
Step-by-step explanation:
Firstly, to get the slope intercept form, we need to find the slope and the y-intercept. To find the slope, we can use the slope formula and calculate the "rise over run" for these two points. The coordinate of the first point is (0, 1) , and the coordinate of the second point is (4, 4). If x1 = 0, x2 = 4, y1 = 1, and y2 = 4, we can plug those values into the slope formula that I mentioned earlier, which is [tex]\frac{y_{2}-y_{1}}{x_{2}-{x_{1}}}[/tex]. So, after we plug in those values we get in the two points, we can see that [tex]\frac{4-1}{4-0}[/tex], so the slope is [tex]\frac{3}{4}[/tex]. The x moves right 4 times and the y goes up 3 times. Finally, the y-intercept value is 1 because when x = 0, y is 1, and the point we used for the slope formula (0, 1) proves that. For the slope-intercept form, [tex]mx+b[/tex], where m is the slope and b is the y-intercept, m is [tex]\frac{3}{4}[/tex] and b is 1. So, our final answer for the slope-intercept form is [tex]y=\frac{3}{4}x+1[/tex]. Now we can find the general form. To do this, we must get one side of the equation to equal 0. Using our slope-intercept equation, [tex]y=\frac{3}{4}x+1[/tex], we can subtract y from both sides to get 0 on the left, like this: [tex]0=\frac{3}{4}x+1-y[/tex]. Then, we can rearrange the variables to general form: [tex]0=\frac{3}{4}x-y+1\\[/tex]. That is our general form answer. To recap, to find the slope, find the coordinates of the two points, and then plug in those points into the slope formula to find the steepness of the line. Then, add the y intercept that we can see on the graph. For general form, subtract y from both sides and rearrange the equation. Hope this helps!
Lauren's birthday is in January. Determine the approximate probability that her brother, Adam, also has a birthday in January.
A) 1/2
b) 1/6
c) 1/12
d) 1/144
Please helpp!!
Quinn returned home one summer's day to find it sweat-inducingly hot! He turned the air conditioner on and fell asleep. The room's temperature decreased by 0.5^\circ0.5
∘
0, point, 5, degrees Celsius each minute, and Quinn woke up 606060 minutes later when it was 10^\circ10
∘
10, degrees Celsius.
Answer:
[tex]f(x)=-0.5x+40[/tex]
Step-by-step explanation:
To solve this problem, we need to find the linear function. We know that the constant rate of change is -0.5° Celsius per minute. Also, after 60 minutes the temperature was 10° Celsius. So, we have a one point and the slope of the linear function, let's use the point-slope formula
[tex]y-y_{1} =m(x-x_{1} )\\y-10=-0.5(x-60)\\y=-0.5x+30+10\\y=-0.5x+40[/tex]
Where the y-intercept is at (0, 40).
Now, we have two points to graph the relation between minutes and Celsius degrees.
Therefore, the room's temperature as a function of time is
[tex]f(x)=-0.5x+40[/tex]
Its graph is attached.
Answer:
Put one of the dots 2 spaces obove 60 and the other dot 3 spaces above 50.
Step-by-step explanation:
Given the directrix of y = 6 and focus of (0, 4), which is the equation of the parabola?
y = −one fourthx2 + 5
y = −one fourthx2 − 5
y = one fourthx2 + 5
y = one fourthx2 − 5
Answer:
a) The equation of the parabola
[tex]y = \frac{-x^{2} }{4} +5[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given the directrix of the parabola y = 6
Focus of the parabola S(0,4)
The standard equation of the parabola
( x- h)² = 4 a (y-k)
(h,k) is the vertex of the parabola
Axis of the parabola is parallel to y-axis
Given the directrix of the parabola y = 6
The directrix of the parabola y = k -a = 6
k-a =6 ...(i)
The focus of the parabola
S( h , K+a) = (0,4)
so h = 0 and K+a =4
K+a =4 ....(ii)
Step(ii):-
Solving (i) and (ii) equations , we get
Adding (i) and (ii) equations and we get
K-a + k+a = 6 +4
2 K = 10
K =5
Substitute K =5 in equation (i)
K -a =6
5 -a =6
5-6 =a
a = -1
Step(iii):-
we have (h,k) =( 0,5) and a = -1
The equation of the parabola
( x- h)² = 4 a (y-k)
( x- 0)² = 4 (-1) (y-5)
x² = -4 y + 20
-4 y = x² - 20
dividing '-4' on both sides, we get
[tex]y = \frac{x^{2} }{-4} +\frac{-20}{-4}[/tex]
[tex]y = \frac{-x^{2} }{4} +5[/tex]
Final answer:-
The equation of the parabola
[tex]y = \frac{-x^{2} }{4} +5[/tex]
The volume of a cube is represented by the polynomial 8x³ - 60x² + 150x - 125. Determine the measure of the edge of that cube.
Answer:
Edge = 2.5
Step-by-step explanation:
Pls help me with this questions
Step-by-step explanation:
6a
Sn = n/2 [2a + (n-1) d]
(2Sn)/ n = 2a + (n - 1) d
2a + (n-1) d = (2Sn)/n
(n-1) d = (2Sn - 2a)/n
[tex]d = \frac{2sn \: - 2a}{(n(n - 1))} [/tex]
[tex]d = \frac{2(sn - a)}{ {n}^{2} - n} [/tex]
6b
[tex]d = \frac{2(56 - 25)}{ {32}^{2} - 32} [/tex]
d = ¹/16
7a.
E = (mv²)/2 + mgh
E = m( v²/2 + gh)
E/m = v²/2 + gh
E/m - gh = v²/2
2(E/m - gh) = v²
so
[tex]v = \sqrt{2( \frac{e}{m} - gh)}[/tex]
7b.
[tex]v = \sqrt{2( \frac{4900}{20} - 9.8 \times 15)}[/tex]
v = 14 m/s
Given: y // z Prove: measure of angle 5 plus measure of angle 2 plus measure of angle 6 equals 180 degrees
Step-by-step explanation:
Given: y // z Prove: measure of angle 5 plus measure of angle 2 plus measure of angle 6 equals 180 degrees
A swimming pool is being drained at a constant rate of 800 gallons per hour. After 5 hours of draining, 11,000 gallons of water remain in the pool.
Answer:
Step-by-step explanation:
In 5th hour remainder is 11,000 gal
Therefore at 4th hour 11,800 gal
At 3rd hour 12,600 gal
At 2nd hour 13,400 gal
at 1st hour 14,200 gal
Part B
At the beginning there is 15,000 gal
Before the draining began, the pool contained 14,200 gallons of water.
The water is being drained at a rate of 800 gallons per hour.
The function f(t) = 14,200 - (800t - 800)
49 - 3 + 9 times 8 divided by 2
Answer:
82
Step-by-step explanation:
49 - 3 + 9 times 8 divided by 2
Answer:
82
Step-by-step explanation:
49 -3 + 9*8/2
PEMDAS
Multiply and divide from left to right
49 -3 + 72/2
49 -3 + 36
Add and subtract from left to right
46 +36
82
Jennifer can do 8 math problems in 20 minutes. How long would it take her to complete a 10 question test at the same rate?
Answer:
25 minutes
Step-by-step explanation: 20 divided by 8 equals 2.5 so she take 2 and a half minutes per question. 2.5 plus 2.5 equals 5 so just add five minutes on her original time. 25 minutes
Answer:
25 minutes
Step-by-step explanation:
→You can set this problem up as a proportion, like so:
[tex]\frac{8}{10} =\frac{20}{x}[/tex]
→Cross multiply:
[tex]\frac{8x}{200}[/tex]
→Divide 200 by 8:
x = 25
There are 15 students going on a field trip. If 3/5 of them pack there lunches, how many students pack their lunches?
Answer:
9 pack their lunches
Step-by-step explanation:
Take the number of students and multiply by the fraction that pack their lunches
15 *3/5 =
15/5 * 3
3*3
9
Hannah babysits to earn money. She charges $6.50 to babysit for the first hour. She charges $5.75 for each additional hour. Let "n" equal the number of hours after the first hour. Which expression represents how much Hannah charges? *
[tex] \sqrt[4]16 - 6 \sqrt[3]343 + 18 \sqrt[5]243 - \sqrt{196} [/tex]
Answer:
Step-by-step explanation:
= 2- 6*7 + 18*3 - 14
=2-42+54-14
=2 + 12- 14
= 14-14
=0
Answer:
the ans is 0
Step-by-step explanation:
=2- 6*7 + 18*3 - 14
=2-42+54-14
=2 + 12- 14
= 14-14
=0
please help! find the area is the parallelogram.
Answer:
24cm^2
Step-by-step explanation:
3cm times 8cm = 24cm^2
Answer:
A=b*h
Step-by-step explanation:
base=5
height=3
5*3=15
15 is the answer
Carl wants to put up a glow-in-the-dark sticker display on his bedroom ceiling. He needs a gallon of black paint which costs $12. The stickers cost $18 per package and he wants to buy 2 packages. Which of the following is a good estimation of how much change Carl will get back if he gives the cashier $60?
Answer:3a ?
Step-by-step explanation:
Answer:
✈️?
Step-by-step explanation:
If there are 16 ounces in a pound. How many pounds are in 24 ounces?
Answer: 1.5 pounds
Step-by-step explanation: 16 oz(one pound) + 8oz(half a pound)= 24oz
The graph of which function passes through the point (0,2/pi)?
y=cos-1(x)
y=csc-1(x)
y=sec-1(x)
y=sin-1(x)
thanks!
Answer:
[tex]y=sin^{-1}x[/tex]
Step-by-step explanation:
Given: A point is [tex](0,2\pi)[/tex]
To find: function whose graph passes through the given point
Solution:
A trigonometry explains the relationship between the sides and the angles of the triangle.
The inverse trigonometric functions [tex]sin^{-1}x\,,\,cos^{-1}x\,,\,tan^{-1}x[/tex] help to find the value of an unknown angle of a right triangle when length of two sides are given.
Consider [tex]\sin y=x[/tex]
Put [tex]y=2\pi[/tex]
[tex]sin 2\pi=0[/tex]
So, point [tex](0,2\pi)[/tex] satisfies the function [tex]y=sin^{-1}x[/tex]
Therefore, graph of function [tex]y=sin^{-1}x[/tex] passes through [tex](0,2\pi)[/tex]
Answer:it’s A y=cos^1(x)
Step-by-step explanation:
Edge 2020
The formula f(x + 1) = Two-thirds(f(x)) defines a geometric sequence where f(1) = 18. Which explicit formula can be used to model the same sequence?
Answer:
The explicit formula is Tn = 18[(2/3)^(n-1)]
Where n is the term we are looking for
Step-by-step explanation:
Here, we want to get an explicit formula to model the equation
Now, F(2) = 2/3 * f1 = 2/3 * 18 = 12
F(3) = 2/3 * f(2) = 2/3 * 12 = 8
F(4) = 2/3 * F(3) = 2/3 * 8 = 16/3
F(5) = 2/3 * 16/3 = 32/9
Thus, seeing how the equations are progressing, we can definitely see a pattern.
That is Tn = (2/3)^(n-1)(18)
Answer:
Answer in image.
Step-by-step explanation:
Solve for x. Round your answer to the nearest thousandth. a. 8.691 c. 6.474 b. 6.252 d. 12.956
Answer:
The answer is B 6.252
Step-by-step explanation:
Solve the simultaneous equation
y=9-x
y= 2x^2+4x+6
Answer:
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The intersecting points of given two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
Step-by-step explanation:
Explanation:-
Step(i):-
Given simultaneous equation
y = 9-x ...(i)
y = 2 x² +4 x+6 ..(ii)
Equating (i) and (ii) equations , we get
9 -x = 2 x² +4 x+6
⇒ 2 x² +4 x + 6- 9 +x =0
⇒ 2 x² + 5 x - 3 =0
⇒ 2 x² +6 x -x -3 =0
⇒ 2 x ( x +3) -1 ( x+3) =0
⇒ (2 x -1 ) ( x+3) =0
⇒ (2 x -1 ) = 0 and ( x +3 ) =0
[tex]2 x =1[/tex] and x = -3
x = 1/2 and x =3
Step(ii):-
x = 3 ⇒ y = 9 - 3 =6
A( 3 ,6)
[tex]x = \frac{1}{2} , y = 9 - \frac{1}{2} = \frac{17}{2}[/tex]
[tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
Final answer:-
The intersecting points of two simultaneous equations are
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The solution of the given two simultaneous equation
A( 3 ,6) and [tex]B(\frac{1}{2} ,\frac{17}{2} )[/tex]
The solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)
From the question,
We are to solve the given simultaneous equations
The given equations are
y = 9-x ---------- (1)
y = 2x²+4x+6 ---------- (2)
Substitute equation (1) into equation (2)
y = 2x²+4x+6
That is
9-x = 2x²+4x+6
Simplifying, we get
0 = 2x² +4x +x +6 -9
0 = 2x² +5x -3
∴ 2x² +5x -3 = 0
Now, solving the quadratic equation
2x²+6x -x -3 = 0
Factorizing
2x(x+3) -1(x+3) = 0
Then, we get
(2x -1)(x+3) = 0
∴ 2x - 1 = 0 OR x + 3 = 0
2x = 1 OR x = -3
∴ x = 1/2 OR x = -3
Now, substitute the values of x into equation (1) to determine the values of y
y = 9-x
When x = 1/2
y = 9 - 1/2
y = 8 1/2
and when x = -3
y = 9 --3
y = 9+3
y = 12
Hence, the solution to the given simultaneous equation is (1/2, 8 1/2) and (-3, 12)
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David wants to hang a mirror in his room. The mirror and frame must have an area of 8 square feet. The mirror is 2 feet wide and 3 feet long. Which quadratic equation can be used to determine the thickness of the frame, x?
Answer:
4x^2+10x-2=0
Step-by-step explanation:
So the total area of mirror: 2*3 = 6 ft sq
8-6 = 2 ft sq is the area of the frame
x is the thickness of the frame
so we have (2*x)*2+(3*x)*2+x*x*4= 2
4x+6x+4x^2=2
-> 4x^2+10x-2=0
A circle representing a pool is graphed with a center at the origin. Grant enters the pool at point A and swims over to a friend who is located at point B. A coordinate plane with a circle drawn. The center of the circle is the origin, (0, 0). The circle has a diameter of 16 units. There is a line segment drawn from Point A at (8, 0), passing through (0, 4) to Point B at (negative 4, 6). Which equation represents Grant’s path? y = 2 – 4x y = 4 – y = 6 – y = 8 – 2x
Answer:
y = 4 - x/2
Step-by-step explanation:
Since the line passes through the points A(8,0) and B(4,6), we find that gradient of that lime m = (y₂ - y₁)/(x₂ - x₁) where (8,0) = (x₁, y₁) and (-4,6) = (x₂, y₂).
So, m = (6 - 0)/(-4 - 8) = 6/-12 = = -1/2.
Since the line passes through the point (0,4), the equation of the line is
m = (y - y₃)/(x - x₃) where (x₃, y₃) = (0,4)
So, -1/2 = (y - 4)/(x - 0)
= (y - 4)/x
-x/2 = y - 4
y = 4 - x/2
which is the equation of the line.
Answer:
B
Step-by-step explanation:
Which interval for the graphed function contains the local
minimum?
O f-1,1]
(1.2)
O(-3,-1)
O (-5, -3)
C is the midpoint of AD. B is the midpoint of AC. BC = 14. What is
the length of BD?
Answer:
Length of segment BD = 42 units
Step-by-step explanation:
Since C is the midpoint of AB,
Then segment AC = segment CD
Since B is the midpoint of BC,
Then the length of segment AB = Length of segment BC = 14 units
Length of AC = 2 × (14)
= 28 units
Length of AC = length of CD = 28 units
Length of segment BD = Length of BC + length of CD
= 14 + 28
= 42 units
Therefore, length of segment BD is 42 units.
Find the value of 4 + (27 - 12 ∙ 2) ÷ 2.
Step-by-step explanation:
4 + (27 - 12 * 2) / 2
4 + (27 - 24) / 2
4 + 3/2
5 1/2
Answer:
5 1/2
Step-by-step explanation:
4 + (27 - 12 ∙ 2) ÷ 2=
4 + (27 - 24) ÷ 2=
4 + 3/2= 5 1/2
Solve the system using elimination.
-9x - 4y = 1
3x + 3y = 3
([?], [])
Step-by-step explanation:
-9x-4y=1....eq1
3x+3y=3.....eq2
multiply eq2 by 3
to get
9x+9y=9....eq3
add eq1 and 3
0+5y=10
5y=10
divide both sides by 5
y=2
substitute y=2 in to eq1
-9x-4(2)=1
-9x-8=1
grouping of like terms
-9x=1+8
-9x=9
divide both sides by -9
x= -1
now the answer is
x= -1, y=2
