Answer:
n = -15 and n = 9. n = -15 is not reasonable because you can't have negative boxes or negative units of measurement.
Step-by-step explanation:
8(n + 2)(n + 4) = 1,144
(n + 2)(n + 4) = 143
n^2 + 2n + 4n + 8 = 143
n^2 + 6n - 135 = 0
(n + 15)(n - 9) = 0
n + 15 = 0
n = -15
n - 9 = 0
n = 9
I got two solutions: n = -15 and n = 9. Only one is reasonable because you cannot have a negative number of boxes or negative weight.
Hope this helps!
Simplify the equation, and set it equal to zero to prepare for factoring.
Multiply the two factors in parentheses using the distributive property:
8(n2 + 2n + 4n + 8) = 1,144
Combine like terms inside the parentheses:
8(n2 + 6n + 8) = 1,144
Multiply the terms inside the parentheses by 8 using the distributive property:
8n2 + 48n + 64 = 1,144
Set the equation equal to zero by subtracting 1,144 from each side:
8n2 + 48n − 1,080 = 0
Factor out the GCF, which is 8:
8n2 + 48n − 1,080 = 0
8(n2 + 6n − 135) = 0
Divide both sides of the equation by 8:
n2 + 6n − 135 = 0
Compare the equation with the standard form ax2 + bx + c = 0, and get a, b, and c:
a = 1, b = 6, c = -135
The leading coefficient of the equation is 1. So, find two numbers that have a sum of 6 and a product of -135:
6 = -9 + 15
-135 = -9 • 15
The two numbers are -9 and 15. Use the two numbers to write the factors of the quadratic expression:
(n − 9)(n + 15) = 0
Use the zero product property, and solve for n:
n − 9 = 0 or n + 15 = 0
n = 9 or n = -15
There are two solutions for n. But since n represents the width of the helmet box, it can’t be negative. Therefore, the only reasonable solution is n = 9
“a railroad bridge spans a gorge 40 feet wide and connects two cliffs at heights of 98 and 158 feet above the bottom of the gorge. a train is crossing this gorge from the higher cliff to the lower. when the front of the train has traveled three-fourths of the bridge's length, how many feet is it above the bottom of the bottom of the gorge?”
Answer:
Height above the bottom gorge is 113 feet
Step-by-step explanation:
The width of the gorge = 40 feet
The height of the higher cliff = 158 feet
The height of the lower cliff = 98 feet
The length of the bridge = √((158-98)² + 40²) = 72.11 feet
The slope of the bridge = (158-98)/40 = 1.5
The length of 1/4 of the bridge from the lower cliff =72.11 - 3/4×72.11 = 18.03 feet
The angle of inclination of the bridge = tan⁻¹(1.5) = 56.31°
The height above the bottom at 3/4 from the higher cliff = The height above the bottom at 1/4 from the lower cliff = 98+ 18.03×sin(56.31 ) = 113 feet
Which can also be found directly from the heights of the two cliffs knowing that 3/4 from the higher cliff = 1/4 from the lower cliff giving;
Height above the bottom gorge = 98 + 1/4×(158 - 98) = 113 feet.
Simplify this expression: -2x + 3 – (5 – 6x).
Step-by-step explanation:
-2x + 3 – (5 – 6x)
=-2x + 3 - 5 + 6x
= 4x - 2
Answer:
4x - 2
Step-by-step explanation:
We have to combine the like terms which are -2x and 6x. We will get 4x. Next, we have to subtract 3 - 5 and we get -2. This brings us to the conclusion of 4x - 2.
Which of the points listed is the same distance from the y-axis as the point (-4,7.5)?
Answer:
(4,7.5)
Step-by-step explanation:
Reflect (-4,7.5) at the y-axis
the figure is cut into 6 equal pieces shade 1/3 of the figure.
Answer:
Here,
The circle is cut into 6 equal parts.
It means all the piece of circle is divided forming 60°.
And according to the question we have shade its 1/3part.
means 1/3×360°
=120° so, we should shade 2 pieces of circle.
Hope it helps...
first person to answer what 4585 times 5645 CORRECT first gets brainiest
Answer: 25882325
Step-by-step explanation:
Simply do 4585*5645 in a calculator.
hope it helps <3
Answer:
Hey there!
The answer is 25882325.
Hope this helps :)
On a coordinate plane, a line goes through (negative 4, negative 1) and (0, 1). Square a is around (negative 5, negative 2), square b is around (negative 1, 1), square c is around (1, 2), and square d is around (4, 4). The linear equation y = one-half x + 1 is represented by the graphed line. A second linear equation is represented by the data in the table. A 2-column table with 4 rows. Column 1 is labeled x with entries negative 2, 0, 2, 4. Column 2 is labeled y with entries 7, 6, 5, 4. In which square is the solution located?
Answer: D
Step-by-step explanation:
The solution of the two equations does not exist since they are parallel.
What is Slope?Slope of a line is the ratio of the change in y coordinates to the change in x coordinates of two points.
Equation of a line in slope intercept form is y = mx + b, where m is the slope and b is y intercept.
Given linear equation of a line in slope intercept form as,
y = 1/2 x + 1
Here slope = 1/2 and y intercept = 1
y intercept is the y value of a point where it touches the y axis.
A second linear equation is to be found by using the values in the table.
Taking two points (2, 7) and (0, 6).
Slope = (6 - 7) / (0 - 2) = (-1) / (-2) = 1/2
Since the point (0, 6) is given, 6 is the y coordinate when the line touches the Y axis.
y intercept = 6
Equation of the second line is,
y = 1/2 x + 6
Since the slopes of two lines are equal, they are parallel.
There is no solution for two parallel lines.
Hence there is no solution for the linear equations given.
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I WILL GIVE 20 POINTS!!! This three- dimensional figure is a triangular pyramid where the base and lateral are congruent equilateral triangles and the height of each triangular face 17.32 inches The surface are of the figure is Square inches
Answer:
Hey there!
The surface area of the triangular pyramid can be expressed as: 4 times the area of one triangle.
The area of one triangle is 17.32, so the total surface area is 69.28.
Hope this helps :)
The surface area of the triangular pyramid will be equal to 692.8 square inches.
What is surface area?The space occupied by any two-dimensional figure in a plane is called the area. The area of the outer surface of any body is called the surface area.
Given that:-
Three- dimensional figure is a triangular pyramid where the base and lateral are congruent equilateral triangles.The height of each triangular face is 17.32 inchesThe formula for the surface area of the pyramid is given as follows;-
SA = Base area + (1/2) [ Perimeter x Slant height ]
SA = [ (1/2) x 20 x 17.32)] + (1/2) [ 60 x 17.32 ) ]
SA= [ 173.2 + 519.6 ]
SA = 692.8 squarer inches
Therefore the surface area of the triangular pyramid will be equal to 692.8 square inches.
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find the sum of the following ap .1) 1/15, 1/12, 1/10,....,to 11 terms
Answer:
33/20
Step-by-step explanation:
1/12 - 1/15 = 5/60 - 4/60 = 1/60
d = 1/60
a_n = a_1 + d(n - 1)
a_11 = 1/15 + (1/60)(11 - 1)
a_11 = 1/15 + 1/6
a_11 = 4/60 + 10/60
a_11 = 14/60
a_11 = 7/30
a_12 = 14/60 + 1/60
a_12 = 15/60
a_12 = 1/4
s_n = n(a_1 + a_n)/2
s_11 = 11(1/15 + 7/30)/2
s_11 = 11(2/30 + 7/30)/2
s_11 = 11(9/30)/2
s_11 = 99/60
s_11 = 33/20
Determine whether the triangles are congruent. Explain you reasoning.
Triangles are congruent
Step-by-step explanation:
Law of Side, Side, Angle
Thier base are same (PR).
Thier 1 side is equal to 2 inch (PS = RQ).
Thier 1 angle is equal (/_ PRQ = /_ RPS)
So, Its prove that both triangles are congruent.
what happens to the resistance as the conductor is made thicker
Answer:
The resistance decreases.
Step-by-step explanation:
The resistance decreases as the conductor is made thicker.
First of all, resistance is like some sort of an obstacle right?
So if the conductor is made thicker it will be easy for the electrons to pass through.
And if the conductor is made thinner it won't be easy for the electrons to pass through. Which makes the resistance increase as there will be collision between the electrons.
Hope this helped ;) ❤❤❤
The circumference of the base of a cone is 24 inches. The slant height of the cone is 20 inches. What is the surface area of the cone? Express the answer in terms of .
Answer:
Step-by-step explanation:
Given data:
Circumference of the base of the cone = 24in.
Recall that circumference (in this case) is the distance round the base of the cone and from here the diameter D=12in. Radius = 6in
Surface area l = pie x radius ( slant height + radius)
= 3.142 x 6 (20 + 6)
= 3.142 x 6 (26)
= 3.142 x 156
= 490.152in^2
Answer:
384pi inches hop it halp!!!
Step-by-step explanation:
A Line Segment has the points (1,-2), and (3,-2). What are the new points after its dilated by a scale factor of 3/2 or 1.5
Answer:
The new points after dilation are
(3/2, -3) and (9/2,-3)
Step-by-step explanation:
Here in this question, we want to give the new points of the line segment after it is dilated by a particular scale factor.
What is needed to be done here is to multiply the coordinates of the given line segment by the given scale factor.
Let’s call the positions on the line segment A and B.
Thus we have;
A = (1,-2) and B = (3,-2)
So by dilation, we multiply each of the specific data points by the scale factor and so we have;
A’ = (3/2, -3) and B’= (9/2,-3)
can I help someone with math
Answer:
please mark my answer brainliest
Step-by-step explanation:
can you tell me a subscript n =sin to the power theta +cosec to the power n theta...and a subscript 1 =2...then prove that a subscript n =2...
Solve.
6x + y = 14
-2x - y = -4
Enter your answer, in the form (x, y), in the boxes.
Answer:
[tex]\huge\boxed{(2.5,\ -1)}[/tex]
Step-by-step explanation:
[tex]\underline{+\left\{\begin{array}{ccc}6x+y=14\\-2x-y=-4\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad4x=10\qquad\text{divide both sides by 4}\\.\qquad\dfrac{4x}{4}=\dfrac{10}{4}\\.\qquad\boxed{x=2.5}\\\\\text{put it to the first equation}\\6(2.5)+y=14\\15+y=14\qquad\text{substract 15 from both sides}\\15-15+y=14-15\\\boxed{y=-1}[/tex]
Answer:
x = 5/2, y = -1
Step-by-step explanation:
6x + y = 14
-2x - y = -4
Add the two equations together to eliminate y
6x + y = 14
-2x - y = -4
-----------------------
4x = 10
Divide by 4
4x/4 = 10/4
x = 5/2
Now solve for y
-2x -y = -4
-2( 5/2) -y = -4
-5 -y = -4
Add 5 to each side
-5+5 -y =-4+5
-y = 1
Divide by -1
y = 1
The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day. Which statements are true based on the model?
Answer:
Options (1), (2) and (5)
Step-by-step explanation:
Outcomes from the quadratic function given in the graph,
1). Negative y-intercept of the graph represents the loss to the store when x = 0 Or the loss when no clerk is working.
2). Peak of the parabola represents a point (vertex) with x-coordinate as number of clerks working = 4 and y-coordinate as maximum profit earned by the store = $400,000
3). x-intercept of the graph shows the number of clerks working at store when profit earned by the store is zero.
Graph reveals that the store is in loss when number of clerks is zero and 8.
Summarizing these outcomes from the graph,
Options (1), (2), (5) are the correct options.
The function graphed models the profits, P(c), in thousands of dollars a store earns as a function of the number of clerks, c, working that day.
Which statements are true based on the model?
Which one of the following would most likely have a positive linear correlation coefficient?
A. temperature of a refrigerator compared to the number of items inside of it
B. amount of money spent on baby food as a child ages
C. length of a driveway compared to number of cars owned
D. distance driven in a car compared to the hours spent driving
Answer:
this question is not clear please send clear question
SOMEONE PLEASE HELPPPPPPPPPPPPPPPP!!!!!!!!!!!!!!!!!!!!11
The red graph is the black graph reflected in the y axis, y = f(-x)
It's an odd way to write it, but the answer is:
Answer: D
Find: ∠a ∠b ∠c Plaese help
Answer:
i believe a=105, b=29, and c=45
If gear A has 400 teeth and drives another gear B with 1200 teeth. Determine gear ratio.
Divide the two numbers to find the ratio:
400 / 1200 = 1/3
The ratio is 1:3
Answer:
B
Step-by-step explanation:
Gear A has 400 teeth.
Gear B has 1200 teeth.
Write as a ratio of gear A to gear B.
400:1200
Simplify the ratio.
4:12
1:3
Simplfiy the expression 96 ÷4+5x2²
Answer:
44
Step-by-step explanation:
96 divided by 4 add 5 times 2 squared equals 44
Answer:
44
Step-by-step explanation:
BIDMAS
B: Brackets
I: Indices
D: Division
M: Multiplication
A: Addition
S: Subtraction
96 divided by 4 + 5 x 2^2
96 divided by 4 + 5 x 4
96 divided by 4 = 24
24 + 5 x 4
24 + 20
24 + 20 = 44
Name the algebraic property demonstrated in the example below: (1 point) x ⋅ y ⋅ z = y ⋅ x ⋅ z
Answer:
commutative property of multiplication
Step-by-step explanation:
10. Read the following word problem, then choose which linear equation models the problem.
The length of a rectangle is six feet more than twice the width. The rectangle’s perimeter is 84 feet. Find the width and length of the rectangle.
A. 2w + 6 + w = 84
B. 2(2w + 6) + 2w = 84
C. 2(2w +6) • (2w) = 84
D. (2w + 6) • (w) = 84
Answer:
D. ( 2w+6). (w)
i tried my best
hope this is the answer
stay at home stay safe
Assume EFG JKL. If m J = 90 , m K = 26 , and m L = 64 , what is the measure of E?
Answer:
I think its 90
Step-by-step explanation:
Answer:
E=90
Step-by-step explanation:
because EFG=JKL E=J F=K G=L
This is probably pretty easy, I could solve all the other ones but I got stuck on this one.
Answer:
78
Step-by-step explanation:
Let x be the score on the next test
We are averaging 6 tests and want an average of 75
( 82+91+38+78+83+x) /6 = 75
Multiply each side by 6
( 82+91+38+78+83+x) = 75*6
( 82+91+38+78+83+x) =450
Combine like terms
x+372 = 450
Subtract 372 from each side
x+372-372 = 450-372
x =78
A rectangle measures 6 cm by 4 cm. Another rectangle with adjacent sides 8 cm and x cm is geometrically similar to it. Find the two possible value of x.
Answer:
5 1/3 or 5.33333333333333333333333333333333333333333333333333333
Step-by-step explanation:
to find the scale factor, you must divide the two equal sides.
[tex]\frac{6}{8}[/tex]
which equals
[tex]\frac{3}{4}[/tex] or 0.75
Now, the way to get the value of x is to divide 4 by 3/4 0r 0.75
[tex]\frac{4}{0.75}[/tex]
Which equals
5.333 repeating or 5 1/3
Hope this helps. If you have any follow-up questions, feel free to ask.
Have a great day! :)
PLZ HELP Which represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3
Answer:
f(x) = -7x² - x + 2
Step-by-step explanation:
Quadratic functions are set up in the form ax² + bx + c. f(x) = 0x² + 3x -3 is also set up in this format but 0x² would simplify to 0 which means the equation is actually f(x) = 3x-3 and does not fit in the quadratic function format. The other equations are also not set up in ax² + bx + c.
Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
A polynomial with degree 2 is called a quadratic equation.
The quadratic equation is in the form of ax² + bx + c.
The equation that represents a quadratic equation is
f(x) = -7x² - x + 2.
It is in the form of ax² + bx + c
Where a = -7, b = -1, and c = 2
Option B is the correct answer.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
A polynomial with degree 2 is called a quadratic equation.
The quadratic equation is in the form of ax² + bx + c.
Now,
f(x) = 2x³ + 2x² - 4
This is not a quadratic equation since it has a degree of 3.
f(x) = -7x² - x + 2
This is a quadratic equation since its degree is 2.
It is in the form of ax² + bx + c
Where a = -7, b = -1 and c = 2
f(x) = -3x + 2
This is not a quadratic equation.
Its degree is 1.
f(x) = 0x² + 3x - 3
f(x) = 3x - 3
This is not a quadratic equation.
Thus,
The equation that represents a quadratic equation is
f(x) = -7x² - x + 2.
It is in the form of ax² + bx + c
Where a = -7, b = -1, and c = 2
Option B is the correct answer.
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Please help me with atleast some of them❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
Answer:
1. 24 x
Step-by-step explanation:
Area = (6x +1)(6x-1)
which means
length = 6x+1
width = 6x -1
as perimeter = 2 (length + width)
= 2 (6x +1+6x -1)
= 2(12x)
=24x
Plz help pre calc!!!!
find the area of a sector of a circle with radius 6 centimetre if angle of sector is 60 degree
Answer:
Step-by-step explanation:
[tex]area=\frac{\pi r^2 \times\theta}{360} =\frac{\pi 6^2 \times 60}{360} =6 \pi \approx 18.85~ cm^2[/tex]
Amanda is cooking a turkey for dinner. The recipe says that the turkey should cook for 1\dfrac121 2 1 1, start fraction, 1, divided by, 2, end fraction hours. She has been cooking the turkey for 252525 minutes. According to the recipe, how many more minutes does the turkey need to cook?
Answer:
The turkey needs to cook for 5 more minutesStep-by-step explanation:
According to recipe, Amanda should cook for total of 1/2 hour which is 30 minutes. If she has been cooking for 25 minutes, the remaining time needed for the turkey to cook will be the difference between the total time and the time she has already spent in cooking.
[tex]minutes\ left = 30 minutes - 25 minutes\\\\munites\ left = 5 minutes[/tex]
Hence, the turkey needs to cook for 5 more minutes