Answer:
B
Step-by-step explanation:
For each box, there is 1 defective lightbulb. Therefore, a delivery of 4 boxes will have 4 defective lightbulbs. A delivery of 2 boxes has 2 defective lightbulbs. 4 defective lightbulbs subtracted by 2 defective lightbulbs equals 2 more defective lightbulbs in 4 boxes than 2. Therefore, it is B.
What is the product ? 2x(x-4)
Answer:
2x^2- 8x
Step-by-step explanation:
2x(x-4)
distribute; multiply parenthesis by 2 x
2x * x-2x *4
calculate products
2x^2- 8x
Answer: The required product is [tex]2x^2-8x.[/tex]
Step-by-step explanation: We are given to find the following product :
[tex]P=2x(x-4).[/tex]
To find the above product, we need to multiply 2x to every term ithin the bracket.
The multiplication is as follows :
[tex]P\\\\=2x(x-4)\\\\=2x\times x-2x\times4\\\\=2x^2-8x.[/tex]
Thus, the required product is [tex]2x^2-8x.[/tex]
if x^1/2 = 8, what is the value of x?
a. 4
b. 8
c. 16
d. 64
Answer:
d. 64
Step-by-step explanation:
x^1/2 = 8
Square each side
(x^1/2 )^2=( 8)^2
x = 64
Answer:
(d) 64
Step-by-step explanation:
Please write either x^(1/2) or x^0.5 or √x, to reduce the chances of misinterpreting your input.
√x = 8 becomes x = 64 when both sides are squared.
This corresponds to answer (d).
Find the quotient,a. 70 /10 =a
Find the value of y for a given value of x, if y varies directly with x
Answer:
[tex]y=-222[/tex]
Step-by-step explanation:
When "y varies directly with x" this means that:
[tex]y=k\times x[/tex]
where k is a number we need to find out (called the constant of proportionality if you care about that).
We can figure out what k is because they tell us when y= -252, x=84. Substituting those values into our equation we get:
[tex]-252 = k \times 84[/tex]
and therefore:
[tex]k=-3[/tex].
So our equation or formula between y and x is:
[tex]y= -3x[/tex].
So when x = 74, then:
[tex]y=-3 \times 74 = -222[/tex]
Seven times a number minus the number is -48. Find the number. In the form of a paragraph, explain in complete sentences the next steps necessary to completely solve the equation for the unknown value. Include the final answer in your explanation. Complete your work in the space provided or upload a file that can display math symbols if your work requires it
Let x represent the unknown number.
7x - x = -48
Group like terms together.
6x = -48
Divide both sides by 6.
x = -8
Hence, the number is negative eight.
Answer:x=-8
Step-by-step explanation:
What I did was set up my equation and my equation was 7x-x=-48. My second step was to combine like terms and then I had 6x=-48 lastly I divided both sides by 6x then my final answer was x=-8.
The graph of a certain hyperbola, y=h(x) is shown in the standard (x,y) coordinate plane below
Among the following graphs, which best represents y= -h(x)?
Answer:
Step-by-step explanation:
B
Among the following graph option (A) graph best represents y= -h(x)
What is hyperbola?A hyperbola is a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone.Hyperbola is a plane curve generated by a point so moving that the difference of the distances from two fixed points is a constantHyperbola is a curve formed by the intersection of a double right circular cone with a plane that cuts both halves of the coneHow to solve this problem?The steps are as follow:
Given the graph of a certain hyperbola, y=h(x) in the standard (x,y) coordinate planeWe have to find which graph represents the y= -h(x)Since there is refraction around x-axis we can conclude that option (A) graph represents best y= -h(x)Learn more about hyperbola here:
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Identify the translation rule on a coordinate plane that verifies that triangle A(-5,1), B(-2,7), C(0,1) and triangle A'(-6,0), B'(-3,6), C'(-1,0) are congruent.
A) (x, y) → (x - 1, y - 1)
B) (x, y) → (x + 2 , y + 1)
C) (x, y) → (x - 2, y + 1)
D) the triangles are not congruent
Answer:
A) (x, y) → (x - 1, y - 1)Step-by-step explanation:
A(-5, 1) → A'(-6, 0)
-5 - 1 = -6
1 - 1 = 0
B(-2, 7) → B'(-3, 6)
-2 - 1 = -3
7 - 1 = 6
C(0, 1) → C'(-1, 0)
0 - 1 = -1
1 - 1 = 0
Which number line shows the solution set for |p-3|=9?
Answer:
Option b
[tex]p = -6[/tex] or [tex]p = 12[/tex]
Step-by-step explanation:
The absolute value is a function that transforms any value x into a positive number.
Therefore, for the function [tex]f(x) = |x|[/tex] x> 0 for all real numbers.
Then the equation:
[tex]|p-3| = 9[/tex] has two cases
[tex](p-3) = 9[/tex] if [tex]h > 3[/tex] (i)
[tex]-(p-3) = 9[/tex] if [tex]h < 3[/tex] (ii)
We solve the case (i)
[tex]p = 9 + 3\\p = 12[/tex]
We solve the case (ii)
[tex]-p +3 = 9\\p = 3-9\\p = -6[/tex]
Then the solution is:
[tex]p = -6[/tex] or [tex]p = 12[/tex]
Answer:
b
Step-by-step explanation:
please help me I really need this for school to get a good grade on my report card
Answer: 0.29
Step-by-step explanation: The first thing that you need to know is that a ton equals 2,000 pounds. Therefore, 6,000 pounds of rocks cost $1,740. In order to solve the problem you need to divide $1,740 by 6,000. 1,740 / 6,000 = .29
Each pound cost $ 0.29. (29 cents)
Answer: $0.29 per pound
Step-by-step explanation:
[tex]\dfrac{price}{pound}:\ \dfrac{\$1,740}{3\ tons}\times \dfrac{1\ ton}{2,000\ pounds}=\dfrac{\$1,740}{6,000\ pounds}=\large \boxed{\dfrac{\$0.29}{1\ pound}}[/tex]
please help me with 13 and 14
Answer:
13. x = 6
14. x = 3.5
Step-by-step explanation:
13. To find x when f(x) = -17, set the equation f(x) equal to -17 and solve.
-3x + 1 = -17 Subtract 1 from both sides
-3x = -17 - 1
-3x = -18 Divide by -3
x = 6
14. To find x when g(x) = 31, set the equation g(x) equal to 31 and solve.
10x - 4 = 31 Add 4 to both sides
10x = 31 + 4
10x = 35 Divide by 10
x = 3.5
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.
choose the graphic representation of the quadratic function
The answer is: The first graphic representation.
Why?We are given a quadratic equation, meaning that it could be two possible solutions for the exercise, however, we are talking about time, so we have to consider only the obtained positive values.
Let's make the equation equal to 0 in order to find the values of "t"
[tex]h(t)=-16.1t^2 + 150\\0=-16.1t^2 + 150\\16.1t^2=150\\t^2=\frac{150}{16.1}=9.32\\t=+-\sqrt{9.32}=+-3.05\\t1=3.05\\t2=-305[/tex]
So, discarding the negative value, we can use the possitive value to find the correct graphic representation.
To find the correct graphic representation we must take into consideration the following:
- We must remember that the sign of the coefficient of the quadratic term (t^2) will define if the parabola opens downward or upward.
From the given quadratic (or parabola) equation we have:
[tex]a=-1\\b=0\\c=150[/tex]
So, since the coefficient of the quadratic term is negative, the parabola opens downward.
- Since we are looking for a graphic that represents the change in height over time, we need to look for a graphic that shows only positive values for the x-axis (time)
- We are looking for a parabola which y-axis intercept is equal to 150.
Therefore, the graphic representation of the quadratic function that models a ball's height over time is the first graphic representation.
Have a nice day!
Answer: A
Step-by-step explanation:
find the amount to which $500 will grow in five years following 12% compound annually
The amount to which $500 will grow to is $881.17.
How to calculate the amountFrom the question, we have the following parameters that can be used in our computation:
Principal = 500
Rate = 12%
Time = 5 years
The future value is calclated as
FV = P * (1 + r)ⁿ
substitute the known values in the above equation, so, we have the following representation
FV = $500 * (1 + 0.12)⁵
Evaluate
FV = $881.17
Hence, the amount is $881.17
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You decide to make a beanbag in the shape of a sphere with a diameter of 120 millimeters. You will need to find the volume to know how many beans to put in the bag. What is the volume? Use 3.14 to approximate pi.
Answer:
The volume is [tex]904,320\ mm^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]r=120/2=60\ mm[/tex] ----> the radius is half the diameter
[tex]\pi=3.14[/tex]
substitute the values
[tex]V=\frac{4}{3}(3.14)(60)^{3}=904,320\ mm^{3}[/tex]
Final answer:
The volume of a sphere-shaped beanbag with a diameter of 120 millimeters is calculated using the formula V = (4/3)πr³, resulting in a volume of approximately 904.32 cubic centimeters.
Explanation:
To calculate the volume of a beanbag in the shape of a sphere, we use the formula for the volume of a sphere, which is V = (4/3)πr³. Given that the diameter of the beanbag is 120 millimeters, we first need to find the radius, which is half of the diameter, so r = 60 millimeters or 6 centimeters. Plugging the values into the formula, we get:
V = (4/3) × 3.14 × (6 cm)³
V = (4/3) × 3.14 × 216 cm³
V = (4/3) × 3.14 × 216
V = (4) × 3.14 × 72
V = 904.32 cm³
Therefore, the volume of the beanbag is approximately 904.32 cubic centimeters (cm³).
Eric traveled to three cities on a single highway. The distance from his original location to the first city was 100 miles more than the distance from the first city to the second city. The distance from the second city to the third city was 10 miles less than the distance from the first city to the second city. If the distance from his original location to the first city and the distance from the second city to the third city were the same, what was the total distance Eric traveled?
A. 120 miles
B. 200 miles
C. 280 miles
D. 360 miles
E. 400 miles
Answer:
B
Step-by-step explanation:
*cough cough*
The diagram shows a semi circle inside a rectangle of length 150 m. The semi circle touches the rectangle at a b and c. Calculate the perimeter of the shaded region.
Answer:
Perimeter of the shaded region is 268 m
Step-by-step explanation:
In this diagram a semi circle is drawn inside a rectangle of length 150m.
Length of diameter of a semicircle = 150 m
So radius of the semicircle = [tex]\frac{150}{2}=75 m[/tex]
We have to find the perimeter of the shaded region.
Perimeter of the shaded region = length of tangents drawn on the circle at A and B + m(arc AB)
Length of tangents = radius of the semi circle = 75 m
and m(arc AB) = [tex]\frac{\text{Perimeter of the circle}}{4}=\frac{2\pi r}{4}[/tex]
= [tex]\frac{2\pi (75)}{4}[/tex]
= [tex]\frac{2(3.14)(75)}{4}[/tex]\
= [tex]\frac{471}{4}[/tex]
= 117.75 m
Now Perimeter of the shaded region = 75 + 75 + 117.75
P = 267.75 ≈ 268 m
Given the image showing a rectangle that is 150 cm long with a semicircle inside of it, the perimeter of the shaded region is: 267.8 m
Recall:
Perimeter of a circle = [tex]2 \pi r[/tex]
Thus, given the semicircle in the diagram below, where:
Length of rectangle = 150 m
Radius of semi circle = half of 150 m = 75 m
Thus,
The width of the circle = 75 m
The shaded region is bounded by the circumference of a quarter circle (AB) and two sides measuring 75 m each.
Perimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \pi r[/tex]
SubstitutePerimeter of Quarter circle = [tex]\frac{1}{4} \times 2 \times \pi \times 75 = 117.8 m[/tex]
Perimeter of the shaded region = 117 + 75 + 75 = 267.8 m
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Darpana solved the equation s = a+b+c/3 for a. Her steps are shown below:
1. Multiply by 3: s=a+b+c/3
3s=a+b+c
2. Subtract b: 3s-b=a+b+c-b
3s-b=a+c
3. Divide by c: 3s-b/c=a
Which statement about Darpana’s work is true?
In step 1 she needed to divide by 3 rather than multiply.
In step 2 she needed to add b rather than subtract.
In step 3 she needed to subtract c rather than divide.
Darpana solved the equation correctly.
Answer: Third option (In step 3 she needed to subtract c rather than divide)
Step-by-step explanation:
When she subtract b from both sides of the equation, she obtained:
[tex]3s-b=a+c[/tex]
Therefore, to leave the a alone at one member of the equation, she needs to subtract c from both sides of the equation.
Then, she would obtain the following:
[tex]3s-b-c=a+c-c\\3s-b-c=a\\a=3s-b-c[/tex]
Therefore the answer is the third option: In step 3 she needed to subtract c rather than divide.
Answer:
The true statement is: In step 3 she needed to subtract c rather than divide.
Step-by-step explanation:
Lets solve our equation [tex]s=\frac{a+b+c}{3}[/tex] step by step.
Step 1. Since 3 is the denominator of the right hand side, we need to multiply both sides of the equation by 3:
[tex]3s=\frac{3(a+b+c)}{3}[/tex]
Now we can cancel the 3 in the numerator and the 3 in the denominator to get
[tex]3s=a+b+c[/tex]
As you can see, the first statement is false
Step 2. Since we want to isolate the variable [tex]a[/tex], we need to subtract b from both sides of the equation:
[tex]3s=a+b+c[/tex]
[tex]3s-b=a+b+c-b[/tex]
[tex]3s-b=a+c[/tex]
The second statement is also false
Step 3. The last thing we to do to isolate [tex]a[/tex] (and solve for it) is subtract c from both sides of the equation:
[tex]3s-b-c=a+c-c[/tex]
[tex]3s-b-c=a[/tex]
[tex]a=3s-b-c[/tex]
Therefore, the third statement is true: In step 3 she needed to subtract c rather than divide.
Which solid figure does this net represent? 40 Points
A) cone
B) square pyramid
C) rectangular prism
D) triangular pyramid
Answer:
C.) Rectangular prism
Step-by-step explanation:
Answer:
[tex]\Large \boxed{\mathrm{Rectangular \ prism}}[/tex]
Step-by-step explanation:
The net represents a three-dimensional shape.
The figure that the net represents is a rectangular prism.
Find the average rate of change for f(x)=x^2 -3x-10 from x=4 to x=6
Answer:
7
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ 4, 6 ]
f(b) = f(6) = 6² - 3(6) - 10 = 36 - 18 - 10 = 8
f(a) = f(4) = 4² - 3(4) - 10 = 16 - 12 - 10 = - 6, hence
average rate of change = [tex]\frac{8-(-6)}{6-4}[/tex] = [tex]\frac{14}{2}[/tex] = 7
the library has enough DVDs to display an equal number of them in groups of 3,5, or 9. What is the least number of DVDs the library has?
Answer: 45 DVDs
Step-by-step explanation:
45 is the least common multiple of 3, 5, and 9.
45 can be equally divided by 3, 5, and 9:
45 ÷ 3 = 15
45 ÷ 5 = 9
45 ÷ 9 = 5
Are the arcs below congruent?
Answer:
There is not enough information
Step-by-step explanation:
In Circle 1
Minor Arc : [tex]\widehat{AB}=140^{\circ}[/tex]
Radius = AO=OB
In Circle 2
Minor Arc : [tex]\widehat{GH}=140^{\circ}[/tex]
Radius =OG =OH
We need to show that the arcs are congruent .
Since the length of the radii are not given .
So, There is not enough information to prove that the arcs are congruent.
Hence Option D is true.
Answer: d/ there is not enough information to determine
Step-by-step explanation:
I just did this on a p e x
write an equation in slope intercept form for the line that passes through (4, -4) and is parallel to 3x+4x=2y-9
Answer:
[tex]\large\boxed{y=\dfrac{7}{2}x-18}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
Convert the equation of a line 3x + 4x = 2y - 9 to the slope-intercept form:
[tex]3x+4x=2y-9[/tex]
[tex]7x=2y-9[/tex] add 9 to both sides
[tex]7x+9=2y[/tex] divide both sides by 2
[tex]\dfrac{7}{2}x+\dfrac{9}{2}=y\to y=\dfrac{7}{2}x+\dfrac{9}{2}[/tex]
Parallel lines have the same slope. Therefore we have the equation:
[tex]y=\dfrac{7}{2}x+b[/tex]
Put the coordinates of the point (4, -4) to the equation:
[tex]-4=\dfrac{7}{2}(4)+b[/tex]
[tex]-4=7(2)+b[/tex]
[tex]-4=14+b[/tex] subtract 14 from both sides
[tex]-18=b\to b=-18[/tex]
Finally we have the equation:
[tex]y=\dfrac{7}{2}x-18[/tex]
Factor the following polynomial completely.
1,280x^11 - 405x^7
Answer:
[tex]5x^7(16x^2+9)(16x^2-9)[/tex]
Step-by-step explanation:
we have
[tex]1,280x^{11}-405x^{7}[/tex]
we know that
[tex]1,280=(2^8)(5)[/tex]
[tex]405=(3^4)(5)[/tex]
substitute
[tex](2^8)(5)x^{11}-(3^4)(5)x^{7}[/tex]
Factor 5x^7
[tex]5x^7[(2^8)x^{4}-(3^4)][/tex]
[tex]5x^7[256x^{4}-81][/tex]
Applying difference of square
[tex][256x^{4}-81]=(16x^2+9)(16x^2-9)[/tex]
substitute
[tex]5x^7(16x^2+9)(16x^2-9)[/tex]
Answer:
5x^7(4x-a 3)(4x+3)(16x^2+9)
Step-by-step explanation:
Q : For each of the following cases, either explain why the case cannot occur or give an example to show how it can.
b. Two negative numbers whose product is in between the two numbers
c. Two negative numbers whose product is less than both numbers
b. Any two negative numbers when multiplying gives positive answers which are never between negative numbers. -9*-3=27
c. same logic, positive answer so never less than either negative number.
The product of two negative numbers will always be positive, so both cases described in the question are not possible. This is due to the property of real numbers which states that the product of two negative numbers results in a positive number.
Explanation:b. The product of two negative numbers will always be positive, so the case where the product of two negative numbers falls between the two numbers is not possible.
c. The product of two negative numbers is always positive, which is larger than their negatives. Therefore, the scenario of two negative numbers having a product that is less than both numbers cannot occur.
These conclusions are based on the property of real numbers which specifies that the product of two negative numbers is a positive number. For example, if you multiply -3 by -2, the result is 6, which is a positive number and larger than both -3 and -2.
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What is the difference between the mean and median (rounded to the nearest tenth) of these numbers 6,6,6,7,7,7,8,8,8,9
The median is the moddle number of a data set. If the number of numbers is even add the 2 middle numbers and divide by 2.
Median = (7+7)÷2 = 7
The mean is the averagw value in a data set. You find it be adding all the numbers and then divide the answer by the number of numbers.
Mean: (6+6+6+7+7+7+8+8+8+9) ÷ 10
= 72 ÷ 10 = 7.2
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Jayden needs to store boxes that are 4 feet long, 3 feet wide, and 2 feet high. The boxes must remain upright with one of the 4-foot by 3-foot sides on top. Jayden's storage locker is 12 feet long, 6 feet wide, and 9 feet high. What is the greatest number of boxes that he can store in the locker?
The dimensions of the box are = 4 feet (length); 3 feet(width); 2 feet(height)
So, volume of the box is = [tex]4\times3\times2=24[/tex] cubic feet
The dimensions of the storage locker are = 12 feet(length); 6 feet(width) ; 9 feet(height)
So, volume of the storage locker is = [tex]12\times6\times9=648[/tex]
So, the greatest number of boxes that can be stored are =
[tex]\frac{648}{24}= 27[/tex] boxes
Hence, a maximum of 27 boxes are stored.
Jayden's storage locker has a volume of 648 cubic feet, and each of his boxes has a volume of 24 cubic feet. By dividing the locker's volume by the volume of a single box, we find that Jayden can store a maximum of 27 boxes in the locker.
Explanation:To determine the greatest number of boxes Jayden can store in the storage locker, we need to calculate the volume of the storage locker and the volume of one box. The storage locker is 12 feet long, 6 feet wide, and 9 feet high, so its volume is calculated as follows:
Storage Locker Volume = length × width × height = 12 ft × 6 ft × 9 ft = 648 cubic feet.
The box has dimensions of 4 feet long, 3 feet wide, and 2 feet high. Thus, its volume is:
Box Volume = length × width × height = 4 ft × 3 ft × 2 ft = 24 cubic feet.
Now, to find the greatest number of boxes that can fit into the locker, we divide the volume of the storage locker by the volume of one box:
Number of Boxes = Storage Locker Volume / Box Volume = 648 cubic feet / 24 cubic feet.
When we perform the division, we get:
Number of Boxes = 27.
Hence, Jayden can store a maximum of 27 boxes in the storage locker when placed upright with a 4-foot by 3-foot side on top.
SOMEBODY HELP ME PLEASE
Solve by equation by factoring. 4) x^2+11x+28=0
.
.
.
Find the product. Write your answer in standard form. 5) (3a+8)(3a^2-a-7)
[tex]4) \: {x}^{2} + 11x + 28 = 0 \\ \Leftrightarrow {x}^{2} + 7x + 4x + 28 = 0 \\ \Leftrightarrow x(x + 7) + 4(x + 7) = 0 \\ \Leftrightarrow (x + 4)(x + 7) = 0 \\\Leftrightarrow x = - 4 \: \vee \: x = - 7 \\ \\ 5) \: (3a + 8)(3 {a}^{2} - a - 7) \\ = 9 {a}^{3} - 3 {a}^{2} - 21a + 24 {a}^{2} - 8a - 56 \\ = 9 {a}^{3} + 21 {a}^{2} - 29a - 56[/tex]
Write an integer that represents this situation (be sure to include or-): a weight loss of 20 pounds
Answer:
(-20)
Step-by-step explanation:
loss = a negative integer.
Find the measure of RUS
Answer:
The measure of angle <RUS is 23°
Step-by-step explanation:
In this problem we know that
82°+24°+<RUS+51°=180°
solve for < RUS
157°+<RUS=180°
<RUS=180°-157°
<RUS=23°
Answer:
Step-by-step explanation:
23
Ella completed the division problem below.
Answer:
option B
Elia multiply the dividend by 100 instead of 10.
Step-by-step explanation:
Given that,
divisor = 0.6
dividend = 1.848
Elia decided to multiply each by 10 to get
divisor = 0.6 x 10 = 6dividend = 1.848 x 10 = 18.48but unfortunately she multiply the dividend by 100
As,
1.848 x 100 = 184.8
So,
Elia's error was that she multiply the dividend by 100 instead of 10.
find the reference angle for the given angle. show your work -404degree
recall that the reference angle, is the angle made by the terminal point with the x-axis.
Check the picture below.