Answer:
x=7
Step-by-step explanation:
[tex]1 + 3x = - 13 + 5x[/tex]
Collect like terms and simplify
[tex]3x - 5x = - 13 - 1 \\ - 2x = - 14[/tex]
Divide both sides of the equation by -2
[tex] \frac{ - 2x}{ - 2} = \frac{ - 14}{ - 2} [/tex]
Simplify
[tex]x = 7[/tex]
Answer:
Step-by-step explanation:
1 + 3x = 5x - 13
-2x + 1 = -13
-2x = -14
x = 7
what is 84.637 minus 28.56
Answer:
56.077
Step-by-step explanation:
Answer:
56.077
Step-by-step explanation:
i did it in my caculator lol :)
Rank the items from 1 to 4 based on their unit prices.
Use the drop-down menus to label the least expensive
item per pound with "1" and the most expensive item
per pound with "4."
Avocados:
Broccoli:
Carrots:
Onions:
Answer:Avocados:4
Broccoli:3
Carrots:2
Onions:1
Step-by-step explanation:I did the question it is correct.
shipping box that is length=3 3/4ft width=3ft height=3 1/4 what is the volume and how to work it out
Answer:
36 9/16 ft^3
Step-by-step explanation:
volume = length * width * height
volume = 3 3/4 ft * 3 ft * 3 1/4 ft
Change all mixed numerals to fractions.
volume = 15/4 * 3/1 * 13/4 ft^3
volume = 585/16 ft^3
volume = 36 9/16 ft^3
Point T is on line segment SU. Given ST 2x + 1, SU = 4x, and
TU = 5x 4, determine the numerical length of ST.
Answer:
Step-by-step explanation:
3
Find and simplify the following for f(x)= x(21-x), assuming h#0 in (C). (A) f(x +h) (B) f(x+h) – f(x) (C) f(x+h) – f(x) (D) f(x+h)=
Answer:
A
[tex]f(x + h) = 21x -x^2 -2xh+ 21h+h^2[/tex]
B
[tex]f(x-h)-f(x) = 21h+h^2 -2xh[/tex]
C
[tex]\frac{f(x-h)-f(x)}{h} = 21+h -2x[/tex]
Step-by-step explanation:
From the question we are told that
The equation given is
[tex]f(x) = x (21 - x )[/tex]
Considering A
[tex]f(x + h) = (x + h) (21 - (x + h))[/tex]
[tex]f(x + h) = (x + h) (21 - x - h)[/tex]
[tex]f(x + h) = 21x -x^2 -2xh+ 21h+h^2[/tex]
Considering B
[tex]f(x + h)-f(x) = 21x -x^2 -2xh+ 21h+h^2 -[ x(21 -x)][/tex]
[tex]f(x + h)-f(x) = 21x -x^2 -2xh+ 21h+h^2 -21x + x^2[/tex]
[tex]f(x-h)-f(x) = 21h+h^2 -2xh[/tex]
Considering C
[tex]\frac{f(x-h)-f(x)}{h} = \frac{21h+h^2 -2xh}{h}[/tex]
[tex]\frac{f(x-h)-f(x)}{h} = \frac{h(21+h -2x)}{h}[/tex]
[tex]\frac{f(x-h)-f(x)}{h} = 21+h -2x[/tex]
You buy a new wheel for your bicycle. Thaw diameter of the bicycle wheel is 22 inches.What is the radius of the bicycle wheel?What is the circumference of the bicycle wheel?What is the area of the bicycle wheel?
Answer:
Radius= 11
Circumference= 69.12
Area= 380.133
Step-by-step explanation:
Radius is half of the diameter.
Circumference is 2[tex]\pi[/tex]r.
Area is [tex]\pi r^2[/tex].
ILL GIVE YOU BRAINLIST !!!
HAVE TO GET IT RIGHT
Evaluate the expression given the replacement values.
Answer:
[tex]-\frac{15}{16}[/tex]
Step-by-step explanation:
[tex]\frac{1}{4} ^{2}[/tex]= [tex]\frac{1}{16}[/tex]
2*(pq)= 2([tex]\frac{1}{6}[/tex])= [tex]\frac{1}{3}[/tex]
-3[tex]q^{2}[/tex]= -3[tex](\frac{4}{9} )[/tex]= [tex]-\frac{4}{3}[/tex]
[tex]\frac{1}{16} +\frac{1}{3}-\frac{4}{3}[/tex]=
[tex]\frac{1}{16} -1[/tex]=
[tex]-\frac{15}{16}[/tex]
Use the slope formula to find the slope of the line through the points (1, -2) and (-2,8).
Sorn thatic in
Answer:
Step-by-step explanation:
(8 + 2)/(-2 - 1)= -10/3
5. Based on the data in the table, how many
members would you expect in the band in 2018?
Year
Year Number of Band
Members
2014 40
2015 46
2016 54
2017 64
A sequence is defined as an arrangement of numbers in a particular order.
The number of Band members in the year 2018 is expected to be 76.
What is a sequence?A sequence is defined as an arrangement of numbers in a particular order.
We have,
Year Number of Band members
2014 40
2015 46
2016 54
2017 64
We can make a sequence with the number of band members that increases each year.
i.e
40 46 54 64
We see that,
46 - 40 = 6
54 - 46 = 8
64 - 54 = 10
We see that the difference between the consecutive terms is increasing by 2.
So, the next term in the sequence will be 64 + 12 = 76.
Thus the number of band members in the year 2018 is expected to be 76.
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Xavier caught a football and ran for eight yards before being pushed 17 yards backward.
Which equation correctly shows his change in yardage?
А
8 + (-17) = -9
-17 + (-8) = -25
B
С
17 + (-8) = 9
D
8 + 17 = 25
Answer:
Answer A
Step-by-step explanation:Option B is saying that he went back 8 yards and was pushed even farther. Option C is saying he ran foward 17 yards and got pushed back 8. Option D is saying he got pushed foward 17 yards.
Option A is saying that he ran 8 yards and then lost 17 by getting pushed back.
design a Boolean circuit that verifies whether a given integer 0 ≤ x < 16 is divisible by 5
This question is incomplete, the complete question is;
Your boss asks you to design a Boolean circuit that verifies whether a given integer 0 < x < 16 is divisible by 5.
Every such number is represented in binary using four bits, say b₃b₂b₁b₀, and so your Boolean circuit will have four inputs. For instance, the number 13 is written in binary as 1101 and so to test its divisibility by 5 a user would feed the values b₀ = 1, b₁ = 0, b₂ = 1, and b₃ = 1 into the inputs of your circuit.
The Boolean circuit will have a single output, which should deliver the value 1 if the iput values represent a number that is divisible by 5 and 0 otherwise.
a) write down the truth table of the Boolean function F(b₀,b₁,b₂b₃) that implements this "divisible by 5" operation
b) construct a Boolean expression in disjunctive normal form that implements the Boolean function yo wrote down in a)
Answer:
Given that;
integer range = 0≤ x ≤ 16
within 4bits, we can represnt each number
(0,5,10,15)
a)
Truth table for function that implements divisible by 5
Integer B3 B2 B1 B0 Y
0 0 0 0 0 1
1 0 0 0 1 0
2 0 0 1 0 0
3 0 0 1 1 0
4 0 1 0 0 0
5 0 1 0 1 1
6 0 1 1 0 0
7 0 1 1 1 0
8 1 0 0 0 0
9 1 0 0 1 0
10 1 0 1 0 1
11 1 0 1 1 0
12 1 1 0 0 0
13 1 1 0 1 0
14 1 1 1 0 0
15 1 1 1 1 1
b)
Boolean expression that implements the Boolean function from a)
from the truth table;
Boolean expression Y is;
Y = b⁻₃b⁻₂b⁻₁b⁻₀ / y₁ + b⁻₃b₂b⁻₁b₀ / y₂ + b₃b⁻₂b₁b⁻₀ / y₃ + b₃b₂b₁b₀ / y₄
Answer:
circuit is in the second attachment
Step-by-step explanation:
Attached is a truth table for the desired circuit, where b3–b0 are the input bits, MSB–LSB. We notice that the output is true whenever b3=b1 and b2=b0. This can be written in DNF as ...
[tex]Y=b_3'b_2'b_1'b_0'+b_3b_2'b_1b_0'+b_3'b_2b_1'b_0+b_3b_2b_1b_0[/tex]
More compactly, it can be written in terms of the exclusive-nor function as ...
[tex]y=(b_3\odot b_1)\wedge(b_2\odot b_0)[/tex]
A circuit diagram showing this circuit is the second attachment. (A–D are the input bits, in order MSB–LSB (or its reverse)).
Find equations of the spheres with center(3, −4, 5) that touch the following planes.a. xy-plane b. yz- plane c. xz-plane
Answer:
(a) (x - 3)² + (y + 4)² + (z - 5)² = 25
(b) (x - 3)² + (y + 4)² + (z - 5)² = 9
(c) (x - 3)² + (y + 4)² + (z - 5)² = 16
Step-by-step explanation:
The equation of a sphere is given by:
(x - x₀)² + (y - y₀)² + (z - z₀)² = r² ---------------(i)
Where;
(x₀, y₀, z₀) is the center of the sphere
r is the radius of the sphere
Given:
Sphere centered at (3, -4, 5)
=> (x₀, y₀, z₀) = (3, -4, 5)
(a) To get the equation of the sphere when it touches the xy-plane, we do the following:
i. Since the sphere touches the xy-plane, it means the z-component of its centre is 0.
Therefore, we have the sphere now centered at (3, -4, 0).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, -4, 0) as follows;
[tex]d = \sqrt{(3-3)^2+ (-4 - (-4))^2 + (0-5)^2}[/tex]
[tex]d = \sqrt{(3-3)^2+ (-4 + 4)^2 + (0-5)^2}[/tex]
[tex]d = \sqrt{(0)^2+ (0)^2 + (-5)^2}[/tex]
[tex]d = \sqrt{(25)}[/tex]
d = 5
This distance is the radius of the sphere at that point. i.e r = 5
Now substitute this value r = 5 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 5²
(x - 3)² + (y + 4)² + (z - 5)² = 25
Therefore, the equation of the sphere when it touches the xy plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 25
(b) To get the equation of the sphere when it touches the yz-plane, we do the following:
i. Since the sphere touches the yz-plane, it means the x-component of its centre is 0.
Therefore, we have the sphere now centered at (0, -4, 5).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (0, -4, 5) as follows;
[tex]d = \sqrt{(0-3)^2+ (-4 - (-4))^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(-3)^2+ (-4 + 4)^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(-3)^2 + (0)^2+ (0)^2}[/tex]
[tex]d = \sqrt{(9)}[/tex]
d = 3
This distance is the radius of the sphere at that point. i.e r = 3
Now substitute this value r = 3 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 3²
(x - 3)² + (y + 4)² + (z - 5)² = 9
Therefore, the equation of the sphere when it touches the yz plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 9
(b) To get the equation of the sphere when it touches the xz-plane, we do the following:
i. Since the sphere touches the xz-plane, it means the y-component of its centre is 0.
Therefore, we have the sphere now centered at (3, 0, 5).
Using the distance formula, we can get the distance d, between the initial points (3, -4, 5) and the new points (3, 0, 5) as follows;
[tex]d = \sqrt{(3-3)^2+ (0 - (-4))^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(3-3)^2+ (0+4)^2 + (5-5)^2}[/tex]
[tex]d = \sqrt{(0)^2 + (4)^2+ (0)^2}[/tex]
[tex]d = \sqrt{(16)}[/tex]
d = 4
This distance is the radius of the sphere at that point. i.e r = 4
Now substitute this value r = 4 into the general equation of a sphere given in equation (i) above as follows;
(x - 3)² + (y - (-4))² + (z - 5)² = 4²
(x - 3)² + (y + 4)² + (z - 5)² = 16
Therefore, the equation of the sphere when it touches the xz plane is:
(x - 3)² + (y + 4)² + (z - 5)² = 16
By using the general sphere equation and what we know about planes, we will get:
a) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2b) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2c) (x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2.General sphere equation.The general sphere of radius R centered in the point (a, b, c) is given by:
(x - a)^2 + (y - b)^2 + (z - c)^2 = R^2
If we want a sphere centered in (3, -4, 5) we will have:
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = R^2
a) We want the sphere to touch the xy-plane, (with z = 0) then the radius must be at least equal to the z-component of the point, so we have R = 5, then the equation is:
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 5^2
b) This time is the yz-plane, so the radius must be equal to the x-component.
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 3^2
c) Finally, the xz-plane, this time the radius must be equal to the y-component.
(x - 3)^2 + (y + 4)^2 + (z - 5)^2 = 4^2
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The question is Find the area.
Answer:
the area is 9in^3
Step-by-step explanation:
the formula for area of a triangle is 1/2bh, so it's 1/2 x 7.2 x 2.5
what are the steps for multiplying monomial algebraic terms where they have exponents with like bases
Answer:
See below.
Step-by-step explanation:
Rule:
[tex] a^m \times a^n = a^{m + n} [/tex]
Explanation:
When multiplying monomials with the same base, write the same base and add the exponents.
A small apple weighs 4.5 ounces. if
it is divided into 4 equal Pieces, how
much dose each piece weighs
Answer:
1.125
Step-by-step explanation:
Each piece weighs 1.125 ounces
What is the fundamental principle of multiplication?Multiplication is the mathematical operation that is used to determine the product of two or more numbers. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.
We are given that small apple weighs 4.5 ounces.
if it is divided into 4 equal Pieces then
Therefore, Weight of apple = 4.5 ounces
Total pieces = 4
Now Weight of 1 piece = 4.5 ÷ 4
= 1.125
Hence the answer is 1.125 ounces
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The costs per load (in cents) of 47 dish-washing detergents tested by a consumer organization are shown here. Find the standard deviation of the sample.
Write a number that is 90,000 greter than 8,304,088
find the interval between: 8:40 pm and 9:30 am
Answer:
12 hours 50 minutes
Step-by-step explanation:
8:40 pm to 9:30 am
8:40 pm to 8:40 am = 12 hours
8:40 am to 9:30 am = 50 minutes
The interval between 8:40 pm and 9:30 am is 12 hours and 50 minutes
What is an Interval?
An interval is measured in terms of numbers. An interval includes all the numbers that come between two particular numbers. This range includes all the real numbers between those two numbers.
Given data ,
Let the interval be denoted as [ a , b ] , where a is the start point and b is the final point
Now ,
a = 8:40 pm
b = 9:30 am
The interval can be calculated by ( b - a )
8:40 pm → 8:40 am = 12 hours
8:40 am → 9:30 am = 50 minutes
Therefore , total interval = 12 hours and 50 minutes
Hence , The interval between 8:40 pm and 9:30 am is 12 hours and 50 minutes
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The revenue from the sale of specialty golf hats is given by the function R(x) = 31x, where x is the number of hats sold.
a. What is R(200)? Interpret this result
b. What is the revenue from the sale of 3000 hats? Write this in functional notation.
a. R(200) =
Answer:
[tex]R(200) = 6200[/tex]
[tex]R(3000) = 93000[/tex]
Step-by-step explanation:
Given
[tex]R(x) = 31x[/tex]
Solving (a): R(200)
[tex]R(x) = 31x[/tex]
Substitute 200 for x
[tex]R(200) = 31 * 200[/tex]
[tex]R(200) = 6200[/tex]
This means that the revenue from 200 hats is 6200
Solving (b): Revenue from 3000 hats
[tex]R(x) = 31x[/tex]
Substitute 3000 for x
[tex]R(3000) = 31 * 3000[/tex]
[tex]R(3000) = 93000[/tex]
The above represents the functional notation and the revenue sale is 93000
Round each decimal to the place value stated and enter the value in the box a Round 3.892 to the nearest tenth. b. Round 5.424 to the nearest hundredth. c. Round 124.62 to the nearest whole number.
Answer:
A) [tex]\huge\boxed{3.9}[/tex]
B) [tex]\huge\boxed{5.42}[/tex]
C) [tex]\huge\boxed{125}[/tex]
Step-by-step explanation:
A) 3.892
To round off to nearest tenth, we'll see the digit in hundredths place. If it is greater than 5 or equal to 5, 1 will be added to the tenths place. If it's not, it will remain the same.
So, it will be like:
=> 3.9
B) 5.424
To round off to nearest hundredth, we'll see the digit in thousandths place. If it is greater than 5 or equal to 5, 1 will be added to the hundredths place. If it's not, it will remain the same.
So, it will be like:
=> 5.42
C) 124.62
To round off to nearest whole number, we'll see the digit in tenths place. If it is greater than 5 or equal to 5, 1 will be added to the ones place. If it's not, it will remain the same.
So, it will be like:
=> 125
what is 8 x 5 = 4 x _______
Step-by-step explanation:
[tex] \\ 8 \times 5 = 40 \\ 40 = 4 \times 10 \\ \\ 8 \times 5 = 4 \times 10[/tex]
6. Use the data to find the following (Please show work)
2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18
a. Mean
b. Median
C. Mode
d. Range
Answer:
1. [tex] \boxed{ \boxed{ \sf{mean = 10}}}[/tex]
2. [tex] \boxed{ \boxed{ \sf{median = 10.5}}}[/tex]
3. [tex] \boxed{ \boxed{ \sf{mode = 11}}}[/tex]
4. [tex] \boxed{ \boxed{ \sf{range = 16}}}[/tex]
Step-by-step explanation:
1. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18
Σx = 2 + 3 + 5 + 7 + 8 + 10 + 11 + 11 + 13 + 15 + 17 + 18 = 120
N ( total number of items ) = 12
Finding the mean
To find the mean, divide the sum of all the items by the number of items.
[tex] \boxed{ \sf{mean = \frac{Σx}{N} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = \frac{120}{12} }}[/tex]
[tex] \dashrightarrow{ \sf{mean = 10}}[/tex]
Mean = 10
----------------------------------------------------------
2. Given data : 2 , 3 , 5 , 7 , 8 , 10 , 11 , 11 , 13 , 15 , 17 , 18
N ( total number of items ) = 12
Finding the position of median
[tex] \boxed{ \sf{median = { \frac{n + 1}{2} }^{th \: item}}} [/tex]
[tex] \dashrightarrow{ \sf{median = {( \frac{12 + 1}{2}) }^{th \: } item}}[/tex]
[tex] \dashrightarrow{ \sf{median = {( \frac{13}{2}) }^{th \: }item }}[/tex]
[tex] \dashrightarrow{ \sf{median = {6.5}^{th \: }}} [/tex] item
[tex] \sf{ {6.5}^{th} }[/tex] item is the average of 6 th and 7 th items.
[tex] \sf{∴ \: median = \frac{ {6}^{th}item + {7}^{th} item}{2}} [/tex]
[tex] \dashrightarrow{ \sf{median = \frac{10 + 11}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{median = \frac{21}{2} }}[/tex]
[tex] \dashrightarrow{ \sf{median = 10.5}}[/tex]
Median = 10.5
-----------------------------------------------------------
3. The mode of a set of data is the value with the highest frequency.
Given data : 2, 3, 5, 7, 8, 10, 11, 11, 13, 15, 17, 18
Here, 11 has the highest frequency.
So, Mode = 11
----------------------------------------------------------
4. Highest number = 18
Lowest number = 2
[tex] \boxed{ \sf{range = highest \: number - lowest \: number}}[/tex]
[tex] \dashrightarrow{ \sf{range = 18 - 2}}[/tex]
[tex] \dashrightarrow{ \sf{range = 16}}[/tex]
Hope I helped!
Best regards! :D
Which set of points are NOT collinear?
A
B
D
A and E
E and B
OD and B
OC and A
Mary brought chocolate and vanilla cupcakes to school for her birthday. 21 students picked a vanilla cupcake and 7 students picked a chocolate cupcake. What percentage of the students picked a vanilla cupcake?
Answer:
75%
Step-by-step explanation:
Total = 21 + 7
= 28 cupcakes
Vanilla cupcakes = 21 / 28 x 100
= 0.75 x 100
= 75%
Answer:
75%
Step-by-step explanation:
21+7=28
21 divided by 28 is equal to 0.75. 0.75 x 100 = 75%
Please choose my answer as the brainliest. It gets me to the next level!
Please answer this correctly without making mistakes
She will most likely finish graduation portraits.
I'm not to sure so try not to pick my answer.
What is the value of the product (3 – 2i)(3 + 2i)? 5 9 + 4i 9 – 4i 13
Answer:
13
Step-by-step explanation:
(3-2i)(3+2i)
as (a+b)(a-b) =a²-b²
3²-(2i)²
=9-(4*-1)
=9-(-4)
=9+4
=13
Hope this helps you!
Answer:
13
Step-by-step explanation:
3^2=9, 2i*(-2i)=-4i^2=4
the 6i and -6i cancel leaving the positive 9 and 4
9+4=13
The vertical intercept of the line will always be a snap point.
A. True
B. False
Answer:
False because the vertical intercept is not always a snap point.
Step-by-step explanation:
In a line graph, the vertical intercept of a line will not always be a point snap. This is because snap points rest on nodes and are used to define boundary or shape of objects in a line graph. So in a case whereby the intercept of the line doesn't rest on a node that defines the boundary or shape of the object, then the vertical intercept may not be a snap point.
False
A vertical intercept is a point where a line crosses the vertical axis, or [tex]\boldsymbol{y-}[/tex]axis.
The vertical intercept of a line in a line graph is not always a snap point. Snap points are used to define the boundary or shape of objects in a line graph, rely on nodes. In the event when the line's intercept does not rest on a node that defines the object's boundary or shape, the vertical intercept may not be a snap point.
False, the vertical intercept of the line may not always be a snap point.
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what is 3/2 (7/3n +1)= 3/2
*!* find the area and perimeter of the shapes below.
Answer:
a: 15 in
b:210 cm
c: 21 yds
Step-by-step explanation:
a: to find the area of a triangle multiply the base and the height, then divide the result by two.
b: to find the area of a trapezoid, multiply the median ( the point where the opposite corners cross) and the height.
c: to find the area of a parallelogram, multiply the lenght and the height.
Hope this helps!
f(x) = -x² – 10x + 16
Find f(-7)
Answer:
-5
Step-by-step explanation:
or, f(x) = -x^2+10x+16
or, f(7) = (-7)^2+10*-7+16 (-7*-7=49)
=49-70+16
=65-70
=-5