Answer:
Option B==========================
The distributive property is:
a(b + c) = ab + acApply this to the options:
A) 2(2 + 3) = 2*2 + 2*3 = 4 + 6, not matching, no;B) 2(x + 3) = 2x + 2*3 = 2x + 6, matching, yes;C) 2(x + 3) = 2x + 6, as above, not matching, no;D) 2(2 + 3) = 4 + 6, not matching, no.Answer:
b) 2(x + 3) = 2x + 6
Step-by-step explanation:
The formula we refer to is,
→ a × (b + c) = (a × b) + (a × c)
The option obeys distributive law is,
→ 2 × (x + 3) = (2 × x) + (2 × 3)
→ 2(x + 3) = 2x + 6
Hence, option (b) is correct.
25) Which of these numbers cannot be a probability? (There is more than one answer.)
A -0.02
B0
C 1.002
D 1
Answer:
1.002, -0.02
Step-by-step explanation:
Probabilities range between 0 and 1.
Simplify to create an equivalent expression.
−
5
(
1
−
5
k
)
−
4
(
2
k
+
5
)
Answer:
Step-by-step explanation:
1) Distribute the numbers outside of the parenthesis to the numbers inside the parenthesis. This means multiple the outside number to all the numbers that are inside the parenthesis:
-5+25k-8k-20
2) Combine the like terms. The number with k get combined together since they both have a k. The numbers without a k get combined together. When you combine, you ADD the numbers together.
-13k+5
That should be right!
In 2008, the number of digital cameras shipped totaled 186 million. There were 24 million shipped in 2013. Find and
interpret the average rate of change in the number of digital cameras shipped per year.
Step-by-step explanation:
the average change rate for a function g(x) is defined for an interval of x values as
(g(interval end) - g(interval begin))/(interval end - interval begin)
in our case that is
(g(2013) - g(2008))/(2013 - 2008) =
= (24 mil. - 186 mil)/5 = -162 mil./5 =
= -162,000,000 / 5 = -32,400,000
that means that as a mean value there were 32,400,000 digital cameras shipped less every year.
in other words, fewer and fewer digital cameras are sold. the demand is strongly declining.
actually, following the mean values and their trend, there should have been no new digital cameras shipped in 2014 anymore (as 24 mil. - 32.4 mil is less than 0).
Determine whether each equation represents a proportional relationship. If it does, identify the constant of proportionality
The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.
According to the statement
We have to find that the constant of proportionality.
So, For this purpose, we know that the
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
From the given information:
each equation represents a proportional relationship.
Then
We know that the A proportional relationship is one in which two quantities vary directly with each other
That's why
An equation has a proportional relationship if it can be written in the form y=kx where k is the constant of proportionality.
A linear function of x is given as y = 0.5x - 2.
Yes, this function of x represents a proportional relationship between x and y.
The constant of proportionality is given to be 0.5 provided that the dependent variable y has an initial value of - 2 at x = 0.
The graph of this equation will be a straight line and that means that the equation consists of a proportional relationship.
So, The proportional relationship of the given statement is a between x and y and the constant of proportionality is 0.5.
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Disclaimer: This question was incomplete. Please find the full content below.
Question:
Determine whether each equation represents a proportional relationship. if it does identify the constant of proportionality. y = 0.5 x -2
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IS 303 2022 Summer Packet for Incoming
Ms. Hamilton wants to put a decorative iron fence (rather like Winnie's in Tuck Everlasting)
around her yard. The yard is a perfect rectangle: its length is 24.75 feet and its width is 12.75
feet. Home Depot charges $50 a yard for iron fencing.
66.) How many feet of fencing does Ms. Hamilton need to buy?
67.) What do you call the distance around a rectangle?
Math in the Real World (Leave in packet)
68.) Write a detailed explanation of at least 3 ways that you used math this summer (other
completing this packet). How did these skills help you be successful in the real world? W
skills do you hope to develop this year in math?
66) The number of feet of fencing that Ms. Hamilton needs to buy is 75 feet.
67) The distance around a rectangle is called a perimeter.
68) What are the instances of the use of Maths skills?The use of Mathematics skills is all-encompassing. Every activity involves some mathematical calculations and the use of mathematical operations, like additions, subtractions, divisions, and multiplication.
When you visit a Merchandise Store, you undertake some mathematical activities by computing how much is needed and the balance you will get. Future projections depend on maths skills.
For instance, budgeting how much it costs you weekly to maintain your hairstyle also involves maths skills.
As you return to school after the summer breaks, you decide how much savings you must spend. It is maths. Any time calculations are involved, it requires maths.
Data and Calculations:Length of the yard = 24.75 feet
Width of the yard = 12.75 feet
Perimeter of the yard = 75 feet (24.75 + 12.75)2
Charges for a yard of iron fencing = $50 per yard
3 feet = 1 yard
75 feet = 25 yards (75/3)
The cost of 25 yards = $1,250
Thus, Ms. Hamilton will need to spend $1,250 on this decorative iron fence project.
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Kyla earns $21 per hour tutoring student-athletes at Eastern University. If Kyla tutored for 12 hours this month, how much money did she earn this month?
Answer: $252
Step-by-step explanation:
21$ an hour x 12 hours = $252 total :)
Answer:
She earned $252 thsi month.
Step-by-step explanation:
1 hour = $21
12 hours = $?
21*12 = 252
where RS=8y+5, ST=3y+4, and RT=97.
a. What is the value of y?
b. Find RS and ST
The answer of part a is y = 8
The answer of part b is RS = 69, ST = 28
Step-by-step explanation:
a. Since RT = RS + RT, subsitute values of RS and RT in the equation
97 = (8y + 5) + (3y + 4)
97 = 11y + 9
97 - 9 = 11y
88 = 11y
y = 8
b. Subsitute the value of y in RS and ST just like done in part a
Simplify the quantity 9 minus two thirds times the square root of 9 end quantity squared plus the quantity 1 minus 6 end quantity squared.
74
24
495
1,225
The correct answer is option A that is 74.
First, we need to put the expression in the form of mathematical equation. A mathematical equation may be defined as the combination of numbers and arithmetic symbols which are related to each other according to the expression given. The expression in the form of mathematical expression can be written as:
(9 - 2/3×√9)² + (1-6)²
Solving the brackets separately.
(9 - 2/3×3)² + (-5)²
Now in the next step, simplify the equation.
=>(9 - 2)² + 25
=>(7)² + 25
=>49 + 25
=>74.
Therefore, the required answer is 74.
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See the attached screenshot.
The Area of the given composite shape is; 40 square units
What is the Area of the Composite Shape?
We can breakdown the shape into triangle and rectangle and as such we know that;
Formula for area of triangle is;
Area = ¹/₂ * base * height
Formula for area of rectangle is;
Area = Length * Width
Thus;
Area of composite shape = (10 * 3) + (¹/₂ * 10 * 2)
Area of composite shape = 30 + 10
Area of composite shape = 40 square units
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question is in picture please help
Answer:
[tex] \sf {a}^{6} [/tex]
Step-by-step explanation:
Given expression
[tex] \sf \: {a}^{0} \: • \: \: {a}^{6} [/tex]
To find expression solution
power rule[tex] \sf \: {a}^{m} \: {a}^{n} = {a}^{m + n} [/tex]
[tex] \sf {a}^{0} + {a}^{6} = {a}^{0 + 6} [/tex]
[tex] \sf \therefore \: {a}^{6} [/tex]
[tex] \: \Large \mathbb{SOLUTION:}[/tex]
[tex] \: \: \rm{ {a}^{0} \times {a}^{6} }[/tex]
[tex] \: \: \text{Calculate the power }[/tex]
[tex] \: \: \underline{\underline{\rm{{a}^{6} }}}[/tex]
The sum of 4 consecutive even integers is the same as the least of the integers find the integers
The four numbers are: -4, -2 ,0, 2 Answer.
How do you solve this: the sum of four consecutive even integers is equal to least of the integer
Solution: Let the numbers be n, n+2, n+4 and n+6.
Their sum = 4n+12 = n or
3n+12 = , or
3n = -12,
n= -4
therefore we get -4, -2, 0, 2
The four numbers are: -4, -2 ,0, 2 . Answer.
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Please help, This is urgent 7th-grade math.
There was 2/3 of a pan of lasagna in the refrigerator. Bill and his friends ate half of what was left. Write a number sentence and draw a model to represent the problem. How much of the pan did they eat?
Explanations/Answers, please!
PLEASE HELP I WILL GIVE BRAINLIEST AND 50 POINTS !!!!
A circle has equation x^2+y^2=100 Tangents meet the circle at R(-6,-8) and S(-8,6)
Find the equation of these tangents.
Find the coordinates of the point where these tangents meet.
Answer:use demos cauculator
Step-by-step explanation:
What is 22 divided 2.630 and what’s the remainder
Answer:
22 divided by 2.630= 8 remainder 0.96
Answer: 22/2.630 is 8, remainder is 0.365 or 73/200
Find the slope of the line if it exists.
Answer:
The slope would be [tex]-\frac{4}{3}[/tex]
Step-by-step explanation:
Select the approximate value of 9 - √7 on a number line.
The value of 9 - √7 is between 6 and 7:
4 < 7 < 9
⇒ √4 < √7 < √9
⇒ 2 < √7 < 3
⇒ -3 < -√7 < -2
⇒ 9 - 3 < 9 - √7 < 9 - 2
⇒ 6 < 9 - √7 < 7
NO LINKS!! Please help me with these problems. Part 11a1
y = 3x^2
Domain: (−∞,∞) , {x|x ∈ R}
Range: [0,∞) , {y|y ≥ 0}
Continuity: y=3x^2 is a parabola opening upwards, the vertex is at (0,0) and the focus is (0,1/12)
Max's and Min's: the minimum and maximum x value goes to infinity while for the y value the minimum is 0 and goes up to infinity.
Intervals: both x and y start to increase from the origin
Symmetry: the axis of symmetry is x=0 so therefore there the parabola is symmetrical
Answer:
Domain: (-∞, ∞)Range: [0, ∞)Continuity: Function is continuous on its domain (-∞, ∞). Minimum stationary point (turning point) at (0, 0).Increasing function: (0, ∞)Decreasing function: (-∞, 0)Symmetry: Even (symmetry about the y-axis).Step-by-step explanation:
Given function:
[tex]y=3x^2[/tex]
DomainThe domain is the set of all possible input values (x-values).
The domain of the given function is unrestricted.
Therefore, the domain is (-∞, ∞).
RangeThe range is the set of all possible output values (y-values).
As x² ≥ 0, the range of the given function is [0, ∞).
ContinuityA function f(x) is continuous when, for every value [tex]c[/tex] in its domain:
[tex]\text{$f(c)$ is de\:\!fined \quad and \quad $\displaystyle \lim_{x \to c} f(x) = f(c)$}[/tex]
Therefore, the function is continuous on its domain (-∞, ∞).
Maximums and MinimumsStationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
[tex]\begin{aligned}y & = 3x^2\\\implies \dfrac{\text{d}y}{\text{d}x} & = 6x\\\\\dfrac{\text{d}y}{\text{d}x} & = 0\\\implies 6x & = 0\\x & = 0\end{aligned}[/tex]
[tex]\textsf{When} \:x = 0 \implies y=3(0)^2=0[/tex]
Therefore, the stationary point of the given function is (0, 0).
To determine if a stationary point is minimum or maximum, differentiate the function again and substitute the x-value of the stationary point:
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & = 6x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6 \end{aligned}[/tex]
As the second derivative is positive regardless of the x-value of the stationary point, the stationary point is a minimum.
Increasing/Decreasing Function[tex]\textsf{A function is \textbf{increasing} when the \underline{gradient is positive}} \implies \dfrac{\text{d}y}{\text{d}x} > 0[/tex]
[tex]\textsf{A function is \textbf{decreasing} when the \underline{gradient is negative}} \implies \dfrac{\text{d}y}{\text{d}x} < 0[/tex]
Increasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & > 0 \\ \implies 6x & > 0 \\ x & > 0\end{aligned}[/tex]
Decreasing
[tex]\begin{aligned}\dfrac{\text{d}y}{\text{d}x} & < 0 \\ \implies 6x & < 0 \\ x & < 0\end{aligned}[/tex]
Therefore:
The function is increasing in the interval (0, ∞).The function is decreasing in the interval (-∞, 0).Symmetry[tex]\textsf{A function is \underline{even} when $f(x) = f(-x)$ for all $x$.}[/tex]
[tex]\textsf{A function is \underline{odd} when $-f(x) = f(-x)$ for all $x$.}[/tex]
As x² ≥ 0 and there is symmetry about the y-axis,
[tex]\textsf{then $f(x)=f-x)$ for all $x$,}[/tex]
so the function is even.
Why was his velocity 0? Explain.
In general, a
person is 1% shorter in the evening than in the
morning. Use your height to write a conditional
that uses this fact.
The conditional statement is that; If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.
How to write conditional statements?
First, we will calculate how much is one percent of your height and then subtract that percentage from the total height to get your" height in the evening".
For example:
If my height is 1.64 m, then;
0.01 * 1.64 m = 0.0164 m
Step 2 is;
1.64m - 0.0164m = 1.62326 m
Now, using these height, let's write a conditional that uses the described fact:
Conditional:
If generally a person is 1% shorter in the evening than in the morning, then my height is about 1.62326 m in the evening.
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Please help me yall!! This is due tomorrow… I would really appreciate it if y’all could give me some feedback!! Please and thank you!!
Answer:
[tex]\sf (A' \cap B) \cup (A' \cap C') =\{1,6,7\}[/tex]
Step-by-step explanation:
[tex]\begin{array}{|c|c|l|} \cline{1-3} \sf Symbol & \sf N\:\!ame & \sf Meaning \\\cline{1-3} \{ \: \} & \sf Set & \sf A\:collection\:of\:elements\\\cline{1-3} \cup & \sf Union & \sf A \cup B=elements\:in\:A\:or\:B\:(or\:both)}\\\cline{1-3} \cap & \sf Intersection & \sf A \cap B=elements\: in \:both\: A \:and \:B} \\\cline{1-3} \sf ' \:or\: ^c & \sf Complement & \sf A'=elements\: not\: in\: A \\\cline{1-3} \sf - & \sf Difference & \sf A-B=elements \:in \:A \:but\: not\: in \:B}\\\cline{1-3} \end{array}[/tex]
Given sets:
Universal = {1, 2, 3, 4, 5, 6, 7, 8}A = {2, 4, 5, 8}B = {1, 4, 6}C = {1, 2, 3, 4, 5}Therefore, the complement sets are:
[tex]\begin{aligned}\sf A' & = \text{U}-\sf A\\& = \{1,2,3,4,5,6,7,8 \}- \{2,4,5,8 \}\\& = \{1,3,6,7 \}\end{aligned}[/tex]
[tex]\begin{aligned}\sf B' & = \text{U}-\sf B\\& = \{1,2,3,4,5,6,7,8 \}- \{1,4,6 \}\\& = \{2,3,5,7,8 \}\end{aligned}[/tex]
[tex]\begin{aligned}\sf C' & = \text{U}-\sf C\\& = \{1,2,3,4,5,6,7,8 \}- \{1,2,3,4,5 \}\\& = \{6,7,8 \}\end{aligned}[/tex]
Solution
[tex]\begin{aligned}\sf (A' \cap B) \cup (A' \cap C') & = \sf \left(\{1,3,6,7 \} \cap \{1,4,6\} \right) \cup \left(\{1,3,6,7 \} \cap \{6, 7, 8 \} \right)\\\\& = \sf \{1,6\} \cup \{6,7 \} \\\\& = \sf \{1,6,7\} \end{aligned}[/tex]
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Write the decimal equivalent of:
Three hundred three and two hundredths
Answer: 303.002
Step-by-step explanation:
(x,y) —> (y,x)
I can’t do this one
Answer:
I legit don't remember lol
in the u.s government a memeber if the senate serves for 4 years longer than a member of the House of Representatives. If a member of the House of Representatives serves for h years, write an expression for how many years a member of the senate serves .
A member of the senate will serve for (h+4) years.
An expression, in mathematics, is a finite set of combinations and/ or numbers and variables that accurately represents the the context in question. When two or more expressions are connected using the equality sign then an equation is formed.
Here, we are given that in the US government a member of the senate serves for 4 years longer than a member of the House of Representatives.
Also the House of Representatives serves for- h years
Thus, the number of years a member of the Senate will serve will be 4 more than the number h
= h + 4
Thus, a member of the senate serves for (h+4) years.
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The table below models a particular physical situation.
x −9 −3 4 10
y 9 1 −7 10
Find the piecewise linear equation that models the data above. Round to three decimal places if needed.
y={
___ x + ___. −9 ≤ x ≤ −3
___ x + ___. −3 < x ≤ 4
___ x + ___. 4 < x ≤ 10
The piecewise linear function that models the situation is given as follows:
y = -4/3x + b, −9 ≤ x ≤ −3,y = -8/7x - 17/7, −3 < x ≤ 4,y = 17/6x - 110/6, 4 < x ≤ 10.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.A piecewise function is a function that has different definitions based on the input.
For x between -9 and -3, the function decreases by 8 when x increases by 6, hence the slope is given by:
m = -8/6 = -4/3, hence:
y = -4/3x + b.
When x = -9, y = 9, hence we use it to find b as follows:
9 = -4/3(-9) + b
9 = 12 + b
b = -3.
Thus the first definition is:
y = -4/3x + b, −9 ≤ x ≤ −3
For x between -3 and 4, the function decreases by 8 when x increases by 7, hence the slope is given by:
m = -8/7
y = -8/7x + b.
When x = -3, y = 1, hence we use it to find b as follows:
1 = -8/7(-3) + b
1 = 24/7 + b
b = -17/7
Thus the second definition is:
y = -8/7x - 17/7, −3 < x ≤ 4.
For x between 4 and 10, the function increases by 17 when x increases by 6, hence the slope is given by:
m = 17/6
y = 17/6x + b.
When x = 10, y = 10, hence we use it to find b as follows:
10 = 17/6(10) + b
b = 10 - 170/6
b = -110/6
Thus the third definition is:
y = 17/6x - 110/6, 4 < x ≤ 10
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Which numbers are between 5 & 6 not including 5 & 6
Answer:5.1,5.2,5.3,5.4,5.6,5.7,5.8,5.9,
Step-by-step explanation:
At what coordinate would you place point e so that is partitions df in a ratio of 5:3
∠1 and ∠2 form a linear pair. If m ∠1 is eight more than m ∠2 find the measures of both angles
A linear pair is formed of ∠1 and ∠2. The measures of the angle ∠1 is 20 and ∠2 is 160.
Given that,
A linear pair is formed of ∠1 and ∠2.
We have to find the measurements of both angles if m∠1 is eight more than m∠2.
When they refer to something as "linear," they mean that two angles create a straight line (or, 180 degrees). In other words, the two angles add up to 180.
Let us take the ∠1 as x
Then ∠2 will be 8x.
Now, we can write as
x+8x=180
9x=180
x=180/9
x=20
Therefore, the measures of the angle ∠1 is 20 and ∠2 is 8×20=160.
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Solve for x in the diagram below.
(2x+45)
Answer:
Step-by-step explanation:
you can't really solve for x because there is no equal sign to determine how much x needs to be in order to get the sum.
which of the following statements is true about the function f in the equation f(10)=5
The cordinates of the turning point of the graph of y=f(x) occurs at (1.1) and (5/3, 23/27)
2
(x−2)+1
Now, differentiating w.r.t. x, we get
f
′
(x)=2(x−1)(x−2)+(x−1)
2
=(x−1)[2(x−2)+x−1]
=(x−1)[3x−5]
Hence,
f
′
(x)=0 implies x=1 and x=
3
5
Corresponding values of y are y=1 and y=
27
23
respectively.
∴ Co-ordinates of turning point of the graph of f(x) occurs at (1,1) and (
3
5
,
27
23
)
Now,
f(x)=(x−1)
2
(x−2)+1
=(x
2
−2x+1)(x−2)+1
=x
3
−2x
2
−2x
2
+4x+x−2+1
=x
3
−4x
2
+5x−1
The value of p for which the equation f(x)=p has 3 distinct solutions lies in interval (
27
23
,1)
Area enclosed by f(x),x=0,y=1 and x=1 is
A=∫
0
1
(1−f(x))dx
⇒∫
0
1
(4x
2
−x
3
−5x+2) dx
⇒A=
12
7\
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Kenna has a 80.3 foot length of pipe to cut into pieces. Each piece must be 9.4 feet long. How many pieces of this length can Kenna get from this one length of pipe?
Step-by-step explanation:
80.3÷9.4
80/3÷9/4
80/3×4/9
26.6×4/9
=17.733
This means that Kenna will get 18 pieces from one lenght of pipe