Answers
ANSWER
y = 130 degrees
STEP-BY-STEP EXPLANATION
Key points to note in the provided figure
Alternate exterior angles are equal
The sum of supplementary angles is 180 degrees
From the figure given, angle y and angle 5x are alternate exterior angles
Since alternate exterior angles are equal. Hence, angle y = angle 5x
y = 5x
Also, angle (2x - 2) and y are supplementary angles
Recall, the sum of supplementary angles is 180 degrees
Hence, we have
y + (2x - 2) = 180
Note, y = 5x
substitute y = 5x into the above equation
5x + (2x - 2) = 180
Open the parenthesis
5x + 2x - 2 = 180
Collect the like terms
5x + 2x - 2 = 180
7x - 2 = 180
Add 2 to both sides of the equation
7x - 2 + 2 = 180 + 2
7x = 182
Divide both sides by 7
7x/7 = 182/7
x = 26 degrees
Since we have gotten the value of x = 26 degrees. Hence, we can now find the value of y
Recall, y = 5x
y = 5(26)
y = 130 degrees
Related Questions
find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. x^2+10x+n
Answers
From the problem, we have :
[tex]x^2+10x+n[/tex]To make it a perfect square trinomial, we will use the formula :
[tex]n=(\frac{b}{2a})^2[/tex]and we can factor the trinomial as :
[tex](x+\frac{b}{2a})^2^{}[/tex]a = 1 and b = 10
so n will be :
[tex](\frac{b}{2a})^2=(\frac{10}{2\times1})^2=5^2=25[/tex]The value of n is n = 25
and the factor of the trinomial will be (x + 5)^2
Answer: the answer is (x + 5)^2
Step-by-step explanation:
Given x = pi/3, what is the exact value of cos (pi+x)?
Answers
Using the unit circle above you can identify the cosine as the x-coordinate.
Then, the cosine of (4pi/3) is -1/2
Suppose we interpret 20 ÷ 8. How many groups of 8 are in 20? Show how we think we could draw a diagram for this (optional)
Answers
To find number of groups of 8 are in 20
Divide 20 by 8 :
20 ÷ 8. = 2
Number of groups = 2
how to solve this question?
Answers
Answer:
2+4+2= 8
Step-by-step explanation:
(9x10 to the 7th power) (7x10 to the 9th power) in scientific notation.
Answers
The value of the expression in scientific format is 6.3 x 10¹⁷
How to determine the expression in scientific format?From the question, we have the following parameters that can be used in our computation:
(9x10 to the 7th power) (7x10 to the 9th power)
To start with, we need to represent the above expression using numbers and mathematical operators
So, we have the following representation
(9 x 10⁷) (7 x 10⁹)
Next, we combine the brackets using a product sign
This gives
(9 x 10⁷) x (7 x 10⁹)
Next, we remove the brackets from the expression
This gives
9 x 10⁷ x 7 x 10⁹
Evaluate the products of 9 and 7
63 x 10⁷ x 10⁹
Apply the law of indices to evaluate the final products
63 x 10¹⁶
Rewrite as
6.3 x 10¹⁷
Hence, the solution is 6.3 x 10¹⁷
Read more about scientific notation at
https://brainly.com/question/27862246
#SPJ1
#13, can you please try to give a detailed run-through on how to identify the variables, and do the problem step by step, I have trouble learning math.
Answers
Given the general expression of a quadratic function,
[tex]f(x)=ax^2+bx_{}+c[/tex]The given function is,
[tex]f(x)=(x-3)(x+8)[/tex]Expanding the right-hand side of the equation
[tex](x-3)(x+8)[/tex]Apply FOIL method:
[tex]\begin{gathered} \mleft(a+b\mright)\mleft(c+d\mright)=ac+ad+bc+bd \\ \end{gathered}[/tex]Therefore,
[tex]\mleft(x-3\mright)\mleft(x+8\mright)=x\times x+x\times8-3\times x-3\times\: 8=x^2+8x-3x-24[/tex]Simplify
[tex]x^2+8x-3x-24=x^2+5x-24[/tex]Therefore, the function in standard form is
[tex]f(x)=x^2+5x-24[/tex]Now, comparing the general quadratic function and the function given.
[tex]\begin{gathered} ax^2=x^2 \\ \frac{ax^2}{x^2}=\frac{x^2}{x^2} \\ \therefore a=1 \end{gathered}[/tex][tex]\begin{gathered} bx=5x \\ \frac{bx}{x}=\frac{5x}{x} \\ \therefore b=5 \end{gathered}[/tex][tex]c=-24[/tex]Hence, the answers are
[tex]\begin{gathered} a=1 \\ b=5 \\ c=-24 \end{gathered}[/tex]3. The vertex of the graph of y = ax + b is at the ?, and the vertex of the graph of y = a + b is at the ?
Answers
3. The vertex of the function y=|ax+b| happens at y=0, where the function changes its direction.
Then, the value of x at that point is x=-b/a.
The vertex happens at (-b/a,0). This is the x-intercept
In the second function y=a|x|+b, the vertex happens when x=0 and y=b. This is the y-intercept.
Answer: Option B: x-intercept, y-intercept.
A bad contains 31 red blocks, 46 green blocks, 23 yellow blocks, and 25 purple blocks. You pick one block from the bag at random. Find the indicated theoretical probability. Pr(green or red) = ______
Answers
SOLUTION
The probability of the event is given by the formula
[tex]\text{Probability}=\frac{\text{required outcome }}{total\text{ oucome }}[/tex]From the question, we have
[tex]\begin{gathered} \text{Red}=31,\text{green}=46,\text{ yellow=23, Purple=25} \\ \text{Total blocks=31+46+23+25=125} \end{gathered}[/tex]The indicated probability is
[tex]P(\text{green or red )=Pr(gr}een)+Pr(red)[/tex]where
[tex]Pr(\text{green)}=\frac{\text{Number of gre}en}{total\text{ blocks }}=\frac{46}{125}[/tex]Also, we have
[tex]Pr(\text{red)}=\frac{\text{Number of red }}{total\text{ blocks }}=\frac{31}{125}[/tex]Hence
[tex]Pr(\text{green or red )=}\frac{31}{125}+\frac{46}{125}=\frac{31+46}{125}=\frac{77}{125}[/tex]Therefore
The Pr(green or red ) will be 77/125
A surveyor measures the distance across a straight river by the following method: Starting directly across from a tree on the opposite bank, he walks x = 116 m along the riverbank to establish a baseline. Then he sights across to the tree. The angle from his baseline to the tree is = 29.2°. How wide is the river?
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Step 2:
The details of the solution are as follows:
The width of the river can see calculated thus:
[tex]\begin{gathered} \\ Using\text{ Trignometry, we have that:} \\ tan\text{ 29.2}^0\text{ =}\frac{opposite\text{ }}{adjacent}=\frac{y}{116} \end{gathered}[/tex][tex]\begin{gathered} cross-multiply,\text{ we have that:} \\ y\text{ = 116 x tan 29.2}^0 \\ Then,\text{ } \\ y\text{ = 116 x 0.5589} \\ y\text{ = 64.8324 m} \\ y\text{ }\approx\text{ 65 m \lparen to the nearest metre\rparen} \end{gathered}[/tex]CONCLUSION:
The width of the river is:
[tex]y=\text{ 65 m \lparen correct to the nearest metre\rparen}[/tex]8. Mel's mean on 10 tests for the semester was 89. She complained to the teacher that she should be given an A because she missed the cutoff of 90 by only a single point. Explain whether it is clear that she really missed an A by only a single point if each test was based on 100 points. Explain how many points she actually missed.
Answers
Answer
Check Explanation
Explanation
The mean of a group of numbers is the average of these numbers.
Mathematically, the mean is the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
So, when Mel's mean is 89 for 10 tests, this means
Mean = 89
N = Number of variables = 10
So, we can calculate the sum of all of Mel's scores
Mean = (Σx)/N
Cross multiply,
Σx = N [Mean]
Σx = 10 (89) = 890
For Mel to have an average score of 90 from 10 tests,
Mean = 90
N = Number of variables = 10
So, we can calculate the sum of all of Mel's scores
Mean = (Σx)/N
Cross multiply,
Σx = N [Mean]
Σx = 10 (90) = 900
So, we can see that Mel does not actually need 1 point to score an A (90), Mel needs 10 extra points gathered from the 10 tests, to get the extra average 1 point.
Hope this Helps!!!
graph the following system of inequalities and the solution set.y>2x+1y
Answers
Problem
graph the following system of inequalities and the solution set.
y>2x+1
ySolution
For this case when we create the plot we got:
And we can see that the solution set in terms of x is given by:
[tex](-\infty,-3)[/tex]And for y:
[tex](-\infty,-5)[/tex]
In circle E with mZDEF 36 and DE = 15 units find area of sector DEF. Round to the nearest hundredth. E F D
Answers
Given:
m∠DEF = 36
DE = 15 units
Let's find the area of the sector.
To find the area of the sector, apply the formula:
[tex]A=\frac{\theta}{360}\ast\pi r^2[/tex]Where:
radius, r = DE = 15 units
θ = 36
Substitute values into the formula:
[tex]\begin{gathered} A=\frac{36}{360}\ast\pi\ast15^2 \\ \\ A=\frac{1}{10}\ast\pi\ast225 \end{gathered}[/tex]Solving further:
[tex]\begin{gathered} A=0.1\pi\ast225 \\ \\ A=70.69\text{ square units} \end{gathered}[/tex]Therefore, the area of the sector rounded to the nearest hundredth is 70.69 square units
ANSWER:
[tex]\begin{gathered} ^{} \\ \text{ 70.69 units}^2 \end{gathered}[/tex]Given BA=DCCB=ADWhich postulate/theorem will be sufficient to prove ∆ABC= ∆CDB
Answers
We are given two triangles and we are told that
[tex]\begin{gathered} BA=DC \\ CB=AD \end{gathered}[/tex]since the triangle share side BD this means that the triangles have the same side length, therefore, congruency can be proved by SSS (Side Side Side).
$3.40 for a box of 20 trash bags. Find unit cost
Answers
Answer:
$0.17
Explanation:
To find the unit cost, we need to divide the total cost by the number of units, so
$3.40 divided by 20 is
$3.40/20 = $0.17
Therefore, the unit cost is $0.17
Expand binomial using binomial expansion (x-y)^3
Answers
The expression is,
[tex](x-y)^3[/tex]Expanding the expression we get,
[tex](x-y)^3=(x-y)(x-y)^2\ldots.(1)[/tex]We have,
[tex](x-y)^2=x^2-2xy+y^2\ldots..(2)[/tex]Substituting equation 2 in equation 1, we get,
[tex]\begin{gathered} (x-y)^3=(x-y)(x^2-2xy+y^2) \\ \text{ =}x(x^2-2xy+y^2)-y(x^2-2xy+y^2) \\ \text{ =}x^3-2x^2y+xy^2-yx^2+2xy^2-y^3 \\ \text{ =x}^3-y^3+3xy^2-3x^2y \end{gathered}[/tex]Find the value of an investment of $15,000 for 13 years at an annual interest rate of 3.15%
Answers
EXPLANATION:
We are given an investment of $15,000 invested for 13 years at an annual rate of 3.15%.
To calculate the Simple Interest on this investment, the formula given is;
[tex]I=PRT[/tex]Where the variables are;
[tex]\begin{gathered} P=15000 \\ R=3.15\% \\ T=13 \end{gathered}[/tex]We now have;
[tex]I=15000\times0.0315\times13[/tex][tex]I=6142.5[/tex]The value at the end of the investment period is now derived as;
[tex]A=P+I[/tex][tex]A=15000+6142.5[/tex][tex]A=21,142.5[/tex]To calculate value of this investment using the compound interest formula, we shall apply the formula which is;
[tex]A=P(1+r)^t[/tex]Given the same variables as earlier, we simply substitute and solve as shown below;
[tex]A=15000(1+0.0315)^{13}[/tex][tex]A=15000(1.0315)^{13}[/tex][tex]A=15000(1.49658028574)[/tex][tex]A=22448.7042861[/tex]We can round this to 2 decimal places and we'll have;
[tex]A=22,448.70[/tex]ANSWER:
Amount of the investment after 13 years will be $22,448.70
Kate started with a piece of bubblegum that was 5/8 in wide . She later blew a bubble that was 2 7/8 in wide how much wider was Kate's bubble than the original piece of bubblegum
Answers
The answer is 23/5 or 4.6
Don’t get part ii of this question ? I needed help with this, please help me as I am confused.
Answers
We are given the following function:
[tex]y=\frac{1-10x}{(2x-1)^5}[/tex]We are asked to differentiate with respect to "x". To do that we need to have into account that the function is rational and therefore, we need to use the quotient rule for derivatives, which is the following:
[tex]\frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{f^{\prime}(x)g(x)-f(x)g^{\prime}(x)}{g^2(x)}[/tex]Therefore, we need to determine the derivatives of f(x) and g(x). In this case, we have:
[tex]\begin{gathered} f(x)=1-10x \\ g(x)=(2x-1)^5 \end{gathered}[/tex]Now, we determine the derivative of f(x):
[tex]\frac{d}{dx}(f(x))=\frac{d}{dx}(1-10x)[/tex]First, we distribute the derivative:
[tex]\frac{d}{dx}(f(x))=\frac{d}{dx}(1)-\frac{d}{dx}(10x)[/tex]The first, derivative is the derivative of a constant and therefore is zero:
[tex]\frac{d}{dx}(f(x))=-\frac{d}{dx}(10x)[/tex]For the second derivative we use the following rule:
[tex]\frac{d}{dx}(ax)=a[/tex]Applying the rule we get:
[tex]\frac{d}{dx}(f(x))=-10[/tex]Therefore:
[tex]f^{\prime}(x)=-10[/tex]Now, we determine the derivative of g(x):
[tex]\frac{d}{dx}(g(x))=\frac{d}{dx}(2x-1)^5[/tex]Now, we determine the derivative using the following rule:
[tex]\frac{d}{dx}(g(x))^n=n(g(x))^{n-1}(g^{\prime}(x))[/tex]Applying the rule we get:
[tex]\frac{d}{dx}(g(x))=5(2x-1)^4(2)[/tex]Simplifying:
[tex]\frac{d}{dx}(g(x))=10(2x-1)^4[/tex]Therefore, we have:
[tex]g^{\prime}(x)=10(2x-1)^4[/tex]Now, we substitute the function in the quotient rule:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{(-10)(2x-1)^5-(1-10x)(10)(2x-1)^4}{((2x-1)^5)^2}[/tex]Now we simplify the denominator:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{(-10)(2x-1)^5-(1-10x)(10)(2x-1)^4}{(2x-1)^{10}}[/tex]Now, we take (2x - 1)^4 as a common factor on the numerator:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{(2x-1)^4((-10)(2x-1)^{}-(1-10x)(10))}{(2x-1)^{10}}[/tex]Now, we simplify the function:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{((-10)(2x-1)^{}-(1-10x)(10))}{(2x-1)^6}[/tex]Now, we apply the distributive property on the numerator:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{-20x+10^{}-10+100x}{(2x-1)^6}[/tex]Now, we cancel out the 10 and add like terms:
[tex]\frac{d}{dx}(\frac{1-10x}{(2x-1)^5})=\frac{80x}{(2x-1)^6}[/tex]Since we can't simplify any further this is the final answer.
PLS ANSWER, will mark brainliest
The total cost after tax to repair Deborah’s computer is represented by 0.08(50h)+50h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
Answers
Answer:
The expression of the total cost after tax, 0.08(50h) + 50h, has a tax part and a cost part.The tax part is 0.08(50h).The cost part is 50h.What is tax?Tax is the amount paid by the consumer to the government for the use of goods and services produced in/by the country.It is charged over the total cost for the particular good or service, at a pre-determined rate called the rate of tax.How to solve the question?In the question, we are informed that the total cost after tax to repair Deborah's computer is represented by 0.08 (50h) +50h, where h represents the number of hours it takes to repair Deborah's computer.We are asked what part of the expression represents the amount of tax Deborah has to pay.We know that the total cost = Tax + Fixed Cost,where tax = tax rate * fixed cost.Therefore, we write the total cost function like this:Total cost = Tax Rate(Fixed cost) + Fixed Cost.Comparing the given expression of the total cost, 0.08(50h) + 50h, with this expression, we can say that 0.08(50h) represents the tax part, where 0.08 is the tax rate and 50h is the fixed cost.Learn more about taxes atbrainly.com/question/5022774#SPJ2
Step-by-step explanation:
Which equation is perpendicular to y= 1/2x + 4
Answers
The equation is given as
[tex]y=\frac{1}{2}x+4[/tex]For finding the perpendicular line,
The product of slope is -1.
For the given equation , the slope is 1/2.
Now find the slope of perpendicular line.
[tex]\frac{1}{2}\times m=-1[/tex][tex]m=-2[/tex]Hence the slope of perpendicular line is -2.
Now the perpendicular equation to the given line can be
y=-2x+b.
Where assume b=1.
Then the equation perpendicular to the given line is
[tex]y=-2x+1[/tex]PLS HELP FOR BRAINLIEST
Answers
Answer:
the answer is
5 cupcakes and 8 muffins
5+8=13
2(5)+1.5(8)=22
Put a T for a true or a F for false .and don't worry this is just a practice :)and let me know if you can see the picture !!
Answers
1)
Working with inequalities, when you draw them in a number line or a coordinate system. The Open circle, or "blank dot" indicates that the number itself is not included in the definition, while the closed circle or "blak dot" indicates the value is included.
For example:
The inequality marked in the number line can be expressed symbolically as:
[tex]x<2[/tex]So the first statement is True.
2)
When an inequality includes a variable (letter) this one can be writen in terms of said variable following almost the same rules as when you calculate the value of a variable in an equation.
The greatest exception is that when you divide by a negative number, the direction of the inequality changes.
So for the given inequality:
[tex]-10w>100[/tex]To determine one possible value of w you have to divide both sides of the expression by "-10" and when you do so, the direction of the inequality gets inverted from > to <
[tex]\begin{gathered} -10w>100 \\ w<\frac{100}{-10} \\ w<-10 \end{gathered}[/tex]So this statement is False.
3)
This statement is True, when the variable is "alone" the coefficient is 1. Since multiplying a number by one results in said number it is redundant to write it, but altough "invisible" one is the coefficient of any variable that is "alone" in any given expression.
4)
"At most" indicates that it is the maximum value possible for the determined inequality. So the inequality can be equal or less than the determined value.
For example, "The cell phone repair will cost at most $100" → You know that you will pay no more than $100 dollars for the repair, it can be less but not more.
Let "x" symbolize the repair cost, you can express this as:
[tex]x\leq100[/tex]So this statement is True
5)
"Minimum" indicates that is the lowest value of the inequality, it is the startpoint, from the determined value onwards.
Could I please get help on finishing this math problem.
Answers
The triangles ABC and DEF have identical angles and one correspondent side identical. Therefore, they are congruent (AAS congruency).
The triangles UVW and XYZ have identical angles but there is no confirmation if they have identical correspondent sides. Therefore, they are not necessarily congruent.
The triangles GHI and JKL are congruent since they have three identical sides (SSS congruency).
Compute.-2.65 - 16.3 =23.5 + ( -62.74) =
Answers
Given:
There are given the expression:
[tex]\begin{gathered} -2.65-16.3\text{ and} \\ 23.5+(-62.74) \end{gathered}[/tex]Explanation:
To find the value of the expression, we need to subtract 16.3 from the -2.65.
Then,
[tex]-2.65-16.3=-18.95[/tex]And,
In the next expression, we need to add 23.5 with (-62.74).
So,
[tex]\begin{gathered} 23.5+(-62.74)=23.5-62.74 \\ =-39.24 \end{gathered}[/tex]Final answer:
Hence, the value of the expressions is shown below:
[tex]undefined[/tex]In the diagram of △△ADC below, EB∥∥DC, AE=2, AB=10, and BC=45. What is the length of AD?
Answers
Answer:
11 units
Explanation:
Given that lines EB and DC are parallel, we use the proportional division theorem:
[tex]\frac{AE}{ED}=\frac{AB}{BC}[/tex]Substitute the given values:
[tex]\begin{gathered} \frac{2}{ED}=\frac{10}{45} \\ \text{Cross multiply} \\ ED\times10=2\times45 \\ \text{Divide both sides by 10} \\ \frac{ED\times10}{10}=\frac{2\times45}{10} \\ ED=9 \end{gathered}[/tex]Next, find the length of AD:
[tex]\begin{gathered} AD=AE+ED \\ =2+9 \\ =11\text{ units} \end{gathered}[/tex]The length of AD is 11 units.
Alternate Method
[tex]ED=AD-2[/tex]So, we have that:
[tex]\frac{AE}{ED}=\frac{AB}{BC}\implies\frac{AE}{AD-2}=\frac{AB}{BC}[/tex]Substitute the given values:
[tex]\frac{2}{AD-2}=\frac{10}{45}[/tex]Cross multiply:
[tex]undefined[/tex]statement if p then not q this is different statement than the one give in the notes
Answers
Solution:
Given:
The conditional statement;
[tex]\begin{gathered} \text{If p, then not q} \\ p\rightarrow\text{ \textasciitilde{}q} \end{gathered}[/tex]A converse statement is a result of reversing its two constituent statements.
[tex]\begin{gathered} \text{Conditional statement-If p, then not q} \\ \text{Converse statement-If not q, then p} \end{gathered}[/tex]Therefore, the converse statement is: If not q, then p
The inverse statement assumes the opposite of each of the original statements.
[tex]\begin{gathered} \text{Conditional statement-If p, then not q} \\ I\text{nverse statement-If not p, then q} \end{gathered}[/tex]Therefore, the inverse statement is: If not p, then q
To get the contrapositive statement, we interchange the conclusion of the inverse statement.
[tex]\begin{gathered} \text{Conditional statement-If p, then not q} \\ I\text{nverse statement-If not p, then q} \\ \\ \text{Hence, the contrapositive statement is gotten by reversing the conclusion of the inverse statement.} \\ \text{Contrapositive statement-If q, then not p} \end{gathered}[/tex]
Therefore, the contrapositive statement is: If q, then not p
{57, 53, 53, 71, 73, 57, 61, 58, 78. 64, 54, 69, 56, 58, 49, 56, 53, 52, 82, 62, 61, 60, 71, 75, 60} Whats the mean?. and the iqr? what is the five number summary? what is Q3? The Median is 60.
Answers
Given the data set:
[tex]\lbrace57,53,53,71,73,57,61,58,78,64,54,69,56,58,49,56,53,52,82,62,61,60,71,75,60\rbrace[/tex]• You can find the Mean by adding all the values and dividing the sum by the number of values in the data set:
[tex]Mean=\frac{57+53+53+71+73+57+61+58+78+64+54+69+56+58+49+56+53+52+82+62+61+60+71+75+60}{25}[/tex][tex]Mean\approx61.72[/tex]• By definition the term for the third quartile can be found with this formula:
[tex]\frac{3}{4}(n+1)[/tex]Where "n" is the number of observations.
In this case:
[tex]n=25[/tex]Then:
[tex]\frac{3}{4}(25+1)\approx19.5[/tex]Since it is an integer, you get that the position of the terms is:
[tex]Q_3=\frac{69+71}{2}=70[/tex]Because, when you order the data set, 69 is the 19th value and 71 is the 20th value. Then, the third quartile is the average between them:
[tex]\lbrace49,52,53,53,53,54,56,56,57,57,58,58,60,60,61,61,62,64,69,71,71,73,75,78,82\rbrace[/tex]• By definition:
[tex]IQR=Q_3-Q_1[/tex]And the term position of the first quartile is found with:
[tex]\frac{n+1}{4}[/tex]You get:
[tex]\frac{25+1}{4}=6.5[/tex]Therefore, you can determine that:
[tex]Q_1=\frac{54+56}{2}=55[/tex]Then:
[tex]IQR=70-55=15[/tex]• By definition, the Five-Number Summary is:
- The minimum value:
[tex]Minimum=49[/tex]- The first quartile:
[tex]Q_1=55[/tex]- The median:
[tex]Median=60[/tex]- The third quartile:
[tex]Q_3=70[/tex]- The maximum value:
[tex]Maximum=82[/tex]Hence, the answers are:
• Mean:
[tex]Mean\approx61.72[/tex]• IQR:
[tex]IQR=15[/tex]• Five-Number Summary:
[tex]Minimum=49[/tex][tex]Q_1=55[/tex][tex]Median=60[/tex][tex]Q_3=70[/tex][tex]Maximum=82[/tex]• Third quartile:
[tex]Q_3=70[/tex]Which of the following is a quadraticfunction?F. f(x) = -x4 + x + 11G. f(x) = 5x2-8H. f(x) = x3 - 7x + 12J. f(x) = 47 - X
Answers
The qudratic function is the function that the x-variable has a power to the power of two
Hence, the quadratric function is G
f(x) = 5x²-8
Write √32 in simplest radical form4√22√42√168√2
Answers
Answer:
4√2
Explanation:
To write √32 in its simplest radical form:
Express it as a product of two factors where one is a perfect square.
[tex]\sqrt[]{32}=\sqrt[]{16\times2}[/tex]Next, we can separate the product of radicals as follows:
[tex]\begin{gathered} =\sqrt[]{16}\times\sqrt[]{2} \\ =4\times\sqrt[]{2} \\ =4\sqrt[]{2} \end{gathered}[/tex]The simplest radical form is 4√2.
Determine whether the given ordered pair is a solution of the system.
y = 6
2x - 5y = 24
Is (2,-4) a solution of the system?
Answers
Answer:
[tex](2, -4)[/tex] is not a solution.
Step-by-step explanation:
The ordered pair [tex](2, -4)[/tex] cannot be a solution of the system since, given the first equation of [tex]y=6[/tex], the only possible value for [tex]y[/tex] is 6. In other words, the only possible value that makes [tex]y=6[/tex] true is 6.
Therefore, to figure [tex]x[/tex], we substitute 6 for [tex]y[/tex] in the second equation and solve:
[tex]2x-5y=24[/tex]
[tex]2x-5(6)=24[/tex]
[tex]2x-30=24[/tex]
[tex]2x=54[/tex]
[tex]x=27[/tex]
The ordered pair, then, that solves the system is [tex](27,6)[/tex].