Let the first number be x and the second number be y.
Since the sum of the numbers is 70, it follows that the equation that shows the sum of the numbers is:
[tex]x+y=70[/tex]The difference between the two numbers is 30, hence, the equation that shows the difference is:
[tex]x-y=30[/tex]The system of equations is:
[tex]\begin{cases}x+y={70} \\ x-y={30}\end{cases}[/tex]Make x the subject of the first equation:
[tex]x=70-y[/tex]Substitute this into the second equation:
[tex]\begin{gathered} 70-y-y=30 \\ \Rightarrow70-2y=30 \\ \Rightarrow-2y=30-70 \\ \Rightarrow-2y=-40 \\ \Rightarrow\frac{-2y}{-2}=\frac{-40}{-2} \\ \Rightarrow y=20 \end{gathered}[/tex]The second number is 20.
Substitute y=20 into the equation x=70-y to find x:
[tex]x=70-20=50[/tex]Answers:
The equation that shows the sum of the numbers is x+y=70.
The equation that shows the difference between the numbers is x-y=30.
The numbers are x=50 and y=20.
Don’t get part ii of this question ? I needed help with this, please help me as I am confused.
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.
In the diagram of △△ADC below, EB∥∥DC, AE=2, AB=10, and BC=45. What is the length of AD?
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]Could I please get help on finishing this math problem.
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).
You are interested in purchasing a $144,000 home. You plan to make a 25% downpayment and obtain an 8% mortgage for 20 years for the remaining amountthrough City Savings and Loan. Complete the form below to determine the totalclosing cost.
Cost of the house = $144,000
25% down payment = 25 / 100 * $144,000 = $36,000
Amount of mortgage = $144,000 - $36,000 = $108,000.
The closing costs are detailed in the form, and two rows need to be filled in and get the total closing costs row.
The first missing row is the Loan origination fee that corresponds to 2% of the mortgage:
2% of $108,000 = 2 / 100 * $108,000 = $2,160
The last row corresponds to 3/16 of the total interest on the mortgage.
Calculate the final value of the mortgage:
[tex]\begin{gathered} FV=\$108,000\cdot(1+0.08)^{20} \\ FV=\$503,383.37 \end{gathered}[/tex]The total interest is:
I = $503,383.37 - $108,000
I = $395,383.37
3/16 * $395,383.37 = $74,134.38
Write √32 in simplest radical form4√22√42√168√2
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.
Write equation below matches the following statement?Five more than two times a number,n, is sixteen.
"Five more than two times n" indicates that you have to multiply n by 2 and add 5, the result of this operation is 16, so the expression is:
[tex]2n+5=16[/tex]Given x = pi/3, what is the exact value of cos (pi+x)?
Using the unit circle above you can identify the cosine as the x-coordinate.
Then, the cosine of (4pi/3) is -1/2
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
The answer is 23/5 or 4.6
find the value of n so that the expression is a perfect square trinomial and then factor the trinomial. x^2+10x+n
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:
Find the value of an investment of $15,000 for 13 years at an annual interest rate of 3.15%
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
how to solve this question?
Answer:
2+4+2= 8
Step-by-step explanation:
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) = ______
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
$3.40 for a box of 20 trash bags. Find unit cost
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
Which equation is perpendicular to y= 1/2x + 4
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
Answer:
the answer is
5 cupcakes and 8 muffins
5+8=13
2(5)+1.5(8)=22
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.
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:
#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.
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]Compute.-2.65 - 16.3 =23.5 + ( -62.74) =
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]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.
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!!!
How many solutions exist for the equation cos 2θ − sin θ = 0 on the interval [0, 360°)?
We are given the following equation
[tex]\cos 2\theta-\sin \theta=0[/tex]Let us solve the above trigonometric equation.
Using the double angle identity,
[tex]\cos 2\theta=1-2\sin ^2\theta[/tex]So, the equation becomes
[tex]\begin{gathered} \cos 2\theta-\sin \theta=0 \\ 1-2\sin ^2\theta-\sin \theta=0 \end{gathered}[/tex]Now, let us solve the equation by substitution
Let sinθ = u
[tex]\begin{gathered} 1-2\sin ^2\theta-\sin \theta=0 \\ 1-2u^2-u=0 \\ -2u^2-u+1=0 \end{gathered}[/tex]Let us solve the above equation using the quadratic formula
[tex]u=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]The coefficients are
a = -2
b = -1
c = 1
[tex]\begin{gathered} u=\frac{-(-1)\pm\sqrt[]{(-1)^2-4(-2)(1)}}{2(-2)} \\ u=\frac{1\pm\sqrt[]{1+8}}{-4} \\ u=\frac{1\pm\sqrt[]{9}}{-4} \\ u=\frac{1\pm3}{-4} \\ u=\frac{1-3}{-4},\; \; u=\frac{1+3}{-4} \\ u=\frac{-2}{-4},\; \; u=\frac{4}{-4} \\ u=\frac{1}{2},\; \; u=-1 \end{gathered}[/tex]So, the two possible values are u = 1/2 and u = -1
Substitute them back into sinθ = u
[tex]\begin{gathered} \sin \theta=\frac{1}{2},\; \; \sin \theta=-1 \\ \theta=\sin ^{-1}(\frac{1}{2}),\; \; \theta=\sin ^{-1}(-1) \\ \theta=\frac{\pi}{6}\; and\; \frac{5\pi}{6},\; \; \theta=\frac{3\pi}{2}\; \\ \theta=30\degree\; and\; \; 150\degree,\; \; \theta=270\degree \end{gathered}[/tex]Therefore, the two solutions of the given equation are θ = 30°, θ = 150°, θ = 270° on the interval [0, 360°)
Answer:
I got it correct, by graphing on desmos
Step-by-step explanation:
Look at picture
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?
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].
graph the following system of inequalities and the solution set.y>2x+1y
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]
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 !!
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.
If this represents the sides of a triangle, classify it by it being an acute triangle, obtuse triangle, right triangle, or not being a triangle.
1. Determine if it is a rtiangle by using the triangle inequality: the sum of any two sides of a triangle is greater than or equal to the third side.
[tex]\begin{gathered} 13+14\ge16 \\ 27\ge16 \\ \\ 14+16\ge13 \\ 30\ge13 \\ \\ 13+16\ge14 \\ 29\ge14 \end{gathered}[/tex]It is a triangle
2. To classify a triangle knowing its sides you use the next: In a triangle ABC with longest side c
Acute:
[tex]c^2Right:[tex]c^2=a^2+b^2[/tex]Obtuse:
[tex]c^2>a^2+b^2[/tex]For the given triangle;
- Find the square of the longest side:
[tex]16^2=256[/tex]-Find the sum of the squares of the other sides:
[tex]13^2+14^2=169+196=365[/tex]As the sum of the squares of the to smallest sides (365) is greater than the square of the longest side (256) it is an acute triangle.Answer: Acute triangle{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.
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]Point D is in the interior of
The given problem can be exemplified in the following diagram:
The conditions are:
[tex]\begin{gathered} m\angle ABD=6x+5 \\ m\angle ABC=10x+7 \\ m\angle DBC=36 \end{gathered}[/tex]We also have the following relationship:
[tex]m\angle ABD+m\angle DBC=m\angle ABC[/tex]Substituting the values we get:
[tex]6x+5+36=10x+7[/tex]Solving the operations:
[tex]6x+41=10x+7[/tex]Now we solve for "x", first by subtracting 10x on both sides:
[tex]\begin{gathered} 6x-10x+41=10x-10x+7 \\ -4x+41=7 \end{gathered}[/tex]Now we subtract 41 on both sides:
[tex]\begin{gathered} -4x+41-41=7-41 \\ -4x=-34 \end{gathered}[/tex]Now we divide both sides by -4
[tex]x=-\frac{34}{-4}=\frac{17}{2}[/tex]Now we replace the value of "x" in the expression for angle ABD:
[tex]\angle ABD=6x+5[/tex]Replacing the value of "x":
[tex]\angle ABD=6(\frac{17}{2})+5[/tex]Solving the operations:
[tex]\angle ABD=3(17)+5=56[/tex]Therefore angle ABD is 56 degrees.
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 ?
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.
In circle E with mZDEF 36 and DE = 15 units find area of sector DEF. Round to the nearest hundredth. E F D
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]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
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
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)
To find number of groups of 8 are in 20
Divide 20 by 8 :
20 ÷ 8. = 2
Number of groups = 2