The perimeter (P) and area (A) of a square of sides a = 9 in, are given by:
[tex]\begin{gathered} P=4a=4\cdot(9in)=36in, \\ A=a^2=(9in)^2=81in^2. \end{gathered}[/tex]Answer
• Perimeter = 36 in
,• Area =, ,81 in²
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].
Choose all of the expressions that are equivalent to 2 1/2 divided by 1 2/6A 5/2 times 6/8B 2/5 times 6/8C 1 2/6 divided by 2 1/2D 5/2 divided by 8/6
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:
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.
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.
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:
Jim borrows $300 at 7% per annum compounded quarterly for 7 years. Determine the interest due on the loan.
Answer:
[tex]I=\text{ \$187.62}[/tex]Step-by-step explanation:
Compounded interest is represented as;
[tex]\begin{gathered} A=P(1+\frac{r}{n})^{nt} \\ \text{where,} \\ P=\text{ principal } \\ r=\text{ interest rate} \\ n=\text{ times compounded per unit time} \\ t=\text{ time in years} \end{gathered}[/tex]Therefore, for a principal of $300 at 7% per annum compounded quarterly;
[tex]\begin{gathered} A=300\cdot(1+\frac{0.07}{4})^{4\cdot7} \\ A=487.62 \\ \text{Then, the interest due would be the subtraction of A-P} \\ I=487.62-300 \\ I=\text{ \$187.62} \end{gathered}[/tex]Which point has the coordinates (-2.5, 5.5)? A.point EB.point FC.point GD.point H
I need to know the sum of the two terms
Answer: 194 degrees
From the given figure, we can see a transversal forming between the pairs of parallel lines.
Let us focus on the lines n, a, and e. Here, we can see a pair of parallel lines a and e, cut by a transversal n.
We are given a measurement for angle 4, which is 97. Then we are asked to find the sum of angle 2 and angle 4.
One theorem with respect to transversals that we must be familiar with is the Alternate Interior Angles Theorem which states that:
When two parallel lines are cut by a transversal, the resulting alternate interior angles are congruent.
With this, we can see from the figure that angle 2 and angle 4 are actually alternate interior angles.
Since they are alternate interior angles, and they are congruent, this would mean that angle 2 also measures 97.
[tex]m\angle4=97;m\angle2=97[/tex]With this, we can now add the two measurements, and that would give us:
[tex]97+97=194[/tex]The sum of angle 2 and angle 4 is 194 degrees.
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
$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
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).
The area of the parallelogram is 273in squared what’s the height ?
The formula for determining the area of a parallelogram is expressed as
Area = base x height
Given that
base = 39
area = 273
Then,
273 = 39 x height
height = 273/39
height = 7 ft
After paying $7 for a movie ticket Grace still had $3.75 how much money did Grace have before buying the ticket A. $3.25B. $10.25C. $4.52D. $10.75
D. $10.75
To solve this we have to write an equation:
Movie ticket price: $7
Money left : $3.75
Original amount: x
The original amount (x) minus the price of the ticket(7) must be equal to the money left after the purchase (3.75)
x-7 =3.75
Solving for x:
x = 3.75+7
x = 10.75
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.
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
If △STU is similar to △XYZ, the sides of △STU must be congruent to thecorresponding sides of △XYZ.A. TrueB. False
Similar triangles are triangles that have the same interior angles and the corresponding sides are proportional, that is, for triangles STU and XYZ we have the proportion:
[tex]\frac{ST}{XY}=\frac{TU}{YZ}=\frac{SU}{XZ}[/tex]The corresponding sides are congruent only if the proportion rate is 1, but that is not always true and it's not necessary.
Therefore the correct option is B: False
If the corresponding sides are congruent, the triangles are congruent.
writing exponential functions (4, 112/81), (-1, 21/2)
The given points are (4, 112/81) and (-1, 21/2).
To find an exponential function from the given points, we have to use the forms.
[tex]\begin{gathered} y_1=ab^{x_1} \\ y_2=ab^{x_2} \end{gathered}[/tex]Now, we replace each point in each equation.
[tex]\begin{gathered} \frac{112}{81}=ab^4 \\ \frac{21}{8}=ab^{-1} \end{gathered}[/tex]We solve this system of equations.
Let's isolate a in the second equation.
[tex]\begin{gathered} \frac{21}{8}=\frac{a}{b} \\ \frac{21b}{8}=a \end{gathered}[/tex]Then, we replace it in the first equation
[tex]\frac{112}{81}=(\frac{21b}{8})\cdot b^4[/tex]We solve for b.
[tex]\begin{gathered} \frac{112\cdot8}{81\cdot21}=b\cdot b^4 \\ \frac{896}{1701}=b^5 \\ b=\sqrt[5]{\frac{896}{1701}}=\frac{2\sqrt[5]{4}}{3} \\ b\approx0.88 \end{gathered}[/tex]Once we have the base of the exponential function, we look for the coefficient a.
[tex]a=\frac{21b}{8}=\frac{21}{8}(\frac{2\sqrt[5]{4}}{3})=\frac{7\sqrt[5]{4}}{4}[/tex]Therefore, the exponential function is[tex]y=\frac{7\sqrt[5]{4}}{4}\cdot(\frac{2\sqrt[5]{4}}{3})^x[/tex]The image below shows the graph of this function.
Evaluate each of the following. Illustrate with a point on the graph g(-2)=g(3)=g(0)=g(7)=
Solution
From the graph given we have this:
g(-2)= -3
g(3)= 4
g(0)= -3
g(7)= 0
why aren't 38 and 40 relatively prime
No they aren't relatively because they don't come from the same prime number
A scatter plot showed a positive correlation for 11 bowlers. As the number of strikes, s, a bowler made in a game increased, the number of points, p, the bowler scores also increased. The equation for the line of best fit for the data is p = 25s + 40. Estimate the number of strikes made by a bowler with 140 points. A) 4B) 6C) 25D) 40
The model variables the relationship between the strikes (s) and the number of points scored (p)
[tex]p=25s+40[/tex]To determine the number of strikes made, so that 140 points where scored, you have to replace the model with p=140 and solve for s
[tex]140=25s+40[/tex]The first step is to pass "40" to the others side of the equal sing, by performing the inverse operation "-40" to both sides of the expression
[tex]\begin{gathered} 140-40=25s+40-40 \\ 100=25s \end{gathered}[/tex]Then you have to divide both sides of the expression by 25 to determine the value of s
[tex]\begin{gathered} \frac{100}{25}=\frac{25s}{25} \\ 4=s \end{gathered}[/tex]The bowler made s=4 strikes, the correct choice is A.
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 triangleA fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
Problem
A fruit bowl contains 4 green apples, 7 red apples, and 5 yellow apples. What is the probability that a randomly selected apple will NOT be red?
Solution
For this case we can find the total number of apples like this:
4+7+5= 16 apples
And the number of apples not red are:
4 + 5= 9 apples
Then the probability of being not red would be:
p = 9/16
3|x + 1| - 9 = 0? Solution set?
x = (2, -4)
Explanation:Given:
[tex]\begin{gathered} 3|x+1|-9=0 \\ \\ 3|x+1|=9 \\ \\ |x+1|=3 \\ \\ x+1=3 \\ \Rightarrow x=2 \\ \\ OR \\ -(x+1)=3 \\ \\ -x-1=3 \\ \\ -x=3+1 \\ \\ -x=4 \\ \\ x=-4 \end{gathered}[/tex]x = (2, -4)
What is the slope of the line that passes through the points (9, 5) and (21,-5)?
The equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
How does the slope intercept form made?The slope-intercept form of an a line is a method of writing the equation of a line so that the slope as well as y-intercept are easily identifiable.The the line's slope represents its steepness, and also the y-intercept is the point at which the line intersects a y-axis.For the given question;
The line passes through points are-
(x1, y1) =(9, 5) and
(x2, y2) = (21,-5)
Slope = m = (y2 - y1)/(x2 - x1)
m = (-5 - 5)/(21 - 9)
m = -10/12
m = -5/6
Equation of the line is found using slope intercept form.
y - y1 = m (x - x1)
y - 5 = (-5/6)(x - 9)
y = (-5/6)x - 25/2
Thus, the equation of the line that passes through points (9, 5) and (21,-5) isy = (-5/6)x - 25/2.
To know more about the slope intercept form, here
brainly.com/question/1884491
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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
Out of 50 students, 17 want pepperoni pizza, 19 want sausage pizza and the rest want a supreme pizza. What percent of the students want a supreme pizza?
First, lets find how many students want the supreme pizza. Let 'x' be the number of those students. Then, given the information, we have:
[tex]x+17+19=50[/tex]solving for 'x', we get:
[tex]\begin{gathered} x+17+19=50 \\ \Rightarrow x+36=50 \\ \Rightarrow x=50-36=14 \\ x=14 \end{gathered}[/tex]we have that x = 14 students want a supreme pizza.
Now, if we suppose that the 50 students are the 100%, then, using a rule of three, we get:
[tex]\begin{gathered} 50\rightarrow100\% \\ 14\rightarrow y\% \\ \Rightarrow y=\frac{14\cdot100}{50}=\frac{1400}{50}=28 \\ y=28\% \end{gathered}[/tex]therefore, 28% of the students want a supreme pizza
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]If you will conduct a research about the poor study habits of Grade 7 students, how will you present your research problem using mathematical function?
I would define what a poor study habit is, using a parameter like study time in hours or days.
Let a study time of at least 2 hours per day be good, and less than 2 hours per day be poor.
Let f(x) be the study habit of a particular grade, so we write:
Good study time as:
[tex]f(x)\ge2[/tex]Bad study time as:
[tex]f(x)<2[/tex]The last one can represent the study habits of Grade 7 students.
0 2 4 6 8 10 12 14 16 What is the interquartile range of plot A
The given Data set can be arranged in the ascending order as,
0,2,4,6,8,10,12,14,16.