Answer:
56.25
Explanation:
We are told that the side lengths of the smaller figure are 3/4 the length of the larger figure.
[tex]S_{small}=\frac{3}{4}\times S_{large}[/tex]Now since the area is proportional to the equal of the side lengths, we have
[tex]A_{small}=S_{small}^2^[/tex][tex]A_{small}=(\frac{3}{4})^2\times S_{large}^2[/tex][tex]=A_{small}=(\frac{3}{4})^2\times A_{large}^2[/tex]The last is true since A_large = S^2_large.
Now we are told that A_large = 100 square units; therefore,
[tex]A_{small}=(\frac{3}{4})^2\times100[/tex][tex]\Rightarrow A_{small}=\frac{9}{16}\times100[/tex]which we evaluate to get
[tex]A_{small}=\frac{9}{16}\times100=56.25[/tex][tex]\boxed{A_{small}=56.25.}[/tex]Hence, the area of the smaller figure is 56.25.
Lisa is four years younger than her sister. Which expression below stands for the sum of Lisa’s age and her sister’s age?
A. x − (x − 4)
B. (x + 4) − x
C. None of these
D. (x − 4) − x
The expression for the sum of Lisa and her sister's age is (x - 4) + x which is the third option that is none of these form the given options.
It is given in the question that Lisa is four years younger than her sister.
Let Lisa's sister's age be x years.
Hence, according to the data given on the question, we can write,
Lisa age = (x - 4) years
Hence, the expression for the sum of the ages of Lisa and her sister will be = (x - 4) + x years.
It is not given in any of the options, hence the answer is none of these.
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Factor Problem Completely 16n^3 - 56n^2 + 8n - 28
Given
The equation is given as
[tex]16n^3-56n^2+8n-28[/tex]Explanation
Factorisation the equation,
[tex]4(4n^3-14n^2+2n-7)[/tex]Factorise the polynomial.
[tex]4(2n-7)(2n^2+1)[/tex]AnswerHence the answer is
[tex]4(2n-7)(2n^2+1)[/tex]w=3? What is the value of the expression below when w = 5w+ 2
Answer:
The value of the expression at w=3 is;
[tex]17[/tex]Explanation:
Given the expression;
[tex]5w+2[/tex]Then when w=3, the value of the expression is;
[tex]\begin{gathered} 5w+2 \\ =5(3)+2 \\ =15+2 \\ =17 \end{gathered}[/tex]The value is gotten by replacing/substituting w with 3 in the expression;
Therefore, the value of the expression at w=3 is;
[tex]17[/tex]$1750 is invested in an account earning 3.5% interest compounded annualy. How long will it need to be in an account to double?
Given :
[tex]\begin{gathered} P\text{ = \$ 1750} \\ R\text{ = 3.5 \%} \\ A\text{ = 2P} \\ A\text{ = 2}\times\text{ 1750 = \$ 3500} \end{gathered}[/tex]Amount is given as,
[tex]\begin{gathered} A\text{ = P( 1 + }\frac{R}{100})^T \\ 3500\text{ = 1750( 1 + }\frac{3.5}{100})^T \\ \text{( 1 + }\frac{3.5}{100})^T\text{ = }\frac{3500}{1720} \end{gathered}[/tex]Further,
[tex]\begin{gathered} \text{( 1 + }\frac{3.5}{100})^T\text{ = 2} \\ (\frac{103.5}{100})^T\text{ = }2 \\ (1.035)^T\text{ = 2} \end{gathered}[/tex]Taking log on both the sides,
[tex]\begin{gathered} \log (1.035)^T\text{ = log 2} \\ T\log (1.035)\text{ = log 2} \\ T\text{ = }\frac{\log \text{ 2}}{\log \text{ 1.035}} \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} T\text{ = }\frac{0.3010}{0.0149} \\ T\text{ = 20.20 years }\approx\text{ 20 years} \end{gathered}[/tex]Thus the required time is 20 years.
what are the two moves you can use to get the first figure to the second figure (dilation,rotation, reflection,and translation)
ANSWER:
Dilation and translation
EXPLANATION:
Looking at the figures, the two moves used to get the first figure to the second figure is dilation and translation.
The figure was translated 6 units right and 7 units down.
The translation rule that occured here is==> (x+6, y-7)
Also, a dilation with a scale factor of 2 occured here.
Therefore, a dilation and translation occured in order to get the first figure to the second figure.
Problem Solving
20. A city is building 3 parks in a new subdivision. Each park
will be 1.25 acres. How many total acres will the 3 parks
be?
According to the solving all three parks will cover surface of 37.5 acres in total.
How much area of land is in acres?The imperial and US customary systems both utilize the acre as a unit of land area. An acre is approximately equal to approximately 4,047 [tex]m^{2}[/tex].
How much area will 3 parks cover?Area covered by 3 parks can be calculated by multiplying the area of one park by three.
so, area covered by 3 parks=3×1.25
area covered by 3 parks=3.75
As you know multiplication is the repeated addition so we can obtain the same results by adding 1.25 three times to itself.
These three parks will cover total area of 3.75acres.
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The pentagonal prism below has a height of 13 units and a volume of 247 units ^3. Find the area of one of its bases.
• Volume of pentagonal prism = area of base x height
Volume = 247 unis^3
height = 13 units
Replacing:
V = A x h
A = V / h
A = 247/13 = 19 units^2
Is x5 + x2 + x a polynomial? Explain why or why not.
A polynomial is a mathematical expression formed by variables and coefficients, that involves only the operations of addition, subtraction, multiplication and non-negative integer exponentiation of variables.
The expression:
[tex]x^5+x^2+x[/tex]Is formed by the addition of three terms, each consisting of the variable x raised to a positive integer quantity. Therefore, the given expression is a polynomial.
Fill in the blanks. (6x)^2 = _x^_
Step-by-step explanation:
[tex](6x) {}^{2} = -x { }^{?} - [/tex]3. The data in the table gives the number of barbeque sauce bottles (y) that are sold with orders of chicken wings (x) for each hour on a given day at Vonn's Grill. Use technology to write an equation for the line of best fit from the data in the table below. Round all values to two decimal places.
1) Let's visualize the points
2) To find the equation for the line of best fit we'll need to follow some steps.
2.1 Let's find the mean of the x values and the mean of the Y values
2.2 Now It's time to find the slope, with the summation of the difference between each value and the mean of x times each value minus the mean over the square of the difference of the mean of x and x.
To make it simpler, let's use this table:
The slope then is the summation of the 5th column over the 6th column, we're using the least square method
[tex]m=\frac{939.625}{1270.875}=0.7393\cong0.74[/tex]The Linear coefficient
[tex]\begin{gathered} b=Y\text{ -m}X \\ b=14.625-0.73(19.875) \\ b=0.11625\cong0.12 \end{gathered}[/tex]3) Finally the equation of the line that best fit is
[tex]y=0.73x+0.12[/tex]Translate the sentence into an equation.Eight more than the quotient of a number and 3 is equal to 4.Use the variable w for the unknown number.
We are to translate into an equation
Eight more than the quotient of a number and 3 is equal to 4.
Let the number be w
Hence, quotient of w and 3 is
[tex]\frac{w}{3}[/tex]Therefore, eight more than the quotient of a number and 3 is equal to 4
Is given as
[tex]\frac{w}{3}+8=4[/tex]Solving for w
we have
[tex]\begin{gathered} \frac{w}{3}=4-8 \\ \frac{w}{3}=-4 \\ w=-12 \end{gathered}[/tex]Therefpore, the equation is
[tex]\frac{w}{3}+8=4[/tex]What is the y-intercept of the line x+2y=-14? (0,7) (-7,0) (0,-7) (2,14)
Debra the trainer has two solo workout plans that she offers her clients: plan A and plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did plan A and 3 who did plan B. On Thursday there were 7 clients who did plan A and 9 who did plan B. Debra trained her Wednesday clients for a total of 6 hours and her Thursday clients for a total of 12 hours. How long does each of the workout plans last?
The solo plans Debra offers her clients are plan A and plan B. Each client can only do one plan .
According to the question the plan only ran on wednesday and thursday.
Wednesday = plan A has 5 client and plan B has 3 clients.
Thursday = plan A has 7 client and plan B has 9 clients.
On wednesday she trained her client for 6 hours.
On thursday she trained her client for 12 hours.
let
x = hour of plan A workout for each client
y = hour of plan B workout for each client
[tex]\begin{gathered} 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}\mathrm{}(i) \\ 7x\text{ + 9y = 12}\ldots\ldots\ldots\text{.(2)} \\ 3y\text{ = 6 - 5x} \\ y\text{ = }\frac{6}{3}\text{ - }\frac{5}{3}x \\ y\text{ = 2 - }\frac{5}{3}x \\ 7x\text{ + 9(2 - }\frac{5}{3}x\text{) = 12} \\ 7x\text{ + 18 - }\frac{45}{3}x\text{ = 12} \\ 7x\text{ + 18 - }15x\text{ = 12} \\ -8x\text{ = 12 - 18} \\ -8x\text{ = - 6} \\ x\text{ = }\frac{6}{8} \\ x\text{ = }\frac{3}{4} \\ 5x\text{ + 3y = 6}\ldots\ldots\ldots\text{.}(i) \\ 5(\frac{3}{4})\text{ + 3y = 6} \\ \frac{15}{4}\text{ + 3y = 6} \\ 3y\text{ = 6 - }\frac{15}{4} \\ 3y\text{ = }\frac{24-15}{4} \\ 3y\text{ = }\frac{9}{4} \\ y\text{ = }\frac{9}{4}\text{ }\times\text{ }\frac{1}{3} \\ y\text{ = }\frac{9}{12} \\ y\text{ = }\frac{3}{4} \end{gathered}[/tex]on wednesday plan A lasted for 5 * 3/4 = 15/4 hrs and plan B lasted for 3 * 3/4 = 9/4 hrs
On thursday plan A lasted for 7* 3/4 = 21/4 hrs and plan B lasted for 9 * 3/4 = 27/4 hrs
Each of the work out lasted for 3/4 hrs = 0.75 hrs
Describe it and decide if normal curve could be used as model
Answer:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
Explanation:
The normal distribution is symmetric and unimodal, where the mode, the median, and the mean are equal. This distribution has the following shape
Therefore, the normal curve can be used as a model for the distribution.
So, the answers are:
The symmetric is symmetric
The distribution is unimodal
The mean, median, and mode are equal
A normal distribution is appropriate
factor the following by taking on the greatest common factor 14a^3 + 35a^2 +42a
Let's break apart each term into its factors:
[tex]\begin{gathered} 14a^3=2\cdot7\cdot a\cdot a\cdot a \\ 35a^2=5\cdot7\cdot a\cdot a \\ 42a=2\cdot3\cdot7\cdot a \end{gathered}[/tex]The common factors are
7 * a
That is,
[tex]7\cdot a=7a[/tex]Now, factorizing the expression, we have:
[tex]\begin{gathered} 14a^3+35a^2+42a \\ =7a(2a^2+5a+6) \end{gathered}[/tex]Answer[tex]7a(2a^2+5a+6)[/tex]Determine if the 2 lines are parallel, perpendicular, or neither based on their slope-intercept equations.
Equations of lines G & H;
Line G: y=-6x + 14
Line H: y=6x-14
O Perpendicular
O Not Enough Information
O Parallel
O Neither
POSS
10 11
12 13 14 15
Answer:
perpendicular because the slopes are opposite
Step-by-step explanation:
writing equations in slope-intercept form common core algebra 1question 1
The equation of the line in the slope-intercept form is y = mx + b, where "m" is the slope and "b" is the y-intercept.
"b" is the point (0, yi).
"m" can be found using 2 points P₁ (x₁, y₁) and P₂ (x₂, y₂), according to the formula below:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]So, to solve this question, follow the steps below.
(a) First graph
Step 01: Find the y-intercept and another point in the graph.
To find the points in the graph, choose a x-value and find its corresponding y-value.
Choosing x = 0, y = 2.
P₁ = (0, 2).
Choosing x = -3, y = -2.
P₂ = (-3, -2).
Step 02:
A cone has a base radius of length r, and an perpendicular height length h. If the height remains the same, and the radius is multiplied by 3, then the volume is multiplied by:A. 27B. 2C. 9D. 4/3
ANSWER
C. 9
EXPLANATION
The volume of a cone is:
[tex]undefined[/tex]A square paddock has an area of 7140.25m².
How long is each side?
Answer:
it's 84.5 m ...................
Find ( f+g ) (x) for each of the following functions
Answer:
(f + g)(x) = 2x³ + 3x² + x + 2
Explanation:
If f(x) = 2x³ - 5x² + x - 3 and g(x) = 8x² + 5, we can calculate (f + g)(x) as follows
(f + g)(x) = f(x) + g(x)
(f + g)(x) = (2x³ - 5x² + x - 3) + (8x² + 5)
Then, we can simplify the expression adding the like terms, so
(f + g)(x) = 2x³ - 5x² + x - 3 + 8x² + 5
(f + g)(x) = 2x³ + (-5x² + 8x²) + x + (-3 + 5)
(f + g)(x) = 2x³ + 3x² + x + 2
Therefore, the answer is:
(f + g)(x) = 2x³ + 3x² + x + 2
The ratio of students polled in 6th grade who prefer lemonade to iced tea is 8:4, or 2:1. If there were 39 students in 6th grade polled, explain how to find the number of students that prefer lemonade and the number of students that prefer iced tea. Be sure to tell how many students prefer each.
Since we know the ratio is 2:1, then to find the number of students who like iced tea we convert the ratio to a fraction:
[tex]\frac{1}{2}[/tex]this means that one of two students preferred iced tea.
To find the number of students who prefer iced tea we multiply the total number of students by the fraction, then:
[tex]39\cdot\frac{1}{2}=\frac{39}{2}=19.5[/tex]Since we can't have a fraction of a student, we conclude that 19 students prefer iced tea and 20 prefer lemonade.
write each of the following numbers as a power of the number 2
Answer
The power on 2 is either -3.5 in decimal form or (-7/2) in fraction form.
Explanation
To do this, we have to first note that
[tex]\begin{gathered} \sqrt[]{2}=2^{\frac{1}{2}} \\ \text{And} \\ 16=2^4 \end{gathered}[/tex]So, we can then simplify the given expression
[tex]\begin{gathered} \frac{\sqrt[]{2}}{16}=\frac{2^{\frac{1}{2}}}{2^4}=2^{\frac{1}{2}-4} \\ =2^{0.5-4} \\ =2^{-3.5} \\ OR \\ =2^{\frac{-7}{2}} \end{gathered}[/tex]Hope this Helps!!!
Question 39.Find the inverse of the given function. Graph both functions on the some set of axes and show the line y=x as a dotted line in the graph.
First, to find the inverse of a function, call the original function "x" and call call "x" in the original function as the inverse function:
[tex]\begin{gathered} f(x)=5x+1 \\ x=5f^{-1}(x)+1 \end{gathered}[/tex]Now, we solve for the inverse function:
[tex]\begin{gathered} x=5f^{-1}(x)+1 \\ 5f^{-1}(x)+1=x \\ 5f^{-1}(x)=x-1 \\ f^{-1}(x)=\frac{x}{5}-\frac{1}{5} \end{gathered}[/tex]To graph lines, we can find two points in it and draw a line that passes through both.
Let's pick x = 0 and x = 1 for the first equation:
[tex]\begin{gathered} f(0)=5\cdot0+1=1 \\ f(1)=5\cdot1+1=6 \end{gathered}[/tex]So, we plot the points (0, 1) and (1, 6).
For the inverse, we can simply invet the coordinates, which is the same as picking x = 1 and x = 6:
[tex]\begin{gathered} f^{-1}(1)=\frac{1}{5}-\frac{1}{5}=0 \\ f^{-1}(6)=\frac{6}{5}-\frac{1}{5}=\frac{5}{5}=1 \end{gathered}[/tex]Thus, we have the points (1, 0) and (6, 1).
The line y = x is jus the diagonal that passes though point (0, 0) and (1, 1), for example.
Putting these points and drawing the lines, we get:
I resolved this problem for a test already but it looks like the graph it’s not ok can you help me?
SOLUTION
The function given is
[tex]f(x)=2x+1[/tex]To obtain the slope, we compare the equation above with the standard form of a slope intercept form.
Hence,, slope intercept is given as
[tex]\begin{gathered} y=mx+c \\ \text{Where m=slope.c=intercept on y (0,c)} \end{gathered}[/tex]Comparing with the function given, we have
[tex]\begin{gathered} M=2,c=1 \\ \text{Hence } \\ \text{slope}=2,\text{ y-intercept=(0,1)} \end{gathered}[/tex]Therefore
The slope = 2 and the y-intercept= (0,1 )
The graph of the functionis given in the image below
Henry has 3 3/5 metres of rope, and Sam has a piece of rope that is 1 1/2 metres
shorter. What is the total amount of rope that the boys have together?
A rational number is one that can be stated mathematically as the ratio or fraction p/q of two numbers, where p and q are the numerator and denominator, respectively. For instance, every integer and 3/7 are rational numbers.
The answer to the puzzle is 21 divided by ten.
What factors make a number rational?
It is possible to express rational numbers in the form pq, where p and q are integers and q0. Fractions cannot have a negative numerator or denominator, which is what distinguishes them from rational numbers.
Rates and ratios compare two different numbers. Simply put, a rate is a particular kind of ratio. The distinction is that a rate involves comparing two numbers.
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Which statement best describes the area of the triangle shown below?
ANSWER
Option D - The area of this triangle is one-half of that of a square that has area of 12 square units
EXPLANATION
We want to the best description of the area of the triangle given.
To do this, we have to first find the area of the triangle.
The area of a triangle is given as:
[tex]A\text{ = }\frac{1}{2}(b\cdot\text{ h)}[/tex]Where b = base and h = height
From the diagram, we have that:
b = 4 units
h = 3 units.
Therefore, the area of this triangle is:
[tex]\begin{gathered} A\text{ = }\frac{1}{2}(4\cdot\text{ 3)} \\ A\text{ = }\frac{1}{2}(12) \\ A\text{ = 6 square units} \end{gathered}[/tex]Checking through the options, we see that the only correct option is Option D.
This is because the area of this triangle (6 square units) is one-half of that of a square that has area of 12 square units
want to graph xdont you need to find out what x is?-3x-6y=0
We have a equation of a line in the form:
[tex]-3x-6y=0[/tex]This goes through the point (0,0).
With another point, we can graph the line.
For example, for x=2, we have:
[tex]\begin{gathered} -3(2)-6y=0 \\ -6-6y=0 \\ -6y=6 \\ y=-1 \end{gathered}[/tex]So the point (2,-1) belongs to the line.
We can graph the line passing through those points:
StatusRecovery8Help ResourcessAABC ~ AXYZFind the missing side length, s.B.3 65А&Х-ZCross multiplySE ][?] = [ ]153s
Since triangles ABC and XYZ are similar, the ratio between their corresponding sides is constant; thus,
[tex]\begin{gathered} \frac{AB}{XY}=\frac{BC}{YZ} \\ \Rightarrow\frac{3}{5}=\frac{6}{s} \end{gathered}[/tex]Solving for s,
[tex]\begin{gathered} \frac{3}{5}=\frac{6}{s} \\ \Rightarrow\frac{3}{5}\cdot s=\frac{6}{s}\cdot s \\ \Rightarrow\frac{3s}{5}=6 \\ \Rightarrow\frac{3s}{5}\cdot5=6\cdot5 \\ \Rightarrow3s=30 \\ \Rightarrow s=\frac{30}{3} \\ \Rightarrow s=10 \end{gathered}[/tex]Thus, the result of the cross multiplication is 3s=30 and the answer is s=10
Solve the inequality and write the solution using:
Inequality Notation:
The answer of the given inequality is x < 16
Difference between equality and inequality equations
Both mathematical phrases, equations and inequalities, are created by connecting two expressions.The equal sign (=) indicates that two expressions in an equation are believed to be equivalent. The symbols show that the two expressions in an inequality are not always equal: >, <, ≤ or ≥. Or in simple words the equation which has '=' sign is an equality equation while the inequality equation has the signs are >, <, ≤ or ≥.
The inequality expression is ,
(1 * x) /4 < 4 or x/4 < 4
=> x < 4 * 4
=> x < 16
Therefore, the answer is x < 16.
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Expand and simplify 3(3x - 4) - 2(2x - 1)
Answer:
5x-10
Step-by-step explanation:
expand to 9x-12-4x+2
collect like terms.
5x-10
