The area of the rectangle is given as 16 units squared
The length = x
The width = x-6
The area of a rectangle is given by the formula;
A= l * w
A= x {x-6}
16 = x^2 -6x -----------form a quadratic equation as;
[tex]x^2-6x-16\text{ =0}[/tex]Find the factors of -16 that can add or subtract to give -6
The factors will be -8 and 2
Factorize the equation as ;
[tex]x^2+2x-8x-16=0[/tex][tex]x(x+2)-8(x+2)=0[/tex][tex](x+2)(x-8)=0[/tex]Finding the real values of x , take that which will result to a positive length
( x-8) = 0
x-8 = 0
x= 8 units
So ; Length = x = 8 units
Width = x- 6 = 8-6 = 2 units
Answers
Length = 8 units
Width = 2 units
The following are the amounts contributed by 6 friends contributed fortrekking.$2, $9, $8, $7, $9, $7Find the standard deviation.
The given data are
2, 9, 8, 7, 9, 7
To find the standard deviation we will find the mean at first
[tex]Mean=\frac{sum}{no.}[/tex]The sum = 2 + 9 + 8 + 7 + 9 + 7 = 42
The no. = 6, then
[tex]\begin{gathered} Mean=\frac{42}{6} \\ \\ Mean=7 \end{gathered}[/tex]Then we will square the difference between each number and the mean
[tex]\begin{gathered} (2-7)^2=25 \\ (9-7)^2=4 \\ (8-7)^2=1 \\ (7-7)^2=0 \\ (9-7)^2=4 \\ (7-7)^2=0 \end{gathered}[/tex]Add all the answers
[tex]\sum_^(x-M)^2=25+4+1+0+4+0=34[/tex]Divide it by the no. and find the square root
[tex]\begin{gathered} \sigma=\sqrt{\frac{\sum_^(x-M)^2}{N}} \\ \\ \sigma=\sqrt{\frac{34}{6}} \\ \\ \sigma=2.380476143 \end{gathered}[/tex]The standard deviation is about 2.38 to the nearest hundredth
i need help on this, please help me if you can.
Given:
We're given two sections right and left and we need to match the correct options relating to each other.
Step-by-step solution:
1) We're given a diagram of a line passing through the circle and cutting two points on the circle.
Answer: Secant
2) A segment between the center of the circle and the point on the circle:
Answer: Radius
3) The distance along the circle, between two points of the circle:
Answer: Arc length
4) A figure of line cutting on one point of the circle:
Answer: tangent
5) The distance around a circle:
Answer: Circumference
6) A figure of a line joining two points of the circle (not passing through the circle):
Answer: Chord
# 8-13 classifying the polygon the number of sides.Tell weather the polygon is equilateral,equilangular,or regular. Explain your answer
EXPLANATION:
8..This is an octagon and it is a regular polygon because its sides and interior angles are equal or measure the same.
9.This is a pentagon and it is a regular polygon because its sides and interior angles are equal or mesure the same.
10.This is an equilateral triangle that means that its three sides are equal, and its three internal angles are also equal.
11.This triangle has two equal sides and one unequal, which is why it is an obtuse triangle;that is, it is equiangular, it only has two equal sides.
12.This is a regular square because all four sides are equal.
13.This is an equiangular polygon is a type of polygon whose vertex angles are equal. they are equiangular polygons because they alternate sides of two lengths.
Aidan walked 440 feet in one minute. Find his average rate in miles per hour.
Take into account the following equivalences as conversion factors:
1 mi = 5280 ft
1 h = 60 min
Then, you have:
[tex]440\frac{ft}{\min}\cdot\frac{1mi}{5280ft}\cdot\frac{60\min }{1h}=5mph[/tex]Hence, the average rate is 5 miles per hour
What is the slope of a line that is perpendicular to y = 2x - 6?a.2b.-1/2c.-2d.1/2
When two lines are perpendicular to each other, their slope are inverted. This means that if the slope of a line is "m", then the one that is perpendicular to it should be "-1/m". The slope-intercept equation of a line is given by:
[tex]y=mx+b[/tex]Where "m" is the slope. The line from this problem has the slope equal to 2, therefore the slope of the line that is perpendicular to it is:
[tex]m_2\text{ = }\frac{1}{m}=-\frac{1}{2}[/tex]I NEED THIS ASAP!!!
The Helping Hands Student Club set a goal to raise $2,000 by the end of the school year for a project. After 3 months, it reaches 37% of its goal. How much was raised during the first 3 months?
Answer:
$740
Step-by-step explanation:
You want to know the amount that is 37% of $2000.
AmountThe amount can be found by multiplying the fraction by the total:
0.37 × $2000 = $740
During the first 3 months, $740 was raised.
<95141404393>
What is the surface area of 1 Katie's chests? What is the surface area of all four chests Katie needs to paint?
We have to add the areas from A to F.
We then can write:
[tex]S=A+B+C+D+E+F[/tex]As each area is a rectangle, the area is the product of the sides.
We can also simplify and see that:
[tex]A=E=16\cdot13=208[/tex][tex]B+C+D+F=25\cdot(13+16+13+16)=25\cdot58=1450[/tex]Then:
[tex]\begin{gathered} S=A+(B+C+D+F)+E \\ S=208+1450+208 \\ S=1866in^2 \end{gathered}[/tex]The surface of one chest is 1866 square inches.
The four chests will represent:
[tex]4\cdot1866=7464in^2[/tex]If each can paints 933 square inches, she will need:
[tex]\frac{7464}{933}=8\text{ cans}[/tex]Answer:
Each chest has a surface of 1866 sq. in.
The four chest represent 7464 sq. in. of surface area.
She needs 8 cans of paint to paint all 4 chests.
How did I get this wrong I need help with this problem ( please show work) P.s I don’t know what’s wrong with the quality
Answer:
a. 0.01%
b. 99.22°F
Explanation:
We know that the temperature follows a normal distribution with a mean of 98.18 °F and a standard deviation of 0.63 °F.
Part a.
If 100.6 °F is the lowest temperature that they consider fewer, we need to calculate the following probability
P( T > 100.6)
To calculate this probability, we first need to standardize 100.6 as follows
[tex]\begin{gathered} z=\frac{temp\text{ - mean}}{\text{ standard deviation}} \\ \\ z=\frac{100.6-98.18}{0.63}=3.84 \end{gathered}[/tex]Therefore, the probability is equivalent to
P(T > 100.6) = P(Z > 3.84)
Now, we need to use the table for positive z scores, but it gives the probability P (Z < z), so we can calculate P(Z > 3.84) as follows
P(Z > 3.84) = 1 - P(Z < 3.84)
P(Z > 3.84) = 1 - 0.9999
P(Z > 3.84) = 0.0001
Therefore, the percentage is 0.0001 x 100% = 0.01%. So 100.6 °F is appropiate because the probability that a healtly person is considered to have fewer is 0.01%
Part b.
If we want a temperature such that 5.0% exceed it, we need to find a value of z that satisfies
P(Z > z) = 0.05
P(Z < z) = 1 - 0.05
P(Z < z) = 0.95
Using the table, we get that z = 1.645. Then, we can find the temperature as follows
[tex]\begin{gathered} \text{ temp = z}\cdot\text{ \lparen standard deviation\rparen + mean} \\ \text{ temp = 1.645\lparen0.63\rparen+98.18} \\ \text{ temp = 1.036+98.18} \\ \text{ temp = 99.22 }\degree F \end{gathered}[/tex]Therefore, the answer for part b is 99.22°F
A researcher randomly purchased several different kits of a popular building toy. The following table shows the number of pierces in each kit in the sample. Find the mode of the data
The modes of the data are 62, 282, and 367
Explanation:The mode of a distibution is the number with the highest frequency. That is, the number with the highest number of appearances.
By considering the data in the table shown:
62 appears twice
282 appears twice
367 appears twice
The other numbers appear only one time each
This means that the distribution is multimodal
The modes of the data are 62, 282, and 367
I'm not sure how to start this problemApproximate (b) to nearest 10th
ai) y = 3.32673x + 86.32673
ii) r = 0.944502376
b) 179.5 cm
Explanation:Regression equation model is in the form:
[tex]\begin{gathered} y\text{ = ax + b} \\ a\text{ = slope} \\ b\text{ = y-intercept} \end{gathered}[/tex]To get the model that shows the relationship between x and y, we will use a regression calculator:
[tex]\begin{gathered} \text{The model is given by:} \\ y=3.32673x+86.32673 \end{gathered}[/tex]ai) a = slope, b = y-intercept of the function
[tex]\begin{gathered} \text{from the model we got:} \\ m\text{ = }3.32673 \\ \text{slope = }3.32673 \\ b\text{ = y-intercept} \\ b\text{ = }86.32673 \end{gathered}[/tex][tex]\begin{gathered} aii)\text{ r = correlation coefficient} \\ r\text{ = }\frac{S_{xy}}{\sqrt[]{S_{x\times\text{ }\times}S_{yy}}} \\ \\ \text{From the model, r = }0.944502376 \end{gathered}[/tex]b) when feet = 28 cm long, height = ?
x = 28, y = ?
[tex]\begin{gathered} \text{substitute for x in the model:} \\ y=3.32673x+86.32673 \\ y=3.32673(28)+86.32673 \\ y=\text{ }179.47517 \end{gathered}[/tex]To the nearest tenth number, the height 179.5 cm
Find the measure Z BCD in thefollowing parallelogram.ADх2x2xХСBmZBCD = [ ? 10
Ok, so
We got the following parallelogram:
We want to find the value of the angle BCD.
For this, remember that the sum of the internal angles of a parallelogram must be always equal to 360°.
So, we could write:
[tex]\begin{gathered} 2x+2x+x+x=360 \\ 6x=360 \\ x=\frac{360}{6} \\ x=60 \end{gathered}[/tex]The value of x is equal to 60°. Now, the angle BCD is an angle that measures 2x degrees.
So, BCD measures 2*60, which is 120°.
Use a system of linear equations with two variables and two equations to solve.
A number is 11 more than another number. Twice the sum of the two numbers is 14. Find the two numbers. (Enter your answers as a comma-separated list)
In order to solve linear equations in two variables two equations are needed. The solution of the equations 2(x + y) = 14 and y = 11 + x is x = -2 and y = 9.
What is a system of linear equations?A system of linear equations is a group of equations having same number of variables and degree.
For the n number of variables n number of equations are required.
On the basis of number of solutions a system of equations can be classified as consistent and inconsistent.
Given that,
One of the number is 11 more than the other,
And, twice the sum of two numbers = 14.
Suppose one of the number be x.
And, the other number is y.
Then as per the question the pair of equations can be formed as,
2(x + y) = 14 (1)
y = 11 + x (2)
In order to solve these equations, multiply equation (2) by 2 and then substract it from equation (1) as,
2(x + y) - 2y = 14 - 2(11 + x)
=> 2x = 14 - 22 - 2x
=> 2x + 2x = -8
=> 4x = -8
=> x = -2
Substitute x = -2 in equation (2) to obtain y as,
y = 11 - 2
y = 9.
Hence, the equations for the given case are 2(x + y) = 14 and y = 11 + x and their solution is x = -2 and y = 9.
To know more about system of equations click on,
brainly.com/question/24065247
#SPJ1
Which of these square numbers also happens to be the sum of two smaller square numbers? Select one:a. 16b. 25c. 36d. 49
Notice that:
[tex]25=9+16.[/tex]Recall that:
[tex]\begin{gathered} 3^2=9, \\ 4^2=16. \end{gathered}[/tex]Answer: Option b.
can you tell me if I did the equation right
Answer: The equation is correct
Clearly and neatly show all work for each problem. Round all final answers to thenearest dollar. Do not round intermediate work.Fitzwilliam is buying a new car. The sticker price for the base model is $10,000,but the options he wants will cost him an extra 15%. He then talks the dealer intogiving him 10% off. Fitzwilliam has also decided to put down a 25% downpayment on the car.Find Fitzwilliam's down payment on the car.Find the balance that Fitzwilliam needs to finance.
Given:
Sticker price of car = $10,000
His options will cost him extra 15% = 0.15
Percentage discount = 10% = 0.10
Down payment = 25% = 0.25
Let's solve for the following:
• (a). Find Fitzwilliam's down payment on the car.
Given that his options will cost him extra 15% and he got a percentage discount of 10%, the total amount he will pay for the car will be:
[tex]\begin{gathered} T=10000(1+(0.15-0.10)) \\ \\ T=10000(1+0.05) \\ \\ T=10000(1.05) \\ \\ T=10500 \end{gathered}[/tex]The total cost of the car will be $10,500
Now, to find the down payment, we have:
Down payment = 25% of Tottl cost
Down payment = 0.25 x 10500
Down payment =2625
Therefore, his down payment s $2625
• (,b). Find the balance that Fitzwilliam needs to finance.
To find the amount he needs t balance, apply the formula:
Balance = Total cost - down payment
Balance = 10500 - 2625
Balance = 7875
Therefore, the balance he will need to finance is $7875
ANSWER:
(a). $2625
(b). $7875
Meiling has 1/ 1 4 liter of orange juice. She drinks 1/3 liter how much orange juice does she have left
Litres left can be solve as shown below
[tex]\begin{gathered} 1\frac{1}{4}\text{ - }\frac{1}{3} \\ using\text{ the LCM, we have} \\ \frac{5}{4}-\frac{1}{3} \\ \frac{15\text{ - 4 }}{12}=\frac{11}{12} \end{gathered}[/tex]how do I find AC if AE = x + 50 and CE = x + 32
ANSWER
AC = 18
EXPLANATION
Let us draw a diagram to represent the situation:
From the diagram, we see that:
AC + CE = AE (since they are colinear)
So, we have that:
AC + x + 32 = x + 50
=> AC = x + 50 - x - 32
AC = 18
That is the value of AC.
A prism is completely filled with 72 cubes that have edge lengths of 1/2 in.What is the volume of the prism?Enter your answer in the box. in³
Given:
A prism is completely filled with 72 cubes that have edge lengths of 1/2 in.
Required:
To find the volume of the prism.
Explanation:
The volume of the each cube is
[tex]\begin{gathered} =(\frac{1}{2})^3 \\ \\ =\frac{1}{8}in^3 \end{gathered}[/tex]So the volume of the complete prism is
[tex]\begin{gathered} =72\times\frac{1}{8} \\ \\ =9in^3 \end{gathered}[/tex]Final Answer:
The volume of the prism is
[tex]9in^3[/tex]Question Help 7.4.PS-12 Juan is designing an exercise room in his house. How many square feet of rubber flooring will he need to cover the floor? The product is sold in whole square yards. How many square yards should he buy? Explain. 10 ft 3 ft 9 ft 13 ft TUJIU . une lola alea O Te exeICISE TOUNT IS THIS IS also the lurar ammouTCOI Tuppen Houming mat Juan must have. (Type a whole number.) The number of square yards equivalent to this totallarea is 11.4 square yards. (Round to the nearest tenth as needed.) Since rubber flooring is sold in whole sq. yards, Juan must purchase exactly square yards. (Round up to the nearest square yard.) Enter your answer in the answer box and then click Check Answer. Check Answer Clear All All parts showing Review progress Next → Question Back of 10 6
The figure can be divided into a 2 shape. It can be divided into 2 rectangle. Let us find the individual areas and sum to get the area of the entire figure.
Area of first rectangle
[tex]\begin{gathered} \text{area}=lw \\ \text{area}=3\times4=12ft^2 \end{gathered}[/tex]Area of the second rectangle
[tex]undefined[/tex]Swimming pool A is 20 yards long and 10 yards wide. Swimming pool B is 40 yardslong and 20 yards wide.Pool A20 ydsPool B20 deIn terms of area, how many times bigger is Pool B in relation to Pool A?The area of Pool B is ten times the area of Pool A.The area of Pool B is 50 percent larger of Pool A.The area of Pool B is four times the area of Pool A.The area of Pool B is twice the area of Pool A.Both pools have the same area
Data
Swimming pool A Swimming pool B
20 yards long 40 yards long
10 yards width 20 yards width
Area of a rectangle
Area = length x width
Substitution
Area A = 20 x 10 Area B = 40 x 20
Simplification
Area A = 200 yards 2 Area B = 800 yards 2
Proportion
Area B/A = 800 / 200
Result
Area B/A = 4
The area of Pool B is four times the area of Pool A.
Consider the equation V = 4h where V is the volume (in cubic centimeters) of a box with a variable height h in centimeters and a fixed base of area 4 cm².
complete the table below to satisfy
Using linear function given, the value of v when h is 2, 6, 7 and 9 are 8cm³, 24cm³, 28cm³ and 36cm³ respectively
Linear FunctionA linear function is a function that represents a straight line on the coordinate plane. For example, y = 3x - 2 represents a straight line on a coordinate plane and hence it represents a linear function. Since y can be replaced with y, this function can be written as y = 3x - 2.
In the relation, V = 4h. All we need to do is substitute the value of h into the formula and find v for that value of h.
When h = 2
v = 4h
v = 4 * 2 = 8cm³
When h = 6
v = 4 * 6 = 24cm³
when h = 7
v = 4 * 7 = 28cm³
when h = 9
v = 4 * 9 = 36cm³
Learn more on linear function here;
https://brainly.com/question/4025726
#SPJ1
Look at the figure which now shows the value of x for DS. Write the similarity ratio as a fraction in simplest form
Since both figures are similar, we have the following proportions:
[tex]\frac{HP}{GD}=\frac{PT}{DS}[/tex]in this case, we have that HP=4, GD=8, PT=6 and DS=12, then we have:
[tex]\frac{4}{8}=\frac{6}{12}[/tex]the ratio in its simplest form is 1/2, since:
[tex]\frac{6}{12}=\frac{4}{8}=\frac{1}{2}[/tex]Please help:The graph of f(x)=x^2 is shown. Use the parabola tool to graph the function g(x)=(12x)^2.To graph a parabola, first plot the vertex then plot another point on the parabola.
The equation of the graph show is given as
f(x) = x^2
Which can also be given as:
f(x) = x^2 - 12x + 17
Based on its form, it is a parabola.
First, we will factor the quadratic equation.
f(x) = (x - 9)(x - 3)
To lot the graph on x-y plane, we will generate a table by assigning values to x and then get the y values.
x y
1 16
2 7
3 0
0 27
-1 40
-2 55
-3 72
The height of the object at 1 second is what amount of feet?
If t= 1s. Then let's replace t-value in the equation:
[tex]\begin{gathered} \text{ -16t}^2\text{ + 1130= } \\ \text{ -16 \lparen1\rparen + 1130= } \\ \text{ -16 + 1130= } \\ 1,114\text{ feet. } \end{gathered}[/tex]The height of the object at 1 second is 1,114 feet.
A person wants to increase a (5 in. x 7 in.) photo to an (8 in. x 10 in.) but since the aspect ratios are not the same some of the picture will get chopped off. ti 8" original picture blown-up picture with frame shown What percentage of the picture can be used in the (8 in. x 10 in.) frame?
Using the properties of aspect ratio we calculate that approximately 89.3% of the picture will be used in the new frame.
The original picture has the dimension 5 × 7 inches .
The new dimension is 8 by 10.
Now let us consider that the height is 8 inches but the width will be x for the increased size picture.
Now we will us ratio to find the width.
original / new = 5/8 = 7 / x
or, x = 11.2 inches.
Area of the new picture = 11.2 × 8 = 89.6 square inches.
Area of the picture frame = 8 × 10 = 80 square inches.
Percentage of picture used
= 80 /89.6 × 100 %
= 89.268...
≈ 89.3%
Therefore using the properties of aspect ratio we calculate that approximately 89.3% of the picture will be used in the new frame.
to learn more about aspect ratio visit:
https://brainly.com/question/18492629
#SPJ9
Hi, no explication/steps required I just need the final answer
SOLUTIONS
Graph the vertical and horizontal asymptote of the function below:
[tex]f(x)=\frac{4}{x-4}[/tex]The above graph represent the vertical and horizontal asymptote of the function, using desmos calculator.
determine whether the following graphs are functions using the vertical line test. what is the vertical line test?
The vertical line test is a method that is used to determine whether a given relation is a function or not. The approach is rather simple. Draw a vertical line cutting through the graph of the relation, and then observe the points of intersection.
The vertical line test supports the definition of a function. That is, every x-value of a function must be paired to a single yy-value. If we think of a vertical line as an infinite set of x-values, then intersecting the graph of a relation at exactly one point by a vertical line implies that a single x-value is only paired to a unique value of y.
If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.
If a vertical line intersects the graph in some places at more than one point, then the relation is NOT a function.
With the above illustration,
Graph 3 is not a function using vertical test because it has infinitely many solutions
Graph 4 is not a function because the vertical cuts the graph and intersect at a points
Graph 5 is a constant function because it has a repeated value of x and a constant y value
Graph 6 is not a function because the x-values which is the domain is repeated for different values of y
Graph 7 is not a function because the vertical line cuts the graph at two-point
Graph 8 is a function because it has one point intersection and each value of x have a corresponding value of y
Solve for x. Round to the nearest tenth, if necessary.V4.1U43°W
For the angle 43 degree, perpendicular side is 4.1 and base side is x.
Determine the length of side x by using trigonometry.
[tex]\begin{gathered} \tan 43=\frac{4.1}{x} \\ x=\frac{4.1}{\tan 43} \\ =4.396 \\ \approx4.4 \end{gathered}[/tex]So value of x is 4.4
Find a linear inequality for the graph.y ≥ 3y > 3x ≤ 3x < 3
Given:
A graph is given
Required:
To tell whose inequality is this.
Explanation:
[tex]\begin{gathered} This\text{ graph shows the inequality of } \\ y\ge3 \end{gathered}[/tex]Required answer:
Option A is correct.
The cost of 42 grams of a nitric acid is $14.40. Type 1 nitric acid costs 45€ a gramtype 2 nitric acid costs 30¢ a gram. How many grams of each nitric acid were usecform the compound?
Solution:
Given:
Let the amount of Type 1 nitric acid used be represented by a
Let the amount of Type 2 nitric acid used be represented by b
Hence, the system of equations is;
[tex]\begin{gathered} Total\text{ }grams\text{ used is 42g} \\ a+b=42.................(1) \\ \\ \\ Cost\text{ of type 1 nitric acid is }0.45a \\ Cost\text{ of type 2 nitric acid is 0.30b} \\ Total\text{ cost of 42g used is \$14.40} \\ Hence, \\ 0.45a+0.30b=14.40...............(2) \end{gathered}[/tex]Thus, solving the system of equations simultaneously,
From equation (1),
[tex]\begin{gathered} a=42-b \\ \\ Substitute\text{ into equation \lparen2\rparen} \\ 0.45(42-b)+0.3b=14.4 \\ 18.9-0.45b+0.3b=14.4 \\ 18.9-0.15b=14.4 \\ 18.9-14.4=0.15b \\ 4.5=0.15b \\ \\ Hence, \\ \frac{4.5}{0.15}=b \\ b=30 \end{gathered}[/tex]Solving for a,
[tex]\begin{gathered} a=42-b \\ a=42-30 \\ a=12 \end{gathered}[/tex]Therefore, the answer is;
12 grams of Type 1 and 30 grams of Type 2