Let's begin by listing out the information given to us:
[tex]\begin{gathered} |XY|=x+7 \\ |XZ|=152 \\ |YZ|=2|XY|\Rightarrow|XZ|=|XY|+|YZ| \\ But\colon|YZ|=2|XY|\Rightarrow|XZ|=|XY|+2|XY|\Rightarrow|XZ|=3|XY| \\ |XZ|=3|XY| \\ But\colon|XY|=x+7,|XZ|=152 \\ 152=3(x+7)\Rightarrow152=3\cdot x+3\cdot7\Rightarrow152=3x+21 \\ 152=3x+21 \\ \text{Subtract 21 from each side, we have:} \\ 152-21=3x+21-21\Rightarrow131=3x\Rightarrow3x=131 \\ 3x=131 \\ \text{Divide each side by 3, we have:} \\ \frac{3x}{3}=\frac{131}{3}\Rightarrow x=43\frac{2}{3}\approx43.667\cong43.7 \\ x=43.7(ToNearestTenth) \end{gathered}[/tex]Carmen drove 240 miles using 9 gallons of gas. At this rate, how many gallons of gas would she need to drive 216 miles? gallons
We are given that 240 miles are driven using 9 gallons of gas. To determine the gallons of gas needed to drive 216 miles we use a rule of three like this:
[tex]\begin{gathered} 240mi\rightarrow9gal \\ 216mi\rightarrow x \end{gathered}[/tex]Now, we cross multiply:
[tex](240mi)x=(216mi)(9gal)[/tex]Now, we divide both sides by 240 mi:
[tex]x=\frac{(216mi)(9gal)}{240mi}[/tex]Now, we solve the operations:
[tex]x=8.1gal[/tex]Therefore, 8.1 gallons are needed.
A manager chooses 2 months of the year during which to have training. What is the size of the sample space in this experiment?
The sample space refers to all possible ways of choosing two months. Since we have 12 months to choose from, the number of ways would be
12C2
We are applying combination because the order of the months doesn't matter. From our calculator,
12C2 = 66
the size of the sample space in this experiment is 66
PLS HELP ASAP POINTS WILL BE GIVEN AND BRAINY
make y the subject of this formula
W = [tex]\frac{5y -t}{r}[/tex]
Variable y as the subject of the formula of the equation W = ( 5y - t )/r is y = (Wr + t)/5
How to solve for y as a subject formula?The subject of a formula is simply a specific variable that is being worked out.
Given the formula in the question;
W = ( 5y - t )/r
To solve for y, first multiply both sides by r
W × r = ( 5y - t )/r × r
In the right side of the equation, r cancels out r.
W × r = ( 5y - t )
Wr = 5y - t
To isolate the term with y, add t to both sides
Wr + t = 5y - t + t
In the right side of the equation, t cancels out t.
Wr + t = 5y
Reorder equation
5y = Wr + t
Divide both sides by the coefficient of y
5y/5 = (Wr + t)/5
y = (Wr + t)/5
Therefore, solving for y as subject of the formula is y = (Wr + t)/5.
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help meeeeeeeeee pleaseee
The domain of the relation represented in the graph as given in the task content is; [2, infinity).
The range of the relation is; (-infinity, infinity).
What is the domain and range of the relation?It follows from the task content that the domain and range of the relation are to be determined from the graph given.
Since the range is the set of all possible output, y-values, it follows from the arrows in the graph that the range is the set of all real numbers and hence can be represented using interval notation as; (-infinity, infinity).
Also, the domain is the set of all possible input, x-values and can be determined from the graph as numbers greater or equal to 2 as 2 is the minimum of the curve.
Domain = [2, infinity).
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combining functions to write a new function that models a real world solution please help!!!
SOLUTION
The standard charge is
[tex]S=0.60M+18.95[/tex]And the insurance charge is
[tex]I=0.15M+4.80[/tex]The total cost will be given as:
[tex]C=S+I[/tex]Substitute for S and I into the equation
[tex]C=0.60M+18.95+0.15M+4.80[/tex]Simplify the equation:
[tex]C=0.75M+23.75[/tex]Therefore the required answer is:
[tex]C=0.75M+23.75[/tex]Determine whether A ABC is similar to ADEF. If so state how do you know.E
Given data:
In triangle DEF ,
DF = 25
DE = 41
EF = 40
In triangle ABC,
AB = 96
AC = 61
BC = 96
From above it is clear that , corresponding sides of triangle are not similar
Therefore, the triangle are not similar.
Solve for n1/2(12n- 4) =14-10n
1/2(12n- 4) =14-10n
First, apply the distributive property to solve the parenthesis
1/2 (12n)+1/2 (-4) = 14-10n
6n-2 =14-10n
Combine like terms
6n+10n = 14+2
16n=16
Divide both sides of the equation by 16
16n/16 =16/16
n= 1
Name the quadrant in which each of the points lies -1, -8
Given the point ( -1, -8 )
The x-coordinate of the point = -1
The y-coordinate of the point = -8
So, x < 0, y < 0
So, the point lies in the third quadrant
So, the answer will be Quadrant 3
x+6=4x+1-3xsolve for x
we place the x's on the same side and the number on the other side
[tex]\begin{gathered} x-4x+3x=1-6 \\ (1-4+3)x=-5 \\ 0x=-5 \\ 0=-5 \end{gathered}[/tex]x is removed, and equality is meaningless, so x has no solution
Please help with the problem
An equilateral triangle has an
area of 97.5 square meters. If the
height of the triangle is 13 meters,
find the perimeter of the triangle.
The perimeter of the equilateral triangle is 45 meters.
What is the perimeter?An equilateral triangle is a polygon that has three sides that are of equal length. The sum of angles in an equilateral triangle is 180 degrees. The perimeter of an equilateral triangle is the distance round the triangle. It can be determined by adding the length of the three sides of the triangle together.
The first step is to determine the side length of the triangle. The base can be determined from the area.
Area of a triangle = 1/2 x base x height
97.5 = 1/2 x 13 x b
b = (97.5 x 2) / 13
b = 15 meters
Perimeter = 15 x 3 = 45 meters
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The dimensions of portable kennel can be expressed as width x, height x-0.2 and length x+0.4.What are dimensions of portable kennel with a volume of 7.4 ft^3?Use a graphing calculator to solve.
Assuming the portable kennel is a box (rectangular prism), the volume is:
[tex]V=WHL[/tex]Where W is the width, H is the height, and L is the length.
We are given the values:
W = x
L = x + 0.4
H = x - 0.2
The volume is:
[tex]V=x(x+0.4)(x-0.2)[/tex]The volume is known to be 7.4, thus:
[tex]x(x+0.4)(x-0.2)=7.4[/tex]We cannot directly solve the equation by algebraic methods, so we use a graph. Define the function:
[tex]y=x(x+0.4)(x-0.2)-7.4[/tex]We need to find the value of x that makes the value of y equal to 0.
The graph of the function is shown below:
We can see the solution for x is a value near x = 1.8. Zooming the graph around the solution:
Now we have a more accurate solution at x = 1.9.
The dimensions of the kennel are:
W = 1.9
L = 1.9 + 0.4 = 2.3
H = 1.9 - 0.2 = 1.7
Checking: 1.9 × 2.3 × 1.7 = 7.43
The volume is approximately equal to 7.4
Find the missing number so that the equation has no solutions.
?missing number? x+18=5x–12
Answer:
x=1.5
Step-by-step explanation:
Simplifying
5x + 12 + -1x = 18
Reorder the terms:
12 + 5x + -1x = 18
Combine like terms: 5x + -1x = 4x
12 + 4x = 18
Solving
12 + 4x = 18
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-12' to each side of the equation.
12 + -12 + 4x = 18 + -12
Combine like terms: 12 + -12 = 0
0 + 4x = 18 + -12
4x = 18 + -12
Combine like terms: 18 + -12 = 6
4x = 6
Divide each side by '4'.
x = 1.5
Simplifying
x = 1.5
Answer:
Firstly: collect like terms
Secondly: simplify
Lastly: divide the number you got from the one without the letter x by the number you got with the letter x
Over a specified distance, rate varies inversely with time. If a car on a test track goes a certaindistance in one-half minute at 166 mph, what rate is needed to go the same distance intwo-thirds minute?
124.5 mph is needed to go the same distance in two-thirds minute
Explanation:Let rate = r
and time = t
Since rate varies inversely with time, we have:
r = k/t ....................................................(1)
Where k is constant
Given
r = 166 mph, and t = 1/2, we can find the value of k as follows:
166 = k/(1/2)
k = 1/2 * 166
= 83
Substituting the value of k into equation (1)
r = 83/t ....................................................(2)
For r = ? and t = 2/3, we have:
r = 83/(2/3)
= 83 * 3/2
= 124.5 mph
124.5 mph is needed to go the same distance in two-thirds minute
10. Dice A has six sides and dice B has ten sides. What is the probability of NOT rolling a 1 with both dice A and dice B?
Answer:
66.7 percent hope this helps
Step-by-step explanation:
Determine whether the statement is always, sometimes, or never true. Complete the explanation.If line m is parallel to linen and the slope of line m is greater than 1, then the slope of linen is greaterthan 1.This statement is (select) true. If line m is parallel to line n, then the lines have (select)slope. Therefore, if the slope of line m is greater than 1, the slope of line m (select) greater than 1.
The given statement is
If line m is parallel to linen and the slope of line m is greater than 1, then the slope of linen is greater
than 1.
This statement is always true because parallel lines have the same exact slope, otherwise they wouldn't be parallel.
Therefore, the complete statement would be
This statement is always true. If line m is parallel to line n, then the lines have an equal slope. Therefore, if the slope of m is greater than 1, the slope of n is always greater than 1.
I NEED THIS ANSWER SOON!
Rewrite the expression 6a + 21 to demonstrate the distributive property. Describe how the rewritten expression can be verified to be equivalent to 6a + 21.
Answer:
it can be verified as 2a + 7
help me please
thank you
Answer:
is a functiondomain: [-6, 2]range: [-4, 0]Step-by-step explanation:
You want to know if the graph of the semicircle centered at (-2, 0) with radius 4 extending below the x-axis is a function. You also want to know its domain and range.
FunctionThe graph passes the vertical line test. That is, no vertical line intersects the graph in more than one place. That means the relation is a function.
DomainThe domain of the function is the horizontal extent of the graph. The solid dots at the extreme points of (-6, 0) and (2, 0) indicate those points are part of the domain. The domain also includes all x-values between them. In interval notation, the domain -6 ≤ x ≤ 2 is written as ...
[-6, 2]
RangeThe range is the vertical extent of the graph. The semicircle extends from a low point of (-2, -4) to high points on the x-axis. Thus its range is -4 ≤ y ≤ 0, written in interval notation as ...
[-4, 0]
__
Additional comment
The brackets used in interval notation are square brackets if the end points are included in the interval. Otherwise, they are round brackets (parentheses).
PLEASE HELP ASAPPPP!!!
Create a scatter plot using the data below.
week 1: $27,188,270 week 2: $34,664,856 week 3: $38,086,246 week 4: $40,603,493 week 5: $42,272,097 week 6: $43,514,327 week 7: $44,665,033 week 8: $45,900,553 week 9: $46,861,913 week 10: $47,881,047. Be sure to label your x and y axis and use appropriate scales and consistent intervals for each axis.
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities or events, scatter plots are crucial in statistics (called variables).
Explain about scatter plot?In an effort to demonstrate the degree to which one variable is influenced by another, scatter plots are used to plot data points on a horizontal and vertical axis. The values of the columns set on the X and Y axes determine the position of the marker that represents each row in the data table.
A scatter plot is a form of plot or mathematical diagram that uses Cartesian coordinates to display values for typically two variables for a collection of data. It is also known as a scatter graph, scatter chart, scatter gram, or scatter diagram.
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When moving from Chicago to Milwaukee, your salary went from $65,000 per year to $55,000 per year. By what percent does your salary decrease? Round your answer to the nearest tenth of a percent (one decimal place).
Data:
Initial salary: $65,000
Salary after decrease: $55,000
To find the percentage of decrease you use the next formula:
[tex]D=\frac{O-N}{O}\cdot100[/tex]Where:
D is the percentage of decrease
O is the original value
N is the new value
Then, you have the next:
O=$65,000
N= $55,000
[tex]\begin{gathered} D=\frac{65000-55000}{65000}\cdot100 \\ \\ D=\frac{10000}{65000}\cdot100 \\ \\ D=0.1538\cdot100 \\ \\ D=15.38 \end{gathered}[/tex]Then, the percentage of decrease is 15.4% (round to the nearest tenth)Using the graph, determine the value of the slope. y What is the slope? 2. e about the graph? -3 -2 Y 2 0 -2 3 no slope 4
What is a slope?
It shows how inclinated is a line. It goes from zero, 0 (no inclination - horizontal line), no infinity (total inclination - vertical line).
It can also be representated by negative numbers
Since the line of the graph is horizontal, we can say its slope, m, is given by zero : m = 0Use the picture to fill in the green box Inequalities in two triangles
Step 1
Given;
Step 2
The size of the angle facing any side of a triangle determine how size or length of that side. The bigger the angle, the longer the side.
In a triangle, the largest side is opposite the largest angle and vice versa and the shortest side is opposite the smallest angle and vice versa
[tex]\begin{gathered} The\text{ angle facing x=63}^{\circ} \\ The\text{ angle facing y=62}^{\circ} \end{gathered}[/tex]Thus, 63 is bigger than 62. So we conclude that;
[tex]x>y[/tex]Answer;
the grades on the second statistics test for Mr. Montgomery’s class are in the following list. complete the frequency distribution table for the grades. A,A,D,D,A,B,A,D,D,D,F,F,C,C,A,C,B,A,C,F,F
The frequency table can be filled by counting the number of each grades in the list.
The grade A is 6 times, grade B is 2 times, grade C is 4 times, grade D is 5 times, grade F is 4 times.
Answer:
Grade Frequency
A 6
B 2
C 4
D 5
F 4
Please solve with explanation so I can use as reference in the future thank you!
Answer:
x=24
Step-by-step explanation:
y = x*c
x=2, y=7
2*c=7 => c=7/2
x*7/2 = 84
x = 84*2/7
x = 12*2
x = 24
I hope this helps TwT
Put these numbersmin order from least to greatest 3/103/89/100.63
A hall has square tables that can seat 4 people each, When there are more than 4 people in a group, the tables are moved together. what is the greatest number of people who can sit at 7 tables lines up in a row?
28 people can sit on 7 tables in a row
Explanations:Number of people that can sit on a square table = 4
The greatest number of people that can sit on 7 tables = 7 x ( Number of people that can sit on a table)
The greatest number of people that can sit on 7 tables in a row = 7 x 4
The greatest number of people that can sit on 7 tables in a row = 28
Two tables are placed side by side. One table is 5 feet 4 inches wide, and the other is 5 feet 9 Inches wide. Together, how wide are they?Write your answer in feet and inches. Use a number less than 12 for inches.
The widths of the tables are 5 feet 4 inches wide and 5 feet 9 Inches wide.
The first step is to add the dimensions in feet. We have
5 + 5 = 10 feet
The next step is to ad the dimensions in inches. We have
4 + 9 = 13 inches
Recall,
1 foot = 12 inches
Thus means that 13 inches = 1 foot and 1 inch. Adding 1 foot and 1 inch to 10 feet, the total width would be
11 feet 1 inch
Suppose that x and y vary inversely and that y= 1/6 when x = 3. Write a function that models the inverse variation and find y when x = 10.
The function that models the inverse variation is: y = 1/2x.
When x = 10, y = 1/20.
What is a Function that Models an Inverse Variation?The function that models an inverse variation between two variables, x and y, can be expressed as:
y = k/x.
Given that y = 1/6 when x = 3, find the value of the constant, k, by substituting the values of x and y into y = k/x:
1/6 = k/3
Multiply both sides by 3
1/6(3) = k/3(3)
1/2 = k
k = 1/2.
The function for the inverse variation would be, y = 1/2/x
y = 1/2x
To find y when x = 10, substitute the value of x = 10 into the equation y = 1/2x:
y = 1/2(10)
y = 1/20
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which set of output values correctly completes the function table?
EXPLANATION
Applying the relationship output = input * 4 give us the appropiate y-value as shown as follows:
x y
-5 -5*4= -20
12 12*4 = 48
32 32*4 = 128
The answer is the second option.
is 0.49 a rational or irrational number? Explain how you know.
The decimal 0.49 is a rational number.
What is a rational number?Any number that can be expressed as a fraction and where the denominator (the bottom number) and the numerator (the top number) are both integers is considered a rational number. In other words, p/q, where p and q are both integers, can be used to represent a rational number.
A rational number is a number that can be expressed as a fraction where the numerator is a whole number and the denominator is a whole number .
In this case, 0.49 is the same as 0.49 over 1. In other words, it can be seen that 0.49 can be written with a numerator and denominator like 49/100.
Therefore, it's a rational number.
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