We can find the value of x, by using the property of issoceles triangle:
A isosceles triangle is a triangle that has two sides of equal length.
In the given figure, triangle have two sides of equal length 21, thus the given triangle is issoceles.
Since, the angle opposite to the equal sides are equal,
so, the third angle of the given triangle is x
The sum of all angles in a triangle is equal to 180 degrees.
In the given figure : x, x & 34
[tex]\begin{gathered} x\text{ + x +34=180} \\ 2x+34=180 \\ 2x=180-34 \\ 2x=146 \\ x=\frac{146}{2} \\ x=73 \end{gathered}[/tex]So, x = 73º
Answer: D) 73º
A group of people were asked "What time do you prefer to see a movie? The two way tablebelow represents the results by their age.Morning 4 2 12 25 4316-20 21-25 26-30 Over 30 TotalsAfternoon 8 12 18 32 70EveningTotals28 34 28 11 101Late Night 34 18 21 4 7774 66 79 72 291What the approximate probability that a person will be over 30 given they prefer afternoonmovies?
From theinformation given,
total number of people = 291
Number of persons over 30 that prefer afternoon movies = 32
Number of persons that prefer afternoon movies = 70
This is a conditional probability.
Recall, Probability of event A given event B = P(A and B)/P(B)
Thus,
Probability that a person will be over 30 given that they prefer afternoon movies = 32/70
By multiplying by 100, it becomes
32/70 x 100
= 46%
Probability that a person will be over 30 given that they prefer afternoon movies = 46%
A dilation by a scale factor od 2 centered at (2,-1) is performed on the triangle shown draw the resulting triange
Explanation:
The vertices of the triangle are:
• (2, -1)
,• (-3, -1)
,• (1,2)
The triangle is dilated by a scale factor of 2 with the center of dilation at (2, -1).
The coordinates of the image triangle are (-2,1), (0,5) and (-8, -1).
Answer:
The triangle and its image are attached below:
find the slope of the line passing through the points (-6,4) and (2,4)
To find the slope, we will use the formula below:
[tex]\text{slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]x₁= -6 y₁=4 x₂=2 y₂=4
substitute the values into the formula
[tex]\text{slope =}\frac{4-4}{2+6}[/tex][tex]\text{slope}=\frac{0}{8}[/tex][tex]\text{slope = 0}[/tex]A boat is heading towards a lighthouse, where Dalvin is watching from a vertical distance of 138 feet above the water. Round your answer to the nearest tenth of a foot if necessary.
To find the first distance we use:
[tex]\begin{gathered} tan13=\frac{138ft}{x} \\ x=\frac{138ft}{tan13º} \\ x=\frac{138ft}{0.23} \\ x=\text{ 600ft} \end{gathered}[/tex]For the second distance, we change 13º to 45º and 77º to 45º as well.
So:
[tex]\begin{gathered} tan45=\frac{138ft}{x} \\ 1=\frac{138ft}{x} \\ x=138ft \end{gathered}[/tex]So the distance from point A to B is=600ft - 138ft = 462ft
What is the positon of the letter E on the number line and how can i write it as a fraction or mixed number
We are asked to identify the position of the letter E on the number line.
First of all, count the total number of spacings between 2 and 3.
There are a total of 7 spacings.
The letter E is at the 6th spacing.
So, we can write the position of the letter E in the mixed form as
[tex]2\frac{6}{7}[/tex]We can also re-write the above mixed number as a fraction
[tex]2\frac{6}{7}=\frac{2\times7+6}{7}=\frac{14+6}{7}=\frac{20}{7}[/tex]So, the position of the letter E on the number line as a fraction is 20/7
A. Show all of your work to solve each equation and to check for extraneous solutions:4. [√(2x^2 - 1)]=x
ANSWER:
x = 1
STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\sqrt{2x^2-1}=x[/tex]We solve for x:
[tex]\begin{gathered} 2x^2-1=x^2 \\ \\ 2x^2-x^2=1 \\ \\ x^2=1 \\ \\ x=\sqrt{1}=\pm1 \\ \\ \text{ we check:} \\ x=1 \\ \\ \sqrt{2\left(1\right)^2-1}=1 \\ \\ \sqrt{2-1}=1 \\ \\ 1=1 \\ \\ x=-1\rightarrow\text{ true} \\ \\ \sqrt{2\left(-1\right)^2-1}=-1 \\ \\ \sqrt{2^-1}=-1 \\ \\ 1=-1\rightarrow\text{ false} \end{gathered}[/tex]Therefore, the solution of the equation is x = 1
Last year. Kareem deposited into an account that paid 4% interest per year and $6000 into an account that paid 9% interest per year. No with withdrawals were made from either account. No rounding needed What was the total interest earned at the end of 1 year? What was the percent interest for the total deposited?
Find the distance between the points (-5,4) and (-2,-1)
Answer
√34
Step-by-step explanation
Distance formula
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]where
• d: distance between two points
,• (x₁, y₁): coordinates of the first point
,• (x₂, y₂): coordinates of the second point
Substituting into the formula with the points (-5,4) and (-2,-1), we get:
[tex]\begin{gathered} d=\sqrt{(-2-(-5))^2+(-1-4)^2} \\ d=\sqrt{3^2+(-5)^2} \\ d=\sqrt{9+25} \\ d=\sqrt{34} \end{gathered}[/tex]How many routes does this function have Y= -2x^2+12x-10
We have that the equation is equal to
[tex]-2(x-1)(x-5)[/tex]So the equation have two roots, x = 1 and x = 5.
On a set of architectural drawings for a new school building the scale is 1/4 inch = 2 feet. Find the missing lengths of the rooms.
We have a scale for the drawing that is 1/4 inch = 2 feet.
This means that 1/4 inch in the drawing represent 2 feet in the real world.
1. Lobby.
The actual length is 16 feet.
If 2 feet are drawn in 1/4 inch (0.25), the drawing length is 2 inches
[tex]\frac{16*0.25}{2}=\frac{4}{2}=2[/tex]2. Principal's office
The drawing length is 1.25 inches.
We can calculate the actual length as:
[tex]1.25\cdot\frac{2}{0.25}=\frac{2.50}{0.25}=10[/tex]3. Library
The actual length is 20 feet.
We have discovered that we can transform this in drawing units (inches) multypling by 0.25/2=0.125.
[tex]20\cdot0.125=2.5[/tex]The drawing length is 2.5 inches.
4. School room
The drawing length is 3 inches.
We have discovered that we can transform this in actual length units by dividing by 0.125, or multiplying by 2/0.25=8:
[tex]3\cdot8=24[/tex]The actual length is 24 feet.
5. Science lab.
In the drawing has 1.5 inches, so we multiply by 8 and we get 1.5*8=12 feet.
The actual length is 12 feet.
6. Cafeteria
The actual length is 48 feet.
Then, the drawing length is 48*0.125=48/8=6 inches.
7. Music room
The drawing length is 4 inches.
Then, the actual length is 4*8=32 feet.
8. Gymnasium
The drawing length is 13 inches, so the actual length is 13*8=104 feet.
9. Auditorium
The actual length is 56 feet, so the drawing length is 56/8=7 inches.
10. Teachers lounge
The drawing length is 1.75 inches, so the actual length is 1.75*8=14 feet.
We can calculate the scale factor drawing to actual length as:
[tex]\frac{\text{drawing}}{\text{actual}}=\frac{\frac{1}{4}in}{2\text{ feet}}=\frac{1}{8}\cdot\frac{in}{\text{ feet}}\cdot\frac{1\text{ feet}}{12\text{ in}}=\frac{1}{96}[/tex]The scale is 1:96.
12) If the scale is 12 inches = 1 foot, the scale factor is:
[tex]\frac{\text{drawing length}}{\text{actual length}}=\frac{12\text{ in}}{1\text{ ft}}\cdot\frac{1\text{ ft}}{12\text{ in}}=1[/tex]The scale in this case is 1:1 (the drawing has the same size as the actual object).
14) We have a road which length is 30 cm.
The scale is 1 cm = 3.5 m.
We can calculate the actual length of the road as:
[tex]\text{Actual length}=30cm\cdot\frac{3.5\text{ m}}{1\text{ cm}}=105\text{ m}[/tex]The actual legth of the road is 105 meters.
in the figure below, points D, E, and F are the midpoints of sides ABC. suppose AC =58, DF =26, and AB =38. find the following lengths. DE, BC, and CE
The values of the lengths DE, BC, and CE are 29, 52, and 26 respectively which can be found out by using the relations for mid-points of triangle.
In the figure, it is given to us that -
Points D, E, and F are the midpoints of sides AB, BC, and AC of the ΔABC respectively.
AC = 58
DF = 26
and, AB = 38
We have to find out the values of the lengths DE, BC, and CE.
Now, AC = 58 is parallel to the mid-segment DE
=> The mid-segment DE is half of the AC.
=> DE = AC/2
=> DE = 58/2
=> DE = 29
Similarly, the mid-segment DF = 26 is parallel to BC
=> BC = Twice the mid-segment DF
=> BC = 2*26
=> BC = 52
Now, E is the midpoint of BC of the ΔABC.
=> CE = BC/2
=> CE = 52/2
=> CE = 26
Through the formulas for mid-points of triangle, we find out that the values of the lengths DE, BC, and CE are 29, 52, and 26 respectively.
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Karina purchased 5 yard a fabric costing $7.99/yard, two spools of thread at $1.25/spool and a pattern costing $5.25 . what was the total amount of her purchase before tax?
Given:
She purchased:
5 yard of fabric at $7.99/yard
2 spools of thread at $1.25/spool
1 pattern at $5.25
We can calculate the total amount of her purchase before tax by summing the cost of each item without tax.
The total amount:
[tex]\text{Total amount = cost of yard }\times\text{ number of yards purchased + cost of thread }\times\text{ number of spools + cost of pattern }\times Number\text{ of pattern}[/tex]Substituting we have:
[tex]\begin{gathered} \text{Total amount = 7.99}\times\text{ 5 + 1.25}\times2\text{ + 5.25 }\times\text{ 1} \\ =47.7 \end{gathered}[/tex]Hence, the total amount of her purchase before tax is $47.7
Answer: $47.7
Could you please help me out with this question ??
Given the polynomial function:
[tex]x^3-2x^2-x+2[/tex]Group the functions:
[tex](x^3-2x^2)-(x-2)[/tex]Factor out the greatest common factor from the parenthesis
[tex]\begin{gathered} x^2(x-2)-1(x-2) \\ (x^2-1)(x-2) \end{gathered}[/tex]Simplify fully to have:
[tex]\begin{gathered} (x^2-1)(x-2) \\ \lbrack(x^2-1^2)\rbrack(x-2) \\ (x+1)(x-1)(x-2) \end{gathered}[/tex]This gives the factored form of the given polynomial.
Type the equation for the graphbelow.Pi/3 2piy = [?] sin([ ]x)
To find the equation of the graph, what we do is to recognize some characteristics of a sine function:
- Amplitude: The amplitude of the sine function is the distance from the middle value or line running through the graph up to the highest point. In this case, the amplitude is 1.
- Period: The period of a sine function is defined as the length of one complete sine wave or one complete cycle of the curve. It can be found using the equation: P=2pi/B.
Why are these characteristics important?
Because the sine function has the following general form:
In this problem, we have A=1 and we know that the period equals 2pi/3. So,
Therefore, the equation of the graph is:
James and Susan wish to have $10,000 available for their wedding in 2 years.
How much money should they set aside now at 6% compounded monthly in
order to reach their financial goal?
They need to set aside $8871.86
A tailor cut 1/2 inch off a skirt and 1/6 inch off a pair of pants. which garment had the greater amount cut off
The garment that had the greater amount cut off is the skirt
Explanation:
Amount cut off from skirt = 1/2
Amount cut off from pants = 1/6
To determine the grament witht he greater cut, we need to find the LCM of the fractions
[tex]\text{LCM of the denominator, 2 and 6 = 12}[/tex][tex]\begin{gathered} \frac{1}{2},\frac{1}{6}=\frac{6(1),2(1)}{12}=\frac{6,\text{ 2}}{12} \\ \text{the fraction with higher number of numerator had the greater amount cut off} \end{gathered}[/tex]The fractor with higher number in the numerator = 1/2 has it has 6 has the numerator
In other words, 1/2 > 1/6
The garment that had the greater amount cut off is the skirt
A baseball player went up to bat 500 times in a season. He hit the ball 150 times. Find the rate of balls hit to times at bat. Express as a ratio.
To find the answer, we just divide
[tex]\frac{150}{500}=0.30[/tex]As ratio would be
[tex]\frac{150}{500}=\frac{15}{50}=\frac{3}{10}[/tex]Hence, his rate is 3/10, three hits every 10 attempts.Roseanna, Kennedy and Guadalupe had a super mean Math teacher who made them come up with a probability game where the chances of winning was 1/7. Roseanna’s idea was to have 5 red blocks and 30 blue blocks all in a bag. Each player gets one chance to pull out a block and if they pull out a red one they win Kennedy’s idea was the same as Roseanna’s except to have 1 red block and 7 blue blocks.Guadalupe’s idea was to have a seven sided die with a number 1 through 7 on each side. Each player rolls the die once and wins if they get a 3Whose game has a 1/7 chance of winning? Whose game doesn’t? For each game that doesn’t, show one way to change it so that it does have a 1/7 chance.
We are asked to determine which games have a 1/7 chance of winning. -
In the case of Roseanna's game, we have that there are 5 red blocks and 30 blues blocks. If the winner is the person that pulls out a red block then to determine the probability we must determine the quotient between the number of red blocks and the total number of blocks, like this:
[tex]P(red)=\frac{5}{5+30}[/tex]Solving the operations:
[tex]P(red)=\frac{5}{35}=\frac{1}{7}[/tex]Therefore, Roseanna's game has a 1/7 probability.
In the case of Kennedy's game, there are 1 red block and 7 blue blocks, therefore, the probability of getting a red block is:
[tex]P(red)=\frac{1}{7+1}=\frac{1}{8}[/tex]Therefore, Kennedy's game has not a chance of 1/7 but 1/8 of winning.
For Kennedy's game to have a probability of 1/7 he could remove one of the blue blocks, that way the probability is:
[tex]P(red)=\frac{1}{6+1}=\frac{1}{7}[/tex]In the case of Guadalupe's game, we have that there is a dice with 7 sides numbered from 1 to 7. This means that the probability of getting a 3 is:
[tex]P(3)=\frac{1}{7}[/tex]Therefore, Guadalupe's game has a probability of 1/7.
1. Which of the following is the value of -13 - 51 – 3? (A) -5 (B) -1 (C) 0 (D) 1 M
The value of -|3-5|-3 is,
[tex]\begin{gathered} -|3-5|-3=-|-2|-3 \\ =-2-3 \\ =-5 \end{gathered}[/tex]Hence, Option A is right.
What are the magnitude and direction of w = ❬–5, –14❭? Round your answer to the thousandths place.
To solve the question, we will have to determine the quadrant within which the point falls
Since both values are negative
[tex](x,y)=(-5,-14)[/tex]So the values are in the third quadrant
So we will have to get the magnitude first
[tex]\begin{gathered} \text{Magnitude}=\sqrt[]{x^2+y^2} \\ \text{Magnitude}=\sqrt[]{(-5)^2+(-14)^2} \\ \text{Magnitude}=\sqrt[]{25+196} \\ \text{Magnitude}=221 \\ \text{Magnitude}=14.866 \end{gathered}[/tex]Next, we will have to get the direction
[tex]\begin{gathered} \text{direction}=\tan ^{-1}(\frac{y}{x}) \\ \text{direction}=\tan ^{-1}(\frac{-14}{-5}) \\ \text{direction}=\tan ^{-1}(2.8) \\ \text{direction}=70.346^0 \end{gathered}[/tex]So, since we know that the point is on the third quadrant, then
We will add 180 degrees (90 degrees from first and 90 degrees from the second quadrant)
So we will have
[tex]180^0+70.346^0=250.346^0[/tex]Thus the answer is
[tex]\mleft\Vert w\mleft\Vert=\mright?\mright?14.866,\theta=250.346^0[/tex]In the figure XYZ ~ ABC.Find cosB, tanB, and sinB.Round your answers to the nearest hundredth.
we have the following;
1. Cos B:
[tex]\begin{gathered} CosB=\frac{a}{h} \\ CosB=\frac{15.4}{17}=0.91 \end{gathered}[/tex]2. Tan B:
[tex]\begin{gathered} TanB=\frac{o}{a} \\ TanB=\frac{7.2}{15.4}=0.48 \end{gathered}[/tex]1. Sin B:
[tex]\begin{gathered} SinB=\frac{o}{h} \\ SinB=\frac{7.2}{17}=0.42 \end{gathered}[/tex]Marge makes four payments each year of $175 for her auto insurance. Howmuch must she budget weekly to cover this fixed expense?a. $13.46b. $.84c. $58.33d. $ 700
Since she makes four payments each year, the total amount she pays in a year is
[tex]\$175\times4=\$700[/tex]Now there are 52 weeks in a year, divide the total amount of what she pays in a year by the number of weeks in a year.
[tex]\$700\div52=\$13.46[/tex]Therefore, she must budget weekly $13.46 to cover for this fixed expense.
Use the formula t= ln2 over k that gives the time for a population, with growth rate k, to double, to answer the following questions. The growth model A=6e^0.001t describes the population, A, of a country in millions, t years after 2003. A. What is the country's growth rate? B. (After answering A I will assistance for question B following question A)
Answer:
A. k = 0.001
B. 693 years
Explanation:
An exponential function has the following form:
[tex]y=a\cdot e^{kt}[/tex]Where a is the initial value and k is the growth or decay rate.
So, if the equation is:
[tex]A=6e^{0.001t}[/tex]Therefore, the growth rate is 0.001.
Now, to know how long will it take the country to double its population, we can use the equation:
[tex]t=\frac{\ln 2}{k}[/tex]Where k is the growth rate. So, replacing k by 0.001, we get:
[tex]\begin{gathered} t=\frac{\ln 2}{0.001} \\ t=693.14\approx693\text{ years} \end{gathered}[/tex]Therefore, the country will double its population 693 years after 2003
refer to the figure to complete thus proportion. c/a = a/?
Here, we want to compare triangles and such write the equivalent ratio on both
Mathematically, if two triangles are similar, the ratio of their sides are fixed
In the triangle consisting of c and a, we can see that c is the hypotenuse( the side facing the right-angle) while a represents the base
Now, in the triangle where we have a as the hypotenuse, we can see that the measure r reresents the base of the triangle
Thus, we can complete the proportion as;
[tex]\frac{c}{a}\text{ = }\frac{a}{r}[/tex]What is the value of 2x in this equation?3(2x-5)-4x+8=-2x+1a. 8 b. -1c. 4d. -4
The value of (2x) after the solving the equation
[{3(2x-5) - 4x + 8} = (-2x + 1)] for the variable "x" will be 4.
As per the question statement, we are provided with an equation:
[{3(2x-5) - 4x + 8} = (-2x + 1)],
And we are required to calculate the value of (2x) from the solution of the above mentioned equation.
Given, [{3(2x-5) - 4x + 8} = (-2x + 1)]
Or, [{(6x - 15) - 4x + 8)} = (-2x + 1)]
Or, [{(6x - 4x) + (8 - 15)} = (-2x + 1)]
Or, [(2x - 7) = (-2x + 1)]
Or, [(2x + 2x) = (7 + 1)]
Or, (4x = 8)
Or, [x = (8/4)]
Or, (x = 2)
Or, [2x = (2 * 2)]
Or, (2x = 4)
Equation: An equation is a mathematical statement that determines the relation of equality among two or more expressions, by a connector "equal to" sign in between.To learn more about Equations, click on the link below.
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What graph is the function of the table shown ?
Answer:
Explanation:
The table contains corresponding values of x and y
We would look at the points in the graph that contains these corresponding values of x and y. Looking at the graphs,
5x - 2 + 10 = 20 - 32
In this case the answers is very simple. .
We must apply algebraic rules to find the solution.
5x - 2 + 10 = 20 - 32
5x = 20 - 32 + 2 - 10
5x = (20 + 2) + (- 32 - 10)
5x = 22 - 42
5x = -20
x = -20 / 5
x = -4
The answers is:
x = -4
A community service group spent Planet summer planting trees in City park the table shows the total of number of trees after a certain number of weeks how many trees were already planted in the park before the community group started to plant?
If we consider the number of weeks equals 0 as the moment where the group started to plant, we can notice that at this point there were already 16 trees, then the answer is 16 trees
The length of a rectangle is 4 in longer than its width. If the perimeter of the rectangle is 362 in, find it's area.
The length of a rectangle is 4 in longer than its width, which means
Length = 4 in + width
P = 362 in = 2L + 2W
362in = 2(4 in + W) + 2W = 8in+2W+2W = 8in + 4W
362in = 8in + 4W
Solve for W
362 in - 8in = 4W
354 = 4W
354/4 = W
88.5 = W
Replace W in the Length
Length = 4 in + W
Length = 4 in + 88.5in
Length = 92.5in
The formula for the area is A = Length * Width = L * W
Replace the values and find the area
A = L* W
A = 92.5in * 88.5in
A = 8186.25 in²
The graph of function fis shown.YA-10X-5g(x)ENTEENENEN-10-2-325(0,-2)-5Function g is represented by the table.-10(2,8)-1-16BUDETETIEREDIVITETITENTENTENDEUREN MEDIOEMED MERDENDENDIENTEDETETTETTEN VEDIMENMEDITED RENDUER TRENINEEEEE5ENITEDIOUS0-8101-42-2
For function f:
According to the graph in the interval [0,2] the function is increasing.
Rate: 8 - 0 = 8
For function g:
According to the table g function is increasing.
Rate: -2 - ( -8) = -2 + 8 = 6
Answer: C. both functions are increasing but f is increasing faster