Answers
Answer
Angle PQR = 82°
Explanation
Tosolve this, we just need to note one thing about the properties of a rhombus;
The diagonals of a rhombus bisects its angles into two equal parts.
So, this means that
4x - 27° = 2x + 7°
4x - 2x = 27° + 7°
2x = 34°
Divide both sides by 2
(2x/2) = (34°/2)
x = 17°
We are then asked to solve for Angle PQR
Angle PQR = 4x - 27° + 2x + 7°
Angle PQR = 6x - 20°
Recall that x = 17°
Angle PQR = 6x - 20°
Angle PQR = 6(17°) - 20°
Angle PQR = 102° - 20°
Angle PQR = 82°
Hope this Helps!!!
Related Questions
-15y^2+3[-y^2-2(5-y^2)]
Answers
We have to simplify the expression:
[tex]\begin{gathered} -15y^2+3\mleft[-y^2-2\mleft(5-y^2\mright)\mright] \\ -15y^2+3\lbrack-y^2-10+2y^2\rbrack \\ -15y^2+3\lbrack y^2-10^{}\rbrack \\ -15y^2+3y^2-30 \\ -12y^2-30 \\ -6(2y^2-5) \end{gathered}[/tex]Answer:
We can express the simplified expression as -12y^2-30 or factorized as -6(2y^2-5).
lilla On a coordinate plane, point J is located at (-1, -2) and point K is located at (8, 10). What is the distance, in units from point J to point K? Enter youh answer in the space provided.
Answers
Using the distance formula;
[tex]|d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]From the points given:
x₁=-1 y₁=-2 x₂=8 y₂=10
substitute the values into the formula;
[tex]|d|=\sqrt[]{(8+1)^2+(10+2)^2}[/tex][tex]=\sqrt[]{9^2+12^2}[/tex][tex]=\sqrt[]{81+144}[/tex][tex]=\sqrt[]{225}[/tex][tex]=15[/tex]The distance is 15 units.
Which proportion can you use to convert 5 gallons to quart?
Answers
Given:
5 gallons
To convert into quarts:
We know that 1 gallon = 4 quarts
So, 5 gallons is,
[tex]5\times4=12\text{ quarts}[/tex]Hence, the proportion is,
[tex]1\colon4[/tex]In each pair of graphs shown here, the values of function g are the values of function f multiplied by a scale factor. Express g in terms of f using function notation.
Answers
From the given graph, we can note that
[tex]\begin{gathered} f(0)=-8 \\ \text{and} \\ g(0)=-13.6 \end{gathered}[/tex]the factor between these values is
[tex]\frac{-13.6}{-8}=1.7[/tex]this implies that
[tex]g(0)=1.7f(0)[/tex]and this relationship applies for every point in the graph. Therefore, the answer is
[tex]g(x)=1.7f(x)[/tex]Find the solutions to the equation below. Check all that apply. 20x^2 - 26x + 8 =0
Answers
Answer
B. x=1/2
D. x=4/5
Explanation
[tex]20x^2-26x+8=0[/tex]Divide by 2 both sides:
[tex]10x^2-13x+4=0[/tex]Factoring:
[tex](2x-1)(5x-4)=0[/tex]And we have 2 options:
[tex]\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}[/tex]and
[tex]\begin{gathered} 5x-4=0 \\ 5x=4 \\ x=\frac{4}{5} \end{gathered}[/tex]
Find the slope and tell what kind of slope each line illustrates.
Answers
step 1
Find out the slope
we need two points
looking at the graph
we take the points (-4,4) and (-3,-2)
m=(-2-4)/(-3+4)
m=-6/1
m=-6
the slope is -6
Is a negative slope ( that means, is a decreasing function)
2. Stacey is factoring the expression, 12x^2-4x. After factoring completely, Stacey got 4x(3x-1). How can she check to see if she factored correctly? Explain and show work to support your explanation
Answers
She can check that by expanding the factored equation, if she gets the original expression, then the factoring is correct
[tex]4x(3x-1)=12x^2-4x[/tex]Answer:
She is correct!
Step-by-step explanation:
She would check if it is correct by doing this.
You would factor out 4.
[tex]4 (3x^{2} - x )[/tex]
Then you would consider [tex]3x^{2} -x[/tex]. Factor out [tex]x[/tex].
[tex]x (3x-1)[/tex]
Then rewrite the complete factored expression.
[tex]4x(3x-1)[/tex]
Therefore, Stacey is correct.
Hope this helps! :))
help please I need 5 points total. i need 2 to left of vertex. i need vertex. i need 2 to right of vertex. Please, quickly, I am timedgraph only goes up to 14. thank you
Answers
The graph is displayed below:
• The points are: (2, 11), (3, 6), (7, 6), and (8, 11)
• The vertex is (5, 2). ,This is because the graph opens up and the lowest point is always the vertex for this type of graphs.
For each expression, write an equivalent expression in standard form. Show your reasoning. [tex](x - 2)( x + 2)[/tex]
Answers
(x - 2) (x+2)
we will expand by opening the parenthesis
x(x+2) - 2(x+2)
x² + 2x - 2x - 4
x² - 4
Mario made five phone calls lasting 4,6, 8, 15, 21 minutes. After another call, the median length of the phone calls were 10 minutes. What was the mean length of the six calls?
Answers
Explanation
We are given that Mario made 5 phone calls which lasted 4, 6, 8, 15, and 21 minutes
We are then asked to determine the mean length of the 6 calls after another call has been made
Let the 6th call be x
So that the median of 4, 6, 8, 15, 21, and x minutes be 10
[tex]4,6,8,\text{ x,15, 21}[/tex]The value of x cannot be after 21 because, this will mean that x is greater than 21 minutes, which will not give us a median of 10 minutes
The median of the values is
The median
[tex]\frac{8+x}{2}=10[/tex]If we make x the subject of the formula
[tex]\begin{gathered} 8+x=20 \\ x=20-8 \\ x=12\text{ minutes} \end{gathered}[/tex]So we can then compute the mean of the six calls as
[tex]mean=\frac{4+6+8+12+15+21}{6}=11\text{ minutes}[/tex]The mean length of the calls is 11 minutes
Alex wants to know the volume of sand in an hourglass when all the sand is in the bottom, he stands a ruler up beside the hourglass and estimates the height of the cone of sand.a. What else does he need to measure to find the volume of sand? b. If the volume of sand is increasing at a constant rate, is the height increasing at a constant rate? Explain.
Answers
Notice that Alex measured the height of the hourglass. To find its volume he also has to measure the radius of the circumference of the base.
(b)We know that the height and radius of the volume are directly proportional, which means if one increases then the other one also increases. Therefore, the answer is yes, if the volume of sand is increasing at a constant rate, the height is increasing at a constant rate because those magnitudes are directly proportional.
lan likes to play online games. There is an online gaming company where he can download games.There are two pricing options, he can become a member and pay $15 per year and $0.99 per gamedownload. If he decides to not become a member he will have to pay $1.29 per game download.a) Write an equation that sets the two plans equal to each other.b) Solve the equation you wrote from a)c) Interpret the solution from a) within the context of the problem
Answers
Answer:
a) The equation, if the two plans are equal is
15 + 0.99x = 1.29x
b) The solution to the equation is
x = 50
c) The solution x = 50 means he can download a total of 50 games with either plan
Explanation:
The first pricing option, where he can pay $15 per year and $0.99 per game, may be represented by the equation:
15 + 0.99x
Where x is the number of games he plays per year.
The second pricing option, where he can pay $1.29 per game, may be represented by the equation:
1.29x
a) If the two plans are equal to each other, then we have
15 + 0.99x = 1.29x
b) Solving the equation in a)
15 + 0.99x = 1.29x
Subtract 0.99x from both sides of the equation
15 + 0.99x - 0.99x = 1.29 - 0.99x
15 = 0.3x
Divide both sides by 0.3
15/0.3 = 0.3x/0.3
50 = x
Therefore, x = 50
c) The solution x = 50 means the total number of games he can download with either plan is 50, since the plans are equal.
Approximate the area under the graph of f(x) over the specified interval by dividing the interval into the indicated number of subintervals and using the left endpoint of each subinterval. f(x) -; interval [1, 5); 4 subintervals x2 O 1.4636 O 1.4236 O 0.4636 0 2.0833
Answers
The approximate area under the curve using the left-end points is 1.4236
Here; f(x) = 1/x^2 , [a,b] = [1,5] and n = 4
We start by calculating the width of each of the triangles on the interval
Mathematically, that would be;
[tex]\frac{b-a}{n}\text{ = }\frac{5-1}{4}\text{ = 1}[/tex]Since there are 4 sub-intervals, there are 4 rectangles
So using the left end-points, we have;
[tex]1\text{ }\times\text{ f(1) + (1 }\times\text{ f(2)) + (1 }\times\text{ f(3)) + (1 }\times\text{ f(4))}[/tex]where;
[tex]\begin{gathered} f(1)\text{ = }\frac{1}{1^2}\text{ = 1} \\ \\ f(2)\text{ = }\frac{1}{2^2}\text{ = 0.25} \\ \\ f(3)\text{ = }\frac{1}{3^2}=\text{ }\frac{1}{9}\text{ = 0.11111} \\ \\ f(4)\text{ = }\frac{1}{4^2}\text{ = }\frac{1}{16}\text{ = 0.0625} \end{gathered}[/tex]So the approximate area under the curve will be;
[tex]1\text{ + 0.25 + 0.1111 + 0.0625 = 1.4236}[/tex]How many solutions does this system of equations have? Explain how you know.y + 2/3x = 42x = 12 - 3y
Answers
Lets start by rewrite both equations:
We realize that the first equation multiplied by 3 is equal to the second equation, that means that this system has infinite solutions because both equations represents the same line.
Find the a area and b perimeter of the figure. Dimensions are in feet.
Answers
a. Area
The area of the figure is the sum of the area of the rectangle and the area of the triangle. Therefore:
Area of triangle is given by
[tex]A=\frac{1}{2}bh[/tex]First, we find the height of the triangle using the Pythagorean theorem:
[tex]\begin{gathered} h^2+b^2=c^2 \\ h^2+12^2=(10+5)^2 \\ h^2+144=225 \\ h^2+144-144=225-144 \\ h^2=81 \\ h=\sqrt[]{81} \\ h=9 \end{gathered}[/tex]So, the area is:
[tex]\text{Area}=\frac{1}{2}(12)(9)=\frac{108}{2}=54[/tex]Area of rectangle is given by
[tex]\text{Area}=length\times width=5\times4=20[/tex]The area of the figure is:
[tex]\text{Area of figure=54+20=}74[/tex]Answer: area = 74 ft^2
b. Perimeter
Perimeter is the sum of all sides, therefore:
[tex]\text{Perimeter}=10+4+5+4+12+9=44[/tex]Answer: perimeter = 44 ft
Einstein's equation for mass-energy equivalence, E = mc2, qives the equivalent energy of an object, E, where m is the mass of the object and c is the speed of light.Solve for m in terms of E and c.m=
Answers
1) In this literal equation problem, let's perform some algebraic manipulations:
[tex]\begin{gathered} E=mc^2 \\ \frac{E}{m}=\frac{mc^2}{m} \\ c^2=\frac{E}{m} \\ mc^2=E \\ \frac{mc^2}{c^2}=\frac{E}{c^2} \\ m=\frac{E}{c^{2}} \end{gathered}[/tex]Note that the point here is to isolate m on the left side, so we needed to divide both sides and then cross multiply them.
translate to an algebraic expression and simplify the product 8 anf-13.
Answers
1,320,000,000 fish were sold in 2005. 4,220,000,000 fish were sold in 2006. Which is the best estimate of the number of fish sold in 2005 and 2006?A.3,000,000,000B.5,000,000,000C.5,540,000,000D.6,000,000,000
Answers
The Solution:
The number of fish sold in 2005 is 1,320,000,000
The number of fish sold in 2006 is 4,220,000,000
Adding the two numbers above together, we have
[tex]1,320,000,000+4,220,000,000=5,540,000,000[/tex]Thus, the best estimate of the number of fish in both years (2005 and 2006) is 5,540,000,000 (option C)
what is the slope of the blue line?what is the slope of a parallel line?
Answers
To find the slope (m) of a line given two points (x1, y1) and (x2, y2), we can use the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Points (-3,2) and (0,-2) lies on the blue line, then its slope is:
[tex]m_1=\frac{-2-2}{0-(-3)}=-\frac{4}{3}[/tex]Two lines are parallel if they have the same slope. Then,
Original slope: -4/3
Parallel slope: -4/3
Find the common difference of the arithmetic sequence. 4, 3 2/3, 3 1/3, 3, .... The common difference is ?
Answers
The numbers of the seria are:
[tex]4,3\cdot\frac{2}{3},3\cdot\frac{1}{3},3[/tex]so to find the diference we made the rest of two numbers so:
[tex]3\cdot\frac{2}{3}-4=-\frac{1}{3}[/tex]So the difference is -1/3
choose all that are correct:all 4 sided shapes are parallelogramsall rhombuses are parallelogramssome rectangles are squares same rectangles are squaresall squares are parallelograms
Answers
Number 1 statement is false
Not all 4 sided shapes are parallelograms
Number 2 statement is true
All rhombuses are paralleogram
Number 3
some rectangles are square though not all rectangles are square
Number 4
All squares are paralleloprams, this is also true
Express the following percent into lowest term : 12.5%: options- a)1/8 b)1/4 c)1/12
Answers
Answer:
[tex]A\colon\text{ }\frac{1}{8}[/tex]Explanation:
Here, we want to express the given percentage as a fraction
What we have to do here is just to divide the percentage by 100
Mathematically, we have this as follows:
[tex]12.5\text{ \% = }\frac{12.5}{100}\text{ = }\frac{1}{8}[/tex]Order these numbers from least to greatest. -6.44, 12/50, 0.2, -40.
Answers
To answer this question, we need to take into account that negative numbers are always lesser than a positive number, and, between two negative numbers, the one that has the greatest distance from 0 is lesser than the other negative number.
We have the numbers:
[tex]-6.44,\frac{12}{50},\bar{0.2},-\sqrt[]{40}[/tex]With the help of a calculator, we can find the value of all these numbers in decimal expression:
[tex]\frac{12}{50}=\frac{6}{25}=0.24[/tex]The number above is a terminating decimal. Only have two decimals.
[tex]\bar{0.2}=0.222222222222\ldots[/tex]The latter is a periodic decimal number.
[tex]-\sqrt[]{40}=-6.32455532034[/tex]Now, we can observe the negative numbers:
[tex]-6.44,-\sqrt[]{40}=-6.32455532034[/tex]The number with the greatest absolute value, that is, with the greatest distance from 0 is -6.44, since:
[tex]|-6.44|=6.44,|-6.32455532034|=6.32455532034[/tex]Therefore, we have the least number is -6.44, then -√40.
Now, which one is the greatest?:
[tex]\frac{12}{50}=0.24,\bar{0.2}=0.222222222\ldots[/tex]We can apply the same here. The one with the greatest absolute value is 0.24.
Therefore, to order these numbers from least to greatest is:
[tex]-6.44<-\sqrt[]{40}<\bar{0.2}<0.24[/tex]Accountants often use the median when studying salaries for various businesses what is the median of the following salary list 32,023; 21,983; 27,503; 43,702; 38,850; 25,997
Answers
Explanation
The median is the middle number in a sorted, ascending or descending list of numbers, to find the median we need
Step 1
given the set
[tex]32,023;21,983;27,503;43,702;38,850;25,997[/tex]a): Arrange the scores in numerical order ( ascending),so
[tex][/tex]3A. Explain in your own words how to find the domain of a function if you know its equation.B. Find the domain of f (x) =19-7x6x2.-13x-15Be sure to show relevant work.
Answers
A)
The domain of a function can be found using its rule of correspondence. If it is given as an algebraic equation, then we can analyze the restrictions over the variable of the function.
Those restrictions include that the denominator of an expression cannot be 0, and the radicand of a root with even index cannot be negative. Then, if the variable appears on the denominator of an expression or inside a radical with even index, we can apply those restrictions to find the values which x cannot take.
B)
Analyze each algebraic equation to find the restrictions over the variable x.
1.-
[tex]f(x)=19-7x[/tex]In this case, the variable x has no restrictions. Then, the domain of the function is the set of all real numbers, which can also be written as:
[tex](-\infty,\infty)[/tex]2.-
[tex]f(x)=6x^2-13x-15[/tex]In this case, the variable x has no restrictions. Then, the domain of the function is the set of all real numbers, which can also be written as:
[tex](-\infty,\infty)[/tex]hi, I need help with this. I don’t need an explanation just the answer.. it’s due in 5 minutes and my last tutor didn’t help..
Answers
Given that KN represents a proportional relationship and coordinate of N is (18,12)
Therefore, coordinate of K must be (2,3) as no other coordinates are in proportional relationship with N
Hence, correct option is (B)
Hi Ms or Mr i need help with this problem could you guide me here step by step
Answers
When two parallel lines are intercepted by another line, the angles formed between the two lines parallel lines and the one that intercepted them are congruent in alternated sides. This means that the angle AEF is congruent to DFE, Therefore:
[tex]\begin{gathered} \measuredangle DFE=\measuredangle AEF \\ \measuredangle DFE=40 \end{gathered}[/tex]The angle DFE is 40 degrees.
Number problem. The sum of the digits in a three-digitnumber is 14. The sum of the hundreds digit and the unitsdigit is equal to the tens digit. If the hundreds digit and theunits digit are interchanged, the number is increased by 297.What is the original number?
Answers
Answer: 275
Explanation:
Let x represent the hundred digit
Let y represent the tens digit
Let z represent the unit digit
The sum of the digits in a three-digit number is 14. This means that
x + y + z = 14
The sum of the hundreds digit and the units digit is equal to the tens digit. This means that
x + z = y
If the hundreds digit and the units digit are interchanged, the new digit would be x + 10y + 100z. If the number is increased by 297, then
x + 10y + 100z = 100x + 10y + z + 297
x - 100x + 10y - 10y + 100z - z = 297
- 99x + 99z = 297
Substituting y = x + z into the first equation, we have
x + x + z + z = 14
2x + 2z = 14
Dividing through by 2,
x + z = 7
Substituting x = 7 - z into - 99x + 99z = 297, we have
- 99(7 - z) + 99z = 297
- 693 + 99z + 99z = 297
99z + 99z = 297 + 693
198z = 990
Dividing both sides by 198, we have
z = 990/198
z = 5
x = 7 - z = 7 - 5
x = 2
y = x + z = 2 + 5
y = 7
Thus, the original number is
275
here is a pattern of dots. how many dots will there be in step 10
Answers
Given data:
The given pattern is shown.
The expression for the dot pattern is,
[tex]a_n=n^2+1_{}[/tex]For step 10 subtitute 10 for n in the above expression.
[tex]\begin{gathered} a_{10}=10^2+1 \\ =101 \end{gathered}[/tex]Thus, the numbers of dots in step 10 are 101.
if the temperature rises 4 degrees in 10 hours, what is the constant of proportionality
Answers
4 degrees in 10 hours, means 4/10 = 0.4 degrees per hour
So the constant of proporcionality is 0.4
Answer: 0.4 degrees per hour