Answers
From the given diagram, PQ is a diameter and since the triangle inside a semicircle is right angled, hence triangle PQR is a right triangle.
Also since the side QR is parallel to OS, hence the line PR is perpendicular to the lines QR and OS
Hence;
PR ⊥ QR and OS ⊥ PR
Proof that From △PRQ,
Since OS ⊥ PR, hence △PSR is divided into two similar triangles by the line OS showing that the base angles (
Recall that for an isosceles triangle, the base angles and two opposite sides are equal. Based on the proof above, we can conclude that;△PSR is isosceles triangle showing that SP = SRRelated Questions
ху Evaluate when x = 6 and y = 13. x + y
Answers
EXPLANATION
When x=6 and y=13 x+y = 6 + 13 = 19
x + y = 19
In 2009, Mariana paid $5,160 in federal income tax. In 2010, she paid 70% more than in 2009. How much did Mariana pay in 2010?
finishing. What is the percent of decrease in the number of finishers?
Answers
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{70\% of 5160}}{\left( \cfrac{70}{100} \right)5160}\implies 3612~\hfill \underset{for~2010}{\stackrel{5160~~ + ~~3612}{\text{\LARGE 8772}}}[/tex]
Answer:
3,612
Step-by-step explanation:
70% of 5,160
0.70•5,160= 3612
7. Elena wanted to find the slope and y-intercept of the graph of 25x – 20y = 100. Shedecided to put the equation in slope-intercept form first. Here is her work:-25x - 20y = 10020y = 100 - 25x5y = 5 - 2x-4She concluded that the slope isand the y-intercept is (0,5).a. What was Elena's mistake?b. What are the slope and y-intercept of the line? Explain or show your reasoning.
Answers
The slope-intercept form for an equation of a line looks like this:
[tex]y=mx+b[/tex]Where m is the slope and (0,b) the y-intercept. Let's take the equation given by the question, operate and write it in slope-intercept form and see which was Elena's mistake. So we have:
[tex]25x-20y=100[/tex]We can substract 25x from both sides:
[tex]\begin{gathered} 25x-20y-25x=100-25x \\ -20y=100-25x \end{gathered}[/tex]Here we can see Elena's mistake. Instead of the equation I just wrote she got:
[tex]20y=100-25x[/tex]This doesn't have the negative sign in 20y. This was her mistake and answer to part a.
Now let's continue, we can divide both sides by -20:
[tex]\begin{gathered} -\frac{20y}{-20}=\frac{100-25x}{-20} \\ y=-\frac{100}{20}+\frac{25}{20}x \\ y=\frac{5}{4}x-5 \end{gathered}[/tex]Which means that the slope is 5/4 and the y-intercept is (0,-5).
2 hours reading1 hour playing with friendsRate ? Ratio only ? Or a proportion?
Answers
Answer:
[tex]\text{Ratio Only}[/tex]Explanation:
We get a rate when we consider how a quantity changes in relation to another
When we compare two quantities, we have a ratio
Equating two ratios, we have a proportion
From the question, we are comparing the number of reading hours to the number of playing hours
That means we have a ratio only
⦁ The total cost after tax to repair Deborah’s computer is represented by 0.08(50h)+50h, where h represents the number of hours it takes to repair Deborah’s computer. What part of the expression represents the amount of tax Deborah has to pay? Explain.
Answers
The part of the expression that represents the amount of tax Deborah will pay is 0.08(50h).
What part of the expression represents taxes?The given expression is known as a linear equation. A linear expression is an expression that has a single variable raised to the power of 1.
Tax is the compulsory amount levied by on goods and services. Tax is usually a percentage of the price of a good and service. Taxes increases the price of a good or service. The tax paid would increase with the total income earned.
Tax = tax percentage x total cost
Tax = 0.08 x (total hours worked x cost per hour)
Tax = 0.08 x (50 x h)
Tax = 0.08(50h)
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Need help with finding the vertex and the Y intercept of the quadratic function and use them to graph the function for number 21
Answers
EXPLANATION
Given the function y=-2x^2 -12x -5
[tex]\mathrm{The\: vertex\: of\: an\: up-down\: facing\: parabola\: of\: the\: form}\: y=ax^2+bx+c\: \mathrm{is}\: x_v=-\frac{b}{2a}[/tex][tex]\mathrm{The\: parabola\: params\: are\colon}[/tex][tex]a=-2,\: b=-12,\: c=-5[/tex][tex]x_v=-\frac{b}{2a}[/tex][tex]x_v=-\frac{\left(-12\right)}{2\left(-2\right)}[/tex][tex]\mathrm{Simplify}\colon[/tex][tex]x_v=-3[/tex]Plug in x_v=-3 to find the y_v value:
[tex]y_v=-2\mleft(-3\mright)^2-12\mleft(-3\mright)-5[/tex]Computing the powers and multiplying terms:
[tex]y_v=-18+36-5[/tex]Adding and subtracting numbers:
[tex]y_{v\text{ }}=13[/tex]Therefore, the parabola vertex is:
(-3,13)
Now, we need to compute the y-intercept
[tex]y\mathrm{-intercept\: is\: the\: point\: on\: the\: graph\: where\: }x=0[/tex][tex]\mathrm{Apply\: rule}\: 0^a=0[/tex][tex]0^2=0[/tex][tex]y=-2\cdot\: 0-12\cdot\: 0-5[/tex]Multiplying numbers:
[tex]y=-5[/tex]The y-intercept is at (0,-5)
In conclusion, the graph of the function is as follows:
A third box is designed so that it is also a cube that has sides that are half of solid 1's. find the volume of solid 3. then find the ratio of the volume of solid 1 to the volume of solid 3. explain why the ratio is not 2 to 1
Answers
Given :
Solid 1:
The side of the cube is, a = 8 cm.
Solid 3:
The side of the cube is, b = 4 cm.
The volume of the third cube can be calculate as,
[tex]V=b^3=(4cm)^3=64cm^3[/tex]The volume of first cube is,
[tex]V^{\prime}=a^3=(8cm)^3=512cm^3[/tex]Thus, the ratio can be calculated as,
[tex]\frac{V^{\prime}}{V}=\frac{512}{64}=\frac{8}{1}[/tex]Thus the required ratio is 8:1.
Since the volume is proprtional to the cube of the side, the ratio will also be in the range of cube of the fractional difference between the sides.
Which of the following Platonic solids is made from squares? Check all thatapply.A. icosahedronB. cubec. tetrahedronD. octahedronE, hexahedronF. dodecahedron
Answers
From the information on platonic solids, we can say that cube is the only platonic solid that is made from squares. Thus, option B is correct.
Platonic solids, also referred to as regular solids or regular polyhedrons, are the types of solids that have identical faces composed of congruent regular convex polygons.
A platonic solid can be defined as a 3D shape where each face is similar to a regular polygon and consists of same number of faces that meet at each vertex of the polygon.
There are 5 different types of platonic solids that are -
Tetrahedron - A tetrahedron is referred to as a triangular pyramid in geometry. The tetrahedron comprises of 4 triangular faces, 6 straight edges, and 4 vertex corners.Cube - A cube can be defined as 3D solid object with 6 square faces and consists of the sides that are of the same length. The cube is also called as a regular hexahedron which is a box-shaped solid with 6 equivalent square faces.Octahedron - An octahedron is in fact, a polyhedron consisting of 8 faces, 12 edges, and 6 vertices and at each of the vertices, the 4 edges coincide. The faces of an octahedron are shaped in the form of an equilateral triangle.Dodecahedron - A dodecahedron is referred to as a platonic solid comprising of 12 sides and 12 pentagonal faces. Icosahedron - An icosahedron is a platonic solid with 20 faces, 30 edges, and 12 vertices. The shape of an icosahedron consists of equilateral triangle faces.Thus, from the above information on platonic solids, we can say that cube is the only platonic solid that is made from squares. Thus, option B is correct.
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To get the 10% discount, a shopper must spend no less than $400.Use d to represent the spending (in dollars) of a shopper who gets the discount.
Answers
d represents the amount spent by a shopper who gets the discount.
The expression for d would be
[tex]d\text{ }\ge400[/tex]d is greater than or equal to 400I’m done answering. Do you understand my explanation?
Which equation represents a line which is parallel to the y-axis?a) x=4yb) x=1/4yc) x=3d) y=-6
Answers
The graph of x = 3 is a line parallel to the y-axis, which passes through the point (3, 0). This means that x = 3 for every value of y.
11) The table below represents a linear equation. If the y-intercept is at point (0, b), what is the value of b?X-125Y-1817
Answers
step 1
Find the slope of the linear equation
we take the points
(-1,-1) and (2,8)
so
m=(8+1)/(2+1)
m=9/3
m=3
step 2
Find the equation of the line in sloe intercept form
y=mx+b
we have
m=3
point (2,8)
substitute
8=3(2)+b
solve for b
8=6+b
b=2
the equation is
y=3x+2
and the value of b is 2
help me on this math question! please
Answers
Answer:
X: -2, -1, 0, 1, 2
Y: -3, -1, 1, 3, 5
Step-by-step explanation:
A problem solver site says the table will look like this
(d) 8x + 3y = -45x + 2y = 6Solve the following simultaneous linear equation
Answers
To solve the following simultaneous linear equation, we are going to solve for y on the first equation and replace it on the second as:
[tex]\begin{gathered} 8x+3y=-4 \\ 3y=-4-8x \\ y=\frac{-4-8x}{3} \\ y=\frac{-4}{3}-\frac{8x}{3} \end{gathered}[/tex]Replacing it on the second equation and solving for x, we get:
[tex]\begin{gathered} 5x+2y=6 \\ 5x+2(\frac{-4}{3}-\frac{8x}{3})=6 \\ 5x-\frac{8}{3}-\frac{16x}{3}=6 \\ 5x-\frac{16}{3}x=6+\frac{8}{3} \\ \frac{-1}{3}x=\frac{26}{3} \\ -x=26 \\ x=-26 \end{gathered}[/tex]Finally, replacing x on the first equation and solving for y, we get:
[tex]\begin{gathered} 8x+3y=-4 \\ 8(-26)+3y=-4 \\ 3y=-4+208 \\ 3y=204 \\ y=\frac{204}{3}=68 \end{gathered}[/tex]Answer: x = -26 and y = 68
To make subtraction of 5x - 16x/3, we can use the following equation:
[tex]\frac{a}{b}-\frac{c}{d}=\frac{a\cdot d-b\cdot c}{b\cdot d}[/tex][tex]\begin{gathered} 5x-\frac{16x}{3}=\frac{5x}{1}-\frac{16x}{3}=\frac{5x\cdot3-1\cdot16x}{1\cdot3}=\frac{15x-16x}{3}=\frac{-1x}{3} \\ \end{gathered}[/tex]How do I solve this I think I did it incorrectly
Answers
Given:
The diameter of the circle = d = 14 cm
The radius of the circle = r = d/2 = 7 cm
The circumference is given by the formula: 2πr
so, the exact value = 2π * 7 = 14π cm
The approximated value to the nearest hundredth = 43.98 cm
The area of the circle is given by the formula: πr²
The exact value of the area = π * 7² = 49π cm²
The approximated value to the nearest hundredth = 153.94 cm²
the U.S senate has 100 members. there are 6 more democrats than republicans, with no other parties represented. how many memebr of each party were there in the senate
Answers
The number of republicans and democrats will be 47 and 53 respectively.
Define equation.Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side. It shows that the expressions printed on the left and right sides have an equal relationship. In any mathematical equation, we have LHS = RHS (left hand side = right hand side). Equations can be solved to find the value of an unknown variable that represents an unknown quantity.
Given data -
Total number of members in U.S senate = 100
Let the number of republicans in U.S senate be x members
As republicans outnumber democrats by six,
Therefore, number of democrats = (x+6) members
According to the given data,
x + (x+6) = 100
2x + 6 = 100
2x = 94
x = 47
Number of members as a republicans will be 47.
Number of members as a democrats will be (100-47) = 53
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The data points on the scatter plot below show the amount of natural snow received and the amount of artificial snow made by a ski resort for each of 25 weeks. Draw the line of best fit for these data points. (It doesn't have to be the exact line of best fit. Just draw your best approximation.)
Answers
We need to draw the line of best fit for the data points in the scatter plot.
One way of drawing this line is by leaving approximately the same amount of points above and below it:
Notice that the line has to follow the trend of the points: the amount of artificial snow made decreases as the amount of natural snow received increases.
What is the intensity of an earthquake in Hawaii
which measured 3.92 on the richter scale?
Use the formula M = log(i/s)
S= 1 micron
- 7,943 microns
- 6904 microns
- 8318 microns
- 2818 microns
Answers
8318 microns is the intensity of an earthquake in Hawaii.
What is Richter scale?The Richter scale was originally developed to measure the magnitude of moderate earthquakes (magnitude 3 to magnitude 7) by assigning numbers so that the magnitude of one earthquake can be compared to another. This scale was developed for the Southern California earthquake recorded by the Wood He Anderson seismograph whose epicenter was less than 600 km (373 mi) from the seismometer location. However, today's seismometers can be calibrated to calculate the Richter magnitude, and modern methods of measuring earthquake magnitude are designed to give results consistent with those measured using the Richter scale. Developed.
The magnitude of an earthquake is determined using the logarithm of the amplitude (height) of the largest seismic wave, calibrated to scale by the seismograph.
Using the formula,
[tex]M = log \frac{i}{s}\\ 3.92 = log\frac{i}{1 micron} \\10^3.92 = \frac{i}{s} \\i = 8318[/tex]
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heights of men on a basketball team have a bell shaped distribution with the mean of 177 cm and a standard deviation if 5 cm. using the empirical rule, what is the approximate percentage of the men between 162 cm and 192 cm?
Answers
The variable
X: height of a basketball team
This variable has a bell shaped distribution (Normal distribution) with mean μ=177cm and a standard deviation of δ=5cm
The empirical rule states that
68% of the distribution is within one standard deviation away from the mean
[tex]\begin{gathered} \mu\pm\sigma=0.68 \\ 177\pm5 \\ (172;182) \end{gathered}[/tex]95% of the distribution is within two standard deviations away from the mean
[tex]\begin{gathered} \mu\pm2\sigma=0.95 \\ 177\pm2\cdot5 \\ (167,187) \end{gathered}[/tex]99.7% of the distribution is within three standard deviations away from the mean
[tex]\begin{gathered} \mu\pm3\sigma=0.997 \\ 177\pm3\cdot5 \\ (162,192) \end{gathered}[/tex]So, following the empirical rule, 99.7% of the men are between 162 cm and 192 cm
Which equation represents a line which is parallel to the line by – 7x = 24?:A) y=7/6x+3B) y=6/7x-2C) y=-7/6x-1D)y=-6/7x+7
Answers
We have the equation 6y-7x=24, and want to know what of the options represents a line parallel to that one.
First we need to write our equation in the form of the options:
[tex]\begin{gathered} 6y-7x=24 \\ 6y=7x+24 \\ y=\frac{7x+24}{6}=\frac{7x}{6}+\frac{24}{6} \\ y=\frac{7}{6}x+4 \end{gathered}[/tex]Now, we know that two lines are parallel if and only if they slopes are equal, so the slope of our line is 7/6 and the option that has the same slope is the option A.
So te correct answer is the option A
Which of the following lines is NOT parallel toy = 3x + 4?
Answers
We are to look for lines that are not parallel to y=3x + 4
Comparing the above equation with y=mx + b, the slope(m) = 3
Equations of lines are said to be parallel, if they have the same slope
So, we need to re-write each equation in the slope-intercept form to see which is NOT parallel to the given equation
OPTION A
3y - 9x - 6 = 0
[tex]y=\frac{9x}{3}+\frac{6}{3}[/tex][tex]y=3x+2[/tex]slope = 3 which implies. it is parallel to the given equation
OPTION B
-2y + 6x + 4 = 0
[tex]2y=6x+4[/tex]Divide through by 2
[tex]y=3x\text{ + 2}[/tex]slope = 3 which implies the line is parallel to the given line
OPTION C
2y - 6x - 4 = 0
[tex]2y=6x\text{ + 4}[/tex]Divide through the equation by 2
[tex]y=3x\text{ + 2}[/tex]slope = 3 which implies the line is parallel to the given line
OPTION D
2y - 4x - 8 = 0
[tex]2y=4x\text{ + 8}[/tex]Divide through the equation by 2
[tex]y=2x\text{ + 4}[/tex]slope = 2, which means tthe line is NOT parallel to the given line.
Therefore, the line which is NOT parallel to y=3x+ 4 is D. 2y - 4x - 8 = 0
f(x) = 8x⁵-7x⁴-73x³+23x²-20x-5÷8x+1
Answers
f(x) = 8x⁵-7x⁴-73x³+23x²-20x-5÷8x+1
[tex]f\mleft(x\mright)=\frac{8x^{5}-7x^{4}-73x^{3}+23x^{2}-20x-5}{8x+1}[/tex]For 97.1 seconds, a remote-controlled helicopter flew at an altitude of 3 meters and a constant velocity of 19.0 meters per second to the west. During this time, how far did the helicopter fly?
Answers
The relationship between time, distance and velocity is:
[tex]v=\frac{d}{t}[/tex]In this case, we need to find the distance, d
We can solve for d:
[tex]v=\frac{d}{t}\Rightarrow d=v\cdot t[/tex]The velocity of flight is v = 19 m/s and the time of flight is t = 97.1s
Then:
[tex]d=19\frac{m}{s}\cdot97s[/tex][tex]d=1844.9m[/tex]The answer is 1844.9m
If FG= 9x-2 and jk=3x+10, what value of x will make FG and JK congruent
Answers
ANSWER
x = 2
EXPLANATION
If we want FG and JK to be congruent, then we have to see which value of x makes:
[tex]FG=JK[/tex]true.
What is the average rate of change of the function f(x) = x^2 – 2x + 4 over the interval –2 ≤ x ≤ 3?
Answers
The rate of change of a function is the increase or decrease that a function experiences as the independent variable changes from one value to another.
The corresponding equation of the average rate of change is:
[tex]TVM(x_1,x_2)=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]In this case, x1 is 3 and x2 is 3
Remember that according to the notation of the limits, they take the values of 2 and 3.
Now, we solve f(3) and f(2)
[tex]\begin{gathered} f(3)=3^2-2\cdot(3)+4 \\ f(3)=9-6+4 \\ f(3)=7 \end{gathered}[/tex][tex]\begin{gathered} f(2)=2^2+2\cdot(2)+4 \\ f(2)=4-4+4 \\ f(2)=4 \end{gathered}[/tex]This way now we can replace the values in the TVM equation and I will solve this.
[tex]\begin{gathered} TVM(3,2)=\frac{7-4}{3-1_{}} \\ TVM(3,2)=\frac{3}{1}=3 \end{gathered}[/tex]In conclusion, the average rate of change of the function
How is this equation true?4/4 * x/1 + 1/4 = 4x/4 + 1/4 = 4x+1/4
Answers
Given
[tex]\frac{4}{4}*\frac{x}{1}+\frac{1}{4}[/tex]Simplify as shown below,
[tex]\begin{gathered} \frac{4}{4}*\frac{x}{1}+\frac{1}{4}=\frac{4*x}{4*1}+\frac{1}{4} \\ =\frac{4x}{4}+\frac{1}{4} \\ =\frac{4}{4}*x+\frac{1}{4} \\ =1*x+\frac{1}{4} \\ =x+\frac{1}{4} \end{gathered}[/tex]If the initial equation is correct, the last equality in the question tab is incorrect. The simplification is x+1/4, not 4x+1/4.
what do you know one step equations x+7=15
Answers
We will see how to evaluate one step equations. The following equation is given as follows:
[tex]x\text{ + 7 = 15}[/tex]A one-step equation is accompained by a ( single mathematical operation ). A mathematical operation can be classified into:
[tex]\text{Multiplication , Division, Addition, Subtraction}[/tex]We can use either of the above mathematical operations to solve for the variable ( x ) given in the equation.
We see that a constant ( 7 ) is added to the variable ( x ). We need to isolate our variable ( x ) on the left hand side of the " = " sign. To do that we will seek help of a " Subtraction " operation.
We will subtract the constant ( 7 ) on both sides of the equation as follows:
[tex]\begin{gathered} x\text{ + 7 = 15 } \\ x\text{ + 7 - 7 = 15 - 7} \\ \textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 8}} \end{gathered}[/tex]We have abotained a solution for the variable ( x ) using a single ( on-step ) mathematical operation as follows:
[tex]\textcolor{#FF7968}{x}\text{\textcolor{#FF7968}{ = 8}}[/tex]9 Is the sentence correct? Select Yes or No. A. O Yes O No 2 3 B. O Yes O No c. > O Yes O No D. too O Yes O No 8 E. O Yes O No F.
Answers
9 a) 1 /2 = 1/ 3 NO
b) 4/ 6 < 5/6 YES
c ) 5/ 6 > 5/8 YES
d) 4/8 < 7/8 YES
e) 3/3 = 3/ 8 NO
f) 1/4 < 3/4 YES
A factory makes candles. Each candle is in the shape of a triangular prism, as shown below. If the factory used 14,700 cm^3 of wax,how many candles did the factory make?
Answers
Answer:
Explanation:
Step 1
First, we find the volume of one the triangular prism shaped candles.
The volume of a prism is calculated using the formula:
[tex]V=\text{ Cross-Sectional Area}\times\text{ Length}[/tex]The cross section of the prism is a triangle with:
• Base = 10cm
,• Height = 7cm
Length of the Prism = 6cm
Therefore:
[tex]\begin{gathered} V=\frac{1}{2}bh\times L \\ =\frac{1}{2}\times10\times7\times6 \\ =210\;cm^3 \end{gathered}[/tex]The volume of one of the candles is 210 cubic cm.
Step 2
Next, divide the volume of wax used by the factory by the volume of one candle.
[tex]\text{Number of candles made}=\frac{14700}{210}=70[/tex]Rewrite the expression with a positive rational exponent. Simplify, if possible.100-1/2
Answers
We need that the 100 has a 2 in the denominator. To do this, we can multiply on top and bottom by 2:
[tex]100\cdot\frac{2}{2}=\frac{200}{2}[/tex]Now, we can make the subtraction:
[tex]\frac{200}{2}-\frac{1}{2}=\frac{199}{2}[/tex]The answer is 199/2
which of the following expression has a coefficient of 10 and a constant of 5 10+5x. 10+5. 10 - 5. 10x+5
Answers
the coefficient is the number that accompanies the variable, in this case it would be the number that accompanies the x
and a constant is a number without company
so, the expression is
[tex]10x+5[/tex]the last option