Answer: If you are simplifying the expression, 8m-1 is your answer.
If you are finding the roots of this polynomial, 1/8 is your answer. (Can also be written as 0.125, 2^-3)
The standard height from the floor to the bull's-eye at which a standard dartboard is hung is 5 feet 8 inches. A standard dartboard is 18 inches in diameter.
Suppose a standard dartboard is hung at standard height so that the bull's-eye is 12 feet from a wall to its left.
Brian throws a dart at the dartboard that lands at a point 11.5 feet from the left wall and 5 feet above the floor.
Does Brian's dart land on the dartboard?
The equation of the circle that represents the dartboard is (x - 12)² + (y - 17/3)² = 9/16, where the origin is the lower left corner of the room and the unit of the radius is feet.
The position of Brian's dart is represented by the coordinates (11.5, 5). Brian's dart does land on the dartboard.
What is the equation of a circle?Mathematically, the standard form of the equation of a circle is represented by this mathematical expression;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r represents the radius of a circle.From the question, we have the following information:
The height of this standard dartboard, k = 5 feet, 8 inches.
The diameter of this standard dartboard = 18 inches.
The bull's eye, h = 12 feet.
Next, we would convert the all of the units in inches to feet as follows:
Height, k = 5 + 8/12
Height, k = 5 + 2/3
Height, k = 17/3 feet.
For the diameter, we have:
Diameter = 18/12
Diameter = 3/2 feet.
Also, we would determine the radius as follows:
Radius, r = diameter/2
Radius, r = (3/2)/2
Radius, r = 3/4 feet.
Substituting the parameters into the standard equation, we have;
(x - 12)² + (y - 17/3)² = (3/4)²
(x - 12)² + (y - 17/3)² = 9/16
Next, we would determine whether Brian's dart land on the dartboard:
(x - 12)² + (y - 17/3)² < 9/16
(x - 12)² + (y - 17/3)² < 9/16
(11.5 - 12)² + (5.5 - 5.67)² < 0.5625
0.25 + 0.0289 < 0.5625
0.2789 < 0.5625 (Yes, it does land because it's within the circumference of this standard dartboard).
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Choose all equivalent expression ( s). (4) ^ (3z ^ 2); (4) ^ (- 3x ^ 2); (1/4) ^ (3z ^ 2); (pi/4) ^ (3x)
Answer:
B, C
Step-by-step explanation:
You want to find the equivalent expressions among ...
4^(3x^2)4^(-3x^2)(1/4)^(3x^2)(x/4)^(3x)Rules of exponentsThe relevant rule of exponents is ...
a^b = (1/a)^-b
Equivalent expressionsExpressions with the same base and different exponents will not be equivalent. (A≠B).
Expressions with different bases and the same exponent will not be equivalent. (A≠C).
A variable in the base cannot replace a variable in the exponent. (A≠D).
The rule of exponents tells us replacing the base by its reciprocal and negating the exponent will result in an equivalent expression. (B=C).
The equivalent expressions are 4^(-3x^2) and (1/4)^(3x^2).
please help me brainliest?
Answer:
See below.
Step-by-step explanation:
Given multiplication:
[tex]3 \dfrac{1}{5} \times 2 \dfrac{5}{8}[/tex]
Convert the mixed numbers into improper fractions by multiplying the whole number by the denominator of the fraction, adding this to the numerator of the fraction, and placing the answer over the denominator:
[tex]\implies \dfrac{3 \times 5+1}{5} \times \dfrac{2 \times 8+5}{8}[/tex]
[tex]\implies \dfrac{15+1}{5} \times \dfrac{16+5}{8}[/tex]
[tex]\implies \dfrac{16}{5} \times \dfrac{21}{8}[/tex]
[tex]\textsf{Apply\;the\;fraction\;rule} \quad \dfrac{a}{b} \times \dfrac{c}{d}=\dfrac{ac}{bd}:[/tex]
[tex]\implies \dfrac{16 \times 21}{5 \times 8}[/tex]
[tex]\implies \dfrac{336}{40}[/tex]
Reduce the fraction by dividing the numerator and denominator by the common factor of 8:
[tex]\implies \dfrac{336 \div 8}{40 \div 8}[/tex]
[tex]\implies \dfrac{42}{5}[/tex]
Divide the numerator by the denominator:
[tex]\implies 42 \div 5=8\;\textsf{remainder}\;2[/tex]
The mixed number answer is the whole number and the remainder divided by the denominator:
[tex]\implies 8 \dfrac{2}{5}[/tex]
Step-by-step explanation:
when you want to start solving it you will do 16 over 5 * 21/8equals 8 whole number 2/5
it will give you 336 all over 40 if you divide by 8 you will get 42/5 which is 8 whole number 2/5
harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 3 years how much will they be able to spend
harry and marie despoit $800.00 into a savings account which earns 9% interest compounded monthly they want to use the money in the account to go on a trip in 2 years how much will they be able to spend
we know that
The compound interest formula is equal to
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
P=$800
r=9%=9/100=0.09
n=12
t=2 years
substitute in the expression above
[tex]\begin{gathered} A=800(1+\frac{0.09}{12})^{12\cdot2} \\ \\ A=800(\frac{12.09}{12})^{(24)} \\ A=\$957.13 \end{gathered}[/tex]the answer is $957.13Poland Spring Hotel is a 500-room property that offers only rooms, no F&B service. You are in the process of evaluating the business as an investment. Calculate the breakeven sales and rooms using the information below
Answer: GAS
Step-by-step explanation:
7/8 × 9/8 , but the answer as a fraction
We are given the following multiplication problem.
[tex]\frac{7}{8}\times\frac{9}{8}[/tex]To perform the fractional multiplication, simply multiply the numerators and the denominators
[tex]\frac{7}{8}\times\frac{9}{8}=\frac{7\times9}{8\times8}=\frac{63}{64}[/tex]Therefore, the result of the multiplication is 63/64
Divide 6.1 x 10^20 by 3.2 x 10^5. Express your answer in scientific notation.
PLEASE HELP!!!!
The division of the two numbers in scientific notation is equal to 1.91*10^15
Division of NumbersTo solve this problem, we have to divide the two numbers in scientific notation and to do this, we can simply apply division law of indices here;
We can first divide 6.1 by 3.2.
This will give us 1.90625 which is approximately 1.91.
Then applying the law of indices and subtract the power from one another. This becomes 20 - 5 = 15
The final value will be 1.91 * 10^15
The division of 6.1*10^20 by 3.2*10^5 is equal 1.91 *10^15
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(x ^ 2 + 11x + 18) / (x + 3) =
Answer:
x+8 - 6/x+3
Step-by-step explanation:
use reference angle to find the exact value of the expression, do not use a calculator sin 2(pi)/3
Given the expression below:
[tex]\sin (\frac{2\pi}{3})[/tex]To find the exact value of the expression, let us determine the quadrant of the expression. It should be noted that the value of angles compare with the quadrants is as shown below
[tex]\begin{gathered} First\text{ quadrant, the measure of reference angle in radian is } \\ 0-\frac{\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{second quadrant, the measure of reference angle in radian is} \\ \frac{\pi}{2}-\pi \end{gathered}[/tex][tex]\begin{gathered} \text{third quadrant, the measure of reference angle in radian is} \\ \pi-\frac{3\pi}{2} \end{gathered}[/tex][tex]\begin{gathered} \text{fourth quadrant, the measure of reference angle in radian is} \\ \frac{3\pi}{2}-2\pi \end{gathered}[/tex]It can be observed that the expression given in the question is a fraction of (pi), greater than half of (pi) but less than (pi). This means that it lies in the second quadrant.
It should be noted that sine is positive in the second quadrant
The equivalent of the expression in the first quadrant is as shown below:
[tex]\begin{gathered} \sin (\frac{2\pi}{3})=\sin (\pi-\frac{2\pi}{3}) \\ =\sin (\frac{3\pi-2\pi}{3}) \\ =\sin (\frac{\pi}{3}) \end{gathered}[/tex][tex]\begin{gathered} \text{Therefore,} \\ \sin (\frac{2\pi}{3}),in\text{ second quadrant is the same } \\ \sin (\frac{\pi}{3}),in\text{ first quadrant.} \\ \sin (\frac{\pi}{3})=\frac{\sqrt[]{3}}{2} \end{gathered}[/tex]Hence, the exact value of the expression is √3/2
At 30 mph a trip from Town A to Town B takes 6 hours. If the speed were doubled, how many hours would the trip take?
The time taken by Town A to Town B will be 3 hours.
What is speed?Speed is defined as the ratio of the time distance traveled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance traveled by time. The unit of speed in miles per hour.
Given that at 30 mph a trip from Town A to Town B takes 6 hours.
The time taken will be calculated as,
Total distance = 30 x 6 = 180 meters
Speed = 30 x 2 = 60 mph
The time,
T = 180 / 60= 3 hours
Therefore, the time taken by Town A to Town B will be 3 hours.
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A local farm raises horses and goats. • Let x represent the number of horses on the farm. • The number of goats is 3 times the number of horses. • The total number of horses and goats on the farm is 96. What is x, the number of horses on the farm?
The number of horses on the harm will be 24.
What is an expression?
Expression in math is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that;
A local farm raises horses and goats.
The total number of horses and goats on the farm is 96.
Let number of horses = x
Since, The number of goats is 3 times the number of horses.
Then, Number of goats = 3x
The total number of horses and goats on the farm is 96.
Hence, we can formulate;
x + 3x = 96
4x = 96
x = 24
Thus, The number of horses on the harm will be 24.
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4505 x 219 standard algorithm
After throughfall calculating the multiplication 4505 x 219 in standard algorithm, we have come to find that product is 986595
What is standard algorithm?In elementary math, a standard algorithm or method is a particular computation technique that is typically taught for resolving particular mathematical issues. In general, these techniques include exchanging, regrouping, long division, long multiplication using a standard notation, and standard formulas for average, area, and volume.
These techniques can vary somewhat by country and time, but they typically include these techniques. Similar techniques are also available for more complex functions like square roots, but they are no longer taught in general mathematics classes because calculators are more convenient.
4505 x 219 in standard algorithm is as follows:
⇒ 4 5 0 5
× 2 1 9
4 0 5 4 5
+ 4 5 0 5
+ 9 0 1 0
9 8 6 5 9 5
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however, she is not quite sure where to start. Using complete sentences, describe to Erika how to solve this equation
Explanation:
For the given equation
[tex]50^x=17[/tex]For Erika to resolve the question
Step 1: We will take the logarithm of both sides
[tex]\log (50^x)=\log (17)[/tex]Step 2: Simplify the expression
Thus
[tex]x\log 50=\log 17[/tex]Step 3: Solve for x
[tex]x=\frac{\log 17}{\log 50}[/tex][tex]x=0.724[/tex]can you help please this is really important
The value of x is 10 and the length of SU is 50.
Here SU is the line and T is the mid-point of the line
So from this we have
SU = ST + TU
ST = TU
SU = 2ST = 2TU
ST = 3x - 5 and TU = 2x + 5
As ST = TU
3x - 5 = 2x + 5
x = 10
SU = 2ST
= 2( 3x - 5)
= 2( 3 × 10 - 5)
= 2( 30 - 5)
= 2× 25
= 50
Therefore the value of x is 10 and the length of SU is 50.
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Question #36 Multiple-Choice Reduce -2 + b2 by 7 + b2. C5 0 2b2-7 C9
Answer:
[tex]-2+b^2-7-b^2=-9[/tex]Step-by-step explanation:
Reduce the following expressions:
[tex]-2+b^2-(7+b^2)[/tex]Operate like terms:
[tex]-2+b^2-7-b^2=-9[/tex]The list price of a DVD player is $129. Sam found the player on sale for $90.30. What was the percent discount?
A percent discount of 30%
Explanation:
Since $129 represent 100% of the price, then the new price $90.30 represent 70 %
129 * 100 / 90.30 = 70 %
Since from the 100% of the price, it went to 70% of it, there was a discount of 30%
100 - 70 = 30%
What is the slope of the line that contains these points? 9 X 17 13 21 -24 -21 -18 Y - -15 slope:
We have to use the slope formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Let's replace the points (9,-24) and (13,-21). Where
[tex]\begin{gathered} x_1=9 \\ x_2=13 \\ y_1=-24 \\ y_2=-21 \end{gathered}[/tex][tex]m=\frac{-21-(-24)}{13-9}=\frac{-21+24}{4}=\frac{3}{4}[/tex]Hence, the slope is 3/4.Graph the equation using the slope and the y-interceptY=-8/5x-4
We got the linear equation:
[tex]y=\frac{-8}{5}x-4[/tex]The slope of this line will be -8/5 and the y-intercept will be -4.
To graph it, first find the intercept with x - axis.
We can find it if we equal the equation to zero.
[tex]\begin{gathered} \frac{-8}{5}x-4=0 \\ \\ -\frac{8}{5}x=4 \\ \\ x=-\frac{20}{8}=-\frac{10}{4}=-\frac{5}{2} \end{gathered}[/tex]Now, we got two points:
[tex](-\frac{5}{2},0),(0,-4)[/tex]To graph the function, we only join these points:
So that's the graph for the function.
Maya has 846 beads. She is making bracelets with 18 beads on each. How many bracelets is she able to make?
Answer:
maya is able to make 47 bracelets
Step-by-step explanation:
You have one box that is 2 and 5 11 feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for 2 and 5 11. If you stack the boxes, about how tall will the stack be
You have one box that is 2 and 5/11
feet tall and a second box that is 2.45 feet tall. Write the decimal expansion for
2 and 5/11. If you stack the boxes, about how tall will the stack be
we have that
[tex]2\frac{5}{11}=2+\frac{5}{11}=\frac{22+5}{11}=\frac{27}{11}=2.454545\ldots[/tex]If you stack the boxes,
we have
2.45+2.45=4.90 ft
ANSWER ONLY A-Ca. what is the students speed from the 3rd to 5th minute?b. at what times during the bike ride did the student come to a stop?c. During what time intervals did the students speed increase?
SOLUTION:
Case: Distance time graph
Method:
a) the students speed from the 3rd to 5th minute
[tex]\begin{gathered} Speed,s \\ s=\frac{4-2.25}{5-3} \\ s=\frac{1.75}{2} \\ s=0.875miles\text{ }per\text{ }minute \end{gathered}[/tex]b) the times during the bike ride did the student come to a stop
d and h
8 minutes and 23 minutes
c) the students speed increase during.
b to c. 1 and 3 minutes
e to f. 11 and 15 minutes
f to g. 15 and 17 minutes
Given the function: f(x) = (x − 3)(x + 7)(x − 1)its f-intercept is:its x-intercepts are:
Given: Given the function: f(x) = (x − 3)(x + 7)(x − 1)
Required: its f-intercept and its x-intercepts.
Explanation:
[tex]f(x)=(x-3)(x+7)(x-1)[/tex]For f-intercept, put x = 0
[tex]\begin{gathered} f(0)=(0-3)(0+7)(0-1) \\ f(0)=21 \end{gathered}[/tex]So the f-intercept is (0,21).
For x-intercepts, put f(x) = 0
[tex]\begin{gathered} 0=(x-3)(x+7)(x-1) \\ x=3,-7,1 \end{gathered}[/tex]So x-intercepts are (3,0),(-7,0) and (1,0).
Final Answer:
f-intercept: (0,21)
x-intercept: (3,0),(-7,0),(1,0).
Given lines l, m and n are all parallel and cut by two transversal lines, find the value of 2. 2 12 6. т х 33 n
Answer:
66
Explanation:
By the Thales theorem, if we have the following figure:
Then, the following equation applies:
[tex]\frac{a}{c}=\frac{b}{d}[/tex]So, in this case, we can formulate the following equation:
[tex]\frac{6}{12}=\frac{33}{x}[/tex]Then, solving for x, we get:
[tex]\begin{gathered} 6\cdot x=33\cdot12 \\ 6x=396 \\ \frac{6x}{6}=\frac{396}{6} \\ x=66 \end{gathered}[/tex]Therefore, the value of x is 66.
What is the polynomial function of lowest degree with rational real coefficients and roots 2 and squared root 5?
The polynomial having the above quantities is expressed as x³ - 2x² - 5x + 10 = 0
The above situations will form a Cubic polynomial. A Cubic polynomial function may be defined as an expression which can be written in the form of ax³ + bx² + cx + d = 0 where a, b, c and d are coefficients and x is the independent variable. Since, the polynomial should have real coefficients so its multiplicity will be equal to 1. Now, the roots of the polynomial are given as 2 and √5. Since, square roots always occur in pair so the polynomial will have -√5 as its root. Now, the polynomial formed will be
(x - 2) (x - √5) (x + √5) = 0
(x - 2) (x² - 5) = 0
x³ - 5x - 2x² + 10 = 0
=> x³ - 2x² - 5x + 10 = 0 which is the required polynomial.
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BE is the diameter of circle A. What's the measure of ∠BCE?Question 12 options:1) 90°2) 88°3) 180°4) 93°
Since BCE is an inscribed angle, it measures half the measure of the inscribed arc.
Angle BCE inscribes the arc BE of 180°, we have:
[tex]\begin{gathered} \text{BCE}=\frac{BE}{2} \\ BCE=\frac{180}{2} \\ \text{BCE}=90\degree \end{gathered}[/tex]Therefore the correct option is 1)
The length of the smaller rectangle is 12 inches and the width is x inches. The length of the larger rectangle is 20 inches and the width is 15 inches. What is the area of the smaller rectangle?
The area of the smaller rectangle is 108 inches².
What is the Area of a Rectangle?The area of a rectangle is calculated to determine the area occupied by the rectangle within its boundary. A rectangle's area (A) is the product of its length 'a' and width or breadth 'b'. As a result, the Area of the Rectangle = (a × b) square units.
Given the dimensions of the smaller rectangle:
Length = 12 inches
Width = x inches
Given the dimensions of the larger rectangle:
Length = 20 inches
Width = 15 inches
To find the value of x we use proportion,
[tex]\frac{12}{x} = \frac{20}{15}[/tex]
Cross-multiplying, we get
12 × 15 = 20x
x = 180/20 = 9
Hence, the width of the smaller rectangle is 9 inches.
Area of the smaller rectangle = length × width
= 12 × 9
= 108 inches²
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Express your answer in scientific notation.
5.4x10^5 + 6.7x10^4
Answer:
Step-by-step explanation:
5.4*10*10*10*10*10+6.7* 10*10*10*10
540,000+6.7*10,000
540,000+60,000
114,000=1.14*10^5
Identify the segments that are skew to line EF. There are four answers.
The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.
The four lines that are skew to line EF are AB, GB, CH, and DC.
What are skew lines?The lines that are not intersecting and perpendicular to each other, are not parallel to each other, and are not coplanar are called skew lines.
We have,
A line EF on the given square figure.
We have the following lines on the given figure.
DG, CB, HA, FA, FG, GB, AB, EH, ED, DC,CH,
We see that,
FG, FA, EH, and ED are perpendicular and intersecting to line EF.
DG, CB, and HA are parallel to line EF.
So the remaining lines will be skew to line EF
i.e AB, GB, CH, and DC
Thus,
The four lines that are skew to line EF are AB, GB, CH, and DC.
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A print shop borrows $4200 from a credit union for 178 days. The credit union charges simple interest at an annual rate of 6.5% for this loan. Assume each day is 1/365 of a year.
round your final answers to the nearest cent.
A) Find the interest that will be owed after 178 days.
B) Assuming the print shop doesn't make any payments, find the amount owed after 178 days.
Using percentages, the answer to both the subparts are:
(A) Interest that will be owed after 178 days: $4,336.5(B) Interest after 178 days if sop doesn't repay: $4,473What is the percentage?A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Although the abbreviations "pct.", "pct.", and occasionally "pc" is also used, the percent symbol, "%," is frequently used to indicate it. A % is a number without dimensions and without a standard measurement.So, since the interest is annual 6.5%:
(A) Interest that will be owed after 178 days:
Interest/2 ⇒ 6.5/2 ⇒ 3.25%Now, 3.25% of 4200:
4200/100 × 3.25 = 136.5$4,336.5(B) Interest after 178 days if sop doesn't repay:
Interest ⇒ 6.5%Now, 6.5% of 4200:
4200/100 × 6.5 = 273$4,473Therefore, using percentages, the answer to both the subparts are:
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12Solve using the Quadratic Formula for 2x2 + 5x – 3 = 0x = -5, 7b. X = -12,2X = -3,42
2x² + 5x - 3 = 0
Multiply the coeeficient of x² and the constant (-3)
That is 2 ( - 3) = -6
Find the numbers whose sum is 5 and whose product is -6
The number is 6 and -1
Replace 5x by the numbers
2x² + 6x - x - 3 = 0
2x( x + 3) - 1 ( x + 3) = 0
(2x - 1 ) ( x + 3) = 0
Either 2x -1 = 0 or x + 3 = 0
2x = 1
x = 1/2 or x = -3