Fractions
Ivanna has to drive 12 miles. She has already driven 1/4 so far.
The distance she has driven is:
[tex]\frac{1}{4}\cdot12=\frac{12}{4}=3[/tex]Ivanna has driven 3 miles so far
Name an angle supplementary to
Supplementary angles are angles that add up to 180 degrees.
To find the supplementary angle to ∠EOD, we find the angle with ∠EOD that makes up a straight line.
Looking at the figure, EC is a straight line and both ∠EOD and ∠DOC fall on this line. These two angles make up 180 degrees.
Thus,
The one supplementary angle to ∠EOD is ∠DOC.
AnswerB#WT 10, 4). 47-3, -1), and Y-5. 11) classify A#XY by its sides ae: Vanhem
Answer:
Isosceles triangle
Explanation:
An isosceles triangle is one in which two side lengths are congruent while the third is not.
Looking at the triangle given we see that the two side lengths WY and WX are the same; therefore, the triangle is isosceles.
What would the Outputs be when the Inputs are 1,7,-3, and -5 if the function is Y=x
The function is:
[tex]y=x[/tex]This means that the output of the function is equal to the input. So when the inputs are 1,7,-3 and -5. The outputs will also be 1, 7, -3 and -5.
In the game of Monopoly, a player is sent to jail if he or she rolls doubles with a pair of dice 3 times in a row.What is the probability of rolling doubles on a single turn? (Enter your probability as a fraction.) _______What is the probability of rolling doubles 3 times in succession? (Enter your probability as a fraction.) _______
The probability of rolling doubles on a single turn is the number of favorable cases over the number of total cases, the favorable cases are those when you get a double, the number of total cases is the number of total possible outcomes.
Now, the number of total possible outcomes is
[tex]6\times6=36.[/tex]The number of favorable cases is
[tex]6.[/tex]Therefore, the probability of rolling doubles is:
[tex]\frac{6}{36}=\frac{1}{6}\text{.}[/tex]Now, the probability of rolling double 3 times in succession is the product of rolling a double in a single turn, therefore:
[tex]P=\frac{1}{6}\times\frac{1}{6}\times\frac{1}{6}=\frac{1}{216}.[/tex]Answer:
The probability of rolling doubles on a single turn is:
[tex]\frac{1}{6}\text{.}[/tex]The probability of rolling doubles 3 times in succession is:
[tex]\frac{1}{216}\text{.}[/tex]10 ydFind the surface area of the closed hemisphere.Enter your answer in terms of A and rounded to thenearest tenth.The surface area is ]# yd? or approximatelyyd?
We have the following:
[tex]A=2\cdot\pi\cdot r^2[/tex]we have that the radius is half the diameter, therefore
[tex]\begin{gathered} r=\frac{d}{2}=\frac{10}{2} \\ r=5 \end{gathered}[/tex]replacing:
[tex]\begin{gathered} A=2\cdot\pi\cdot5^2 \\ A=50\pi\cong157 \end{gathered}[/tex]The surface area is 50*pi yd^2 or approximately 157 yd^2
Consider the first 2 terms of the sequence 28, 14, ...
Determine whether the sequence is arithmetic or geometric. Explain your reasoning.
please help me with 1 and 2
With the first term being 28 and the difference being 2, this geometric progression is finite because 28 is divided by 14 and then that number is divided by 2 and so on.
What is geometric progression?
A mathematical sequence known as a geometric progression (GP) is one in which each succeeding term is generated by multiplying each preceding term by a fixed number, or "common ratio." This progression is also referred to as a pattern-following geometric sequence of numbers. A geometric progression is a series in which each term can be obtained by multiplying or dividing the term before it by a predetermined amount. Infinite GP sum refers to the total number of terms in an infinite GP. S_ = a/(1 - r), where an is the first term and r is the common ratio, is the formula for calculating the sum of an infinite geometric progression.
Here,
This is geometric progression with first term 28 and difference 2 and this is finite GP as 28 is divided by 14 then 14 is divided by 2 so on as the definition of GP says, "a series of numbers with a fixed ratio between each and the previous one (e.g., each subsequent number is increased by a factor of 3 in the progression 1, 3, 9, 27, 81 )".
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Write the slope-intercept form of the equation of the line described. 11.) through: ( 1 , 2 ) , perpendicular to Y= -1/5x +2
We would like to find the equation of the line that passes through the point (1.2) and is perpendicular to the line y=-1/5 x +2, and write in slope intercept form. To do this first we have to remeber that the equation of a line is given by
[tex]y-y_1=m(x-x_1)[/tex]and that to find it we need a point and the slope. In this case we have the point but we don't know the slope yet. To find the slope we notice that the line has to be perpendicular to the line y=-1/5 x +2. We need to remember that two lines are perpendicular if and only if
[tex]m_1m_2=-1[/tex]where m1 and m2 are the slopes of the lines.
The line y=-1/5 x +2 is wirtten in the slope-intercept form:
[tex]y=mx+b[/tex]from this we notice that its slope is -1/5, then using the relation for perpendicular lines we have that
[tex](-\frac{1}{5})(m)=-1[/tex]Solving for m we have that
[tex]\begin{gathered} m=\frac{-1}{-1}(5) \\ =5 \end{gathered}[/tex]So, our line passes through the point (1,2) and has an slope equal to 5. Plugging this values on the equation for a line we have
[tex]\begin{gathered} y-2=5(x-1) \\ y-2=5x-5 \\ y=5x-5+2 \\ y=5x-3 \end{gathered}[/tex]so the equation of the line we were looking for is y=5x-3. (Notice that it is already written in the adequate form).
22. [-/2 Points]DETAILS OSELEMALG1 1.4.325.Translate to an algebraic expression, but do not simplify.the quotient of -4 and the sum of a and b†
Given:
The quotient of -4 and the sum of a and b.
Required:
To translate to an algebraic expression.
Explanation:
The sum of a and b is
[tex]a+b[/tex]The quotient of -4 and the sum of a and b is
[tex]\frac{-4}{a+b}[/tex]Final Answer:
[tex]-\frac{4}{a+b}[/tex]What is the equation of the line of best fit for the following data? Round theslope and y-intercept of the line to three decimal places.ху2258.7.109111113
Answer:
Explanation:
The equation o
I am having a little bit of trouble on this (help)
Answer:
D
Step-by-step explanation:
We should use ratio.
AB is 5
DE is 10
AB/DE = 1/2
BC is 12 and EF is 24
BC/EF=1/2
AC is 13 and DF is 26
AC/DF= 1/2
So we can write the equation like D choice.
Solve the following equation for x.x^2−47=17List your answers separated by a comma, not using a ± sign and do not include x= in your answer.Question 2 options:3, 5-9, 9-8, 8-30, 0
ANSWER :
The values of x are -8 and 8
EXPLANATION :
From the problem, we have the equation :
[tex]x^2-47=17[/tex]Add 47 to both sides :
[tex]\begin{gathered} x^2-47+47=17+47 \\ x^2=64 \end{gathered}[/tex]Take the square root of both sides :
[tex]\begin{gathered} \sqrt{x^2}=\sqrt{64} \\ x=\pm8 \end{gathered}[/tex]May you solve the system of linear equations by graphingm?
We shall begin by plotting the graph of the equations given which are;
[tex]\begin{gathered} y=\frac{1}{3}x+6 \\ y=-\frac{2}{3}x+3 \end{gathered}[/tex]The black line shows the graph of y = [1/3]x + 6
The red line shows the graph of y = [-2/3]x + 3
The solution to these system of equations is at the point (-3, 5)
mrs corwin has a contractor install a new quarter circle window in her house like shown at right. what is the area of the window? use 3.14 pi. round to the nearest tenth
The area of a circle is given by:
[tex]A=\pi r^2[/tex]Since it is a quarter of the circle, the area is:
[tex]\begin{gathered} A=\frac{\pi r^2_{}}{4} \\ where \\ r=7 \\ \pi=3.14 \\ so\colon \\ A=\frac{(3.14)(7^2)}{4} \\ A\approx38.5in^2 \end{gathered}[/tex]Carter plays 5/8 of a basket ball game. The basket ball game is 40 minutes long. Which if the following shows how to find the number of minutes carter plays?how do we do it?
Answer:
C.
Explanation:
The number of minutes played by Carter is given below:
[tex]\begin{gathered} \text{Multiply the fraction of time Carter played by the total time of a basketball game:} \\ =\frac{5}{8}\times40 \\ =\frac{5\times40}{8} \\ =25 \end{gathered}[/tex]Hence, C is the correct option
Need help with relationship between measures of two given angles
Note that in the picture we are asked about the angles QRW and RWQ. This two angles are part of the the same triangle. So we can ignore the rest of the image and focus only on the triangle that contains both. We have the following
Using this information, we can see that the measure of the three sides of the triangle are different. This means that the triangle is a scalene triangle. This type of triangles have the property that the measure of each angle is different from the other. So, we know that the measure of angles QRW and RWQ are different.
To dig deeper in the problem, we will use the sines law for triangle, which states the following. If we have a triangle of the form
Then, we have the following
[tex]\frac{\sin A}{a}=\frac{\sin B}{b}=\frac{\sin C}{c}[/tex]In this case, we have c=45 and a=47, so we have
[tex]\frac{\sin A}{47}=\frac{\sin C}{45}[/tex]where A is the angle RWQ and C is the angle QRW, if we multiply both sides by 45, we get
[tex]\sin C=\frac{45}{47}\cdot\sin A[/tex]In this case, we have that 45/47 < 1. Since angles A and C are less than 180° degrees, the sine of this angles is a positive number, so we have that
[tex]\sin C=\frac{45}{47}\cdot\sin A<\sin A[/tex]Note also that angles A and C should have a measure less than 90°. Over this interval, the sine function is an increasing function, which means that if sin(C)So we have that the measure of angle QRW is less than the measure of angle RWQ.
Construct a Venn diagram where U={a,b,c,d,e,f,g}, A={b,d,f,g}, and B={b}.Move each of the lettered points to an appropriate region on the Venn diagram.
Explanation:
Given the universal set, U and subsets A and B as follows:
• U={a,b,c,d,e,f,g}
,• A={b,d,f,g}
,• B={b}
Answer:
The Venn diagram representing the sets is given below:
Note:
• The ,letter b is common to both A and B,, so we put it in the intersection of both sets.
,• The ,letters a, c, and e do not belong to either A or B,, so we place it outside of the two sets.
He cosed that the system has an esse number of solutions. Which is the BEST evaluation of Alfred's conclusion
At for any positive value of the corresponding value of is negative, which means the system has no solution
08 Nescored both equations describe lines that have infinitely many solutions
00 scored if the st equation is moped by a and added to the second equation, the result is 136, which leads to exactly one solution
00 escorect if the fest equation is multiplied by 4 and subtracted from the second equation, the result is 3a8y--14, which means the
system has an inte number of solutions SO HELP
Answer: 08
Step-by-step explanation:
Jane is a software saleswoman. Her base salary is $1500, and she makes an additional $110 for every copy of English isFun she sells.Let P represent her total pay (in dollars), and let N represent the number of copies of English is Fun she sells. Write anequation relating P to N. Then use this equation to find her total pay if she sells 29 copies of English is Fun.
You know that "P" represents her total pay (in dollars) and "N" represents the number of copies of English is Fun Jane sales.
According to the information given in the exercise, Jane makes $110 for every copy of English is Fun, then you can set up the following expression for this:
[tex](110)(N)=110N[/tex]Knowing that her base salary is $1500, you can conclude that her total pay "P" will be the sum of her base salary and the amount of money she makes for every copy she sells. Based on this, you can write the following equation relateion "P" to "N":
[tex]P=1500+110N[/tex]If Jane sales 29 copies of English is Fun, then:
[tex]N=29[/tex]Substituting this value into the equation and evaluating, you get:
[tex]\begin{gathered} P=1500+(110)(29) \\ P=1500+3190 \\ P=4690 \end{gathered}[/tex]The answers
- Equation:
[tex]P=1500+110N[/tex]- Solution:
[tex]P=4690[/tex]Her total pay if she sells 29 copies of English is Fun, is $4690
what is the slope formula (-12,-2) and (18,4) ?
The slope is given by:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]In thie case we have:
[tex]\begin{gathered} m=\frac{4-(-2)}{18-(-12)} \\ =\frac{4+2}{18+12} \\ =\frac{6}{30} \\ =\frac{1}{5} \end{gathered}[/tex]therefore the slope between this points is 1/5.
Which of the following equations describes the graph? (options included)
So,
Given a quadratic equation of the form:
[tex]y=ax^2+bx+c[/tex]There's some important facts we could use to determine which options are not correct.
First fact: the y - intercept of the graph is the number c. So, if our graph intercepts at y=1, that means that c=1.
For that reason, option A is not correct, because c=1.
Second fact: the sign of the number "a", will determine the concavity of the graph. This is, in other words:
That means that if "a" is positive, the graph will has the form of the left, and if "a" is negative, it will take the form of the right side.
Based in this, we can see that our graph has the form of the left side, so "a" has to be positive.
For that reason, options A and C are incorrect.
Now we should pick between B or D.
The third fact, is that, when the sign of "b" is negative, our graph seems to be moved to the right.
When the sign of b is positive, the graph seems to be moved to the left.
As you can see, our graph seems to be moved to the right, so the sign of b should be negative.
For these reasons, the appropiate answer is D.
[tex]y=\frac{1}{2}x^2-2x+1[/tex]
If a number is raised to a power of 2, it is A. CubbedB. Powered C. Squared
If we raise a number to a power of 2, we can represent the result graphically as shown below (where n is the number to be raised to a power of 2)
This is a square of side equal to n.
Therefore, the answer is option C, squared.
What is thX= ら*e coefficient of the term x³y5 in the expansion of the binomial expression (2x − y)³?
The coefficient of the term x²y in the binomial expansion of (2x − y)³ is -12.
The expression (2x − y)³ can be simplified as
8x³−12x²y+6xy²−y³ .
Thus the coefficient of the binomial expansion is -12.
Of the use of the binomial theorem, it is possible to determine the expanded value of either formula with the form (x + y)ⁿ.
The values of (x + y)², (x + y)³, and (a + b + c)² can be easily determined by adding the integers algebraically in accordance with the exponent value.
The binomial theorem was first mentioned by a well-known Greek mathematician by the name of Euclid in the fourth century BC.
According to the binomial theorem, which represents it as a sum of terms using distinct exponents of the variables x and y, the algebraic statement (x + y)ⁿ can be expanded. A coefficient, or numerical value, is assigned to each word in a binomial expansion.
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PLEASE HELP ME ASAP!!!! I NEED YOU!
2. Consider the linear expression.
3.2a - 1 - 4 1/3 + 7 - a
(a) What are the like terms in the expression?
(b) Simplify the linear expression.
Please answer question in this format:
(expression)
= (next step)
= (next step)
= (next step)
= (answer)
1) 3.2a , a and 1 , 4 1/3 , 7 are the like terms in the expression.
2) 2.2a + 1.66 is the simplified linear expression
What is linear expression ?The greatest power of a variable in a linear equation is always equal to 1. A one-degree equation is another name for it. A linear equation with one variable is typically expressed as Ax + B = 0. Here, the variables x and A and B are constants and coefficients, respectively.
Calculation1 ) Merger of similar items 3.2a , a
and 1 , 4 1/3 , 7
2 ) 3.2 a -1 - 4 1/3 + 7 -a
= 3.2a - a - 1 - 4 1/3 + 7
= 2.2a + 6 - 13/3
= 2.2a + 6 - 4.34
= 2.2a + 1.66
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a car rental company leases automobiles for a charge of 20 birr / day plus 2birr/km write an equation for the cost y birr in terms of the distance X driven , if the car is leased for 5 days.
The equation for the cost y birr in terms of the distance X driven is y = 20 + 2x.
When the car is leased for 5 days, the cost is 100 + 2x.
How to calculate the value?From the information, the car rental company leases automobiles for a charge of 20 birr / day plus 2birr/km.
The equation for the distance x will be:
= 20 + (2 × x)
= 20 + 2x.
When the car is leased for 5 days, this will be:
= 5(20) + 2x.
= 100 + 2x
= 100 + 2x
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7. What equation is represented by this illustration?OOOOOOOOO A 2x + 4 = 8x +1OB. 42 - 2 = 2 - 8O 0.42 +2 = 8O D.4.2 + 2 = 2 +8
We have 4 x's and 2 "units" in the left side. We know that this is equal or equivalent to one X and 8 units, pictured in the right side.
So we can write the left side as: 4x+2
And the rigth side as: x+8
As both sides are equal, we can write:
[tex]4x+2=x+8[/tex]The answer is Option D: 4x+2=x+8
Write an equivalent expression for each expression without drawing a diagram: a) (x + 2)(x+6) b.) (x + 5)(2x + 10)
For the experiment, determine the two given events are independent. The answers are guessed on a twenty-question multiple-choice test. The events are "the first question is correct" and "the second answer is correct". Are the two events independent or not independent?
Two events are independent when one of the events happen and the result does not affect on the result for the second event.
In this case if we have multiple-choice answers on the test the probability of having the correct answer for both of them is the same, however if we get the first one correct it does not mean that we will have the second answer correct.
For this reason the events are independent.
Perform the following operationand express the answer inscientific notation.5.7365x10-5 = 3.4891x10-8[ ? ]x10?)Coefficient (green)Exponent (yellow)Enter
Both numerator and denominator have 5 significant figures, then the quotient will have 5 significant figures too.
Choose the best selection for thequadrilateral with vertices at thefollowing points:(4,0), (8,0), (4,-4), (8,-4)Hint: Start by graphing the points.Distance Formula: d= (x2 – x1)2 + (y2 - y1)2A. RectangleB. SquareC. RhombusD. Trapezoid
We are given coordinates of four points and we are asked to find the best selection of the shape.
In order to know what shape this is, we simply graph all the points and see what shape we get.
Using a graphing calculator, the points make up the following shape:
Now that we have the shape, we know that it can either be a Rectangle or a Square.
If the shape is a rectangle, the lengths x and y are not equal. If the shape is a square, lengths x and y are equal.
In order to find x and y, we use the distance formula given to us as:
[tex]\begin{gathered} |d|=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)^2} \\ \text{where,} \\ (x_2,y_2)\to\text{ Second point} \\ (x_1,y_1)\to\text{ First point} \end{gathered}[/tex]Now let us find x and y.
x:
The points that make up the length x are:
(4, 0), and (4, -4)
Therefore, length x can be gotten as:
[tex]\begin{gathered} x_2=4,y_2=0,x_1=4,y_1=-4 \\ |x|=\sqrt[]{(4-4)^2+(0--4)^2} \\ |x|=\sqrt[]{4^2} \\ \\ \therefore|x|=4 \end{gathered}[/tex]Now we find y.
y:
The points that make up the length y are:
(4, 0) and (8, 0)
Therefore, length y can be gotten as:
[tex]\begin{gathered} x_2=4,y_2=0,x_1=4,y_1=-4 \\ |x|=\sqrt[]{(4-4)^2+(0--4)^2} \\ |x|=\sqrt[]{4^2} \\ \\ \therefore|x|=4 \end{gathered}[/tex]i have the first answer but keep getting the second one wrong please help!!
Kenyan = k
$3.50 per pound
Sri Lankan = s
$5.60 per pound
6lbs of blend
$28.35
s+k = 6
3.50k + 5.60s = 28.35
where:
k = lbs of kenyan
s = lbs of Sri Lankan
Solve the system
s+k = 6
3.50k + 5.60s = 28.35
solve the first equation for s:
s = 6-k
Replace in the second equation:
3.50k + 5.60 (6-k) = 28.35
3.50k + 5.60(6)+ 5.60(-k) = 28.35
3.50k + 33.6 - 5.60k = 28.35
3.50k - 5.60k = 28.35-33.6
-2.1k= -5.25
k= -5.25/-2.1
k= 2.5 lbs
Replace k on any equation and solve for s
s+k= 6
s+ 2.5 = 6
s= 6-2.5
s= 3.5 lbs