Final answer:
To simplify the expression, factorize the numerator and then cancel out any common terms with the denominator, resulting in the expression 1 / 3 + 2 / (3x).
Explanation:
To simplify the given expression 2x2 - 10x - 28 over 6x × (6x - 7), we need to factorize the numerator and see if any terms cancel out with the denominator. The factored form of the numerator is (2x + 4)(x - 7). The denominator can be written as 6x(6x - 7).
When we place the numerator over the denominator, we see that (x - 7) cancels out, simplifying our expression to (2x + 4) / 6x. This can further be simplified to 1 / 3 + 2 / (3x) by dividing both terms in the numerator by 6x
Please help 30 points Asap
40 units2˛
Looking at the figure, the rectangle has the vertexes (2,1), (3,-3), (-5,-5) and (-6,-1). The parallelogram has the vertexes (2,7), (3,3), (3,-3), and (2,1).
The area of a parallelogram is base times height. We have 2 vertical lines at x=2 and x=3, so the height is 1. And the length of the line from (3,3) to (3,-3) is 6, so the base is 6. Therefore the area of the parallelogram is 1*6 = 6.
The rectangle is a tad trickier since it's not aligned with either the x or y axis. But we can use the Pythagorean theorem to get the lengths.
L = sqrt((2 - -6)^2 + (1 - -1)^2)
L = sqrt(8^2 + 2^2)
L = sqrt(64 + 4)
L = sqrt(68) = 2*sqrt(17)
W = sqrt((2-3)^2 + (1- -3)^2)
W = sqrt((-1)^2 + 4^2)
W = sqrt(1 + 16)
W = sqrt(17)
And the area is length * width, so:
2*sqrt(17)*sqrt(17) = 2 * 17 = 34
And the total area is the sum of the areas, so
34 + 6 = 40
So the area of the figure is 40 square units.
Answer:
40 units ^2
Step-by-step explanation:
when finding an odd shaped figure, make sure to divide it up into porportions. Then figure out the square and then the triangles.
the answer would be: 40 units ^2
hope this helps!!
In what quadrant of the coordinate plane is the graph of the direct proportion located which is parallel to the graph, expressed by the formula:
Note: Please answer both questions in the same format (The direct proportion is ____. The graph is located on quadrants ___ and ___.).
Answer:
Part 1) The direct proportion is [tex]y=0.8x[/tex]. The graph is located on quadrants I and III
Part 2) The direct proportion is [tex]y=-0.4x[/tex]. The graph is located on quadrants II and IV
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Part 1) we have
[tex]y=0.8x-1.6[/tex]
Remember that
If two lines are parallel, then their slopes are the same
In this problem, the slope of the given line is [tex]m=0.8[/tex]
therefore
The direct proportion is [tex]y=0.8x[/tex]
The graph is located on quadrants I and III
see the attached figure to better understand the problem
Part 2) we have
[tex]y=-0.4+1[/tex]
Remember that
If two lines are parallel, then their slopes are the same
In this problem, the slope of the given line is [tex]m=-0.4[/tex]
therefore
The direct proportion is [tex]y=-0.4x[/tex]
The graph is located on quadrants II and IV
see the attached figure to better understand the problem
A game for $40 and the sales tax is two dollars what percent of the game price are you paying sales tax
Answer: 5%
Step-by-step explanation: In order to calculate the sales tax rate you divide the amount of the sales tax by the purchase price.
$2/40 = .05 = 5%
The interest rate is 5%.
Carrie can print 24 photos in 8 minutes.At this rate, how many can she print in 3 minutes
[tex]24 \div 8 = 3 \: photos \: in \: 1 \: minute[/tex]
[tex]3 \: photos \: per \: 1 \: minute\: \times 3 \: minutes \: \\ = 9 \: photos \: per \: 3 \: minutes[/tex]
9 photos
50 POINTS PLEASE HELP ME!!!!!!!! HURRY!!!!
Evaluate
6!
8P5
12C4
what are we supposed to evaluate, here? i dunno what your asking us to do
A tangent to a circle at point A is given, and point A is an endpoint of a chord, which is the same length as radius of the circle. What is the measure of angle between the tangent and the chord?
PLS HELP SQDANCEFAN!!!!! I NEED HELP I DON'T GET IT :((((
Answer:
30°
Step-by-step explanation:
Call the other end of the chord point B and the center of the circle point O. Then triangle AOB is an equilateral triangle, since OA = OB = AB.
Angle OAB is the internal angle of that triangle, so is 60°. Since OA is perpendicular to the tangent line (makes an angle of 90°), The angle between the tangent line and the chord must be ...
90° - 60° = 30°
___
The other way you know this is that central angle AOB is 60°, and the tangent-to-chord angle is half that, or 30°.
_____
One way to remember the angle relationship between a tangent line and a chord is this:
Consider a point C on long arc AB. The measure of inscribed angle ACB is half the measure of central angle AOB, no matter where C is on the circle. (If C happens to be on the short arc AB, then central angle AOB is a reflex angle, but the relationship still holds.) Consider what happens when C approaches A. The angle at vertex C is still the same: 1/2 the measure of central angle AOB. This remains true even in the limit when points A and C become coincident and line AC is a tangent at point A.
The figures below are similar. Compare the smaller figure to the larger. Which of the following is the ratio of the perimeters of the figures?
Answer: first option
Step-by-step explanation:
As you can see in the figures shown in the image attached, the lenght of a side of the smaller figure is 2 inches and the the lenght of a side of the larger figure is 4 inches.
Therefore, you can find the ratio as following:
[tex]ratio=\frac{2in}{4in}[/tex]
Now, you must reduce the fraction. Therefore, you obtained that the ratio of the perimeters of the figures is:
[tex]ratio=\frac{1}{2}[/tex]
Which can be written in the following form:
[tex]ratio=1:2[/tex]
Then, the answer is the first option.
What basic trigonometric identity would you use to verify that sinx + 1/ sinx = 1+ cscx
Answer:
C) We use csc = [tex]\frac{1}{sinx}[/tex] to verify.
Step-by-step explanation:
Given : [tex]\frac{sinx+ 1}{sinx}[/tex] = 1 +csc x.
To find : What basic trigonometric identity would you use to verify.
Solution : We have given that [tex]\frac{sinx+ 1}{sinx}[/tex] = 1 +csc x.
To verify we need to show left hand side equal to right hand side.
For right hand side
1 +csc x
By csc = [tex]\frac{1}{sinx}[/tex].
Plug the value csc = [tex]\frac{1}{sinx}[/tex].
1 + [tex]\frac{1}{sinx}[/tex].
Taking least common multiple
[tex]\frac{sinx +1}{sinx}[/tex] = left hand side.
We can see this is equal to left hand side
Hence , left hand side = right hand side.
Therefore, C) We use csc = [tex]\frac{1}{sinx}[/tex] to verify.
What is the domain of the function below
F(x)=(52)(47)^(x-4)
Answer:
[tex]\large\boxed{x\in\mathbb{R}}[/tex]
Step-by-step explanation:
[tex]f(x)=(52)(47)^{x-4}[/tex]
It's an exponential function.
The domain of an exponential function is the set of all real numbers.
Please help! I give brainliest!
Answer:the answer is c I literally just took this lol can I get brainliest pls
Step-by-step explanation:it would be helpful and my first
A line has a slope of -3 and y-intercept of 5. write the equation of the line in slope intercept. form and explain how you would use the slope and y-intercept to graph the equation.
Equation: y= mx + b
y = -3x +5
Graph the y intercept first.
Go down three times on the y axis.
Go across one because of -3/1 .
The equation of the line is y = -3x + 5. To graph the equation, plot the y-intercept and use the slope to find additional points on the line.
Explanation:
The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. In this case, the slope is -3 and the y-intercept is 5, so the equation of the line is y = -3x + 5. To graph the equation, start by plotting the y-intercept of (0, 5). Then use the slope to find additional points on the line. For every increase of 1 on the x-axis, the y-value decreases by 3. You can use this pattern to plot more points and draw a straight line connecting them.
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similarities between finding the perimeter and area of a polygon with and without the coordinate plane
A Polygon is shape with straight sides and must be closed. Polygon sides never touch and are classified according to the number of its sides. So:
A Triangle is any polygon with exactly 3 sidesA Quadrilateral is any polygon with exactly 4 sides. A Pentagon is any polygon with exactly 5 sides. An Hexagon is any polygon with exactly 6 sides. A Heptagon is any polygon with exactly 7 sides. An Octagon is any polygon with exactly 8 sides. A Nonagon is any polygon with exactly 9 sides. Decagon is any polygon with exactly 10 sides.1. WITH THE COORDINATE PLANE:If you have the coordinate plane, there are several ways to calculate the perimeter and area. If the polygon meaning that every side must have the same length and every angle must have the same measure, you just need the coordinates of two points and by using the distance formula you can calculate the length of that side. Then you must multiply the number of sides by that distance and this is the perimeter, but if the polygon is irregular you must calculate the length of each side of the polygon using the distance formula and then make the sum. To compute the area, you must divide the entire polygon in triangles, rectangles, parallelograms, etc, and then calculating the area of each figure using the formulas known for each type of figure.
2. WITHOUT THE COORDINATE PLANE:If you don't have the coordinate plane, you need to have the length of each side to calculate the perimeter or each side should be calculated by using trigonometry and other mathematical skills. If the polygon is regular or is a known figure (trapezoid, parallelogram, triangle) you can use the formulas you know to compute the area of that figure. On the other hand, if the polygon is irregular you should divide the polygon in other simple figures and calculate each area and then making the sum.
_______________________
In conclusion, for both ways you need to have the length of each side to find the perimeter and can use well known formulas to find the area of the figure.
Patrick is buying a new pair of shoes. The expression shown below represents the sales tax on the price of the shoes,s. 0.06s By what number can Patrick multiply the price of the shoes, s, to determine the total amount he will need to pay for them including the tax?
Answer: 1.06
Step-by-step explanation:
This is the answer because the price of the shoes is s, and the tax is 0.06s. The total cost of the shoes with tax is s+0.06s= 1.06s
Answer:
Your answer is 1.06
Step-by-step explanation:
A certain drug is made from only two ingredients: compound A and compound B. There are 3 milliliters of compound A used for every 4 milliliters of compound B. If a chemist wants to make 533 milliliters of the drug, how many milliliters of compound B are needed?
Answer:
[tex]304\dfrac{4}{7}\ milliliters[/tex]
Step-by-step explanation:
If there are 3 milliliters of compound A used for every 4 milliliters of compound B, then we can denote that we use 3x milliliters of compound A and 4x milliliters of compound B to get 533 milliliters of the drug. Thus,
[tex]3x+4x=533,\\ \\7x=533,\\ \\x=\dfrac{533}{7}\ milliliters.[/tex]
Hence, a chemist must take
[tex]4\cdot \dfrac{533}{7}=\dfrac{2132}{7}=304\dfrac{4}{7}\ milliliters[/tex]
of compound B.
Answer:
228.43 ml
Step-by-step explanation:
The ratio of compound A to compound B will be; 4: 3
4:3 is the same as 4x:3x where 4x is compound A and 3x is compound B.
We can solve for "x":
If amount of compound A is 4x and compound B is 3x;
Then; 4x + 3x = 533
7 x = 533
x = 533/7
Then amount of compound B is 3x = 3(533/7)
= 228.43 ml
A figure is translated using the rule (x, y) → (x – 3, y + 6). Which describes how the figure is moved? left 3 units and down 6 units right 3 units and down 6 units left 6 units and down 3 units left 3 units and up 6 units
Answer:
left 3 units and up 6 units
Step-by-step explanation:
we know that
The rule of the translation is equal to
[tex](x,y)------> (x-3,y+6)[/tex]
That means
(x-3)-----> The figure is moved 3 units to the left, because the number is negative
(y+6)----> The figure is moved 6 units up because the number is positive
Answer:
left 3 units and up 6 units
Step-by-step explanation:
Ava put 10 spoons of sugar in 5 coffees. How many spoons of sugar does Ava put in one coffee
Answer:
2 spoonfuls of sugar in each coffee.
Step-by-step explanation:
If there are 10 spoonfuls of sugar in 5 coffees, simply divide 10 by 5. Then you find that for every 1 coffee, she puts 2 spoonfuls.
Answer:
Ava puts two spoons of sugar in each coffee.
Step-by-step explanation:
We can find this by dividing the total number of spoons of sugar by the total number of coffees.
10 spoons/5 coffees = 2 spoons per coffee
tabitha defines a sphere as the set of all points equidistant from a single point. Is Tabitha's definition valid?
answer; it is valid because all spheres fit this definition, and figures that are not spheres do not fit this definition.
definition is valid since center is exactly 1radius away from any point on the outersurface.
other figures do not fit this defn
Answer:
Tabitha's defintion is valid.Step-by-step explanation:
Her definition is valid because the sphere is basically defined by its radius, which is the equidistant points towards a center. If points are not equidistant, then that's not a sphere.
Also, Tabitha is considering "a set of points" referring to infinite points on the surface of the sphere. The single point she mentioned is the center.
Therefore, Tabitha's definition is valid because she's considering all elements that define a sphere.
Calculate the Difference Quotient for f(x)=2x^2-3
Answer:
Calculate the Difference Quotient for f(x)=2x^2-3
Find f(x+h) and f(x), and plug these values into the difference quotient formula.
4x+2hHas the marrying age of a man changed over the years? The United States Bureau of the Census takes a formal count of everyone in the U.S. every 10 years and has provided the following data that gives the median age of an American man at the time of his first marriage.
Year / Median Age
1910 / 25.1
1920 / 24.6
1930 / 24.3
1940 / 24.3
1950 / 22.8
1960 / 22.8
1970 / 23.2
1980 / 24.7
1990 / 26.1
2000 / 26.8
Determine the average rate of change in median age per year from 1950 to 1990.
a.) 0.0825 years of age per year
b.) 0.825 years of age per year
c.) 1.21 years of age per year
d.) -1.21 years of age per year
Answer:
a.) 0.0825 years of age per year
Step-by-step explanation:
By the given table,
The median age at the time of first marriage on 1950 = 22.8 years,
While, the median age on 1990 = 26.1 years,
Hence, the average rate of change in median age per year from 1950 to 1990
[tex]=\frac{22.8 - 26.1}{1950 - 1990}[/tex]
[tex]=\frac{-3.3}{-40}[/tex]
[tex]=0.0825\text{ years of age per year}[/tex]
That is, OPTION a) is correct.
Answer:
It is D
Step-by-step explanation:
got it right on edge
Two geometry questions! Double the points thanks in advance!
2x-4+50=100
2x-4=50
2x=54
x=27º
2x+4x=90
6x=90
x=15º
1. Simplify 100 = (2x - 4) + 50
x = 27
2. Complementary mean the angles equal 90 degrees when added, so
90 = 2x + 4x
x = 15
Me banks left work at 5:15cpm it took him 1 1/4 hours to drive home at what time did me banks arrive home
Answer:
the answer would be 6:30 pm
Step-by-step explanation:
if you left work at 5:15 and it took 1 1/4 min to get home
you would
find 1/4 witch would be 15 min because 60/4= 15
then add 1:15 to 5:15
1:15 + 5:15 = 6:30 pm
you arrived home at 6:30 pm
Mr. Banks would get home at 6:30 PM after leaving work at 5:15 PM and driving for 1 hour and 15 minutes.
The student asked what time Mr. Banks would arrive home if he left work at 5:15 PM and took 1 and 1/4 hours to drive home. To solve this, we need to add the travel time to the departure time. Since 1 and 1/4 hours is the same as 1 hour and 15 minutes, we simply add this to 5:15 PM. Adding 1 hour to 5:15 PM, we get 6:15 PM. Then, adding the remaining 15 minutes, we get 6:30 PM. This means Mr. Banks would arrive home around 6:30 PM.
need help filling in the blanks.. (comparing depreciation methods.)
Answer:
Refer to step-by-step.
Step-by-step explanation:
Fixed Cost Per Deck = Total Fixed Cost/Estimated Deck Sales
Fixed Cost Per Deck = 85000/13000
Fixed Cost Per Deck = $7.08
Break Even Point in Units = Fixed Costs/ Sales Price per Unit - Variable Cost
Break Even Point in Units = 85000/11.95 - 3
Break Even Point in Units = 9497
Fixed Cost Per Deck = Total Fixed Cost/Estimated Deck Sales
Fixed Cost Per Deck = 85000/10000
Fixed Cost Per Deck = $8.50
Break Even Point in Units = Fixed Costs/ Sales Price per Unit - Variable Cost
Break Even Point in Units = 85000/12.95 - 3
Break Even Point in Units = 8543
Break Even Point in Units = Fixed Costs/ Sales Price per Unit - Variable Cost
Break Even Point in Units = 85000/13.45 - 3
Break Even Point in Units = 8134
1.Total Cost = Variable Cost/unit x Units Produced + Fixed cost
Total Cost = (3 x 13000) + 85000
Total Cost = 39000 + 85000
Total Cost = $124000
2.Total Cost = Variable Cost/unit x Units Produced + Fixed cost
Total Cost = (3 x 10000) + 85000
Total Cost = 30000 + 85000
Total Cost = $115000
3. $12.95 and $13.45.
Because the total cost is greater than the revenue.
Let's try at $12.95:
Revenue = 12.95 x 8000
Revenue = $103600
Total Cost = (3 x 8000) + 85000
Total Cost = 24000 + 85000
Total Cost = $109000
Profit = Revenue - Total Cost
Profit = 103600 - 109000
Profit = $-5400
Now at $13.45:
Revenue = 13.45 x 7000
Revenue = $94150
Total Cost = (3 x 7000) + 85000
Total Cost = 21000 + 85000
Total Cost = $106000
Profit = Revenue - Total Cost
Profit = 94150 - 106000
Profit = $-11850
4. The fixed costs to produce $13.45 decks is so much greater than the fixed costs to produce 10.95 due to the estimated deck sales.
In a city school, 60% of students have blue eyes, 55% have dark hair, and 35% have blue eyes and dark hair. What is the probability (rounded to the nearest whole percent) that a randomly selected student will have dark hair, given that the student has blue eyes?
Hint:
P(A|B)=P(A∩B) / P(B)
64%
58%
80%
20%
Answer:
58%
Step-by-step explanation:
This is a problem of conditional probability.
Let A represent the event that student has dark hair.
So P(A) = 55% = 0.55
Let B represents the event that student has blue eyes.
So, P(B) = 60% = 0.60
Probability that student has blue eyes and dark hairs = P(A and B) = 35% = 0.35
We are to find the probability that a randomly selected student will have dark hair, given that the student has blue eyes. Using the given formula and values, we get:
[tex]P(A|B)=\frac{P(A \cap B)}{P(B)}\\\\ P(A|B)=\frac{0.35}{0.60}\\\\ P(A|B)=0.58[/tex]
Therefore, there is 0.58 or 58% probability that the student will have dark hairs, given that the student has blue eyes.
A cone with a radius 2 units is shown below. Its volume is 29 cubic units. Find the height of the cone
Answer:
The height of the cone is [tex]6.9\ units[/tex]
Step-by-step explanation:
we know that
The volume of the cone is equal to
[tex]V=\frac{1}{3}Bh[/tex]
where
B is the area of the circular base of the cone
h is the height of the cone
In this problem we have
[tex]V=29\ units^{3}[/tex]
[tex]r=2\ units[/tex]
Find the area of the base B
[tex]B=\pi r^{2}[/tex]
substitute the value of r
[tex]B=\pi (2)^{2}=4 \pi\ units^{2}[/tex]
Find the height of the cone
[tex]29=\frac{1}{3}(4 \pi)h[/tex]
[tex]h=29*3/(4 \pi)[/tex]
assume [tex]\pi=3.14[/tex]
[tex]h=29*3/(4*3.14)=6.9\ units[/tex]
A triangle has a base of 8 cm and a height of 12 cm. What is the area of the triangle? Enter your answer in the box. Cm?
Answer:
The area is 48 cm^2
Step-by-step explanation:
The formula for area of a triangle is
A = 1/2 b*h
A = 1/2 * 8cm*12cm
A = 1/2 *96cm^2
A = 48 cm^2
The area is 48 cm^2
Answer:
A = 48 cm^2
Step-by-step explanation:
k12
Given sin0=6/11 and sec 0<0 find cos0 and tan0 (picture provided)
Answer:
[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]
[tex]tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]
Step-by-step explanation:
We know by definition that:
[tex]cos ^ 2(x) = 1-sin ^2(x)[/tex]
We also know that:
[tex]tan(x) = \frac{sin(x)}{cos(x)}[/tex]
[tex]sec(x) = \frac{1}{cos(x)}[/tex]
Then we can use these identities to solve the problem
if [tex]sin(0\°) = \frac{6}{11}[/tex] then [tex]cos^2(0\°) = 1-(\frac{6}{11})^2[/tex]
[tex]cos(0\°) = \±\sqrt{\frac{85}{121}}\\\\cos(0\°)=\±\frac{\sqrt{85}}{11}[/tex]
As [tex]sec(x) <0[/tex] then [tex]cos(x) <0[/tex]. Therefore we take the negative root:
[tex]cos(0\°)=-\frac{\sqrt{85}}{11}[/tex]
Now that we know [tex]sin(0\°)[/tex] and [tex]cos(0\°)[/tex] we can find [tex]tan(0\°)[/tex]
[tex]tan(0\°) = \frac{sin(0\°)}{cos(0\°)}\\\\tan(0\°) = \frac{\frac{6}{11}}{\frac{-\sqrt{85}}{11} }\\\\tan(0\°) = -\frac{6}{\sqrt{85}}\\\\[/tex]
which is a true statement about 10 days of production?
A. Plant C is just beginning to produce actual widgets.
B. None of these plants is yet producing actual widgets.
C. Plant A is the closest to producing actual widgets.
Answer:
B. None of these plants is yet producing actual widgets.
Step-by-step explanation:
As we can see in the graph, the number of days is on the x axis, and the number of widgets at y axis.
At 10 days, no line is above the '0' means no one is producing widgets at 10 days point.
Since the y axis represents number of widgets produced, this means none of the plants have produced more than 0 widgets yet.
So, option B is the answer.
Oliver has 5 pieces of string that are each
4
2
12
feet long. Destiny has 4 pieces of string that are each
5
14
16
feet long. Use an estimation strategy to determine who has the most string. Choose the name and number to complete the statement.
is estimated to have more feet of string.
So to estimate, I would look at each set of numbers and determine which ones have higher numbers. For example in the first set the highest I see is 12x5=60
In the second set I see 14 AND 16 automatic telling me to estimate that Destiny has more using 14x4=56, but keeping in mind there is a 16 as well...
Lori bought gifts for her 3 borthers and 6 cousins. She bought 4 toy cars for each
Answer: 36 toy cars
Step-by-step explanation: If Lori bought gifts for her 3 brothers and 6 cousins then she bought gifts for 9 people (3+6). Since she bought 4 toy cars for each of them she bought 36, which is calculated by multiplying 9 x 4.
9 x 4 = 36
Lori bought a total of 36 gifts for her three brothers and six cousins since she bought four gifts for each of them. This was calculated by multiplying the total number of recipients (3+6) by the number of grants each person got (4).
Explanation:The question is asking how many gifts Lori bought in total. Since Lori bought four toy cars for each of her three brothers and six cousins, we need to multiply the total number of recipients by the number of gifts per person. This gives us (3 brothers + 6 cousins) * 4 skills = 36. So, Lori bought a total of 36 grants.
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HELP! Nine friends share 3 pumpkin pies equally. What fraction of a pumpkin pie does each friend get? Please explain or show your work! :)
Answer:
1/3 of a pie.
Step-by-step explanation:
Givens
There are 3 pies
There are 9 people
Answer
Each person gets 3/9 or 1/3 of a pie
So each pie is cut into thirds.