(b)
using the 'laws of exponents '
[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex]
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex]
2² × [tex]\frac{2}{2^{4} }[/tex] = [tex]\frac{2^{3} }{2^{4} }[/tex] = [tex]2^{(3-4)}[/tex] = [tex]2^{-1}[/tex]
What number must you add to complete the square? x^2+14x=-5
A. 14
B. 28
C. 7
D. 49
D
since the coefficient of the x² term is 1, then
add (half the coefficient of the x-term )² to both sides
that is ([tex]\frac{14}{2}[/tex])² = 49
Explain how you can tell the function f (x) = |x + 4| is not linear by using points on its graph.
If there are any three points on the graph that are not on the same line, the function is nonlinear. Such points might be ...
... (-5, 1), (-4, 0), (-3, 1)
40 POINTS TO WHO EVER CAN ANSWER THIS!!!!!
Which quadratic function does the graph represent? The vertex is at (-2,-3) and the point is at (0,7)
A.)f(x)=5/2(x+2)^2-3
B.) f(x)= 10/9(x+2)^2-3
C.) f(x)=7(x-2)^2-3
D.)f(x)=5(x-2)^2-3
Answer:
y = 2.5(x + 2)^2 - 3
The answer is A
Step-by-step explanation:
The general equation for the vertex is
y = a (x + b)^2 + c
a we are not certain about
b = 2
c = - 3
y = a(x + 2)^2 - 3 Now we have to solve for a.
a is found by using the one point we know (0,7) It means when x = 0 y = 7 so just put those two numbers in.
7 = a(0 - 2)^2 - 3
7 = a (- 2)^2 - 3 Add 3 to both sides.
7 + 3 = a(4) Combine 7 and 3
10 = 4a Divide by 4
10/4 = a Do the actual division
2.5 = a
Answer: See above
A
the equation of a parabola in vertex form is
y = a(x - h )² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
here the vertex = (- 2, - 3 ), thus
y = a(x + 2 )² - 3
to find a substitute (0, 7 ) into the equation
7 = 4a - 3 ( add 3 to both sides )
10 = 4a ( divide both sides by 4 )
a = [tex]\frac{10}{4}[/tex] = [tex]\frac{5}{2}[/tex]
y = [tex]\frac{5}{2}[/tex](x + 2 )² - 3
Point A is located at (3,4) and is rotated 90 degrees counterclockwise about the origin. What is the new point of A?
A'(- 4, 3 )
Under a counterclockwise rotation about the origin of 90°
a point (x, y ) → (- y, x )
A(3, 4 ) → A'(- 4, 3 )
Beth swam laps to raise money for a charity. Beth raised $15 plus $0.65 per lap that she swam. She raised a total of $80. Let x represent the number of laps Beth swam. What expression completes the equation to determine the total number of laps Beth swam? How many laps did Beth swim? Enter your answers in the boxes.
______= 80
______ Laps
The amount Beth raised by swimming is ...
... x · $0.65
In addition, she had a contribution that was not related to the number of laps. Her total can be expressed as
... 15 + 0.65x = 80
_____
Subtract 15 and divide by 0.65 to find
... x = (80 -15)/0.65 = 65/0.65 = 100
Beth swam ...
... 100 Laps
1.994 x 10^-23 1.67 x 10^-24 what are the difference
Answer:
1.827 x 10^-23
Step-by-step explanation:
(1.994 x 10^-23) - (1.67 x 10^-24) = 1.827 x 10^-23
Jesse used 5 gallons of gasoline to drive 50 miles. How much gasoline will he need to travel 170 miles?
5/50 = x / 170
solve for x by multiplying both sides by 170
Jesse used 5 gallons of gasoline to drive 50 miles. the gasoline he will need to travel 170 miles will be 17 gallons.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Jesse used 5 gallons of gasoline to drive 50 miles.
Let x be the gasoline he will need to travel 170 miles
5/50 = x / 170
x = 170 (1/10)
x = 17
Hence, the gasoline he will need to travel 170 miles will be 17 gallons.
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plz help geometry question is below, asap
I would say the answer is b. It sounds like the best choice
hope i helped!
What is the additive identity of the complex number 14 + 5i?
A) 14 – 5i
B) 0
C) 1
D) –14 – 5i
Answer: B) 0
Step-by-step explanation:
1. When you add complex numbers you must add the whole parts and then the imaginary parts.
2. One of the properties of complex numbers is called "Additive identity" which is represented by:
[tex]0+0i[/tex]
3. Then, for the complex number [tex]14+5i[/tex], you have:
[tex](14+5i)+(0+0i)=(14+0)+(5+0)i=14+5i[/tex]
4. Therefore, the answer is the option B.
Answer:
The answer is B. 0
cersei is 3 times older than Arya. In 15 years their combined ages will be 94.How old are each of them now (please show work)
The "work" can be all in your head. In 15 years, their combined ages will have increased by 30 years over what it is now*, so their combined age now must be 64 year. If the ratio of their ages is 3:1, the youngest must be 1/(3+1) = 1/4 of the total, or 16 years.
Arya is 16 years old; Cersei is 48 years old.
_____
* Each person ages one year each year, so their combined age increases by 2 years each year. In 15 years, their combined age will increase by 30 years.
_____
If you insist on an equation, let "a' represent Arya's age. Then 3a represents Cersei's age. The relationship given in the problem is ...
... (a +15) + (3a +15) = 94
... 4a +30 = 94 . . . . . . . . . . collect terms
... 4a = 64 . . . . . . . . . . . . . . subtract 30
... a = 64/4 = 16 . . . . . . . . . multiply by 1/4
This equation and its working should look a lot like the verbal reasoning we did above.
Can someone please help me with business math
Answer:
1721 $
1612.80
Step-by-step explanation:
Straight line depreciation means depreciation is the same spread over for all the years. The spread over amount is nothing but total cost of equipment - salvage value.
Here we have
Cost of equipment(Purchase cost) ... 18000
Shipping costs ... 620
Installation costs ... 590
Total cost of equipment ... 19210
Less: salvage value at the end ... 2000
Net cost of equipment for 10 years ... 17210
Depreciation per year = Net cost /number of years of life
= 17210/10 = 1721/-
Hence answer is 1721/- for all years and also hence for year 2.
--------------------
Peach tree has an average life of 12 years. First 3 years no benefit would arise, 4 to 8 would be peak and after that slowly decreasing.
Hence in 9th year there would be least value and least depreciation.
Hence answer is $1612.80
which of the following equations is equivalent to 1/4x -1/2y =8? a) 2x-4y=8. b)2x-4y =64. c) 4x-2y =64
If you multiply the original equation by 8, you get
... 8(1/4x -1/2y) = 8(8)
... 8/4x -8/2y = 64
... 2x -4y = 64 . . . . . matches choice b)
Round off 620,000 to the nearest ten thousand
620,000 = 620,000 it remains the same because of the 0.
it will be 600,000 your welcome
Please help! easy points
Name two corresponding angles to ∠1.
∠6 and ∠15
∠5 and ∠6
∠13 and ∠15
∠5 and ∠13
we know that
Corresponding angles:
the angles which occupy the same relative position at each intersection where a straight line crosses two others
If the two lines are parallel, the corresponding angles are equal
so, the angles with same positions to ∠1 are
∠13 and ∠5
so,
∠5 and ∠13..................Answer
Answer:
The answer is 5 and 13.
This is because they are on the same side but in other place. You can see this as a square, each square has 4 numbers.
-7p^ 3(4p ^2 + 3p - 1)
- 28[tex]p^{5}[/tex] - 7[tex]p^{4}[/tex] + 7p³
distributing and adding exponents of like terms gives
- 28[tex]p^{3+2}[/tex] - 7[tex]p^{3+1}[/tex] + 7p³
= - 28[tex]p^{5}[/tex] - 7[tex]p^{4}[/tex] + 7p³
A tennis ball machine serves a ball vertically into the air from a height of 2 feet, with an initial speed of 120 feet per second. After how many seconds does the ball attain it's maximum height?
Answer:
The maximum height is reached after 3.75 seconds.
Step-by-step explanation:
Assuming the deceleration due to gravity is unaided by air resistance, gravity causes the ball to lose vertical speed at the rate of 32 ft/s every second. The initial vertical speed of 120 ft/s will decline to zero when t satisfies ...
... 120 ft/s - (32 ft/s²)t = 0
... (120 ft/s)/(32 ft/s²) = t = 3.75 s
The ball will not go any higher after its vertical speed is zero.
Y=-5/2x-5 find the slope of each line
slope = - [tex]\frac{5}{2}[/tex]
the equation of a line in slope-intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = - [tex]\frac{5}{2}[/tex] x - 5 is in this form
with slope m = - [tex]\frac{5}{2}[/tex]
The slope of the equation
[tex]Y=\dfrac{-5}{2}x-5[/tex] is [tex]-\dfrac{5}{2}[/tex] .
A line's steepness or inclination can be measured by a line's slope. It specifies the amount of rise or fall a line experiences for each unit of horizontal distance. In other words, it measures how quickly the vertical (y) and horizontal (x) coordinates of points on a line change with time.
Given equation is
[tex]Y=\dfrac{-5}{2}x-5[/tex] consider it as equation (1)
This is in the form of slope-intercept equation y = mx +b consider it as equation (2).
Where m represents the slope and b represents the intercept term.
On comparing the equation (1) and equation (2)
[tex]m=-\dfrac{5}{2}[/tex]
Hence, the slope of the given equation is given by [tex]-\dfrac{5}{2}[/tex] .
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Answers in Scientific Notation.
one way is to factor the expressions
(a)
[tex]10^{5}[/tex] (1.2 + (5.35 × [tex]10^{1}[/tex]))
= [tex]10^{5}[/tex] (1.2 + 53.5)
= 54.7 × [tex]10^{5}[/tex] = 5.47 × [tex]10^{1}[/tex]× [tex]10^{5}[/tex] = 5.47 × [tex]10^{6}[/tex]
(b)
[tex]10^{-3}[/tex]((6.91 × [tex]10^{1}[/tex]) + 2.4)
= [tex]10^{-3}[/tex](69.1 + 2.4)
= 71.5 × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{1}[/tex] × [tex]10^{-3}[/tex] = 7.15 × [tex]10^{-2}[/tex]
(c)
[tex]10^{5}[/tex]((9.7 × [tex]10^{1}[/tex]) + 8.3)
= [tex]10^{5}[/tex](97 + 8.3)
= 105.3 × [tex]10^{5}[/tex] = 1.053 × [tex]10^{2}[/tex] × [tex]10^{5}[/tex] = 1.053 × [tex]10^{7}[/tex]
(d)
[tex]10^{1}[/tex]((3.67 × [tex]10^{1}[/tex]) - 1.6)
= [tex]10^{1}[/tex](36.7 - 1.6)
= 35.1 × [tex]10^{1}[/tex] = 3.51 × [tex]10^{1}[/tex] × [tex]10^{1}[/tex] = 3.51 × [tex]10^{2}[/tex]
(e)
[tex]10^{-6}[/tex]((8.41 × [tex]10^{1}[/tex]) - 7.9)
= [tex]10^{-6}[/tex](84.1 - 7.9 )
= 76.2 × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{1}[/tex] × [tex]10^{-6}[/tex] = 7.62 × [tex]10^{-5}[/tex]
(f)
[tex]10^{4}[/tex]((1.33 × [tex]10^{1}[/tex]) - 4.9 )
= [tex]10^{4}[/tex](13.3 - 4.9) = 8.4 × [tex]10^{4}[/tex]
Two students rotate the given figure around the origin.
Lance rotates the figure 180°.
Celina rotates the figure 90° counterclockwise.
Drag the result of each student’s rotation into the table.
Answer:
Given is that Lance rotates the figure 180° and Celina rotates the figure 90°
Now, when the figure is rotated 180 degrees, it will be turned around the origin in a way that the new place of the image will lie in a straight line in accordance to the original position. So, the second image is Lance's image.
When a figure is rotated 90 degrees counterclockwise, this means the figure will turn to the left and the point of the figure will be downwards. So, the first image is Celina's image.
Answer:
See below: Brainliest would help?
Step-by-step explanation:
Please help! Answer only if you know
area = 20 units²
construct a square of side 6 units around the given figure, then the area of the figure is given by area of square minus 4 congruent triangles
A = 6² - 4 × [tex]\frac{1}{2}[/tex] × 4 × 2
= 36 - 16 = 20 units²
An analog clock loses 2 minutes every 3 hours. What is the shortest interval of time after which the clock will show the correct time?
(I have answered this question about half an hour before - repeating here)
In order to show the correct time again, the clock has to be exactly 12 hours, or 12*60=720 minutes, behind. With 2 minutes per 3 hours, the clock will have to run for 3 * 720/2 = 1080 hours. 1080 hours = 45 days. The shortest interval the clock need to show the correct time is 45 days.
The shortest interval of time after which the clock will show the correct time is 1.5 hours.
Explanation:To find the shortest interval of time after which the clock will show the correct time, we need to determine the total time it takes for the clock to lose 2 minutes and reset to the correct time. Since the clock loses 2 minutes every 3 hours, it loses 1 minute per 1.5 hours. Therefore, it will take 1.5 hours for the clock to lose 2 minutes and show the correct time again. So, the shortest interval of time is 1.5 hours.
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Find the equation of the line in slope-intercept form. Slope is −7 and through (−3, 16)
It is convenient to start with the point-slope form and then simplify it to the desired form.
The point-slope form of the equation for a line with slope m through point (h, k) can be written as ...
... y = m(x -h) +k
You have m=-7 and (h, k) = (-3, 16), so you can fill in the numbers to get ...
... y = -7(x +3) +16
... y = -7x -21 +16 . . . eliminate parentheses
... y = -7x -5 . . . . the form you are looking for
Based on the diagrams, which statement is true?
Using a somewhat liberal interpretation of "the angles shown in the diagrams", we can conclude that the appropriate choice is ...
... A. The value of x should be 75, because the angles shown in the diagrams are congruent.
_____
There are 8 angles shown in each of 4 diagrams. All 32 angles are not congruent. Taken literally, "the angles shown in the diagrams are congruent" is a false statement. Rather, the marked pair of angles in each diagram are congruent angles.
Im begging u, plzzzzzzzz help
a.) Describe a transformation sequence that will transform pentagon ABCDE into pentagon A’B’C’D’E’.
b.) There is more than one way to transform pentagon ABCD into pentagon A’B’C’D’. Describe a second sequence of transformations that will accomplish this goal. Explain what tool you used as an aid in identifying a transformation sequence.
a) The orientation of the figure ABCDE is clockwise. The orientation of figure A'B'C'D'E' is counterclockwise, so at least one reflection is involved. The direction of AB is North, while the direction of A'B' is West, so a rotation of 90° is involved. Both of these can be accomplished by a reflection across the line that has a direction halfway between these, Northwest. The x-coordinate of point D is the same as that of D', so it is convenient to put point D on the line of reflection.
A transformation sequence that maps ABCDE to A'B'C'D'E' is ...
reflection across the line x+y=-2translation down 2 unitsThe attachment shows the result of reflecting the figure across the line.
b) About any reflection will give the figure the proper orientation. Depending on what it is, some amount of rotation and/or translation may be required.
We can reflect point D across the line y=-2 to put it where point D' is. That reflection changes the direction of AB to South, so we need to rotate the figure 90° CW to get AB to point West. Since we want point D' to be invariant, we can use that point as the center of rotation.
A second transformation that gives the same mapping is ...
reflection across the line y = -2rotation 90° CW about the point (-1, -3)A hybrid car can get 54 mpg when traveling at an average speed of 40 mph. You travel in this car at that speed for 45 miles to your grandparents’ house. Gas at your nearest station cost $3.23. Use this information to complete the statements. It will take________ Hours to get to your grandparents’ house. Your car will use______gallons of gas on the trip. You will spend________on gas for the trip.
A) The time to travel 45 miles at a speed of 40 mph can be found from ...
... time = distance / speed
... time = (45 mi)/(40 mi/h) = 9/8 h = 1 hr 7 min 30 sec
B) The gas consumption can be found from ...
... (45 mi)/(54 mi/gal) = 5/6 gal
C) The cost of gas can be found from ...
... ($3.23/gal)×(5/6 gal) ≈ $2.69
_____
The units of the numbers tell you what needs to be multiplied or divided to give the answer quantity with correct units. It pays to keep the units with the numbers. They can be treated as though they were a variable.
Kerry bought 5 packs of Jasmine rice from an online store if each pack holds 1 9/10 pounds of rice how many pounds of rice did kerry purchase in total
Answer:
9.5 lbs
Step-by-step explanation:
To find the total package weight, add up the weights of the packages, or use the shortcut to repeated addition that is called multiplication.
... 1.9 + 1.9 + 1.9 + 1.9 + 1.9 = 5×1.9 = 9.5 . . . pounds
Keith left his house, rode his bike 3 miles along one road, took a 90 degree turn, and rode 3 miles to the local swimming pool. If he had ridden directly to the pool, how much distance would be have saved? Round to the nearest tenths of a mile.
riding directly to the pool would be 4.2 miles, so he would have saved 1.8 miles
In the right △ABC with m∠C=90°, m∠B=75°, and AB=12 cm. Find the area of △ABC. without trigonometry! worth 49 points
There might be two ways to go about this
(1) I am going to assume that we can construct a second (reference) triangle - and you confirmed that it is ok to use trigonometry on that, and then we use the relationship between areas of similar triangles to get what we want. I choose a triangle DEF with same angles, 15, 75, and 90 degrees, and the hypotenuse DE a of length 1 (that is a triangle similar to ABC). I use sin/cos to determine the side lengths: sin(15)=EF and cos(15)=DF and then compute the area(DEF) =EF*DF/2. This turns out to be 1/8 = 0.125.
Now one can use the area formula for similar triangles to figure out the area of ABC - this without trigonometry now: area(ABC)/area(DEF)=(12/1)^2
so area(ABC)=144*area(DEF)=144*0.125=18
(2) Construct the triangle ABC geometrically using compass, protractor, and a ruler. Draw a line segment AB of length 12. Using the compass draw a (Thales') semi-circle centered at the midpoint of AB with radius of 6. Then, using the protractor, draw a line at 75 degrees going from point B. The intersection with the semicircle will give you point C. Finally. draw a line from C to A, completing the triangle. Then, using ruler, measure the length BC and AC.
Calculate the area(ABC)=BC*CA/2, which should come out close to 18, if you drew precisely enough.
Answer: 18 square cm
Step-by-step explanation:
*picture very note to scale im sorry lol*
Given: △ABC, m∠C=90°, m∠B=75°, AB=12 cm
m∠A = 15° (sum of all angles in a triangle is 180 degrees and 180-90-75=15)
CM - median to hypotenuse
CL - altitude
m<CLB = m<CLM = 90 degrees (def of altitude)
CM=MA=MB=1/2 AB = 6 cm (median to hypotenuse theorem)
m<MBC=m<BCM=75 degrees (base angles theorem of iso triangle)
m<BMC = 30 degrees (sum of all angles in a triangle, 180-75-75 = 30)
m<LCM = 60 degrees (sum of all angles in a triangle of triangle LCM, 180-90-30=60)
so now we know that triangle LCM is a 30-60-90 triangle with a hypotenuse of CM (6 cm)
LC = 1/2 of MC = 3 cm (leg opposite to 30 degree <)
So now we know that the height (altitude) of the triangle is 3 cm and the length is 12 cm.
Then, we can find the area by doing the (height * length)/2 = (3*12)/2, which brings us to our answer of 18 cm.
lmk if you don't understand anything in here i'm happy to clarify!
hope this helps!
PLZ HELP GEOMETRY BELOW
This is known as Einstein's proof, not because he was the first to come up with it, but because he came up with it as a 15 year old boy.
Here the problem is justification step 2. The written equation
BC ÷ DC = BC ÷ AC
is incorrect, and wouldn't get us our statement 2, which is correct.
For similar triangles we have to carefully pair the corresponding parts to get our ratios right:
ABC ~ BDC means AB:BD = BC:DC = AC:BC so BC/DC=AC/BC.
Justification 2 has the final division upside down.
Consider the scatter plot.
Describe the outliers from the scatter plot.
the outliers (8,25) and (39,16)
Answer:
The outliers are (8,25), and (39,16)
Step-by-step explanation:
These two points are outliers because they have a great value difference when compared to the other values.