A computer desk, originally priced at $83, is now on sale for $78.85
originally priced at $83. After discount the price becomes $78.85
Discount amount = $83 - $78.85 = $4.15
Decrease rate = discount amount divide by original price
Decrease rate = [tex]\frac{4.15}{83}= 0.05[/tex]
Decrease rate = 0.05
To find percent of decrease we multiply by 100
0.05 * 100 = 5%
Decrease percentage = 5%
Jonathan used completing the square to find the maximum value of the quadratic expression -x^2 - 4x + 1. What is the maximum value of the expression, and at what x value does it occur?
Answer:
Maximum value of the expression = 5
X value it occurs at = 2
Step-by-step explanation:
Please view the image I provided.
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
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
Solve for c. (1/4) to the power of c−2=64
Rewrite the equation so both sides have the same base, then equate exponents and solve for c.
[tex]\displaystyle\left(\frac{1}{4}\right)^{c-2}=64\\\\\left(4^{-1}\right)^{c-2}=4^{3}\\\\-(c-2)=3\\\\-1=c[/tex]
The value of c is -1.
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
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]
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!
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.
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
What is the value of g(−3) when g(x)=2x−2 ?
To solve a function like this, simply put the numerical value in place of the unknown variable for which you have to find the solution, for instance '-3' in this case.
g(x) = 2x-2
so to find g(-3), we just need to replace the x in the given expression by '-3'. Working is shown below:
g(x) = 2x-2
putting '-3' in place of x
g(-3) = 2(-3) - 2
g(-3) = -6 -2
g(-3) = -8
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
plz help geometry question is below, asap
I would say the answer is b. It sounds like the best choice
hope i helped!
A theater can seat 672 people. The number of rows is 4 less than the number of seats in each row. How many rows of seats are there?
24 rows of seats
let n be the number of rows
then the number of seats per row = n + 4
number of seats = number of rows × number of seats per row
n(n + 4 ) = 672
n² + 4n - 672 = 0 ← in standard form
the factors of - 672 which sum to + 4 are + 28 and - 24
(n + 28)(n - 24) = 0
equate each factor to zero and solve for n
n + 28 = 0 ⇒ n = - 28
n - 24 = 0 ⇒ n = 24
number of rows n > 0
number of rows = 24 and number of seats per row = 28
24 × 28 = 672 as a check
-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
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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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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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:
A farmer is considering four different sizes of cylindrical silos. Which silo will provide the greatest storage capacity?
Corn Silos
Silo
Radius
Height
A
6 feet
60 feet
B
8 feet
50 feet
C
10 feet
34 feet
D
12 feet
20 feet
Answer:
Cylinder C is the right answer.
Step-by-step explanation:
We have to find the storage capacity or the volume of cylindrical silos.
A. radius 6 feet; height 60 feet
Volume = [tex]\pi r^{2} h[/tex]
V = [tex]3.14\times6\times6\times60=6782.40[/tex] cubic feet
B. radius 8 feet; height 50 feet
V = [tex]3.14\times8\times8\times50=10048[/tex] cubic feet
C. radius 10 feet; height 34 feet
V = [tex]3.14\times10\times10\times34=10676[/tex] cubic feet
D. radius 12 feet; height 20 feet
V = [tex]3.14\times12\times12\times20=9043.20[/tex] cubic feet
Comparing all the volumes, we can see that cylinder C has the heighest volume.
Therefore, cylinder C is the right answer.
Triangle ABC is similar to triangle PQR, as shown below:
Two similar triangles ABC and PQR are shown. Triangle ABC has sides AB equals c, BC equals a, and AC equals b. Triangle PQR has
Which equation is correct?
c is the correct equation
given ΔABC is similar to ΔPQR
then the ratios of corresponding sides are equal.
the sides a, b and c inΔABC correspond to the sides p, q and r in ΔPQR
thus the following ratios are equal
[tex]\frac{a}{p}[/tex] = [tex]\frac{b}{q}[/tex] = [tex]\frac{c}{r}[/tex]
from this we can see that [tex]\frac{c}{r}[/tex] = [tex]\frac{a}{p}[/tex] → c
Find the restricted values of x for the following rational expression. If there are no restricted values of x, indicate "No Restrictions". −8x/8x2+2x Answer How to enter your answer
Given rational expression is
[tex]-\frac{8x}{8x^2+2x}[/tex]
Now we need to find the restricted values if any for this rational expression.
Restricted values means the possible values of the used variable (x) that will make denominator 0 as division by 0 is not defined.
So to find the restricted values, we just set denominator equal to 0 and solve for x
[tex]8x^2+2x=0[/tex]
[tex]2x(4x+1)=0[/tex]
2x=0 or 4x+1=0
x=0 or 4x=-1
x=0 or x=-1/4
Hence final answer is x=0, -1/4
To find the restricted values of a rational expression, set the denominator equal to zero and solve for x.
Explanation:To find the restricted values of the rational expression, we need to determine the values of x that will make the denominator of the expression equal to zero. When the denominator is zero, the expression is undefined.
In this case, the denominator is 8x2 + 2x. We set this equal to zero and solve for x:
8x2 + 2x = 0
Factor out 2x:
2x(4x + 1) = 0
Set each factor equal to zero:
2x = 0, 4x + 1 = 0
Solve each equation:
x = 0, x = -1/4
Therefore, the restricted values of x for the given rational expression are 0 and -1/4.
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Kierra purchase candy from the bulk section. The equation c=0.99p represents the cost of the candy per pound. What is the unit rate for the cost of the candy?
Answer:
The answer would be 0.99/1 pound
Step-by-step explanation:
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
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)
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
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.
is it possible to find a side length that would be perfect for a square with an area of 45 square units?
If a square has an area of 45 square units its side has a length of
[tex]s=\sqrt{45} = 3 \sqrt{5}[/tex]
units. Is that a perfect length? I don't know, but I know it's perfect for a square whose area is 45.
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.
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
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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