Answer:
28 cm
Step-by-step explanation:
Area = 46.75 = l * (l-3) shows l = 8.5 cm (using Quadratic Formula)
then w = 5.5
perimeter = 2 * ( 8.5+5.5) = 28 cm
The perimeter of the given card is 28 cm.
What is perimeter?Perimeter of an object is given by adding the side lengths of the object.
Given that, the width w of a credit card is 3 cm shorter than the length. The area is 46.75 cm².
We need to find the perimeter of the credit card,
Let the length be l,
Therefore,
Area = length x width
46.75 = l x (l-3)
46.75 = l² - 3l
l² - 3l - 46.75 = 0
Finding l, we get,
l = 8.5, l = -5.5
Since, length cannot be negative so, l = 8.5 cm
So, width = 8.5 - 3 = 5.5 cm
Perimeter = 2(l+w)
= 2(5.5+8.5) = 28 cm
Hence, the perimeter of the given card is 28 cm.
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A bag contains 15 beads that are either red or yellow.
The probability of randomly removing a red bead is 20%.
What is the probability of randomly removing a yellow bead?
The probability of randomly removing a yellow bead is 0.8 or 80% if the bag contains 15 beads that are either red or yellow the probability of randomly removing a red bead is 20%.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
We have the probability P(R) of randomly removing a red bead is 20%.
Let's suppose the number of red beads is n(R)
[tex]\rm P(R) = 20\% \Rightarrow 0.20\\\\\rm \frac{n(R)}{15} = 0.20[/tex]
n(R) = 15×0.20
n(R) = 3
Number of yellow beads = 15 -3 = 12
The probability randomly removing a yellow bead:
[tex]=\rm \frac{12}{15}[/tex]
= 0.8 or 80%
Thus, the probability of randomly removing a yellow bead is 0.8 or 80% if the bag contains 15 beads that are either red or yellow the probability of randomly removing a red bead is 20%.
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3x⁵. 2xy - x²y. 4x⁴ simplified
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
Let's solve ~
[tex]\qquad \tt \dashrightarrow \:(3 {x}^{5} \times 2xy) - ( {x}^{2} y \times 4 {x}^{4} )[/tex]
[tex]\qquad \tt \dashrightarrow \:6 {x}^{6} y - 4 {x}^{6} y[/tex]
[tex]\qquad \tt \dashrightarrow \:2 {x}^{6} y[/tex]
= (3x^5× 2xy) — (x^2y × 4x^4)
= 6x^6y - 4x^6y
= 2x^6y
The product of 4 and 3 is raised to the 5th
power. Which expression shows this?
A (4 X 3) 5
B(4/3)5
C 4 X 35
D 4/35
Write each quadratic equation in general form.
I need help direly
Answer:
9. 3x² +x -2y +5 = 0
10. 4x² +x -y +4 = 0
11. 9x² -6x -3y -12 = 0
Step-by-step explanation:
"General form" of a polynomial equation is ...
f(x, y) = 0
where the terms are arranged in lexicographical order and decreasing degree. That is, for terms of the same degree, x-terms are listed before y-terms, and xy terms are listed before y-only terms.
The leading coefficient can be positive or negative, your choice. (Positive is generally preferred.) For linear equations, "standard form" has the coefficients mutually prime. Making that happen for a general form polynomial would be your choice.
__
9.The highest-degree term is 3x². If we keep the leading coefficient positive, we can get general form by subtracting the expression on the left side of the equal sign.
3x² +x -2y +5 = 0
__
10.Subtracting the right side gives ...
4x² +x -y +4 = 0
__
11.Subtracting the left side gives ...
9x² -6x -3y -12 = 0
or
3x² -2x -y -4 = 0 . . . . . . remove a common factor of 3
Isabel wants a coat that costs $60. She has saved $42. What fraction of the
amount she needs has she saved?
A) 21/30
B) 4/6
C) 8/12
D) 1/3
coat cost= $60.
to find:the fraction of amount she needs to save.
solution:saved/ actual cost
= $42/ $60 ÷ 2/2
= 21/30
answer= option a) 21/30
Which of the following best describes a circle?
A. The set of all points in a plane at a given distance from a given
point
O B. The set of all points in a plane that are equidistant from two points
C. The set of all points in a plane that are equidistant from a given
point and a given line
D. The set of all points smaller than or equal to a given distance from
a given point
Help me with this question about vectors.
Answer:
parallelogram
Step-by-step explanation:
sr/pq=sp/rq
ab/dc=ad/bc
Answer:
Proven.
Step-by-step explanation:
So, fasten your seatbelts, we're about to go on a long ride(◠‿・)—☆
» In a parallelogram, opposite sides are equal in length.
This can be represented (in the vector way) by
'QR = '-SP = 'PS and 'RS = 'QS (let “'” represent a vector)
'QR + 'SP= 0 and 'RS-'QS = 0
Note the signs. The signs are determined by the arrows in the diagram. [A reminder: If you walk from a point A to a point B, your displacement vector is 'AB. If you walk back, that is, from B to A; your displacement vector is 'BA which is also equal to '-AB.]
This means: to prove that PQRS is a parallelogram, we must prove that
'QR + 'SP= 0 and/or 'RS-'QS = 0.
In this solution, we will only work on the first equation.
Permit me to remove this ' sign.
QR = QC+CR ...1
QR= QB+BA+AD+DR...2
ADD 1 TO 2
2QR= QC+CR+QB+BA+AD+DR
[LOOK CLOSELY, QC+QB=0 ; CR+DR=0. This is because BQ+QC = BC
BUT, BQ=QC= (BC)/2
QC-BQ= 0
AND, -BQ= QB
QC+QB= 0 ;)]
2QR= BA+AD...3
★
SP = SA+AP...4
SP= SD+DC+CB+BP...5
ADD 4 TO 5
2SP = SA+AP+SD+DC+CB+BP
[AGAIN, SA+ SD = 0 ; AP+ BP = 0]
2SP= DC+CB...6
3+6
2QR+2SP= BA+AD+DC+CB
[ BA+AD+DC+CB, IN A SIMPLE WAY, MEANS:
you start from B, and move to A (BA); from A to D (AD); from D to C (DC); and from C to B (CB). Therefore, you have gone from B to B (from your starting point and back). Hence, your total DISPLACEMENT is zero (you haven't changed your position).
2(QR+SP) = 0
'QR+'SP= 0
PROVEN
You can work out the other equation, but it is evident that PQRS is a parallelogram.
Given the same type of golf ball scenario with an equation
y=-0.005x2 +1.8x, horizontal distance of 360 feet, maximum
height of 162 feet, and using the helpful projectile motion formulas
below, answer the following.
x(t)=v, cos(6)y(t)= h, + v, - sin(0).4-1612
. 0
a.) What is the angle at which the ball takes off?
[ Select]
b.) How long is the ball in the air? (Select]
c.) What is the ball's speed when it hits the ground?
[ Select
The angle at which the ball takes off, distance the ball in the air, the ball's speed is mathematically given as
theta=60d=6.3658vo=116.486What is the angle at which the ball takes off?Generally, the equation for the verticle component is mathematically given as
[tex]y=xtan\theta-\frac{16x^2}{v0cos^2\theta}\\\\Therefore\\\\\theta=tan^{-1}(1.8)[/tex]
theta=60
b)
hmax=vo^2sin^2\theta/2g
vo=116.486
Therefore, distance the ball in the air
[tex]d=\frac{2*114.486*0.874*2}{32}[/tex]
d=6.3658
c)
The ball's speed when it hits the ground will be vo
vo=116.486
Read more about Angle
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Why is it wrong to draw y=ln(2x-5) this way?
well because he did not do it
Notice how
2x-5 = 2x - 2*2.5 = 2(x-2.5)
This means we can replace x with x-2.5 in the second step, in the "wrong way" column.
So,
y = ln(2x)
y = ln( 2(x-2.5) )
y = ln( 2x - 2*2.5 )
y = ln( 2x - 5 )
In the second step, the x-2.5 tells the reader to shift the curve 2.5 units to the right. Therefore, the 1/2 = 0.5 would shift to 0.5+2.5 = 3 as indicated by the correct graph.
Katie has these 2 boxes shaped likerectangular prísms. How do the volumes of the two bones compare?
A. Box 2 and Box 1 have the same volume.
B. Box 2 has 3 times the volume of Box1
C. Box2 has 9 times the volume of Box 1.
cm
D. Box 2 has 27 times the volume of Box1.
2 cm
1.5 cm
1.5cm
25
25 am
Box1
Box 2
Answer:
Box 2 has 3 times the volume of Box 1....
Which description most accurately describes the motions for the calculation -5+ (-37)?
The motions for the calculation -5+ (-37) is given as a small movement to the left followed by a large movement to the left.
What is an equation?An equation is an expression used to show the relationship between two or more numbers and variables.
The expression -5+ (-37) can be solved using a number line. The motions for the calculation -5+ (-37) is given as a small movement to the left followed by a large movement to the left.
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Answer:
small movement to the left followed by a large movement to the left.
Step-by-step explanation:
Henry has 1.20 pounds of cat food. He uses 0.15 pound of cat food to feed one cat. How many cats can Henry feed with the cat food he has?
∣_7x+4∣=<18 absolute value
Step-by-step explanation:
|7x+4|≤18
7x+4≤ 18. 7x+4≥-18
x≤2. x≥-22/7
2≤x≤-22/7
25 Points! Please tell me how to answer this.
Answer: ....
Ok done. Thank to me :>
An amount of 47,000 is borrowed for 12 years at 8.25% interest, compounded annually. If the loan is paid in full at the end of that period, how much must be paid back?
Use the calculator provided and round your answer to the nearest dollar.
Answer:
$121,683.79
Step-by-step explanation:
A= P(1+ r)^t
A= Amount, P = Principal, r = Rate (decimal form), t= time
A = 47000(1+0.0825)^12
A = 47000(1.0825)^12
A = 47000(2.589016751)
A = 121683.7873
Rounded Answer = $121,683.79
(If there is meant to be no cents then $121,684). Good luck :)
I hate math. Can someone pls help me?
Answer:
∠s = 158
Step-by-step explanation:
Since lines a and b are parallel,
∠s and 158 are alternate exterior angles.
Alternate exterior angles are equal if two lines are parallel.
So,
∠s = 158
Answer: 22°.
Step-by-step explanation: We're given the angle 158°, which is all we need. Angle u and 158°, have to add up to 180°. 180° - 158° = 22°, which is the angle measure of u. You're probably wondering how this will help us. The answer to that is it gives us the measurement of angle t, which is 158°. Now, we'll do the same thing we did with angle u, which was to make angle u add up with 158° to make 180°. We'll apply this to angle t and angle s. We already know that angle t is 158°, so angle s has to be 22° in order to add up to 180°. Therefore, your answer is 22° for angle s.
Let me know if this is right! :)
Noah writes the equation 3(x+7)=57 to represent the situation. Use the distributive property to write this equation another way.
Answer:
3x+21=57
Step-by-step explanation:
When we use distributive property we do
[tex]3*x[/tex] and [tex]3*7[/tex] which will like this when rewritten [tex]3x+21=57[/tex]
Check answer:
[tex]3x+21=57\\-21=-21\\3x=36[/tex] [tex]\frac{3x}{3} =\frac{36}{3}[/tex]
x=12 3(12)+21=57
36+21=57
While on vacation, the Garner family paid $120 for 3 tickets to a water park. How much money would they have spent on 5 tickets?
Answer:
$ 200
Step-by-step explanation:
$ per ticket = $ 120 / 3 tix
Price for 5 $120 / 3 tix * 5 tix = $ 200
Find the slope of the line passing through the points , 2−6 and , −9−6
I will assume that we are trying to find the slope between (2,-6) and (-9,-6)
The slope's equation ⇒ [tex]\frac{y2-y1}{x2-x1}[/tex]
Let's set the variables:
(x1, y1) --> (2, -6)
(x2, y2) --> (-9, -6)
Now let's plug them in:
[tex]Slope = \frac{-6--6}{-9-2} =\frac{0}{-11} =0[/tex]
Thus the slope of the line is 0.
Hope that helps!
What is 4,321,109,432 rounded to the nearest billion?
Answer:
I think 4000000000
Answer: 4,321,109,432 rounded to the nearest billion is 4,000,000,000
Step-by-step explanation:
First, you find the billions place which is right here:
4,321,109,432
Look to the number to the right of it. Is it greater or less than 5? Since it's less, you round down to 0, leaving a 4 and 3 sets of 3 zeroes.
Complete the following sentence.
13 cm
8 cm
8 cm
The composite figure is made up of a rectangular prism and a
Answer:
Triangular prism
Step-by-step explanation:
There is one rectangular prism at the bottom and one triangular prism at the top.
Answer:
It is a square pyramid
Step-by-step explanation:
Predicted distance traveled in 10 minutes: 3 km
(b) Lena is deciding how many people to take to the movies. The table below
shows the cost for different sized groups of people.
Number in group
4
8
9
Cost (in dollars)
36
64
72
O The cost for each person is not always the same.
O The cost for each person appears to be the same.
Predicted number in group for a cost of $80:
Explanation
Check
Answer:
Cost for person is not always the same
For 80 dollars predicted would be 10 people
Step-by-step explanation:
4 people 36 dollars = 9 each
8 people 64 dollars = 8 each
9 people 72 dollars = 8 each seems to flatten at 8 dollars each
A boat is heading towards a lighthouse, where Meena is watching from a vertical
distance of 120 feet above the water. Meena measures an angle of depression to the
boat at point A to be 18º. At some later time, Meena takes another measurement and
finds the angle of depression to the boat (now at point B) to be 44º. Find the distance
from point A to point B. Round your answer to the nearest foot if necessary.
Answer:
245 ft
Step-by-step explanation:
The geometry of the problem can be modeled by a right triangle in which Meena's height is the side opposite the angle of depression, and the distance to the boat is the side adjacent to the angle of depression. The mnemonic SOH CAH TOA reminds us of the relation ...
Tan = Oppsite/Adjacent
__
The more useful trig function for this problem is the inverse of the tangent function, the cotangent. Using that function, we have ...
cot(angle) = (distance to boat)/(Meena's height)
Then the distance to the boat is ...
distance to boat = (Meena's height)×cot(angle)
The change in distance from A to B is then ...
A -B = (120 ft)(cot(18°) -cot(44°))
= (120 ft)(3.0777 -1.0355) ≈ 245.06 ft
The distance from point A to point B is about 245 feet.
Yan had 5 trading cards, and then his friend gave him more cards. Now he has 16 trading cards. Let t represent the number of cards his friend gave him. Write both an addition equation and a subtraction equation to model the problem.
PLEASE ANSWER IN THE NEXT 1 MINUTE.
1. Quinn's test scores are 95, 90, and 83. What must she score on the next test to have an average
score of 90 on the four tests?
Answer:
92
Step-by-step explanation:
Add 95, 90, and 83 all together
add 92 to that total
divide by 4
NEED HELP ASAP!!!!
A) 12 sq. cm.
B) 6 sq. cm.
C) 12 cm
D) 6 cm
Answer:
its B- 6 sq. cm.
Step-by-step explanation:
1/2 times base times height
1/2 x 4 x 3
6
Answer:
The answer is given below
Step-by-step explanation:
[tex]area = \frac{1}{2} \times base \times perpendicular[/tex]
[tex]area = \frac{1}{2} \times 3 \times 4[/tex]
Area = 1/2 * 12
Area = 6
Help me please permutations and computations?
Answer:
i think it's 14c5 sincce theres 5 colors to choose from .
What is x in this equation?
Answer:
x = 6.08 units
Step-by-step explanation:
For a right triangle
sin = opp leg / hyp
for this triangle sin 34 = 3.4 / x re-arrange to
x = 3.4 / sin34 = 3.4 / .5591 = 6.08
What is the ratio of the radius to the circumference of any circle, using 3.14 for pi?
Answer:
1 : 6.28Step-by-step explanation:
The circumference formula is
C = 2πr orC = 2(3.14)r = 6.28rThe ratio of the radius to the circumference is
r/C = 1/6.28or
r : C = 1 : 6.28r : C = 1 : 6.28
Formula's:
circumference of any circle: 2πr
radius: r
Their ratio:
radius : circumference
r : 2πr
r : 2(3.14)r
1 : 6.28
what is approximate distance between (-1, 3) and (2, -4)
Answer:
d= 7.62
Step-by-step explanation:
(-1,3)(2,-4)
the formula of distance is-
[tex]d=\sqrt{((x_{2}-x_{1})^2 + (y_{2}-y_{1})^2)} \\\\d=\sqrt{(2+1)^2+(-4-3)^2}\\ d=7.62[/tex]