This question is solved applying the formula of the area of the rectangle, and finding it's width. To do this, we solve a quadratic equation, and we get that the cardboard has a width of 1.5 feet.
Area of a rectangle:
The area of rectangle of length l and width w is given by:
[tex]A = wl[/tex]
w(2w + 3) = 9
From this, we get that:
[tex]l = 2w + 3, A = 9[/tex]
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}[/tex]
[tex]\Delta = b^{2} - 4ac[/tex]
In this question:
[tex]w(2w+3) = 9[/tex]
[tex]2w^2 + 3w - 9 = 0[/tex]
Thus a quadratic equation with [tex]a = 2, b = 3, c = -9[/tex]
Then
[tex]\Delta = 3^2 - 4(2)(-9) = 81[/tex]
[tex]w_{1} = \frac{-3 + \sqrt{81}}{2*2} = 1.5[/tex]
[tex]w_{2} = \frac{-3 - \sqrt{81}}{2*2} = -3[/tex]
Width is a positive measure, thus, the width of the cardboard is of 1.5 feet.
Another similar problem can be found at https://brainly.com/question/16995958
GIVEN THAT GENERAL TERM =7n+4
evaluate sum of 5th termand 6th term
Answer:
general term - 7n+4
5th term - 7(5) + 4 = 39
6th term - 7(6) + 4 = 46
Consider the graph of the quadratic function. Which
interval on the x-axis has a negative rate of change?
3
0-2 to-1
2
O -1.5 to 0
O 0 to 1
-3
-2
21
2
3
x
О 1 to 2.5
Answer:
1 to 2.5
Step-by-step explanation:
A negative rate of change requires the instantaneous slope to be negative, and the interval from 1 to 2.5 is the only place segment where that can happen.
the product of two rational number is _______ number
give answers this question
Answer:
rational number
Step-by-step explanation:
multiplying two rationals is the same as
multiplying two such fractions, which will
result in another fraction of this same form
since integers are closed under
multiplication. Thus, multiplying two rational numbers produces another rational number.
"The product of two rational number is rational" So, multiplying two rationals is the same as multiplying two such fractions, which will result in another fraction of this same form since integers are closed under multiplication.Sep 5, 2020
Is speed the rate of change in the velocity of a moving body?
No, speed is the rate of change of distance.
Velocity is the rate of change of displacement.
Distance is scalar quantity, it has just magnitude.
Displacement is vector quantity, it has both magnitude as well as direction. So, speed and velocity are scalar and vector respectively too.
Name the number that is
represented by the letter Y.
Y
Z
WVX
+
-10 -5
+
5
0
10
Answer:
y is 8 if you count towards the right side of the screen you will figure out that y is 8 followed by 9 leading you to 10, therefore x is 11.
I hope this helps
The second term in a geometric sequence is 50. The forth term in the same sequence is 112.5. what is the common ratio in this sequence?
Answer:
1.5
Step-by-step explanation:
Let the first term be a and the common ratio be r
ATQ, ar=50 and ar^3=112.5, divide these two. r^2=2.25, r=1.5
Terrell loves to listen to music, so he buys a subscription to a music-streaming service. He pays $4.99 each month. How much does the streaming service cost per year?
Translate the sentence into an equation.
Four times the sum of a number and 7 equals 3
Answer:
[tex]4(x+7)=3[/tex]
Step-by-step explanation:
Since the sum is being multiplied 4 different times, it's best to write the equation of the sum and the number 4 being in the outside. and since it's saying it equals 3, just add the equal sign
Hope this helps!
- doomdabomb
3 and 4 are complementary
Complementary angles are those whose sum is 90° hence angles 3 and 4 will not be complementary angles but they will have adjacent angles so it will be true.
What is an angle?An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.
The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.
In another word, the angle is the measurement of the angular distance for example for linear motion we have a meter inch but for angular rotation, we don't have the measurement so the angle is useful to measure the angular rotation.
Given,
Angle 3 and angle 4 are only two angles of a single line
So,
∠3 + ∠4 = 180°
So they will be supplementary angle not complimentary angle.
Angle 3 and 4 are adjacent angle because they are neighbors of each other.
Hence, they will not be complementary angles but will be the adjacent angle.
For more about the angle
brainly.com/question/13954458
#SPJ5
prove it using mathematical induction
Answer:
Mathematical induction can be used to prove that an identity is valid for all integers n≥1. Here is a typical example of such an identity: 1+2+3+⋯+n=n(n+1)2. More generally, we can use mathematical induction to prove that a propositional function P(n) is true for all integers n≥1.
Step-by-step explanation:
I'd really appreciate a brainleast please:)
Of every 300 magic cakes Farah makes, 90 are chocolate, what percentage of chocolate cakes Farah makes?
De cada 300 pasteles mágicos que hace Farah, 90 son de chocolate, ¿qué porcentaje de pasteles de chocolate hace Farah?
Answer:
Total magic cakes =300
chocolate cakes =90
so if you want the percentage of chocolate you will divide the number of chocolate cakes over the total number of chocolates
% of chocolate cakes = 90/300×100%
=30%
I will mark as brainliest:)
Answer:
Point E.
.................
What are the coordinates of point S"?
Answer:
point s: (-2,6)
-2 is the x coordinate
6 is the y coordinate
The area of a parallelogram is 60 f2.
The height is 5 ft. How long is the
base?
Answer:
12 feet
BRAINLIEST, PLEASE!
Step-by-step explanation:
Area = base x height
60 = base x 5
base = 60/5
base = 12
Helppppppp
What’s is the equation of the new function?
Answer:
C
Step-by-step explanation:
If the graph is shifted 10 units down, the equation will be sqrt(x) + 10
Describe and correct the error in determining the formula for the sequence below
Answer:An arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant. For instance, the sequence 5, 7, 9, 11, 13, 15.. . is an arithmetic progression with a common difference of 2.
Step-by-step explanation:
Write the equation in standard form.
x2 + 6 = 5x
Answer:
Step-by-step explanation:
x2 + 6 = 5x
2x-5x = -6
3x = -6
x = -6/3
x = -2
Answer:
[tex]x^{2} -5x + 6 =0[/tex]
Step-by-step explanation:
How much state tax is withheld from $36,200 if the tax rate is 4%?
Answer:
$1448
Step-by-step explanation:
Tax=rate*amount=(4/100)*36200=1448
A nurse is preparing to administer cefaclor 40 mg/kg/day PO divided in equal doses every 8 hr to a child who weighs 48 lb. Available is cefactor
suspension 375 mg/5 ml. How many mL should the nurse administer per dose? (Round the answer to the nearest tenth. Use a leading zero if it
applies. Do not use a trailing zero.)
This question is solved by proportions.
Step 1:
A nurse is preparing to administer cefaclor 40 mg/kg/day.
This means that the first step is finding the baby's weight in kg.
The child weighs 48lb. Each lb has 0,453592kg.
So the child weighs 48*0.453592 = 21.7724kg.
Step 2:
Here, we find the daily dose.
For each kg, the baby is administered 40 mg.
Since the baby weighs 21.7724 kg, the daily dose is of 40*21.7724 = 870.896 mg.
Step 3:
Here, we find how many mL in a day.
For 375 mg, 5 mL are administered. How many mL for 870.896 mg?
375 mg - 5 mL
870.896 mg - x mL
Applying cross multiplication:
[tex]375x = 5*870.896[/tex]
[tex]x = \frac{5*870.896}{375}[/tex]
[tex]x = 11.6[/tex]
Step 4:
Here, we find how many mL per dose.
Equal doses every 8 hours, so 24/8 = 3 doses per day.
11.6/3 = 3.9
Thus, the nurse should administer 3.9 mL per dose.
For more on proportional variables, you can check https://brainly.com/question/23536327.
Answer:
x = 3.9 ml quantity of ml / dose
Step-by-step explanation:
The child weighs 48 lbs.
Then the weigh in kgs is 48 * 0.454 = 21.792 kgs (since 1000 lbs = 454 kgs)
If the nurse has to prepare doses according to 40 mg/kg/day then for a child of 21.792 kgs it is needed 21.792*40 mg or 871.68 mg/day, and the fact that he or (she) need to take three doses then each dose will be of
871.68/3 = 290.56 mg
So far we know that each dose should contain 290.56 mg, now we have the cefactor in a suspension wich density is 375 mg/5 ml or 75 mg/ml
Then by rule of three
if 75 mg ⇒ 1 ml
290.56 mg ⇒ x (ml)
x = 290.56/75 ( mg*ml)/ mg
x = 3.87 ml round to the nearest tenth
x = 3.9 ml
How many real solutions does this system of equations have? x2 +3 = y
3х — у+1 = 0
Answer:
Step-by-step explanation:
y = x²+3
y = 3x+1
x² + 3 = 3x +1
x² - 3x + 2 = 0
(x-2)(x-1) = 0
x = 2, 1
Two solutions
(2,7) and (1,4)
Find the volume of the following figure round your answer to the nearest tenth if necessary
Answer:
5.3
Step-by-step explanation:
2×2×4/3
= 5.3 (rounded to the nearest tenth)
The capacity of a small container is 380 ml. and the capacity of a big container is 1250 ml. If Akash uses 8 small containers and 1 big container to fill up an empty tank, then what is the capacity of the tank? With statements
Answer:
3290 ml
Step-by-step explanation:
he fills into the tank 8×380 ml and 1×1250ml.
that is all there is to it.
so,
capacity tank = 8×380 + 1250 = 3040 + 1250 = 3290 ml
8. Point Mis 6 units away from the origin. Circle the letter by each pair of possible coordinates. A. (3.0) B. (4.2) C. (5,3) D. (0.6) E. (4.4) F. (1,5)
9514 1404 393
Answer:
D. (0, 6)
Step-by-step explanation:
The origin is where the axes cross. The coordinates of that point are (0, 0). The distance of a point (x2, y2) from point (x1, y1) is given by the distance formula ...
d = √((x2 -x1)² +(y2 -y1)²)
When (x1, y1) = (0, 0), this reduces to ...
d = √(x² +y²)
We want to find (x, y) such that d=6. This can be a little easier if we square both sides of the equation to eliminate the radical.
x² +y² = 6² = 36
This is the equation of a circle of radius 6 centered at the origin: all points that are distance 6 from the origin. So, any point on the circle will be at a distance of 6 from the origin.
__
The sum of squares in each case is ...
A. 3² +0² = 9 . . . inside the circle
B. 4² +2² = 20 . . . inside the circle
C. 5² +3² = 34 . . . inside the circle
D. 0² +6² = 36 . . . on the circle at a distance of 6 from the origin
E. 4² +4² = 32 . . . inside the circle
F. 1² +5² = 26 . . . inside the circle
PLEASE HELP!!!
The following data are the distance from the workplace ( in miles) for the 5 employees of a small business.
10,17,12,14,12
Assuming that these distance constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.
Answer:
stdev= 2.366431913
Step-by-step explanation:
10 stdev= 2.366431913
17
12
14
12
Which polynomial can be factored using the binomial theorem?
64x2 + 200x + 625
64x2 + 400x + 625
14,641x4 - 11,979x3 + 9,801x2 – 8,019x + 6,561
14,641x4 - 23,958x3 + 19,602x2 – 16,038x + 6,561
Answer:
B
Step-by-step explanation:
64x2 + 400x + 625=(8x+25)^2
Which expression is equivalent to: 16x - 16
4(2x - 2)
4(4x - 16)
4(4x - 4)
Answer:
4(4x-16)
Step-by-step explanation:
If you like my answer than please mark me as brainliest
The distribution of SAT scores is approximately normal with a mean of 1500.
If 1628 is the 90th percentile, what is the standard deviation?
Answer:
Hello,
Answer
[tex]\sigma=457,95...[/tex]
Step-by-step explanation:
p(z<a)=0.9
p(z<1.29)=0.9015
p(z<1.28)=0.8997
using linear interpolation: with 4 decimals
p(z<1.282)<0.9
[tex]\dfrac{1628-1500}{\sigma} =1.282\\\\\sigma =\dfrac{1628-1500}{1.282}\\\\\sigma=457,95...\\[/tex]
Amy, Hong, and David have a total of $102 in their wallets. Amy has $6 less than Hong. David has 4 times what Hong has. How much does each have?
Answer:
12,18, and 72 respectively
Step-by-step explanation:
102=A+H+D
A+6=H
D=4H=4(A+6)=4A+24
102=A+H+D=A+A+6+4A+24
102=6A+30
6A=72
A=12
H=18
D=72
what is the lub of 0.2,0.23,0.234,0.2343,0.23434,0.234343
Answer:
The lub is 0.2343, while the glb is 0.2
Step-by-step explanation:
btw the 43 seems to be repeating for the lub.
Have a good day!
5 5 I think of a number, treble it then add on 3, the result is equal to 6. Find the value of the original number I thought of.
Let the number be x
If 3 is added to tripple the number then the result is 6[tex]\\ \sf\longmapsto 3x+3=6[/tex]
[tex]\\ \sf\longmapsto 3x=6-3[/tex]
[tex]\\ \sf\longmapsto 3x=3[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
Answer:
The number is 1
Step-by-step explanation:
If you like my answer than please mark me brainliest thanks
