Answer:
450 m²
Step-by-step explanation:
Let x = length of rectangle and y = width of the rectangle.
Therefore,
2x + y = 60...............(1)
Making y subject of the formula, we have:
y = 60 - 2x............... (2)
We know area of a rectangle is length * width i.e A = x*y
Let's substitute (60-2x) for y,
A = x * (60-2x)
= 60x - 2(x)²
= -2x² + 60x
[tex] \frac{dA}{dx} = -2x^2 + 60x = [/tex]
-4x + 60 = 0
-4x = -60
[tex] x = \frac{-60}{-4} = 15 [/tex]
Let's substitute 15 for x in equation 2, we have:
y = 60 - 2(15)
= 60 - 30
y = 30
Since x = 15 & y = 30, the area would be:
A = xy
A = 15 * 30
A = 450 m²
The maximum area of the dog pen is 450m²
How do I Graph y=-2x+5
Answer:
Slope-Intercept Form y = mx + b
Y = 5
Slope = -2/1
Step-by-step explanation:
Slope-Intercept Form y = mx + b
m = Slope; Rise over Run; Remember there is always an understood 1 in the denominator. If the slope is positive it goes up and to the right and if the slope is negative it goes down and to the right.
b = Y-intercept; This is where the line crosses the y-axis at. If it's positive it's above the x-axis and if negative below.
If f(x)=5x2−3x+8, find f(0)
Answer:
8
Step-by-step explanation:
f(x)=5x^2−3x+8
Let x=0
f(0) = 5(0) -3(0) +8
= 8
Kia is saving money to buy a Six Flags ticket. She worked for 6 hours at the library and earns the same amount each hour. Her grandmother then gave her $20. In all,she has $53.
Answer:
She earns 5.5 dollars per hour at the library
Step-by-step explanation:
I am going to assume that the questions is "how much she earns per hour at the library?"
Let's call x the amount of dollars earn by hour at the library. We know that she worked for 6 hours, thus she made 6x dollars.
Later her grandma gave her 20 dollars and she has now 53 dollars.
Let's write the equation and solve it
Amount earned + Amount given by her grandma = 53
[tex]6x+20=53\\6x=33\\x=\frac{33}{6}\\x=5.5[/tex]
Thus, based on this information we would have that Kia earns 5.5 dollars per hour.
Which statement about the parabola is not true?A. The focus lies on the axis of symmetry.B.The directrix of the parabola is parallel to the axis of symmetry.C. Each point on the parabola is equidistant from the directrix and the focus
Answer:
Option B
The directrix of the parabola is parallel to the axis of symmetry
Step-by-step explanation:
The directrix of the parabola is not parallel to the axis of symmetry. It is as a matter of fact, perpendicular to it.
A parabola is actually a set of points that are equidistant from a given point, the focus, and a given line the directrix.
The axis of symmetry is a line that divides the parabola into two equal halves and it always passes through the focus.
The directrix of the parabola is always perpendicular to this axis of symmetry as they always intersect at right angles.
We want to see which one of the given statements is false. We will see that the false one is B: "The directrix of the parabola is parallel to the axis of symmetry"
So in a parabola, we define the axis of symmetry as the vertical line that divides the parabola in two equal parts.
For a general parabola:
y = a*x^2 + b*x + c
The line of symmetry is at:
x = -b/2a
While we know that in a parabola the directrix is a horizontal line.
So the axis of symmetry and the directrix are perpendicular lines.
Then the statement that is false is B: "The directrix of the parabola is parallel to the axis of symmetry"
If you want to learn more, you can read:
https://brainly.com/question/3283347
Use a net to find the surface area of the prism 8 in 6 in 15 in
Write an inequality for each sentence.
The elephant weighs more than 12,000 pounds.
Answer:
e > 12000 pounds
Step-by-step explanation:
Since the elephant weighs over 12000 pounds it would not be greater than or equal to or less than or less tan or equal to so
if elephant = e than
e > 12000 pounds
Correct answers only!
To the nearest cent, how much will he have in 2 years?
Use the formula B = p(1 + r)t, where B is the balance (final amount), p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years.
Answer: $44.10
Step-by-step explanation:
We are given our p, r, t in the problem.
p=40 (starting amount)
r=0.05 (5%)
t=2 (years)
With the given information, we can plug this into our equation.
B=p(1+r)^t
B=40(1+0.05)^2
B=44.1
Terry is buying juice. He needs 3 liters. A half-liter of juice costs $2.39. A 250 -milliliter container of juice cost $ 1.69. What should Terry buy so he gets 3 liters at the lowest price? Explain
Answer:
Terry should buy half a liter because if he buys 250 millimeters, he will need to pay $20.28, which is more than 14.34.
When you add fractions is the sum always greater than 1?
Answer:
Not always
Step-by-step explanation:
Some fractions, like 1/2, if you add it with 1/2, it equals one.
Halves will always equal one, and they are fractions too, so technically not all addition of fractions are greater than 1.
hope this helped
A waitress serves $950. Worth of dinners and recieves &95.00 in tips how much less in tips did she receive if she had gotten her 15% of the cost of meals
Answer:
She receives $47.5 less
Step-by-step explanation:
Now, the first thing to do here is to calculate what 15% if the total amount is
That would be 15/100 * 950 = $142.5
The amount she receives less is thus $142.5 -$95 = $47.5
Answer:
The amount less that she received than if she had received 15% of the cost of the meal is $47.5
Step-by-step explanation:
Here we have the amount of dinners served by the waitress = $950
Amount received in tips = $95.00
Amount the waitress would have received if she had gotten 15% of the cost of meals served = 15/100 × $950 = $142.5
Therefore, since she received $95.00, the amount less that she received than if she had received 15% of the cost of the meal is thus;
$142.5 - $95 = $47.5.
Solve the equation.
6+q=1
Answer:
-5
Step-by-step explanation:
6 - 5 = 1
so 6 + -5 is also equal to 1
Answer:
q = -5
Step-by-step explanation:
Step 1 : Simplify: 6/q
Step 2 :
Rewriting the whole as an Equivalent Fraction
Equation at the end of step 2 :
(6 - q)
——————— - 2 = 0
q
Step 3 :
Rewriting the whole as an Equivalent Fraction
Step 4 :
Pulling out like terms
Answer: q = -5
Hope this helps.
i need help i don't understand can someone help me plz :)
Find the surface area.
Any help will be appreciated thank you!
Answer:
580 cm^2
Step-by-step explanation:
H = Height
L = length
W = width
2(HL)+2(WH)+2(WL)
= 2(20*10)+2(3*20)+2(3*10)
= 2(200)+2(60)+2(30)
= 400+120+60
= 580
Question 4 11 point)
Four hundred grocery store shoppers were surveyed to determine their favorite fruit. How many shoppers prefer bananas?
Favorite Fruit
Bananas Apples
32%
35%
Cherries
33%
Os 32
Answer:
128
Step-by-step explanation:
128 is the right
peanut butter
The zero(s) of the function : f(x)=x² - 2x +3 are_____________ *
Answer:
x = 1 ± i√2
Step-by-step explanation:
hope i helped
Mrs. Dominguez asked her students to plot the number of books they read over the summer.
Using the dot plot, how many students read two books?
1
2
3
6
Answer:
6
Step-by-step explanation:
Answer:
6 students read 2 books
Step 2: Radii OK and NL are perpendicular to OM because of the radius-tangent theorem. By definition of perpendicular, angles KOM and LNM are right angles. This means that triangles KOM and LNM are right triangles. Angle LMN is common to both right triangles, so by the _________________________, triangles KOM and LNM are similar. please fill in the blank
Answer:
AAA postulate.Step-by-step explanation:
Givens
Angles KOM and LNM are congruent, because both are right.Angle LNM is common to both triangles.If two internal angles of two triangles are congruent, then the third angle is also congruent.
Therefore, the similarity is proven by AAA postulate, which states that if we have three corresponding angles congruent, then those triangles are similar.
Remember that similarity is about proportion between sides and congruence between angles.
Which arc measures 180°
А.
8
AE
BD
d or DC
Hope this helps!! :)
Help asap! giving brainliest!
Answer: understand The problem
Gather reasources
check your answer to a solution
come to an answer
vvvvvvv help me plzzzzzzzzzzzzzzz
Answer:
the answer is 0
Step-by-step explanation:
she had -27 in her bank the she added 27
pls pls pls pls pls pls pls pls pls pls help
an airplane takes off from an airport at 11 am. fifteen minutes later, its shadow is 360000 feet away from the take off point and its altitude is 24000 ft. what is the exact distance the plane traveled in 15 minutes
Answer:
what grade are you in so i can help
Step-by-step explanation:
Complete the point-slope equation of the line through (-9,6)(−9,6)left parenthesis, minus, 9, comma, 6, right parenthesis and (-7,-8)(−7,−8)?
Answer:
Step-by-step explanation:
hello : here is an solution
The equation of the line in point-slope form is y - 6 = -7(x+9)
The equation of a line in point-slope form is expressed as:
y-y0 = m(x-x0)
m is the slope of the line
(x0, y0) is any point on the line
Given the coordinate points (-9, 6) and (-7, -8)
Get the slope of the line:
slope = -8-6/-7+9
Slope = -14/2
Slope = -7
Using the point (-9, 6), the required slope is expressed as:
y - 6 = -7(x-(-9))
y - 6 = -7(x+9)
Hence the equation of the line in point-slope form is y - 6 = -7(x+9)
Learn more here: https://brainly.com/question/24642959
What is the volume? Please answer asap.
Answer:
20
Step-by-step explanation:
solve the following
2(X+3)=X-4
Answer:
2(x+3)=x-4
2x+6=x-4
2x-x=-4-6
x=-10
fathi has $1.10 in his printing account. each sheet of paper he uses reduces his printing account balance by $0.25. Fathi wants to print out a PDF document that is 47 pages long. To save paper, he decides to print on both sides of each sheet and to print two pages on each sides of the sheet.
Answer:
IF THE question is After Fathi prints, what will be the balance in his printing account?
then it is: $1.9
There are 47 pages.
Printing on both sides would divide the number of pages into half.
47/2 = 23.5
2 pages on each side would mean 4 pages on one sheet. Therefore, the number of pages will be further divided by 2.
23.5/2 = 11.75
There cannot be 11.75 pages so we will round it up to 12 pages.
Each page costs $0.25 so 12 pages will cost:
12 x 0.25 = $3
Faithi has $1.1 so new account balance will be:
1.1 - 3 = $-1.9
Therefore, Fathi's balance in his printing account would be negative $1.9.
Answer:
The answer is $-1.90
Meagan knits 1/10 of q scarf in 3/4 of annhour.What fraction of a scaf can megan knit in 1 hour
Answer:
2/15
Step-by-step explanation:
To solve this problem we just need to use a rule of three, relating the fraction of the scarf knitted and the amount of time.
So we have that:
1/10 of the scarf -> 3/4 hour
x of the scarf -> 1 hour
x * (3/4) = 1/10
x = (1/10) / (3/4)
x = (1/10) * (4/3)
x = 4/30 = 2/15
In one hour, Meagan knit 2/15 of the scarf.
How do I calculate this parent function of a linear function? The parent function of a linear function is y=x. When the parent function is changed to y=x+5, how does the graph transform?
Step-by-step explanation:
This only moves the linear function up 5 units. So, before the y-intercept and the x-intercept both was (0,0). Now, the y-intercept is (0,5) because the graph was shifted up 5 units.
hope this helps :)
Find the volume of the cone khan academy
Answer:
V= 1/3 pi*r^2*
Step-by-step explanation:
The reason the volume of a cone involves using the fraction 1/3, is because it takes three cones to fill up a cylinder. So, if the volume of a cylinder is pi*r^2*h, and a cone is 1/3 the size, then the volume of a cone(which uses the same formula) has to have the 1/3rd in front.
Which equation demonstrates the additive identity property?
(7 + 4i) + (7-4i) = 14
(7 + 4i) + 0 = 7 + 4i
(7 + 4i) ( 1 ) = 7 + 4i
(7 + 4i) + (-7- 4i) = 0
the answer for the question is b! :)
1 1/7 times 3/5 plz answer now
Answer:
24/35 or 0.6857142
Step-by-step explanation:
Answer:
[tex] \frac{24}{35} [/tex]
alternative form:
[tex] 0.685714286 [/tex]
Step-by-step explanation:
[tex]1 \frac{1}{7} \times \frac{3}{5} \\ multiply \: 1 \: and \: 7 \\ \\ \frac{7 + 1}{7} \times ( \frac{3}{5} ) \\ add \: 7 \: to \: 1 \\ \\ \frac{8}{7} \times ( \frac{3}{5} ) \\ remove \: parenthesis \: and \: put \\numerator \: times \: numerator \: and \\ denominator \: times \: denominator \\ \\ \frac{8 \times 3}{7 \times 5} \\ do \: the \: multiplications \\ \\ \frac{24}{35} [/tex]
