Answer:
y = 2x - 11Step-by-step explanation:
[tex]\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================[/tex]
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-slope\\b-y-intercept\\\\==========================[/tex]
[tex]\text{We have the equation of a line:}\ y=2x-7\to m_1=2.\\\\\text{The slope of a parallel line:}\ m_2=m_1=2.\\\\\text{We have the equation:}\\\\y=2x+b\\\\\text{Put the coordinates of the point (5, -1) o the equation:}\\\\-1=2(5)+b\\-1=10+b\qquad\tex\text{subtract 10 from both sides}\\-11=b\to b=-11\\\\\text{Finally:}\\\\y=2x-11[/tex]
Simplify the expression.
20*5^-2
What is the following product? square root 10× square root 10
[tex]\huge{\boxed{10}}[/tex]
We can rewrite this using an exponent. [tex]\sqrt{10}^2[/tex]
When you square a square root, you basically just cancel out the square root, leaving whatever was inside the square root symbol. In this case, you end up with a final answer of [tex]\boxed{10}[/tex].
Step-by-step explanation:
First, you must find the square root of 10, which is 3.16.
Now, multiply 3.16x3.16, or find 3.16 squared.
This is 9.98
The length of each leg of an isosceles right triangle is 4 cm. What is the length of the hypotenuse
Answer:
5.65 cm
Step-by-step explanation:
We are given that the length of each leg of an isosceles right triangle is 4 cm and we are to find the length of the hypotenuse.
For this, we will use the Pythagoras Theorem:
[tex] a ^ 2 = b ^ 2 + c ^ 2 [/tex]
where [tex]a[/tex] is the hypotenuse.
[tex] a ^ 2 = 4 ^ 2 + 4 ^ 2 [/tex]
[tex] \sqrt { a ^ 2} = \sqrt { 3 2 } [/tex]
[tex] a = 5 . 6 5 [/tex]
Therefore, the length of the hypotenuse is 5.65 cm.
Answer:
hypotenuse = 4√2
Step-by-step explanation:
It is given that, the length of each leg of an isosceles right triangle is 4 cm
To find the hypotenuse
From the given information we get the given triangle is a right triangle with angles 45°, 45° and 90°
Therefore the side are in the ration 1 : 1 : √2
Here two legs are give
leg1 : leg2 : hypotenuse = 4 : 4 : 4√2
Therefore hypotenuse = 4√2
Calculate the slope of the line that contains the points (-2, 3) and (5,-3).
Answer:
Step-by-step explanation:
Answer:
-6/7
Step-by-step explanation:
To find the slope of a line given two points on that line, you can use the slope formula: [tex]\frac{y_2-y_1}{x_2-x_2}[/tex] where you have points [tex](x_1,y_1) \text{ and } (x_2,y_2)[/tex].
When using that formula, do not put the subscripts when plugging in the answers.
Something that is equivalent to that formula and I think is easier to remember is:
Lining up the points and subtracting vertically and then putting 2nd difference over first difference.
Like this:
(-2 , 3)
- ( 5 , -3)
-------------
-7 6
So the slope is 6/-7 or -6/7.
It doesn't matter what order you do the points. You have done the (5,-3) on top instead.
Like this:
( 5, -3)
- (-2, 3)
--------------
7 -6
The slope is still -6/7.
If you don't like that and you do just directly like using that formula, then I will do it that way too.
So applying the formula either gives you: [tex]\frac{3-(-3)}{-2-5)}[/tex] or [tex]\frac{-3-3}{5-(-2)}[/tex]. Both will give us the same number.
[tex]\frac{3-(-3)}{-2-5)}=\frac{6}{-7}=\frac{-6}{7}[/tex]
[tex]\frac{-3-3}{5-(-2)}=\frac{-6}{7}[/tex]
Because of a problem in the program, the timer in a video player did not begin counting until the video had been playing for several seconds. The player began counting at 0 seconds, even though the video had already played 190 frames. The video plays 25 frames per second. How many frames had the video already played when the time was equal to -3 2/5 seconds?
Answer:
105 frames
Step-by-step explanation:
Given that 25 frames are played per second
25 frames= 1 sec
The video already played 3 and 2/5 seconds before the player started to count 0
Write 3 and 2/5 seconds as an improper fraction
=(5*3)+2 / 5 = 17/5 seconds
Multiply by 25 frames
17/5 *25 =85 frames
So according to the video counter,after 17/5 seconds,it should count 85 frames.However,at 0 seconds,it indicated a count of 190 frames.Thus,to get the number of frames that were already in count you subtract 85 frames from the 190 frames.
190-85=105 frames.
The video had played 275 frames when the timer showed [tex]-3\frac{2}{5}[/tex] seconds.
To determine how many frames had been played when the timer showed [tex]-3\frac{2}{5}[/tex] seconds, we first need to convert [tex]-3\frac{2}{5}[/tex] seconds to an improper fraction or decimal. We have [tex]-3\frac{2}{5}[/tex] = [tex]-\frac{17}{5}[/tex] seconds.
Since the video plays at a rate of 25 frames per second, we can calculate the number of frames played during [tex]-\frac{17}{5}[/tex] seconds as follows:
Total frames = 25 frames/second × [tex]-\frac{17}{5}[/tex] seconds = -85 frames.
This means that 85 frames had been played before the timer started counting (since negative time indicates frames played before the recorded start time).
Since at 0 seconds, the video had already played 190 frames, we add the frames played during the negative time interval:
Total frames = 190 frames (initial) + 85 frames = 275 frames.
Select the two binomials that are factors of this trinomial.
x^2+6x+8
Answer:
(x + 4)(x + 2)
Step-by-step explanation:
Consider the factors of the constant term ( + 8) which sum to give the coefficient of the x- term ( + 6)
The factors are + 4 and + 2, since
+ 4 × + 2 = + 8 and + 4 + 2 = + 6, hence
x² + 6x + 8 = (x + 4)(x + 2) ← in factored form
The two binomials that are factors of this trinomial x^2+6x+8 would be (x + 4)(x + 2).
What is factorization?Factorization is expressing a mathematical quantity in terms of multiples of smaller units of similar quantities.
For an integer, factorization is the decomposition of that integer in terms of smaller integers which when multiplied with each other give back that considered number.
Those composing integers are called factors of that considered integers.
Consider the factors of the constant term ( + 8) which sum to give the coefficient of the x- term ( + 6)
x² + 6x + 8
The factors are - 4 and + 2, since
+ 4 × + 2 = + 8 and + 4 + 2 = + 6,
hence , in the factored form
x² + 6x + 8 = (x + 4)(x + 2
Learn more about factorization here:
https://brainly.com/question/10454590
#SPJ2
Need help with this problem
[tex](a^2+3a)^2+(2a+5)-(a^4-3a+2)=\\a^4+6a^3+9a^2+2a+5-a^4+3a-2=\\6a^3+9a^2+5a+3[/tex]
Multiply
6.421. 10 =
0.6421
• 64.21
64210
6,421
Gujb
Answer:
64.21
Step-by-step explanation:
Here we are given with the a number in decimals and need to find its product with 10.
please note the rule of multiplication in decimals . When we multiply any decimal with 10, 100, 1000 , 10000 and so on.. the position of decimal in the number given to us shifts to its right by the number of places as we have the number of 0 in the multiplier
6.421 X 10
here we have only one 0 in the multiplier , hence the position of decimal in 6.421 will be shifted to one place towards right
6.421 x 10 = 64.21
Answer:
64.21
Step-by-step explanation:
Please help with this word problem would be a huge help!!
Answer:
11.2 miles
Step-by-step explanation:
What has been describe here is a right triangle.
He went 10 miles east, and he turned left and went 5 miles. He started at home ended at work. We want to make a road from his home directly to his workplace (no turns; straight there).
So we have by Pythagorean Theorem:
[tex]5^2+10^2=c^2[/tex]
[tex]25+100=c^2[/tex]
[tex]125=c^2[/tex]
Square root both sides:
[tex]\sqrt{125}=c[/tex]
[tex]11.2 \approx c[/tex]
11.2 miles would be the length of that direct path.
A hamburger bun merchant can ship 8 large boxes or 10 small boxes of hamburger buns into a carton for shipping. In one shipment, he sent a total of 96 boxes of hamburger buns. If there are more large boxes than small boxes, how many cartons did he ship?
Answer:
11 cartons
Step-by-step explanation:
Number of large boxes that can be contained in a carton = 8
Number of small boxes that can be contained in a carton = 10
Total number of boxes sent in one shipment = 96
This shipment contains both large and small boxes. Let there be x cartons of large boxes and y cartons of small boxes in one shipment. So, we can say,
Total number of large boxes in one shipment = Number of boxes in one carton * Total number of cartons = 8x
Similarly,
Total number of small boxes in one shipment = 10y
Since, total number of boxes in one shipment is 96, we can set up the equation as:
8x + 10y = 96
This equation can have following possible solutions:
x =2, y = 8x = 7, y = 4x = 12, y = 0We are given in the statement that are more large boxes than the small boxes, the valid solutions are:
x = 7, y = 4x = 12, y = 0Assuming that he sent both large and small boxes, the only valid solution will be:
x = 7, y = 4This means, the merchant sent 7 cartons of large boxes i.e. 56 large boxes and 4 cartons of small boxes i.e. 40 small boxes. So in total he sent 11 cartons.
Answer:
11 boxes total 4 small 7 large
Step-by-step explanation:
1 small box *10 = 10 96-10 = 86 (NO MULTIPLE OF 8)
2 small boxes*10=20 96-29=76 ( no multiple of 8)
3 small boxes *10=30 96-30= 66(no multiple of 8)
4 small boxes*10 = 40 96-40 = 56 (YES multiple of 8) 56/8 = 7 (7 large boxes)
4 large boxes and 7 large boxes
if f(x)=4x2=1 and g(x)=x2-5, find (f-g)(x)
A:3x2+6
B:5x2-6
C:3x2-4
D:5x2-4
For this case we have the following functions:
[tex]f (x) = 4x ^ 2 + 1\\g (x) = x ^ 2-5[/tex]
We must find[tex](f-g) (x):[/tex]
By definition of operations with functions we have:
[tex](f-g) (x) = f (x) -g (x)[/tex]
So:
[tex](f-g) (x) = f (x) -g (x) = 4x ^ 2 + 1- (x ^ 2-5) = 4x ^ 2 + 1-x ^ 2 + 5 = 3x ^ 2 + 6[/tex]
Answer:
Option A
[tex]3x ^ 2 + 6[/tex]
A picture frame is 30 cetimeters by 50 centimeters this includes a border 5 centimeters wide surronding the picture itself what is the area of this shaded border in square cm?
Answer:
700 cm^2
Step-by-step explanation:
The area of the picture + frame = L * W
L = 50 cmW = 30 cmArea = 50 * 30
Area = 1500
=====================
Area of inside area
L = 50 - 10 = 40 (Remember both ends have to be shortened)W = 30 - 10 = 20 ( Remember again both ends have to be shortened)Area = L * W
Area = 40 * 20
Area = 800
======================
Now the frame is going to take up the difference.
Area Frame = Entirie area - inside area
Area Frame = 1500 - 800
Area Frame = 700
Step 1: -10 + 8x < 6x-4
Step 2: -10 <-2x - 4
Step 3: -6 <-2x
Step 4:
What is the final step in solving the inequality --215-4x)
6x - 4?
O x<-3
O x>-3
O x<3
O x>3
Help!!
Answer:
The final step in solving inequality is x>3.
Step-by-step explanation:
To solve this problem, first thing to do is switch sides of -2x>-6, and divde -2 from both sides.
-2x>-6
-2x/-2>-6/-2
Divide numbers from left to right.
-6/-2=3
The final step in solving the inequality is x>3, which is our answer.
I hope this helps!
Thank you! for submitting question on Brainly.
If DB is drawn, what is the measure of TDB?
Answer:
90°
Step-by-step explanation:
we know that
The side TD is perpendicular to the plane formed by the square base ABCD of the cube
therefore
The measure of angle ∠TDB is 90 degrees
The correct answer is d) 90
Step-by-step explanation:
The graph of f(x) = x^5 + 2x^4 - x - 2 is given. How many complex zeros does the function have?
Answer:
According to the graph of f(x), the function has three real solutions to x= -2, x= -1 and x=1.
Then, given that the function is a 5 degree polynomial, we can conclude that the function has 2 complex zeros.
If it takes Tom 15 minutes to eat a burger and then 5 minutes to eat a portion of fries, how many burgers and portions of fries would he be able to eat in one hour?
But my options are, 3,6,2,and 5
Answer:
6
Step-by-step explanation:
In this question it appears that for each burger Tom then has to eat 1 portion of fries. This combination would take 15 + 5 = 20 minutes.
Since 60/20 = 3, he would be able to eat 3 burgers and 3 portions of fries in 60 minutes. Making up a total of 3+3 = 6
Answer:
Tom eats 3 burgers and 3 portions of fries in 1 hour.
Step-by-step explanation:
Tom eats a burger in 15 minutes and a portion of fries in 5 minutes.
Total time he spent = 15 + 5 = 20 minutes in eating both
We have to calculate the number of burgers and fries he is able to eat in one hour.
∵ In 20 minutes Tom eats burger and fries = 1
∴ In 1 minutes he would be able to eat = [tex]\frac{1}{20}[/tex]
∴ In 60 minutes he would be able to eat = [tex]\frac{60}{20}=3[/tex] sets of burgers and fries.
Therefore, Tom eats 3 burgers and 3 portions of fries in 1 hour.
The variable t in the formula d = rt stands for
Answer:
The distance formula d = rt, 'd' stands for distance, 'r' stands for rate and 't' stands for time.
It's a well known formula used in physics to solve problems that involves questions like "how fast", "how far", or "for how long".
In the formula d = rt, the variable t represents time. It's a consistent representation across situations whenever you are dealing with equations for motion, speed, or other physics contexts.
The variable t in the formula d = rt stands for time. This formula is used to calculate distance based on the rate of speed (r) and the time (t) traveled. To solve for time, you would rearrange the formula to t = d/r, which means time equals distance divided by rate.
In various physics and mathematical contexts, as shown in the reference information, the letter t consistently represents time. It could be the time an object takes to cover a certain distance at a given rate, or more complex scenarios involving non-Euclidean worlds or quantum mechanics. Nevertheless, whenever you see t in such equations, it is typically referring to time, unless otherwise specified.
If a+ b + c= -6 and x +y = 5, what is 9y +9x - 10a-10c -10b ?
Answer:
9y +9x - 10a-10c -10b = 105
Step-by-step explanation:
Given
a+b+c = -6 and x+y = 5
We have to find 9y +9x - 10a-10c -10b
Rearranging the terms
9x+9y-10a-10b-10c
Simplifying will give us:
= 9 (x+y) - 10(a+b+c)
Putting the values of x+y and a+b+c
= 9(5) -10(-6)
=45+60
=105
Therefore,
9y +9x - 10a-10c -10b = 105 ..
Answer:
9y + 9x - 10a - 10c - 10b = 105
Step-by-step explanation:
It is given that, a+ b + c = - 6 and x + y = 5
To find the value of given expression
Let the expression be 9y +9x - 10a-10c -10b
9y +9x - 10a -10c -10b = 9(y + x) - 10(a + c + b )
= 9(x + y) - 10(a + b + c)
= 9 * (5) - 10 * (-6)
= 45 + 60
= 105
Therefore 9y + 9x - 10a - 10c - 10b = 105
I need 12 and 13 plzzz
Evaluate: 5P5
A:120
B: 1
C: 132
D: 126
(This is permutations btw)
[tex]_nP_k=\dfrac{n!}{(n-k)!}\\\\\\_5P_5=\dfrac{5!}{0!}=120[/tex]
Answer:
A. 120.
Step-by-step explanation:
5P5 = 5! / (5-5)!
= 5! / 0!
= 5!/1
= 5!
= 120.
Which is a graph of f(x) = (6x-2)/(x-3), with any vertical or horizontal asymptotes indicated by the dashed lines?
Answer:
to find the vertical asymptote, you have to put the rational function in the simplest form, which means to cancel any common factor between the numerator and denominator. here we don't have anything to cancel. then take the denominator and equal it to 0. x-3=0 ,x=3
to find the horizontal asymptote, in this situation, the degree of the numerator and denominator are the same which is 1. therefore, y=the coefficient of the numerator ÷ the coefficient of the denominator. y=6÷1 ,y=6
Answer with explanation:
The given function is:
[tex]f(x)=\frac{6x-2}{x-3}[/tex]
Horizontal Asymptote
[tex]y= \lim_{x \to \infty} \frac{6x-2}{x-3}\\\\\text{Dividing Numerator and Denominator by ,x}\\\\\Rightarrow y=\lim_{x \to \infty} \frac{6-\frac{2}{x}}{1-\frac{3}{x}}\\\\\Rightarrow y=\frac{6-0}{1-0}\\\\\Rightarrow y=6[/tex]
Vertical Asymptote
→Substitute Denominator of f(x) =0
⇒x-3=0
⇒x=3
⇒x=3 is Vertical Asymptote , and y=6 is horizontal Asymptote.
Matching with all the options
Option D
[tex]25.643 - 18.21 = [/tex]
Answer:
The answer is 7.433
Step-by-step explanation:
Bc:
25.643 the 5 turned to 15, and the 2 is a 1.
- 18.210
7.433
Hope my answer has helped you, if not i'm sorry.
Answer:
7.433
Step-by-step explanation:
To solve this problem, you'd need to subtract the numbers from left to right.
25.643-18.21=07.433=7.433
So, the correct answer is 7.433.
I hope this helps!
Thank you for submitting your question!
Ken wants to purchase a boat. The purchase price of the boat is $ 15 , 000. The dealership will allow him to pay cash or finance the boat for a down payment of $ 3 , 000.00 and 48 monthly payments of $ 300.00. Ken chose to finance the boat.
In finance, the buyer pays more when choosing to finance the boat rather than paying cash upfront due to additional fees included in the payments.
Explanation:The subject area of the question is Mathematics, specifically Financial Mathematics. The question is asking about the total cost Ken will pay for the boat if he chooses to finance it. The down payment is $3000 and he will make 48 monthly payments of $300, totaling $14,400. Therefore, Ken will pay a total of $17,400 when financing the boat, which is $2,400 more than the cash purchase price.
Learn more about Financial Mathematics here:https://brainly.com/question/28975181
#SPJ12
To find the total amount paid for the boat, add the down payment to the product of the monthly payments and the number of payments.
Explanation:To find the total amount paid for the boat, we need to calculate the total future amount. The down payment is $3,000 and there are 48 monthly payments of $300 each.
The total future amount can be calculated using the formula:
Total Future Amount = Down Payment + Monthly Payments * Number of Payments
Plugging in the values, we get:
Total Future Amount = $3,000 + $300 * 48 = $17,400
Therefore, Ken will pay a total of $17,400 for the boat.
Learn more about Calculating the total amount paid for the boat here:https://brainly.com/question/34045673
#SPJ12
The vet told Jake that his dog, Rocco, who weighed 55 pounds, needed to lose 10 pounds. Jake started walking Rocco every day and changed the amount of food he was feeding him. Rocco lost half a pound the first week. Jake wants to determine Rocco’s weight in pounds, p, after w weeks if Rocco continues to lose weight based on his vet’s advice.
Answer:it would take him five weeks to lose ten pounds
Step-by-step explanation:
Answer: To determine Rocco´s weight jake must use this expression
p = 55 - 0.5 wStep-by-step explanation:
Hi to solve this problem we have to analyze the information given:
Rocco´s initial weight: 55 pounds Pounds lost per week: 0.5 poundsSo, we have to write an equation where p is Rocco's weight after w weeks.
Each week Rocco will lose 0.5 pounds so the expression is 0.5w, where w is the number of weeks.
Mathematically speaking:
p = 55 - 0.5 wBy replacing w by the number of weeks, Jake will obtain Rocco´s weight.
For example, if the number of weeks is 20:
p= 55-0.5x 10
p= 55 - 20
p= 35
After 20 weeks Rocco will lose 10 pounds.
The height y (in feet) of a ball thrown by a child is
y=−1/12x^2+6x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y when x=0)
Your answer is y=_______
(b) What is the maximum height of the ball? _______
(c) How far from the child does the ball strike the ground? ______
Answer:
Step-by-step explanation:
a)
y=−1/12x^2+6x+3
y=−1/12(0)^2+6(0)+3
y = 3
b)
y=−1/12x^2+6x+3
y = -1/12 (x^2-72x) + 3
y = =-1/12 (x^2-72x+1296-1296) +3
y = -1/12(x^2 -72x +1296) + 108 + 3
y = -1/12 (x - 36)^2 +111
maximum height of the ball is 111 feets
c)
y = -1/12 (x - 36)^2 +111
0 = -1/12 (x - 36)^2 +111
-111 = -1/12 (x - 36)^2
1332 = (x - 36)^2
36.497 = x - 36
x = 72.497
How far from the child does the ball strike the ground = 72.497 feets
The ball is 3 feet high when it leaves the child's hand. The maximum height of the ball is 6 feet. The ball strikes the ground 2 feet from the child.
Explanation:(a) To find the height of the ball when it leaves the child's hand, we need to substitute x=0 into the equation for y. Therefore, y=(-1/12)(0)^2+6(0)+3=3. So, the ball is 3 feet high when it leaves the child's hand.
(b) The maximum height of the ball can be found by determining the vertex of the parabolic equation. The equation is in the form of y=ax^2+bx+c, where the vertex is located at x=-b/2a. In this case, a=-1/12 and b=6. Therefore, x=-6/(2(-1/12))=-6/(-1/6)=-6(-6)=6 feet. So, the maximum height of the ball is 6 feet.
(c) To determine how far from the child the ball strikes the ground, we need to find when the ball's height is 0. Set y to 0 and solve for x. 0=(-1/12)x^2+6x+3. This equation can be solved using factoring or the quadratic formula. The solutions are x=-36 and x=2. Therefore, the ball strikes the ground 2 feet from the child.
I need help!!!!!!!!!!! PLEASE EXPLAIN! I'M SO CONFUSED! PLEASE!
Answer:
2
Step-by-step explanation:
There are four 11-year olds and x amount of 14-years old.
We are given the average of this group of 11 and 14 year olds is 12.
This gives us the following equation to solve for x:
[tex]\frac{4(11)+x(14)}{4+x}=12[/tex]
Doing some simplifying on the left and writing 12 as 12/1 on the right because I'm going to cross-multiply in the step to follow:
[tex]\frac{44+14x}{4+x}=\frac{12}{1}[/tex]
Cross multiplying:
[tex]1(44+14x)=(4+x)(12)[/tex]
Distribute:
[tex]44+14x=48+12x[/tex]
Subtract 12x on both sides:
[tex]44+2x=48[/tex]
Subtract 44 on both sides:
[tex]2x=4[/tex]
Divide both sides by 2:
[tex]x=2[/tex]
There are two 14-year olds.
Let's confirm.
You have four 11 year olds and two 14 years old.
So you have:
11,11,11,11,14,14
We want to find the average of this set of numbers.
You add the numbers and divide by the number of numbers.
[tex]\frac{11+11+11+11+14+14}{6}=\frac{72}{6}=12[/tex]
This is the average the problem wanted us to obtain so the work we did above is correct.
Solve for x 3 - square root of x = 0
Answer:
x = 9Step-by-step explanation:
[tex]3-\sqrt{x}=0\\\\\text{Domain:}\ x\geq0\\\\3-\sqrt{x}=0\qquad\text{add}\ \sqrt{x}\ \text{to both sides}\\\\3=\sqrt{x}\to\sqrt{x}=3\\\\\text{Use the de}\text{finition of a square root:}\ \sqrt{a}=b\iff b^2=a\\\\\sqrt{x}=3\iff x=3^2\\\\x=9[/tex]
Use multiples to write 2 fractions equivalent to 7/9
Answer:
14/18 and 49/63
Step-by-step explanation:
14/18 and 49/63 are equivalent to 7/9.
7 x 2 = 14
9 x 2 = 18
Therefore, 14/18
7 x 7 = 49
9 x 7 = 63
Therefore, 49/63
Answer:
21/27 and 42/54
Step-by-step explanation:
therefore, 21/27 and 42/54 are equivalent to 7/9
7 x 3=21
9 x 3= 27
Therefore, 21/27
7 x 6= 42
9 x6 = 54
Therefore, 42/54
Nasheem is going to make breakfast for his family. He has a carton of dozen eggs and uses 2/3 of them. How many eggs did Nasheem use? How many eggs does he have left?
Answer:
Step-by-step explanation:
He uses (2/3)(12 eggs) = 8 eggs.
He has (12-8), or 4, eggs left.
Answer:
Step-by-step explanation:
Number of eggs = 1 dozen = 12 eggs
Number of used eggs = 2/3 * 12 (Total eggs will be multiplied by used eggs)
2/3*12
2*4
=8 eggs
Number of used eggs= 8 eggs
To find the number of left eggs. Simply subtract the used eggs from total eggs
12-8 = 4eggs
4 eggs were left....
John has a rectangular picture which is 43 inches long and 27 inches wide. He wants to build a wooden gram for the picture but she only has 800 square inches of wood available. How wide will the border be?
Answer:
The border will be 18.6 inches wide
Step-by-step explanation:
Let the width be w
The length = 43 inches
Total wood = 800 square inches
Formula for area of rectangle = length x width
800 = 43 x w
w = 800/43
w = 18.6 inches
Therefore, the border will be 18.6 inches wide.
!!
Answer:
5 inches
Step-by-step explanation:
Let x be the width ( in inches ) of the border,
Given,
The length of the picture = 43 inches,
And, width of the picture = 27 inches,
So, the length of whole frame ( picture with border ) = 43 + 2x,
Its width = 27 + 2x
Thus, the area of the whole frame,
[tex]A=(43+2x)(27+2x)-----(1)[/tex]
Now, the area of the picture,
[tex]A_1=43\times 27=1161\text{ square inches}----(2)[/tex]
We have, the area of the border,
[tex]A_2=800\text{ square inches}----(3)[/tex]
Thus,
[tex]A=A_1+A_2[/tex]
Equation (1) (2) and (3),
[tex](43+2x)(27+2x) = 1161+800[/tex]
[tex]1161 + 86x+54x+4x^2=1161+800[/tex]
[tex]4x^2+140x-800=0[/tex]
[tex]x^2+35x-200=0[/tex]
[tex]x^2+40x-5x-200=0[/tex]
[tex]x(x+40)-5(x+40)=0[/tex]
[tex](x-5)(x+40)=0[/tex]
[tex]\implies x=5\text{ or }x=-40[/tex]
∵ Width can not be negative,
Hence, the width of the border is 5 inches.