Answer:
The dimensions have to be reduced by 2 inches
Step-by-step explanation:
Given that the dimensions are: 6 by 8 inches which means that the area is 48 square inches.
Let x be the amount to make a new photo which is half of the area that means
The new dimensions will be: (8-x) by (6-x) and as the area is half
The area of new photo will be: 48/2 = 24
Putting it mathematically
[tex](8-x)(6-x) = 24\\8(6-x)-x(6-x)=24\\48-8x-6x+x^2=24\\48-14x+x^2=24\\x^2-14x+48-24=0\\x^2-14x+24=0\\x^2-12x-2x+24=0\\x(x-12)-2(x-12)=0\\(x-2)(x-12)=0\\x-2=0 => x=2\\x-12=0 =>x=12[/tex]
Subtracting 12 from both dimensions will make them negative so 12 cannot be the solution.
Hence,
The dimensions have to be reduced by 2 inches
We want to see by how much we must reduce the dimensions of the photograph in order to reduce its area to half. We will find that we must reduce each measure by 2 inches.
The original measures of the photograph are:
length = 6 inwidth = 8 in.Then the area is:
A = (6 in)*(8 in) = 48 in^2
Now we want to define a new length and a new width:
L' = (6 in - n)W' = (8in - n)such that:
A' = L'*W' = 24 in^2
(6 in - n)*(8in - n) = 24 in^2
48in^2 - n*14 in + n^2 = 24 in^2
n^2 - n*14 in + 24in^2 = 0
This is a quadratic equation, we can solve this for n by using Bhaskara's formula, we will get:
[tex]n = \frac{14in \pm \sqrt{(-14)^2 - 4*1*24in^2} }{2*1} \\\\n = 7in \pm 5 in[/tex]
The only solution that makes sense is:
n = 7in - 5in = 2in
This means that we need to reduce each measure by 2 inches.
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After releasing of radioactive material into.The atnosphere from.A nuclear.Powe plant in a country in 1988, the hay in that country was contaminayed by radioactive.Isotope remains, how long did the famers need to.Wait to use this hay
Answer:
the question is incomplete, so I looked for a similar one:
After the release of radioactive material into the atmosphere from a nuclear power plant, the hay was contaminated by iodine 131 ( half-life, 8 days). If it is all right to feed the hay to cows when 10% of the iodine 131 remains, how long did the farmers need to wait to use this hay?
iodine's half life (we are given x, we need to find b):
0.5A₀ = A₀eᵇˣ
x = 8 days
we eliminate A₀ from both sides
0.5 = eᵇ⁸
ln 0.5 = ln eᵇ⁸
-0.69315 = b8
b = -0.69315 / 8 = -0.08664
since the farmers need to wait until only 10% of the iodine remains (we already calculated b, now we need to find x):
0.1A₀ = A₀eᵇˣ
0.1 = eᵇˣ
ln 0.1 = bx
where b = -0.08664
x = ln 0.1 / -0.08664 = -2.302585 / -0.08664 = 26.58 days
What is the value of k in the equation StartFraction k Over 3 EndFraction minus 5 = 34?
[tex]\huge\text{$k=\boxed{117}$}[/tex]
[tex]\displaystyle\frac{k}{3}-5=34[/tex]
To find the value of [tex]k[/tex], we need to isolate it on one side of the equation. Add [tex]5[/tex] to both sides of the equation, then multiply both sides of the equation by [tex]3[/tex].
[tex]\displaystyle\begin{aligned}\frac{k}{3}-5+5&=34+5\\\frac{k}{3}&=39\\\frac{k}{3}*3&=39*3\\k&=\boxed{117}\end{aligned}[/tex]
what would the answer be?
Answer:
-2y
Step-by-step explanation:
10x+ -2y = 3
-10 -10
-2y = -7
-2 -2
Neil has 3 partially full cans of white paint.They contain 1/3 gallon, 1/5, gallon, and 1/2, gallons of paint About how much paint dose Neil have in all?
Answer:
1 and 1/30 gallons
Step-by-step explanation:
First, convert all the fractions to a common denominator. I'm choosing 30.
1/3=10/30 1/5=6/30 1/2=15/30
Now, you can add them together to get 31/30, so a little more than a gallon
GEOMETRY HELP ILL VOTE YOU BRAINLIEST I PROMISE PLEASE
Answer:
x=29
Step-by-step explanation:
4x-18+5x-71=180
9x=269
x=29
A hobby shop sells small and large toy cars. A small toy car is $5.50, and a large toy car is $9. What is an equation that relates the cost, Cin dollars
with the number of small toy cars, S, and the number of large cars, L. purchased?
Answer:
C = 5.50S + 9L
.............
The equation that relates the cost, Cin dollars with the number of small toy cars, S, and the number of large cars, L is C = 5.50S + 9L.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
It is given that:
A hobby shop sells small and large toy cars. A small toy car is $5.50, and a large toy car is $9.
Let S be the number of a small toy car and L be the number of a large toy car.
The equation can be made:
Total cost:
C = 5.50S + 9L
Thus, the equation that relates the cost, Cin dollars with the number of small toy cars, S, and the number of large cars, L is C = 5.50S + 9L.
Learn more about the linear equation here:
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From A to B a private plane flies 2.8 hours at 110 mph on a bearing of 64 degrees . It turns at point B and continues another 1.7 hours at the same speed, but on a bearing of 154 degrees to point C. Round each answer to three decimal places. a. At the end of this time, how far is the plane from its starting point? b. On what bearing is the plane from its original location?
Answer:
a. 360.323 m
b. [tex]95.265^{o}[/tex]
Step-by-step explanation:
Distance covered from A to B = speed x time
= 110 x 2.8
= 308 m
Distance covered from B to C = speed x time
= 110 x 1.7
= 187 m
The sum of angles at B = [tex]64^{o}[/tex] + [tex]26^{o}[/tex]
= [tex]90^{o}[/tex]
a. The distance of the plane from it starting point to C can be determined by applying the cosine rule.
[tex]b^{2}[/tex] = [tex]a^{2}[/tex] + [tex]c^{2}[/tex] - 2ac Cos B
Sot hat;
[tex]b^{2}[/tex] = [tex]187^{2}[/tex] + [tex]308^{2}[/tex] - 2(187 x 308) Cos [tex]90^{o}[/tex]
But, Cos [tex]90^{o}[/tex] = 0
So that,
[tex]b^{2}[/tex] = [tex]187^{2}[/tex] + [tex]308^{2}[/tex]
= 34969 + 94864
= 129833
b = [tex]\sqrt{129833}[/tex]
= 360.323
The distance from A to C is 360.323 m.
b. Applying the sine rule;
[tex]\frac{a}{SinA}[/tex] = [tex]\frac{b}{SinB}[/tex]
[tex]\frac{187}{SinA}[/tex] = [tex]\frac{360.323}{Sin90^{o} }[/tex]
[tex]\frac{187}{SinA}[/tex] = [tex]\frac{360.323}{1}[/tex]
Sin A = [tex]\frac{187}{360.323}[/tex]
= 0.5190
⇒ A = [tex]Sin^{-1}[/tex] 0.5190
= [tex]31.265^{o}[/tex]
The bearing of the plane from its original location = [tex]64^{o}[/tex] + [tex]31.265^{o}[/tex]
= [tex]95.265^{o}[/tex]
Using the Sine and Cosine rule on the triangle generated using the information given, the distance and bearing of the plane from its original location are :
360.32 mile 95.26°Using the Cosine Rule :
b² = a² + c² - 2abCosBb² = 187² + 308² - 2(187)(308)Cos(90°)
b² = 187² + 308² - 0
b² = 129833
b = √129833
b = 360.32 miles
B.)
Using the Sine rule :
a/sinA = b/SinB = c/SinC
187/sinA = 360.32/sin90
187/sinA = 360.32/1
sinA × 360.32 = 187
sinA = 187 / 360.32
sinA = 0.51898
A = Sin¯¹(0.51898)
A = 31.264
Hence, bearing of C from A = (64° + 31.264) = 95.26°
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U GET BRAINLIEST IF U ANSWER
WHICH ONES ARE POSITIVE OR NEGATIVE SUMS
–5 + (–2)
Choose...
5 + (–2)
Choose...
-3 + 4
Choose...
0 + (–3)
SPACE THEM OUT SO I KNOW
THANKSSSSSSSSSSS
Answer:
Below :)
Step-by-step explanation:
-5+(-2)= -7
5+(-2)= 3
-3+4= 1
0+(-3)= -3
1 and 4 are negative sums, 2 and 3 are positive! :)
Answer:
-5+(-2) will be -7 so negative sum
5+(-2) will be 3 so postive sum
-3+4 will be 1 so postive sum
and finally 0 + (-3) is -3 so negative sum
hope this helps!
I need help pls pls pls pt.2
Answer:
where is the Worksheet
Step-by-step explanation:
there is no Worksheet
Can someone please help me!?!?!?
3. Alt. Interior Angles
4. definition of midpoint
HELP!!!!!!
The line graphed by the equation, y =2/3 x +1/4 , has a slope of 1/4 and a y-intercept of 2/3. True False
Answer:
Um, no lo sé, lo siento, solo necesito los puntos
Step-by-step explanation:
Answer:
False; the slope is 2/3 and the y intercept is 1/4
I hope this is good enough:
Ms. Reyes buys three types of flowers. She buys 20 roses, 24 carnation, and 36 tulips. She plans to group the flowers into more than a bouquet. She wants to put the same number of each type of flower into each bouquet. What is the greatest number of bouquets Ms. Reyes can make?
Answer:
The greatest number of bouquets Ms. Reyes can make is 4 bouquets
Step-by-step explanation:
Ms. Reyes buys three types of flowers. She buys 20 roses, 24 carnation, and 36 tulips.
To find the greatest number of bouquets she can make, we solve using Greatest Common Factor method.
We find the factors of 20, 24 and 36
The factors of 20 are: 1, 2, 4, 5, 10, 20
The factors of 24 are: 1, 2, 3, 4, 6, 8, 12, 24
The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
Then the greatest common factor is 4.
Hence, the greatest number of bouquets Ms. Reyes can make is 4 bouquets
How many solutions does 2x + 6 = -2 (x - 3)
Answer: x=0
Step-by-step explanation:
2x+6=-2x+6
2x+2x=6-6
4x=0
x=0/4
x=0
What is 0.8 as a fraction?
Answer:
8/10
Step-by-step explanation:
Answer: 0.8 = [tex]\frac{4}{5}[/tex]
Step-by-step explanation: We need to change 0.8 into a fraction.
0.8 = [tex]\frac{8}{10}[/tex]
[tex]\frac{8}{10}\\[/tex] = [tex]\frac{4}{5}[/tex]
Therefore, your answer is [tex]\frac{4}{5}[/tex]
hope this helps!
lovelymoonlight
3.7(x−5.9)=−26.64
help
Answer: -1.3
Step-by-step explanation:
4. How do you solve x2 + 9x - 3 = 0 using the completing-the-square method?
Answer:
i used to have a problem with this
Step-by-step explanation:
When 4(0.5x+2.5y - 0.7x- 1.3y +4) is simplifted, what is resulting expersion
URGENT!! I WILL GIVE BRAINLIEST TO CORRECT ANSWER!!
find the length of side x in simplest radical form with a rational denominator
Answer:
x = [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Because of 45 45 90 triangle rule, we can see that the length opposite of the right angle is [tex]\sqrt{6}[/tex]. Using the 45 45 90 triangle rule, the side opposite to the right angle is x[tex]\sqrt{2}[/tex]. Then we solve for x and get x=[tex]\sqrt{3}[/tex].
Hope this helps and have a nice day!
Each dimension of a parallelogram is multiplied by a positive number n. Write an expression for the area of the new parallelogram. Let b represent the base and h represent the height of the original parallelogram.
what is the expression for the area of the new parallelogram???
Answer:
b*h
Step-by-step explanation:
therethere are four sides to a parallelogram and two of them would be h and b and you must multiply that by n then each other
New area:
(b*n) * (h*n) = (b*h)n^2
A car covered a certain distance at a speed of 24 mph. While returning, the car covered the same distance at a speed of 16 mph. What was the average speed of the car for the entire journey?
please healp
Answer:
(96/5) mph, or 19.2 mph
Step-by-step explanation:
Average speed = (total distance traveled) / (total time elapsed)
Here we need to calculate the two elapsed times (going and returning)
Going: t1 = d/(24 mph)
Returning: t2 = d/(16 mph)
Less time is required for the outward bound trip.
16d + 24d
Total time elapsed: t = t1 + t2 = d/24 + d/16 = ------------------- = (5/48)*d hr
16*24
Thus, the average speed is (total distance traveled) / (total elapsed time)
2d
which here is --------------------- = (96/5) mph, or 19.2 mph
(5/48)d
If we take average speed into account in any direction, it equals (24 + 16) / 2 = 40 / 2 = 20mph.
What is average speed?Average speed is calculated by dividing a number by the time it takes to obtain that number. The SI unit of speed is meters per second.The average speed is represented by a scalar value. The magnitude indicates its absence of direction.Since this distances were the same, the average speed can be calculated directly by adding the speeds and dividing by 2. There is no need to weigh anything.If we consider speed in any direction, the average speed is:
(24 + 16) / 2 = 40 / 2 = 20mph
However, if direction is important, one number must be negative because the directions are opposite:
(24 - 16) / 2 = 8 / 2 = 4mph (in the positive direction)
Depending on the circumstances, either of these could be your response.
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Find the slope of the line that passes through the points (2, -3) and (5, -4).
2/3(9x-6)= 4x + 10
3
6x-4=4x+10
What is the value of x in the equation?
A X = 7
B X = 8
B X = 3.2
D X = -12
Answer:
the answer will be A. x=7
Your answer should be 7
What is the volume of the rectangular prism?
Answer:
180
Step-by-step explanation:
5 time 6 times 6 is 180
2y - 7 = 35
A
28
B
21
C
14
D
9
Answer:
Do u know the answer to
Step-by-step explanation:
Triangle ABC is a right triangle. The length of the legs are 3 in and 6 in, how long is the hypotenuse? (Round to the nearest tenth if necessary)
A) 3.3 in
B) 6.7 in
C) 7.9 in
D) 9.0 in
Answer:
21
Step-by-step explanation:
2y-7=35
2(21)-7 = 35
42-7= 35
35 =35
Zahra was given two data sets, one without an outlier and one with an outlier. Data without an outlier: 15, 19, 22, 26, 29 Data with an outlier: 15, 19, 22, 26, 29, 81 How is the median affected by the outlier? The outlier slightly affected the median. The outlier made the median much higher than all the other values. The outlier made the median much lower than all the other values. The median is the exact same number in both data sets.
Answer:
The outlier slightly affected the median.
Step-by-step explanation:
Given :
Data without an outlier: 15, 19, 22, 26, 29
Data with an outlier: 15, 19, 22, 26, 29, 81
The median :
Data without outlier :
0.5(n + 1) th term
n = 5
0.5(5 + 1) = 0.5(6) = 3rd term
3rd term = 22
Data with outlier :
0.5(n + 1) th term
n = 6
0.5(6 + 1) = 0.5(7) = 3.5th term
(3rd term + 4th term) /2
(22 + 26) / 2
48 / 2
= 24
From the result obtained ; The outlier slightly affected the median.
Answer:
A) The outlier slightly affected the median.
Step-by-step explanation:
Without the outlier, the median is 22, and with the outlier, the median is 24. So the outlier slightly affected the median.
Hope this helps :)
=Evaluate the function f(x) = –2x2 – 3x + 5 for the input value –3.
−22
–4
2
32
Answer:
The correct answer is -4.
Step-by-step explanation:
have a good day yall
Evaluating the function, f(x) = –2x² – 3x + 5 for x = -3, we would have: f(-3) = -4. (option B).
How do you Evaluate a Function?To evaluate a function, plug in the given value of the input (x) and simplify.
Thus:
f(x) = –2x² – 3x + 5
Substitute x = -3 into the function
f(-3) = –2(-3)² – 3(-3) + 5
f(-3) = -2(9) + 9 + 5
f(-3) = -4
Therefore, evaluating the function, f(x) = –2x² – 3x + 5 for x = -3, we would have: f(-3) = -4. (option B).
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Find the slope (m) and the y intercept please show work
Answer:
m=2/5
b=3.8
Step-by-step explanation:
To find slope you need to use slope formula which is (y2-y1)/(x2-x1) so you need two points from the table and plug them into this. I'll use the first two points (-2, 3) and (-1, 5)
(5-3)/(3--2)
2/5
our slope is 2/5(m)
now to find the y int(b)
we have out slope intercept formula which is y=mx+b
plug in our slope
y=2/5x+b
now take a random point from our tabell and apply it to our equation I'll use (-2, 3) again.
3=2/5(-2)+b
3=-4/5+b
3=-0.8+b
add 0.8 to each side
3.8=b
b=3.8
which expression has the same value as 7 ÷ 9/10
A) 7 x 10/9
B) 1/7 ÷ 910
C) 7 x 9/10
D) 1/7 ÷ 10/9
Answer
A.) 7* 10/9
When you divide fraction you change the symbol and flip the fraction and A is that equation.
Answer:
7 ÷ 9/10 = 7.777
a. 7 × 10/9 = 7.777
b. 1/7 ÷910 = 0.000
c. 7 × 9/10 = 6.3
d. 1/7 ÷ 10/9 = 0.128
therefore the answer is a
Step-by-step explanation:
Hope this helped!!! have a wonderful day!! :):):):)
Independent Practice : Rectangular Prism
GRAHAM CRACKERS A manufacturer wants to double the volume of the graham cracker box.
The manufacturer will either double the height or double the width.
GRAHAM
CRACKERS
a. Which option uses less cardboard? Justify your answer.
h 9 in
w 2 in
16 in.
b. What is the volume of the new graham cracker box?
Answer:
a). Amount of cardboard required will be less when manufacturer doubles the width.
b). Volume of the new cracker box = 216 in³
Step-by-step explanation:
Volume of the Graham cracker box = volume of the rectangular prism formed
= Length × Width × Height
= 6 × 2 × 9
= 108 in³
a). To double the volume of the rectangular prism, manufacturer either doubles the height or doubles the width.
When manufacturer doubles the height,
Amount of cardboard required = surface area of the rectangular prism
= 2(lw + wh + hl)
= 2(6×2 + 2×18 + 18×6)
= 2(12 + 36 + 108)
= 2(66)
= 132 in²
When manufacturer doubles the width,
Surface area of the rectangular prism = 2(6×4 + 4×9 + 9×6)
= 2(24 + 36 + 54)
= 2(114)
= 228 in²
Therefore, amount of cardboard required will be less when manufacturer doubles the width.
b). Volume of the new Graham box = 2(Volume of the old box)
= 2 × 108
= 216 in³
Helppppppppppppppppppp
Answer:
2^3 * 7 + 7^2
Step-by-step explanation:
1) divide 28 by 2 = 14
2) divide 14 by 2 = 7
3) this means that 2 * 2 * 7 = 28
4) you can then take those 2 twos and multiply them with the first 2 and make 2^3
5) the square root of 49 is 7 so that is just 7^2
6) plug in all these new values for the originals and you get the answer above
Answer:
first you gotta calculate 2 -28 +49
After getting the answer solve the expressions to see which one is equivalent to 2-28 +49 (I think)