Answers
Answer:
-b[a + (c-d)^2]
-(-8)[3/4 + (-2 -3)^2]
8 [3/4 + (-5)^2]
8 [3/4 + 25]
8 [25.75]
206
=======================================
Work Shown:
a = 3/4
b = -8
c = -2
d = 3
----------------
c-d = -2-3 = -5
(c-d)^2 = (-5)^2 = 25
a+(c-d)^2 = 3/4 + 25 = 3/4 + 100/4 = 103/4
-b * [ a + (c-d)^2 ] = -(-8)*103/4 = 8*103/4 = (8/4)*103 = 2*103 = 206
----------------
Another way to show the steps could be
[tex]-b[a+(c-d)^2]\\\\-(-8)\left[\frac{3}{4}+(-2-3)^2\right]\\\\8\left[\frac{3}{4}+(-5)^2\right]\\\\8\left(\frac{3}{4}+25\right)\\\\8\left(\frac{3}{4}+\frac{100}{4}\right)\\\\8\left(\frac{3+100}{4}\right)\\\\8\left(\frac{103}{4}\right)\\\\\frac{8}{4}*103\\\\2*103\\\\206\\\\[/tex]
Which is more or less the same thing as the previous section.
----------------
So ultimately,
[tex]-b[a+(c-d)^2] = 206[/tex]
when a = 3/4, b = -8, c = -2, and d = 3.
Related Questions
A country has a 7 digit phone number system of the form ABC-DEFG. The first digit 'A' can be any number except O or 1. The next 2 digits , B' and 'C, can be any digit , except they cannot repeat . The last 4 digits can be any single digit number 0-9 . How many unique phone numbers are possible?
Answers
Answer:
7,200,000
Step-by-step explanation:
Number of Possibilities for
A) First Digit
There are 10 digits (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) of which 0 and 1 is not allowed.
Hence there are 8 possibilities for the first digit
B) Second digit
There are 10 posibilities
C) Third digit
Since it mustn't be the same as Second digit....
There are 9 possibilities
D) Forth digit
There are 10 possibilities
E) Fifth digit
There are 10 possibilities
F) Sixth digit
There are 10 possibilities
E) Seventh digit
There are 10 possbilities
Total possible ways for the 7-digit phone number is...
8×10×9×10×10×10×10
=7,200,000 possible phone numbers
Of the 2254 students at a liberal arts college, 257 are fifth year students. Among a sample of 321 of the students from this college, 257are fifth year students. Find the sample proportion of fifth year students, rounded to two decimal places as needed.
Answers
Answer:ifk
Step-by-step explanation:
please help!!!!! thank uuuuuuu
Answers
Step-by-step explanation:
here's the answer
Hope it helps◉‿◉
Marissa is writing a book. The ratio of the number of pages she has written so far to the
number of hours she has spent writing is 5:8. Which statement is true?
On average, Marissa wrote 1 page every 3 hours.
On average, Marissa wrote 3 pages each hour.
On average, Marissa wrote 5 pages every 8 hours.
On average, Marissa wrote 8 pages every 5 hours.
Answers
Answer:
On average, Marissa wrote 5 pages ever 8 hours.
Step-by-step explanation:
The ratio is the number of pages to the number of hours she has spent writing so 5:8 means 5 pages every 8 hours.
On average, Marissa wrote 5 pages every 8 hours. Therefore, option C is the correct answer.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of the number of pages she has written so far to the number of hours she has spent writing is 5:8.
In 8 hours Marissa is writing 5 pages
Therefore, option C is the correct answer.
To learn more about the ratio visit:
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Answer please ! I’ll give 25 points !! Thank you
Answers
Answer:
a. 7%
b. 13%
c. 3%
d. I can conclude that poor nutrition affects academic performance because the chart shows that people with poor nutrition got the worst scores out of the people with better nutrition. The chart also shows that there are more kids below average than kids with excellent nutrition. Kids with poor nutrition also have less people above average then any other category.
Step-by-step explanation:
For the percentages, it is just a number out of the total, which is 1000.
Percentages are a number out of 100. Like, 35/100 is 35%. So the total is 1000 and if you divide it by 10, you'll get 100. That means you have to only divide the amount of kids in a category by 10, and you'll get the percentage.
Below average kids with poor nutrition has 70 kids.
70/1000. Divide 1000 by 10 to get 100. Since you divided the denominator, 1000, by 10, you need to do the same for the numerator, which is 70. 70 divided by 10 is 7, so it's 7%. It is sort of like a ratio!
Average kids with poor nutrition has 130 kids.
130/1000. Divide 1000 by 10 to get 100. Since you divided the denominator, 1000, by 10, you need to do the same for the numerator, which is 130. 130 divided by 10 is 13, so it's 13%.
Above average kids with poor nutrition has 30 kids.
30/1000. Divide 1000 by 10 to get 100. Since you divided the denominator, 1000, by 10, you need to do the same for the numerator, which is 30. 30 divided by 10 is 3, so it's 3%.
Use the method of Lagrange Multipliers to find any maximum or minimum values of the function f(x,y)=x2+y2 subject to the constraint xy=1.
Answers
Answer:
possible maximum and minimum values : f (1,1), f (-1,-1)
Step-by-step explanation:
Given function :
f(x,y) = x^2 + y^2
constraint = xy = 1
attached below is the detailed solution of the method of using Lagrange method of Multipliers to find the maximum and minimum values of the function
A cell phone company charges $15 for 120 minutes. What is the cost per minute? Round to the nearest cent.
Answers
Answer: The cost per minute is $0.13 or 13 cents.
Step-by-step explanation:
If it charges $15 for 120 minutes then to get to one minute we will have to divide it by 120.
so 15/120 = 0.125 which rounds to 0.13 to the nearest cent.
Answer:
Step-by-step explanation:
simplify the expression. -6(-8 + 3s) =
Answers
Answer:
The correct answer is 48 - 18s.
Step-by-step explanation:
To simplify this problem, we have to use the distributive property. To do this, we must multiply each term inside the parentheses by -6 (what is outside of the parentheses). This is modeled below:
-6(-8 + 3s)
= (-8 * -6) + (-6 * 3s)
Now, we can simplify what is inside the parentheses.
= 48 - 18s
Therefore, the correct answer is 48 - 18s.
Hope this helps!
At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml.
(a) The normal distribution should be used for the sample mean because:________.
1. the sample population has a large mean.
2. the population distribution is known to be normal.
3. the population standard deviation is known.
4. the standard deviation is very small.
(b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance.
The hypothesis for a two-tailed decision is:_______.
1.. H0: μ ≠520, H1: μ = 520, reject if z < −1.96 or z > 1.96
2. H0: μ ≠520, H1: μ = 520, reject if z > 1.96 or z < −1.96
3. H0: μ = 520, H1: μ ≠ 520, reject if z > 1.96 or z < −1.96
4. H0: μ =520, H1: μ ≠ 520, reject if z > −1.96 or z < 1.96
Answers
Answer:
A) Population standard deviation is known.
B) Option 3
H0: μ =520,
H1: μ ≠ 520
z > 1.96 or z < -1.96
Step-by-step explanation:
A) The normal distribution should be used for the sample mean because the population standard deviation is known. Usually, when the standard deviation is unknown we don't use normal distribution except there is an underlying normal approximation.
B) Null Hypothesis:H0: μ =520,
Alternative hypothesis H1: μ ≠ 520
At 5% level of significance, from standard tables, we will reject H0 if;
The test statistic; z > 1.96 or z < -1.96
What is construction
Answers
Answer:
Consrution is the steps of building buildings or town.
Step-by-step explanation:
CONSTRUCTION IS THE ACT OF MAKING 《OR》BUILDING SOMETHING.......
HOPE IT HELP.......❣❣❣
x^2+6x-6=10 what’s the solution?
Answers
Answer:
-8,2
Step-by-step explanation:
Factoring:
(x+8)(x-2)
x is -8 or 2
Answer:
-8 and 2
Step-by-step explanation:
option 2 or b
Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x, y) = 2x2y, 2x2 + 4y2 = 12
Answers
Answer:
f(-2,-1) = -8 is the minimum value of f(x,y)
f(2,1) = 8 is the maximum value of f(x,y)
Step-by-step explanation:
f(x,y) = 2x²y under the constraint 2x² + 4y² = 12
Let g(x,y) = 2x² + 4y² - 12
df/dx = 4xy, df/dy = 2x², dg/dx = 4x and dg/dy = 8y
Now, using the principle of Lagrange multipliers,
df/dx + λdg/dx = 0 and df/dy + λdg/dy = 0.
Substituting the values of the variables, we have
df/dx + λdg/dx = 0 and df/dy + λdg/dy = 0.
4xy + 4xλ = 0 (1) 2x² + 8λy = 0 (2)
xy + xλ = 0
x(y + λ) = 0
x = 0 or y + λ = 0
Since x ≠ 0, y = -λ
Substituting y = -λ into (2), we have
2x² + 8λy = 0
2x² + 8λ(-λ) = 0
2x² - 8λ² = 0
2x² = 8λ²
x² = 4λ²
x = ±2λ
Substituting the values of x and y into the constraint equation, we have
2x² + 4y² = 12
2(±2λ)² + 4(-λ)² = 12
2(4)λ² + 4λ² = 12
8λ² + 4λ² = 12
12λ² = 12
λ² = 1
λ = ±1
Substituting the value of λ into x and y, we have
x = ±2λ = ±2(±1) = ±2
y = -λ = -(±1) = ±1
The minimum values of x and y are -2 and -1 respectively. Substituting these int f(x,y), we have
f(-2,-1) = 2(-2)²(-1) = 2 × 4 × (-1) = -8
So f(-2,-1) = -8 is the minimum value of f(x,y)
The maximum values of x and y are 2 and 1 respectively. Substituting these int f(x,y), we have
f(2,1) = 2(2)²(1) = 2 × 4 × 1 = 8
So f(2,1) = 8 is the maximum value of f(x,y)
What decimal number does point A on the number line below represent? −0.75 0.75 −1.25 1.25
Answers
Answer:
-1.75
Step-by-step explanation:
Point A is in between - 1 and -2
This interval is split in 4 equal parts and has 3 marker points.
Point A is on the bottom marker point, which indicates:
-1 * 3/4 = - 3/4 = - 0.75Since it is below -1, we add up - 1 and - 0.75:
- 1 + (-0.75) = - 1.75Point A represents: -1.75 on the number line
Answer:
-0.75678obsf
Step-by-step explanation:
12/5x - 2x = 3/10
solve for x
And show steps plz
Answers
Answer:
x=3/4
Step-by-step explanation:
First, we must combine like terms and find the common denominator (which is 5):
12/5x-2x
12/5x-10/5x=2/5x
Then, we cross multiply
[tex]\frac{2x}{5} =\frac{3}{10}[/tex]= 2x(10)=(3)(5)=20x=15
Then, we divide by 20 to get x:
x=15/20
and finally, we simplify the fraction
x=3/4
What is the first step to solving this equation? -5c + 6 = -4
Answers
Answer:
subtract 6 from both sides.
-5c = -10
then divide both sides by -5 (negative divided by a negative is a positive)
c = 2
Step-by-step explanation:
Step-by-step explanation:
Hey, there!!
The given equation is : -5c + 6 = -4
The first step olis to take (+6) in right side,
[tex] - 5c = - 4 - 6[/tex]
now, another step is add ( -4 and -6)
[tex] - 5c = - 10[/tex]
Now, divide -10 by -5.
[tex]c = \frac{ - 10}{ - 5} [/tex]
Therefore, c= 2.
Hope it helps..
Is the following an Arithmetic Sequence? 4, 6, 8, 10, 12
Answers
Answer:
Yes
Step-by-step explanation:
For a sequence to be arithmetic, it must have a common difference, which means that the difference between any two consecutive terms must be the same. If we check the terms in our sequence, we see that 6 - 4 = 2, 8 - 6 = 2, 10 - 8 = 2 and 12 - 10 = 2. Since we got the same answer (2) every time, the answer is yes, it is an arithmetic sequence.
A record weight for a red snapper was 46 pounds. A record weight for a sturgeon was 468 pounds. About how many times heavier than the red snapper was the sturgeon?
Answers
Answer:
10.17
Step-by-step explanation:
To find the answer the this question we must divide "468" by "46". We then get the answer 10.173913....... I rounded it to the hundredths place.
4. A ship traveled a distance of 50 km from port O at a bearing of 120°, then another 100 km to port B at a bearing of 200 °. What is the distance between ports O and B?
Answers
Step-by-step explanation:
Jesu
Quadrilateral $ABCD$ has right angles at $B$ and $D$, and $AC=3$. If $ABCD$ has two sides with distinct integer lengths, then what is the area of $ABCD$? Express your answer in the simplest radical form.
Answers
Answer:
[tex]\sqrt{2}+\sqrt{5}[/tex]
Step-by-step explanation:
Since there are 2 diagonal angles that are 90 degrees, we can figure out the shape is made of 2 right triangles, so we can use the Pythagorean theorem to find out the length of each side.
The problem said that there must be 2 distinct sides with integer lengths, but there are no 2 integers that satisfy [tex]x^2+y^2 = 3^2[/tex] so we can deduce that both right triangles contain 1 integer value side and 1 non-integer value side.
There are only 2 positive integer values that would fit in [tex]x^2+y^2 = 3^2[/tex] for x: 1 and 2. That means the 2 triangles' equation is:
[tex]1^2+\sqrt{8}^2 = 3^2[/tex] and [tex]2^2 + \sqrt{5}^2 = 3^2[/tex].
Now, since these are right triangles, their areas are just going to be their 2 legs multiplied by 1/2.
The first triangle's area is:
[tex]1\cdot\sqrt{8}\cdot1/2 = 1\cdot2\sqrt{2}\cdot1/2 = \sqrt{2}[/tex]
The second triangle's area is:
[tex]2\cdot\sqrt{5}\cdot1/2 = \sqrt{5}[/tex]
The total area of the quadrilateral would be the sum of the 2 triangles, which is just [tex]\sqrt{2}+\sqrt{5}[/tex].
I hope this helped you.
The total area of the quadrilateral ABCD is [tex](\sqrt{2}+ \sqrt{5} )[/tex] and this can be determined by using the formula of the area of the triangle.
Given :
Quadrilateral ABCD has right angles at B and D, and AC=3. ABCD has two sides with distinct integer lengths.The following steps can be used in order to determine the area of ABCD:
Step 1 - Let the length of the segment AD be 'x' and the length of the segment CD be 'y'.
Step 2 - Now, apply the Pythagorean theorem on the triangle ACD.
[tex]x^2+y^2= 3^2[/tex]
Step 3 - According to the given data, ABCD has two sides with distinct integer lengths. So, there are two possibilities:
[tex]1^2+(\sqrt{8} )^2= 3^2[/tex]
[tex](2)^2+(\sqrt{5} )^2=3^2[/tex]
So, the possible sides of the quadrilateral will be [tex]\rm 1, \;2,\; 2\sqrt{2},\;and \;\sqrt{5}[/tex].
Step 4 - So, the area of the triangle ABC is:
[tex]A=\dfrac{1}{2}\times \sqrt{8} \times 1\\A = \sqrt{2}[/tex]
Step 5 - Now, the area of the triangle ACD is:
[tex]A'=\dfrac{1}{2}\times \sqrt{5} \times 2\\A' = \sqrt{5}[/tex]
Step 6 - So, the total area of the quadrilateral ABCD is:
[tex]{\rm Area } = \sqrt{2} + \sqrt{5}[/tex]
The total area of the quadrilateral ABCD is [tex](\sqrt{2}+ \sqrt{5} )[/tex].
For more information, refer to the link given below:
https://brainly.com/question/25240753
Decide whether the pair of lines is parallel, perpendicular, or neither.
2x + 3y = 7
2x + 3y = 9
Answers
Answer:
the pair of lines are parallel
x2-8x-9-y2+10y solve this
Answers
Answer:
in descending order, your answer would be x^2-y^2+2y-9. Hope this helps!
Step-by-step explanation:
Answer:-6x-9+8y.
Step-by-step explanation: 2x-8x-9-2y+10y -6x-9-2y+10y -6x-9+8y
A car is driving 90 kilometers per hours how far in meters does it travel in 3 second
Answers
Answer:
I hope it will work
Step-by-step explanation:
as given
speed = v = 90 km/hr convert to meter and sec we get
v =( 90 *1000 meter)/(3600 sec)
v=25 m /sec
as given t= 2 sec so
v=s/t
s= v*t
s=25*2
s=50 meter
if its help-full hit the stars and brain list it thank-you
3(x-8) = -29.7 please solve for x
Answers
Answer:
The answer is x= -1.9.
Use the 3 to multiply the number and the letter in the bracket... which is...
3x-24=-29.7.
3x=-29.7+24.
3x=-5.7.
x=-5.7/3.
x=-1.9.
x is -1.9
Solve 3(x-8) = -29.7
Remove the brackets by dividing both sides by 3:
3(x-8) / 3 = -29.7 / 3
You will be left with:
x - 8 = -9.9
Take -8 to the other side so that you can be left with x. When you do this, the sign will change from negative to positive:
x = -9.9 + 8
x = 1.9
x is therefore -1.9
Find out more at https://brainly.com/question/17289311.
4. The Emerson First National Bank is lending you money to buy a new car. The loan agreement will probably state
that you must carry
insurance.
A no-fault
B. collision
C. medical
D. liability
Answers
Answer:
D. liability
Step-by-step explanation:
The Emerson First National Bank is lending you money to buy a new car.
Before an agreement will be reached for any Organization to lend someone money there have to be something like a collateral.
The agreement will in it's document state that there must be a form of a reliability to hold on, such that if something's happen to the car, or you don't meet the paying up time, or something happens to you,they will see something to hold on.
Answer:
COLLISION insurance.
Step-by-step explanation:
How long will it take you to ski a distance of 36 miles at a speed of 3 miles per 30 minutes.
Answers
Answer:
6 hours
Step-by-step explanation:
Since there are 60 minutes in one hour, you can ski 3 * 2 = 6 miles per hour. Therefore, it will take you 36 / 6 = 6 hours to ski that distance.
anyone help if you guys help me the next question i will give u more points the screenshot is attached below
Answers
Answer:
69°
Step-by-step explanation:
To obtain the value of w, we must first obtain the value y as shown in the attached photo.
The value of y can be obtained as follow:
y + (w + 37) = 180 (sum of angle on a straight line)
y + w + 37 = 180
Make y the subject by rearranging
y = 180 – 37 – w
y = 143 – w
Finally, we shall determine the value of w as follow:
w + (w – 32) + y = 180 (sum of angles in a triangle)
y = 143 – w
w + (w – 32) + (143 – w) = 180
w + w – 32 + 143 – w = 180
Rearrange
w + w – w – 32 + 143 = 180
w + 111 = 180
Collect like terms
w = 180 – 111
w = 69°
Therefore, the value of w is 69°
Help me please thank you
Answers
Answer:
x = 7
Step-by-step explanation:
To make L II M, the two angles ([2x - 3] & [x + 4]) have to be the same.
2x - 3 = x + 4 is the equation.
Simplify, and you will get x = 7
Hope this helps! Please tell me if I did anything wrong, thank you!
A pool measures 15 feet by 17 feet. A cement walkway is added around the pool,
to both the width and the length. The area of the pool and the cement walkway is
now 483 square feet. What is the width of the cement walkway?
Answers
Answer:
Width of the walkway = 3 feet
Step-by-step explanation:
Dimensions of a pool = 15 feet × 17 feet
After the addition of a cement walkway around the pool,
New dimensions of the pool (including walkway) = (l + 2x)(w + 2x)
Area of the pool and the cement walkway = 483 square feet
(15 + 2x)(17 + 2x) = 483 [Since, l = 15 feet and w = 17 feet]
255 + 30x + 34x + 4x² = 483
4x² + 64x = 483 - 255
4x² + 64x = 228
4x² + 64x - 228 = 0
x² + 16x - 57 = 0
By using quadratic formula,
[tex]x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}[/tex]
x = [tex]\frac{-16\pm \sqrt{(16)^2-4(1)(-57)}}{2\times 1}[/tex]
x = [tex]\frac{-16\pm 22}{2}[/tex]
x = 3.0 ft, -19 ft
Since, dimension can't be negative.
Therefore, width of the walkway = 3 ft
The width of the walkway is 3 ft
The pool measures 15 feet by 17 feet. This means the pool is rectangular.
Properties of a rectangle:Opposite sides are equal to each otherOpposite sides are parallel to each otherarea of the pool = lw
area = 15 × 17 = 255 ft²
A cement walkway is added around the pool, to both the width and the length.
area of the pool and the cement walkway = 483 ft²
Therefore,
area = lw
The width and length was added on both sides.
let
the side added to the width = x
the side added to the length = x
length = 2x + 17
width = 2x + 15
483 = (2x + 17)(2x + 15)
483 = 4x² + 30x + 34x + 255
4x² + 64x - 228 = 0
x² + 16x - 57
x² - 3x + 19x - 57
x(x - 3) + 19(x - 3)
(x + 19)(x - 3) = 0
x = -19 or 3
we can only use positive value of x. Therefore, x = 3
length = 2(3) + 17 = 23 ft
width = 2(3) + 15 = 21 ft
Therefore, the width of the walkway is 21 - 15 / 2 = 3 ft
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The final cost of a bookstore purchase with a $5 coupon in a state that charges 8% sales tax is given by this expression. The variable x represents the amount of the purchase before the sales tax and the coupon are applied. 1.08(x−5) What does (x−5) represent?
a. the total charge after tax
b. the rate at which the total cost increases
c. the total charge before applying sales tax
d. the cost before applying the coupon
Answers
Answer:
B.the total charge before applying sales tax
Step-by-step explanation:
Angle Pairs Introduction
1. A shirt is priced $24.99. and is on sale for 20% off and subject to 5% sales tax.
final cost of the shirt?
I
Answers
Answer:
$20.99
Step-by-step explanation:
The sale causes the original price to be multiplied by 1 - 20% = 80%. The tax causes the sale price to be multiplied by 1 + 5% = 105%. The net effect is that the original price is multiplied by the product of these values:
final cost = $24.99(0.80)(1.05) = $20.99