W=L+2
A=48=L*W
48=L*(L+2)
48=L^2+L*2
0=L^2+L*2-48
L1=6
L2=-8 (can't be used since it's negative)
Lenght=6
Width=8
The values of x and y vary directly
and one pair of values are given.
Write an equation that relates x
and y. Simplify completely.
x = 0.1, y = 0.9
A
y = [? ]x
Direct variation equation is y=kx . Your k is your variation or you could look at it as your slope. y=kx Plug in what you know, 4=k12 Divide both sides by 12 to cancel out your 12 that is being multiplied by k.
4(/12)=k12(/12) Simplify
1/3=k
y=1/3x This is your direct variation equation.
Answer:
Step-by-step explanation:
1) y=kx
plug in the #s
(0.9)=k(0.1)
divide both sides by 0.1
k=9
plug in k and that is your equation (y=9x)
find the slope and y-intercept of the line that is perpendicular to y=-2/3x+5 and passes through the point (5,7).
The slope of line perpendicular to given line is is 3/2 and y-intercept is: -1/2
Step-by-step explanation:
Given equation of line:
[tex]y = -\frac{2}{3}x+5[/tex]
The given equation of line is in slope-intercept form so the co-efficient of x will be the slope of the line
Let m_1 be the slope of given line
[tex]m_1 = -\frac{2}{3}[/tex]
As we know that the product of slopes of perpendicular lines is -1
Let m_2 be the slope of required line
So,
[tex]m_1.m_2= -1\\-\frac{2}{3} . m_2 = -1\\m_2 = -1 * -\frac{3}{2}\\m_2 =\frac{3}{2}[/tex]
The lope-intercept form is:
[tex]y =m_2x+b[/tex]
Putting the value of m2
[tex]y = \frac{3}{2}x+b[/tex]
To find the value of y-intercept, putting (5,7) in the equation
[tex]7 = \frac{3}{2}(5) + b\\7 = \frac{15}{2} + b\\7 - \frac{15}{2} = b\\b =\frac{14-15}{2}\\b = -\frac{1}{2}[/tex]
Putting the values of slope and y-intercept
[tex]y = \frac{3}{2}x - \frac{1}{2}[/tex]
Hence,
the slope is 3/2 and y-intercept is: -1/2
Keywords: Slope, y-intercept
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In a group 120 children there are teice as many boys as girls. How many girls are there?
Answer:
40 girls 80 boys
Step-by-step explanation:
80/2=40
40+80=120
Answer:
80 girls
Step-by-step explanation:
120/3 = 40.
40 x 2 = 80
1.
Marcy is comparing prices of
bottled water for 16.9-ounce
bottles. The table shows the
price for each brand. Complete
the table to sort the brands
from least to greatest price per
bottle. Round each unit price
to the nearest thousandth
dollar. 7.RP.2, 7.RP.2b
Answer:
Here is the complete question (in attachment).
The least price is for Water Spring brand and the greatest price is of Clear Mountain brand.
Step-by-step explanation:
To find the unit price we have to divide the full price with the whole of the quantity.
From least to greatest unit prices are arranged below.
Water Springs [tex]=\frac{19.99}{48}=0.416\$[/tex]Nature's River [tex]=\frac{20.35}{48}=0.423\$[/tex]Forest Air [tex]=\frac{10.49}{24}=0.437\$[/tex]Iceland Springs [tex]=\frac{5.49}{12}=0.457\$[/tex]Clear Mountain [tex]=\frac{11.99}{24}=0.499\$[/tex]In ascending order the number are.
[tex]0.416 < 0.423< 0.437< 0.457< 0.499[/tex]
So the least price is for Water Spring brand,and the greatest price is for Clear Mountain brand.
-3x – 4y=2
6x + 6y = -6
Final answer:
To solve the system of equations -3x - 4y = 2 and 6x + 6y = -6, multiply the first equation by 2 to eliminate the coefficients of y, and then add the equations together. The solution is x = -2 and y = 1.
Explanation:
To solve the system of equations:
-3x - 4y = 2
6x + 6y = -6
First, multiply the first equation by 2 so that the coefficients of y will cancel when adding the equations together.
-6x - 8y = 4
Next, add the modified first equation to the second equation.
(-6x - 8y) + (6x + 6y) = 4 + (-6)
-8y + 6y = -2
-2y = -2
Divide both sides of the equation by -2 to solve for y.
y = 1
Substitute the value of y back into either equation to solve for x.
-3x - 4(1) = 2
-3x - 4 = 2
-3x = 6
x = -2
The solution to the system of equations is x = -2 and y = 1.
Paula bought a ski jacket on sale for $6 less than half it’s original price.She paid $86 for the jacket.What was the original price
Answer: Original price $184
Step-by-step explanation:
(X/2) - 6 = 86
X/2 = 86+6
X/2 = 92
X = 92*2
X = 184
explanation of two column proofs? (geometry)
Answer:
Two Column Proofs. Two column proofs are organized into statement and reason columns. Each statement must be justified in the reason column. Before beginning a two column proof, start by working backwards from the "prove" or "show" statement. The reason column will typically include "given", vocabulary definitions, conjectures, and theorems.
Step-by-step explanation:
hope this helps :)
A scientist measured the width of a square flake of gold to be7.3 x 10 -4mm what is the area of the flake
The area of square flake of gold is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]
Solution:Given that width of square flake of gold is [tex]7.3 \times 10^{-4}[/tex] millimeter
To find : Area of square flake
Since gold flake is in shape of square, we can use area of square formula
The formula for area of square is given as:
[tex]area = s^2[/tex]
where "s" is the length of one side
[tex]\begin{array}{l}{\text { Area of a square flake }=\left(7.3 \times 10^{-4}\right) \times\left(7.3 \times 10^{-4}\right)} \\\\ {\text { Area of a square flake }=53.29 \times 10^{8}}\end{array}[/tex]
Hence , the calculated area of flake is [tex]53.29 \times 10^{-8} \mathrm{mm}[/tex]
BEST ANSWER WILL GET BRAINLIEST! which number line correctly shows 47/10, 4 2/5, and 24/5 brainly
Answer:
The third number line
Step-by-step explanation:
first, make each fraction a complex fraction
47/10 = 4 7/10, so you know its the 7th dash from the left.
for 4 2/5 you need to make the denominator 10 by multiplying the numerator and denominator by 2 to get 4 4/10; this should be the 4th dash.
divide 24/5 to get 4 4/5. Multiply the numerator and denominator of the fraction part to get a denominator of 10. you should get 4 8/10; this is on the 8th dash from the last
You would have a dot on the 4th 7th and 8th dash altogether
if 12^-x=5, what does 12^2x equal
Answer:
0.04
Step-by-step explanation:
12^(-x) = 5 (taking log on both sides)
log [ 12^(-x)] = log 5
-x log 12 = log 5
-x = log 5 / log 12
x = - (log 5/log12)
x = -0.6477
12^(2x)
= 12^[2(-0.6477)]
= 12 ^ (-1.295)
= 0.04
what is 1 5/8 divided by 5 1/7
Answer: 91/288
Step-by-step explanation: To divide mixed numbers, first write the mixed numbers as improper fractions.
We can do this by multiplying the denominator by the whole number and then adding the numerator. Then, we put our new numerator over our old denominator.
So here, we can write 1 and 5/8 as the improper fraction 13/8 and we can write 5 and 1/7 as the improper fraction 36/7.
So here, we have 13/8 ÷ 36/7.
Dividing by a fraction is the same as multiplying by the reciprocal of that fraction.
So here, 13/8 ÷ 36/7 is the same as 13/8 × 7/36.
So now we are simply multiplying fractions and we do this by multiplying across the numerators and multiply across the denominators.
[tex]\frac{13}{8} x \frac{7}{36} = \frac{91}{288}[/tex]
So now we have 91/288 which is in lowest terms.
This means that 1 and 5/8 divided by 5 and 1/7 is 91/288.
Your have 100$ in your savings account and plan to deposit 20$ each month. Write and graph a linear equation that represents the balance in your account
Answer:
Formula - y=mx+b
You have $100 and you're increasing it by $20 each month.
m=slope, b= initial value.
Thus, y=20x+100, is your linear equation.
Hope This Helps! :D
Answer:
.
Step-by-step explanation:
Find the value of "k" such that 1/2 is a root of 2x^2+11x=-k
The value of k is -6
Step-by-step explanation:
The general form of the quadratic equation is y = ax² + bx + c
The roots of the equation is the values of x when y = 0ax² + bx + c = 0, is used to find the roots∵ 2x² + 11x = -k
- Add k to both sides
∴ 2x² + 11x + k = 0
∵ The roots of the quadratic equations is the values of x when y = 0
∵ [tex]\frac{1}{2}[/tex] is a root of the equation
- Substitute x by [tex]\frac{1}{2}[/tex] in the equation above to find k
∵ 2( [tex]\frac{1}{2}[/tex] )² + 11( [tex]\frac{1}{2}[/tex] ) + k = 0
∴ 2( [tex]\frac{1}{4}[/tex] ) + [tex]\frac{11}{2}[/tex] + k = 0
∴ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] + k = 0
- Add the like terms
∵ [tex]\frac{1}{2}[/tex] + [tex]\frac{11}{2}[/tex] = [tex]\frac{12}{2}[/tex] = 6
∴ 6 + k = 0
- Subtract 6 from both sides
∴ k = -6
The value of k is -6
Learn more:
You can learn more about the quadratic equations in brainly.com/question/8196933
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Final answer:
By substituting x = 1/2 into the equation [tex]2x^2 + 11x = -k[/tex] and simplifying, we find that k must equal -6 for 1/2 to be a root of the equation.
Explanation:
To find the value of k such that 1/2 is a root of the quadratic equation [tex]2x^2 + 11x = -k[/tex], we can substitute x = 1/2 into the equation and solve for k.
First, substitute x = 1/2:
[tex]2(1/2)^2 + 11(1/2) = -k[/tex]
Then, simplify the equation:
2(1/4) + 11/2 = -k
1/2 + 11/2 = -k
Now, combine the terms:
(1 + 11)/2 = -k
12/2 = -k
6 = -k
Finally, multiply both sides by -1 to find k:
k = -6
Write the slope intercept form of the equation of the line through the given points and slope 1,1 and slope of -3/5
Slope is already given in the question so we only need to solve for the y-intercept.
Slope intercept form: y = mx + b
m = slope
b = y-intercept
-3/5 = -0.6
1 = -0.6(1) + b
1 = -0.6 + b
1 + 0.6 = -0.6 + b + 0.6
1.6 = b
Now, write in slope-intercept form.
y = -3/5x - 1.6
______
Best of Luck,
Wolfyy :)
The sum of two non-negative numbers is 4. Find the numbers if the sum of the square of one and the cube of the other is to be a maximum.
^ My brain is saying 2+2 here pals. I have no idea where to start. Okay so, I was out most of the last week because I was sick. And now there's a test on this optimization weird application idea in my pre-calc class. I could probably figure this out if I needed to in a bizarre backwards way, but knowing how to find it properly with a procedure and all will help very much. Thanks!
Answer:
I would say you're right, 2 + 2
Step-by-step explanation:
Final answer:
The mathematics optimization problem involves finding the maximum sum of the square of one non-negative number and the cube of the other, with their total being 4. Calculus is applied by taking the derivative of the function representing the sum, setting it to zero to find critical points, and checking the second derivative to ensure a maximum is found. The optimized numbers are x and 4-x, based on the critical point found.
Explanation:
To solve the optimization problem, we need to use calculus to find the maximum value of the sum of the square of one number and the cube of the other, given that the sum of the two numbers is 4. Let's call these numbers x and y, with x + y = 4. We want to maximize S = x^2 + y^3.
Since x + y = 4, we can express y as y = 4 - x. Substituting this into S, we have S = x^2 + (4-x)^3. This becomes a function of one variable.
To find the maximum value, we differentiate S with respect to x, set the derivative equal to zero, and solve for x. We can check the second derivative to ensure it is a maximum. The function S' will have a maximum when the first derivative is zero (S'(x) = 0) and the second derivative is negative (S''(x) < 0).
Therefore, the two non-negative numbers that maximize S are x and 4-x, with x being the value at which S' equals zero with S'' negative.
Three more than the product of 12 and jose’s score
Answer:
the answer will be 48
Step-by-step explanation:
The answer 48 because 12 times 3 is 36 and then you add Jose's score and you get 48
Madison has $6.50. Potatoes are $0.50 per pound. How many pounds of potatoes can Madison afford to buy?
In two or more complete sentences write and solve an inequality for this situation. Explain how you would solve this inequality.
Answer to the first step:
3 Pounds of Potatoes.
6.50 / 0.50 = 13 or 650 / 50 = 13
Then, in two or more complete sentences, explain the steps you used to add the mixed numbers.
Answer:
x will be number of pounds
.5x is less than or equal to 6.50
She can afford 13 pounds of potatoes
You would solve the inequality by dividing each side by .5 to isolate x then write it as x is less than or equal to 13.
Part A:
You are given the amount of money Madison can spend and the price per pound for the potatoes. To find how many pounds Madison can buy, you would need to divide the amount of money she has by the price per pound.
The equation would be Pounds of potatoes = 6.50 / 0.50
Part B:
The only step required to solve the equation from part A is division.
Dividing 6.50 by 0.50 = 13. This means Madison can buy 13 pounds of potatoes.
How many square feet of outdoor carpet will
we need for this hole?
11 ft
13 ft
2 ft
3 ft
Answer:
39 square feet
Step-by-step explanation:
The outdoor carpet consists of two rectangles.
The area of the rectangle is
[tex]A=\text{Length}\times \text{Width}[/tex]
1st rectangle:
Length = 11 ft
Width = 3 ft
Area [tex]=11\cdot 3=33 \ ft^2[/tex]
2nd rectangle:
Length = 3 ft
Width = 2 ft
Area [tex]=3\cdot 2=6 \ ft^2[/tex]
Total area:
[tex]33+6=39\ ft^2[/tex]
Determine whether the sequence 7, 21, 35, 49 is geometric. If so, find its common
ratio.
Answer:
a. no
b. yes, common ratio of 14
c. yes, common ratio of 2
Answer:
B
Step-by-step explanation:
Answer:
a. no
Step-by-step explanation:
The sequence is arithmetic. It has a common difference of 14.
7 + 14 = 21
21 + 14 = 35
35 + 14 = 49
A geometric series has a common ratio (multiplication). For example:
7 × 3 = 21
21 × 3 = 63
63 × 3 = 189
Help!! Please!!
Basketball star Mumford (a six foot senior forward) places a mirror on the ground x ft. from the base of a basketball goal. He walks backward four feet until he can see the top of the goal, which he knows is 10 feet tall. Determine the how far the mirror is from the basketball goal. Justify your answer.
Step-by-step explanation:
x=10+4=14
14+14=28
the answer is 28 fts
Answer:
The answer is 6.67 feet, approximately.Step-by-step explanation:
The image attached shows the context that the problems refered.
Notice that two acute angles from those triangles are congruent, just because their complement are also congruent.
[tex]\angle AOB \cong \angle COD[/tex]
[tex]\angle AOB= \angle COD=90\° - a[/tex]
Remember that the tangent function is defined as
[tex]tan(\theta)=\frac{Opposite \ Leg}{Adjacent \ Leg}[/tex]
Replacing each equiavlence, we have
[tex]tan(90-a)=\frac{6}{4}=\frac{10}{x}[/tex]
Then, we solve for [tex]x[/tex]
[tex]\frac{6}{4} =\frac{10}{x}\\ x=\frac{40}{6}\\ x \approx 6.67 ft[/tex]
Thereofre, the answer is 6.67 feet, approximately.
100 POINTS and BRAINLIEST to get both of these answer the third question on my profile :)
Answer:
1. f
2.b
3. d
4. a
5. e
6. g
7. c
Step-by-step explanation:
The parent function is [tex]y = 3 (5)^{x}[/tex].
So,
1. [tex]y = - 3 (5)^{x} + 4[/tex] ≡ f. reflected across x-axis and 4 units up
2. [tex]y = 3 (5)^{x - 4} - 4[/tex] ≡ b. 4 units down and 4 units right.
3. [tex]y = 3 (5)^{x + 4} + 4[/tex] ≡ d. 4 units up and 4 units left.
4. [tex]y = - 3 (5)^{x} - 4[/tex] ≡ a. reflected across x-axis and 4 units down.
5. [tex]y = 3 (5)^{x} - 4[/tex] ≡ e. 4 units down
6. [tex]y = 3 (5)^{x} + 4[/tex] ≡ g. 4 units up.
7. [tex]y = 3 (5)^{x - 4}[/tex] ≡ c. 4 units right. (Answer)
what is the quotient when the sum of 0.2 and 0.05 is divided by the product of 0.2 and 0.05
Answer:
25
Step-by-step explanation:
0.25/0.01
=25
Find the difference between -14w - 3 and 5w.
-9 w - 3
-19 w + 3
-19 w - 3
-22 w
Answer:
C) -19w-3
Step-by-step explanation:
(-14w-3)-5w
-14w-3-5w
-19w-3
A)11%
B)16%
C)19%
D)30%
Answer: C) 19%
Step-by-step explanation:250 +200 + 150 + 125 + 50 = 775 total complaints. 150 rude sales clerks out of 775 total complaints equals 150/775 = 0.1935 which is a 19 percent. So 19 percent of the complaints are about rude sales clerks.
line m contains the points -3,4 and 1,0. write the equation of a line that would be perpendicular to this one and pass through the point -2,6
How do you solve that
For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
According to the statement we have two points through which the line passes:
[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 1,0)[/tex]
We found the slope:
[tex]m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {0-4} {1 - (- 3)} = \frac {-4} { 1 + 3} = \frac {-4} {4} = - 1[/tex]
By definition, if two lines are perpendicular then the product of their slopes is -1.
Thus, a perpendicular line will have a slope: [tex]m_ {2} = \frac {-1} {- 1} = 1[/tex]
Thus, the equation will be of the form:
[tex]y = x + b[/tex]
We substitute the given point and find "b":
[tex]6 = -2 + b\\6 + 2 = b\\b = 8[/tex]
Finally, the equation is:
[tex]y = x + 8[/tex]
Answer:
[tex]y = x + 8[/tex]
expand (3x+7)(3x-7) =
Answer:
[tex]9 {x}^{2} - 49[/tex]
Step-by-step explanation:
Do FOIL, first outside inside last
3x × 3x = 9x^2
3x × -7 = -21x
7 × 3x = 21x
7 × -7 = -49
[tex]9 {x}^{2} - 21x + 21x - 49 \: midde \: cancels \: each \: other \: out[/tex]
So it would just be 9x^2 - 49
(3x + 7)(3x - 7) =
= 9x² + 21x - 21x - 49
= 9x² - 49
1. Find the slope of a line passing through (56, 67) and (-12, -50)
Answer:
117/78
Step-by-step explanation:
(-50-67)/(-12-56)=-117/-78=117/78
Pen Packages
Pen Color
Number of Pens
8. Higher Order Thinking Carla buys
two packages of pens. She buys
49 pens in all. Which color pens does
Carla buy? Show how you found the
answer.
Blue
25
Black
12
Red
24
Green
33
Carla bought one package each of Blue and Red pens. These are the only two packages that when combined bring the total number of pens to 49.
Explanation:This problem revolves around simple arithmetic and logical reasoning. What we need to do is to figure out which combination of pen packages adds up to make 49 pens.
By looking at the numbers given, we can see that the only combination that adds up to 49 would be one package of Blue pens (25 pens) and one package of Red pens (24 pens). There is no other combination of two packages which would result in a total of 49.
Therefore, Carla would have bought one package of Blue pens and one package of Red pens to have a total of 49 pens.
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Are the fractions 3/9 ,3/10, 3/11, and 3/12 arranged in order from least to greatest or greatest to least? Explain.
Answer:
They are arranged greatest to least
BC is parallel to DE.what is the length of CE?
Answer:
Option B [tex]2\frac{2}{3}\ units[/tex]
Step-by-step explanation:
we know that
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
In this problem
Triangles ABC and ADE are similar by AA Similarity Theorem
so
[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]
substitute the given values
[tex]\frac{3}{3+2}=\frac{4}{AE}[/tex]
Solve for AE
[tex]\frac{3}{5}=\frac{4}{AE}[/tex]
[tex]AE=5(4)/3[/tex]
[tex]AE=\frac{20}{3}\ units[/tex]
Find the length of CE
[tex]AE=AC+CE\\CE=AE-AC[/tex]
substitute the values
[tex]CE=\frac{20}{3}-4[/tex]
[tex]CE=\frac{8}{3}\ units[/tex]
Convert to mixed number
[tex]\frac{8}{3}\ units=\frac{6}{3}+\frac{2}{3}=2\frac{2}{3}\ units[/tex]