Answer:
[tex]r = 16[/tex], [tex]s = -48[/tex]
Step-by-step explanation:
The values of [tex]r[/tex] and [tex]s[/tex] can be found with the help of algebraic manipulation on the second-order polynomial described on statement:
[tex]f(x) = 3\cdot x^{2} - 24\cdot x + \frac{1}{3}[/tex]
[tex]f(x) = 3\cdot (x^{2} - 8\cdot x) + \frac{1}{3}[/tex]
[tex]f(x) = 3\cdot (x^{2} - 8\cdot x + 16 - 16) + \frac{1}{3}[/tex]
[tex]f(x) = 3\cdot (x^{2}-8\cdot x + 16) + \frac{1}{3} - 48[/tex]
By comparing each expression, the results are presented below:
[tex]r = 16[/tex], [tex]s = -48[/tex]
Stephen uses \dfrac{2}{25}
25
2
start fraction, 2, divided by, 25, end fraction kilograms of tofu in each serving of his famous tofu dish. He has 1\dfrac{1}{10}1
10
1
1, start fraction, 1, divided by, 10, end fraction kilograms of tofu.
How many servings can Stephen make?
Answer:
[tex]13\dfrac{3}{4}$ servings[/tex]
Step-by-step explanation:
Stephen uses [tex]\dfrac{2}{25}[/tex] kilograms of tofu in each serving of his dish.
He has [tex]1\dfrac{1}{10}[/tex] kilograms of tofu.
We want to determine how many servings Stephen can make.
To do this, we divide the total weight of tofu by the weight per serving.
[tex]\dfrac{\text{Total Weight(in kg)}}{\text{Weight(kg) per serving}} =\dfrac{1\dfrac{1}{10}}{ \dfrac{2}{25}}\\ = \dfrac{11}{10}\div \dfrac{2}{25}\\\\= \dfrac{11}{10}X \dfrac{25}{2}\\\\= \dfrac{11X25}{10X2}\\\\= \dfrac{275}{20}\\\\=13\dfrac{3}{4}$ servings[/tex]
Stephen can make [tex]13\dfrac{3}{4}$ servings[/tex] .
Find the equation of the parabola with vertex at the origin, focus at (3m, 0) and directrix with equation x=–3m.
Answer:
The equation of the parabola is:
[tex]x = 12\cdot m \cdot y^{2}[/tex]
Step-by-step explanation:
The equation of the parabola is:
[tex]x = 4\cdot p \cdot y^{2}[/tex]
Where [tex]p[/tex] is equal to the distance between focus and vertex. Then,
[tex]p = 3\cdot m[/tex]
Lastly, the equation of the parabola is:
[tex]x = 12\cdot m \cdot y^{2}[/tex]
Answer: x = (1/12m)(y^2)
Step-by-step explanation:
Focus at (3m, 0)
Directrix equation, x = -3m
Distance from focus = distance from directrix
√(x-3m)^2 + (y-0)^2 = √(x - (-3m))^2 + (y -y)^2
(x - 3m)^2 + y^2 = (x + 3m)^2
y^2 = (x + 3m)^2 - (x - 3m)^2
y^2 = x^2 + 6mx + 9m^2 - x^2 +6mx - 9m^2
Collecting like terms and simplifying
y^2 = 6mx + 6mx
y^2 = 12mx
x = (1/12m)(y^2)
The cost of 6 tennis balls in a sports store is $4.60. Wyatt bought 9 tennis balls from the store. What is the cost of 9 tennis balls?
Answer:
$6.90 is the cost of 9 tennis balls
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Answer:
C
Step-by-step explanation:
[tex]x^2-2x-80=[/tex]
[tex](x-10)(x+8)[/tex]
You can confirm this by expanding this:
[tex](x-10)(x+8)=[/tex]
[tex]x^2-10x+8x-80=[/tex]
[tex]x^2-2x-80[/tex]
Therefore, the answer is choice C. Hope this helps!
Answer:
C
Step-by-step explanation:
x^2-2x-80
(x^2+8)+(-10x-80)
factor out the -10 for -10x-80
=x(x+8)-10(x+8)
(x+8)(x-10)
pls mark me brainliest
Rewrite as a simplified fraction.
2.31 with the 1 repeating
Answer: [tex]\frac{104}{45}[/tex]
Step-by-step explanation:
[tex]2.31^-[/tex]
Let x be equal to that.
[tex]x=2.31^-[/tex]
Multiply by 1 followed by as many zeros as repeating numbers. In this case it's just one repeating decimal, therefore, 1 followed by 1 zero or 10.
[tex]10x=2.31^-*10[/tex]
This basically moves the decimal point one number to the right.
[tex]10x=23.11^-[/tex]
Subtract the first equation from this new equation.
[tex]10x=23.11^-\\-x=2.31^-[/tex]
--------------------------
The repeating decimal is eliminated and we are left with:
23.1
- 2.3
---------
20.8
We also have 10 - 1 = 9. We are left with:
[tex]9x=20.8[/tex]
Divide by 9.
[tex]x=\frac{20.8}{9}[/tex]
To get rid of the decimal, multiply by 1 followed by as many zeros as decimals. In this case 1.
[tex]x=\frac{20.8}{9} (\frac{10}{10} )[/tex]
[tex]x=\frac{208}{90}[/tex]
Let's simplify.
208/2=104
90/2=45
[tex]x=\frac{104}{45}[/tex]
Help does any one know how to type out the variable that looks like a cursive E??
Answer:
why don't you copy and paste it
The function f (t) =-16t^2 = 576 represents the height of a freely falling ballast bag that starts from rest on a ballon 576 feet above the ground. After how many seconds t does the ballast bag hit the ground.
Answer:
The ballast bag hits the ground after 6 seconds.
Step-by-step explanation:
Suppose there was a small typing mistake.
The height of the ball, after t seconds, is given by the following equation:
[tex]f(t) = -16t^{2} + 576[/tex]
After how many seconds t does the ballast bag hit the ground.
This is t for which f(t) = 0. So
[tex]f(t) = -16t^{2} + 576[/tex]
[tex]-16t^{2} + 576 = 0[/tex]
[tex]16t^{2} = 576[/tex]
[tex]t^{2} = \frac{576}{16}[/tex]
[tex]t^{2} = 36[/tex]
[tex]t = \pm \sqrt{36}[/tex]
Time is a positive measure, so
[tex]t = 6[/tex]
The ballast bag hits the ground after 6 seconds.
Please help. I also will post another question I need help with. Thank you if you help.
Geometric progression, first term 5, common ratio 3.
Answer: 5, 15, 45, 135
How many solutions does this equation have?
–2 − 10z = –4 − 10z
Answer:
No solutions
Step-by-step explanation:
To find out how many solutions there are you must solve:
- 2 - 10z = - 4 - 10z
Add 10z to both sides:
-2 = -4
Since the two terms are different from one another, that means that there are no solutions for this equation.
1. Use Euler’s formula to find the number of vertices in a polyhedron with 18 edges and 9 faces
use formula: F+V = E+2
please help!
Answer: 11 vertices
Step-by-step explanation:
Hi, to answer this question we simply have to substitute E=18 and F= 9 on Euler's formula:
F+V = E+2
Where:
F = number of faces
V = number of vertices
E= number of edges
Replacing with the values given:
9+V = 18+2
Solving for V:
V =18+2-9
V = 11
Feel free to ask for more if needed or if you did not understand something.
Mrs.Garcia is making bread using a total of 400 grams of gluten free flour.The recipe calls for 70% of the flour to be almond flour. She needs to know how much almond flower to use.
Answer:
She needs 280 grams of almond flour.
Step-by-step explanation:
This question can be solved using a rule of three.
400 grams is 100% = 1. How much is 70% = 0.7?
400 grams - 1
x grams - 0.7
x = 400*0.7
x = 280
She needs 280 grams of almond flour.
Answer:
120g
Step-by-step explanation:
70% of flour in 400g is expressed as
= 70/100×400
=0.7×400
=280g
Therefore, the amount of almond flour to be used by Mrs Garcia in making the recipe is
=400g-280g
=120g
Thus, Mrs Garcia requires 120g of almond flour
Carmine has a total of 9 7/8 gallons of milk in his refrigerator. For breakfast, his nephew Silvio puts 3/4 of the milk into his cereal bowl. How many gallons of milk does Silvio get in his cereal
Answer:
The volume of gallons used by Silvio = [tex]7\frac{13}{32}[/tex] gallons
Step-by-step explanation:
Total volume of milk = [tex]9\frac{7}{8}[/tex] = [tex]\frac{79}{8}[/tex]
amount used by Silvio = [tex]\frac{3}{4}[/tex] of total volume
This means that if the total volume of milk were divided into four parts, Silvio takes 3 out of 4 parts, and this is converted to volume as follows:
∴ amount used by Silvio = [tex]\frac{3}{4}[/tex] × [tex]\frac{79}{8}[/tex] = [tex]\frac{237}{32}[/tex] = [tex]7\frac{13}{32}[/tex] gallons
Did Julio verify the solution?
O No. He substituted 4 and -2 for the wrong
variables.
O No. He did not check the point in the second
equation
O No. He simplified the equation incorrectly.
Yes. He verified that (4, -2) is a solution to the
system of equations.
ASAP
Answer:
No. He did not check the point in the second equation.
Step-by-step explanation:
Took the assignment
Answer:
no he did not check his second equation
Step-by-step explanation:
Just took it hope this helps.
Follow the steps to finish solving the equation -3x + 18 = 7x
1. Add 3x to both sides to isolate the variable term.
2. Divide both sides by 10.
Xa
Answer:
Don’t really know what the question is, but these are the answers for x
Does anybody know how to solve this? (Click for full picture if it doesn’t show up)
Step-by-step explanation:
angle A = 38
now come with me inside the triangle ABC
use two property of isoceles traingle and sum of angles of triangle
you get x= 71°
Answer:
x = 71°
Step-by-step explanation:
Notice that angle D is the inscribed angle of arc BC. By definition of inscribed angles, the measure of an arc's inscribed angle is half the measure of the arc. Also we see that angle A is the central angle of arc BC. By definition, the central angle measure is equal to the arc measure.
Here, ∠D = 19, which means arc BC = 19 * 2 = 38°. Then, that means ∠A = 38.
Notice that ABC forms a triangle and remember that all the angles of a triangle add up to 180°. Since ΔABC is isosceles, we know that the base angles are congruent, so let's say they're both x. Since ∠A = 38°, ∠B = ∠C = x, we can add them up to get 180:
∠A + ∠B + ∠C = 180
38 + x + x = 180
38 + 2x = 180
2x = 142
x = 142/2 = 71
Thus, x = 71°.
Four students were asked to write an expression which has terms that have a greatest common factor of 8c.
the expressions provided by the students are shown below.
Tanya
32C+16cd
Wyatt
8c-48cd
Xavier
36c-24c yang. 8c+40
Which student wrote the correct expression?
Answer:
Wyatt
Step-by-step explanation:
Tanya: 32c+16cd=16c(2+d)
The GCD of the terms is 16cWyatt : 8c-48cd=8c(1-6d)
The GCD of the terms is 8cXavier :36c-24c =12c(3-2)
The GCD of the terms is 12cYang: 8c+40=8(c+5)
The GCD of the terms is 8Since the expression is required to have a GCD of 8c, Wyatt wrote the correct expression.
Answer:
wyatt answered correctly
Step-by-step explanation:
Crunch Bunch cereal boxes come in two sizes. The mini What is the height of the standard size box of Crunch
cereal box of Crunch Bunch is a reduction of the
Bunch?
standard box
1.6 inches
8 in
6.4 inches
10 inches
15.2 inches
Standard Box
Mini Box
The answer is 10
Answer:
10 inches
Step-by-step explanation:
For we solve this, we can use proportionality
Using the following method
Mini box: height 4 inches and width 3.2 inches
The proportion is: 4 in (height) / 3.2 in (width)
Standard box: height x inches and width 8 inches
x in (height) / 8 in ( width)
So:
x /8= 4/ 3.2
Solving for x:
x = (4/ 3.2) 8
x = 10 inches
As the answer
Answer:
10 inches
Step-by-step explanation:
which rational number does not have a reciprocal
Answer:
the rational numbers that doesn’t have a reciprocal are [math]0 [/math] (which can also be expressed as [math]\frac {0} {x}, x \neq 0 [/math] ), and any number of the form [math]\frac {x} {0} [/math].
Step-by-step explanation:
What is the volume, in cubic m, of a cube with an edge length of 18m?
Answer:
The answer is 5832
Step-by-step explanation:
18 ^3 is 5832
b) Imagine that you earned $8,425 in one year. If the government enforces a 15% income tax, how
much money would you owe in taxes at the end of the year? Show your work. (5 points)
Answer:
$1,263.75
Step-by-step explanation:
8425×0.15=1263.75
Answer: $1263.75
Step-by-step explanation:
$8425 (the amount you earned) multiplied by 0.15 (the tax rate as a decimal) is equal to 1263.75.
So, you would owe $1263.75 in taxes at the end of the year.
Nadia has a box of quarters and dimes on her dresser. There are 5 times as many
quarters as dimes in the box. The total number of quarters and dimes is 96. How
many of each coin is in the box?
Answer:
480= 96x5
Step-by-step explanation:
multiply on a caluculater
What is the product of (-a + 3)(a + 4)?
Answer:
-a^2-a+12
Step-by-step explanation:
(-a+3)(a+4)
-a^2-4a+3a+12
-a^2-a+12
Anyone understand how to do this?
Answer:
f ( x ) = - 2x^2 + 3x + 1
Step-by-step explanation:
If f (x ) extends to → − ∞, as x→ − ∞ , provided f(x) → − ∞, as x → +∞, we can rewrite this representation as such;
− ∞ < x < ∞, while y > − ∞
Now the simplest representation of this parabola is f ( x ) = - x^2, provided it is a down - facing parabola;
If we are considering a down - facing parabola, the degree of this trinomial we should create should be even, the LCM being negative. Knowing that we can consider this equation;
Solution; f ( x ) = - 2x^2 + 3x + 1, where the degree is 2, the LCM ⇒ - 2
If a 30-foot ladder leaning against a building makes a 62° with the ground. How many feet from the base of the building is the bottom of the ladder? Assume you hired an excellent contractor, and your building's wall is perpendicular to the ground. Round to the nearest tenth of a foot.
Answer: 14.1 feet
Step-by-step explanation:
Hi, since the situation forms a right triangle (see attachment) we have to apply the trigonometric functions.
cos α = adjacent side / hypotenuse
Where α is the angle of elevation of the ladder to the ground, the hypotenuse is the longest side of the triangle (in this case is the length of the ladder), and the adjacent side (x) is the distance from the base of the building to the bottom of the ladder
Replacing with the values given:
cos 62 = x/ 30
Solving for x
cos62 (30) =x
x= 14.1 feet
Feel free to ask for more if needed or if you did not understand something.
Please Help!! In a discount store, 12% of the 100 cups in stock have some unnoticeable defect. What is the probability of buying 12 cups that don’t have any defect? And what is the probability of getting all 12 cups having a defect?
≈Answer:
a)What is the probability of buying 12 cups that don’t have any defect?
0.1955
b) And what is the probability of getting all 12 cups having a defect?
9.52 × 10⁻¹⁶
Step-by-step explanation:
In the question,we are given the following values:
12% of the 100 cups in stock have some unnoticeable defect.
The number of cups that have defect in stock is calculated as:
12/100 × 100 = 12 cups
The number of cups that doesn't have defect is calculated as:
Total number of cups in stock - Number of cups in stock that have defect.
100 - 12 = 88 cups
a) What is the probability of buying 12 cups that don’t have any defect?
Probability Formula = Number of events/ Number or possible outcomes.
The probability of buying cups that don't have any defect =
88/100 × 87/99 × 86/98 × 85/97 × 84/96 × 83/95 × 82/94 × 81/93 × 80/92 × 79/91 × 78/90 × 77/89 = 0.1955138721
Approximately = 0.1955
b) And what is the probability of getting all 12 cups having a defect?
Probability Formula = Number of events/ Number or possible outcomes.
= 12/100 × 11/99 × 10/98 × 9/97 × 8/96 × 7/95 × 6/94 × 5/93 × 4/92 × 3/91 ×2/90 × 1/89
= 9.519991996 ×10⁻¹⁶
Approximately = 9.52 × 10⁻¹⁶
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Answer:
z=2
Step-by-step explanation:
z^2 - 4z+4 =0
Factor recognizing
a^2 - 2ab - b^2 = (a-b)^2
(z-2)^2 =0
Using the zero product property
z-2 = 0
z=2
A soccer field is a rectangle 40 yards long and 30 yard wide. The coach asks the players to run from one corner to the other corner diagonally across. What is the distance?
Answer:
50 yards
Step-by-step explanation:pythogourus theorem apply here
a²+b²=c²
40²+30²=c²
c²=2500
c=√2500
c=50 yards
hope this helps
plz mark me brainliest
On a test, Robert has been presented with 15 vocabulary words and 15 definitions. He is being asked to match each vocabulary word to appropriate definition. How many different ways are there for Robert to do the matching?
Answer:
15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
Step-by-step explanation:
It will be 15! = 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1
Because the first vocab has 15 definitions to match
the second then be left with 14 definitions ( cause the first one match with 1 def already
the third has 13 definition
so on ...
hope this help
Answer:
15! ways
Step-by-step explanation:
15! =1.307 × 10¹²
For the first word, he has 15 options
For the second word, 14 options
.
.
.
For the last word, 1 option
Total possibilities:
15 × 14 × 13 × 12 × ...... × 1 = 15!
Solve the following:
a)
3x + 4 /2 = 9.5
7 + 2x /3 = 5
b)
Which ists the steps in the correct order to fnd the medan of this data set? 24 16 23 30, 18 29 1 Put the numbers in order 2. Cross off highvlow pairs 3 Add the leftover numbers 4. Divsde the sum by 1 Pt the numbers in order 2. Cross of highlow pairs 1 Cross off hightow pars 2. Add the 3 Divsle the sum by over numbers 1 Cross of highlow pars
Answer:
1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
Step-by-step explanation:
Given:
24, 16, 23, 30, 18, 29
The ordered steps involved in Calculating the median of the data set given :
1.) put the numbers in order: This involves arranging the numbers in the dataset usually in ascending order :
16, 18,23,24,29,30
2.) Cross off high/low pairs: take out equal amount of input from both the left and right hand side. Here we have (23, 34) left
3) Add the leftover numbers: Since the values left is more than one, both values are summed, we have (23+24) = 47
4.) Divide the sum by 2 : Get the average of the two numbers to obtain the median value. Here the average is (23+24)/2 = 47/2 = 23.5
Answer:
A: 1. Put the numbers in order.
2. Cross off high/low pairs.
3. Add the leftover numbers.
4. Divide the sum by 2.
Step-by-step explanation:
edg2020
