Answer:
(6, 3)
Step-by-step explanation:
Given the 2 equations
3x + 6y = 36 → (1)
3x - 6y = 0 → (2)
Add the 2 equations term by term to eliminate the y- term
(3x + 3x) + (6y - 6y) = (36 + 0)
6x = 36 ( divide both sides by 6 )
x = 6
Substitute x = 6 into either of the 2 equations and solve for y
(1) : 18 + 6y = 36 ( subtract 18 from both sides )
6y = 18 ( divide both sides by 6 )
y = 3
Solution is (6, 3)
Answer:
the solution is (6, 3)
Step-by-step explanation:
Subtract the second equation from the first, as indicated:
3x+6y=36
-( 3x-6y=0)
-----------------
12y = 36. Then y = 36/12 = 3.
Subbing 3 for y in the second equation, we get 3x - 6(3) = 0, or 3x = 18, or x = 6.
Thus, the solution is (6, 3).
The function p(x) = –2(x – 9)2 + 100 is used to determine the profit on T-shirts sold for x dollars. What would the profit from sales be if the price of the T-shirts were $15 apiece?
Answer:
$28
Step-by-step explanation:
Put the given value into the formula and do the arithmetic.
p(15) = -2(15 -9)^2 +100
= -2(6^2) +100
= -72 +100
= 28
The profit on T-shirts selling for $15 would be $28.
Answer:
B -$28
Step-by-step explanation:
A zip line is setup 150ft in the air, where a person can expect to zip line at a safe declining speed to the ground as they pass over a body of water, said to be 40 ft in length. Assuming that this cable were stretched tight, where the zip liner is approaching the ground at a 40∘ angle (not the top angle), how many feet of ground would be covered horizontally by the zip liner, not including the body of water? Round to the nearest foot
Answer:
139 ft
Step-by-step explanation:
So the zip line forms a right triangle. The height of the triangle is 150 ft, and the opposite angle is 40°. The horizontal distance covered by the zip liner can be found with trigonometry, specifically with tangent.
tan 40° = 150 / x
x = 150 / tan 40°
x ≈ 179 feet
But this includes the 40 ft long body of water, so the amount of ground covered is:
179 ft - 40 ft = 139 ft
The legs of a right triangle have lengths of 28 and 16. What's the length of the hypotenuse, rounded to the nearest hundredth? A. 32.25 B. 32.45 C. 22.98 D. 22.94
Answer:
h = 32.25.
Step-by-step explanation:
h^2 = 28^2 + 16^2 (Pythagoras theorem).
h = √1040
h = 32.25.
Using the Pythagorean theorem, the length of the hypotenuse in a right triangle with legs of lengths 28 and 16, rounded to the nearest hundredth, is 32.25.
The question asks for the length of the hypotenuse in a right triangle with legs of lengths 28 and 16. To find this, we use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the two legs (a and b). Thus, according to the equation a² + b² = c², we substitute the given values to find the hypotenuse length.
Using the given lengths:
a = 28
b = 16
We calculate:
c = √(28² + 16²)
c = √(784 + 256)
c = √(1040)
c = 32.249
Rounded to the nearest hundredth, the length of the hypotenuse is therefore 32.25.
PARKS Anika is hiking on a rectangular trail at the national park. There are four resting spots along the corners of the trail. On the map, they are marked with coordinates of (-2, 2), (1, 2), (1, -2), and (-2, -2). If each unit represents 1 mile, find the perimeter of the trail in miles, using the coordinates.
Answer:
[tex]14\ miles[/tex]
Step-by-step explanation:
Let
[tex]A(-2, 2), B(1, 2), C(1, -2),D(-2, -2)[/tex]
Plot the coordinates
see the attached figure
we know that
The perimeter is equal to
[tex]P=2(AB+AD)[/tex]
we have
[tex]AB=(1-(-2))=3\ units[/tex]
[tex]AD=(2-(-2))=4\ units[/tex]
substitute
[tex]P=2(3+4)=14\ units[/tex]
Convert to miles
If each unit represents 1 mile
then
[tex]14\ units=14\ miles[/tex]
Answer:
15 units sq
Step-by-step explanation:
Good job
Which system could be used to solve the following:
A manager is comparing two companies.
Company A charges $50 plus $7 per item.
Company B charges $30 plus $9 per item.
For what number of items will the cost be the same at both companies?
(A) y=7+50x
y=30+9x
(B) y=50+7x
y=30x+9
(C) y=50+7x
y=30+9x
(D) y=50x+7
y=30x+9
Answer:
(C)
10
Step-by-step explanation:
Let y = cost of items
Let x = number of items
Total cost = fixed charge + (cost per item x number of items)
Given:
company A fixed charge = $50 , cost per item = $7
company B fixed charge = $30 , cost per item = $9
For company A,
Total Cost = $50 + ($7 x number of items),
or
y = 50 + 7x
Similarly for company B,
Total Cost = $30 + ($9 x number of items),
or
y = 30 + 9x
Hence (C) is the correct answer.
For the cost to be the same, Total cost for A = total cost for B
i.e 50 + 7x = 30 + 9x
x = 10 items (Answer)
The correct system to solve the problem is y=50+7x and y=30+9x. The cost will be the same at both companies when there are 10 items.
Explanation:The correct system that could be used to solve the problem is (C) y=50+7x and y=30+9x.
To find the number of items where the cost will be the same at both companies, we need to set the two equations equal to each other and solve for x.
50+7x = 30+9x
20 = 2x
x = 10
Therefore, the cost will be the same at both companies when there are 10 items.
Learn more about System of Equations here:https://brainly.com/question/21620502
#SPJ12
Answer the following questions.
1. How many favorable outcomes are expressed in the probability 7/9 ?
2. How many possible outcomes are expressed in the probability 14/25 ?
3. What fraction correctly shows the probability of 14 favorable outcomes out of 21 possible outcomes?
(Enter
as a reduced fraction using / for the fraction bar. Do not use any spaces in your answer.. Example: 1/2 is 1/2
4. Which probability is least likely; 17/35, 5/13, 132/425, 1/2?
Answer:
1. 7
2. 25
3. 2/3
4. 132/425
Step-by-step explanation:
Probability is the likelihood of an event occurring and it can be computed by:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}[/tex]
1. So when you are given a probability of 7/9:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{7}{9}[/tex]
So the answer is 7.
2. Given the probability is 14/25:
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{25}[/tex]
The number of possible outcomes is 25.
3. You have 14 favorable outcomes out of 21 possible outcomes.
[tex]Probability=\dfrac{favorable\hspace{1mm}outcomes}{all\hspace{1mm}possible\hspace{1mm}outcomes}=\dfrac{14}{21}\div \dfrac{7}{7}=\dfrac{2}{3}[/tex]
The answer is 2/3.
The least likely even would be the smallest fraction. If you want to do this the easy way, just change them all to decimal and find the value with the least.
17/35 = 0.49
5/13 = 0.38
132/425 = 0.31
1/2 = 0.5
Since 132/425 = 0.31 is the smallest, then it is the least likely probability.
A new unit has been formed in the army . In this until, 1 member is a staff sergeant , 3 are sergeants,21 are PFC's and 35 are PVT's . What percent of the soldiers are in the army
Answer:
93%
Step-by-step explanation:
1 + 3 + 21 + 35 = 60 = 100%
21 + 35 = 56 = x%
60 = 100%
56 = x%
60x = 56 * 100
x = 56* 100 / 60
x = 2*23*2*2*5*5 / 2*2*3*5
x = 23*2*5/3
x = 93%
To find the percent of soldiers in the new army unit, you divide the number of soldiers in the unit by the total number of soldiers in the army and multiply by 100. However, the question doesn't provide the total number of soldiers in the army, making it impossible to calculate this percentage.
Explanation:The question is asking what percent of the soldiers in the newly formed army unit consists of the total personnels. The total number of soldiers in the unit is the sum of staff sergeants, sergeants, PFCs, and PVTs which is 1 + 3 + 21 + 35 = 60 soldiers. The percent of soldiers in the army is the number of soldiers in the unit divided by the total number of soldiers in the army multiplied by 100. However, without the context of the total number of soldiers in the army, it is impossible to calculate this percentage. For example, if the total army size is 600, then the percent of soldiers in this unit would be (60/600)*100 = 10%. The keywords here are
percent
,
total soldiers
, and
army unit
.
Learn more about percentages here:https://brainly.com/question/30697911
#SPJ12
PLZ HELP ME!!! I NEED THIS DONE BY TONIGHT!!!
1. This kite has a 90 degree angle, which is equivalent to angle B.
2. Distance RB is 2.
3. Distance SB is 1.
4. The kite forms a right triangle.
5. Distance RS is the hypotenuse which has not been given. We can call RS by any variable of choice.
The unit cost, in dollars, to produce bins of cat food is $3 and the fixed cost is $6972. The price-demand function, in dollars per bin, is
p
(
x
)
=
253
−
2
x
Find the cost function.
C
(
x
)
=
syntax error
Find the revenue function.
R
(
x
)
=
syntax error
Find the profit function.
P
(
x
)
=
syntax error
At what quantity is the smallest break-even point?
Answer:
Revenue , Cost and Profit Function
Step-by-step explanation:
Here we are given the Price/Demand Function as
P(x) = 253-2x
which means when the demand of Cat food is x units , the price will be fixed as 253-2x per unit.
Now let us revenue generated from this demand i.e. x units
Revenue = Demand * Price per unit
R(x) = x * (253-2x)
= [tex]253x-2x^2[/tex]
Now let us Evaluate the Cost Function
Cost = Variable cost + Fixed Cost
Variable cost = cost per unit * number of units
= 3*x
= 3x
Fixed Cost = 6972 as given in the problem.
Hence
Cost Function C(x) = 3x+6972
Let us now find the Profit Function
Profit = Revenue - Cost
P(x) = R(x) - C(x)
= [tex]253x-2x^2 - (3x+6972)\\253x-2x^2-3x-6972\\253x-3x-2x^2-6972\\250x-2x^2-6972\\-2x^2+250x-6972\\[/tex]
Now we have to find the quantity at which we attain break even point.
We know that at break even point
Profit = 0
Hence P(x) = 0
[tex]-2x^2+250x-6972[/tex]=0
now we have to solve the above equation for x
[tex]-2x^2+250x-6972 = 0[/tex]
Dividing both sides by -2 we get
[tex]x^2-125x+3486 = 0\\[/tex]
Now we have to find the factors of 3486 whose sum is 125. Which comes out to be 42 and 83
Hence we now solve the above quadratic equation using splitting the middle term method .
[tex]x^2-42x-83x+3486 = 0\\x(x-42)-83(x-43)=0\\(x-42)(x-83)=0\\[/tex]
Hence
Either (x-42) = 0 or (x-83) = 0 therefore
if x-42= 0 ; x=42
if x-83=0 ; x=83
Smallest of which is 42. Hence the number of units at which it attains the break even point is 42.
Final answer:
The cost function is C(x) = $6972 + ($3 × x). The revenue function is R(x) = 253x - 2x². The profit function is P(x) = (253x - 2x²) - ($6972 + $3x). The smallest break-even point is where P(x) = 0.
Explanation:
To answer the student's series of questions involving cost, revenue, and profit functions, as well as the break-even quantity, we need to derive these functions from the given information and perform the necessary calculations. The unit cost to produce bins of cat food is $3, and the fixed cost is $6972. Meanwhile, the price-demand function is given by p(x) = 253 - 2x.
The cost function, C(x), which represents the total cost of producing x units, can be expressed as:
C(x) = Fixed Costs + (Variable Cost per Unit × x)
Thus, C(x) = $6972 + ($3 × x).
The revenue function, R(x), is the total income from selling x units, defined by:
R(x) = Price per Unit × x
So, using the price-demand function, R(x) = (253 - 2x)x = 253x - 2x².
The profit function, P(x), is found by subtracting the cost function from the revenue function:
P(x) = R(x) - C(x)
Therefore, P(x) = (253x - 2x²) - ($6972 + $3x).
To calculate the break-even point, where profit is zero, you need to solve the equation P(x) = 0 for x.
Carl's Candies has determined that a candy bar measuring 3 inches long has a z-score of +1 and a candy bar measuring 3.75 inches long has a z-score of +2. What is the standard deviation of the length of candy bars produced at Carl's Candies?
Answer:
0.75 inches
Step-by-step explanation:
The value that has z=2 is 2 standard deviations from the mean. The value that has z=1 is 1 standard deviation from the mean. The difference between these two values is 1 standard deviation:
1 standard deviation = 3.75 in - 3 in = 0.75 in
Answer:
0.75
Step-by-step explanation:
Can someone please help me? Will give the brainlest!!
Step-by-step explanation:
The ratio of the perimeters = the scale
P₂ / P₁ = 6 / 4 = 3 / 2
The ratio of the areas = the square of the scale
A₂ / A₁ = (6 / 4)² = (3 / 2)² = 9 / 4
Same for the triangles:
P₂ / P₁ = 6 / 3 = 2
A₂ / A₁ = (6 / 3)² = (2)² = 4
please help asap will mark brainliest
Answer:
29; 30
Step-by-step explanation:
1. To the nearest whole number.
Whole numbers are numbers like 27, 28, 29, and 30.
A is between 28 and 29, but it is closer to 29.
To the nearest whole number, A = 29.
2. To the nearest 10
The tens are numbers like 10, 20, 30, and 40.
A is between 20 and 30, but it is closer to 30.
To the nearest ten, A = 30.
Help please. Select all correct answers
We're given pairs (A,B) and asked if we have
enough calcium,
5A + 4B >= 24
enough iron
4A + 6B >= 15
and enough vitamins
7A + 4B >= 15
We check each constraint on each pair; if we find any false we can stop for that pair.
(A,B)=(1,4)
5(1)+4(4)=21 under 24, NO CHECK
(A,B)=(1,5)
5(1) + 4(5) = 25, bigger than 24, good
4(1) + 6(5) = 34, bigger than 15, good
7(1) + 4(5) = 27, bigger than 15, good CHECK
(A,B)=(2,3)
5(2)+4(3)=22, NO CHECK
(A,B)=(3,2)
5(3)+4(2)=23, NO CHECK
(A,B)=(4,1)
5(4) + 4(1) = 24, ok
4(4) + 6(1) = 22, ok
7(4) + 4(1) = 32, ok, CHECK
Answer:
(1,5), (4,1)
Step-by-step explanation:
Let's check the possible answers and see if they will Steve to meet his requirements:
We'll start by looking if each answer (dose) will provide enough calcium first. If it does, we'll get iron and vitamins if needed.
a) (1,4)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (1) + 4 (4)
24 ≤ 5 + 16
24 ≤ 21
NO!
b) (1,5)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (1) + 4 (5)
24 ≤ 25 YES!
Iron, at least 15 mg
15 ≤ 4x + 6y
15 ≤ 4(1) + 6(5)
15 ≤ 34 YES!
Vitamins, at least 16 mg
16 ≤ 7x + 4y
16 ≤ 7 (1) + 4 (5)
16 ≤ 27 YES
YES, YES, YES...
c) (2,3)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (2) + 4 (3)
24 ≤ 22 NO!
d) (3,2)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (3) + 4 (2)
24 ≤ 23 NO!
e) (4,1)
Calcium, at least 24 mg
24 ≤ 5x + 4y
24 ≤ 5 (4) + 4 (1)
24 ≤ 24 YES!
Iron, at least 15 mg
15 ≤ 4x + 6y
15 ≤ 4(4) + 6(1)
15 ≤ 22 YES!
Vitamins, at least 16 mg
16 ≤ 7x + 4y
16 ≤ 7 (4) + 4 (1)
16 ≤ 32 YES
YES, YES, YES...
You plan to use 170 feet of fencing to enclose a Rectangular play area of 2800 square feet. You plan to build the play area so it is centered against the back of your home which is 50 feet in length. Determine the dimensions necessary to enclose the required area.
Answer:
40 ft by 70 ft
Step-by-step explanation:
The 50 ft side of the house can add to the total perimeter of the play area, allowing it to be 170+50 = 220 feet. Then the sum of length and width will be half that, or 110 feet.
Factors of 2800 that have a sum of 110 are 40 and 70.
The play area fence can extend 10 ft either side of the house, out 40 ft, then 70 ft across the back, for a total length of 170 ft. Dimensions of the play area are 40 ft by 70 ft.
The density of granite is about 2.75 grams per cubic centimeter. Suppose you have a granite countertop for a kitchen that is 1 meter wide, 3 meters long, and 4 centimeters thick. Which of the following equations will give you its mass, in kilograms? View Available Hint(s) The density of granite is about 2.75 grams per cubic centimeter. Suppose you have a granite countertop for a kitchen that is 1 meter wide, 3 meters long, and 4 centimeters thick. Which of the following equations will give you its mass, in kilograms? 2.75 gcm3×1 m×3 m×4 cm×1000 g1 kg 2.75 gcm3×1 m×3 m×(100 cm1 m)2×4 cm×1 kg1000 g 2.75 gcm3×1 m×3 m×4 cm×1 m100 cm×1 kg1000 g 2.75 gcm3×1 m×3 m×4 cm×1 kg1000 g 2.75 g3cm3×1 m×3 m×(100 cm1 m)2×4 cm×(1 kg1000 g)3 2.75 gcm3×1 m×3 m×(1 m100 cm)2×4 cm×1 kg1000 g
Answer:
[tex]330\ kg[/tex]
Step-by-step explanation:
Remember that
1 kg=1,000 g
1 m= 100 cm
The volume of the granite countertop in cubic centimeters is equal to
[tex]V=(100)(300)(4)\ cm^{3}[/tex]
The density in kg per cubic centimeter is equal to
[tex]D=2.75(\frac{1}{1,000}) \frac{kg}{cm^{3}}[/tex]
Multiply the density by the volume
[tex]2.75(\frac{1}{1,000})(100)(300)(4)[/tex]
[tex]2.75(120)=330\ kg[/tex]
which of the following is NOT equal to 50 millimeters?a. 5,000,000 nanometersb. 0.05 metersc. 5 centimetersd. 50,000 micrometers
Answer:its a. 5,000,000
Step-by-step explanation:
Final answer:
Option a, 5,000,000 nanometers, is the correct choice as it does not equate to 50 millimeters; it equates to 5 millimeters instead, making it not equal to the other options listed.
Explanation:
The question asks which of the provided options is not equal to 50 millimeters. We can convert each option to see which one does not equal 50 mm:
a. 5,000,000 nanometers (nm) - This equates to 5,000,000 nm × 1 m / 1,000,000,000 nm = 0.005 m or 5 mm, which is not equal to 50 mm.
b. 0.05 meters (m) - This is equal to 0.05 m × 1000 mm / 1 m = 50 mm, which is equal to 50 mm.
c. 5 centimeters (cm) - This is equal to 5 cm × 10 mm / 1 cm = 50 mm, which is equal to 50 mm.
d. 50,000 micrometers (µm) - As 1 µm is 1/1000 mm, this is equal to 50,000 µm × 1 mm / 1000 µm = 50 mm, which is equal to 50 mm.
Therefore, the correct answer is a. 5,000,000 nanometers, as it is the only option that does not equate to 50 mm.
What is the value of n?
-4n = 696
A)
n = -2,784
B)
n = -174
C)
n = 174
D)
n = 2,784
Answer:
n = -174
Step-by-step explanation:
What I did was 696 divided by -4 and got B) n = -174.
Please mark brainliest and have a great day!
Solve for the zeros
x^2+10x+21
(x+3)(x+7)= 0
x^2+7x+3x+21= x^2+10x+21
x+3-3= 0-3
x+7-7= 0-7
Answers are :
x= -3 , x= -7
Answer:
x=-7,-3
Step-by-step explanation:
An election was contested by 3 candidates.A got 345983 votes. His nearest rival, Candidate B won elections by 15967 votes. Candidate C got 279845 votes and 39823 votes were declared invalid. Find total number of votes polled.
Final answer:
To find the total number of votes polled in the election with three candidates and invalid votes, the sum of votes received by each candidate and the invalid votes is calculated. The total number of votes polled is 1,027,601.
Explanation:
The question pertains to vote totals and calculating the overall number of votes polled in an election with three candidates. To solve this, we will perform simple addition of the votes received by each candidate and also include votes that were declared invalid.
Candidate A received 345,983 votes. Candidate B won the election by a margin of 15,967 votes more than Candidate A, which means Candidate B received 345,983 + 15,967 = 361,950 votes. Candidate C received 279,845 votes, and there were 39,823 invalid votes.
To find the total number of votes polled, add together all the votes:
Votes for Candidate A: 345,983
Votes for Candidate B: 361,950 (since Candidate B won by 15,967 votes more than Candidate A)
Votes for Candidate C: 279,845
Invalid votes: 39,823
Adding these together:
345,983 + 361,950 + 279,845 + 39,823 = 1,027,601
Therefore, the total number of votes polled in the election is 1,027,601.
What are the solutions of the equation 9x4 – 2x2 – 7 = 0? Use u substitution to solve. tions of the equation 9
Answer:
Step-by-step explanation:
Let [tex]u^2=x^4\\u = x^2[/tex]
Subbing in:
[tex]9u^2-2u-7=0[/tex]
a = 9, b = -2, c = -7
The product of a and c is the aboslute value of -63, so a*c = 63. We need 2 factors of 63 that will add to give us -2. The factors of 63 are {1, 63}, (3, 21}, {7, 9}. It looks like the combination of -9 and +7 will work because -9 + 7 = -2. Plug in accordingly:
[tex]9u^2-9u+7u-7=0[/tex]
Group together in groups of 2:
[tex](9u^2-9u)+(7u-7)=0[/tex]
Now factor out what's common within each set of parenthesis:
[tex]9u(u-1)+7(u-1)=0[/tex]
We know this combination "works" because the terms inside the parenthesis are identical. We can now factor those out and what's left goes together in another set of parenthesis:
[tex](u-1)(9u+7)=0[/tex]
Remember that [tex]u=x^2[/tex]
so we sub back in and continue to factor. This was originally a fourth degree polynomial; that means we have 4 solutions.
[tex](x^2-1)(9x^2+7)=0[/tex]
The first two solutions are found withing the first set of parenthesis and the second two are found in other set of parenthesis. Factoring [tex](x^2-1)[/tex] gives us that x = 1 and -1. The other set is a bit more tricky. If
[tex]9x^2+7=0[/tex] then
[tex]9x^2=-7[/tex] and
[tex]x^2=-\frac{7}{9}[/tex]
You cannot take the square root of a negative number without allowing for the imaginary component, i, so we do that:
[tex]x=[/tex]±[tex]\sqrt{-\frac{7}{9} }[/tex]
which will simplify down to
[tex]x=[/tex]±[tex]\frac{\sqrt{7} }{3}i[/tex]
Those are the 4 solutions to the quartic equation.
The height of a kicked football can be represented by the polynomial –16t2 + 32t + 3 where t is the time in seconds. Find the height (in feet) of the football after 1.2 seconds. A. 18.75 feet B. 18.25 feet C. 18.36 feet D. 18.05 feet
To find the height of the football after 1.2 seconds, we substitute t with 1.2 in the polynomial −16t2 + 32t + 3, simplifying to 18.36 feet, which corresponds to answer option C.
Explanation:The student asked to find the height of a kicked football after 1.2 seconds, with the height given by the polynomial −16t2 + 32t + 3, where t is the time in seconds. To solve for the height after 1.2 seconds, we substitute t with 1.2 in the polynomial, which gives us:
−16(1.2)2 + 32(1.2) + 3
Calculating this gives:
−16(1.44) + 38.4 + 3
−23.04 + 38.4 + 3
15.36 + 3
18.36 feet.
Therefore, after 1.2 seconds, the height of the football is 18.36 feet, making the correct answer option C.
Which shows the correct substitution of the values a, b, and c from the equation 0 = – 3x2 – 2x + 6 into the quadratic formula? Quadratic formula: x =
Answer:
[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]
Step-by-step explanation:
The given quadratic equation is
[tex]-3x^2-2x+6=0[/tex] .... (1)
If a quadratic equation is defined as
[tex]ax^2+bx+c=0[/tex] .... (2)
then the quadratic formula is
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
On comparing (1) and (2), we get
[tex]a=-3,b=-2,c=6[/tex]
Substitute [tex]a=-3,b=-2,c=6[/tex] in the above formula.
[tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex]
Therefore, the correct substitution of the values a, b, and c in the quadratic formula is [tex]x=\frac{-(-2)\pm \sqrt{(-2)^2-4(-3)(6)}}{2(-3)}[/tex].
How are the graphs of the functions f(x) = /16x and g(x) = 3/64x related
Answer:
the functions f(x) and g(x) are equivalent
Step-by-step explanation:
Your full question is attached below
The equations of your problem are
f(x) = √(16^x)
f(x) = √(4^(2x))
f(x) = √(4^(2x)) = √(4^x.4^x)
f(x) = 4^(x)
and
g(x) = ∛64^x
g(x) = ∛4^(3x)
g(x) = ∛4^(3x) = ∛4^(x) .4^(x) .4^(x)
g(x) = 4^(x)
Thus, the functions f(x) and g(x) are equivalent
Given the statement "If a line is horizontal, then it has slope equal to zero," what is its contrapositive?
Answer:
if a line has a slope equal to zero, then it is horizontal
Step-by-step explanation:
Answer:
If a line does not have zero slope, then it is not a horizontal line.
Step-by-step explanation:
edg
Solve for a.
a = 0
a = -1
a = 1
none
Answer:
None.
Step-by-step explanation:
5/a - 2 / (1 - a) = 2 (a - 1)
Multiply each term by a(1 - a)(a - 1):
5 (1 - a)(a - 1) - 2a(a - 1) = 2a(1 - a)
5( a - 1 - a^2 + a) - 2a^2 + 2a = 2a - 2a^2
5(-a^2 + 2a - 1) - 2a^2 + 2a = 2a - 2a^2
-5a^2 + 10a - 5 - 2a^2 + 2a - 2a + 2a^2 = 0
-5a^2 + 10a - 5 = 0
-5(a^2 - 2a + 1) = 0
= -5(a - 1)^2 = 0
So a = 1.
But a = 1 cannot be a root because 2/ 1 - a would be 2/0 which is undefined.
Also 2 / (a - 1) is undefined.
can anyone help with problems 6 and 8 those are the only ones I cannot figure out
Answer:
[tex](f + g) (x)=x^2 +x +3[/tex]
[tex](f - g) (x)=-x^2 +5x +1[/tex]
Step-by-step explanation:
We have the following functions:
[tex]f(x)=3x +2\\[/tex] and [tex]g(x) = x^2 -2x +1[/tex]
First we find [tex](f + g) (x)[/tex]
To find [tex](f + g) (x)[/tex] we must add the function f(x) with the function g(x)
[tex](f + g) (x)=3x +2 + x^2 -2x +1[/tex]
[tex](f + g) (x)=x^2 +x +3[/tex]
Now we find [tex](f - g) (x)[/tex]
To find [tex](f - g) (x)[/tex] we must subtract the function f(x) with the function g(x)
[tex](f - g) (x)=3x +2 - (x^2 -2x +1)[/tex]
[tex](f - g) (x)=3x +2 - x^2 +2x -1[/tex]
[tex](f - g) (x)=-x^2 +5x +1[/tex]
Solve for x: √3-x+13=1
Answer:
√3 + 12 = x
Step-by-step explanation:
Simplify both sides of the equation, isolating the variable.
A basket contains 13 pieces of fruit five apples five oranges and three bananas Jonas takes piece of fruit at random from the basket in Bethex if you summon what is the probability that Jonas will get orange and Beth will get an apple
Answer:1 out of 13
Step-by-step explanation:
because you take both of them and add them together and if one gets a banana and the other one gets an orange that will be one out of thirteen
Which postulate can be used to prove that the triangles are congruent?
A. SAS
B. SSS
C. ASA
D. not congruent
Answer:
D. not congruent
Step-by-step explanation:
Only two pairs of congruent sides are given to us, when we need either 3 pairs of congruent sides (SSS) or two pairs of congruent sides & 1 pair of congruent angles (SAS), or two pairs of congruent angles & one pair of congruent sides (ASA).
~
If there are 25 questions in a test, and I got an 84% grade, how many questions did I get wrong? Please explain!
-sunny
Answer:
4 wrong
Step-by-step explanation:
Just do .84 times 25.
.84(25)=21
That means you got 21 questions right.
Answer:
You missed 4 questions.
Step-by-step explanation:
If you have a 100 questions test with 1 point each and you get and 84% that means you missed 16 questions. Since there was 25 questions on this test that is 1 quarter of 100. Divide the number of questions missed on a 100 questions test by the fraction of the actual test. So by 4. 16 divided by 4 = 4