The discriminant of the quadratic equation -2x²-5x+7=0 is 81 units when formula of discriminant is (b²-4ac).
What is the discriminant of the quadratic equation?Keeping in mind that a, b, and c are the coefficients of your quadratic in standard form, the discriminant is calculated using the formula b squared minus 4ac. It reveals how many possible answers there are to a quadratic equation. There are two solutions if the discriminant is greater than zero. The square root's argument (i.e., its contents), which is the expression b²-4ac, is known as the "discriminant" because using its value, you can "discriminate" between (i.e., be able to distinguish between) the different solution types.
Here,
-2x²-5x+7=0
discriminant=(b²-4ac)
=(-5)²-(4*-2*7)
=25+56
=81 units
When the discriminant formula is (b²-4ac), the discriminant of the quadratic equation (-2x²-5x+7=0) is 81 units.
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A candy company sells peanut brittle and almond bark. The information for both types of candy is shown.
graph labeled Peanut Brittle with x axis labeled weight in ounces and y axis labeled cost in dollars with a line from point 0 comma 0 going through 10 comma 10
Almond Bark
Weight (ounces) 2 6 14
Cost (dollars) 3 9 21
Determine how much more one candy costs per ounce than the other candy.
Peanut brittle costs $0.50 more per ounce than almond bark.
Almond bark costs $0.50 more per ounce than peanut brittle.
Peanut brittle costs $0.33 more per ounce than almond bark.
Almond bark costs $0.33 more per ounce than peanut brittle.
The difference between the cost of one candy per ounce and the other candy is that: Almond bark costs $0.50 more per ounce than peanut brittle.
How to determine the cost of candy?Mathematically, a direct proportion can be represented the following mathematical expression:
y = kx
Where:
x represents the weight in ounces of a candy.y represents the cost in dollars of a candy.k represents the constant of proportionality.Next, we would determine the constant of proportionality (k) for each candy as follows:
For Peanut Brittle, we have the following:
Constant of proportionality (k) = 10/10
Constant of proportionality (k) = 1.0
For Almond Bark, we have the following:
Constant of proportionality (k) = 3/2
Constant of proportionality (k) = 1.5
Next, we would determine the difference in cost:
Difference in cost = 1.5 - 1.0
Difference in cost = $0.50.
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Part A
A model car is for sale online. Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day the car sells.
If the original price of the model car was $40, how much did the car sell for to the nearest cent?
Part B
What percent discount does this represent from the original price? Round to the nearest whole percent.
The car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.
According to the question,
We have the following information:
Beginning on day one, the owner discounts the price by 5% each day until it sells. On the third day the car sells. And the original price of the model car was $40.
The first day:
40*5/100
200/100
2
The price on the first day = $38
The second day:
38*5/100
190/100
1.9
The price on the second day = 38-1.9
The price on second day = 36.1
The third day:
36.1*5/100
180.5/100
1.805
The price on third day = $34.295 (36.1-1.805)
1 dollar = 100 cents
Price of car in cents = 3429.5 cents
B) Percent discount from the original price:
Let's take it to be x.
40 - (40x/100) = 34.295
-40x/100 = 34.295-40
-40x/100 = -5.705
40x = 570.5
x = 570.5/40
x = 14.265%
Hence, the car was sold for 3429.5 cents and the percent discount from the original price is 14.265%.
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How does knowing how ACT essays are scored help
you with writing your own?
Answer:
Generally, more selective schools may require or recommend a writing score, while less selective ones may not (though there certainly are exceptions). It's worth noting that most schools no longer require the ACT with Writing, though many schools recommend it.
Step-by-step explanation:
whats 28.2 × 4.42= in decimal form? lol
Answer:
124.644
Step-by-step explanation:
28.2*4.42=124.644.
Answer:
28.2 × 4.42= 124.644
and in non-decimal it's 124644 removing 3 decimal places
Step-by-step explanation:
Brainiest, please
thank you
Choose a variable, write a inequality, and solve the inequality.
The sum of a number and -2 is no more than 6
Answer: 4
Step-by-step explanation: your going to divide -2 by 1 and you get 2 then add 4 and you get 6 pls give me brainliest :)
A water tank holds a total of 5,600 gallons in the tank has three pipe through which water drains what water is drained from the tank pipe B drains twice as much as pipe a pipe C drain 65 gallons more than pipe B how many gallons of water does each pipe
The amounts drained by each pipe, considering a system of equations, are given as follows:
Pipe A: 1107 gallons.Pipe B: 2214 gallons.Pipe C: 2279 gallons.What is the system of equations?The variables to the system of equations are presented as follows:
Variable x: amount of water drained by Pipe A.Variable y: amount of water drained by Pipe B.Variable z: amount of water drained by Pipe C.A water tank holds a total of 5,600 gallons, hence:
x + y + z = 5600.
Pipe B drains twice as much as pipe A, hence:
y = 2x.
Pipe C drains 65 gallons more than pipe B, hence:
z = 65 + y = 65 + 2x.
Replacing the last two equations into the first, the amount drained by Pipe A is obtained as follows:
x + y + z = 5600.
x + 2x + 65 + 2x = 5600
5x = 5535
x = 5535/5
x = 1107 gallons.
Hence the remaining amounts are given as follows:
Pipe B: y = 2x = 2 x 1107 = 2214 gallons.Pipe C: z = y + 65 = 2214 + 65 = 2279 gallons.More can be learned about a system of equations at https://brainly.com/question/24342899
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A sporting goods store manager was selling a ski set for a certain price. The manager offered the markdowns shown, making the one-day sale price of the ski set 327$. Find the original selling price of the ski set.
Answer:$583.93 is the original price
find the slope of the line passing through the points (-2,2) and (-5,5)
Answer:
The slope of the line passing through the points [tex](-2, 2)[/tex] and [tex](-5, 5)[/tex] is equal to: [tex]-1[/tex]
Step-by-step explanation:
The slope of a line can be found with the following formula
[tex]m=\frac{y_2 - y_1}{x_2 - x_1}[/tex]
Where [tex]x_2 > x_1[/tex]
Then substituting the values with the given ones we have
[tex]m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{2-5}{-2-(-5)}=\frac{-3}{-2+5}=\frac{-3}{3} =-1[/tex]
So the slope of the line passing through the given points is [tex]-1[/tex]
solve for x;
2/7 x + 1/5 x=51
Answer:
x = 105
Step-by-step explanation:
To solve for x, we simply need to isolate it:
[tex]\frac{2}{7}x+\frac{1}{5}x=51\\ \frac{17}{35}x=51\\ x=105[/tex]
For the piecewise function, find the values h(-5), h(0), h(5), and h(9).
- 3x-13, for x < -5
h(x) = 5,
h(0) =
h(-5) = (Simplify your answer.)
=(Simplify your answer.)
(Simplify your answer.)
(Simplify your answer.)
=
h(5)=
X+ 7,
h(9) =
for 5≤x<5
for x ≥ 5
2
Answer:
h(-5) = 5, h(0) = 5, h(5) = 12, h(9) = 16==========================
The given function is the combination of three lines:
h(x) = - 3x - 13, for x < - 5,h(x) = 5, for - 5 ≤ x < 5,h(x) = x + 7, for x ≥ 5.The values of the function at the given points are:
h(-5) = 5, corresponds to second equation,h(0) = 5, same as above,h(5) = 5 + 7 = 12, corresponds to third equation,h(9) = 9 + 7 = 16, same as above.Ken, Mike, and Ariel are eating out at their favorite restaurant. They each order a sandwich combo and plan to split the bill evenly. The service they receive at the restaurant is amazing, so they decide to leave a 30% tip. Their bill total is $50.88 before tax. If Florida’s sales tax is 6%, how much will each person pay? Round your answer to the nearest hundredth.
Each individual paid the sum of $23.4 including state tax at the restaurant
PercentageIn mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%".
In the problem, their total bill is $50.88 and they gave a 30% tip
We should fid 30% of 50.88
0.3 * 50.88 = $15.264
30% of $50.88 is $15.264
If we add this up and then find the state tax to it.
15.264 + 50.88 = 66.144.
Find 6% of 66.144 to determine the state tax.
0.06 * 66.144 = 3.96864
The total amount spent is 66.144 + 3.96864 = 70.11264
We can divide this equally amongst the three people to get the individual payment = 70.11264/3 = 23.37088
Rounding this to the nearest cent, we have 23.4.
We can say each person paid $23.4 at the end of the day
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what does (cot0)(sin0)(sec0) simplify to
Answer: c. 1
Step-by-step explanation:
[tex]\displaystyle\\(cot\theta)(sin\theta)(sec\theta)=\\\\\frac{cos\theta}{sin\theta}(sin\theta)\frac{1}{cos\theta} =\\\\\frac{cos\theta (sin\theta)(1)}{sin\theta(cos\theta)}=\\\\1[/tex]
1. Write the radical below in the simplest radical form. Decimals are not allowed.
√175
2. Write the radical in simplest radical form. Decimals not allowed
√5/12
number 2 is a fraction btw
The simplest radical form of the radicals given are:
1. The simplest radical form of √175 is 5 √7.
2. The simplest radical form of √5 / 12 is √5 / 12.
First, let us understand the radical:
A radical can also be called a surd. A surd is an irrational number. We say that it is irrational because it can not be expressed as a terminating decimal.
1.
We are given:
√175
We need to write in the simplest radical form.
175 can be written as:
175 = 5 * 5 * 7
√175 = √ 5 * 5 * 7
√175 = √ 5 * 5 * √7
√175 = 5 √7
So, the simplest form of √175 is 5 √7.
2.
We are given:
√5 / 12
We need to write in the simplest radical form.
√5 / 12 is already in the simplest form.
So, the simplest form of √5 / 12 is √5 / 12.
Thus, the simplest radical form of the radicals given are:
1. The simplest radical form of √175 is 5 √7.
2. The simplest radical form of √5 / 12 is √5 / 12.
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Suppose $18,000 is deposited into an account paying 8.5% interest, compounded continuously. How much money is in the account after 10 years if no withdrawals or additional deposits are made?
This question requires you to find simple interest. Total money in the account after 10 years is $189,000
The total money can be calculated as follows:
First, multiply all the things known from the question, deposit, interest, and years of saving.Given,
=Deposit×Interest×Year
=18,000×8.5%×10
=18,000×[tex]85/100[/tex]×10
=$171,000
Next, we need to add up the deposit above with the initial deposit=$171.000+$18.000
=$189,000
Hence, the simple interest or total money in the account after 10 years without any withdrawals of additional deposits is $189,000.
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The amount of money in the account after 10 years will be $42113.64.
What is compound interest?Compound interest is applicable when there will be a change in the principle amount after the given time period.
For example, if you give anyone $500 at the rate of 10% annually then $500 is your principle amount. After 1 year the interest will be $50 and hence principle amount will become $550 now for the next year the interest will be $550, not $500.
As per the given,
Principle amount P = $18000
Rate of interest r = 8.5% = 0.085
Time t = 10
By continuous compounding interest formula,
P = (18000)[tex]e^{0.085\times10}[/tex]
P = $42113.64
Hence "The amount of money in the account after 10 years will be $42113.64".
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NO LINKS!! Please help me with the Segment Proofs Part 2
Answer:
1. Given.
2. Definition of congruent segments.
3. Segment Addition Postulate.
4. Substitution Property of Equality.
5. Transitive Property of Equality.
6. Subtraction Property of Equality.
7. Definition of congruent segments.
Step-by-step explanation:
Statement 1
[tex]\overline{AB} \cong \overline{CD}; \; \overline{CE} \cong \overline{AE}[/tex]
Reason: Given.
Statement 2
[tex]AB=CD; \;CE=AE[/tex]
Reason: Definition of congruent segments.
Congruent segments are segments that have the same length.
Statement 3
[tex]AE+EB=AB; \; CE+ED=CD[/tex]
Reason: Segment Addition Postulate.
A line segment divided into smaller pieces is the sum of the lengths of all those smaller segments.
Statement 4
[tex]CE+EB=CD[/tex]
Reason: Substitution Property of Equality.
For all numbers a and b, if a=b, then a may be replaced by b in any equation or expression.
Statement 5
[tex]CE+ED=CE+EB[/tex]
Reason: Transitive Property of Equality.
For all numbers a, b and c, if a=b and b=c, then a=c.
Statement 6
[tex]ED=EB[/tex]
Reason: Subtraction Property of Equality.
For all numbers a, b and c, if a=b, then a-c=b-c.
Statement 7
[tex]\overline{ED} \cong \overline{EB}[/tex]
Reason: Definition of congruent segments.
Congruent segments are segments that have the same length.
Last week, a candy store sold 6 13 pounds of white chocolate. It sold 4 times as much milk chocolate as white chocolate.
How many more pounds of milk chocolate were sold than white chocolate at the candy store last week?
A)19
B)19 2/3
C)18
D)18 2/3
Answer: 25 1/3
Step-by-step explanation:
X:
6. A two-story building measures 21 feet from
the ground. A scale model shows the building
to be 3 inches tall. How many inches would an
84-foot building be in the model?
height:
Answer:
12 inches
Step-by-step explanation:
Let be "x" the top inches (in the model) of a eighty four foot building.
According to the information provided in the exercise, we be aware of that the top of a two-story establishing is 21 toes and in the scale model its top is 3 inches.
Knowing this, we can set up the following proportion: 3/21=x/84
The final step is to get to the bottom of for "x" in order to calculate its value.
The half-life of radium is 1690 years. If 30 grams are present now, how much will be present in 720 years?
Answer:
22.3 gm
Step-by-step explanation:
720 is this many half lives : 720 / 1690
so there will be this much left 30 gm ( 1/2)^(720/1690) = 22.3 gm
Smith forecasts that interest rates will rise over a 5-year period according to a force of interest function given by delta = .08 + .025t/(t+1) for 0<=t<=5.
Step-by-step explanation:
if p(A)=0.17, p(B)=0.42 and p(AorB)=0.59, are A and B mutually exclusive
Evaluate the following algebraic expression:
64-9p when p = 7
O 14
O 63
O 36
01
Answer:
63 is the answer.
Step-by-step explanation:
9p=9xp, p=7, so 9x7=63. ;)
1/3 of the guests choose beef
5/12 choose chicken
69 are vegeterian
How many guests are at the wedding
The number of guests at the wedding is 276.
How to calculate the number of guests?Since 1/3 of the guests choose beef and 5/12 choose chicken, the fraction for vegetarian will be:
= 1 - (1/3 + 5/12)
= 1 - 3/4
= 1/4
Therefore, let the total number of guests be x.
This will be illustrated as:
1/4 × x = 69
0.25x = 69
Divide
x = 69 / 0.25
x = 276
Therefore, there are 276 guests.
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Suppose a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual
percentage rate of growth?
A. 20%
B. 3.7%
C. 8.2%
If a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%
The initial population was 5000
The population in 2015 is 6000
let the rate of growth be r
aₙ = arⁿ-¹
6000 = 5000 r⁵⁻¹
6000/5000 = r⁴
6/5 = r⁴
r = 1.2⁻⁴
r = 0.48
r = 48%
the annual percentage rate of growth 48/5 = 9.6
Therefore, if a population was 5000 in 2010 and grew to 6000 by 2015. What is the annual percentage rate of growth is 9.6%
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A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles
from the ship located at point A. How far apart are the ships? Round your answer to the nearest tenth of a mile.
According to the given depression angle, ship is 4.4 miles apart from ship B.
Depression angle:
Depression angle refer an angle that is formed with the horizontal line if the line of sight is downward from the horizontal line.
Given,
A pilot is flying over the ocean. She determines that the angles of depression to two ships are 74° and 48°, as shown in the figure below. The plane is 5 miles from the ship located at point A.
Here we need to find the distance between the two ships.
Here we know the following,
Distance between plane and Ship A = 5 miles.
And the depression angle = 74°, 48°
Let us consider the following, that they sit on a line,
So under this situations,
=> 80 - 48 - 74 = 58 degrees.
The next thing we have to do is bring this 74 degree angle inside the diagram. Because it is congruent to this interior angle because they are alternate.
Then it can be written as,
=> x = sin 74°/5
=> x = 4.4
Therefore, the two ships are 4.4 miles apart from each other.
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please help
Our class is studying the effects of mindfulness on mental health. To help with data collection, we will have the support of ten grade 9, eleven grade 10, twelve grade 11 and thirteen grade 12 students. Showing your calculations,how many different groups of 12 volunteers can we make if:
a) the group must have the same number of students from each grade?
b) the group must have at least two grade 9 students? [2A]
c) the group must have James and Lucy (both grade 11 students) in it? [2A]
The number of groups, using the combination formula, for each case, is given as follows:
a) Same number of students from each grade: 1,245,816,000
b) At least two grade nine students: 31,650,886,995.
c) James and Lucy are in it: 2,481,256,778.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, obtained by the following formula, involving factorials.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
For item a, the groups are taken as follows:
3 students from grade 9, from a set of 10.3 students from grade 10, from a set of 11.3 students from grade 11, from a set of 12.3 students from grade 12, from a set of 13.Hence the number of groups is:
[tex]C_{10,3}C_{11,3}C_{12,3}C_{13,3} = \frac{10!}{7!3!} \times \frac{11!}{8!3!} \times \frac{12!}{9!3!} \times \frac{13!}{10!3!} = 120 \times 165 \times 220 \times 286 = 1,245,816,000[/tex]
For item b, the total number of groups, without considering the restriction, is:
[tex]C_{46,12} = \frac{46!}{12!34!} = 38,910,617,655[/tex]
The number of groups with none students from grade 9 is:
[tex]C_{36,12} = \frac{36!}{12!24!} = 1,251,677,700[/tex]
The number of groups with one student from grade 9 is:
[tex]C_{10,1}C_{36,11} = 10 \times \frac{36!}{11!25!} = 6,008,052,960[/tex]
Using complementary events, the number of groups with at least two grade 9 students is:
38,910,617,655 - (1,251,677,700 + 6,008,052,960) = 31,650,886,995.
For item c, considering Jamie and Lucy in it, the remaining 10 students are taken from a set of 44, hence:
[tex]C_{44,10} = \frac{44!}{10!34!} = 2,481,256,778[/tex]
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Resolve:
1:3a + 2a
2:-5b -7b
3:-a² -9a²
4:3a^x-²^+5a^x-²
5:18x - 11x
6:5a - 8a + a -6a + 21a
[tex] \bold{1: 3a + 2a \: = 5a}[/tex]
[tex]\bold{2: - 5b - 7b = - 12b}[/tex]
[tex]\bold{3: - a {}^{2} - 9 a{}^{2} = - 10a {}^{2}}[/tex]
[tex]\bold{4: 3a {}^{x - 2} + 5a {}^{x - 2} = 8a {}^{x - 2}}[/tex]
[tex] \bold{5: 18x - 11x = 7x}[/tex]
[tex]\bold{6: 5a - 8a + a - 6a + 21a = 13}[/tex]
The reduction of similar terms is an operation that aims to convert two or more similar terms into a single term.
In these cases you must add or subtract either addition, subtraction or subtraction and addition, using the law of signs.
[tex]\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {\bold{Law \: of \: signs: }} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times + = + \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times + = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: + \times - = - \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - \times - = + \end{gathered} [/tex]
Juan invested $110,000, 10 years ago at 8% compound quarterly. how much has he accumulated?
use the MS Excel FV function
Answer:
Below
Step-by-step explanation:
The equation ( you need to commit to memory) is:
FV = PV ( 1+i)^n FV = future value PV = present value(110 000)
i = decimal interest per PERIOD = .08 /4 = .02
n = # of periods = 40 (it is a quarterly period by 10 yrs)
FV = 110 000 ( 1 + .02)^40 = 242 884 .36 dollars
find using substitution method
Answer:
x = 4 ; y = -1
Step-by-step explanation:
y = -2x + 7
x + 2(-2x+7) = 2
x -4x + 14 = 2
-3x = 2 -14
-3x = -12
-3/-3 x = -12/-3
x = 4
y = -2* 4 + 7
y = -8 + 7
y = -1
jessie needs to borroe 12,000 from northwestern bank. they offeted her a 5 year loan with an apr of 4.98%. how much will she pay interest over the life of the loan?
Answer:
1580.40----------------------------------
GivenLoan amount P = 12000,Rate r = 4.98% = 0.0498,Time t = 5 years,Number of compounds n = 12.Find the monthly payment[tex]M=\dfrac{P(r/n)(1+r/n)^{nt}}{(1+r/n)^{nt}-1}[/tex][tex]M=\dfrac{12000(0.0498/12)(1+0.0498/12)^{12*5}}{(1+0.0498/12)^{12*5}-1} =226.34[/tex]Find the total amount paid226.34*60 = 13580.40Find the amount of interest13580.40 - 12000 = 1580.40Answer:
$1580.69
Step-by-step explanation:
Monthly Payment Formula
[tex]\sf PMT=\dfrac{Pi\left(1+i\right)^n}{\left(1+i\right)^n-1}[/tex]
where:
PMT = Monthly payment.P = Loan amount.i = Interest rate per month (in decimal form).n = Term of the loan (in months).Given:
P = $12,000i = 0.0498/12 = 0.00415n = 5 years = 60 monthsSubstitute the values into the formula to calculate the monthly payment:
[tex]\implies \sf PMT=\dfrac{12000(0.00415)\left(1+0.00415\right)^{60}}{\left(1+0.00415\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{49.8\left(1.00415\right)^{60}}{\left(1.00415\right)^{60}-1}[/tex]
[tex]\implies \sf PMT=\dfrac{63.84764727}{0.2820812705}[/tex]
[tex]\implies \sf PMT=226.3448656[/tex]
Therefore, the total payments over the life of the loan is the monthly payment multiplied by the total number of months:
[tex]\implies \sf 226.3448656 \times 60=\$13580.69[/tex]
To calculate how much interest Jessie pays over the life of the loan, subtract the original loan amount from the total payments amount:
[tex]\implies 13580.69-12000=\$1580.69[/tex]
Therefore, the interest Jessie will pay over the life of the loan is $1580.69.
5) A woman drinks 8 bottles of water in 2 days. How many bottles of water would she drink in 4 days?
Suppose you invest $2000 in equipment to put pictures on T-shirts. You buy each T-shirt for $4. After you have placed a picture on a shirt, you sell it for $20. How many T-shirts must you sell to break even?
Answer:
25
Step-by-step explanation:
2000/4=500
500/20=25
Answer: 125
Step-by-step explanation: you see if you take your 20$ you ern of of selling a shirt then the price you buy it for 4$ then defied it by 2000$ you get 125.