Answer:
x=2
Step-by-step explanation:
x^2 + 4x - 16 = 0
I'm using the quadratic formula to solve this equation.
A = 1
B = 4
C = -16
x = -b +- [tex]\sqrt{b^2 - 4ac}[/tex]
over 2a
Plug it in:
x= -4 +- [tex]\sqrt{4^2 -4(-16)}[/tex] over 2
x= -4 +- [tex]\sqrt{16+64[/tex] over 2
x = -4 +-[tex]\sqrt{80}[/tex] over 2
x = -4 +- 4[tex]\sqrt{5[/tex]
Divide by 2.
x = -2 +- 2[tex]\sqrt{5[/tex]
Therefore, x would be -2 + 2[tex]\sqrt{5}[/tex], -2 - 2[tex]\sqrt{5}[/tex]
Convert to decimal form: 2.47213595, -6.47213595
Round it: 2.4714595 = 2.5 and -6.47213595 = -6.5
Show that (x+1)(x+3)(x+5) can be written in the form ax^3+bx^2+cx+d where a,b and c are all positive integers, and d is a negative integer
The expression (x+1)(x+3)(x+5) can be expanded to the form ax^3+bx^2+cx+d with a, b, and c as positive integers and d as negative by first multiplying (x+1) and (x+3) to get x^2+4x+3, which is then multiplied by (x+5) to obtain x^3+9x^2+23x+15.
Explanation:To show that
(x+1)(x+3)(x+5)
can be written in the form
ax^3+bx^2+cx+d where a,b and c are all positive integers, and d is a negative integer, perform multiplication for the given factors as follows:
Firstly, multiply (x+1) and (x+3) which yields x^2+4x+3.
Then, multiply this result by (x+5) which gives the final form: x^3+9x^2+23x+15.
So, a=1, b=9, c=23, and d=15 proving the original expression can be written in the stated form.
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Someone please help. Someone please help.
Radius of the hemisphere and the cone base: R = 2 in
Height of the cone: H = 6 - 2 = 4 in
π ≈ 3,14
Ice inside cone:
[tex]V_1=\frac13\pi R^2\cdot H=\frac13\pi\cdot2^2\cdot 4=\frac{16}3\pi[/tex]
Ice outside cone:
[tex]V_2=\frac12\cdot\frac43\pi R^3=\frac23\pi\cdot2^3=\frac{16}3\pi[/tex]
Total of ice:
[tex]V=V_1+V_2=\frac{16}3\pi+\frac{16}3\pi=\frac{32}3\pi\approx\frac{32}3\cdot3,14=33,49(3)\approx33,5[/tex]
There are 33,5 cubic inches of ice in the cone.
What is the domain of the function y=3x?
Answer:
The domain is all real numbers
Step-by-step explanation:
if y = 3x and x can be any number
you can do 3 times -29 or 3 times 1/3
The screen shows Roberto's video game card activity. A negative number represents
money spent on games. A positive number represents money added to the card.
Card Activity
Games
-$2
Deposits
$8
- 4 - 2
0
2
4
6
-10-8-6
S
10
) How much money does Roberto have
on his card?
Answer: 6
Step-by-step explanation:
Which of the following can have a NEGATIVE impact on your credit score
1) paying bills on time
2) paying down balances on your credit card accounts
3) applying for multiple credit cards in a short period of time (e.g., a week)
The answer option which can have a negative impact on your credit score is: 3) applying for multiple credit cards in a short period of time (e.g., a week).
A credit score refers to a numerical expression between 300 to 850, that typically represents an individual's financial history and credit worthiness.
This ultimately implies that, the higher your credit score, the higher and better it is to obtain a credit (money) from a potential lender.
Generally, the ratings of a credit score by FICO include the following;
A credit score ranging from 670 to 739 is considered to be a good credit score.A credit score of 740 to 799 is better.A credit score of 800 to 850 is considered to be excellent.Generally, the best ways to improve your credit score are;
1. You should ensure you don't pay less than the minimum amount due.
2. You should ensure you pay your bills on time or as at when due.
3. You shouldn't move credit card debt around.
4. You should pay down balances on your credit card accounts.
However, when you apply for multiple credit cards in a short period of time (e.g., a week), it is most likely to have a negative impact on your credit score.
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Plz help i will give brainliest
Answer:
$96
Step-by-step explanation:
First, let's find the price for a ticket with the markup.
Normally, you pay for 100% of the ticket price, but now you also have to pay an extra 20% of the ticket price.
100%+20%=120%
So, you are basically paying for 120% of the normal ticket price, $16
Multiply 120% and $16
120%*16
Convert 120% to a decimal by dividing by 100, or moving the decimal place 2 spots to the left
120%/100=1.20
120.0-->12.0-->1.20
1.20*16=19.2
Now, each adult ticket costs $19.20
Next, find how much 5 tickets will cost.
Multiply 5 and $19.20
5*19.20=96
5 adults will pay $96 with the ticket markup
The ___ of a two-dimensional figure can be any side.
Answer:
The area I believe.
Step-by-step explanation:
The Length of a two-dimensional figure can be any side.
What is the length?length is the measure of some distance from one end to another end.
The side is a distance between two vertexes joined with another part of the figure.
We can measure that distance which means it could be a length.
Thus, The Length of a two-dimensional figure can be any side.
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As the administration looks ahead to next year, Kyra is concentrating on finishing up this year well. Students at her school receive 4 quarter grades, a mid-term exam grade, and a final exam grade for each class. The quarter grades are all weighted equally, the mid-term exam grade is double the weight of a quarter grade, and the final exam grade is four times the weight of a quarter grade. What fraction of the final course grade is the final exam grade? Express your answer as a common fraction.
Answer:
2/5
Step-by-step explanation:
Defining x the weight of each quarter grades (4x for the 4 quarter grades), then the weight of the mid-term exam grade is 2x, and the weight of the final exam is 4x. The addition of all grades is 4x + 2x + 4x = 10x (this represents the combination of grades that makes the final course grade).
So, the final exam grade represents 4x/10x = 2/5 of the final course grade.
Answer:
2/5
Step-by-step explanation:
just did the test
Find the percent of change. Round to the nearest tenth of a percent if necessary. 10 inches to 25 inches. ___ % increase.
Answer:
150% change
Step-by-step explanation:
Formula for Percent change = C =[ (new - old)/ old ]* 100%
C = [ (25 in. - 10 in.) / 10 in. ] = [15/10 ] * 100% = 150 %
a sound wave is traveling at 3,810 m/s and has a wave length of 8 m. what is the frequency of the wave?
Answer:
476.25 hertz
Step-by-step explanation:
Since the speed of a wave is the wave length multiplied by the frequency, the frequency can be written as the speed divided by the wave length. 3810/8=476.25 hZ. Hope this helps!
work out the perimeter of a semicircle with radius 3cm.Give answer in terms of pi.
Answer:
15.42477796
Step-by-step explanation:
1/2π x 6 + 6
- sorry if its wrong
Answer:
3pi
Step-by-step explanation:
refer to the picture for steps.
Identify two factors that have a product of 1 7/8.
Will give Brainliest
Answer:
17×1= 17, and 8×1= 8
17 and 8 is ur answer
i hope its right...
Step-by-step explanation:
1 7/8 into an improper fraction is 15/8
You can say that
3 5
---- x ----
2 4
Find the value of r .
Answer:
0.5
Step-by-step explanation:
hypotenuse/adjacent=r
7/14=0.5
What is the mean of the normal distribution shown below?
-3 -2 -1
0
1
2
3
00.00
Answer:
mean = 0
Step-by-step explanation:
-3 -2 -1
0
1
2
3
if your set is -3, -2, -1, 0, 1, 2, 3 the your mean = 0
An icicle drips at a rate that can be represented by the function f(x) = −x2 + 9x − 18, where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. When f(x) is a negative number, the icicle is not dripping. Determine the values when the icicle starts and stops dripping.
x = −3 and x = 6
x = 3 and x = −6
x = 3 and x = 6
x = −3 and x = −6
Answer: x=3 and x=6
Step-by-step explanation:
Put the first equation in math-way and find the roots/zeros
An icicle drips at a rate that can be represented by the function
[tex]f(x) = -x^2 + 9x - 18[/tex], where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen. So, The solution are x = 3 and x = 6.
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
An icicle drips at a rate that can be represented by the function
[tex]f(x) = -x^2 + 9x - 18[/tex],
where 0 ≤ x ≤ 10 and x is the number of hours after the sun has risen.
First, we have to find its solution since it is a quadratic function;
[tex]f(x) = -x^2 + 9x - 18\\\\f(x) = -x^2 + 3x+ 6x - 18\\\\f(x) = x (3-x) - 6(3-x)\\\\f(x) = (3-x)(x-6)[/tex]
So, The solution are x = 3 and x = 6.
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HELP PLEASE VERY QUICK, I'LL MARK AS BRAINLIEST!
Answer:
Greater ; Greater
Smaller ; Greater
Step-by-step explanation:
Slopes
First row
A: 15/2
B: (25-12.5)/(4-2) = 12.5/2
A has a greater slope than B
-4x + 2y = 8
2y = 4x + 8
y = 2x + 4
A: 2
B: 3/2
A has a greater slope than B
Second Row
A: (2.6-2)/(3-0) = 0.6/3 = 0.1
B: (5-4)/(4-0) = 1/4 = 0.25
A has a smaller slope than B
A: 60
B: (325-50)/5-0) = 275/5 = 55
A has a greater slope than B
» Aiden has 27 fewer
crayons this week than
last week. Last week he
had 56 crayons. How
many crayons does
Aiden have this week?
Show your work.
Answer:
He has 29 crayons left
Step-by-step explanation:
56-27=29
All you have to do is subtract since fewer means less and to find less you need to subtract
11
Adimas found the mean of her 11 math test scores for the first semester.
(76 +87 +65 +88 +67+84 +77 +82 +91 +85 +90) 892
81
11
Using 81 as the mean, find the variance of her grades rounded to the nearest hundredth.
02=
Find the standard deviation of her grades rounded to the nearest hundredth.
Answer:
Variance = 78.5
Standard Deviation = 8.86
Step-by-step explanation:
Given
Mean = 81
Required
Find the variance and standard deviation of the given set of data.
Provided that we already know the mean; to calculate the variance, follow the steps below.
1. Subtract the mean from each data.
76 - 81 = -5
87 - 81 = 6
65 - 81 = -16
88 - 81 = 7
67 - 81 = -14
84 - 81 = 3
77 - 81 = -4
82 - 81 = 1
91 - 81 = 10
85 - 81 = 4
90 - 81 = 9
2. Square these results
-5² = 25
6² = 36
-16² = 256
7² = 49
-14² = 196
3² = 9
-4² = 16
1² = 1
10² = 100
4² = 16
9² = 81
3. Sum these results
Sum = 25+36+256+49+196+9+16+1+100+16+81
Sum = 785
4. Calculate variance by dividing the sum by n - 1 where n = 11
So, n - 1 = 11 - 1 = 10
Variance = 785/10
Variance = 78.50
5. Calculate standard deviation by finding the square root of variance
S.D = √78.50
S.D = 8.86 (Approximated)
Answer:
71.36 and 8.45
Step-by-step explanation:
A person places $82100 in an investment account earning an annual rate of 4.3%, compounded continuously. Using the formula V = Pe^{rt}V=Pe rt , where V is the value of the account in t years, P is the principal initially invested, e is the base of a natural logarithm, and r is the rate of interest, determine the amount of money, to the nearest cent, in the account after 2 years.
The future value of $82,100 invested at a 4.3% annual interest rate compounded continuously for 2 years using the formula V = Pe^{rt}, will be approximately $90,137.30.
Explanation:Your question involves the calculation of the future value of an investment using the formula for continuous compound interest, in this case $82,100 invested at an annual rate of 4.3%, over 2 years. This scenario relies on the mathematical concept of compound interest, which means the interest earned on the initial investment is added to the principal, and this combined amount earns interest as well.
Using the formula V = Pe^{rt}. where:
P = principal amount (initial investment) = $82,100,
r = annual nominal interest rate (decimal) = 4.3/100 = .043,
t = time the money is invested for = 2 years,
e = Euler's number (approx. 2.71828).
The calculation then becomes: V = $82,100 * e^(0.043 * 2) = $82,100 * e^(0.086). Using a calculator to do the exponentiation and the multiplication, the balance in the account after 2 years would approximately be $90,137.30.
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Suppose a parabola has vertex (–8, –7) and also passes through the point (–7, –4). Write the equation of the parabola in vertex form.
We have been given that a parabola has vertex [tex](-8,-7)[/tex] and also passes through the point [tex](-7,-4)[/tex]. We are asked to write the equation of the parabola in vertex form.
We know that vertex form of parabola in format [tex]y=a(x-h)^2+k[/tex], with a vertex at point (h,k).
Let us write equation of parabola using our given information as:
[tex]y=a(x-(-8))^2-7[/tex]
[tex]y=a(x+8)^2-7[/tex]
Now we will substitute the coordinates of point [tex](-7,-4)[/tex] to solve for a as:
[tex]-4=a(-7+8)^2-7[/tex]
[tex]-4=a(1)^2-7[/tex]
[tex]-4+7=a-7+7[/tex]
[tex]3=a[/tex]
Therefore, our required equation would be [tex]y=3(x+8)^2-7[/tex].
Josh wanted to buy a new shirt for a school dance. At the store, he couldn't decide between a purple plaid shirt and a scarlet striped shirt. Since the shirts were on sale for $19.95 each, Josh decided to buy them both. He saved a total of $9.10. If he saved the same amount on each shirt, what was the original price of each one? $
Answer:
$24.50
Step-by-step explanation:
Answer:
24.50
Step-by-step explanation:
Given the equation below, what is the value of 3 + 6(79 – s)?
7= -s+ 82
Answer:
1 expression) 477 - 6s
2 equation) s = 75
Step-by-step explanation:
Also, the first expression is simplified
if one letter is chosen at random from the word substitute, what is the probability that the letter chosen will be a "t"?
Please show the work. Thank you
Answer:
3/10
Step-by-step explanation:
there are 10 letters in substitute
there are 3 t's
3/10
The probability of choosing the letter 't' will be 3 / 10.
What is probability?
Probability is defined as the ratio of the number of favourable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.
Given that:-
If one letter is chosen at random from the word substitute.what is the probability that the letter chosen will be a "t"?The probability will be calculated as:-
There are 10 letters in the word SUBSTITUTE.
Out of these 10 letters, t is three times in the word
So probability will be:-
P = 3 / 10
Therefore the probability of choosing the letter 't' will be 3 / 10.
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$ 20,000 is invested at a rate of 5% compounded quarterly. Identify the compound interest function ta model the situation. Then find the balance after 5 years.
Answer:
the balance after 5 years is: 26540.744
Step-by-step explanation:
Given the information:
P = initial balance = $ 20,000r = interest rate (decimal) = 5% = 0.05n = number of times compounded annually = 4t = time = 5We have the compound interest function ta model the situation is:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
<=> A = [tex]20000(1+\frac{0.05}{4} )^{4*5}[/tex]
<=> A = $26540.744
Hence, the balance after 5 years is: $26540.744
Answer:
$25,640.74
Step-by-step explanation:
The total compound interest is $5,640.74.
The final balance is $25,640.74.
with zero additional deposits
hope this helps:)
PLEASE HELP!!!!whats the first step of factoring 4x^2+10x-24
Answer
2(2x-3)(x+4)
Step-by-step explanation:
Answer:
Exponents
Step-by-step explanation:
First its parentheses but you don't have any and then its exponents and then you multiply and divide and lastly you add or subtract
If the perimeter of a square is 60 inches, how long is each side?
Answer:
15
Step-by-step explanation:
Since a square has 4 sides, that means that each side is equal to the other three sides because it is a square. If so, we do 60/4 to get is 15. To check the answer 15x4 is equal to 60.
Answer:
each side will be 15
Step-by-step explanation:
because if its a square and all the sides are the same lengh and one of the sides are 15 then all of the other sides will also be 15,so that will equal 60.
Sara cuts a pie into halves.How many pieces are there?
Answer:
2 Pieces
Mostly depends how much slices are there
Step-by-step explanation:
Every element is called half the whole by all equal sections. Similarly, the half fraction is defined as the whole half component of both of the two equivalent sections of the rectangle.
Hope this helps
Helen is using glass tiles that each measure one square centimeter to make a
decorative square plate. The plate will use 144 square centimeters of glass tiles.
How many glass tiles will Helen use in one row of her plate?
Answer: 12
Step-by-step explanation:
12 times 12 is 144 so 12.in each row
Helen will use 12 glass tiles in one row of her plate, as the square plate has a total area of 144 square centimeters and each tile measures one square centimeter.
Explanation:The student's question involves calculating the number of glass tiles Helen would use in one row of a square plate, given that she has 144 square centimeters of glass tiles and each tile measures one square centimeter. To determine the number of tiles in one row, we need to remember that the area of a square is equal to the side length squared. Since the total area is 144 square centimeters, we take the square root of 144 to find the length of one side, which is 12 centimeters. Therefore, Helen will use 12 glass tiles in one row of her plate, as there would be 12 tiles lengthwise and 12 tiles widthwise to make up the total area of 144 square centimeters.
A golfer hits a golf ball with an initial velocity of 100 miles per hour. The range R of the ball as a function of the angle θ to the horizontal is given by R(θ)=672sin(2θ), where R is measured in feet. Round to two decimal places. Write DNE if the solution does not exist.
A) At what angle θ should the ball be hit if the golfer wants the ball to travel 450 feet (150 yards)?
degrees
B) At what angle θ should the ball be hit if the golfer wants the ball to travel 540 feet (180 yards)?
degrees
" role="presentation" style="position: relative;">C) At what angle θ should the ball be hit if the golfer wants the ball to travel at least 480 feet (160 yards)?
degrees
D) At what angle θ should the ball be hit if the golfer wants the ball to travel 720 feet (240 yards)?
Answer:
A) 21.02°
B) 26.74°
C) 22.79°
D) DNE
Step-by-step explanation:
We can solve the equation for the angle:
D = 672·sin(2θ)
D/672 = sin(2θ)
arcsin(D/672) = 2θ
θ = arcsin(D/672)/2
A) For D = 450, θ = arcsin(450/672)/2 = 21.0198° ≈ 21.02°
B) For D = 540, θ = arcsin(540/672)/2 = 26.7363° ≈ 26.74°
C) For D = 480, θ = arcsin(480/672)/2 = 22.7923° ≈ 22.79°
D) For D = 720, θ = arcsin(720/672)/2 = DNE
What about this one y’all ?
Answer:
y decreases by half everytime
Step-by-step explanation: