Answer: 0=1620=162
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The vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the parabola is open downwards
From the given parabola
The vertex of the parabola is at (-2, 2)
The vertex of the parabola is defined as the the point at the intersection of the parabola and its line of symmetry.
The line of symmetry is at x = -2
The parabola is open downwards
Hence, the vertex of the parabola is at (-2, 2), the line of symmetry of the parabola is at x = -2 and the given parabola is open downwards
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Shandra is preheating her oven before using it to bake. The initial temperature of the oven is 65° and the temperature will increase at a rate of 10° per minute after being turned on. What is the temperature of the oven 8 minutes after being turned on? What is the temperature of the oven tt minutes after being turned on?
Answer:
x=145 at 8 minutes
im not sure what tt means but please read my note at the end.
Step-by-step explanation:
if the initial temp is 65 and it increases at a rate of 10 per min the use
65+10(x)
let x be the number of minutes
65+10(8)
65 +80= 145
after 8 minutes the oven will be at 15 degrees. im not sure what tt is suppose to mean, but to find any other solution just plug it into x multiply x by 10 and add it to 65
15. Find mACB. help me please
The measure of the angle ACB is 87°.
What does the term angle mean?Angles produced by two beams are included in the plane that contains the rays. The intersection of two planes may also produce an angle. Dihedral angles are the name given to them. It is also possible to determine the angle between two crossing curves using the angle created by the rays that are perpendicular to each intersecting curve at that point.
An angle can also refer to a measurement of a rotation or an angle. This number represents the length-to-radius ratio of a circular arc.
When two crossing lines in a plane are not perpendicular to one another, Euclid defined a plane angle as the inclination between those intersecting lines.
In triangle ADE and triangle ACB, the triangles are similar.
So,
∠AED/ ∠ABC = ∠DAE/∠CAB
∠AED = ∠ABC
11x-2 = 6x + 13
11x - 6x = 13 + 2
5x = 15
x = 15/5
x = 3
So, the measure of angle ABC is
∠ ABC = 6(3)+13
∠ ABC = 18+13
∠ ABC = 31°
Now, consider triangle ABC, the sum of all angles = 180°
So, 62° + 31° + ∠ACB = 180°
∠ACB + 93° = 180°
∠ACB = 180° - 93°
∠ACB = 87°
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Given that X is directly proportional to y2. if x=4 units and y=3 units ,then find the value of y when x= 3 units
Answer:
y = 2.60 (to 3sf)
Step-by-step explanation:
Since x is directly proportional to y², then x = ky², where k is a constant.
When x = 4, y = 3,
4 = k(3)²
4 = 9k
9k = 4
∴[tex]k =\frac{4}{9}[/tex]
∴ When x = 3,
[tex]\frac{4}{9}y^{2} = 3[/tex]
∴y = 2.60 (to 3sf)
Which inequality represents the phrase "nine less than two
times a number is no more than 45?"
The expression of the inequality is [tex]9 < 2x\le45[/tex]. It can be obtained using the operations of inequality.
What is inequality?
In matmathematics if two numbers are not equal even then there is a relationship. This relationship can be defined by inequality relationship.
According to the pharase, 9 is less than two times a number. Hence, consider the number is x and its two times means 2x. Now, 9 should be less than this number. Hence, 9<2x. Now, again the number 2x is not more than 45. Means, it can be equal to 45. Hence, it will give the expression [tex]2x\le45[/tex].
Now, combine the two expressions as follows:
9<2x
[tex]2x\le45[/tex]
[tex]9 < 2x\le45[/tex]
Hence, the expression of the inequality is [tex]9 < 2x\le45[/tex].
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help meeeeeeeeeeeeee pleaseeeeeeeeee!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Evaluate the expression.
Do not round your answer.
1/5(3+2+ 5)² =
Answer:
20
Step-by-step explanation:
do parenthesis first
1/5(3+2+ 5)² =
1/5(10)² =
then exponent
1/5(10)² =
1/5(100) =
20
The formula d=16f^2 describes the number of feet d a skydiver falls in t second of free fall. How far does a skydiver fall after 1.5 second?
The skydiver falls a distance of 36 feet after 1.5 seconds.
What is the distance?Distance is a measurement of how far apart two things or points are, either numerically or occasionally qualitatively. The distance can refer to a physical length in physics or to an estimate based on other factors in common usage.Distance is the sum of an object's movements, regardless of direction. The distance can be defined as the amount of space an object has covered, regardless of its starting or ending position.Now, we have:
d=16t²t=1.5 secondsTo calculate distance:
d = 16 * 1.5*1.5d= 36 feetTherefore, the skydiver falls a distance of 36 feet after 1.5 seconds.
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gold miners in alaska have found, on average, 12 ounces of gold per 1,000 tons of dirt excavated with a standard deviation of 3 ounces. assume the amount of gold found per 1,000 tons of dirt is normally distributed. if the miners excavated 1,000 tons of dirt, how little gold must they have found such that they find that amount or less only 15% of the time?
Miners excavated 1000 tons of dirt, and they found 8.892 ounces of gold.
Let X stand for the random variable determining how much gold is discovered for every 1,000 tonnes of dirt dug up. After that, we learn that:
X ~ N (12, 3²)
Let K be the required amount of discovered gold. 15% of the time, less than K worth of gold is discovered. Next, we have:
P (X ≤ K) = 0.15
When we transform this into a typical normal variable, we get:
P [Z ≤ (K - 12) / 3] = 0.15
From the common normal tables, we can deduce:
P (Z ≤ -1.036) = 0.15
Comparing the two equations above, we obtain:
(K - 12) / 3 = -1.036
K = 12 - (1.036 * 3) = 12 - 3.108 = 8.892
As a result, 8.892 ounces of gold are needed.
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An investor borrows r11500 to buy a computer and is charged interest at an annual rate of 6 %per annum compounded quarterly. the loan has to be paid in 3 years. calculate the amount of loan that is outstanding at the end of 2 years
The loan amount at the end of 2 years is Rs. 12,127 .
In the given question we have, amount Rs. 11500 is borrowed by investor at the interest rate of 6% per annum.
compund interest is defined as the addition of interest to the principal of loan.
principal (P) = 11500
If interest is compunded quarterly then time(t) = 3 years = 12 , rate ( r%) = 6/4% = 2/3 %
Using the formula of Amount ,
Amount = P( 1 + r / 100) ᵗ
= 11500( 1 + 2/ 300)⁸
= 12127.83 ~ 12128
compound interest = Amount - principal =
12128- 11500 = Rs. 628
So, An investor has to pay total Rs. 12128 at the end of 2- year.
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Expand and simplify (3x + 4)(2x + 3)
Answer:
6x^2+17x+12
Step-by-step explanation:
(3x+4) * (2x+3)
3x * 2x = 6x^2
3x * 3 = 9x
+4 * 2x = +8x
+4 * +3 = +12
6x^2+ 9x+8x +12
Simplify:
6x^2+17x+12
Clay asks Donte to play the following number puzzle:
Pick a number
Add 4
Multiply by 2
Subtract 3
Add your original number
Donte’s final result is 32. Which number did he start with?
Group of answer choices below
A. 7
B. 9
C. 4
D. 23
E. 0
ESSENTIAL
Chuck
Match up each scenario with the equation that models the word problem.
Skate rental charges an additional $3.
Jeff is 3 years less than Tony's age.
Marie buys balloons for a party that
are $3.00 each.
Intro
y=x+3
y=x-3
y = 3x
Done
En this is the answer
The following are the equations which matches the given word problems:
a. Skate rental charges an additional $3 :
y = x+3
b. Jeff is 3 years less than Tony's age:
y=x-3
c. Marie buys balloons for a party that are $3.00 each:
y = 3x
Given, we have the word problems:
a. Skate rental charges an additional $3 :
here, based on the fixed charge, additional charge is taken as $3.
let the total charge be represented as y and
x represent the fixed charge,
hence the equation we get is:
y = x+3
b. Jeff is 3 years less than Tony's age.
let y represent the age of Jeff
and x represent the age of Tony.
hence we frame the equation as:
y = x - 3
c. Marie buys balloons for a party that are $3.00 each:
let the cost of the balloon be represented as y
and x represent the number of balloons Marie wants to buy for $3 each.
hence the equation we frame is:
y = 3x
Hence we get the required equations.
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simplify (4i+1)^2
show all work
The simplified answer is 8i-15.
What do you mean by iota?
Iota is a mathematical concept that is represented by the symbol i and has the value of [tex]i^{2}=-1[/tex] , or i =[tex]\sqrt{-1}[/tex] . It is an imaginary unit number that is denoted by i. You could have run into instances when the discriminant is negative while attempting to solve quadratic equations.
According to the given question,
We have: [tex](4i+1)^{2}[/tex]
Now, we will solving this by formula,
[tex](a+b)^{2}=a^{2} +b^{2}+2ab[/tex]
Putting the values in it,
[tex](4i+1)^{2}=(4i)^{2}+1^{2}+2(4i)(1)\\=16i^{2} +1+8i\\ =16(-1)+8i+1\\=8i-16+1\\=8i-15[/tex]
Therefore, the required answer is 8i-15.
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if the interest for 5 years on Rs 3000 is Rs 525, find the interest on Rs 2200 for 6 years at the same rate of interest.
Using the formula of simple interest, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
In the given question,
The given principal amount = Rs 3000
The given time = 5 years
Interest amount = 525
Now finding the rate of interest.
As we know that the formula of simple interest.
I = P*R*T/100
525 = 3000*R*5/100
Multiply by 100 on both side we get
52500 = 15000*R
Divide by 15000 on both side
R = 52500/15000
R = 3.5
In the question we have to find the interest on Rs 2200 for 6 years at the same rate of interest.
To find the interest put the value in I = P*R*T/100
As given P=2200, R=3.5%, T=6 years
I = P*R*T/100
I = 2200*3.5*6/100
I = 462
Hence, the interest on Rs 2200 for 6 years at the same rate of interest is Rs 462.
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5-(40/5)
Step A: 5+ (4)
Step B: 5+8
Step C: 13
In which step did the student first make an error? Be sure to include the correct value of
the expression in simplest form in your answer.
Explain your answer.
Answer:
5 - [tex]\frac{40}{5}[/tex] = 5 - 8 = -3
Step-by-step explanation:
The first mistake made by the student is in Step A where the problem was not copied down correctly.
If a+4/a = 4 then find the value of a^5-1/a^5
pls answer this one as quick as possible.
Value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
What do you mean by algebraic expression?
In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.). Terms comprise expressions.
There are 3 main types of algebraic expressions which include:
Monomial Expression
Binomial Expression
Polynomial Expression
An algebraic expression which is having only one term is known as a monomial.
Given expression:
a + 4/a = 4
We need to simplify the above expression and will find the value of a.
[tex]a+\frac{4}{a}=4[/tex]
⇒ [tex]\frac{a^2+4}{a}=4[/tex]
⇒ [tex]a^{2}+4=4a[/tex]
⇒ [tex]a^2-4a+4=0[/tex]
⇒ [tex]a^2-2a-2a+4=0[/tex]
⇒ a(a-2) -2(a-2) = 0
⇒ (a-2)(a-2) = 0
⇒ a = 2
Now, substitute this value of a in expression , [tex]a^5-\frac{1}{a^5}[/tex]
[tex]2^5-\frac{1}{2^5}[/tex]
= 32 - 1/32
= [tex]\frac{1024-1}{32} =1023/32 = 31.97[/tex]
Therefore, value of [tex]a^5-\frac{1}{a^5}[/tex] is 31.97.
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Each month Edna spends all her income on rent, on travel and on other living expenses She spends 1/3 of her income on rent. she spends 1/5 of her income on travel. She spends $420 of her income on other living expenses. Work out her income each month.
Answer:I think $1064
Step-by-step explanation:
First you multiply 1/5 by 420 and then add, so 1/5 x 420 = 84 & 420 + 84 = 504. Then you multiply 1/3 by 420 and also add, so 1/3 x 420 = 140 & 420 + 140 = 560. After you add both totals to get your final answer, so 504 + 560 = 1064. Her income each month is $1064.
suppose the insect population doubled after 15 hours. how long (in hours) will it take the insect population to grow to eight times its initial size? (simplify your answer completely.)
Using population growth modeling it is concluded that the population of insects after 1 hour will be about 1.05 times.
What is growth and decay modeling?The method used to calculate the growth and decay of insects or bacteria are called growth and decay modeling.
Let us assume n₀ is the initial population, then the total population n(t) after t time is given by the formula:
n(t) = n₀ [tex]e^{rt}[/tex], where r = the relative rate of growth.
Suppose an initial number of insects is x and after 15 hours it becomes 2x.
2x = x[tex]e^{15r}[/tex]
[tex]e^{15r}[/tex] = 2
Take the log of both sides of the equation
ln [tex]e^{15r}[/tex]= ln 2
15r = ln 2
r = 0.693147/15
Now, population after 1-hour = x [tex]e^{r}[/tex]
= 1.047
≈ 1.05
Hence the population of insects after 1 hour will be about 1.05 times.
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Complete the statement. 48 cm = mm
Answer:
48cm = 480mm
Step-by-step explanation:
1cm = 10mm
48cm = 48 X 10 mm
48cm = 480mm
Answer:
480mm
When converting from cm to mm, multiply by 10.
48 x 10 = 480
Hi if someone could help me I would be very grateful.
I submitted a photo of the questions
Answer:
5/12
6/15
10/18
Step-by-step explanation:
help quick!!
Find the equation of the Axis of symmetry and the coordinates of the vertex of the graph of each function
y = 4x² – 2
Answer: (0,-2)
Step-by-step explanation: just multiply
Решите пожалуйста приведенные ниже файлы, срочно
Step-by-step explanation:
the answer is Y=-1/2×+5
Explanation:
You put the gradient in M for Y=M×+C (substitute) then you substitute the coordinates it has given you into the X and Y part of linear equation. (x,y)
HELP PLEASE ASAP!!!!!!!!
The missing angle is as follows:
m∠C = 30 degrees.How to find congruent triangle?When two triangles are congruent they will have exactly the same three sides and exactly the same three angles.
In other words, two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal.
Therefore, the triangle ABC is congruent to EDF.
Hence,
∠A = ∠D
∠B = E
∠C = ∠F
Therefore,
m∠C = x
m∠F = 2x - 30
Hence,
m∠C = m∠F
x = 2x - 30
x - 2x = -30
-x = -30
x = 30
m∠C = 30 degrees
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Omar compro 3.5k de cebolla a 8.90 el kilo. Cuanto pago por las cebollas
The amount that Omar will pay when he bought 3.5k of onions are 8.90 per kilo is $31.15.
What is money?From the information given, Omah wants to know the total amount that he will pay for the onions. It's important to know the cost for each kilogram of onion and then multiply it but the number of kilograms that are bought.
In this case, Omar bought 3.5k of onions are 8.90 per kilo.
The amount that Omar will pay for the onions will be:
= Number of kilograms × Cost per kg
= 3.5 × 8.90
= $31.15
In conclusion, the amount is $31.15.
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Tell whether x and y show a positive, negative, or no relationship
Answer:
negative, as the points are slowly making their way "down" the graph :)
a positive integer divisor of 12! is chosen at random. the probability that the di-visor chosen is a perfect square can be expressed asmn, wheremandnare relativelyprime positive integers. what ism n?
The probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
What exactly is meant by probability?Probability is synonymous with possibility. It is a mathematical branch that deals with the occurrence of a random event. The value ranges from zero to one. Probability has been introduced in mathematics to predict the likelihood of events occurring.Given: Randomly, a positive integer divisor of 12! is selected.
Prime factorization of 12! = 2¹⁰ × 3⁵ × 5² × 7¹ × 11
Total divisors of 12! = 11 × 6 × 3 × 2 × 2
Each number in the prime factorization must have an even exponent in order to construct a perfect square divisor. In the prime factorization, the divisor cannot have any factors of 7 and 11 because there is only one of each in 12!. There are 6 × 3 × 2 perfect squares as a result.The probability that the divisor chosen is a perfect square is given as:
(6 × 3 × 2)/(11 × 6 × 3 × 2 × 2)
= 1/22
=m/n
Therefore, the probability that the divisor chosen is a perfect square is found to be 1/22 which is m:n.
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help help help helppp
The coordinate of image of P is (-6,-4)
What in math is a coordinate?
a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).
P (-2,2)
Translation (x,y)=(x-4,y-6)
x= -2
y= 2
x-4= -6
y-6= -4
Hence the coordinate of image of p is (-6,-4)
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Pls help me and give steps as to how to do it thank you
Answer: [tex]x=13, y=132[/tex]
Step-by-step explanation:
Using the same-side interior angles theorem, [tex]y=132[/tex].
Using the alternate interior angles theorem, [tex]5x-17=48 \implies x=13[/tex]
find the inequality 2x/3 <4
Answer:
x<6
Step-by-step explanation:
2x/3<4
2x<12
x<6
Answer:
x < 6
Step-by-step explanation:
[tex]\frac{2x}{3}[/tex] < 4 ( multiply both sides by 3 to clear the fraction )
2x < 12 ( divide both sides by 2 )
x < 6
