Using equations,
A: y=-x²+6x-5
y=3
3=-x²+6x-5
y=0
B: (x-2) (x-4) =0
C: x-2=0 OR x-4=0
D: x=2 OR x=4
What are equations?An equation is a mathematical statement that contains the symbol "equal to" between two expressions with identical values. as in 3x + 5 = 15, for example. There are many different types of equations, including linear, quadratic, cubic, etc.
Y=-x²+6x-5
Y=3
Using substitution:
3 = - x²+6x- 5
x²- 6x+8 = 0
Now factor your equation:
x²- 6x+8 = 0
⇒ x² -2x - 4x + 8 = 0
⇒ x (x-2) -4(x-2) = 0
⇒ (x- 2) (x-4) =0
Identify the x-values of the solutions:
x-2=0 or x-4 =0
x=2 or x=4
Identify the solution to the system:
x=2 y=3 and
x=4 y=3
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help fast
Using a standard deck of cards, a gamer drew one card and recorded its value. They continued this for a total of 100 draws. The table shows the frequency of each card drawn.
Card A 2 3 4 5 6 7 8 9 10 J Q K
Frequency 4 7 5 6 7 6 8 10 7 10 8 12 10
Based on the table, what is the experimental probability that the card selected was a K or 6?
one over 26
four over 25
one fourth
8 over 13
The experimental prοbability that the card selected was a K οr 6 is fοur οver 25.
What is the prοbability?The study οf prοbability examines the likelihοοd that a particular οutcοme will οccur; this likelihοοd is determined by the ratiο οf the preferred and pοssible cases.
The frequency οf K and 6 is 8 and 7 respectively.
Therefοre, the tοtal frequency οf K οr 6 is 8 + 7 = 15.
The tοtal number οf cards drawn is 100.
Hence, the experimental prοbability οf drawing a K οr 6 is:
15/100 = 3/20
Hence, the answer is fοur οver 25.
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Please help me it's about percentages
Answer:
A) 0.5%
Step-by-step explanation:
Hope this helps! Pls give brainliest!
Answer:
0.5%
Step-by-step explanation:
7 out of 1400 walk
7/1400 = 1/ 200 divide by 2 equals 0.5/100=0.5%
Here is a graph of function f and a graph of function g. Express g in terms of f using function
notation.
y = g(x)
Answer:
Step-by-step explanation:
Carl is boarding a plane. he has 2 checked bags of equal weight and a backpack that weighs 4kg. The total weight of Carls baggage is 35 kg.
2w + 4= 35
2w=31
w= 31/2
w=15.5
The weight of each bag is 15.5 kg.
Find the difference for 5 1/4 - 2 3/4
Answer: 2.5 (or 2 1/2 as a mixed number)
Step-by-step explanation:
Answer:
5/2 or 2.5
Step-by-step explanation:
[tex]5 \frac{1}{4} - 2\frac{3}{4}[/tex] = 5.25 - 2.75 = 2.5 = 5/2
Among 300 elementary school students,
258 said they like chocolate ice cream, 142
like vanilla ice cream and 102 like both.
Find the probability that a randomly
selected student likes:
A. Vanilla ice cream or chocolate ice
cream, but not both.
B. Neither of the 2 flavors.
C. Vanilla ice cream but not chocolate ice
cream.
To solve this problem, we can use the formula for probability:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
A. To find the probability that a student likes vanilla or chocolate ice cream, but not both, we need to subtract the number of students who like both from the total number of students who like vanilla or chocolate:
Number of students who like vanilla or chocolate = 258 + 142 = 400
Number of students who like both = 102
Number of students who like only vanilla or only chocolate = 400 - 102 = 298
Probability = 298/300 = 0.9933
B. To find the probability that a student likes neither vanilla nor chocolate ice cream, we need to subtract the total number of students who like either or both flavors from the total number of students:
Total number of students = 300
Number of students who like vanilla or chocolate = 258 + 142 = 400
Number of students who like both = 102
Number of students who like neither flavor = 300 - 400 + 102 = 2
Probability = 2/300 = 0.0067
C. To find the probability that a student likes vanilla ice cream but not chocolate ice cream, we need to subtract the number of students who like both from the total number of students who like vanilla:
Number of students who like vanilla = 142
Number of students who like both = 102
Number of students who like only vanilla = 142 - 102 = 40
Probability = 40/300 = 0.1333
Each of the given linear systems is in row echelon form.
Solve the system.
x + y − z + 2w=4
w=5
The solution as an ordered quadruple:
(0, -6 - z, z, 5)
HOW TO SOLVE A LINEAR SYSTEM?
The given linear system is:
x + y - z + 2w = 4
w = 5
This system is already in row echelon form. We can use back substitution to solve for the variables. Since we already know the value of w, we can substitute w = 5 into the first equation:
x + y - z + 2w = 4
x + y - z + 2(5) = 4
x + y - z + 10 = 4
Simplifying, we get:
x + y - z = -6
Now we have two equations:
x + y - z = -6
w = 5
We can solve for x, y, and z using the first equation. To do this, we can use the fact that the system is in row echelon form, which means that the leading coefficients are all 1 and there are no variables to the left of the leading coefficients. We can start by solving for z since it has a leading coefficient of 1:
z = x + y + 6
Next, we can use the second equation to solve for y:
y = -x - z - 6
Finally, we can use the third equation to solve for x:
x = y + z + 6
Substituting the expressions for y and z into the equation for x, we get:
x = (-x - z - 6) + (x + y + 6) + 6
Simplifying, we get:
2x = 0
Therefore, x = 0. Substituting this value into the expressions for y and z, we get:
y = -z - 6
z = y + 6
We have now solved the system and found that:
x = 0
y = -z - 6
z = y + 6
w = 5
We can write the solution as an ordered quadruple:
(0, -6 - z, z, 5)
where z can take on any value. This means that the system has infinitely many solutions, since we can choose any value for z and obtain a corresponding solution for x, y, and w.
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Write an exponential function for the graph that passes through the points (0, –3) and (4, –48)
Answer:
y = (-3)2^x
Step-by-step explanation:
We can substitute the two points in the equation y = abˣ and we get two equations. By solving the two equations, we can find the values of a and b.
Substitute (0, -3) in the equation y = abˣ
-3 = a * b⁰
-3 = a * 1
[tex]\boxed{\bf a = -3}[/tex]
Substitute (4, -48) in the equation y =abˣ
-48 = (-3) * b⁴
[tex]\dfrac{-48}{-3}=b^4\\\\ b^4 = 16\\\\b^4 = 2^4\\\\ \boxed{\bf b = 2}[/tex]
Exponential function:
[tex]y = (-3)2^x[/tex]
Which statement about the function is true?
The function is increasing for all real values of x where
x < 0.
The function is increasing for all real values of x where
x < –1 and where x > 4.
The function is decreasing for all real values of x where
–1 < x < 4.
The function is decreasing for all real values of x where
x < 1.5.
The appropriate choice is for all actual x values of x 1.5, the function is declining.
Define linear polynomialsA linear polynomial is a polynomial of degree one, which means it is a polynomial that has only one variable raised to the power of one and no other variables or exponents.
A function f(x), which is made up of two linear polynomials, is given as follows:
f(x)=(x-4)(x+1)
We now know that when we multiply the two linear polynomials, a quadratic polynomial results.
As a result, the function f(x) will be shown as:
f(x)=x(x+1)-4(x+1)
f(x)=x²+x-4x-4
f(x)=x²-3x-4
In order to determine which claims about the function are accurate, we shall plot the function's graph.
1) The function increases for all real x values greater than zero.
Since we get from the graph that function f(x) is decreasing for x<0.
This statement is false.
2)The function is increasing for all real values of x where x < –1 and where x > 4.
This option is incorrect as the function is decreasing for x<-1
whereas it is increasing for x>4.
3)Where -1 <x<4, the function decrements for all real values of x.
This is the incorrect choice.
Because of the function's dual trend of growing and dropping in the interval (-1,4).
4)For all actual x values of x< 1.5, the function is declining.
This choice is the best one.
since, it is obvious from the graph that the function declines for x<1.5.
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The complete question is;
The graph of the function f(x) = (x – 4)(x + 1) is shown below. Which statement about the function is true? The function is increasing for all real values of x where x < 0. The function is increasing for all real values of x where x < –1 and where x > 4. The function is decreasing for all real values of x where –1 < x < 4. The function is decreasing for all real values of x where x < 1.5.
Find the missing side lengths. Leave your answers as radicals in simplest form.
Answer:
x = y = 10
Step-by-step explanation:
This is a 45-45-90 triangle. This means the values of x and y are equal.
The formula for hypotenuse of this type of triangle s[tex]\sqrt{2}[/tex] where s is the side length.
s[tex]\sqrt{2}[/tex] = 10[tex]\sqrt{2}[/tex]
Therefore, s = 10; x = y = 10.
Note that the side lengths of 45-45-90 triangles are equal because their angles are equal. 45-45-90 triangles are also isosceles right triangles.
The total value of some coins is $1.50. The
coins contain nickels, dimes, and quarters only. The collection must contain at least one of each kind. What is the fewest number of coins possible?
F. 5
G. 6
H. 7
J. 8
K. 9
Answer: J. 8 Coins
Step-by-step explanation: 5 quarters ($1.25 worth), 2 dimes ($0.20 worth ) and 1 nickel ($0.05 worth) is the only way you can get to the value of $1.50 total using 8 coins while using every coin at least once.
each of the small squares in the figure measures 2 meters on each side. what is the area of the triangle?
Answer: you good day
Step-by-step explanation:
What is √-36 in simplest form?
In conclusion √-36 can be simplified to 6i.
How to simplify and what does a square root mean?
The square root of a negative number is not a real number, as any real number squared gives a non-negative result. Therefore, the expression √-36 cannot be simplified in terms of real numbers.
However, in some mathematical contexts, we define the imaginary unit i as √-1. With this definition, we can write:
√-36 = √(36)√(-1) = 6i
Therefore, in this context, √-36 can be simplified to 6i.
In mathematics, the square root of a non-negative real number is a number that, when multiplied by itself, gives the original number. The square root is denoted by the symbol √.
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(1) Jackson deposits $2,000 into a bank account that earns 3.7% interest per year. What is the total amount in the account after 2 years?
(2) Jen deposits $9,500 into a bank account that pays her 4.5% simple interest for 5 years. How much interesrt will she earn over 5 years
Answer:
Question 1) $2150.74
Step-by-step explanation:
100 + 3.7 = 103.7
Divide this by 100 to give you 1.037
Then multiply this by 2,000
$2000 x 1.037^2 = $2150.74
Make sure the square is there to represent the years
This is your answer for 2 years.
A rectangle has a length of 40 cm and width of 21 cm. If a new rectangle is formed by adding the same amount to both the length and width the new area is 2262 cm. Find the dimensions of the rectangle.
Step-by-step explanation:
the area of a rectangle is
length × width.
so, the original area is
40 × 21 = 840 cm²
now, we add x to length and width, and we get :
(40 + x) × (21 + x) = 2262 cm²
let's do the multiplication :
40×21 + 40x + 21x + x² = 2262
840 + 61x + x² = 2262
x² + 61x = 1422
x² + 61x - 1422 = 0
a quadratic equation
ax² + bx + c = 0
has the general solution
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 61
c = -1422
x = (-61 ± sqrt(61² - 4×1×-1422))/(2×1) =
= (-61 ± sqrt(3721 + 5688))/2 =
= (-61 ± sqrt(9409))/2 =
= (-61 ± 97)/2
x1 = (-61 + 97)/2 = 36/2 = 18
x2 = (-61 - 97)/2 = -158/2 = -79
x2 would make the side lengths negative, and that does not make any sense for an actual shape, so
x = 18
is our valid solution.
that means the new length is
40 + 18 = 58 cm
the new width is
21 + 18 = 39 cm
Please help me answer these two questions!!!
2. IN THE ALPHABEIC ORDER IF WE GO A-B SO I THINK ITS 10
Find the distance, d, of AB.
A = (3,7) B=(7,11)
Thus, the distance of the line segment AB for the given coordinates is found as: d = 16√2 units.
Explain about the distance formula:The Pythagorean theorem serves as the foundation for the distance formula. A line connecting two sites of interest is the hypotenuse of the a right triangle, and this particular line connects the two points of interest.
The neighbouring side is obtained by uniting the x-coordinates of both the two points in a horizontal line, whereas the opposing side is obtained by joining the y-coordinates. Let's assume that d is the hypotenuse's length. Given two locations' coordinates, length of both the adjacent side:
(x1,y1) = A(3,7)
(x2,y2) = B(7,11)
[tex]d = \sqrt{(x_{1} - x_{2} )^{2} + (y_{1} - y_{2}) ^{2} }[/tex]
[tex]d = \sqrt{(3 - 7) ^{2} + (7 - 11 ^{2})}[/tex]
[tex]d = \sqrt{16 + 16}[/tex]
d = [tex]\sqrt{32}[/tex]
d = 16√2
Thus, the distance of the line segment AB for the given coordinates is found as: d = 16√2 units.
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Please answer question 15, with diagrams.
The 60 m length of PS and the 21° angle ∠QKR, 41° angle ∠KSR, 17° angle ∠KSR, and the time of flight of 2 minutes, indicates that the distance |PQ| and the aeroplane speed are;
(a) The distance |PQ| is about 2,020.5 meters
(b) The speed of the aeroplane is about 60.6 km·h⁻¹
What is the speed of an object in motion?The speed of an object is a measure of how fast the object is moving, and the unit of speed is the distance per unit time. The speed of an object is the magnitude of the velocity vector of the object.
(a) The direction of flight of the aeroplane = Horizontally
Therefore;
PS = QR
PS = 600 m (the dimension on the diagram)
Therefore; QR = PS = 600 m
QR/KR = tan(21°)
KR = QR/tan(21°)
Therefore;
KR = 600/tan(21°) ≈ 1,563.05
PQ and SR are horizontal segments and PS and QR are vertical, therefore;
PQ ║ SR and PS ║ QR, therefore, quadrilateral PQRS is a parallelogram
PS and QR are vertical therefore, ∠PSR and ∠QRS are 90° angles, (definition of vertical segment PS is perpendicular to the horizontal segment segment SR)
Therefore, the parallelogram PQRS is a rectangle (Properties of a rectangle)
PQ ≅ SR (Facing sides of a rectangle)
∠SKR = 180° - (41° + 17°) = 122°
∠SKR = 122°
KR/sin(41°) = SR/sin(122°)
SR = sin(122°) × KR/sin(41°)
SR = sin(122°) × KR/sin(41°)
SR = sin(122°) × 1,563.05/sin(41°) ≈ 2,020.5
SR = PQ ≈ 2,020.5
|PQ| = 2,020.5 meters(b) The aeroplane flies from P to Q in 2 minutes
The conversion of the units are obtained as follows;
2,020.5 meters = 2.0205 km
1 minutes = (1/60) hour, therefore, 2 minutes = (2/60) hour = (1/30) hourThe time of 2 minutes = 120 seconds, therefore;
The speed of the aeroplane ≈2.0205 km/((1/30) h) ≈ 60.6 km·h⁻¹Learn more on distance, speed and time here: https://brainly.com/question/4931057
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*Algebra 1
Give the domain and range of each question. Tell whether the relation is a function or not and explain.
The relations that are functions are the ones in options 12 and 13
which ones of the relations are functions?A relation is a function only if each one of the inputs is mapped to a single one output, so if you see a relation where the same input is mapped into different outputs, this is not a function.
Then the relations that are functions are options 12 and 13, in the other two we can see that there are multiple outputs for the same inputs.
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Please solve the following
For the given graph of the function: Period = π, Domain = [0,π], Range = (-∞, + ∞), Asymptotes at x = 0.
Explain about the period of function:Period:
A function is referred to as periodic if it repeats a pattern, such as sine or cosine. The shortest interval with exactly one instance of the repeating pattern is said to have a period, which is its length.
Period = π
Domain:
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x).
Domain = [0,π]
Range:
A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values.
Range = (-∞, + ∞)
Asymptotes:
The graph of the a function approaches an asymptote as either x or y approach positive or negative infinity, respectively.
Asymptotes at x = 0.
As a result, whenever x = 0, the function possesses a vertical asymptote.
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the radius of a scooter wheel is 14cm how many revolutions does the wheel make if the scooter travels 4.4km
If the scooter travels 4.4km with the given radius, the wheel have number of revolutions about 1567 times.
In order to solve this issue, we must first determine the scooter wheel's circumference, which is given by the formula C = 2[tex]\pi[/tex]r, where r is radius of the wheel. Hence, the circumference of a wheel with a 14 cm radius would be:
C = 2[tex]\pi[/tex](14cm) = 28[tex]\pi[/tex] cm
We must translate the distance from kilometres to centimetres in order to determine how many revolutions the wheel completes if the scooter travels 4.4 kilometres. 1 km equals 100,000 cm, so 4.4 km is equal to 440,000 cm.
Now, we can calculate the number of rotations by dividing the distance travelled by the wheel's circumference:
Distance travelled divided by circumference equals the number of revolutions.
440,000 cm / 28 cm divided by the number of revolutions
1566.99 revolutions were made.
Therefore if the scooter travels 4.4km, the wheel will turn about 1567 times.
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5x + 1 over 4 y2
What is the value of the expression above when x = 3 and y = 2? You must show all work and calculations to receive full credit. (4 points)
Answer:
1
Step-by-step explanation:
5x + 1 / 4y²
5(3) + 1 / 4(2)²
15 + 1 / 4(4)
16 / 16 = 1
Solve the following question
cot θ = 7/4 and θ in degrees = 29.744881 degrees. In this case, the adjacent side is 7 and the opposite side is 4.
What is cot?Cotangent (cot) is the ratio of the adjacent side to the opposite side of a right triangle.
In this right angle triangle, cot θ can be calculated using the formula
cot θ = adjacent/opposite.
In this case, the adjacent side is 7 and the opposite side is 4.
Therefore, cot θ = 7/4.
Now, to find theta in degrees, we can use the inverse cotangent function, arccot.
arccot (cot θ) = θ.
Therefore, θ = arccot (7/4).
Using a calculator, arccot (7/4) = 29.744881 degrees
Therefore, cot θ = 7/4 and θ in degrees = 29.744881 degrees.
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Suppose you will need $12,000 in 3 years. How much do you need to invest per month in order to have $12,000 if money earns an annual rate of 6% compounded monthly?
Assumptions for above case:
1-Equal payments are made monthly.
2-Total amount deposited throughout the year are compounded by end of the year.
3-Annual interest is 6%
4-Total Amount invested plus interest at maturity are reinvested the following year.
Given above, if you create a table in excel for those calculations, you would get $296.330 /month which amounts to $12,000.00 in 3 years approximately.
Year 1 = $3,555.96 Pre-interest =>$3769.32 Post 6% interest
Year 2 = $7,325.28 Pre-interest =>$7,325.28 Post 6% interest
Year 3= $11,320.75 Pre-interest =>$12,000.00 Post 6% interest.
The way to calculate pre interest for each year is just $296.330*12=$3555.96
Afterwards just multiply by the annual interest rate to get the full amount invested + interest (6%) =>$3555.96*(1.06)= $3769.32
Then As per step 1, add another 3555.96 and multiply it all by 1.06, to get 305.06
x = $305.06
Question: 6982×283
Im stuck on this question
If you jave na answer please write it
Thanks you!
Answer:
1,975,906
Step-by-step explanation:
Answer:
The answer is 1975906
Explanation:
If you pick up a Calculator and you input this on it It will give you the answer if u don't have a calculator search on the internet how to multiply numbers
help pls show ur work
The missing variables of the triangle is given as follows:
17.) X=20
18.) X= 32
19) X = 31
20) X= 149
21) X= 125
22.) X= 10
23.) X= 13
How to calculate the missing parts of the triangle?To calculate tye variables the formula SOHCAHTOA is used.
For question 17.)
The adjacent of the triangle = 14
The hypotenuse of the triangle = X
The given angle = 45°
Therefore Cos ∅ = 14/X
X = 14/cos∅
X = 14/0.707106781
X = 20( approximately)
For question 18.)
The opposite of the triangle = x
The hypotenuse of the triangle = 45
The given angle = 45°
Therefore sin ∅ = opposite/hypotenuse
sin 45° = X/45
X = sin45°×45
X = 0.707106781×45
X = 32 (approximately)
For question 19.)
The opposite of the triangle = 22
The hypotenuse of the triangle = x
The given angle = 45°
Therefore sin∅ = opposite/hypotenuse
sin45° = 22/X
X= 22/0.707106781
X= 31
For question 20.)
The opposite of the triangle = x
The hypotenuse of the triangle = 210
The given angle = 45°
Therefore sin ∅ = opposite/hypotenuse
sin45° = X/210
X= 0.707106781×210
X= 149 (approximately)
For question 21.)
The opposite of the triangle = 88
The hypotenuse of the triangle = x
The given angle = 45°
Therefore sin ∅ = opposite/hypotenuse
sin∅ = 88/X
X= 88/0.707106781
X= 125(approximately)
For question 22.)
The opposite of the triangle = 5√2
The hypotenuse of the triangle = x
The given angle = 45°
Therefore sin ∅ = opposite/hypotenuse
Sin∅= 5√2/X
X= 7.071067811/0.707106781
X= 10
For question 23.)
The opposite of the triangle = 9
The hypotenuse of the triangle = x
The given angle = 45°
Therefore sin ∅ = opposite/hypotenuse
Sin∅ = 9/X
X = 9/0.707106781
X = 13(approximately)
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If you get the answer correct ill give brainliest and thanks :))
Answer:
B.
Step-by-step explanation:
Just pick a point on the graph like F
( -1, 3)
(-5,-4)
so its -4 for x and -7 y
How many total workers are needed to ship 110,550 units for the shift
Answer: 402 is the workers should be picking in order to ship 110,550 units for the shift. Hence, option E is correct.
Step-by-step explanation:
A laptop computer is purchased for $1450. After each year, the resale value decreases by 25%. What will the resale value be after 4 years?
Answer:
see step by step
Step-by-step explanation:
so a laptop starts at 1450 this means the equation is
y=1450(0.75)^x and plug in 4 for x and you get $458.79
Ms. Hernandez writes this expression on the board. 1/2 divide by 3 1/6
Answer:
[tex] \frac{1}{2} \div 3 \frac{1}{6} [/tex]
[tex] \frac{1}{2} \div \frac{19}{6} = \frac{1}{2} \times \frac{6}{19} = \frac{3}{19} [/tex]
The answer is 3/19.
right triangle abc has area 32square root 3 cm squared. the measure of the angle a =30.
The length of BC is 16cm, the length of AB is 8√3cm, and the length of AC is 8cm. In a right triangle, the side opposite the right angle is the hypotenuse, while the other two sides are the legs.
Let's label the sides of the triangle ABC as follows:
BC is the hypotenuse, opposite to the right angle at B.
AB is a leg, adjacent to the angle A.
AC is a leg, opposite to the angle A.
Given that the area of the triangle is 32√3cm^2, we have:
(area) = (1/2) x (base) x (height)
Substituting the values we know, we get:
32√3 = (1/2) x AB x AC
Simplifying, we get:
AB x AC = 64√3
We also know that <A = 30 degrees, which means that <C = 60 degrees (since the angles in a triangle add up to 180 degrees).
Now we can use the trigonometric ratios to find the lengths of the sides. We have:
sin(30) = AC/BC
cos(30) = AB/BC
Solving for AC and AB, we get:
AC = BC x sin(30) = BC/2
AB = BC x cos(30) = BC√3/2
Substituting these values into the equation we got earlier, we get:
(BC/2) x (BC√3/2) = 64√3
Simplifying, we get:
BC^2 = 256
Taking the positive square root, we get:
BC = 16
Substituting this value into the equations we got for AB and AC, we get:
AB = BC√3/2 = 8√3
AC = BC/2 = 8
Therefore, the length of BC is 16cm, the length of AB is 8√3cm, and the length of AC is 8cm.
The complete question is:
right triangle ABC has area 32√3cm^2. The measure of <A = 30, m<B=90. What is the length of BC? AB? AC? Express all answers in simplest radical form.
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