The equation (in slope-intercept form) of the line passing through the points (5,3) and (4,1) is y = 2x -7
How to find equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + c
where
m = slope of the linec = y-interceptlet's find the slope as follows:
(5, 3)(4, 1)
m = 1 - 3 / 4 - 5
m = - 2 / -1
m = 2
Therefore, let's find the y-intercept using (4, 1)
y = 2x + c
1 = 2(4) + c
c = 1 - 8
c = -7
Therefore, the equation of the line is y = 2x -7
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If anyone could take some time and look at the photo and explain a little bit? Thank you I’m grateful for the help :)
Answer:
C= 31in
Step-by-step explanation:
First you must know the circumference equation. The circumference equation is C=2πr, with r being the radius. Since we are given the radius, we will fill in the radius given for r. So then we will fill in and solve:
C=(2)(π)(5in)
C=(10)(π)
C=31.4in...
C=31in
Hope this helps!
Organic sugar used to be sold at a bulk price of $5 per pound. The price was recently increased by 20%. What is the current price per pound?
please helpp
Answer:
$6
Step-by-step explanation:
5 x 0.20=1
5+1=6
Solve for x and y . Special right triangle lesson
Answer:
hope this helps!!!
Help I know the answer just need to know that it is correct
what the question............
Your teacher will grade your responses to questions 4–8 to ensure you receive proper credit for your answers.
A carpenter cut the top section of a window frame with a 37º angle on each end. The side pieces each have a 50º angle cut at their top ends, as shown. Will the side pieces of the frame be parallel? Explain. Diagram not to scale.
SOMEONE PLEASE HELP ME!
Based on the given parameters about a carpenter cutting the top section of a window frame, the side pieces of the frame are not parallel.
How to show that the side pieces of the frame are parallel?Parallel lines are lines which are equally distant from one another at all points.
To show that the side pieces of the frame are parallel:
The interior angles are equal in measure and the sum of the interior angles must be equal to 180°
The two given side pieces of the window frame are also equal in measure.
If the sum of both side angles is equal to 180∘, then, the sides are parallel.
Adding one side of the interior angle:37∘ + 50∘ = 87∘
Adding both sides of the angle:2(37∘ + 50∘)
= 2(87∘)
= 174∘
Hence,
174∘ < 180∘
So therefore, the sides pieces of the window frame cut by the carpenter are not parallel.
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mary invests 12500 in savings rate of 1.5 percent for 2 years
Answer:The question is very brief, im not sure if i understand what your asking
Step-by-step explanation:
Consider the equation and the following ordered pairs: (1,y) and (x,3).
6x+1.2y=−2.4
The value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
We have to find the values of the variable in the given ordered pairs: (1,y) and (x,3).
Equation is 6x + 1.2y = −2.4
For ordered pairs: (1,y)
6(1)+1.2y =-2.4
1.2y=-8.4
y=-7
For Pair (x,3)
6(x)+1.2(3) =-2.4
6x = -6
x=-1
Hence, the value of the variable in the given ordered pairs: (1,y) and (x,3) are x = -1 and y = -7.
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Find a degree 3 polynomial with real coefficients having zeros 3 and 4 i and a lead coefficient of 1. Write P in expanded form. Be sure to write the full equation, including P ( x ) = .
Answer:
[tex]P(x)=x^3-3x^2+16x-48[/tex]
Step-by-step explanation:
Given information:
Polynomial function with real coefficients.Zeros: 3 and 4iLead coefficient of 1.For any complex number [tex]z=a+bi[/tex], the complex conjugate of the number is defined as [tex]z^*=a-bi[/tex].
If f(z) is a polynomial with real coefficients, and z₁ is a root of f(z)=0, then its complex conjugate z₁* is also a root of f(z)=0.
Therefore, if P(x) is a polynomial with real coefficients, and 4i is a root of f(x)=0, then its complex conjugate -4i is also a root of P(x)=0.
Therefore, the polynomial in factored form is:
[tex]P(x)=1(x-3)(x-4i)(x-(-4i))[/tex]
[tex]P(x)=(x-3)(x-4i)(x+4i)[/tex]
Expand the polynomial:
[tex]P(x)=(x-3)(x^2+4ix-4ix-16i^2)[/tex]
[tex]P(x)=(x-3)(x^2-16(-1))[/tex]
[tex]P(x)=(x-3)(x^2+16)[/tex]
[tex]P(x)=x^3+16x-3x^2-48[/tex]
[tex]P(x)=x^3-3x^2+16x-48[/tex]
Vonna scored 48 goals in her soccer kicking practice. If her success-to-failure rate was 3:2, how many times did she attempt a goal?
The number of attempts Vonna made is 80.
Given,
Vonna scored 48 goals in her scoccer kicking practice.
Her success to failure rate is 3:2
Vonna scored 48 goals" means that there were 40 successes,
= 48 goals
= 3:2
= 48:3
= 16
x = 6 positive integer
hence let 3x:2x
= 3(16) = 48
= 2(16) = 32
Total attempts = 48+32
= 80
Hence the total number of attempts Vonna made is 80.
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Eleanor and Luke started on a trip to the mountains with their six-year old car. Their
odometer read 87,236.2 miles at the start of the trip and 87,626.2 miles at the end of the trip.
They used 14.5 gallons of gas on the trip. How many miles per gallon did they achieve with
their car?
They achieved 26.9 miles per gallon approximately with that car in this trip.
Given that the initial odometer reading is = 87236.2 miles
Final odometer reading after trip is = 87626.2 miles
So the distance of the total trip is = 87626.2-87236.2 = 390 miles
They used 14.5 gallons of gas on the tri[p.
So the mileage is = 390/14.5 = 26.9 miles per gallon approximately.
Their car achieved 26.9 miles per gallon approximately.
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Solve the following equation. 8x-6=10
Answer:
x = 2
Step-by-step explanation:
8x - 6 = 10 ( add 6 to both sides )
8x = 16 ( divide both sides by 8 )
x = 2
Answer:
x = 2
Step-by-step explanation:
8x-6 = 10
8x-6+6 = 10+6
8x = 16
8x/8 = 16/8
x = 2
x -1 , 3, 7 , 11 and y 3, 6, 10, 15 is the relationship linear, exponential, or neither
Answer:
Yes i the relationship linear,exponential,or neither
What sentence represents this equation?
8 3/4=17−x
The sentence that represents this equation 8 3/4 = 17 - x is B) 8 3/4 is the same as 17 decreased by a number.
What is an equation?An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.
It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
In this case, 8 3/4 is the same as 17 decreased by a number will be 8 3/4=17−x.
Therefore, the correct option is B.
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Complete question
What sentence represents this equation?
8 3/4 = 17 - x
A) A number is the same as the difference of 17 and 8 3/4.
B) 8 3/4 is the same as 17 decreased by a number.
C) 17 decreased by 8 3/4 is the same as a number.
D) 8 3/4 is the same as a number decreased by 17.
Determine an nth degree polynomial that satisfies the aforementioned conditions.
The polynomial of p(x) is -24 (x² + 15x + 54) with the satisfying's conditions degree 3.
Given,
An nth degree polynomial p meets the requirements listed below:
p is of degree 3.
-9 is a zero, with multiplicity 2, of p.
-6 is a zero, with multiplicity 1, of p.
p(-1) = -960
We have to determine an nth degree polynomial that satisfier the conditions.
Let the polynomial be p(x) whose zero are -9 and -6
a be the coefficient.
p(x) = a (x+9) (x+6)
p(x) = a(x² + 6x + 9x + 54)
p(x) = a(x² + 15x + 54)
Now, take x = -1
p(-1) = a (-1² + 15 x -1 + 54)
-960 = a ( 1 - 15 + 54)
-960 = a x 40
a = -960/40
a = -24
We get,
p(x) = -24 (x+9) (x+6)
p(x)= -24 (x² + 15x + 54)
Therefore, the polynomial of p(x) is -24 (x² + 15x + 54) with the satisfying's conditions degree 3.
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complete the missing numbers, please .
The cost of the sweater is $ 30 and
1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos.
Mathematical Operations:Mathematical Operations are activities or mathematical processes used to solve given problems. The most used mathematical activities are adding, subtracting, multiplying, and dividing.
The basic operations and their symbols are given below
Addition (+); Subtraction (-); Division (÷); and Multiplication (x).
Here we have
Priya exchanged 250 dollars for 4250 pesos
[Here we used division and multiplication to solve the problem ]
Then the value of 1 dollar in pesos = [tex]\frac{4250}{250}[/tex] = 17 pesos
⇒ 1 dollar = 17 pesos
⇒ 25 dollars = 25 × 17 = 425 pesos
⇒ 3 dollar = 3 × 17 = 51 pesos
Given the cost of the sweater = 510 pesos
The cost of the sweater in pesos = [tex]\frac{250}{4250} \times510[/tex] = 30
Therefore,
The cost of the sweater is $ 30 and
1 dollar = 17 pesos, $ 25 = 425 pesos and $ 3 dollar = 51 pesos
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Determine whether the series converges or diverges
Please, check the image
The series as represented in the task content is divergent and hence; diverges.
What convergence and divergence in series?It follows from the task content that the series defined by the summation expression as represented above is to be identified as divergent or convergent.
It is noteworthy to know that;
If a sequence converges, it means that the limit of the sequence exists as n → ∞. Also, if the limit of the sequence as n → ∞ does not exist, Then, such series is said to diverges.
Therefore, by evaluation as the limit of the expression k sin²k / 1 + k³ as k → ∞ is; Undefined and hence does not exist.
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Given a quadratic function in vertex form:
a) A vertical stretch happens for values of a such that |a| > 1.
b) A vertical compression happens for values of a such that |a| > 0.
c) For a vertical stretch, the graph increases vertically, and for a vertical compression, the graph increases horizontally.
d) A reflection across the x-axis takes place when a < 0.
How to obtain the transformations?The definition of the quadratic function is given as follows:
f(x) = a(x - h)² + k.
The transformations to the function are given as follows:
Vertical stretch: multiplication of the function by a value with absolute value greater than 1, hence |a| > 1, increasing the graph vertically.Vertical compression: multiplication of the function by a value with absolute value less than 1, hence |a| < 1, increasing the graph horizontally.Additionally, for a reflection over the x-axis, the function is multiplied by a negative number, hence:
a < 0.
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what is the kinetic energy of a 158 kg Green Sea Turtle swimming at 0.42 m/s? With work shown
Kinetic energy is defined as the work required to accelerate a body of a given mass from rest to its stated speed. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes.
Mass - (Measured in Kilogram) - Mass is the amount of matter in a body, regardless of its volume or the forces acting on it.
Velocity - (Measured in Meters per Second) - Velocity is a vector quantity (has both magnitude and direction) and is the rate of change of an object's position with respect to time.
What is the kinetic energy of a 158 kg Green Sea Turtle swimming at 0.42 m/s? With work shownWe have that the data is:
m = 150 kgv = 0.42 m/sThe formula to calculate kinetic energy is:
Ec = m * v²/2
Since it only asks us to calculate the kinetic energy, it is not necessary to clear the formula.
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*\left(0.42 \ \frac{m}{s}\right)^2 }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=\dfrac{158 \ kg*0.1764 \ \frac{m^2}{s^2} }{2} }}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ kg*\dfrac{m^2}{s^2} }}[/tex]
We work with the units, in this case with m^2 = m*m.
[tex]\boldsymbol{\sf{Ec=13.9356 \boxed{\boldsymbol{\sf{Kg*\frac{m}{s^2} }}}*m }}[/tex]
Newton's units are: Kg*m/s^2.
[tex]\boldsymbol{\sf{Ec=13.9356 \ N*m \longmapsto Joule \ units=N*m}}[/tex]
[tex]\boldsymbol{\sf{Ec=13.9356 \ J}}[/tex]
The kinetic energy (E) of a body with mass m = 158 kilograms and speed v = 0.42 m/s is equal to 13.9356 JBut if you need the rounded answer, then 13.94 Joules.
The equation of line L1, is y=5x+1
The equation of line L2, is 2y-10x+3=0
Answer:
y = 5x + 1
y = 5x + [tex]\frac{-3}{2}[/tex]
When the slopes are the same (5) the equations are parallel.
Step-by-step explanation:
You can look at the graph of the two equaions attached to see that there paralle.
2y - 10x +3 = 0 Add 10 to both sides of the equation
2y -3 = 10x Add three to both sides of the equation
2y = 10x -3 Divide all the way through by 2
y = 5x + [tex]\frac{-3}{2}[/tex]
1.
Find the values of the sine, cosine, and tangent for
It depends on how accurate you want to be, but two straight lines between 0° and 30° and 30° and 90° will not be too bad for Sine.
Thus for angles less than 30°
sinx≈x/60
and for angles greater than 30°
sinx≈(30+x)/120
For Cosine you use the identity
cosx=sin(90−x)
And for Tangent you use the identity
tanx=sinxcosx
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Suppose that you borrow $17,000 for five years at 6% toward the purchase of a car. Find the monthly payments and the
total interest for the loan.
The monthly payment is $
The amount of the monthly payments is $368.34, and the total interest on the loan is $5,100.
The initial amount of money that we borrow is $17,000. We borrow this amount for a total of five years. The interest charged is 6%. We borrowed the money for the purchase of a car. We need to find the monthly payments and the total interest for the loan.
Let the total amount to be paid and the interest be denoted by the variables "A" and "I", respectively.
I = P*R*T
I = $17,000*0.06*5
I = $5,100
The total amount of money to be paid is the sum of the initial amount and the interest charged.
A = P + I
A = $17,000 + $5,100
A = $22,100
The total number of months in five years is 12*5 = 60.
The amount of the monthly payment is the ratio of the total amount to be paid to the total number of months.
M = $22,100/60
M = $368.34
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The top face of the latest music player measures 4.33 inches by 1.54 inches. Find the perimeter of the rectangular face.
Answer: 11.74
Step-by-step explanation:
4.33+4.33+1.54*1.54+11.74
A rectangle has two pairs of equal sides.
The table shows telephone charges for different companies. Which table shows a linear relationship between length of call and the cost
Answer: they both go up in cents by 5s. they may not be only five but five's. Therefore, they are adding by 5s and that is the linear relationship
Step-by-step explanation:
To solve the system of equation below zach isolated X^2 in the first equation and then substituted into the second equation. What was the resulting equation
{x^2 + y^2 = 25
{x^2/16 - y^2/9 = 1
The resulting equation of isolation and substitution is 9y⁴-466 y² + 5481 = 0
How to get the resulting equation?
Given:
{x² + y² = 25
{x²/16 - y²/9 = 1
Zach isolated x² in the first equation, we have:
x² + y² = 25
x² = 25- y²
Zach then substituted the x² into the second equation:
x²/16 - y²/9 = 1 (put x² = 25- y²)
(25- y²)²/16 - y²/9 = 1 (Expand the bracket)
(625- 50y²+y⁴)/16 - y²/9 = 1 The LCM of 9 and 16 is 144
( 9(625- 50y²+y⁴) - 16 y² ) /144 = 1 Cross multiply
9(625- 50y²+y⁴) - 16 y² = 144
5625 - 450y² + 9y⁴-16 y² = 144
9y⁴-466 y² + 5625 = 144
9y⁴-466 y² + 5625-144 = 0
9y⁴-466 y² + 5481 = 0
Therefore, the resulting equation is 9y⁴-466 y² + 5481 = 0
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The Singapore Navy acquired 4 Swedish- build Sjoormen class submarine to beef up its defence capabilities in the late 1990s. The submarine is capable of attaining a top speed of 16 knots (nautical miles per hour) when submerged. Convert 16 knots to (a) km/h (b) m/s. (Take 1 nautical mile to be 1 853 m.)
The speeds when converted are 29.648 km/h and 8.24 m/s
How to convert the units of speed?From the question, we have the following parameters that can be used in our computation:
Speed = 16 knots
Also, from the question, we have
1 nautical mile to be 1853 m
This means that
Speed = 16 * 1853 m per hour
Convert meters to kilometers
So, we have
Speed = 16 * 1.853 km per hour
Evaluate the products
Speed = 29.648 km/h
Also, we have
Speed = 16 * 1853 m per hour
Convert hour to seconds
So, we have
Speed = 16 * 1853/3600 m/s
Evaluate
Speed = 8.24 m/s
Hence, the speed in m/s is 8.24 m/s
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A car dealership increased the price of a certain car by 6%. The original price was $33,600.
(a) Fill in the blank to write the new price in terms of the original price.
Write your answer as a decimal.
New Price = blank * Original Price
(b) Use your answer in part (a) to determine the new price.
The new price for the car when there's an increase of 6% is $35616.
How to calculate the new price?Given that the dealership increased the price of a certain car by 6% and the original price was $33,600.
The new price will be:
= Original price + Increase in price
= $33600 + (6% × $33600)
= $33600 + $2016
= $35616
The new price is $35616.
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Which is the graph of f(x) = 3 sqrt 3
Answer: I think it’s the first one.
Step-by-step explanation:
A chemical company mixes pure water with their premium antifreeze solution to create an inexpensive antifreeze mixture. The premium antifreeze solution contains 60% pure antifreeze. The company wants to obtain 180 gallons of a mixture that contains 35% pure antifreeze. How many gallons of water and how many gallons of the premium antifreeze solution must be mixed?
The gallons of water and premium antifreeze solution that must be mixed are equal to 60 gallons and 120 gallons respectively.
How to determine the gallons of water and premium antifreeze solution?In order to calculate the gallons of water and premium antifreeze solution, we would assign variables to the gallons of water and premium 60% antifreeze that is required, and then translate the word problem into algebraic equation as follows:
Let the variable x represent the gallons of water.Let the variable y represent the premium 60% antifreeze.Since the premium antifreeze solution contains 60% premium antifreeze, we have the following mathematical expression:
x + y = 180 ....equation 1.
0.60y = 0.40(180) ....equation 2.
From equation 2, we have:
0.60y = 0.40(180)
0.60y = 72
y = 72/0.60
y = 120 gallons of premium antifreeze.
For the gallons of water, we have the following:
x + y = 180
x = 180 - y
x = 180 - 120
x = 60 gallons of water.
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-7) El promedio de 3, 8, 9 y 12 es 8.
a) O Cierto
b)
Falso
Previous
El promedio de los números enteros 3, 8, 9 y 12 es igual a 8. (Opción correcta: Cierto)
¿Cómo determinar el promedio de un conjunto de datos?
En este problema tenemos un conjunto de cuatro números enteros positivos, del cual debemos comprobar si el promedio uniforme es igual a 8. El promedio uniforme es definido por la siguiente operación:
[tex]\bar {x} = \frac {1}{n} \cdot \sum \limits_{i = 1}^{n} x_{i}[/tex]
Donde:
[tex]\bar x[/tex] - Promedio uniforme del conjunto de datos.n - Cantidad de elementos del conjunto de datos. [tex]x_{i}[/tex] - Elemento i-ésimo del conjunto de datos.Si sabemos que n = 4, x₁ = 3, x₂ = 8, x₃ = 9 y x₄ = 12, entonces el promedio uniforme del conjunto de datos es:
[tex]\bar {x}[/tex] = (3 + 8 + 9 + 12) / 4
[tex]\bar x[/tex] = 8
El promedio del conjunto de datos, correspondiente a los números enteros positivos 3, 8, 9 y 12, es igual a 8.
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you are making purple paint in the ratio of 2 cups blue paint to 1/4 cups of red paint use the information in the table to complete the rest of the table
The table to show the number of cups for the colors will be:
Red cups Blue cups
1. 8
2. 16
3. 24
How to illustrate the information?Given that the person is making purple paint in the ratio of 2 cups blue paint to 1/4 cups of red paint.
Therefore, for every 1 cup of red paint, the number of blue paint will be:
= 2 ÷ 1/4
= 2 × 4
= 8 cups
Therefore, to get other values, you simply have to multiply by 8.
2 red paint will be:
= 2 × 8
= 16 blue cups.
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