The equation of the line that has a slope of 1/3 and passes through the point (-2, 1) is y = 1/3x + 5/3.
Explanation:The subject of this question is the representation of a line in the form of an equation, specifically a line that has a slope of 1/3 and passes through a given point, (-2, 1). We can use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Substituting the given values, we have y - 1 = 1/3(x - (-2)). Or simplified to y - 1 = 1/3(x + 2). From here, we can rearrange this into slope-intercept form (y = mx + b) by distributing the 1/3 to x and 2, thus giving us y = 1/3x + 2/3 + 1. Finally, simplifying the equation gives y = 1/3x + 5/3, which is the equation of the line that has a slope of 1/3 and passes through the point (-2, 1).
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What is 62 divided by 5,841
Answer:
5,841 divided by 62 is 94.2
Identify the vertex, the axis of syn
y = x2 + 8x + 16
The vertex is
. (Type an ordere
What is the min and max porabala
Good evening ,
Answer:
Vertex (-4 , 0)
axis x = -4
It’s a parabola.
Min = 0
Step-by-step explanation:
x2 + 8x + 16 = (x + 4)².
the product of a 3x3 and a 6x6 matrix would be
54 54 54
54 54 54
54 54 54
Solve x2 + 2x = 4 for x by completing the square. x equals plus or minus square root of 5 plus 1 x equals plus or minus square root of 5 minus 1 x = 1 x = 3
Answer:
x equals plus or minus square root of 5 minus 1
Step-by-step explanation:
we have
[tex]x^{2} +2x=4[/tex]
Divide by 2 the coefficient of the x-term
[tex]2/2=1[/tex]
squared the number
[tex]1^2=1[/tex]
Adds both sides
[tex]x^{2} +2x+1=4+1[/tex]
[tex]x^{2} +2x+1=5[/tex]
Rewrite as perfect squares
[tex](x+1)^{2}=5[/tex]
take the square root both sides
[tex]x+1=(+/-)\sqrt{5}[/tex]
[tex]x=(+/-)\sqrt{5}-1[/tex]
therefore
x equals plus or minus square root of 5 minus 1
Answer - B. x = ± [tex]\sqrt{5[/tex] - 1
I don’t know where to start with this problem
Answer:
√(4/5)
Step-by-step explanation:
First, let's use reflection property to find tan θ.
tan(-θ) = 1/2
-tan θ = 1/2
tan θ = -1/2
Since tan θ < 0 and sec θ > 0, θ must be in the fourth quadrant.
Now let's look at the problem we need to solve:
sin(5π/2 + θ)
Use angle sum formula:
sin(5π/2) cos θ + sin θ cos(5π/2)
Sine and cosine have periods of 2π, so:
sin(π/2) cos θ + sin θ cos(π/2)
Evaluate:
(1) cos θ + sin θ (0)
cos θ
We need to write this in terms of tan θ. We can use Pythagorean identity:
1 + tan² θ = sec² θ
1 + tan² θ = (1 / cos θ)²
±√(1 + tan² θ) = 1 / cos θ
cos θ = ±1 / √(1 + tan² θ)
Plugging in:
cos θ = ±1 / √(1 + (-1/2)²)
cos θ = ±1 / √(1 + 1/4)
cos θ = ±1 / √(5/4)
cos θ = ±√(4/5)
Since θ is in the fourth quadrant, cos θ > 0. So:
cos θ = √(4/5)
Or, written in proper form:
cos θ = (2√5) / 5
What is the slope of the line?
Answer:
[tex]\displaystyle 2[/tex]
Step-by-step explanation:
Starting from the y-intercept of [tex]\displaystyle [1, 1],[/tex]you do [tex]\displaystyle \frac{rise}{run}[/tex]by either moving two blocks south over one block west or two blocks north over one block east [west and south are negatives]. Doing this will give you the equation below:
[tex]\displaystyle y = 2x + 1[/tex]
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How are the graphs of the functions f(x) = 16and g(x) = 3/64"related?
Answer:
The graphs of the functions are both straight lines and parallel to x-axis
Step-by-step explanation:
The graph of f(x) is the line y = 16 which is parallel to x-axis.
This is because for every value of x the function f(x) only takes the value 16
Similarly the graph of g(x) is also a straight line but is characterized by y = 3/64. This line is also parallel to the x-axis.
For every value of x the function g(x) only takes the value 3/64
Given the function y = 1/2x - 1
Find and plot the points for x = -4, X = 2, and x = 6
please show me the graph
Answer:
Step-by-step explanation:
if y = 1/2x - 1 is the function
y = 1/2(-4) - 1
y = -2 - 1
y = -3
(-4, -3)
y = 1/2(2) -1
y = 1 - 1
y = 0
(2, 0)
y = 1/2(6) - 1
y = 3 - 1
y = 2
(6, 2)
the pictures should be in order
Answer:
[tex]\displaystyle 2 = f(6), 0 = f(2), -3 = f(-4)[/tex]
Step-by-step explanation:
[tex]\displaystyle \frac{1}{2}[6] - 1 = 3 - 1 = 2 \\ \\ \frac{1}{2}[2] = 1 - 1 = 0 \\ \\ \frac{1}{2}[-4] - 1 = -2 - 1 = -3[/tex]
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the child weighs 55 lbs. Calculate the child’s weight in pounds to kilograms
Which expressions are equivalent to 6^-10 6^-8
Answer:
The equivalents are 1/6¹⁰ and 1/6⁸
Step-by-step explanation:
1. Let's recall the rule about the negative exponents to find the equivalents to the expressions provided:
The rule says that any number different than zero, raised to a negative power equals its reciprocal raised to the opposite positive power.
Thus, x ⁻ⁿ = 1/x ⁿ
2. Now, let's find the equivalents after following the rule:
6 ⁻ ¹⁰ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ¹⁰
6 ⁻ ⁸ = 1 ÷ 6 * 6 * 6 * 6 * 6 * 6 * 6 * 6 = 1/6 ⁸
Mr. Milligan bought a puppy for $287 and
sold him for $324. Find his gross profit.
How much money did he have
Answer:
His profit would be $37 of the money he got back.
Step-by-step explanation:
Darren has a piece of wood that is 7 in by 8 in. Explain how he could divide this large rectangle into smaller rectangles
The rectangle can be divided into 6 ways as, 1 × 56 or 56 × 1, 2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.
What is rectangle?An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel, opposite sides. Since a rectangle is a two-dimensional form, it has two dimensions: length and width. The rectangle's longer side is its length, while its shorter side is its breadth.
Given:
Darren has a piece of wood that is 7 in by 8 in
The area of the rectangle can be given by,
[tex]Area = Length\times width[/tex]
Area = 7 × 8
Area = 56
You can now divide the length and width as shown below,
Rectangle = 1 × 56 or 56 × 1
Rectangle = 2 × 28 or 28 × 2
Rectangle = 4 × 14 or 14 × 4
Therefore, the rectangle can be divided into 6 ways as 1 × 56 or 56 × 1, 2 × 28 or 28 × 2, and 4 × 14 or 14 × 4.
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solve quadratic equation using factoring
z^2-5z+4=0
Answer:
[tex]z^2-5z+4=(z-4)(z-1)[/tex]
Step-by-step explanation:
To factorize a cuadratic equation, one must use the well known formula to find the roots of the equation: [tex]\frac{-b(+-)\sqrt{b^2-4ac} }{2a}[/tex], where a (a=1) is the coefficient that accompanies the cuadratic term, b is the coefficient that accompanies the linear term (b=-5) and c is the constant (c=4).Then, applied to this specific case, the previous formula results: [tex]\frac{5(+-)\sqrt{(-5)^2-4\times{1}\times{4}} }{2\times1}[/tex]. Then, the two roots of the equation come from [tex]\frac{25(+-)\sqrt{9} }{2}[/tex].Consecuently, [tex]z_1=\frac{5+\sqrt{9}}{2} =4[/tex], and [tex]z_2=\frac{5-\sqrt{9}}{2} =1[/tex].Finally, the cuadratic function can be expressed like this: [tex](z-4)(z-1)[/tex] (which comes from the fact that any polynomial can be expressed as the product of [tex](x-x_i)[/tex], where i are the roots of the polynomial). To corroborate that the procedure is correct, you can resolve this product, and you will obtain the inicial expression.2. When Mrs. Romano was pricing cans of tomato sauce, she noticed the following prices.
1 can (28 ounces) cost $1.89
1 can (32 ounces) costs $2.95
Which is the better deal?
need to know the unit rate too please.
Answer:
28 oz can is the better deal.
Step-by-step explanation:
In order to compare the two, we need to find the unit rate for each can. In this case, the unit rate will be in dollars per oz.
For the 28 oz can,
unit rate = $1.89 ÷ 28 = $0.675 / oz
For the 32 oz can
unit rate = $2.95 ÷ 32 = $0.922 / oz
comparing the unit rates, we can see that the unit rate for the 28 oz can is lower (i.e it costs less per oz for the 28 oz can compared to the 32 oz can)
Hence the 28 oz can is the better deal.
mio bought a tablet and pays monthly for internet service for it. she graphed the relationship between the number of months she has had the tablet and the total amount she has spent on it.
what does the y-intercept represent in this context?
A) the number of months after which the total cost is 0 dollars
B) the cost of buying the tablet
C) the cost per month
D) none of the above
In the context of the question, the Y-intercept represents the cost of the tablet that Mio purchased before counting the ongoing costs per month for internet service.
Explanation:In the context of this problem, the Y-intercept in the graph represents the cost of buying the tablet. Using the algebraic equation for a line, which is y = b + mx, the 'b' term is the Y-intercept. When x (in this case, the number of months) equals zero, y is the initial cost, which serves as our Y-intercept. This is the starting point on the Y-axis, and in the context of Mio's spending, this would be her initial expenditure which is the cost of the tablet itself.
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What is the difference between an equation with a variable and an inequality with a variable?
Answer:
An equation is a statement that maintains the equal value of two mathematical expressions. If the statement is true for all variable values, it is called an identity. ... An equation shows the equality of two variables while an inequality shows the inequality of two variables
An equation with a variable expresses a precise equality between expressions, while an inequality with a variable represents a range of possible values expressing that one value is greater or less than another. Equations typically have a definitive set of solutions, whereas inequalities signify a continuum of solutions that satisfy the relational condition.
Explanation:The difference between an equation with a variable and an inequality with a variable lies in the relationship they describe between the variables. An equation states that two expressions are equal by means of the equal sign (=), implying a specific value or set of values for the variables involved. For example, in the equation of a line y = mx + b, where x and y are the variables on the horizontal and vertical axis respectively, and b and m represent the y-intercept and the slope, we can see a direct relationship between x and y that determines the position of a point on a Cartesian plane. Conversely, an inequality such as x > y or x < 10 indicates a range of possible values rather than a single specific value, expressing a relationship where one value is either greater than or less than another value, but not equal to it.
In the context of a graph, the independent variable typically plotted on the x-axis is assumed to be the cause or input which then determines the value of the dependent variable, depicted on the y-axis. The dependent variable changes in response to the independent variable, thereby showing their relationship. This is often represented by inequalities when a range of outcomes is possible, extending beyond the linear relationship that might be depicted with an equation.
Ms. Hartman’s class is going on a field trip to planetarium. There are 25 students in the class, and each students need to purchase a day pass to the planetarium and a lunch ticket. The day pass costs $10 and the lunch ticket costs t dollars
Pick all the expressions that represent the total costs for the field trip
250+10t
t(25+10)
250+25t
25(10+t)
the sum of two numbers is 32. the sum of 3 times the larger and 7 times the smaller is 128
Answer:
Smaller number = 8 (x)
Larger number = 24 (y)
Step-by-step explanation:
x+y=32
7x+3y=128
Solving by Elimination
-3x-3y= -96
7x+3y=128
4x=32
4x/4=32/4
x=8
-7x-7y= -224
7x+3y=128
-4y= -96
-4y/-4= -96/-4
y=24
Check answer
x+y=32
8+24=32
7x+3y=128
7(8)=3(24)=138
56+72=128
128=128
984÷x=3 remainder:84
The value of x in 984 ÷ x = 3 remainder: 84 is 300
Step-by-step explanation:
In the division problem A ÷ B = Q [tex]\frac{R}{B}[/tex], where
A is the dividendB is the divisorQ is the quotientR is the remainderIf A is divisible by B, then R = 0
Examples:
23 ÷ 5 = 4 [tex]\frac{3}{5}[/tex] , The dividend is 23, the divisor is 5, the quotient is 4, and the remainder is 354 ÷ 6 = 9, 54 is divisible by 6 , then the remainder = 0The rule of the dividend is ⇒dividend = (divisor × quotient) + reminder
Let us use this rule to find x
984 ÷ x = 4, remainder 84
∵ Dividend = 984
∵ Divisor = x
∵ Quotient is 3
∵ Remainder = 84
- Substitute these values in the rule of dividend above
∵ 984 = (x × 3) + 84
∴ 984 = 3x + 84
- Subtract 84 from both sides
∴ 900 = 3x
- Divide both sides by 3
∴ 300 = x
∴ The value of x = 300
The value of x in 984 ÷ x = 3 remainder: 84 is 300
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6. Suppose an Olympic-size swimming pool in the
shape of a rectangular solid has a volume of 4000
cubic meters, a length of 80 meters, and a width of
20 meters. What is the depth of the pool? Round
your answer to one decimal place.
A) 1.5 meters
B) 2.5 meters
C) 4 meters
D) 6 meters
E) 3.5 meters
To find the depth of the swimming pool, use the formula for the volume of a rectangular solid and substitute the given values to calculate the depth as 2.5 meters.
The depth of the Olympic-size swimming pool can be calculated using its volume, length, and width.
First, use the formula for the volume of a rectangular solid:
Volume = Length x Width x Depth
4000 = 80 x 20 x Depth
Depth = 4000 / (80 x 20) = 2.5 meters
Depth = 2.5 meters
Need help asap !!!!!
Answer:
The answer is x = 5.
Step-by-step explanation:
Given:
Δ ABC is an Isosceles triangle with AB = CA
m∠ ABC = ( 6x + 4 )°
m∠ BAC = 73°
m∠ BCA = ( 8y - 7 )°
To Find:
x = ?
Solution:
Properties of an Isosceles Triangle.
Base angles or two angles are equal.Any two sides are equal.Here , Δ ABC is an Isosceles triangle with AB = CA
∴ m∠ BAC = m∠ BCA
[tex]73= 8y-7\\8y=73+7\\8y=80\\y=\frac{80}{10} \\y=10[/tex]
∴ m∠ BCA = ( 8y - 7 )°
= 8 × 10 - 7
m∠ BCA = 73 Which is same as ∠ CAB
Property of a Triangle is Sum of the measures of the angle of a triangle is 180°.
[tex]\angle ACB + \angle CAB + \angle CBA = 180[/tex]
Substituting the values we get,
[tex]73 + 73 + (6x+4) = 180\\6x+4=180-146\\6x=34-4\\6x=30\\x=\frac{30}{6} \\x=5\\[/tex]
The answer is x = 5.
PLEASE HELP ASAP!!!!
Compose two complete sentences that each include a dependent clause and an independent clause. Identify the subject and predicate of each. Do not use any of the examples in #1 above.
Example: After the meal (S) was served (P), we (S) lounged around with full bellies (P).
Answer:
An independent clause is a group of words that contains both a subject and a predicate. It expresses a complete thought and can stand alone as a sentence. It can also be joined to other dependent or independent clauses to make a more interesting and complex sentence.Step-by-step explanation:
Two hundred thousand twenty five
confused as to what you want but if you want to see the number then its 200,025
Answer:
200,025
Step-by-step explanation:
200 1000s so 200,0000 and add 25
Can someone please help?
Answer:
a. .3
b. .7
c. The car is fairly reliable because there is more people with no mechanical issues than there is people with mechanical issues
Step-by-step explanation:
Answer:
A. 3
B. .7
C. The car is fairly reliable, their is more people with no mechanical issues than their is people with mechanical issues
Step-by-step explanation:
Please answer this correctly
Answer:
120 50 pound bags
Step-by-step explanation:
first you see how much 50 pounds is to one ton which one 50 pound bag is equal to .025 tons
then you multiply .025 by 120 to get 3 (tons)
that shows that the answer is correct
A school receives a shipment of books. There are 60 cartons, and each carton weighs 42 pounds. The school’s elevator can hold 2200 pounds. What is the greatest number of cartons that can be carried on the elevator at one time if no people ride with them? Show all of your work. Then, explain your solution.
Answer:
52
Step-by-step explanation:
2200 / 42 = 52.381
You cannot bring a section of a carton, and 53 cartons is too much
53 * 42 = 2226. This goes over the weight limit.
52 * 42 = 2184. 2184 is less than 2200, so 52 is the greatest number you can bring
By dividing the elevator's weight capacity of 2200 pounds by the weight of one 42-pound carton, we find it can carry a maximum of 52 whole cartons simultaneously without exceeding the weight limit.
Explanation:To solve this problem, we can use simple mathematical analysis. We need to calculate how many 42-pound cartons can fit into an elevator that has a maximum capacity of 2200 pounds without exceeding this limit.
We start with the equation:
Divide the maximum weight the elevator can hold by the weight of one carton. 2200 pounds ÷ 42 pounds/carton = 52.38 cartons.Since you can't have a fraction of a carton, you need to round down to the nearest whole number. The greatest number of whole cartons is 52.Therefore, the elevator can safely carry 52 cartons at once, without any people in it.
Please answer this correctly
Is the answer
10:07pm
12:32am
1:32am
11:32pm
Answer:
Step-by-step explanation:
12:32 am
Answer:
1:32 AM
Step-by-step explanation:
Arriving in Oklahoma City, the time is already 12:32 AM since it is past midnight. From Mountains to Central, time moves forward by 1 hour. 12:32 + 1 hour is 13:32 or 1:32 AM. Since the time is still past midnight, the time is AM.
A linear function has an x-intercept of 12 and a slope of 3/8. How does this function compare to the linear function that is represented by the table?
Answer:
We rewrite the statement correctly:
"A linear function has an y-intercept of 12 and a slope of 3/8"
Therefore, the linear function is:
y = (3/8) x + 12
We look for the linear function of the table:
y-yo = m (x-xo)
Where,
m = (y2-y1) / (x2-x1)
m = ((- 3/8) - (- 3/4)) / ((1/3) - (- 2/3))
m = ((- 3/8) - (- 6/8)) / (3/3)
m = ((- 3 + 6) / 8) / (1)
m = 3/8
(xo, yo) = (- 2/3, -3/4)
Substituting:
y + 3/4 = (3/8) (x + 2/3)
y = (3/8) x + 2/8 - 3/4
y = (3/8) x + 1/4 - 3/4
y = (3/8) x + -2/4
y = (3/8) x + -1/2
The lines are:
y = (3/8) x + 12
y = (3/8) x + -1/2
Answer:
It has the same slope and a different y-intercept
Step-by-step explanation:
Answer:
B same slope but different y intercept
Step-by-step explanation:
-3(×+2)=12 what is x equal to
Answer:
x=-6
Step-by-step explanation:
Follow along:
1. Distribute the -3 to those within the parenthesis.
-3x-6=12
2. Move the whole numbers to one sides, isolate the variable.
-3x=18
3. Divide both sides by -3
x=-6
Claire has a hot tub with a diameter of 7 feet. She wants to purchase a cover to protect the hot tub. What is the area
of the cover? Use pi = 3.14 and round the answer to the nearest square foot.
Answer:
The area of the cover for the hot tub must be:
38 square feet.Step-by-step explanation:
First, you must understand that since a hydromassage tub is mentioned and the diameter, it is assimilated that it is round in its upper part, which is why the formula is used to find the area of a circle:
Area of a circle = pi * radius ^ 2 (you must know that the radius is half the diameter)Since the diameter is mentioned, it can be replaced in the formula:
Area of a circle = 3.14 * (3.5 feet) ^ 2 Area of a circle = 38,465 square feet. Approximately 38 square feet.Answer:
I believe it is 38
Step-by-step explanation:
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