The equation of line passes through the point (1, -5) will be;
⇒ y = - 3x - 14
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (1, -5).
And, The slope of the line is,
⇒ m = - 3
Now,
Since, The equation of line passes through the point (1, -5).
And, Slope of the line is,
⇒ m = - 3
Thus, The equation of line with slope - 3 is,
⇒ y - 1 = - 3 (x - (-5))
⇒ y - 1 = - 3 (x + 5)
⇒ y - 1 = - 3x - 15
⇒ y = - 3x + 1 - 15
⇒ y = - 3x - 14
Therefore, The equation of line passes through the point (1, - 5) will be;
⇒ y = - 3x - 14
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1: A is directly proportional to B.
When A = 12, B = 3
Direc
(a) Find a formula for A in terms of B.
(b) Find the value of A when B = 5
(c) Find the value of B when A= 36
Answer:
a)A=4B
b)A=20
c)B=9
If it is directly proportional it means that A=kB.
you can substitute the numbers to find k.
12=k3
k=4
so the formula is A=kB.
For part b and c it is just substitution
Let d represent:
I do not drink bottled water.
Lett represent:
I eat pizza.
What is the symbolic representation of the following statement?
I do not eat pizza or I do not drink bottled water
I eat pizza or drink bottled water, for example, is a symbolic representation of the following statement.
What is meant by symbolic representation?Traditionally, symbolic representation is defined as the representation of a principal, such as a nation, through a symbol, such as a flag, that evokes specific meanings and emotions about the nation. The use of physical or psychological processes to represent an object (either another object or an idea) in a symbolic form is referred to as symbolic representation (Carlson, Sroufe, & Egeland, 2004). A written character or mark that is used to represent something; a letter, figure, or sign that is traditionally used to represent some object, process, etc. (Oxford English Dictionary). Figures denoting the planets, signs of the zodiac, and so on are examples of something visible that represents something else that is invisible by association or convention. Synonyms include symbol, symbolization, and symbolization.To learn more about symbolic representation, refer to:
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please help me with this.
Answer:
Option A
Step-by-step explanation:
→ Multiply both sides by 2
2s = a + b + c
→ Minus b and c from both sides
2s - b - c = a
At the beginning of the lesson, Jacob determined that there was a problem with the sail length measurements of 7.5 meters, 4.8 meters, and 2.5 meters. Explain how Jacob was able to determine there was a problem with the specifications of the triangular sail.
Answer:
Jacob was able to determine there was a problem with the specifications of the triangular sail because of the Pythagorean theorem.
Step-by-step explanation:
Assume the triangular sail is a right triangle.
The Pythagorean theorem says: [tex]A^{2} + B^{2} = C^{2}[/tex]
If A = 4.8, B = 2.5, and C = 7.5, then [tex]4.8^{2} + 2.5^{2} = 7.5^{2}[/tex].
[tex]4.8^{2} + 2.5^{2} = 23.04 + 6.25 = 29.29[/tex]
[tex]7.5^{2} = 56.25[/tex]
In conclusion, [tex]29.29 \neq 56.25[/tex], so there is a problem with the sail.
Can anyone state the vertex of the graph?
Given the graph, the vertex does not exist and the transformations from are
Vertical shift down 2Horizontal shift left 4How to calculate the vertex of the graph?The graph represents the given parameter
In the above graph, we can see that the graph is a cubic function
By definition, cubic functions do not have vertex. This is because they have no minimum or maximum
So, we can conclude that the graph has no vertex
The transformation from the parent functionIn (a), we have
We can see that the graph is a cubic function
This function is represented as
y = ∛x
In this graph, we can see that the graph is 4 units to the left
i.e. y = ∛(x - 4)
And 2 units below the origin
i.e. y = ∛(x - 4) + 2
So, the transformation is (b) and (c)
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Solve for the value of v.
50⁰
(V-7)
The value of v as required to be solved for in the task content is; 47.
What is the value of according to the right triangle?It follows from the complete task content that a right triangle in which case the angle measures are; 50°, (v - 7)° and 90° is to be solved for variable v.
Recall from triangle geometry that the algebraic sum of angles in a triangle is; 180°.
Therefore, we have;
50° + (v - 7)° + 90° = 180°
v - 7 + 140 = 180
v = 180 - 140 + 7
v = 47.
On this note, the value of variable, v as required to be determined is; 47.
Completed question; The complete question is such that a right triangle with two other angles 50° and (v - 7)° is given.
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Find the highest common factor (HCF) of 72 and 90
Answer:
Step-by-step explanation:
Factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, and 90
The six frequent factors between 72 and 90 are 1, 2, 3, 6, 9, and 18.
Consequently, 18 is the number that links 72 and 90 most frequently.
an ant walks along a straight path. After traveling for 1 meter it stops, turns through an angle of 90 degrees in an anticlockwise direction and sets off in a straight line covering a distance of half a meter. Again, the ant turns through an angle of 90 degrees in an anticlockwise direction and sets off in a straight line covering a quarter of a meter. The ant continues in this manner indefinitely.
a) How many turns will the ant have made after covering a distance of 63/32 meters?
b)How far will the ant "eventually" travel?
The description of the motion of the ant which is a geometric series is as follows;
a) After covering 63/32 meters, the ant will have made 6 turns
b) The distance the ant will eventually travel is 2 meters
What is a geometric series?Geometric series is an infinite sum of terms in which the ratio between consecutive terms is a constant.
The distances traveled by the ant is a geometric progression of the form;
aₙ = a·rⁿ⁻¹The sum of the distance is given by the sum of the geometric progression as follow;
[tex]S_n = \dfrac{a\cdot \left(1 - r^n \right)}{(1 - r)}[/tex]
Where;
aₙ = The distance traveled in the nth turn
Sₙ = The sum of the distances
a = The first term = 1 meter
r = The value of the common ratio = 0.5 meter ÷ 1 meter = 0.5
a) The number of turns the ant will have made after covering a distance of 63/32 meters is therefore;
[tex]S_n =\dfrac{63}{32} = \dfrac{1\times \left(1 - 0.5^n \right)}{(1 - 0.5)}[/tex]
31.5 = 32 × (1 - 0.5ⁿ)
32 × 0.5ⁿ = 32 - 31.5 = 0.5
0.5ⁿ = 0.5 ÷ 32
n = ln(0.5 ÷ 32) ÷ ln(0.5) = 6
After covering a distance of 63/62 meters, the ant will have made 6 turnsb) The distance the ant travels eventually is given by the formula for the sum to infinity of a geometric progression as follows;
[tex]S_{\infty} = \dfrac{a}{1-r}[/tex]
Which gives;
[tex]S_{\infty} = \dfrac{1}{1-0.5} = 2[/tex]
The distance the ant eventually travels is 2 meters
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write down the value of 9 and a half?
The value of 9 and a half will be 9 1/2.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
Here, we want to find the value of 9 and half. This will be:
= 9 + 1/2
= 9 1/2
The value is 9 1/2.
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Karl bought 1.6 pounds of oranges and 2.4
pounds of pears. They each cost $1.48 per pound
Use properties to find the total cost.
Answer:
$5.92
Step-by-step explanation:
1.6 lbs. + 2.4 lbs. = 4 lbs.
4 x 1.48 = 5.92
Since it doesn't specify whether the oranges and apples cost differently you can add both of them. Then you multiply it by 1.48 because that's the cost per pound.
48) in how many ways can a photographer at a wedding arrange 6 people in a row from a group of 10 people, where the bride and the groom are among these 10 people, if a) the bride must be in the picture?
The number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
What is permutation and combination?
A permutation is an orderly arrangement of things or numbers.
Combinations are a means to choose items or numbers from a collection or set of items without worrying about the items' chronological order.
The amount of two-letter words that can be created using the letters in a word, like GREAT, is an illustration of permutations: ⁵P₂ = 5!/(5-2)!
How many different ways we may write the words utilizing the vowels in the word GREAT is an example of a combination: ⁵C₂ = 5!/[2! × (5-2)!]
Given, 6 people are to be selected from a group of 10, where the bride must be in the picture.
Following the statements in question, the bride since always there assists for filling five empty spaces using 9 people.
Since five positions are to be filled by nine people, the total number of ways possible = 9 × 8 × 7 × 6 × 5 = 15120
Thus, the number of ways a photographer can arrange 6 people in a row from a group of 10 people if the bride must be in the picture is 15120.
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Please help, I am timed and I have no clue what to do here!
Answer:
Step-by-step explanation:
Re-order terms so constants are on the left
Then divide both sides by the same factor its -2
then Simplify answer is 1
What is the speed of a jet plane that travels 3,000 meters in 100 seconds?
Answer:
Step-by-step explanation:Answer: 108,000m/h (108km/h or 30m/s)
5(x+2)-3(x-2)+7x
PLEASE HELP ME RMS IS KILLING ME HOLY COW
Answer:
9x + 16
Step-by-step explanation:
Let's simplify step-by-step.
5(x+2)−3(x−2)+7x
Distribute:
=(5)(x)+(5)(2)+(−3)(x)+(−3)(−2)+7x
=5x+10+−3x+6+7x
Combine Like Terms:
=5x+10+−3x+6+7x
=(5x+−3x+7x)+(10+6)
=9x+16
Please give me brainiest!
determine whether the lines are parallel, intersect, coincide y = x-7, y = -x + 3
The given two equations are Perpendicular to each other .
What is intersection of lines ?
It is known as an intersection of lines when two lines have exactly one point in common. A point is shared by the connecting lines. The point of intersection is the same place that may be found at the intersection of all intersecting lines. When two or more straight lines cross each other in a plane, they are said to be intersecting lines. An intersection point will be present for the two non-parallel straight lines that are coplanar. The point of intersection, which can be found on all intersecting lines, is where the intersecting lines share a common point.
Here the equation of line is y=mx+b .
Where m = slope . then,
=> y = x-7 where here slope m1= 1 and
=> y = -x+3 where here slope m2 = -1 .
Here the m1= -m2
Hence the given two equations are Perpendicular to each other .
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if a loading ramp is placed next to a truck, at a height of 4 feet, and the ramp is 17 feet, what angle does the ramp make with the ground? round to 2 decimal places.
The angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
What is trigonometry?
The study of the relationship between the sides and angles of the right-angle triangle is essentially the focus of the field of mathematics known as "trigonometry". Therefore, employing trigonometric formulas, functions, or trigonometric identities can be helpful in determining the missing or unknown angles or sides of a right triangle. Angles in trigonometry can be expressed as either degrees or radians.
Given, the length of the ramp = h = 17 feet
Height at which ramp is placed on truck = p = 4 feet
Let the angle that the ramp makes with the ground = ∅
Taking the length and height of ramp as basis, on assuming a right triangle with the length as hypotenuse and the height as perpendicular, we have:
sin ∅ = Perpendicular/Hypotenuse = h / p = 17/4 = 4.25
⇒ ∅ = sin⁻¹ (4.25) ⇒ ∅ = 10.48°
Thus, the angle that the ramp makes with the ground rounded off to two decimal places is 10.48°.
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can 2 parabolas have the same vertex but different directions of opening?
Answer:
Step-by-step explanation:
Yes, of course!
A parabola's direction is based on whether its "a" value is positive or negative and whether it is opening vertically or horizontally (y= or x =)!
quadrilateral rstu has vertices R(2,4) ,s (-2,2), T(-1,0)and (3,2)
Verify:
i) quadrilateral rstu is a rectangle
ii) the diagonals of the rectangle bisect each other and are equal in lengths .
As RS=TU and ST=UR by distance formula, The given quadrilateral RSTU is rectangle and The diagonals RT=US so they are equal and bisect each other at right angle.
What is rectangle?A quadrilateral with parallel sides that are equal to one another and four equal vertices is known as a rectangle. It is also known as an equiangular quadrilateral for this reason. Rectangles can also be referred to as parallelograms because their opposite sides are equal and parallel. 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. A rectangle has two dimensions—length and width—because it is a two-dimensional shape. The rectangle's longer side is its length, and its shorter side is its width.
Here,
Calculate the length of sides by distance formula.
RS=√(y2-y1)²+(x2-x1)²
=√(2-4)²+(-2-2)²
=√4+8
=√(12
=2√3 units
ST=√(y2-y1)²+(x2-x1)²
=√(0-2)²+(-1-(-2))²
=√(4+1)
=√5 units
TU=√(y2-y1)²+(x2-x1)²
=√(2-0)²+(3-(-1))²
=√(4+8)
=√12
=2√3 units
UR=√(y2-y1)²+(x2-x1)²
=√(4-2)²+(3-2)²
=√(4+1)
=√5 units
RT=√(y2-y1)²+(x2-x1)²
=√(0-4)²+(-1-2)²
=√(16+9)
=√25
=5 units
US=√(y2-y1)²+(x2-x1)²
=√(2-2)²+(-2-3)²
=√(0+25)
=√25
=5 units
Because the given quadrilaterals, RS=TU and ST=UR, are rectangles and the diagonals, RT=US, are equal and at right angles to one another, according to the distance formula.
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Please help! The total cost after tax to buy floor tiles is represented by 14f+0.096(14f), where f represents the number of square feet of tile are need to cover the floor.
a. What part of the expression represents the amount of tax that must be paid? Explain. (3 pts)
b. What would the expression be if the cost per square foot was $15 (plus tax)? (3 pts)
Considering the expression in this problem, it is found that:
a) The part of the expression that gives the amount of taxes that has to be paid is: 0.096(14f).
b) The expression would be of: C(f) = 15f + 0.096(15f).
What is the meaning of the expression?The expression for the total cost in this problem is presented as follows:
C(f) = 14f + 0.096(14f).
The meaning of each term is given as follows:
14f means that the cost of each square feet of tile is of 14 f.0.096 x 14f means that an additional 0.096 = 9.6% is paid of tax for each square feet of tile purchased.If the cost per square foot was of $15 instead of $14, the complete expression would be as follows:
C(f) = 15f + 0.096(15f).
That is, the two instances of 14 in the equation were replaced by 15.
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ksiodhhhwdaaaaaaaaaaoidjooaaaaaaaaaaaaaaaaaaa
Answer:
vyfyxfrr6c*"8&"; hxh6 byhd,tf7zg5gzyfe55eE4E45w522
Step-by-step explanation:
6dyxg9yyfz6t bztrfr 4.Sabina the tortoise is an 56,123 way of Policy for recharge of the angles and tricks of Policy in order for me and I have a wonderful experience and a
a hamburger regularly cost $6.00 each additional topping cost $0.59. on Monday the cost of hamburger only is half off
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
A burger consistently cost $6.00 each extra fixing cost $0.59.
Let 'c' be the cost and 't' be the cost of topping. Then the equation is given as,
c = 0.59t + 6
On Monday the expense of the burger just is half off. Then the equation is given as,
c = 0.50(0.59t + 6)
c = 0.295t + 3
The equation that represents the cost of the hamburger with additional topping will be c = 0.295t + 3.
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Classify the angle pair as corresponding, alternate interior, alternate exterior, or consecutive interior angles. Then, select the transversal that connects them.
∠1 and ∠14
corresponding
alternate interior
alternate exterior
consecutive interior angles
p
q
r
s
The identification of the missing angles and their congruency names are;
a. ∠4 and ∠7 = Consecutive interior
b. ∠2 and ∠11 = alternate exterior angles
c. ∠12 and ∠16 = corresponding angles
d. ∠8 and ∠13 = alternate interior angles
e. ∠11 and ∠15 = corresponding angles
f. ∠7 and∠10 = none
g. ∠1 and ∠14 = alternate exterior angles
h. ∠12 and ∠15 = Consecutive interior
i. ∠6 and ∠7 = none
j. ∠1 and ∠3 = corresponding angles
k. ∠12 and ∠16 = corresponding angles
l. ∠6 and ∠15 = alternate exterior angles
m. ∠5 and ∠10 = alternate interior angles
n. ∠8 and ∠14 = corresponding angles
How to classify congruent angles?Corresponding angles are defined as the angles which are formed in corresponding corners with the transversal in a case where two parallel lines are intersected by any other line.
Alternate interior angles are defined as the angles formed when a transversal intersects two coplanar lines.
Alternate exterior angles are defined as the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.
Therefore, the angles given can be classified similarly using the image as:
a. <4 and <7 are Consecutive interior angles
b. <2 and <11 are alternate exterior angles
c. <12 and <16 are corresponding angles
d. <8 and <13 are alternate interior angles
e. <11 and <15 are corresponding angles
f. <7 and <10 are none
g. <1 and <14 are alternate exterior angles
h. <12 and <15 are Consecutive interior
i. < 6 and <7 are none
j. <1 and <3 are corresponding angles
k. <12 and <16 are corresponding angles
l. <6 and <15 are alternate exterior angles
m. <5 and <10 are alternate interior angles
n. <8 and <14 are corresponding angles
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$12000 into an investment account for 5 years. The investment earns 6% interest per
annum, compounding quarterly.
What is the interest rate per quarter?
Answer:
We may use the logarithm formula,
N = ln(EV/SV) ÷ ln(1+r), where (1+ r) is the value of 1 plus interest for 1 year.
EV is end value, SV is start value.
EV is 20000, SV is 12000, interest is 5.6% semi annual
(1+r) is obtained as,
Step-by-step explanation:
Give the domain and range of the relationship. List items from least to greatest. Do not include duplicates. Determine whether or not the relationship is a function.
Answer:
Domain: {2, 3, 4, 5} Range: {12, 13, 14}
Step-by-step explanation:
The relationship is a function even though two different inputs have the same output.
4. The drama club is printing t-shirts for its members. The printing company chargesa certain amount for each shirt plus a setup fee of $40. There are 21 students in the drama club.
a. If there are 21 students in the club and the t-shirt order costs a total of $187, how much does each t-shirt cost? Show your reasoning.
Answer:
$7
Step-by-step explanation:
You want the cost of a shirt when the cost of 21 shirts plus a $40 setup fee is $187.
CostThe total cost of the order is the sum of the setup fee and the extended cost of the shirts.
cost = (setup fee) + (number of shirts) × (cost per shirt)
187 = 40 + 21 × (cost per shirt)
Subtracting 40 gives ...
147 = 21(cost per shirt)
Dividing by 21, we have ...
7 = cost per shirt
Each T-shirt costs $7.
10. A life insurance company found that
among its last 200 claims, there were six
dozen smokers. What is the ratio of smokers
to nonsmokers in this group of claimants?
Write in lowest terms.
for homework .
Multiply (0.000302)(1000)
Answer:
0.302
Step-by-step explanation:
Answer: 0.302
Step-by-step explanation:
after euclid high school's last basketball game, it was determined that 1/4 of the team's points were scored by alexa and 2/7 were scored by brittany. chelsea scored 15 points. none of the other 7 team members scored more than 2 points. what was the total number of points scored by the other 7 team members?
The total number of points scored by the other 7 team members in Euclid high school's last basketball game is 11.
What is defined as the term two variable equation?If an equation is written in the form ax + by + c=0, where a, b, and c are real integers as well as the coefficients of x and y, i.e., a and b, respectively, really aren't equal to zero, then it is said to be a linear function in two variables.For the given question.
Let 't' be the total points scored.
Alexa = 1/4 t.
Brittany = 2/7 t
Chelsea = 15
Let 'x' be the points scored by remaining 7 team.
Thus, the two variable equation becomes.
1/4 t + 2/7 t + 15 + x = t .....eq 1
Where, x ≤ 14 ( for 7 terams)
Simplifying eq 1.
15 + x = 13/ 28 t
28x + 28 = 13 t
Now, t must be divisible by 28.
Let t = 28 u, u ≥ 0 and divisible by 28.
Thus,
x + 15 = 13u.
Then, u = 2( t = 56) has been the only candidates for which x = 11.
Thus, the total number of points scored by the other 7 team members is 11.
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a concert venue is determining the ticket price for concerts in a particular series. the sales team finds that at a price of $38 per ticket, attendance averages 1,000 people per concert. each decrease in price of $5 adds 50 people to the average attendance. find an equation for revenue, r, as a function of p, the price of tickets. what is r(25)?
An equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
Given that;
The cost of tickets for a specific series of concerts is set by a concert venue. The sales team discovers that 1,000 people on average attend concerts with tickets costing $38. The average attendance increases by 50 persons for every $5 decrease in price. Then,
Let 'T' be the number of times the price is decreased.
So, price;
p = 38 – 5x
x = (38 - p) / 5
And as per the given condition attendance;
a = 1000 + 50x
So, the Revenue is;
To develop an equation for revenue (r) as a function of p, the price of tickets;
R = p * a
R= p * (1000 + 50x)
But, x = (38 - p) / 5
Then,
R = P * (1000 + 50(38 - p)/5)
= p * (1000 + 380 - 10p)
= p * (1380 – 10p)
= 1380p - 10p² → (I)
To get R(25) from (I);
R(25) = 1380(25) - 10(25)²
= 34500 - 6250
= 28250
Hence, an equation for revenue (r) as a function of (p) is R = 1380p - 10p²,
and R(25) = 28250.
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find the intervals of increase and decrease of 3/512(x-4)^2(x-8)(x-10)(x^2+16)
The given function is strictly decreasing in interval (−∞, 4) & trictly increasing in interval (4, −∞).
What is an increasing and decreasing functions?
For a given function, y = F(x), the function is known as an increasing function if the value of y increases as the value of x increases, and the function is known as a decreasing function if the value of y decreases as the value of x increases.
We have,
[tex]\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]\frac{d}{dx}\left(\frac{5}{512}\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]=\frac{5}{512}\frac{d}{dx}\left(\left(x-4\right)^2\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)[/tex]
[tex]f'(x)=\left(x-4\right)^2,\:g=\left(x-8\right)\left(x-10\right)\left(x^2+16\right)[/tex]
[tex]=\frac{5}{512}\left(\frac{d}{dx}\left(\left(x-4\right)^2\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\frac{d}{dx}\left(\left(x-8\right)\left(x-10\right)\left(x^2+16\right)\right)\left(x-4\right)^2\right)[/tex][tex]=\frac{5}{512}\left(2\left(x-4\right)\left(x-8\right)\left(x-10\right)\left(x^2+16\right)+\left(4x^3-54x^2+192x-288\right)\left(x-4\right)^2\right)[/tex]
[tex]f'(x)=\frac{5\left(x-4\right)\left(3x^4-53x^3+300x^2-816x+1856\right)}{256}[/tex]
The roots (zeros) are the x values where the graph intersects the x-axis. To find the roots (zeros), replace y with 0 and solve for x.
x = 4, 4i, −4i, 10, 8
∴ f′(x) = 0
x = 4,
Now, the point 4 divides the real line into two disjoint intervals i.e., (−∞, 4) and (4, −∞)
In interval (−∞, 4), f′(x) < 0
Hence, the given function (f) is strictly decreasing in interval (−∞, 4)
In interval (4, −∞), f′(x) > 0
Hence, the given function (f) is strictly increasing in interval (4, −∞)
To learn more about the increasing and decreasing functions visit,
https://brainly.com/question/13157110
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