Answer:
y = (2/3)y - 2
Step-by-step explanation:
Linear equations of the form y=mx+b, describe the slope, m, and the y-intercept, b (the value of y when x=0).
Line K
y = -(3/2)x + 1 tells us that it has a slope of -(3/2) and crosses the y axis (x=0) at y = 1.
Perpendicular Lines
Perpendicular lines have a useful property in that they have a slope that is the "negative inverse" of the line they are perpendicular to. If, for example, we were ever asked what is the slope of a line perpendicular to Line L (yes, it happens), we could, with minimal effort, respond "It is the negative inverse of -(3/2)," which is a slope of (2/3).
Line L
We just accidently answered a key question when we found the negative inverse of the slope for Line K, (2/3). That will be the slope of Line L that will make it perpendicular to Line K.
Line L will have the form y = (2/3)x + b
This line will be perpendicular to Line K, no matter the value of b. But we want a perpendicular line that goes through point (6,2), so we need to find a value of b that will force it to go through that point.
The role b has in our equation is simply moving it up or down. If b were 0, the line will go through the origin (0,0). If b were 5, it would interect the y axis at 5 (0,5). We could draw a graph and get a pretty good idea what b would have to be for the line to go throgh (6,2), but most prefer the easier route: Use the (x,y) value in the above equation and solve for b. Its easy, and works great:
y = (2/3)x + b for (6,2)
2 = (2/3)(6) + b
b = 2 - (2/3)*(6)
b = 2 - 4
b = -2
The equation for Line L is thus: y = (2/3)y - 2
See the attached graph. Included are equations [marked Demo Line 1 and 2] with 2 random values of b (1 and 0), in order to:
demonstrate how b impacts the line, andsuggest try using DESMOS as a free online graphing tool.
Hi I'm honestly really confused on this problem and have no idea what I'm meant to do. It'd be helpful if someone could explain this
As corresponding angles ∠5 and ∠8 are equal. Hence line x is parallel to line z by converse of corresponding angles theorem.
What does converse of corresponding angles theorem states?
If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel.
How can we show two lines are parallel to each other?
We can show lines are parallel by finding a pair of corresponding angles that are congruent.
Proving if two lines are parallel then third line is parallel too.
According to the given data:
It is given in the question that line x is parallel to line yTherefore, ∠5 ≅ ∠7 (i.e. corresponding angles)
∠5 = ∠7
Similarly as given line y is parallel to line z∠6 ≅ ∠8 (Corresponding angles are equal)
∴ Measure of angles is also equal ⇒ ∠6 = ∠8
∠5 = ∠8 (transitive property of equality of angles which says if
∠a = ∠b and ∠b = ∠c then ∠a = ∠c)
∠5 ≅ ∠8 (If measure of angles is same then they are congruent)
Therefore, line x || line z
(Converse of the Corresponding Angles Theorem).
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A tree that is 10 feet tall casts a shadow that is 8 feet long. What is the distance from the top of the tree to the tip of the shadow? Round to the nearest tenth.
9.4 feet
12.8 feet
3.2 feet
2.8 feet
The distance from the top of the tree to the tip of the shadow is 12.8 ft
Pythagorean theorem:
According to the Pythagorean theorem, In a right-angled triangle, the sum of the squares of the side will equal the square of the hypotenuse.
Here hypotenuse is the longest side.
=> Hoptenuse² = side² + side²
Here we have
The length of the tree = 10 feet
Length of shadow = 8 feet
Here we need to find the distance from the top of the tree to the tip of the shadow
If we join the top of the tree to the tip of the shadow we will observe a right-angled triangle as shown below
From the figure,
AC² = AB² + BC² [ ∵ ABC is right angle triangle ]
=> AC² = 10² + 8²
=> AC² = 100 + 64
=> AC² = 164
=> AC = 2√41
=> AC = 12.8 ft
Therefore,
The distance from the top of the tree to the tip of the shadow is 12.8 ft
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Answer:
b) 12.8 feet
Step-by-step explanation:
Now we have to,
→ find the required distance.
Forming the equation,
→ x² = 10² + 8²
Then the distance will be,
→ x² = 10² + 8²
→ x² = 100 + 64
→ x² = 164
→ x = √164
→ [ x = 12.8 feet ]
Hence, distance is 12.8 ft.
HELPPP MEEeeeeeeeeee
When Lily left her house in the morning, her cell phone battery was partially charged. The charge remaining in Lily's battery, as a percentage, can be modeled by the equation B=-4t+52,B=−4t+52, where t is the number of hours since Lily left her house. What is the x-intercept of the equation and what is its interpretation in the context of the problem?
The x-intercept of the equation is 13 and its interpretation in the context of the problem is the number of time in hours for which Lily left her house.
What is x-intercept?In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).
Next, we would determine the number of time for which Lily has left her house since in the morning by substituting the value of B with zero (0) as follows:
B = -4t + 52
0 = -4t + 52
4t = 52
Time, t = 52/4
Time, t = 13 hours.
Therefore, the x-intercept of the given equation is (0, 13).
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a pair of shoes is on sale, the original price is $150.99 and they are 30% whats a new price after the discount?
Answer:
Price after discount is $105.69Step-by-step explanation:
It is assumed 30% is the discount.
Original price is $150.99, discount is 30%, sale price is:
150.99 - 30% = 150.99 × (1 - 0.3) = 150.99 × 0.7 = 105.69 (rounded)There are 103 fifth graders at brookside elementary .for a read thon 5 students read for 100 minutes 25 students read for 50 minutes and rest of the fifth graders read for 30 minutes . how many minutes did the fifth graders read.
The fifth graders are read for total 180 minutes.
What do you mean by minutes?
A 60-second interval of time. In an hour, there are 60 minutes. For illustration, the time 10:35 is 35 minutes after 10 o'clock. A minute is equivalent to 1/60th of a degree in terms of angles.
According to the given question,
First 5 students read for 100 minutes.
Then, next 25 studenda read for 50 minutes.
And the rest of the fifth graders read for 30 minutes.
Now, we will adding all the minutes to obtain the answer or total minutes of fifth grader read,
Total minutes of fifth graders read= 100+50+30
=180 minutes.
Therefore, the fifth graders take 180 minutes to read.
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a box of buttons contains the same number of each type of button
it contains 220g of buttons
how many of each button are in the box
Button A=8 grams
Button B = 12 Grams
The number of buttons A will be 11. And the number of buttons B will be 11.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
A container of buttons contains a similar number of each kind of button it contains 220g of buttons. The weight of the button is given as,
Button A=8 gramsButton B = 12 GramsLet x be the number of each button. Then the equation is given as,
8x + 12x = 220
20x = 220
x = 11
The number of buttons A will be 11. And the number of buttons B will be 11.
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the little twelve basketball conference has two divisions, with six teams in each division. each team plays each of the other teams in its division twice and every team in the other division once. how many conference games are scheduled?
There are 96 basketball conference games are scheduled.
What is termed as the division?Multiplication is the reciprocal of division. If 3 groups of 4 add up to 12, then 12 classified into three groups of equal size results in 4 in each group. Developing equal groups or defining how many people are within each group after a fair distribution is the basic function of division.For the given question;
Every squad competes in ten games within its own division and six games against opponents from the opposing division. The 12 teams thus play a total of 16 conference games.There are N games on the schedule because there are two teams in each game.
N = 12×16/2
N = 96
Thus, there are 96 basketball conference games are scheduled.
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Feng invests money in an account paying simple interest. He invests $70 and no money is added or removed from the investment. After one year, he has $70.70. What is the simple percent interest per year?
The simple interest is given as PRT/100, thus the simple percent interest per year is 1%.
What is simple interest?Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time.
Unlike compound interest, which adds the interest from the principal of prior years to determine the interest of the following year.
As per the given,
Investment = $70
Investment after one year is $70.70
Interset = 70.70 - 70 = $0.70
The interest is given as = PRT/100
0.70 = PR(1)/100
R = (0.70×100)/70
R = 1%
Hence, "The simple interest is given as PRT/100, thus the simple percent interest per year is 1%".
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Which equations are true? Select all that apply.
Answer:
The equation that is true is equation two
HELP the price of gasoline purchased varies directly with the number of gallons purchased if 10 gallons of gasoline are purchased for$23 what will be the price of 50 gallons be?
Answer:
Step-by-step explanation:
It will be 115$
Answer: the answer is $21.7391304348 or round to $21.74 is the cost for 50 gallons
Step-by-step explanation: I did the calculations and it costs $2.30 a gallon
Point O is the center of this circle. What is mzBCA?
A. 56
B. 62
C. 72
D.76
Answer:
B
Step-by-step explanation:
∠ ADB and ∠ AOB sum to 180° , that is
56° + ∠ AOB = 180° ( subtract 56° from both sides )
∠ AOB = 124°
An angle on the circle is half the central angle subtended on the same arc , so
∠ BCA = [tex]\frac{1}{2}[/tex] ∠ AOB = [tex]\frac{1}{2}[/tex] × 124° = 62°
0.1 times n equals 89.5
Answer: n=895
Step-by-step explanation:
Answer:
n = 895
Step-by-step explanation:
Here we want to find n , 1st form the Equation then solve it for n
0.1 times n = 0.1n
0.1 times n equal 89.5
Then 0.1n = 89.5
Solve for n , b dividing both sides by 0.1
n = 89.5 / 0.1 = 895
Walt Disney Co paid a $1.42 annual dividend on a day it closed at a price of $96 per share.
What was the annual dividend for 500 shares?
The annual dividend for 500 shares was $710.
How is the annual dividend computed?The annual dividend is a function of the dividend per share and the number of shares held by a stockholder.
Dividends are always declared per share with a stated dollar amount or percentage.
Dividends represent the portion of the profits earned by an entity that it decides to distribute to the shareholders.
Dividends are a kind of financial reward to stockholders for their investment in the entity.
The dividend per share = $1.42
Market price per share = $96
The number of shares held = 500
The dividend received for the year = $710 ($1.42 x 500)
Thus, the holder of 500 shares in Walt Disney Co. will get $710 in a year the company declared and paid a $1.42 annual dividend.
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125 in the ratio 2:3
Answer:
50:75
Step-by-step explanation:
let the ratio of 2:3 be x
now,
125=2+3x
or,5x=125
therefore,x=125/5
x=25
now,
2x=25*2
=50
3x=25*3
=75
work out
5/6 × 48
120 x 2/3
Answer:
1. 130/6
2. 240/3
Step-by-step explanation:
make the whole numbers into a fraction by putting 1 as the denominator.
48/1.
then multiply together.
48 x 5 = 130
6 x 1 = 6
130/6
do the same with the other
120 x 2 = 240
1 x 3 = 3
240/3
Answer:
40
80
Step-by-step explanation:
5/6 × 48
5 × 48 = 240
240/6
= 40
120 × 2/3
120 × 2 = 240
240/3
= 80
Use Heron's Formula to find the area of AHKP if h' = 24 ft, k = 21 ft, and p = 13 ft. *
(1 Point)
192. 67 sq units
435. 90 sq units
113. 38 sq units
136. 23 sq units
The area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
Define the term Heron's Formula?This formula is well-known for its straightforward computation that supports the length for three triangle sides. If the lengths of the 3 sides are a, b, and c, the semi-perimeter is; s = (a+b+c)/2.Area ; A = √s(s−a)(s−b)(s−c)The three sides of the triangle are-
h = 24 ft, k = 21 ft, and p = 13 ft.
s = ( 24 + 21 + 13 ) / 2
s = 29
s - a = 29 - 24 = 5
s - b = 29 - 21 = 8
s - c = 29 - 13 = 16
Put in the formula,
Area = √s(s−a)(s−b)(s−c)
A = √ 29 x 5 x 8 x 16
A = 136.23
Thus, the area of the triangle HKP found by the Heron's Formula is 136.23 sq. ft.
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the product of 180 and the positive integer n is a perfect cubic number. what is the least possible value of n?
The least possible value of n, where the product of 180 and the positive integer n is a perfect cubic number is 150.
so, by the question,
n×180 is a perfect cube
on the prime factorization of 180, we get
180 = 2²×3²×5
so the number should be
n = 2 × 3 × 5² =150
when we multiply both of them we get
180×n = (2²×3²×5)×(2 × 3 × 5²)
= (2³×3³×5³)
=(2×3×5)³
=(30)³
=27000
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Please answer part d
Answer:
∆JGF ≅ ∆GJH by the SAA Postulate
Step-by-step explanation:
Given a figure showing two triangles with a common side, and two marked angles not at either end of that side, you want to know the applicable congruence postulate.
SAAThe letters S and A in the congruence postulate references refer to "Side" and "Angle". The sequence of the letters corresponds to the sequence of corresponding parts in the triangles.
In the given figure, two angles in each triangle are marked with a single arc and a double arc. The triangles share a side that has the double-arc angle at one end. Hence, the sequence of corresponding parts can be seen to be (common) Side - (double-arc) Angle - (single-arc) Angle. The SAA congruence postulate applies.
∆JGF ≅ ∆GJH by the SAA Postulate
A soft drink manufacturer has a daily production cost of C = 70,000 - 120x + 0.055x ^ 2 , where C is the total cost (in dollars) and x is the number of units produced. How many units should they produce each day to yield a minimum cost?
Show all work please.
They should produce 1091 units each day to yield a minimum cost.
What is the vertex formula?
When the graph crosses its symmetry axes, the vertex formula aids in determining the vertex coordinate of a parabola. The vertex point is often represented by (h, k).
We know that a parabola's conventional equation is y=ax²+bx+c. The vertex in this case should be near the base of the U-shaped curve if the coefficient of x² is positive. The vertex should be at the peak of the U-shaped curve if the coefficient of x² is negative.
We have,
C = 70,000 - 120x + 0.055x²
C = 0.055x² - 120x + 70,000
Hence, for this equation, the graph will be parabola opening upward.
For that, the vertex will be the minimum cost
x = (-b) / 2a
Here, a = 0.055 , b = -120
Now, find and put the values of x.
minimum cost (x) = ( -(-120) ) ÷ ( 2 × 0.055 )
= 120 ÷ 0.11
= 120 ÷ 0.11
= 1090.90 ≈ 1091 units
The minimum cost will be yield for 1091 units.
Therefore, They should produce 1091 units each day to yield a minimum cost.
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Find the value of x.
What is Angle?
An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
From the figure, we can tell that a transversal is passing through the two parallel lines which makes corresponding angles.
In the given figure 14x+7 and 10x+5 are the two angles formed by the transversal.
14x+7=10x+5
Now take all the variable terms to one side
14x-10x=5-7
4x=-2
Divide both sides by 4
x=-2/4
Divide numerator and denominator by 4
x=-1/2
Hence the value of x is -1/2
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Please help me solve as soon as possible
Using the given expression, the number of tiles Mr. Grants will need to buy is 48
Solving an expression to determine the number of tilesFrom the question, we are to use the given expression to determine the number of tiles Mr. Grant would have to buy
From the given information,
The given expression is,
27 ÷ s²
and
Mr. Grants decides to buy square tiles that have side lengths of 3/4 foot
That is,
s = 3/4
Now,
Using the given expression
27 ÷ s²
We get
27 ÷ (3/4)²
27 ÷ 9/16
= 27 × 16 / 9
= 3 × 16
= 48
Hence, he will need to buy 48 of the tiles
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Find the x- and y-intercepts of the graph of 8x - 10y = 32. State each
answer as an integer or an improper fraction in simplest form.
The first container has 3 gallons 3 quarts 1 pint of diesel fuel, the second container has 5 gallons 2 quarts of diesel fuel, and the third container has 6 gallons 1 quart 1 pint of diesel fuel. what is the total quantity of diesel fuel?
The total quantity of diesel fuel is 15.75 gallons.
The total quantity of diesel fuel can be calculated by summing up all the values. But, firstly converting quarts and pint into gallons.
1 quart = 0.25 gallon
For first container, 3 quarts = 0.25 × 3
3 quarts = 0.75 gallon
For second container, 2 quarts = 0.25 × 2
2 quarts = 0.5 gallon
For third container, it has 0.25 gallon
1 pint = 0.125 gallon
For first and third container, it has 0.125 gallon
So, amount of diesel fuel in first container = 3 + 0.75 + 0.125
Amount of diesel fuel in first container = 3.875 gallons
Amount of diesel in second container = 5 + 0.5
Amount of diesel in second container = 5.5 gallons
Amount of diesel in third container = 6 + 0.25 + 0.125
Amount of diesel in third container = 6.375 gallons
So, the total quantity of diesel fuel = 3.875 + 5.5 + 6.375
The total quantity of diesel fuel = 15.75 gallons
Hence, the total quantity is 15.75 gallons.
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if f represents the number of lots of fliptop pens to produce and t represents the number of lots of tiptop pens to produce, the linear programming model for this problem is:
The linear programming model for this problem is Max 1000F + 1000T
Given that,
If the quantity of flip top pens to be produced is f and the quantity of tiptop pens to be produced is t, then
Number of lots of Flip top pens to produce = F
Number of lots of Tip top pens to produce = T
Therefore, The linear programming formulation is given by:
Max 1000F + 1000T
s.t.
Plastic: 3F + 4T <= 39
Ink Assembly: 5F + 4T <= 45
Molding time: 5F + 2T <= 37
F, P >= 0
Hence, the linear programming model for this problem is Max 1000F + 1000P
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solve the system by substitution
Answer:
Step-by-step explanation:
since x=y, you can either substitute for x or for y,
lets do x
-3x - x = 4
-4x=4
x=-1
Now we can just plug in
-3(-1) - y = 4
3-y = 4
y=-1
A share of Southside stock sold for $37. The annual dividend is $1.85. Three years later the stock has increased 17% in value and the dividend has increased 5%.
What is the yield 3 years later? Round to the nearest tenth of a percent.
The price of the share 3 years later, given the increase in value, can be found to be $43.29
How to find the price per share?The value of the Southside stock sold was $ 37 at the current age. Three years later, this value had increased by 17 %.
This means that the price of the share 3 years later would be:
= Share price currently x ( 1 + increase in value)
= 37 x ( 1 + 17 % )
= 37 x 1. 17
= $ 43. 29
The price is $43.29
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does this equal to 10 or 5 I’m confused I’ll brainlist .
Answer:
x = 5
Step-by-step explanation:
3x + 5 = 2x + 10
subtract 5 from both sides:
3x + 5 - 5 = 2x + 10 - 5
3x = 2x + 5
subtract 2x from both sides:
3x - 2x = 2x + 5 - 2x
x = 5
can someone do these for me pls i’m lazy
In peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses
Step-by-step explanation:
In Peter class three times as many students who wear glasses are those who do not.there are 28 students in the class. How many students do not wear glasses?
with glasses: x
without glasses: 3x
x + 3x = 28
4x = 28
x = 7 with glasses
7 * 3 = 21 without glasses
