The slope of a line perpendicular to the line is 5/4
What is the slope of a straight line?A straight line of the form
y = mx + c
has its slope as 'm'
It is constant for a line. The more the slope is, the steeper the line is.
Sign convention takes bottom left to top right going line as positive sloped. And that line which goes from bottom right to top left is taken to have negative slope. Horizontal line has 0 slope and vertical line has infinite slope, as it is now at maximum steepness.
If two lines are perpendicular, their slopes are negative reciprocals, which means that their product is -1
Given;
4x+5y=35
We can write the equation as;
4*x + 5*y - 35 = 0
5*y = - 4*x + 35 or
y = -(4/5)*x + 35
m= -4/5
So, now the slope of this line is -4/5 and line perpendicular slope will be 5/4
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The monthly cost (in dollars) of a long-distance phone plan is a linear function of the total calling time (in minutes). The monthly cost for 40 minutes of calls is $16.03 and the monthly cost for 81 minutes is $19.72. What is the monthly cost for 64 minutes of calls?
Answer:
18.19
Step-by-step explanation:
$ = linear f(t)
$16.03 = f(40) = fixed fee + per min fee = x + 40y
$19.72 = f(81) = fixed fee + per min fee = x + 81 y
use above 2 equations to minus the other
you get:
19.72-16.03 = 41y
so y = 0.09
so x = 16.03 - 40*0.09 =12.43
so for 64 mins
cost = 12.43 + 0.09*64 =18.19
Colin had $23 to spend on four raffle tickets after buying them had $11 how much did each raffle ticket cost what’s the equation HELPPP
Colin had $23 to spend on four raffle tickets after buying them had $11. So each raffle ticket cost is $3 and the equation is 4x + 11 = 23.
Colin had $23 to spend on four raffle tickets after buying them had $11
We have to determine how much each raffle ticket cost and the equation.
Let the cost of one raffle is x.
So the cost of four raffle is 4x.
Colin has total $23.
Colin has left money = $11
So the required equation should be
4x + 11 = 23
Now solving the equation
Subtract 11 on both side, we get
4x = 12
Divide by 4 on both side, we get
x = 3
The cost of one raffle is $3.
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The table shows the costs of movie tickets and large bags of popcorn for two groups of people.
a. Can you determine how much each ticket costs? Explain.
b. A third group buys 5 tickets and 4 large bags of popcorn for $82. How much more does a ticket cost than a large bag of popcorn?
According to the unitary method,
(a) Ticket cost for 5 people is $28.75
(b) The cost for ticket is $28.75 and the cost for popcorn is $53.25
In math the term called unitary method is defined as a basic concept to find the value of a single unit and then using that value to find the value of multiple units.
Here we have know that each person in a group buys a movie ticket, a drink, and a popcorn.
And the cost for each of the product is listed as Ticket is $5.75, Drink is $2.00 and Popcorn is $3.25.
Then the cost of 5 people is calculated as,
=> 5.75 x 5
=> 28.75
And the third group buys 5 tickets and 4 large bags of popcorn for $82.
Then the cost of the ticket is calculated as,
=> 82 - 28.75
=> 53.25
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Two Javan Rhinoceroses share a zoo exhibit. The younger one weighs tons, while the older one weighs 2,400 pounds. Which one weighs more?Explain
Answer:
if younger one weighs 1 ton, then older one is heavier
Step-by-step explanation:
1 ton = 2000lbs
Find the measure of angles 1 and 2.
Explain your reasoning as to how you determined the measurements of angles 1 and 2.
The required values of the angle ∠1 and ∠2 are 135°and 135°respectively.
Explain about angle.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint. The Latin word "angulus," which meaning "corner," is the source of the English term "angle." The shared terminus of two rays is known as the vertex, and the two rays are referred to as sides of an angle.
According to question:We need to find angle 1 and 2
So, by using corresponding angle theorem,
∠1 = 135°
Similarly for ∠2
By using vertically opposite angle,
∠2 =135°
Thus, required value of the angle are ∠1 = 135°, ∠2 =135°.
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In a school containing 360 children, 198 are girls. What percent of all the students are girls? What percent of the children are boys? The number of girls is what percent of the number of boys?
- 5x15x + 12x - 4x I don’t know how to solve this
Answer:
Step-by-step explanation:
Multiply the numbers:
-5x*15x + 12x - 4x.
Which should get you: -75xx + 12x - 4x
Then combine exponents : -75xx + 12x - 4 = -75x^2 + 12x - 4x
Combine like terms: -75x^2 + 8x
Then find common factor with is -1
Lastly, rewrite in factored form : -1(75x^2 + 8x) = -1(75x - 8)x
Calculate the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec. Model the dancer as a cylinder (I = MR 2) with a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m.
The angular momentum of an object can be calculated using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.
In the case of the ballet dancer, we are told that they are spinning at 1.5 rev/sec, and that they can be modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m, and a radius of 0.16 m.
We can calculate the moment of inertia of the cylinder using the formula I = (1/2) MR^2, where M is the mass and R is the radius.
Plugging in the values we have, I = (1/2)(62 kg)(0.16 m)^2 = 3.072 kg-m^2
We can then calculate the angular momentum of the dancer by plugging in the values we have into the formula L = Iω,
L = (3.072 kg-m^2)(1.5 rev/sec) = 4.608 kg-m^2/s
So the angular momentum of a ballet dancer who is spinning at 1.5 rev/sec, modeled as a cylinder with a moment of inertia of 22 MR^2, a mass of 62 kg, a height of 1.6 m and a radius of 0.16 m is 4.608 kg-m^2/s.
PLSSS HELP IF YOU TURLY KNOW THISSS
Answer:
8
Step-by-step explanation:
x= 24/3 = 8
Answer:
[tex] \sf \: x = 8[/tex]
Step-by-step explanation:
Given equation,
→ 3x = 24
Now the value of x will be,
→ 3x = 24
→ x = 24 ÷ 3
→ [ x = 8 ]
Hence, the value of x is 8.
a piece in a wooden toy set is a sphere of radius 7cm , with a cylindrical hole of radius 1cm drilled through the center. find the volume of this piece. write the exact answer. do not round.
The volume of the piece is: 4489.33
To find the volume of this piece, we need to subtract the volume of the cylindrical hole from the volume of the sphere.
The volume of the sphere is given by the formula: V = (4/3) * pi * r^3
Where r is the radius of the sphere, so in this case: V = (4/3) * pi * (7cm)^3 = 1436 * 3.14 cm^3 = 4511.32 cm^3
The volume of the cylinder is given by the formula: V = pi * r^2 * h
Where r is the radius of the cylinder and h is the height of the cylinder, since the hole is drilled through the center of the sphere, the height of the cylinder is equal to the radius of the sphere, so: V = 3.14 * (1cm)^2 * 7cm = 21.99 cm^3
So the volume of the piece is: 4511.32 - 21.99 = 4489.33 cm^3
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A popular gaming console that retails for $299,
was sold out for quite some time. Jake finally
found it on a resale platform, but it was marked
up 40%.
If Jake finally found the gaming console on a resale platform, it was marked up 40% ,then the amount that Jake has to pay to buy it is $418.6 .
The retail price of the gaming console is = $299 ;
the markup in the price of the gaming console is = 40% ;
then the new price of the gaming console is = 299 + 40% of $299 ;
= 299 + 0.40 × 299 ...because 40% is 0.40
Simplifying further ,
we have ;
= 299 + 119.6
= 418.6
Therefore , Jake has to pay $418.6 for the gaming console to buy from the resale platform .
The given question is incomplete , the complete question is
A popular gaming console that retails for $299, was sold out for quite some time. Jake finally found it on a resale platform, but it was marked up 40% , Find the amount that Jake has to pay to buy it .
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Can someone please help me? I need help ASAP
I need to show work btw
Answer:
Step-by-step explanation:
yes the triangle can be formed
h(x) = 3x; Find h(-6)
The points plotted on the coordinate grid represent the rule y = x + 4. Which table also represents this rule?
Answer:
See below
Step-by-step explanation:
No table was given but it should look something like
x y
-3 1
-2 2
-1 3
0 4
1 5
2 6
3 7
Whatever number you select for x add 4 to it and that will give you your y value
Workers in an office of 40 staff were asked their favourite type of take-away. The results are summarised in the table. Take-away Frequency Angle Pizza 3 a Curry 12 b Fish & chips 7 c Kebab 3 d Other 15 e Work out the size of each angle to draw a pie chart.
The measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
Given that, workers in an office of 40 staff were asked their favorite type of take-away.
Fraction of a person = 1 degree
Here, 360° = 40 people
So, 1 degree = 40/360 =1/9
Now, angle a =6/40 ×360
= 54°
Angle b= 2/40 ×360
= 18°
Angle c= 12/40 ×360
= 108°
Angle d = 9/40 ×360
= 81°
Angle e =11/40 ×360
= 99°
Therefore, the measure of angles a, b, c, d and e are 54°, 18°, 108°, 81° and 99°.
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Researchers created a new fertilizer. They conducted an experiment to compare the new fertilizer to the old fertilizer. They divided tomato plants into two groups. They applied the new fertilizer to one group and the old fertilizer to another group. The variable is the number of tomatoes per plant on a randomly selected day.
Which one of the following statements is valid?
A. The new formula of fertilizer works better. Plants with the new fertilizer had more tomatoes.
B. The old formula of fertilizer was better because the plant with the most tomatoes was treated with the old fertilizer.
C. The average number of tomatoes per plant with the old fertilizer is higher than the average amount of tomatoes per plant with the new fertilizer.
D. We can make no conclusions from this data about which fertilizer is better because the two groups have a different number of plants
The plant that produced the most tomatoes was treated with the old fertilizer, thus it was better. So statement B is correct.
A line plot is one type of graph that helps us to represent the data along the number line. This plot is also referred to as a dot plot. In this plot, we show the data as a check or point above a number line. Each point or check in this plot represents the frequency of each value.
The given plot about fertilizers is a line plot. In this plot, 1 dot over 2 in the old fertilizer treatment means about 2 plants have one tomato.
By comparing the line plot for both the new fertilizer and old fertilizer, we will be able to say that there are more tomatoes produced when the old fertilizer is used than the new fertilizer.
Nearly 65 tomatoes were produced when old fertilizer is used but only 58 tomatoes were produced when new fertilizer is used. Therefore, statement B is correct.
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A table shows miles and hours for today and yesterday. The number of miles is 15 for today and m for yesterday. The number of hours is 2.5 for today and 4 for yesterday.
The distance covered on the yesterday was 24 miles.
What is proportion?Proportion is a mathematical comparison between two numbers. According to proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other.
Given that, The number of miles is 15 for today and m for yesterday. The number of hours is 2.5 for today and 4 for yesterday, the rate is same for both the days, therefore, this will represent a proportion,
Therefore, establishing the proportion,
15 / 2.5 = m / 4
15 × 4 / 2.5 = m
m = 24
Since, we got the value of m is 24 miles.
Hence, the distance covered on the yesterday was 24 miles.
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3/5=?/10=33/?
Complete the empty places
The values in the empty places are 0.6 and 3.3 respectively.
What is division and multiplication?Multiplication is the process of adding a number repeatedly. When m is multiplied by n, m is being added to itself n times in total. The multiplication sign is "." A way to divide or distribute a number into equal parts is by division. The two key arithmetic operations in mathematics are multiplication and division. Similar to addition and subtraction, the processes of multiplication and division are intimately tied to one another. All real numbers are subjected to these processes.
The value of 3/5 can be calculated by dividing the numerator and the denominator.
3/5 = 0.6
The given expression is:
10 = 33/ x
Isolate the value of x:
10x = 33
x = 33/10
x =3.3
Hence, the values in the empty places are 0.6 and 3.3 respectively.
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Mateo has 8 liters of punch for a party. Each glass holds 1/5
liter of punch.
How many glasses can Mateo fill with punch?
amswer in simplest from fraction
Mateo can fill 40 glasses with punch and this can be calculated as :
8 liters = 8 x (5/1) = 40 liters
By solving the above equation following will be obtained.
Therefore, Mateo can fill 40 glasses with punch.
Mathematics, where the numerator and denominator are divided. Each is an integer in a simple fraction. Whether it is in the numerator or denominator, a complex fraction contains a fraction. The numerator and denominator of a correct fraction are opposite each other.
If numerator value is less than the denominator value, it is a proper fraction.If a numerator value is greater than denominator value, then it is called an improper fraction.
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noah spent 150$ to buy movie tickets for 15 students and 3 adults. Adult tickets cost $4 more than student tickets Use A as the price for an adult price and S for the price of student tickets.
The amounts of each ticket that were purchased are given as follows:
Adult: $11.67.Student: $7.67.How to obtain the amounts?The amounts are obtained using a system of equations, for which the variables are given as follows:
Variable a: number of adult tickets.Variable s: number of student tickets.Noah spent $150 to buy movie tickets for 15 students and 3 adults, hence:
3a + 15s = 150
a + 5s = 50
a = 50 - 5s
Adult tickets cost $4 more than student tickets, hence:
a = 4 + s.
The solution for s is then obtained as follows:
50 - 5s = 4 + s
6s = 46
s = 46/6
s = $7.67.
Then the price of an adult ticket is of:
7.67 + 4 = $11.67.
Missing InformationThe problem asks for the amounts of each ticket that were purchased.
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Determine the lowest common denominator for each sum or
13/24 • 7/12
Common Denominator: 10 Common Denominator: 12
Common Denominator: 24
7/6 • (-5/12)
344 • (-2/3)
5 - 7/10
1/8 - 5/3
3/2 -4/5
The expressions which are having common denominator 24 are
13/24 + 7/12 , 1/8 - 5/3 and for 10 are 5 - 7/10 , 3/2 - 4/5 and for 12 are
7/6 - 5/12, -3/4 - 2/3.
What is Algebraic expression ?
Algebraic expression can be defined as the combination of variables and constants.
Given ,
So given expressions are,
13/24 + 7/12 = 13+ 7*2 / 24 = 13+14 / 24 = 27/24
7/6 - 5/12 = 7*2 - 5 / 12 = 14-5/12 = 9/12
-3/4 - 2/3 = - (3/4 + 2/3 ) = - ( 9 + 8 / 12) = -17/12
5 - 7/10 = 5*10 - 7 / 10 = 50 - 7 / 10 = 43/10
1/8 - 5/3 = 3 - 8*5 / 24 = 3-40 / 24 = -37 / 24
3/2 - 4/5 = 3*5 - 2*4 / 10 = 15-8 / 10 = 7/10
Therefore, The expressions which are having common denominator 24 are 13/24 + 7/12 , 1/8 - 5/3 and for 10 are 5 - 7/10 , 3/2 - 4/5 and for 12 are 7/6 - 5/12, -3/4 - 2/3.
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Which of the following is an equation of the line through 11,3 and7,9
The linear equation for the coordinate points given is obtained as y = -3/2x + 19.5.
What is a linear equation?
A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.
The coordinate points for the lines are (11,3) and (7,9).
The slope-intercept form of an equation/function is - y = mx + b
To find the slope m use the formula -
(y2 - y1)/(x2 - x1)
Substituting the values in the equation -
[9 - 3]/[7 - 11]
(6)/(-4)
3/-2
So, the slope point is obtained as m = 3/-2.
The equation becomes - y = -3/2x + b
To find the value of b substitute the values of x and y in the equation -
3 = -3/2(11) + b
3 = -33/2 + b
b = 3 + 33/2
b = (6 + 33)/2
b = 39/2
b = 19.5
So, the value for b is 19.5.
Now, the equation becomes -
y = -3/2x + 19.5
The graph for the equation is plotted.
Therefore, the equation is obtained as y = -3/2x + 19.5.
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Earth is about 9. 27 x 107 miles from the Sun. Venus is about 6. 68 x 107 miles
from the Sun. About how much farther from the Sun is Earth than Venus?
Earth is 2.59 x 10⁷ miles farther from the Sun than Venus.
Let us assume that d₁ represents the distance between the earth and the sun.
d₂ represents the distance between the earth and the Venus.
The distance between the earth and the sun is 9.27 x 10⁷ miles.
d₁ = 9.27 x 10⁷ miles
And the distance between the Sun and the Venus is about 6. 68 x 10⁷ miles.
⇒ d₂ = 6. 68 x 10⁷
To find : by how much farther from the Sun is Earth than Venus
We need to find the absolute difference between d₁ and d₂
Let d be the absolute difference between d₁ and d₂
d = |d₁ - d₂|
d = | (9.27 x 10⁷) - (6. 68 x 10⁷ )|
d = |(9.27 - 6.68) x 10⁷ |
d = 2.59 x 10⁷ miles
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graph the quadrilateral with the given vertices in a coordinates plane then show that the quadrilateral is a parallelogram E(-3,0),F(-3,4),G(3,-1),H(3,-5)
If one set of the opposite sides of a quadrilateral is equal and parallel, the shape is referred to as a parallelogram.
Is quadrilateral is a parallelogram?A quadrilateral is a parallelogram if each pair of opposite angles in it is equal. The quadrilateral ABCD is a figure in which A = C and B = D. We are aware that a quadrilateral's angles add up to 360 degrees. ABCD is therefore a parallelogram.
A quadrilateral is a parallelogram if one pair of its opposite sides is both equal and parallel. A quadrilateral becomes a parallelogram if its diagonals cut each other in half.
The opposite sides of a parallelogram are equal to one another. A parallelogram's diagonals are consistently equal. The diagonals do not cross each other in a parallelogram. The diagonals in a parallelogram are always at right angles to one another.
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It takes Julie 4 minutes to run a kilometer. How many kilometers can she run in 12 minutes?
Answer: 180 kilometers
Step-by-step explanation:
Answer:
I think she runs 1 kilometer every 5 minutes
Step-by-step explanation:
1 1/5 - 1/3 greater or less than 1
Answer:
LESS THAN ONE
Step-by-step explanation:
1 1/5 - 1/3=0.86666666666
0.86666666666
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when the data have the properties of interval data and the multiplication or division of two values is meaningful, the variable has which scale of measurement?
When the data have the properties of interval data and the multiplication or division of two values is meaningful, the variable has which scale of measurement is referred to as Ratio Scale.
Now, According to the question:
A scale of measurement can be defined as a classification which is used to illustrate the attributes of the values that are assigned to variables associated with a data set.
The scales of measurement.
Generally, there are four (4) basic scale of measurement for a variable and these include the following;
Interval scaleRatio scaleOrdinal scaleNominal scale
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Three rectangular prisms are shown below. Prism A is a rectangular prism with a height of six inches, length of three inches, and a width of two inches. Prism B is a rectangular prism with a height of three inches, length of five inches, and a width of two inches. Prism C is a rectangular prism with a height of two inches, length of seven inches, and a width of two inches. Which statement is true? (4 points) a The volume of Prism A is less than the volume of Prism C. b Prism B has the greatest volume. c Prism B has a greater volume than Prism C. d Prism B and Prism C have the same volume.
The true statement is, c.) Prism B has a greater volume than Prism C.
What is volume?In mathematics, volume is the space taken by an object. Volume is a measure of three-dimensional space. It is often quantified numerically using SI derived units or by various imperial or US customary units. The definition of length is interrelated with volume.
here, we have,
Prism A is a rectangular prism with a height of six inches, length of three inches, and a width of two inches.
Prism B is a rectangular prism with a height of three inches, length of five inches, and a width of two inches.
Prism C is a rectangular prism with a height of two inches, length of seven inches, and a width of two inches.
now,
volume of prism=V = B*H
where, B is the area of base.
so, by calculating we get,
V-prism A= 36 inch^3
V-prism B= 30inch^3
V-prism C=28 inch^3
Hence, c.) Prism B has a greater volume than Prism C.
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Answer:
C
Step-by-step explanation:
4. The two trapezoids below are similar. What
is the length of segment EF?
24 am
A
D
30 cm
B
C
G.
7.5 cm
X
E
H
Help please
The length of the segment EF for the given trapezoids is 6 cm.
How do trapezoids work?Quadrilaterals called trapezoids have two parallel and two non-parallel sides. It also goes by the name Trapezium. A trapezoid is a closed, four-sided shape.
An opposing set of sides are parallel. The four angles of a trapezium add up to 360 degrees, and their diagonals cut each other in half. It has four odd-numbered sides. Thus, the opposing sides of an isosceles trapezium are congruent, as well as the diagonals.
Trapezoids ABCD and EFGH are similar,
Hence, corresponding sides ratio are equal:
Thus, AB/EF = DC/HG
24/x = 30/7.5
30x = 180
x = 180/30
x= 6
Hence, the length of the segment EF is 6 cm.
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Please help me out on my homework
Answer:
no solutions
Step-by-step explanation:
8(2w - 3) = 4(4w - 8)
Use distributive property.
16w - 24 = 16w - 32
subtract 16w from both sides.
-24 = -32
When the variable falls out of the equation as you are working on it, and you're left with a false statement, there is no solution.
Answer:
no solution
Step-by-step explanation:
to find the value of w, we have to isolate it on one side of the equation.
first, we distribute the numbers outside of the parentheses and multiply them to each term on the inside. this gives us:
16w - 24 = 16w - 32
next, we move 24 to the other side of the equation by adding 24 to both sides. by doing this, we get rid of 24 on the left side by making its value 0, and we add it to -32 on the right side. this gives us:
16w = 16w - 8
after this, we do the same with the 16w on the right side and subtract it from both sides. however, you might notice that there's a problem here.
when you try to move the 16w on the right side to the left side, you subtract 16w from itself, which gets rid of the variable entirely. whenever this happens, there are no values of the variable that make the equation possible- meaning that the answer is no solution.
hope this helped, good luck!