The graph of the line of the proportional relationship is added as an attachment
The unit rate is 7/6
How to graph the line of the proportional relationshipFrom the question, we have the following parameters that can be used in our computation:
An increase of 6 units in t This corresponds to an increase of 7 units in dThis means that
d : t = 7 : 6
Express as fraction
So, we have
d/t = 7/6
Multiply both sides by t
d = 7t/6
So, the equation is d = 7t/6
This also means that the unit rate is 7/6
See attachment for the graph
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K=ºC+273.15
Slope
Y-intercept
The slope of the straight line equation as required to be determined in the task content is; 1.
The y-intercept of the straight line equation as represented in the task content is; 273.15.
What values correctly represent the slope and y-intercept of the given equation?It follows from the task content that the values which correctly represents the slope and y-intercept of the given equation be determined.
Since the given equation is;
K = ºC + 273.15
By comparison with the slope-intercept equation of a straight line; y = mx + c where y = K and x = °C.
It follows that the slope, m = 1 and the y-intercept, c = 273.15.
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Find the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ in standard position on the coordinate plane with the point (−3,−5) on its terminal side.
sinθ=
cosθ=
tanθ=
cscθ=
secθ=
cotθ=
The values sinθ=-5/√34, cosθ=-3/√34, tanθ = 5/3, cotθ = 3/5, secθ = -√34/3 and cscθ = -√34/5
What is Trigonometry?Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.
We have to find the values of sine, cosine, tangent, cosecant, secant, and cotangent for the angle θ in standard position on the coordinate plane with the point (−3,−5) on its terminal side
r=√9+25
=√34
sinθ=y/r
sinθ=-5/√34
cosθ=x/r
cosθ=-3/√34
tanθ = y/x
tanθ = 5/3
cotθ = x/y
cotθ = 3/5
secθ = r/x
secθ = -√34/3
cscθ = r/y
cscθ = -√34/5
Hence, values sinθ=-5/√34, cosθ=-3/√34, tanθ = 5/3, cotθ = 3/5, secθ = -√34/3 and cscθ = -√34/5
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What is a number that when you add 5 to it and then multiply the sum by 3 will equal 27?
Use strategic thinking to find the solutions to these questions.
a. How much is 50 % of 10 liters of milk?
b. How far is 50 % of a 2,000- kilometer trip?
c. How long is 50 % of a 24 hour day?
Using strategic thinking, the solutions to the following questions are:
a) 5 liters of milkb) 1,000 kilometersc) 12 hours.What is strategic thinking?Strategic thinking involves using rational thought processes to focus on workable solutions to business problems.
Strategic thinking concentrates on the future based on its changing environments.
In this situation, 50% of a number represents one-half of the given value. We can divide each number by 2 to find the solutions.
a) 50% of 10 liters of milk = 5 liters (10 x 50%)
b) 50% of 2,000 kilometers = 1,000 kilometers (2,000 x 50%)
c) 50% of 24 hours = 12 hours (24 x 50%)
Thus, strategically thinking, half of each value represents its 50%.
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Which event will have a sample space of S = {g, b}?
A. Flipping a fair, two-sided coin
B. Rolling a six-sided die
C. Flipping a two-sided coin with one side green and the other side blue
D. Choosing a tile from a pair of tiles, one with the letter A and one with the letter B
An event that will have a sample space of S = {g, b} include the following: C. Flipping a two-sided coin with one side green and the other side blue.
What is a sample space?In Mathematics and statistics, a sample space can be defined as a set or collection of possible outcomes (results or outputs) that are obtainable from a random experiment. Mathematically, a sample space is represented or denoted by using the symbol, "S."
Additionally, a sample space may contain a number of outcomes (results or outputs) that depends on the experiment. Generally speaking, the subset of possible outcomes (results or outputs) of that are obtainable from an experiment is typically referred to as events.
In this context, we can reasonably infer and logically deduce that "Flipping a two-sided coin with one side green and the other side blue" is an event which would have a sample space that is modeled by this mathematical expression;
S = {g, b}
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Answer: C: Flipping a two-sided coin with one side green and the other side blue.
Solve for the balloon volume using the
equation below where:
volume = v
circumference = c
V=
The volume of the balloon is 1441.64cm³.
How to calculate the volume?To calculate the volume these are few ways
Solve for Volume by space. All physical objects occupy space, and you can find the volume of some of them by measuring their physical dimensions. Solve for Volume by Density and Mass. Density is defined as an object's mass per a given unit of volume. Solve for Volume by Displacement.The radius of the balloon is given as 7 cm. Also, the equation to calculate the volume is given as c³/6π²
The circumference c will be:
= 2πr = 2 × 22/7 × 7
= 44
The volume will be:
= c³/6π²
= 44³/(6 × 3.14²)
= 85284/(59.1576)
= 1441.64
Therefore, volume of the balloon will be 1441.64 cm³.
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You now have a lot of experience working with equations that compare two quantities. For example, while working on the Big Race, you found relationships of the form y = mx + by=mx+b, which compared x (time in seconds) with y (distance in meters). If a participant's race can be modeled with the equation y= 3x+4y=3x+4: a. How much of a head start did the participant get? How can you tell from the equation? b. What was participant's rate of speed? That is, how fast did they go? Justify your answer.
The participant received a head start of 4 meters. The 4 in the equation represents the initial position of the participant.
The participant's rate of speed of the participant is 3 meters per second.
How to determine how much of a head start the participant gets?a. The participant received a head start of 4 meters.
The 4 in the equation represents the initial position (y-intercept, c) of the participant, so this is the head start that the participant received.
b. The participant's rate of speed of the participant is 3 meters per second.
This means that for every 1 second (represented by x in the equation), the participant covers a distance of 3 meters. So the participant's rate of speed is 3 meters per x second
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local salesman receives a base salary of $875 monthly. He also receives a commission of 6% on all sales over $1450. How much would he have to sell in a month if he needed to have a monthly income of $2800?
The total sales required to earn the desired income of $2800 is calculated to be $6,375.
What is sale?Sale is a business transaction involving the exchange of goods or services for money. It can refer to the act of selling, or the thing that is sold. Sales are typically the main source of revenue for businesses. The process of selling involves finding potential customers, negotiating a price, and delivering the product or service. The ultimate goal is to make a profit.
In order to earn a monthly income of $2800, a local salesman would need to sell $6,375 worth of goods in a month. This is calculated by subtracting the base salary of $875 from the desired income of $2800, which leaves $2,925. Then, 6% of $1450 is $87, so the remaining $2,838 must be made up of 6% of the sales above $1450. By dividing this amount by 6%, the total sales required to earn the desired income of $2800 is calculated to be $6,375.
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what is the answers for these questions
Answer:
1) 6 kids have hamsters
13 kids have dogs
2) Tia scored more in English
She scored around 15 points more
Her range is around 15
Step-by-step explanation:
Answer:
for the first three questions:
1. fill out two boxes in the cat section
2. 6 students
3. 13 students
for the last questions:
1. just fill the lines up to the numbers in the question
2. english
3. about 18%? (not sure)
Step-by-step explanation:
Ivanna needs 201 programs for the school play on Thursday. How many boxes of programs will she need, given that each box contains 46 programs?
boxes
31
E
The number of boxes of programs that she needed will be 5.
What is Algebra?Algebra is the study of algebraic expressions, while logic is the manipulation of those concepts.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to answer the problem correctly and precisely.
Ivanna needs 201 programs for the school play on Thursday. If each box contains 46 programs.
Then the number of boxes of programs that she needed will be given as,
⇒ 201 / 46
⇒ 4.369
The number of boxes cannot be in decimal form. Then the number of boxes will be 5.
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A construction worker needs 3 2/3 pounds of concrete mix. He has 1 1/2 pounds of concrete mix in one bag, and he has 3/10 pound of concrete mix in another bag.
How many more pounds of concrete mix does the construction worker need?
Enter your answer as a mixed number in simplest form by filling in the boxes
On solving the provided question, we cam say that - by unitary method the answer is 4/5
What is unitary method ?The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.
here, construction worker = 2/3 pounds
he has = 1/2
so the answer is 4/5
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(a) An angle measures 55 degrees . What is the measure of its complement?
(b) An angle measures 82 degrees. What is the measure of its supplement?
Answer:
a) 35 degrees
b) 98 degrees
Step-by-step explanation:
Complementary angles measure up to 90 degrees. So if one angle measures 55 degrees, the other would have to be 35 degrees as
55 + 35 = 90
Supplementary angles measure up to 180 degrees. So if one angle measures 82 degrees, the other would have to be 98 degrees as
82 + 98 = 180
Let R be the region enclosed by the graph of f(x) x^4-2.3x^3+4 and the horizontal line y=4, as shown in the figure above.
a. Find the volume of the solid generated when R is rotated about the horzontal line y=-2
b. Region r is the base of a solid. for this solid, each cross section perpendicular to the x-axis is an isosceles right triangle with a leg in r. find the volume of the solid.
c. The vertical line x = k divides R into two regions with equal areas. Write but do not solve, an equation involving integral expressions whose solution gives the value k
The volume of the solid generated when R is rotated about the horizontal line y=-2 is 98.868.
The volume of the solid:3.574
The equation involving integral expressions:
[tex]\int\limits^k_0 {(4-f(x))} \, dx =\int\limits^2_0 {(4-f(x))} \, dx[/tex]
The given equation is f(x)=x^4-2.3x^3+4
f(x)=4 ⇒x=0,x=2.3
Now, substitute the values in the equation:
⇒ Volume= [tex]\pi \int\limits^2_0 {(4-(-2)^2)} \, dx -(f(x)-(-2)^2)dx[/tex]
By solving the equation we get:
volume=98.868
b) consider the point r in the graph which is perpendicular to the x-axis that an isosceles right triangle with a leg in r.
Area of cross-section:
A=1/2(leg)(leg)=1/2(4-f(x))^2
Volume=∫(1/2(4-f(x))^2)dx ∴with limits (0 to 2.3)
Solving the function we get:
Volume=3.574
c)given the vertical line x=k divides R into two regions with equal areas.
∫(4-f(x))dx=∫(4-f(x))dx
2∫(4-f(x))dx=∫(4-f(x))dx ∴with limits 0 to 2.3 and 0 to k
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Please :) !!
Find the value of b in each parallelogram. Then find each side length or
angle measure.
Answer:
Step-by-step explanation:
Six friends went to the movies, if the total cost was $27.00, how much was each ticket?
Answer:
$4.50 each
Step-by-step explanation:
27/6=4.50
a) Write - x² - 14x + 9 in the form -(x + c)² +d, where c and d are numbers. What are the values of c and d?
b) Hence, write down the coordinates of the turning point of the
curve y = -x² - 14x + 9.
a) The values of c and d are 7 and 58.
b) The coordinates of the turning point of the curve y = -x² - 14x + 9 is,
⇒ (- 7, 58)
What is Quadratic equation?An algebraic equation with the second degree of the variable is called an Quadratic equation.
Given that;
The expression is,
⇒ - x² - 14x + 9
Now, Simplify the expression to change in the form of -(x + c)² + d as;
⇒ - x² - 14x + 9
⇒ - (x² + 14x) + 9
⇒ - (x² + 14x) - 49 + 49 + 9
⇒ - (x² + 14x + 49) + 49 + 9
⇒ - (x + 7)² + 58
By comparing, we get;
The values of c and d are,
⇒ c = 7
⇒ d = 58
And. To find the coordinates of the turning point of the curve
y = -x² - 14x + 9, we can differentiate it with respect to x and equate it to zero.
⇒ y = -x² - 14x + 9
⇒ dy/dx = - 2x - 14 = 0
⇒ - 2x = 14
⇒ x = - 7
And,
⇒ y = -x² - 14x + 9
⇒ y = - (-7)² - 14×- 7 + 9
⇒ y = - 49 + 98 + 9
⇒ y = 58
Thus, The coordinates of the turning point of the curve y = -x² - 14x + 9 is,
⇒ (- 7, 58)
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A cow is tied with a rope in the centre of a circular lawn of diameter 28cm.If the length of the rope is 7cm, find the area of the lawn which the cow graze.Also find the remaining area of thelawn.
Diameter of Lawn = 28 cm
Length of rope tied at the centre of lawn = 7cm.
As the cow, tied to the rope grazes the lawn it forms a circle with radius 7cm.
Area of lawn grazed by cow
= pi*7^2. ( pi = 3.14)
= 3.14 * 49
= 153.86 sq. cm
Area of the lawn with radius 14 cm
= pi * 14^2. (pi = 3.14)
= 3.14 * 14^2
= 615.44 sq cm
Remaining area = Area of the Lawn - Area of the lawn grazed by cow
= 615.44 - 153.86
= 461.58 sq cm
PLEASE HELP DONT IGNORE ASAP.
Determine if the situations described below are proportional or not proportional.
Answer: both are proportional
Step-by-step explanation:
Both. ..............................
Which expression is equivalent to
5
NIF
NIN
X
no
5/5
PA
2
y
? Assume y* 0.
Expression [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex] is equal to [tex]x^{2/7} /y^{-3/7}[/tex]
The correct option is 1.
What is algebraic expression?An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations (addition, subtraction, etc.). Expressions are made up of terms.
Examples:
3x + 4y – 7, 4x – 10, etc.
Given expression is
[tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex]
⇒[tex]x^{2.1/7} /y^{3.1/5}[/tex]
⇒[tex]x^{2/7} /y^{3/5}[/tex]
⇒[tex]x^{2/7} . y^{-3/5}[/tex]
Hence [tex]\frac{\sqrt[7]{x} ^{2} }{\sqrt[5]{ y^{3}} }[/tex] is equivalent to [tex]x^{2/7} /y^{-3/7}[/tex].
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help please i don’t understand this!!!
Each side length of an equilateral triangle is (6x³+9x)/3 units
What is perimeter?
The complete length of a shape's edge serves as its perimeter in geometric terms. Adding the lengths of all the sides and edges that surround a form yields its perimeter. It is calculated using linear length units such centimeters, meters, inches, and feet.
An equilateral triangle has all the sides equal in length
Let each side be y
Perimeter is the sum of all sides
So, Perimeter = y+y+y = 3y
Given, Perimeter = 6x³+9x
=> 3y= 6x³+9x
=> y= (6x³+9x)/3
Thus, each side length of an equilateral triangle is (6x³+9x)/3 units
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2. A doctor's office casts a shadow that is 21 feet long. At the same time of day, a nearby tree standing 7 feet tall casts a 3 -foot-long shadow. How tall is the doctor's office?
25 ft.
49 ft.
9 ft.
34 ft.
The height of the doctor's office is solved using similar triangles to give
49 feetWhat are similar triangles?When the corresponding sides of two triangles are proportionate and their corresponding angles are congruent, The triangles are said to be similar.
As a result, the triangle's side should be proportionate if its corresponding angles are congruent.
Examining the descriptions shows that pair of equivalent sides are
height of tree and shadow of tree,
height of doctor's office and shadow's of doctor's office
The solution is worked out
height of tree / shadow of tree = height of doctor's office / shadow's of doctor's office
7 / 3 = height of doctor's office / 21
cross multiplying
3 * height of doctor's office = 7 * 21
height of doctor's office = 7 * 21 / 3
height of doctor's office = 49 feet
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46. A microscope shows an image of an object that is 70 times the object's actual size. So, the
scale factor of the enlargement is 70. An insect has a body length of 6 millimeters. What is the
body length of the insect under the microscope?
42 millimeters
420 centimeters
420 millimeters
4,200 millimeters
Answer:
420 millimeters
Step-by-step explanation:
If the scale factor of the enlargement is 70, and the body length of the insect is 6 millimeters, then the body length of the insect under the microscope is 6 millimeters * 70, which is 420 millimeters. So the correct answer is 420 millimeters.
Hello! Please help asap.
The line graph of the inequality is represented by an open circle at x = - 9 going towards negative infinity.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
The given inequality is x + 3 < - 6.
x < - 6 - 3.
x < - 9.
The line graph of the inequality will be represented as an open circle at
x = - 9 extending towards negative infinity because x is strictly smaller
than 9.
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There are two sets of rainfall data for two different time periods in the same location.
Period 1: 2.3, 2.1, 2.2, 2.2, 2.2, 2.1, 2.4, 2.5, 2.2, 2.0, 1.9, 1.9, 2.1, 2.2, 2.3
Period 2: 2.3, 2.1, 3.3, 1.5, 3.6, 1.6, 3.0, 1.1, 4.7, 2.1, 2.4, 1.9, 2.8, 0.5, 2.3
Draw a conclusion based on the data provided.
has to be a sentence
Comparing the two sets of rainfall data for two different time periods in the same location, it can be concluded that the amount of rainfall in Period 1 was fairly constant whereas the amount of rainfall in Period 2 varied greatly.
What conclusion can be drawn from the rainfall data?The rainfall data for two different time periods in the same location provides information about the pattern of rainfall over the time periods.
The rainfall data over the period did not vary widely apart. The data shows that the amount of rainfall did not change too much.
However, for Period 2, the amount of rainfall had very different values.
Hence, it seems rainfall was more precise in frequency in Period 1 than in Period 2.
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TJ Maxx's stock from Tuesday to Wednesday went from $22 to $25. Find the percent increase in the stock
Jordan is painting her kitchen.
To get the color she wants, she mixes 2 parts red paint and 6 parts yellow paint.
If she needs 18 parts of yellow paint, how much red paint will she need?
Answer:
1. 1/3 or 1 red paint : 3 yellow paint
2. 3/1 or 3 or 3 yellow paint: 1 red paint
Step-by-step explanation:
This velocity-time graph shows 8 seconds of a car journey.
What was the total distance travelled by the car during this time?
If your answer is a decimal, give it to 1 d.p.
Velocity (m/s)
20
15
10
5
0
Time(s)
The distance covered by the car in 8 seconds of the journey is 100 meters.
What is the distance?The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.
Given:
Velocity (m/s) = 20, 15, 10, 5, 0
Calculate the distance as shown below,
[tex]Distance = velocity \times time[/tex]
Distance = 0 × 20 + 15 × 2 + 10 × 4 + 5 × 6 + 0 × 8
Distance = 0 + 30 + 40 + 30 + 0
Distance = 100 meter
Thus, the distance covered by the car is 100 meters.
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Write the equation of the line that passes through the points (-3,-1) and (5, -1).
Put your answer in fully simplified point-slope form, unless it is a vertical or
horizontal line
The equation of line passes through the points (-3, -1) and (5, -1) will be;
⇒ y = - 1
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;
Two points on the line are (-3, -1) and (5, -1).
Now,
Since, The equation of line passes through the points (-3, -1) and (5, -1)
So, We need to find the slope of the line.
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (- 1 - (-1)) / (5 - (-3))
m = 0/8
m = 0
Thus, The equation of line with slope 0 is,
⇒ y - (-1)= 0 (x - (-3))
⇒ y + 1 = 0
⇒ y = - 1
Therefore, The equation of line passes through the points (-3, -1) and (5, -1) in slope intercept form is,
⇒ y = - 1
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Chelsea is sewing handmade scarves she has 7 1/2 yards of material and needs 2 1/4 yards of material for each scarf
Chelsea is sewing handmade scarves she has 7 1/2 yards of material and needs 2 1/4 yards of material for each scarf, so the number of scarves can she make with the existing material = 3. This can be solved using the concept of fractions.
What is fractions?In mathematics, the portion or component of the complete item is represented by a fraction. It stands for the equal components of the whole. Both the numerator and denominator are components of a fraction. The top number is referred to as the numerator, while the bottom number is referred to as the denominator.
Total material = [tex]7\frac{1}{2}[/tex] yards
[tex]= 7\frac{1}{2} = 7 + \frac{1}{2} = \frac{15}{2}[/tex] yards
Materials required for each scarf = [tex]2\frac{1}{4}[/tex] yards
Number of scarfs she make with the existing material
= Total Material ÷ Material required for each scarf
= [tex]\frac{15}{2}[/tex] ÷ [tex]\frac{9}{4}[/tex]
= [tex]\frac{15}{2}[/tex] × [tex]\frac{4}{9}[/tex]
= [tex]\frac{10}{3}[/tex]
= [tex]3\frac{1}{3}[/tex] ≈ 3
Hence, the number of scarves can she make with the existing material = 3.
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etermine T10 of the following geometric sequences
a)T2=-10 and T6=-160
The T10 of the sequence is
T10 =-10.00
What is a geometric sequence?Generally, To determine the T10 of a geometric sequence, you will need to know the common ratio of the sequence.
If T2=-10 and
T6=-160, we can use these terms to find the common ratio.
The formula for any term in a geometric sequence is:
Tn = a * r^(n-1)
Where
Tn is the nth term, a is the first term, and r is the common ratio.We can use the terms you provided to find the common ratio:
-160 = -10 * r^(6-1)
-160 = -10 * r^5
r = (-160/-10)^(1/5)
Now that we know the common ratio, we can find T10:
T10 = a * r^(10-1)
T10 = -10 * r^9
So the T10 of the geometric sequence is
T10= -10 * (-160/-10)^(1/5)^9
T10 =-10.00
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