In linear equation, 60m is the height of flagpole c .
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
Height/ Shadow
Shadow of the pole = 12 m
Height of the pole = x m
Tim's shadow = Height of the pole - Tim's distance
12 m - 10 m = 2 m
Tim's height = 2 m
Hence:
x/12 = 2/10
Cross Multiply
2x = 12 × 10
x = 120/2
x = 60 m
Approximately = 60m
Hence, the height of the flagpole = 60m
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solve
(2x-3) (x2+4x-5)
Answer: 2x^3 + 5x^2 - 10x + 15
Step-by-step explanation:
To multiply two polynomials, you can use the distributive property and multiply each term of one polynomial by each term of the other. In this case, the two polynomials are (2x - 3) and (x^2 + 4x - 5), so we have:
(2x - 3) * (x^2 + 4x - 5) =
2x * x^2 + 2x * 4x - 2x * 5 +(-3) * x^2 + (-3) * 4x - (-3) * 5
Expanding the products, we get:
2x^3 + 8x^2 - 10x - 3x^2 - 12x + 15
Combining like terms, we get: 2x^3 + 5x^2 - 10x + 15
the sum of 3 consecutive multiples of 8 is 888 find the multiples
[tex]\fbox{\textbf{288, 296, and 304}}
[/tex]
Step-by-step explanation:Let's assume the first multiple of 8 is x, then the second multiple is x+8, and the third multiple is x+16.According to the problem statement, the sum of these three multiples is 888:x + (x+8) + (x+16) = 888Simplifying the left side:3x + 24 = 888Subtracting 24 from both sides:3x = 864Dividing both sides by 3:x = 288Therefore, the first multiple of 8 is 288, the second is x+8 = 296, and the third is x+16 = 304.So, the three consecutive multiples of 8 that add up to 888 are 288, 296, and 304Which number is a factor of 24 but not a multiple of 12
Convert 2 pints into milliliters. Round your answer to the nearest whole number.
Answer: 946 ml
Step-by-step explanation: 1 pint= 473.2
2*
473.2= 946.4
=946 ml
Select all of the expressions that have a positive value based on the positions of a and b.
(Select all that apply.)
1. -b
2. a+b
3.a-b
4. a*b
5. -b/a
The expressions that have a positive value based on the positions of a and b are a + b and a×b. options 2 and 4
What are algebraic expressions?Algebraic expressions are defined as expressions that are made up of terms, variables, factors and constants.
These expressions are also composed of mathematical operations such as;
SubtractionBracketParenthesesMultiplicationAdditionDivisionFloor divisionGiven the expressions;
a+ b and a×b.
They have the variables both positive
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a || b and p is a transversal. If m 1 = 140°, find the
measure of each angle giving one reason for each answer.
(The first one is done for you.)
Answer:
Angle 4 = 140
Angle 3= 40
Angle 5=140
angle 6=40
angle 7=40
Step-by-step explanation:
Adjacent angles are congruent. Thats how I can tell angle 4 is 140. And also how i can tell angle 3 is 40. Any questions?
im not explaining the rest im too tired
btw I also do 8th math lol it stinks.
Two important ingredients for baking bread are
yeast and flour. To make a loaf of bread of at
most
30 servings, maintain a yeast to
flour ratio of 1:200. If you're making a loaf of more than 30
servings, use a ratio of 1:180.
If you're making 30 servings
of bread and using 0.25 oz of yeast, how many ounces of flour do you
need?
If you're making 60 servings of bread and using 540 oz of flour, how many ounces of yeast do you
need?
NOTE: Enter only numerals for each of your answers.
If you're making 60 servings of bread and using 540 oz of flour, then the number of ounces of yeast you need is 3 oz.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, to make a loaf of bread of at most 30 servings, maintain a yeast to flour ratio of 1:200. If you're making a loaf of more than 30 servings, use a ratio of 1:180.
If you're making 30 servings of bread and using 0.25 oz of yeast, then
0.25/Flour = 1/200
Flour = 50 oz
If you're making 60 servings of bread and using 540 oz of flour, then
Yeast/540 = 1/180
Yeast = 3 oz
Therefore, if you're making 30 servings of bread and using 0.25 oz of yeast, then the number of ounces of flour you need is 50 oz.
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The table below shows the ratios of black to white keys on pianos of various sizes.
Black A 18 45 72
White 13 B 65 C
Determine which table has the correct values for A, B, and C.
Black 8 18 45 72
White 13 25 65 105
Black 9 18 45 72
White 13 26 65 104
Black 9 18 45 72
White 13 39 65 117
Black 1 18 45 72
White 13 26 65 104
Using the given ratios found the values of A, B and C, and completed the table as follows:
Black 9 18 45 72
White 13 26 65 104
What is meant by the ratio?
A ratio in mathematics demonstrates how many times one number is present in another. A ratio is what a fraction looks like when it is written as a:b. A ratio is the comparative or condensed version of two quantities of the same type.
Given the table:
Black A 18 45 72
White 13 B 65 C
The table represents the ratios of black keys to white keys on pianos of various sizes.
The ratio of keys of the piano always remains constant.
So we can write as follows:
A/13 = 18/B = 45/65 = 72/C
To find A, we take the following ratios.
A/13 = 45/65
On solving, we get
A = 45 * 13 / 65 = 585/65 = 9
To find B, we take the following ratios.
18/B = 45/65
B = 18 * 65 / 45 = 1170/45 = 26
To find C, we take the following ratios.
72/C = 45/65
C = 72 * 65 / 45 = 104
Therefore using the given ratios we can complete the table using the values of A, B and C,
Black 9 18 45 72
White 13 26 65 104
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x^2+y^2=100 is it a function?
The equation x^2+y^2=100 is not a function
How to determine if it is a functionFrom the question, we have the following parameters that can be used in our computation:
x^2 + y^2 = 100
The above equation is a circle equation
As a general rule, we have
Circle equations are not functions and they do not represent a function on a graph
Hence, x^2+y^2=100 is not a function
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can someone explain the questions attached? thanks
The probability of landing on the head side of coin and rolling a 3 on the die is found as 1/12.
Explain about the term sample space?A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of feasible experiment results. Depending on the experiment, a sample area could contain a variety of results.Sample space for tossing a coin: (H,T)
P(head) = 1/2
Sample space for tossing a dice : (1, 2, 3, 4, 5, 6)
P(3) = 1/6
So,
Probability of head with 3 on the die = 1/ 2* 1/6 = 1/ 12
Thus, the probability of landing on the head side of the coin and rolling a 3 on the die is found as 1/12.
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The correct question is-
A coin is tossed and a single 6-sided die is rolled. Find the probability of landing on the head side of the coin and rolling a 3 on the die.
Enter your answer as a fraction in the form a/b (for example 2/3, 5/7) or as an integer.
How many nets are there for a triangular pyramid?
The net of a triangular pyramid consist of a total of 4 triangles. it has 4 faces with the base being one of them which is also in the shape of a triangle.
A net of the triangular pyramid is the pattern formed when the surface of it is laid out flat showing each triangular face of the figure, therefore we know that the net of a triangular pyramid consist of a total of 4 triangles.
Triangular pyramid is a pyramid which has a triangular base. In geometry, vertices are essentially corners. All triangular-based pyramids, either regular or irregular, have four vertices.
It has 6 edges, 4 faces, 4 vertices.
A regular triangular pyramid has equilateral triangles all four faces
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What is the degree of 7c3d2
The degree of the expression 7c³d² is 2
How to determine the degreeFrom the question, we have the following parameters that can be used in our computation:
Expression = 7c³d²
The degree of an expression is the highest power in the expression
In this case,
7c³ = Constant
d² = Variable
The highest power of the variable is 2
Hence, the degree is 2
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Select all the equations that are equivalent.
52 = 8n + 4
4(2n + 1) = 52
4 = 52 – 8n
4n = 48
n = 6
The equivalent equations are 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
To determine which equations are equivalent to each other, we can simplify and manipulate each equation to see if they have the same solution(s).
52 = 8n + 4 can be simplified by subtracting 4 from both sides:
48 = 8n
n=6
Now 4(2n + 1) = 52
8n+4=52
8n=48
n=6
So the 52 = 8n + 4 and 4(2n + 1) = 52 are equivalent equations.
Now 4 = 52 – 8n
8n=52-4 is also equivalent equation.
4n=48 and n=6 are also equal but they are not in the same form as above equations.
Hence, 52 = 8n + 4, 4(2n + 1) = 52 and 4 = 52 – 8n are equivalent equations.
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Which statements are correct about the average rate of change for the function
given in the table?
x y
1 1
2 3
3 7
4 15
Select all correct answers.
Select 2 correct answer(s)
The correct answer is the rate of change is 6 over interval 1 ≤ x ≤ 4 and the rate of change is 6 over interval 2 ≤ x ≤ 4
What is the rate of change?Rate of change is used to mathematically describe the percentage change in value over a defined period of time, and it represents the momentum of a variable. In general, the formula for rate of change is: R = (D2 - D1)/T. where: R = rate of change.
Given that is a table, we need to find the average rate of change for the function,
a = 1, f(a) = 1
b = 2, f(b) = 3
Average rate of change is given by = f(b)-f(a) / b-a
= 3-1 / 2-1
= 2
a = 3, f(a) = 7
b = 4, f(b) = 15
Average rate of change is given by = f(b)-f(a) / b-a
= 15-7 / 4-3
= 8
a = 2, f(a) = 3,
b = 3, f(b) = 7
Average rate of change is given by = f(b)-f(a) / b-a = 4
Hence, the correct answer is the rate of change is 6 over interval 1 ≤ x ≤ 4 and the rate of change is 6 over interval 2 ≤ x ≤ 4
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8 A crystal paperweight
is shaped like a cylinder with a star-shaped hole. The
top of the star-shaped hole is shaped like a square with four points that are
identical equilateral triangles. The height of the cylinder is 3 centimeters. Find
the volume of the paperweight.
Please Help ASAP!!!
The volume of the paperweight is 79.3 cm³.
What is a cylindrical shape?A cylinder is a three-dimensional solid object with two bases that are identically circular and are connected by a curving surface that is located at a specific height from the center.
Examples of cylinders are toilet paper rolls and cold beverage cans.
The volume of a cylinder is πr²h.
Curved surface area = 2πrh.
Total surface area = 2πr(h + r).
From the given information, The area of the star-shaped cutout is,
A square has a side length of 2 cm, and four equilateral triangles have a side and a height of 2 cm.
So, The area of the star-shaped cutout is,
= (2×2) + 4×(1/2)×2×2.
= 4 + 8.
= 12 cm.
Now, The volume of the star-shaped cut-out is,
= 12×height,
= 12×3.
= 36 cm³.
And the volume of the cylinder is,
= π(1 + 2 + 0.5)²×3.
= π(3.5)²×3.
= 115.4 cm³
Therefore, The volume of the paperweight is,
= 115.4 - 36 cm³.
= 79.3 cm³.
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If you take - 3/10 of a number and add 1, you get 10. Write an equation to represent the situation. What is the original number
Answer: -30
Let's call the original number "x". Then, we can write the equation as follows:
-3/10 x + 1 = 10
To find the original number, we can isolate x by subtracting 1 from both sides and then multiplying both sides by 10/3:
-3/10 x = 9
x = (9 * 10)/(-3)
x = -30
So, the original number is -30.
Suppose that n 0 and n 1. Show that the substitution v = y^1-n transforms the Bernoulli equation dy/dx + P (x) y = Q(x) y^n into the linear equation dy/dx +(1-n)p(x)v(x)=(1-n)q(x).
The substitution, transforms the Bernoulli equation dy/dx + P(x)y = Q(x)y^n into the linear equation dv/dx+(1-n)P(x)v(x) = (1 - n)Q(x). It is done as:
The equation is in the form
dy/dx +P(x)y=Q(x)yⁿ, where P and Q are functions of x or constants, this is called Bernoulli's equation.
Now, we have to substitution using
[tex]v = {y}^{1 - n} [/tex]
Differentiating both side with respect to 'x'
[tex]v' = (1 - n) {y}^{ - n} y' \\ \frac{dx}{dy} = \frac{1}{1 - n} {y}^{n} v'[/tex]
we get,
[tex]= \frac{1}{1 - n} {y}^{n} v' + p(x)y \\ = q(x) {y}^{n} \\ = v' + (1 - n)p(x) {y}^{1 - n} \\ = (1 - n)q(x)[/tex]
Now, by using
[tex]v' = {y}^{1 - n} [/tex]
The given equation is expressed as:
[tex]v + (1 - n)p(x)v = (1 - n)q(x)[/tex]
or dv/dx + (1-n)P(x)v(x) = (1 - n)Q(x)
The Bernoulli equation simply states that total energy per unit mass of flowing fluid, at any point in the subsurface, is the sum of the kinetic, potential, and fluid-pressure energies and is equal to a fixed value. The Bernoulli Equation can be viewed as a statement of the conservation of energy principle applicable to flowing fluids.
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A car is bought for £8500
In it's first year it's price reduces by 10%
Each year after that it decreases by 5%
What is the price after 3 years?
Answer: The price after 3 years is £6904.15
Step-by-step explanation:
After 1 year, 8500*0.9= 7650
7650*0.95=7267.5
7267.5*0.95=6904.125
The price after 3 years is £6904.15
1. Arturo earns n dollars per hour. Next month
he will receive a 2% raise in pay per hour. The
expression n +0.02n is one way to represent
Arturo's pay per hour after the raise. Write
an equivalent simplified expression that will
represent his pay per hour after the raise.
The equivalent simplified expression is 1.02n.
What is an equivalent expression?Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Given that, Arturo earns n dollars per hour. Next month he will receive a 2% raise in pay per hour.
The expression n +0.02n is one way to represent Arturo's pay per hour after the raise.
Here, the equivalent expression is n +0.02n= 1.02n
Therefore, the equivalent simplified expression is 1.02n.
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PLEASE ANSWER ASAP THANKS
The value of x is 97.
What are corresponding angles?The angles that are in the same position on a given two parallel lines intersected by a transversal line are called the corresponding angles.
Corresponding angles are always equal.
We can also have alternate angles which are always equal.
We can also have alternate interior and exterior angles which are equal.
The angles on the same side make upto 180 degrees
We have,
From the figure,
(x - 5) and (x - 9) forms a straight angle.
This means,
x - 5 + x - 9 = 180
Solve for x.
2x - 14 = 180
2x = 180 + 14
2x = 194
x = 97
Thus,
The value of x is 97.
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-3x² + 2x-5 = y
-x+2=-y
Answer: \left(h,\:k\right)=\left(\frac{1}{3},\:\frac{14}{3}\right),\:p=\frac{1}{12\
Step-by-step explanation:
Solve for x . circles tangent 1 A. 12 B. 10 C. 42 D. 9
8 is the measure if the angle x in the given diagram.
Circle geometryThe point where two lines meet is known as an angle. The given diagram is a circle geometry.
Using the theorem, angle at the arc is twice the angle at the vertex, we will have:
80 = 2(4x + 8)
80/2 = 8x + 8
40 = 4x + 8
4x = 40 - 8
4x = 32
x = 32/4
x = 8
Hence the value of x from the diagram given is 8
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A cylinder-shaped scoop has a base radius of 2 centimeters and a height of 5 centimeters. The scoop has a mass of 14.9 grams when empty. The scoop is completely filled with water. One cubic centimeter of water has a mass of one gram. What is the mass of the scoop of water in grams, including the mass of the scoop? Describe how you found your answer. Round to the nearest tenth.
Answer:
77.7 g
Step-by-step explanation:
You want the mass of a cylindrical scoop of radius 2 cm and height 5 cm when it is filled with water at 1 g/cm³, and has an empty mass of 14.9 g.
WaterThe mass of the water will be the product of its volume and its density. The volume is that of a cylinder with radius 2 cm and height 5 cm. That volume is given by the formula ...
V = πr²h = π(2 cm)²(5 cm) ≈ 62.83 cm³
The mass of the water is then ...
(62.83 cm³) × (1 g/cm³) = 62.83 g
Total massThe total mass of the water-filled scoop is the sum of its empty mass and the mass of the water:
scoop + water = 14.9 g + 62.8 g = 77.7 g
The mass of the scoop and water is 77.7 grams.
One way to establish validity of a questionnaire is my measuring:A) The correlation between the score on the questionnaire and another measure of the same conceptB) The alpha value of the reliability coefficientC) How well sunjects perform on the questionnaire at one time compared to another timeD) The consistency by which multiple sunjects are able to complete the questionnaire without error
The correct option is Option D) The consistency with which several individuals can complete the questionnaire without making an error is one technique to determine a questionnaire validity.
A questionnaire is a sort of research tool used to collect data from respondents for a survey or statistical analysis. It consists of a collection of questions (or other forms of prompts). Typically, a research questionnaire will have both closed-ended and open-ended questions. Long-term, open-ended inquiries provide the respondent the chance to go into more detail. The Statistical Society of London created the research questionnaire in 1838. Despite the fact that surveys are frequently created so that the answers may be statistically analyzed. Consequently, it may not be practical to conduct a survey using a questionnaire for some demographic groups.
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What is the result of multiplying the first equation by 2 and adding to the second equation?
6x − y = 7
2x + y = 5
A. 14x + 3y = 19
B.14x + y = 19
C.14x - y = 19
Simplify the following by rationalizing the denominator. need rightnow pahelp.
Answer:
Step-by-step explanation:
Multiply the numerator and denominator by the conjugate.
Exact Form:
3√2+2
7
Decimal Form:
0.89180581
…
Raul is wrapping a cylindrical package with wrapping paper. He has two different packages to choose from:
Package A has a radius of 1.5 inches and a height of 6 inches
Package B has radius of 2 inches and a height of 3 inches
He has 70 in2 of wrapping paper and he will need to cover all sides of the package.
Using the formula SA = 2π
rh + 2π
r2, determine which of the following packages Raul will have enough wrapping paper to cover.
Package A has a surface area of
Choose...
in2. Package B has a surface area of
Choose...
in2.
Raul will have enough paper to wrap
Choose...
The package that will have enough wrapping paper to cover is package B
Package A has a surface area of 70. 65 in²
Package B has a surface area of 62. 8 in²
How to determine the surface areaThe formula for the surface area of a cylinder is expressed as;
SA = 2πrh + 2π
Given that the parameters are;
r is the radiush is the height of the cylinderFor Package A, substitute the values
= 2 × 3.14 × 1.5 × 6 + 2 × 3.14 × (1.5)²
Multiply the values, we have;
= 70. 65 in²
For package B, substitute the values, we get;
= 2 × 3.14 × 2 × 3 + 2× 3.14 × (2)²
Multiply the values
= 62. 8 in²
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What is the average increase in pennies for Daisy's piggy bank over the first 2 days (starting with day 0)?
The average increase in first 2 days is 1.5 pennies/day.
What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.Given is a tabular data about Daisy's piggy bank.
The average increase in first 2 days -
{a} = (7 - 4)/(2 - 0)
{a} = 3/2
{a} = 1.5
Therefore, the average increase in first 2 days is 1.5 pennies/day.
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Penny is vacationing at the beach and decides to purchase a pair of swim goggles and a
sand bucket which she randomly selects off the shelf. When she realizes that they are
both green, she states that "because she selected a green pair of swim goggles, she was
more likely to select a green sand bucket." Do you agree or disagree with Penny's
statement? Justify your thinking
Answer: I disagree with Penny's statement. The probability of her selecting a green pair of swim goggles and then a green sand bucket is the product of their individual probabilities. The fact that she selected a green pair of swim goggles does not change the probability of selecting a green sand bucket. Each selection is independent of the other, and the probabilities of each event remain the same. So, Penny's statement that "because she selected a green pair of swim goggles, she was more likely to select a green sand bucket" is not valid.
Step-by-step explanation:
You must spend at least $10 at the grocery store to get a free greeting card
Answer:
I spent 13.32 at the store the other day...?
Step-by-step explanation:
What is the question.