Answer: To find the length of an object in a scale drawing, you need to use the scale to convert the length on the drawing (measured in inches) to the actual length (measured in feet).
The scale of the drawing is given as 0.5 inches = 10 feet, which means that 1 inch on the drawing represents 10 feet in reality.
So, if the length of the object on the scale drawing is L inches, then the actual length of the object in feet would be:
Length (ft) = (Length (in) * 10 ft/0.5 in) = (L*20)
To find the actual length of the object in feet, you need to know the length of the object in inches from the scale drawing.
Once you have that measurement, you could then simply multiply it by 20.
Step-by-step explanation:
The table below shows information about how many fans there were at two
football matches in a local tournament.
What is the difference between the number of away fans at the semi-final and at
the final?
Semi-final
Final
Total number of fans
250
400
Ratio of home fans
to away fans
6:4
7:3
The fans at the semi final is less than the fans at the final .
What is the away goal rule in FIFA?The implementation of the away goals rule makes any goals scored away from home effectively count twice when the scores are tied, as is customary in matches with home and away legs, such as the knockout stage of the Champions League.
In the UCL, do away goals still count?Champions League and Europa League, two of its premier club championships, starting in the 2021–22 season.
Semi final : 250*4/6+4 = 100
Final : 400*3/7+3= 120
Hence, The fans at the semi final is less than the fans at the final .
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Can u please help me with this question.
Answer:
you can use compass to make straight line
What is the difference between a difference of two squares and a perfect square trinomial?
Depending on whether a and b are real numbers, they can factor as (a + b) (a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
what is perfect square ?When you square an integer, you get perfect squares. The number 81, for example, is a perfect square since it can be derived by squaring 9: 99=81. Because 12 can be squared to make 144, 144 is a perfect square. 13 may be squared to make 169, which is a perfect square. Mathematics-related language. Informally: When an integer (a "whole") number is multiplied by itself, whether the result is positive, negative, or zero, the result is referred to as a square number, a perfect square, or simply "a square." All square numbers are therefore 0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on.
given
Perfect square trinomials, also referred to as trinomial squares, are the squares of binomial expressions.
Depending on whether a and b are real numbers, they can factor as (a + b)(a + b) or (a - b)(a - b). Forms like (a + b)(a - b) are unique products also known as the difference of squares.
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Simplifying algebraic expression
Answer:
-33
Step-by-step explanation:
Plug 9 in for c, then simplify the resulting expression.
5c - 9c + 3
5(9) - 9(9) + 3
↓ execute multiplication
45 - 81 + 3
↓ simplify by adding 81 and 3
45 - 84
↓ execute subtraction
-33
Answer:
[tex] \sf \: - 33 \: (if \: c = 9)[/tex]
Step-by-step explanation:
Given expression,
→ 5c - 9c + 3
Now we have to use,
→ c = 9
Simplifying the given expression,
→ 5c - 9c + 3
→ 5(9) - 9(9) + 3
→ 45 - 81 + 3
→ -36 + 3
→ -33 => (answer)
Hence, required answer is -33.
Write a proportion to find how many points az a student needs to score on a test worth 50 points
to get a test score of 40%.
Answer:The student needs to score 20 points
Step-by-step explanation:
? /50= 40/100Cross multiply:100*? = 40*50⇒? = 40*50/100= 20
PLEASEEE HELPPP !!
picture attached
If m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles, find m ∠ Q.
The value of m ∠ Q is 23°.
What are complementary angles?
Because the three angles of a triangle sum up to 180° and the right angle has already taken up 90°, the two non-right angles in a right-angled triangle are complementary. We say two angles "Complement" one other when their sums equal 90 degrees.
Here, we have
Given: m ∠ P = (12x + 7), m ∠ Q = (6x - 7), and ∠ P and ∠ Q are complementary angles.
The sum of the measures of two complementary angles is 90°.
So, m∠P + m∠Q = 90°
Substitute 12x+7 for m∠P and 6x−7 for m∠Q.
12x+7 + 6x−7 = 90°
18x = 90°
x = 5°
To find m∠Q, substitute 5 for x in 6x−7.
6×5 - 7 = 23°
m ∠ Q = 23°
Hence, the value of m ∠ Q is 23°.
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7. Mai and Tyler are selling items to earn money for their elementary school. The school
earns w dollars for every wreath sold and p dollars for every potted plant sold. Mai
sells 14 wreaths and 3 potted plants and the school earns $70.50. Tyler sells 10
wreaths and 7 potted plants and the school earns $62.50.
This situation is represented by this system of equations:
[ 14w + 3p = 70.50
10w+7p = 62.50
Explain why it makes sense in this situation that the solution of this system is also a
solution to 4w + (-4p) = 8.00.
On solving the provided question we can say that - her in the equation 14w + 3p = 70.50 and 10w+7p = 62.50 , w = 12; p = 18
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
[tex]14w + 3p = 70.50 \\[/tex]
10w+7p = 62.50 ,
[tex]w = 12\\[/tex]
p = 18
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It takes 126 cubes that have edge lengths of 1/3 ft to completely fill a plastic bin. What is the area of the base of the bin?
The area of the base of the bin is 9 ft^2.
The given information states that the bin is filled with 126 cubes that have edge lengths of 1/3 ft. To determine the area of the base of the bin, we must first determine the total volume of the bin.
Since each cube has a volume of 1/27 ft^3, the total volume of the bin is 126/27 ft^3. Since the volume of a rectangular prism is equal to the length times the width times the height, we can solve for the area of the base of the bin by rearranging the formula to A = V/h, where A is the area, V is the volume, and h is the height.
We can substitute the values given to obtain A = 126/27 ft^3/h. Since the height of the bin is equal to the edge length of the cubes, which is 1/3 ft, we can substitute that value into the equation to get A = 126/27 ft^3/1/3 ft = 9 ft^2. Therefore, the area of the base of the bin is 9 ft^2.
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EMERGENCY i need thissss helpp. tysmm <33
Please help I have no idea
Answer:
The surface area of this cuboid is 420 square inches.
Step-by-step explanation:
All we have to do is calculate each rectangle. For the width, we have 10 x 5 which is 50. Then we multiply it by 2 because we have two of those sides. Then we get 100. Then we have 11 x 5 which is 55. We multiply that by 2 and we get 110. Then we do that to the final two sides and we get 220. So the final answer if we add them all up is 420 square inches.
The table shows the amount of certain school supplies left over in the school bookstore at the end of the year.
Item Total
Pens 36
Markers 48
Erasers 24
The bookstore manager will make packages of the remaining school supplies and sell them for $5 per package. Each package will be identical and contain the same number of items, and there will be none left over. The manager wants to create the greatest number of packages possible. How much will the bookstore earn if all of the packages of supplies are sold?
Multiple choice question.
The amount earned by the bookstore if all of the packages of supplies are sold is given as follows:
$60.
How to obtain the amount earned?Before obtaining the amount earned, we must obtain the number of packages, with is given by the greatest common factor of the amounts of each item.
The amounts of each item are given as follows:
36, 48 and 24.
Their greatest common factor is obtained factoring them simultaneously by the same prime factors as follows:
36 - 48 - 24|2
18 - 24 - 12|2
9 - 12 - 6|3
3 - 4 - 2
Hence:
gcf(36, 48, 24) = 2² x 3 = 12.
Which is the number of packages. As each package sells for $5, the amount earned is given as follows:
12 x 5 = $60.
Each package is composed by:
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decide whether the function is a polynomial function. If so right it in standard form and state it’s degree type in leading coefficient if so write it in standard form and state its degree type in leading coefficient P(x)=-3x^2+10-4x
For the polynomial p(x) = -3x² - 4x + 10, the degree is 2 and the leading coefficient is -3
What is an polynomial?Polynomials consist of exponents of variables and numbers forming an equation using operations of addition and subtraction.
Polynomial is an expression composed of variables, constants and exponents combined using mathematical operations such as addition, subtraction, multiplication
Given the polynomial:
p(x) = -3x² + 10 - 4x
Rewriting the polynomial in standard form is done by rearranging based on exponents. Hence:
p(x) = -3x² - 4x + 10
The degree is 2 (x²) and the leading coefficient is -3(-3x²)
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A sine function has the following key features:
Period = 4
Amplitude = 4
Midline: y = 1
y-intercept: (0, 1)
The function is not a reflection of its parent function over the x-axis.
The sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].
What is sine function?
The trigonometric functions in mathematics are real functions that relate the right-angled triangle's angle to the ratios of its two side lengths. They are extensively used in all fields of geometry-related science, including geodesy, solid mechanics, celestial mechanics, and many others.
The general sine function is
[tex]y = Asin(b(x+c)+D[/tex]
Where
Amplitude = A
Period = [tex]\frac{2\pi }{B}[/tex]
Phase shift = c
Vertical shift = D
Given:
A = 4 (amplitude)
[tex]\frac{2\pi }{B} = 4[/tex] (period)
[tex]B = \frac{\pi }{2}[/tex]
Since midline: y = 1
And we know that graph of [tex]4sin(\frac{\pi }{2}x)[/tex], midline to be y = 1.
It must have vertical shift D = 1.
Since, y - intercept (0, 1)
⇒ x = 0, y = 1
⇒ It has no phase shift ⇒ c = 0
Since it satisfy [tex]y = 4sin(\frac{\pi }{2}(x+c))+D[/tex]
The graph of the sine function is attached below.
Hence, the sine function becomes, [tex]y = 4sin(\frac{\pi }{2}x) + 1[/tex].
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A group consisting of 14 aggressive zombies quadruples in size every hour. Which equation matches the number of zombies after 6 hours?
The exponential equation that matches the number of zombies after 6 hours is the possible option;
Z = 14 × 4⁶
What is an exponential equation?An exponential equation is one in which the argument is an index or power of a constant.
The initial number in the group of zombies = 14
The amount by which the group increases every hour = The group quadruples every hour
The required equation; The equation that matches the number of zombies after 6 hours
The information in the question indicates that the sequence is a exponential, which can be presented using the following equation;
Z = a·rⁿ
Where;
Z = The number of zombies after n hours
a = The first term = The initial number of zombies in the group = 14
r = The common ratio = The amount that multiplies members of the group every hour = 4
n = The number of hours after which the number in the group is evaluated
Therefore, after 6 hours, n = 6, and we get;
a₆ = 14 × 4⁶ = 14 × 4⁵ = 14336
The equation from the possible options, obtained from a similar question posted online, that matches the number of zombies after 6 hours is therefore;
Z = 14 × 4⁶
The possible options are;
Z = 4·(14)⁶
Z = 4·(1 + 14)⁶
Z = 14·(1 + 4)⁶
Z = 14·(4)⁶
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Reduce 22/154
to its lowest form.
Answer: 1/7
Step-by-step explanation: Find the GCD (Greatest Common Denominator) of the numerator and denominator. The GCD of 22 and 154 is 22. Divide both the numerator and denominator by the GCD = 22 ÷ 22; 154 ÷ 22. Reduced fraction: 1/7. Therefore, 22/154 simplified to lowest terms is 1/7.
is 120,110,105… a geometric sequence
Answer: No
Step-by-step explanation:
Look at the 3 numbers in the sequence,
Geometric sequence means the ratio between two consecutive numbers in the sequence is a constant (eg. 10, 5, 2.5 is a geometric sequence as the ratio is a constant at 1/2)
However, for the sequence listed above
Looking at 1st and 2nd term,
Ratio = 110/120 = 11/12
Looking at 2nd and 3rd term,
Ratio = 105/110 = 21/22 which is not the same as 11/12.
Hence, since the ratio is not the same, this sequence is not a geometric sequence.
HELP THIS IS URGENT!!!! During a sale, a store offered a 35% discount on a camera that originally sold for $750. After the sale, the discounted price of the camera was marked up by 35%. To the nearest whole number, what percent of the original price was the price after markup?
Answer:
the percentage is 62%
Step-by-step explanation:
What is the ratio of sin t?
Sine of an angle is defined as the ratio of the side opposite (perpendicular side) to that angle divided by hypotenuse of the triangle.
sin is a trigonometric ratio.
If θ is one of the acute angles in a triangle, then the sine of theta is the ratio of the opposite side to the hypotenuse.
sin Q = perpendicular / hypotenuse.
sin Q is the base of the trigonometry ratios and it is one of the ratio.
sine is an acute angle.
some formula of sine angle are ,
1- sine Q = 1/ cosec Q .
2- sin ^2 Q = 1- cos^2 Q .
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this is my quation kfwn vehfwqkn uewfhkjn uewfhskj uefwshjl efwuhskcj fwqeukjscngefww
Answer:
1/6
Step-by-step explanation:
There are 6 letters and the spinner lands on one at a time
How many 0's are located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/2^5.5^8 ?
There are seven zeroes located to the right of the decimal point and before the first non-zero digit in the terminating decimal representation of 1/(2^5.5^8).
Terminating decimal is a decimal number which have a finite number of digits after the decimal point. Decimals like 3.45, 6.78, 1.987 are terminating decimals. Decimals which have 0 as the non terminating digit like 3.7800000.. are also called as terminating decimals.
Let P=1/(2^5.5^8)
Multiplying and dividing the numerator by 2^3
P= 2^3/(2^5.5^8.2^3)
P=8/(2^8.5^8)
P=8/10^8
P=0.00000008
The number of zeroes located to the right of the decimal point and before the first non-zero digit are seven.
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Find m angle Bm∠Bm, angle, B.
Note that m angle Bm∠Bm, angle, B is acute. Round to the nearest degree
The measure of angle B where angle B is an acute angle by using the Law Of Sines is 61° .
What is an Acute Angle ?
The Acute Angle can be defined as an angles that measure less than 90° , the acute angle is smaller than Right Angle and also smaller than the Linear Angle ( measuring 180° ).
From the figure ,
we can see that the measure of the sides are given as a = 9 , b = 8 and
the measure of angle A is 79° .
By Applying the Law Of Sines ;
we get ,
[tex]\frac{SinA}{a} =\frac{SinB}{b}[/tex]
Substituting the values in the above equation ,
we get ;
[tex]\frac{Sin79\textdegree}{9} =\frac{SinB}{8}[/tex]
Simplifying further ,
we get ;
[tex]SinB = \frac{Sin79\textdegree}{9} \times 8[/tex]
substituting the value of Sin79° as 0.9816 ;
we get ;
[tex]SinB = \frac{0.9816}{9} \times 8[/tex]
[tex]SinB=0.8725[/tex]
So , B ≈ 61° .
Therefore , the measure of angle B is 61° .
The given question is incomplete , the complete question is
Find the measure of Angle B in the given figure .
Note that the angle B is acute . Round to the nearest degree .
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vivian and her dad drive from Boston to niagara falls it takes them 9 hours to drive 495 miles what is their driving rate in miles per hour.
Answer:
55 miles per hour
Step-by-step explanation:
The equation is:
R = d / s
We know
d = 495 miles
s = 9 hours
Let's solve
R = 495 / 9
R = 55 miles per hour
So, their driving rate is 55 miles per hour
Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown. If he used the
same amount concrete to construct a spherical barrier, how tall would it be? Express your answer in terms of π?
Is it:
A)1 2/3 π
B)3 2/3 π
C)4 1/3 π
D)5 π
The volume of the cone is (2/3)π cubic feet. And the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft. The correct option is A.
What is volume?Space occupied by an object in three-dimensional space is called as volume of an object. In simple words, space is taken by object.
Given:
Tobias is constructing barriers to prevent cars from driving on a bike path. He can make conical pylons using the dimensions shown.
He used the same amount of concrete to construct a spherical barrier.
According to the information given in the exercise, the height and the radius of the pylons are the following:
Height h = 2 ft
Radius r = 1 ft
So, the volume of the cone,
= (1/3)πr²h
= (1/3)π(1)²(2)
= (2/3)π cubic feet.
And the volume of the sphere is twice the volume of the cone.
So, the volume of the sphere,
4πr³/3 = 2π/3
2r³ = 1
r³ = 1/2 = 0.5
r = ∛0.5 = 0.8 ft.
Therefore, the radius of the spherical barrier would be 0.8 ft. and the height would be 2r = 2(0.8) = 1.6 ft.
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find the total surface area of this triangular prism
The surface area of the triangular prism is 156cm² when the triangle sides are 8cm and 15 cm rectangle sides are 17cm and 2 cm.
Given that,
We have to find the total surface area of the triangular prism in the given picture.
We know that,
First, we need to calculate the area of the triangle
a = area of triangle
a = 1/2 ×15 cm × 8 cm
a = 60 cm²
Now,
We must determine the three rectangles' areas.
a₁ = 2cm × 17cm
a₁ = 34cm²
a₂ = 2cm × 15cm
a₂ = 30cm²
a₃ = 2cm ×8cm
a₃ = 16cm²
Now, we must multiply the triangle by two and sum all the estimated areas.
a₁ + a₂ + a₃ + 2a =60cm² + 34cm² + 30cm² + 2 × 16cm² = 156cm²
Therefore, The surface area of the triangular prism is 156cm² when the triangle sides are 8cm and 15 cm rectangle sides are 17cm and 2 cm.
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Please help
The graph shows the reciprocal parent function
Which statement best describes the function
The statement that best represents the function must be identified by reading the graph.
Let's check which of the following statements best characterizes the function:A) When x < 0, the function is negative.
This is accurate; as you can see, the function is negative for x < 0 because it is below the horizontal axis.
We shall see that choice A is the proper one. "When x < 0, the function is negative."
The function tends to infinity on the positive side at an x close to zero.
The function tends to negative infinity at x close to zero on the negative side.
The function tends to zero as x's absolute value grows.
So we can conclude that this is an inverse function similar to:
y = f(x) = 1/x
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Please help me with my HW
Answer:
Step-by-step explanation:
(9a⁴b⁷) x (6a³b⁸)
(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)
54 x a⁷ x b¹⁵ = 54a⁷b¹⁵
Answer:
(9a⁴b⁷).(6a³b⁸)
=54a⁷b¹⁵
Consider your construction of pentagon ABCED.
What segments, if any, are parallel? Explain how you made your
determination.
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
Define pentagonal.Pentagons are two-dimensional polygons having five sides and fifth angles. When we mix the Greek terms "penta" and "gon," which mean "five" and "angles," respectively, we have the word "pentagon."
Here,
we know that a pentagonal prism has five rectangular sides in addition to two pentagonal bases at the top and bottom.
Pentagonal prisms are pentagon-shaped if we look at them from the bottom.
When viewed from the side, a pentagonal prism would have a rectangular shape.
If we were to look at the pentagonal prism from the front, it would appear rectangular.
Therefore , the solution of the given problem of pentagonal comes out to be Nadia has created a pentagonal prism as a result.
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halfway between -5/6 and 1/3 on a number line
The halfway between the number is -1/4 on the number line.We can find halfway by using midpoint formula.
How do we show number on number line?If the given number is positive mark it on the right side of the origin. If it is a negative number mark it on the left side of zero.Then divide each unit into the values equal to the fraction's denominator.
What is a Number Line in Math?A number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides horizontally or vertically.
Now
Using midpoint formula
[tex]x_{1}[/tex]+[tex]x_{2}[/tex]/2 =-5/6 +1/3 divide 2
Find common denominator and write the numerators above common denominator
-5+2/12 =-3/12
=-1/4
Hence we find midpoint between numbers.
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Find an equation for the line that passes through the points (-5, 2) and (3, 4)
A website lists homes for sale in a suburban town. The site provides information including neighborhood, selling price, number of bedrooms, and whether the home has a garage. What are the individuals in this setting?
homes
neighborhoods
selling prices
bedrooms
answer is homes
Based on the description above, the individuals in this setting is option A: homes.
Whys the setting home?The website lists homes for sale in a suburban town and provides information such as neighborhood, selling price, number of bedrooms, and whether the home has a garage.
In this case each house is an instance or a data point of a "home" object, these objects have different attributes or features like neighborhood, selling price, number of bedrooms and garage, these attributes are used to describe the characteristics of the home, they are also called features.
Therefore, each home is an individual unit being sold on the market. Neighborhoods, selling prices, and bedrooms are attributes or characteristics of the homes, and they help provide more information about each individual home being listed.
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