The solution to the set of equations is (x, y) = (8, 17).
What is system of linear equations?
A system of linear equations is a set of two or more equations with two or more variables that are to be solved simultaneously. Each equation in the system is linear, meaning it can be written in the form of ax + by + cz + ... = d, where a, b, c, and d are constants and x, y, z, and other variables are unknowns.
The goal of solving a system of linear equations is to find the values of the variables that satisfy all of the equations in the system. The solution of a system of linear equations is a set of values for the variables that make all of the equations true.
There are different methods to solve systems of linear equations, such as substitution method, elimination method, and matrix method. These methods involve manipulating the equations in the system to isolate one variable, substitute its value into another equation, and eventually find the values of all the variables.
Systems of linear equations are used in many areas of mathematics, science, engineering, and economics to model real-world situations and solve practical problems.
To find the solution to the set of equations, we need to determine the values of x and y that satisfy both equations simultaneously. One way to do this is to use substitution or elimination methods.
However, the given answer choices do not seem to be the steps of a solution process. We need to use both equations to find a solution. Here is one possible way to do it:
Equation S: y = x + 9
Equation T: y = 2x + 1
Since both equations equal to y, we can set them equal to each other:
x + 9 = 2x + 1
Simplifying this equation, we get:
x = 8
Now that we know the value of x, we can substitute it into either Equation S or Equation T to find the value of y. Let's use Equation S:
y = x + 9
y = 8 + 9
y = 17
Therefore, the solution to the set of equations is (x, y) = (8, 17).
None of the given answer choices matches this solution process.
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Determine the slope and intersection with the y-axis of each graph
y=-2x-1
[tex] \mathbb{ANSWER:}[/tex]
The slope is -2 while the y-intercept is -1.
[tex] \mathbb{EXPLANATION:}[/tex]
The slope and the intersection with the y-axis of the graph or the y-intercept is already given if you will just simply look at the equation. An equation written in y = mx + b is in slope-intercept form, where m is the slope and b is the y-intercept. So, the number being multiplied to x or the coefficient of x is the slope while the constant is the y-intercept.
Debra has two different square baking dishes.one has a side length of 8 inches, and the other has a side length of 9 inches. what is the difference in the area of Debra's two square baking dishes?
Debra's two area baking plates are 17 square inches different in size.
What distinguishes an area from a perimeter?The area surrounding a shape forms its perimeter. Area is a unit of measurement for interior space. Surface area is a measurement of a solid shape's exposed surface, whereas area is a two-dimensional measurement of the size of a flat surface (three-dimensional).
The square baking dish has the following surface area with an 8-inch side length:
Area of first square = (side length)² = 8² = 64 square inches
Similarly, the surface area of a square baking dish with 9-inch sides is:
Area of second square = (side length)² = 9² = 81 square inches
Difference in area = |Area of second square - Area of first square|
Difference in area = |81 - 64|
Difference in area = 17 square inches
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I'm so confused on thins can someone PLEASE help me??? It's Algebra by the way
Answer:
Degree: The degree of the function is 3.
X-Intercepts with multiplicity greater than 1: x = -2 and x = 0
How many distinct x-intercepts?: There are two distinct x-intercepts.
How many zeros are there?: There are three zeros, one at x = -2 and two at x = 0 (with a multiplicity of 2).
HELPPPP ASAP PLEASE HURRY 50 POINTS
The interval giving the middle 68% of the lifetime of bulbs in hours is given as follows:
(1350, 1450).
What does the Empirical Rule state?The Empirical Rule states that, for a normally distributed random variable, the symmetric distribution of scores is presented as follows:
The percentage of scores within one standard deviation of the mean of the distribution is of approximately 68%.The percentage of scores within two standard deviations of the mean of the distribution is of approximately 95%.The percentage of scores within three standard deviations of the mean off the distribution is of approximately 99.7%.The middle 68% of scores is within one standard deviation of the mean, hence the bounds of the interval are given as follows:
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A firm manufactures a product that sells for $13 per unit. Variable cost per unit is $2 and fixed cost per period is $1540. Capacity per period is 2500 units. (a) Develop an algebraic statement for the revenue function and the cost function. (b) Determine the number of units required to be sold to break even. (c) Compute the break-even point as a percent of capacity. (d) Compute the break-even point in sales dollars.
(a) Revenue function: R = 13x
Cost function: C = 2x + 1540
(b) Break-even point: 2x + 1540 = 13x
x = 1540/11
x = 140 units
(c) Break-even point as a percent of capacity: 140/2500 x 100% = 5.6%
(d) Break-even point in sales dollars: 13 x 140 = $1820
(a) The revenue function is R(x) = 13x, where x is the number of units sold. The cost function is C(x) = 2x + 1540, where x is the number of units sold.
(b) To find the break-even point, we set R(x) = C(x):
13x = 2x + 1540
11x = 1540
x = 140
So the firm needs to sell 140 units to break even.
(c) The break-even point as a percent of capacity is 140/2500 = 0.056 or 5.6%.
(d) The break-even point in sales dollars is 140 units * $13/unit = $1820.
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7. You have a 8-kilogram bag of dog food. You give your dog 100 grams of food
oqeach day. How many days does the bag of food last?
teris fiel even uoy ob enjur to equo
pje ever vo
We can start by converting the mass of the bag of dog food from kilograms to grams:
8 kilograms = 8,000 grams
Then, we can divide the total mass of the bag of food by the daily amount given to the dog:
8,000 grams ÷ 100 grams/day = 80 days
Therefore, the bag of dog food will last for 80 days.
what is the slope intercept for
(5,1) and (2,16)
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
What distinguishes a linear equation?If an equation is expressed in the form y=mx+b, where m denotes the slope and b the y-intercept, it is said to be linear.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope of the line passing through the two given points (5,1) and (2,16), we can use the formula:
m = (y2 - y1)/(x2 - x1)
where (x1, y1) = (5,1) and (x2, y2) = (2,16)
m = (16 - 1)/(2 - 5) = -5
So the slope of the line is -5.
To find the y-intercept b, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Using the point (5,1) and the slope m = -5, we get:
y - 1 = -5(x - 5)
Simplifying this equation, we get:
y = -5x + 26
So the slope-intercept form of the equation of the line passing through the two given points is:
y = -5x + 26
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a company is building square-bottomed boxes with no tops. the material for the bottom costs $2 per cm2 and the material for the sides costs $1 per cm2. the company has budgeted $96 to build one box. what is the box of largest volume the company can build for $96
The box of largest volume the company can build for $96 is the box that costs exactly $96.
The company can build a box of the largest volume for $96 by calculating the area of the bottom and sides of the box. To calculate the area of the bottom, use the formula A=l x w, where l is the length of one side and w is the width of one side. Since the bottom is square, l=w. Thus, A=l^2. The area of the bottom is then multiplied by the cost of the material for the bottom, which is $2 per cm2, to calculate the total cost of the bottom.
Similarly, to calculate the cost of the sides, use the formula A=2lh + 2wh, where h is the height of the box. The area of the sides is then multiplied by the cost of the material for the sides, which is $1 per cm2, to calculate the total cost of the sides.
The total cost of the box is the cost of the bottom plus the cost of the sides. Since the company has budgeted $96 to build one box, the total cost of the box must not exceed $96. Therefore, the box of largest volume the company can build for $96 is the box that costs exactly $96.
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20. Let V be an Euclidean space and letx,y∈V. (a)†If∥x+y∥=∥x−y∥then determine⟨x,y⟩. (b) * Show that2⟨x,y⟩≤∥x∥2+∥y∥2. (c) If(z,y)=0for allz∈Vthen show thaty=0. (d) †If∥x∥=∥y∥for somex,y∈Vthen⟨x+y,x−y⟩=0. (e)†Pythagorean theorem: Show that⟨x,y⟩=0if and only if∥x+y∥2=∥x∥2+∥y∥2.
Pythagorean theorem: Show that ⟨x, y⟩ = 0
Let V be an Euclidean space and let x, y ∈ V.(a) If ∥x + y∥ = ∥x − y∥ then determine ⟨x, y⟩.We know that ∥x + y∥² = ⟨x + y, x + y⟩ = ⟨x, x⟩ + ⟨x, y⟩ + ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ⟨x − y, x − y⟩ = ⟨x, x⟩ − ⟨x, y⟩ − ⟨y, x⟩ + ⟨y, y⟩ = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x + y∥ = ∥x − y∥, we have ∥x∥² + 2⟨x, y⟩ + ∥y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²⟨x, y⟩ = 0(b) Show that 2⟨x, y⟩ ≤ ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x + y∥² ≥ 0So ∥x∥² + 2⟨x, y⟩ + ∥y∥² ≥ 0⟨x, y⟩ ≤ (∥x∥² + ∥y∥²)/2(c) If (z, y) = 0 for all z ∈ V then show that y = 0.Let z = y, then (y, y) = 0⟨y, y⟩ = ∥y∥² = 0∥y∥ = 0So y = 0(d) If ∥x∥ = ∥y∥ for some x, y ∈ V then ⟨x + y, x − y⟩ = 0.We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²And ∥x − y∥² = ∥x∥² − 2⟨x, y⟩ + ∥y∥²Since ∥x∥ = ∥y∥, we have ∥x∥² = ∥y∥²So ∥x + y∥² − ∥x − y∥² = 4⟨x, y⟩ = 0⟨x, y⟩ = 0(e) Pythagorean theorem: Show that ⟨x, y⟩ = 0 if and only if ∥x + y∥² = ∥x∥² + ∥y∥².We know that ∥x + y∥² = ∥x∥² + 2⟨x, y⟩ + ∥y∥²If ⟨x, y⟩ = 0, then ∥x + y∥² = ∥x∥² + ∥y∥²If ∥x + y∥² = ∥x∥² + ∥y∥², then 2⟨x, y⟩ = 0⟨x, y⟩ = 0
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If 2x-1 is a factor of 24x^4 - 2x^2 +2x +f find f
If 2x-1 is a factor of 24x⁴ - 2x² +2x +f , the value of f is 1 - 2x.
Describe Long division?Synthetic division is a method of polynomial division used to divide a polynomial by a linear expression of the form x - a, where a is a constant. It is a shorthand way of performing long division for polynomials and is particularly useful when the divisor is of the form x - a, as it eliminates the need for writing out the full divisor in each step of the division process.
Since 2x-1 is a factor of the given polynomial, we know that it will divide exactly into the polynomial, leaving no remainder. Therefore, we can use polynomial long division to find the quotient when 24x⁴ - 2x² + 2x + f is divided by 2x-1:
12x³ + 5x² - 3x - f/2 + 1/4
____________________________________
2x - 1 | 24x⁴ + 0x³ - 2x² + 2x + f
- (24x⁴- 12x³)
----------------------
12x^3
- (12x³ - 6x^2)
----------------------
5x^2
- (5x² - 2.5x)
----------------------
2.5x
- (2.5x - f/4)
-----------------------
f/4 + 2x/4 - 1/4
Since there is no remainder, the last term in the quotient must be zero. Therefore:
f/4 + 2x/4 - 1/4 = 0
Simplifying and solving for f, we get:
f/4 = 1/4 - 2x/4
f = 1 - 2x
Therefore, f = 1 - 2x.
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The diameter of a cylindrical construction pipe is 3ft. If the pipe is 17ft long, what is its volume?
Use the value 3.14 for /pi, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answer:
First, we need to find the radius of the pipe by dividing the diameter by 2:
radius = 3ft / 2 = 1.5ft
Next, we can use the formula for the volume of a cylinder:
V = πr²h
where V is volume, π (pi) is approximately 3.14, r is the radius, and h is the height (or length) of the cylinder.
Plugging in the values we have:
V = 3.14 x (1.5ft)² x 17ft
V = 3.14 x 2.25ft² x 17ft
V = 3.14 x 38.25ft³
V ≈ 120ft³
Rounding to the nearest whole number and including the unit:
The volume of the pipe is about 120 cubic feet.
[tex]\bold{Work \ Shown:}[/tex]
[tex]d = 3 = diameter[/tex]
[tex]r = d\div2 = 3\div2 = 1.5 = radius[/tex]
[tex]h = 17 = height \ or\ length \ of \ the\ pipe[/tex]
[tex]\pi = 3.14\ approximately[/tex]
[tex]V = volume \ of \ the \ cylinder \ pipe[/tex]
[tex]V = \pi \times r^2 \times h[/tex]
[tex]V = 3.14 \times (1.5)^2\times 17[/tex]
[tex]V = 120.105[/tex]
[tex]V=120[/tex]
The cylindrical pipe's volume is about 120 cubic feet.
The sum of four times a number x and another number y is 65. The difference of five times the number x and three times y is 94. What is the value of y?
The value of y is -3. The equation formed from the question is 4x + y = 65 and 5x -3y = 94.
First, we will solve for x
Multiplying the 4x + y = 65 equation by 3 we get
12x +3y =195
Now solving both the equation
The variable y gets cancelled because of having the same value
∴ 17x = 289
x= 17
Now putting the value of x in equation 4x + y = 65 to get the value of y
4*17 +y =65
68 +y = 65
y= -3
Now putting the value of x in equation 5x -3y = 94 to get the value of y
5*17 -3y =94
85 -3y =94
-3y = 94-85
y= -3
Therefore, the value of y is -3
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bvement of the progress bor moy be uneven becouse questions can be worth more or less Rewrite ((1)/(3))^(-4)=81 as a logarithmic equation.
The logarithmic equation that is equivalent to the given exponential equation
The logarithmic equation that is equivalent to the exponential equation [tex]((1)/(3))^-4=81 (is) log(1/3) 81 = -4[/tex]
To rewrite an exponential equation as a logarithmic equation,
we can use the following formula:
bx = y → logb y = x
In this case, b = (1/3), x = -4, and y = 81. So, we can plug these values into the formula to get the logarithmic equation:
[tex]log(1/3) 81 = -4[/tex]
This is the logarithmic equation that is equivalent to the given exponential equation.
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For parallelogram ABCD, Find m∠1.
The measure of angle 1 would be equal to 59 degrees.
What is a parallelogram?That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
We have been given the angles as 31 degrees and 90 degree
We know that the sum of angle of triangle is 180 then the angle 1 will be;
31 + 90 + m∠1 = 180
m∠1 = 180 - 90 - 31
m∠1 = 59
Hence, m∠1 = 59
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how can jamie rewrite the expression 1/1-sin theta so that the fraction has cos^2 theta in the denominator
0 she can multiply the numerator and denominator by cos theta
0 she can mulitply the numerator and denominator by tan theta
0 she can mulitply the numerator and denominator by 1- cos theta
0 she can multiply the numerator and denominator by 1+ sin theta
As a result, Jamie could rewrite the equation as (1+sin theta)/cos² theta by multiplying both the denominator and the numerator by (1+sin theta), and then replacing 1-sin² theta with cos² theta.
What exactly is a fraction in mathematics?A ²is part of a whole. The number is expressed mathematically as a quotient, which divides the denominator and the numerator. Both are integers in a simple fraction. A complicated fraction contains a fraction in the numerator or denominator. The denominator of a correct fraction is greater than the numerator
Jamie can double the numerator and write 1/(1-sin theta) to ensure that the fraction's denominator is cos² theta. Neither 1-cos theta nor any other option, but the numerator by (1+sin theta):
1/(1-sin theta) × (1+sin theta)/(1+sin theta) = (1+sin theta)/(1-sin² theta)
We may replace cos² theta for 1-sin² theta using the identity sin² theta + cos² theta = 1:
(1+sin theta)/cos² theta
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Mark is training for a mini triathlon he rode his bike 3/4 Mille ran 2/4 milks and swam 1/4 mile each day how does the distance he biked in 3 days compare to the distance he swam in 3 days in 5 days in 6 days why
The comparison between the distance he biked and swam is 3 : 1.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
From the given information the comparison of the distance he swam to the distance he biked can be represented in the form of ratios.
Given, He rode his bike 3/4 miles and swam for 1/4 mile.
Therefore, The ratio of biking : swimming = 3/4 : 1/4.
Now, Multiplying by 4 to get rid of the denominator we have,
Biking : Swimming = 3 : 1.
As the days in both comparisons increase in the same manner the ratio will remain the same.
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12. WRITE The sketch shows the side view of a sculpture that is
being designed by an artist. Determine whether AABC=
ADCA. If yes, then provide a paragraph proof. If no, then
explain your reasoning.
B
Note that in the above sketch, ΔABC ≇ ΔDCA. That is they are NOT congruent. The proof is that ∠ADC which is supposed to be = ∠BAC are not equal. Thus, line AC which is supposed to be equal to Line BC are not equal.
When two triangles are congruent, it means they are exactly the same in terms of their shape and size, so all corresponding sides and angles are equal.
In ΔABC,
Line AB = 8ft
Line BC = 11ft
Line AC = 13.6ft
∠ABC = 90°
∠BAC = 53.97°
∠ACB = 36.03°
As you can see,
Where as, ∠ADC = 62° - given
∠BAC = 53.97°
Also
Where as:
AC (The Hypotenuse ΔABC which is also the Adjacent Side of ΔACD) = 13.6ft
BC (The adjacent side of ΔABC) = 11ft.
Note that in order to prove congruence, at least two angles and one side from both Triangles must be equal (Angle Angle Side Theorem). Or
Two sides and one angle from both Triangles must be equal (Side - Angle - Side).
Or All three angles (Angle - Angle - Angle);
Or All three Sides (Side - Side Side).
In this case, only one side from both Triangles AC is common to both Triangles.
On the basis of the above, therefore, ΔABC ≇ ΔDCA.
The calculations showing how we arrived at the missing sides and angles are given below:
ΔABC:
AC = √(AB² + BC²)
AC = √(8² + 11²)
AC = √(64 + 121)
AC = √(185)
AC = 13.6014705087
AC [tex]\approx[/tex] 13.60
∠ ACB = arcsin (AB/AC)
∠ ACB = arcsin (8/13.6014705087)
= arcsin(0.58817169767505)
∠ ACB = 0.6288 rad converted to degrees
∠ ACB = 36.03°
Thus, since the sum of Angles in a Triangle is 180°
∠BAC = 180-36.03° -90°
∠BAC = 53.97°
ΔACD
y (AD) = AC / sin(β)
y (AD) = 13.6/ sin(62°)
y (AD) = 13.6/0.88294759285
AD = 15.40°
CD = √(AD² - AC²)
CD = √(15.4029526893712 - 13.62)
CD = √52.290951550999
CD = 7.23
The outstanding angle in ΔACD is ∠CAD
Since the sum of Angles in a Triangle is 180°
∠CAD = 180 - 90 - 62
∠CAD = 28°
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Full Question:
Although part of your question is missing, you might be referring to this full question: See attached Image.
Shaun goes to a fast food restaurant and orders some tacos and burritos. He sees on the nutrition menu that tacos are 160160 calories and burritos are 320320 calories. If he ordered 1515 items and consumed a total of 36803680 calories, how many tacos and how many burritos did Shaun order and eat?
Tacos eaten:
Burritos eaten:
Shaun ordered 7 tacos and 8 burritos, for a total of 160160 calories from tacos and 320320 calories from burritos.
To solve this problem, we need to use a system of equations. Let's call the number of tacos Shaun ordered x and the number of burritos he ordered y. We can then write the following equations:
160x + 320y = 3680 (the total number of calories consumed)
x + y = 15 (the total number of items ordered)
We can rearrange the second equation to get y = 15 - x and then substitute that into the first equation to solve for x:
160x + 320(15 - x) = 3680
160x + 4800 - 320x = 3680
-160x = -1120
x = 7
Now that we know x, we can plug it back into the second equation to solve for y:
7 + y = 15
y = 8
So, Shaun ordered and ate 7 tacos and 8 burritos.
Tacos eaten (x) : 7
Burritos eaten (y) : 8
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A European company is selling a new brand of headphones. For h headphones sold, in thousands, a profit of E(h) = -4h^(4) + 7h^(3) - 7h + 20, in ten thousands of Euros, will be earned. How much will be earned in profit for selling 1,500 headphones?
The European company will earn 128,750 Euros in profit for selling 1,500 headphones.
How to find sale profitTo find the profit for selling 1,500 headphones, we need to plug in the value of h into the profit function E(h) and simplify.
Since h is measured in thousands of headphones, we need to divide 1,500 by 1,000 to get h = 1.5.
Now we can plug in h = 1.5 into the profit function and simplify:
E(1.5) = -4(1.5)^(4) + 7(1.5)^(3) - 7(1.5) + 20
E(1.5) = -4(5.0625) + 7(3.375) - 10.5 + 20
E(1.5) = -20.25 + 23.625 - 10.5 + 20
E(1.5) = 12.875
So the profit for selling 1,500 headphones is 12.875 ten thousands of Euros, or 128,750 Euros.
Therefore, the European company will earn 128,750 Euros in profit for selling 1,500 headphones.
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(Please answer quickly!!!)Which graph represents the solution to one seventh m is less than or equal to negative one twenty second?
number line with closed circle on point negative 14 over 11 and arrow shaded to the right
number line with closed circle on point negative 7 over 22 and arrow shaded to the right
number line with closed circle on point negative 14 over 11 and arrow shaded to the left
number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Option D i.e. number line with closed circle on point negative 7 over 22 and arrow shaded to the left represents the solution to the inequality.
What is inequality?A comparison between two or more mathematical expressions is known as an inequality.
We are given an inequality as one seventh m is less than or equal to negative one twenty second.
So, from the above information, we get the inequality as
m/7 ≤ −1/22
Now, on solving the above inequality, we get the following
⇒m/7 ≤ −1/22
⇒m ≤ −7/22
Hence, Option D i.e. number line with closed circle on point negative 7 over 22 and arrow shaded to the left represents the solution to the inequality.
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How do you find the scale factor of a shape. For common core? And what is the sequence of transformations?
The process to find the scale factor of a shape and the concept of sequence of transformations is explained below.
In order to find the scale factor of a shape, we need to compare the corresponding side lengths of the original shape to the corresponding side lengths of the new shape after a dilation.
The scale factor is the ratio of any two corresponding side lengths.
The sequence of transformations is defined as the order in which different transformations are applied to a shape.
For example, if we have a triangle and we first translate it, then rotate it, and then dilate it, the sequence of transformations would be : translate → rotate → dilate.
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The given question is incomplete, the complete question is
How do you find the scale factor of a shape? And What is the sequence of transformations?
The pyramid and prism above have the
the prism?
OA. 84 cm
OB &3 cm³
OC. 42 cm³
OD. 7cm³
width, length, and height. The volume of the pyramid is 21 cm. What is the volume of
According to the information we can infer that the volume of the prism would be 63cm³
How to find the volume of the prism?To find the volume of the prism we must perform the following mathematical operation:
First of all we must find the cube root of each of the options.
[tex]\sqrt[3]{84} = 4,3795191398878892657\\\sqrt[3]{63} = 3,9790572078963918596\\\sqrt[3]{42} = 3,4760266448864497867\\\sqrt[3]{7} = 1,9129311827723891012[/tex]
Once we find these values we must check them with the formula for the volume of a pyramid. In this case, it would be the area of the base times the height. Then we must take into account that the cube root of these numbers would be the equivalent to the side length of the figures.
In the case of 63, the procedure would be as follows:
3.9790572078963918596 * 3.9790572078963918596 = 15.832896315.8328963 / 3 = 5.27763215.2776321 * 3.9790572078963918596 = 21Then we can establish that this value corresponds to the length of the sides and the height of the pyramid because as a result it gives us the volume of the pyramid. So to find the volume of the prism we must do the following operation:
3.9790572078963918596 * 3.9790572078963918596 * 3.9790572078963918596 = 63Learn more about area in: https://brainly.com/question/27683633
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Which is closest to the surface area of the figure below?
Responses
1463.8 m2
578.1 m2
923.2 m2
3692.6 m2
The surface area of the cone is 578.1 square feet.
How to get the surface area of the cone?We know that for a cone of radius R and slant height H the surface area is given by the formula:
S = pi*R^2 + pi*R*(H)
with pi = 3.14
On the diagram we can see that H = 19.3ft, and the diameter of the base is 14 ft, then the radius is:
R = 14ft/2 = 7ft
REplacing these values in the formula above we will get:
S = 3.14*(7ft)^2 + 3.14*7ft*(19.3ft) = 578.1 ft²
So the correct option is the second one.
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The Patel family looks at a map to plan their family vacation. They plan to travel from Smithville to Jonesville, which are 3 3/4 inches apart on the map. Then they plan to travel from Jonesville to Clarksville, which are 5 1/4 inches apart on the map. The scale on the map is 12 inch equals 4 miles. What is the actual distance the Patel family will travel by the time they reach Clarksville?
the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.
What is the distance in math?
As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.
Smithville to Jonesville distance in map = 3(3/4) inches = (15/4) inches .
given that,
(1/2) inch = 4 miles .
1 inch = 8 miles .
Distance from Smithville to Jonesville = (15/4) * 8 = 30 miles .
similarly,
Jonesville to Clarksville distance in map = 5(1/4) = (21/4) inches .
Distance from Jonesville to Clarksville = (21/4) * 8 = 42 miles .
The actual distance the Patel family will travel by the time they reach Clarksville = 30 + 42 = 72 miles
Hence, the actual distance the Patel family will travel by the time they reach Clarksville is 72 miles.
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Write the expression as a single power using only positive exponents, if possible. Assume no denominator equals zero.
PLS ANSWER ASAP, I need to know in at least under 3 minutes, your help would be very much appreciated.
d^5/d^-3
Possible answers:
A.) d^2
B.) 1/d^2
C.) 1/d^8
D.) d^8
Answer:
Step-by-step explanation:
d^2
When dividing subtract indices OR
dxdxdxdxd /dxdxd
d's cancel out leaving dxd=d^s
What is the surface area for a box with 12 as length, 10 as height and 3 as width.
Answer: 372 units²
Step-by-step explanation:
We can use this formula to solve for the surface area:
Surface Area = 2lw + 2lh + 2hw
We will substitute the known values and solve:
Surface Area = 2lw + 2lh + 2hw
Surface Area = 2(12)(3) + 2(12)(10) + 2(10)(3)
Surface Area = 372 units²
In 2011, there were approximately 2.8 million nurses in a large country, with demand for nurses expected to increase by 0.044 million each year. a. Assuming the number of nurses in 2011 represents the demand for that year, express the demand for nurses in the country, D, in millions, as a function of the number of years after 2011,x. b. If the demand increases as expected, during which year will demand for nurses in the country reach 3.5 million? a. D(x)=
The demand for nurses in the country can be expressed as the function D(x) = 2.8 + 0.044x. The year in which the demand for nurses in the country will reach 3.5 million is in 2027.
a. The demand for nurses in the country can be expressed as a function of the number of years after 2011, x, by using the equation D(x) = 2.8 + 0.044x. This equation represents the initial demand in 2011 (2.8 million) plus the expected increase in demand each year (0.044 million) multiplied by the number of years after 2011 (x).
b. To find the year in which the demand for nurses will reach 3.5 million, we can set D(x) equal to 3.5 and solve for x:
3.5 = 2.8 + 0.044x
0.7 = 0.044x
x = 0.7 / 0.044
x = 15.9
Since x represents the number of years after 2011, we can add 15.9 to 2011 to find the year in which the demand will reach 3.5 million:
2011 + 15.9 = 2026.9
Therefore, the demand for nurses in the country will reach 3.5 million during the year 2027.
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in Chicago, the temperature was 3 degrees. By 5am, it had dropped 15 degrees. What was the temperature at 5am?
PLS HELP OML IM STRUGGLINGGG !!!!!! best answer = brainliest !!!
Answer:
Area = 15.6
Perimeter = 20.6
Step-by-step explanation:
Both smaller triangles are right triangles
The left triangle is isosceles right triangle since 2 angles are 45o so AB is hypotenuse and the other 2 sides are equal
so c^2 = a^2 + b^2
c^2 = 2a^2
(3√2)^2 = 2a^2
2a^2 = 18
a^2 = 9
a = 3
For the right triangle the angle at B is 60o, hypotenuse is BC
so cos(60) = adjacent/hypotenuse
1/2 = 3/BC
=> BC = 6
sin(60) = opposite/hypotenuse
√3/2 = opp/6
opp = 3√3
so AC = 3 + 3√3 = 6√3
Area of triangle = A = 1/2bh = 1/2(6√3)(3) = 9√3 = 15.6
Perimeter = 3√2 + 6√3 + 6 = 20.6
I am needing some help with this
The volume of the cone is 1004.8 cm³.
How to find the volume of a cone?Let's calculate the volume of the cone with radius 8 cm and the slant height is 17 cm. Therefore, let's find the volume of the cone as follows:
volume of a cone = 1 / 3 πr²h
where
r = radiush = height of the coneTherefore,
h² = 17² - 8²
h = √289 - 64
h = √225
h = 15 cm
Therefore,
volume of a cone = 1 / 3 × 3.14 × 8² × 15
volume of a cone = 1 / 3 × 3.14 × 64 × 15
volume of a cone = 3014.4 / 3
volume of a cone = 1004.8 cm³
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