Triangle D has been dilated to create triangle D′. Use the image to answer the question.
image of a triangle labeled D with side lengths of 2.7, 4.8, 4.2 and a second triangle labeled D prime with side lengths of x, 1.6, 1.4
Determine the scale factor used.
2
3
one third
one half
The scale factor is 1/3.
What is the scale factor?
The difference in scale between an original object's scale and a new object that is its representation but is larger or smaller is known as a scale factor. For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.
Here, we have
Given: Triangle D has been dilated to create triangle D′.
To find the scalar value, simply choose one side of D and one did of D’ and divide them to find the scalar. We can verify that we have the correct scalar by performing this division on each related edge. Below I will do D to D’ represented like D/D’:
4.8 / 1.6 = 3
4.2 / 1.4 = 3
2.7 / x = 3
Knowing that the scaling for each edge is 3, we can solve for x.
2.7 / 3 = x
0.9 = x
The edges for D are 4.8, 4.2, and 2.7 respectively to D’ scaled by 1/3. So we can determine that the edges for D’ are 1.6, 1.4, and 0.9 respectively to D scaled by 3.
So if we go D’ to D, we scale by 3. If we go D to D’, we scale by 1/3.
Hence, the scale factor is 1/3.
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answer these questions in detail
Answer:
5. x = 60
6. F' (1, 4)
Step-by-step explanation:
5. The angles shown are same side exterior angles, so they are supplementary (add to 180)
(x + 85) + 35 = 180
x + 120 = 180
x = 180 - 120 = 60
x = 60
6. The line x = 1 is a vertical line, passing through the x=axis at (1, 0). All x coordinates on this line equal 1.
The point F (3,4) is reflected in the line x = 1 at the point F' (1, 4)
7.
Colin uses
cup of vegetable oil in each cake that he makes for his father's beker
If Colin made 8 cakes, how much oil did Colin use in all?
Mark only one oval.
I added 13:5
A. 51/3 cups
OB. 41/3 cups
OC. 51/2 cups
OD.41/2 cups
Spain
42°
The number of cups of vegetable oil used by Colin to make 8 cakes is given by A = 5 1/3 cups
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data,
Let the equation be represented as A
Now, the value of A is
Substituting the values in the equation, we get
Let the number of cups of vegetable oil used by Colin to make 8 cakes be represented as A
Now , the number of cups of vegetable oil used by Colin to make 1 cake is given by = ( 2/3 ) cups of oil
And , number of cups of vegetable oil used by Colin to make 8 cakes A =
A = 8 x number of cups of vegetable oil used by Colin to make 1 cake
On simplifying the equation, we get
[tex]\text{A} = 8 \times \huge \text{(} \dfrac{2}{3} \huge \text{)}= \dfrac{16}{3}[/tex]
[tex]\boxed{\bold{A = 5 \dfrac{1}{3} \ cups}}[/tex]
Therefore, the value of A is 5 1/3 cups
Hence, the number of cups of vegetable oil required is 5 1/3 cups
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Complete question is-
Colin uses 2/3 cup of vegetable oil in each cake that he makes for his father's bakery.
If Colin made 8 cakes, how much oil did Colin use in all?
A. 5 1/3 cups
B. 7 1/3 cups
C. 8 2/3 cups
D. 16 1/3 cups
I believe I missed the lesson on how to solve for x and y from this photo. Any help would be appreciated!
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
Explain about the Pythagorean theorem:The Pythagorean Theorem, a well-known geometric principle that states that the square just on hypotenuse (the side across from the right angle) of a right triangle equals the sum of the squares on its legs, is also known as the
a² + b² = c².
For the larger triangle, applying Pythagorean theorem:
4² + (4√3)² = x²
x² = 16 + 16*3
x² = 16 + 48
x² = 64
x = 8
Then, x - 6 = 8 - 6 = 2
Now applying Pythagorean theorem for smaller triangle:
y² + (x - 6)² = 4²
y² = 4² - 2²
y² = 16 - 4
y² = 12
y² = √12
y = 2√3
Thus, the value of x and y for the given right angled triangle are found as: x = 8 and y = 2√3.
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Can you please help me with this.
The probability that a committee of 10 members consisting of 6 males and 4 females will be selected is 0.3633.
The total number of ways to develop the complex would be 665, 280 ways.
How to find the probability ?To find the probability that a committee of 10 members consisting of 6 males and 4 females be selected for this committee, we need to calculate the number of possible ways to choose 6 males from the 28 males and 4 females from the 12 females.
Using combinations, we have:
Number of ways to choose 6 males = C(28, 6) = 28! / (6! x (28 - 6)!)
Number of ways to choose 4 females = C(12, 4) = 12! / (4! x (12 - 4)!)
Now, we find the probability:
Probability = (Number of ways to choose 6 males * Number of ways to choose 4 females) / Total ways to choose 10 members
Probability = (C(28, 6) x C(12, 4)) / C(40, 10)
Probability = 0.3633
How to find the number of ways ?To find the number of different ways the complex can be developed given the basic designs, we need to consider the following:
The number of ways to arrange the remaining 5 unique designs on the 5 stands is a permutation of 11 designs taken 5 at a time:
P(11, 5) = 11! / (11 - 5)!
Total ways to develop the complex = 12 x P(11, 5)
= 12 x 55440 = 665,280 ways
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Name
Date
- Sarah received a coupon for 15% off the total purchase price at a shoe store. Let p be the
original price of the purchase. Use the expression p-0.15p for the new price of the purchase.
Write an equivalent expression by combining like terms.
What does a residual value of –0.8 mean in reference to the line of best fit?
The given point is 0.8 units above the line of best fit.
The given point is 0.8 units below the line of best fit.
The line of best fit is not appropriate to the data.
The line of best fit has a slope of 0.8.
Which equation represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page?
y = –55x + 407
y = –41x + 814
y = –38x + 922
y = –26x + 723
Answer: A residual value of –0.8 means that the given point is 0.8 units above the line of best fit.
The equation that represents the approximate line of best fit for data, where x represents font size and y represents the number of words on one page is:
y = –38x + 922.
Therefore, the answer is y = –38x + 922.
Step-by-step explanation:
the 3rd and 6th term in fibonacci sequence are 7 and 31 respectively find the 1st and 2nd terms of the sequence
Answer:
7 and 31 it asks
the 3rd and 6th is
The 1st and 2nd terms of this Fibonacci sequence, given the 3rd and 6th terms would be 2 and 5.
How to find the Fibonacci sequence terms ?Let's denote the first and second terms of the Fibonacci sequence as F1 and F2. The Fibonacci sequence is defined by the recurrence relation:
F(n) = F(n-1) + F(n-2)
We are given that the 3rd term (F3) is 7 and the 6th term (F6) is 31. We can use this information to set up the following equations:
F3 = F2 + F1 = 7
F6 = F5 + F4 = 31
We can also express F4 and F5 in terms of F1 and F2:
F4 = F3 + F2 = (F2 + F1) + F2 = F1 + 2F2
F5 = F4 + F3 = (F1 + 2F2) + (F2 + F1) = 2F1 + 3F2
Now, let's substitute equation (4) into equation (2):
F6 = 2F1 + 3F2 + F1 + 2F2 = 31
3F1 + 5F2 = 31
By trial and error, we can find the possible values for F1 and F2 that satisfy this equation:
F1 = 1, F2 = 6: 3(1) + 5(6) = 3 + 30 = 33 (not a solution)
F1 = 2, F2 = 5: 3(2) + 5(5) = 6 + 25 = 31 (solution)
The solution is F1 = 2 and F2 = 5, so the first two terms of the Fibonacci sequence are 2 and 5.
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C. The table below shows the ages in years of 42 children at a birthday party. AGE(YEARS) NO OF CHIDREN 7 2x 8 3x 9 4x-1 10 X 11 X-2 (i). Find the value of x. (ii). Calculate, correct to the nearest whole number the mean age. (iii). Find the probability of selecting at random a child whose age is less than 9 years. 12 x-3 CURT
(1) The value of X is equal to 4 (2) The mean age is 3. (3) The probability of randomly selecting a child under the age of 9 is approximately 0.83.
How to calculate the average?
The formula for calculating the average of given numbers is equal to the sum of all values divided by the total number of values. There are three main types of averages: mean, median, and mode. All of these techniques work slightly differently and often give slightly different typical values.
(i). Given that there are a total of 42 children on the birthday, finding the value of x:
2x + 3x (4x-1) + x + (x-2) + (x-3) = 42
11x - 6 = 42
11x = 48
x = 4
Therefore, the value of x is equal to 4.
(ii). To find the average age, we need to calculate the sum of all the ages and divide by the total number of children:
Average age = (7 x 2 + 8 x 3 + 9 x (4-1) +10 x 4 +11 x (4-2) 12 x (4-3)) / 42
= (14 + 24 + 27 + 40 + 22 +12) / 42
= 139/42
= 3.31
Rounded to the nearest whole number, the average age is 3.
(iii). The probability of randomly selecting a child under 9 is obtained by adding the number of children aged 7, 8 or 9 (because we want children under 9) and dividing by the total number of children:
Number of children under 9 years = 2x + 3x + (4x-1)
Number of children under 9 years = 9x - 1
Number of children under 9 = 9(4)–1
Number of children under 9 years = 35
Probability of choosing a child under 9 = number of children under 9 / total number of children
Probability of choosing a child under 9 = 35/42
The probability of choosing a child under 9 years old is ≈ 0.83
Thus, the probability of randomly selecting a child under the age of 9 is approximately 0.83.
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if a square has length of its side is 8cm then find length of its diagonal
Answer:
8√2 cm
Step-by-step explanation:
yara said that the vertical distance between two points is -5 units how do you know that yara's statement is incorrect
Stop using brainly. This whole website has became a big money grab over the last few months and they will remove all your posts and answers unless you pay them money. I've had it happen several times now.
Convert the equation f(t) = 227e b= -0.09€ to the form f(t) = ab* Give answers accurate to three decimal places
Jackson has a loyalty card good for a 10% discount at his local hardware store. What would his total in dollars and cents be, after the discount and before tax, if the total cost of all the items he wants to buy is $27.40? Round to the nearest cent.
Jackson's total cost after the discount and before tax would be $24.67.
Calculating discounted price :When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.
To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).
Here we have
Jackson has a 10% discount at his local hardware store.
Let 'x' be the cost before tax
After a 10% discount,
The amount that Jackson could pay 90% of the cost
Given that he wants to buy $ 27.40
The cost of items after discount = 90% of 27.40
= [ 90/100 ] × 27.40
= [ 0.9 ] × 27.40
= 24.66
Therefore,
Jackson's total cost after the discount and before tax would be $24.67.
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Write the absolute value equation that has the following solutions.
One solution: x = 15
The absolute value equation is:
|x - 15| = 0
How to write the absolute value equation?We want an absolute value equation that only has the solution x = 15.
So we must have something equal to zero (so we avoid the problem with the signs that we can have with other numbers)
So the equation will be something like:
|x - a| = 0
And the solution is 15, so:
|15 - a | = 0
then a = 15
The equation is:
|x - 15| = 0
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i don't understand this question please help me answer it :)
The number of deer on an island is given by D=200+100sin( 2 π x), where x is the number of years since 2000. Which is the first year after 2000 that the number of deer reaches 150 ?
Therefore, the first Leap year after 2000 that the number of deer reaches 150 is 2000.1, or 2000 and 1/10 of a year.
What are a leap year and a year?If you sum up all the days on a calendar from January to December, there are 365 in a regular year. But about every four years, February has 29 days rather than 28. Therefore, a year has 366 days. There is a term for it: a leap year.
We must find x in the equation D=150 in order to determine the year that the number of deer exceeds 150 for the first time after 2000.
150=200+100sin(2πx)
Subtracting 200 from both sides, we get:
-50 = 100sin(2πx)
Dividing both sides by 100, we get:
-0.5 = sin(2πx)
To find the value of x that satisfies this equation, we can take the inverse sine of both sides:
sin⁻¹(-0.5) = 2πx
Using a calculator, we find that sin⁻¹(-0.5) = -π/6.
-π/6 = 2πx
Solving for x, we get:
x = -1/12
Since x is the number of years since 2000, we need to add 1/12 to find the first year after 2000 that the number of deer reaches 150:
2000 + 1/12 ≈ 2000.1
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Which is more, 19 ounces or 1 pound?
Consequently, 1 pound weighs more than 19 ounces.
What additional weight units are there?
The weight can also be expressed in terms of grams, kilograms, pounds, and tons.
What is a pound?Pound has two different definitions. When used as a noun, it refers to a 16 oz. weight unit. Or it can be used as a verb to strike or hit hard and frequently.
What does ounce mean?The weight unit known as an ounce is 1/16th of a pound.
What fraction of a ton is one pound?A ton weighs 2000 pounds.
16 ounces make up one pound. Consequently, 1 pound weighs more than 19 ounces.
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What fractions are close to 1 than to 0
The answer of the given question based on the fraction is , a value that is greater than 1/2.
What is Fraction?A fraction is mathematical expression that represents part of whole or ratio between the two numbers. It is expressed in the form of a ratio of two integers, with a numerator and a denominator separated by a horizontal or slanted line called a fraction bar.
Fractions that are closer to 1 than to 0 have a value that is greater than 1/2. This is because 1/2 is exactly halfway between 0 and 1 on the number line.
So, any fraction that has a numerator greater than its denominator is closer to 1 than to 0. For example:
2/3 is closer to 1 than to 0 because it is greater than 1/2
7/8 is closer to 1 than to 0 because it is greater than 1/2
3/4 is closer to 1 than to 0 because it is greater than 1/2
On the other hand, fractions that have a value less than 1/2 are closer to 0 than to 1. For example:
1/4 is closer to 0 than to 1 because it is less than 1/2
3/10 is closer to 0 than to 1 because it is less than 1/2
2/5 is closer to 0 than to 1 because it is less than 1/2
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Which is the best estimate of the difference between 67/8 and 1/82
Answer:
8.36
Step-by-step explanation:
67 - 1
8. 82
= 2747 - 4
328
=2743
328
= 8.36
Oriana's Pizza Kitchen has an oven that is shaped like a
rectangular prism. Inside, the oven is 5 feet wide and 4
feet deep so it can bake
their super large pizzas. It is also 3 feet high. What is
the oven's volume?
12 ft³
15 ft3
60 ft³
20 ft³
Answer:
Step-by-step explanation:
If y = x and y = 4, then what is (x + y)² ? A. 0 B. 16 C. 25 D. 64
Step-by-step explanation:
y = x and y = 4
(x + y)²
(4 + 4)² = (8)² = 64
For #1 - 6, use the information given to write the equation of the line in slope intercept form.
1. Line where slope is -32 and y-intercept is 7
1. Line where slope is 5 and x -intercept is 2
1. Line going through the points (-1, -5) and (4, -2)
1. Line going through the points (0, 1) and (2, -2)
1. Line where m = 4 and and b = -76
1. Line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0
An equation of a line where slope is -32 and y-intercept is 7 is y = -32x + 7.
An equation of a line where slope is 5 and x-intercept is 2 is y = 5x - 10.
An equation of a line that is going through the points (-1, -5) and (4, -2) is y = 3x/5 - 22/5
An equation of a line that is going through the points (0, 1) and (2, -2) is y = -x/2 + 1
An equation of a line where m = 4 and and b = -76 is y = 4x - 76.
An equation of a line that passes through the points (1, 3) and (4, 12) with a y-intercept of 0 is y = 3x + 0.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.First of all, we would determine the slope of this line;
Slope (m) = (y₂ - y₁)/(x₂ - x₁)
Slope (m) = (-2 + 5)/(4 + 1)
Slope (m) = 3/5
At data point (-1, -5) and a slope of 3/5, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y + 5 = 3/5(x + 1)
y = 3x/5 + 3/5 - 5
y = 3x/5 - 22/5
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In 1870, the French writer Jules Verne
In 1870, the French writer Jules Verne published his novel "Twenty Thousand Leagues Under the Sea", which tells the story of an underwater adventure aboard the submarine Nautilus.
Who is the French writer?The novel is considered one of Verne's most popular and well-known works, and it has been translated into many languages and adapted into numerous films, TV shows, and stage productions. "Twenty Thousand Leagues Under the Sea" is known for its imaginative portrayal of futuristic technology, such as the advanced submarine Nautilus, and its detailed descriptions of underwater life and exploration.
Therefore, The novel has also been praised for its themes of adventure, exploration, and the relationship between man and nature. It remains a classic in science fiction and adventure literature, and continues to be read and enjoyed by readers around the world.
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A recliner is discounted by $190. If the original price is $800, estimate the sale price by first rounding each number to the nearest hundreds
all u got to do is subtract
The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 12 , 18 , 27 , . . . Find the 8th term.
Answer: 205.031(nearest thousandth)
or 205.03125
Step-by-step explanation:
Solve the inequality for x.
−8+ x/3>-7
Simplify your answer as much as possible.
Answer:
x > 3
Step-by-step explanation:
−8 + x/3 > -7
x/3 > 1
x > 3
We can't simplify anymore, so the answer is x > 3
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Therefore , the solution of the given problem of angles comes out to be the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6.
An angle's meaning is what?The point of intersection of the paths joining a skew ends yields the skew's greatest and smallest walls. A crossroads may be where two paths converge. Angle is another outcome of two things interacting. They approach dihedral shapes more than anything. A two-dimensional curve can be created by arranging two line beams in various configurations between their endpoints.
Here,
Regarding the illustrated diagram, the appropriate statements are:
=> m∠3 + m∠4 + m∠5 = 180°
This is accurate since every triangle's internal angles add up to 180°.
=> m∠5 + m∠6 = 180°
This is true because a triangle's internal angle and outside angle are always equal to 180 degrees.
=> m∠2 + m∠3 = m∠6
This is accurate because, based on the information provided,
the exterior angle at angle 2 (m2) of the triangle is equal to the corresponding interior angle at angle 6 (m6) of the triangle.
Therefore, the three propositions m∠3 + m∠4 + m∠5 = 180°, m∠5 + m∠6 = 180°, and m∠2 + m∠3 = m∠6. are always true in relation to the given figure.
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Helppppppppppppppppppppp
5. Jay cuts identical squares from the corners of a
rectangular sheet of paper as shown in the adjoining
figure. Find the area of remaining portion.
The area of the remaining portion of the sheet is -4x² + 12x + 6.
How to find the area of a figure?Jay cuts identical squares from the corners of a rectangular sheet of paper as shown in the adjoining figure.
Therefore, the area of the remaining portion can be found as follows:
area of the rectangle = 3(4x + 2)
area of the rectangle = 12x + 6
Therefore,
area of each square cut out = x²
area of the 4 square cut out = 4x²
Therefore,
area of the remaining portion = 12x + 6 - 4x²
area of the remaining portion = -4x² + 12x + 6
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Ejercicio 2.- La temperatura ambiente a las 8 am era de 61 grados Farenheit. Fue aumentando de forma lineal hasta la 1 pm en que el termómetro marcó 81 grados. a) Escriba una ecuación lineal que muestre la temperatura en función de la hora en ese intervalo. b) Calcule con esa ecuación la temperatura a las 11:15 am. Aproxime a la décima de grado Farenheit si fuera necesario. oprondamos a hacer ecuaciones y resolver
a)Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es T(h) = 4h + 29
b) Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
what is aproximadamente ?
"Aproximadamente" is a Spanish word that means "approximately" or "roughly" in English. It is often used to indicate that a value or measurement is not exact, but rather an estimation or approximation.
In the given question,
a) La ecuación lineal que relaciona la temperatura con la hora en ese intervalo es:
T(h) = m*h + b
donde T es la temperatura en grados Farenheit, h es la hora en formato de 24 horas, m es la pendiente de la recta y b es el término independiente.
Primero encontramos la pendiente m:
m = (81 - 61) / (13 - 8) = 4
Luego, encontramos el término independiente b utilizando uno de los puntos:
61 = 4*8 + b
b = 29
Por lo tanto, la ecuación lineal que representa la temperatura en función de la hora es:
T(h) = 4h + 29
b) Para encontrar la temperatura a las 11:15 am, primero convertimos el tiempo a horas decimales:
11:15 am = 11 + 15/60 = 11.25 horas
Luego, sustituimos este valor en la ecuación lineal:
T(11.25) = 4(11.25) + 29 = 75.25
Por lo tanto, la temperatura a las 11:15 am aproximadamente es de 75.3 grados Farenheit.
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