If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.
In the question ,
it is given that ,
The triangle CDE is dilated by scale factor of 1/4
and the new triangle formed after dilation is C'D'E' .
it is given that the measure of the side D'E' = 3.5 .
let the measure of the the side DE = x
So , according to the question ,
x *(1/4) = 3.5
On cross multiplication,
we get ,
x = 4* 3.5
x = 14
Therefore , If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.
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please help!! i do not understand
Answer:
Step-by-step explanation:
Hi, Julia, they are trying to ask about error, or the confidence that there is not an error. It's kinda like saying, we're 100% sure the answer is correct, mostly :DDDD which really lowers your confidence about the 100% correct statement. Anyway, sooo then they give the way to show deviation, from something. if you've had Calculus one, this is the same thing as the Delta , Epsilon thing, about a small distance away from the target is still with in a certain range. I feel like if they had written the inequality like this...
( p' - E) < p < (p'+E) it would be clearer about the inequality. E is just a tiny distance away in the positive and negative direction. E plays the role of epsilon. the numbers they give are the range of the confidence. I don't think they ask a very clear question.
0.056<p<0.112
p is kinda like our "best guess" answer, and we're giving it this range that it's probably within, for a certain level of confidence. You can see, that as the confidence goes down, that range can become bigger.
Describe the end behavior of each function using the leading coefficient and degree, and state
the domain and range.
1. f(x) = 3x^4
2.f(x) = -2x^3
3.f(x) = -1/2x^5
4.f(x)=3/4x^6
Answer:
1. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: [0, ∞)
2. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: (-∞, ∞)
3. y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: (-∞, ∞)
4. y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞; Domain: (-∞, ∞); Range: [0, ∞)
Step-by-step explanation:
Rule for end behavior of polynomials:
(a) Positive leading coefficient, even degree: y ⇒ ∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞
(b) Negative leading coefficient, even degree: y ⇒ -∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞
(c) Positive leading coefficient, odd degree: y ⇒ ∞ as x ⇒ ∞ AND y ⇒ -∞ as x ⇒ -∞
(d) Negative leading coefficient, odd degree: y ⇒ -∞ as x ⇒ ∞ AND y ⇒ ∞ as x ⇒ -∞
Domain and range for a polynomial function with an odd degree will always be all real numbers, whether or not there's a constant or not.
Domain will always be all real numbers for a polynomial function with an even, whether or not there's a constant.
For a polynomial function with an even degree, the range will extend from the y-coordinate of the vertex to ∞, if the leading coefficient is positive
For a polynomial function with an even degree, the range will extend from -∞ to the y-coordinate of the vertex if the leading coefficient is negative.
The graph of y = f(x) is graphed below. What is the end behavior of f(x)?
Answer:
The third option, as x approaches infinity y approaches infinity and as x approaches negative infinity y approaches negative infinity.
Step-by-step explanation:
In ΔQRS, s = 7.9 cm, ∠Q=125° and ∠R=23°. Find the length of q, to the nearest 10th of a centimeter.
The length of q, to the nearest 10th of a centimeter, is 8.8 cm.
We are given the following;
In ΔQRS, s = 7.9 cm, ∠Q=125° and ∠R=23°.
The third angle can be calculated using the angle sum property:
angle Q + angle R + angle S = 180 degrees
125 degrees + 23 degrees + angle S = 180 degrees
angle S = 180 - (125 + 23) degrees
angle S = 180 - 148 degrees
angle S = 32 degrees
To find the length of q we shall apply the Sine rule.
q / Sin Q = s / Sin S
q / Sin 125 = 7.9 / Sin 32
by cross multiplication we will get;
q = (7.9 x Sin 125) / Sin 32
q = (7.9 x 0.61) / 0.55
q = 8.8 cm (approximately)
So, the length of q is 8.8 cm.
Thus, the length of q, to the nearest 10th of a centimeter, is 8.8 cm.
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Michael is working two summer jobs, making $19 per hour lifeguarding and making
$14 per hour clearing tables. In a given week, he can work at most 17 total hours and
must earn a minimum of $280. If a represents the number of hours lifeguarding and
y represents the number of hours clearing tables, write and solve a system of
inequalities graphically and determine one possible solution.
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
What is inequality?It shows a relationship between two numbers or two expressions.
There are commonly used four inequalities:
Less than = <
Greater than = >
Less than and equal = ≤
Greater than and equal = ≥
We have,
Two summer jobs:
Lifeguarding.
x = number of hours
= $19 per hour
Cleaning tables.
y = number of hours
=$14 per hour
Total hours in a week = 17 hours
Minimum earning = $280
The inequality represents the above situation.
x + y ≥ 17
19x + 14y ≥ 280
Solving for x and y.
x + y = 17 _____(1)
x = 17 - y
19x + 14y = 280 ______(2)
Putting (1) in (2) we get,
19(17 - y) + 14y = 280
323 - 19y + 14y = 280
323 - 5y = 280
323 - 280 = 5y
43 = 5y
y = 43/5
y = 8.6
y = 9
Now,
x = 17 - y
x = 17 - 8.6
x = 8.4
x = 8
Thus,
The possible solutions are 8 hours and 9 hours.
The number of hours for lifeguarding is 8 hours.
The number of hours for clearing tables is 9 hours.
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Please help with the following question.
Answer:
Step-by-step explanation:
C
Given: AB is parallel to CD and BD bisects AC.
Prove: triangle ABE is congruent to triangle CDE.
Check the picture below.
The lifeguards on a beach in Hawaii found a correlation between the height of a wave (y) and the number of surfers on the beach (x). The equation they calculated was y = 0.95x + 20. If the wave height was 4 feet, about how many surfers would be on the beach?
Answer:
Step-by-step explanation:
hope this helps
please help
The equation the quantity x plus 56 end quantity over 3 equals 5 times x models the workload of a class project, where x is the number of hours each student must contribute. How many hours does each student work on the project?
10 hours
9 hours
7 hours
4 hours
Each student should work for 7 hours on the project.
Given, the equation the quantity x plus 56 end quantity over 3 equals 5 times x models the workload of a class project,
where x is the number of hours each student must contribute.
Now, according to question,
56 - 3x = 5x
56 = 5x + 3x
8x = 56
x = 7
So, x = 7 hours
Hence, each student should work for 7 hours on the project.
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Answer:
4 hours
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x = 14/3
Decimal Form:
x = 4.6
Mixed Number Form:
x = 4 2/3
Therefore, 4 hours is how much the students work on the project.
What is the equation for the line that is perpendicular to y=−1/2x+5 and passes through the point (0, 7)?
The equation of line passes through the point (0, 7) will be;
⇒ y = 1/2x + 7
What is Equation of line?
The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The point on the line are (0, 7).
And, The perpendicular line is,
⇒ y = -1/2x + 5
Now,
Since, The equation of line passes through the point (0, 7).
So, We need to find the slope of the line.
Since, The product of slope of the perpendicular lines is - 1.
Hence, Slope of the perpendicular line is,
y = -1/2x + 5
m₁ = dy/dx = - 1/2
m₁ = - 1/2
So, The slope of the line,
m₂ = - (- 1/2)
= 1 / 2
Thus, The equation of line with slope 1/2 is,
⇒ y - 7 = 1/2 (x - 0)
⇒ y - 7 = 1/2 x
⇒ y = 1/2x + 7
Therefore, The equation of line passes through the point (0, 7) will be;
⇒ y = 1/2x + 7
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a dish contains 2 yellow triangles, 3 yellow squares, and 1 green square two shapes are drawn in a sequence with replacement. what is the probability of drawing a green triangle on a second draw given the first draw was a yellow shape?
Answer: I don't know
Step-by-step explanation:
I have no idea
A small theatre's profit, P(x), from selling concert tickets is P(x) = −15x2 + 60x + 30, where x is the number of $2 price increases of each ticket. Use the graph below to answer the question.
Graph of function p of x equals negative 15 x squared plus 60 x plus 30. The graph has the x-axis labeled as number of price increases, and the y-axis labeled as profit. The curve begins at (0, 30) and increases to (2, 90) and then decreases through (4.449, 0).
How many price increases maximized the theatre's profit?
0
1.5
2
4.5
Using the vertex of the quadratic equation, it is found that the profit will be maximized when each ticket price is sold for $2.
What is the vertex of a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
Considering the coefficient a, we have;
If a < 0, the vertex is a maximum point.
If a > 0, the vertex is a minimum point.
In this question, the function is modeled as follows, considering x as the price divided by $2.
P(x) = -15x² + 60x + 30.
The coefficients are a = -15 < 0, b = 60, c = 30, therefore the x-value of the vertex is given by:
V = -b/2a
V = -60/2(-15)
V = -60/-30
V = 2
Hence, the profit will be maximized when each ticket price is sold for $2.
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Kye's current credit card balance is $3,109.87 with a minimum payment of $159.00. Over the next month he spends $532.42. If the APR is 27.99% (billed monthly), what will Kye's new balance be, with interest?
Therefore , the solution of the given problem of interest comes out to be $4,088.14 is the new balance.
What exactly does interest mean?Divide the number by the expense of borrowing, the remaining time, and other factors to get the simple interest rate. In marketing, the straightforward return plan is principal interest payments plus hours. This technique is the simplest way to figure out interest. The most common way to determine income is as a percentage of the principal sum.
Here,
We must first figure out the interest on the present balance.
The interest rate is 27.99%/12, or 0.0233, per month.
As a result, the current balance's interest rate is:
=> 3,109.87 x 0.0233 = $72.43
When this interest is added to the outstanding amount, Kye's new balance is as follows:
=> 3,109.87 + 72.43 + 532.42 = $3,714.72
The minimum payment for the new amount must now be determined:
=> 3,714.72 x 0.02 = $74.29
Kye's minimum payment for the following month will be $159.00 because the minimum payment is the higher of $74.29 or that amount.
Kye's new balance with interest as a result of making the required minimum contribution and spending $532.42 is as follows:
=> 3,714.72 - 159.00 + 532.42 = $4,088.14.
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3-4x/9 = 9 Simplify your answers. Type an integer or a fraction. Use a comma to separate answers as needed.)
Answer:
"Multiply to remove the fraction then set it equal to 0 and solve."
Exact form
x = - 39/2
Decimal Form:
x = -19.5
Mixed Number Form:
x = - 19 1/2
Hope this helped...!
4/3 pi (2)^3 + 1/3 (2)(4)
Students in a cooking class made 4 1 2 quarts of soup. They served 4 5 of the soup to friends. Each serving is 3 5 quart. Hector incorrectly says that there were 3 3 5 servings of soup. What is the correct number of servings? What did Hector do wrong?
The correct number of servings would be = 12/25
What is a cooking class?A cooking class is defined as the class that is made up of students that are being thought how to prepare and serve different types of food.
The total amount of quarts of food made by the students = 4½.
The number of servings to friends = ⅘
The quantity of quarts in each serving = ⅗ quarts
Total number of quarts served = ⅘ × ⅗= 12/25
The correct number of servings = 12/25
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During the time Tommy eat two bowls of ice cream, Robert eats three bowls of ice cream. The two boys ten bowls of ice cream in one hour. How many bowls did Tommy eat? Show working
Answer:20
Step-by-step explanation:
Write y=-|x-3|+2 as a piecewise function.
The equation y = -|x - 3| + 2 written as a piecewise function is;
f(x) = {y = x - 1, if x < -3
{y = -x + 1, if x ≥ -3
How to define piecewise functions?A function can be written as piecewise function if it changes its behavior ( increasing or decreasing ) about a point.
The function f(x) = y = |x| changes its behavior at |x| = 0 i.e , x = 0 .
y = | x | = x , if x < 0
= - x , if x > 0
| x | = a => x = ± a
• | x | ≥ a ( a ≥ 0 ) => x € ( -∞ , -a ] U [ a , ∞ )
• | x | ≤ a ( a ≥ 0 ) => x € [ -a , a ]
The given function is : y = -|x - 3| + 2
The function will change its behavior when; -| x - 3 | = 0
-x + 3 = 0
x = -3
If x < -3 , then ;
y = -(-(x - 3)) + 2
y = x -3 + 2
y = x - 1
If x ≥ -3, then ;
y = -(x - 3) + 2
y = -x + 3 + 2
y = -x + 1
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10x+2y=41
Solve for y and x
Answer:
{x,y}={25/7,41/7}
Step-by-step explanation:
A truck travels 50 m/s in a 30 second time frame what is the average speed
The average speed of the truck is 50 m/s .
We know that the average speed of any vehicle is calculated by total distance divide by total time.
Now the truck travels at 50 m/s for 30 seconds.
Distance covered in 30 seconds = 50 × 30 = 1500 meters
Time taken = 30 seconds
average speed = 1500 / 30 = 50 m/s
The average speed now accounts for the majority of the distance travelled. Average speed is essentially a method for calculating distance and the rate of transit time.
Knowing the average speed is crucial because it is clear that the pace will vary throughout the voyage. The average speed of a vehicle or an object can be determined using a variety of methods.
That is the most popular and simple way for figuring your average speed. It functions best when the object's speed remains constant throughout the journey, never rising or falling.
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Brand A has a box of 25 forks for 1.99 and Brand B has a box of 42 totals for 3.89. What is the unit price for each brand and what brand is a better buy based on unit price
Answer:
Brand A
Step-by-step explanation:
Brand A has a box of 25 forks for 1.99
Take the price per fork
1.99 /25 = .0796
.08 per fork
Brand B has a box of 42 totals for 3.89
3.89 / 42
.092319048
.09 per fork
The bookshop received a shipment of identification books. 1/3 of them were bird books, 1/2 of the rest of the books
were about plants, and 1/4 of the remaining books were mammal books. The 12 books that were left were insect
books. How many books were in the shipment?
Answer:
48
Step-by-step explanation:
1/3+(1/2*2/3)+(1/4*1/3)=3/4
1-3/4=1/4
So 12 book were 1/4 of the shipment.
So 48 book sis total.
Step A
Let x = Elijah’s age.
x + 4 = James’s age
2(x +4) = Bryan’s age.
Step B
x + x + 4 + 2(x +4) = 80.
Step C 4x + 12 = 80
X = 17
Step D James is 21.
1. Above is a solution to a verbal problem on the Algebra 1 test. Write the word problem that the student was solving.
2. If the equation in step B had been 2(x + 4) = 80, would the wording of the word problem change or stay the same? If it changed, what would it say now?
1. Elijah is the smallest sibling among his brother who is 4 years older than her and Bryan is the eldest sibling who is twice as James, what is his age of James if the sum of their ages is 80 years?
2. If the equation in step B had been 2(x + 4) = 80, the changed statement would be Bryan is 80 years old.
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.
Here we are converting a numerical expression into a statement.
Given,
Step A
Let x = Elijah’s age.
x + 4 = James’s age
2(x +4) = Bryan’s age.
Step B
x + x + 4 + 2(x +4) = 80.
Step C 4x + 12 = 80
X = 17
Step D James is 21.
The verbal problem to the algebra test can be stated as
Elijah is the smallest sibling among his brother who is 4 years older than her and Bryan is the eldest sibling who is twice as James, what is the age of James if the sum of their ages is 80 years?
If the equation in step B had been 2(x + 4) = 80, the changed statement would be Bryan is 80 years old.
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Given f(x) = x³ + kx + 3, and x + 3 is a factor of f(x), then what is the value of
k?
If (x + 3) is a factor of f(x) = x³ + kx + 3 , then the value of k is -8 .
In the question ,
it is given that ,
the function is f(x) = x³ + kx + 3 ,
and also given that (x+3) is a factor of f(x) , that means
x + 3 = 0
x = -3
x = -3 should satisfy the function ,
So , substituting x = -3 in the function f(x) = x³ + kx + 3,
we get
f(-3) = (-3)³ + k(-3) + 3 = 0
-27 -3k + 3 = 0
-3k - 24 = 0
-3k = 24
k = 24/(-3)
k = -8
Therefore , If (x + 3) is a factor of f(x) = x³ + kx + 3 , then the value of k is -8 .
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What are the domain and range of the function f(x) = 2x^3/4 respectively?
Answer:
Domain: [0,∞), {x|x ≥ 0}
Range: [0,∞), {y|y ≥ 0}
Step-by-step explanation:
1. Find where the FUNCTION is DEFINED.
A function is a set of ordered pairs where each first element is paired with one, and only one, second element. No element in either pair is without a partner.
2. Find the DOMAIN: The set of all x-values that a function passes through. Also, it is the left coordinate in a coordinate pair.
3. The RANGE: the set of all y-values that a function passes through. Also, it is the right coordinate in a coordinate pair.
(8.4x10^11)/(5.25x10^2)(8.0x10^3) express in scientific notation
The following equation expressed in scientific notation would be as follows:
SCIENTIFIC NOTATION FORM:
[tex]1.28*10^1^3[/tex]
Hope this helps!
Joan has a vegetable garden in her backyard that measures 8 feet
7 feet. Which expression would not calculate the garden's perimeter
A. 8 + 7/3 + 8 = + 7/3/
B. 27 +28
C. 2 (8² • 7 - - )
D. 2 (8 + 7 )
The expression will be i.e., 2(8 + 7).
The correct option is (D)
Given,
In the question:
Joan has a vegetable garden in her backyard that measures 8 feet 7 feet.
To find the which expression would not calculate the garden's perimeter?
Now, According to the question;
Based on the given conditions:
Formulate:
Measurement of garden is :
Length and breadth is 7 ft. and 8 ft.
Calculate:
2 x (7 + 8)
= 30
Hence, The expression will be i.e., 2(8 + 7).
The correct option is (D)
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3. Cameron has been given 4 boxes with samples
of soil. If all of the samples can either be
classified as mineral-rich, mineral-neutral, or
mineral-poor, how many different ways could
Cameron possibly classify all 4 samples, given
that they could all be classified as the same type
if that were the case?
A. 3
B. 4
C. 12
D. 81
Answer: D. 81
Step-by-step explanation:
Box A: 3 possibilites
Box B: 3 possibilites
And so on, so you get 3^4, which is 81
This is a scale drawing of an apartment. The actual apartment has a perimeter of 160 ft. Draw another scale drawing of the apartment using the scale 20 ft to 1 unit from the apartment to the drawing Explain your reasoning
pls help someone
According to the scale factor, When the scale is changed to 20 feet to 1 unit, then the drawing would be exactly the same shape, here only each side would have half the original drawing units.
Scale factor:
The ratio between the scale of a given original object and a new object, which is its representation but of a different size (bigger or smaller) is known as scale factor.
Given,
This is a scale drawing of an apartment. The actual apartment has a perimeter of 160 ft.
Here we need to find the reason for the scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment
Here we know that the actual apartment has a perimeter of 160 ft.
And we have to draw another scale drawing of the apartment using the scale 20 feet to 1 unit from the apartment to the drawing.
So, as per the given details, the perimeter lies along the edges of squares and we count 16 sides of squares as we work around the perimeter, this means that each square is calculated as,
=> 160 / 16 = 10 feet on a side.
Therefore, 10 feet in real life plots to 1 unit on the drawing
Therefore, if we change the scale to 20 feet to 1 unit , then the drawing would be exactly the same shape, only each side would have half the original drawing units.
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The length of the rectangular lot is 25 ft longer than twice the width. If the perimeter of the lot cannot exceed 350 ft, what is the greatest width possible?
The greatest width possible if the length of the rectangular lot is 25 ft longer than twice the width and if the perimeter of the lot cannot exceed 350 ft is 50 ft.
We are given,
The length of the rectangular lot is 25 ft longer than twice the width.
The perimeter of the lot cannot exceed 350 ft.
Let the width of the rectangular lot be x.
So, the length of the rectangular lot = 2x + 25
We know that the perimeter of the rectangle is given by:
P = 2(L + W)
Substitute the given values in the above formula;
350 = 2(2x +25 + x)
350 / 2 = 3x + 25
175 - 25 = 3x
x = 150 / 3
x = 50 ft
So, the width of the rectangular lot = 50 ft
And, the length of the rectangular lot = 2 * 50 + 25 = 125
Thus, the greatest width possible if the length of the rectangular lot is 25 ft longer than twice the width and if the perimeter of the lot cannot exceed 350 ft is 50 ft.
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