Answer:
The area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2
Step-by-step explanation:
To increase the size of a triangle by a scale factor of 10/3, you can multiply each side length of the triangle by 10/3.
The new dimensions of the triangle would be (10/3) * 9ft = 30ft and (10/3) * 12ft = 40ft.
The area of a triangle is given by the formula A = (1/2) * b * h, where b is the length of the base and h is the height of the triangle.
Using the new dimensions of the triangle, the area of the new triangle would be A = (1/2) * 30ft * 40ft = (1/2) * 1200ft^2 = 600ft^2.
Find the compound ratio of 2:3 and 5:4
The compound ratio of natural number ratios 2 : 3 and 5 : 4 is equal to 5 : 6.
How to determine a compound ratio
Herein we must determine a compound ratio, that is, the product of two ratios, whose definition is shown below:
For a : b and c : d, where a, b, c, d are natural numbers, the compound ratio is equal to (a · c) / (b · d).
If we know that a : b = 2 : 3 and c : d = 5 : 4, then the compound ratio is equal to:
r = (2 · 5) : (3 · 4)
r = 10 : 12
Finally, we simplify the resulting expression:
r = 5 : 6
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Two straight lines are perpendicular to each other at point M. One of the lines passes through (2, 6) and the equation of the other line is 2y + 3x -5 = 0. Calculate the co-ordinates of M.
Answer: The equation of a line in the form y = mx + b can be written as y - mx - b = 0. So we can rewrite the equation of the line as 2y - 3x + 5 = 0. This means that the slope of the line is -3/2.
The slope of a line perpendicular to this line would be the negative reciprocal of -3/2, which is 2/3. Let's call the point M (x, y). We know that the line passing through (2, 6) has a slope of 2/3. So we can write the equation of this line as:
y - (2/3)x - b = 0
Substituting the point (2, 6) into this equation, we get:
6 - (2/3)(2) - b = 0
b = 4
So the equation of the line passing through (2, 6) is:
y - (2/3)x - 4 = 0
To find the coordinates of point M, we need to find the point where these two lines intersect. Setting the two equations equal to each other and solving for x and y, we get:
2y - 3x + 5 = y - (2/3)x - 4
5 - 2y = y - (5/3)x + 4
(5/3)x = 3 - y
x = (3 - y) * (3/5)
Substituting this expression for x into one of the original equations, we can solve for y:
2y - 3((3 - y) * (3/5)) + 5 = 0
2y - (9 - 3y)(3/5) + 5 = 0
(10/5)y - (9/5) + 5 = 0
y = (9/5) + (5/5)
y = 2
Substituting this value for y back into the expression for x, we get:
x = (3 - 2) * (3/5)
x = 1
So the coordinates of point M are (1, 2).
Step-by-step explanation:
(tan A)/(sec(A) - 1) + (tan A)/(sec(A) + 1) = 2cos ecA
Answer:
Step-by-step explanation:
LHS = tanθ/secθ - 1 + tanθ/secθ + 1
Cross multiplication,
tanθ(1 - secθ) - tanθ(1 + secθ)/1 + sec^2θ
= tanθ(1 - secθ - 1 - secθ)/-tan^2θ
= -2secθ/-tanθ
= 2 x 1/cosθ / sinθ/cosθ
= 2cosecθ = RHS
Hence proved.
(100 points) Need help asap!
The function f(x) is defined below. What is the end behavior of f(x)?
[tex]f(x)=\frac{1}{9} x^{12}[/tex]
A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞
C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞
The function f(x) is defined below. What is the end behavior of f(x)?
[tex]f(x)=-\frac{1}{10} x^{18}[/tex]
A. as x→−∞,f(x)→−∞ and as x→∞,f(x)→∞
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞
C. as x→−∞,f(x)→∞ and as x→∞,f(x)→−∞
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞
The end behavior of the function f(x) = 1/9 x¹² is
D. as x→−∞,f(x)→∞ and as x→∞,f(x)→∞The end behavior of the function f(x) = -1/10 x¹⁸ is
B. as x→−∞,f(x)→−∞ and as x→∞,f(x)→−∞What is end behavior?The end behavior of function typically says the characteristics of the function at the ends
How to find the end behavior of functionThe given function is:
f(x) = 1/9 x¹²
The positive exponents will mean that x will always yield positive values hence f(x) is always positive
f(x) = -1/10 x¹⁸
The positive exponents will mean that x will always yield positive values however the negative constant -1/10 will make f(x) always negative hence f(x) is always negative
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Dan is training his puppy, Lola, to sit. Dan holds a treat 5 feet above the ground until Lola
sits. As soon as she does, he drops the treat, and Lola catches it in her mouth 1.5 feet above
the ground.
To the nearest tenth of a second, how long does the treat fall before Lola catches it?
Hint: Use the formula h = -16t² + s.
The distance the treat falls before Lola catches the treat is 3.5 feet.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
The distance of the treat from the ground = 5 feet.
The distance the dog jumps to catch the treat from the ground = 1.5 feet.
Now,
The distance the treat fall before Lola catches.
= 5 - 1.5
= 3.5 feet
Thus,
The treat falls for 3.5 feet.
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Pls help! Step by step
Answer:
x = 6[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the cosine ratio in the right triangle and the exact value
cos45° = [tex]\frac{1}{\sqrt{2} }[/tex] , then
cos45° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{6}{x}[/tex] = [tex]\frac{1}{\sqrt{2} }[/tex] ( cross- multiply )
x = 6[tex]\sqrt{2}[/tex]
This is the exact value for x. It may be rounded if you wish
Answer:
[tex]x=6\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9.4 cm}\underline{Trigonometric ratios} \\\\$\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}$\\\\where:\\ \phantom{ww}$\bullet$ $\theta$ is the angle. \\ \phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle. \\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle. \\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse (the side opposite the right angle). \\\end{minipage}}[/tex]
From inspection of the given right triangle:
θ = 45°A = 6H = xSubstitute the given values into the cosine trigonometric ratio and solve for x:
[tex]\implies \cos(45^{\circ})=\dfrac{6}{x}[/tex]
[tex]\implies \dfrac{\sqrt{2}}{2}=\dfrac{6}{x}[/tex]
[tex]\implies x\sqrt{2}=6 \cdot 2[/tex]
[tex]\implies x\sqrt{2}=12[/tex]
[tex]\implies x=\dfrac{12}{\sqrt{2}}[/tex]
[tex]\implies x=\dfrac{12}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}[/tex]
[tex]\implies x=\dfrac{12\sqrt{2}}{2}[/tex]
[tex]\implies x=6\sqrt{2}[/tex]
Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. What is the ratio of the number of burgers without onions to the number of burgers with onions?
The ratio of number of burgers without onions to the number of burgers with onions is 4:1.
Ratio of numbers.The ratio of numbers implies the relationship between the numbers when expressed in its simplest fraction. The relationship can be written in form of a/ b or a:b.
Given in the question that Julia's Burger Place made 3 burgers with onions and 12 burgers without onions. Then the ratio required can be expressed as;
ratio of number of burgers without onions to burgers with onions = (number of burgers without onions)/ (number of burgers with onions)
= 12/ 3
= 4/ 1
The ratio of number of burgers without onions to burgers with onions = 4:1
Therefore, the ratio of the number of burgers without onions to the number of burgers with onions is 4:1.
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What is the slope for y=-3/4x+7
Answer:
-3/4
Step-by-step explanation:
y=mx+b is in slope-intercept form, in which m=-3/4 and b=7, describing the slope and y-intercept of a linear equation respectively.
Find the slope of the line in which x=-24
Answer:
it is undefined
Step-by-step explanation:
Slope of the line x=-24 is undefined. We'll compare the line x = -24, with x = h. So this line is a vertical line that is parallel to the y-axis. We know that the slope of the y-axis is undefined. Since x=-24 and y-axis are parallel, so x=-24 will have the same slope, that is undefined.
Answer:
undefined slope
Step-by-step explanation:
When you have the line x=-24, you have a vertical line, where the x-value is constant, given in the equation, but the y-value varies between negative infinity and positive infinity. If we were to plug two points into the slope formula, we would get: [tex]\frac{y_2-y_1}{-24-(-24)}\to\frac{y_2-y_1}{0}[/tex], because there is no change in x, the x values are the same. Thus it is said that the slope is undefined.
Given it was not a strike, what is the probability it was a knuckle
ball? Enter the answer as a percent (%)to the nearest tenth.
On solving the provided question, we can say that - here in the percentage obtained = 500 => so, 500/1000X100 = 50%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is = 1000
obtained = 500
so, 500/1000X100 = 50%
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Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. What is the probability that the area of triangle XYD is at most 20?
The probability that the area of the triangle is at most 20 is 5/9
What is probability?Probability is a measure of the likelihood of an event occurring. The probability formula is defined as the possibility of an event happening is equal to the ratio of the number of favorable outcomes and the total number of outcomes. Probability of event to happen P(E) = Number of favorable outcomes/Total Number of outcomes.
Given here: Right triangle XYZ has legs of length XY = 12 and YZ = 6. Point D is chosen at random within the triangle XYZ. Thus area of triangle XYZ is
1/2×12×6=36
Now if the area of the triangle is at most 20 then the required probability is = 20/36
=5/9
Hence, The probability that the area of the triangle is at most 20 is 5/9
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An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram. What is the area, in square units, of parallelogram ABCD? Enter your answer in the box.
In the new logo, what fraction of the parallelogram is shaded.
a. The area of the parallelogram ABCD in this problem is given as follows: 24 units squared.
b. The fraction of the area of the parallelogram that is shaded is given as follows: 1/4. (option C).
How to obtain the area of a parallelogram?The area of a parallelogram is given by the multiplication of the length of the base by the height, as follows:
Area = base x height.
The base and the height for this problem are obtained counting the number of dots, hence:
Base: 4 units.Height: 6 units.Hence the area is given as follows:
Area = 4 x 6
Area = 24 units squared.
The shaded region is composed by a triangle with base 4 and height 3, hence:
Area shaded = 0.5 x 4 x 3 = 6 units squared.
(formula for the area of the triangle).
Meaning that the fraction is given as follows:
6/24 = 1/4.
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Select the correct answer from each drop-down menu. Graph of a four-sided polygon on a coordinate plane at A (minus 1, minus 1), B (0, 1), C (2, 2), and D (2, minus 1). In the figure, polygon ABCD is dilated by a factor of 2 to produce A′B′C′D′ with the origin as the center of dilation. Point A′ is at (-2, -2) , and point D′ is at (4, -2) .
The coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
The vertices of the original polygon for this problem are given as follows:
A(-1,-1), B (0, 1), C (2, 2), and D (2, -1).
The scale factor for the dilation in this problem is given as follows:
k = 2.
Hence the coordinates of the vertices of polygon A'B'C'D' after the dilation are given as follows:
A'(-2, -2), B'(0, 2), C'(4,4), D'(4,-2).
(as each coordinate of each vertex was multiplied by the scale factor of 2).
Missing InformationThe problem is incomplete, hence the coordinates of the vertices of the image after the dilation were obtained to show how the dilation works.
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Given the number 254, 476, 951
What number is in the TEN THOUSAND's SPOT?
Step-by-step explanation: 1 is in the ten thousand places and has a place value of 10,000. 3 is in the thousand's place and has a place value of 3,000. 5 is in the hundreds and has a place value of 500.
Pls help with my math
This is the hard question for me
Thnx
Find the product. Enter your answer in the box below as a fraction, using the
slash mark (/) for the fraction bar. 4/3*5/3
The solution to the product expression 4/3 * 5/3 is 20/9
How to evaluate the product expression?From the question, we have the following parameters that can be used in our computation:
The product 4/3*5/3
To start with, we need to represent the statement as an expression
So, we have the following representation
4/3 * 5/3
Using a calculator, we multiply the numerator
So, we have the following representation
4/3 * 5/3 = 20/3 * 1/3
Using a calculator, we multiply the denominator
So, we have the following representation
4/3 * 5/3 = 20/9
Hence, the solution is 20/9
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Simplify (-8-r)+(2r-4) Plato question
Answer:
−12r+32−2r 2
Step-by-step explanation:
(−8−r)(2r−4)
Apply the distributive property by multiplying each term of −8−r by each term of 2r−4.
−16r+32−2r
2
+4r
Combine −16r and 4r to get −12r.
Answer:
R-12
Step-by-step explanation:
Open the parenthesis, then solve
-8-r + 2r-4
-r+2r-8-4
r-12
Your answer will be R-12
If some one makes and many slices of toast of toast as possible in 4 minutes and 40 seconds how many slices they can make?
Therefore , the solution of the given problem of expression comes out to be probably 4 slices.
Who or what is expression?In mathematics, it is possible can multiply, division, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression. Expressions and phrases can be contrasted.
Here,
you figure if a toaster takes about 1-2 minutes to toast a piece of bread and a toaster usually can fit 2 slices at a time i would say 4.
Preheat oven broil to high. Move oven rack to highest position.
Place sliced bread on an ungreased baking sheet. 4 slices of bread.
Broil bread for 1 minute, or until golden brown, then flip and broil for another 20-30 seconds. ...
Top with butter, jam, or any other favorite topping!
The temperature needed for the hot ambient air in a toaster, which makes the bread turn brown, is around 310°F (146°C). The heating element inside a toaster is a nickel-chromium alloy. The electrical current that runs through it heats it to make it red hot, with a temperature of 1,100°F to 1,200°F (519°C to 566°C).
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guys please help its due today!
Answer:
Step-by-step explanation:
the answer is 6
Minimum or maximum value
The minimum is the smallest value in the data set. The maximum is the largest value in the data set.
To find the minimum or maximum value of a function:We will set the first derivative of the function to zero and solve for x to get the critical point. If we take the second derivative or f''(x), then we can find out whether this point will be a maximum or minimum. If the second derivative is positive, it will be a minimum value.
A minimum or a maximum is called an extreme point. A local extreme point is the smallest or largest value in its neighborhood. If it is also the smallest or largest at the entire domain of the function, it is called a global extreme point. The local minima and maxima can be found by solving f'(x) = 0.
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Complete question is: What is the difference between Minimum or maximum value?
Which equation has 1 solution? A. (W)=-2. B. (W)=1. C. (W)=-1. D. (W)=0
An equation which has one (1) solution include the following: D. |W| = 0.
What is an absolute value function?In Mathematics, an absolute value function can be defined as a type of function that is composed of an algebraic expression, which is placed within absolute value symbols and measures the distance of a point on the x-coordinate to the x-origin (0) of a cartesian coordinate (graph).
Mathematically, an absolute value function can be represented by this mathematical expression:
|x| = x, x ≥ 0.
|x| = x, x < 0.
Generally speaking, an equation or absolute value function would have exactly one (1) solution when there is only one (1) value for the variable (W) that makes the equation to be true as shown below:
|W| = 0
W = ±0
W = 0
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Find the distance between the points.
(-2.5,3), (5,3)
The distance is
Answer:
7.5 units
Step-by-step explanation:
5-(-2.5)=7.5
Complete the following indirect proof (proof by contradiction).
Given: Adjacent angles LA and ZB, formed by the intersection of two lines
Prove: At least one of the angles LA and B has measure 90° or greater
First, we assume that this conclusion is false. In other words, we assume that the contrary statement "none of the two angles has measure [tex]90^{\circ}[/tex] or greater" is true.
The assumption is equivalent to the following two statements:
(1) [tex]m\angle A\text{ } \boxed{ < 90^{\circ}}[/tex]
(2) [tex]m\angle B\text{ } \boxed{ < 90^{\circ}}[/tex]
Using (1) and (2) and the addition properties of inequalities, we conclude that [tex]m\angle A+m\angle B \text{ } \boxed{ < } \text{ } 180^{\circ}[/tex].
On the other hand, two adjacent angles form a linear pair. Thus, the last statement contradicts the Linear Pair Property, which states that for a linear pair of angles [tex]\angle A[/tex] and [tex]\angle B[/tex], [tex]m\angle A+m\angle B \text{ } \boxed{=} \text{ } 180^{\circ}[/tex].
Therefore, the assumption made is false, and the statement "at least one of the angles [tex]\angle A[/tex] and [tex]\angle B[/tex] has measure [tex]90^{\circ}[/tex] or greater" is true.
I need help, and I forgot how to do this
Answer: 5. 2x+8 6. 5(x-9) 7. -3x+-21
Step-by-step explanation: Multiply the number outside the parenthesis by everything inside it
Please help will mark Brainly
Answer:
Step-by-step explanation:
the ratio of the circumference of any circle to the diameter of that circle. Regardless of the circle's size, this ratio will always equal pi. In decimal form, the value of pi is approximately 3.14.
A random sample of 250 campers at a summer camp were surveyed to see what water activities they were most interested in participating in. The study found that 110 campers were not interested in paddleboarding. The study also showed that 64 of the campers who were interested in paddleboarding were also interested in waterskiing and 90 of the students were not interested in waterskiing. Based on the given information, which of the following relative frequency tables summarizes the data?
The relative frequency table that summarizes the data is given by the image at the end of the answer.
What is Relative frequency?The number of desired experiment results divided by the total number of experiment results is used to compute the relative frequency of an event in an experiment.
Given:
The percentage of people interested in waterskiing
= 90/250 x 100
= 36%.
Thus, the percentage of people that was not interested in waterskiing is
=100-36
= 64%
Now, the percentages related to paddle boarding are :
Yes: 72/250 = 28.8%.
No: 18/250 = 7.2%.
Of those not interested in waterskiing, the percentages related to paddle boarding are
Yes: 112/250 = 44.8%.
No: (120 - 72)/250 = 19.2%.
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how long would it tak to go 75 miles if you can go 45 mph
How many Proper Fractions are there?
How can you divide polynomials? What are the different methods you can use?Which method do you prefer and why?
(6 × 10a) + (6 × 10b) + (6 × 10c) = 6006.6
Write down a possible set of values of a, b and c.
The values of a , b and c from the equation is ( 3 , 0 , -1 )
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
( 6 × 10ᵃ ) + ( 6 × 10ᵇ ) + ( 6 × 10^c ) = 6006.6 be equation (1)
Now , the number 6006.6 is written as
6000 + 6 + 0.6 = 6006.6
On simplifying the equation , we get
( 6 × 10ᵃ ) = 6000
Divide by 6 on both sides of the equation , we get
10ᵃ = 1000
So , 10ᵃ = 10³
Therefore , the value of a = 3
Now , ( 6 × 10ᵇ ) = 6
Divide by 6 on both sides of the equation , we get
10ᵇ = 1
when b = 0
10⁰ = 1
Therefore , the value of b = 0
Now , ( 6 × 10^c ) = 0.6
Divide by 6 on both sides of the equation , we get
10^c = 0.1
when c = -1
10⁻¹ = 0.1
Therefore , the value of c = -1
Hence , the value of a , b and c is 3 , 0 and -1 respectively
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