write the following symbolically 'Triangle is equilateral or isosceles'.

False

If it doesn't have an equal sign ( = ), it's not an equation. It would be considered an expression.

Answer: False

Step-by-step explanation:

Answer:

(4x+1) (x+6)

(y-1)(5y+3)

(k-2)(7k+5)

Step-by-step explanation:

Answer:

Step-by-step explanation:you such a nerd and I will never help u

Answer:

2 1/2

Step-by-step explanation:

Answer:

See below

Step-by-step explanation:

Solve the equation using the quadratic formula

[tex]\displaystyle x^2-2x+2=0\\\\x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(2)}}{2(1)}\\ \\x=\frac{2\pm\sqrt{4-8}}{2}\\ \\x=\frac{2\pm\sqrt{-4}}{2}\\ \\x=\frac{2\pm2i}{2}\\ \\x=1\pm i[/tex]

Discriminant and Solution Analysis

As we determined in the quadratic formula, our discriminant is -4 because [tex]b^2-4ac=(-2)^2-4(1)(2)=-4[/tex], under the radical. Because it is negative, our solutions must be imaginary since the square root of a negative number is not real.

Answer: Yes

Step-by-step explanation:

3 is a factor of 81 because on dividing 81 by 3, we get no remainder and 27, that is, the quotient in this division, which is also a factor of 81.

The approximate speed of a vehicle that left a skid mark measuring 100 feet is 47.63 miles per hour

Given the formula:

0.75d = s² / 30.25

Where,

d = length of the vehicle’s skid marks in feet = 100 feet

s = speed in miles per hour

Substitute d = 100 feet into the equation

0.75d = s² / 30.25

0.75(100) = s² / 30.25

75 = s² / 30.25

cross product

75 × 30.25 = s²

2,268.75 = s²

find the square root of both sides

s = √2,268.75

s = 47.63 miles per hour

Ultimately, 47.63 miles per hour is the approximate speed of the vehicle.

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An integer is a whole number that can be positive, negative, or zero and is pronounced as "IN-tuh-jer."

Integers include things like -5, 1, 5, 8, 97, and 3,043.

5.643.1, -1.43, 1 3/4, 3.14,.09, and other non-integer numbers are a few examples.

Formally, the following describes the set of numbers designated Z:

Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

The four most frequent ones are p, q, r, and s.

An infinite set is the set Z. In spite of the possibility of an unlimited number of items in a set, denumerability refers to the property that each element in the set can be represented by a list that implies its identity. The fact that 356,804,251 and -67,332 are integers whereas 356,804,251.5, -67,332.89, -4/3, and 0.232323... are not can be inferred from the list "..., -3, -2, -1, 0, 1, 2, 3,...."

There are no elements missing from either set when pairing the components of Z with N, the set of natural numbers. Let N = {1, 2, 3, ...}. Following that, the pairing may go like this:

The key criterion for assessing cardinality, or size, in infinite sets is the presence of a one-to-one relationship. Z shares the same cardinality with the sets of natural and rational numbers. Real, fictitious, and complex number sets, however, have cardinality that is more than Z.

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Answer: I don't know if this is what you wanted, but two ways to represent 4/5 are 0.8 and 4 divided by 5.

Step-by-step explanation:

4/5 = 8/10

8/10 = 0.8

fraction symbol means to divide.

I hope this helps!

The probability that a muffin picked at random contains raisins is 3/5.

The probability that a muffin picked at random contains raisins is calculated as follows:

The number of muffins that are not frozen = 30 - 14

The number of muffins that are not frozen = 16

The number of muffins that are not frozen but contain raisins = 16 - 4

The number of muffins that are not frozen but contain raisins = 12

The total number of muffins that contain raisins = 12 + 6

The total number of muffins that contain raisins = 18

The probability that a muffin contains raisins, P(contain raisins) = 18/30

P(contain raisins) = 3/5

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Based on the formula [tex]C (t) = 0.8 (1.2)^{t}[/tex] it is expected for the concentration of organisms to increase over time (third option).

To determine how the formula or function affects the number of organisms, let's use two different times in order to compare the results:

C (t) = 0.8 (1.2)^{t}

Let's find out the concentration of organisms with the times 2 and 5:

2:

C (t) = 0.8 (1.2)^{2}

C (t) = 0.8 x 1.44 = 1.152

5:

C (t) = 0.8 (1.2)^{5}

C (t) = 0.8 x 2.48 = 1.99

Based on this, it can be concluded that as time increases the concentration increases too.

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Answer:

Step-by-step explanation:

ill explain How to solve.

A:    

     x+4>15

     15-4=11

      x<11

C:

     6b=>54

     54/6=9

      b=>9

USE A WEBSITE CALLED DESMOS

-pi is the  phase shift of y = -cos ( 1/2 x + pi/2 )

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given function is y = -cos ( 1/2 x + pi/2 )

Standard form of the cosine function is y=acos(bx+c)+d

Phase shift is -c/b

b=1/2 and c is pi/2

Now phase shift=-(pi/2)/(1/2)

=-pi

Hence, -pi is the  phase shift of y = -cos ( 1/2 x + pi/2 )

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The function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

7) The given functions are f(x)=2x+3 and g(x)=x²-3x-6.

Here, f·g(x) =f(x)×g(x)

f·g(x) = (2x+3)×(x²-3x-6)

f·g(x) = 2x(x²-3x-6)+3(x²-3x-6)

f·g(x) = 2x³-6x²-12x+3x²-9x-18

f·g(x) = 2x³-3x²-21x-18

8) The given functions are f(x)=4x-5 and g(x)=2x+8

f·g(x) =f(x)×g(x)

f·g(x) = (4x-5)×(2x+8)

f·g(x) = 4x(2x+8)-5(2x+8)

f·g(x) = 8x²+32x-10x-40

f·g(x) = 8x²+22x-40

Therefore, the function f·g(x) for the functions f(x)=4x-5 and g(x)=2x+8 is 8x²+22x-40.

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The statement "if a > √n and b > √n, then n ≠ ab" is saying that if two positive integers, a and b, are both greater than the square root of another positive integer n, then the product of a and b is not equal to n. This statement can be proven by contradiction.

Suppose the opposite is true, and that n = ab, where a and b are positive integers such that a > √n and b > √n. Then, because n = ab, we have n/a = b and n/b = a. But because both a and b are greater than the square root of n, we have √n < a and √n < b. This leads to a contradiction, because it means that n/a = b > √n, but √n is the largest possible value of b such that b < n/a.

Thus, we have proven that if a > √n and b > √n, then n cannot equal ab, and our original statement is true.

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The difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

When you hear the phrase "difference quotient formula," what comes to mind? Difference and quotient resemble the slope formula in appearance. Yes, the difference quotient formula does really provide the slope of a secant line drawn to a curve. What is a secant line? A line that joins any two points on a curve is known as the secant line.

Given that the function is f(x) = x³

The value of f(8 + h) = (x+ h)³ = x³ + 3x²h + 3xh³ + h³

The value of f(8) = (8)³ = 512

Substituting the value of f(8 + h) and f(8) we have:

f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h

Hence, the difference quotient of f(8 + h) - f(8) / h = x³ + 3x²h + 3xh³ + h³ - 512 / h.

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The value of c at which the function is continuous is 5/6.

For a function to be continuous at a point, the left and right limit of the function must exist and be equal at that point. In this case, the point is x = -5.

The function f(x) = c for x = -5, f(x) = 4 for x = 1, and f(x) = (x^2 - 25) / (x + 5)(x - 7) for x ≠ -5 and x ≠ 7.

To determine the value of c, we need to find the limit of f(x) as x approaches -5 from the left and from the right.

From the left, we have:

lim x→−5− f(x) = lim x→−5− (x^2 - 25) / (x + 5)(x - 7) = 5/6

From the right, we have:

lim x→−5+ f(x) = 5/6

For the function to be continuous at x = -5, we must have:

lim x→−5− f(x) = lim x→−5+ f(x) = c

c = 5/6

--The question is not readable, answering to the question below--

"For what value of c is the function continuous at x = -5?

f (x) = c for x=-5; f(x)=4 for x=1; f(x) = x^2-25 / (x+5)(x-7) otherwise"

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By Solving by factorization method of equation 5x² - 3x - 2 = 0

x = 1 , [tex]\frac{-2}{5}[/tex]  

Given data :

Given equation is, 5x² - 3x - 2 = 0

Solving by factorization method,

5x² - 3x - 2 = 0

5x² - 5x + 2x - 2 = 0

( 5x + 2 ) ( x -*1 ) = 0

x = 1 , [tex]\frac{-2}{5}[/tex]

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Yes, that's correct. When a figure is dilated from the origin, each ordered pair of the figure is transformed according to the rule

What is dilation in maths ?

A dilation is a function f from a metric space M into itself that fulfils the identity d=rd for all locations x, y in M, where d is the distance between x and y and r is some positive real number.

Yes, that's correct!

When a figure is dilated from the origin, each ordered pair of the figure is transformed according to the rule (x, y) → (kx, ky), where k is the scale factor. The scale factor determines the size of the dilation; if k > 1, the dilation increases the size of the figure, while if 0 < k < 1, the dilation decreases the size of the figure. If k = 1, the figure remains unchanged.

It's important to note that dilations preserve the orientation of the figure and can be thought of as a non-uniform scaling of the figure.

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The new price for each pillow case is Php 27.50.

The concept used in this problem is markup pricing, where a certain percentage is added to the cost price of a product to arrive at the selling price.

Markup is the difference between a product's selling price and cost as a percentage of the cost. For example, if a product sells for $125 and costs $100, the additional price increase is ($125 – $100) / $100) x 100 = 25%.

As given, Mr. Mosquera plans to add 10% to the original price which is Php 25. 00 each,

Php 25 * 10/100

= Php 2.50 for each pillow case.

So, the new price for each pillow case is

Php 25 + Php 2.50

= Php 27.50.

Therefore, the new price for each pillow case is Php 27.50.

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Mr. Mosquera ' price for each pillow is 27.50 php. His price for each pillow is 27.50 php.

Here, these values are given,

Total no. of pillows = 50

Original price of each pillow = 25.00 php

Original price of 50 pillows= 125000 php

After, planning to add 10% to the original price'

New price of pillow will increase after adding 10% to the previous price.

New price of each pillow became 25+ 25 of 10%

= 25+ 25 × 10/100

= 25+ 5/2

= 55/2

=27.50 php

New price of each pillow became 27.50 php.

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(a)  The function f: r -> r is not one-to-one (injective) since there are two separate inputs (2 and -2) that have the same result. It is defined as f (x) = x2 - 4x + 9. (9).

(b)  The element (-1) that occurs in the codomain of the function f: r -> r, which is defined by f (x) = x2 - 4x + 9, prevents the function from being onto (surjective).

As a result, neither one-to-one nor onto are applicable to the function

f: r -> r defined by f (x) = x2 - 4x + 9.

According to the Question

We must demonstrate that if a function f(x1) = f(x2), then x1 = x2 in order to establish whether the function is one-to-one (injective). To put it another way, no two unique inputs produce the same outcome.

We must demonstrate that there exists an x in the domain of f such that f(x) = y for every element y in the codomain of f in order to establish if a function f is onto (surjective). Alternatively expressed, each output in the codomain has an associated input in the domain.

For the function f: r → r defined by f (x) = x^2 - 4x + 9, we can easily see that it is not one-to-one since f(2) = f(-2) = 9.

It is also not onto, as the codomain of f is all real numbers and there is no real number x such that f(x) = -1.

So, we can conclude that the function f: r → r defined by f (x) = x^2 - 4x + 9 is neither one-to-one nor onto.

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15

Step-by-step explanation:

20/8 =2.5

6x2.5=15

therefore, 15

All people come very close to being able to float in water. therefore, 0.007 is the volume (in cubic meters) of a 50-kg woman.

Correct answer will be a. 0.007

The volume of a person in water is determined by their body density and the amount of air in their lungs. The volume can be estimated using the principle of buoyancy, which states that a body floating in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the body.

In this case, we are given the weight of a 50-kg woman and asked to determine her volume in cubic meters. To do this, we can use the formula for buoyancy: Fb = ρf * V * g, where Fb is the buoyant force, ρf is the density of the fluid (water), V is the volume of the woman, and g is the acceleration due to gravity.

Since the woman is floating, the buoyant force is equal to her weight, so we can set these two equal to each other: ρf * V * g = 50 kg * 9.8 m/s^2. Solving for V, we find that V = 50 kg / (ρf * g) = 50 kg / (1000 kg/m^3 * 9.8 m/s^2) = 0.005 m^3.

Comparing this answer to the options given, we can see that the closest option is 0.007 m^3 (choice a), which is our final answer.

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If there is a correlation between two variables a and b, it may be because a causes b, or because b causes a, but it cannot be both is a False .

Any statistical association between two random variables or bivariate data, whether causal or not, is referred to in statistics as correlation or dependency. Although "correlation" can mean any kind of association in the broadest sense, in statistics it typically refers to the strength of a pair of variables' linear relationships.

In mathematical modelling, statistical modelling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are examined under the assumption or requirement that they are dependent on the values of other variables due to some law or rule (for example, a mathematical function). In the context of the experiment in question, independent variables are those that are not perceived as dependant on any other factors.

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Answer:

Step-by-step explanation:

The slope for the function f(t) = 3 - 3/5t at point (3/5, 2) is 5/3.

What is slope?

A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.

The given function is - f(t) = 3 - 3/5t.

The data points are - (3/5, 2)

Rewrite the function -

f(t) = 3 - 3/5 t^-1

Differentiate with respect to t. Use the difference rule.

d/dt (3) - d/dt (3/5 t^-1)

Use the constant rule and the constant multiple rule.

0 - 3/5 d/dt (t^-1)

Use the power rule.

-3/5(-1)t^(-1 - 1)

3/5t^-2

Now plug in 3/5 for t on the derivative in order to find the slope at point (3/5, 2).

3/5(3/5)^-2

3/5(5/3)^2

3/5 × 25/9

5/3

Therefore, the slope value is 5/3.

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Find the slope of the graph of the function at the given point.

Function Point f(t) = 3 - 3/5t (3/5, 2)

Answer:

6a + 12b + 18c

Step-by-step explanation:

Distribute 6 to all numbers in the parenthesis.

(6(a) + 6(2b) + 6(3c))

[6a + 12b + 18c]

The value of g(f(-5)) is 5.

In mathematics, a function is represented as a rule that produces a distinct result for each input x. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

f(x)= |2x+ 9|

Now, g(f(-5))

f(-5) = |2(-5)+9|

       = |-10 + 9|

       = |-1|

       = 1

and, g(f(-5)) = g(1)

So, from the graph we can see that the value of g(1) is 5.

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The slope of lines a, b, c, and d are 1/3, 1/4, 1/3, and -4 respectively. Line a is parallel to line c. Line b and line d are perpendicular to each other.

What is a line?

A line is an object in geometry that is infinitely long and has neither width nor depth nor curvature. Since lines can exist in two, three, or higher-dimensional spaces, they are one-dimensional objects. The term "line" can also be used to describe a line segment in daily life that has two points that serve as its ends.

The slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is m = (y₂ - y₁)/(x₂ - x₁).

Line a passes through points (-1,4) and (5,6).

The slope of line a is (6-4)/(5-(-1)) = 2/6 = 1/3

Line b passes through points (-1,1) and (3,2).

The slope of line b is (2-1)/(3-(-1)) = 1/4

Line c passes through points (-3,-2) and (3,0).

The slope of line c is (0-(-2))/(3-(-3)) = 2/6 = 1/3

Line d passes through points (1,6) and (3,-2).

The slope of line d is (-2-6)/(3-1) = -8/2 = -4.

The slopes of line a and line c are the same, thus line a is parallel to line c.

If two lines are perpendicular to each other, then the product of therir slope is -1.

The product of slopes of line b and line d is

1/4 × (-4) = -1

Thus line b and line d are perpendicular to each other.

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The temperature is a function of time, as there is a single temperature for each instant of time.

A relation represents a function when each input value is mapped to a single output value.

For the set in this problem, we have that:

As there are no repeated inputs, the temperature is in fact a function of time.

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