Write the absolute value equations in the form x−b =c (where b is a number and c can be either number or an expression) that have the following solution sets: Two solutions:
x=1/2, x=-1/3

Answer:

x - 17.95 = 71.80, $89.75

Step-by-step explanation:

Let the original price of the headphones be x

Amount of coupon = $17.95

You pay the final amount for the headphones after using the coupon = $71.80

So to find the original price of the headphones, the equation will be

x - 17.95 = 71.80

x = 17.95 + 71.80

x = $89.75

The original price of the headphones would be $89.75

Answer:

p=89.85

Step-by-step explanation:

p-17.95=71.80

+17.95  +17.95

p=89.85

Answer:

1 / 3 (one third)

Step-by-step explanation:

Divide the number of chickens by the number of people:

1 / 3

Answer:

Radius= 11

Circumference= 69.12

Area= 380.133

Step-by-step explanation:

Radius is half of the diameter.

Circumference is 2\(\pi\)r.

Area is \(\pi r^2\).

Answer:

Step-by-step explanation:

At least 9 means more than 9 and includes 9

x ≥ 9     and    [9,  +∞)

At most 9 means numbers less than 9

x≤9       and  (-∞, 9]

more than 9 means bigger than 9 but not including 9

x > 9     and    (9,  +∞)

fewer than 9 means less than 9 but not including 9

x<9       and  (-∞, 9)

strictly between 7 and 9   means between 7 and 9 but not including

7<x<9      and    (7,9)       (This is the only one I'm unsure of.  Strictly, not sure if it includes or doesn't include, usually it just says include or doesn't include)

between 7 and 7 inclusive.   means it's just =7  There's no boundaries

x=7

no more than 7 means less than 7 and includes 7

x ≤ 7   and   (-∞, 7]

Answer:

-1/2

Step-by-step explanation:

y = -1/2x+ 1/4

The equation of a line is given by

y = mx+b where m is the slope and b is the y intercept

-1/2 is the slope and the y intercept is 1/4

Answer:

\(t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116\)    

The degrees of freedom are given by:

\(df=n-1=50-1=49\)  

Now we can calculate the p value with the following probability:

\(p_v =P(t_{(49)}>1.116)=0.135\)  

Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.

Step-by-step explanation:

Information provided

\(\bar X=74.1\) represent the sample mean

\(s=13.1\) represent the sample standard deviation

\(n=50\) sample size  

\(\mu_o =72\) represent the value that we want to test

\(\alpha=0.1\) represent the significance level

t would represent the statistic

\(p_v\) represent the p value

Hypothesis to test

We want to analyze if the true mean for this case is higher than 72, the system of hypothesis would be:  

Null hypothesis:\(\mu \leq 72\)  

Alternative hypothesis:\(\mu > 72\)  

The statistic is given by:

\(t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}\)  (1)  

Replacing the info we got:

\(t=\frac{74.1-72}{\frac{13.3}{\sqrt{50}}}=1.116\)    

The degrees of freedom are given by:

\(df=n-1=50-1=49\)  

Now we can calculate the p value with the following probability:

\(p_v =P(t_{(49)}>1.116)=0.135\)  

Since the p value is higher than the significance level provided of 0.1 we have enough evidence to FAIL to reject the null hypothesis and we can conclude that the true mean is not significantly higher than 72 per hour.

Hello!

The distance, d, is less than 200 miles.

B. d > 200

Answer:

the answer is B (0, -2)

Step-by-step explanation:

To find the point on the curve y = -x^2 - 2 that is closest to the point (0,1), we can use the method of least squares.

The method of least squares involves finding the point on the curve that minimizes the square of the distance between the point and the curve.

To begin, we can define a function d(x) = (y - (-x^2 - 2))^2 which represents the square of the distance between the point (x,y) on the curve and the point (0,1)

then we need to find the derivative of d(x) and set it to zero to find the minimum,

d'(x) = 2(y + x^2 + 2 - 1) = 2(y + x^2 + 1)

by setting d'(x) = 0 we get y = -x^2 - 1,

so the point on the curve that is closest to (0,1) is (0, -1) and the answer is B (0, -2)

Note that the point (0,-1) is on the curve y = -x^2 - 2 but not the point on the closest.

Answer:

25 cents per lemon

Step-by-step explanation:

Simply divide

Answer:

See below

Step-by-step explanation:

When solving real world problems relating to unit price, divide the cost by the amount.

2.5/10

The unit price is 0.25.

-hope it helps

Answer:

the answer is c, it fits the ratio given and is 2:3

Answer:

An acute angle is an angle that has a measure that is less than 90 degrees. Any measure that is less than 90 degrees could be an acute angle. For example, 8°, 15°, °26°, and 89° are all acute angles. Anything that is 90 degrees is a right angle and greater than 90 degrees is an obtuse angle. An acute angle can have all of the following measures except 90 degrees or greater than 90 degrees.

Answer:

0 is not an acute angle

Step-by-step explanation:

if the measurement of an angle is between 0 and 90 degrees then we called it an acute angle. it means acute angle is greater than 0 and less than 90 degrees. among the the other options it is between 0 and 90 therefore 0 is not it

hope this helps

Answer:  = (-8,-4)(-6,-1)=54

Step-by-step explanation:

__(x-3)+(-2x-8)= -3x-5

___ x - 3 -2x - 8 = -3x - 5

____ -x -11 = - 3x - 5 (This is not an equality)

If we replace the blank with - 1, we will have:

- 1 (x - 3) + (-2x - 8) = -3x - 5

-x + 3 -2x -8 = -3x - 5

-x -2x + 3 - 8 = -3x -5

-3x -5 = - 3x - 5 (This is a verifiable equality)

The correct answer is that we can fill the blank with - 1

Answer:

x = 15

Step-by-step explanation:

4(x - 20) = - 20 ( divide both sides by 4 )

x - 20 = - 5 ( add 20 to both sides )

x = 15

Arjun is not entirely correct. A fraction with a denominator of 12 will not necessarily produce a repeating decimal, although many others will do.

A fraction in its reduced form (i.e., when the numerator and denominator have no common factors) will produce a repeating decimal if and only if its denominator is not divisible by any prime number other than 2 and 5.

In the case of 1/2 and 2/12, both fractions have denominators divisible only by 2, which is why they produce terminating decimals. However, 1/3 and 5/12 have denominators that are not divisible only by 2 or 5, so they produce repeating decimals.

Therefore, it is incorrect to say that all fractions with a denominator of 12 will produce a repeating decimal, but many wills.

So, Arjun is not correct.

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Answer:

A,E

Step-by-step explanation:

Operation: Minus

To find how far Sam ran, we need to subtract 2.3 from Dean's distance of 6.8 km.

6.8 km - 2.3 km = 4.5 km

Therefore, Sam ran 4.5 km, since Dean ran 2.3 km fewer than Sam.

Answer:

a and e

Step-by-step explanation:

got it right on homework

So on solving the provided question we can say that here, in triangle ABC and XYZ;  by SSS property they are similar.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

here,

AB = XY

AC = XZ

BC = ZY

by SSS property, they are similar.

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Part 1

\(a=\sqrt{12^2 + 21^2 -2(12)(21) \cos 35^{\circ}} \approx \boxed{13}\)

Part 2

\(\frac{\sin B}{b}=\frac{\sin A}{a}\\\\\sin B=\frac{b\sin A}{a}\\\\\sin B=\frac{12 \sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}}\\\\B=\sin^{-1} \left(\frac{12\sin 35^{\circ}}{\sqrt{12^2 +21^2 -2(12)(21) \cos 35^{\circ}}} \right)\\\\B \approx \boxed{32^{\circ}}\)

Part 3

\(\angle C=180^{\circ}-\angle A -\angle B=\boxed{113^{\circ}}\)

Answer:

\(8 {x}^{2} - 6x - 5 = x\)

\(8 {x}^{2} - 7x - 5 = 0\)

x = (7 + √((-7)^2 - 4(8)(-5)))/(2×8)

= (7 + √(49 + 160))/16

= (7 + √209)/16

= -.4661, 1.3411 (to 4 decimal places)

Answer:

C . neither 8500 nor 850,000

Answer:

Step-by-step explanation:

Answer:

3

---

8

Step-by-step explanation:

the ratio of cakes to pies will be 3:8 if pies to cakes is 8:3

the fraction is 3/8

Answer:

I think the answer would be 96cm³

Step-by-step explanation:

have a great rest of ur dayy

Answer:

C

Step-by-step explanation:

Multiply the exponents

Reduce the gcf

Hope ghis helps! :)

We can conclude that the hypotheses of the Existence and Uniqueness Theorem are satisfied in any rectangular region in the ty-plane that does not contain the curve t² + y² = -1.

The Existence and Uniqueness Theorem for first-order ordinary differential equations states that if a differential equation of the form y' = f(t, y) satisfies the following conditions in some rectangular region in the ty-plane:

1. f(t, y) is continuous in the region.

2. f(t, y) satisfies a Lipschitz condition in y in the region, i.e., there exists a constant L > 0 such that |f(t, y₁) - f(t, y₂)| ≤ L|y₁ - y₂| for all t and y₁, y₂ in the region.

then there exists a unique solution to the differential equation that passes through any point in the region.

In the case of the differential equation y' = (y cot(2t)) / (t² + y² + 1), we have:

f(t, y) = (y cot(2t)) / (t² + y² + 1)

This function is continuous everywhere except at the points where t² + y² + 1 = 0, which is the curve t² + y² = -1 in the ty-plane. Since this curve is not included in any rectangular region, we can say that f(t, y) is continuous in any rectangular region in the ty-plane.

To check if f(t, y) satisfies a Lipschitz condition in y, we can take the partial derivative of f with respect to y and check if it is bounded in any rectangular region. We have:

∂f/∂y = cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²

Taking the absolute value and simplifying, we get:

|∂f/∂y| = |cot(2t) / (t² + y² + 1) - (2y² cot(2t)) / (t² + y² + 1)²|

= |cot(2t) / (t² + y² + 1)| * |1 - (2y² / (t² + y² + 1)))|

Since 0 ≤ (2y² / (t² + y² + 1)) ≤ 1 for all t and y, we have:

1/2 ≤ |1 - (2y² / (t² + y² + 1)))| ≤ 1

Also, cot(2t) is bounded in any rectangular region that does not contain the points where cot(2t) is undefined (i.e., where t = (k + 1/2)π for some integer k). Therefore, we can find a constant L > 0 such that |∂f/∂y| ≤ L for all t and y in any rectangular region that does not contain the curve t² + y² = -1.

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Answer:

Step-by-step explanation:

Quadratic equation has been given as,

\(y=-x^{2} +6x+4\)

Converting this equation into vertex form,

\(y=-(x^{2}-6x)+4\)

\(y=-[x^{2}-2(3x)+9-9]+4\)

\(y=-[x^{2}-2(3x)+3^2]+4+3^2\)

\(y=-(x-3)^2+4+9\)

\(y=-(x-3)^2+13\)

By comparing this equation with the vertex form of a quadratic equation,

y = (x - h)² + k

Here, (h, k) is the vertex of the parabola.

Vertex of the parabola → x = 3, y = 13

Axis of symmetry → x = 3

Answer:

y=-7x+3

since the formula is y=mx+b where m is the slope and b is the y-intercept.

Answer:

30 movies

Step-by-step explanation:

Let Number of movies = x

Member :

Membership fee + 2x

45 + 2x - - - (1)

Non members :

3.50x - - - (2)

Equate (1) and (2)

45 + 2x = 3.50x

45 = 3.50x - 2x

45 = 1.50x

x = 45 / 1.50

x = 30

30 movies

A' - (-1,4)

B' - (-1,8)

C' - (-5,4)

hope this helps