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Dafna1 [17]
3 years ago
6

Find the x- and y-intercepts of the function f(x) = log(2x + 1) − 1.

Mathematics
1 answer:
sleet_krkn [62]3 years ago
6 0
<span>Alright, here's your answer.

y-intercept is computed (not found) by assigning x = 0 and computing y: here that is f(0) = Log(2*0 + 1) – 1 = Log(1) – 1 = 0 – 1 = -1 
y-intercept is (0, -1) 

x-intercept is computed by solving f(x) = 0 for x: here that is 
0 = Log(2x + 1) – 1 → 1 = Log(2x + 1) 

Assuming the Log cited is base 10, then 10^1 = 10^Log(2x + 1) = 2x + 1 

That’s 10 = 2x + 1 

Therefore 9 = 2x 
x = 9/2 = 4.5 
Check this result in the original equation, I did! 

Your answer is - x-intercept is (4.5, 0)

I hope I helped! :)

</span>
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How to find slope intercept form with one point and the slope?
andre [41]
Slope intercept form is y = mx + b...ur slope will be in the m position and ur y int will be in the b position

examples : slope = 2 , (1,3)....x = 1 and y = 3

y = mx + b
slope(m) = 2
(1,3)...x = 1 and y = 3
now we sub and find b, the y int
3 = 2(1) + b
3 = 2 + b
3 - 2 = b
1 = b

so in slope intercept form, ur equation is : y = 2x + 1
================
another example : slope = 3 , (-2,-4)

y = mx + b
slope(m) = 3
(-2,-4)...x = -2 and y = -4
now sub and find b, the y int
-4 = 3(-2) + b
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so ur equation is : y = 3x + 2

7 0
2 years ago
After a game, Coach Jones wants to serve punch to the players on her soccer team. She will mix 2 quarts of ginger ale and 1 gall
Zinaida [17]
The answer would be 24 8-ounce cups.

First you would find how many quarts over all she has which is 6, then multiply that by 32(which is the amount of ounces are in a quart), then you would get 192 which you divide by 8 to find the total amount of cups you would have which is 24.
6 0
2 years ago
8 miles is approximately equal to 6 km how many km are equal to 28 miles ? How many miles are equal to 42km
Snowcat [4.5K]

28/8 = 3.5

3.5*6 = 21 km


42/6=7

7*8 = 56 miles

7 0
2 years ago
Big babies: The National Health Statistics Reports described a study in which a sample of 354 one-year-old baby boys were weighe
Vedmedyk [2.9K]

Answer:

Yes. The data provide enough evidence to support the claim that the mean weight of one-year-old boys is greater than 25 pounds.

P-value=P(t>2.84)=0.0024

Step-by-step explanation:

Hypothesis test on the population mean.

The claim is that the mean weight of one-year-old boys is greater than 25 pounds.

Then, the null and alternative hypothesis are:

H_0: \mu=25\\\\H_a:\mu>25

The significance level is α=0.05.

The sample size is n=354. The sample mean is 25.8 pounds and the sample standard deviation is 5.3 pounds. As the population standard deviation is estimated from the sample standard deviation, we will use a t-statistic.

The degrees of freedom are:

df=n-1=354-1=353

The t-statistic is:

t=\dfrac{\bar x-\mu}{s/\sqrt{n}}=\dfrac{25.8-25}{5.3/\sqrt{354}}=\dfrac{0.8}{0.2817}=2.84

For a right tailed test and 353 degrees of freedom, the P-value is:

P-value=P(t>2.84)=0.0024

As the P-value is smaller than the significance level, the effect is significant and the null hypothesis is rejected.

There is enough evidence to support the claim that the mean weight of one-year-old boys is greater than 25 pounds.

7 0
2 years ago
How to work vector algebra
erica [24]

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Unit vectors:

A unit vector is a vector of unit length. A unit vector is sometimes denoted by replacing the arrow on a vector with a "^" or just adding a "^" on a boldfaced character (i.e., ). Therefore, Any vector can be made into a unit vector by dividing it by its length. Any vector can be fully represented by providing its magnitude and a unit vector along its direction.

Base vectors and vector components:

Base vectors are a set of vectors selected as a base to represent all other vectors. The idea is to construct each vector from the addition of vectors along the base directions. For example, the vector in the figure can be written as the sum of the three vectors u1, u2, and u3, each along the direction of one of the base vectors e1, e2, and e3, so that Each one of the vectors u1, u2, and u3 is parallel to one of the base vectors and can be written as scalar multiple of that base. Let u1, u2, and u3 denote these scalar multipliers such that one has<span> </span><span>The original vector</span><span> </span><span>u</span><span> </span><span>can now be written as </span><span>The scalar multipliers</span><span> </span><span>u</span><span>1</span><span>,</span><span> </span><span>u</span><span>2</span><span>, and</span><span> </span><span>u</span><span>3</span><span> </span><span>are known as the components of</span><span> </span><span>u</span><span> </span><span>in the base described by the base vectors</span><span> </span><span>e</span><span>1</span><span>,</span><span> </span><span>e</span><span>2</span><span>, and</span><span> </span><span>e</span><span>3</span><span>. If the base vectors are unit vectors, then the components represent the lengths, respectively, of the three vectors</span><span> </span><span>u</span><span>1</span><span>,</span><span> </span><span>u</span><span>2</span><span>, and</span><span> </span><span>u</span><span>3</span><span>. If the base vectors are unit vectors and are mutually orthogonal, then the base is known as an orthonormal, Euclidean, or Cartesian base.</span>

 

A vector can be resolved along any two directions in a plane containing it. The figure shows how the parallelogram rule is used to construct vectors a and b that add up to c. <span>In three dimensions, a vector can be resolved along any three non-coplanar lines. The figure shows how a vector can be resolved along the three directions by first finding a vector in the plane of two of the directions and then resolving this new vector along the two directions in the plane. </span><span>When vectors are represented in terms of base vectors and components, addition of two vectors results in the addition of the components of the vectors.</span>

8 0
3 years ago
Read 2 more answers
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