a recipe for cookies calls for 2/3 of a cup of sugar per batch. elena used 6 2/3 cups of sugar to make multiple bathes did she m
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15. The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26
17. The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5
Step-by-step explanation:
Any quadratic function has:
1. A vertex form form f(x) = a(x - h)² + k, where (h , k) are the
coordinates of its vertex point
2. A standard form g(x) = ax² + bx + c, where a , b , c are constant and
a is the coefficient of x², b is the coefficient of x and c is the
y-intercept
3. the x-coordinate of the vertex point h = and
k = f(h)
15.
∵ f(x) = x² + 8x - 10
∴ a = 1 and b = 8
∵ h =
∴ h =
∴ h = -4
∵ k = f(h)
∴ k = f(-4)
- Substitute x by -4 in f(x)
∴ k = (-4)² + 8(-4) - 10
∴ k = 16 - 32 - 10
∴ k = -26
∴ f(x) = (x - -4)² + (-26)
∴ f(x) = (x + 4)² - 26
The vertex form of f(x) = x² + 8x - 10 is f(x) = (x + 4)² - 26
17.
∵ g(x) = (x + 3)² - 4
- Lets solve the power 2 of the bracket:
(1st + 2nd)² = (1st)(1st) + 2(1st)(2nd) + (2nd)(2nd)
∵ (x + 3)² = (x)(x) + 2(x)(3) + (3)(3)
∴ (x + 3)² = x² + 6x + 9
∴ (x + 3)² - 4 = (x² + 6x + 9) - 4
∵ 9 - 4 = 5
∴ (x + 3)² - 4 = x² + 6x + 5
The standard form of g(x) = (x + 3)² - 4 is g(x) = x² + 6x + 5
Learn more:
You can learn more about the vertex form of quadratic function in brainly.com/question/9390381
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Answer:
Option D, 1
Step-by-step explanation:
<u>Step 1: Determine what x1, x2, y1, y2 are</u>
Slope =
(x1, y1) is (2, 8)
(x2, y2) is (6, 12)
<u>Step 2: Plug into the formula to get the slope</u>
Slope =
Slope =
Slope =
<em>Slope = 1</em>
<em />
Answer: Option D, 1
Answer:
The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.
Step-by-step explanation:
An automobile manufacturer has given its van a 59.5 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating:
At the null hypothesis, we test if the mean is the same, that is:
At the alternate hypothesis, we test that it is different, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
59.5 is tested at the null hypothesis:
This means that
After testing 250 vans, they found a mean MPG of 59.2. Assume the population standard deviation is known to be 1.9.
This means that
Value of the test statistic:
Pvalue of the test and decision:
The pvalue of the test is the probability of finding a mean that differs from 59.5 by at least 0.3, which is P(|Z|>-2.5), which is 2 multiplied by the pvalue of Z = -2.5.
Looking at the z-table, Z = -2.5 has a pvalue of 0.0062
2*0.0062 = 0.0124
The pvalue of the test is 0.0124 < 0.1, which means that there is sufficient evidence at the 0.1 level to support the testing firm's claim.