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3 years ago

Find the zeros of the function. Enter the solutions from least to greatest.

Mathematics

2 answers:

Yuki888 [10]3 years ago

6 0

Answer:

Lesser x is -13.

Greater x is 1.

Step-by-step explanation:

We have the function:

$f(x)=(x+6)^2-49$

And we want to find the zeros of the function.

So, set f(x) to 0 and solve for x:

$(x+6)^2-49=0$

Add 49 to both sides:

$(x+6)^2=49$

Take the square root of both sides. Since we're taking an even root, we will need plus/minus:

$x+6=\pm 7$

Subtract 6 from both sides:

$x=\pm7-6$

Evaluate for each case:

Case 1; 7 is positive:

$x=7-6=1$

Case 2; 7 is negative:

$x=-7-6=-13$

So, our zeros are:

$\{x|-13, 1\}$

Our lesser x is -13, and our greater x is 1.

And we're done!

Gnoma [55]3 years ago

6 0

Answer:

Our lesser x is -13, and our greater x is 1.

Step-by-step explanation:

You might be interested in

A rectangle is 6yards longer than it is wide. Find the dimensions of the rectangle if it’s area is 187 square yards

emmasim [6.3K]

Answer:

Width = 11 yards

Length = 17 yards

Step-by-step explanation:

First of all, the length of the rectangle is 6 yards longer than the width, this means, length = width + 6 yards. This dimensions can be represented on figure 1, where <em>w</em> is width, and <em>l</em>, for length.

We know the area of a rectangle is A = width x length

For our case 187 = w . (w + 6)

Using the Distributive Property for the multiplication we obtain

$187 = w^{2} +6w$

$w^{2} +6w-187 =0,$

Using the quadratic formula $w=\frac{-b\±\sqrt{b^{2}-4ac } }{2a}$ where a = 1, b = 6, c = - 187 and replacing into the formula, we will have:

$w=\frac{-6\±\sqrt{6^2-4(1)(-187)} }{2(1)}$

$w=\frac{-6\±\sqrt{36+748} }{2}=\frac{-6\±\sqrt{784} }{2}=\frac{-6\±28}{2}$

We have two options: $w=\frac{-6+28}{2}=\frac{22}{2}=11 yards$

$w=\frac{-6-28}{2}=\frac{-34}{2}=-17 yards$ But a distance (width) can not be negative so, this answer for w must be discarded.

The answer must be width = 11 yards.

To find the length $l =\frac{187}{11}=17 yards$

6 0

3 years ago

1. The national mean (μ) IQ score from an IQ test is 100 with a standard deviation (s) of 15. The dean of a college wants to kno

Nat2105 [25]

Answer:

We conclude that the mean IQ of her students is different from the national average.

Step-by-step explanation:

We are given that the national mean (μ) IQ score from an IQ test is 100 with a standard deviation (s) of 15.

The dean of a college want to test whether the mean IQ of her students is different from the national average. For this, she administers IQ tests to her 144 students and calculates a mean score of 113

Let, Null Hypothesis, $H_0$ : $\mu$ = 100 {means that the mean IQ of her students is same as of national average}

Alternate Hypothesis, $H_1$ : $\mu\neq$ 100 {means that the mean IQ of her students is different from the national average}

(a) The test statistics that will be used here is One sample z-test statistics;

T.S. = $\frac{Xbar-\mu}{\frac{s}{\sqrt{n} } }$ ~ N(0,1)

where, Xbar = sample mean score = 113

s = population standard deviation = 15

n = sample of students = 144

So, test statistics = $\frac{113-100}{\frac{15}{\sqrt{144} } }$

= 10.4

Now, at 0.05 significance level, the z table gives critical value of 1.96. Since our test statistics is more than the critical value of z which means our test statistics will fall in the rejection region and we have sufficient evidence to reject our null hypothesis.

Therefore, we conclude that the mean IQ of her students is different from the national average.

3 0

4 years ago

A wheel with radius 1 m is rolled in a straight line through one complete revolution on a flat horizontal surface. How many metr

Artyom0805 [142]

Answer:

6.28 m

Step-by-step explanation:

If a wheel travels with one full revolution, it would have travelled the circumference's distance from it's starting point.

The circumference of a circle is $2\pi r$

Let's assume $\pi$ is 3.14 and solve for the equation.

$2\cdot3.14\cdot1\\6.28$

Hope this helped!

4 0

3 years ago

Find the value of x and y..

Tomtit [17]

Answer:

x=30° y=110°

Step-by-step explanation:

80+70=150

180-150=30° 》》》》 angles in a triangle add up to 180°

x=30° opposite angles are equal

180-140=40° angles on a straight line add up to 180°

30+ 40=70

180-70=110°

y=110°

7 0

3 years ago

The value of 4√(10) -2 is

ira [324]

Answer:

8√2

Step-by-step explanation:

4√(10) -2

= 4√8

=4√4×2

=4×2√2

=8√2

5 0

3 years ago