Steven purchases a bowl. The diameter of the

Given the diagram below, find the value of x. Then find AC,

Stels [109]

Answer:

$x=5,\\AC=14$

Step-by-step explanation:

Since one triangle is inscribed in another, the two triangles are similar. As marked in the diagram, the sides of the larger triangle are exactly two times larger than the corresponding sides of the smaller triangle.

Therefore, we have:

$2(x+2)=4x-6,\\2x+4=4x-6,\\10=2x,\\x=\boxed{5}$

Since AC is marked by $4x-6$ :

$AC=4(5)-6,\\AC=20-6,\\AC=\boxed{14}$

7 0

3 years ago

11) If the point (2, -5) is reflected in the line y=x, then

svet-max [94.6K]

(-2,5) ... not sure what “if noun 4’ means”

6 0

3 years ago

If sin theta = (sqrt 3)/2, which could not be the value of theta? A. 60 degrees B. 120 degrees C. 240 degrees D. 420 degrees I k

sineoko [7]

Your are right, $\pi /3$ and 2 $\pi /3$ are solutions.
Of course each of these solutions can be replaced by the same number +k2 $\pi$ (with k being an element of Z) since sin x=sin (x+k2 $\pi$ ) with k being an element of Z.
Those are angle measures expressed in radians.
If you translate in degrees you basically have to know that $\pi$ radian=180 degrees
so $\pi /3$ radian=60 degrees and 2 $\pi /3$ =120 degrees. So this two could be values of theta (A and B).
On top of that $\pi /3+2 \pi$ could also be a solution (x+k2 $\pi$ with k=1). This can be translated to 60+360=420 degrees which is solution D.
So C. 240 degrees is the only one that could not be a value of theta.

6 0

4 years ago

The diameter of holes for a cable harness is known to have a normal distribution with a standard deviation of 0. 01 inch. A rand

Sindrei [870]

For the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.

As given in the question,

Confidence interval for population mean is given by:

$\bar{x}$ ± z × ( σ / √n)

Where,

σ = population standard deviation.

n= sample size

$\bar{x}$ = Sample mean

Given values from the random sample size are :

σ = 0.01 inches

n= 10

$\bar{x}$ = 1.5045

Critical value confidence interval (using x-value table)

z for 99% = 2.576 and Significance level = 0.01

z for 95% = 1.960 and Significance level = 0.05

99% two-sided confidence interval on the mean hole diameter is equal to :

$\bar{x}$ ± z × ( σ / √n)

= 1.5045 ± 2.576 × ( 0.01 / √10)

= 1.5045 ± 0.00815 (approximately)

= 1.5045 - 0.00815 , 1.5045 + 0.00815

= ( 1.49635 , 1.51265 )

95% two-sided confidence interval on the mean hole diameter is equal to :

$\bar{x}$ ± z × ( σ / √n)

= 1.5045 ± 1.960 × ( 0.01 / √10)

= 1.5045 ± 0.00620 (approximately)

= 1.5045 - 0.00620 , 1.5045 + 0.00620

= ( 1.4983 , 1.5107 )

Therefore, for the given standard deviation and sample mean the two sided confidence interval on mean diameter foe 95% and 99% is given by ( 1.4983 , 1.5107 ) and ( 1.49635 , 1.51265 ) respectively.

Learn more about standard deviation here

brainly.com/question/16555520

#SPJ4

4 0

1 year ago

given the trinomial x^2+bx-c where both the first sign is positive and the second sign is negative, the signs of the factors wil

geniusboy [140]

The signs of the factors will be different. (One will be positive and one will be negative.)

_____

Here, the "first sign" is considered to be the sign of x², and the "second sign" is considered to be the sign of c. The above statement will be true regardless of the sign of b. The "signs of the factors" is considered to refer to the signs of the constant terms in the binomial factors.

For (x +p)(x -q) where p and q are both positive so the signs are as shown, the product is x² +(p-q)x -pq. That is x² is positive and -pq is negative, regardless of the relative magnitudes of p and q (thus the sign of p-q).

_____

If something else is meant by the terminology used, it isn't clear what the intended answer is supposed to be.

Both x² +3x -10 and x² -3x -10 have factorizations that have different signs in the two factors. The first is (x+5)(x-2); the second is (x+2)(x-5). The signs of the factors are all positive: (x+5), not -(x+5), for example.

On the other hand x² -3x +2 = (x-2)(x-1) has same signs in and of the factors. That is, by themselves, the sign of x² (first sign) and the sign of 3x (second sign) don't guarantee the signs in the factors are anything in particular, except that at least one sign in the factors must be negative if the first (x²) and second (3x) signs differ.

5 0

4 years ago

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