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3 years ago

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Mathematics

1 answer:

Alecsey [184]3 years ago

6 0

Answer: =5x−10

Step-by-step explanation: hope this help

Let's simplify step-by-step.

3(3x−4)−2(2x−1)

Distribute:

=(3)(3x)+(3)(−4)+(−2)(2x)+(−2)(−1)

=9x+−12+−4x+2

Combine Like Terms:

=9x+−12+−4x+2

=(9x+−4x)+(−12+2)

Answer: =5x+−10

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raph the equation with a diameter that has endpoints at (-3, 4) and (5, -2). Label the center and at least four points on the ci

andreyandreev [35.5K]

Answer:

Equation:

${x}^{2} + {y}^{2} + 2x - 2y - 35= 0$

The point (0,-5), (0,7), (5,0) and (-7,0)also lie on this circle.

Step-by-step explanation:

We want to find the equation of a circle with a diamterhat hs endpoints at (-3, 4) and (5, -2).

The center of this circle is the midpoint of (-3, 4) and (5, -2).

We use the midpoint formula:

$( \frac{x_1+x_2}{2}, \frac{y_1+y_2,}{2} )$

Plug in the points to get:

$( \frac{ - 3+5}{2}, \frac{ - 2+4}{2} )$

$( \frac{ -2}{2}, \frac{ 2}{2} )$

$( - 1, 1)$

We find the radius of the circle using the center (-1,1) and the point (5,-2) on the circle using the distance formula:

$r = \sqrt{ {(x_2-x_1)}^{2} + {(y_2-y_1)}^{2} }$

$r = \sqrt{ {(5 - - 1)}^{2} + {( - 2- - 1)}^{2} }$

$r = \sqrt{ {(6)}^{2} + {( - 1)}^{2} }$

$r = \sqrt{ 36+ 1 } = \sqrt{37}$

The equation of the circle is given by:

$(x-h)^2 + (y-k)^2 = {r}^{2}$

Where (h,k)=(-1,1) and r=√37 is the radius

We plug in the values to get:

$(x- - 1)^2 + (y-1)^2 = {( \sqrt{37}) }^{2}$

$(x + 1)^2 + (y - 1)^2 = 37$

We expand to get:

${x}^{2} + 2x + 1 + {y}^{2} - 2y + 1 = 37$

${x}^{2} + {y}^{2} + 2x - 2y +2 - 37= 0$

${x}^{2} + {y}^{2} + 2x - 2y - 35= 0$

We want to find at least four points on this circle.

We can choose any point for x and solve for y or vice-versa

When y=0,

${x}^{2} + {0}^{2} + 2x - 2(0) - 35= 0$

${x}^{2} +2x - 35= 0$

$(x - 5)(x + 7) = 0$

$x = 5 \: or \: x = - 7$

The point (5,0) and (-7,0) lies on the circle.

When x=0

${0}^{2} + {y}^{2} + 2(0) - 2y - 35= 0$

${y}^{2} - 2y - 35= 0$

$(y - 7)(y + 5) = 0$

$y = 7 \: or \: y = - 5$

The point (0,-5) and (0,7) lie on this circle.

3 0

3 years ago

nicole is flying two kites. she has 104 feet of string out to one kite and 110 feet out to the other kite. the angle formed by t

Gnesinka [82]

Answer:

48.49 feet

Step-by-step explanation:

The diagrammatic sketch of the information provided in the question was attached in the image below.

From the image below, the distance between the two kites is denoted by (c) and can be determined by using the cosine angle rule which is expressed as:

$c^2 = a^2 + b^2 -2ab cos \ C$

where;

a = 110

b = 104

Cos C = 26°

Then;

$c^2 = 110^2 + 104^2 -2(110)(104) cos \ 26 \\ \\ c^2 = 12100 + 10816- 22880 ( 0.8988) \\ \\ c^2 = 22916- 20564.544 \\ \\ c^2 = 2351.456 \\ \\ c= \sqrt{2351.456} \\ \\ \mathbf{ c = 48.49 \ feet}$

4 0

3 years ago

A CD usually sells for $17.00. If the CD is 20% off, and sales tax is 6%, what is the total price of the CD, including tax?

Alinara [238K]

Answer:

14.42

Step-by-step explanation:

17.00 x .80 20% off means price is 80% (or .80) of price

=13.6

13.6 x .06 = .82 sales tax

13.60 + .82 = 14.42 sales price plus sales tax

8 0

3 years ago

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the

a_sh-v [17]

Answer:

Probability that the sample proportion will be less than 0.03 is 0.10204.

Step-by-step explanation:

We are given that a courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.04.

Also, 469 are sampled.

<em>Let </em> $\hat p$ <em> = sample proportion</em>

The z-score probability distribution for sample proportion is given by;

Z = $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion

p = true proportion = 0.04

n = sample size = 469

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, probability that the sample proportion will be less than 0.03 is given by = P( $\hat p$ < 0.03)

P( $\hat p$ < 0.03) = P( $\frac{ \hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < $\frac{0.03-0.04}{\sqrt{\frac{0.03(1-0.03)}{469} } }$ ) = P(Z < -1.27) = 1 - P(Z $\leq$ 1.27)

= 1 - 0.89796 = 0.10204

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.27 in the z table which has an area of 0.89796.

Therefore, probability that the sample proportion will be less than 0.03 is 0.10204.

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3 years ago

vWhat is the probability of drawing either a king, a queen, or a jack from a deck of 52 playing cards

Bas_tet [7]

Answer:

20 por ciento de probabilidad de que elijas una de esas cartas

Step-by-step explanation:

20 por ciento de probabilidad de que elijas una de esas cartas

6 0

3 years ago

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