Y=2 when x is 8. Write a Direct Variation

Write the general equation for the circle that passes through the points: (1, 7) (8, 6) (7, -1)

Naddika [18.5K]

Answer:

$x^{2} +y^{2} +(-8)\times x+ (-6)\times y = 0$

Step-by-step explanation:

General equation of circle is $x^{2} +y^{2} +2\times g \times x+2\times f\times y+c = 0$ ---------------------(1)

This circle passes through the given three points, (1,7) , (8,6) and (7,-1).

Substitute (1,7) in (1),

1 + $7^{2} +2\times g\times 1 + 2\times f\times 7 +c$ =0

2g + 14f + c = -50 -------------(2)

Substitute (8,6) in (1),

$8^{2} + 6^{2} +2\times g \times 8+2\times f\times 6 +c=0$

16g + 12f + c = -100 -----------(3)

Substitute (7,-1) in (1),

$7^{2} + (-1)^{2} +2\times g \times 7+2\times f\times (-1) +c=0$

14g - 2f + c = -50 ---------------(4)

Solving (2),(3) amd (4) simultaneously,

g = -4

f = -3

c = 0

Equation of circle is

$x^{2} +y^{2} +(-8)\times x+ (-6)\times y = 0$

7 0

3 years ago

The cost of toner cartridges is 19.50 more than the cost of an ink cartridge. Colleen ordered 11 ink and 4 toner cartridges and

blagie [28]

Answer:

Toner = $45.00; ink = $25.50

Step-by-step explanation:

Let T = the cost of a toner cartridge and I = the cost of an ink cartridge

We have two conditions:

(1) T = I + 19.50

(2) 4T + 11I = 460.50 Substitute (1) into (2)

4(I + 19.50) + 11I = 460.50 Remove parentheses

4I + 78.00 + 11I = 460.50 Combine like terms

15 I + 78.00 = 460.50 Subtract 78.00 from each side

15I = 382.50 Divide each side by 15

(3) I = 25.50

=====

Substitute (3) into (1)

T = 25.50 + 19.50

T = 45.00

=====

Check:

(1) 45.00 = 25.50 + 19.50

45.00 = 45.00

(2) 4×45.00 + 11×25.50 = 460.50

180.00 + 280.50 = 460.50

460.50 = 460.50

6 0

3 years ago

A random sample of 500 adult residents of Maricopa County found that 356 were in favor of increasing the highway speed limit to

zzz [600]

Answer:

$z=1.04$

$p_v =2*P(Z>1.04)\approx 0.298$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the proportion of people in favor of the increased speed limit not differs significantly between the two groups.

Step-by-step explanation:

1) Data given and notation

$X_{PC}=297$ represent the number of residents of Pima County in favor of the increased speed limit

$X_{MC}=356$ represent the number of residents of Maricopa County in favor of the increased speed limit

$n_{PC}=400$ sample of Pima County selected

$n_{MC}=500$ sample of Maricopa County selected

$p_{PC}=\frac{297}{400}=0.743$ represent the proportion of residents of Pima County in favor of the increased speed limit

$p_{MC}=\frac{356}{500}=0.712$ represent the proportion of residents of Maricopa County in favor of the increased speed limit

z would represent the statistic (variable of interest)

$p_v$ represent the value for the test (variable of interest)

$\alpha=0.05$ significance level given

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if is there is a difference in the support for in increasing the speed limit between the residents of the two counties, the system of hypothesis would be:

Null hypothesis: $p_{PC} - p_{MC}=0$

Alternative hypothesis: $p_{PC} - \mu_{MC} \neq 0$

We need to apply a z test to compare proportions, and the statistic is given by:

$z=\frac{p_{PC}-p_{MC}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{PC}}+\frac{1}{n_{MC}})}}$ (1)

Where $\hat p=\frac{X_{PC}+X_{MC}}{n_{PC}+n_{MC}}=\frac{297+356}{400+500}=0.726$

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

$z=\frac{0.743-0.712}{\sqrt{0.726(1-0.726)(\frac{1}{400}+\frac{1}{500})}}=1.04$

4) Statistical decision

Since is a two side test the p value would be:

$p_v =2*P(Z>1.04)\approx 0.298$

Comparing the p value with the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can't say that the proportion of people in favor of the increased speed limit not differs significantly between the two groups.

8 0

3 years ago

Factor out the greatest common factor. 10a3b−6a2b2

podryga [215]

Answer:

2a^2b(5a-3b)

If not then the other way is

5a-3b

Step-by-step explanation:

The GCF of 10a^3b and -6a^2b^2 is 2a^2b

So divide by that you will get

2a^2b(5a-3b)

4 0

3 years ago

PLEASE HELP! WILL MARK BRAINLIEST

omeli [17]

1)

v - 6 ≥ 4

+6 +6

v ≥ 10

Graph: 10 -----------------→ the dot at 10 is filled in because of the "equal to" symbol

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2)

-5x < 15

$\frac{-5x}{-5} > \frac{15}{-5}$ divided by a negative so the symbol flipped

x > -3

Graph: -3 o------------------→ the dot at -3 is NOT filled in because it's NOT "equal to"

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3)

3k > 5k + 12

-5k -5k

-2k > 12

$\frac{-2k}{-2} < \frac{12}{-2}$ divided by a negative so the symbol flipped

k < -6

Graph: ←------------o -6 the dot at -6 is NOT filled in because it's NOT "equal to"

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5)

2t ≤ 4 or 7t ≥ 49

$\frac{2t}{2} \leq\frac{4}{2}$ or $\frac{7t}{7} \geq \frac{49}{7}$

t ≤ 2 or t ≥ 7

Graph: ←------- 2 7 ---------→ the dots at 2 and 7 are filled in

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6)

| n + 2 | = 4

n + 2 = 4 or n + 2 = -4

-2 -2 -2 -2

n = 2 or n = -6

Answer: n = {2, -6}

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7)

| 2x - 7 | > 1

2x - 7 > 1 or 2x - 7 < -1

+7 +7 +7 +7

2x > 8 or 2x < 6

$\frac{2x}{2} > \frac{8}{2}$ or $\frac{2x}{2} < \frac{6}{2}$

x > 4 or x < 3

Graph: ←----------o 3 4 o------------→

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8)

A = {1, 2, 3, 4, 5, 6, 7, 8, 9} B = {2, 4, 6, 8}

A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9} union combines both sets

A ∩ B = {2, 4, 6, 8} intersection includes only those that are in BOTH sets

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9)

P = {1, 5, 7, 9, 13} R = { 1, 2, 3, 4, 5, 6, 7} Q = {1, 3, 5}

P ∩ R ∩ Q = {1, 5}

P ∩ R = {7} disregard 1 & 5 since they are already in P∩Q∩R

R ∩ Q = {3} disregard 1 & 5 since they are already in P∩Q∩R

P ∩ Q = { } disregard 1 & 5 since they are already in P∩Q∩R

P no intersection = {9, 13)

R no intersection = {2, 4, 6}

Q no intersection = { }

If you can't figure out how to draw it based on the information I provided, please see the attached diagram. Note: Usially, you would only identify P, Q, R. I identified the intersections so you would understand why those specific numbers are placed in the designated sections.

4 0

3 years ago