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2 months ago

D(-3+x)=kx+9 solve for x

Mathematics

1 answer:

Zina [12.3K]2 months ago

5 0

d(-3 + x) = kx + 9

Distribute d within the parentheses:

-3d + dx = kx + 9

Subtract kx from both sides:

-3d + dx - kx = 9

Add 3d to both sides:

dx - kx = 9 + 3d

Factor x from dx - kx:

x(d - k) = 9 + 3d

Divide both sides by (d - k):

x = $\frac{9+3d}{d-k}$

To further simplify, factor 3 out of the numerator.

x = $\frac{3(d + 3)}{d-k}$

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The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight

Leona [12618]

To convert, divide each tire's weight by 453.592 grams per pound:

800 grams ÷ 453.592 = 1.76 pounds
700 grams ÷ 453.592 = 1.54 pounds

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2 months ago

Determine if JK and LM are parallel ,perpendicular, or neither. J(13,-5) K(2,6) L(-1,-5) M(-4,-2)

tester [12383]

Answer:

The lines are parallel

Step-by-step explanation:

it's established that

To find the slope between two points, we use the formula

$m=\frac{y2-y1}{x2-x1}$

Keep in mind

If lines are parallel, their slopes must be identical

When lines are perpendicular, their slopes are negative reciprocals (the product equals -1)

step 1

Determine the slope of JK

we have

$J(13,-5),K(2,6)$

insert the values

$m=\frac{6+5}{2-13}$

$m=\frac{11}{-11}$

$m_J_K=-1$

step 2

Compute the slope of LM

we have

$L(-1,-5),M(-4,-2)$

insert the values

$m=\frac{-2+5}{-4+1}$

$m=\frac{3}{-3}$

$m_L_M=-1$

step 3

Analyze the slopes

$m_J_K=-1$

$m_L_M=-1$

thus

$m_J_K=m_L_M$

hence

The lines are parallel

7 0

1 month ago

An experiment was conducted to record the jumping distances of paper frogs made from construction paper. Based on the sample, th

tester [12383]

Answer:

$9.9676 - 2.326*0.5904 =8.594$

$9.9676 + 2.326*0.5904 =11.341$

Step-by-step explanation:

Notation

$\bar X$ is the sample mean

$\mu$ indicates the population mean (the variable of interest)

s signifies the sample standard deviation

n denotes the sample size

Solution to the problem

The mean's confidence interval is derived from the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In this instance, the 9% confidence interval corresponds to:

$8.8104 \leq \mu \leq 11.1248$

We can determine the mean using the following:

$\bar X = \frac{8.8104 +11.1248}{2}= 9.9676$

Additionally, the margin of error can be calculated as:

$ME= \frac{11.1248- 8.8104}{2}= 1.1572$

The margin of error for this situation is expressed as:

$ME = t_{\alpha/2}\frac{s}{\sqrt{n}} = t_{\alpha/2} SE$

Next, we find the standard error:

$SE = \frac{ME}{t_{\alpha/2}}$

The critical value for a 95% confidence interval using a normal standard distribution is roughly 1.96, and substituting gives us:

$SE = \frac{1.1572}{1.96}= 0.5904$

For the 98% confidence interval, the significance corresponds to $\alpha=1-0.98= 0.02$ and $\alpha/2 = 0.01$ with a critical value of 2.326, yielding a confidence interval of:

$9.9676 - 2.326*0.5904 =8.594$

$9.9676 + 2.326*0.5904 =11.341$

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1 month ago

Andros has an oil fired heating system. In a 30-day period he used a full tank of oil at a constant rate per day. At a different

Leona [12618]

To resolve this, we multiply the 30-day timeframe by 7, resulting in a total of 210 days.

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22 days ago

Gus has a fish tank that holds 471047104710 inches^3 3 cubed of water. He is using a cylinder shaped bucket with a radius of 555

tester [12383]

Answer:

Gus must fill the cylindrical bucket three times to get it filled for the tank

Step-by-step explanation:

Extracting essential details from the query:-

*** A fish tank has a volume of 4710 inches^3

*** The tank owner utilizes a cylindrical bucket for filling the tank

*** The bucket has a radius of 5 inches and a height of 20 inches

*** We need to compute how many times Gus has to fill the bucket to fully fill the fish tank.

Since the container used for filling the tank is cylindrical, we will apply the formula for finding a cylinder's volume to derive the bucket's volume used for filling the tank.

Volume of a cylinder = π × r^2 × h. The radius of the cylindrical bucket is stated as 5 inches while the height is mentioned as 20 inches.

The bucket's volume is therefore calculated as 3.14 × 5^2 × 20 = 1570 inches^3

Next, it is given that the fish tank’s capacity is 4710 inches^3. To find out how many times the bucket can fill the tank, we must divide the tank's volume by the bucket's volume:

4710/1570 = 3 full buckets.

Thus, Gus has to fill the bucket three times for filling the fish tank completely without spillage.

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1 month ago