Elijah has $1.60 worth of nickels and dimes. He has 5 more nickels than dimes. Determine the number of nickels and the number of dimes that Elijah has.

An equation in slope-intercept form for the line that passes through (9,12) and is parallel to y=4 is y= 4x -24.

What is Parallel lines?

Parallel lines in geometry are coplanar, straight lines that don't cross at any point. In the same three-dimensional space, parallel planes are any planes that never cross. Curves with a predetermined minimum distance between them and no contact or intersection are said to be parallel.

Parallel lines will have the same slope but different y-intercepts  so again we can  use the coordinates to determine the y intercept of the new equation.

So we know that the slope intercept formula is y=mx + b where m is the slope and b is the y-intercept so we will input the x and y coordinates to solve for b.

12 = 4(9) + b

12 = 36 + b

b = -24

The equation will be y= 4x -24.

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Answer:

brainliest please, i need it and it takes one click

Answer: C. 26°

Step-by-step explanation:

Right triangle: a triangle in which one of the interior angles measures 90°.

This type of angle can be solved using trigonometrical functions. As the measure of the sides given are h and k, then we will use:

In our case, it would be:

cosa = adjacent/hypotenuse

Replacing the values:

cosa = h/k

Solving for a:

cosa-1(cosa) = cos-1(8.1/9)

a = cos-1(8.1/9)

a≈ 25.8 ≈26

Answer: C. 26°

Answer:

C) 11.4

Step-by-step explanation:

Answer:

3.82 km

Step-by-step explanation:

Assuming that the change in elevation is linear, we can calculate the elevation change per km traveled.  The known values are the start (0km) and the sign (3km).  The elevation gain over that interval is (0.95-9.0)km = 0.5km.  That was for an distance interval of  3km, so we can write:

(0.5km elevation gain)/(3km distance)

We can use this as a rate change and and use it in a linear equation to predict the elevation as a function of distance.

Let y be the elevation and x the distance, both in km.

y = (0.183)(x)+b, where b is the elevation at the start of the trail.  We can find b by using this equation and entering one of the two data points.  Lets use the elevation of 0.95m at 3km distance:

y = (0.183)(x)+b

0.95 = (0.183)(3)+b

b = 0.4km

The full equation is :

y = (0.1833)X + 0.4

Enter 1.1 km for y and calculate x, the distance to reach 1.1 km altitude.

1.1 = (0.1833)X + 0.4

X = 3.82 km

Answer:

m> 55 (you only flip the direction of the sign when you divide by a negative number)

Step-by-step explanation:

Answer:

m > 55

Step-by-step explanation:

simplify both sides of the inequality

m - 19 > 36

Add 19 to both sides

36+19

m>55

Hope this helps :D

Answer: A and C

Step-by-step explanation:

The given rational expression is 4y + 16 y + 4. To find the restricted values of y, we need to identify any values of y that would make the expression undefined.

In this case, the expression is in the form of a sum, so we don't have any denominators that could lead to division by zero. Therefore, there are no restricted values of y for this rational expression.

The expression 4y + 16 y + 4 is defined for all real numbers. We can evaluate it for any value of y without encountering any restrictions.

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To solve 3x − 4 = 6 using the change of base formula, we first isolate the variable by adding 4 to both sides of the equation.

The given equation is 3x − 4 = 6. To solve for x, we want to isolate the variable on one side of the equation.

Step 1: Add 4 to both sides of the equation:

3x − 4 + 4 = 6 + 4

3x = 10

Step 2: Apply the change of base formula, which states that log(base b)(x) = log(base a)(x) / log(base a)(b), where a and b are positive numbers not equal to 1.

In this case, we will use the natural logarithm (ln) as the base:

ln(3x) = ln(10)

Step 3: Solve for x by dividing both sides of the equation by ln(3):

(1/ln(3)) * ln(3x) = (1/ln(3)) * ln(10)

x = ln(10) / ln(3)

Using a calculator, we can approximate the value of x to the nearest thousandth:

x ≈ 1.660

Therefore, the solution for x in the equation 3x − 4 = 6, using the change of base formula, is approximately x ≈ 1.660.

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The general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is: y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

To solve this differential equation, we can use separation of variables.

First, we can rearrange the equation to get dy/dx on one side and the rest on the other side:

dy/dx = 1/3(sin x − xy^2)

dy/(sin x - xy^2) = dx/3

Now we can integrate both sides:

∫dy/(sin x - xy^2) = ∫dx/3

To integrate the left side, we can use substitution. Let u = xy^2, then du/dx = y^2 + 2xy(dy/dx). Substituting these expressions into the left side gives:

∫dy/(sin x - xy^2) = ∫du/(sin x - u)

= -1/2∫d(cos x - u/sin x)

= -1/2 ln|sin x - xy^2| + C1

For the right side, we simply integrate with respect to x:

∫dx/3 = x/3 + C2

Putting these together, we get:

-1/2 ln|sin x - xy^2| = x/3 + C

To solve for y, we can exponentiate both sides:

|sin x - xy^2|^-1/2 = e^(2C/3 - x/3)

|sin x - xy^2| = 1/e^(2C/3 - x/3)

Since the absolute value of sin x - xy^2 can be either positive or negative, we need to consider both cases.

Case 1: sin x - xy^2 > 0

In this case, we have:

sin x - xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(sin x - 1/e^(2C/3 - x/3))/x]

Note that the initial condition y(0) = 5 only applies to the positive square root. We can use this condition to solve for C:

y(0) = √(sin 0 - 1/e^(2C/3)) = √(0 - 1/e^(2C/3)) = 5

Squaring both sides and solving for C, we get:

C = 3/2 ln(1/25)

Putting this value of C back into the expression for y, we get:

y = √[(sin x - e^(x/2)/25)/x]

Case 2: sin x - xy^2 < 0

In this case, we have:

- sin x + xy^2 = 1/e^(2C/3 - x/3)

Solving for y, we get:

y = ±√[(e^(2C/3 - x/3) - sin x)/x]

Again, using the initial condition y(0) = 5 and solving for C, we get:

C = 3/2 ln(1/25) + 2/3 ln(5)

Putting this value of C back into the expression for y, we get:

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x]

So the general solution to the differential equation dy/dx = 1/3(sin x − xy^2), y(0)=5 is:

y = ±√[(sin x - e^(x/2)/25)/x], if sin x - xy^2 > 0 and y(0) = 5

y = -√[(e^(2/3 ln 5 - x/3) - sin x)/x], if sin x - xy^2 < 0 and y(0) = 5

Note that there is no solution for y when sin x - xy^2 = 0.

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The correct statement is The image segment is longer than the original segment.

To determine the image of the line segment after dilation, we can use the formula for dilation in the coordinate plane. The formula states that the coordinates of the image point (x', y') are related to the coordinates of the original point (x, y) by the following equation:

(x', y') = (h + k(x - h), v + k(y - v))

Where:

(h, v) represents the center of dilation.

k represents the scale factor.

In this case, the center of dilation is (0, 6), and the scale factor is 3. The endpoints of the line segment are P(2, 3) and Q(4, 6). Let's find the image points P' and Q' after dilation.

For point P(2, 3):

x' = 0 + 3(2 - 0) = 0 + 3(2) = 6

y' = 6 + 3(3 - 6) = 6 + 3(-3) = 6 - 9 = -3

Therefore, the image point P' after dilation is P'(6, -3).

For point Q(4, 6):

x' = 0 + 3(4 - 0) = 0 + 3(4) = 0 + 12 = 12

y' = 6 + 3(6 - 6) = 6 + 3(0) = 6 + 0 = 6

Therefore, the image point Q' after dilation is Q'(12, 6).

Now, let's analyze the coordinates of the image points P' and Q' to determine which statement is true.

The image segment is longer than the original segment.

The image segment is shorter than the original segment.

The image segment has the same length as the original segment.

To compare the lengths of the line segments, we can use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

For the original segment PQ:

Distance(PQ) = √((4 - 2)² + (6 - 3)²) = √(2² + 3²) = √(4 + 9) = √13

For the image segment P'Q':

Distance(P'Q') = √((12 - 6)² + (6 - (-3))²) = √(6² + 9²) = √(36 + 81) = √117

Since √13 is approximately 3.6056 and √117 is approximately 10.8167, we can conclude that the image segment P'Q' is longer than the original segment PQ.

Therefore, the correct statement is:

The image segment is longer than the original segment.

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When the radius is 9 cm, the area of the circular pool is increasing at a rate of 288π cm square/min.

To find how fast the area of the circular pool is increasing when the radius is 9 cm, we can use the formula for the area of a circle, which is A = πr^2, where A represents the area and r represents the radius.

Given that the radius is increasing at a rate of 4 cm/min, we can differentiate the formula for the area with respect to time (t) using the chain rule:

dA/dt = dA/dr * dr/dt

Here, dA/dt represents the rate of change of the area with respect to time, dr/dt represents the rate of change of the radius with respect to time, and dA/dr represents the derivative of the area with respect to the radius.

To find dA/dr, we can differentiate the formula for the area of a circle:

dA/dr = d/dt (πr^2)

= 2πr * dr/dt

Plugging in the given values, we have:

dr/dt = 4 cm/min

r = 9 cm

Substituting these values into the equation for dA/dr:

dA/dr = 2π(9) * 4

= 72π cm^2/min

Now, we can find dA/dt by multiplying dA/dr by dr/dt:

dA/dt = (72π cm^2/min) * (4 cm/min)

= 288π cm^2/min

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The limit does not exist.

In order for such a limit to occur, the fraction \(\frac{x^{2} }{x^{2} +y^{2} }\) must be comparable to the same value \(L\), regardless of the way we take to get there \((0,0)\).

Try approaching \((0,0)\) along the x-axis.

This means setting \(y=0\) and finding the limit \(lim_{x-0} \frac{x^{2} }{x^{2} +y^{2} }\).

We obtain:

\(lim_{x-0,y=0}\frac{x^{2} }{x^{2} +y^{2} } =lim_{y=0}}\frac{x^{2} }{x^{2} +0 }\\=lim_{x-0}} \frac{x^{2} }{x^{2} } \\\\=lim_{x-0}}1\\=1\)

Now evaluate approaching \((0,0)\) along the y-axis.

This means setting \(x=0\) and finding the limit \(lim_{y-0} \frac{x^{2} }{x^{2} +y^{2} }\).

\(lim_{y-0,x-0} \frac{x^{2} }{x^{2} +y^{2} } =lim_{y-0} \frac{0}{0+y^{2} } \\=lim_{y-0} \frac{0}{y^{2} } \\=lim_{y-0} 0\\=0\)

Approaching the origin via these two methods results in distinct limits.

\(lim_{x-0,y-0} \frac{x^{2} }{x^{2} +y^{2} }\) ≠ \(lim_{y-0,x-0}\frac{x^{2} }{x^{2} +y^{2} }\)

Therefore the limit does not exist.

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The correct question is given below:

Find the limit, if it exists, or show that the limit does not exist.

\(lim_{(x,y) -(0,0)} \frac{x^{2} }{x^{2} +y^{2} }\)

Answer:

2nd option is the correct answer.

\( 5\frac{1}{3}\: units\)

Step-by-step explanation:

\( In\:\triangle XWZ, \: \angle XWZ= 90°

\\ \: \&\: WY \perp XZ\\\)

Therefore, by geometric mean postulate:

\( WY^2 = XY\times YZ\\

\therefore 4^2 = 3\times a\\

\therefore 16 = 3a

\therefore a = \frac{16}{3}\\\\

\huge \red {\boxed {\therefore a = 5\frac{1}{3}\: units}} \)

Answer:

its 62!

p-by-step explanation:

Answer:

62.

Step-by-step explanation:

A=2(wl+hl+hw)=2·(3·5+2·5+2·3)=62

Answer:

4/8 is one half

Step-by-step explanation:

ANSWER

0.3783

EXPLANATION

The lengths of the pregnancies, X, is normally distributed with a mean of 246 days and a standard deviation of 13 days,

We have to find the probability that a randomly selected pregnancy lasts less than 242 days,

For this, we have to standardize the variable X with the formula,

So the probability we have to solve is,

This is equivalent to,

Which is also equivalent to,

We have to find these equivalences because, usually, normal distribution tables show the probabilities for positive z-scores and to the left of those values - i.e. less than those values. Find z = 0.31 in a z-table,

So, the probability is,

Hence, the probability that a randomly selected pregnancy lasts less than 242 days is 0.3783.

the average rate of change in the number of cattle from 2006 to 2014 is approximately -1.1125 million head of cattle per year.

To find the average rate of change in the number of cattle from 2006 to 2014, we need to divide the total change in the number of cattle over that period by the number of years.

The total change in the number of cattle is:

87.7 million - 96.6 million = -8.9 million

The number of years is:

2014 - 2006 = 8

So, the average rate of change is:

-8.9 million / 8 years = -1.1125 million per year

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A significance level of 0.10, we have enough evidence to conclude that the new copy machines have a significantly faster mean repair time compared to the older model.

To test if the new copy machines are faster to repair, we can set up the following null and alternative hypotheses:

Null Hypothesis (H₀): The mean repair time for the new copy machines is the same as the mean repair time for the older model.

Alternative Hypothesis (H₁): The mean repair time for the new copy machines is less than the mean repair time for the older model.

Let's perform a one-sample t-test to test these hypotheses. The test statistic is calculated as:

t = (sample mean - population mean) / (sample standard deviation / √(sample size))

Given:

Population mean (μ) = 93 minutes

Sample mean (\(\bar x\)) = 86.8 minutes

Sample standard deviation (s) = 14.6 minutes

Sample size (n) = 18

Significance level (α) = 0.10

Calculating the test statistic:

t = (86.8 - 93) / (14.6 / sqrt(18))

t = -6.2 / (14.6 / 4.24264)

t ≈ -2.677

The degrees of freedom for this test is n - 1 = 18 - 1 = 17.

Now, we need to determine the critical value for the t-distribution with 17 degrees of freedom and a one-tailed test at a significance level of 0.10. Consulting a t-table or using statistical software, the critical value is approximately -1.333.

Since the test statistic (t = -2.677) is less than the critical value (-1.333), we reject the null hypothesis.

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Answer:

Step-by-step explanation:

To the 4th power means that all the items in the parenthesis is mulitplied 4 times

(9m)⁴

=9*9*9*9*m*m*m*m*m  or

= (9m)(9m)(9m)(9m)

Answer:

7.396 × 10-5

Step-by-step explanation:

To convert 0.00007396 into scientific notation, follow these steps:

Move the decimal 5 times to right in the number so that the resulting number, m = 7.396, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -5

Write in the scientific notation form, m × 10n

= 7.396 × 10-5

Answer:D

0.00007395999999999999 7.396x10-5 7.396e-5 7.396 x 10-5

The value of IQR is 90 when box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290.

Given that,

For box plot data where Q₁ = 200, Q₂ = 250, and Q₃ = 290

We have to find the data of IQR.

We know that,

IQR is define as the variation in the distribution of your data's middle quartile is measured by the interquartile range (IQR). It is the range that corresponds to your sample's middle 50%. Measure the variability where the majority of your numbers are by using the IQR.

IQR Formula is Q₃ - Q₁

So,

Q₃ = 290

Q₁ = 200

Then ,

IQR = Q₃ - Q₁

IQR = 290 - 200

IQR = 90

Therefore, The value of IQR is 90.

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Answer:

4.) log2(10)=3x

Step-by-step explanation:

I think it's correct

Answer:

Step-by-step explanation:

Step-by-step explanation:

the general equation of a parabola is

y = a(x – h)² + k.

(h, k) is the vertex of the parabola.

comparing it to

y = 3(x + 4)² - 2

we see that (h, k) = (-4, -2).

the student made a sign mistake. it is "- h" in the squared factor. so, "+4" indicates "-4" as "h".

but the student simply used "+4".

Answer:

1, -2

Step-by-step explanation:

The x axis is 1 to the right, and the y axis is 2 down.

The solution is, 128 combinations.

In mathematics, a combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

here, we have,

We are told in the question that a frozen yogurt shop has:

8 flavors of frozen yogurt

2 kinds of syrup

8 toppings.

The combinations that can be made with one flavor of frozen yogurt, one syrup, and one topping is calculated as:

8 × 2 × 8

= 128 combinations

Therefore, the combinations that can be made with one flavor of frozen yogurt, one syrup, and one topping is 128 combinations.

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Answer:it will be c

Step-by-step explanation:

9514 1404 393

Answer:

  C.  7.1

Step-by-step explanation:

The distance is found using the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((1-(-6))² +(1-2)²) = √(7² +(-1)²) = √50

  d ≈ 7.07107 ≈ 7.1 . . . . . matches choice C

Answer:

ans - 25.77°

Step-by-step explanation:

tan a = 14/29

a = tan ^ -1 14/29

a = 25.77°

Answer:

25.77

Step-by-step explanation:

It's logically impossible for this angle to be .008.

Alternatively (the harder way), use trigonometric ratios to solve this problem.

Since you know the adjacent and opposite angle, you need to use tangent ratio.

tan = a/o

Use \(tan^-1\)

 \(tan^-1(14/29)\)

a = 25.76932762, ~25.77

Answer:

26.93

Step-by-step explanation:

The right polygon is the first one scaled down by 1.33 so we can multiply the values on the 2nd one by 1.33 to get the first one.

y+1 = 21*1.33

y+1 =27.93

y=26.93