A raft left port A traveling towards port B. At the same time a motorboat left port B traveling towards port A. How many hours since the departure will the two meet if the raft can cover the distance between ports A and B in 30 hours and the boat can cover the same distance in 6 hours?

Answer:

SAS

Step-by-step explanation:

pretty sure since the angle z is connected to both right triangles the sides become congruent.

Answer:

4x - y = -8

Step-by-step explanation:

y = 4x+8

-8 + y = 4x

-8 = 4x - y

4x - y = - 8

Answer:

D. SSA

Step-by-step explanation:

The SSA postulate does not exist because an angle and two sides does not guarantee that the two triangles are congruent. This is because if two triangles have two congruent sides but a non-included congruent side, this does not indicate that it is necessarily congruent.

Answer:

6

Step-by-step explanation:

Answer:

Step-by-step explanation:

x 2 + y 2 = 9

is not a function

Explanation:

In order for an equation to represent a function any single value of  

x

must have at most one corresponding value of  

y

which satisfies the equation.

For  x2 + y 2= 9 XXXX

if (for example)  

x = 0 XXXX

there are two values for  

y  (namely  + 3  and  − 3 ) which satisfy the equation

and therefore the equation is not a function.

So general equation of circle

(h,k) is centre and r is radius

here radius is

So equation

9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

The angle bisector divides the sides proportionally.

  (3x -12)/6 = 21/14

  3x -12 = 9 . . . . . . . multiply by 6 and simplify

  x -4 = 3 . . . . . . . .  divide by 3

  x = 7 . . . . . . . . . . . add 4

\(\textit{exponential form of a logarithm} \\\\ \log_a(b)=y \qquad \implies \qquad a^y= b \\\\[-0.35em] ~\dotfill\\\\ \log_2(x)=-5\implies 2^{-5}=x\)

Answer:

y=mx+b

Step-by-step explanation:

Answer:

B. StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction

i.e \(\frac{RY}{RS}\) = \(\frac{RX}{RT}\) = \(\frac{XY}{TS}\)

Step-by-step explanation:

Two or more shape or figures are similar when their sides and angles can be compared appropriately.

In the given figure, ΔRXY is within ΔRST. Since the two triangles are similar, then their length of sides can be compared in the form of required ratios.

So that by comparison,

\(\frac{RY}{RS}\) = \(\frac{RX}{RT}\) = \(\frac{XY}{TS}\)

Therefore, the correct option to the question is B.

Answer:

option B: StartFraction R Y Over R S EndFraction = StartFraction R X Over R T EndFraction = StartFraction X Y Over T S EndFraction

The equation of the plane passing through the point (1, 4, -4) with normal vector 〈3, 5, -2〉 can be written as:

3(x - 1) + 5(y - 4) - 2(z + 4) = 0

Expanding and rearranging terms, we get:

3x + 5y - 2z - 23 = 0

To parameterize this plane, we can let:

x = s

y = t

z = (3s + 5t - 23) / 2

Therefore, the parameterization of the plane is:

r (s,t) = <s, t, (3s + 5t - 23) / 2>

By definition, "to parameterize" means "to express in terms of parameters". A mathematical technique known as parameterization involves representing the state of a system, process, or model as a function of a set of independent variables known as parameters.

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Answer:30 degrees

Step-by-step explanation:There are a couple of ways to do this.

This is the straightforward, “follow-your-nose” way. Find a point on each line. (Say, (1,2) on the line with slope 2 and (-1,1) on the line with slope -1. Then the angle in the triangle formed by the origin (0,0) and these other two point is the desired angle. One can find the cosine of angle in the triangle using the Law of Cosines, since the lengths of all of the sides can be found directly from the distance formula and the coordinates of the points. Finally, use arccosine to get from the cosine of the angle to the angle itself.

There is also a “slick” way, which relies on remembering the subtraction formula for tangents. tan(u-v) = [tan(u) - tan(v)] / [tan(u) + tan(v)]. Consider u as the angle between the positive x-axis and the line with slope -1, and v as the angle between the positive x-axis and the line with slope 2. Then the requested angle is u-v. We know tan(u) = -1 and tan(v) = 2, so substituting into the subtraction formula for tangents allows us to find tan(u-v). Finally, use arctangent of that value to find u-v.

Considering the density curve, the percent of the area under the

density curve where x is less than 2 is 375.5%

The total area under the curve is by the formula of a trapezoid

= 1/2 (sum of parallel lines) * height

= 1/2 * (0.25 + 0.75) * 2

= 0.5 * 1 * 2

= 1

Area of the curve where x < 2

= 1/2 (sum of parallel lines) * height

= 1/2 * (0.25 + 0.5) * 1

= 0.5 * 0.75 * 1

= 0.375

the percent area

= area of area where x is less than 2

= 0.375 / 1 * 100

= 37.5%

the percent area is 37.5

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Answer:

Constant of proportionality is y divided by x.  y is 2 and x is 4.  2 divided by 4 is 1/2.

Let me know if that is correct.

Step-by-step explanation:

Answer:

the answer is £1.47

Step-by-step explanation:

on a calculator time's your number by 0.12 and that's how you found your answer

Answer:

Step-by-step explanation:

Shiredddddd

a) The upper bound of the 95% confidence interval is given as follows: 1024 hours.

b) The lower bound of the 95% confidence interval is given as follows: 1004 hours, which is the same difference from the mean as the upper bound, just below the mean.

We use the t-distribution to obtain the confidence interval when we have the sample standard deviation.

The equation for the bounds of the confidence interval is presented as follows:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

The variables of the equation are presented as follows:

The critical value, using a t-distribution calculator, for a two-tailed 99% confidence interval, with 25 - 1 = 24 df, is t = 2.0639.

The parameters for this problem are given as follows:

\(\overline{x} = 1014, s = 25, n = 25\)

The lower bound of the interval is then given as follows:

1014 - 2.0639 x 25/5 = 1004.

The upper bound of the interval is then given as follows:

1014 - 2.0639 x 25/5 = 1024.

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The answer is 1004.

Given data: $n=25$, $\bar{x}=1014$ and $\sigma=25$.

The sample mean $\bar{x}$ = 1014 and sample size n = 25We can construct 95% confidence interval as follows:Step 1: Find the sample mean $\bar{x}$ = 1014Step 2:

Find the standard error,SE = $\frac{\sigma}{\sqrt{n}}$ =$\frac{25}{\sqrt{25}}$=5Step 3: Find the margin of error,

ME = $z_{\frac{\alpha}{2}}$ x SE , where $\alpha$=0.05, z-value for 0.025 = 1.96ME=1.96 x 5 = 9.8Step 4: Find the lower and upper limit for the confidence interval.

Lower limit = $\bar{x}$ - ME= 1014 - 9.8= 1004.2Upper limit = $\bar{x}$ + ME= 1014 + 9.8= 1023.8Thus the 95\% two-sided confidence interval is $(1004,1024)$.Lower-confidence bound on the mean life with 95% CI is:

Lower confidence bound = $\bar{x}$ - $z_{\alpha}$ x $\frac{\sigma}{\sqrt{n}}$=1014 - 1.96 x $\frac{25}{\sqrt{25}}$=1014-1.96x5=1004.2.

Comparing the lower bound of this confidence interval with the one in part (a), the lower bound in part (b) is the same as the lower limit in part (a). Therefore, the answer is 1004.

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If a set of data has a normal distribution with a mean of 50 and a standard deviation of 8. the percent of data within the interval less than 50 is; C. 50%.

Based on the details given the percent of data within the interval less than 50 is not 34% or 68% or 97.5% but rather the percent of data  is 50%.

The reason why it is 50% is that  the mean is 50 in which the data has a normal distribution, 50 is the center of the distribution.  Based on this half the data falls above the mean and half the data falls below the mean.

Therefore the correct option is C.

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Step-by-step explanation:

The slope of a line given two points can be found by using the formula

\(m = \frac{ y_2 - y _ 1}{x_ 2 - x_ 1} \\\)

From the question we have

\(m = \frac{ - 22 - - 2}{ - 4 - - 4} = \frac{ - 22 + 2}{ - 4 + 4} = - \frac{20}{0} \\ \)

Any number divided by zero is undefined so the slope of the line is undefined.

Hope this helps you

Answer:

Step-by-step Explanation:

We need to find the slope of the line joining the points (-4, -2) and (-4, -22).

We know that, Slope is the difference of abcsissa (x - coordinate) / difference of ordinates (y-coordinate)

\(m = \dfrac{y2 - y1}{x2 - x1} \)

Here:

Plugging these values:

\(m = \dfrac{ - 22 - ( - 2)}{ - 4 - ( - 4)} \)

This can be written as:

\(m = \dfrac{ - 22 + 2}{ - 4 + 4} \)

\(m = \dfrac{ - 20}{0} = \infty \)

Here, The slope of the line is infinite or undefined. An undefined slope (or an infinitely large slope) is the slope of a vertical line!

Answer:

Step-by-step explanation:

2(√x+2/2 - 1)² + 4 (√x+2/2 - 1)

2((√x+2/2)² + 1² - 2(√x+2/2)(1)) + 4√x+2/2 - 4

2(x+2/2 + 1 - 2(√x+2/2)) + 4√x+2/2 - 4

x + 2 + 2 - 4√x+2/2 + 4√x+2/2 - 4

x + 4 - 4

x

Answer:

the answer is x

Step-by-step explanation:

The value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

Time t = 11 sec

Initial velocity u = 25 kmph

u = (25 × 1000)/(60 × 60) = 6.9 m/s

final velocity v = 75 kmph

v = (75 × 1000)/(60 × 60) = 20.83 m/s

From the first equation of motion;

v = u + at

Put the values;

20.83 = 6.9 + 11a

20.83 - 6.9 = 13a

11a = 13.93

a = 13.93 / 11

a = 1.26 m/s²

Thus, the value of the acceleration is 1.26 m/s² for the automobile advertised by the makers.

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The molarity of acetic acid in the vinegar is 0.561 M and the mass percent of acetic acid in the vinegar is 33.6%.

In this problem, we are given the volume and concentration of the base (NaOH) used to titrate a sample of vinegar, and we need to find the molarity of acetic acid in the vinegar and the mass percent of acetic acid.

To start, we can use the balanced chemical equation for the reaction between acetic acid and NaOH to find the moles of NaOH used in the titration:

CH₃COOH + NaOH → CH₃COONa + H₂O

From the equation, we can see that the ratio of moles of acetic acid to moles of NaOH is 1:1. Therefore, the number of moles of NaOH used is the same as the number of moles of acetic acid in the original vinegar sample.

Molarity of acetic acid in the vinegar:

moles of NaOH = concentration of NaOH × volume of NaOH used

moles of acetic acid = moles of NaOH

molarity of acetic acid = moles of acetic acid / volume of vinegar sample

Substituting the given values, we get:

moles of NaOH = 0.231 M × 0.02430 L = 0.00561 moles

moles of acetic acid = 0.00561 moles

molarity of acetic acid = 0.00561 moles / 0.0100 L = 0.561 M

Mass percent of acetic acid in the vinegar:

mass of acetic acid = density × volume × molarity × molecular weight

mass percent = (mass of acetic acid / mass of vinegar sample) × 100%

Substituting the given values and the molecular weight of acetic acid (60.05 g/mol), we get:

mass of acetic acid = 1.01 g/mL × 0.0100 L × 0.561 mol/L × 60.05 g/mol = 3.39 g

mass percent = (3.39 g / (1.01 g/mL × 0.0100 L)) × 100% = 33.6%

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Using a system of equations, it is found that:

--------------------------

In a triangle, the sum of the interior angles is of 180º, thus:

\(x + y + z = 180\)

The second angle of the triangle  has a measure equal to the sum of two times the other two angles, then:

\(y = 2(x + z)\)

\(x + z = 0.5y\)

Replacing into the first equation, we find the second angle:

\(x + y + z = 180\)

\(0.5y + y = 180\)

\(1.5y = 180\)

\(y = \frac{180}{1.5}\)

\(y = 120\)

The measure of the second angle is of 120º.

Now, working to find the measures of the first and of the third angles:

\(x + z = 0.5y \rightarrow x + z = 60 \rightarrow x = 60 - z\)

The third  angle has a measure equal to ten less than the first angle, then:

\(z = x - 10\)

Since \(x = 60 - z\)

\(z = 60 - z - 10\)

\(2z = 50\)

\(z = \frac{50}{2}\)

\(z = 25\)

And

\(x = 60 - z = 60 - 25 = 35\)

The measure of the first angle is of 35º.

The measure of the third angle is of 25º.

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Answer:

Circumcenter of a triangle is formed by joining the perpendicular bisectors of three sides of triangle.

As we draw perpendicular bisectors of three sides, they will intersect at one point(say O) which lies inside the circle.

From that point of intersection, draw a circle touching each of the vertex of a triangle and we get a circumcircle. And O becomes centre of the circle.

Hence, circumcenter lies inside the triangle.

Point Z is the intersection of the medians. Then the correct option is A.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

Z is the centroid of the triangle ΔUVW.

The circumcenter of a triangle is framed by joining the opposite bisectors of three sides of the triangle. But the perpendicular bisectors are not shown.

The opposite sides are bisects. Then point Z is the intersection of the medians.

Thus, the correct option is A.

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The impedance of the circuit element is (4 + 5i) ohms

Impedance is a measure of the opposition to electrical flow in an alternating current circuit. The unit of impedance is ohms. It is given by:

Impedance (Z) = Voltage (V) / Current (I)

Given that V = 35 + 13i, I = 5 - 3i, hence:

Z = (35 + 13i) / 5 - 3i

Z = (4 + 5i) ohms

The impedance of the circuit element is (4 + 5i) ohms

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Answer:

a would be 0 and b would be 33

Step-by-step explanation:

that's what I think the answer is-

EXPLANATION

We can affirm that the length of the adjacent leg is 5 units and the length of the hypotenuse is 8 units.

As given, the length of the third side is 6.245 units.

Now, computing sin A give us the following expression:

The solution is 1249/1600

pneumonoultramicroscopicsilicovolcanoconiosis

a chronic lung disease caused by the inhalation of fine silicate or quartz dust. More examples. Pneumono refers to the lung.

we can use the information given about its growth rate and the height after 4.5 years:So, it took 7 years from the time Vlad moved in until the tree was 357 centimeters tall.

Height increase per year = 26 centimeters
Years since Vlad moved in = 4.5 years
Height after 4.5 years = 292 centimeters
To calculate the initial height of the tree, we can multiply the growth rate by the number of years and add it to the starting height:
Initial height = Height after 4.5 years - (Height increase per year x Years since Vlad moved in)
Initial height = 292 - (26 x 4.5)
Initial height = 168 centimeters
Therefore, the tree was 168 centimeters tall when Vlad moved into the house.
To find out how many years passed from the time Vlad moved in until the tree was 357 centimeters tall, we can use the same formula and solve for the number of years:
Height increase per year = 26 centimeters
Initial height = 168 centimeters
Final height = 357 centimeters
To calculate the number of years, we can rearrange the formula as follows:
Years = (Final height - Initial height) / Height increase per year
Years = (357 - 168) / 26
Years = 6.04 years (rounded to two decimal places)
Therefore, it took approximately 6 years and 1 month for the tree to grow from 168 centimeters to 357 centimeters tall.
To determine the height of the oak tree when Vlad moved into the house, we can use the given information. The tree grows by 26 centimeters each year, and it was 292 centimeters tall after 4.5 years.
First, let's find the total growth during the 4.5 years:
26 cm/year * 4.5 years = 117 cm
Now, subtract the total growth from the current height to find the initial height:
292 cm - 117 cm = 175 cm
So, the oak tree was 175 centimeters tall when Vlad moved into the house.
To find out how many years passed until the tree was 357 centimeters tall, we can use the growth rate again:
First, find the difference in height between the target height (357 cm) and the initial height (175 cm):
357 cm - 175 cm = 182 cm
Now, divide the difference in height by the growth rate to find the number of years:
182 cm / 26 cm/year = 7 years

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Answer:

x=-2

Step-by-step explanation:

6(x + 1) = -2(3x + 9)​

Distribute 6 and -2.

6x+6=-6x-18

Move the variable to the left-hand side and move the constant to the right and change their signs.

6x+6x=-18-6

Collect like terms.

12x=-24

Divide both sides of the equation by 12.

x=-2

Hope this helps :)

SSS congruence rules states that if three sides of one triangle are equal to the three sides of another triangle, then the two triangles are congruent.

The SSS (Side-Side-Side) congruence rule states that if three sides of one triangle are equal to the three sides of another triangle, equal, and the two triangles share the same dimensions then the two triangles are congruent. This means that all of the angles and sides of the two triangles are In order for two triangles to be congruent according to the SSS congruence rule, the lengths of the three corresponding sides of the two triangles must be equal. If all three of these conditions are met, then the two triangles are congruent and can be used to solve a variety of geometric problems.

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The SSS congruence rule is rule that is used to prove two triangles congruent . Its full form is Side-Side-Side Congruence .

The Two Triangles can be called as  Congruent Triangles if their sides have same length and the angles also have the same measure.

One of the 4 rules in proving the triangles congruent is SSS .

The SSS Congruence Rules also called as (Side-Side-Side) Rule means that if all the three sides of one triangle are equal to the corresponding three sides in the other triangle ,

then we can say that the two triangles are congruent by SSS (Side-Side-Side) Rule .

Therefore , The SSS Congruence rule means Side-Side-Side Congruence .

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The quadratic function representing the given graph is f(x) = 2(x - 1)^2 - 3. This quadratic function is obtained by observing the key features of the graph, namely the vertex and the direction of the parabola.

In the given graph, the vertex of the parabola is at the point (1, -3). This gives us the vertex form of the quadratic function: f(x) = a(x - h)^2 + k, where (h, k) represents the vertex coordinates.

Since the vertex is at (1, -3), we substitute these values into the vertex form and solve for the coefficient a. This gives us f(x) = a(x - 1)^2 - 3.

To determine the value of a, we can use another point on the graph. From the graph, we can observe that when x = 0, y = -1. Substituting these values into the equation, we get -1 = a(0 - 1)^2 - 3, which simplifies to -1 = a - 3.

Solving for a, we find a = 2. Substituting this value back into the equation, we obtain the quadratic function f(x) = 2(x - 1)^2 - 3 as the desired function representing the given graph.

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