for what value of k, the line joining 3x-ky+7=0 is perpendicular to the line joining (4 ,3) and ( 5, -3).

The value for each interior angle in the polygon will be 147.27°.

The total angles in the 11 sided polygon will be:

= (n - 2) × 180

= (11 - 2) × 180

= 9 × 180°

= 1620°

Each angle will be:

= 1620°/11

= 147.27°

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15 gallons of 35% peroxide solution contains 0.35 × 15 = 5.25 gallons of hydrogen peroxide. The rest of the volume is made up of 15 - 5.25 = 9.75 gallons of water.

If we add [tex]x[/tex] gallons of water to the solution, the amount of hyrdrogen peroxide in the solution stays the same, but the volume of water increases to [tex]9.75+x[/tex] gallons, and the total volume increases to [tex]15+x[/tex] gallons.

To get a concentration of 8% in this diluted solution, we add [tex]x[/tex] gallons of water such that

[tex]\dfrac{5.25}{15+x} = 0.08[/tex]

Solve for [tex]x[/tex].

[tex]5.25 = 0.08 (15 + x)[/tex]

[tex]5.25 = 1.2 + 0.08x[/tex]

[tex]0.08x = 4.05[/tex]

[tex]x = 50.625[/tex]

To get the desired concentration, one must add 50.625 gallons of water, and one will end up with a total volume of 65.625 gallons of solution.

The solutions when y = 0 are x = -4.796 and x = 4.796

The function is given as:

[tex]y = (\frac{x + 5}{x + 1} \div \frac{(x + 3)(x - 2)}{(x -4)(x + 1)})- \frac{1}{x - 2}[/tex]

See attachment for the graph of the function

When the function is simplified, we have:

(x +3)(x -2) at the denominator of one of the terms

Set this factor to 0

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

Expand

x + 3 = 0 and x -2 = 0

Solve for x

x = -3 and x = 2

Hence, the vertical asymptotes are x = -3 and x = 2

The feature at x = -1 is a hole and, not a vertical asymptote.

This is so because the absolute value of -1 is less than the absolute values of the vertical asymptotes at x = -3 and x = 2

From the attached graph, we have:

x = -4.796 and x = 4.796 when y = 0

Hence, the solutions when y = 0 are x = -4.796 and x = 4.796

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The solution to the graph given is 7/16.

It should be noted that a graph is used to show the relationship between the variables illustrated.

Here, the successive approximation is used to solve equations.

This is done by the comparison to the sequence of the known quantities.

Here, the equation given is 4(-)x + 5 = 3^x + 4. solution to the graph given is 7/16. This is based on the graph given.

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Answer:

Step-by-step explanation:

Answer:

wouldn't it be 0.1

Step-by-step explanation:

Answer:

5x + 25

Step-by-step explanation:

2x+29+3x+4

Step 1: Arrange it:- 2x+3x+29-4

Step 2:- Add and Subtract the terms:- 5x + 25

HOPE IT HELPS!

Hey there!

EQUATION:
2x + 29 + 3x - 4

COMBINE the LIKE TERMS

(2x + 3x) + (29 - 4)

2x + 3x + 29 - 4

SIMPLIFY IT!

5x + 25

Therefore, your answer should be:

5x + 25

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

Step-by-step explanation:

Answer: can you show us the graph?

Step-by-step explanation:

Answer:

66 dollars

Step-by-step explanation:

15+6=22

15×2=30

15+22+30=66

Answer:

Tim had 15 dollars. Paul had 6 dollars more than Tim. Rick had double Tim’s money. How much did they have ALTOGETHER is 66 dollars.

Step-by-step explanation:

→ Is know :

→ Asked :

How much did they have ALTOGETHER ?

→ Solution :

[tex] \bf{x =Tim's \: \: money + Paul's \: \: money + Rick's \: \: money }[/tex]

[tex]\bf{x =15 + (15 + 6) + (2 \times 15) }[/tex]

[tex]\bf{x =15 + 21 + 30 }[/tex]

[tex]\bf{x =36 + 30 }[/tex]

[tex]\bf{x =66 \: \: dollars }[/tex]

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Answer: m∡B°=38,2°.

Step-by-step explanation:

a=3,  b=5,  c=7  ∡B°=?

[tex]b^2=a^2+c^2-2*a*ccosB^0\\2*a*c*cosB^0=a^2+c^2-b^2\\cosB^0=\frac{a^2+c^2-b^2}{2*a*c} \\cosB^0=\frac{3^2+7^2-5^2}{2*3*7} \\cosB^0=\frac{9+49-25}{2*3*7} \\cosB^0=\frac{33}{42} \\cosB^0=\frac{11}{14}\\[/tex]

m∡B°=arccos[tex](\frac{11}{14})[/tex]

m∡B°≈38,2°.

Good luck!

Answer: B, D, E

Step-by-step explanation:

Statement 1 cannot be true because f(1)<0.

Statement 2 might be true.

Statement 3 cannot be true because if f is continuous, then for some value between -1 and 0, f(x) is positive by the Intermediate Value Theorem.

Statement 4 might be true.

Statement 5 might be true

The solutions are given below:

1. 3y- 9 = 2x

2.  2/3.

3. y/x

4.  y = (2/3)x + 3

The equation of a line with one given point (x1, y1) is (y - y1) = m(x - x1). Here m is the slope of the line.

The complete question is:

On a coordinate plane, a line goes through (0, 3) and (x, y). A triangle has a rise of 2 and run of 3. A larger triangle has a rise of 5 and run of 7.

Use similar triangles to determine the equation of the line with a slope of 2/3 that passes through the point (0, 3).

What is the ratio of the rise to the run in the smaller triangle in the diagram?

What is the ratio of the rise to the run in the larger triangle in the diagram?

What is the equation of the line in slope-intercept form?

1. slope= 2/3

coordinates= (0, 3)

y-y1 = m(x-x1)

y-3 = 2/3(x-0)

y-3 = 2/3x

3y- 9 = 2x

2. The ratio of the rise to the run in the smaller triangle in the diagram

is y/x = 2/3

3. The ratio of the rise to the run in the larger triangle = y/x

4. The equation of the line in slope-intercept form is given by:

  y = (2/3)x + 3

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Absolutely, over result will match in part b and c

Geogebra tools are software which is used to study an absolute geometry with zero errors.

Since, Geogebra contains various tools, In part b we have drawn a square through polygon command. Its allows  to select the number of sides, so we select 4 cause square requires 4 equal sides.
Now, we very it in c part just by drawing a 4 connected lines which have 90° adjacent angles.
                    Here, by comparing their geometry it seems identical

Thus, the result, in part b and c matches for each other.

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The x- and y-coordinates of point C, which partitions the directed line segment from A to B into the ratio 3:10 is; (-2.6, 5.2)

The coordinate of the points are given as:

A(-4, 8)

B(2, -4)

Ratio of partition is given as; 3:10

Now, the point at the given ratio is calculated from the formula;

C = [(mx2 + nx1)/(m + n)], [(my2 + ny1)/(m + n)]

Thus;

C = [(3*2 + 10*-4)/(3 + 10)], [(3*-4 + 10*8)/(3 + 2)]

C = (-34/13, 68/13)

C = (-2.6, 5.2)

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Answer:

-2.6, 5.2

Step-by-step explanation:

Answer:

  C.  Ian rode less than 1 hour

Step-by-step explanation:

It never hurts to think about what the problem statement is telling you. Ian rode at a speed that would take him 18 miles in 1 hour.

Clearly, Ian would pass the 15-mile mark in a 1-hour ride before an hour had elapsed. If he only rode 15 miles, he rode less than 1 hour.

The actual time Ian rode is given by the relation between speed, time, and distance.

  time = distance/speed

  time = (15 mi)/(18 mi/h) = (15/18) h = 5/6 h

Ian's riding time was 5/6 of an hour, which is less than 1 hour.

Answer:

The independent variables in most cases is input variable. That is a value that does not depend on any other value and it can change independently.

Step-by-step explanation:

The answer is 1/2 .

In given question ,

Dalinda spins a spinner = 60 times.

                           blue = 30

The probability that the pointer will land on blue =   30 / 60  ⇒ 1/2

Therefore, the answer is 1/2 .

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I am unfortunately not too sure about this, I have not heard of a proportional equation before even after getting my degree, because an equation usually isn't proportional, only expressions are and there are usually 2 terms.

Here's my best attempt. The first equation isn't proportional since y is inversely proportional to the 7 in the denominator. The second is proportional, and the k constant is 10.

I cannot provide any further explanations.

Let me know if this was helpful!

Answer: Since y is inversely proportional to the 7 in the denominator, the first equation cannot be a proportional expression. The k constant is 10 and the second is proportional.

Step-by-step explanation:

Minimizing the sum of the squared deviations around the line is called Least square estimation.

It is given that the sum of squares is around the line.

Least squares estimations minimize the sum of squared deviations around the estimated regression function. It is between observed data, on the one hand, and their expected values on the other. This is called least squares estimation because it gives the least value for the sum of squared errors. Finding the best estimates of the coefficients is often called “fitting” the model to the data, or sometimes “learning” or “training” the model.

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Answer:

(x - 2)² + (y + 7)² = 64

(fourth option listed / option D)

Step-by-step explanation:

as you likely know, the equation of a circle (centered at origin) is x²+y²=r²

now, let's say we want to write this using the center (the origin), it could look like this:

(x - 0)² + (y - 0)² = r²

(the center is 0,0)

[we write this in parentheses when we are shifting the location of a point--similar to when we move a line on a graph]

We can use this for any center, and we write our circle equation as:

(x - h)² + (y - k)² = r²

(h, k) is the center

So, let's apply the information we know

our (h, k) is (2, -7)

so let's fill that in:

(x - h)² + (y - k)² = r²

(x - 2)² + (y - -7)² = r²          (simplify)

(x - 2)² + (y + 7)² = r²

now, we also know that our "r" (r is the radius) is 8, so let's fill that in too:

(x - 2)² + (y + 7)² = r²

(x - 2)² + (y + 7)² = 8²   (simplify)

(x - 2)² + (y + 7)² = 64

So, we have found the equation of our circle to be:

(x - 2)² + (y + 7)² = 64

hope this helps! (and hope this makes sense) have a lovely day :)

The value of x in the congruent triangles abc and dec is 1

The question implies that the triangles  abc and dec are congruent triangles.

The congruent sides are:

ab = de

bc = ce = 4

ac = cd = 5

The congruent side ab = de implies that:

4x - 1 = x + 2

Collect like terms

4x - x = 2 + 1

Evaluate the like terms

3x = 3

Divide through by 3

x = 1

Hence, the value of x is 1

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Complete question

Two triangles, abc and cde, share a common vertex c on a grid. in triangle abc, side ab is 4x - 1, side bc is 4, side ac is 5. in triangle cde, side cd is 5, side de is x + 2, side ce is 4. If Δabc ≅ Δdec, what is the value of x? a. x = 8 b. x = 5 c. x = 4 d. x = 1 e. x = 2

Hello,

Answer: We have f(x) = g(x) when x ≈ 1

(a) x = 1, is an approximate solution for f(x) = g(x).

Here, we have,

given that,

A graph of two functions is shown

f(x) and, g(x)

now, we have,

The graph has two functions, which are f(x) and g(x) and a graph.

In the graph, we can follow their intersections.

Those would be the parts of the line that would make the functions to have the same value.

The first intersection is really close to 1,

and second is very unclear, most likely beyond -2.5.

Since the highest number is 1 and the intersection is very close to 1,

we have to go with the approximate answer.

We have f(x) = g(x) when x ≈ 1.

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Switch the variable x and y with each other. Then the correct option is B.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = 3x – 10

Then the inverse function of the f(x) will be

Put y in place of f(x).

    x = 3y – 10

  3y = x + 10

    y = (x + 10) / 3

Switch the variable x and y with each other.

Then the correct option is B.

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The number of boys and girls assigned to each team is 6 and 15 respectively.

= 63/3

= 21 students

Number of girls = 5/7 × 63

= 315/7

Number of girls = 45 students

Number of boys = 63 - 45 = 18 students

If the three groups have equal composition of boys and girls, then,

Number of boys and girls in each group is 6 and 15 respectively.

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(a) i. See comment...

(a) ii. We have

[tex]\vec p = 6\,\vec\imath - 3\,\vec\jmath + 9\,\vec k[/tex]

and

[tex]\vec q = 3\,\vec\imath - 6\,\vec\jmath - 3\,\vec k[/tex]

(b) We can parameterize the line segment from P to Q by the vector function

[tex]\vec r(t) = (1-t) \vec p + t \vec q = (6-3t) \, \vec\imath + (-3-3t) \,\vec\jmath + (9-6t) \,\vec k[/tex]

with [tex]0\le t\le1[/tex]. The point R is located 1/3 of the way along this line segment, i.e. at [tex]t=\frac13[/tex], so its position vector is

[tex]\vec r\left(\dfrac13\right) = 5\,\vec\imath -4\,\vec\jmath + 7\,\vec k[/tex]

and hence its coordinates are [tex]\boxed{(5,-4,7)}[/tex].

Answer:

radius = 5

Step-by-step explanation:

Since the line is a tangent, that means the PT and OP are perpendicular (they make a right angle) Sooo, the triangle is a right triangle. Use Pythagorean Theorem to calculate or Pythagorean Triples for a shortcut (5, 12, 13)

r^2 + 12^2 = 13^2

r^2 + 144 = 169

Subtract 144

r^2 = 25

Squareroot both sides.

sqrt(r^2) = sqrt25

r = 5

The radius is 5.

Answer:

The slope formula is used to find the slope of a line that joins two points (x₁, y₁) and (x₂, y₂). Using this formula, the slope of the line is, m = (y₂ - y₁) / (x₂ - x₁). We can use the same formula to find the slope of a line from its graph also.

Answer:

∠C and ∠F are right angles

Step-by-step explanation:

To prove that two triangles are congruent using HL, one must have:

For this problem, there are two sides of the triangle already congruent:  one could be the hypotenuse (if the right angle were across from it), and the other congruent side could be a leg.  So, if we can prove either that angles C & F are right angles, or that angles A & D are right angles, that would be enough to use HL congruence.

Hence, from the answer choices provided, proving that angle C and angle F are both right angles would be sufficient to prove the triangles are congruent via HL congruence.

Side note:  Proving angles B and E would not be enough to use HL congruence, because the hypotenuse is always across from the right angle.  So, if angle B were a right angle, it would mean that side AC was the hypotenuse (which hadn't yet been proven or stated to be congruent).

While not enough to prove triangle congruence via HL, if angle B and E were congruent at all (right angles or not), it would be enough to prove that the triangles were congruent by SAS (side-angle-side) because it would have proven that two sides and the included angle were congruent.