What is the rule for the reflection

x/2 + 10 = 35 - 2x

x/2 + 2x = 35 - 10

5x/2 = 25

5x = 25.2

5x = 50

x = 50/5

x = 10

The number is 10

Let's take it step by step to find the number for the given situation:
Step 1: Define the variable.
Let's denote the number we are trying to find as \( x \).
Step 2: Set up the equation based on the given information.
The problem statement says "Half a number increased by 10 is equal to 35 less than twice the number." This gives us the equation:
\[ \frac{1}{2}x + 10 = 2x - 35 \]
Step 3: Solve the equation.
Now we'll solve for \( x \). To do this, we need to get all terms involving \( x \) on one side and the constant terms on the other. Start by subtracting \( \frac{1}{2}x \) from both sides to get rid of the \( x \) term on the left-hand side:
\[ 10 = \frac{3}{2}x - 35 \]
Now, add 35 to both sides to isolate the \( x \)-related term on the right-hand side:
\[ 10 + 35 = \frac{3}{2}x \]
\[ 45 = \frac{3}{2}x \]
Next, to solve for \( x \), multiply both sides by \( \frac{2}{3} \) to cancel out the fraction:
\[ \frac{2}{3} \cdot 45 = x \]
\[ x = 30 \]
Step 4: Verify the solution.
Plugging the value of \( x \) back into the original equation to check:
\[ \frac{1}{2} \cdot 30 + 10 = 2 \cdot 30 - 35 \]
\[ 15 + 10 = 60 - 35 \]
\[ 25 = 25 \]
The equation is true, confirming that the solution \( x = 30 \) is correct.
Therefore, the number we were trying to find is 30.

Answer:

4

Step-by-step explanation:

Let's call the width W and the length L.

We know the width is 3 less than the length, so:

W = L - 3

And we know the area is 28, so:

28 = WL

If we solve for L in the first equation:

L = W + 3

And substitute into the second equation:

28 = W (W + 3)

28 = W² + 3W

0 = W² + 3W - 28

0 = (W + 7) (W - 4)

W = -7, 4

Since W can't be negative, W = 4 units.

The width, in units, of the rectangle, if the area of the rectangle is 28 units, is  4 units.

The measurement that expresses the size of a region on a plane or curved surface is called an area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Given:

The width of a rectangle is 3 units less than the length. The area of the rectangle is 28 units,

Write the equation as shown below,

b = l - 3   (Here, l is the length and b is the width)

l × b = 28

Solve the above equations,

l = 7 units and b = 7 - 3 = 4 units

Therefore, the width, in units, of the rectangle, if the area of the rectangle is 28 units, is  4 units.

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Answer:

The values of x are x= 2i and x= -2i

Step-by-step explanation:

We need to solve the equation:

2x^2 + 8 =0

Taking 2 common

2(x^2 +4) =0

Dividing both sides by 2

x^2+4 =0

Adding -4 on both sides

x^2 +4 -4 = 0-4

x^2 = -4

Taking square root on both sides we get

√x^2 = √-4

we know √4 = 2 and √-1 = i so answer is:

x = ± 2i

The values of x are x= 2i and x= -2i

The graph is shown in figure attached.

To solve 2x² + 8 = 0 by graphing, one plots the corresponding quadratic function f(x) = 2x² - 8, which is a parabola that opens upwards. The equation has no real solutions as the function does not cross the x-axis, indicating that the original quadratic equation has no real roots.

To solve the quadratic equation 2x² + 8 = 0 by graphing the related function, we first need to rewrite the equation in the standard form of a quadratic function, which is f(x) = ax² + bx + c. In this case, the equation becomes f(x) = 2x² + 0x - 8.

The roots of the equation are the values of x where the function crosses the x-axis. To find these, we set the function equal to zero and solve for x. Subtracting 8 from both sides gives us 2x² = -8. Dividing by 2, we get x² = -4. Taking the square root of both sides, we see that x could be either positive or negative square root of -4, which does not have a real solution since you can't have a real number whose square is negative. Therefore, the graph of the function will not cross the x-axis and there are no real roots to this equation.

If we were to graph this function, we would plot the quadratic curve and notice that it is a parabola opening upwards because the coefficient of x² is positive. However, as we have established there are no real solutions, this would be confirmed by the fact that the vertex of the parabola is above the x-axis.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}2x-5y=9&\text{multipy both sides by 4}\\3x+4y=2&\text{multiply both sides by 5}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}8x-20y=36\\15x+20y=10\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad23x=46\qquad\text{divide both sides by 23}\\.\qquad x=2\\\\\text{put it to the second equation}\\\\3(2)+4y=2\\6+4y=2\qquad\text{subtract 6 from both sides}\\4y=-4\qquad\text{divide both sides by 4}\\y=-1[/tex]

D is the correct graph follows into whatever

Answer: OPTION C.

Step-by-step explanation:

Given a function f(x), the range of the inverse of f(x) will be the domain of the function f(x) and the range of the domain of f(x) will be the range of the inverse function.

For example, if the point (2,1) belongs to f(x), then the point (1,2) belongs to the inverse of f(x).

Observe that in the graph of the function f(x) the point (-3,1) belongs to the function, then the point (1,-3) must belong to the inverse function.

Therefore, you need to search the option that shown the graph wich contains the point (1,-3).

Observe that the Domain f(x) is (-∞,0) then the range of the inverse function must be (-∞,0).

This is the graph of the option C.

Answer:

(3x^2-5x-5)/(x^2+x) <--- answer  

Step-by-step explanation:

3x/(x+1) - 5/x = (3x^2 - 5(x+1) )/[ x(x+1) ]  

= (3x^2 - 5x - 5)/(x^2 + x)

The difference between the rational expressions 3x+1/x and 5/x is 3x - 4/x.

The difference between these two rational expressions will be obtained by subtracting the second expression from the first. To do this, we first need to simplify the expressions wherever possible. The first expression, 3x + 1/x, remains as it is. The second expression, 5/x, is a simple fraction and can't be simplified any further either.

Subtracting the second from the first, you get (3x + 1/x) - (5/x) which simplifies to 3x - 4/x. The difference between these two rational expressions is hence 3x - 4/x.

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P: padre de Luis

h: hijo

P=32+h

P+h=78

Método: sustitución

*p + h = 78

(32 + h) + h = 78

32 + h + h = 78

2h + 32 = 78

2h = 78 - 32

2h = 46

[tex]h = \frac{46}{2} \\ \\ h = 23[/tex]

El hijo tiene 23 años

EL padre tiene 55 años

P = 32 + h

P = 32 + 23

P = 55

Answer:

It is correct.

Step-by-step explanation:

Orange to Apple juice = 3:1.

Work out the 'multiplier':

3 + 1 = 4.

3 parts are orange so we need 3 * the multiplier = 3*4 = 12  litres.

Answer: None of them are equal

Step-by-step explanation:

Answer: I hope this helps with any confusion

A) x + 4

Step-by-step explanation:

x(x + 9) + 20

x + 5

x2 + 9x + 20

x + 5

(x + 4)(x + 5)

x + 5

x + 4

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}m+4n=8&(1)\\m=n-2&(2)\end{array}\right\\\\\text{substitute (2) to (1):}\\\\n-2+4n=8\qquad\text{add 2 to both sides}\\5n=10\qquad\text{divide both sides by 5}\\n=2\\\\\text{put the value of}\ n\ \text{to (2):}\\\\m=2-2\\m=0[/tex]

100,000

For each possible combination digit, there are 10 options: 0-9. Multiply ten by itself five times (for five digits) to find the number of combinations. This gives you 100,000 possible combinations.

Answer:

a) [tex]a_n = 50 (0.52) ^ {n-1}[/tex]

b) [tex]a_6 = 50 (0.52) ^ 5 = 1.90\ cm[/tex]

Step-by-step explanation:

If each curved path has 52% of the previous height this means that [tex]\frac{a_{n+1}}{a_n} = 0.52[/tex]

Then the radius of convergence is 0.52 and this is a geometric series.

The geometric series have the form:

[tex]a_n = a_1 (r) ^ {n-1}[/tex]

Where

[tex]a_1[/tex] is the first term of the series and r is the radius of convergence.

In this problem

[tex]a_1 = 0.5[/tex] meters = 50 cm

[tex]r = 0.52[/tex]

a) Then the rule for the sequence is:

[tex]a_n = 50 (0.52) ^ {n-1}[/tex]

b) we must calculate [tex]a_6[/tex]

[tex]a_6 = 50 (0.52) ^ 6-1\\\\a_6 = 50 (0.52) ^ 5 = 1.90\ cm[/tex]

Answer:

[tex] \frac{4}{5} \div \frac{2}{3} = n[/tex]

[tex] \frac{4}{5} = n \times \frac{2}{3} [/tex]

[tex] \frac{3}{2} \div \frac{4}{5} = n [/tex]

[tex] \frac{4}{5} = n \times \frac{2}{3} [/tex]

[tex] \frac{2}{3} \times n = \frac{4}{5} [/tex]

Part A: Scatter plot with best-fit line attached. You'll find the line to have equation (approximately)

[tex]y=51.34+3.98x[/tex]

The positive slope suggests that test scores and study time are directly are proportional.

Part B: Same as in a previous question you had posted. Pick two points on the provided line and compute the slope as best you can. For example, I might pick (2, 30) and (4, 40), which gives a slope of

[tex]\dfrac{40-30}{4-2}=5[/tex]

and assuming the line passes through (2, 30) exactly, it would have equation

[tex]y-2=5(x-30)\implies y=5x-148[/tex]

Answer:

Sorry, all I know is that after he got the 7 blocks of spruce he will have $3,600  left over. I don't know how many blocks he can buy with that.

Step-by-step explanation:

Answer:

Ted can buy 8 blocks of mahogany.

Step-by-step explanation:

Total amount Ted wishes to spend this month is $5000.

Mahogany costs $450 per block, and he has already bought 7 blocks of spruce at $200 each.

So, money spent on spruce = [tex]7\times200=1400[/tex] dollars

Money left after buying spruce = [tex]5000-1400=3600[/tex] dollars

Now as $450 will be spent on buying 1 block of mahogany.

So, $3600 will be spent on buying [tex]\frac{3600}{450}= 8[/tex] blocks of mahogany.

The answer is 8 blocks.

The correct answer is D, since if you simplify the equation 11 + 4 < -8 you get      x < -2. Since -2 is greater than x, the arrow would need to point to the left signifying that it is a lesser value.

Answer:

x = 3

Step-by-step explanation:

You can multiply by 2x^2, then subtract x

2x = x +3 . . . . . multiply by 2x^2

x = 3 . . . . . . . . . subtract x

___

The attached graph shows the difference between the left side of the equation and the right side. When that difference is zero, the value of x is a solution. There is one solution at x=3. (x=0 is not in the domain of the relation. There is a vertical asymptote there.)

Answer:

0.04

Step-by-step explanation:

Looking at the chart we can see that there are 0, 1, 2 and 3 defective parts in one column while the other column says the probability of each happening. Look at the probability of there being 2 defective parts and that will be your answer.

Answer:

0.04

Next answer is 0.15.

Step-by-step explanation:

Answer:

P = 4s

Step-by-step explanation:

We see that on every point on the line, the perimeter is 4 times the side length. For example, when the [tex]P[/tex] is 24, [tex]s[/tex] is 6. When [tex]P[/tex] is 20, [tex]s[/tex] is 5. So our answer is [tex]\boxed{P = 4s}[/tex]

Answer:

1 = 60, 4 = 30, 5 = 30, 6 = 150, 7 = 110, 8 = 30, 9 = 60, 10 = 90.  2 = 47.5, 3 = 132.5

Step-by-step explanation:

Starting with angle 5:  knowing that arc BC = 30 and angle 5 is a central angle, it has an angle measure equal to the measure of the arc it intercepts.

Angle 6 is supplementary to angle 5, so 180 - 30 = 150.

Angle 9 = 60.  Ch is a diameter, so that means it splits the circle into 2 congruent halves, each measuring 180 degrees around the outside.  So if arcs AB and CB both measure 30, then arc AH measures 180 - 30 - 30 = 120.  By definition, the measure of angle 9 is half the measure of the arc it intercepts.

Angles 4 and 8 = 30 each.  Because you have AH parallel to CG, then CH is a transversal, creating a pair of alternate interior angles that are congruent.  Those angles are 4 and 8.  We find 8 to be an inscribed angle, cutting off arc ABC which measures 60 degrees.  An inscribed angle is half the measure of the arc it intercepts. Because angle 4 measures 30 degrees and is inscribed, the arc it cuts off, arc GH, measures twice the angle cutting it.  So arc GH measures 60.

Again, since CH is a diameter, then the semicircle CDEG measures 180.  Since we know from the description that arcs CD and DE are congruent, then arc CD + arc DE + arc EG (given as 50) + arc GH = 180.  Since arcs CD and DE are congruent, lets just call them "x" and we have two of them.  That gives us that 2x + 50 + 60 = 180.  x = 35.  Angle 1 is equal to half of the sum of its intercepted arcs ( 35 + 35 + 50) which is 60.

Angle COE intercepts arc CDE, and is central, so angle COE measures 70, and since angle 7 is supplemetray to angle COE, then angle 7 measures 180 - 70 = 110.

Angle 10 by definition is a right angle (refer to the theorem regarding a tangent line to a point on a circle).

Angle 2 is half of the sum of 35 (arc CD) and 60 (arc GH), so angle 2 measures 47.5 and that means that angle 3, supplementary to angle 2, measures 180 - 47.5 = 132.5.  I think those are all correct.  The only one I'm unsure of is angle 2.  

Answer:

Final answer is [tex](3x-y)(x+y)[/tex].

Step-by-step explanation:

Given expression is [tex]3x^2+2xy-y^2[/tex].

Now we need to factor the given expression [tex]3x^2+2xy-y^2[/tex] completely. Let's use factor by grouping method.

[tex]3x^2+2xy-y^2[/tex]

[tex]=3x^2+3xy-xy-y^2[/tex]

[tex]=3x(x+y)-y(x+y)[/tex]

[tex]=(3x-y)(x+y)[/tex]

Hence final answer is [tex](3x-y)(x+y)[/tex].

(3x−y)(x+y) is the answer but did you mean to put 3x^2 + 2xy - y^2 as your answer?

Answer:

Step-by-step explanation:

if i had to guess i would say a

ANSWER

The midpoint is a) (m,n)

EXPLANATION

The point O has coordinate (0,0) and the point A has coordinate (2m,2n)

The x-coordinate of the midpoint is

[tex]x = \frac{0 + 2m}{2} [/tex]

[tex]x = \frac{2m}{2} [/tex]

[tex]x = m[/tex]

Also,

[tex]y = \frac{0 + 2n}{2} [/tex]

[tex]y = \frac{ 2n}{2} [/tex]

[tex]y = n[/tex]

The answer is A

Answer:

[tex]p=-9[/tex]

Step-by-step explanation:

We want to solve the linear equation;

[tex]7p=-63[/tex]

We divide both sides of the given linear equation by 7 to obtain;

[tex]\frac{7p}{7}=\frac{-63}{7}[/tex]

This implies that;

[tex]p=\frac{-63}{7}[/tex]

[tex]p=\frac{-9\times7}{7}[/tex]

We now cancel out the common factors to get:

[tex]p=-9[/tex]

In this figure, ∠a and ∠b are supplementary. The answer is OPTION C.

A. Complementary angles are two angles whose sum is equal to 90 degrees. Since no information is given about the angles Za and Zb in the figure, we cannot determine if they are complementary. Therefore, this answer choice is not supported by the given information.

B. Equal angles have the same measure. Again, no information is given about the angles Za and Zb, so we cannot determine if they are equal. Thus, this answer choice is not supported by the given information.

C. Supplementary angles are two angles whose sum is equal to 180 degrees. Since the figure does not provide any specific angle measurements, we cannot directly determine if Za and Zb are supplementary. However, this answer choice is a possibility as supplementary angles are commonly encountered in geometry.

D. Vertical angles are a pair of non-adjacent angles formed by intersecting lines. Without any information about the lines or angles in the figure, we cannot determine if Za and Zb are vertical angles. Therefore, this answer choice is not supported by the given information.

In conclusion, the most accurate answer choice based on the given information is C. supplementary. However, without additional context or measurements, we cannot definitively determine the relationship between Za and Zb.

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According to the given figure, ∠a and ∠b are complementary angles.

The correct answer to the given question is option A.

These two could be any pair of angles and the relationship between them depends on their relative positions. If ∠a and ∠b are complementary, that means that the sum of their angle measures is 90 degrees.

This usually happens when two angles together form a right angle. On the other hand, if ∠a and ∠b are equal, that means that they have the same angle measure.

This usually happens when the angles are opposite each other in a shape with symmetry, such as an isosceles triangle or a rectangle. Should ∠a and ∠b be supplementary, it means that the sum of their angle measures is 180 degrees.

This usually happens when two angles form a straight line or the angles on a straight line sum to 180 degrees.

Finally, if ∠a and ∠b are vertical, that means they are opposite each other when two lines intersect.

Hence, ∠a and ∠b are complementary angles.

Therefore, the correct answer to the given question is option A.

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A)x+4x = Juice and water

x = Water

4.00 is total juice relative to water

  +

1.00 is total water

B) 4 liters

(1 liter)+4(1 liter) = Total

1 + 4 = 5

Answer:

Width=5

Step-by-step explanation:

Answer:

the answer is: 6z^3

Step-by-step explanation:

We need to solve this equation:

[tex]\sqrt{36z^6}[/tex]

We know that 6X6 = 36

and √ = 1/2

Solving:

[tex]=\sqrt{6*6*z*z*z*z*z*z}\\We\,\,know\,\,6X6=6^2\,\, and \,\,z*z=z^2\\=\sqrt{6^2*z^2*z^2*z^2} \\=(6^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}*(z^2)^{1/2}\\=6*z*z*z\\=6z^3[/tex]

So, the answer is: 6z^3

Answer:

Step-by-step explanation:

D

area of rectangle=25*12=300

6 % of area=300*6 %=18

area of D=1/2 *6*6=18

so  D

The question about the shape representing 6% of a rectangle requires more information about the dimensions or sizes involved to be answered accurately in the context of Mathematics.

The question regarding which shape represents 6% of the rectangle pertains to understanding fractions or percentages of shapes and is related to the concepts of area and proportion within the field of Mathematics. To answer this, one would need more information about the dimensions of the rectangle or the sizes of the shapes involved.

The reference information provided seems unrelated to calculating percentages of a rectangle, and thus it is not possible to give a precise answer regarding the shape without additional context or clarification.

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It would be 93,000 because it’s closed to 93,000 than 94,000

heya dear

93000.........

Answer:

c = [tex]\frac{27}{40}[/tex]

Step-by-step explanation:

To eliminate the fractions, multiply all terms by the lowest common multiple of 8 and 5

The lowest common multiple of 8 and 5 is 40

5 + 40c = 32 ( subtract 5 from both sides )

40c = 27 ( divide both sides by 40 )

c = [tex]\frac{27}{40}[/tex]