3(2x-4)- 4x+7<9 solve fr x

Answer: OPTION D.

Step-by-step explanation:

Rectangles have four right angles (angles of 90 degrees).

The point of intersection of the diagonals divides each one of them into two equal parts.

Knowing this, we can conclude that:

[tex]m\angle c=m\angle b=55\°[/tex]

(Observe the figure)

Therefore, since the sum of the interior angles of a triangle is 180 degrees, we can find the value of "x":

[tex]x+m\angle c+m\angle b=180\°\\x=180\°-55\°-55\°\\x=70\°[/tex]

Answer:

70 degrees

Step-by-step explanation:

55*2= 110

180-110=70

Answer:

        [tex]P(t)=\frac{R(t)}{A(t)} =\frac{5000(1.111)^t}{200(1.1)^t}[/tex]

         [tex]P(t)=25(1.01)^t[/tex]

Explanation:

I will rewrite the question removing the errors, for better understanding:

You must depart from the equation that relates revenue (R), price (P), and number of items sold.

There you see that you can solve for P(t), which is the unknown function:

Substituting you get:

Divide the coefficients (5,000 / 200) and apply the power properties for the quotients of powers with the same power:

Answer:

x=6.6 cm

Step-by-step explanation:

The angle force at the point where the tangent touches the circle is 90° hence the  triangle is a right angle triangle . We can apply the Pythagorean relationship in this case

Given the hypotenuse as x+ 8.45  and the base as x and height as 13.5 then;

a²+b²=c²  .................where a=x  , b= 13.5 and c x+8.45

x² +13.5²= (x+8.45)²

x²+182.25=x²+8.45x+8.45x+71.4025

x²+182.25=x²+16.90x+71.4025-----------------collect like terms

x²-x²+ 182.25-71.4025=16.90x

110.8475=16.90x-------------------divide by 16.90 to remain with x

110.8475/16.90 = x

x=6.5590

x= 6.6 cm

The function f(x) = 86(1.29)x represents a weekly weed growth rate of 29%. To convert this to a daily growth rate, we use the formula (1+0.29)^(1/7) - 1, which equates to an approximate daily growth rate of 4%. Therefore, the function can be rewritten as: f(x) = 86(1.04)x.

Your question involves the function that represents the weed growth in a garden: f(x) = 86(1.29)x. Here, 1.29 refers to the growth rate of 29% per week. However, you want to rewrite the function to show how quickly the weeds grow each day.

To get a daily growth rate from a weekly one, we use the formula: daily growth rate = (1 + weekly growth rate)^(1/7) - 1. For the given function, this translates to a daily growth rate of (1 + 0.29)^(1/7) - 1, which is approximately 0.04, or 4%. Therefore, the function rewrite will be:

This function shows that the weeds grow at approximately 4% each day. So, the correct answer is Option B: f(x) = 86(1.04)x; grows approximately at a rate of 4% daily.

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To find the daily growth rate of the weeds, we divide the weekly growth rate by 7. The correct function is f(x) = 86(1.04)x, which represents a daily growth rate of approximately 0.4%.

To find how quickly the weeds grow each day, we need to convert the rate of growth from weekly to daily.

Since there are 7 days in a week, we can divide the weekly growth rate by 7 to get the daily growth rate.

In this case, the function f(x) = 86(1.29)x represents the weekly weed growth, so to find the daily growth rate, we use the function f(x) = 86(1.29/7)x.

Simplifying this expression, we get f(x) = 86(1.04)x.

Therefore, the correct answer is A. f(x) = 86(1.04)x; it grows approximately at a rate of 0.4% daily.

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Answer:

[tex]\text{D. }\left[\begin{array}{cc}0&4\\-6&1\\3&-4\end{array}\right][/tex]

Step-by-step explanation:

It would be helpful to know the numbers of rows and columns, so we don't have to guess.

Any number of on-line calculators and/or graphing calculators can multiply these matrices for you. Excel and other spreadsheets can do this, too. Forming the 6 sums of 2 products is tedious to do by hand.

For example, the term in the product matrix at row 1 column 2 is the sum of products of the numbers in row 1 of the first matrix and column 2 of the second matrix:

  4·1 + 0·1 = 4

_____

The attachment shows the matrix multiplication on a TI-84 calculator.

Vectors can be multiplied by scalars, where each component of the vector is multiplied by the scalar. In the student's question, direct multiplication isn't possible due to different number of components in both vectors. However, we can partially apply the concept to illustrate vector and scalar multiplication.

The question being asked here is about multiplying vectors within the subject of Mathematics. It's important to note that vectors can be multiplied by scalars, and each component of the vector is multiplied by the scalar. In this question, it seems there might be a typo because the two vectors have a different number of components and cannot be multiplied directly.

However, multiplication of vectors by scalars does not involve reversing signs or changing magnitude based on whether the scalar is negative or positive. If Vector A is multiplied by a scalar c, all components of Vector A are simply multiplied by c.

So, applying this concept to part of the vectors in the question, we would get [0, 4, -3] when [4, 0, -1] is multiplied by the scalar 0 and 1 respectively.

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Answer:

  a. Using multiplication and addition to check the digits, it is invalid because the total is 51 and does not end in a 0

Step-by-step explanation:

The sum of alternate digits is multiplied by 3. Those digits are ...

 0 3 5 0 1 1 . . . . sum of 10

The sum of remaining alternate digits is added to that.

  7 8 2 0 3 1 . . . . sum of 21

The result of the arithmetic ...

  mod(3×10 + 21, 10) = 1 . . . . . should be zero for valid GTIN-12 UPC code

Answer: Option d

They are opposites and parallel.

Step-by-step explanation:

Although they have the same magnitude, one can not say that a and b are equal because they have opposite directions.

If we know that both vectors have opposite directions then necessarily a and b must be parallel.

So what we know about a and b is that they are parallel and opposite.

The correct answer is the option d

Answer:

guy above is right

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. The number of candies in the machine is the product of the number of pounds of candy and the number of candies in a pound:

  (15 lbs)(180 candies/lb) = 2700 candies

__

2. c(0) = 2700; c(n) = c(n-1) -7 . . . . the new number of candies is 7 fewer than after the previous customer. After no customers, the number is the original 2700 candies.

__

3. As the recursive formula tells us, the initial number of candies is 2700, and the number decreases at the rate of 7 per customer. The number remaining after n customers is ...

  c(n) = 2700 -7n

__

4. Evaluating the above formula for n=1, 2, 3, we get ...

  c(1) = 2700 -7 = 2693 . . . . candies remaining after 1 customer

  c(2) = 2700 -7·2 = 2686 . . . 2 customers

  c(3) = 2700 -7·3 = 2679 . . . 3 customers

ANSWER

[tex](9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729} [/tex]

EXPLANATION

The given expression is

[tex](9 {c}^{ - 9} )^{ - 3} [/tex]

Recall that:

[tex] ({a}^{m} )^{n} = {a}^{mn} [/tex]

We use the law of exponents to get

[tex](9 {c}^{ - 9} )^{ - 3} = 9^{ - 3} {c}^{ - 9 \times - 3} [/tex]

Let us multiply in the exponents to get:

[tex](9 {c}^{ - 9} )^{ - 3} = 9^{ - 3} {c}^{ 27} [/tex]

Recall again that:

[tex] {a}^{ - m} = \frac{1}{ {a}^{m} } [/tex]

This implies that:

[tex](9 {c}^{ - 9} )^{ - 3} = \frac{1}{ {9}^{ 3} } \times {c}^{ 27} [/tex]

We expand the power to get:

[tex](9 {c}^{ - 9} )^{ - 3} = \frac{1}{9 \times 9 \times 9} \times {c}^{ 27}[/tex]

[tex](9 {c}^{ - 9} )^{ - 3}=\frac{1}{729} \times {c}^{ 27} [/tex]

We multiply out to get:

[tex](9 {c}^{ - 9} )^{ - 3}=\frac{{c}^{ 27} }{729} [/tex]

Answer:

Step-by-step explanation: the answer is b

Answer:

24 hours.

Step-by-step explanation:

This is one of those problems where the easiest way to do is just to reason it out without trying to devise a formula.

Call the water in the basement = w

Therefore w/2 = 4*x where x is the rate of the pump. The statement means that 1/2 the water in the basement is pumped out by x in 4 hours.

Now x and y work together. They (together ) pump out the rest of the water which is also w/2

w/2 = 3x + 3y              Now you can equate the two values for w/2

4x = 3x + 3y                Subtract 3x from both sides.

4x-3x = 3x-3x + 3y

x = 3y

Now you have to be very careful in interpreting what you found. It takes pump y three times as long to do anything as it does x.

So here's the reasoning part.

x by itself will empty the basement in 8 hours. It takes x four hours to get 1/2 the water out.

It will take pump y 3 times as long to pump out that basement. 3*8 = 24 hours

Answer:

Step-by-step explanation:

A cross section is the intersection of a cut plane with the object of interest. In a classroom setting, we often try to do the cross sectioning mentally or with diagrams, rather than physically cutting anything. Sometimes, there is no substitute for actually performing the cut to see what the cross section looks like.

For certain samples that don't take kindly to cutting, we sometimes encase them in a block of material that helps them hold their shape during the process. Sometimes the "cutting" is performed by grinding away the portion of the material on one side of the cut plane.

Answer: Place 3 points on 2 or 3 edges or faces.

Connect the points to form a triangle.

Extend the triangle to form a plane.

Determine where the plane intersects the edges of the solid.

Step-by-step explanation:

Answer:

8 inches

Step-by-step explanation:

Area (A) of a triangle = [tex]\frac{1}{2}[/tex] × base (b) × height (h)

72 square inches = [tex]\frac{1}{2}[/tex] × 18 × h

9h = 72

h = 8 inches

Follow below steps:

The area of a triangle: A = 1/2 * base * height. Given area = 72 sq in and base = 18 in, we can calculate the height:

72 = 1/2 * 18 * height

height = 8 inches

Answer: Option 'c' is correct.

Step-by-step explanation:

Since we have given that

If a transversal intersects two parallel lines, then _____ angles are supplementary.

Since the sum of interior angle on the same side is supplementary.

Supplementary angles are those angles whose sum is 180°.

Hence, Option 'c' is correct.

If a transversal intersects two parallel lines, then alternate interior angles are supplementary.

When a transversal intersects two parallel lines, alternate interior angles are formed. Alternate interior angles are pairs of nonadjacent interior angles located on opposite sides of the transversal and between parallel lines.

These angles have equal measures and are supplementary, meaning they add up to 180 degrees. This property holds true for any pair of parallel lines intersected by a transversal, providing a relationship between the angles that helps in solving geometric problems and proofs.

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Answer:

x^2 + 7x - 3 = 0

Step-by-step explanation:

I think you meant "width of the frame" from outside of frame to outside of mirror.

Let x represent the width of the frame.

Area of mirror is (3 ft)(4 ft) = 12 ft^2.  Total area of mirror and frame is 15 ft^2.  The 3 ft^2 difference is the area of the frame.

But you were asked to find a quadratic equation that would give you the "width" of the frame.  

The "new" width would be 3 + x and the "new" height would be 4 + x.

Then the area of the mirror and frame together would be

A = (3 + x)(4 + x) = 15 ft^2, or

      12 + 7x + x^2 = 15 ft^2, or

x^2 + 7x - 3 = 0.  This is the desired quadratic equation.

When answer choices are given, please share them when you post a question.  Thank you.

Answer: Graph D

Step-by-step explanation:

in slope intercept form, the equation is y</= 1/2x-6

Since it's </=, the line is solid instead of dashed

The graph that matches the inequality is:

                         Graph D

We are given a inequality as:

[tex]y+4\leq \dfrac{1}{2}x-2[/tex]

i.e. it could also be represented in the form:

[tex]y\leq \dfrac{1}{2}x-2-4\\\\i.e.\\\\y\leq \dfrac{1}{2}x-6[/tex]

The graph of this inequality is a straight solid line ( since the inequality is not strict i.e. it is a inequality with a equality sign) that passes through (0,-6) and (12,0) .It also passes through (4,-4) and the shaded region is away from the origin.

Hence, the graph which satisfies all the above property is:

                           Graph D

For this case we discard options A and B, since by definition, the graph does not correspond to the function of the Neperian logarithm.

We tested option C:

[tex]y = e ^ x[/tex]

Doing [tex]x = 0[/tex]we have:

[tex]y = e ^ 0[/tex]

Every number raised to zero power is 1.

So, we have:

[tex]y = 1[/tex]

We have the point (0,1)

If we try option D:

[tex]y = e ^ x + 1[/tex]

Doing x = 0 we have:

[tex]y = e ^ 0 + 1\\y = 1 + 1\\y = 2[/tex]

We have the point (0,2)

So, we note that the correct option is option C

ANswer:

Option C

Answer: Third option.

Step-by-step explanation:

Observe that the graph tends to zero when [tex]x<0[/tex] and "y" tends to infinite when [tex]x>0[/tex]

The function [tex]y=lnx[/tex] is not defined for values of "x" less than zero, therefore the equations of the options 1 and 2 do not represent the graph attached.

Observe that the function cuts the y-axis at [tex]y=1[/tex], while the function [tex]y=e^x+1[/tex] cuts the y-axis at [tex]y=2[/tex], therefore the equation of the last option does not represent that graph.

Finally, the equation that represents the graph is:

[tex]y=e^x[/tex]

Answer:

  7 days

Step-by-step explanation:

We assume that "by day 4" means "at the end of day 3." Since Curtis had run 9 miles in 3 days, his average rate is 9/3 = 3 miles per day.

It will take Curtis ...

  (21 mi)/(3 mi/day) = 7 days

to run 21 miles at that rate.

_____

Comment on the question

There is nothing in the problem statement to suggest that the number of miles run each day is the same. A different assumption than the one we have made will give a different answer.

Answer:

  9 1/16 in

Step-by-step explanation:

When chords cross, the distances from their point of intersection to the circle have the same product for each chord. For the 9-in chord, those two distances are 4.5 inches. For the diameter, the distances are 4 in and (d-4) in, where d is the diameter of the circle. Then ...

  4.5^2 = 4(d -4)

  d = 4.5^2/4+4 = 9 1/16 . . . . inches

The diameter is 9 1/16 inches.

_____

Comment on the diagram

The fact that the 9-inch chord looks very much like a diameter tells you the actual diameter won't be much different than that. These figures are not always drawn to scale, and are sometimes misleading. However, if the actual diameter were in the neighborhood of 16 inches, the perpendicular bisector shown would need to be about 1.4 inches instead of 4 inches.

for two figures to be proportional, their corresponding pair of sides must retain a proportion, regardless of rotation or translation of the figure.

so if we simply verify that all corresponding pairs of sides are proportional under transformation, if they are, then the figures are similar.

Answer:

The correct option is C. Verify corresponding pairs of sides are proportional by dilation

Step-by-step explanation:

The scale factor is the ratio between the dimensions in two similar figures. The term "similar figures" refers to figures that have the same shape but different sizes.

So, a dilation is a transformation created by a scale factor.

That is, a dilation that is smaller or larger than the original figure can be created.

To obtain a measure of the large figure and have the value of the small figure, this value is multiplied by the scale factor.

To obtain a measure of the small figure and the value of the large figure, this value is divided by the scale factor.

In other words, the scale factor is the radius that determines the proportional relationship between the sides of similar figures. In order for the pairs of sides to be proportional to each other, they must have the same scale factor. That is, similar figures have congruent angles (Dilation keeps the measure of the corresponding angles are equal) and sides with the same scale factor.

For example, a scale factor of two means that each side of the larger figure is exactly twice as large as the corresponding side in the smaller figure.

Given the above, the correct option is C. Verify corresponding pairs of sides are proportional by dilation

For this case we have by definition that the volume of a cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

r: It's the radio

h: It's the height

We have as data that:

[tex]V = 324 \pi\\r = 12[/tex]

Substituting:

[tex]324 \pi = \pi * (12) ^ 2 * h[/tex]

We cleared h:

[tex]324 \pi = \pi * 144 * h\\324 = 144 * h\\h = \frac {324} {144}\\h = 2.25[/tex]

Thus, the height of the cylinder is 2.25 inches.

Answer:

[tex]h = 2.25[/tex]

Answer:

the anser is d

Step-by-step explanation:

Answer:

  192 m²

Step-by-step explanation:

If it were as long as it is wide, the area would be that of an 8-meter square:

  (8 m)² = 64 m²

It is 3 times as long, so the area is 3 times that value:

  3 × 64 m² = 192 m²

Answer:

192 m²

Step-by-step explanation:

The width of the playground is 8m.

Now it's length is three times more than its width.

thus its length is 8*3 = 24.

The area thus is 24*8 = 192 m²

Answer:

f(6) = 82

Step-by-step explanation:

f(x) = 2x^2+5 sqrt(x-2)

Let x =6

f(6) = 2(6)^2+5 sqrt(6-2)

    = 2 * 36 + 5 sqrt(4)

    = 72+5*2

    = 72+10

    =82

f(6) = 82

Answer:

It's B.

Step-by-step explanation:

It might be a square because  a rhombus is defined as a parallelogram with 4 equal sides. A square is a rhombus with each angle = 90 degrees and has 4 equal sides.

Answer:

x = 16

Step-by-step explanation:

From the first statement, we can say that:

Angle A is equal to angle D,

Angle B is equal to and E.

Since measure of Angle B and E are given and they are equal, we equate them and solve for x.

[tex]B=E\\x+15=6x-65\\15+65=6x-x\\80=5x\\x=\frac{80}{5}\\x=16[/tex]

Hence x = 16

Answer:

The probability that the dart lands inside the triangle is 0.25

Step-by-step explanation:

* Lets explain how to find the probability of an event

- The probability of an Event = Number of favorable outcomes ÷ Total

  number of possible outcomes

- P(A) = n(E) ÷ n(S) , where

# P(A) means finding the probability of an event A

# n(E) means the number of favorable outcomes of an event

# n(S) means set of all possible outcomes of an event

- P(A) < 1

* Lets solve the problem

- A rectangular dartboard has an area of 648 cm²

- The triangular part of the dartboard has an area of 162 cm²

- A dart is randomly thrown at the dartboard

- The dart lands in the rectangle

∴ The area of the rectangle is the set of all possible outcomes n(S)

- The probability P(A) that the dart lands inside the triangle

∴ The area of the triangle is set of favorable outcomes of an

   event n(E)

∵ P(A) = n(E) ÷ n(S)

∴ P(T) = area of the triangle ÷ area of the rectangle

∵ Area of the rectangle is 648 cm²

∴ n(S) = 648

∵ The area of the triangle is 162 cm²

∴ n(E) = 162

∴ P(T) = 162 ÷ 648 = 1/4 = 0.25

* The probability that the dart lands inside the triangle is 0.25

Answer:

(1/2, 0)

Step-by-step explanation:

The solution to a system of equations graphically is where they intersect on the graph.  In a coordinate, the x is first and the y is second.  Where our lines cross is ON the x-axis.  This means that y = 0 here.  Because we are to the right of the origin, we are in positive x values.  Because we are between x = 0 and x = 1, the best estimate from our choices is x = 1/2.  The coordinate for the solution is best represented by (1/2, 0)

Answer:

  (x, y) = (4, 0)

Step-by-step explanation:

It is convenient to first put the equations into standard form by eliminating common factors. The first equation has a factor of 2 that can be removed; the second equation has a factor of 3 that can be removed. Then you have ...

Subtracting the second equation from the first eliminates the x variable. That gives you ...

  (x +2y) -(x -y) = (4) -(4)

  3y = 0 . . . . . . simplify

  y = 0 . . . . . . . divide by 3

Substituting this value into either equation above, you get ...

  x + 0 = 4

  x = 4

The solution is (x, y) = (4, 0).

Answer:

  C.  1.8 m × 1.1 m

Step-by-step explanation:

Actual dimensions will be 18 times those shown:

The approximate window dimensions are 1.8 m × 1.1 m.

Answer:

d

Step-by-step explanation:

explanation- I think there a dent or something like the surface of the number seven being slightly high blocking the pointer and causing it to stop.

The statement that BESTexplains the results obatined is, the bottom of the spinner is not flat.

There is ony one explanation to the reason why the pointer will land on te section labled 7 four out of the five times.

The bottom of the spinner may not be flat and the section labled 7 could also be dented causing the spinner to land at this section each time it is spinned.

Thus, we can conclude that, the statement that BESTexplains the results obatined is, the bottom of the spinner is not flat.

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Answer:

  about 26 min

Step-by-step explanation:

Let x represent the time spent rowing distance d upstream. Then the time spent rowing downstream is ...

  time = distance/speed . . . . speed × time = distance

  downstream time = (4.5 km/h)(x)/(5.5 km/h)

So, the total time in both directions is ...

  x + 4.5/5.5x = 48 min

  x(1 + 9/11) = 48 min

  x = (48 min)/(20/11) = 26.4 min

Rounded to the nearest minute, Toni spent about 26 minutes rowing upstream.