What is 5x-2.5+6x-3 equivalent to

Answer:

y=3x

Step-by-step explanation:

If y is the total distance from the shore and it increases by 3 miles every hour, then by plugging in the amount of hours that have passed into x we will find the distance they have traveled. For example, if they have been out for 5 hours then you would do y=3(5) which would be 15 miles from the shore.

The correct equation to represent the relationship between Mary's distance from shore and time is y=3x. This is a linear equation, with 3 representing the rate of increase in distance for each time unit (each hour).

In this case, Mary is moving at a constant rate, which means we are dealing with a linear relationship. The problem states that her distance from shore, y, increases by 3 miles for each hour, x. Therefore, the correct equation to model this scenario would be y=3x.

This is an equation of a line where 3 is the slope, signifying the change in distance for each time unit (in this case, an hour), and x is the time in hours. So, as time increases, the distance from the shore also increases at a rate of 3 miles per hour.

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Answer:

G x 3 = 48

Step-by-step explanation:

let G be Greg's score

And product means multiplication.

so G x 3 = 48.

finding Greg's score means 3g = 48.

g = 48/3

g = 16.

Answer:

441

Step-by-step explanation:

The ratio of sidelengths squares is the ratio of the areas, so the ratio of the area of the smaller triangle's area to the larger triangle's is 25:49.

Using ratios, you figure out that the area of the larger triangle must be 225/25 *49, which is equal to 9*49 = 441

Final answer:

The area of the larger triangle, given a scale factor of 5:7 and the smaller triangle's area of 225cm squared, is 441cm squared. The areas scale as the square of the scale factor, in this case, 25:49.

Explanation:

The question involves working with the scaling of the area of a triangle when given a scale factor between two similar triangles. Since the scale factor of the linear dimensions between the two triangles is 5:7, the ratio of the areas is the square of the scale factor, which is (5:7)2 or 25:49.

If the area of the smaller triangle is 225 cm², to find the area of the larger triangle, we need to use the area ratio. Given that 25 parts correspond to 225 cm²in the smaller triangle, we can calculate the value of 1 part as 225 cm² / 25 = 9 cm2. Hence, the area of the larger triangle corresponds to 49 parts, which gives us 49 * 9 cm² = 441 cm².

Answer: mean, median, mode and range

Step-by-step explanation:

The measures of centre are referred to as mean, median, mode and range.

Mean also referred to as average, it is the sum of values in a data set divided by the number of values in the given data set.

Median is the middle point number in a given data set. Median of an even data set is the average of two values in the middle of the data set.

Mode is the most occurring number in the given data set. It is the number with the highest frequency in the set.

Range is the difference between the highest number and the lowest number in a given data set.

I hope this answers your question.

The measures of center in a dataset are statistical values that represent the central point of the data. These include the mean (arithmetic average), median (middle value), and mode (most frequent value). Another common measure of center is the weighted mean, which is used when some data points carry more significance than others.

Measures of the center are statistical measures that provide information about the central point of a dataset. The main measures include the mean, median, and mode.

The mean is the arithmetic average of the data set. This is usually the sum of all data points divided by the number of data points.

The median is the middle value of the data set when it is ordered from smallest to largest. If there is an even number of data points, the median would be the average of the two middle numbers.

The mode is the data point that occurs most frequently in the data set. A data set may have one mode, more than one mode, or no mode at all.

Another common measure of center is the weighted mean, which is useful when some data points carry more significance than others. For example, you might want to calculate the average grade in a class where some assignments are worth more than others.

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Answer: No

Step-by-step explanation:

10x + 11 when x= 1 is equal to 21

While 5x + 11, when x=1 is equal to 16

The volume of a conical pile of dirt with an 11-meter radius and a 6-meter height is approximately 754.24 cubic meters.

The question is asking for help in calculating the volume of a conical pile of dirt.

The formula for finding the volume of a cone is  [tex]V = (1/3) \pi r^2h[/tex], where V is the volume, r is the radius, and h is the height of the cone.

Substituting the given values, the radius r is 11 meters, the height h is 6 meters, and using 3.14 for
π, the calculation would be -

V = (1/3) * 3.14 * 112 * 6.

To find the volume: V = (1/3) * 3.14 * 121 * 6

= 3.14 * 40.333333 * 6  

= 754.24 cubic meters.

So, there are approximately 754.24 cubic meters of material in the conical pile of dirt.

Multipli the numbers

$7.00

21/3=7, and 21 is 3/4 of 7*4

y = ([tex]\frac{3}{2}[/tex])x -2 is the equation of the required line

Step-by-step explanation:

Step 1 :

Equation of the given line is 3x-2y=14

Re writing this in the form y = mx + c , we have

-2y = -3x +14

 y = ([tex]\frac{3}{2}[/tex])x - 7

The co efficient of x , m is the slope of the line. So for the given line the slope is  [tex]\frac{3}{2}[/tex]

Step 2 :

We have to find  equation of a line which is parallel to this line. All parallel lines will have the same slope. Hence the required line has a slope of [tex]\frac{3}{2}[/tex].

Step 3 :

Equation of line with slope m and passing through a point ([tex]x_{1} ,y_{1}[/tex]) is

(y-[tex]y_{1}[/tex]) = m((x-[tex]x_{1}[/tex])

So equation of line passing through (-6,-11) and with a slope of  [tex]\frac{3}{2}[/tex] is

(y-(-11)) = [tex]\frac{3}{2}[/tex] ( x - (-6))

y + 11 = [tex]\frac{3}{2}[/tex] ( x + 6)

y = ([tex]\frac{3}{2}[/tex])x + 9 - 11

y = ([tex]\frac{3}{2}[/tex])x -2

Step 4 :

Answer  :

y = ([tex]\frac{3}{2}[/tex])x -2 is the required equation

The given equation has the slope 3/2 after converting to the slope-intercept form. Because parallel lines share the same slope, the equation for the line parallel to the given line, passing through the point (-6,-11), is found to be y = (3/2)x - 9 using the point-slope form.

To find an equation that is parallel to a given equation, we must first find the slope of the given line. The equation provided is in the form Ax + By = C. To convert this into slope-intercept form (y = mx + b), where m is the slope, we rearrange the equation to get y = (3/2)x - 7. Therefore, the slope of the given line is 3/2.

Parallel lines share the same slope, the equation of the line parallel to the given one that passes through point (-6,-11) will also have the slope 3/2. We stick this and our point into the point-slope form of a line (y - y1 = m(x - x1)) to get: y + 11 = 3/2(x + 6). Simplifying, we get y = (3/2)x - 9 which is the equation of the line parallel to the given equation that passes through the point (-6,-11).

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Answer:

252

Step-by-step explanation:

Multiply 350 by the decimal form of 72%. To find the decimal form of 72%, divide 72 by 100 or move every number two places to the right:

72/100 = 0.72

Then multiply 350 by 0.72:

350 x 0.72 = 252

I hope this helps!

Answer:

Step-by-step explanation:

Let c represent the speed of the current. The travel time is inversely proportional to the travel speed. In one direction the current speed is added to the boat speed; in the other direction, it is subtracted. You can write the relation ...

  (10 +c)/(10 -c) = 3/2

  2(10 +c) = 3(10 -c) . . . . . . "cross multiply"

  20 +2c = 30 -3c . . . . . . . eliminate parentheses

  5c = 10 . . . . . . . . . . . . . . . add 3c -20

  c = 2 . . . . . . . . . . . . . . . . . divide by 5

The speed of the current is 2 miles per hour.

__

The speed downstream is then (10 +2) = 12 miles per hour. The travel time in that direction is 2 hours, so the distance covered is ...

  (12 mi/h)(2 h) = 24 mi

The one-way distance of the trip is 24 miles.

Answer:

Step-by-step explanation:

[tex]k^2+5k+6=k^2+2k+3k+6=k(k+2)+3(k+2)\\\\=(k+2)(k+3)[/tex]

Other method:

[tex]k^2+5k+6=(k+2)(k+x)\qquad\text{use}\ FOIL\\\\k^2+5k+6=(k)(k)+(k)(x)+(2)(k)+(2)(x)\\\\k^2+5k+6=k^2+kx+2k+2x\\\\k^2+5k+6=k^2+(x+2)k+2x\Rightarrow x+2=5\ \wedge\ 2x=6\\\\x+2=5\qquad\text{subtract 2 from both sides}\\x=3\\\\2x=6\qquad\text{divide both sides by 2}\\x=3[/tex]

Answer:

The integer values of x are 5 and 6

Step-by-step explanation:

we have

Inequality A

[tex]4x-2>17[/tex]

solve for x

adds 2 both sides

[tex]4x>19[/tex]

divide by 4 both sides

[tex]x> 4.75[/tex]

solution A is the interval (4.75,∞)

Inequality B

[tex]3x+5<24[/tex]

solve for x

subtract 5 both sides

[tex]3x<19[/tex]

divide by 3 both sides

[tex]x<6.33[/tex]

solution B is the interval (-∞,6.33)

The solution of the inequality A and the inequality B is

(4.75,∞) ∩  (-∞,6.33)=(4.75,6.33)

The integer values of x are 5 and 6

Final answer:

The integer value of x for which both inequalities 4x - 2 > 17 and 3x + 5 < 24 are true is x = 5.

Explanation:

To find the integer value of x for which the inequalities 4x – 2 > 17 and 3x + 5 < 24 are both true, we solve each inequality step by step.

Answer:

116.3

Step-by-step explanation:

Supplementary angles add to 180

One angle is 63.7, the other is x

63.7+x = 180

Subtract 63.7 from each side

63.7-63.7+x = 180-63.7

x = 116.3

Answer:

0

Step-by-step explanation:

78/17 gives 4.588

In rounding up numbers, 1 to 4 is rounded up to zero, while numbers 5 to 9 will be rounded up to 1.

In the question above, we are asked to round up to the nearest 10. And then 78/17 gives 4.588

This number is between 0 and 10.

The whole number there is 4. Therefore, 4 will be rounded up to Zero.

If the question and us to round up to the nearest whole number, as we have 4.588

The number before the whole number 4 is 5 (the tenth digit), and then 5 will be rounded up to 1. That 1 will hence be added to 4.

4+1= 5. To nearest whole number, it is 5 but to nearest ten, it is 0

Answer:

[tex]y=-3x+4[/tex]

Answer: -72√3

Step-by-step explanation:

(-9√2)(4√6)

−9√2*4√6

-9*4√2*6

-9*4√12

-9*4*2√3

-72√3

Hope this helps, now you know the answer and how to do it. HAVE A BLESSED AND WONDERFUL DAY! :-)  

- Cutiepatutie ☺❀❤

Final answer:

To simplify (-9√2)(4√6), we multiply numerical coefficients (-9) and (4), and the square roots √2 and √6, simplifying to get -72√3 which is option B.

Explanation:

To simplify the expression (-9√2)(4√6), we need to follow the rules of algebraic multiplication for square roots. Here are the steps to simplify the expression:

The correct option from the given choices is thus B. -72√3.

For the graph, the image of triangle ABC after a reflection across the x-axis, the vertices of the image will be called A” B” , and C” are respectively,  (-3, 4),  (-3, 1),  (-1, 1)

Reflection about the axis is a transformation in geometry where a figure is flipped across a line or plane, producing a mirror image of the original figure. The line or plane across which the figure is reflected is called the axis of reflection.

Given that,

A graph, having triangle ABC

The reflection points, A', B', C'  = ?

All the vertices and their mirror image will be at equal distance from the x-axis

So, y-coordinate will be equal in magnitude but different in sign for all the vertices and their mirror image

x-axis is axis of reflection,

there will be no change in x-coordinates

So, x-coordinates will be same in magnitude and in sign as well

Now, Mirror image points can be written as,

A' = (-3, 4)

B' = (-3, 1)

C' =  (-1, 1)

Hence, the points are  (-3, 4),  (-3, 1),  (-1, 1)

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Answer:

The population density in people per square meter is 0.005377 people per square meter.

Answer: [tex]0.005377\frac{people}{m^{2}}[/tex]

Step-by-step explanation:

You want to convert [tex]\frac{people}{km^{2} }[/tex] to [tex]\frac{people}{m^{2}}[/tex]

To do this, multiply [tex]\frac{people}{km^{2} }[/tex] * [tex]\frac{1 km}{1000 m}[/tex] * [tex]\frac{1 km}{1000 m}[/tex]=[tex]\frac{people}{1000 * 1000 m^{2}}[/tex]

sub in 5377 for people to get

[tex]\frac{5377people}{1000 * 1000 m^{2}}=0.005377\frac{people}{m^{2}}[/tex]

Step-by-step explanation:

(a)

[tex] In\: \triangle ABC \& \triangle DEF \\\\

\frac {AB} {DE} = \frac {40} {48} = \frac {5} {6}...(1)\\\\

\angle ABC \cong \angle DEF... (each\: 90°)...(2)\\\\

\frac {BC} {EF} = \frac {30} {36} = \frac {5} {6}...(3)\\\\[/tex]

From equations (1), (2) & (3)

[tex] \triangle ABC \sim \triangle DEF[/tex]

(By SAS Postulate)

Hence both of the triangles are similar.

(b)

Prism DEF will have greater volume, because length of its sides are larger than that of prism ABC.

6/5 = 1.2 times greater.

Answer:

7.9

4.2

9.3

17.8

Step-by-step explanation:

8. √63

the square of 8 is 64 √63 is close to 64 so we can say it's 7.9 approximately

9. √18

the square of 4 is 16, √18 is greater than 16 so we can say it's 4.2 approximately

10. √87

the square of 9 is 81, √87 is greater than 81 so we can say the value of it is approximately 9.3

11. √319

the square of 18 is 324, √319 is smaller than 324 so we can say it's 17.8

The question is about finding the total count of possible 5-digit numbers that either has identical adjacent digits or differ from its neighbor digits by exactly 1 and containing at least one 5. Providing an exact solution without knowing students' pre-existing knowledge on the subject can be difficult. This kind of problem typically involves methodologies like recursive relationships.

This question pertains to combinatorics, a topic in mathematics that deals with countable structures. Specifically, the question is asking how many five-digit numbers are there that follows the conditions given in the question.

The condition that the number contains the digit 5 is applicable for both the cases where the digit is the same as or differs by 1 from its neighbors. This is because 5 is a middle digit from 0 to 9, and it can satisfy both conditions.

The problem can be approached by finding the total count of five digit numbers that satisfy just the adjacent difference conditions, and then subtracting the count of such numbers that do not contain the digit 5.

However, providing a step-by-step solution to this problem would be complex and lengthy, especially without the proper context of the student's pre-existing knowledge. The method to solve it would involve recursive relationships and possibly programming or usage of a suitable mathematical software.

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Answer:

3x - 24

Step-by-step explanation:

9x - 6x - 24

3x - 24

Answer:

Red is 19

Blue is 57

Step-by-step explanation:

According to the question,it says Sam has 25% red marble out of the 76.

It means 25/100×76

It gives 19

To get the value for blue

Blue + red=76

Red is 19

Blue + 19=76

Blue=76-19

Blue=57

Therefore,red is 19 and blue is 57

Answer:

x > 2/7

Step-by-step explanation:

Step 1:  Make an inequality

3/14 + x > 1/2

Step 2:  Solve for x

3/14 + x - 3/14 > 1/2 - 3/14

x > 2/7

Answer:  x > 2/7

Answer:

.50 for one donut

Step-by-step explanation:

do a ratio 6$ for 12 donuts

so for $ for 1 donut

reduce the first equation for a ration of $1 per two donuts

so it be 50 cents

$6. $0.50

____ = ______

12 donuts. 1 donut

The positive solution to the equation 4x^2 + 12x = 135 is; x = 9/2

By quadratic formula;

where, a = 4, b = 12 and c = -135.

By solving the equation quadratically;

The solutions are;

In essence, the positive solution of the equation is; x = 9/2

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The positive solution to the equation 4x^2 + 12x = 135 is found using the quadratic formula, resulting in a positive root of approximately x ≈ 3.375.

The positive solution to the equation 4x^2 + 12x = 135 can be found by first rearranging the equation into the standard quadratic form of ax^2 + bx + c = 0. Bringing all terms to one side gives us 4x^2 + 12x - 135 = 0. This equation can be solved by either factoring, completing the square or using the quadratic formula. Since the original equation does not easily factor into a product of binomials, and the instructions indicate a preference for recognizing a perfect square when possible, we should attempt to complete the square or use the quadratic formula.

To complete the square, we would add (b/2a)^2 to both sides of the equation after dividing the linear coefficient by 2 and squaring the result. However, in this case, it's more straightforward to employ the quadratic formula, which is x = (-b ± sqrt(b^2 - 4ac)) / (2a). Plugging in the values from our equation gives two roots, but since we are only interested in the positive root, we take the solution where the square root term is added to the negative b value.

After calculating, we find that the positive root is x ≈ 3.375, which is the solution to the equation in question.

Answer:

957.62

Step-by-step explanation:

Given the house price, P=$197,000, [tex]n=12\times 30=360, i=0.0415/12[/tex], the monthly payments, M, can be calculated as:

[tex]M=P[\frac{i(1+i)^n}{(1+i)^{360}-1}]\\\\M=[\frac{\frac{0.0415}{12}(1+\frac{0.0415}{12})^360}{(1+\frac{0.0415}{12})^{360}-1}]\\\\M=957.62[/tex]

Hence, the monthly payment of the baloon mortgage is $957.62

Answer:

yesyesyesyes

Step-by-step explanation:

yesyesyesyesyes

Answer:

yesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyesyes