The sum of two consecutive negative integers whose product is 156. Find the integers

Answer:

Step-by-step explanation:

[tex]3x+2=x+4(x+2)\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\\\3x+2=x+(4)(x)+(4)(2)\\\\3x+2=x+4x+8\qquad\text{combine like terms}\\\\3x+2=(x+4x)+8\\\\3x+2=5x+8\qquad\text{subtract 2 from both sides}\\\\3x+2-2=5x+8-2\\\\3x=5x+6\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\3x-5x=5x-5x+6\\\\-2x=6\qquad\text{divide both sides by (-2)}\\\\\dfrac{-2x}{-2}=\dfrac{6}{-2}\\\\x=-3[/tex]

(3, - 4)

Imagine a rectangle with one corner on the origin and the opposite on the point. Rotate the rectangle about the origin and see where the point lands.

To find the new coordinates of point B after a 90° clockwise rotation around the origin, you apply the rotation rule: (x, y) becomes (y, -x). The original coordinates are needed to calculate the exact new position of point B.

The student is asking about the result of a 90° clockwise rotation of a point around the origin in the Cartesian coordinate system. To find the new coordinates of point B after the rotation, we use the rule for 90° clockwise rotation, which is (x, y) becomes (y, -x). If the original coordinates of point B are (x₂, y₂), the new coordinates after the rotation will be (y₂, -x₂).

Without knowing the original coordinates of point B, we cannot give the exact new coordinates. However, if the student provides the initial coordinates, the new coordinates can be calculated using the rotation rule mentioned.

1 minute has 60 seconds. So dividing the number of seconds jack has to walk from school to home by 60 will give us minutes.

[tex]t=\dfrac{360\mathrm{s}}{60}=\boxed{6\mathrm{min}}[/tex]

Hope this helps.

Answer:

$25.30

Step-by-step explanation:

The final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

It is given that:

You get a haircut that cost $23.if you tip the barber 10% of the total hair cut cost.

Let x be the final bill amount.

The value of x can be found as follows:

x = $23 + 10% of $23

x = 23 + (10/100)23

x = 23 + 0.1(23)

x = 23 + 2.30

x = $25.30

Thus, the final bill was $25.30 if you get a haircut that cost $23.if you tip the barber 10% of the total haircut cost.

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Answer:

no solution

Step-by-step explanation:

well first you gotta distribute

-5(-3 - w) + 4 = -5/6(24 - 6w)

15 + 5w + 4 = -20 + 5w

19 + 5w = -20 + 5w

+20           +20

39 + 5w = 5w

      -5w    -5w

39 ≠ 0

therefore there is no solution (which is the answer)

Answer:

[tex]x=30\°[/tex]

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

m∠LOM+m∠MON=m∠LON ----> by angle addition postulate

we have

m∠LOM=2x°

m∠MON=x°

m∠LON=90° ----> is a right angle

substitute the values

[tex]2x+x=90[/tex]

solve for x

[tex]3x=90[/tex]

[tex]x=30\°[/tex]

Answer:

0.3 > 0.09

Step-by-step explanation:

The comparison 0.3 > 0.09 is true.

0.3 = 0.300

0.300 > 0.009

All other options are false. They should have a less than sign instead of a greater than sign.

Final answer:

Upon comparison of decimal values in the given options, Option A (0.3 > 0.09) is the true comparison as 0.3 is greater than 0.09 when comparing the tenths place.

Explanation:

When comparing decimal numbers, you should look at the largest place value first and work your way to smaller place values to determine which number is larger. Let's evaluate each option:

A. 0.3 > 0.09: Comparing the tenths place, 3 is greater than 0. Therefore, this statement is true.

B. 0.04 > 0.2: Comparing the tenths place, 0 is less than 2. Therefore, this statement is false.

C. 0.29 > 0.38: Comparing the tenths place, both numbers are equal, but in the hundredths place, 9 is less than 8. Therefore, this statement is false.

D. 0.24 > 0.67: Comparing the tenths place, 2 is less than 6. Therefore, this statement is false.

E. 0.55 > 0.600: Comparing the tenths place, both numbers are equal, and in the hundredths place, 5 is equal to 0 followed by an additional 0, thus both numbers are equal and this statement is false.

Based on the above analysis, the correct answer is Option A. 0.3 > 0.09.

Answer:

44°

Step-by-step explanation:

The sum of the angles in a triangle = 180°

In an isosceles triangle the base angles are equal, thus

base angle = [tex]\frac{180-92}{2}[/tex] = [tex]\frac{88}{2}[/tex] = 44°

The number is 7

Step-by-step explanation:

Let x be the number

then according to given statement

[tex]2(x+2) = 5x-17[/tex]

Simplifying

[tex]2x+4 = 5x-17[/tex]

Adding 17 on both sides

[tex]2x+4+17 = 5x-17+17\\2x+21 = 5x[/tex]

Subtracting 2x from both sides

[tex]2x+21-2x = 5x - 2x\\21 = 3x\\3x = 21[/tex]

Dividing both sides by 3

[tex]\frac{3x}{3} = \frac{21}{3}\\x = 7[/tex]

Hence,

The number is 7

Keywords: Linear equation, variables

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9514 1404 393

Answer:

  (x, y) = (43/53, 18/53)

Step-by-step explanation:

If we want to eliminate the x-terms, we multiply the first equation by 7 (opposite of the x-coefficient in the second equation), and we multiply the second equation by 5 (x-coefficient in the first equation). Then we add the result.

  7(5x -9y) +5(-7x +2y) = 7(1) +5(-5)

  35x -63y -35x +10y = 7 -25

  -53y = -18 . . . . simplify. Note the x-terms are gone.

  y = 18/53 . . . . . divide by -53

__

Putting this value of y in the first equation, we get ...

  5x -9(18/53) = 1

  5x = 1 + 162/53 = 215/53 . . . . . add 9y to both sides, simplify

  x = 43/53 . . . . . . . . . . divide by 5

The solution is (x, y) = (43/53, 18/53).

Answer:

If you were asking how many miles in total: 290 miles.

If you were asking how many miles in the 2 hours: 122 miles

Step-by-step explanation:

In the first 168 miles,

[tex]Since \\v_1=168miles/3h=56 miles/h\\\\Thus  \\v_2=v_1+5=56+5=61miles/h\\\\X_1=168miles\\X_2=v_2*2h=61*2=122miles\\X_1+X_2=168+122=290miles\\\\[/tex]

A, D & E

Cells store energy in the form ATPs. These molecules power al the biochemical activities that would not occur spontaneously. Examples of these bioactivities are the contraction of actin filaments, glycolysis cycle, replication of DNA, cell division, gene expression, cell repair and etcetera.

Step-by-step explanation:

All ATPs are not spent at the same time, and futhermore, they are constantly replaced by the continuous process of cellular respiration that captures the chemical energy in the glucose molecules and stores them in ATP. During the release of this energy to power the biochemical reactions, much of it is lost as heat energy and this is why living organisms are always warm.

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Answer: The multiple choice answers would be, A, D, and E.

Step-by-step explanation:

Problem 1

A = 5! = 5*4*3*2*1 = 120 ways to arrange the math books

B = 4! = 4*3*2*1 = 24 ways to arrange the French books

C = 2! = 2*1 = 2 ways to arrange the biology books

D = 3! = 3*2*1 = 6 ways to arrange the three blocks of books, each block a different subject

E = A*B*C*D = 120*24*2*6 = 34560 different ways to arrange the books such that the subjects stick together

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

========================================

Problem 2

Group all the math books to form one "book". This is the same as taking out the 5 math books and replacing it with one single math book. This single math book acts as a placeholder for all of the five books together as one block.

We have

1 math "book"

4 French books

2 biology books

So there are 1+4+2 = 7 "books" total and

7! = 7*6*5*4*3*2*1 = 5040 different ways to arrange those "books"

Within the math block of books, there are 5! = 120 ways to arrange things.

So overall we have 120*5040 = 604800

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

Answer:

(b) The number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.

Step-by-step explanation:

The amount of berries in first basket = 3 3/8 pounds

Now, [tex]3\frac{3}{8}  = 3+\frac{3}{8} = 3 + 0.375 = 3.375[/tex]

So, the amount of berries in first basket = 3.375 pounds

The amount of berries in second basket = 2 7/8 pounds

Now, [tex]2\frac{7}{8}  = 2+\frac{7}{8} = 2 + 0.875 = 2.875[/tex]

So, the amount of berries in second basket = 2.875 pounds

Now, the total berries = Berries in ( First + Second)  basket

                                      = 3.375 pounds +  2.875 pounds  

                                    = 6.25 pounds

So, the number of pounds each person would have = [tex]\frac{\textrm{Total weight of viable berries}}{\textrm{4}}  = \frac{6.25}{4} = 1.5625[/tex]

Now, [tex]1.5625 = 1 + 0.5625  = 1 + \frac{5625}{10000}  = 1 + \frac{5}{8}  = 1\frac{5}{8}[/tex]

So, the number of pounds of berries each person would receive is [tex]1\frac{5}{8}[/tex]pounds.

Answer:

(11/4)x units

Step-by-step explanation:

for a rectangle,

perimeter = 2(length) + 2(width)

given:

length = x

width = (3/8)x

hence,

perimeter = 2(length) + 2(width)

perimeter = 2x + 2(3/8)x

perimeter = 2x + (3/4)x

perimeter = [2 + (3/4)]x

perimeter = (11/4)x

(C) 7/10 cup is the correct answer

Step-by-step explanation:

First of all we will calculate the 40% of grandmother's recipe then add it to the given flour in grandma's recipe

So,

The amount of flour in grandma's recipe = F_g = 1/2 cups

Calculating percentage

[tex]=40\%\ of\ \frac{1}{2}\\=\frac{40}{100}*\frac{1}{2}\\=\frac{2}{10}[/tex]

So Evelyn needs to add 2/10 cups more to the original quantity.

So,

Flour used by Evelyn:

[tex]=\frac{1}{2}+\frac{2}{10}\\\\=\frac{5+2}{10}\\\\=\frac{7}{10}\ cups[/tex]

Hence,

(C) 7/10 cup is the correct answer

Keywords: Percentage, Quantity

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Final answer:

The sum of two positive numbers always has a positive sign, so the sum of 3/5 + 3/5 is positive.

Explanation:

The question what is the sign of 3/5 + 3/5 involves understanding the rules of addition for numbers with the same sign. According to the rules of addition:

When two positive numbers add, the answer has a +ve sign.

Since both fractions 3/5 and 3/5 are positive, their sum will also have a positive sign. Therefore, the sign of the sum 3/5 + 3/5 is +ve, which means the answer is also positive.

The volume of the silo is 461.81 m³

Step-by-step explanation:

A barn silo, excluding the top, is a cylinder

We need to find the volume of the silo

∵ The silo is shaped a cylinder

∵ The volume of a cylinder = base area × height

∵ The base is shaped a circle

∵ Area a circle = π r², where r is the radius of the circle

∴ The volume of the silo = π r² × h

∵ The diameter of the silo = 7 m

∵ The radius of a circle is half the diameter

∴ The radius of the silo = [tex]\frac{1}{2}[/tex] × 7 = 3.5 m

∵ The height of the silo = 12 m

- Substitute the values of r and h in the rule of volume

∴ The volume of the silo = π (3.5)² × 12

∴ The volume of the silo = 147 π = 461.81 m³

The volume of the silo is 461.81 m³

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Final answer:

The volume of a barn silo that is shaped like a cylinder with a diameter of 7 meters and a height of 12 meters is approximately 461.7 cubic meters.

Explanation:

To calculate the volume of the silo which is in the shape of a cylinder, we use the formula V = πr²h, where V is the volume, r is the radius, and h is the height. The diameter of the silo is given as 7 meters, so the radius is half of that, which is 3.5 meters. The height of the silo is 12 meters. Plugging these values into the formula gives:

V = π × (3.5 m)² × 12 m

V = π × 12.25 m² × 12 m

V = π × 147 m³

Assuming π to be approximately 3.14159, the calculation results in:

V = 3.14159 × 147 m³ = 461.7 m³ (approx)

So, the volume of the silo is approximately 461.7 cubic meters.

Answer:1 C milk

Step-by-step explanation:

1/2 C milk = 2 C chocolate

1 C milk = 4 C chocolate

Answer:

1 cup of milk

Step-by-step explanation:

If 1/2 cup of milk is needed for 2 cups of chocolate, and you need to find how much milk is needed for 4 cups, then you'd follow the same steps as going from 2 cups to 4, multiplying by 2.

2 cups chocolate x 2 = 4 cups chocolate

1/2 cup milk x 2 = 1 cup

Answer:

A) The smaller angle between 12 and 3 is 90°  and that is [tex]\frac{1}{4}[/tex]th coordinate

B) The smaller angle between 2 and 3 is 30°  

C) The angle between 4 and 6 is 60°

D) the angle between 6  and 9 is 90°  

D) The angle between 6 and 12 is 180°

E) The angle between 7 and 8 is 30°    

Step-by-step explanation:

Given as :

It is shown in diagram as ;

The circle with different angles from angle 1 to angle 12

Now, The figure is the complete circle, and the measure of all angles in a circle = 360°

The measure of semicircle = 180°

and each quadrant is divided in to 3 angles

Each right angle is further divided into three 30° angles  

Again ,

A) The smaller angle between 12 and 3 is 90°  and that is [tex]\frac{1}{4}[/tex]th coordinate

B) The smaller angle between 2 and 3 is 30°  

C) The angle between 4 and 6 is 60°

D) the angle between 6  and 9 is 90°  

D) The angle between 6 and 12 is 180°

E) The angle between 7 and 8 is 30°    Answer

Answer:

y-6=-3/4(x+4)

Step-by-step explanation:

y-y1=m(x-x1)

m=-3/4

y-6=-3/4(x-(-4))

y-6=-3/4(x+4)

Answer:

x=-10/23

Step-by-step explanation:

-23x=10

x=10/-23

x=-10/23

Answer:

x = -15 thus c: is your answer

Step-by-step explanation:

Solve for x:

10 = (-2 x)/3

10 = (-2 x)/3 is equivalent to (-2 x)/3 = 10:

(-2 x)/3 = 10

Multiply both sides of (-2 x)/3 = 10 by -3/2:

(-3 (-2) x)/(2×3) = (-3)/2×10

(-3)/2×(-2)/3 = (-3 (-2))/(2×3):

(-3 (-2))/(2×3) x = (-3)/2×10

(-3)/2×10 = (-3×10)/2:

(-3 (-2) x)/(2×3) = (-3×10)/2

(-3)/3 = (3 (-1))/3 = -1:

(-2-1 x)/2 = (-3×10)/2

(-2)/2 = (2 (-1))/2 = -1:

--1 x = (-3×10)/2

(-1)^2 = 1:

x = (-3×10)/2

10/2 = (2×5)/2 = 5:

x = -35

-3×5 = -15:

Answer:  x = -15

Answer:

6/8

Step-by-step explanation:

3/4 into eighths would be 6/8. She said she had 5/8 cups of flour.

Answer:

c. two places to the left

Step-by-step explanation:

Answer:

two places to the left

Step-by-step explanation:

Final answer:

The perimeter of the isosceles triangle with a base of 20 meters and height of 24 meters is 60 meters.

Explanation:

The formula for the area of a triangle is 1/2 × base × height.

In this case, the base of the isosceles triangle is given as 20 meters and the corresponding height is given as 24 meters.

Answer: perpendicular

Step-by-step explanation:

Final answer:

The slopes of the two lines given by the equations 3x-6y=2 and 18x+9y=8 are 1/2 and -2 respectively. Since these slopes are neither equal nor negative reciprocals, the lines are neither parallel nor perpendicular.

Explanation:

To decide whether the pair of lines is parallel, perpendicular, or neither, we need to find the slopes of the lines. The lines are given by the equations 3x-6y=2 and 18x+9y=8. To find the slope of each line, we must rewrite the equations in slope-intercept form (y=mx+b), where m represents the slope

For the first line, 3x-6y=2, we isolate y:

So the slope of the first line is 1/2.

For the second line, 18x+9y=8, we isolate y:

The slope of the second line is -2.

Since the slopes of the two lines are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.

Answer:

∠A=67°

∠B=70°

∠C=43°

Step-by-step explanation:

The correct question in English is

Determines the measurement of each of the angles of the triangle ABC if it is known that A=(3x+1)°,B=(3x+4)° and C=(2x-1)°.

we know that

The measure of the interior angles in a triangle must be equal to 180 degrees

so

∠A+∠B+∠C=180°

substitute the given values

[tex](3x+1)\°+(3x+4)\°+(2x-1)\°=180\°[/tex]

solve for x

[tex](8x+4)\°=180\°[/tex]

[tex]8x=180-4[/tex]

[tex]x=22[/tex]

Find the measure of each angle

∠A=(3(22)+1)=67°

∠B=(3(22)+4)=70°

∠C=(2(22)-1)=43°

The width of a rectangular farm with area of 1/2 square mile and length of 1/3 mile is 1 1/2 miles.

The area of a rectangle is found by multiplying length times width. In this case, we know that the area is 1/2 square mile and the length is 1/3 mile.

So the width of the farm is 1 1/2 miles.

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Answer: 204 teddy bears

Step-by-step explanation:

Answer:

17 x 12 = 204 teddy bears

Step-by-step explanation:

17 cases, 12 bears in each case

You could round 17 --> 20

You could round 12 --> 10

20×10=200