Rewrite the following expression using the distributive property and the GCF: 36+48

Answer:

2

Step-by-step explanation:

3x-4 =-1/2x+3

3x+1/2x=3+4

6x+x/2=7

6x+x=14

7x=14

x=14/2

x= 2

Answer:

X = 2

Step-by-step explanation:

- Add 1/2 to both sides

3x - 4 + 1/2x = -1/2x + 3 + 1/2x

7/2x - 4 = 3

- Add 4 to both sides

7/2x - 4 + 4 = 3 + 4

7/2x = 7

- Multiply both sides by 2/7

(2/7) X (7/2x) = (2/7) X (7)

x = 2

The equation has only one solution that is x = -15

Step-by-step explanation:

We have to convert the given statement in  form of equation to find the number

Let x be the number

then

According to given statement,

[tex]2x-7 = 3x+8\\-7 = 3x-2x+8\\-7 = x+8\\x = -7-8\\x = -15[/tex]

The equation has only one solution that is x = -15

Keywords: Linear equation, variables

Learn more about linear equation at:

#LearnwithBrainly

Final answer:

The equation 'twice a number minus seven equals eight greater than three times the number' simplifies to 2x - 7 = 3x + 8, which has one solution: x = -15.

Explanation:

The original question asks us to solve an algebraic equation where twice a number minus seven is equal to eight greater than three times that number.

To translate this into an algebraic expression, let the unknown number be x.

This gives us the equation 2x - 7 = 3x + 8.

To solve this equation, we can subtract 2x from both sides to get -7 = x + 8 and then subtract 8 from both sides to isolate x, resulting in x = -15.

To answer part B, this type of linear equation will only have one solution because it’s a linear equation with a non-zero coefficient in front of the variable x.

Dimensions are length 20 meter and width 14 meter

Solution:

Let "a" be the length of rectangle

Let "b" be the width of rectangle

Given that,

A rectangle has width that is 6 meters less than the length

Width = length - 6

b = a - 6

The area of the rectangle is 280 square meters

The area of the rectangle is given by formula:

[tex]Area = length \times width[/tex]

Substituting the values we get,

[tex]Area = a \times (a-6)\\\\280 = a^2-6a\\\\a^2-6a -280=0[/tex]

Solve the above equation by quadratic formula

[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]

[tex]\mathrm{For\:}\quad a=1,\:b=-6,\:c=-280:\quad a_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:1\left(-280\right)}}{2\cdot \:1}[/tex]

[tex]a =\frac{6 \pm \sqrt{36+1120}}{2}\\\\a = \frac{6 \pm \sqrt{1156}}{2}\\\\a = \frac{6 \pm 34}{2}\\\\Thus\ we\ have\ two\ solutions\\\\a = \frac{6+34}{2} \text{ or } a = \frac{6-34}{2}\\\\a = 20 \text{ or } a = -14[/tex]

Since, length cannot be negative, ignore a = -14

Thus solution of length is a = 20

Therefore,

width = length - 6

width = 20 - 6 = 14

Thus dimensions are length 20 meter and width 14 meter

Answer: 0.8mile/min

Step-by-step explanation:please see attachment for explanation

Answer:

The simplified expression is

[tex]\frac{4}{5}(\frac{1}{4}c-5)=\frac{c}{5}-4[/tex]

Step-by-step explanation:

Given expression is

[tex]\frac{4}{5}(\frac{1}{4}c-5)[/tex]

To simplify the given expression:

[tex]\frac{4}{5}(\frac{1}{4}c-5)[/tex]

[tex]\frac{4}{5}(\frac{1}{4}c-5)=(\frac{4}{5}\times \frac{1}{4}c)-(\frac{4}{5}\times 5)[/tex] ( here using the distributive property )

[tex]=(\frac{1}{5}c)-(4\times 1)[/tex] (simplify the factors )

[tex]=\frac{1}{5}c-4[/tex] or

[tex]=\frac{c}{5}-4[/tex]

Therefore the simplified expression is

[tex]\frac{4}{5}(\frac{1}{4}c-5)=\frac{c}{5}-4[/tex]

The correct answer is "no solution."

Let's first rewrite the second equation in the system in slope-intercept form (y = mx + b) to make it easier to work with:

[tex]\[ -5y = 10x + 20 \][/tex]

Divide both sides by -5:

[tex]\[ y = -2x - 4 \][/tex]

Now we have the system of equations:

[tex]\[ y = -2x + 5 \][/tex]

[tex]\[ y = -2x - 4 \][/tex]

To find the solution to the system, we can set the two equations equal to each other since they both equal y:

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

Now, we can solve for x:

[tex]\[ 5 = -4 \][/tex]

This equation is not true, which means there is no value of x that satisfies both equations simultaneously. Therefore, the system has no solution.

Answer:

Step-by-step explanation:

This Sequence is  Geometric Progression

a = 16

r = 8/16 = 1/2

nth term = ar^(n-1) = 16*(1/2)^(n-1)

The nth term of the geometric sequence 16, 8, 4, 2, 1 can be found using the formula an = 16 * (1/2)^(n-1), where n is the position of the term in the sequence.

The sequence given is 16, 8, 4, 2, 1, which is a geometric sequence where each term is half of the previous term. This means the common ratio r is 1/2. The nth term of a geometric sequence is given by the formula a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

To find the nth term for our sequence, we plug in the values: a_1 = 16 and r = 1/2. Thus, the formula for the nth term becomes an = 16 * (1/2)^(n-1).

Answer:

0.42

Step-by-step explanation:

use the attached as reference

recall that for a right (90°) triangle, with any acute angle θ,

cos θ = length of adjacent side / length of hypotenuse

in our case, for angle I, the adjacent side is HI = 36 units and the hypotenuse is IJ = 85 units

by the above formula,

cos I = length of adjacent side / length of hypotenuse

= 36 / 85

= 0.42353

= 0.42 (rounded to nearest hundredth)

Answer:

-18.4z+6

Step-by-step explanation:

1. Always

2. x^2 − 14x + 49

3. x^2 + 10x + 25

4. x^2 − 9

5. 16x^2 − 24xy + 9y^2

6. 4x^2 + 20xy + 25y^2

7. 9x^2 − 49y^2

Some of these may be incorrect as you didn't probably right down the problems... I had to guess what was exponents/ <3

Answer:

Not a polyhedron and it's a sphere

Step-by-step explanation:

It's not a polyhedron because a polyhedron has to have faces more than 6

The solution is x = 2 and y = -11

Solution:

Given system of equations are:

x + y = -9 --------- eqn 1

5x - 2y = 32 ------------- eqn 2

We have to solve the system of equations

We can solve the system by substitution method

From eqn 1,

x + y = -9

Isolate "y" to one side

y = -9 - x ---------- eqn 3

Substitute eqn 3 in eqn 2

5x -2(-9 - x) = 32

5x + 18 + 2x = 32

Combine the like terms

7x = 32 - 18

7x = 14

x = 2

Substitute x = 2 in eqn 3

y = - 9 - 2

y = -11

Thus the solution is x = 2 and y = -11

Answer:

infinite solutions

Step-by-step explanation:

−2(2x+3)=−4(x+1)−2 multiply -2 and -4 with inside the parenthesis

-4x -6 = -4x -4 -2 now add like terms

-4x -6 = -4x -6 ➡ -4x +4x = -6+6

that makes equation 0 = 0 this is called infinite solutions which means whatever number you use instead of x there will always be a solution.

Answer:

19 ft i think

Step-by-step explanation:

hop ethis helps :) have a nice day

Step-by-step explanation:

If two lines cross each other the angles opposite of each other are the same. So left=right and top=bottom. Knowing this the bottom angle must be 120°. if 3x=120° then x=40°

Answer:280 square feet per hour.

Step-by-step explanation:

Answer:

144 pages

Step-by-step explanation:

Johan has read [tex]\frac{1}{4}[/tex] of the book that is 36 pages.

To find the total number of pages in the book, note that

[tex]\dfrac{1}{4}\ - \ 36\ \text{pages}\\ \\1\ - \ x\ \text{pages}[/tex]

Then

[tex]\dfrac{\frac{1}{4}}{1}=\dfrac{36}{x}\\ \\\dfrac{1}{4}x=36\\ \\x=4\cdot 36\\ \\x=144\ \text{pages}[/tex]

a. The equation of the line is [tex]y = \frac{28}{15}x+\frac{41}{30}[/tex]

b. The equation of the line is [tex]y = \frac{-7}{5}x+\frac{1}{5}[/tex]

The general equation of the line in slope-intercept form is:

y = mx + c

where m is the slope and c is the y-intercept

1. To get the slope:

[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

where (x₁ , y₁) and (x₂ , y₂) are two points that belong to the line

2. To get the y-intercept:

We pick any point (x , y) that belong to the line and use this point to substitute in the general equation:

y = mx + c

m is calculated from part 1 and (x , y) is a known point on the line. So, we solve for c which is the only unknown.

Now, for the required lines:

Part a:

The two given points are (2, 5.1) and (-1, -0.5)

representing (x₁ , y₁) and (x₂ , y₂)

i. Getting the slope:

[tex]m = \frac{-0.5 - 5.1}{-1 -2}=\frac{28}{15}[/tex]

ii. Getting the y-intercept:

I will use the point (-1, -0.5)

y = mx + c

[tex]-0.5 = \frac{28}{15}(-1)+c\\\\-0.5=\frac{-28}{15}+c\\ \\ c = \frac{41}{30}[/tex]

iii. Based on the above calculations, the equation of the line is:

[tex]y = \frac{28}{15}x+\frac{41}{30}[/tex]

Part b:

The two given points are (-2, 3) and (3, -4)

representing (x₁ , y₁) and (x₂ , y₂)

i. Getting the slope:

[tex]m = \frac{-4-3}{3--2}=\frac{-7}{5}[/tex]

ii. Getting the y-intercept:

I will use the point (3, -4)

y = mx + c

[tex]-4 = \frac{-7}{5}(3) + c\\ \\-4 = \frac{-21}{5}+c\\ \\c=\frac{1}{5}[/tex]

iii. Based on the above calculations, the equation of the line is:

[tex]y = \frac{-7}{5}x+\frac{1}{5}[/tex]

Hope this helps :)

Step-by-step explanation:

x-1=2 therefore x is 3 so 2x squared is 36

Answer:

1.22474487139

Step-by-step explanation:

x = 3

so if 2x^2 - 1 = 2

add 1 to both equations

2x^2 = 3

next, divide 2 from both sides

x^2 = 3/2

x^2 = 1.5

now find the square root of 1.5

the answer is:

1.22474487139

Answer:

Angle 1:  100

Angle 2:  80

Step-by-step explanation:

A linear pair of angles is formed when two lines intersect.  The measure of a straight angle is 180 degrees, so a linear pair of angles is equal to 180 degrees.

Angle 1: x

Angle 2: (x * 3/4) + 5

x + (x * 3/4) + 5 = 180

x + 3/4x + 5 = 180

1 3/4x + 5 - 5 = 180 - 5

1 3/4x = 175

1 3/4x / 1 3/4 = 175 / 1 3/4

x = 100

Check:

(x * 3/4) + 5

(100 * 3/4) + 5

75 + 5

80

100 + 80 = 180

To find the measure of both angles that form a linear pair, set up an equation and solve for x.

To find the measure of both angles, let's assume that one angle is x degrees. According to the given information, the other angle is 3/4 of x degrees plus 5. So the measure of the other angle is (3/4)x + 5 degrees. Since the two angles form a linear pair, their measures sum up to 180 degrees. Therefore, we can write the equation: x + (3/4)x + 5 = 180. Solving this equation, we can find the value of x and then calculate the measures of both angles.

Answer:

D

Step-by-step explanation:

95/100 is equal valent to 95℅.

Answer:

The price of the shoes should be $13.12

Answer:

54/5

Step-by-step explanation:

(3/5)(18)=54/5

Answer:

Step-by-step explanation:

Increases weight  = 80 - 40 = 40 lbs

Percent increase = (40/40)*100 = 1*100 = 100%

Answer:

The percent change is 50%.

Step-by-step explanation

1) 80-40=40

2) 40 divided by 80 which equals 0.5

3) 0.5 multiplied by 100

4) 0.5 x 100=50

The formula for percent change is change divided by the original amount then multiply the answer from that problem by 100.

Step-by-step explanation:

parallelogram is a simple quadrilateral with 2 pairs of. parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Thanks..... hope it helped.

Marco scored 876 more points than Jasmine.

To find how many more points Marco scored than Jasmine, we subtract Jasmine's score from Marco's score.

Marco scored 1,753 points while Jasmine scored 877 points.

Thus, Marco scored 1,753 - 877 = 876 more points than Jasmine.

Answer:

x=-2, y=3. (-2, 3).

Step-by-step explanation:

y=-x+1

y=3

----------

-x+1=3

-x=3-1

-x=2

x=-2

y=-(-2)+1

y=2+1=3

Answer:

Step-by-step explanation:

2x3/5+1/5

Going by BoDMAS

Multiplication comes before addition

2x3/5+1/5 = 6/5 + 1/5 = (6+1)/5

= 7/5 = 1 2/5

Final answer:

The expression 2x3/5+1/5 is solved by first multiplying 2 by 3/5 to get 6/5 or 1.2, and then adding this to 1/5 to get the final answer of 7/5 or 1.4.

Explanation:

To solve the expression 2x3/5+1/5, you first need to perform the multiplication before the addition, according to the order of operations (PEMDAS/BODMAS). So, you need to multiply 2 by 3/5:

2 x 3/5 = 6/5 or 1.2

Now add this result to 1/5:

6/5 + 1/5 = 7/5 or 1.4

Therefore, the answer is 7/5 or 1.4.

Answer: 12 I saw your comment lol