A snake accelerates from 2 m/s to 10 m/s in 4 seconds. What is the snake’s average acceleration?

Answer:

c = 7

Step-by-step explanation:

Solve for 'c'

-7c - 5 = -9c + 9

-5 -9 = -9c + 7c

-14 = -2c

c = 7

Therefore 'c' equals 7

Answer:

c=7

Step-by-step explanation:

-7c-5=-9c+9

Add 9c to each side

-7c+9c-5=-9c+9c+9

2c -5=9

Add 5 to each side

2c-5+5 = 9+5

2c = 14

Divide each side by 2

2c/2 = 14/2

c=7

Answer:

65

Step-by-step explanation:

You multiply the factors by each other.

Answer:

65

Step-by-step explanation:

13 x 5 = 65

Answer:

2:45

Step-by-step explanation:

Expanding parentheses,

➝ (x - 3)(x + 7)

➝ x(x + 7) - 3(x + 7)

➝ x² + 7x - 3x - 21

➝ x² + 4x - 21

Option B

Expanding brackets involves removing the brackets by multiplying each term in the brackets by every term outside of the brackets. The process of expansion is also known as the distributive law. When expanding brackets be very careful of negative numbers. 

Once a set of brackets has been expanded, it is possible for several like terms to appear. 

When this is the case you can use the box method or FOIL to ensure you expand the set of brackets properly. In general:

[tex] \large{ \boxed{ \rm{(a + b)(c + d) = ac + ad + bc + bd}}}[/tex]

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Answer:

12,662 books

Step-by-step explanation:

Total number of books = 75,972

No. of science books = ⅓ of 75,972 = ⅓*75,972 = 25,324 books.

No. of business books = 75% of the remaining books = 75% of (75,972 - 25,324)

= [tex] \frac{75}{100}*50,648 = 37,986 [/tex]

No. of business books = 37,986

No. of maths books in the math section = 75,972 - (25,324 + 37,986)

= 75,972 - 63,310

= 12,662 books

The height of house is 26.53 m

The angle of elevation and angle of depression are opposites of each other. In an angle of elevation, the object is placed above the observer, while in the case of the angle of depression, it is placed below the observer.

If you are standing at your terrace and looking at the sun, then the angle of elevation will be formed. On the other hand, if you will look at the dog standing on the road from your terrace, then the angle of depression will be formed. In both cases, we use trigonometry angles to find the heights and distances.

Given:

Window height = 20 m

angle of elevation =5

angle of depression= 15

Using trigonometry

tan 15 = P/B

0.2679= 20/B

B= 74.654 m

Again

tan 5 =P/B

0.0874 = P/ 74.645

P= 6.5305 m

Hence, height of the tree is 6.53 + 20= 26.53 m

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Answer: Three gallons will be enough to make 128 servings.

Step-by-step explanation: In Three gallons there are 64 cups. if 5 cups makes 10 servings, that is 1/2 cup per serving. So 64 cups will make 128 servings.

The original price is 100%, a 15% discount means the shoes are now ( 100-15 = 85) 85% of the original price,.

Multiply the original price by 85%

60 x 0.85 = 51

The price is $51

Answer:

$51

Step-by-step explanation:

15% discount means that the new price is 85% of the original one. Therefore we just need to multiply 60 by 0.85 to find 85% of the number.

60x0.85=$51

The new price would be $51.

Similarly you could also have divided 60 by 100 to find one percent of it (60/100=0.6) and then multiplied it by 85 to find 85%. (0.6x85=51)

Hope this helped!

Answer:

m = 1.2

Step-by-step explanation:

12m = 14.4

Divide each side by 12

12m/12 = 14.4/12

m = 1.2

m = 1.2  is the answer

because..

12m = 14.4

Divide each side by 12

12m/12 = 14.4/12

m = 1.2

hope this helped ヾ(•ω•`)oヾ(•ω•`)o

Answer:   see proof below

Step-by-step explanation:

Use the Pythagorean Identity: cos²Ф + sin²Ф = 1

Use the Difference Identity: cos(A - B) = cosA · cosB + sinA · sinB

Use the Double Angle Identity: cos 2Ф = 1 - 2sin²Ф

Proof LHS → RHS

LHS:                                          (cosA - cosB)² + (sinA - sinB)²

Expand:          cos²A - 2cosA · cosB + cos²B + sin²A - 2sinA · sinB + sin²B

Pythagorean Identity:   2 - 2cosA · cosB  - 2sinA · sinB

Factor:                           2(1 - (cosA · cosB  + sinA · sinB))

Difference Identity:       2(1 - (cos(A - B))

Let Ф = (A-B)/2:             2(1 - cos2Ф)

Double Angle Identity:  2(1 - (1 - 2sin²Ф))

Simplify:                         2(1 - 1 + 2sin²Ф)

                                   = 4sin²Ф

Substitute (A-B)/2=Ф:    4sin²(A-B)/2

LHS = RHS: 4sin²(A-B)/2 = 4sin²(A-B)/2   [tex]\checkmark[/tex]

Answer:

0.074 or 37/500

Step-by-step explanation:

also 7.4%

Answer:

X÷5y

Step-by-step explanation:

5 x y is 5y and then we divide

The expression for the given phrase is 5y/x.

Given that, x divided by the product of 5 and y.

An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.

Here,

The product of 5 and y =5×y

= 5y

x divided by the product of 5 and y

= 5y/x

Therefore, the expression for the given phrase is 5y/x.

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Answer:

x = 30    Quadrilateral

x = 20    Triangle

Step-by-step explanation:

Quadrilateral

A quadrilateral has a sum of 360 degrees for its interior angles.

So

x + 2x + 4x + 5x = 360       Find the sum of the 4 angles

12x = 360                           Divide by 12

12x = 360/12                      

x = 30                                 Answer

Triangle

A triangle has an interior angle sum of 180 degrees.

2x + 5x  + (x + 20) = 180         Remove the brackets

2x + 5x  + x + 20 = 180           Add the angles

8x + 20 = 180                           /subtract 20 from both sides

8x = 180 - 20

8x = 160                                 Divide by 8

x = 160/8

x = 20    

Answer:

B and D

Step-by-step explanation:

A can't be correct because the length of a segment is always positive. B is correct because we have to take the absolute value of the distance between endpoints to find the length of the segment. C is not correct because AC is obviously longer than BC so how would AB + AC = BC? D is correct because it models the Parts Whole Postulate.

Answer:

2,irrational,2,irrational :)

Step-by-step explanation:

Answer: I think its a tell me if im wrong

Step-by-step explanation:

Answer:

[tex] w = \frac{11}{35} [/tex]

Step-by-step explanation:

To solve, [tex] \frac{3}{5w} - \frac{2}{7w} = 1 [/tex], make both fractions on your left as one fraction by finding a common denominator.

Common denominator of 5w and 7w is 35w

Thus,

[tex] \frac{7(3) -5(2)}{35w} = 1 [/tex]

[tex] \frac{21 - 10}{35w} = 1 [/tex]

[tex] \frac{11}{35w} = 1 [/tex]

Multiply both sides by 35w

[tex] \frac{11}{35w}*35w = 1*35w [/tex]

[tex] 11 = 35w [/tex]

Divide both sides by 35

[tex] \frac{11}{35} = \frac{35w}{35} [/tex]

[tex] \frac{11}{35} = w [/tex]

[tex] w = \frac{11}{35} [/tex]

Answer:

4 terms

Step-by-step explanation:

First rearrange the expression from largest to smallest:

-9x^4-3x^2+5x+2

Now count how many terms their are,

-9x^4=1 term

-3x^2=2 terms

5x=3 terms

2=4 terms

Therefore, there are 4 terms in the expression

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one-half=[tex]\frac{1}{2}[/tex]

one-fifteenth=[tex]\frac{1}{15}[/tex]

[tex]\frac{1}{2}*\frac{1}{15} = \frac{1}{30}[/tex]

To multiply fractions, you multiply the numerator (top number) by the numerator (top number and the denominator (bottom number) by the denominator (bottom number).

Numerator: 1×1=1

Denominator: 2×15=30

So the product of one-half times one-fifteenth is one over thirty.

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The product of one-half times one-fifteenth is equal to 1/30.

A fraction is a number that represents a part of a whole. Fractions are written as two numbers separated by a fraction bar.

The number on top of the fraction bar is called the numerator, and the number on the bottom of the fraction bar is called the denominator.

We have:

One-half, which is equal to 1/2.

One-fifteenth, which is equal to 1/15.

In mathematics, product means multiplication

Multiplying two fractions is the same as multiplying the numerators and the denominators.

Thus, the product of one-half times one-fifteenth is:

1/2 * 1/15 = (1*1)/(2*15)

               = 1/30

The product of one-half times one-fifteenth is 1/30.

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Answer:

m=[tex]\frac{23}{3}[/tex] simplest form if you need it as a decimal its m=7.6

Step-by-step explanation:

Answer: X= -1 OR X= 11

Step-by-step explanation:

Step 1 : Equate ( x-5)² since it occurred twice, hence the reason 2 is added in front of (x-5)²

= (x-5)²

= (x-5)(x-5)

= (x²-5x-5x+25)

= (x²-10x+25)

Step 2: multiply the result by two since it occurs twice and also bring the equation

= 2 (x²-10x+25) +7 = 79

= 2x²- 20x+50+7 = 79

= 2x²- 20x+57 =79

Step 3: most quadratic equation are always equal to zero, let's make this one equal to Zero by subtracting 79 from both sides

= 2x²-20x+57-79 = 79-79

= 2x²-20x-22=0

Step 4: divide the equation by a common number to get the least coefficient of the three coefficients

Dividing the three by 2

(2x²-20x-22)/2 = x²- 10x- 11

Step 5: Factorise completely

Sub step 1 : the first term in the equation is X² which makes the first term coefficient 1; the second term in the equation is -10x which makes the second term coefficient -10, the constant has a coefficient of -11

Sub step 2: multiply the coefficient of the first term (1) and the constant (-11) which gives us (-11)

1*-11 = -11

Sub step 3: Get two numbers in such a way that the addition of the first number and the second number gives the second coefficient in the quadratic equation and the multiplication of the two numbers will give us the product of the first coefficient and the constant.

And the two numbers is +1 and -11, the sum of the two numbers will give us -10 and the product will give us -11.

Step 6: slot the two numbers (+1, -11) into the equation by making themr replace the second coefficient

x²-10x-11=0

= x²+x-11x-11 =0

Step 7: split the equation into two and Factorise further

= (x²+x)(-11x-11) =0

= x(x+1)-11(x+1) = 0

= x+1= 0 or x-11 =0

Step 8 split them into individual equation

= x+1= 0.

Subtract 1 from both sides

= X+1-1=0-1

= x= -1

Or X should be

= x-11=0

Add 11 to both sides

= X-11+11 = 0+11

= x= 11

Answer:

150 miles

Step-by-step explanation:

15÷100×1000=150

Step-by-step explanation:

From graph of g(x), it is observed that y - intercept is 6.

Therefore,

[tex]6 = 2(3)^{0} + k[/tex]

[tex]k \: = 4[/tex]

The value of k is equal to 4

Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given here the functions  f(x)=2(3)ˣ and g(x)=f(x)+k when x=0 we get

f(0)=2  and from the graph we can clearly observe that g(0)=6

Thus putiing in the values we get k=4

Hence, The value of k is equal to 4

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Answer:

64

Step-by-step explanation:

let the number be x, then

[tex]\frac{1}{8}[/tex] x + 5 = 13 ( subtract 5 from both sides )

[tex]\frac{1}{8}[/tex] x = 8 ( multiply both sides by 8 )

x = 64

The number is 64

Answer:

The number is 64

Step-by-step explanation:

Let x be the number

1/8 x +5 = 13

Subtract 5 from each side

1/8x +5-5 = 13-5

1/8 x = 8

Multiply each side by 8

8*1/8x = 8*8

x = 64

Answer:

21.69% decrease.

Step-by-step explanation:

We want to determine the percent change from 16.6 to 13.

First, since 13 is smaller than 16.6, we know that this is decrease.

Percent change is given by the formula:

[tex]\displaystyle PC=\frac{ \text{New - Old}}{\text{Old} } \cdot100\%[/tex]

The new value is 13 and the old value is 16.6. Substitute:

[tex]\displaystyle PC=\frac{(13)-(16.6)}{16.6} \cdot100\%[/tex]

Evaluate:

[tex]\displaystyle PS = -\frac{3.6}{16.6} \cdot 100 \%[/tex]

Use a calculator:

[tex]\displaystyle PS\approx-0.2169\cdot100\% \\ \\ PS\approx21.69\%[/tex]

We ignore the negative because the negative simply tells us that it's decreasing. (Likewise, if the answer's positive, it's an increase.)

In conclusion, the percent change is an approximate 21.69% decrease.

Answer:

The answer is 51

Step-by-step explanation:

Because 18 + 23 = 51

Answer:

Step-by-step explanation:

the length of EG is 6 so G is 6 units away from E. If E is at 3, then G is at 3+6 = 9

X is 12 units away from E so X is at 3 + 12 = 15

This assumes you are not using negative numbers.

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Number line are used to represent numbers on a line at regular intervals. The possible coordinates of G is either 10 or -14.

Given that:

[tex]G = 2[/tex]

[tex]EG = 12[/tex]

The equation that calculates EG is:

[tex]EG = |E - G|[/tex]

So, we have:

[tex]12 = |2 - G|[/tex]

Remove absolute brackets

[tex]2 - G = \± 12[/tex]

Add 2 to both sides

[tex]-G =2 \± 12[/tex]

Rewrite as:

[tex]G =-2 \± 12[/tex]

Split

[tex]G =- 2 - 12[/tex] or [tex]G = -2 + 12[/tex]

[tex]G = -14[/tex] or [tex]G = 10[/tex]

The possible coordinates of G are: 10 or -14.

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Answer:

127x

Step-by-step explanation:

The expression 127x will represent this situation.

Since x represents the number of textbooks, we can put the coefficient 127 in front of it to include the cost.

For example, 2 textbooks will be $254 if we plug in 2 as x into the expression, since 127(2) = 254.

Answer:

y > -255, or (-255, infinity)

Step-by-step explanation:

y + 51 > - 204

Solve for y:  subtract 51 from both sides, obtaining:

y > -255, or (-255, infinity)

The solution of the inequality is y > -255.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

Given that translate and solve: 51 more than y is greater than −204. The inequality expression can be written as:-

y + 51 > - 204

Solve for y:  subtract 51 from both sides, and solve the inequality:-

y > -255,

Hence, the solution to the inequality is y > -255.

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Answer:

w=sa

Step-by-step explanation:

move the a into multiplication on the other side so

w=sa

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Answer:

W = SA

Step-by-step explanation:

S = W/A

Multiply both sides by 'A'

S* A = [tex]\frac{W}{A }*A[/tex]

SA = W

W = SA