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Answer: 3.215 × 10^-7

Step-by-step explanation:

The exponent is smaller than all of the others, so it's the smallest.

Values needed to complete the X diagram are:

On top -28, On the bottom: -3 and On the sides: -7 and 4.

An algebraic expression is factorised when it is written as the product of its factors.

The given equation is :

F(x) = x²-3x-28

finding factors,

=  x²-7x+4x-28

= x(x-7) +4(x-7)

= (x-7)(x+4)

Given general equation is ax²+bx+c,

on comparing with  x²-3x-28

a = 1

b = -3

c = -28

ac = 1*(-28) = -28

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The principal amount invested by Shen in the saving bond is $9,000.

As per the given question;

The formula for simple interest is-

SI = PRT/100

Put the values;

SI = PRT/100, write the formula in the terms of P

P = 100×SI/RT

P =  100×1620 / (3×6)

On simplification;

P = 9,000

Thus, the amount invested by Shen in the saving bond is $9,000.

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Using division we can calculate that 8 books can fit in the 14 inch long bookshelf .

Division is one of the four basic arithmetic operations, or the process by which two numbers are added together to produce a new number. Multiplication, addition, and subtraction make up the remaining operations.

length of book shelf = 14 inch

length of each book = 1 3/5 inch = 1.6 inches

Number of books = 14 ÷ 1.6 = 8.75 books

Hence by division we get that 8 book can be put in the  bookshelf.

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Answer: w = -238

Step-by-step explanation:

[tex]34=\frac{-w}{7}[/tex]

Switch sides

[tex]\frac{-w}{7} =34[/tex]

Multiply both sides by 7

[tex]\frac{7\left(-w\right)}{7} =34\cdot \:7[/tex]

Simplify

-w = 238

Divide both sides by -1

[tex]\frac{-w}{-1}=\frac{238}{-1}[/tex]

Simplify

w = -238

If I made any mistakes, please let me know!

 I hope this helped :)

Step-by-step explanation:

x(c - b) = g

divide through by (c - b)

x(c - b) = g

(c - b) (c - b)

x = g/ (c - b)

Answer:

The restaurant is at a profit of $250

Maggie's mistake on the solution of the expression for x was when she subtracted 7x to both sides, the result should have been -3x and not 3x.

The equation is given as follows, as the angles are congruent, that is, they have the same measure:

4x + 2 = 7x - 25.

First, we isolate x on the left side of the equality, subtracting 7x from both sides, hence:

4x + 2 - 7x = 7x - 25 - 7x

Then the correct expression is:

-3x + 2 = -25

Which is where Maggie's mistake happened, on the subtraction of 4x and 7x.

Then, isolating x, we subtract 2 from both sides of the equality, to remove the +2 term on the left side of the equality.

-3x = -27

3x = 27

x = 27/3

x = 9.

The correct solution is x = 9.

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Answer: Ray BA and Ray BC

Explanation:

A ray starts at at a fixed point and moves forever in one direction. If we break line AC into two parts BA and BC, then we can form two opposite rays. Another ray points to the right but the letter marked for this isn't clear, so I'm not sure what to write for that ray. Same goes for the dashed ray that points to the left.

BD is a segment because both endpoints are fixed. We don't have either side extending forever in that direction.

The value of x is 9 and the mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.

When any two straight lines intersect each other, then four angles are formed. The angles that are directly opposite to each other are known as opposite angles. They are also called vertical angles or vertically opposite angles.

Now, from the image attached, we see that the two given angles are opposite angles and as such they are congruent. Thus, we have;

4x + 2 = 7x - 25

Rearrange to collect like terms on same side to get;

7x - 4x = 25 + 2

3x = 27

x = 27/3

x = 9

The mistake that Maggie made is that she did use the proper operation sign when rearranging the numbers.

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The value of Chrissy's height from the problem is 76

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Let x represent Chrissy's height. 55 is the difference of Chrissy's height and 21. Hence:

x - 21 = 55

x = 76

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The fraction of the students in the classroom that like both flavors is 1/4.

From the information, three-fourths of students in the classroom like chocolate chip cookie dough ice cream and one-half of these same students also like mint-flavored ice cream.

The fraction of the students in the classroom that like both flavors will be the addition of both flavors subtracted from 1. This will be illustrated as:

= (3/4 + 1/2) - 1

= 3/4 + 2/4 - 1

= 5/4 - 1

= 1/4

The fraction is 1/4.

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The sinusoidal function that matches the graph given is:

g(x) = 4cos((π/7)x) - 2.

The cosine function is defined as follows:

g(x) = acos(bx)+d.

The coefficients have these following roles:

For this problem, we use a cosine function because the function is not zero at the origin, while for the sine it is.

From the graph of this function, the maximum value is of 2, while the minimum value is of -6, hence the amplitude is found as follows:

2a = 8 (difference between these values).

a = 4.

Then:

g(x) = 4cos(bx) + d.

A function with amplitude of 4 should oscillate between -4 and 4, while this one oscillates between -6 and 2, meaning that it was shifted 2 units down, hence d = -2 and:

g(x) = 4cos(bx) - 2.

The period is of 14 units, hence:

2π/b = 14

14b = 2π

b = π/7

Hence the function is:

g(x) = 4cos((π/7)x) - 2.

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Answer:

y = 1/4x + 1

1/4 is the slope and 1 is the y-intercept

Answer: the function only intersects the y axis

Step-by-step explanation:

Answer:

The function only intersects the y axis.

Step-by-step explanation:

See the attached worksheet.

Answer:

See below

Step-by-step explanation:

Plug in x = 3   And  y = 1 to see

3(3) + 10(1)  >= 20 ?

9     + 10 >= 20?

19 >= 20     Not true  ....the point does not make the inequality true

Answer:

The correct option is (b) truth value. If we are given two statements, the first statement is called the hypothesis and the second is its conclusion.

Answer:

all students their favorite subject in school

465/48

Step-by-step explanation:

1 ⅞ miles × 5⅙ = 465/48

________ _______

1 hour × 5⅙ = 5⅙ hours

The true statement about the function are;

⇒ The function is positive for all real values of x, where x < –1.

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The graph of the function;

f(x) = –(x + 3)(x – 1)

Now,

Graph of the function is shown in attached image.

Which is a parabola, It goes through (- 3, 0), has a vertex at (- 1, 4), and goes through (1, 0).

Clearly, When x < -1

Take x = 0 < -1

The value of function;

f(x) = –(x + 3)(x – 1)

    = - (0 + 3) (0 -1)

    = -3 x -1

    = 3

The function is positive.

Thus, The true statement about the function are;

⇒ The function is positive for all real values of x, where x < –1.

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One possible solution for the system of inequalities that models the situation is: (5,7), when he purchases 5 drinks and 7 tacos.

A system of inequalities is when multiple variables are related in a context, and then inequalities are built to find the numeric range of values that each variable can assume, according to the constraints in this problem.

For this problem, the variables are defined as follows, as stated in the text:

Both amounts cannot assume negative values, hence the first constraints are:

He must buy at least 14 drinks, hence:

x + y ≥ 14.

He must spend at most $40, hence, considering the price of each item, the constraint is given by:

2x + 4y ≤ 40.

The graphic solution to the inequality is given at the end of the answer. One possible solution is of (5,7), meaning that he buys 5 drinks and 7 tacos.

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Answer:

a)16777216

b)279936

c)32768

d)49

Plss mark as brainliest

Answer:

ok!

a) 4^9 ×4^3=4^9+3=4^12

b) 6^5 ×6^2=6^5+2=6^7

c) 8^6 ÷8=8^6-1 =8^5

d) 7^8÷7^6=7^8-6=7^2

Pls mark me as brainliest.

I answered first.

Step-by-step explanation:

It's simple!

If there is multiplication, add the powers.

If there is division, subtract the powers.

The smallest such whole number is 11 which is, Which is divided by 3, the remainder is 2, f it, divided by 4, the remainder is 3

Let the number be x

Here we have to find the whole number which is Divided by 3,4 the remainder is 2,3 respectively,

x+(3–2)= x +1 is multiple of 3

Div by 4 remainder is

3x+(4–3) = x+1 is multiple of 4

So LCM of 3,4 is 3×4 = 12

Hence,x=12 –1 =11

The smallest such whole number is 11 which is divided by 3, the remainder is 2, if it divided by 4, the remainder is 3.

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replace 'x' with 'y'

15y - 14 = x; solve for y

15y = x + 14

y = (x+14)/15

Provided the figures we have that describe the mass of Earth and the mass of Jupiter, we can conclude that Jupiter is 318 times greater than the mass of Earth.

From the figures we have, we can see that the mass of Jupiter is greater than the mass of Earth because it has more zeros.

So, we have to divide the value of the mass of Jupiter by the mass of the earth as follows:

1.9 x 10^27

5.97 X 10^24

=1. 9 ÷ 5.97 × 10^27 - 10^24

= 0.318... ×10³

= 318

Do note that when we have to divide figures that are raised to some figures, the rule will be to subtract the figures as we find in the fact that 27 - 24 is equal to 3. And when we multiply, we arrive at the stated figure.

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Answer:

the answer is c

Step-by-step explanation:

3 x 5 x 5 x 8 x 10 = 6,000

3 x 5 = 15, 15 x 5 = 75.

8 x 10 = 80.

75 x 80 = 6,000