Fill in each box to make the statements true.

The ____ function is written f(x) = ⌊x⌋ and rounds numbers ___ to the nearest integer. The graph of f(x) = ⌊x⌋ includes the point (174, ___ ).

Answer:

all positive real numbers, (0, ∞)

Step-by-step explanation:

The log function is not defined for 0 or for negative numbers.

The domain of the log function is all positive real numbers.

Answer: all positive real numbers

Answer:

A. x + 5

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \frac{x^2 - 25}{x - 5}[/tex]

Step 2: Simplify

Answer:

[tex](1,\, 10)[/tex].

Step-by-step explanation:

Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to [tex]x[/tex]. Make use of the power rule to find the following:

[tex]g^\prime(x) = 3\, x^2 - 2\, a\, x[/tex].

[tex]h^\prime(x) = 2\, (2\, x) + b = 4\, x + b[/tex].

The question states that the graphs of [tex]g(x)[/tex] and [tex]h(x)[/tex] touch at [tex]x = 1[/tex], such that [tex]g^\prime(1) = h^\prime(1)[/tex]. Therefore:

[tex]3 - 2\, a = 4 + b[/tex].

On the other hand, since the graph of [tex]g(x)[/tex] and [tex]h(x)[/tex] coincide at [tex]x = 1[/tex], [tex]g(1) = h(1)[/tex] (otherwise, the two graphs would not even touch at that point.) Therefore:

[tex]1 - a + 6 = 2 + b + 3[/tex].

Solve this system of two equations for [tex]a[/tex] and [tex]b[/tex]:

[tex]\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}[/tex].

Therefore, [tex]a = -3[/tex] whereas [tex]b = 5[/tex].

Substitute these two values back into the expression for [tex]g(x)[/tex] and [tex]h(x)[/tex]:

[tex]g(x) = x^3 + 3\, x^2 + 6[/tex].

[tex]h(x) = 2\, x^2 + 5\, x + 3[/tex].

Evaluate either expression at [tex]x = 1[/tex] to find the [tex]y[/tex]-coordinate of the intersection. For example, [tex]g(1) = 1 + 3 + 6 = 10[/tex]. Similarly, [tex]h(1) = 2 + 5 + 3 = 10[/tex].

Therefore, the intersection of these two graphs would be at [tex](1,\, 10)[/tex].

Answer:

y=3x + 1

Step-by-step explanation:

slope is same

insert coordinates into x and y values

determine y-intercept

Answer:

113.04 is the answer

Step-by-step explanation:

Use the formula for finding the area of a circle.

Area= pi times radius to the second power.

First you had to divide your diameter by 2 to get 6. Then 6 squared, to get 36. Then finally 36x3.14.

Answer:

6

Step-by-step explanation:

Answer:

91 - 120 minutes

Step-by-step explanation:

In a histogram, the bar highest suggests the most common, so most students spend 91 - 120 minutes in this histogram.

Answer:

In other words y = 2-x

Put in some values of x and see which graph matches the given ys.

The last graph

Answer:

b

Step-by-step explanation:

Answer:

5.4 units

Step-by-step explanation:

Hi there!

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]

Plug in the given points (1,5) and (3,0)

[tex]d=\sqrt{(3-1)^2+(0-5)^2}\\d=\sqrt{(2)^2+(-5)^2}\\d=\sqrt{4+25}\\d=\sqrt{29}\\d=5.4[/tex]

Therefore, the distance between the two points when rounded to the nearest tenth is 5.4 units.

I hope this helps!

Answer:

Let's define:

S as the rate at which Sara can weed a garden.

We know that:

S*30min = 1 garden

And let's define H as the rate at which Hamdan can weed a garden, we know that when they work together, they can complete the job in 20 minutes, then

(S + H)*20min = 1 garden

a) Here we get:

H*n = 1 garden

where n is the number of hours that he would take (note that in two previous equations we have minutes, so we need to use a change of units)

b) The equation is

(S + H)*20min = 1 garden

c) ok, we know two things:

(S + H)*20min = 1 garden

S*30min = 1 garden

first, let's convert both times to hours:

60 min = 1 hour

then:

30 min = (30/60) hours = 0.5 hours

20 min = (20/60) hours = 0.33 hours

Then the equations become:

(S + H)*0.33 hours = 1 garden

S*0.5 hours = 1 garden

Le's solve the second equation for S:

S = (1 garden /0,5 hours) = 2 gardens/hour.

Now we can replace this in the other equation to get:

(2 garden/hour + H)*0.33 hours = 1 garden

2 garden/hour + H = (1 garden)/(0.33 hours) = 3 gardens/ hour

H = 3 gardens/hour - 2 gardens/hour = 1 gardens/hour

This means that the rate of Hamdan is 1 gardens/hour, so he can weed a garden in one hour.

Then:

(1 garden/hour)*n = 1 garden

n = ( 1 garden)/((1 garden/hour)) = 1 hour

Answer:

1.) 8 ; (2.) 200 ; (3.) 5 ; (4.) 6

Step-by-step explanation:

1.)

Number of apple baskets = 11

Total number of apples = 88

Number of apples per basket = 88 / 11 = 8

2).

Number of words per minute = 40

Number of words that can be typed in 5 minutes :

40 * 5 = 200 words

3.)

Number of balloons = 20

Number of friends = 4

Number of balloons per friend = 20/4 = 5

4.)

Time required to make 1 greeting card = 5 minutes

Number of greeting cards that can be made in 30 minutes :

30 minutes / 5 minutes = 6 greeting cards

Answer:

[tex]C=28.3m[/tex]

Step-by-step explanation:

From the question we are told that:

Diameter [tex]d=9m[/tex]

Radius[tex]r=4.5m[/tex]

Generally the equation for Circumference of a circle is mathematically given by

[tex]C=2\pi r\\\\\C=2*\pi*4.5m[/tex]

[tex]C=28.3m[/tex]

Answer:

Step-by-step explanation:

From the question we are told that:

Diameter

Radius

Generally the equation for Circumference of a circle is mathematically given by

Have a good day

Step-by-step explanation:

Answer:

B.) 75

Step-by-step explanation:

Answer: B 75

Step-by-step explanation:

9514 1404 393

Answer:

  2

Step-by-step explanation:

Each orange vertex is twice as far from the origin as the corresponding black vertex. Each orange line segment is twice as long as the corresponding black line segment. The scale factor is 2.

Answer:

4 and 5

Step-by-step explanation:

Let the numbers be x and y

If their sum is 9, hence;

x + y = 9 ....1

When reversed

10y+x = 2(10x+y)

10y+x = 20x + 2y

10y - 2y = 20x - x

8y = 19x

y = 10x/8 ...2

Substitute equation 2 into 1;

From 1;

x+y = 9

x +(10x/8) = 9

18x/8 = 9

18x = 72

x = 72/18

x = 4

Since x+y =9

y = 9-x

y =9-4

y = 5

Hence the numbers are 4 and 5

Answer:

please mark as brilliant

Answer:

Step-by-step explanation:

[tex] {10}^{ - 4} [/tex]

Answer:

Vertex is (-a, -6), where a ≠ 0.

General Formulas and Concepts:

Algebra I

Algebra II

Vertex Form: y = a(bx - h)² + k

Step-by-step explanation:

Step 1: Define

y = -3(x + a)² - 6

↓ Identify variables

a = -3

b = 1

(h, k) = (-a, -6)

Answer:

V = 12,348·π

Step-by-step explanation:

The given parameters of the glass Vase are;

The shape of the glass vase = A sphere

The radius of the vase, r = 21 inches

The given formula for finding the volume of a sphere is [tex]V = \dfrac{4}{3} \cdot \pi \cdot r^3[/tex]

Therefore, when r = 21 inches, we get;

[tex]V = \dfrac{4}{3} \cdot \pi \cdot 21^3 = {12,348 \cdot \pi}[/tex]

Therefore, the expression for finding the equation of the spherical glass vase, V = 12,348·π

Answer:

B

Step-by-step explanation:

These are corresponding angles if i remember correctly.

Answer:

Supplementary

Step-by-step explanation:

The angles add up to 180 degrees

Answer:

(3,-5)

Step-by-step explanation:

We first cal ulate the distance

Answer:

Step-by-step explanation:

Biking is x and bussing is y. We know that the total distance is 325. Thus, the first equation in this system is

x + y = 325 (which says that the km traveled by bike plus the km traveled by bus totaled 325 km).

We also know that the pair biked 75 km more than they rode, giving us the second equation in our system:

x = y + 75. Now we use simple substitution and plug y + 75 in for x in the first equation:

(y + 75) + y = 325 and

2y + 75 = 325 and

2y = 250 so

y = 125 km. They rode the bus for 125 km and biked for 325 - 125 which is 200. And the difference is 75 km, as it should be!

Answer:

Step-by-step explanation:

please type it correctly and i can help Step-by-step explanation:

Complete question:

4x³ - 4x + 3 is divided by (2x - 1). Find the quotient and the remainder

Answer:

The quotient =  2x² +  x  - ³/₂  and the remainder = ³/₂

Step-by-step explanation:

Given function;

4x³ - 4x + 3 divided by (2x-1)

Use long division method to obtain the remainder and the quotient.

                               2x² +  x  - ³/₂

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

                 2x - 1 √4x³ - 4x + 3

                           - (4x³ - 2x²)

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

                                    2x²  - 4x + 3

                                 - ( 2x² - x)

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

                                        -3x + 3

                                      -(-3x + ³/₂)

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

                                            ³/₂

Therefore, the quotient =  2x² +  x  - ³/₂  and the remainder = ³/₂

Answer:

add

Step-by-step explanation:

The exponent "product rule" tells us that, when multiplying two powers that have the same base, you can add the exponents. In this example, you can see how it works. Adding the exponents is just a short cut! The "power rule" tells us that to raise a power to a power, just multiply the exponents.

Hope this is helpful

Answer:

Add

Step-by-step explanation:

Hope it helps you

Please mark as brainliest

Thank You

Answer:

Step-by-step explanation:

1)

9:10

+ 0:45

9:55      

so at 9:55 she finished her eating.

2)

  10:25

- 2:15

8:10

so test started at 8:10

3)

9:15

-7:30

2:15    

si games duration was 2;15

4)

2:40

+25

3:05

 se reached home at 3:05

Given:

The rule of translation is:

[tex](x+3,y-2)[/tex]

The trapezoid ABCD on the graph.

To find:

The coordinates of the point C'.

Solution:

From the given graph, it is clear that the coordinates of point C are (-2,4).

The rule of translation is:

[tex](x,y)\to (x+3,y-2)[/tex]

Using this rule of translation, we get

[tex]C(-2,4)\to C'(-2+3,4-2)[/tex]

[tex]C(-2,4)\to C'(1,2)[/tex]

Therefore, the coordinates of the point C' are (1,2).