Which point is on the graph of f(x) = 2.5^x
А. (1, 10)
в. (0, 0)
с. (0, 10)
D. (10, 1)

Answer:

5y - 4x = 5. This gives you your points with a slope of 4/5

Answer:

[tex]y=\frac{4}{5}x+1[/tex]

Step-by-step explanation:

We are given the slope, and the y-intercept. So we can use the slope-intercept equation. Which is as follows:

[tex]y=mx+b[/tex]

where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (the value of [tex]y[/tex] when [tex]x=0[/tex]).

The information that we have is that the slope of the line is:

[tex]m=\frac{4}{5}[/tex]

and that the line crosses the y-axis at (0, 1).

From this point we can find the y-intercept [tex]b[/tex], because b is the value of [tex]y[/tex] when [tex]x=0[/tex].

And since the line passes through (0, 1) when [tex]x = 0[/tex], [tex]y =1[/tex]. Thus, the y-intercept is:

[tex]b=1[/tex]

substituting the values of the slope and the y-intercept into the equation:

[tex]y=mx+b\\y=\frac{4}{5}x+1[/tex]

the answer is:   [tex]y=\frac{4}{5}x+1[/tex]

In total, there are 200 students from North Beach.

Of those 200 students, 110 attended the game.

Because it is only asking for the probability that a student from North Beach attended, the answer would be 110 / 200, or 0.55.

Therefore, the answer would be C.

Hope this helps! :)

Answer:

0.314

Step-by-step explanation:

Given:

total number of students=350

total number of students that attented= 170

students that attended from North beach =110

probability that a student attended the game, given that the student is from North Beach= 110/350

                    =0.314 !

Answer:

1. C) 5.50x + 10

2. 54

Step-by-step explanation:

1. C) 5.50x + 10

You have a static fee of $10 which does not need to be attached to a variable as it will not change. You also have a fee of $5.50, which may be charged depending on the amount of classes. Since this is dependent on something, it includes a variable.

Therefore, your terms are:

5.5x

10

Simply add them together for your equation.

[tex]5.5x+10[/tex]

2. 54

To solve, simply plug in 8 to your equation which you created in part 1. This is possible because x stands for the amount of classes and, as the question tells us, 8 is the amount of classes.

[tex]5.5(8)+10\\44+10\\54[/tex]

Answer:

[tex]\large\boxed{x=-\dfrac{8}{3}\ or\ x=\dfrac{7}{2}}[/tex]

Step-by-step explanation:

[tex]6x^2-5x=56\qquad\text{subtract 56 from both sides}\\\\6x^2-5x-56=0\\\\6x^2+16x-21x-56=0\\\\2x(3x+8)-7(3x+8)=0\\\\(3x+8)(2x-7)=0\iff 3x+8=0\ \vee\ 2x-7=0\\\\3x+8=0\qquad\text{subtract 8 from both sides}\\3x=-8\qquad\text{divide both sides by 3}\\\boxed{x=-\dfrac{8}{3}}\\\\2x-7=0\qquad\text{add 7 to both sides}\\2x=7\qquad\text{divide both sides by 2}\\\boxed{x=\dfrac{7}{2}}[/tex]

Answer:

2¹⁵x¹⁵ (2nd option)

Step-by-step explanation:

When you expand (2x+10y)¹⁵ you would get:

32,768x¹⁵ + 2,457,600x¹⁴y + 86,016,000x¹³y² + 1,863,680,000x¹²y³+

27,955,200,000x¹¹y⁴+307,507,200,000x¹⁰y⁵ + 307,507,200,000x¹⁰y⁵ + ... so on and so forth.

Since you are not interested in anything else but the first term, observe that the first term is:

32,768x¹⁵

That is equal to: 2¹⁵x¹⁵

What happened there is you need to distribute the exponent to the coefficient of the term as well, so you need to distribute it to 2 as well.

Answer:

OB. (f+g)(x) = x^2-2x-13

Step-by-step explanation:

Given

f(x) = 2x-5

and

g(x) = x^2-4x-8

We have to find (f+g)(x)

So,

(f+g)(x) = f(x) + g(x)

= 2x-5 + (x^2-4x-8)

= 2x-5+x^2-4x-8

= x^2+2x-4x-5-8

=x^2-2x-13

Therefore, Option B is correct ..

ANSWER

[tex]{j}^{16} [/tex]

EXPLANATION

The given expression is

[tex]( {j}^{ - 8} )^{ - 2} [/tex]

To simplify this expression, we use the law of exponents.

Recall that:

[tex] {(a}^{m} )^{n} = {a}^{mn} [/tex]

We need to multiply the exponents to get:

[tex]( {j}^{ - 8} )^{ - 2} = {j}^{ - 8 \times - 2} [/tex]

[tex]( {j}^{ - 8} )^{ - 2} = {j}^{16} [/tex]

Therefore after simplification, Clyde got:

[tex]{j}^{16} [/tex]

Answer:

Clyde should have applied the power of a power rule and multiplied the exponents instead of adding them. The simplified form should be j to the 16th power.

Step-by-step explanation:

The exponents should be multiplied.

The simplified form should be j^16

Answer:

[tex]\log_3(a)=n[/tex] has exponential form [tex]3^n=a[/tex].

[tex]\log(3a)=n[/tex] has exponential form [tex]10^{n}=3a[/tex].

Please let me know if neither of my interpretations of your problem/question is correct.  That is I can either assume you wrote [tex]\log_3(a)=n[/tex]  or [tex]\log(3a)=n[/tex].

If something else was intended, please let me know. Thanks kindly.

Step-by-step explanation:

Let's assume: [tex]\log_3(a)=n[/tex].

The base is 3.

The exponent is n. (Just remember the logarithm is the exponent.)

So we have [tex]3^n=a[/tex]

In general these forms are equivalent:

[tex]log_b(a)=y \text{ is equivalent to } b^y=a[/tex].

[tex]\log(3a)=n[/tex] is the same as [tex]\log_{10}(3a)=n[/tex]

The base is 10 (if you don't see a base and log is written).

The exponent is n.

So we have [tex]10^n=3a[/tex].

To transform the logarithmic function log3 a = n into an exponential form, we apply the rule that if logb a = n, then b^n = a. Therefore, the exponential form is 3^n = a.

The student's question is about transforming a logarithmic equation into an exponential form. This is a common request in mathematics, particularly in algebra and precalculus.

The given equation is log3 a = n. The exponential form of a logarithmic equation is based on this relationship: If logba = n, then the exponential form is bn = a. Applying this rule to the provided equation gives 3n = a as the exponential form.

This transformation is based on the definition of logarithms, which are the inverses of exponential functions. The logarithm of a number to a particular base is the exponent to which the base must be raised to get that number. So in this case, n is the power you need to raise 3 to in order to get a.

https://brainly.com/question/37287488

#SPJ3

Answer:

y = -2x/3 + 6

Step-by-step explanation:

y = mx+b

m = y2-y1/x2-x1

m = 2 - 6/6 - 0

m= -4/6 = -2/3

b = y-intercept = 6

Answer:

Step-by-step explanation:

The given question is that the volume of a cube depends on the length of its sides.This can be written in function notation  as v(s). What is the best interpretation of v(3)=27.

Solution:

According to the question the volume of a cube depends on the length of its sides. According to the statement we will apply the formula of volume of a cube.

V(s)=s³

In this question we have given s=3ft.

So, we will put the value of 's' in the formula.

V(s)=s³

V(3)=3³

Multiply 3 three times to get the answer.

V(3)=3*3*3

V(3)=27 ft³

This means that the cube has a volume of 27ft³ with the length of its sides 3ft....

Answer:

The correct answer is last option 3√2 units

Step-by-step explanation:

From the figure we can see that two small  right angled triangle.

These two triangle combined to form a large right angled triangle.

To find the value of x

Consider the small triangle with hypotenuse x and one side 3 units.

The angles of this triangle be 45°, 45° and 90°, then the sides are in the ratio 1 : 1 : √2

Therefore we can write,

3 : 3 : x = 1 : 1 : √2

x = 3√2

The correct answer is last option 3√2 units

Answer:

Arc length = (30/360)(2π)(14)

= (7/3)π cm = about 7.33 cm

Answer:

B

Step-by-step explanation:

Look for an expression with (x - 5 ) as this will give zero when x = 5, that is

x - 5 = 5 - 5 = 0

The only expression with a factor of (x - 5 ) is B

Answer:

My man above in Correct

Step-by-step explanation:

Answer: x^3 + 1x^2 - 18x - 8

Step-by-step explanation: Using the box method, we get the values x^3, 5x^2, 4x^2, 20x, 2x, and 8. Then you add the like terms to get your final answer.

lol my diagram got glitched out when uploading, sorry if its hard to understand

Answer:

[tex]b/a\ hours[/tex]

Step-by-step explanation:

we know that

Betsy can clean a/b of the house in an hour

The whole house (100%) correspond to the number 1

so

using proportion

Find out how long will it take her to clean the whole house

[tex]\frac{(a/b)}{1}=\frac{1}{x} \\ \\x=1/(a/b)\\ \\x=b/a\ hours[/tex]

Answer:

D

Step-by-step explanation:

Reminder:  A function returns ONLY ONE y value for each input value.  

We immediately discard possible answer A, since 2 points have input 1 with different outputs.

Same for B:  discard this.

Same for C:  discard this.

D is a function.  All of the inputs are unique (no duplication).

Answer:

x+3 is a factor of P

Step-by-step explanation:

By the factor theorem:

P(a)=0 <-> x-a is a factor of P.

You have P(-3)=0.

This implies x-(-3) is a factor of P.

Note: x-(-3)=x+3.

Answer:

=5.1 units

Step-by-step explanation:

To use the sine rule to find the length of c we first need to find the angle at C.

C=180-(13+12)

C=180-25

C=155°

a/Sin A=c/Sin C

Calculating for the value of c using the sine rule:

12/Sin 13=c/Sin 155

c=12 sin 155

=5.07 units

Thus to 1 decimal places, the value of c is 5.1 units.

A: decreased

B: increased

C: increased

D: decreased

E: decreased

F: increased

Answer:

∵ Change = final value - initial value,

If change > 0, then the value is increased,

if change < 0, then the value is decreased,

a. 45° F to -10° F,

Change = -10° F - 45° F = -55° F < 0° F,

Thus, temperature is decreased,

b. 35° C to 80° F

∵ 35° C = 95° F  ( by the formula (°C × 9/5) + 32 = °F )

Change = 80° F - 95° F = -5° F < 0° F,

Thus, temperature is decreased,

c. -19° C to 49° C,

Change = 49° C - (-19)° C = 68° C > 0° C,

Thus, temperature is increased,

d. 137° C to 0° C,

Change = 0° C - 137° C = -137° C < 0° C,

Thus, temperature is decreased,

e. 5° C to 19° F,

∵ 5°C = 41°F

Change = 19° F - 41° F = -22° F < 0° F,

Thus, temperature is decreased,

f. 68° F to 29° C,

∵ 29°C = 84.2°F

Change = 84.2°F - 68° F = 16.2° F > 0° F,

Thus, temperature is increased.

Answer:

There are several ways to make 380 with whole numbers. For example:

Answer: [tex]\frac{3}{8}x-\frac{41}{5}[/tex] or  [tex]\frac{3}{8}x-8\ \frac{1}{5}[/tex]

Step-by-step explanation:

Given the following expression:

[tex]\frac{3}{4}(\frac{1}{2}x-12)+\frac{4}{5}[/tex]

You can follow these steps in order to simplify it:

1.  You need to apply Distributive property:

[tex]=\frac{3}{8}x-9+\frac{4}{5}[/tex]

2. And now you must add the like terms. Then:

[tex]=\frac{3}{8}x-\frac{41}{5}[/tex]

Therefore you get the following answer:

[tex]\frac{3}{8}x-\frac{41}{5}[/tex] or  [tex]\frac{3}{8}x-8\ \frac{1}{5}[/tex]

Answer:

B'(-5,-6)

Step-by-step explanation:

The mapping for 180° clockwise rotation about the origin is:

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

The find the image of B(5,6), we plug in x=5 and y=6 into the rule.

[tex](5,6)\to (-5,-6)[/tex]

Therefore the coordinates of B' are (-5,-6).

Point B with coordinates (5, 6) will have coordinates (-5, -6) after a 180° clockwise rotation about the origin.

Triangle ABC has coordinates A(2, 4), B(5, 6), and C(1, 4). If the triangle is rotated 180° clockwise about the origin, we need to find the coordinates of B'.

To rotate a point (x, y) 180° about the origin, we can multiply the coordinates by -1. So, the coordinates of B' after rotation will be (-5, -6).

Answer: 595 Dollars

Step-by-step explanation:

16 1/2 times 18 1/2 = 305.25

one square yard = nine feet

305 devided by nine 33.9166667 (round to 34)

34 times 17.50 = 595

Answer:

$593

Step-by-step explanation:

We have been that a customer wants to buy carpet for a room that is 16 1/2 feet by 18 1/2 feet in size.

First of all, we will find area of carpet by multiplying both side lengths as:

[tex]\text{Area of carpet}=16\frac{1}{2}\text{ ft}\times 18\frac{1}{2}\text{ ft}[/tex]

Convert mixed fraction into improper fraction:

[tex]16\frac{1}{2}\Rightarrow \frac{16\times2+1}{2}=\frac{32+1}{2}=\frac{33}{2}[/tex]

[tex]18\frac{1}{2}\Rightarrow \frac{18\times2+1}{2}=\frac{36+1}{2}=\frac{37}{2}[/tex]

[tex]\text{Area of carpet}=\frac{33}{2}\text{ ft}\times \frac{37}{2}\text{ ft}[/tex]

[tex]\text{Area of carpet}=\frac{1221}{4}\text{ ft}^2[/tex]

[tex]\text{Area of carpet}=305.25\text{ ft}^2[/tex]

1 square feet equals 0.111 square yards.

[tex]305.25\text{ ft}^2=305.25*0.1111\text{ yards}^2[/tex]

To find the cost to carpet the room, we will multiply area of carpet by cost $17.50 per square yards.

[tex]305.25\times 0.1111\text{ yards}^2\times\frac{\$17.50}{\text{ yard}^2}[/tex]

[tex]305.25\times 0.1111\times\$17.50[/tex]

[tex]\$593.4823125\approx \$593[/tex]

Therefore, the cost to carpet the room would be $593.

Answer:

24.4

Step-by-step explanation:

16.667 + 7.66 becomes 16.7 + 7.7, which, in turn, is 24.4

Answer:

24.4

Step-by-step explanation:

The nearest tenth is the first decimal place.  We look at the second decimal place.  If it is 5 or above we round up

16.667 to the nearest tenth = 16.7

7.66 to the nearest tenth = 7.7

16.7 + 7.7 = 24.4

Answer:

Part 1) The rate of change is [tex]2,000\ \$/year[/tex]

Part 2) The equation of the line into slope intercept form is [tex]y=2,000x+73,000[/tex]

Part 3) Tom's salary would be [tex]\$93,000[/tex] in ten years

Step-by-step explanation:

Let

x ------> the number of years worked

y -----> Tom's salary amount in dollars

we have the points

A(1, 75,000) and B(4,81,000)

step 1

Find the rate of change (slope)

The slope is equal to

[tex]m=(81,000-75,000)/(4-1)=2,000\ \$/year[/tex]

step 2

Find the equation of the line into slope-intercept form

we know that

[tex]y=mx+b[/tex]

where

m is the slope

b is the y-intercept

we have that

[tex]m=2,000\ \$/year[/tex]

point A(1, 75,000)

substitute

[tex]75,000=(2,000)(1)+b[/tex]

[tex]b=75,000-2,000=73,000[/tex]

The equation of the line is

[tex]y=2,000x+73,000[/tex]

step 3

What will Tom's salary be in ten years?

For x=10 years

Substitute in the linear equation

[tex]y=2,000(10)+73,000=\$93,000[/tex]

Answer:

The increment in salary is $1500 each year. The slope intercept form is [tex]y=1500x+75000[/tex] and the salary in 10 years will be $90000.

Step-by-step explanation:

Consider the provided information.

The starting is $75,000 per year.

Let x is the number of years worked and y is Tom's salary amount in dollars.

When he has 0 yr of experience, his salary is $75000 per year.

it can be written as (0,75000).

His salary will probably be $81,000 in four years.

It can be written as (4,81000).

STEP 1:

Find the rate of change by using the formula slope=[tex]m=\frac{rise}{run}[/tex].

Determine the rise by subtracting 75000 from 81000.

Rise = 81000 - 75000 = 6000

Now determine the run by subtracting 0 from 4.

Run = 4 - 0 = 4

Substitute the respective values in the above formula.

[tex]slope=m=\frac{6000}{4}\\slope=m=1500[/tex]

Therefore, the rate of change, or the salary increase per year is $1500.

STEP 2:

Write the slope intercept form by using the formula:

[tex](y-y_1)=m(x-x_1)[/tex]

Substitute m = 1500 and [tex](x_1,y_1)=(0,75000)[/tex] on the above formula.

[tex](y-75000)=1500(x-0)\\y-75000=1500x\\y=1500x+75000[/tex]

Thus, the slope intercept form is [tex]y=1500x+75000[/tex].

STEP 3:

The salary in 10 years. can be calculated as:

Substitute the value of x = 10 in [tex]y=1500x+75000[/tex].

[tex]y=1500(10)+75000\\y=15000+75000\\y=90000[/tex]

Hence, the salary in 10 years will be $90000.

Answer:

A

n=27, n+2=29, n+4=31

The correct option is A: n + n + 2 + n + 4 = 87; n -27, n + 2 - 29, n + 4 - 31.

Let's denote the three consecutive odd integers as n, n + 2, and n + 4. The sum of these integers is given as 87.

The correct equation to represent this situation is:

n + (n + 2) + (n + 4) = 87

Now let's solve for n:

3n + 6 = 87

Subtract 6 from both sides:

3n = 81

Divide both sides by 3:

n = 27

n + (n + 2) + (n + 4) = 87

27 + 29 + 31 = 87

The three consecutive odd integers are 27, 29, and 31.

Answer: [tex]x=1[/tex]

Step-by-step explanation:

In order to find the value of "x", it is important to remember that:

[tex]Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)[/tex]

 We can identify in the figure that:

[tex]Tangent\ chord\ angle=(43x)\°\\\\Intercepted\ arc=AB[/tex]

Then:

[tex]43x=\frac{1}{2}AB[/tex]

Solving for AB:

[tex]2(43x)=AB\\\\AB=86x[/tex]

Now, since there are 360° in a circle, we know that:

[tex]AB+(272x+2)=360[/tex]

Then we can substitute [tex]AB=86x[/tex] into [tex]AB+(272x+2)=360\°[/tex] and solve for "x". This is:

[tex](86x)+(272x+2)=360\\\\358x=360-2\\\\x=\frac{358}{358}\\\\x=1[/tex]

Answer:

Yes, no two ordered pairs in this list have the same first coordinate

Step-by-step explanation:

we know that

A function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

That means that there can be only one ordered pair with the same value of x.

therefore

In this problem F is a function, because all the ordered pairs of the list don't have the same first coordinate