In general, the y-intercept of the function F(x) = a • bx is the point _____.A.(0, b)B.(0, a)C.(0, x)D.(0, 1)
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The y-intercept of a function is the point where the function crosses the y axis and where x = 0
[tex]\begin{gathered} We\text{ are asked to find the y intercept of an exponential function, y = a*b}^x \\ When\text{ x = 0, b}^x\text{ =1 for any value of b} \\ We\text{ are then left with y = a*1 when x =0} \end{gathered}[/tex]The y intercept is therefore given by:
(0,a) --> option B
Related Questions
46. Identify the center and radius of a circle given the equation is (x - 2)^2 + (y + 4)^2= 36
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Answer: Center: (2, –4); Radius: 6.
Explanation
The equation of a circle in standard form is:
[tex](x-h)^2+(y-k)^2=r^2[/tex]where (h, k) is the center and r is the radius. Thus, in our given equation:
[tex]\left(x-2\right)^2+(y+4)^2=36[/tex]• h = 2
,• k = –4 (it is negative as negative sign times negative sign equals positive sign)
,• r² = 36
Therefore, the center is (2, –4) and the radius is:
[tex]r^2=36[/tex][tex]\sqrt{r^2}=\sqrt{36}[/tex][tex]r=6[/tex]Is the LCD Going to be 5 • 7 •z = 35 ?
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To add these fractions, we can do the following steps.
Step 1: Simplify each fraction.
[tex]\frac{25}{5y}=\frac{5\cdot5}{5y}=\frac{5}{y}[/tex][tex]\frac{64}{8y}=\frac{8\cdot8}{8y}=\frac{8}{y}[/tex]Step 2: We add the numerators since the fractions have the same denominator.
[tex]\frac{5}{y}+\frac{8}{y}=\frac{5+8}{y}=\frac{13}{y}[/tex]Therefore, the result of adding the fractions is 13/y.
Where would 5pi be located on a number line? Show all thoguhts.
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In order to locate 5π in a number line, you consider that π = 3.141516...
When this irrational number is multiplied by 5 you obtain:
5 x π = 5 x 3.141516... = 15.70796...
Then, if you have a number line with ten subdivisions between units, the position of 5π on the number line can be as follow:
1. At first street elementary school, about 21% of the 645 students ride bicycles to school. About how many students ride bicycles to school? 2. A team of biologists captured and tagged 50 deer in a forest. Two weeks later, the biologists captured a sample of 20 deer from the same forest, and found that 5 of them were tagged. How many deer would they estimate are in the forest.
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1 Given that about 21% of the 645 students ride bicycles to school
The number of students that ride bicycles to school
= 21% * 645
= 21/100 * 645
= 135.45
Hence about 135 students ride bicycles to school.
In a direct variation, y = -18 when x = -3. Write a direct variation equation that shows therelationship between x and y.Write your answer as an equation with y first, followed by an equals sign.Submit
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The direct variation between y and x has the following
Thursday: Word Problems 1 The plant growth is proportional to time. When Tia bought the plant, it measured 2 cm. It measured 2.5 cm exactly one week later. If the plant continues to grow at this rate, determine the function that represents the plant's growth.
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We have the next informtion
initial measure = 2 cm
after
Which is not a true equation?O A. -12 · 4 = -3O B. 100 = -25 = -4O C. -72 = -9 = 80 D. –32 - 0 = 32
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In the last option:
-32 / 0 = 32
But we can not divide by 0, it is undefined in mathematics, so this is not a true equation.
Answer: Option D
7. Let f(x) = 3x and g(x) = (x + 2)^2. Find the value of (f og)(-5)A.135B. -27 C. 169. D.27.
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f(x)= 3x
g(x)= (x+2)²
State the solution in terms of x 4^x+6 = 20
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We have the question as
[tex]4^{x+6}=20[/tex]Let us introduce logarithms to base 4 to both sides of the equation:
[tex]\log _44^{x+6}=\log _420[/tex]Applying the law of logarithm that states
[tex]\log A^B=B\log A[/tex]we have
[tex](x+6)\log _44=\log _420[/tex]Applying the law that states
[tex]\log _nn=1[/tex]we have
[tex]\begin{gathered} (x+6)\times1=\log _420 \\ x+6=\log _420 \end{gathered}[/tex]Collecting like terms, we have
[tex]x=-6+\log _420[/tex]Therefore, the answer is OPTION C.
Write in descending order.420t + 201 to the 3rd power -210t to the 2nd power
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To answer this, we need to see the polynomial. Descending order is in a way that the first term of the polynomial will be three, the second (in descending order, two....and so on).
420t+20t3-210t2
In descending order is:
20t^3 - 210t^2 + 420t
So, the option is number two.
If each side of an equilateral triangle is 2 inches long, then what is the area of the triangle?
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Solution:
The image below represents the equilateral triangle of 2 inches long
From the triangle above, the given values include
[tex]\begin{gathered} a=2in \\ b=2in \\ c=2in \end{gathered}[/tex]Concept:
To calculate the area of the triangle, we will use Heron's formula below
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ \text{where,s = semi perimter} \\ s=\frac{a+b+c}{2} \end{gathered}[/tex]Step 1:
Calculate the semi perimeter s
[tex]\begin{gathered} s=\frac{a+b+c}{2} \\ s=\frac{2in+2in+2in}{2} \\ s=\frac{6in}{2} \\ s=3in \end{gathered}[/tex]Step 2:
Substitute the value of s,a,b,c in the heron's formula
[tex]\begin{gathered} A=\sqrt[]{s(s-a)(s-b)(s-c)} \\ A=\sqrt[]{3(3-2)(3-2)(3-2)} \\ A=\sqrt[]{3\times1\times1\times1} \\ A=\sqrt[]{3} \\ A=1.73in^2 \end{gathered}[/tex]Hence,
The area of the triangle = 1.73 squared inches
Triangle ABC has coordinates A(-6,2), B(-3,6), and C(5,0). Find the perimeter of the triangle. Express your answer in simplest radical form.
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we must know the measure of each side, for this we must calculate the distance between points
the formula is
[tex]d=\sqrt[]{(x1-x2)^2+(y1-y2)^2}[/tex]AB
[tex]\begin{gathered} \sqrt[]{(-6-(-3))^2+(2-6)^2} \\ \sqrt[]{25} \\ AB=5 \end{gathered}[/tex]AC
[tex]\begin{gathered} \sqrt[]{(-6-5)^2+(2-0)^2} \\ \sqrt[]{125} \\ AC=5\sqrt[]{5} \end{gathered}[/tex]BC
[tex]\begin{gathered} \sqrt[]{(-3-5)^2+(6-0)^2} \\ \\ \sqrt[]{100} \\ BC=10 \end{gathered}[/tex]now add all sides to find the perimeter
[tex]\begin{gathered} 5+5\sqrt[]{5}+10 \\ \end{gathered}[/tex]the perimeter is
[tex]15+5\sqrt[]{5}\approx26.18[/tex]An astronaut on the moon throws a baseball upward. The astronaut is 6 ft, 6 in tall, and the initial velocity of the ball is 30 ft per sec. The height s of the ball in feet isgiven by the equation s= -2.7t^2 + 30t + 6.5, where t is the number of seconds after the ball was thrown. Complete parts a and b.a. After how many seconds is the ball 18 ft above the moon's surface?After ____ seconds the ball will be 18 ft above the moon's surface.(Round to the nearest hundredth as needed. Use a comma to separate answers as needed.)
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In order to find when the ball will be 18 ft above the moon's surface, we need to equal the expression to 18
[tex]18=-2.7t^2+30t+6.5[/tex]then, solve the associated quadratic expression
[tex]\begin{gathered} 0=-2.7t^2+30t+6.5-18 \\ 0=-2.7t^2+30-11.5 \\ using\text{ }the\text{ }quadratic\text{ }formula \\ x=\frac{-30\pm\sqrt{(30)^2-4\ast(-2.7)\ast(-11.5)}}{2\ast(-2.7)} \\ x_1\cong0.40 \\ x_2\cong10.72 \end{gathered}[/tex]answer:
after 0.40 seconds the ball will be 18 ft above the surface
3. A savings account is started with an initial deposit of $1500.The account earns 1.8% interest compounded annually.(a) Write an equation to represent the amount of money inthe account as a function of time in years. 5 Points(B) how much more interest would be earned if the initial deposit is allowed to earn interest for 20 years vs 10 years
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a) We would apply the formula for determining compound interest which is expressed as
A = P(1 + r/n)^nt
where
A = the total amount in the account at the end of t years
r = interest rate
n = the periodic interval at which it was compounded
P = the principal or initial amount deposited
From the information given,
P = 1500
r = 1.8/100 = 0.018
n = 1 because it is compounded once in a year
Thus, an equation to represent the amount of money in the account as a function of time in years ia
A = 1500(1 + 0.018/1)^1 * t
A = 1500(1.018)^t
B) If t = 20, then
A = 1500(1.018)^20
A = 2143.12
The interest earned would be the total amount - the principal
Interest earned after 20 years = 2143.12 - 1500 = 643.12
If t = 10, then
A = 1500(1.018)^10
A = 1792.95
Interest earned after 10 years = 1792.95 - 1500 = 292.95
Thus, the difference in interest earned between both years is
643.12 - 292.95
= $350.17
From the graph identify the zeros of the quadratic function
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The zeros of the function are the points where it crosses the x axis:
Answer: (1,0) and (3,0)
if a=5x-2 and b=5x-22 , what is the value of x ?
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Trigonometry
We are given the following condition:
sin (a) = cos (b)
Since both angles are acute, the following relationship must apply:
a = 90° - b
Both angles must be complementary
Substituting the values for each angle:
a = 5x - 2
b = 5x - 22
We have:
5x - 2 = 90 - (5x - 22)
Removing brackets:
5x - 2 = 90 - 5x + 22
Adding 5x:
5x - 2 + 5x = 90 + 22
Adding 2:
5x + 5x = 90 + 22 + 2
Simplifying:
10x = 114
Dividing by 10:
x = 114/10
x = 11.4
Correct choice: C)
6:4= :2 I dont know what that is
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Answer: x = 3
Let the missing number be x
6 : 4 = x : 2
ratio is the same as fraction
6/4 = x/2
Step2 : cross multiply
x * 4 = 6 * 2
4x = 12
Divide both sides by 4
4x/4 = 12/4
x = 3
Therefore, the missing number is 3
Help Please!!use the drawing to form the correct answers on the graph complete the function table for the given domain and plot the points on the graph
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The Solution:
The given function is
[tex]f(x)=-x^2+2x+5[/tex]Step 1:
We shall complete the table.
Explanation of how the table was completed:
Substituting each value of x to obtain the corresponding value of y.
[tex]\begin{gathered} f(-1)=-(-1)^2+2(-1)+5=-1-2+5=2 \\ f(0)=-(0)^2+2(0)+5=5 \\ f(1)=-(1)^2+2(1)+5=-1+2+5=6 \\ f(2)=-(2)^2+2(2)+5=-4+4+5=5 \\ f(3)=-(3)^2+2(3)+5=-9+6+5=2 \end{gathered}[/tex]l will send u the pic
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as they are in the same line, the measures of angles AOD and angle DOC they measure 180°
Hannah reads at a constant rate of 3 pages every 8 minutes. Write an equation that shows the relationship between p, the number of pages she reads, and m, the number of minutes she spends reading. Report a probler
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Since we have that Hannah reads 3 pages every 8 minutes, we will construct the function by first knowing how many pages she reads in 1 minute, that is:
She reads 3/8 pages each minute, then we will construct the function as follows:
[tex]p=\frac{3}{8}m[/tex]Where p is the number of pages and m is the number of minutes that she reads. We can see that this describes is if we solve for 1 minute and 8 minutes. If we solve for 1 minute, we get she read 3/8 pages and if we replace 8 minutes, we will get that she reads 3 pages.
differentiate y=4x√3x²-8x
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Okay, here we have this:
Considering the provided function, we are going to perform the requested operation, so we obtain the following:
[tex]\begin{gathered} y=4x\sqrt{3}x^2-8x \\ \\ y=4\sqrt{3}x^3-8x \\ \\ \frac{dy}{dx}=\frac{d}{dx}(4\sqrt{3}x^3)-\frac{d}{dx}(8x) \\ \\ \frac{dy}{dx}=12\sqrt{3}x^2-8 \end{gathered}[/tex]Finally we obtain that dy/dx is equal to: 12sqrt(3)x^2-8
guys please help
60% of = 45
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Answer:
Step-by-step explanation:
Answer: 75
Use the equation is/of = %/100
Plug in the numbers to get 45/x = 60/100
Cross Multiply and you get 60x = 4500
Divide both sides by 60
X = 75.
Suppose that the functions g and h are defined for all real numbers x as follows. 9g(x) = 2x ^ 2 h(x) = x - 3Write the expressions for (hg)(x) and (h + g)(x) and evaluate (h - g)(- 3) .
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Given
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]To write the expressions of
[tex]\begin{gathered} (h\cdot g)(x) \\ (h+g)(x) \end{gathered}[/tex]And to evaluate,
[tex](h-g)(-3)[/tex]Explanation:
It is given that,
[tex]\begin{gathered} g(x)=2x^2 \\ h(x)=x-3 \end{gathered}[/tex]Then,
[tex]\begin{gathered} (h\cdot g)(x)=h(x)\cdot g(x) \\ =\left(x-3\right)\cdot\left(2x^2\right) \\ =2x^3-6x^2 \end{gathered}[/tex]Also,
[tex]\begin{gathered} (h+g)(x)=h(x)+g(x) \\ =(x-3)+2x^2 \\ =2x^2+x-3 \end{gathered}[/tex]And,
[tex]\begin{gathered} (h-g)(-3)=h(-3)-g(-3) \\ =(-3-3)-2(-3)^2 \\ =-6-(2\times9) \\ =-6-18 \\ =-24 \end{gathered}[/tex]Hence, the answer is,
[tex]\begin{gathered} (h\cdot g)(x)=2x^3-6x^2 \\ (h+g)(x)=2x^2+x-3 \\ (h-g)(-3)=-24 \end{gathered}[/tex]Create an expression that can be used to find the value of x
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There are two possible expressions that can help to calculate "x"
First
[tex]\begin{gathered} \text{ cos 28 = }\frac{42}{x} \\ \text{ } \end{gathered}[/tex]Second
[tex]\text{ sec 28 = }\frac{x}{42}[/tex]Both are possible to find "x".
What is the sum of the first 19 terms of the sequence 9,2,-5,-12....2SEE ANSWERS
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ANSWER
-1026
EXPLANATION
The sum of the first n terms in an arithmetic sequence is,
[tex]S_n=\frac{n(a_1+a_n)}{2}[/tex]As we can see, we have to find the nth term of the sequence,
[tex]a_n=a_1+(n-1)d[/tex]In this case, the first term is 9 and the common difference is -7 - note that each term is the previous one minus 7. So the formula for the nth term is,
[tex]a_n=9-7(n-1)[/tex]We have to find the 19th term,
[tex]a_{19}=9-7(19-1)=9-7\cdot18=9-126=-117[/tex]So the sum of the first 19 terms is,
[tex]S_{19}=\frac{19\cdot(9+(-117))}{2}=\frac{19\cdot(9-117)}{2}=\frac{19\cdot(-108)}{2}=\frac{-2052}{2}=-1026[/tex]Hence, the sum of the first 19 terms of the given sequence is -1026.
Suppose f(x)=5x+6 . Describe how the graph of g compares with the graph of f . g(x)=f(x+5)
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g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
What is a function?The link between two independent variables and one dependent variable is described by a mathematical expression, rule, or law (the dependent variable).
An example of a rule is a function, which produces one output for a single input. Y=X2 is an illustration of this. You only get one output for y if you enter anything for x. We can infer that y is a function of x because x is the input value.
The function is given as:
f(x) = 5x+6
g(x) = f(x)+5
this gives,
g(x) = 5x+6+5
g(x) = 5x+11
g(x) = f(x) + 5 relates to f(x) by shifting f(x) 5 units up.
To know more about functions visit:
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What is the perimeter of the dinning room? Perimeter is distance around the room, rounded to the nearest hundredth
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To answer this question, we will use the following formula to determine the perimeter of the dining room:
[tex]P=2w+2l,[/tex]where w is the width and l is the length.
Substituting w=9 feet and l=10feet 8 inches=, we get:
[tex]P=2(9ft)+2(10ft8in)=18ft+2(10ft+\frac{8}{12}ft)\text{.}[/tex]Simplifying the above result, we get:
[tex]P=18ft+20ft+\frac{16}{12}ft=38ft+\frac{16}{12}ft=\frac{118}{3}ft\text{.}[/tex]Answer: The perimeter is 39.33ft.
I need help please Question 9 Help for my homework
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Given the figure of a triangular prism.
We will find the amount of wood to make the wooden play block
So, we will find the volume of the given block
As shown: the triangular side has a base of 4 cm and a height of 6 cm
The area of the triangular base =
[tex]\frac{1}{2}*4*6=12\text{ }cm^2[/tex]the length between the triangular sides = 12 cm
So, the volume = base area * length =
[tex]12*12=144\text{ }cm^3[/tex]So, the answer will be the first option 144 cm³
6x-(2x+5) need help please
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we have the expression
6x-(2x+5)
remove the parenthesis
6x-2x-5
Combine like terms
4x-5
therefore
the answer is 4x-5which statement is true if the graph of the linear function passes through the points (-1, -6)and (5,6) function first if needed
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The correct option is C
Explanation:We check through each of the options to see if they are true
Option A is not true
The slope of the graph is as follows:
(6 - (-6))/((5 - (-1))
= (6 + 6)/(5 + 1)
= 12/6
= 2
Option B is not true
The zero of the graph is the point on the x-axis where y = 0, this is x = 2
Option C is true
The x-intercept is the point where the graph crosses the x-axis. This is (2, 0)
Option D is not true