ANSWER:
1st option: The y-intercept of f(x) is equal to the y-intercept of g(x).
STEP-BY-STEP EXPLANATION:
The y-intercept can be determined when x = 0, therefore:
For f(x):
[tex]\begin{gathered} f\mleft(0\mright)=-3\mleft(1.02\mright)^0 \\ f(0)=-3\cdot1 \\ f(0)=-3 \\ \text{the y-intercept is (0, -3)} \end{gathered}[/tex]In the function g(x), we can see that when x = 3, g(x) = -3, which means that the y-intercept is (0,-3)
Which means that the intercept is the same for both functions.
The correct answer then would be:
The y-intercept of f(x) is equal to the y-intercept of g(x).
Writing Solve the system using addition. Use pencil and paper. Explain why the addition method is agood choice for solving the system. If you wanted to solve for x first, is the addition method still a goodchoice? Explain.X-3.3y = 5.6- X+4.9y = -8.8
Given the two equations
[tex]\begin{gathered} x-3.3y=5.6 \\ -x+4.9y=-8.8 \end{gathered}[/tex]If we have to solve this question, we will do so easily using the addition method because we can easily eliminate x. Also because we will avoid using fractions to get our answers
Thus if we add the two equations
[tex]\begin{gathered} -3.3y+4.9y=5.6-8.8 \\ 1.6y=-3.2 \\ y=-2 \end{gathered}[/tex]Then, the value of x from the first equation
[tex]\begin{gathered} x-3.3y=5.6 \\ x-3.3(-2)=5.6 \\ x+6.6=5.6 \\ x=5.6-6.6 \\ x=-1 \end{gathered}[/tex]Therefore
[tex]x=-1,y=-2[/tex]If we wanted to solve for x first, this method of addition would not be convenient because the coefficients of y in the two equations are neither the same nor equal to one.
Paul took a total of 30 pages of notes during 15 hours of class. In all, how many hours willPaul have to spend in class before he will have a total of 32 pages of notes in his notebook?Assume the relationship is directly proportional.
ANSWER:
16 hours
STEP-BY-STEP EXPLANATION:
Since the relationship is directly proportional, we can establish the following relation:
If there are 30 pages in 15 hours, how many hours will the 32 pages be:
[tex]\frac{15}{30}=\frac{x}{32}[/tex]Solving for x:
[tex]\begin{gathered} x=\frac{15\cdot32}{30} \\ x=16 \end{gathered}[/tex]The number of hours is 16
18 = 9 ( x + 8 ) solve for x
Answer:-6
Step-by-step explanation:
18=9x(n+8) so if "n" = -7 then -6+8 is 2, and 2x9 is 18
ons belo Situation Cone Diagrams 6 in need to be placed on the boxes. 1. Dylan used a styrofoam cone to make a floral arrangement. The cone had a radius of 4.5 Inches and a height of 6 inches. What is the volume of this cone? 4.5 in Shane used day to make a cone with a height of 6 inches and a diameter of 4.5 inches for a sculpture. What is the volume of this cone? 4.5 in 6 in. Jake made a wooden cone with a diameter of 6 inches and a height of 4.5 inches. What is the volume of this cone? Grace made a cone for her sand castle with a radius of 6 inches and a height of 4.5 Inches. What is the volume of this cone? 6 in Type here to search ה 7 4:27 PM 10/6/2020
Answer
Check Explanation
Explanation
The volume of cone is given as
Volume of a cone = ⅓ (πr²h)
where
r = radius of the cone
h = height of the cone
also note that radius of a cone = ½ (Diameter of the cone)
1) Dylan's cone
Radius = 4.5 inches
Height = 6 inches
Volume = ⅓ (πr²h)
= ⅓ (π × 4.5² × 6)
= ⅓ (381.7035)
= 127.23 in³
2) Shane's cone
Radius = ½ (Diameter of the cone)
Diameter of the cone = 4.5 inches
Radius = ½ (4.5) = 2.25 inches
Height = 6 inches
Volume = ⅓ (πr²h)
= ⅓ (π × 2.25² × 6)
= ⅓ (95.426)
= 31.81 in³
3) Jake's cone
Radius = ½ (Diameter of the cone)
Diameter of the cone = 6 inches
Radius = ½ (6) = 3 inches
Height = 4.5 inches
Volume = ⅓ (πr²h)
= ⅓ (π × 3² × 4.5)
= ⅓ (127.2345)
= 42.41 in³
4) Grace's cone
Radius = 6 inches
Height = 4.5 inches
Volume = ⅓ (πr²h)
= ⅓ (π × 6² × 4.5)
= ⅓ (508.938)
= 169.65 in³
Hope this Helps!!!
Point O is the center of this circle. What is mZCAB?A. 55 degrees B. 48 degrees C. 45 degrees D. 35 degrees
We are asked to find the measure of the angle CAB in the given figure.
Recall that the central angle is twice any inscribed angle subtended by the same arc.
For the given case, the central angle is given that is 96°
This means that the angle CAB must be half of the central angle.
[tex]m\angle CAB=\frac{1}{2}\cdot96\degree=48\degree[/tex]Therefore, the measure of the angle CAB is 48°
трана s 11 27-1.5 - 10 720 1 0 - Ayo ys agoga vo Anto 36-18-22 А) tarao utas se terre doүчно y-studio Critical thinking questions ту 25) Write a system of equations with the solution (4, -3).
We have to solve the system:
[tex]\begin{gathered} -\frac{5}{7}-\frac{11}{7}x=-y \\ 2y=7+5x \end{gathered}[/tex]To solve this system by elimination we have to add or substract a linear combination of the second equation from the first equation in order to eliminate one of the variables.
In this case we can multiply the first equation by 2 and add it to the second equation:
[tex]\begin{gathered} -y\cdot2=(-\frac{5}{7}-\frac{11}{7}x)\cdot2 \\ -2y=-\frac{10}{7}-\frac{22}{7}x \end{gathered}[/tex][tex]\begin{gathered} -2y+2y=(-\frac{10}{7}-\frac{22}{7}x)+(7+5x) \\ 0=-\frac{10}{7}-\frac{22}{7}x+7+5x \\ \frac{22}{7}x-5x=7-\frac{10}{7} \\ \frac{22x-5\cdot7x}{7}=\frac{7\cdot7-10}{7} \\ 22x-35x=49-10 \\ -13x=39 \\ x=\frac{39}{-13} \\ x=-3 \end{gathered}[/tex]Now we can use any of the two equations to find y:
[tex]\begin{gathered} -y=-\frac{5}{7}-\frac{11}{7}x \\ y=\frac{5}{7}+\frac{11}{7}(-3) \\ y=\frac{5}{7}-\frac{33}{7} \\ y=-\frac{28}{7} \\ y=-4 \end{gathered}[/tex]Answer: x=-3 and y=-4
Use a table to solve the following proportion word problems. Then choosethe correct answer.10. The ratio of sand to cement used for making a concrete walkway is1 to 2. If there are 16 pounds of cement, how many pounds of sandare needed?1ySand (in pounds)Cement (in pounds)2.16Aà pound of sandB32 pounds of sandC8 pounds of sand
Let:
x = pounds of sands
y = pounds of cement
[tex]\begin{gathered} y=\frac{1}{2}x \\ \text{if y=16} \\ 16=\frac{1}{2}x \\ \text{Solve for x:} \\ x=16\times2 \\ x=32lb \end{gathered}[/tex]32 pounds of sand are needed
find the equation of a line that passes through (-3,10) and is perpendicular to y=3
Answer:
x = -3
Step-by-step explanation:
The line y = 3 is a horizontal line. So a perpendicular line is a vertical line. The form of the equation for a vertical line is
"x = anumber"
The information we have to work with is the point (-3, 10) A point is in the form (x,y). So we know that x is -3 and y is 10.
We need the x.
x = -3
This is the equation of the vertical line through (-3,10). It is perpendicular to the horizontal line
y = 3.
Answer:
x = -3
Given the equation negative 26 equals y over 13, solve for y.
Answer:
y = -338
Step-by-step explanation:
The equation will be,
→ -26 = y ÷ 13
→ y/13 = -26
Now the value of y will be,
→ y/13 = -26
→ y = -26 × 13
→ [ y = -338 ]
Hence, the value is -338.
HELP ME WITH THIS QUESTION PLEASE 35 POINTS
Answer:
Step-by-step explanation:
Ok:
So this means 3/4 of one big square it is asked to find=75 percent= 75/100=0.75
=
Abigail Henderson has $3400.00 budgeted for spending money on an upcoming trip to Country A and Country B.
Country A's currency is trading at $1.30 per currency A, and Country B's currency is trading at $1.60 per currency B.
She plans to spend more time in Country A, so she wants to have four times as much of currency A as currency B. Set
up and solve a system of equations to model this problem, and explain what the answer means in practical terms.
The amounts that she has to spend are of $2000 in Country A and $500 in Country B, using a system of equations.
What is the system of equations?
The first step in building the system of equations is identifying the variables, as follows:
Considering the total amount of $3400 that she has to spend, and the rates of each country, the following equation is established:
1.3x + 1.6y = 3400.
She wants to have four times as much of currency A as she wants of currency B, hence the second equation of the system is presented as follows:
x = 4y.
Then the amount that she will have to spend in Country B is calculated replacing x = 4y on the first equation as follows:
1.3(4y) + 1.6y = 3400
6.8y = 3400
y = 3400/6.8
y = $500.
The amount that she has to spend in Country A is given as follows:
x = 4y = 4 x 500 = $2000.
More can be learned about a system of equations at https://brainly.com/question/24342899
#SPJ1
Find the product 1. 61 X 63
The product of 1. 61 and 63 gives 101.43
what is the value of 8 to the power of minus 3 over 4
The value of the number "8 to the power of minus 3 over 4" is found as -6561/16777216.
What is meant by the term power of a number?The power of a number is the number of multiples of that number. An exponent is a symbol that represents a number's power.When a number is "raised to a second power," it indicates that it has been multiplied together twice. Whenever a number is "raised to the fifth power," it indicates it has been multiplied by five. The reciprocal of the base is used to calculate the value of the number raised to the power of the a negative number.For the given number,
8 to the power of minus 3 over 4 can be written as;
= (-3/8)⁸
Expand the number to the 8th power.
= (-3/8)×(-3/8)× (-3/8)× (-3/8)× (-3/8)× (-3/8)× (-3/8)× (-3/8)
= -6561/16777216
Thus, the value of the number "8 to the power of minus 3 over 4" is found as -6561/16777216.
To know more about power of a number, here
https://brainly.com/question/17738075
#SPJ1
To estimate the percentage of a states voters who support the current governor for reelection, three newspapers each survey a simple random sample of voters. Each paper calculates the percentage of voters in its sample who support the governor and uses that as an estimate for the population parameter. Here are the results:
When doing a sample of this kind, the papers are attempting to determine the actual percentage of voters that will vote a ceirtain way. The most accurate way to do this would be to ask everyone. As they cannot feasibly do this, the paper that asks the most number of people will likely be the most accurate.
The Tribune interviewed the most people at n= 900
Correct option: The Tribune at 73%
thirteen and thirteen thousandths decimal form
another ratio that is equivalent to the ratio 4:6. Your answer
The given ratio is 4:6
We can determine another ratio that is equivalent bymultiplying or dividing both numbers by a common factor.
If we divide by a common factor, we would be reducing the ratio to its lowest term. If we divide by 2, the equivalent ratio woyld be
4/2 : 6/2
= 2:3
Another equivalent ratio is 2:3
85. What is the value of x?والے1040)DDrawing not to scaleA 38°B. 128°C. 76D. 52°
Given:
One of the angle of a triangle is 104°.
The objective is to find the missing angle x.
If two sides of a triangle are equal, then it is an isosceles triangle.
In an isosceles triangle, the angle formed by the equal sides is also equal.
Then, the value of angle x can be calculated angle sum property of triangle.
[tex]\begin{gathered} x+x+104\degree=180\degree \\ 2x+104\degree=180\degree \\ 2x=180\degree-104\degree \\ 2x=76\degree \\ x=\frac{76}{2} \\ x=38\degree \end{gathered}[/tex]Hence, option (A) is the correct answer.
Tommy spent $16 on two toys. The cost of each toy was a multiple of $4. What are the possible prices of the toys?
ok
Possible prices
Toy 1 Toy 2 Total Price
$12 $4 $16
$8 $8 $16
$4 $12 $16
These are the possible prices:
What is the slope to question 1,3,4,5,7
Answer:
The image is blurry, I cannot see it. Maybe take a better pic.
Step-by-step explanation:
through (-2,3) and (0,2 )
The slope of the line that passes through the points (x1, y1) is computed as follows:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given that the line passes through (-2,3) and (0,2), then its slope is:
[tex]m=\frac{2-3}{0-(-2)}=-\frac{1}{2}[/tex]The slope-intercept form of a line is:
y = mx + b
where m is the slope and b is the y-intercept
Replacing the point (0, 2) and m = -1/2 into the general equation, we get:
2 = -1/2(0) + b
2 = b
Then, the equation of the line is:
y = -1/2x + 2
Select the three equations that pass through the points (–4, –16) and (5, 2):
A) y + 4 = 2(x – 16)
B) y – 2 = 2(x – 5)
C) y = 2x – 8
D) y + 16 = 2(x + 4)
The equations of the line can be:
B) y – 2 = 2(x – 5)
C) y = 2x – 8
D) y + 16 = 2(x + 4)
What is the Equation of a Line?The equation of a line can be expressed in either ways below:
In point-slope form as y - b = m(x - a) [(a, b) is a point on the line, m is the slope of the line]In slope-intercept form as y = mx + b [m is the slope of the line, and b is the y-intercept of the line.The points that the line passes through are given as:
(-4, -16) and (5, 2)
Slope of the line (m) = change in y / change in x
Slope of the line (m) = (2 -(-16))/(5 -(-4))
Slope of the line (m) = 2
Substitute (a, b) = (-4, -16) and = 2 into y - b = m(x - a):
y - (-16) = 2(x - (-4))
y + 16 = 2(x + 4)
We can also plug in the second point (5, 2) and the slope to get the equation of the line as y – 2 = 2(x – 5).
Any of the equation could also be rewritten in the form of the slope-intercept form as y = 2x - 8.
Learn more about equation of a line on:
https://brainly.com/question/13763238
#SPJ1
siin. The scale used for a model of a kitchen isdimensions of the kitchen?1ft. In the model, the kitchen measures $2in. by 3 in.
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data
Model
1 / 4 in = 1 1/2 ft
dimensions of the kitchen
2 1/2 in by 3 in
Step 02:
[tex]1\text{ }\frac{1}{2}\text{ ft = 1 + }\frac{1}{2}\text{ = }\frac{2+1}{2}=\frac{3}{2}\text{ ft}[/tex][tex]2\text{ }\frac{1}{2}in\text{ = 2 +}\frac{1}{2}\text{ = }\frac{4+1}{2}\text{ =}\frac{5}{2}in[/tex]Step 03:
1 / 4 in = 3 / 2 ft
[tex]\frac{5}{2}in\cdot\text{ }\frac{3\text{ / 2 ft}}{1\text{ /4 in }}\text{ = }\frac{5\text{ }}{2\text{ }}in\cdot\text{ }\frac{3\cdot4\text{ ft}}{2\cdot1\text{ in}}[/tex][tex]\frac{5}{2}in\cdot\text{ }\frac{12ft}{2in}\text{ = }\frac{5\cdot12\text{ }}{2\cdot2}=\text{ }15ft[/tex][tex]3\text{ in }\cdot\text{ }\frac{12ft}{2in}\text{ = }\frac{3\cdot12}{2}=18ft[/tex]The answer is:
b. 15 ft by 18 ft
what is the value of g(f(2))
First we need to find f(2), this is when x=2 on the funciton F
from the table we can notice when x=2 f is 3
now, we need to find g(3), it is when x is 3 on the funcion G
from the table we can notice wen x=3 G is -2
so
[tex]g(f(2))=-2[/tex]Find the area of a triangle whose sides are 3cm,6cm and 7cm
Answer:
See below
Step-by-step explanation:
It is NOT a RIGHT triangle so you cannot use 1/2 b * h
but you can use Heron's Formula
Area = sqrt( s (s-a)(s-b)(s-c) )
s = semi- perimeter = (3+6+7)/2 = 8
Area = sqrt ( 8 ( 8-3)(8-6)(8-7) ) = sqrt ( 80) = 8.9 cm^2
The following data represents the age of 30 lottery winners Complete the frequency distribution for the data
EXPLANATION
We can complete the frequency table by arranging each given value with its corresponding age class, as shown as follows:
Age class Frequency
20-29 1
30-39 4
40-49 2
50-59 7
60-69 11
70-79 4
80-89 1
The complete frequency distribution for the data is,
Age Frequency
20-29 1
30-39 4
40-49 2
50-59 7
60-69 11
70-79 4
80-89 1
We have to given that;
The following data represents the age of 30 lottery winners.
Now, We can formulate;
By given table,
Age Frequency
20-29 1
30-39 4
40-49 2
50-59 7
60-69 11
70-79 4
80-89 1
Learn more about the equation visit:
brainly.com/question/28871326
#SPJ6
i need help please help me
Answer
Check Explanation
Explanation
We've been told that 2 cups of mix corresponds to 1.5 cups of water.
2 cups of mix = 1.5 cups of water
Let 8 cups of mix be equal to x cups of water
2 cups of mix = 1.5 cups of water
8 cups of mix = x cups of water
We can write a mathematical relationship by cross multiplying
2 × x = 8 × 1.5
2x = 12
Divide both sides by 2
(2x/2) = (12/2)
x = 6 cups of water
Let y cups of mix correspond to 4 cups of water
2 cups of mix = 1.5 cups of water
y cups of mix = 4 cups of water
We can write a mathematical relationship by cross multiplying
1.5 × y = 2 × 4
1.5y = 8
Divide both sides by 1.5
(1.5y/1.5) = (8/1.5)
y = 5.33 cups of mix
b) To write the proportional relationship represented by the table,
We can see that the cups of mix is proportional to the cups of water,
2 cups of mix = 1.5 cups of water
Dividing both sides by 2
1 cup of mix = 0.75 cup of water.
Hope this Helps!!!
Find the antilog of 3.8226
Answer:
6646.6
Step-by-step explanation:
You want the antilog of 3.8226.
AntilogA scientific or graphing calculator, or any spreadsheet can tell you the value of 10 to that power, assuming this is a common log.
10^3.8226 ≈ 6646.6
__
Additional comment
If this is a natural log, then the base is e ≈ 2.718281828459045... instead of 10.
Most calculators have keys dedicated to the antilog functions. (Antilog may be a "2nd" or "Shift" function of a logarithm key.)
The width of a rectangular flower shop is 20 feet less than twice the length The perimeter is more than 70 feet Which inequality can be used to hnd a possible length of the shop in feet?
width (w)= 20 feet less than twice the length = 2x-20
x = length
Perimeter is more than 70 feet
Perimeter = 2w+2x
Replacing:
P= 2 (2x-20)+ 2x
Since the perimeter is more than 70:
2 (2x-20)+ 2x > 70
Write an equation of the line that is perpendicular to 3x + y = 7 and passes through the point (6,4).
Firstly, we proceed to write the given equation in the standard form of the slope-intercept
That is written as;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and b represents the y-intercept
In this case, we can write the given equation as;
[tex]y\text{ = -3x + 7}[/tex]From above, we can see the slope as -3 and the y-intercept as 7
If two lines are perpendicular to each other, then the product of the slopes of the two lines is equal to -1
Let us call the given line, line 1 and the other line, line 2
Thus, we have;
[tex]\begin{gathered} m_1\text{ }\times m_2\text{ = -1} \\ \\ -3\text{ }\times m_2\text{ = -1} \\ \\ m_2\text{ = }\frac{-1}{-3}\text{ = }\frac{1}{3} \end{gathered}[/tex]So now, we want to write the equation of a line with slope of 1/3 with the line passing through the point (6,4)
We can use the one-point slope form for this
This can be written as;
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ y\text{ - 4 = }\frac{1}{3}(x-6) \\ \\ 3(y-4)\text{ = x-6} \\ \\ 3y\text{ - 12 = x - 6} \\ \\ 3y\text{ = x-6+12} \\ \\ 3y\text{ = x + 6} \end{gathered}[/tex]The graph of the function f is shown below Find one value of x for which f(x) =2 and find f(2)A- One value of X for which f(x)=2: B- f(2) =
To find the corresponding x where the function assumes a certain value, we draw a horizontal line on the desired function value. For f(x) = 2, we have:
The intercept between the horizontal line and our graph happens at (0, 2), therefore, we have:
[tex]f(x)=2\implies x=0[/tex]To evaluate graphically a function, we check the corresponding value for the desired x value on the horizontal axis. For x = 2, we have:
Then
[tex]f(2)=1[/tex]