The y-intercept of linear function (f- g)(x) is (0,9)
How to determine the y-intercept?The table of values is given as:
x -6 -4 -1 3 4
f(x) 15 11 5 -3 -5
g(x) -36 -26 -11 9 14
The equations of the functions is calculated using:
[tex]y = \frac{y_2 -y_1}{x_2-x_1} * (x -x_1) + y_1[/tex]
So, we have:
[tex]f(x) = \frac{11 -15}{-4 + 6} * (x + 6) + 15[/tex]
Evaluate
f(x) = -2x + 3
Also, we have:
[tex]g(x) = \frac{-26 + 36}{-4 + 6} * (x + 6) - 36[/tex]
Evaluate
g(x) = 5x - 6
Next, we calculate (f - g)(x) using:
(f - g)(x) = f(x) - g(x)
This gives
(f - g)(x) = -2x + 3 - 5x + 6
Substitute 0 for x
(f - g)(0) = -2(0) + 3 - 5(0) + 6
Evaluate
(f - g)(0) = 9
Hence, the y-intercept of (f- g)(x) is (0,9)
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Given the following exponential function, identify whether the change represents
growth or decay, and determine the percentage rate of increase or decrease.
y = 4200 (1.07)
For the given exponential function there will be an exponential growth of 7%.
What is a function?A function is defined as the expression that set up the relationship between the dependent variable and independent variable.
we have
[tex]f(x) = 4200(1.07)^x[/tex]
This is an exponential function of the form
[tex]f(x)=ab^x[/tex]
where
a - is the initial value
b - is the base
If b > 1 ----> is a exponential growth
0 < b < 1 ----> is a exponential decay
r is the per cent rate
b = 1 + r
In this problem we have
a = 4200
b = 1.07
We can see that 1.07 > 1 -----> is a exponential growth
Find out the per cent rate
b = 1 + r
r = 1.07 - 1
r = 0.07
r = 7 x 100 = 7%
Therefore the given exponential function there will be an exponential growth of 7%.
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use the probability model listing all 6 possible outcomes when rolling a six-sided number cube. what is the probability of rolling 5 or greater
Answer:
The probability of it rolling 5 or above is 45%
Step-by-step explanation:
I have passed the test of it
i need to fine the value of x
Please help soon!!!!!!
Solving the exponential function, it is found that the times that will take to have the desired measures are given by:
a) 3.6 hours.
b) 38.51 hours.
c) 56.98 hours.
What is the exponential function for the amount of Carbon-10 after t hours?The function is given by:
[tex]A(t) = 140(0.5)^{\frac{t}{19.255}}[/tex]
Solving for t, we have that:
[tex](0.5)^{\frac{t}{19.255}} = \frac{A(t)}{140}[/tex]
[tex]\log{(0.5)^{\frac{t}{19.255}}} = \log{\frac{A(t)}{140}}[/tex]
[tex]\frac{t}{19.255} = \frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
[tex]t = 19.255\frac{\log{\frac{A(t)}{140}}}{\log{0.5}}[/tex]
In item A, we have that A(t) = 123, hence:
[tex]t = 19.255\frac{\log{\frac{123}{140}}}{\log{0.5}}[/tex]
t = 3.6 hours.
In item B, we have that A(t) = 35, hence:
[tex]t = 19.255\frac{\log{\frac{35}{140}}}{\log{0.5}}[/tex]
t = 38.51 hours.
In item C, we have that A(t) = 18, hence:
[tex]t = 19.255\frac{\log{\frac{18}{140}}}{\log{0.5}}[/tex]
t = 56.98 hours.
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Please helpp!!!!!! Quick
The area of the parallelogram in the given diagram is 103.68 cm²
Calculating area of ParallelogramFrom the question, we are to determine the area of the given parallelogram
The area of a parallelogram can be calculated by using the formula,
A = bh
Where A is the area
b is the base
and h is the perpendicular height
From the given diagram,
b = 14.4 cm
h = 7.2 cm
Putting the parameters into the equation, we get
A = 14.4 × 7.2
A = 103.68 cm²
Hence, the area of the parallelogram in the given diagram is 103.68 cm²
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4.5:2.25 in n:1 how would i solve this
The required ratio is 2:1.
We have given that,
4.5:2.25
Since we have given that
We need to find the ratio in the form of n:1.
What is the ratio?
A ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six. Similarly, the ratio of lemons to oranges is 6:8 and the ratio of oranges to the total amount of fruit is 8:14.
so, it becomes,
[tex]=\frac{4.5}{2.25}:1\\\\=2:1[/tex]
Hence, the required ratio is 2:1.
Express the ratio in the simple form
4.5:3 1/2.
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Despite control measures, the pigeon population in Winchester is increasing by 10% each year. If there are currently 9,520 pigeons, how many pigeons will there be in 13 years?
If necessary, round your answer to the nearest whole number.
Using an exponential function, it is found that there will be 32,866 pigeons in 13 years.
What is an exponential function?An increasing exponential function is modeled by:
[tex]A(t) = A(0)(1 + r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.The initial value and the growth rate are given by:
A(0) = 9520, r = 0.1.
Hence the function is given by:
[tex]A(t) = 9520(1.1)^t[/tex]
Hence in 13 years, the amount of pigeons will be of:
[tex]A(13) = 9520(1.1)^{13} = 32866[/tex]
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Please help!! Will give brainliest
Answer:
The first choice
Step-by-step explanation:
7/8 x + 3/4 = -6
6 (x/8) + 3/4 = -6
Donna is making a cookie recipe that calls for 1 ¾ cups of sugar. However, when she
goes to take out the measuring cups she can only find the one-half cup measuring cup. How many one-half cups will she need to fill to get the correct amount of sugar for her cookie recipe?
Answer:
3 and 1/2 half-cups
Step-by-step explanation:
We are asked to find the number of half-cups that will equal 1 3/4 cups.
__
Let the desired number be represented by n. Then we require ...
n × 1/2 = 1 3/4 . . . . some number of 1/2-cups will give 1 3/4 cups
Using a common denominator, we have ...
n × 2/4 = 7/4
Multiplying by the inverse of the coefficient of n gives ...
n × 2/4 × 4/2 = 7/4 × 4/2
n = 7/2 = 3 1/2 . . . . . simplify
That is, Donna can measure 1 3/4 cups of sugar by using her 1/2-cup measure 3 times, and filling it half-full for the final 1/4 cup she needs.
She needs 3 1/2 half-cups to get the correct amount.
Through a regular hexagon whose base edge is 8cm and whose height ii 12cma hole in the shape of the right prism with ots end being rhombus with diagonals of 6cm and 8cm is drilled find the total surface area and volume of the remaining soild?
The total surface area of the remaining solid is 48(4+✓3) centimeters square.
How to calculate the surface area?Through a regular hexagonal prism whose base edge is 8 cm and the height is 12 cm, a hole in the shape of a right prism.
The formula for the total surface area will be:
= Total surface area=2(area of the base)+ parameter of base × height
where,
Height= 8cm
Parameter of base=12(2) = 24
Area of the base= 6×✓3/4×4² = 64✓3/4
The surface area of the remaining solid will be:
= 2(64✓3/4) + 24 × 8
= 2(64✓3/4 + 192
With the hole is a rhombus prism with the following parameters:
diagonal 1 = 6, diagonal 2 = 8, height = 12
The volume is:
V1 =0.5 × d1 × d2 × h
V1 = 0.5 × 6 × 8 × 12
V1 = 96
The dimensions of the hexagonal prism are:
Base edge (a) = 8
Height (h) = 12
The volume is
V2 = (3✓(3)/2)a²h
V2 = (3✓3)/2) × 8² × 12
V2 = 1152✓3
The remaining volume is
V = V2 -V1
V = 1152✓3 - 96
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PLEASE HELP!
The chart shows the relationship between the cost of internet service per month and degree of customer satisfaction.
Based on a linear model, what would you expect a customer to rate their satisfaction for an internet plan that costs $10 per month. Give your answer to 2 decimal places
A customer that uses an internet plan that costs $10 per month is expected to give a customer rating of 6
How to determine the customer rating?We start by calculating the regression equation of the table of values using a graphing calculator.
Using the graphing calculator, we have:
y = 0.04x + 5.75
When the cost is $10 per month, it means that
x = 10
So, we have:
y = 0.04 * 10 + 5.75
Evaluate
y = 6.15
Approximate
y = 6
Hence, a customer that uses an internet plan that costs $10 per month is expected to give a customer rating of 6
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Please help it’s easy, I just need help on the state the problem questions. Make sure to put the number by the answer.
The property of the questions are correctly stated below.
Properties of the various given equations Commutative property of addition: This is represented by equation 7Commutative property of multiplication: This is represented by equation 5.Associative property of addition: This is represented by equation 4.Associative property of multiplication: Not represented with any equation.Additive identity property: This is represented by equation 10.Multiplicative identity property: This is represented by equation 1.Multiplicative property of zero: This is represented by equation 8.Multiplicative inverse property: Not represented with any equation.Distribution property: This is represented by equation 2.Reflexive property: This is represented by equation 3.Symmetric property: Not represented with any equation.Transitive property: This is represented by equation 2.Substitution property: This is represented by equation 2.Learn more about equations here:
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Problem 3
The √2-1.4142135... This expansion is not exact (a finite decimal expansion cannot give the exact
5
10,000,000
10,000,000
14,142,135 is close to √2 and in fact, is within
(or half the size of the
answer). The fraction
denominator); however, the denominator is too large. There are fractions that match this
approximating power with much smaller denominators.
Part A: Find the fraction with the smallest denominator that matches √2 to three places.
Answer:
5,000,000^2
Step-by-step explanation:
half of 10,000,000 sqrt of 2
Please help I don't Understand!
Answer: SAS similarity theorem
Proportional relationship:
[tex]\sf \dfrac{AB}{AC} = \dfrac{AM}{AN}[/tex]
insert values
[tex]\rightarrow \sf \dfrac{21+9}{14+6} = \dfrac{21}{14}[/tex]
simplify
[tex]\rightarrow \sf 1 = 1[/tex]
L.H.S = R.H.S
The triangles are congruent and follows the rule SAS similarity theorem.
The triangles has/starts from the same angle, corner (A).
What table represents a linear function
Considering the constant rate of change, it is found that table 1 represents a linear function.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.From the concept of the slope, we have that the rate of change of a linear function is constant, that is, when x changes by 1, y has to change always by the same amount, which happens in table 1, with a constant rate of change of 1/2 = 0.5.
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On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 3, negative 7) and (0, 2). Everything to the left of the line is shaded.
Which is the graph of the linear inequality y < 3x + 1?
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a solid straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the left of the line is shaded.
On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 1, negative 2) and (0, 1). Everything to the right of the line is shaded.
The attached graph represents the graph of the inequality
How to determine the graph of the inequality?The points on the line are given as:
(-3,-7) and (0,2)
Start by calculating the linear equation using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1}(x -x_1) + y_1[/tex]
This gives
[tex]y = \frac{2 + 7}{0 + 3}(x -0) + 2[/tex]
Evaluate the fraction expression
y = 3(x -0) + 2
Evaluate the difference
y = 3x + 2
From the question, we understand that the line of the inequality is a dashed line and the left of the line is shaded.
This means that the inequality is greater than i.e. >
So, we have:
y > 3x + 2
See attachment for the graph of the inequality
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solve
[tex] \frac{2x - 3}{4} = 3x[/tex]
with working out pls
[tex]~~~~~~\dfrac{2x-3}{4} = 3x\\\\\implies 2x-3 = (3x)(4)\\\\\implies 2x -3 = 12x \\\\\implies 12x -2x = -3\\\\\implies 10x = -3\\\\\implies x = -\dfrac{3}{10}[/tex]
Answer:
x = -3/10
Step-by-step explanation:
Given :
[tex]\frac{2x-3}{4} = 3x[/tex]
============================================================
Multiply both sides with 4 :
⇒ [tex]4 \times \frac{2x-3}{4} = 4 \times 3x[/tex]
⇒ 2x - 3 = 12x
============================================================
Subtract 2x from both sides :
⇒ 2x - 3 - 2x = 12x - 2x
⇒ -3 = 10x
⇒ x = -3/10
a fruit vendor bought 75 Kg of bananas she gave 10kg of the bananas to a poor family she sold the remainder at $28 per kg if she make a loss of $55 on the transaction calculate the cost price of the bananas
Answer:
$25
Step-by-step explanation:
the fruit vendor sold 75-10 = 65 kg of bananas. 65*28 = 1820 dollars. so the fruit vendor earned 1820 dollars.
since she lost 55 dollars, 75 * cost = 1875, divide by 75 to get cost = 25
On a coordinate plane, triangle B C D is rotated 180 degrees clockwise to form triangle B prime C prime D prime. Identify the angle of rotation that maps triangle BCD to triangle B’C’D’. What is the angle of rotation? 90° 180° 270° 360°
Answer:
180
Step-by-step explanation:
Find the measure of center:
1, 2, 3, 4, 5, 6, 7
Answer:
Mean: 4
Median : 4
Mode: 1, 2, 3, 4, 5, 6, 7
Step-by-step explanation:
Measure of center is:
Mean: Average
Median: Middle number
Mode: Often number
Mean: Add all number then divide by the total number in data set.
1 + 2 + 3 + 4 + 5 + 6 + 7 = 28
28/7 = 4
Median: Middle number
1,2,3,4,5,6,7
Mode: most often number
1,2,3,4,5,6,7
Kavinsky
Answer:
(a)no mode
(b)mean= 4
(c)median= 4
Step-by-step explanation:
the measure of centre are the mode, mean and median
mode: this is the heighest occuring number or the number with the heighest frequency.
mean: this is the average number. it's obtained by adding the data values in a set of numbers and dividing the sum by the number of data items.
meadian: this is the middle number when the data is ordered or when the data is arranged in ascending or descending order.
from the data,
mode: no number occured more than the other. therefore, there is no mode
mean = 1+2+3+4+5+6+7 = 28/7= 4
median= 1,2,3,4,5,6,7
the middle numbers is 4
3x^2-8=5x solve using quadratic equation
Answer:
x = -1 or x = 8/3
Step-by-step explanation:
3x² - 8 = 5x
3x² - 5x - 8 = 0
3x² - 8x + 3x - 8 = 0
(Here you find two numbers which have a sum of -5 and a product of 3×-8= -24. These two numbers are -8 and 3. -8 + 3 = -5 and -8 × 3 = -24.)
(3x² - 8x) (3x - 8) = 0
x(3x - 8) +1(3x - 8) = 0
(x + 1) (3x - 8) = 0
x + 1 = 0 OR 3x - 8 = 0
x = -1 3x = 8
x = [tex]\frac{8}{3}[/tex]
What is the Solution to 1-x<5
[tex]~~~~~1-x < 5\\\\\implies -x < 5-1\\\\\implies -x < 4\\\\\implies x > -4\\\\\text{Interval notation:}~ (-4, \infty)[/tex]
An angle cannot be the complement of one angle and the supplement of another angle at the same time. is this true or false?
An angle cannot be the complement of one angle and the supplement of another angle at the same time. Then the given statement is false.
What is an angle?The angle is the distance between the intersecting lines or surfaces. The angle is also expressed in degrees. The angle is 360 degrees for one complete spin.
Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.
Complementary angle - Two angles are said to be complementary angles if their sum is 90 degrees.
An angle cannot be the complement of one angle and the supplement of another angle at the same time.
Then the given statement is false.
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Will be marked the brainliest if correct
Answer:
6 is the answer
Hope that helps.
Let me know if im wrong :)
Step-by-step explanation:
Make 2 sets of data 8 numbers each between 1 and 25. Then calculate the median and IQR for each data set.
Due in 25 mins please help quick!!
The median of the data set will be 15.5. The data set is in between the 1 to 25.
What is median?Median is such a number for the arranged data set in ascending or descending order, such that to its left and to its right belong the same number of observations.
The data set between the number is;
1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25
The value of IQR for data set is;
First Quartile Q1 = 6.5
Second Quartile Q2 = 13
Third Quartile Q3 =19.5
The median of the data set is;
[tex]\rm Median= \frac{15+16}{2} \\\\ Median= 15.5[/tex]
Hence, the median of the data set will be 15.5.
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Jasper buys ten bagels with a listed price of $2 each. Which of these coupons will deduct the most from Jasper's purchase price?
A. Free bagel
B. Save 10%
C. $5 off
D. Buy 8, Get 2 free
Answer:
c. $5 off
Step-by-step explanation:
If jasper buys 10 bagels $2 each then it'll cost $20. With a free bagel it'll deduct $2. With 10% off it'll deduct $2. Buy 8, get 2 free deducts $4. Therefore $5 off is the most
Simplify..
Please show work
I give Brainliest
Answer:
[tex]\frac{4}{n^{2} }[/tex]
Step-by-step explanation:
(2nm⁻³) * 2m³n⁻³
First, focus on the coefficients, 2*2 = 4.
Now the n, n * n⁻³ = n⁻²
Now the m, m⁻³ * m³ = m⁰ = 1
Now multiply altogether, 4n⁻²(1) = [tex]\frac{4}{n^{2} }[/tex]
Please help
Francine has a picture with a length its width. She wants to enlarge the picture to have an area of 375 in2. What will the dimensions of the enlarged picture be? Model the scenario and solve. Then, explain in at least one sentence your solution and include the reasonableness of your solution.
Answer:
25 in x 15 in
Step-by-step explanation:
Given:
Length = 3/5 the widthArea = 375 in²Let width = [tex]x[/tex]
Therefore, length = 3/5 [tex]x[/tex]
First create an equation for the area of the picture based on the given information for its width and length:
[tex]\begin{aligned} \implies \textsf{Area of original picture} & = \sf width \times length\\& = x\left(\dfrac{3}{5}x\right)\\& = \dfrac{3}{5}x^2\end{aligned}[/tex]
We are told the area of the enlarged picture is 375 in². Therefore, substitute this into the equation and solve for [tex]x[/tex] to find the width of the enlarged picture:
[tex]\begin{aligned}\textsf{Area} & = 375\\ \implies \dfrac{3}{5}x^2 & = 375\\ x^2 & =375 \cdot \dfrac{5}{3}\\ x^2 & =625\\ x & = \sqrt{625}\\ x& = 25\end{aligned}[/tex]
Therefore, the width of the enlarged picture is 25 in.
Substitute the found value of [tex]x[/tex] into the expression for length to find the length of the enlarged picture:
[tex]\begin{aligned}\sf Length & = \dfrac{3}{5}x\\\\\implies \sf Length & = \dfrac{3}{5}(25)\\\\& = 15\: \sf in\end{aligned}[/tex]
Therefore, the dimensions of the enlarged picture are 25 in x 15 in. The width is 25 in and the length is 15 in, as the length is 3/5 of the width.
Answer:
correct
Step-by-step explanation:
please answer!!
Use the parabola tool to graph the quadratic function.
f(x)=3x^2+6x−24
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
See below
Step-by-step explanation:
[tex]f(x)=3x^2+6x-24\\\\f(x)=3(x^2+2x-8)\\\\f(x)+3(9)=3(x^2+2x-8+9)\\\\f(x)+27=3(x^2+2x+1)\\\\f(x)=3(x+1)^2-27[/tex]
Here, we can see that the vertex of the parabola is [tex](-1,-27)[/tex] when we compare to the equation [tex]y=(x-h)^2+k[/tex] with vertex [tex](h,k)[/tex].
A second point you could plot is the y-intercept, when [tex]x=0[/tex]:
[tex]f(0)=3(0+1)^2-27\\\\f(0)=3-27\\\\f(0)=-24[/tex]
So, your y-intercept is [tex](0,-24)[/tex].
!!! PLEASE HELP FAST !!!!
The school that Nicole goes to is selling tickets to a play. On the first day of
ticket sales the school sold 7 adult tickets and 5 student tickets for a total of
$105. The school took in $84 on the second day by selling 7 adult tickets and 2
student tickets. What is the price each of one adult ticket and one student
ticket?
A) adult ticket: $7, student ticket: $10
C) adult ticket: $11, student ticket: $6
B) adult ticket: $5, student ticket: $10
D) adult ticket: $10, student ticket: $7
Answer:
the answer is d
Step-by-step explanation:
1st day : 7 × 10 = 70
5 × 7 = 35 70+ 35= 105
2nd day : 7 × 10 = 70
2 × 7 = 14 70+14 = 84