Part of the graph of the function f(x) = (x + 4)(x-6) is
shown below.
Which statements about the function are true? Select two
options.
The vertex of the function is at (1,-25).
The vertex of the function is at (1.-24).
AO
The graph is increasing only on the interval -4< x < 6
The graph is positive only on one interval, where x <
4.
6
-
The graph is negative on the entire interval
4
True options:
1. The vertex of the function is at (1,–25).
5. The graph is negative on the entire interval –4 < x < 6.
Step-by-step explanation:
Part of the graph of the function f(x) = (x + 4)(x – 6) is shown in attached diagram.
This graph intesects the x-axis at points (-4,0) and (6,0). So, the x-coordinate of the vertex is \dfrac{-4+6}{2}=\dfrac{2}{2}=1
The y-coordinate of the vertex is
y=(1+4)(1-6)=5\cdot (-5)=-25
Hence, the vertex is ar the point (1,-25) - frist option is true, second option is false.
For all x<1 the graph is decreasing, for all x>1 the graph is increasing. So, third option is false.
The graph is positive (placed above the x-axis) for all x<-4 or x>6. This means fourth option is false.
The graph is negative (placed below the x-axis) for all -4<x<6. This means fifth option is true.
hope this helps homie
-21(a + 2b) + 14a - 9b
It’s hard I’m only a 7th grader
Answer:
-7a-51b
Step-by-step explanation:
-21(a+2b)+14a-9b
-21a-42b+14a-9b
-21a+14a-42b-9b
-7a-42b-9b
-7a-51b
Answer: -7a - 51b
Step-by-step explanation:
see photo for work
2. Ron lives in Seattle, but he is going to be in Hawaii for 13 days during the month of
March. There are 30 days in March. What would you subtract to find out how many days
in March Ron will be in Seattle?
We will subtract 13 from the days of March to find out the days in March Ron will be in Seattle.
Step-by-step explanation:
Given,
Number of days Ron will be in Hawaii = 13 days
Number of days in March = 30 days
As Ron will be in Hawaii for 13 days, the remaining days he will be in Seattle.
So we will subtract 13 from days of March to find out the number of days in March, Ron will be in Seattle.
Number of days in Seattle = Days of March - Number of days in Hawaii
Number of days in Seattle = 30 - 13 = 17 days
We will subtract 13 from the days of March to find out the days in March Ron will be in Seattle.
Keywords: subtraction
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what is 6x - 3y if x = 5 and y = 3
Answer:
21
Step-by-step explanation:
Answer:
21
Step-by-step explanation:
x = 5
y = 3
6(5) - 3(3)
30 - 9
21
Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1:4:6. If 20 buckets of sand are used, how many buckets of cement and sand will be needed?
Buckets of cement needed is 5 and sand needed is 20
Solution:
Given that Concrete tiles are made using buckets of cement, sand and gravel mixed in the ratio 1 : 4 : 6
cement : sand : gravel = 1 : 4 : 6
Let the cement needed be "1x"
Let the sand needed be "4x"
Let the gravel needed be "6x"
Given that 20 buckets of sand used
4x = 20
x = 5
Thus buckets of cement needed = 1x = 1(5) = 5
Buckets of sand needed = 4x = 4(5) = 20
5 buckets of cement and 20 buckets of sand are needed
Visitor attendance at the nature center in December is one-quarter the attendance in September.
In December, 94 people visit the nature center.
How many people visit the nature center in September?
376 people visited the nature center in September.
Step-by-step explanation:
Given,
Number of visitors in December = 94 people
This number is one quarter of the number of people in September.
One quarter = [tex]\frac{1}{4}[/tex]
Let,
x represent the number of visitors in September.
[tex]\frac{1}{4}x=94[/tex]
Multiplying both sides by 4
[tex]4*\frac{1}{4}x=94*4\\x=376\\[/tex]
376 people visited the nature center in September.
Keywords: fraction, multiplication
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210 ÷ ☐ = 15
Please help I did it on my calculator and i cant find it
210 / x = 15
--> 210/15 = x
--> x = 14
Helllp!! Analyze the diagram below and answer the question that follows.
The parallel lines are:
▪ Option D that's FL // GKKnow more:-
In geometry, parallel lines are lines in a plane which do not meet; they do not intersect at any point and keeps a fixed minimum distancefind the value of x that satisfies the equation 25 degrees =sin(x)
Answer:
5
Step-by-step explanation:
Marissa bought four bottles of water Each bottle of water is 0.95 cents Write an equation with the same product as the total cost but different factors SHOW IN OWN WORDS SHOW YOUR WORK
Answer: Total cost = Cost of each bottle × Number of bottles
Step-by-step explanation: If each bottle of water Marissa bought cost 0.95cents. This means four bottles will cost = 0.95 + 0.95 + 0.95 + 0.95 = 3.80 cents
This can be written simply as 0.95 × 4 = 3.80 cents
Therefore, a general equation for calculating the total cost of bottle water will be;
Total cost = Cost of each bottle × Number of bottles.
Please respond to the question below in your own words with proper explanations and use of math vocabulary. Here is a function.
What is the function equation in function notation?
Enter your answer in the box. Show your work. Explain how you found your numbers for the slope and y-intercept.
Answer:
Slope = - 3, y-intercept is 4 and the equation is y = - 3x + 4.
Step-by-step explanation:
Slope of a straight line passing through two given points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is given by the formula
[tex]m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex].
Now, the given graph of the straight line passes through the points (0,4) and (1,1) points.
Hence, the slope of the straight line will be = [tex]\frac{1 - 4}{1 - 0} = - 3[/tex]
Again, the straight line intersects the y-axis at point (0,4) point. hence, its y-intercept is 4.
Therefore, the straight line has equation
y = - 3x + 4 (Answer)
the sale of KIDZ sneakers rice from $1.5 billion to $2.8 billion.find the percent of increase.Round to the nearest tenths of a percent where necessary.
First: work out the difference (decrease) between the two numbers you are comparing.
Decrease = Original Number - New Number
Then: divide the decrease by the original number and multiply the answer by 100.
% Decrease = Decrease ÷ Original Number × 100
If your answer is a negative number then this is a percentage increase.
Thus, the answer is a 86.7% (rounded) increase.
Final answer:
The sale of KIDZ sneakers increased by $1.3 billion, representing an 86.7% increase when rounded to the nearest tenth of a percent.
Explanation:
To find the percent of increase for the sale of KIDZ sneakers, we subtract the original amount ($1.5 billion) from the new amount ($2.8 billion) and then divide by the original amount. The difference between the two values is $2.8 billion - $1.5 billion = $1.3 billion. To calculate the percentage increase, we divide $1.3 billion by $1.5 billion, which gives us approximately 0.8667. To get the percentage, we then multiply by 100, resulting in an 86.67% increase. Finally, rounding to the nearest tenth of a percent, we get an increase of 86.7%.
find the solution to the systems of equations y=-7x+3 and y=-x-3
Answer:
x=1, y=-4. (1, -4).
Step-by-step explanation:
y=-7x+3
y=-x-3
-------------
-7x+3=-x-3
-7x-(-x)+3=-3
-7x+x=-3-3
-6x=-6
6x=6
x=6/6
x=1
y=-1-3=-4
19. If the scale is 1:100 on a plan, and a fence is 7,500 mm,
how many millimetres will it measure on the plan?
mm
Answer:
It will measure 75 millimetres on the plan.
Step-by-step explanation:
Given:
Scale on the plan = 1:100
Length of the fence = 7,500 mm
To find:
how many millimetres will it measure on the plan
Solution:
As the ratio on the plan is 1: 100, the for 7500 the ratio will
x : 7500
Now by cross multiplication we get
[tex]7500 \times 1 = x \times 100[/tex]
[tex]7500 = 100x[/tex]
[tex]x =\frac{ 7500}{100}[/tex]
x = 75
Final answer:
The fence will measure 75 millimeters on the plan.
Explanation:
To find out how many millimetres a fence that is 7,500 mm long in reality would measure on a plan with a scale of 1:100, you would convert the actual size to the scale size. You do this by dividing the actual size by the scale factor.
Here is the calculation for this scale conversion:
Actual length of the fence = 7,500 mmScale = 1:100Scaled length on the plan = Actual length / Scale factorScaled length on the plan = 7,500 mm / 100Scaled length on the plan = 75 mmThe fence would measure 75 mm on the plan.
Using only the numbers 1 through 14. Add the numbers to get 28 (using 4 numbers), 14 (using 3 numbers), 30 (using 4 numbers), and 33 (using 3 numbers)
Answer:
10 + 9 + 7 + 2 = 28 (Getting 28 using 4 numbers from 1 to 14)8 + 5 + 1 = 14 (Getting 14 using 3 numbers from 1 to 14)11 + 12 + 4 + 3 = 30 (Getting 30 using 4 numbers from 1 to 14)14 + 13 + 6 = 33 (Getting 33 using 3 numbers from 1 to 14)Step-by-step explanation:
The given numbers:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14
Getting the number 28 (using 4 numbers):
If we add the following 4 numbers from 1 to 14, we would get 28.
10 + 9 + 7 + 2 = 28
Getting the number 14 (using 3 numbers):
If we add the following 3 numbers from 1 to 14, we would get 14.
8 + 5 + 1 = 14
Getting the number 30 (using 4 numbers):
If we add the following 4 numbers from 1 to 14, we would get 30.
11 + 12 + 4 + 3 = 30
Getting the number 33 (using 3 numbers):
If we add the following 3 numbers from 1 to 14, we would get 33.
14 + 13 + 6 = 33
Keywords: addition, number
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Look at the example problem. Suppose Alana walks 6.6 miles the next day. Complete the steps below to find the number of miles she walks in two days.
Answer:
Looking at the example Alana will walk. 15.23 miles in two days
step-by-step explanation:
Looking at the example and using place value system
8.63 + 6.60= 15.23 miles
Sum = 14 ones + 8 tenths + 6 hundredths
= 4 ones + 2 tenths + 3 hundredths
= 1 ten + 4 ones + 2 tenths + 3 hundredths
Alana walks 12.3 miles in two days.
In the given problem, Alana walks 6.6 miles on the first day.
To find the total distance she walks in two days, we perform a multi-digit addition.
We start by adding the ones place, which gives us 14 ones. Moving to the tenths place, we add 8 tenths to the existing sum.
In the hundredths place, we have 6 hundredths. This gives us a total of 14 ones, 8 tenths, and 6 hundredths.
Next, we simplify this into a mixed decimal, resulting in 4 ones, 2 tenths, and 3 hundredths.
Converting to place value, this becomes 1 ten, 4 ones, 2 tenths, and 3 hundredths.
Therefore, Alana walks a total of 12.3 miles in two days.
This process involves careful consideration of place value and addition to accurately determine the distance covered over the two-day period.
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complete question should be:
Look at the example problem. Suppose Alana walks 6.6 miles the next day. Complete the steps below to find the number of miles she walks in two days.
Alana walks ____ miles in 2 days.
50.48=-22.02+5x what is the solution to the equation?
Answer:
x=14.5
Step-by-step explanation:
50.48=-22.02+5x
5x=50.48-(-22.02)
5x=50.48+22.02
5x=72.5
x=72.5/5
x=14.5
If f(x) = x2 − 6x + 19, complete the square and determine the minimum or maximum value of the function.
A) f(x) = (x + 3)2 + 28 and f(x) has a maximum value f(3) = 28.
B) f(x) = (x + 3)2 + 28 and f(x) has a minimum value f(3) = 28.
C) f(x) = (x − 3)2 + 10 and f(x) has a maximum value f(3) = 10.
D) f(x) = (x − 3)2 + 10 and f(x) has a minimum value f(3) = 10. Eliminate
Final answer:
To complete the square for f(x) = x^2 - 6x + 19, we create a perfect square trinomial to rewrite the function as f(x) = (x - 3)^2 + 10, which has a minimum value at the vertex (3, 10).
Explanation:
To complete the square for the quadratic function f(x) = x2 - 6x + 19, we need to form a perfect square trinomial from the x2 and the -6x terms and then adjust the constant term accordingly.
First, we divide the coefficient of the x term, which is -6, by 2, getting -3, and then square it to get 9. We add and subtract this number inside the function to maintain the equality:
f(x) = (x2 - 6x + 9) - 9 + 19
Now, f(x) becomes:
f(x) = (x - 3)2 + 10
Since the coefficient of the x2 term is positive, the parabola opens upward, and the vertex represents the minimum value of the function.
The vertex of the parabola is at (3, 10), so f(3) = 10 is the minimum value of f(x). Therefore, the correct answer is:
D) f(x) = (x - 3)2 + 10 and f(x) has a minimum value f(3) = 10.
Helene invested a total of 1,200 $
U can use a common denominator and rewrite 3/5 divided by 1/10 as
Answer:
6
Step-by-step explanation:
3/5 = 6/10
6/10 / 1/10
6/10 times 10/1
60/10
6
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They’re 80 skittles in a bag 20% of them are read how many skittles a red
Answer: 16
Step-by-step explanation: 80x20=1600
Put the decimal place where it belongs
80% of 20=16
Hope this helps!
To find the number of red skittles in the bag, multiply the total number of skittles by the percentage of red skittles (in decimal form). In this case, there are 16 red skittles in the bag. So, there are 16 red skittles in the bag.
Explanation:To find the number of red skittles in the bag, we can use the concept of percentages. We know that 20% of the skittles are red, and there are 80 skittles in total. To find the number of red skittles, we multiply 80 by 20% (or 0.20).
80 * 0.20 = 16
So, there are 16 red skittles in the bag.
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Identify the relationship between the graphs of
these two equations.
5y = 6x +1 6y = -5x – 4
Click on the correct answer.
parallel
perpendicular
neither
Answer:
perpendicular
Step-by-step explanation:
Convert into y = mx + b form
5y = 6x + 1
y = 6/5x + 1/5
6y = -5x - 4
y = -5/6x - 2/3
Since the y int are different, and the slopes are perpendicular (neg reciprocal), the 2 lines are perpendicular
The sum of three consecutive numbers is eighty-four what is the smallest of the three numbers
Answer:
Step-by-step explanation:
consecutive numbers are one right after the other...
ur 3 consecutive numbers are :
x and x + 1 and x + 2.....and they total 84
x + x + 1 + x + 2 = 84.....combine like terms
3x + 3 = 84
3x = 84 - 3
3x = 81
3x = 81/3
x = 27
x + 1 = 27 + 1 = 28
x + 2 = 27 + 2= 29
so your 3 numbers are 27,28,29 with the lowest being 27
Answer: 24
Step-by-step explanation: This problem states that the sum of 3 consecutive numbers is 84 and it asks us to find the smallest number.
3 consecutive numbers can be represented as follows.
X ⇒ first number
X + 1 ⇒ second number
X + 2 ⇒ third number
Since the sum of our 3 consecutive numbers is 84, our equation will read X + X + 1 + X + 2 = 84.
Simplifying on the left we get 3x + 3 = 84.
Subtracting 3 from both sides, we have 3x = 81.
Now we can divide both sides by 3 to get x = 27.
This means that 27 will be the smallest number.
When is a long-term purchase on a credit card better than taking out a loan?
Long-term purchase on a credit card better than taking out a loan when interest rate is 0% or very lower than loan, or any other benefits
Explanation:We can use a credit card for long term purchases if there is a 0% interest rate on purchase is allowing you to pay off your shopping with no additional cost for an introductory period. Or some of the credit cards may offer interest-free purchases for 3 to 6 months others can run for as long as 12 to 14 months. An interest-free period could be considered long-term if it lasts between 12 and 14 months or more.
We could benefit from one of these cards if you are making a large purchase and need more breathing room to pay it off without any interest. This is especially useful if you have a high spending period such as an overseas holiday coming up.
A long term purchase with loan or with a credit card will depends upon the interest rates offered in both the schemes.
In order to understand that what is more beneficial for us a long term purchase or taking out a loan we have to see the interest rates of the both the schemes.
If the interest rate of loan is higher than the interest rate offered by credit card then we must go for long term purchase on credit card and the amount can be paid later .
Also credit cards often offer other benefits too. These options can also be seen as a determining parameters of whether to take loan or a long term purchase on credit card is beneficial.
Also we can have a look at the period of interest free purchase offered by the credit card.
Depending upon the credit card and its usage they can vary from three months to one year with multiple other benefits which promote the use of credit card.
so we can conclude that
A long term purchase with loan or with a credit card will depends upon the interest rates offered in both the schemes.
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Find g(-1)).
g[(-1)) =
Answer:
Step-by-step explanation:
Incomplete question.
What time is 5 1/ 2 hours after 7:00 pm?
Answer:
5 1/2 hours past 7:00 would be 12:30
Step-by-step explanation:
Answer:
12:30 a.m.
Step-by-step explanation:
You can automatically add 5 to the 7, 5 + 7 = 12. Then add 30 to the minuets. 00 + 30 = 30.
So, your answer is 12:30.
Hope this helps!!
10x^3 - 6x^2 + 50x - 30
Answer:
Step-by-step explanation:
22
Answer:
Factored :
2 (5x-3)(x^2+5)
Roots :
[tex]x=\frac{3}{5} , i\sqrt{5} , -i\sqrt{5} \\[/tex]
Step-by-step explanation:
a closet has 10 pairs of sneakers and 4 pairs of flip flops. write the ratio of pairs of flip flops to the total pairs of sneakers in simplest form
Answer:
2:5
Step-by-step explanation:
The ratio of pair of flip flop to pair of sneakers is 4:10 we simplify it to 2:5 by dividing both sides by 2
30 treadmills to 36 elliptical machines the ratio in simplest form
Circumcenter of triangle with coordinates of (1,1) (1,-3) (7,-3)
Answer:
Circumcenter of triangle [tex](4,-1)[/tex]
Step-by-step explanation:
Given coordinates are [tex](1,1)(1,-3)(7,-3)[/tex]
We will draw these points on the graph.
Let [tex]A(1,1)[/tex], [tex]B(1,-3)[/tex] and [tex]C(7,-3)[/tex]
We can see it is a right-angle triangle.
Let [tex]O[/tex] be the midpoint of line [tex]AC[/tex]
So, the coordinate of the point [tex]O[/tex] will be
[tex]A(1,1)\ C(7,-3)\\\\Midpoint\ O\ will\ be\\\\O=(\frac{1+7}{2},\frac{1+(-3)}{2})\\ \\O=(\frac{8}{2},\frac{-2}{2})\\\\O=(4,-1)[/tex]
Also, we know the coordinates of circumcenter of a right angle triangle will be midpoint of its hypotenuse.
So, coordinates of circumcenter is [tex](4,-1)[/tex]