Answer:
D. The graph contains the point (4, -10)
Step-by-step explanation:
We have been given an equation of a function: [tex]y=4x-10[/tex]. We are asked to find which of the given statements are not true about our given function.
A. The slope of the line can be written as 4/1.
We can see from our given equation that slope is 4 we can write 4 as 4/1 as it will not change value of 4, therefore, option A is true.
B. The graph crosses the y-axis 10 units below the origin.
Since we know that b represents y-intercept, where line crosses y-axis. y-intercept for our given equation is -10, which means that our given line crosses y-axis at -10 (10 units below the origin), therefore, option B is true.
C. The line has a constant rate of change.
We can see that slope of line is 4 which means with each increase in x, y will increase by 4 units, which remains constant, therefore, option C is true indeed.
D. The graph contains the point (4, -10)
Since we know that y-intercept is -10, which occurs at x equals 0, therefore, the graph does not contain the point (4,-10) and option D is not true.
the sum of the perimeter of two squares is 40cm while the sum of the area is 58cm². Find length the side of the square.
[tex]a,\ b-the\ length\ of\ sides\\\\(1)\qquad4a+4b=40\qquad\text{divide both sides by 4}\\\\a+b=10\to a=10-b\\\\(2)\qquad a^2+b^2=58\\\\\text{Substitute}\ (1)\ \text{to}\ (2):\\\\(10-b)^2+b^2=58\qquad\text{Use}\ (x-y)^2=x^2-2xy+y^2\\\\10^2-2(10)(b)+b^2+b^2=58\\\\100-20b+2b^2=58\qquad\text{subtract 58 from both sides}\\\\42-20b+2b^2=0\\\\2b^2-20b+42=0\qquad\text{divide both sides by 2}\\\\b^2-10b+21=0\\\\b^2-7b-3b+21=0\\\\b(b-7)-3(b-7)=0\\\\(b-7)(b-3)=0\iff b-7=0\ \vee\ b-3=0\\\\\boxed{b=7\ \vee\ b=3}[/tex]
[tex]\text{Put the values of b to }\ (1):\\\\for\ b=7\to a=10-7=3\\\\for\ b=3\to a=10-3=7\\\\Answer:\ \boxed{7cm\ and\ 3cm.}[/tex]
The sides of the squares will be 3 and 7.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
Area of square = Side²
The perimeter of the square = 4× side
Length of diagonal of square = √(2) × side
Let's say the side of the first square is a while the second is b
Now,
the sum of the perimeter of two squares is 40cm
4a + 4b = 40
a + b = 10
Now,
The Sum of the area is 58cm²
So,
a² + b² = 58
By substituting,
a² + (10 - a)² = 58
a² - 10a + 21 = 0
a² - 7a - 3a + 21 =0
a(a - 7) - 3(a - 7) = 0
(a-3)(a - 7) = 0
a = 3 ,7
Corresponding to 3 and 7
b = 10 - 3 = 7 and b = 10 - 7 = 3.
Hence "The sides of the squares will be 3 and 7".
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Write an expression equivalent to the one below
5(x + 6)-2x + 9
Answer:
5x+30-2x+9
Step-by-step explanation:
first you have to do the ''distributive property'' then you will get 5x+30-2x+9
Question
Write an expression equivalent to the one below
5(x + 6)-2x + 9
Answer:
2x + 10 + 29 + xStep-by-step explanation:
5(x + 6)-2x + 9 =
5x + 30 - 2x + 9 =
3x + 39
----------------------------
2x + 10 + 29 + x =
3x + 39
buses on your route run every 8 minutes from 7:00 am to 11:00 am. you arrive at the bus stop at 8:19. how long will you wait for the bus?
a: 1 minutes
b: 3 minutes
c: 7 minutes
d: 8 minutes
Answer:
A: 1 Minute
Step-by-step explanation:
Buses start running at 7 and run every eight minutes. This means that:
Bus 1: 7:00 AM
Bus 2: 7:08 AM
Bus 3: 7:16 AM
Bus 4: 7:24 AM
Bus 5: 7:32 AM
Bus 6: 7:40 AM
Bus 7: 7:48 AM
Bus 8: 7:56 AM
Bus 9: 8:04 AM
Bus 10: 8:12 AM
Bus 11: 8:20 AM
The waiting time of the bus is 7 minutes,
To calculate the waiting time, we need to break down the time difference between your arrival (8:19 am) and the next bus arrival (scheduled to come every 8 minutes). Let's start by determining the time between 8:19 am and the next scheduled bus at 8:20 am. This is only 1 minute of waiting time.
However, you want to know how long you'll have to wait until the next bus after 8:20 am, which means we need to consider the remaining time until the next 8-minute interval. From 8:20 am to 8:24 am, the bus does not arrive yet, resulting in an additional 4 minutes of waiting time
=> (8:24 am - 8:20 am = 4 minutes).
Now, we have reached the second 8-minute interval from 8:24 am to 8:28 am. As you arrived at 8:19 am, you will have to wait for 5 more minutes
=> (8:28 am - 8:19 am = 7 minutes)
to catch the bus.
So, the Main Answer: c: 7 minutes.
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Which equation is graphed here
A) y=2x+3
B) y=2x-3
C) y=3x+2
D) y=3x-2
Answer:
C) y=3x+2
Step-by-step explanation:
Looking at the graph, we can see the y intercept is at 2.
All of the answers are in the form y = mx +b
where b is the y intercept
y = mx+2
The only answer that has the y intercept of 2 is y = 3x+2
Plz help me answer A and B
For both questions, you essentially use the equation r = d/t
a. 34/7 = about 4.86 dollars per hour
b. 4/10 = 0.40 dollars per pound.
The sum of three consecutive numbers is 129 what is the smallest of the three numbers
Answer: n=42
Step-by-step explanation: Lets suppose n is a number. Since the numbers are consecutive, they would be:
n
n+1
n+2
If the sum is 129, then an equation would be
n+n+1+n+2=129
3n=126
n=42
So, the smallest number would be 42
Denise bought a t-shirt at the sale price of $25 the original cost of the T-shirt was $40 what percent represents the discount that Denise received when buying the T-shirt
Answer:
37.50%
Step-by-step explanation:
Use the formula: Old Value minus New Value (in absolute value bars) divided by Old Value times 100
New Value = $25 / Old Value = $40
$40 - $25 = $15
$15 divided by $40 is 0.375
0.375 times 100 (0.375 x 100) is 37.50
some one answer ASAP!! in trail mix, there are nuts and dried fruit. In one mix there is 40% dried fruit. In another, there is 60% dried fruit. How many pounds of each mix is needed to make 5 pound mix that is 55% dried fruit?
let x= The amount of 40% fruit mix
let y=the amount of 60% fruit mix
what is the solution to the system
[tex]p\%=\dfrac{p}{100}\\\\40\%=\dfrac{40}{100}=\dfrac{4}{10}=0.4;\ 60\%=\dfrac{60}{100}=\dfrac{6}{10}=0.6;\ 55\%=\dfrac{55}{100}=0.55\\\\\left\{\begin{array}{ccc}x+y=5&\to x=5-y\\0.4x+0.6y=0.55\cdot5\end{array}\right\\\\\text{Use substitution method}\\\\0.4(5-y)+0.6y=2.75\qquad\text{use distributive property}\\\\(0.4)(5)+(0.4)(-y)+0.6y=2.75\\\\2-0.4y+0.6y=2.75\qquad\text{subtract 2 from both sides}\\\\0.2y=0.75\qquad\text{multiply both sides by 5}\\\\\boxed{y=3.75}[/tex]
[tex]\text{Put the value of y to the first equation}\\\\x=5-3.75\\\\\boxed{x=1.25}\\\\Answer:\ x=1.25\ and\ y=3.75.[/tex]
Leo weighs 10 pounds of dog food at the pet store. The scale mistakenly lists the bag at 11.5 pounds
Answer:
percent error = 15%
Step-by-step explanation:
The following question is missing: What is the percent error?
percent error = (measure error/ actual weight)*100
where:
measure error = incorrect weight - correct weight = 11.5 - 10 = 1.5 pounds
percent error = (1.5/10)*100 = 15%
At the start of the 20th century,there were about 100,000 tigers in the wild.In 2014 there were about 3,200.What percent did the population decrease
The population decreased 96.8%.
Initial value = 100,000
Final value = 3,200
The percentage decrease is
= (Final value - initial value) * 100% /initial value
= [tex]\frac{\left(3200-100000\right)}{100000}\cdot100 \%[/tex]
= −96.8%
Negative sign because of decrease.
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A water company offers industrial users two different packages. The users can either pay 77 cents per thousand gallons, or pay a fixed amount of $1,232,000 for unlimited water usage for one year. How much water does an industrial user need to use in one year for the fixed amount package to be the less expensive option?
The water used will be greater than 1600000 thousands of gallons for the fixed amount to be less expensive.
How to find amount of water used for it to be less expensive?The users can either pay 77 cents per thousand gallons, or pay a fixed amount of $1,232,000 for unlimited water usage for one year.
Therefore,
77 cents = 0.77 dollars
Hence,
The user can pay 0.77 per thousand gallons.
He can pay a fixed amount of $1,232,000 .
Therefore, the amount of water the company will use for the fixed amount to be less expensive is as follows;
let
x = amount of water use in thousand gallons
Using inequalities,
0.77x ≥ 1,232,000
x ≥ 1,232,000 / 0.77
x ≥ 1600000
Therefore, the water used will be greater than 1600000 thousands of gallons for the fixed amount to be less expensive.
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(14 POINTS!) PLEASE HELP ASAP!! IMAGE PROVIDED!!!
Which table shows a proportional relationship between x and y?
Answer: C
Step-by-step explanation: The equation is y = x/7. For every 7 numbers that x increases, y increases by 1.
For which value of X is the row in the table of values incorrect? The function is the quadratic function Y=3/4x^2
Answer:
The row with x = 2 and y = 4 is incorrect. The y value should be y = 3 when x = 2.
==============================================================
Explanation:
Fractions can be a bit of a pain, so I'm going to be converting to decimal form to help with the computation; however, I will convert the y value results to mix number form so that it matches what the table shows.
Keep in mind that 3/4 = 0.75 when you use a calculator or long division. So a number like 2.75 means 2 & 3/4 (two and three quarters)
---------------
Let's check the first row. Plug in x = 0 and it leads to...
y = (3/4)*x^2
y = (3/4)*0^2
y = (3/4)*0
y = 0.75*0
y = 0
This shows us that row 1 is correct. When x = 0, y = 0 leading to (x,y) = (0,0).
-------------
Repeat the same basic outline of steps, but now use x = 2
y = (3/4)*x^2
y = (3/4)*2^2
y = (3/4)*4
y = 0.75*4
y = 3
So instead of 4, the proper y value is y = 3 when x = 2. This means row 2 is the answer (the row that has the incorrect values).
-------------
For the sake of completeness, let's see if the third row is correct or not. Plug in x = 3
y = (3/4)*x^2
y = (3/4)*3^2
y = (3/4)*9
y = 0.75*9
y = 6.75
y = 6 & 3/4
We see that x = 3 points to y = 6 & 3/4, so we have the correct values in this row. We can cross this off the list of choices.
-------------
Finally, let's check x = 5
y = (3/4)*x^2
y = (3/4)*5^2
y = (3/4)*25
y = 0.75*25
y = 18.75
y = 18 & 3/4
We get the proper y value. So we can also cross this off the list.
Emma buys and sells truck parts. She bought two tires for $35.00 each and later sold them for $65.00 each. She bought three rims for $75.00 each and later sold them for $136.00 each. She bought five headlight covers for $4.00 each and later sold them for $15.00 each. What is Emma's total profi?
Answer:
two tires for $35 -------------------------$70 total
three rims for $75--------------------------- $225
five headlights for $ 4.00 ----------------$20
Emma spends ($225+$70+$20) =$315
Now Emma sells them for 2 tires for $65 =130
3 rims for $136 = $408
5 headlights for $15 = $75
total money Emma makes = $613.
the profit is $613- $315= $298
the profit is $298
Each day a company use 1/5 of a box of paper how many boxes would they have used after four days
Answer:0.8 or 4/5
Step-by-step explanation:1/5 x 4 = 4/5
And to check your work
4/5 / 4 = 1/5
Answer: 4/5
Step-by-step explanation: First you have to set up a multiplacation problem.
1/5 x 4 or 1/5 x 4/1 = 4/5
Leila has scored 33, 28, 24 and points in her three basketball games so far. How many points does she need to score in her next game so that her average (mean) is 27 points per game?
Leila needs to score 23 points in her next game to have an average of 27 points per game.
Explanation:
To find out how many points Leila needs to score in her next game in order to have an average of 27 points per game, we need to use the formula for finding an average. The sum of all the points scored is 33 + 28 + 24 + x (the points in the next game), and we divide this sum by the number of games, which is 4. So, the equation is (33 + 28 + 24 + x) / 4 = 27. To solve for x, we multiply both sides of the equation by 4 to get 33 + 28 + 24 + x = 27 * 4. Simplifying this gives us 85 + x = 108. To isolate x, we subtract 85 from both sides of the equation, which gives us x = 108 - 85. So, Leila needs to score 23 points in her next game to have an average of 27 points per game.
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Why is math important “?
Answer:
Without math, how would we know how to count seconds minutes, etc.?
Math is extremely important for knowing how to do simple things like cooking, you need to know for how much time to put something in the oven or microwave or stove. Those are just the basics. There is a lot more stuff out there that math is used for.
If you want to get a job, you have to know about math. Without math, you will be unable to get a job. Every single job you can get requires math. Even working in a grocery store, you need math. Whether we like it or not, you will have to learn math or you'll end up homeless and without a job.
If the sides of a triangle MNP are MN= 4x+9, NP= x+5, MP= 7x-20, find the range of possible values for x. Please show steps!
Answer:
[tex]6<x<8.[/tex]
Step-by-step explanation:
The sides MN, NP and MP of the triangle MNP should satisfy inequalities:
[tex]MN+NP>MP;[/tex][tex]MN+MP>NP;[/tex][tex]NP+MP>MN.[/tex]Then
[tex]\left\{\begin{array}{l}4x+9+x+5>7x-20\\4x+9+7x-20>x+5\\x+5+7x-20>4x+9\end{array}\right..[/tex]
Simplify this system:
[tex]\left\{\begin{array}{l}4x+x-7x>-9-5-20\\4x+7x-x>20-9+5\\x+7x-4x>20-5+9\end{array}\right.\Rightarrow \left\{\begin{array}{l}-2x>-16\\10x>16\\4x>24\end{array}\right.\Rightarrow \left\{\begin{array}{l}x<8\\x>1.6\\x>6\end{array}\right..[/tex]
Thus, the range of possible values for x is [tex]6<x<8.[/tex]
The question, from high school Mathematics related to geometry and algebra, asks to find the possible values for x using the triangle inequality theorem. These inequalities when solved gives the required range for x.
Explanation:The subject of this question is Mathematics, specifically pertaining to geometry and algebra. This question asks to find the range of possible values for x given that the sides of triangle MNP are MN= 4x+9, NP= x+5, MP= 7x-20.
Firstly, we utilize the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side. With this theorem, we can set up three inequalities:
4x+9 + x+5 > 7x-20 4x+9 + 7x-20 > x+5 x+5 + 7x-20 > 4x+9
Solving these inequalities will provide the range of possible values for x.
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PLEASE HELPPP!!!
WILL GIVE THE BRAINLEST!!!
Answer:
5.) Proportionality is 3/1 or 3 simplified
b x 3 = pb= boxesp= pens in box6.) Proportionality is 1/6
m ÷ 6 = pm = muffinsp= pack(s) of muffinsStep-by-step explanation:
You would take the first column (or in this case row (pens and packs) and place the 2nd row under it in fraction form.
5.) 3/1 = 36.) 1/6 = 1/6That would be your proportion
Then you would (in place of numbers) use letters to symbolize in the equation
5.) p = pens: b= boxes6.) m= muffins; p= packThen create an equation to figure out how to get the correct numbers.
1 box holds 3 pens so:5.) b x 3 = pCheck: 2 boxes x 3 pens per box = 6 pens (check table) Correct!6 muffins in 1 pack so:6.) m ÷ 6 = p12 muffins ÷ 6 muffins in per box = 2 packs (check table) Correct!the grand prix cinema sold 150 tickets to a movie. Some of these were child tickets and the rest were adult tickets. A child ticket costs $7.75 and an adult ticket cost $10.25. if the cinema sold $1470 worth of tickets, which system of equations would be used to determine how many adult tickets, a, and how many child tickets, c, were sold?
The problem requires setting up a system of two equations: one representing the total number of tickets sold (c + a = 150) and the other representing the total revenue from ticket sales (7.75c + 10.25a = 1470). Solving this system will yield the number of adult and child tickets sold.
Explanation:To determine how many adult tickets, a, and child tickets, c, were sold by the Grand Prix Cinema, we need to establish a system of equations based on the given information:
The total number of tickets sold was 150: c + a = 150.The total revenue from tickets was $1470: 7.75c + 10.25a = 1470.These two equations can be used simultaneously to solve for the variables a (adult tickets) and c (child tickets). This problem is an example of a linear system of equations that can be solved by various methods such as substitution, elimination, or matrix operations.
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Which equation and solution represents each situation? Solutions may be rounded to the nearest tenth. What number is 74% of 58?
42.9
Step-by-step explanation:"74% of 58" translates to ...
... 74/100 × 58 = 42.92
Rounded to the nearest tenth, this is 42.9.
_____
Comment on translation
In this context, "of" means "times." Of course, % means /100, so ...
... 74% = 74/100 = 0.74
Help please ASAP!!! I’ll mark brainliest
PLEASE HELP, I WILL MOVE TO A DIFFERENT SCHOOL IF I DONT PASS!!!!
Do number 1 all of the letters, a, b, c, d , e , and f.(its just connecting the equations).
for number 2, just do b and c.
if you know how to do 3, (b and c), that would be great.
plz help me out.
Roger Ratkin has three employees who earn $500, $550, and $700, respectively. How much does Roger owe for the first 12 weeks for SUTA and FUTA? Assume a SUTA rate of 5.3% and a FUTA rate of .8%.
The answer explains how to calculate the SUTA and FUTA amounts owed by Roger Ratkin for the first 12 weeks for his employees' wages.
Explanation:State Unemployment Tax Act (SUTA) and Federal Unemployment Tax Act (FUTA)
Calculate SUTA amount: ($500 + $550 + $700) * 5.3% * 12 weeks = $744.Calculate FUTA amount: ($500 + $550 + $700) * .8% * 12 weeks = $55.20.Therefore, Roger owes a total of $799.20 for SUTA and FUTA for the first 12 weeks for his three employees.1. Two boats A and B depart from a port at the same time, travels to the north at 15 miles per hour, while B travels eastward at 20 mph. How fast boats are separated two hours after they left the port?
Answer:
50 mi
Step-by-step explanation:
Two hours after leaving port,
Boat A has travelled 30 mi north Boat B has travelled 40 mi east.The triangle formed by their tracks and the line joining their current positions is a right-angled triangle.
According to Pythagoras,
a² + b² = c²
30² + 40² = c²
900 + 1600 = c²
2500 = c²
√(2500) = c
c = 50 mi
The boats will be separated by 50 mi two hours after leaving port.
If ABC is congruent to DEC, angle B = 50 degrees and angle E = 5x x=
Answer:
the answer is 10
Step-by-step explanation:
if b is congruent to e
(which it is)
e=50 degrees
50/5=10
x=10
The value of x is 50 degrees.
Explanation:In the given question, if ABC is congruent to DEC and angle B is 50 degrees, we want to find the value of angle E.
Since ABC and DEC are congruent, their corresponding angles are equal.
Therefore, angle E will also be equal to angle B, which is 50 degrees.
So, x = 50 degrees.
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What are the zeros of the quadratic function f(x)=8x2-16x-15
Answer:
x = 2.696, x = -0.696
Step-by-step explanation:
We are given the following function of x and we are to find the zeros for the given quadratic function:
[tex]f(x)= 8x^2-16x-15[/tex]
To find its zeros, we will use the quadratic formula:
[tex]x=\frac{-b+-\sqrt{b^2-4ac} }{2a}[/tex]
Substituting the values in the formula where [tex]a=8[/tex], [tex]b=-16[/tex] and [tex]c=-15[/tex].
[tex]x=\frac{-(-16)+-\sqrt{(-16)^2-4(8)(-15)} }{2(8)}[/tex]
[tex]x=\frac{16+-\sqrt{736} }{16}[/tex]
[tex]x=\frac{16+27.13}{16}[/tex] , [tex]x=\frac{16-27.13}{16}[/tex]
[tex]x = 2.696[/tex] , [tex]x=-0.696[/tex]
Therefore, the solutions are 2.696 and -0.696.
Answer: c on edge
Step-by-step explanation:
x=1-square root 23/8 and x=1+square root 7
What is the domain of f(x)=(1/2)^x
Answer:
Domain: all real numbers
Step-by-step explanation:
The domain of a function is the set of values that x can be replaced with.
In this function, x can be replaced by any real number, so the domain of the function is all real numbers.
Here we need to find the domain of the given function.
We will see that the domain is the set of all real numbers.
The first thing we need to do is to define the domain of a function.
For a given function f(x), we define the domain as the set of possible inputs that we can use on the function.
Usually, we start by defining the domain as the set of all real numbers and then remove from the domain the numbers that cause "a problem" with our function.
Where these "problems" are undefined operations, like the logarithm of a negative number or a zero in a denominator.
Particularly, in our function: f(x) = (1/2)^x
We do not have a denominator that can become zero nor a function that has problems with some given values of x (the exponent of a number can be any real number).
Concluding, because there is no problem with any real value, we can see that the domain is the set of all real numbers.
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A pet store runs two different training programs. The first program charges a $35 membership fee and $5 for each class. The second program does not have a membership fee, but charges $10 for each class. For how many classes will the programs cost the same? The variable c represents the number of classes and t represents the total cost. Which equations create the system to represent the scenario? Check all that apply.
t = c + 35
t = 5c
t = 5c + 35
t = 10c
t = 10c + 35
Answer:
Step-by-step explanation:
the answer is
t=5c+35
t=10c
i just did this problem and got it right.
To represent the scenario of two training programs with different costs, we can use the equations t = c + 35 and t = 5c.
Explanation:In this scenario, we have two different training programs at a pet store. The first program charges a $35 membership fee and $5 for each class.
The second program does not have a membership fee, but charges $10 for each class. We want to find out for how many classes the total cost will be the same for both programs.
To create the system of equations, we can use the variable c to represent the number of classes and t to represent the total cost. The equations that represent the scenario are:
t = c + 35
t = 5c
Determine the slope of the line J(0,0) K(-2,8)
Answer:
slope is -4 or in a fraction, -4/1
Step-by-step explanation:
When you have 2 points, you can find the slope by subtracting them by each other. You must do 8 - 0 which is 8, then -2 - 0 which is -2. Then you get 8/-2. Once simplified, you get -4, and you know if the number is alone, there is always a 1 under it so you get -4/1.
Hello!
Step-by-step explanation:
[tex]Slope=\frac{Y_2-Y_1}{X_2-X_1}=\frac{RISE}{RUN}[/tex]
[tex]\frac{8-0}{(-2)-0}=\frac{8}{-2}=-4[/tex]
Slope is -4
Final answer is -4
*The answer must have a negative sign.*
I hope this helps you!
Have a nice day! :)
-Charlie
:D