The equation for the purchase of n number of notebooks by Caitlin is
4n = c , where c is representing the cost that Caitlin paid.
What is unitary method ?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Finding the value of a single unit using the unitary technique allows us to determine the value of the necessary number of units based on this value.
Calculationthe price for one notebook was = $4 each
n number of notebooks were purchased by caitlin
therefore the cost price of 4 notebooks will be = 4 * n
as per given in the question cost price = c
therefore the equation formed will be
4n = c
learn more about unitary method here :
brainly.com/question/22056199
#SPJ4
50 POINTS
What system of linear inequalities is shown in the graph? Enter your answers in the boxes.
enter your answers in the boxes
□
□
Answer:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
Step-by-step explanation:
Find the equations of the two lines by substituting two points on each line into the slope formula to find the slope, then substituting the found slope and one of the points into the point-slope formula.
Equation of Line 1
Points on the line: (0, 2) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-2}{2-0}=-\dfrac{1}{2}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-2=-\dfrac{1}{2}(x-0)[/tex]
[tex]\implies y=-\dfrac{1}{2}x+2[/tex]
Equation of Line 2
Points on the line: (0, -3) and (2, 1).
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{1-(-3)}{2-0}=-\dfrac{4}{2}=2[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-3)=2(x-0)[/tex]
[tex]\implies y=2x-3[/tex]
When graphing inequalities:
< or > : dashed line.≤ or ≥ : solid line.< or ≤ : shade under the line.> or ≥ : shade above the line.As the line for equation 1 is solid and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y \geq -\dfrac{1}{2}x+2}[/tex]
As the line for equation 2 is dashed and there is shading above the line, the line is represented by the inequality:
[tex]\boxed{y > 2x-3}[/tex]
Therefore, the system of linear inequalities shown in the graph is:
[tex]\begin{cases}y \geq -\dfrac{1}{2}x+2\\\\y > 2x-3\end{cases}[/tex]
how to find the edge of a cube with the volume of 125 inches
Answer:
5 inches
Step-by-step explanation:
Hello!
The volume of a cube is simply the side length cubed, or the side lengthed multiplied by itself 3 times.
So, to find the edge, we can find the cube root of 125 to find that measure.
Find the Side Lengthx³ = 125x = ∛125x = 5The edge is 5 inches.
Calculate the surface area of the can. Area of a circle =
Height = 10cm
Diameter = 7 cm
Please help me thank you!
What is the surface area of the circle?
The surface area of the can is 220cm².
The height of the can is 10cm, and the diameter is 7cm.
height (h) = 10cm
radius(r) = 7/2 cm
The formula to find the surface area of the can = 2πrh
= 2 × 22/7 × 7/2 × 10
= 220cm²
Therefore the surface area of the can is 220cm².
To know more about the surface area refer to the link given below:
https://brainly.com/question/16519513
#SPJ1
6. What is the constant of proportionality of the linear function?
Time, x 12 3 4
Cost ($), y 25 50 75 100
F. 2 G. 12 H. 25 I. 50
Pls help!!
The table has a constant of proportionality of 25
How to determine what is the constant of proportionality?The table represents the given parameter
On the table, we have the following points
(x, y) = (1, 25)
The constant of proportionality of the points is then calculated as
k = y/x
Substitute the known values in the above equation
So, we have
k = 25/1
Evaluate the quotient
So, we have
k = 25
Hence, the constant of proportionality of the table is 25
Read more about constant of proportionality at
brainly.com/question/28413384
#SPJ1
Based on triangle inequality theorem, what are the restrictions on the values of y
The restriction on the the values of y of the triangle is 4 < y < 16
How to find the side of a triangle using the triangle inequality theorem?The triangle inequality theorem describes the relationship between the three sides of a triangle.
According to triangle inequality theorem, for any given triangle, the sum of two sides of a triangle is always greater than the third side.
Therefore, a triangle x, y and z have the following rule:
x < y + z
y < x + z
z < x + y
Hence, the restriction of the on the values of y, third side of the triangle is as follows:
6 < 10 + y
10 < 6 + y
y < 10 + 6, y < 16
Therefore, the restriction is y > 4 and y < 16.
Hence,
4 < y < 16
learn more on triangle here: https://brainly.com/question/1163433
#SPJ1
A box contains 5 reams of paper. How could you estimate the thickness of 2 sheets of paper. One ream is 500 sheets.
Answer:
If one ream is 500 sheets, then that would mean that two reams combined are 1,000 sheets, and the fact that there are 5 reams is just a random number meant to throw you off.
Given: 4+x=16
What is the value of x?
Need this answered ASAP
Answer:
To get the answer for X we have to subtract 16 from 4 which gives us 12
X=12
Hope this helps.
Answer:
4+X= 16
X=16-4
X=12
*To find X , you need to minus 16 by four. That is because you have to move (+4) to the other side (change sides,change signs). So (+4) becomes (-4) so 16-4 =12
If a biker travels 380 meters in 20 seconds at that rate how far could he travel in 3 seconds
I think its 57 meters.
12x + 5y = -24 13x - 5y = 14 Linear Equations By Elimination
Let,
[tex]\begin{gathered} 12x+5y=-24\ldots(1) \\ 13x-5y=14\ldots(2) \end{gathered}[/tex]Perform the operation (1)+(2),
[tex]\begin{gathered} 12x+5y+(13x-5y)=-24+(14) \\ 12x+13x+5y-5y=-10 \\ 25x+0y=-10 \\ 25x=-10 \\ x=\frac{-10}{25} \\ x=\frac{-2}{5} \end{gathered}[/tex]Substitute the value of x=-2/5 in the expression (1).
[tex]\begin{gathered} 12\times\frac{-2}{5}+5y=-24 \\ 5y=-24+\frac{24}{5} \\ 5y=\frac{-96}{5} \\ y=\frac{-96}{5\times5} \\ y=\frac{-96}{25} \end{gathered}[/tex]Thus, the value of x is -2/5 and value of y is -96/25.
Damon drew a scale drawing of a swimming pool. The scale he used was 1 inch : 9 feet. The diving board is 2 inches long in the drawing. How long is the actual diving board?
Since the scale utilized in the draw is 1 inch : 9 feet and the diving board is 2 inches, we need to multiply the 2 inches by the scale:
[tex]2\cdot9ft=18ft[/tex]The actual diving board is 18ft long
(-5 -5) (10 4), point-slope
The slope is 5/3, and the point-slope is y = 5(x+2)/3.
Describe point slope.
A linear equation has the general form y-y1=m (x-x1). It highlights the line's slope as well as one of the line's points (that is not the y-intercept).
The formula provided is to find slope, i.e.
m = (y2 - y1) / (x2 - x1) (x2 - x1)
where (-5, -5) for (x1, Y1) and (x2, Y2) (10, 4)
m = (10 + 5) / (4 + 5)
= 15 / 9
= 5 / 3
Now that we have the slope value, we can easily enter it into the supplied equation.
y - y1 = m(x - x1) (x - x1)
y + 5 = 5/3(x + 5)
Upon resolution, we obtain
y = 5x/3 + 10/3
or, y = 5(x + 2)/3
As a result, the slope is 5/3 and the point-slope is y = 5(x+2)/3.
To read more about point-slope
https://brainly.com/question/24907633
#SPJ10
Don’t ignore help pls I think i know it but I’m not sure
Answer:
The y intercept is 0
Step-by-step explanation:
Where the line crosses the y axis that is your y intercept
Check the picture below.
help me 20 points please
Answer:
Step-by-step explanation:
the one on top is simple it's 120
how would i solve this?
FIRST FIND THE EQUATION OF THE LINE
I WILL USE THE POINTS (-94,24) AND (-54,12)
TO FIND THE GRADIENT
[tex]m = \frac{y2 - y1}{x2 - x1} \\ m = \frac{12 - 24}{ - 54 - ( - 94)} \\ m = \frac{ - 24}{ - 54 + 94} \\ m = \frac{ - 24}{40} \\ m = \frac{ - 3}{5} [/tex]
THE m ABOVE IS THE GRADIENT.
I WILL USE THE POINT (-74,18) TO GET THE VALUE OF C IN THE EQUATION Y=MX+C
[tex]15 = \frac{ - 3}{5} ( - 74) + c \\ 15 = \frac{222}{5} + c \\ c = 15 - \frac{222}{5} \\ c = \frac{ - 147}{5} [/tex]
THEREFORE THE EQUATION NOW IS
[tex]y = \frac{ - 3}{5} x - \frac{147}{5} \\
FOR THE X-INTERCEPT Y=0 SINCE IN THR X-AXIS Y=0..PLUG IN 0 IN THE PLACE OF Y TO GET X-INTERCEPT.
[tex] \frac{ - 3}{5} x - \frac{147}{5} = 0 \\ \frac{ - 3}{5} x = \frac{147}{5} \\ x = \frac{147}{5} \div \frac{ - 3}{5} \\ x = - 49[/tex]
(-49,0)
Which ordered pairs are on the graph of 7x−y=2?
Select ALL that applies.
A. >>(−3,−19)open paren negative 3 comma negative 19 close paren
B. (−1,−9)open paren negative 1 comma negative 9 close paren
C. (0,−2)open paren 0 comma negative 2 close paren
D. (1, 9)(1, 9)
(3, 23)(3, 23)
The ordered pairs which are on the graph of 7x - y = 2 as required in the task content are; Choices B and C; (-1, -9) and (0, -2).
Which ordered pairs are on the graph of 7x - y = 2 as required in the task content?It follows from the task content that the ordered pairs which are on the graph of 7x - y = 2 be determined.
Hence, by testing each pair as follows; we have;
For (-3, -19); we have; 7(-3) - (-19) = 2; -21 + 19 = 2; -2 ≠ 2. Hence, FALSE.For (-1, -9); we have; 7(-1) - (-9) = 2; -7 + 9 = 2; 2 = 2. Hence, TRUE.For (0, -2); we have; 7(0) - (-2) = 2; 0 + 2 = 2; 2 = 2. Hence, TRUE.For (1, 9); we have; 7(1) - (9) = 2; 7 - 9 = 2; -2 ≠ 2. Hence, FALSE.For (3, 23); we have; 7(3) - (23) = 2; 21 - 23 = 2; -2 ≠ 2. Hence, FALSE.Ultimately, the required ordered pairs are; (-1, -9) and (0, -2).
Read more on ordered pairs;
https://brainly.com/question/24880873
#SPJ1
Elena received a $25 gift card to a fun center. She drives a race car which costs $4.75. She also wants to use the gift card to play video games. Each game costs $0.75 which of these inequalities describe this situation, where n is the number of games Elena wants to play.
A. 4.75 + 0.75. ≤ 25
B. 4.75 + 0.75. ≥ 25
C. 4.75 - 0.75. ≥ 25
D. 4.75 - 0.75. ≤ 25
Answer: B - 4.75 + 0.75 is greater than 25
Step-by-step explanation:
so, first you have 4.75 and she want to play video games that cost 0.75 each but we don't know how many video games she played.
so, n = how many video games played4.75 + 0.75n =? which is greater than 25divide 4.75 + 0.75n 0.75 0.75after dividing you will get 4,100 + 1n = which equals 4.101 is greater than 25NEED HELP ASAP - 100 Points (Operations with Polynomials)
In multiple sentences, create your own real-world application problem for either adding or subtracting polynomials. Include a description of how the problem can be solved.
Answer: Well we can look at whether or not cubes may or may not equal the same by using volume and surface area, where the volume can be used as x^3 and the surface area x^2, but the reason why polynomials can help us a great deal in world problems is whether or not measurements are accurate, or just in general for solving big math equations. Hope this helps.
a) How much time do people in Bhutan spend watching TV each night?
Answer:
about 2 hours
Step-by-step explanation:
it is the reported average
Suppose a projectile is fired from a cannon with velocity v0 and angle of elevation θ. The horizontal distance Rθ it travels (in feet) is given by the following. R(θ)=(v0)²sin2θ/32 If v0=80ft/s, what angle θ (in radians) should be used to hit a target on the ground 129 feet in front of the cannon? Do not round any intermediate computations, and round your answer(s) to the nearest hundredth of a radian. (If there is more than one answer, enter additional answers with the "or" button.)
The angle at which the projectile should be launched to hit the target which is 129 feet away is 7/100π.
The projectile fires with a velocity V₀ and angle of elevation θ, then the horizontal distance is given by the R(θ),
R(θ) = V₀²sin2θ/32
The given function in dependent on theta θ,
The angle at which the projectile must be fired so that it reaches the horizontal distance of 129 feet in front of the cannon,
R(θ) = V₀²sin2θ/32
putting R(θ) equal to 129, V₀ = 80ft/s,
129 = (80)²sin2θ/32
sin2θ = (129 x 32)/(80 x 80)
sin2θ = 0.645
Hence,
θ = 7/100π
so, the projectile should be launched at angle of 7/100π.
To know more about projectile, visit,
https://brainly.com/question/12870645
#SPJ9
one number is 9 more than 3 times another. Their product is 9 more than 3 times their sum. Find the numbers. Answer in the form of paired points with the lowest of the two integers first
Let x and y be the two numbers we are trying to find.
'One number is 9 more 3 times another' is equivalent to x=9+3y
'Their product is 9 more than 3 times their sum' is equivalent to xy=9+3(x+y)
We have two equations and two unknowns; therefore, we can solve the problem
[tex]\begin{cases}x=9+3y \\ xy=9+3(x+y)\end{cases}[/tex]Solve it as shown below
[tex]\begin{gathered} x=9+3y \\ \Rightarrow xy=(9+3y)y=9y+3y^2 \\ \text{and} \\ 9+3(x+y)=9+3(9+3y+y)=9+3(9+4y)=9+27+12y=36+12y \\ \Rightarrow9y+3y^2=36+12y \\ \Rightarrow3y^2-3y-36=0 \\ \Rightarrow y^2-y-12=0 \end{gathered}[/tex]Solve the quadratic equation
[tex]\begin{gathered} y^2-y-12=0 \\ \Leftrightarrow(y-4)(y+3)=0 \\ \Rightarrow y=4,y=-3 \end{gathered}[/tex]Finally,
[tex]\begin{gathered} y=4 \\ \Rightarrow x=9+3(4)=21 \\ \Rightarrow(21,4) \\ y=-3 \\ \Rightarrow x=9+3(-3)=0 \\ \Rightarrow(0,-3) \end{gathered}[/tex]The solutions are (21,4) and (0,-3)
Ron's youth group commits to making a certain number of sandwiches for a local soup
kitchen. They make 132 sandwiches, but then they run out of peanut butter. The group still
has 110 sandwiches left to make to meet their commitment.
Use an equation to find the total number of sandwiches the youth group commits to making.
sandwiches
Answer:
242 sandwiches
Step-by-step explanation:
The group wants to make x number of sandwiches.
They have already made 132 sandwiches and still have 110 sandwiches to make.
To find the total, you can add these numbers up, because:
132 + 110 = total sandwiches
This way, you get 242 sandwiches
Jennie drew a scale drawing of her family's game room. The pool table is 4 feet wide in real life. Using a scale of 1 inch: 2 feet, how wide is the pool table in her drawing?
Please answer ASAP.
(Will give brainliest)
When Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
The width of the pool table in real life = 4 feet
The scale of width in drawing to real life = 1 inch : 2 feet
Therefore the equivalent ratio is
1 inch : 2 feet :: x inches : 4 feet
1 / 2 = x / 4
x = (1/2) × 4
= 2 inches
Hence, when Jennie drew a scale drawing of her family's game room. If the pool table is 4 feet wide in real life and using a scale of 1 inches: 2 feet, then the width of the pool table in her drawing is 2 inches
Learn more about ratio here
brainly.com/question/13419413
#SPJ1
BRAINLIEST will be given to the answer
Write in the form (x + p)^2 + q
x^2 - 5x + 3
Answer:[tex][x{-\frac{5}{2}] ^{2} +\frac{-12}{25}[/tex] is in the form [tex][x+p]^{2} +q[/tex]
Step-by-step explanation:
Here given is [tex]x^{2} -5x+3[/tex].................................eq [1]
now we know that [tex][x-\frac{5}{2}] ^{2}[/tex]= [tex]x^{2} -5x+\frac{25}{4}[/tex]............eq [2]
now add and subtract [tex]\frac{25}{4}[/tex] in eq 1
[tex]x^{2} -5x+3+\frac{25}{4} -\frac{25}{4}[/tex]
[tex]x^{2} -5x+\frac{25}{4}+3-\frac{25}{4}[/tex]
[tex][x-\frac{5}{2} ]^{2} +\frac{3*4-25}{4}[/tex]................................from eq[2]
[tex][x{-\frac{5}{2}] ^{2} +\frac{-12}{25}[/tex]
so comparing with the given form [tex][x+p]^{2} +q[/tex]
where p=[tex]\frac{5}{2\\}[/tex] and q=[tex]\frac{-12}{5}[/tex]
ANSWER FAST I WILL GIVE BRAINLIEST
Which graph represents the solution to one seventhm ≤ −1 over 22? number line with closed circle on point negative 14 over 11 and arrow shaded to the right number line with closed circle on point negative 7 over 22 and arrow shaded to the right number line with closed circle on point negative 14 over 11 and arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Answer: arrow shaded to the left number line with closed circle on point negative 7 over 22 and arrow shaded to the left
Step-by-step explanation:
Answer:
for easier explanation.... it's D
Step-by-step explanation:
Ben's monthly housing costs for his new home will be $2100 per month. What
must his monthly net income be to keep housing as 30% of his budget?
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
The monthly net income to keep housing a 30% of his budget is $7000.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Cost of monthly housing per month = $2100
$2100 = 30%
Monthly income = 100%
30% = 2100
Multiply 100/30 on both sides.
100/30 x 30% = 100/30 x 2100
100% = 7000
Thus,
The monthly net income to keep housing a 30% of his budget is $7000.
Learn more about percentages here:
https://brainly.com/question/11403063
#SPJ1
HELP PLEASE I GIVE BRAINY IF U ANSWER RIGHT AND IF I CANT READ THAT THERE IS MORE THEN ONE ANSWER U WONT GET ANYTHING
ANSWER BOTH QUESTIONS PLEASE IF U DON'T I WONT GIVE U A THING
Question 1
Which ordered pairs lie on the graph of the exponential equation
f(x) = 25(2.2)^x ?
Select EACH correct answer.
A. (0, 0)
B. (0.5, 37.08)
C. (1, 55)
D. (2, 121)
THE FIRST PICTURE GOES WITH QUESTION 2 ONLY
Question 2
The function f(x) = (3/8)^x is shown on the coordinate plane.
Determine which expressions describe the end behaviors of the function.
Select EACH correct answer.
A. As x increases without bound, the graph of f(x) decreases without bound.
B. As x increases without bound, the graph of f(x) approaches y = 1.
C. As x decreases without bound, the graph of f(x) increases without bound.
D. As x decreases without bound, the graph of f(x) approaches y = 0.
The ordered pairs lie on the graph of the exponential equation is
(0.5, 37.08) (1, 55) (2, 121)What is exponential equation?Exponents are used in exponential functions, as the name indicates. But take note that an exponential function does not have a constant as its base and a variable as its exponent (if a function has a variable as the base and a constant as the exponent then it is a power function but not an exponential function). One of the following forms can be used for an exponential function.
According to its definition, a fundamental exponential function has the formula f(x) = [tex]b^x[/tex], where b is a constant and x is a variable. The exponential function f(x) = [tex]e^x[/tex], where "e" is "Euler's number," and e = 2.718, is one of the most well-known ones. An exponential function may incorporate a constant if we expand the potential of various exponential functions.
Given function:
f(x) = 25 [tex](2.2)^x[/tex]
Now, taking x=0
y = f(x) = 25
and, x=0.5
y= f(x) = 37.08
and, x = 1
y = 55
and, x=2
y = 121
So, the ordered pairs lie on the graph of the exponential equation is
(0.5, 37.08) (1, 55) (2, 121)2. The given function is [tex]f(x)= (3/8)^x[/tex]
Now, as per the graph As x decreases without bound, the graph of f(x) approaches y = 1.
Or, As x decreases without bound, the graph of f(x) increases without bound.
Learn more about exponential function here:
https://brainly.com/question/14355665
#SPJ1
2. You are riding your bicycle. It takes you 20 minutes to go 5 miles.
a. Find your average speed per minute.
b.
How long would it take you to cycle 12 miles?
Answer:
a= one mile in 4 minutes
b =48 minutes
Step-by-step explanation:
A
t = 20 minutes
d = 5 miles
Average speed = distance ÷ time
5 miles÷ 20 minutes
= 1 mile in 4 minutes
= 0.25 miles in 1 minute
B
0.25 miles in 1 minute
12 miles in g minutes
12 miles in 48 minutes
we get this answer because 0.25 in one minute is 1 ÷4
12÷ 12 × 4
12÷ 48
= 12 miles In 48 minutes
Characterize the slope of the line in the graph,
A. Positive
B. Negative
C. Zero
D. Undefined
Answer:
D. Undefined
Step-by-step explanation:
[tex]m=[/tex] ∞
Hope this helps
Is it possible to have a series of true conditional statements that lead to a false
conclusion? Explain.
It is possible to have a series of true conditional statements that lead to a false conclusion.
How to illustrate the information?Making decisions based on particular situations is made easier with conditional statements.
A conditional statement's truth value can be either true or false. Simply demonstrate that the conclusion is true whenever the hypothesis is true to establish the truth of a conditional.
Simply demonstrating that the conclusion is wrong each time the hypothesis is true suffices to demonstrate that a conditional is untrue.
Learn more about conditional statement on:
https://brainly.com/question/11073037
#SPJ1
An empty swimming pool is shaped like a rectangular prism with a length of 18 feet and a width of 9 feet. once water begins to be pumped into the pool, the depth of the water increases at a rate of 0.5 foot per hour.
Answer:
volume=length×width×depth
Step-by-step explanation: