Answer:
A box of 50 stickers would cost $13
Explanation:
1- getting the equation representing the price:
We have two variables; the number of stickers and the price of the box
We can note that the price is the dependent variable (y) while the number of stickers is the independent one (x)
We are given that:
A box of 15 stickers cost $6..........> first point is (15,6)
A box of 25 stickers cost $8 ........> second point is (25,8)
The general equation of the linear line is:
y = mx + c
where m is the slope and c is the y-intercept
i. getting the slope:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{8-6}{25-15}=0.2[/tex]
The equation now became: y = 0.2x + c
ii. getting the y-intercept:
To get the y-intercept, use any of the given points and substitute in the equation we got in part i. I will use the point (15,6)
y = 0.2x + c
6 = 0.2(15) + c
c = 6 - 0.2(15) = 3
The final equation is:
y = 0.2x + 3
where y is the price of the box and x is the number of stickers it contains
2- getting the price of a box with 50 stickers:
To get the price of a box of 50 stickers, simply substitute with x = 50 in the equation we got from part 1
This is done as follows:
y = 0.2(50) + 3 = 13
Therefore, a box of 50 stickers will cost $13
Hope this helps :)
The formula for the nth term b of a geometric series is b=arn-1. Find n when b=1,024, a=16 and r=2.
[tex]\bf b=ar^{n-1}~~ \begin{cases} b=1024\\ a=16\\ r=2 \end{cases}\implies 1024=16(2^{n-1})~~ \begin{cases} 1024=&2^{10}\\ 16=&2^4 \end{cases} \\\\\\ 2^{10}=2^4(2^{n-1})\implies \cfrac{2^{10}}{2^4}=2^{n-1}\implies 2^{10}\cdot 2^{-4}=2^{n-1}\implies 2^{10-4}=2^{n-1} \\\\\\ 2^6=2^{n-1}\implies \stackrel{\textit{same base, the exponents must be the same}}{6=n-1\implies 7=n}[/tex]
The value of n when b = 1,024, a = 16, and r = 2 is 7.
The student is asking to solve for n in the formula of the nth term of a geometric series given the formula b = ar^(n-1) and the values of b, a, and r. To find the value of n, we can substitute the known values into the formula and solve for n.
b = 1,024
a = 16
r = 2
Using these values:
Substitute the known values into the formula: 1,024 = 16 imes 2^(n-1)
Divide both sides by 16: 64 = 2^(n-1)
Recognize that 64 is 2 to the power of 6: 2^6 = 2^(n-1)
Therefore, n - 1 = 6
Add 1 to both sides to find n: n = 7
The value of n when b = 1,024, a = 16, and r = 2 is 7.
Select all that apply. A point is reflected over the y-axis and translated up 3 units. How will the coordinates change? The x-coordinate will decrease by 3. The x-coordinate's sign will change. The y-coordinate's sign will change. The y-coordinate will increase by 3.
Answer:
Step-by-step explanation:
If the point is translated across the y axis then the x coordinate will change sign.
If the point is translated upwards then the y coordinate will increase by 3
So the answers are B and D.
Find the simplified quotient. (2x^2 + 5x +3 / x^2 - 3x -4) / (4x^2 + 2x - 6 / x^2 - 8x + 16)
ANSWER
[tex]\frac{x - 4}{2x - 2} [/tex]
EXPLANATION
The given expression is;
[tex] \frac{2 {x}^{2} + 5x + 3}{ {x}^{2} - 3x - 4} \div \frac{4 {x}^{2} + 2x - 6}{ {x}^{2} - 8x + 16} [/tex]
We factor to obtain;
[tex] \frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \div \frac{2(x - 1)(2x + 3)}{(x - 4)(x - 4)} [/tex]
Multiply by the reciprocal of the second fraction
[tex]\frac{(x + 1)(2x + 3)}{(x - 4)(x + 1)} \times \frac{(x - 4)(x - 4)}{2(x - 1)(2x + 3)} [/tex]
Cancel out common factors to get,
[tex]\frac{1}{1} \times \frac{(x - 4)}{2(x - 1)} [/tex]
[tex]\frac{x - 4}{2x - 2} [/tex]
Answer:
X-4/2x-2
Step-by-step explanation:
Write the equation of a piecewise function with a jump discontinuity at x =3. Then, determine which step of the 3-step test for continuity that the function
fails.
Answer:
Here's a possible example:
Step-by-step explanation:
[tex]f(x) =\begin{cases} x & \quad x < 3\\x+3 & \quad x \geq 3\\\end{cases}[/tex]
Each piece is linear, so the pieces are continuous by themselves.
We need consider only the point at which the pieces meet (x = 3).
[tex]\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) = \lim_{x \longrightarrow 3^{-}} x = 3\\\\\displaystyle \lim_{x \longrightarrow 3^{+}} f(x) = \lim_{x \longrightarrow 3^{+}} x+3 = 6\\\\f(3) = x + 3 = 6\\\\\displaystyle \lim_{x \longrightarrow 3^{-}} f(x) \neq f(3)[/tex]
The left-hand limit does not equal ƒ(x), so there is a jump discontinuity at x =3.
Final answer:
A piecewise function with a jump discontinuity at x = 3 could be f(x) = 2x for x < 3 and f(x) = 2x + 1 for x ≥ 3. It fails the 3-step test for continuity at x = 3 in the second step, as the limits on either side of the point x = 3 do not match.
Explanation:
To write the equation of a piecewise function with a jump discontinuity at x = 3, we can define one function for values of x less than 3, and another for values of x equal to or greater than 3. For instance:
For x < 3: f(x) = 2xFor x ≥ 3: f(x) = 2x + 1Now, to determine where the piecewise function fails the 3-step test for continuity at x = 3, we assess the following criteria:
The function must be defined at x = 3. Our function is defined at x = 3, so it passes this step.The limit of f(x) as x approaches 3 must exist. Since the left-hand limit as x approaches 3 is 6 and the right-hand limit as x approaches 3 is 7, the limits do not match, and the limit does not exist. Therefore, the function fails the second step of the test for continuity.The limit of the function as x approaches the point must equal the function's value at that point. As the limit does not exist, this step is not applicable.Therefore, the function has a jump discontinuity at x = 3 because it fails the second step of the 3-step test for continuity, where the left and right-hand limits are not equal.
A water sprinkler sends water out in a circular pattern. How many feet away from the sprinkler can it spread water if the area formed by the watering pattern is 1,661.06 square feet?
Check the picture below.
Answer:
The correct answer is 23
Step-by-step explanation:
Find the coordinates of the midpoint of the segment whose endpoints are given. W (-3, -7) and X (-8, -4) (-5/2, -11/2) (-11/2, -11/2) (-5/2, -3/2)
Answer:
[tex]\large\boxed{\left(-\dfrac{11}{2};\ -\dfrac{11}{2}\right)}[/tex]
Step-by-step explanation:
The formula of a midpoint of the segment"
[tex]\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
We have the points W(-3, -7) and X(-8, -4).
Substitute:
[tex]x=\dfrac{-3+(-8)}{2}=\dfrac{-11}{2}\\\\y=\dfrac{-7+(-4)}{2}=\dfrac{-11}{2}[/tex]
The coordinates of the midpoint of a line segment with endpoints (-3, -7) and (-8, -4) are (-5.5, -5.5) using the midpoint formula.
Explanation:The subject of this question is Mathematics, specifically dealing with geometry. The student is asked to find the midpoint of a line segment whose endpoints are given. The coordinates of the endpoints of the line segment are W(-3, -7) and X(-8, -4).
The formula to calculate the coordinates of a midpoint in a Cartesian plane is M = [(x1 + x2)/2, (y1 + y2)/2], where M denotes the midpoint, (x1, y1) and (x2, y2) are the coordinates of the endpoints of the line segment.
Thus, the midpoint M of the line segment WX is calculated as follows: M = [(-3 -8)/2, (-7 -4)/2] = [-11/2, -11/2]. So, the coordinates of the midpoint of the line segment WX are (-5.5, -5.5).
Learn more about Midpoint here:https://brainly.com/question/28224145
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Theo is practicing for a 5 kilometer race. He runs 5 kilometers every day and records his time. His normal time is 25 minutes 15 seconds. Esterday it took him only 23 minutes 49 seconds. How much faster was his time yesterday than his normal time? What are you asked to find? What information do you know? How will you solve the problem? Solve the problem
2 minutes 21 seconds
Find the product
2x(x - 3)(x + 2)
OA. 4x - 1
B. 2x3 -X-6
C. 2x3 - 2x2 - 12x
2x3-12x|
Answer:
2x^3 - 2x^2 - 12x
Step-by-step explanation:
2x(x - 3)(x + 2)
= 2x ( x^2 + 2x -3x - 6)
= 2x (x^2 - x - 6)
= 2x^3 - 2x^2 - 12x (answer).
Answer:
Step-by-step explanation:
Find the product
2x(x - 3)(x + 2)
OA. 4x - 1
B. 2x3 -X-6 Find the product
2x(x - 3)(x + 2)
OA. 4x - 1 Find the product
2x(x - 3)(x + 2)
OA. 4x - 1
B. 2x3 -X-6
C. 2x3 - 2x2 - 12x
2x3-12x|
B. 2x3 -X-6
C. 2x3 - 2x2 - 12x
2x3-12x|
C. 2x3 - 2x2 - 12x
2x3-12x|Find the product
2x(x - 3)(x + 2)
OA. 4x - 1
B. 2x3 -X-6
C. 2x3 - 2x2 - 12x
2x3-12x|
Based on the information marked in the diagram, MNP and QRS must be congruent. True or False. ty for the help! <3
Answer:
True
Step-by-step explanation:
The hypotenuse angle theorem, also known as the HA theorem, states that "If the hypotenuse and an acute angle of one right triangle are congruent to the hypotenuse and an acute angle of another right triangle, then the two triangles are congruent."
In triangles MNP and QRS:
NP=RS (hypotenuses);∠P=∠S (acute angles).Then, triangles MNP and PRS are congruent by HA theorem.
True
Answer:
True (just did it on a pex)
Step-by-step explanation:
Use the parabola tool to graph the quadratic function y=−2x2+12x−14 . Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
(x,12x-18)
Step-by-step explanation:
Answer:
Check attached graph
Step-by-step explanation:
Given equation of the parabola is [tex]y=-2x^2+12x-14[/tex].
Nowe we need to use the parabola tool to graph the quadratic function. Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Compare Given equation with [tex]y=ax^2+bx+c[/tex] we get: a=-2 and b=12
then x-coordinate of vertex [tex]=x=-\frac{b}{2a}=-\frac{12}{2\left(-2\right)}=3[/tex]
plug x=3 into given function
[tex]y=-2x^2+12x-14[/tex]
[tex]y=-2(3)^2+12(3)-14=4[/tex]
Hence vertex is (3,4).
Plug any x-value say x=0 into given function to find other point
[tex]y=-2(2)^2+12(2)-14=2[/tex]
Hence second point is (2,2)
now graph the parabola using both points as shown below:
Chris put $1,500 in a savings account at an annual interest rate of 5%. If Chris does not deposit or withdraw any money, what is the amount of interest Chris will earn the first year her money is in the savings account?
[tex]\bf ~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$1500\\ r=rate\to 5\%\to \frac{5}{100}\dotfill &0.05\\ t=years\dotfill &1 \end{cases} \\\\\\ I=(1500)(0.05)(1)\implies I=75[/tex]
Chris will earn $75 in interest in the first year by depositing $1,500 into a savings account with an annual interest rate of 5%, calculated using the simple interest formula.
To calculate the amount of interest Chris will earn in the first year the money is in the savings account, we will use the formula for simple interest, which is Interest = Principal × Rate × Time. In this case, the principal amount is $1,500, the annual interest rate is 5% or 0.05 when expressed as a decimal, and the time is 1 year since we are looking for the interest for the first year only.
Therefore, the interest Chris will earn after one year is calculated as follows:
Interest = $1,500 × 0.05 × 1
Interest = $75
Thus, at the end of the first year, Chris will have earned $75 in interest.
Scott takes gets a student loan to go to college after high school. If he pays $750 in interest at a rate of 3%, how much must the loan have been for originally?
Answer: 5,000
Step-by-step
Answer:
5,000
Step-by-step explanation:
just got my paper graded
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
If the table is that of f(x), find a point that lies on the graph of f-1(x).
Answer: D) (-5, 1)
Step-by-step explanation:
Inverse is when the x's and y's are swapped.
f(x) has the coordinate (1, -5) --> the inverse of that is (-5, 1), which is option D.
Identify the angle measures of PQRS. I'm so confused, please help me! SHOW YOUR WORK!!
10y + 7 + 3(3y + 7) = 180
10y + 7 + 9y + 21 = 180
19y + 28 = 180
19y = 180 - 28
19y = 152
y = 152/19
y = 8
Plug back into Q and S.
Q = 10y + 7
Q = 10(8) + 7
Q = 80 + 7
Q = 87
S = 3(3y + 7)
S = 9y + 21
S = 9(8) + 21
S = 72 + 21
S = 93
Without solving for x to find the other angles, we can easily see that the answer is choice C.
Answer:
P = 61°
Q = 87°
R = 119°
S = 93°
Done!
Please please help me
Yes.
The triangle inequality theorem states that a triangle is possible if the sum of two sides is larger than the 3rd side.
In this case, the sides are 4, 5 and 6.
4+5 is bigger than 6
4 + 6 is bigger than 5
5 + 6 is bigger than 4.
The sum of any 2 sides is always larger than the 3rd side, so this triangle is possible.
-------------------------------------------------------
Answer: Yes
add 2/3 yards 4/9 yard and 23/36 yard and please show work
Answer:
7/4 yard
Step-by-step explanation:
36 is a suitable common denominator for expressing these fractions. All measures are in yards.
2/3 + 4/9 + 23/36 = (12·2)/(12·3) + (4·4)/(4·9) + 23/36
= 24/36 + 16/36 + 23/36
= 63/36 = (9·7)/(9·4)
= 7/4 = 1 3/4 . . . . . yards
alfred invest $60 a month in annuity that earns 4% ApR and is compounded monthly .what is the future value of alfreds accoint in five years
Answer:
Step-by-step explanation:
Answer:
$934.30
Step-by-step explanation:
We have been given that Alfred invest $60 a month in annuity that earns 4% APR and is compounded monthly. We are asked to find the future value of Alfred's account after 5 years.
[tex]FV=C_0\cdot (1+r)^n[/tex], where,
[tex]C_0=\text{Initial value}[/tex],
[tex]r=\text{APR in decimal form}[/tex],
[tex]n=\text{Number of times interest is compounded per year}[/tex].
[tex]r=4\%=\frac{4}{100}=0.04[/tex]
[tex]FV=\$60\cdot (1+0.04)^{12*5}[/tex]
[tex]FV=\$60\cdot (1.04)^{70}[/tex]
[tex]FV=\$60\cdot 15.57161835[/tex]
[tex]FV=\$934.2971[/tex]
[tex]FV\approx \$934.30[/tex]
Therefore, the future value of Alfred's account in 5 years would be $934.30.
Margret sold 1,392 meatballs on Friday. She sold 1,940 meatballs on Saturday. How many meatballs did she sell on Friday and Saturday?
Margret sold a total of 3,332 meatballs on Friday and Saturday by adding the meatballs sold on each day (1,392 on Friday and 1,940 on Saturday).
Explanation:To find out how many meatballs Margret sold on Friday and Saturday combined, we simply add the number she sold on each day. On Friday, she sold 1,392 meatballs and on Saturday, she sold 1,940 meatballs.
The total number of meatballs sold over the two days is:
1,392 (meatballs on Friday)
+ 1,940 (meatballs on Saturday)
3,332 (total meatballs)
So, Margret sold a total of 3,332 meatballs on Friday and Saturday.
the parent function of the logarithm is f(x) =log x. if g(x) = log(x-4)-3 write down the transformation
The x and y
Answer:
Step-by-step explanation:
The (x - 4) indicates side-to-side movement, and the -3 at the end indicates up and down movement. This log graph has moved 4 units to the right (x - (4)) and down 3 units (-3)
Final answer:
The transformation consists of a horizontal shift to the right by 4 units and a vertical shift downward by 3 units from the parent function f(x) = log x to g(x) = log(x - 4) - 3.
Explanation:
The transformation of the parent function f(x) = log x to g(x) = log(x - 4) - 3 involves a horizontal shift to the right by 4 units and a vertical shift downward by 3 units. This is because for the horizontal shift, the logarithmic function is now evaluating (x - 4) instead of x, indicating a move to the right on the x-axis by 4 units. Similarly, subtracting 3 from the whole function log(x - 4) indicates that every value of the function will be decreased by 3 units on the y-axis.
Molly made 3600 \text{ mL}3600 mL3600, space, m, L of tea for a party, and she served the tea divided equally in 121212 cups.
How many liters of tea did Molly put in each cup?
111 liter =1000=1000equals, 1000 milliliters
Answer:
0.3
Step-by-step explanation:
The circumference (C) of a circle is 16cm. Which formula can you use to find the diameter (d) if you know that C= πd?
The formula is d=C/π.
The diameter is 2 times the radius
The formula for the circumference using the radius is 2πr.
in order to do this backwards, we would have to do 16÷2÷π, but we're not looking for the radius.
Therefore, we take out the ÷2 part, which would be 16÷π
16 is the circumference
16÷π=d
d=C÷π
Answer:
d = /π
Step-by-step explanation:
2. Find the area of the trapezoid. Leave your answer in the simplest radical form.
Answer:
170 ft²
Step-by-step explanation:
First let's calculate the height of this trapezoid. Call it 'h.' Look at the triangle on the right; the base is equal to (22 ft - 12 ft), or (10 ft). Using the tangent function, we can find h:
h
tan 45° = ---------- = 1 and so we know that h = 10 ft
10 ft
The formula for the area of a trapezoid is
A = (average length)*(width)
Here we have:
A = [ (12 ft + 22 ft) / 2 ] * 10 ft, or
A = (17 ft)*(10 ft) = 170 ft²
Which of the following statements describes one part of completing the square for x 2 + 4x = 32? Take the square root of 36 and add 2. Take the square root of 32 and subtract 2. Take the square root of 36 and subtract 2.
take the square root of 36 and subtract 2 because √36= 6-2=4x
Answer:
take the square root of 36 and subtract 2 because √36= 6-2=4x
Step-by-step explanation:
The amount of money an employee earns monthly before taxes, in dollars, after selling n products is $1,300 + $300n. Which statement is correct? A. For every product sold, the employee's earnings increase by $1,300. B. For every product sold, the employee's earnings increase by $1,000. C. For every product sold, the employee's earnings increase by $1,600. D. For every product sold, the employee's earnings increase by $300.
Answer:
The answer is D
Step-by-step explanation:
for every increase in the product sold, the earnings increase by 300 respectively
Let p= x^2-7.
which equation is equivalent to (x^2-7)-4x^2+28 in terms of p
PLZ HELP
Since p = x² - 7, you can substitute/plug in p for x² - 7
So:
(x² - 7)² - 4x² + 28 = 5
(p)² - 4x² + 28 = 5 You can factor out -4 from (-4x² + 28)
p² - 4(x² - 7) = 5 Plug in p
p² - 4p = 5 Subtract 5
p² - 4p - 5 = 0 Your answer is C
To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, substitute x^2-7 with p. The equation equivalent to (x^2-7)-4x^2+28 in terms of p is -4x^2+p+28.
Explanation:To find an equation equivalent to (x^2-7)-4x^2+28 in terms of p, we can substitute x^2-7 with p. So we have (p)-4x^2+28. Now, we combine like terms by adding the coefficients of p and -4x^2, which gives us -4x^2+p+28.
Sam said the square root of a rational number must be a rational number. Jenna disagreed. She said that it is possible that the square root of a rational number can be irrational. Who is correct and why?
Jenna is correct because the square root of a rational number can still be irrational.
Take for example the square root of 2. It is an irrational number than goes 1.41421...
If you multiply just the first however many digits of the result by itself, you will never end up with a perfect 2, because the square root is irrational.
Answer:
Jenna is correct because not all square roots are rational.
Step-by-step explanation:
Given ΔABC, m∠A = 50°, m∠B = 60°, and a = 7. Find c.
Answer:
D) 8.6
Step-by-step explanation:
The Law of Sines tells you ...
c/sin(C) = a/sin(A)
The sum of angles in a triangle tells you ...
C = 180° -A -B = 180° -50° -60° = 70°
Then ...
c = a·sin(C)/sin(A) = 7·sin(70°)/sin(50°) ≈ 8.6 . . . . . above equation multiplied by sin(C)
_____
There are apps available for phone or tablet for solving triangles. Many graphing calculators have functions that will do the same. Also, there are on-line triangle solvers that will give you the answer.
We include the working here because you're supposed to know how to work the problem. If all you want is the answer, that can be found faster a number of different ways.
Help asap 15 points!
What is the approximate area of a sector given Θ≈212 with a radius of 45 m?
Question 1 options:
2613.59 m²
3744.45 m²
3371.26 m²
2928.36 m
What is the approximate area of a sector given Θ≈92 degrees with a diameter of 9m?
Question 2 options:
60 m²
65 m²
15.6 m²
16.2 m
Final answer:
The approximate area of a 212-degree sector with a 45m radius is 3371.26 m², and the approximate area of a 92-degree sector with a 9m diameter (4.5m radius) is 16.2 m².
Explanation:
To find the approximate area of a sector of a circle, we use the formula for the area of a circle, A = πr², and then adjust it for the sector by multiplying by the ratio of the central angle to 360 degrees. For Question 1, the central angle θ is approximately 212 degrees and the radius is 45 m. The formula for the sector area becomes A = (π × (45 m)² × (212/360)). A quick calculation gives us the following area:
For the first sector with a 212-degree angle and a radius of 45m:
A = 3.1415927 × (45 m)² × (212/360) = 3.1415927 × 2025 m² × 0.5889 ≈ 3371.26 m²
For Question 2, the central angle θ is approximately 92 degrees and the diameter is 9m, which makes the radius 4.5m. The formula for the sector area then becomes A = (π × (4.5 m)² × (92/360)). The calculation yields the following area:
A = 3.1415927 × (4.5 m)² × (92/360) = 3.1415927 × 20.25 m² × 0.2556 ≈ 16.2 m²
A water storage tank is in the shape of a hemisphere (half a sphere) If the radius is 15 ft, approximate the volume of the tank in cubic feet
7068.58 cubic feet is the volume
I need help in these questions
Answer:
see explanation
Step-by-step explanation:
All of these questions use the external angle theorem, that is
The external angle of a triangle is equal to the sum of the 2 opposite interior angles.
18
∠3 = 43° + 22° = 65°
19
∠2 + 71 = 92 ( subtract 71 from both sides )
∠2 = 21°
20
90 + ∠4 = 123 ( subtract 90 from both sides )
∠4 = 33°
21
2x - 15 + x - 5 = 148
3x - 20 = 148 ( add 20 to both sides )
3x = 168 ( divide both sides by 3 )
x = 56
Hence ∠ABC = x - 5 = 56 - 5 = 51°
22
2x + 27 + 2x - 11 = 100
4x + 16 = 100 ( subtract 16 from both sides )
4x = 84 ( divide both sides by 4 )
x = 21
Hence ∠JKL = 2x - 11 = (2 × 21) - 11 = 42 - 11 = 31°