Answer:
Option B is correct.
Step-by-step explanation:
300 cm^3 of snow melts into 33 cm^3 water. We need to find how much water is produced if 600 cm^3 of snow is melt.
Solving using unitary method:
300 cm^3 of snow melts into water = 33 cm^3
1 cm^3 of snow melts into water = 33/300
600 cm^3 of snow melts into water = 33/300 *600
= 66 cm^3
So, Option B is correct.
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:
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.
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:
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
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
The SAT math Mattix scores in the state of Florida are approximately normally distributed with a mean of 500 and a standard deviation of 100 using the empirical rule what is the probability that a random selected students math scores between 300 and 700 express your answer as a decimal
Answer:
0.95
Step-by-step explanation:
This is what Algebra Nation told me, I just want to help get the answer correct
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:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!
What are the vertical asymptotes of R(x) =
Answer:
C. x = 2, and x = -2
Answer: C) x = 2 and x = -2
Step-by-step explanation:
Vertical Asymptotes are restrictions on the x-values.
Since the denominator cannot equal zero, then any x-value that makes the denominator equal to zero is a vertical asymptote.
x² - 4 = 0
(x - 2)(x + 2) = 0
x - 2 = 0 x + 2 = 0
x = 2 x = -2
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.
Plz help!!! Questions are in the attachment!!!!! Thank you in Advance
1) If f(x) = -3x⁴ - 2x³ + 3x²
If g(x) = 3x⁴ - 4x³ + x²
Set the equation:
f(x) + g(x) = (-3x⁴ - 2x³ + 3x²) + (3x⁴ - 4x³ + x²)
Rearrange from greatest power sign to the least:
f(x) + g(x) = -3x⁴ + 3x⁴ - 2x³ - 4x³ + 3x² + x²
Combine like terms (terms with the same amount of variables):
f(x) + g(x) = (-3x⁴ + 3x⁴) + (-2x³ - 4x³) + (3x² + x²)
f(x) + g(x) = (0) + (-6x³) + (4x²)
f(x) + g(x) = -6x³ + 4x²
B) -6x³ + 4x² is your answer.
__________________________________________________________
2) If s(x) = 2x² + 3x - 4
If t(x) = x + 4
Set the equation:
s(x) * t(x) = (2x² + 3x - 4) * (x + 4)
To solve for multiplication, choose a parenthesis. Distribute each term within that parenthesis to all terms within the other.
s(x) * t(x) = 2x²(x + 4) + 3x(x + 4) - 4(x + 4)
Simplify.
s(x) * t(x) = 2x³ + 8x² + 3x² + 12x - 4x - 16
Combine like terms.
s(x) * 5(x) = 2x³ + 11x² + 8x - 16
A) 2x³ + 11x² + 8x - 16 is your answer.
~
Find the image of A(4, -2) after it is reflected over the line y = 2, then reflected over the line x = 2.
(-8, 6)
(0, -2)
(0, 6)
(-8, -2)
Answer:
(0, 6)
Step-by-step explanation:
The given point A has coordinates (4,-2).
The mapping for a reflection over the line y=k, is given by:
[tex](x,y)\to (x,2k-y)[/tex]
Therefore the line y=2 is
[tex](4,-2)\to (4,2(2)--2)[/tex]
[tex](4,-2)\to (4,4+2)[/tex]
[tex](4,-2)\to (4,6)[/tex]
When this point is again reflected over the line x=2, we use the mapping
[tex](x,y)\to (2k-xx,y)[/tex]
[tex](4,6)\to (2(2)-4,6)[/tex]
[tex](4,6)\to (4-4,6)[/tex]
[tex](4,6)\to (0,6)[/tex]
Answer:
0,6
Step-by-step explanation:
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:
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
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
Determine whether the point (1,1) is a solution to the system of equations. Explain your reasoning in complete scentences . Graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one the graphs intersect at the point 0 comma 2
Answer:
(1, 1) is NOT a solution
Step-by-step explanation:
The only point of intersection of the graphs is (0, 2). The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection, so is NOT the solution to the system of equations.
The point (1,1) is not a solution to the system of equations because, when we substitute the coordinates into the equations, it matches the second equation but not the first.
Explanation:To determine whether point (1,1) is a solution to the system of equations, we need to substitute the x and y values of the point into each equation and see if they produce true statements.
The first equation in the system is '3 times x plus 2', which we can write as 3x + 2. Substituting x = 1 in this equation gives us 3*1 + 2 = 5, which is not equal to the y-coordinate (1) of our input point.
The second equation is the |x - 1| + 1, which refers to the absolute value of (x minus 1) plus one. If we input x = 1, we get |1 - 1| + 1 = 1, which equals the y-coordinate (1) of our point. However, because the point didn't satisfy both equations, (1,1) is not a solution to the system.
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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|
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.
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).
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Jacob mixes the letters J, K , L, J, K, M, N, and P thoroughly without looking terry draws one letter expressed as a fraction, decimal., and percentage what is the probability that K will not be the letter Terry selects
Answer:
1/4, 0.25, 25%
Step-by-step explanation:
There are 8 letters in total and 2 K's out of those 8. Therefore the fraction is 2/8, and simpfied it would be 1/4. 1/4 is equal to 0.25 and 25%.
Answer:
3/4, 0.75, 75%.
Step-by-step explanation:
J, K , L, J, K, M, N, P.
There are 8 letters and 2 of them are K, therefore 6 of them are not K.
Probability ( Not picking K) = 6/8
= 3/4 or 0.75 or 75%.
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.
Jean throws a ball with an initial velocity of 64 feet per second from a height of 3 feet. Write an equation and answer the questions below. Show all your work for full credit. Use the correct units with your answers.
Answer:
a) The equation is s = 64t - 16.1 t² + 3
b) The ball will take 1.99 seconds to reach its maximum height
c) The maximum height the ball will reach is 66.60 feet
d) The ball will be in the air for 4.02 seconds
Step-by-step explanation:
* Lets revise some rules of distance , velocity and time
- If the displacement is s , initial velocity is u , time is t and acceleration of
free fall is a , then the equation of the trajectory is
s = ut - 1/2 at² ⇒ upward thrown
∵ The acceleration of free fall a = 32.2 feet/sec²
∴ s = ut - 1/2 (32.2) t²
∴ s = ut - 16.1 t²
∵ The initial velocity is 64 feet/second
∴ s = 64t - 16.1 t²
∵ The ball is thrown from a height 3 feet
∴ s - 3 = 64t - 16.1 t² ⇒ add 3 to both sides
∴ s = 64t - 16.1 t² + 3
a) The equation is s = 64t - 16.1 t² + 3
- The ball will reach the maximum height when its velocity (v)
reached to 0
∵ v = ds/dt
∵ s = 64t - 16.1 t² + 3
- The rule of differentiation
# y = ax^n ⇒ dy/dx = a(n) x^(n-1)
# y = ax ⇒ dy/dx = a
# y = a ⇒ dy/dx = 0
∴ ds/dt = 64 - 16.1(2) t + 0
∴ v = 64 - 32.2 t
∵ At maximum height v = 0
∴ 0 = 64 - 32.2 t ⇒ add 32.2 t to both sides
∴ 32.2 t = 64 ⇒ divide both sides by 32.2
∴ t = 1.987577 ≅ 1.99 seconds
b) The ball will take 1.99 seconds to reach its maximum height
- To find the maximum height substitute this value of t in the
equation of trajectory
∵ s = 64t - 16.1 t² + 3
∴ s maximum = 64(1.99) - 16.1(1.99)² + 3 = 66.60
c) The maximum height the ball will reach is 66.60 feet
- To find the time that the ball in the air put s = 0, because the ball will
return to the point of thrown
∵ s = 0
∵ s = 64t - 16.1 t² + 3
∴ 0 = 64t - 16.1 t² + 3 ⇒ multiply both sides by -1
∴ 16.1 t² - 64t - 3 = 0
- Use your calculator to factorize it and find the value of t
∴ t = 4.02 or -0.5
- We will refused the negative answer because there is no negative time
∴ t = 4.02
d) The ball will be in the air for 4.02 seconds
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
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:
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
Identify the measure of arc XY◠. PLEASE HELP!!
Use the intersecting chords theorem: the labeled angle (WVZ) between the given chords has measure that is the average of the two arcs the chords intercept (WZ and XY):
[tex]81^\circ=\dfrac{m\widehat{XY}+52^\circ}2\implies m\widehat{XY}=110^\circ[/tex]
The requried measure of the arc XY is 110°. Option D is correct.
What is an arc?An arc is a portion of the circumference of a circle. It is defined by two endpoints on the circle and all the points on the circle between these endpoints. The length of an arc is proportional to the measure of the central angle that subtends it.
Here,
To use the intersecting chords theorem,
we can state that the measure of the labeled angle (WVZ) between the given chords is equal to the average of the measures of the two arcs intercepted by the chords, namely WZ and XY.
81 = mWZ+ mXY/2
81 = 52 + mXY / 2
mXY = 110°
Thus, the requried measure of the arc XY is 110°. Option D is correct.
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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.
Help please!!! Have to turn my credit by tomorrow or I won’t walk!!!
Ans:63
Exp:The angles is less than 90 so it cant be 92 or 121. It is also compare with the angle 58 but we can see it is not 58, so the only remaining logical answer would be 63.
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°
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:
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: