Answer:
y = -1½x + 3; Parallel Equation: y = -1½x [Direct Variation (y = mx)]
Step-by-step explanation:
Set the equation equal to 6, move -3x to the right side of the equivalence symbol to get 2y = -3x + 6, then divide all terms by 2, to isolate the variable, resulting in y = -½x + 3. Now that we have our equation, we have to the PARALLEL equation [SIMILAR RATE OF CHANGES (SLOPES)] that passes through the origin [0, 0]. To do this, we simply plug these coordinates into the Slope-Intercept Formula, y = mx + b --> 0 = -½[0] + b. It is obvious that your y-intercept IS the origin [so as your x-intercept], so your parallel equation is y = -½x.
NOTE: The parent function of y = mx, is what is known as direct variation.
please help
A manager measured the number of goods, y, that his company produced in x hours. The company produces goods at a rate of 5 per hour. At hour 9, the company had produced 45 goods.
Which equation, in point-slope form, correctly represents the goods produced by the company after x hours?
A.y−45=5(x+9)
B.y−45=5(x−9)
C.y+9=5(x+45)
D.y−9=5(x−45)
Answer:
Option B. [tex]y-45=5(x-9)[/tex]
Step-by-step explanation:
Let
x -----> the number of hours
y ----> the number of goods
we know that
The equation of a line in point slope form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=5\ \frac{goods}{h}[/tex] ----> the rate is the same that the slope of the linear equation
[tex]point\ (9,45)[/tex] --->(At hour 9, the company had produced 45 goods)
substitute
[tex]y-45=5(x-9)[/tex]
Help please thank you!
Answer:
[tex]x_1=-2.9\\x_2=0.2[/tex]
Step-by-step explanation:
The first step is to move the [tex]5x[/tex] to the left side of the equation and then add the like terms:
[tex]4x^2+16x-2=5x\\\\4x^2+16x-2-5x=0\\\\4x^2+11x-2=0[/tex]
Now we can apply the Quadratic formula. This is:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
In this case we can identify that:
[tex]a=4\\b=11\\c=-2[/tex]
Finally, we must substitute these values into the Quadratic formula. Then we get:
[tex]x=\frac{-11\±\sqrt{(11)^2-4(4)(-2)}}{2(4)}[/tex]
[tex]x_1=-2.9\\x_2=0.2[/tex]
A group of 125 teenagers were asked which of the following activities they would most likely choose to spend their free time doing: reading a book, watching television, playing video games, or listening to music. The results are displayed in the circle graph below.
How many teenagers chose watching television?
35
40
45
50
there is an attachment at the bottom.
From the Circle Graph, We can notice that :
★ 32% of 125 teenagers chose watching Television
[tex]:\implies \mathsf{\left(\dfrac{32}{100} \times 125\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \mathsf{\left(\dfrac{32}{20} \times 25\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \mathsf{\left(\dfrac{8}{5} \times 25\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \mathsf{\left(8 \times 5\right)}\;\textsf{teenagers chose watching television}[/tex]
[tex]:\implies \large\boxed{\mathsf{40}}\;\textsf{teenagers chose watching television}[/tex]
Explain what x^(2/3) means using radicals and integer exponents.
Which phrase matches the expression c^3
A.) c cubed
B.) c increased by 3
C.) the sum of 3 and c
D.) 3 cubed
Answer:A
Step-by-step explanation:
Think about it as a process of elimination.
It can't be "B' for the simple fact that "increased by'' is a term that is often used for addition problems.
It can't be "C" because, as previously stated, sum is a term that is used in addition problems.
It can't be "D" because this is a unit that you are using.
A. "c cubed" matches the expression c^3, which means raising c to the power of 3, not the other options.
The correct phrase that matches the expression c^3 is "A.) c cubed."
In mathematics, when you see an exponent of 3 (as in c^3), it indicates that you should multiply the base, c, by itself three times. This is commonly referred to as "c cubed." It signifies that you should raise c to the power of 3, meaning c * c * c. The other options are not accurate representations of c^3:
B.) "c increased by 3" does not involve exponentiation; it implies adding 3 to c.
C.) "the sum of 3 and c" is simply c + 3 and does not involve cubing.
D.) "3 cubed" represents 3^3, which equals 27, and is different from c^3.
For such more questions on expression
https://brainly.com/question/1859113
#SPJ2
Find the value of ax 4 ; a = 2, x = 1.
Select one: a. 2 b. 4 c. 1 d. 8
For this case we have the following expression:
[tex]ax ^ 4[/tex]
We must find the value of the expression when:
[tex]a = 2\\x = 1[/tex]
Substituting the values in the expression we have:
[tex]2 (1) ^ 4 = 2 * 1 = 2[/tex]
Thus, the value of the expression is 2.
Answer:
The value of the expression is 2
Option A
Answer:
The correct answer is A
Step-by-step explanation:
The given expression is [tex]ax^4[/tex].
We want to evaluate this expression for: [tex]a=2,x=1[/tex].
We just have to substitute a=2 wherever we see 'a' in the expression [tex]ax^4[/tex] and x=1 wherever see x in the same expression.
We perform the substitution to get:
[tex]2(1)^4[/tex]
We evaluate the exponent to get:
[tex]2(1)[/tex]
We now multiply to get:
[tex]2[/tex]
Which ratios form a proportion?
1. 4/10 and 10/25
2. 4/11 and 6/13
3. 4/9 and 9/4
4. 3/5 and 9/25
An industrial laser cuts steel plates that are 11.93 meters long. The laser can have an error value of at most 0.02 meters.
The inequality |x − | ≤ can be used to find the range of acceptable lengths for the steel plates.
The range of acceptable lengths for the steel plates is ≤ x ≤
Answer:
| x - 11.93 | ≤ 0.0211.91 ≤ x ≤ 11.95Step-by-step explanation:
Error is the difference from the nominal value, hence the nominal value is what is subtracted from x. We want the magnitude of that difference, | x-11.93 |, to be less than the maximum error value, 0.02, so the inequality is ...
|x -11.93| ≤ 0.02
__
We can solve this by "unfolding" it, then adding 11.93:
-0.02 ≤ x -11.93 ≤ 0.02
11.91 ≤ x ≤ 11.95
The South Company cash account had a balance of $1,202.50 on January 31. A deposit, made on the 31st, in the amount of $100.05 was in transit. The January 31 bank statement presented the following information.
Bank statement balance $1,421.95
NSF charge 18.00
Bank service charge 8.50
Note collected 150.00
South also had outstanding checks in the amount of $196.00. What was South’s reconciled balance?
$1,202.50
$1,326.00
$1,271.95
$1,236.00
Answer:
$1326
Step-by-step explanation:
Follow the format of the reconciliation statement
The adjusted cash balances should match
Cash balance as per the bank statement, January 31 1421.95
Add: Deposit in transit 100.05
Deduct: Outstanding checks (196)
Adjusted cash balance 1326
Balance as per depositor's record, January 31 1202.5
Subtract: NSF check (18)
Subtract: Service charges (8.5)
Add: receivable collected 150
Adjusted cash balance 1326
The reconciled amount is $1326.
!!
Restrict the domain of the function f(x) = (x-2)^2 so it has an inverse. Then determine its inverse function.
Answer:
Look to the bold answer down
Step-by-step explanation:
* Lets explain how to restrict the domain of the quadratic function
- The quadratic function is two-to-one function
- The inverse of it is one-to-two which is not a function
- So we can not find the inverse of the quadratic function until restrict its
domain
- We restrict the domain at the x-coordinate of the vertex of the function
∵ f(x) = (x - h)² + k is the standard form of the quadratic function, where
(h , k) are the coordinates of its vertex
- To restrict the domain we put x > h for the right part of the parabola
or x < h for the left part of the parabola
* Lets solve the problem
∵ f(x) = (x - 2)²
∵ f(x) = (x - h)² + k is the standard form of the quadratic function
∴ h = 2 and k = 0
∴ The vertex of the parabola is (2 , 0)
- We will restrict the domain at x = 2
∴ The domain of the function f(x) to have inverse is x > 2 or x < 2
* The restriction domain is x > 2 or x < 2
- To find the inverse of the function switch x and y and solve for the
new y
∵ f(x) = (x - 2)²
∵ f(x) = y
∴ y = (x - 2)²
- Switch x and y
∴ x = (y - 2)²
- take square root for both sides
∴ ± √x = y - 2
- Add 2 for both sides
∴ ± √x + 2 = y
∴ [tex]f^{-1}=\sqrt{x}+2=====OR=====f^{-1}=-\sqrt{x}+2[/tex]
* For the domain x > 2 of f(x) the inverse is [tex]f^{-1}(x) = \sqrt{x}+2[/tex]
For the domain x < 2 of f(x) the inverse is [tex]f^{-1}(x)=-\sqrt{x}+2[/tex]
candy has to paint a fence. if she can paint 2/3 of each section in 1/2 hour, and there are 9 sections , how long will it take her to paint the entire fence?
[tex]6 \frac{3}{4}[/tex] hours
Step-by-step explanation:First, find the time it takes to paint each section with this formula: [tex]\frac{\frac{1}{2}}{\frac{2}{3}}[/tex]
You can use keep, change, flip, to make this multiplication. [tex]\frac{1}{2} * \frac{3}{2}[/tex]
Multiply the numerators. [tex]1 * 3 = 3[/tex]
Multiply the denominators. [tex]2 * 2 = 4[/tex]
So, it takes [tex]\frac{3}{4}[/tex] hour to paint one section of fence.
Now, we just need to find how long it takes to paint 9 sections. [tex]9 * \frac{3}{4}[/tex]
Multiply. [tex]\frac{27}{4}[/tex]
Finally, simplify. [tex]6 \frac{3}{4}[/tex]
The point (4, 5) is translated two units left and eight units down. What is the y-coordinate of the image?
since 5 is the y coordinate, subtract 8. 5-8=-3!
Answer:-3
Step-by-step explanation:
A wise man once said 200 reduced by 3 times my age is 50. What is his age?
He is 50 years old
200-(3*50)=age
200-150= 50
Answer:
50
Step-by-step explanation:
200-(3x)=50
3x=200-50 (Collect like terms)
3x=150
3x/3=150/3 (Divide through by 3)
x=50
WILL MARK BRAINLIEST
Answer:
587.18 in^2
Step-by-step explanation:
Given:
Diameter = d = 11 inches
Slant height = l =28.5 inches
Radius will be half of diameter
r = d/2 = 11/2 = 5.5 in
We know that the formula for surface area of cone is:
[tex]SA = \pi rl+\pi r^2\\Putting\ the\ values\\SA = (3.14*5.5*28.5)+(3.14 * 5.5 * 5.5 )\\= 492.195+94.985\\=587.18\ in^2[/tex]
Hence, second option is correct ..
Answer: second option.
Step-by-step explanation:
We know that we can calculate the surface area of a cone with this formula:
[tex]SA=\pi rl + \pi r^2[/tex]
Where "r" is the radius and "l" is the slant heigth.
We know that the radius is half the diameter, then the radius of this cone is:
[tex]r=\frac{11in}{2}\\\\r=5.5in[/tex]
Since we know tha radius and the slant height, we can substitute values into the formula, using 3.14 for π.
Therefore, we get:
[tex]SA=(3.14)(5.5in)(28.5in) + (3.14)(5.5in)^2=587.18in^2[/tex]
What is eleven p.m plus six hours
Answer:
5 a.m.
Step-by-step explanation:
From 11 p.m. to midnight is 1 hour. Adding 5 hours to this result is equivalent to "eleven p.m plus six hours" and is 5 a.m.
Which of the following is a solution of y - x < -3?
A. (6, 2)
B. (2, 6)
C. (2, -1)
For this case we have the following inequality:
[tex]y-x <-3[/tex]
We must evaluate each of the points and verify if the inequality is met:
[tex](6,2)\\2-6 <-3\\-4 <-3[/tex]
The inequality is met!
[tex](2,6)\\6-2 <-3\\4 <-3[/tex]
It is not fulfilled!
[tex](2, -1)\\-1-2 <-3\\-3 <-3[/tex]
It is not fulfilled!
Thus, the point that meets the inequality is (6,2)
Answer:
Option A
What number should be added to both sides of the equation to complete the square
Answer:
36
Step-by-step explanation:
You take 1/2 the linear term's coefficient and square it.
The linear term is the term that contains just an x and a number -- in this case 12x
Take 1/2 12 = 6
and square it
6^2 = 36
So when you've done that you should get
x^2 + 12x + 36 = 11 + 36
x^2 + 12x + 36 = 47
Which is greater 4 P 3 or 4 C 3?
Answer:
[tex]\large\boxed{_4P_3>_4C_3}[/tex]
Step-by-step explanation:
[tex]\left\begin{array}{ccc}_nP_r=\dfrac{n!}{(n-r)!}\\\\_nC_r=\dfrac{n!}{r!(n-r)!}\end{array}\right\}\Rightarrow\dfrac{n!}{(n-r)!}>\dfrac{n^!}{r!(n-r)!}\Rightarrow_nP_r>_nC_r\\\\\text{because}\\-\text{the nominators are the same}\\-\text{the denominator}\ (n-r)!\ \text{is graeter than the denominator}\ r!(n-r)![/tex]
[tex]\text{Let's check our example:}\\\\n!=1\cdot2\cdot3\cdot4\cdot...\cdot n\\\\_4P_3=\dfrac{4!}{(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1!}=\dfrac{24}{1}=24\\\\_4C_3=\dfrac{4!}{3!(4-3)!}=\dfrac{1\cdot2\cdot3\cdot4}{1\cdot2\cdot3\cdot1!}=\dfrac{24}{6}=4\\\\24>4\Rightarrow_4P_3>_4C_3[/tex]
[tex]nPr = \dfrac{n!}{(n-r)!} \\ \\ nCr = \dfrac{n!}{r!(n-r)!}\\ \\ \Rightarrow nPr > nCr\\ \\ \Rightarrow \boxed{4P3 > 4C3}[/tex]
A box has a length of 6 inches, a width of 8 inches, and a height of 24 inches. Can a cylinder rod with a length of 63.5 centimeters fit in the box?
Answer:
Yes.
Step-by-step explanation:
The longest diagonal in the box is the line between one of the top corners to the opposite bottom corner.
Calculate the length of the longest diagonal in the box:
The diagonal of the base = √(6^2 + 8^2)
= √100 = 10 inches.
The longest diagonal = √( 24^2 + 10^2)
= √676
= 26 inches
= 26 * 2.54
= 66.04 cms.
Therefore the cylinder (length 63.5 cms) rod can fit in the box.
what is the equation in poiny slope form of the line that is perpendicular to the given line and passes through the point (-4, -3)
Answer:
Step-by-step explanation:
Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].
Ex: 2 --> -½; -2 --> ½
Answer:
Step-by-step explanation:
Well, there is no given equation, but I can tell you that perpendicular lines have OPPOSITE MULTIPLICATIVE INVERSE [RECIPROCAL] rate of changes [slopes].
Ex: 2 --> -½; -2 --> ½
The area of the indoor sports exhibition is shown below.
What is its perimeter?
m
What is its area?
Answer:
Step-by-step explanation:
The perimeter of the circular part of the sports exhibition can be found with the formula [tex]\pi[/tex]r.The equation is halved from the 2[tex]\pi[/tex]r as it is half a circle.
perimeter of circular part=17[tex]\pi[/tex]
Perimeter of the sports exhibition:
(4000/100)+10+10+68+33+17[tex]\pi[/tex]+34+(700/100)
=202+17[tex]\pi[/tex]
=255m(nearest whole number)
For the area, find the total area of the representive shapes
The two rectangles:10*40+68*33
=2644
The area of the semi circle (:[tex]\pi[/tex]r^2)/2
=17*17*[tex]\pi[/tex]/2
=144.5 [tex]\pi[/tex]
Total area:
2644+144.5 [tex]\pi[/tex]
=3098m^2(nearest whole number)
The coordinates of point A on a coordinate grid are (−2, −3). Point A is reflected across the y-axis to obtain point B and across the x-axis to obtain point C. What are the coordinates of points B and C?
ANSWER
[tex]B(2,-3)[/tex]
[tex]C(-2,3)[/tex]
EXPLANATION
The given point has coordinates A(-2,-3).
The rule for the reflection across the y-axis is
[tex](x,y)\to(-x,y)[/tex]
We apply this rule to obtain the coordinates of B.
[tex]A(-2,-3)\to B(--2,-3)[/tex]
Simplify the coordinates of B to get:
[tex]A(-2,-3)\to B(2,-3)[/tex]
The rule for reflection across the x-axis is
[tex](x,y)\to (x,-y)[/tex]
When the point A(-2,-3) is reflected across the x-axis to obtain C, then the coordinates of C are:
[tex]A(-2,-3)\to C(-2,--3)[/tex]
[tex]A(-2,-3)\to C(-2,3)[/tex]
Answer:
B(2 ,-3) and C( -2, 3)
Step-by-step explanation:
i did the test lol :)
What is the factorization of the trinomial below?
4x^2+28x + 48
O A. 4(x+3)(x+4)
O B. 4(x+2)(x+4)
O C. (x+2)(x+16)
O D. (x+3)(x + 4)
[tex]4x^2+28x + 48=\\4(x^2+7x+12)=\\4(x^2+3x+4x+12)=\\4(x(x+3)+4(x+3))=\\4(x+3)(x+4)[/tex]
Answer:
A
Step-by-step explanation:
Given
4x² + 28x + 48 ← factor out 4 from each term
= 4(x² + 7x + 12)
To factor the quadratic
Consider the factors of the constant term (+ 12) which sum to give the coefficient of the x- term
The factors are + 4 and + 3, since
4 × 3 = 12 and 4 + 3 = 7, thus
x² + 7x + 12 = (x + 3)(x + 4) and
4x² + 28x + 48 = 4(x + 3)(x + 4) → A
the height of a ball can be estimated by the following equation h(t) = 8t^2 4t 125 where t is time, in seconds, after the ball was thrown and h(t) is the corresponding height, in meters. what is the height at t=2.3 seconds
Replace t with 2.3 and solve:
8(2.3)^2 +4(2.3) + 125
Simplify:
8(5.29) + 9.2 + 125
42.32 + 9.2 + 125
51.52 + 125
176.52 meters
Answer:
176.52m
Step-by-step explanation:
Given is the height of a ball as
[tex]h(t) = 8t^2+ 4t +125[/tex]
where t is time, in seconds, after the ball was thrown and h(t) is the corresponding height, in meters
When t=2.3, substitute this for t
h(2.3) = [tex]8(2.3)^2 +4(2.3)+ 125 \\=176.52m[/tex]
The PE class has 12 boys and 8 girls. What is the maximum number of teams that the teacher can divide the class into so that each team has an equal number of boys and girls, the greatest common factor of the numbers of girls and boys? Factors of 12: 1, 2, 3, 4, 6, 12 Factors of 8: 1, 2, 4, 8
2
4
24
96
Answer:
4
Step-by-step explanation:
12 can be multipled by 4 and 4 and 8 can be multipled by 4 and 2 so 4 is the greatest common factor
Answer:
4
Step-by-step explanation:
Which lines are parallel? Check all that apply.
b and f
b and c
c and e
c and d
d and f
e and f
Answer:
b and f
c and e
Step-by-step explanation:
Basically, this question is testing your knowledge on supplementary angles (angles that add up to 180) and corresponding angles (angles that are across from each other that have the same value).
Using the information the diagram has given you, you just need to plug in the correct values for each angle. Once you've completed that, you just match them up. If two of the top right corners are 90.5, then they match! I made a little diagram, though it might be a little confusing :/// I hope I helped a little :)
I do not understand how to find Q
Answer:
50
Step-by-step explanation:
You can use that sum of the opposite interior angles is equal to that exterior one.
So (30)+(4x+2)=8+6x
Combine like terms on left
32+4x=8+6x
Subtract 4x on both sides
32=8+2x
Subtract 8 on both sides
24=2x
So x=12
To find Q replace x in 4x+2 with 12 giving you 4(12)+2=48+2=50
just to add to the great reply above
Check the picture below.
Q = 4(12) + 2 = 50.
Explain why the initial value of any function of the form
f(x) = a(b) is equal to a.
Answer:
The answer in the procedure
Step-by-step explanation:
we have
[tex]f(x)=a(b)^{x}[/tex]
This is a exponential function
where
a is the initial value
b is the base
we know that
The initial value of the function is the value of f(x) when the value of x is equal to zero
substitute x=0 in the function
[tex]f(0)=a(b)^{0}[/tex]
Remember that any number to the zero power is one
so
[tex](b)^{0}=1[/tex]
substitute
[tex]f(0)=a*1=a[/tex]
Help please ..someone
Which equation represents the line shown on the graph?
1. y=x+2
2. y=-2x
3. y=2x
4. y=-x+2
Answer:
4
Step-by-step explanation:
Recall that the equation for a straight line is y = mx + b, where m is the slope and b is the y-intercept.
we can see that the slope is negative (i.e graph goes from top left to bottom right). hence the value for m must be negative.
By looking at the answer choices, only 2 and 4 have negative x-terms, hence we can ignore 1 and 3.
Also we notice that the graph intersects the y-axis at y = 2, hence the y-intercept must be 2.
Only Answer 4 satisfies both requirements and is the correct answer.