Gracie’s overtime rate of pay would be $635.06.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.
Gracie earns 17.25/h for a 37.5h week, plus extra for overtime.
For one hour she earns $17.25
For 37.5h she earns = 37.5h x 17.25
= $646.87
The total money she earns = $646.87 + overtime pay
During store inventory, she worked 48.5h. Her gross earnings were $1,471.88.
= 48.5h x 17.25
= $836.625
So, $836.625 + overtime pay = $1,471.88
overtime pay = $1,471.88 - $836.625 = $635.06
Hence, Gracie’s overtime rate of pay would be $635.06.
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Currently,nova is 3 times as old as Damon. in 8 years, she will be as only 2 times as old as Damon. How old will Damon be in 8 years?
Answer:
16
Step-by-step explanation:
consider X = Damon's age
3x + 8 = 2x
x = 8
so Damon will be 16 in 8 years ( 8+8)
Answer:
16
Step-by-step explanation:
24/3 8
24+8=32
8+8=16
16/32=1/2
8) Mark ran a mean distance of 13.2 km in five days. The next day, Mark ran 20 km.
Find the mean distance Mark ran in the six days.
Answer:
16.6
Step-by-step explanation:
Add the numbers together.
13.2+20=33.2
Now divide the number by 2.
33.2/2=16.6
Hope this helps!
If not, I am sorry.
If triangle RST is within Quadrant 2 and csc T = 13/12, what is the value of cotT?
Answer:
[tex]\boxed {cot T = -\frac{5}{12}}[/tex]
Step-by-step explanation:
Finding the missing side :
x² = 13² - 12²x² = 169 - 144x = √25x = 5Taking the cot value :
cot T = adjacent / oppositecot T = -5/12 (As cot is negative in Quadrant 2)Answer:
csc T =13/12
(cot T)^2=csc^2T -1
Cot T)^2=(13/12)^2-1
(cot. T )^2=169/144-1
(cot T)^2=169-144/144
(cot T)^2=25/144
cot T =√ 25/144
cot T=5/12
where cot is negative in WE
so Cot T=-5/12
Step-by-step explanation:
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If two angles have the same angle measure, then they are said to be____.
A. Complementary
B.adjacent
C.congruent
Answer:
C
Step-by-step explanation:
2 equal angles are said to be congruent
Solve the equation.
7h-5(3h-8)= -72
7h-15h+40=-72
40+72=15h-7h
112=8h
h=14
The formula for the area of a rhombus is A = a equals StartFraction one-half EndFraction d 1 d 2.d1d2, where d1 and d2 are the lengths of the diagonals.
Which are equivalent equations? Select two correct answers.
The two equivalent equations are d₁= 2a/d₂ and d₂= 2a/d₁ , Option 2 and 5 is the right answer.
What is a Rhombus ?Rhombus is a quadrilateral with all the sides equal to each other.
It is given that d₁ and d₂ are the lengths of the diagonals.
and Area = a
a = (1/2) d₁ * d₂
2a = d₁ * d₂d₁ * d₂ = 2a
It can be written as
d₁= 2a/d₂
a = (1/2) d₁ * d₂
d₁ * d₂ = 2ad₂= 2a/d₁
Therefore Option 2 and 5 are the correct answer.
The options of this question are:
1. d₁=2Ad₂
2. d₁= 2A/d₂
3. d₂= d₁/2A
4. d₁= 2A/d₂
5. d₂= 2A/d₁
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The area of a square is 256cm2. When each side of the square is increased by x cm, its area becomes 324 cm2.Find the value of x.
Answer: x = 2
Step-by-step explanation:
First, let's take the root of 256 to find the length of each side before the addition of x.
[tex]\sqrt{256} = 16[/tex]
This means 16 cm is the length of each side before the addition of x.
Then increase each side by X to get
[tex](16 + x)(16 + x) = 324[/tex]
[tex]256 + 16x + 16x + x^2=324[/tex]
[tex]x^2+32x -68=0[/tex]
[tex]x=2[/tex] or [tex]x=-34[/tex]
The value cannot be negative so x has to be 2
Probability of Next Candy
Fill in the chart below with the probability of choosing the next candy.
Answer:
8 is correct.
Mark as brainlist, thanks me, and rate. Hope it helps you!!!
Find the minimum value of the following equation:
(Please provide detailed explanations, no links)
Answer:
×=11
Step-by-step explanation:
2×-4×+27-5=0
-2×+22=0
-2×=-22
×=11
what is 2(5+34-67/45*43)^2 equal to?
The value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Evaluating an ExpressionFrom the question, we are to determine the value of
2(5+34-67/45*43)^2
This can be written as
[tex]2 (\frac{5+34-67}{45 \times 43 })^{2}[/tex]
First, we will simplify the bracket
[tex]2 (\frac{-28}{1935 })^{2}[/tex]
Then, we get
[tex]2 \times \frac{-28}{1935 }\times \frac{-28}{1935 }[/tex]
= [tex]\frac{1568}{3744225}[/tex]
= [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
Hence, the value of the give expression is [tex]\frac{313}{748845}[/tex] OR 4.18 × 10⁻⁴
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Choose any set of Pythagorean triplets of your choice and illustrate them using graph sheet.
Example given below:
The required Pythagorean triplets are hypotenuse, perpendicular and base is 13, 12 and 5 respectively.
In a right angled triangle, its side, such as hypotenuse, perpendicular and base is Pythagorean triplets.
We have
Hypohypotenuse = 13
perpendicular = 12
base = 5
Which satisfies the condition of the Pythagorean theorem.
[tex]a^2+b^2=c^2\\12^2+5^2=c^2\\169=c^2[/tex]
and c = 13
Thus, the required value of Pythagorean triplets satisfies the Pythagorean theorem.
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What is the factored form of the following expressions?
x2 – x – 42
Answer:
(x-7)(x+6)
Step-by-step explanation:
Terrence is going on vacation and taking his dog Pickles along. Pickles eats 3 cups of Hungry Hound dog food each day. Terrence wants to know how many days he can feed Pickles from a 15-cup bag of Hungry Hound.
Answer:
Number of Days he can feed Pickles from a 15-cup bag of Hungry Hound = 5 Days
Step-by-step explanation:
this is question based on simple algebraic equations
Simple Algebraic equations - An algebraic equation can be defined as a mathematical statement in which two expressions are set equal to each other. The algebraic equation usually consists of a variable, coefficients and constants. we can apply many operations on algebraic equations like addition, subtraction, multiplication, division and raising to a power, and extraction of a root.
so in the question algebraic operation used to solve is simple division.
therefore, according to the question -
Total cups of Hungry Hound dog food pickles eats each day are - 3 cups
Total number of cups of Hungry Hound Terrence have = 15 cups
Number of days Terrence can feed pickles from these cups are =
15/3 = 5 days
so the correct answer is = 5 Days
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In the equation 17x2 = 12x, the value of c is:
17
12
0
factoris fully 2ab² + 8a²b
Answer:
2ab(b + 4a)
Step-by-step explanation:
2ab² + 8a²b
Factor Out the 2:
2(ab² + 4a²b)
Factor Out the a:
2a(b² + 4ab)
Factor Out the b:
2ab(b + 4a)
What is the slope-intercept equation of the line below?
Answer:
y= 2x - 3
Step-by-step explanation:
To calculate the slope (or gradient) of a line, take two points on the line whose x and y values are easy to read. Then divide the difference of they y-coordinate values by the difference of their x-coordinate values.
Here I have taken the points p (3, 3) and q (1, -1) to calculate the slope.
• slope = [tex]\frac{y_{2} - y_{1} }{x_{2} - x_{1}}[/tex]
= [tex]\frac{3 - (-1)}{3 - 1}[/tex]
= [tex]\frac{4}{2}[/tex]
= 2
The intercept is the y-coordinate value of the point at which the line crosses ("intercepts") the y-axis. I've marked the intercept point with a green line.
• intercept = -3
The slope-intercept equation of a line takes the form:
y = mx + c
where 'm' is the slope and 'c' is the y-intercept.
Substituting the values we found into the equation gives us:
y = 2x + (-3)
∴ y = 2x - 3
In triangle PQR, find the measure of angle Q.
P= 64 degrees
Q= X
R= 2x
Answer:
38.667°
Step-by-step explanation:
the total sum of 3 angles in a triangle is 180
in triangle PQR this means:
P+Q+R = 180
so:
64+x+2x=180
64+3x=180
3x=116
x=116/3=38.667
So Q=X=38.667
experimental verification
See below for the verification of ∠ACD = ∠ABC + ∠BAC
How to verify the angles?The following proof works for both triangles.
The sum of angles in a triangle is 180 degrees.
So, we have:
∠ABC + ∠BAC + ∠ACB = 180
Make ∠ACB the subject
∠ACB = 180 - ∠ABC - ∠BAC
The sum of angles on a straight line is 180 degrees.
So, we have:
∠ACD + ∠ACB = 180
Make ∠ACB the subject
∠ACB = 180 - ∠ACD
Substitute ∠ACB = 180 - ∠ACD in ∠ACB = 180 - ∠ABC - ∠BAC
180 - ∠ACD = 180 - ∠ABC - ∠BAC
Subtract 180 from both sides
- ∠ACD = - ∠ABC - ∠BAC
Multiply both sides by -1
∠ACD = ∠ABC + ∠BAC
Hence, ∠ACD = ∠ABC + ∠BAC has been verified
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Which function represents the inverse of function f?
Answer: Choice [B]
Step-by-step explanation:
Hii, I'd love to help you out! (:
This particular problem is all about finding inverse functions.
This can be done in 3 easy steps, which are shown below.
Replace f(x) with ySwitch x and y placesSolve for yThe process is shown below.
[tex]\multimap\quad \tt f(x)=3x+5 \\ y=3x+5\\ x=3y+5\\Solve\;for\;y[/tex]
[tex]\multimap\quad \tt x=3y+5\\x-5=3y\\\cfrac{x-5}{3}=y[/tex]
Why doesn't our answer show up among the answer choices? Has all of our hardwork been in vain?
Ofc not! There's just one more thing that can be done to simplify our answer.
[tex]\tt \cfrac{x}{5}-\cfrac{5}{3}[/tex]
We're getting closer!
[tex]\tt \cfrac{1}{3}x-\cfrac{5}{3}[/tex]
Voila! There's our answer, cheers! (;
________________
Hope I helped!
Best wishes.
Reach far.
Aim high.
Dream big.
______________
please place the dot for me(20 points will give brainliest!!!)
Answer:
2,
Step-by-step explanation:
The vertex is the very highest or very lowest point. X coordinates are listed first, then Y.
Express ratio 3.5:14 as 1:n
Answer:
1 : 4
Step-by-step explanation:
3.5 : 14 ( divide both parts by 3.5 )
= 1 : 4
Write a system of equations that could be used to solve the situation described below.
You find 12 coins under the couch. Every coin is either a nickel or a penny, and they add up to a total of 32 cents. How many of each type of coin do you have? Let x represent the number of pennies and y represent the number of nickels.
Please select the best answer from the choices provided
A. x+y=12
0.05x+0.01y=0.32
B. x+y=0.32
0.01x+0.05y=12
C. x+y=12
0.01x+0.05y=0.32
D. not enough information
If there are 12 coins under the couch and every coin is either a nickel or a penny and together they are forming 32 cents then the equations which represent the problem will be x+y=12, 0.01x+0.05y=0.32. The correct option is B which is x+y=12, 0.01x+0.05y=0.32.
Given There are 12 coins and total money is 32 cents.
Let the number of pennies be x and the number of nickels be y.
According to question there are 12 coins so the first equation becomes:
x+y=12.
Then we have been told that together they amount to 32 cents.
We know that 1 penny is 1 cent coin and 1 nickel is 5 cent coin so the equation becomes :
1*x+5*x=32
x+5y=32
converting into dollar
0.01x+0.05y=0.32.
Hence the right equations showing the problem of nickel and pennies are x+y=12, 0.01x+0.05y=0.32.
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NEED SOME HELP ASAP PLEASE!!
Step-by-step explanation:
if it is cloudy, then it is snowing. False. This is obviously not true since sometimes it's just cloudy and it's also cloudy when it rains.
all quadrilaterals are rectangles. False. A quadrilateral has four straight sides which don't have to be parallel to each other unlike a rectangle which has four straight sides with all four sides being parallel to one other side.
All chocolates like students? False? Not sure if I'm writing the converse correctly for this one but if I am this isn't true because chocolate doesn't have feelings...
All triangles with two or more congruent angles are a right triangle. False. This is only true when those two congruent angles add up to 90 which is when they're both 45. But they could also both be 30, 29, 28, etc... which won't result in a right triangle.
Answer:
If it is cloudy, then it is snowing.
Counter-argument: It can be cloudy in the summer.
If a figure is a quadrilateral, then it is a rectangle.
Counter-argument: Trapezoids are not rectangles.
If someone likes chocolate, then they are a student.
Counter-argument: many people like chocolate who are not students.
If a triangle has 2 or more congruent angles, then it is a right triangle.
Counter-argument: Equilateral tr6iangles have 3 congruent angles.
None are right angles.
Step-by-step explanation:
Converse statements reverse the If Then in the original.
the graph of F(x) can be stretched vertically and flipped over the x axis to produce the graph of G(x) if F(x)=x^2 which of the following could be the equation of G(x)
A. G(x)=-1/5x^2
B. G(x)=-5x^2
C. G(x)=5x^2
D. G(x)=1/5x^2
Answer:
g(x) = -5x²
(option B)
Step-by-step explanation:
we know that our original graph, f(x) = x² is a parabola.
So, we can consider what happens when we adjust the function/equation of a parabola.
when we "vertically stretch" a parabola, we are increasing the value of x.
think of it this way: the steepness of a slope is rise over run. If we rise ten, and run one, that's going be a lot more steep than if we rise 1, run 1.
Let's say our x = 5
if f(x)=x²
f(5) = 25
> y value / steepness is 25
f(x) = 3x²
f(5) = 75
> y value / steepness is 75
So, we are looking for an equation with an increase in x present.
When a parabola has been flipped over the x-axis, we know that the original equation now includes a negative
suppose that x = 1
if y = x² ; y = 1² = 1
if y = -(x²) ; y = -(1²) ; y = -1
So, when we set x to be negative, we make our y-values end up as negative also (which makes the graph look as if it has been flipped upside-down)
This means that we are looking for a function with a negative x value.
So, we are looking for a negative x-value that is multiplied by a number >1
The graph that fits our requirements is g(x) = -5x²
hope this helps!!
What type of relationship is expressed below?
5x = 2x 9
O equation
O function
O inequality
A running relay team ran a 400 meter race in a record-setting time of 36 seconds. What was their average speed to the nearest tenth of a meter per second?
PLEASE ANSWER ASAP!!!!!11
The nth term of a sequence is represented by 2n^3+25n^2+32n−15/ 6n^4+2n^3−11n^2−2n+17.
What is the limit of the the nth term as x becomes increasingly large?
A. 0
B. 1/3
C. 3
D. The limit does not exist
The limit of the nth term of a sequence does not exist option (D) is correct.
What is the limit?A limit is a value at which a function approaches the output for the given values in mathematics. Limits are used to determine integrals, derivatives, and continuity in calculus and mathematics.
We have an expression:
[tex]= \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
Applying limit:
[tex]= \lim_{n \to \infty} \rm \dfrac{2n^5+25n^2+32n-15}{6n^4+2n^3-11n^2-2n+17}[/tex]
[tex]=\lim _{n\to \infty \:} n \left(\dfrac{2+\dfrac{25}{n^3}+\dfrac{32}{n^4}-\dfrac{15}{n^5}}{6+\dfrac{2}{n}-\dfrac{11}{n^2}-\dfrac{2}{n^3}+\dfrac{17}{n^4}}\right)[/tex]
= ∞ = The limit does not exist
Thus, the limit of the nth term of a sequence does not exist option (D) is correct.
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The radius of a circle is 7 metres. What is the length of a 135° arc?
Answer:
16.5 meters
Step-by-step explanation:
The length of an arc of a circle = 2πr(C/360°) ;where:
C is the central angle of the arc,
R is the radius of the arc
Length of the arc = 2π(7)(135/360)
= 16.493
= 16.5 metres (approx.)
Answer:
Arc Length: 5.25π or [tex]\frac{21}{4} \pi[/tex]
Explanation:
An arc is the part of the circumference of a circle.
Formula:
[tex]\sf Arc \ Length = \dfrac{\theta}{360} \ \times \ 2\pi \ \times radius[/tex]
If applied:
[tex]\sf Arc \ Length = \dfrac{135}{360} \ \times \ 2\pi \ \times 7[/tex]
[tex]\sf Arc \ Length = \dfrac{3}{8} \ \times \ 14\pi[/tex]
[tex]\sf Arc \ Length = \dfrac{21}{4} \pi[/tex]
[tex]\sf Arc \ Length = 5.25 \pi[/tex]
Figure 1 is similar to figure 2. What is TS?
1 unit
4 units
8 units
2 units
Answer:
8 units
Step-by-step explanation:
ratios
(x-3) /( x+1) = (x-2)/(x+3) cross multiply
x^2 -x -2 = x^2 - 9
-x - 2 + 9 = 0
x = 7
so TS = x + 1 = 8 units
Find the x-intercept of the rational function.
A (-5,0)
B (0,-5)
C (0, -1)
D (-1, 0)
Answer:
(-5,0)
Step-by-step explanation:
The x intercept is where it crosses the x axis
It crosses the x axis where x = -5
The y value is 0
(-5,0)
Answer:
A
Step-by-step explanation:
The x -intercept is 'shorthand' for x - AXIS intercept
where the graph crosses the x - axis
this will always have a ZERO value for the 'y'- coordinate
looking at the graph this point is -5,0