Say her hourly pay was $p for the day shift and $1.2p for the night shift.
(1) x = 55. Clearly insufficient: we need to know how these 55 hours are split between the day shift hours and the night shift hour.
(2) Grace's gross pay for the hours she worked on day shift last month was exactly 50% of her total gross pay for last month. Not sufficient.
(1)+(2) Say Grace worked h hours on the day shift and 55-h hours on the night shift. Thus, her pay for the the hours she worked on day shift is $ph and the total gross pay is $ph+(55-h)*1.2p. From (2) we have that ph=0.5(ph+(55-h)*1.2p) --> reduce by p: h=0.5(h+(55-h)*1.2). We have 1 variable, so we can solve for it. Sufficient.
Answer: C.
Find the coordinates of the image of M(−1, 5) after the translation (x, y)→(x+3, y−2).
Answer:
To find a translation image of a shape, you can use the following rule or formula. Suppose you want to translate or slide point P a units horizontally and b units vertically. Then, change the x-values and y-values of the coordinates of P. The points of the triangle of are A(-3, 1), B(-4, 3), and C(-2, 4).
Translation involves moving a point on a coordinate geometry from one position to another position.
Given that:
[tex]M = (-1,5)[/tex] --- point
[tex](x,y) \to (x + 3, y - 2)[/tex] --- translation rule
Substitute -1 for x and 5 for y in [tex](x,y) \to (x + 3, y - 2)[/tex]
So, we have:
[tex](-1,5) \to (-1 + 3, 5 - 2)[/tex]
[tex](-1,5) \to (2, 3)[/tex]
This means that:
[tex]M' = (2, 3)[/tex]
Hence, the image of M after translation is [tex](2, 3)[/tex]
Read more about translations at:
https://brainly.com/question/12463306
What equation represents the parabola with focus (-1,4) and directrix y= -2
Answer:
Hello
y=(x+1)/12 +1
Step-by-step explanation:
[tex]\text{As the directrice is horizontal:}\\\\\\y=-2 ==> k=-2\\\\Focus=(a,b)=(-1,4)\\\\\boxed{y=\dfrac{x-a}{2(b-k)} +\dfrac{b+k}{2} }\\\\\\y=\dfrac{x+1}{2(4+2)} +\dfrac{4-2}{2} }\\\\\boxed{y=\dfrac{x+1}{12} +1}\\[/tex]
Write the quadratic equation whose roots are −3 and 2, and whose leading coefficient is 4.
Answer:
f(x) = 4(x+3)(x-2)
Step-by-step explanation:
The quadratic function is
f(x) = a(x-b1)(x-b2) where a is a coefficient and b1 and b2 are the zeros
f(x) = a(x- -3)(x-2)
f(x) = a(x+3)(x-2)
The leading coefficient is a and we know a =4
f(x) = 4(x+3)(x-2)
Translate this sentence into a equation. The sum of 22 and chau’s are is 54. Use the variable c to represent chums age
Answer:
22+c=54
Step-by-step explanation:
22 + his age =54
six times the difference of a number and 4 is no more than 10.
Answer:
nnnnnnnnnnnnnnnnnnnnnnnnn
Step-by-step explanation:
Please someone tell me the answer of these questions
Answer:
VERTICALLY OPP ANGLES
Step-by-step explanation:
The internal dimension of a lidless wooden box is 48cm × 38cm × 32cm. If the thickness of the tank is 1 cm, find the volume of the wooden box
Step-by-step explanation:
this is confusing.
first the description says "the internal dimensions".
and then it tells us the thickness of the tank walls (1cm).
so, I am not sure what the given numbers describe.
in any case, the volume is length × width × height.
so, either
48×38×32
or
46×36×31 (as for length and width we need to consider 2 walls, one on each end, for the height only one wall, as the tank is open and lidless.
whatever you choose, make sure to mark the result as cm³.
order the following expressions by their values from least to greatest
Find the length of AD in the figure.
A. √26 units
B. √34 units
C. √122 units
D. √130 units
Answer:
√122
Step-by-step explanation:
To find the distance/length between two points
Use this formula: [tex]\sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
[tex]\sqrt{(1 - 2)^2 + (3 + 8)^2}[/tex]
[tex]\sqrt{(-1)^2 + (11)^2}[/tex]
[tex]\sqrt{1 + 121}[/tex]
[tex]\sqrt{122}[/tex]
Resolve into factor :(a+b) ^3+1
use the formula a^3+b^3=(a+b)^3-3ab(a+b)
in above question assume (a+b) as a and 1 as b
take help of file above
In XYZ, what is the cosine ratio of X?
Answer:
c) 12/15 = 4/5
Step-by-step explanation:
imagine we mirror the triangle up, so that Z is on top.
then you can clearly see that 6 is cos(X) times r (and r is then 7.5).
XY is sin(X)×7.5
and again, 7.5 is r (the line making the X angle).
so, the cosine ratio of X is
6 = cos(X)×7.5
cos(X) = 6/7.5 or then 12/15. or simplified 4/5.
pls help, and explain. Will give brainliest
Cost of 12 notebooks = $9
Ratio of number of notebooks to its price
= 12:9
= 4:3 (because we reduced it to the simplest form by dividing both numerator and denominator by 3)
Let the cost of 8 notebooks be x.
Then, 8:x = 4:3
=> 8/x = 4/3
=> (8×3)/4 = x
=> 24/4 = x
=> 6 = x
So, the cost of 8 notebooks is $6.
-k - (-8k)!!!
Hdisidjdidjdkdkdjenenenen
Answer:
7k
Step-by-step explanation:
-k - -(8k): the - sign cancels out the - in 8k so it would only leave -k+8k=7k
Answer:
7k
Step-by-step explanation:
-k - (-8k)
if there is "-" in front on an inner form, change the sign of each quarter to the form.
-k + 8k
Simplify similar tribes with add or subtract.
= 7k
a^2/9=b^2/16 and a^2+b^2=100
Answer:
a=6 and b=8
Step-by-step explanation:
a^2=(9/16)b^2. Substitute this in the second equation, you get b^2+b^2*(9/16)=100, b^2=100*16/25=8 and a=6
Given an arithmetic progression 17,13,9,..... find the number of terms required so that its sum is - 33 .
Answer:
11 terms.
Step-by-step explanation:
We are given the arithmetic sequence:
17, 13, 9, ...
And we want to find the number of terms required such that the sum is -33.
Recall that the sum of an arithmetic series is given by:
[tex]\displaystyle S = \frac{k}{2}\left( a + x_k\right)[/tex]
Where k is the number of terms, a is the first term, and x_k is the last term.
The desired sum is -33. The first term is 17 as well. Thus:
[tex]\displaystyle (-33) = \frac{k}{2} \left( (17) +x_k\right)[/tex]
Simplify:
[tex]-66 = k(17 + x_k)[/tex]
We can write a direct formula to find the last term x_k. The direct formula of an arithmetic sequence has the form:
[tex]x_ n = a + d(n-1)[/tex]
Where a is the initial term and d is the common difference.
The initial term is 17 and the common difference is -4. Hence:
[tex]\displaystyle x_n = 17 - 4(n-1)[/tex]
Then the last term is given by:
[tex]x_k = 17 - 4(k-1)[/tex]
Substitute:
[tex]\displaystyle -66 = k\left( 17 + \left( 17 - 4(k-1)\right)\right)[/tex]
Solve for k:
[tex]\displaystyle \begin{aligned} -66 &= k(17 + (17 - 4k + 4)) \\ -66 &= k(38 -4k) \\ -66 &= -4k^2 + 38k \\ 4k^2 -38k -66 &= 0 \\ 2k^2 - 19k -33 &= 0 \\ (k-11)(2k+3) &= 0 \\ k-11&= 0 \text{ or } 2k+3 = 0 \\ \\ k &= 11 \text{ or } k = -\frac{3}{2}\end{aligned}[/tex]
Since we cannot have a negative amount of terms, we can ignore the second solution.
Therefore, the given sequence must have 11 terms such that it sums to -33.
Answer:
Here is 2 methods
Step-by-step explanation:
1) we use excel to find n=11 for lasy students
2) mathematical method
[tex]u_1=17\\u_2=13=17+(2-1)*(-4)\\u_3=9=17+(3-1)*(-4)\\\\\\\boxed{u_n=17+(n-1)*(-4)}\\\\\\\displaystyle s_n=\sum_{i=1}^nu_i\\=\sum_{i=1}^n(17+(i-1)*(-4))\\\\\\=(\sum_{i=1}^n 17) + (-4)*\sum_{i=1}^n (i) +4*\sum_{i=1}^n (1)\\\\\\=17*n+4*n-4*\frac{n*(n+1)}{2} \\\\\\=21n-2n^2-2n\\\\\\=-2n^2+19n\\\\=-33\\\\\\\Longrightarrow\ 2n^2-19n-33=0[/tex]
[tex]\Delta=19^2+4*2*33=625=25^2\\\\n=\dfrac{19-25}{4} =-1.5\ (excluded)\ or\ n=\dfrac{19+25}{4}=11\\\\[/tex]
!!!!HELP PLS!!!!
WHAT IS:
2.039 x 31.5
Answer:
2039/1000×315/10
642285/10000
=64.2285
can u solve two questions. .. Mark brilliant student
sorry I don't know if you ask to other sure I think they will tell you ans
Plz answer fast!! i need help
Answer: D) w = 9 feet
Work Shown:
[tex]L = \sqrt{w^2+h^2}\\\\L^2 = w^2+h^2\\\\L^2-h^2 = w^2\\\\w^2 = L^2-h^2\\\\w = \sqrt{L^2-h^2}\\\\w = \sqrt{15^2-12^2}\\\\w = \sqrt{225-144}\\\\w = \sqrt{81}\\\\w = 9\\\\[/tex]
That points us to the final answer choice D.
help me please brainliest for the best answer!!
Answer:
The volume of the irregular figure would be 102 [tex]cm^3[/tex].
Step-by-step explanation:
If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is [tex]l*w*h[/tex], where [tex]l[/tex], [tex]w[/tex], and [tex]h[/tex], represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be [tex]6*3*5=30*3=90 cm^3[/tex], and the volume of the smaller rectangular prism would be [tex]3*2*2=6*2=12 cm^3[/tex]. So the volume of the entire irregular figure would be [tex]90+12=102 cm^3[/tex].
Answer:
102
Step-by-step explanation:
Large rectangle:
6 × 3 × 5 = 18 × 5 = 90
Small rectangle:
7 - 5 = 2
3 × 2 × 2 = 6 × 2 = 12
90 + 12 = 102
Hope this helped.
Evaluate the expression. Question 9 options: A) tan π∕56 B) tan 17π∕56 C) –tan 17π∕56 D) –tan π∕56
Answer:
A
Step-by-step explanation:
Note the expansion
tan(a - b) = [tex]\frac{tana-tanb}{1+tanatanb}[/tex]
We are given the right side of the expansion , then left side is
tan([tex]\frac{\pi }{7}[/tex] - [tex]\frac{\pi }{8}[/tex] )
= tan([tex]\frac{8\pi -7\pi }{56}[/tex] )
= tan ([tex]\frac{\pi }{56}[/tex] ) → A
Identify one similarity and one difference between the graph of 2x + 4 and the graph of y= -1/2x + 4
Answer:
Similarity: Both graphs have same y-intercepts.
Difference: Graph 2x + 4 has a slope of 2 while the graphic -½x + 4 has a slope of -½
Step-by-step explanation:
[tex]{ \sf{y = mx + b}}[/tex]
m is the slope
b is the y-intercept
PLS HELP ME ON THIS QUESGTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
The difference between the largest and smallest values in a data set is the ______________.
A. mean
B. mode
C. median
D. range
Answer:
D. Range
Step-by-step explanation:
The definition of range is as the question says, and we can also use the process of elimination to make sure it's not the others.
A mean is the average of a data set.
A mode is the item that appears the most times.
And a median is the middle number.
As you can see, A, B, C all don't fit the given statement in the question, so it is D. Range.
I hope this helped! :D
trigonometric identities
Answer:
answer B:
[tex]x= \dfrac{\pi}{2}\ or\ \dfrac{\pi}{6}\ or\ x=\dfrac{5\pi}{6}[/tex]
Step-by-step explanation:
[tex]2cos^2 x + 3sin x=3\\\\\Longrightarrow\ 2*(1-sin^2 x)+3sin x -3=0\\\\\Longrightarrow\ 2-2sin^2 x+3 sin x -3=0\\\\\Longrightarrow\ -2sin^2 x+3 sin x -1=0\\\\\Longrightarrow\ 2sin^2 x-3 sin x +1=0\\\\\Delta=3^2-4*2*1=1\\\\sin\ x=\dfrac{3-1}{4} \ or\ sin\ x=\dfrac{3+1}{4}\\\\sin\ x=\dfrac{1}{2} \ or\ sin\ x=1\\\\\Longrightarrow\ x= \dfrac{\pi}{6}\ or\ x= \dfrac{5\pi}{6}\ or\ x=\dfrac{\pi}{2} \\[/tex]
Geometry, please answer question ASAP
Answer:
A,53.37°
360-306.63=53.37
Answer:
A
Step-by-step explanation:
a whole circle has 360 degrees (one time all around).
so, going from J over M to L is "using" already 306.63 degrees of that. going then from L to J just finishes the full trip of going one time around the whole circle.
so, LJ is just the missing "piece" to 360 degrees.
LJ = 360 - 306.63 = 53.37
A pet store has 80
80
geckos and anole lizards altogether.
The ratio of geckos to anole lizards is 1:3
1
:
3
.
How many geckos does the pet store have?
Answer:
The ratio of geckos to lizards is 1:3
So, that means 1/(3+1) of the animals are geckos.
1/4 of the reptiles are geckos.
And, there are 20 geckos.
Let me know if you have any other questions!
Ratios are used to show the relationship between related quantities. The number of geckos in the pet store is 20.
Given that:
[tex]Total = 80[/tex]
[tex]Gecko : Anole = 1 :3[/tex]
The number of geckos (n) in the store is calculated as follows:
[tex]n = \frac{Gecko}{Gecko + Anole} \times Total[/tex]
So, we have:
[tex]n = \frac{1}{1+ 3} \times 80[/tex]
[tex]n = \frac{1}{4} \times 80[/tex]
[tex]n = 20[/tex]
Hence, there are 20 geckos in the store
Read more about ratios at:
https://brainly.com/question/19257327
Lena and Jared collected stickers. Lena collected 125. Jared collected 213. How many more stickers did Jared collect?
Answer:
Jared collected 88 more stickers
Step-by-step explanation:
Take the amount Jared collected and subtract the amount Lena collected
213-125
88
Jared collected 88 more stickers
Answer:
88
Step-by-step explanation:
213-125=88
PLSSSS HELP ME!!!!! I HAVE A TEST IN THE MORNING WHOEVER ANSWERS CORRECTLY GETS BRAINLIEST!
1. How would we name the polynomial below? Think about degree and number of terms.
x^4 + 3x^2 - x
2. Simplify by adding
(x + 4) + (2x + 7)
3. Multiply
3x^2(5x^3)
4. Divide
8x^3y^5 / 4x^2y^3
Answer:
2. 3x + 11
3. 15x^5
Step-by-step explanation:
2. Simplify by adding
(x + 4) + (2x + 7)
= x + 4 + 2x + 7
= 3x + 11
3. Multiply
3x^2(5x^3)
= 3 (5x^2 x^3)
= 3 (5x^2+3)
= 15x^5
PLEASEEE HELP!!
___ + 42= -18
and
-56+___=-84
i will give brainlist plus 50 points!!!!!
Answer:
-60 and -28
Step-by-step explanation:
-60 + 42= -18
CHECK:
-42-18=-60
-56+-28=-84
CHECK:
-84+28=-56
Hope this helps <3 Need thanks? Comment /hearthelp
Answer:
-60
-28
Step-by-step explanation:
x +42 = -18
Subtract 42 from each side
x+42-42 = -18-42
x = -60
-56 +y = -84
Add 56 to each side
y = -84+56
y = -28
I need help with this plzzzz and this is the thing to the other thing I posted
Answer:
A. A, B, C, D
Step-by-step explanation:
A. 4.99 ÷ 2.25 = 2.1777...
B. 5.50 ÷ 1.75 = 3.142857143
C. 10.99 ÷ 4.50 = 2.44222...
D. 2.99/0.5 = 5.98/1
Answer:
a. A, C, B, D
Step-by-step explanation:
A. 9/4 = 2.25
2.25/4.99 = 1/x
2.25x ÷ 2.25 = x
4.99 ÷ 2.25 = 2.22
$2.22 per pound
B. 7/4 = 1.75
1.75/5.50 = 1/x
1.75x ÷ 1.75 = x
5.50 ÷ 1.75 = 3.14
$3.14 per pound
C. 9/2 = 4.5
4.5/10.99 = 1/x
4.5x ÷ 4.5 = x
10.99 ÷ 4.5 = 2.44
$2.44 per pound
D. 1/2 = 0.5
0.5/2.99 = 1/x
0.5x ÷ 0.5 = x
2.99 ÷ 0.5 = 5.98
$5.98 per pound
Each coffee pot hold 6 cups of coffee we sell 10 cups of coffee every fifteen minutes how many pots of coffee do I need to make in an hour?
Answer:
7 pots of coffee (If you want to be precise its 6 2/3)
Step-by-step explanation:
So basically you need 10 cups of coffe in fifteen minutes, so 60/15=4 then time 10. so 40 is how much coffee you need in a hour, but we are solving the pot so 40/6= 6 2/3. but it says how many pots so we round it up so its 7. (Unless you wanna be precise)
