Answer:
the distribute property is basically taking the number outside the parenthesis and multiplying with the numbers inside each by each.
Step-by-step explanation:
20(30-15)
20×30= 600, and 20×15=300
finally you just use the new numbers and solve the solution which is 600-300. The answer is 300
Answer: 300
Step-by-step explanation: The distributive property tells us that when there's a number outside a set of parentheses, you can multiply it times each of the terms that are inside the set of parentheses and then add those products together.
So in this problem, we can multiply 20 (30) - 20 (15) which simplifies to 600 - 300 which is 300.
16 store cashiers work average 21 hours per week and paid $8.25 per hour . after store manager hires 2 additionsl cashiers each cashier will be paid .25 more per hour and will work an average of 1.5 fewer hours per week. what will be the change in total amount of money the cashiers are paid each week?
Answer:
The change in total amount of money the cashier are paid each week will be $331.5.
Step-by-step explanation:
16 store cashiers work average 21 hours per week and paid $8.25 per hour.
Now, the store manager hires 2 additional cashiers each cashier will be paid 0.25 more per hour and will work an average of 1.5 fewer hours per week.
Therefore, the two additional cashiers will be paid $8.50 per hour and will work an average of (21 - 1.5) = 19.5 hours per week.
So, the change in the total amount of money the cashiers are paid each week will be (2 × 19.5 × 8.5) = $331.5. (Answer)
Given the function y= 7x - 3 determine the y-intercept of the line.
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You start driving north for 3 miles, turn right, and drive east for another 4 miles. At the end of driving, what is your straight line distance from your starting point?
The straight line distance is 5 miles from starting point.
Step-by-step explanation:
Driving 3 miles north and 4 miles east and then the straight line distance will form a right angled triangle.
Where;
One leg = a = 3 miles
Other leg = b = 4 miles
Hypotenuse = c
Using Pythagoras theorem;
[tex]a^2+b^2=c^2\\(3)^2+(4)^2=c^2\\9+16=c^2\\c^2=25[/tex]
Taking square root on both sides
[tex]\sqrt{c^2}=\sqrt{25}\\c=5[/tex]
The straight line distance is 5 miles from starting point.
Answer:
5
Step-by-step explanation:
3[2]+4[2]=c[2]
9+16=c[2]
[tex]\sqrt{25}[/tex]=5
If the length of a pool is 8 more than twice the width and the total area is 960 square feet, find the length and width of the rectangular landscape element.
Answer:
l=48, w=20
Step-by-step explanation:
Let the width of the pool be w feet, then the length will be:
[tex]l = 2w + 8[/tex]
The area of the pool is 960 square feet.
This means that:
[tex]w(2w + 8) = 960[/tex]
Expand and rewrite in standard form to get:
[tex]2 {w}^{2} + 8w - 960 = 0[/tex]
[tex] {w}^{2} + 4w - 480 = 0[/tex]
[tex]{w}^{2} + 24w - 20w- 480 = 0[/tex]
[tex]{w}(w+ 24) - 20(w + 24) = 0[/tex]
Factor to get:
[tex](w+ 24)(w - 20) = 0[/tex]
[tex]w = - 24 \: or \: w = 20[/tex]
We discard the negative value because magnitude is positive.
This means
[tex]l = 2 \times 20 + 8 = 48[/tex]
if 2a+b=3,find the value of 8a³+b³+18ab
Answer:
531.
Step-by-step explanation:
Let's assume 2(1) + 1 = 3
a = 1 and b = 1
Now we can plug that in
8(1)^3 + (1)^3 + 18(1)(1)
Then we need to multiply together
8^3 + 1^3 + 18
Then do the powers
512 + 1 + 18
Then add them together
531
Hope this helped!
Answer:
27
Step-by-step explanation:
A sum of cubes factors as
a³ + b³ = (a + b)(a² - ab + b²)
Factor the sum of cubes 8a³ + b³
8a³ = (2a)³, thus
8a³ + b³
= (2a)³ + b³
= (2a + b)(4a² - 2ab + b²)
We now have the right side as
(2a + b)(4a² - 2ab + b²) + 18ab ← substitute 2a + b = 3
= 3(4a² - 2ab + b²) + 18ab
= 12a² - 6ab + 3b² + 18ab ← collect like terms
= 12a² + 12ab + 3b² ← factor out 3 from each term
= 3(4a² + 4ab + b²) ← perfect square
= 3(2a + b)² ← substitute 2a + b = 3
= 3 × 3²
= 3 × 9
= 27
Figure ABCD is reflected across the y-axis. What are the coordinates of A' , B' , C' , and D' ?
Answer:
Reflection in the y-axis maps:
(x,y) onto (-x,y)
x coordinate gets multiplied by -1,
y coordinate remains unchanged
Combine the like terms to simplify the polynomial. Show any work. Put your answers in standard form.
(5x^4-3x^3+2x^2-15x+27)+(7x^4+5x^3-x^2+8x-13)
Answer:
12x⁴ + 2x³ + x² - 7x + 14
Step-by-step explanation:
(5x^4-3x^3+2x^2-15x+27) + (7x^4+5x^3-x^2+8x-13)
(5+7)x⁴ + (-3+5)x³ + (2-1)x² + (-15+8)x + (27-13)
12x⁴ + 2x³ + x² - 7x + 14
Write each repeating decimal using bar notation.
5.313131
0.999
2.010101
26.993993
Answer:
1) 5.313131 put the bar over the first 31
2)0.999 put the bar over the first 9
3)2.010101 put the bar over the first 01
4)26.993993 put the bar over the first 993
Step-by-step explanation:
what is the probability of rolling a 4 on a single sided die and then rolling a 6?
Answer:
If it is a six-sided die then it has the probability of 1/6 or .16
Step-by-step explanation:
question 3 - open up to see pic
(12, 11):
2((12) + 3) - (11) = 7 + (12)
2 • 15 - 11 = 19
2 • 4 = 19
8 [tex]\neq[/tex] 19
(1, 0):
2((1) + 3) - (0) = 7 + (1)
2 • 4 = 8
8 = 8
(-5, 1):
2((-5) + 3) - (1) = 7 + (-5)
2 • -2 - 1 = 2
2 • -3 = 2
-6 [tex]\neq[/tex] 2
Hope this helps.
Write the explicit formula for the geometric sequence
The formula [tex]3(4^{n-1})[/tex] represents the geometric sequence.
Step-by-step explanation:
Step 1:
The value of [tex]a_{n}[/tex] is dependent on the value of n.
So n is independent while [tex]a_{n}[/tex] is dependent on n i.e. the value of [tex]a_{n}[/tex]depends on the value of n.
Step 2:
We substitute the values of n in the functions to check which function satisfies the values of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} = -4(3)^{n-1} = -4 (3^{3}) = -108.[/tex] This does not equal the value of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} = 4(3)^{n-1} =-4 (3^{3}) = 108.[/tex] This does not equal the value of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} =3(-4)^{n-1} = 3 (-4^{3}) = -192.[/tex] This does not equal the value of [tex]a_{n}[/tex].
If [tex]n = 4, a_{n} =3(4)^{n-1} = 3 (4^{3}) = 192.[/tex] This equals the value of [tex]a_{n}[/tex].
So the fourth formula represents the geometric sequence.
marco wants to buy 2 books that cost 20$ each. He can save $5 a week. Draw siagrama and write equations to find how many weeks it will take hime to save enough money to buy the books.
Answer: He needs to wait 8 weeks.
Step-by-step explanation: 5•8 equals 40. 2 books, 20$ each and add them together, 40!
To determine the number of weeks Marco needs to save $40 to buy two books at $20 each, an equation can be set up based on his weekly savings of $5. Solving the equation 5 × w = $40 gives us w = 8, meaning Marco will need to save for 8 weeks.
Explanation:The problem given is about Marco who wants to buy two books, each costing $20. He can save $5 a week. To calculate how many weeks it will take for Marco to save enough to buy the books, we can set up an equation. First, we need to determine the total cost of the books:
Cost of one book = $20Cost of two books = 2 × $20 = $40Next, let’s set up our equation. If Marco saves $5 each week, the total amount saved after w weeks will be 5 × w. We want this to be equal to the total cost of the books, so our equation will be:
5 × w = $40
To solve for w, we divide both sides by 5:
w = $40 / 5
w = 8
Therefore, it will take Marco 8 weeks to save enough money to buy the two books.
The queen had 300 servants. there were 10 more butlers than cooks. the number of cooks was twice the number of maids. how many maids worked at the queen palace?
The no. of maids who worked at the queen's palace is 58.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
Given, The queen had 300 servants. there were 10 more butlers than cooks. The number of cooks was twice the number of maids.
Assuming the no. of maids to be 'x', therefore no. of cooks is 2x and the no. of butlers is (2x + 10).
∴ x + 2x + (2x + 10) = 300.
5x = 290.
x = 58.
learn more about numerical expressions here :
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Complete the parts in each step to find the area of each trapezoid?
Press on the picture to see it
The area of the trapezoid is 20 in².
Solution:
Given data:
Length of the bottom base = 7 in
Length of the top base = 3 in
Height of the trapezoid = 4 in
Step 1: Area of the trapezoid formula,
[tex]$A=\frac{b_{1}+b_{2}}{2} \times h[/tex]
Step 2: Substitute the given values in the formula.
[tex]$A=\frac{7+3}{2} \times 4[/tex]
Step 3: Add 7 and 3.
[tex]$A=\frac{10}{2} \times 4[/tex]
Step 4: Divide 10 by 2, we get
[tex]A=5 \times 4[/tex]
Step 5: Multiply 5 by 4, we get
A = 20 in²
The area given in the picture is wrong.
The area of the trapezoid is 20 in².
What is the rate of change for the equation y = 4x +60?
The rate of change is .
The slope represents the rate of change. Then the rate of change will be 4.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The linear equation is given below.
y = 4x + 60
The slope is 4 and the y-intercept is 60.
The slope represents the rate of change. Then the rate of change will be 4.
More about the linear equation link is given below.
https://brainly.com/question/11897796
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The rate of change in the equation y = 4x + 60 is 4, which is the coefficient of x. This means for each unit increase in 'x', 'y' will increase by 4 units.
Explanation:In mathematics, the rate of change in an equation like y = 4x + 60 is represented by the coefficient of the variable x. This is because, in such an equation which is in the form of y = mx + b (a standard linear equation), 'm' represents the rate of change or the slope of the line.
So, in your specific equation y = 4x + 60, the rate of change or slope is 4. This means that for each increment of 1 in 'x', 'y' will increase by 4 units. This value - 4 - is your rate of change in this case.
Learn more about Rate of Change here:https://brainly.com/question/20816247
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abby buys 4 pencils and 2 erasers for $3.58. Micheal buys 1 pencil and 6 erasers for $2.49
what is the cost of 1 pencil and 1 eraser ?
Answer:
1 pencil = $0.75
1 eraser = $0.29
Step-by-step explanation:
4p+2e=3.58 1p+6(0.29)=2.49
1p+6e=2.49 1p+1.74=2.49
p=2.49-6e 1p=0.75
4(2.49-6e)+2e=3.58 p=0.75
9.96-24e+2e=3.58
9.96-22e=3.58
-22e=-6.38
e=0.29
please help. i don’t get this. explain and show work. will give lots of points and mark as brainliest!
The student didn't provide enough information to answer their question. The subject and specific problem were missing from the request. More context or further details are needed to give a correct and applicable tutorial response.
Explanation:Unfortunately, your question did not provide enough information for me to provide a specific answer. The subject and the specific problem you want to explain have not been given. Please provide these details, and I would be more than happy to help you understand any academic problem you're facing, whether it's about Mathematics, English, History, Biology, Physics or any other subject.
Remember that it's always good to include as much information as possible - what particular concept do you struggle with? Is there a specific assignment question that troubles you? This will help tutors provide you with the most accurate, relevant, and helpful answer!
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What is the mad of this set 0,3,6,9,11,13,14
Answer:
When I calculated this I got: 4.2857142857143 but I don't know if that's the correct answer.
Step-by-step explanation:
Find the missing angle measure below:
Answer:
81
Step-by-step explanation:
ANGLES in a TRIANGLE add up to 180
In the Triangle you have 65 and 34
Add them together = 99
Subtract the total from 180
180 - 99 = 81
Answer:
81 degrees
Step-by-step explanation:
The angles of the triangle always add up to 180.
SO you'd do 65+34 which equals 99.
NOW you do 180-99 which equals 81
So you're missing angle would be 81 degrees
Which of the following is another way to express the equation 8 - (-) = 43?
8-d=43
-d + 8 = 43
-8+d=43
O8+ d=43
Question:
Which of the following is another way to express the equation 8 - (-d) = 43?
A.8-d=43
B.-d+8=43
C.-8+d=43
D.8+d=43
Answer:
8 + d = 43 is another way to express the given equation
Solution:
Consider the given equation
[tex]8 - (-d) = 43[/tex]
We have to find the another way to express the above equation
We know that,
We we multiply negative sign number by another negative sign number, then the result is positive sign number
Therefore from given,
[tex]-(-d) = -1 \times -d = d[/tex]
Thus the given equation becomes,
8 + d = 43
Thus option D is correct
Four times a divided by two equals 5.2
Initial equation:
4a / 2 = 5.2
Multiply both sides by 2:
4a = 10.4
Divide both sides by 4:
a = 2.6
Hope this helps!! :)
Answer:
Step-by-step explanation:
2.6 becuase 4a/2= 5.2
4a=10.4
a=2.6
If the volume of the pyramid shown is 216 in 3, what is the area of its base?
Answer:
Step-by-step explanation:
volume =1/3×base area×height
216=1/3× A×6
base area=216/2=108 in²
Answer:
Here is the answer
Step-by-step explanation:
108 in squared
or D
Area of circles
Susan designed a circular pool with a diameter of 25 meters. what is the area of the bottom of the pool? round to rhe nearest.
Step-by-step explanation:
Diameter of circle = 25 m
Therefore, radius of the circle = 12.5 m
[tex]area \: of \: bottom \: of \: pool \\ = \pi {r}^{2} \\ = 3.14 \times ( {12.5)}^{2} \\ = 3.14 \times 156.25 \\ = 490.625 \: {m}^{2} \\ \approx490.63 \: {m}^{2} [/tex]
Which of these absolute values is the greatest?
A.
|140|
B.
|-104|
C.
|104|
D.
|-204|
When doing absolute value, negatives will always be positive.
Option A's absolute value is 140.
Option B's absolute value is 104.
Option C's absolute value is also 104.
Option D's absolute value is 204.
Therefore, the option with the greatest absolute value would be D. |-204|
Answer:
A because is positive and highlights numbers
This is so confusing I don't understand how to do it!
Answer:
494 square feet
494 ft^2
Step-by-step explanation:
Trapezoid:
(20 + 32) ÷ 2 ) × 3
52 ÷ 2 ) × 3
26 × 3
= 78
Rectangle:
32 × 13 = 416
Add:
78 + 416 = 494
Brenda invests $4500 in the savings account earning 5.5% interest compounded quarterly. What will the account balance be after seven years?
The account balance will be $6642 after seven years.
Step-by-step explanation:
It is given that, Brenda invests $4500 in the savings account.The interest rate is 5.5% interest compounded quarterly.To find the amount after seven years, a certain formula is used.
Amount = [tex]P( 1+r/n)^{n\times t}[/tex]
where,
P is the principal amount that is invested in the account.
Therefore, P = 4500 dollars.
r is the rate of interest. (r = 5.5 %)
Therefore, r = 5.5/100 = 0.055
n is the number of time the interest is compounded per year which is n= 4.
t is the time period which is t = 7 years.
Now, substituting all the above values in the formula,
Amount = [tex]4500(1+0.055/4)^{4\times 7}[/tex]
⇒ [tex]4500(4.055/4)^{28}[/tex]
⇒ [tex]4500(1.014)^{28}[/tex]
⇒ [tex]4500\times1.4759[/tex]
⇒ 6641.55 (which is approximately equal to 6642)
⇒ 6642 dollars.
The account balance after 7 years is $6642.
Which of the following describes how to translate the graph y = 1xl to obtain the graph of y = lx - 11 - 1?
1)1 unit left and 1 unit down
2)1 unit left and 1 unit up
3)1 unit right and 1 unit down
4)1 unit right and 1 unit up
Please help
Answer:
3)1 unit right and 1 unit down
Step-by-step explanation:
The parent function is
[tex]y = |x| [/tex]
This is the base of the absolute value functions.
It has its vertex at the origin.
The transformed function is
[tex]y = |x - 1| - 1[/tex]
This absolute value function has its vertex at (1,-1).
This means the parent function has been shifted 1 unit right and 1 unit down to obtain the transformed function.
What is the answer to 50% of $250
Answer:$125
Step-by-step explanation:
50% of 250
50/100 x 250
1/2 x 250=(1x250)/2=250/2=125
Hi I just have a question what is 23+4189
Answer:
4,212
Step-by-step explanation:
Step 1: Add
23 + 4189
4,212
Answer: 4,212
x2 + y2 + 12x + 2y – 1 = 0
Answer:
This question would be related to slopes so the answer is [tex]y=-\frac{7}{2}x+\frac{1}{4}[/tex]
Step-by-step explanation:
[tex]\mathrm{Slope-Intercept\:form\:of}\:\\x2+y2+12x+2y-1=0:\quad y=-\frac{7}{2}x+\frac{1}{4}[/tex]
[tex]\mathrm{Domain\:of\:}\:-\frac{7}{2}x+\frac{1}{4}\::\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<x<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Range\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad \begin{bmatrix}\mathrm{Solution:}\:&\:-\infty \:<f\left(x\right)<\infty \\ \:\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\infty \:\right)\end{bmatrix}[/tex]
[tex]\mathrm{Parity\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{Neither\:even\:nor\:odd}[/tex]
[tex]\mathrm{Axis\:interception\:points\:of}\:\\-\frac{7}{2}x+\frac{1}{4}:\quad \mathrm{X\:Intercepts}:\:\left(\frac{1}{14},\:0\right),\:\mathrm{Y\:Intercepts}:\:\left(0,\:\frac{1}{4}\right)[/tex]
[tex]\mathrm{Inverse\:of}\:-\frac{7}{2}x+\frac{1}{4}:\quad -\frac{4x-1}{14}[/tex]
[tex]\mathrm{Slope\:of\:}-\frac{7}{2}x+\frac{1}{4}:\quad m=-\frac{7}{2}[/tex]
Hope this helps you!
Have a good night!