X → first integer
X + 1 → second integer
X + 3 → third integer
X + X + 1 + X + 2 = 138
3x + 3 = 138
-3 -3
3x = 135
÷3 ÷3
X = 45
X + 1 = 46
X + 2 = 47
23. A glass box shaped like a rectangular prism has width 7 inches, length 9 inches, and height 12 inches. It is being shipped in a larger box with width 10 inches, length 10 inches, and height 15 inches. The space between the glass box and the shipping box will be filled with Styrofoam peanuts. How many cubic inches of space will contain Styrofoam peanuts? Show all work.
The 12 members in Dante's hiking club shared 176 ounces of trail mix equally. How many ounces of trail mix did each member get?
Which algebraic expression represents the phrase “the quotient of negative eight and the sum of a number and three”?
The Side-Angle-Side Similarity Postulate states “If the measures of 2 sides of a triangle are proportional to the measures of 2 corresponding sides of another triangle and the angles between them are congruent, then the triangles are congruent”?
TRUE or FALSE
It takes Makhaya 75 minutes and 3 paper sheets to complete a writing assignment, and it takes him 15 minutes and 1 paper sheet to complete a math assignment. Makhaya is required to spend more than 300 minutes to complete assignments, and he can use at most 20 paper sheets.
Let W denote the number of writing assignments he completes and M the number of math assignments he completes.
Write an inequality that represents the condition based on the number of minutes.
Write an inequality that represents the condition based on the number of paper sheets.
Answer:
Part a) [tex]75W+15M > 300\ minutes[/tex]
Part b) [tex]3W+M \leq 20\ paper\ sheets[/tex]
Step-by-step explanation:
Let
W------> the number of writing assignments that Makhaya completes
M-----> the number of math assignments that Makhaya completes
so
case A) Based on the number of minutes
[tex]75W+15M > 300[/tex] -----> inequality that represent the situation based on the number of minutes
The solution is the shaded area between the positive values of W and M
see the attached figure N 1
case B) Based on the number of paper sheets
[tex]3W+M \leq 20[/tex]-----> inequality that represent the situation based on the number of paper sheets
The solution is the triangular shaded area between the positive values of W and M
see the attached figure N 2
Answer:
First box: 75W+15M>300
Second box: 3W+M≤ 20
Step-by-step explanation:
Did it on Khan
What is the line of symmetry for the parabola whose equation is y = x2 + 10x + 25? x = -10 x = -5 x = 5
Answer:
[tex]y=x^2 + 10x + 25\\\\y=(x+5)^2[/tex]
Used the identity, [tex](a+b)^2=a^2+2ab+b^2[/tex]
The given parabola is of the form , [tex](x+a)^2=y[/tex], having vertex at ,which can be obtained by
x+a=0
x= -a
(-a,0).
So, vertex of the given parabola is , at (-5,0).
The Meaning of term line of symmetry,is that line which divides the parabola in two equal halves.
Drawing the parabola,and finding the line of symmetry,which can be obtained by drawing a line parallel to y axis, passing through (-5,0).
So, the equation of line is : x= -5
Frank is constructing the circumscribed circle for △XYZ. He has already used his compass and straightedge to complete the part of the construction shown in the figure.
Which construction could be his next step?
Place the point of the compass on point Y and draw an arc intersecting the two arcs.
Place the point of the compass on point X and draw an arc intersecting the two arcs.
Place the point of the compass on point Z and draw an arc through points X and Y.
Place the point of the compass on one of the arcs and draw an arc through point X.
Answer:
Place the point of the compass on point X and draw an arc intersecting the two arcs.
Step-by step explanation:
This is to complete the angle bisector.
--9/8x4/3 Please help I will mark brainliest
What is 7200 minutes, in days? (Remember, there are 60 minutes in an hour and 24 hours in a day.)
Answer:
5 Days is the answer
Domain -9,9,93 and Range -1,-5,9,9 is this a function
Please show work! Thank you
Given f(x)=3x^2+10x−8 and g(x)=3x^2−2x .
What is (fg)(x)
Answer:
[tex]\frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
Step-by-step explanation:
The division between functions is defined as:
[tex](\frac{f}{g})(x)=\frac{f(x)}{g(x)} ,\hspace{10}g(x)\neq0[/tex]
So:
[tex](\frac{f}{g} )(x)=\frac{3x^2+10x-8}{3x^2-2x}\\ \\Factor\hspace{3}x\hspace{3}out\hspace{3}the\hspace{3}denominator\\\\(\frac{f}{g} )(x)=\frac{3x^2+10x-8}{x(3x-2)}\\\\Factor\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{4(3x-2)+x(3x-2)}{x(3x-2)}\\\\Factor\hspace{3}3x-2\hspace{3}from\hspace{3}the\hspace{3}numerator\\\\(\frac{f}{g} )(x)=\frac{(3x-2)(x+4)}{x(3x-2)}=\frac{x+4}{x}[/tex]
Since [tex]g(x) \neq0[/tex] , let's find its roots:
[tex]3x^2-2x=0\\\\Factor\\\\x(3x-2)=0\\\\Split\hspace{3}into\hspace{3}two\hspace{3}equations:\\\\(1):x=0\\(2):3x-2=0[/tex]
For (2)
[tex]3x=2\rightarrow x=\frac{2}{3}[/tex]
Therefore the roots are:
[tex]x=0,\hspace{3}x=\frac{2}{3}[/tex]
Finally the complete answer is:
[tex](\frac{f}{g})(x)= \frac{x+4}{x} \hspace{8}where\hspace{8}x\neq0,\frac{2}{3}[/tex]
Dory and Nemo go to Taco Bell for lunch. Dory orders three soft tacos and three double deckers for 11.25. Nemo pays $10 for four soft tacos and two double deckers. Write a system of equations that represents the lunch orders for dory and Nemo.
The equations representing Dory's and Nemo's lunch orders are 3x + 3y = 11.25 and 4x + 2y = 10, respectively.
Let's define the variables first. Let x be the cost of one soft taco, and y be the cost of one double decker.
Dory orders three soft tacos and three double deckers for $11.25. This gives us the first equation:
3x + 3y = 11.25
Nemo orders four soft tacos and two double deckers for $10. This gives us the second equation:
4x + 2y = 10
We now have a system of equations that represents the lunch orders:
3x + 3y = 11.25
4x + 2y = 10
These equations can be solved simultaneously to find the individual costs of the soft tacos and double deckers.
We play a game where there are 50 coins in a row, we take turns taking between 1 and 5 coins however many you like. whoever takes the last coin keeps them all. how can i win everytime and does it matter if i go first
Lucy wants to make different types of Cheesecake, each cheesecake uses 2/3 pound of cream cheese, she has 2 pounds of cream cheese. How many cheesecakes can she make?
A bamboo shoot is 20 inches tall at day 0 and grows 24 inches each day. which function(s) shown below can be used to determine height, f(n), of the bamboo after n days?
I. f(n)=24n+20
II. f(n)=24n+20(n-1)
III. f(n)=f(n-1)+24 where f(0)=20
Answer:
The correct answer is option I
Step-by-step explanation:
Initial height of bamboo [tex]= 20 in\\[/tex]
Height of bamboo grows by [tex]24 in \\[/tex] every day
Let "n" be the number of days
So the height of bamboo after "n" days is
[tex]f(n) = 20 + 24n\\[/tex]
Thus, the correct answer is option I
Use two variables k and total to write a for loop to compute the sum of the squares of the first 50 counting numbers, and store this value in total. thus, your code should put 1*1 2*2 3*3 ... 49*49 50*50 into total. use no variables other than k and total.
Could someone please give me the answer? The subject is math and its Pre- Algebra
Which statement describes the translation of y = −one half (x − 2)2 − 2 from standard position?
Which graph represents the function f(x) = log10(x + 2)?
Answer:
Please see the attachment for graph.
Step-by-step explanation:
Given: [tex]f(x)=\log_{10}(x+2)[/tex]
It is log function. First we take parent function of log
[tex]y=\log_{10}x[/tex]
We have to change y to f(x)
First we draw the graph of parent function.
[tex]y=\log_{10}x[/tex]
Now we shift graph 2 unit left because when x change to x+a , graph shift a unit left or right.
So, f(x) will shift 2 unit left.
[tex]f(x)=\log_{10}(x+2)[/tex]
Consider today's stock listings for bukkia hog farms, shown below. 52 wk high 52 wk low symbol div. close net change 212.45 106.63 bhf 18.95 140.26 8.85 today, ken sold the 116 shares of bukkia hog farms that he purchased yesterday. how much profit did ken make
Answer:
$1026.60
Step-by-step explanation:
Today's stock listing for Bukkia hog farms as shown below :
52 wk high : 212.45
52 wk low : 106.63
symbol : bhf
Div. : 18.95
close : 140.26
net change : 8.85
Since we know net change from yesterday till date is 8.85.
Ken sold shares that he purchased yesterday = 116 × 8.85 = $1026.60
Ken made profit of $1026.60
An advertisement on a billboard measures 22 ft long and 8 ft high. If the ad is transferred to the side of a bus and is 30 in. Long, how tall is the new ad, to the nearest inch
the new ad is 10 ft and 11 inches tall, to the nearest inch.
What is Scale?The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary throughout a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of size significant in two different ways.
Given, An advertisement on a billboard measures 22 ft long and 8 ft high. If the ad is transferred to the side of a bus and is 30 ft. Long.
when the advertisement is 22 ft long then the height is 8 ft.
So,
When the advertisement is 1 ft long then the height is = 8/22 ft.
the advertisement is 1 ft long then the height is = 4/11 ft.
thus,
the advertisement is 30 ft long then the height is = 4/11 * 30 ft.
the advertisement is 30 ft long then the height is = 120/11 ft.
the advertisement is 30 ft long then the height is = 10 ft 11 inches.
Therefore, When the advertisement is 30 ft long then the height is 10 ft 11 inches.
Learn more about scale here:
https://brainly.com/question/1287267
#SPJ1
2) Find the point, M, that is five-sixths of the distance from A(-7, 2) to B(-1, -4).
Consider the expression 625(5xy)^-3/ (5x)^2 y^7
Answer:
1
-----------------
5x^5y^10
Step-by-step explanation:
How much will it cost to mail a first-class letter that weighs 2.8 oz?
The rate is $.22 for the first ounce and $.17 for each additional
ounce or fraction of an ounce.
a. $.56
b. $5.60
c. $.53
d. $.39
Final answer:
The total cost to mail a first-class letter that weighs 2.8 oz is $0.56, which includes $0.22 for the first ounce and $0.34 for the additional weight.
Explanation:
To calculate the cost of mailing a first-class letter that weighs 2.8 oz, you need to know the initial rate for the first ounce and the rate for each additional ounce. According to the given rates, the cost for the first ounce is $0.22, and each additional ounce (or fraction thereof) costs $0.17.
Since the letter weighs 2.8 oz, you have 1.8 oz over the first ounce. Thus, you need to pay for 2 additional ounces.
The total cost = cost for first ounce + cost for additional ounces = $0.22 + 2 x $0.17 = $0.22 + $0.34 = $0.56. Therefore, the correct answer is (a) $.56.
1. Use an inequality symbol (<, >, ≥, =) to compare −26 ____ 54
An inscribed angle has a measure of 48°. Determine the measure of the intercepted arc.
24°
48°
72°
96°
The diagonals of a parallelogram are congruent which could be the same parallelogram ?
A - trapezoid
B - Rectangle
C - Kite
D - rhombus
Answer:
B - Rectangle
Step-by-step explanation:
The diagonals of the parallelogram are given equal.
Diagonals of a parallelogram are equal in a rectangle .
So the given figure in which diagonals are equal is called a Rectangle.
Among the given options Option B is the right answer.
Choose the correct classification of 4x4 − 4x3 + 10x6. (5 points)
The given expression 4x^4 - 4x^3 + 10x^6 is a polynomial of degree 6.
Explanation:The given expression is 4x4 - 4x3 + 10x6.
To classify this expression, we need to look at the highest power of x in the expression. In this case, the highest power is 6, which means it is a polynomial of degree 6.
So, the correct classification of 4x4 - 4x3 + 10x6 is a polynomial of degree 6.
In GHI, HI = IHG =3x + 4, and IGH = 2x - 24. What is HIG?