Answers:
A+B+C = 7x - 9y - zA-B+C = 3x - 3y - 9zA+B-C = -x + y + 11z======================================================
Explanation:
Skip to the "Work Shown" section below to see the steps for each part.
Each variable is a place holder for some unknown number. We can think of it like a box that holds a number. Luckily the letter x is found in the word "box" to help cement this line of thinking.
1x = 1 box
2x = 2 boxes
3x = 3 boxes
and so on
This shorthand notation allows us to quickly add boxes
2 boxes + 3 boxes = 5 boxes
So 2x+3x = 5x
And we can subtract boxes as well
7 boxes - 3 boxes = 7x - 3x = 4x = 4 boxes
The same number must go in box x for this to work out.
When it comes to dealing with negative numbers, it might help to use a vertical number line. I like to think of it like going up and down an elevator on a skyscraper. Negative integers represent basement levels.
It's possible to have boxes within boxes. The box A has the three boxes x-y+z inside it. So wherever we see an "A", replace it with x-y+z. Unfortunately we don't know what numbers go in the boxes for x, -y and z. Use the same type of thinking for B and C.
Don't forget to use the distributive property to distribute the negative through to each term.
Example: (x+y)-(w+z) = x+y-w-z
Many students make the mistake in saying that (x+y)-(w+z) = x+y-w+z which is not true. The +z should be -z at the very end.
Let me know if you have any other questions.
The next section below shows the steps needed to get the three answers.
----------------
Work Shown:
Part (I)
A+B+C = (x-y+z)+(2x-3y+4z)+(4x-5y-6z)
A+B+C = (x+2x+4x)+(-y-3y-5y)+(z+4z-6z)
A+B+C = 7x - 9y - z
Part (II)
A-B+C = (x-y+z)-(2x-3y+4z)+(4x-5y-6z)
A-B+C = x-y+z-2x+3y-4z+4x-5y-6z
A-B+C = (x-2x+4x)+(-y+3y-5y)+(z-4z-6z)
A-B+C = 3x - 3y - 9z
Part (III)
A+B-C = (x-y+z)+(2x-3y+4z)-(4x-5y-6z)
A+B-C = x-y+z+2x-3y+4z-4x+5y+6z
A+B-C = (x+2x-4x)+(-y-3y+5y)+(z+4z+6z)
A+B-C = -x + y + 11z
What is the value of y?
log^464 = y
OA. 16
OB. 8
OC. 3
OD. 4
The value of y in the given logarithmic equation is 3. The correct option is C. 3
Evaluating Logarithmic equationFrom the question, we are to determine the value of y in the given logarithmic equation
The given equation is
[tex]log_{4}64=y[/tex]
By applying one of the laws of logarithm, we get
[tex]64 = 4^{y}[/tex]
Now, express 64 in index form,
[tex]4^{3} = 4^{y}[/tex]
Since the bases are equal, we can equal the powers to get
3 = y
∴ y = 3
Hence, the value of y in the given logarithmic equation is 3. The correct option is C. 3
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Mario has captured many yellow spotted slalmaders. He weighs each and then counts the number of yellow spots on its back. This trend line is a ___ fit for these data.
There is a bag filled with 5 blue and 4 red marbles.
A marble is taken at random from the bag, the colour is noted and then it is replaced.
Another marble is taken at random.
What is the probability of getting 2 of the same colour?
5 blue, 4 red = 9 total
Probability (Blue, Blue) = 5/9 x 5/9 = 25/81 = 0.30864
Probability (Red, Red) = 4/9 x 4/9 = 16/81 = 0.19753
Probability (Blue,Blue) or (Red,Red) = 25/81 + 16/81 = 41/81 = 0.506173
Fraction answer = 41/81
Decimal answer = 0.506173 (round off as needed)
which of the following equations will produce the graph shown below?
A circle can be characterized by its center's location and its radius' length. The correct option is A.
What is an equation of a circle?A circle can be characterized by its center's location and its radius' length. Let the center of the considered circle be at (h,k) coordinate and the radius of the circle be 'r' units. Then, the equation of that circle would be:
(x-h)² + (y-k)² = r²
The given graph is the graph of a circle that has its origin at (0,0) and has a radius of 4 units, therefore, the equation will be,
(x-0)² + (y-0)² = 4²
x² + y² = 16
Multiply both the sides of the equation by 2,
2x² + 2y² = 32
Hence, the correct option is A.
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Zack has 2 feet of balsa wood. he needs twice that amount to finish a project. the cost is $0.05 per inch. how much will the balsa wood cost zack.
Answer:
$1.2
Step-by-step explanation:
There is 12 inches in a foot, and if he needs twice the amount he already has which is 4 then you would multiply 0.05 times 24 and you would get $1.2
Answer: $1.20 for 2 feet of balsa wood
Step-by-step explanation: There are 12 inches in 1 foot, and 24 inches in 2 feet. The cost per inch is 0.05, multiplying 24 (inches) x 0.05 (the cost per inch) would equal $1.20
Banana
23
Apple
18
Orange
34
Peach
27
Pear
18
Using proportional reasoning, about how many students out of the 2,000 would you expect to select an orange as their favorite fruit?
Answer:
almost 567 students
Step-by-step explanation:
all fruits = 23+18+34+27+18 = 120
possibility of selecting an orange as favourite fruits by one student = 34/120 = 17/60
possibility of selecting an orange as favourite fruits by 2000 students = 17/60×2000 =1700/3 = 566.6666...=567 students
Lakeridge health oshawa is a 423 beds hospital with 463 doctors and 4058 staff comprised of nurses and technologists. it is planning to open another 35-bed wing. assuming the same proportionate staffing levels, how many more doctors will need to be hired?
The number of doctors that would be needed for the 35-bed wing is 38.
How many more doctors are needed?The first step is to determine the number of doctors needed for one bed : 463 / 423
The second step is to multiply the ratio gotten in the first step by the number of beds in the new wing: (463 / 423) x 35 = 38.21 = 38
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Find the distance between the points (-6,-4) and (-6,-18)
Answer:
The answer is 16 units.
Step-by-step explanation:
Now we have to use the distance formula i.e distance between two points =root under (x2-x1)^2+(y2-y1)^2
Answer:
22 is the distance between the points
What is the y-intercept of the function f(x) = -2/-9x+1/3?
Answer:
b = 1/3
Step-by-step explanation:
The general structure of equations in slope-intercept form is:
y = mx + b
In this form, "m" represents the slope and "b" represents the y-intercept.
The given equation is already in slope-intercept form. In other words, you have already been given "m" and "b". Therefore, the value which corresponds with the y-intercept is (1/3).
f(x) = mx + b
f(x) = -(2/9)x + 1/3
Question 29 of 49
The pattern below follows the rule, "starting with a value of 3, every
consecutive row has a value that is 2 less than twice the value of the previous
row."
Value
Row 1
3
Row 2
4
Row 3
6
What is the value for the 6th row?
34.............................. ........
Picture has the choices
Answer: 4th option, 28 = 28
Step-by-step explanation:
Cross multiplying means we will multiply the numerator of the first fraction by the denominator of the second. Then we will multiply the denominator of the first by the numerator of the second.
-> See attached for a visual example and my work.
28 = 28, so the fractions are equal.
Answer:
Step-by-step explanation:
2/7=4/14 because 7x4=28 and 2x14=28. so you're gonna see which equals 28. but for example, if it's 10, you do 10/1.
combine like terms to simplify 3x + 5 - 2x
Step-by-step explanation:
3x and 2x are like terms so,
3x + 5 - 2x
3x - 2x + 5 = x + 5
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression
[tex]\star~~\large\pmb{3x+5-2x}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Combine like terms.The like terms here are: 3x-2x; let's combine them:
[tex]\star~\large\pmb{x+5}[/tex]
We can't simplify this any further, because x and 5 are not like terms.
[tex]\ddot\bigstar[/tex] Remember this...
[tex]\fbox{Variables\:and\;numbers\;are\;not\;like\;terms}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
Which of the following proves ABC= DEF?
Answer: A
Step-by-step explanation:
In the diagram, we see that we have two pairs of congruent angles, so it is going to be either ASA or AAS congruence.
To determine if it is ASA or AAS congruence, we can use the fact that for ASA, the side is included between the congruent angles, whereas in AAS, the side isn't.
Since the congruent side is included between the two angles, there is ASA congruence.
At a diner, the lunch special gives you three choices. For the starter, you can pick from 3 choices (soup or salad or fries) For the main item, you can pick from 2 choices (burger or sandwich) For the drink, you can pick from 2 choices (coke or pepsi) If the staff chooses all items for you randomly, figure these probabilities.
1. Probability of getting (soup, burger, coke)
2. Probability of getting (fries, burger, any drink)
Answer:
1/12; 1/6
Step-by-step explanation:
1. the chance of getting soup is 1/3, the chance of getting a burger is 1/2, and the chance of getting coke is 1/2, multiply these chances to get (1/3) *(1/2) * (1/2) = 1/12
2. the chance of getting fries is 1/3, the chance of getting a burger is 1/2, and the chance of getting any drink is 1, multiply these chances to get (1/3) * (1/2) * 1 = 1/6
Which point is on the circle centered at the origin with a radius of 5 units?
Distance formula: StartRoot (x 2 minus x 1) squared + (y 2 minus y 1) squared EndRoot
(2, StartRoot 21 EndRoot)
(2, StartRoot 23 EndRoot)
(2, 1)
(2, 3)
What is the value of x?
Enter your answer in the box.
Answer:
25
Step-by-step explanation:
c^2=a^2+b^2
where c = hypotenuse
so, x^2 = 24^2+7^2
x^2 = 576 + 49
x^2 = 625
x = square root of 625
x = 25
Which transformations could have been used to create A'B'C'? Choose all that apply.
a 180° rotation about the origin and then a translation 3 units up and 1 unit left
a translation 3 units up and 1 unit left and then a 180° rotation about the origin
a 90 degree clockwise rotation about the origin and then a reflection over the Y axis
a 90° counterclockwise rotation about the origin and then a reflection over the X axis
A translation through you to down and one unit right and then I 108° rotation about the origin
The correct transformation is a rotation of 180° around the origin followed by a translation of 3 units up and 1 unit to the left.
Which transformation is used to get A'B'C'?
To analyze this we can only follow one of the vertices of the triangle.
Let's follow A.
A starts at (3, 4). If we apply a rotation of 180° about the origin, we end up in the third quadrant in the coordinates:
(-3, -4)
Now if you look at A', you can see that the coordinates are:
A' = (-4, -1)
To go from (-3, -4) to (-4, -1), we move one unit to the left and 3 units up.
Then the complete transformation is:
A rotation of 180° around the origin, followed by a translation of 3 units up and 1 unit to the left.
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Answer:
A. a 180degree rotation about the origin and then a translation 3 units up and 1 unit left
E. a translation 3 units down and 1 unit right and then a 180degree rotation about the origin
Assume that an economy has 1,000 workers, each working 2,500 hours per year. if the average real output per worker-hour is $20, then total output, or real gdp, will be
Answer:
$50,000,000
Step-by-step explanation:
You want to know the total output (real gdp) of 1000 workers, each working 2500 hours producing real output of $20 per hour.
GDPThe output, called "gross domestic product" or GDP, is the total output of all workers for the hours they work:
(1000 worker) × (2500 hours/worker) × ($20/hour) = $50,000,000
The GDP will be $50,000,000 or 50 million dollars.
2. Use the figures below for parts a through c.
B
45°
15
90% C
105°
120%
105°
W
80
(a) Are the corresponding angles in figures ABCD and WXYZ congruent? (1 pt)
Circle or highlight one:
Yes
No
(b) Are the corresponding sides in figures ABCD and WXYZ proportional? (1 pt)
Circle or highlight one:
Yes
No
Show your work for part b below. (2 pts)
(c) Are figures ABCD and WXYZ similar? (1 pt)
Circle or highlight one:
Yes
45°
No
110
150
120%
Z
90% Y
40
Answer:
see the attachment photo!
1) A survey asked 200 Grade 4 students about their reading preferences. Based on Graph #1, about how many of them would you expect prefer comic books?
x
A. 10
B. 20
C. 60
D. 80
E. 100
help please
Answer:
First send the graph then we can help you in your answer
Answer:
D. 80
Step-by-step explanation:
The graph shows that about 3/8 ( 37.5% ) of the students enjoy comic books.
200 × .375 = 75
75 rounded to the nearest tens value is 80
For anyone wondering, the graph was on a different question that this person asked.
What is the value of the expression?
-16+12
Answer:12-16=-4
Step-by-step explanation:the answer is the same way it’s just flipped
the ratio of new airplanes to old air planes in a fleet of 720 planes of which 240 are old airplanes
Answer:2
Step-by-step explanation:(720-240)/(240)
Needs help no bots please
Directions: Solve each of the following problems. Round answers to the nearest hundredths when applicable.
1) If the height of a parallelogram is 27.3 m and the base is 6.3 m, what is the area of the parallelogram?
2) If the base of a rectangle is 27.4 mm and the area is 420.92 mm2, what is the height of the rectangle?
3) What is the height of a rectangle with perimeter 133.2 mm and base length 30.6 mm?
4) If the base of a parallelogram is 61 m and the area is 645 m2, what is the height of the parallelogram?
5) What is the perimeter of a parallelogram with base 32 cm and side length 34 cm?
6) What is the area of a parallelogram with base 40 mm and height 18 mm?
7) If the height of a rectangle is 8.8 m and the base is 7.9 m, what is the perimeter of the rectangle?
8) If the base of a rectangle is 23 cm and the area is 354 cm2, what is the height of the rectangle?
9) What is the area of a square with a perimeter of 44 mm?
10) What is the area of a square with a perimeter of 55 cm?
11) What is the area of a parallelogram with a height 43 m and base 18 m?
12) What is the perimeter of a parallelogram with side length 35 m and base 25 m?
13) If the base of a rectangle is 16 m and the area is 600 m2, what is the height of the rectangle?
14) What is the area of a rectangle with perimeter 125.6 cm and base length 40.5 cm?
15) If the height of a parallelogram is 64.3 m and the base is 4.3m, what is the area of the parallelogram?
Someone help me with this
Identify the angle of depression.
Answer:
4
Step-by-step explanation:
An angle of elevation is the angle formed by a horizontal line and a line of sight to a point above the line.
An angle of depression is the angle formed by a horizontal line and a line of sight to a point below the line.
∠3 is an angle of elevation because it is formed by the line of sight that is above the horizontal line.
∠4 is an angle of depression because it is formed by the line of sight that is below the horizontal line.
∠5 is neither an angle of depression nor an angle of elevation because it is not formed by the horizontal line and the line of sight.
∠6 is an angle of elevation because it is formed by the line of sight that is above the horizontal line.
Therefore, the angle of depression is ∠4.
please help me (show ur solution)
Answer:
See below ~
Step-by-step explanation:
Q9
x = 200° (arc measure = central angle measure)The inscribed angle y is half of the arc length xy = 1/2xy = 1/2(200°)y = 100°Q10
x + 112 = 180x = 68°y + 81 = 180y = 99°Answer:
9. x = 200 and y = 100
10. x = 68 and y = 99
Step-by-step explanation:
Question 9
The measure of an arc is the measure of its central angle.
⇒ x = 200
This is a non-cyclic quadrilateral as not all its vertices touch the circumference of the circle.
The angle at the center is twice the angle at the circumference.
⇒ y = 200 ÷ 2
⇒ y = 100
Question 10
This is a cyclic quadrilateral as all its vertices touch the circumference of the circle.
The opposite angles in a cyclic quadrilateral add up to 180°.
⇒ x + 112 = 180
⇒ x = 68
⇒ y + 81 = 180
⇒ y = 99
Can someone help me?
Answer:
It's the third one hun :>
Answer:
yup third one
Step-by-step explanation:
parabolas are ALWAYS a U shape ;-)
(2⁄3)3 the 3 is a exponent a answer would help but i would also like a step by step explanation so i can solve it on my own next time
Answer:
8/27
Step-by-step explanation:
So an exponent is basiclly when you multiply the number as many times as the exponent says. In this case it saying 3 so you would do 2/3*2/3*2/3 and then you would get 8/27. I hope this helps.
A cone and a cylinder have the same base and height, as shown below.
The volume of the cylinder is 84 rin.3 What can be concluded about the volume of the cone? Check all that apply.
1
The volume of the cone is the volume of the cylinder.
The volume of the cylinder is 2 times the volume of the cone.
The volume of the cone is less than the volume of the cylinder.
Answer:
The volume of the cone is less than the volume of the cylinder.
Step-by-step explanation:
what is 5 x 9/10 (fraction)
help me please asap