Answer:
x²+2xy-x+y²-y-12
Step-by-step explanation:
(x+y+3)(x+y-4)
= x(x+y-4)+y(x+y-4)+3(x+y-4)
= x²+xy-4x+xy+y²-4y+3x+3y-12
= x²+2xy-x+y²-y-12
The answer is:
The simplified expression is:
[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Why?To solve the problem, we need to remember how to use the distributive property and how to add like terms.
The distributive property can be defined as follow:
[tex](a+b)(c+d)=ab+ad+bc+bd[/tex]
The like terms are the terms that share the same variable and the same exponent, for example:
[tex]3x+x+ x^{2}=x^{2} +4x[/tex]
We were able to add the first and the second term because they share the same variable and the same exponent.
Now, we are given the expression:
[tex](x+y+3)(x+y-4)[/tex]
So, simplifying we have:
[tex](x + y + 3)(x + y - 4)=(x*x)+(x*y)-(4*x)+(y*x)+(y*y)-(4*y)+(3*x)+(3*y)-(3*4)\\\\(x + y + 3)(x + y - 4)=x^{2} +xy-4x+xy+y^{2}-4y+3x+3y-12\\\\(x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Hence, we have that the simplified expression is:
[tex](x + y + 3)(x + y - 4)=x^{2} +y^{2} +2xy-x-y-12[/tex]
Have a nice day!
(04.01 LC)
Which of the tables represents a function
Answer:
Table 2
For every input, there is one output.
Why table 1 is not a function:
The input 5 has two outputs, 3 and 2
Why table 3 is not a function:
The input 1 has two outputs, 2 and 3
Why table 4 is not a function:
The input 4 has three outputs, 2, 3, and 4
Hope this helps!
Which is the better buy?
A. 1,323 ounces of topsoil for $410.13
B. 8 pounds of topsoil for $78.08
Answer:
Option. A
Step-by-step explanation:
Covert Ounces to Pounds, or vice versa, I went with pounds.
1323 ounces = 82 pounds.
find the pound to dollar rate
A; 82 ÷ 410.13 = about 5
B; 8 ÷ 78.08 = 9.76
The better buy is A. 1,323 ounces of topsoil for $410.13.
To determine which is the better buy, we need to calculate the price per ounce for both options and then compare them.
First, let's calculate the price per ounce for option A:
1,323 ounces of topsoil for $410.13.
Price per ounce for A = $410.13 / 1,323 ounces.
Now, let's calculate the price per ounce for option B:
Since 1 pound is equal to 16 ounces, 8 pounds of topsoil is equal to
8 × 16 = 128 ounces.
8 pounds of topsoil for $78.08.
Price per ounce for B = $78.08 / 128 ounces.
Next, we compare the price per ounce for both options:
Price per ounce for A = $410.13 / 1,323 ounces $0.310 / ounce.
Price per ounce for B = $78.08 / 128 ounces $0.609 / ounce.
Since the price per ounce for option A ($0.310) is less than the price per ounce for option B ($0.609), option A is the better buy. The customer gets more topsoil for their money with option A.
What is the best next step in the construction of the perpendicular bisector of
AB?
O
A. It is not possible to bisect AB with this construction.
O
B. Use a compass to draw a circle using the lower intersection of the
circles as the center point.
C. Use a straightedge to draw a line segment that connects the
vertices of the two equilateral triangles that coincide with the
intersections of the circles.
O
D. Use a compass to draw a circle using the upper intersection of the
circles as the center point.
The best next step in the construction of the perpendicular bisector of AB is C. Use a straightedge to draw a line segment that connects the vertices of the two equilateral triangles that coincide with the intersections of the circles.
What is Perpendicular Bisector?Perpendicular bisector is defined as the perpendicular line which bisects another line or an angle.
Given a line AB.
There are also two intersecting circles and two equilateral triangles joining the line AB with the intersecting points.
We have to draw a perpendicular bisector to AB.
We can draw perpendicular bisector by connecting the intersecting points of the circles.
Hence the correct option is C.
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Final answer:
To construct the perpendicular bisector of AB, connect the intersections of the circles drawn from A and B with the same radius using a straightedge.
Explanation:
The student has asked what the best next step is in the construction of the perpendicular bisector of a line segment AB. The correct answer is C, which states that you should use a straightedge to draw a line segment that connects the intersections of the circles. This will create the perpendicular bisector of AB. The process involves drawing two circles with the same radius from points A and B, such that each circle goes through the other point, and then connecting the two points where the circles intersect with a straight line. This line will be the perpendicular bisector because it will be perpendicular to AB and divide it into two equal parts, hence bisecting AB.
the length of a varies string varies inversely as the frequency of its vibrations. A violin string 10 inches long vibrates at a frequency of 512 cycles per second. Find the frequency of an 8-inch string.
Answer:
10(512) = 5,120
8f = 5,120
f = 640 cycles per second
Jenna uses the Fermi process to estimate the number of stickers it would take to cover her bedroom floor. Both her stickers and her floor are rectangular in shape. . She estimates her stickers to be about 2 in. long and 1 in. wide . She estimates her bedroom floor to be about 20 ft long and 10 ft wide Which expression should Jenna use in the process?
Answer:
3x10^4/2x10^0
Step-by-step explanation:
just took the test!!
The expression that Jenna should use in the process is area of floor/area of sticker
How to find the surface area of a figureThe surface area is defined as the sum of area of the faces.
Area of rectangle = lengh * width
Determine the area of the rectangular sticker
The area of the rectagular sticker = 2in * 1in
The area of the rectagular sticker = 2 square inches
Determine the area of the bedroom floor
Area of the floor = 20ft * 10ft
Area of the floor = 200 square feet = 28800 square in
Determine the number of stickers needed
Number of stickers needed = area of floor/area of sticker
Number of stickers needed = 28800/2
Number of stickers needed = 14400 stickers
The expression that Jenna should use in the process is area of floor/area of sticker
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Linear function A and linear function B both have the same input values as shown below. Why will the output values for linear function A always be different than the corresponding output values for linear function B? The initial values of the two functions are different, and the rates of change of the two functions are also different. The initial values of the two functions are different, and the rates of change of the two functions are the same. The initial values of the two functions are the same, and the rates of change of the two functions are different. The initial values of the two functions are the same, and the rates of change of the two functions are also the same.
Answer:The initial values of the two functions are different, and the rates of change of the two functions are the same.
Step-by-step explanation:
The values will start out different. When you apply the rate of change, because they have the same rate of change, you don't risk them coming out with the same value if the values ended up being just right, they will always remain different.
The differences in the output values for linear function A and function B are a result of varying y-intercepts and slopes in each function. When plotted on a graph, these differences become apparent.
Explanation:The output values for linear function A and function B will differ because of variations in their respective initial values (or y-intercepts) and their rates of change (or slopes). When you plot these output values against the shared input values as a graph of y as a function of x, these differences can be seen visually. For instance, consider the linear equation y = mx + b, where m represents the slope of the line and b is the y-intercept. If function A and B have different y-intercepts or slopes, the output values will differ for the same set of input values.
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Helppppppppppppppppppppp!
Answer:
±(√35 i)
Step-by-step explanation:
[tex]\pm\sqrt{-35}[/tex]
We need to solve the above equation using the imaginary unit i.
We know i= √-1
Solving
±√-35 =±( √-1 √35)
= ±(√35 i)Since 35 = 5*7 or 35*1 it cannot be further simplified
So our answer is ±(√35 i).
20,21,23,23,25,29,32,33 -What is the outliner
Answer:
There is not an outlier
Step-by-step explanation:
All the numbers are close together and do not have a big difference from each other
The outlier in the given series of numbers (20, 21, 23, 23, 25, 29, 32, 33) is the number 20, as it deviates significantly from the rest of the data points.
Explanation:In the series given (20, 21, 23, 23, 25, 29, 32, 33), the term that appears to be an outlier is the number 20. An outlier in a number series is a number that is significantly different from the other numbers in that series. It deviates significantly from the rest of the data points. Most of the numbers in the series are in the twenties or thirties, but 20 is distinctly less than the rest. Therefore, in the given number series, 20 is the outlier.
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Write V64 - V-289 as a complex number in the form of a + bi.
A.8+17i
B. 17 + 8i
C. 8-17i
D.-17 - 8i
The correct answer is C. 8 - 17i
What are complex numbers?Complex numbers are numbers that consist of two parts — a real number and an imaginary number.
How to write the given expression in the form of a +ib?
√64 - √-289
= 8 - √-289
= 8 - 17i ( since (17i)² gives -289)
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Carlos graphs the equations y=-1/2 x^2+4 and and y=-1/2 x^2-2x+2 generates the graph below. Which conclusion is supported by the graph?
Answer: The answer is B the second option. I just took the test.
Step-by-step explanation:
Answer:
2nd Option is correct.
Step-by-step explanation:
Given Functions:
[tex]y=\frac{-1}{2}x^2+4[/tex]
[tex]y=\frac{-1}{2}x^2-2x+2[/tex]
We need to find which conclusion supported by graph.
From the given, it is clear that both graph intersecting only at one point.
Also, One graph is translation of another graph.
So, the equation [tex]\frac{-1}{2}x^2+4=\frac{-1}{2}x^2-2x+2[/tex] has only one solution.
Therefore, 2nd Option is correct.
If prism A and Prism B have a ratio of similarity of 2:3, what is the volume of prism A if Prism B's volume is 56 cubic inches
Answer:
16.6 in³
Step-by-step explanation:
Given the ratio of similarity = 2 : 3, then
the ratio of volumes = 2³ : 3³ = 8 : 27
let the volume of prism A be x then by proportion
[tex]\frac{x}{8}[/tex] = [tex]\frac{56}{27}[/tex] ( cross- multiply )
27x = 448 ( divide both sides by 27 )
x = 448 ÷ 27 ≈ 16.6 ( to 1 dec. place )
Prism A has a volume of approx 16.6 in³
Anna wants to put a fence around a rectangular garden plot that measures 9 feet by
18 feet. She wants to place posts at the corners of the plot and every 2 feet around
the perimeter of the plot. How many posts does she need?
The answer is:
Anna will need 27 posts.
Why?To calculate how many post does she need to place at the corners and every 2 feet around, we need to calculate the perimeter of the garden plot.
So, we can calculate the perimeter of the garden plot (rectangle) using the following formula:
[tex]Perimeter=2height+2width[/tex]
We know that:
[tex]height=9ft\\width=18ft[/tex]
Then, calculating the perimeter of the garden plot, we have:
[tex]Perimeter=2height+2width[/tex]
[tex]Perimeter=2*9ft+2*18ft=18ft+36ft=54ft[/tex]
Now, calculating how many post she will need, we have:
[tex]No.Post=\frac{Perimeter}{DistanceBetweenPost}\\\\\frac{54feet}{2feet}=27posts[/tex]
Hence, we have that Anna will need 27 posts.
Solve the quadratic equation by factoring 9x2+24+20=4
Answer:
Final answer is [tex]x=-\frac{4}{3}[/tex] and [tex]x=-\frac{4}{3}[/tex].
Step-by-step explanation:
Given equation is [tex]9x^2+24x+20=4[/tex].
Now we need to solve that by factoring.
[tex]9x^2+24x+20=4[/tex]
[tex]9x^2+24x+20-4=0[/tex]
[tex]9x^2+24x+16=0[/tex]
[tex]9x^2+12x+12x+16=0[/tex]
[tex]3x(3x+4)+4(3x+4)=0[/tex]
[tex](3x+4)(3x+4)=0[/tex]
[tex](3x+4)=0[/tex], [tex](3x+4)=0[/tex]
[tex]3x+4=0[/tex], [tex]3x+4=0[/tex]
[tex]3x=-4[/tex], [tex]3x=-4[/tex]
[tex]x=-\frac{4}{3}[/tex], [tex]x=-\frac{4}{3}[/tex]
Hence final answer is [tex]x=-\frac{4}{3}[/tex] and [tex]x=-\frac{4}{3}[/tex].
In the diagram, lines r and s are parallel to each other and perpendicular to transversal line t. Line w is a transversal to lines r and s. Use properties of special angles, formed by parallel lines, perpendicular lines and their transversals, to describe the relationship between the angles. Choose all of the situations that correctly describe the relationship between the angles. Note: Figure is not drawn to scale
s || r ; s ⊥ t ; r ⊥ t
line w is a transversal
same side interior angles
alternate interior angles
equal angles
alternate exterior angles
supplementary angles
right angles
corresponding angles
vertical angles
The angles do not share a special relationship.
Answer:
equal angles and vertical angles
Step-by-step explanation:
we know that
Vertical Angles are the angles opposite each other when two lines cross. They are always equal
In this problem
∠14=∠16 -----> by vertical angles
therefore
The answer is
equal angles and vertical angles
Answer:
Vertical angles, equal angles
Step-by-step explanation:
when a transversal passes through two lines, then,
Angles formed in the same side and inside the two lines are same side interior angles.
Angles that are formed on opposite sides of the transversal and inside the two lines are alternate interior angles.
Angles formed on opposite sides of the transversal and outside the two lines are alternate exterior angles.
Angles with the same relative position at each intersection are corresponding angles,
While, when two lines intersect each other then the opposite angles formed called vertical angles,
supplementary angles : When the sum of two angles are 180°,
Right angles : angle that has the measurement of 90°,
Equal angles : angles with the same measurement.
Now, vertical angles are always equal angles,
Also, when two parallel lines are cut by the same transversal then the pair of alternate interior angles, alternate exterior angles, corresponding angles are always equal.
Hence, by above definitions it is clear that,
∠16 and ∠14 are vertical and equal angles.
PLEASE CAN SOMEONE HELP FAST BEG U
SIMULTANEOUS EQUATION
P/2 + Q/3 =6
P/3 + Q/3 =0
Answer:
{Q = -(3 P)/2, Q = -6 P}
Step-by
-step explanation:
Round 378,903.97 to the nearest thousand
Answer:
Step-by-step explanation:
378,903,970.
Hudson picked 1 1/4 baskets of apples.Suzy picked 2 baskets of apples. How many more baskets of apples did Suzy pick than Hudson?
Answer: 3/4
Step-by-step explanation:
1 1/4 = 4/4 + 1/4 = 5/4
2 = 8/4
8/4 - 5/4 = 3/4
A 4-foot piece of aluminum wire costs $6.72. What is the price per inch?
Answer:
the answer is 14 cents
Step-by-step explanation:
12 time 4 equal 48 ( this is converting the feet into inches)
48 divided by 6.72 to get 0.14
Answer:
$0.14
Step-by-step explanation:
There are 12 inch in 1 foot.
You are given 4 foot. Find the amount of inch in 4 feet.
1 ft x 12 in/ft = 12 in
4 ft x 12 in/ft = 48 in
There are 48 in. in 4 ft. Divide 48 from $6.72
(6.72)/48 = $0.14
$0.14 is the price per inch.
~
Round 66681 to the nearest ten thousand
Answer:
66,681 rounded to the nearest ten-thousand would be equal to 70,000.
Step-by-step explanation:
any time the number is higher than 5 you round up but if not you round down! i hope this helps!
70,000
When you round you find whatever your rounding, like for this your rounding to the nearest ten thousand, heres a random one thats simple:
89,000 rounded to nearest ten thousand.
If its its higher than 5 then you round up, if its 4 or lower you round down.
so for 89,000 its 90,000.
But for u answer its 70,000 :3
Yw, goodbye hooman who exists
The price of cable service changed from
$35.00 per month to $42.00 per month.
What was the percent of increase?
A. 5%
B. 7%
C. 17%
D. 20%
Answer:
D. 20%
Step-by-step explanation:
percent change = (new number - old number)/(old number) * 100%
The new number is the increased price, $42, and the old number is the original price, $35.
percent change = ($42 - $35)/($35) * 100%
percent change = ($7)/($35 min) * 100%
percent change = 0.20 * 100%
percent change = 20%
Since the percent change is a positive number, it is a percent increase.
The percent increase was 20%.
Answer: D. 20%
1/2x= 3/(x+5)
What is the value of x that makes the statement true
Answer:
.5x = 3x + 15
-2.5 x = 15
x = -6
Step-by-step explanation:
50.
Belinda has 10 cups of flour. She uses 3 cups of it to make a loaf of bread.
She uses 1/4 cup of the remaining flour for each biscuit she wants to make. How
many biscuits can she make with the remaining flour?
Answer:
28 biscuits.
Step-by-step explanation:
Belinda has 10 cups of flour
She uses 3 cups to make a loaf of bread
She uses [tex]\frac{1}{4}[/tex] cup of the remaining flour for each biscuit she wants to make.
There are 10 - 3 = 7 cups of flour remaining
[tex]\frac{1}{4}[/tex] cup of flour makes -> 1 biscuit
7 cups of flour will make;
7 × 1 ÷ [tex]\frac{1}{4}[/tex] = 7 × 4 = 28 biscuits
PLESE HELP ASAP!!!! Worth 15 point plz help!!
Answer:
The last expression is correct
Step-by-step explanation:
We have been given the following expression for simplification;
[tex]4^{4}*4^{-9}[/tex]
The bases of the two expressions are the same. They are both equal to 4. When multiplying numbers with the same base, we simply add their exponents. In this case our exponents are;
4 and -9
adding them we have;
4 + (-9) = -5
The simplified expression thus becomes;
[tex]4^{-5}=\frac{1}{4^{5}}[/tex]
A rectangle has an area of 40,if the length and width are doubled. What is the new area ?
Answer:
160
Step-by-step explanation:
e.g. 5×8 --> 10×16 =160
4×10 --> 8×20 =160
2×20 --> 4×40 =160
160
When you double both the length and width, you are multiplying by 2 twice. Whatever you do to one side of an equation, you have to repeat on the other.
l * w = 40; This is the original equation.
2l * 2w = 40 * 2 * 2; This is when you double the length and the width.
The 2 * 2 on the end can be simplified.
2l * 2w = 40 * 4
Now, simplify 40 * 4.
2l * 2w = 160
So, when you double both the length and the width, you multiply the area by 4, making the area 160.
what is $630,000 divide by 24
$26,250. 630,000 ÷ 24 =26250
Answer: 630,000 / 24= 26250
If you were, for example, to divide $630,000 evenly between you and 24 of your coworkers, you'd each get $26,250.
Hope this helps,
LaciaMelodii :)
Classify the following triangle as acute, obtuse, or right.
Answer:
A. Obtuse
F. Scalene
Step-by-step explanation:
There are two ways to classify a triangle:
by angles:
Obtuse - has one angle that is greater than 90°
Right - has one angle that is 90°
Acute - has all angles less than 90°
and by side lengths:
Equilateral - all sides are equal
Isosceles - two sides are equal
Scalene - no sides are equal
In this triangle, there is an obtuse angle (A. Obtuse).
∡ = 132°, which is greater than 90°.
There are no equal sides (F. Scalene).
6 ≠ 7 ≠ 11.9
What is the measure of the missing angle
The sum of the angles of any quadrilateral is 360 degrees. This means that you can make a formula like the one bellow and solve for x:
72 + 107 + x + 91 = 360
270 + x = 360
(270 - 270) + x = 360 - 270
x = 90
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
x = 90°
Step-by-step explanation:
Angles in a quadrilateral add up to 360°
We are given the following angles : 107°, 72° and 91°
Wee need to find x so,
x + 107° + 72° + 91° = 360°
( Simplify )
x + 270° = 360°
( Minus 270° from both sides to isolate x )
x = 90°
Find the graph of the inequality y>-1/6x+1
what we do is, we simply draw the graph for its EQUALITY counterpart, namely [tex]\bf y=-\cfrac{1}{6}x+1[/tex].
then we check the regions on both sides of the graph, in this case we can check say the point (0,0) for simplicity, and
[tex]\bf y>-\cfrac{1}{6}x+1\qquad (0,0)~~ \begin{cases} x=0\\ y=0 \end{cases}\implies 0>-\cfrac{1}{6}(0)+1\implies 0>1[/tex]
now, is 0 > 1? is 0 really greater than 1? nope, is smaller, thus the area where the point (0, 0) is at is the false region, so that's the area we do NOT shade, thus the other region must be the true region and that's the one we shade.
the ">" sign means, that "y" is greater than, NOT equals to but greater, thus the values at the borderline are not included, and thus is a dashed line.
Check the picture below.
Can Someone Help me with my Algabra 2 Homework 4a-c
Answer:
Step-by-step explanation:
Sigma notation is:
n
∑ ak
k=1
The n on top is the number of terms. ak is the expression for the kth term.
Let's look at the first one. The series is:
-2+4+-8+...+64+-128
There's two things to notice. One, the sign changes back and forth between + and -. Two, the magnitude doubles with each next term. Therefore:
ak = (-2)ᵏ
Next we need to find the number of terms. -128 is the last term, so:
128 = 2ⁿ
n = 7
So the answer is:
7
∑ (-2)^k
k=1
Now the second one. Notice the numerators are all 1 and the denominators are all perfect squares. Therefore:
ak = (1/k)²
The last term is 1/100, so n = 10.
So the answer is:
10
∑ (1/k)²
k=1
Now the last one. Notice that each term is 5 plus the previous term. This is an arithmetic series. So we can say:
ak = 4 + 5(k-1)
ak = 4 + 5k - 5
ak = 5k - 1
The last term is 49, so:
49 = 5n - 1
n = 10
So the answer is:
10
∑ (5n-1)
k=1
Which of the following could be the graph of this equation?
Answer: OPTION C.
Step-by-step explanation:
Given a function f(x), the range of the inverse of f(x) will be the domain of the function f(x) and the range of the domain of f(x) will be the range of the inverse function.
For example, if the point (2,1) belongs to f(x), then the point (1,2) belongs to the inverse of f(x).
Observe that in the graph of the function f(x) the point (-3,1) belongs to the function, then the point (1,-3) must belong to the inverse function.
Therefore, you need to search the option that shown the graph wich contains the point (1,-3).
Observe that the Domain f(x) is (-∞,0) then the range of the inverse function must be (-∞,0).
This is the graph of the option C.
Answer:
C
Step-by-step explanation: