Which of the following must be true for an expression to be a difference of
two squares?
(((a. all variables are raised to an even power
b. there are only two terms
c. both terms have negative coefficients)))
Answers:
O A. a and
O B. a, b, and c
OC. b and
O D. a and b
Answer:
D
Step-by-step explanation:
A difference of squares is represented in general as
a² - b²
Both variables have an even power (2) → a
There are only two terms → b
how do you round the answer to the nearest hundredth by doing 1062.98 * 0.092
Answer:
97.79
Step-by-step explanation:
1062.98 * 0.092 = 97.79416
To the nearest hundredth would be to the second 9. Since 4 is less than 5 just drop the 4 and anything after it.
simplify the expresion 8w+5r-t+9r
To simplify an expression you need to combine like terms.
In the given equation, there are two like terms, 5r and 9r.
There is a plus sing in front of each one, so add those together: 5r + 9r = 14r
There are no ther like terms so the simplified expresssion becomes:
8w + 14r - t
A window is in the shape of a kite. Caleb wants to apply a layer of plastic film on the top half of the window so that the glass appears crackled. What are the dimensions of the layer of film he will apply?
9 inches in width and 7 inches in height
9 inches in width and 14 inches in height
18 inches in width and 7 inches in height
18 inches in width and 14 inches in height
Answer:
18 inches in width and 7 inches in height
Using kite, the dimensions of the layer of film the Caleb will apply is 18 inches in width and and 7 inches in height.
What is Kite?
A Kite is "quadrilateral with two distinct pairs of congruent consecutive sides".
What is relationship between kite and quadrilateral?If a kite is quadrilateral, then "its diagonal are perpendicular and exactly one diagonal each other".
According to the question,
A window is in the shape kite has an height of 14 inches and a width of 18 inches. Caleb wants to apply a layer of plastic film on the top half of the kite shape window. The window has dimensions of width 18 inches and 14 inches of height.
In order to the find new dimensions to apply a layer of plastic film on the top half of the kite shape window only if we divide the height by two then we get new dimensions on the top half of the kite shape window.
= [tex]\frac{14}{2}[/tex]
=7 inches
Hence, new dimensions to apply a layer of plastic film on the top half of the kite shape window is 18 inches in width and and 7 inches in height.
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Convert the mixed numbers into improper fractions. Convert the improper fraction to mixed Numbers.
Answer:
13. 23/4
14. 13/2
15. 6 and 1/2
16. 2 and 7/12
Answer:
13. 23/4
14. 13/2
15. [tex]6\frac{1}{2}[/tex]
16. [tex]2 \frac{7}{12}[/tex]
Step-by-step explanation:
13) 5×4=20
20+3=23
[tex]\frac{23}{4}[/tex]
14) 2×6=12
12+1=13
[tex]\frac{13}{2}[/tex]
15 an 16 divide
HELP ASAP
What is the area of triangle DEF?
A)294 square centimeters
B)490 square centimeters
C)588 square centimeters
D)735 square centimeters
Answer:
The correct answer will be "588 square centimeters"
Step-by-step explanation:
The answer would be 588 squared cm because the area of a triangle is 1/2(base*height).
and The base is 42 cm and the height is 28 cm.
588 square centimeters is the correct answer !
Answer:
C) 588
Step-by-step explanation:
A= 1/2 b*h
First you need to find the base and height
Which is 42 and 28
42*28=1176
1176/2= 588
the graph represents f(x)=[x]+3. what is f(-2.2)?
Answer:
f(-2.2) = 1
Step-by-step explanation:
There is a horizontal blue line with equation y = 1 between x = -3 and x = -2. Thus, f(-2.2) = 1.
Answer:
f(-2.2) = 1
Step-by-step explanation:
There is a horizontal blue line with equation y = 1 between x = -3 and x = -2. Thus, f(-2.2) = 1.
how do i solve this using elimination
Answer:
The value of x=6 and y=4.
Answer:
(6, 4 )
Step-by-step explanation:
Given the 2 equations
4x - 3y = 12 → (1)
x + 2y = 14 → (2)
Multiplying (2) by - 4 and adding to (1) will eliminate the y- term
- 4x - 8y = - 56 → (3)
Add (1) and (3) term by term
(4x - 4x) + (- 3y - 8y) = (12 - 56) ← simplify
- 11y = - 44 ( divide both sides by - 11 )
y = 4
Substitute y = 4 into either (1) or (2)
(2 ) : x + 8 = 14 ( subtract 8 from both sides )
x = 6
Solution is (6, 4 )
evaluate the expression xy for x = 6 and y = 3
Plug in values.
xy=
6(3) =
18 = Answer
I need to know this answer please!
Answer:
3*5=15
15 is your answer
ANSWER
15 square units.
EXPLANATION
Each box is 1 square units.
When we count the number of boxes we obtain 15 boxes.
This implies that the area of the rectangle is 15 square units.
Alternatively, we can observe that:
The rectangle is a 3 by 5 rectangle.
So the area is
[tex]3 \times 5 = 15 \: units \: square[/tex]
The rectangle is 15 units square.
15p!!what is the percent of change from 12 to 19? round to the nearest percent!
Answer:
58%
Step-by-step explanation:
The change between 12 to 19 is 7
The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%
7/12*100
=58.3333333%
=58%(rounded to nearest percent)
58% increase
Percent change = 19 - 1212 × 100 = 58.333333333333 % (increase) Where: 12 and 19 is the new value. In this case we have % of increase because the new value is greater than the old value.
What is percentage change?Percent change differs by the percent increase or percent decrease of the sense that we could see both directions of the change. For example, the percent increase calculator calculates amount of increase, in which we shall say, "x percent increase".
The change between 12 to 19 is 7
The percentage of change is calculated by dividing 7 by 12 and multiplying it by 100%
7/12*100
=58.3333333%
=58%(rounded to nearest percent)
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Lin took 75 boxes of carrots and 80 boxes of potatoes to the market. She sold 68 boxes of carrots and 71 boxes of potatoes. How many boxes of vegetable did she take home?
5. Write and solve the arithmetic problem for each step.
?
Answer the question below. Type your response in the space provided.
How many boxes of carrots are left?
How many boxes of Potatoes are left?
How many boxes altogehter are left?
Answer: 7 boxes of carrots, 9 boxes of potatoes, 18 boxes total
Step-by-step explanation:
75 -68=7 boxes of carrots
80-71=9 boxes of potatoes
For this case we have:
x: Represents the number of carrot boxes
y: Represents the number of boxes of potatoes
Initially we have:
[tex]x = 75\\y = 80[/tex]
If you sold 68 boxes of carrot we have:
[tex]x = 75-68 = 7[/tex]
If you sold 71 boxes of potatoes, we have:
[tex]y = 80-71 = 9[/tex]
The number of boxes I take home is given by:[tex]x + y = 7 + 9 = 16[/tex]
ANswer:
7 boxes of carrots left
There are 9 boxes of potatoes left
A total of 16 boxes remain
Find the distance between the given points.
R(0, 0) and S(6, 8)
Distance =
2√7
√(22)
10
Answer:
The correct answer is last option
10
Step-by-step explanation:
Points to remember
Distance formula
Length of a line segment with end points (x1, y1) and (x2, y2) is given by,
Distance = √[(x2 - x1)² + (y2 - y1)²]
To find the distance between given points
Here (x1, y1) = R(0, 0) and (x2, y2) = S(6, 8)
Distance, RS = √[(x2 - x1)² + (y2 - y1)²]
= √[(6 - 0)² + (8 - 0)²]
= √[6² + 8²]
= √[36 + 64]
= √100
= 10
Therefore the correct answer is last option 10
quadratic function (f)x=2x^2+8x-7
Answer:
See attached images
Step-by-step explanation:
The expression of your question is
f(x) = 2x^2+8x-7
A full analysis of the function is shown in the images below
Factor completely and then place the factors in the proper location on the grid a^2-a-20
Answer:
[tex](x-5)(x+4)[/tex]
Step-by-step explanation:
We have the following quadratic equation
[tex]a^2-a-20[/tex]
The factored expression will have the following form
[tex](x+b)(x+c)[/tex]
Where b and c are two real numbers which when added together result in -1, and multiplying them results in -20
[tex]b*c=-20\\b+c=-1[/tex]
You can verify that the numbers that meet this condition are:
-5 and 4
Then the factors are:
[tex](x-5)(x+4)[/tex]
Kathy runs 16 miles a week. If she continues to run at this rate how many miles will she run a year
Answer:
Remember, 1 is the multiplicative identity. That means that we can multiply a value by 1 and not change the value, only change the units.
For example: If we have 3 dozen eggs, how many eggs do we have?
3 dozen
(3 dozen)*(12 eggs / 1 dozen) = 36 eggs (dozen cancels out, leaving only eggs)
In this problem:
(16 miles / 1 week)
(16 miles / 1 week)*(52 weeks / 1 year) (weeks cancel out, leaving miles/year)
832 miles/year
Note: with either 365 (or 366) days in a year, there are 365/7 = 52.14 weeks in a year, but we'll use 52 because the problem gave miles/week.
Step-by-step explanation:
Find the coordinates of the focus and equation of the directrix for the parabola given by
y2 = −4x.
The general formula for this parabola is y2 = 4px.
Therefore, the value of p is _____
The coordinates of the focus are ______
The equation of the directrix is ______
Answer:
The answers to your three problem question are shown
1) the value of p is
p = -1
2) The coordinates of the focus are
Focus = (-1,0)
3) The equation of the directrix is
Directrix
x = 1
Step-by-step explanation:
The general equation for this parabola is
y^2 = 4px
Problem 1
Find the value of p.
We are told that the equation of the problem is
y^2 = -4x
And the general formula is
y^2 = 4px
From there, we can deduce that
p = -1, because
y^2 = 4(-1)x = -4x
This means that p = -1
Problem 2
Find the focus
To find the focus we can see the equations attached below for the focus, vertex and directrix.
In these case, the equations still apply, even though the variable is inverted, we just need to adjust it
y^2 = -4x =>
x = (-1/4)*y^2
x = a*y^2 + b*y +c
Focus
((4ac -b^2 + 1)/4a, -b/2a)
But, b = 0 and c = 0
=>
(1/4a,0) = (1/4(-1/4),0) = (-1,0)
Focus = (-1,0)
Problem 3
Find the directrix
The equation is
x = c - (b^2 + 1).4a
But, b = 0 and c = 0
x = -4*a
x = -4* (-1/4) = 1
x = 1
Directrix
x = 1
Answer: P is -1
Focus is (-1,0)
Directrix is X= 1
The slope of the line below is -2. Use the coordinates of the labeled point to
find a point-slope equation of the line.
•
4
-6)
Answer: y= -2x+2
Step-by-step explanation: y-y₁=m(x-x₁)
y-(-6)= -2(x-4)
y+6=-2x+8
y=-2x+8-6
y= -2x+2
Answer:
y + 6 = -2(x - 4)Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
We have the slope m = -2 and the point (4, -6). Substitute:
[tex]y-(-6)=-2(x-4)\\\\y+6=-2(x-4)[/tex]
A comedian knows eleven jokes. One joke is old, one joke is new, and the other jokes are somewhere between. If the order in which these jokes are told makes a difference in terms of how they are received, how many ways can they be delivered if the old joke is told first and the new joke is told last?
Answer: I believe nine
Step-by-step explanation: If one and 11 stay in the same place then it would start as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. then it would be 1, 10, 2, 3, 4, 5, 6, 7, 8, 9, 11. then 1, 9, 10, 2, 3, 4, 5, 6, 7, 8,11 and so one.
If
[tex]f(x) = \frac{(3 + x)}{x - 3} [/tex]
what is
[tex]f(a + 2)[/tex]
?
a)
[tex] \frac{3 + f(a + 2)}{f(a) - 1} [/tex]
b)
[tex] \frac{(5 + a)}{(a - 1)} [/tex]
c)
[tex] \frac{(3 + a)}{(a - 3)} + 2[/tex]
Answer:
Option B: [tex]\frac{5+a}{a-1}[/tex]
Step-by-step explanation:
Given function is:
[tex]f(x) = \frac{3+x}{x-3}[/tex]
In order to find f(a+2), we have to put a=2 in place of x in the function
So,
[tex]f(a+2) = \frac{3 + (a+2)}{(a+2)-3}\\ =\frac{3+a+2}{a+2-3}\\ = \frac{5+a}{a-1}[/tex]
Hence, we can see that option b is correct ..
Helppppp me immmm stuckkkkk
Answer:D
Step-by-step explanation: 4y-3x=4 -2x-8y=8
4(-.5)-3(-2)=4 -2(-2)-8(-.5)=8
Work this problem from here
4*-.5= -2
-3*-2=6
6+-2=4
so this is a true statement
-2*-2=4
-8*-.5=4
4+4= 8
so this statement is also true
The surface temperature averages at 15 degrees Celsius and increases 25 degrees Celsius with each kilometer of depth. Let one variable be the distance away from the surface and the other variable be the temperature. Now write an equation that models the relationship between the variables. I choose the variable, d for distance and t for temperature.
Answer:
15+25d=t
Step-by-step explanation:
the initial value is 15 it increases(+) by 25 to each kilometer(distance=d) of depth.
The equation that models the relationship between distance d in kilometers and temperature t in degrees Celsius is t = 25d + 15. This means that for each kilometer increase in depth, the temperature increases by 25 degrees Celsius in addition to the initial 15 degrees Celsius surface temperature.
Explanation:
The relationship between the variables, distance (d) and temperature (t), is described as a linear function. Given that the surface temperature is 15 degrees Celsius and it increases by 25 degrees Celsius with every kilometer, the mathematical model is expressed as:
t = 25d + 15
In this equation, t represents the temperature and d is the distance from the surface in kilometers. This implies that for every kilometer increase in depth, the temperature increases by 25 degrees Celsius on top of the initial 15 degrees Celsius surface temperature.
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The passing yards for the top 5 quarterbacks in the country are 3,832, 3,779, 3,655, 3,642, and 3,579. Find the variance and standard deviation. Round to the nearest hundredth.
(EXPLAIN WORK)
Answer:
variance = 8,732.24standar deviation = 93.45Explanation:
In order to calculate the variance and standard deviation of a set of data, you first must calculate the mean.
Mean = average = μ = ∑ values / (number of data)
Hence, the mean of our data set is:
mean = μ = [ 3,832 + 3,779 + 3,655 + 3,642 + 3,579] / 5 = 18,487 / 5 = 3,697.4Now you can calcuate the variance using the formula.
For a data set (which is all your population and not a sample) the formula is:
Variance = ∑ (value - μ)² / (number of data)That is:
Variance = [ (3,832 - 3,697.4)² + (3,779 - 3,697.4)² + (3,655 - 3,697.4)² + (3,642 - 3,697.4)² + (3,579 - 3,697.4)² ] / 5 Variance = 8,732.24 (rounded to the nearest hundreth)The standard deviation, S.D., is the square root of the variance:
[tex]S.D.=\sqrt{8,732.24}=93.45[/tex] (rounded to the nearest hundresth)Answer:
Variance = 8732.24 and standard deviation = 93.45
Step-by-step explanation:
We have to calculate the variance and standard deviation of the data set
3,832, 3,779, 3,655, 3,642, 3,579
First we calculate the mean of the data
Mean = [tex]\frac{(3,832+3,779+3,655+3,642+3,579)}{5}[/tex]
= [tex]\frac{18487}{5}[/tex]
= 3697.4
Now we calculate the variance by subtracting the mean from value of data set and square it.
3832 - 3697.4 = 134.6² = 18,117.16
3779 - 3697.4 = 81.6² = 6,658.56
3655 - 3697.4 = -42.4² = 1,797.76
3642 - 3697.4 = -55.4 = 3069.16
3579 - 3697.4 = -118.4 = 14,018.56
Add up the squared result and take the mean
= [tex]\frac{(18117.16+6658.56+1797.76+3069.16+14018.56)}{5}[/tex]
= [tex]\frac{43661.2}{5}[/tex]
Variance = 8732.24
To calculate standard deviation, we take the square root of the variance = [tex]\sqrt{8732.24}[/tex]
Standard deviation = 93.44645526 ≈ 93.45
Variance = 8732.24 and standard deviation = 93.45
(a) Find an angle between 0° and 360° that is coterminal with – 120°.
(b) Find an angle between 0 and 2π that is coterminal with 15π/4
Give exact values for your answers.
Answer:
a) [tex]240\degree[/tex]
b) [tex]\frac{15\pi}{4}[/tex]
Step-by-step explanation:
Coterminal angles have the same terminal sides in standard position.
a) To find an angle between [tex]0\degree[/tex] and [tex]360\degree[/tex], that is coterminal with [tex]-120\degree[/tex], we keep adding multiples of [tex]360\degree[/tex] until we get an angle within the specified range.
[tex]-120\degree \implies -120\degree +360\degree=240\degree[/tex].
In some cases you would have to subtract in order to get the specified angle. That is when the angle given is positive.
b) This time we want to find an that coterminal with [tex]\frac{15\pi}{4}[/tex] radians.
We keep subtracting multiples of [tex]2\pi[/tex] until we get an angle measure within the specified range.
[tex]\frac{15\pi}{4}=\frac{15\pi}{4}-2\pi=\frac{7\pi}{4}[/tex]
Dana kicks a soccer ball. The table shows the height of the soccer ball with respect to the time, in seconds, after the ball was kicked.
Time | Height
(Seconds) | (Feet)
~~~~~~~~~~~~~~~
0.5 21
1 34
1.5 39
2 36
2.5 25
3 6
Which Graph best displays the relationship shown in the table?
(i just need confirmation that its C)
Answer: It is!!!!!!!!
Answer:
The correct option is C.
Step-by-step explanation:
The standard form of a parabola is
[tex]y=ax^2+bx+c[/tex]
The table of values represents the coordinate pairs of the parabola. It means the graph of the parabola must be passes through these coordinate pairs.
From the given table it is clear that the parabola passes through the points (0.5,21), (1,34) and (1.5,39).
[tex]21=a(0.5)^2+b(0.5)+c[/tex]
[tex]21=0.25a+0.5b+c[/tex] .... (1)
[tex]34=a(1)^2+b(1)+c[/tex]
[tex]34=a+b+c[/tex] .... (2)
[tex]39=x(1.5)^2+y(1.5)+z[/tex]
[tex]39=2.15a+1.5b+c[/tex] .... (3)
On solving (1), (2) and (3), we get
[tex]a=-16, b=50,c=0[/tex]
The equation of parabola is
[tex]y=-16x^2+50x+0[/tex]
[tex]y=-16x^2+50x[/tex]
The graph of parabola is shown below. It is same as graph in option C.
Therefore the correct option is C.
If h(x)=4x^2-16 we’re shifted 7 units to the right and 3 units down what would the new equation be
Answer:
4(x-7)^2 - 19
Step-by-step explanation:
Shifting 7 units to the right: 4(x-7)^2 - 16.
3 units down: 4(x-7)^2 - 16 - 3, or 4(x-7)^2 - 19
Evaluate sin(arccos(-4/
[tex]evaluate \: sin(arccos( - \frac{4}{ \sqrt{25))[/tex]
Answer:
sin(arccos(-4/√25)) = 0.6
Step-by-step explanation:
The expression you want to evaluate is
sin(arccos(-4/√25))
= sin(arccos(-4/5))
We place this expression into a calculator and get the result
arccos(-4/5) = 2.498 rads = 143.1°
then
sin(143.1°) = 3/5
sin(143.1°) = 0.6
sin(arccos(-4/√25)) = 0.6
Plzzz HELP (3 QUESTIONS!!)
6) Which of the following numbers is written in standard notation for 1.31x10^-5?
a) 11,310
b) -11,310
c) .01131
d) .00001131
7) Select the expression written in scientific notation that is equivalent to 4.8 x 10^5-9.7 x 10^4.
a) -4.83x10^9
b) 480,000-97,000
c) 3.83x10^5
d) 0.000048 – 0.00097
8) Select the expression that is equivalent to (4 x 10^3)(5x10^7).
a) 4.5 x 10^3+7
b) (4+5) (10^3+10^7)
c) 4.5 x 10^3x7
d) ( 4 x 5) (10^3+10^7)
Answer:
6: d, 7: b and c, 8: a
Step-by-step explanation:
6) The answer is (d).
We have,
0.00001131 =1.131×0.00001
= 1.131/100000
= 1.131×10^-5.
So, this is correct answer.
7) This question have two answers (b) and (c), both are correct.
(b) 480000-97000
= 4.8x100000-9.7x10000
=4.8x10^5-9.7x10^4
(c) 4.8x10^5-9.7x10^4
= 4.8x10^5-0.97x10^5
= (4.8-0.97) x10^5
=3.83x10^5
8)(a)
(4 x 10^3)(5x10^7).
= 4x5x10³x10^7
= 4x5x10^(3+7).
What is the value of f(4)in the function below? F(x)=1/4•2^x
Answer:
f(4) = 4
Step-by-step explanation:
F(x)=1/4•2^x
Let x = 4
F(4)=1/4•2^4
= 1/4 * 2^4
= 1/4 *16
= 4
Answer: f(4) = 4
Step-by-step explanation:
f(x) = 1/4 . 2^x
To find f(4) we simply replace x by 4 in the above equation;
f(4) =1/4 . 2^4
f(4) = 1/4 . 16
f(4) = 16/4
f(4) = 4
Therefore f(4) is equal to 4
what is measure of cgf?
Answer:
[tex]<CGF = 130[/tex]
Step-by-step explanation:
A triangle adds up to 180.
180 - 50 = 130
Since both of the missing angles are congruent each of the missing angles is 65 degrees.
130/2 = 65
As per the exterior angle theorem, the measure of the exterior angle is determined by the sum of the opposite interior angles.
65 + 65 = 130
So, the measure of [tex]<CGF = 130[/tex]