Answer:
1) The polynomial [tex]8x^3+1[/tex] represents a sum of cubes
2) The polynomial [tex]49x^2-25[/tex] represents a difference of squares
Step-by-step explanation:
1) To find the polynomials represents a sum of cubes :
[tex]8x^3+1[/tex] represents a sum of cubes
For [tex]8x^3+1[/tex]
[tex]=2^3x^3+1^3[/tex]
[tex]=(2x)^3+1^3[/tex]
Therefore [tex]8x^3+1=(2x)^3+1^3[/tex]
Therefore [tex]8x^3+1[/tex] represents a sum of cubes
2)To find the polynomials represents a difference of squares :
[tex]49x^2-25[/tex] represents a difference of squares
For [tex]49x^2-25[/tex]
[tex]=7^2x^2-5^2[/tex]
[tex]=(7x)^2-5^2[/tex]
Therefore [tex]49x^2-25=(7x)^2-5^2[/tex]
Therefore [tex]49x^2-25[/tex] represents a difference of squares
What’s 186 rounded to the nearest hundred
Answer:
200
Step-by-step explanation:
50 or more round up
49 and down you round to the last whole hundred or number
hope this helped please mark brainliest and rate
What is the following sum?
4 sq root 5+2 sq root 5
will mark brainliest
Answer:
6 sq root 5
Step-by-step explanation:
Answer:
6sqrt(5)
Step-by-step explanation:
Both of these expressions are a number times the square root of 5. By definition, we can simply add the coefficients as these are like terms.
A bakery sells 25rolls for every 35 loaves of bread. At this rate, how many will be sold for every 7 rolls of bread?
At the same rate, the bakery would sell approximately 10 loaves of bread for every 7 rolls.
The bakery sells 25 rolls for every 35 loaves of bread. To find out how many loaves of bread will be sold for every 7 rolls of bread, we need to use a simple proportion based on the given ratio. This can be set up as a fraction, 25 rolls/35 loaves = 7 rolls/x loaves, where x represents the number of loaves sold for every 7 rolls.
We can solve for x by cross-multiplying:
(25 rolls/35 loaves) = (7 rolls/x loaves),
so 25x = 35*7.
The next step is to divide both sides of the equation by 25 to solve for x:
x = (35*7)/25 = 9.8 loaves.
Therefore, the bakery would sell approximately 10 loaves of bread for every 7 rolls, given the same rate.
Find the semiannual payment for a 20 year endowpayment policy with face of $25,000 if the annual premium is $22.24 per $1,000
Answer:
$278
Step-by-step explanation:
There is an endowpayment policy with face of $25,000 with the annual premium $22.24 per $1000.
So, the annual premium of the endowpayment policy with face of $25,000 will be equal to [tex]\frac{25000}{1000}\times 22.24 = 556[/tex] dollars.
And the semi annual payment for this policy will be [tex]\frac{556}{2} = 278[/tex] dollars. (Answer)
PLEASE HELP AND FAST
Which expressions are polynomials?
Select each correct answer.
6x2 + 5x
-x^2+52
-7x^2+5/3x
X^2+5x^1/5
Yo sup??
6x^2+5x is a polynomial
-x^2+52 is also a polynomial
-7x^2+5/3x is not a polynomial as power of x is negative
x^2+5x^1/5 is not a polynomial as power of x is fraction
Hope this helps.
Which expressions are equivalent to the one below? Check all that apply.
log 2 - log 8
Answer:
[tex]\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=-\log 4[/tex]
Step-by-step explanation:
[tex]\log 2-\log 8=\log\frac{2}{8}\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=\log\frac{1}{4}\\\\\log 2-\log 8=\log 1-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \log\frac{a}{b}=\log a-\log b\\\\\log 2-\log 8=-\log 4\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \log 1=0[/tex]
Answer:
log(1/4)
log(2) + log (1/8)
Patricia annual Salary was 52,000. She earned a 6% raise what is her new salary
See picture for solution to your problem.
The function f(x) = g(x), where f(x) = 2x - 5 and g(x) = x2 - 6.
The table below shows the process of solving using successive approximations
NO
--5
-6
T -3
-5
1
-2
13
0
0.25
NE
Continue this process to find the positive solution to the nearest tenth.
Answer:
The positive solution to the nearest tenth is (2.4, - 0.2).Explanation:
I will rewrite the table to understand how the process of solving using succesive approximations is.
Table:
x f(x) g(x)
0 - 5 - 6
1 - 3 - 5
2 - 1 - 2
3 1 3
Those are the points shown in the table.
Now you must continue the process of solving using successive approximations until you find the positive solution to the nearest tenth.
You need to determine whether a "guess" is closer or farther away of the solution.
The first row shows that g(x) is less than f(x) in 1 unit when x = 0 ( -6 - (-5) ) = -1.
The second raw shows that g(x) is less than g(x) in 2 units when x = 1 ( - 5 - (-3) ) = - 2
The third row shows that g(x) is is less than f(x) in 1 unit when x = 2 ( - 2 - (-1) ) = - 1.
The fourth row shows that g(x) is than f(x) in 2 units when x = 3 ( 3 - 1 = 2).
Hence, the trend changed form negative to positive, meaning that, since the functions are continous, there must be an intertemediate value of x (between x = 2 and x = 3) for which f(x) = g(x) and that is the solution.
Therefore, test x = 2.5
f(x) = 2x - 5 = 2(2.5) - 5 = 0g(x) = x² - 6 = (2.5)² - 6 = 0.25g(x) - f(x) = 0.25 Thus the difference is bigger than one tenth (0.1)Test for x = 2.4
f(2.4) = 2(2.4) - 5 = - 0.2g(2.4) = 2.4² - 6 = -0.24g(2.4) - f(2.4) = - 0.24 - (0.2) = -0.04Now the difference is less than 0.1 and the solution to the nearest tenth is (2.4, - 0.2).
Answer:
answer is 2.7
Step-by-step explanation:
I got it right
a border to surround a picture is to be cut from an 11 1/2 in. by 11 1/2 in. mat board. if the picture is 8 3/4 in. by 8 3/4 in., what is the width of the border?
Answer:
Step-by-step explanation:
y (y-4) – (y-2) (y-3)=10
Answer:
y =16
I have solved it . It's in the picture above. Hope it helps
quadrilateral PQRS is a square whos side length is 10. Let X and Y be points outside the square so that XQ = YS = 6 and XP = YR = 8. Find XY^2.
Answer:
392
Step-by-step explanation:
You want the value of the square of the length XY, given X and Y are outside and symmetrically opposite the center of a 10-unit square and each is 6 units and 8 units from the two nearest vertices.
LocationThe attached drawing shows the positions of points X and Y. Each is 4.8 units horizontally and 3.6 units vertically from the nearest vertex of the square. That means their locations relative to each other are ...
horizontally: 2×4.8 +10 = 19.6 units
vertically: 6.4 -3.6 = 2.8 units
DistanceThe square of the distance between X and Y will be given by the Pythagorean theorem:
XY² = 19.6² +2.8² = 384.16 +7.84
XY² = 392
__
Additional comment
The locations of X and Y relative to the side of the square can be found using the "geometric mean" relations for a right triangle. Triangle QXP has side lengths 6, 8, 10, which are a multiple of the well-known {3, 4, 5} right triangle. So ∆QXP is a right triangle with a right angle at X.
The length QX is the geometric mean √(QA·QP), so we have ...
6 = √(10·QA)
36 = 10·QA
QA = 3.6 ⇒ PA = 6.4
and
XA = √(QA·PA) = √(3.6·6.4)
XA = 4.8
The value of [tex]\( XY^2 \)[/tex] is 100.
Let's begin by visualizing the problem. We have a square PQRS with side length 10. Points X and Y are outside the square such that XQ = YS = 6 and XP = YR = 8. We need to find the square of the distance between X and Y, denoted as [tex]\( XY^2 \)[/tex].
To solve this, we can use the Pythagorean theorem. Let's consider triangle XPQ. Since PQRS is a square, angle PQX is a right angle. Therefore, triangle XPQ is a right-angled triangle with PQ as the hypotenuse and XQ and XP as the other two sides.
Using the Pythagorean theorem for triangle XPQ, we have:
[tex]\[ 8^2 = 6^2 + XQ^2 \][/tex]
[tex]\[ 64 = 36 + XQ^2 \][/tex]
[tex]\[ XQ^2 = 64 - 36 \][/tex]
[tex]\[ XQ^2 = 28 \][/tex]
Now, we have found the square of the distance XQ, which is [tex]\( 28 \)[/tex].
Similarly, for triangle YRQ, which is also a right-angled triangle with YR as one leg and YS as the other leg, and RQ as the hypotenuse, we can write:
[tex]\[ 8^2 = 6^2 + RQ^2 \][/tex]
[tex]\[ 64 = 36 + RQ^2 \][/tex]
[tex]\[ RQ^2 = 64 - 36 \][/tex]
[tex]\[ RQ^2 = 28 \][/tex]
We have found that [tex]\( RQ^2 = 28 \)[/tex], which is the same as [tex]\( XQ^2 \)[/tex].
Now, to find [tex]\( XY^2 \)[/tex], we need to consider the distance between points X and Y. Since X and Y are outside the square and their distances to the square are equal (XQ = YS and XP = YR), the line segment XY is parallel to side PQ of the square and is also equal to the side length of the square, which is 10.
Therefore, [tex]\( XY^2 \)[/tex] is simply the square of the side length of the square PQRS:
[tex]\[ XY^2 = PQ^2 \][/tex]
[tex]\[ XY^2 = 10^2 \][/tex]
[tex]\[ XY^2 = 100 \][/tex]
What is the solution to the equation 2 (4 minus 3 x) + 5 (2 x minus 3) = 20 minus 5 x?
x = 3
Step-by-step explanation:
First we would simplify the left hand side of the equation by expanding the brackets
so 2(4-3x) = 8-6x and
5(2x-3) = 10x-15
This gives the left hand side as 8-6x+10x-15. So the overall equation becomes
8-6x+10x-15 = 20-5x.
Grouping the unknown values on one side and integers on one side of the equation gives us
8-15-20=6x-10x-5x (note the sign changes when numbers and unknown values are moved to the other side of the = sign
Solving further, -27 = -9x i.e x = -27/-9 = 3
Hence x = 3
Answer:
3
Step-by-step explanation:
plz help i need helppppppp
Answer:
1) 36
b) 5
c) 3.0
Step-by-step explanation:
1) The recursive formula that defines the given sequence is
[tex]a_1=12 \\ a_n=a_{n-1}+4.[/tex]
That means we keep adding 4 to the subsequent terms:
The sequence will be:
12,16,20,24,28,32,36,...
Therefore the seventh term is 36.
2) The sequence is recursively defined by;
[tex]a_1=20\\ a_n=a_{n-1} - 5[/tex]
This means, we have to keep subtracting 5 from the subsequent terms.
The sequence will be;
20,15,10,5,...
Therefore the fourth term is 5
3) The sequence is recursively defined by:
f(n+1)=f(n)+0.5
where f(1)=-1.5
This means that, the subsequent terms can be found by adding 0.5 to the previous terms.
The sequence will be:
-1.5,-1.0,-0.5,0,0.5,1,1.5,2.0,2.5,3.0,....
Therefore f(10)=3.0
75% of a number is 230. Solve.
Work is attached in the image provided.
6. Calculate the distance Tarryn drives if she
drives 7/8mile each way to and from work,
5 days a week.
Answer:
not that hard sir
Step-by-step explanation:
do 7/8 x 5
Final answer:
Tarryn drives a total of 8.75 miles in a week to and from work, with each one-way trip being 7/8 mile and she works 5 days a week.
Explanation:
Calculating Total Distance Driven
Tarryn drives to and from work 5 days a week, with each trip being 7/8 mile. To calculate the total distance she drives in a week, we need to consider both the trip to work and the return trip. This will give us the daily round trip distance, which we will then multiply by the number of days she works in a week.
First, we calculate the daily round trip distance:
Round trip distance = Distance to work + Distance from work
Round trip distance = 7/8 mile + 7/8 mile
Round trip distance = 7/4 miles (or 1.75 miles)
Then, we calculate the total distance for the week:
Total weekly distance = Daily round trip distance × Number of workdays
Total weekly distance = 7/4 miles × 5 days
Total weekly distance = 35/4 miles (or 8.75 miles)
Therefore, Tarryn drives a total of 8.75 miles over the course of a 5-day workweek.
The sum of eight times a number and negative four exceeds twelve.
8x + -4 > 12
8x > 16
x > 2
Hope this helps! ;)
Answer:8x + -4 > 12
8x > 16
x > 2
Step-by-step explanation:
Equivalent fractions of 8/12
Answer:
Step-by-step explanation:
Simple multiply both 8 and 12 by any number and then equivalent
Answer:
3/4 or 16/24 or 2/3
Step-by-step explanation:
A line is graphed in the xy-plane shown at left. Which of the following is an equation of the line?
A line is graphed in the x-y plane and it will follow a path of straight line and equation for that is, Y = (-3/2)X.
So option (C) is correct.
What is the equation of line?The equation of a straight line is a relationship between x and y coordinates, The equation of a straight line is y = mx + c, where m is the slope of the line and c is the y-intercept.
The net change in y coordinate is written as, Δy and the net change in x coordinate is written as, Δx.
m = change in y coordinate/change in x coordinate = Δy/Δx = y2-y1/x2-x1
In given graph,
Line is passing through the points (2, -3) & (-2 ,3)
Slope = -3-3/2-(-2)
Slope = -3/2
y = (-3/2) x + c ____(i)
by putting point (2, -3) in equation (i)
-3 = (-3/2) 2 + c
c = 0
Hence, The equation is Y = (-3/2)X
To know more about the equation of line check:
https://brainly.com/question/2564656
#SPJ2
simply the expression.
Using the negative exponent rule move x^-2 to the numerator
Answer = 5x^2/y^5
Does 133/9 equals seven
Answer:
No; 14.7777777 or 14.78
Step-by-step explanation:
133 divided by 9 = 14.7777777
this rounds to 14.78
Hope this helped! :)
Answer:
no it does not it is 14.777777778
At 10:00a.m ,pharaoh leaves his office traveling by car to deliver a book to Valerie. He stopped to eat lunch for two hours , and then returned directly to his office , arriving at 2:00pm. If Pharaohs rate going was 60mph and the rate returning was 20 mph, how far is it from pharaohs office to Valerie’s?
30 m
Step-by-step explanation:
Step 1 :
Let x be the distance traveled.
Speed taken while going is given as 60mph.
Hence time taken for the onward journey =x/60
Speed for the return journey is 20mph
Hence time for the return journey is x/20
Step 2:
Total time is from 10 m to 2 pm. Deducting the 2 hours taken for lunch, time spent for the onward and return journey is 2 hrs
=> X/60 + x/20 = 2.
Solving for x we get x = 30
Hence the distance between the office and Valerie's is 30 m
Recipe calls dor 1 3/4 cups of cheese. Only need to make 2/3 of recipe. How much cheese should be used?
[tex]1\frac{1}{6}[/tex] cups of cheese should be used for [tex]\frac{2}{3}[/tex] of the recipe.
Step-by-step explanation:
Given,
Quantity of cheese used in recipe = [tex]1\frac{3}{4}\ cups = \frac{7}{4}\ cups[/tex]
Recipe to made = [tex]\frac{2}{3}[/tex]
Quantity to use in [tex]\frac{2}{3}[/tex] of recipe = [tex]\frac{2}{3}\ of\ quantity\ required\ for\ full\ recipe[/tex]
Quantity to use = [tex]\frac{2}{3}*\frac{7}{4}[/tex]
Quantity to use = [tex]\frac{7}{6} = 1\frac{1}{6}\ cups[/tex]
[tex]1\frac{1}{6}[/tex] cups of cheese should be used for [tex]\frac{2}{3}[/tex] of the recipe.
Keywords: fraction, multiplication
Learn more about fractions at:
brainly.com/question/10989800brainly.com/question/10990024#LearnwithBrainly
The figure shown is made up of 16 equally sized squares. Four of the squares are shaded and 12 are not.
What is the probability that a randomly chosen point on the grid is in the shaded area? Give your answer as a fraction in simplest form.
Answer: 1/4
Step-by-step explanation:
Answer:
1/4
Step-by-step explanation:
i had the same question and 1/4 was right
a checking account earns 2.5% simple interest.how much would be earned by an account with $3,400 in after 3 years
Answer:
Step-by-step explanation:
$3,400*2.5%*3=$255
To calculate the simple interest on $3,400 at a 2.5% interest rate over 3 years, the formula I = P imes r imes t is used, which results in $255 of interest earned in that period.
To calculate the simple interest earned by a checking account with $3,400 at a 2.5% annual interest rate over 3 years, we use the formula for simple interest:
I = P times r times t
where:
I is the interest earnedP is the principal amount (initial amount of money)r is the annual interest rate (as a decimal)t is the time the money is invested or borrowed for, in yearsLet's plug in the values:
I = $3,400 times 0.025 times 3
I = $85 times 3
I = $255
So, the account will earn $255 in simple interest over 3 years.
NEED ANSWERS PLEASE!!
A tee box is 64 feet above its fairway. When a golf ball is hit from the tee box with an initial vertical velocity of 48 ft/s, the quadratic equation 0= -16t^2 + 48t + 64 gives the time, t, in seconds when a golf ball is at height 0 feet on the fairway.
A) Solve the quadratic equation by factoring to see how long the ball is in the air.
B) What is the height of the ball at 1.5 seconds?
C) Is the ball at its maximum height at 1.5 seconds? Explain.
(A) 4 sec the ball is in the air.
(B) Height of the ball = 49 ft.
(C) Yes, the ball is at its maximum height at 1.5 seconds.
Solution:
Given data:
[tex]h(t)=-16t^2+48t+64[/tex]
Initial velocity = 48 ft/s
Height = 64 ft
(A) [tex]-16t^2+48t+64=0[/tex]
a = –16, b = 48, c = 64
We can solve it by using a quadratic formula,
[tex]$\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{(48)^{2}-4 \times(-16)(64)}}{2(-16)}[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{2304+4096}}{-32}[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm \sqrt{6400}}{-32}[/tex]
[tex]$\Rightarrow t=\frac{-48 \pm 80}{-32}[/tex]
[tex]$\Rightarrow t=\frac{-48 + 80}{-32},\frac{-48 - 80}{-32}[/tex]
[tex]$\Rightarrow t=-1,t=4[/tex]
Time cannot be in negative. So neglect t = –1
t = 4 sec
Hence, 4 sec the ball is in the air.
(B) When t = 1.5 sec,
[tex]h(1.5)=-16(1.5)^2+48(1.5)+64[/tex]
h(1.5) = 49 ft
(C) The maximum height occurs at the average of zeros.
Average = [tex]\frac{(-1+4)}{2}=1.5[/tex] sec
Yes, the ball is at its maximum height at 1.5 seconds.
Screenshot will be posted
Answer:
Part 1) [tex]z=121^o[/tex]
Part 2) [tex]x=59^o[/tex]
Part 3) [tex]y=49^o[/tex]
Part 4) [tex]w=72^o[/tex]
Step-by-step explanation:
step 1
Find the measure of angle z
we know that
The sum of exterior angles in a polygon is always equal to 360 degrees
so
[tex]z^o+(z+10)^o+(z-13)^o=360^o[/tex]
solve for z
[tex](3z-3)^o=360^o[/tex]
[tex]3z=363\\z=121^o[/tex]
step 2
Find the measure of angle x
we know that
[tex]z^o+x^o=180^o[/tex] ---> by supplementary angles (form a linear pair)
we have
[tex]z=121^o[/tex]
substitute
[tex]121^o+x^o=180^o[/tex]
[tex]x=180^o-121^o=59^o[/tex]
step 3
Find the measure of angle y
we know that
[tex]y^o+(z+10)^o=180^o[/tex] ---> by supplementary angles (form a linear pair)
we have
[tex]z=121^o[/tex]
substitute
[tex]y^o+(121+10)^o=180^o[/tex]
[tex]y=180^o-131^o=49^o[/tex]
step 4
Find the measure of angle w
we know that
[tex]w^o+(z-13)^o=180^o[/tex] ---> by supplementary angles (form a linear pair)
we have
[tex]z=121^o[/tex]
substitute
[tex]w^o+(121-13)^o=180^o[/tex]
[tex]w=180^o-108^o=72^o[/tex]
What is the equation of the line that passes through the point (-4, -8) and haves a slope of 4
Answer:
y=4x+8
Step-by-step explanation:
y-y1=m(x-x1)
y-(-8)=4(x-(-4))
y+8=4(x+4)
y=4x+16-8
y=4x+8
HURRY
Figure ABCDF is transformed according to the rule R0, 270
What are the coordinates of B?
(-2,3)
(3.-2)
(2-3)
(-3.2)
Answer:
3,-2
Step-by-step explanation:
Answer:
ITS (-3,2)
Step-by-step explanation:
What is the value of x?
Enter your answer in the box.
Answer: X = 27
Step-by-step explanation: The diagram shows two triangles with one triangle cut out from the other. A careful observation would reveal triangle BDR and triangle QDC.
Since line QC is parallel to line BR, that makes triangle QDC similar to triangle BDR. Also the ratio of lines QD and BQ is the same as the ratio of lines CD and RD. The same applies to lines QC and BR.
Therefore,
QD/BQ = CD/RC
Alternatively we can use the ratios,
QD/BD = CD/RD
Using the first ratios, we have
QD/BQ = CD/RC
39/26 = X/18
3/2 = X/18 {the left hand side has been reduced to it's simplest form}
If we cross multiply, we now arrive at
3 × 18 = 2X
54 = 2X
Divide both sides of the equation by 2
27 = X
Lucy's age is a.
Jacob is eight year older than Lucy.
Half of Jayne's age is the same as Jacob's age.
How old is Jayne?
Answer:
a+8 x 2
Step-by-step explanation:
Lucy= a
Jacob= 8 + a
½ Jayne= Jacob or Jayne= 2 Jacob
½ Jayne= 8 + a
Jayne= (8+a)2
= 16 + 2a