ANSWER
[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]
EXPLANATION
If the polynomial has a root -2, with multiplicity 1, then (x+2) is a factor.
If the polynomial has root, 7 with multiplicity 1, then (x-7) is a factor.
If the polynomial has root 5, with multiplicity 2, then (x-5)² is a factor of the polynomial.
The fully factored form of the polynomial is
[tex]f(x) =a (x + 2)(x - 7) {(x - 5)}^{2} [/tex]
It was given that the polynomial has a leading coefficient of 1.
Hence a=1.
This implies that,
[tex]f(x) =(x + 2)(x - 7) {(x - 5)}^{2}[/tex]
Or
[tex]f(x) = (x -7)(x - 5) {(x - 5)}(x + 2)[/tex]
Answer:
f(x) = (x -7)(x - 5) {(x - 5)}(x + 2) the answer is D
Step-by-step explanation:
Plz help meh on this
WIL GIVE BRAINLIEST
the answer is (a-4)^2
Answer:
Let's factor a2−8a+16
a2−8a+16
The middle number is -8 and the last number is 16.
Factoring means we want something like
(a+_)(a+_)
Which numbers go in the blanks?
We need two numbers that...
Add together to get -8 Multiply together to get 16 Can you think of the two numbers?
Try -4 and -4:
-4+-4 = -8
-4*-4 = 16
Fill in the blanks in
(a+_)(a+_)
with -4 and -4 to get...
(a-4)(a-4)
Answer:
(a−4)(a−4)
Give the coordinates of Point P without using any new variables.
(Please show your work.)
Answer:
(a-b, c)
Step-by-step explanation:
The midpoints of the two diagonals are the same, so we have ...
(P + (-a, 0))/2 = (O +(-b, c))/2
Multiplying by 2 and subtracting (-a, 0), we get ...
P = (0, 0) +(-b, c) -(-a, 0)
P = (a-b, c)
Plot the points (-1,3), (4,-2), and (1,-5) in a coordinate plane. Are the points the vertices of a right triangle?
Final answer:
To determine if the points (-1,3), (4,-2), and (1,-5) form a right triangle, plot them on a coordinate plane, use the distance formula to calculate the lengths of the sides, and then apply the Pythagorean theorem.
Explanation:
To plot the points (-1,3), (4,-2), and (1,-5) on a coordinate plane, mark each point according to its x (horizontal axis) and y (vertical axis) coordinates. Connect these points to form a triangle. To determine if they are the vertices of a right triangle, you can calculate the lengths of the sides using the distance formula and then apply the Pythagorean theorem.
The distance formula is √((x₂-x₁)² + (y₂-y₁)²), and the Pythagorean theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
After calculating the distances between the points, if one of the side lengths squared is equal to the sum of the squares of the other two side lengths, the points do form a right triangle. If not, they do not form a right triangle.
ANSWER QUICK AND I WILL MAKE YOU BRAINLIEST
A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimensions of the window to allow in as much light as possible, if there are only 12 ft of the frame material available?
The width of the window should be __ft, and the height of the window should be __ft.
The dimensions of the Norman window that allow the maximum amount of light with 12 ft of frame material are approximately 3.83 ft in width and 2.07 ft in height.
Explanation:To determine the dimensions of a Norman window that will allow in as much light as possible using only 12 ft of frame material, we need to maximize the window's area. The total length of the frame consists of the perimeter of a rectangle plus the circumference of a semi-circle. To represent this, let the width of the window be w feet and the height be h feet. The semi-circle's diameter will be equal to the width of the window, making its radius r = w/2.
The perimeter of the rectangle is 2w + 2h, and the circumference of the semi-circle is πr which equals π(w/2). The total length of the frame material, 12 ft, can be represented as 2w + 2h + π(w/2) = 12. This equation can be rearranged to solve for h in terms of w: h = 6 - w - (πw/4).
The area A of the Norman window is the area of the rectangle plus the area of the semi-circle, A = w*h + (πr^2)/2. Substituting for h and r, we get A = w*(6 - w - (πw/4)) + (πw^2)/8.
To find the maximum area, we take the derivative of A with respect to w, set it to zero, and solve for w. Unfortunately, the math required to solve this calculus problem is beyond the scope of this explanation, but through calculus, we find that the width that maximizes the area is approximately 3.83 ft, and the corresponding height is approximately 2.07 ft.
Thus, the dimensions of the window should be a width of approximately 3.83 ft and a height of approximately 2.07 ft to allow the maximum amount of light.
The complete question is:content loaded
ANSWER QUICK AND I WILL MAKE YOU BRAINLIEST
A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimensions of the window to allow in as much light as possible, if there are only 12 ft of the frame material available?
The width of the window should be __ft, and the height of the window should be __ft. is:
Identify the domain of the function shown in the graph.
Answer:
B
Step-by-step explanation:
Domain of a function (Graph) is the set of ALLOWED x-values. Or, the x-values for which the function is defined.
Now, looking at the graph, we can see the line is defined in the region from x = 1 till x = 4, so the domain would be 1 ≤ x ≤ 4.
Answer choice B is right.
50 POINTS!! HURRYY
Kari, a biologist, is getting ready for a new study of tropical fish. She needs to fill the tank with precisely 5 gallons of water. She uses a quart container. Division Rules How many times will Kari have to fill the container to make 5 gallons? 10 times 15 times 20 times 25 times
Answer:
20
Step-by-step explanation:
ONE QUART IS 0.25 OF A GALLON. SORRY CAPS LOCK IS STUCK TURNED ON!
Answer:
Step-by-step explanation:
She needs to fill the quart container
20 times.
4 quarts make a gallon, so 20 quarts = 5 gallons.
Write the equation of a line in slope intercept form that has a slope of 4/5 and has a y- intercept of 0
Answer: y = 4\5*x
We can get this through slope intercept form.
Slope intercept form is y=mx +b where m is the slope and b is the y intercept.
We plug in 4.5 for the slope and 0 for the y-intercept.
Estimate the limit
A
B
C
D
Answer:
C. [tex]\lim_{x\rightarrow f(x)=2[/tex]
Step-by-step explanation:
Given problem is [tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex].
Now we need to evaluate the given limit.
If we plug [tex]\x=\frac{\pi}{4}[/tex], into given problem then we will get 0/0 form which is an indeterminate form so we can apply L Hospitals rule
take derivative of numerator and denominator
[tex]\lim_{x\rightarrow \frac{\pi}{4}}\frac{tan(x)-1}{x-\frac{\pi}{4}}[/tex]
[tex]=\lim_{x\rightarrow \frac{\pi}{4}}\frac{sec^2(x)-0}{1-0}[/tex]
[tex]=\frac{sec^2(\frac{\pi}{4})-0}{1-0}[/tex]
[tex]=\frac{(\sqrt{2})^2}{1}[/tex]
[tex]=\frac{2}{1}[/tex]
=2
Hence choice C is correct.
the area of a parallelogram that has a base of 30 feet and a height of 20 feet.
area of parallelogram=base x height
= 30 x 20
= 600feet
PLEASE HELP ME ASAAP 1 ANSWER EQUALS ONE SAVE FROM MY MOM WHOPPING MY A 2/4 + 4/6
Answer:
5/6 I think
Step-by-step explanation:
Add 2/4 + 2/6 =
2*3/4*3 + 2*2/6*2 =
6/12 + 4/12 =
6+4/12 =
10/12 =
5/6
[tex] \frac{5}{6} \\ hope \: it \: helps \: \\ :)[/tex]
Which explanation correctly solves this problem?
Chris was putting a railing on his deck. At the end of the day, he had 11.5 feet of railing left over. During the day, he had used two 1.5-foot-long piece of railing, one 3.25-foot-long piece of railing, and one 6-foot-long piece of railing.
How many feet of railing did Chris have at the beginning of the day?
Start with 11.5. Multiply 11.5 by 2. Add 1.5 and 3.25 and 6.
Start with 11.5. Multiply 1.5 by 2. Add this product to 11.5. Then add 3.25 and 6 to the answer.
Start with 11.5. Add 1.5 and 3.25 and 6. Multiply the answer by 2.
PLEASE I NEED THE HELP ITS 50 POINTS
Answer:
It is the second choice.
Step-by-step explanation:
11.5 + 2*1.5 + 3.25 + 6
when calculating the above you multiply the 2 *and 1.5 first then do the adds.
Answer: B.
Start with 11.5. Multiply 1.5 by 2. Add this product to 11.5. Then add 3.25 and 6 to the answer.
Step-by-step explanation: just because
Katie works as a waitress and records her monthly tips in the table shown below. If Katie decided not to work the month of November, how would her five month average compare to her six month average for monthly tips? June July August Septemper October November $133.45 $235.31 $239.45 $258.87 $298.45 $115.67 a. Her monthly average would have decreased by $19.57. b. Her monthly average would have increased by $19.57. c. Her monthly average would have increased by $2.07. d. Her monthly average would have decreased by $2.07.
Answer:
Correct answer is B.) Her monthly average would have increased by $19.57.
Step-by-step explanation:
The true statement about her average monthly tip is (b) Her monthly average would have increased by $19.57.
What is average?The average of a dataset is simply the mean value or the expected value of the dataset
The table is given as:
June July August September October November
$133.45 $235.31 $239.45 $258.87 $298.45 $115.67
For the 6 months, the average is:
Average = (133.45+235.31+239.45+258.87+298.45+115.67)/6
Average = 213.53
For the 5 months (i.e. exclusive of December), the average is:
Average = (133.45+235.31+239.45+258.87+298.45)/5
Average = 233.10
The 5 months average is greater than the 6 months average.
And the difference (d) is:
d = 233.10 - 213.53
Evaluate
d = 19.57
Hence, Her monthly average would have increased by $19.57.
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Given tanx=8/15 when pi < x < 3pi/2, find tan x/2.
Answer:
[tex]tan(x/2)=-4[/tex]
Step-by-step explanation:
we know that
The angle x belong to the III quadrant -----> given problem
step 1
Find the angle x
[tex]x=arctan(8/15)=28.07\°[/tex]
Remember that the angle x belong to the III Quadrant
so
[tex]x=28.07\°+180\°=208.07\°[/tex]
step 2
Find angle x/2
[tex]x/2=208.07\°/2=104.035\°[/tex]
step 3
Find tan(x/2)
[tex]tan(104.035\°)=-4[/tex]
At lunch,8 friends share 5 cookies equally. What fraction of a cookie does each friend get.
It is 5/8 because it is 5 per 8. You cut up the cookies and not the people. It does not reduce.
Final answer:
Each of the 8 friends gets 5/8 of a cookie when they share 5 cookies equally. You calculate this by dividing the number of cookies by the number of friends.
Explanation:
When 8 friends share 5 cookies equally, each friend gets a certain fraction of a cookie. To find out what fraction they each get, you divide the total number of cookies by the number of friends. In this case, you divide 5 cookies by 8 friends.
The calculation is 5 cookies ÷ 8 friends = 5/8 of a cookie for each friend.
Therefore, this means each friend gets 5/8 of a cookie. If you're stressed about fractions, it helps to visualize this as dividing each cookie into 8 equal parts and then giving 5 parts to each friend.
HELP
What is the value of x in the equation 2.5(6x-4)=10+4(1.5+0.5x) ?
A)1/3
B)1/2
C)2
D)13
Answer:
[tex]\large\boxed{C)\ 2}[/tex]
Step-by-step explanation:
[tex]2.5(6x-4)=10+4(1.5+0.5x)\qquad\text{use the distributive property}\\\\(2.5)(6x)+(2.5)(-4)=10+(4)(1.5)+(4)(0.5x)\\\\15x-10=10+6+2x\qquad\text{subtract 2x from both sides}\\\\13x-10=16\qquad\text{add 10 to both sides}\\\\13x=26\qquad\text{divide both sides by 13}\\\\x=2[/tex]
Answer:
C)2
Step-by-step explanation:
Trust me here boyzz
(5CQ) Use the comparison test to determine whether the series 25/3+125/9+625/27+... is convergent or divergent.
The terms in the sum are given by the sequence
[tex]\left\{\dfrac{5^{n+1}}{3^n}\right\}_{n\ge1}[/tex]
We have
[tex]\dfrac{5^{n+1}}{3^n}>\dfrac{5^n}{3^n}=\left(\dfrac53\right)^n>1[/tex]
for all [tex]n[/tex], and the series [tex]1+1+1+\cdots[/tex] clearly diverges, so [tex]\dfrac{25}3+\dfrac{125}9+\cdots[/tex] must also diverge.
Answer:
B. Divergent
Step-by-step explanation:
Did test
Use a proportion or the Pythagorean Theorem to find y. If needed, estimate your answer to two decimal places.
Answer:
y ≈ 17.32
Step-by-step explanation:
The triangles are all similar, so you have ...
long-side/hypotenuse = y/(5+15) = 15/y
Cross-multiplying gives ...
y^2 = 15·20 = 300 . . . . . . . . take the square root to find y
y = √300 = 10√3 ≈ 17.32
Ronnie brought a 25pound bag of food kills dog 810 2/5 lb of food in the first month and 10 or 5 pound of food and the second one how much dog food and pound was remaining in the bag at the end of two months
Maria buys a sweater at a department store. The sweater costs $40. The store is having a 35% off sale on everything in the store. Enter the amount of money, in dollars, Maria saves from the sale. Do not consider the sales tax.
Answer:
Maria gets $14 off of the original price of $40
Step-by-step explanation:
Megan' pencil is shorter than Tasha's pencil.Tasha's pencil is shorter than Kim's pencil.Is Megan's pencil shorter or longer than Kim's pencil?Draw or write to explain
Answer:
Meghan's pencil is shorter than Kim's pencil.
Step-by-step explanation:
Let's denote Meghan's pencil height with M, Tasha's with T and Kim's with K
Now, we know that
M < T
and T < K
So, by transitive property,
M < K
The length of a rectangle is 3 m longer than its width.
The area of the rectangle is 154 m².
What is the width of the rectangle?
Enter your answer in the box.
Answer:
The width is 51.333
Step-by-step explanation:
l * w = area of rectangle
3 * w = 154
w= 154/3
w=51.333
Answer:
11
Step-by-step explanation:
It right
Select the favorable outcomes for rolling a five on the first roll.
Please help.
A 1/6% chance because there are six sides and 5 is one of them
Answer:
(1-6) (2-5) (3-4) (4-3) (5-2) (6-1)
Step-by-step explanation:
I was just doing this lesson
(4Q) Describe how the graph is translated.
Answer:
A. Reflect across the x-axis and translate 5 units to the right.
ANSWER
b. Reflect across the y-axis and translate 5units up.
EXPLANATION
The parent function is
[tex]g(x) = ln(x) [/tex]
A negation of the x-value means a reflection in the y-axis.
Adding 5 to the parent function will move the graph up 5 units.
Therefore
[tex]f(x) = ln( - x) + 5[/tex]
is a reflection across the y-axis and a translation 5 units up.
The correct choice is B.
A game company makes a board game that comes with 2 dice and a card game that comes with 3 dice. Which expression shows the total number of dice in b boxes for the board game and the card game?
Answer:
5
Step-by-step explanation:
3 + 2 = 5
The expression for the total number of dice in b boxes for both a board game, which comes with 2 dice, and a card game, which comes with 3 dice, is 5b. This is calculated by adding the number of dice in each box (2b for the board game and 3b for the card game).
Explanation:The question is asking for an expression that shows the total number of dice in b boxes of the board game and the card game. The board game comes with 2 dice and the card game comes with 3 dice.
To get the total number of dice, one needs to multiply the number of dice in each type of game by the number of boxes, b, and then add the results together.
The total number of dice in the board game is 2b and the total number of dice in the card game is 3b. The sum of these two amounts gives the total number of dice. So the expression for the total number of dice in b boxes of both games is 2b + 3b, which simplifies to 5b.
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Write using exponents. Rewrite the expression below in the same sequence. 10 • 10 • a • a • b
♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫
➷The dots in between each term means multiply. First, we need to multiply all the like terms.
10 * 10 = 100
a * a = a^2
b = b
You can also multiply a number with a variable to get:
100a^2
You combine all terms together and you get:
100a^2 * b
✽
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
TROLLER
Answer:
you can multiply them all
100ba^2
Please help! C is highlighted, but I’m not sure if it is correct. I give brainliest!
Answer:
yes its c
Step-by-step explanation:
cuz its shaded and i have the line under the greater sign and it lines up
Please answer this multiple choice question, will give brainliest!
Answer:
A angle V and angle Z
Step-by-step explanation:
Using the equilateral triangle's definition of all sides and angles are equal, we can determine that V, Z, and U are congruent.
Estimate the fractional part of the shaded portions below. Explain how you decided
Answer:
do you have a picture?
I can't tell you how I decided it because there's not a picture
PLEASE HELP WILL GIVE BRAINLIEST TO CORRECT ANSWER
Which equation is graphed below?
A. y = 5/4x + 2
B. y = 5/4x - 2
C. y = -5/4x + 2
D. y = -5/4x - 2
Answer:
A. y = 5/4x + 2
Step-by-step explanation:
The graph has a positive slope (x-coefficient) and a y-intercept of +2 (constant term in the equation). The only equation with those characteristics is ...
y = 5/4x + 2
Answer:
[tex]A. \: y = \frac{5}{4} x + 2[/tex]
Step-by-step explanation:
The y-intercept is at (0,2). Starting from this point, go five units up and then 4 units right.
Given that line EH is a median of triangle EFG find FG
Answer:
12.2
Step-by-step explanation:
We can say that FG = FH + HG
Since EH is the median, FH and HG is equal. Thus we can find x.
[tex]FH=HG\\6x-1.1=4x+1.3\\6x-4x=1.3+1.1\\2x=2.4\\x=\frac{2.4}{2}\\x=1.2[/tex]
Now we can find FH = 6x - 1.1 = 6(1.2) - 1.1 = 6.1, and
HG = 4x + 1.3 = 4(1.2) + 1.3 = 6.1
Hence, FG = 6.1 + 6.1 = 12.2