Answer:
remainder = 2
Step-by-step explanation:
A polynomial f(x) is divided by (x - a) then the remainder is f(a)
Here f(x) = 4x³ - 5x² + 2x - 14 is divided by (x - 2) then remainder is f(2)
f(2) = 4(2)³ - 5(2)² + 2(2) - 14
= 4(8) - 5(4) + 4 - 14
= 32 - 20 - 10
= 12 - 10
= 2
What is the factorization of 49b2 − 81?
Step-by-step explanation:
The factorisation of 49b^2 - 81 is (7b - 9)(7b + 9). This is because 49 and 81 are the squares of 7 and 9 respectively, so these must be multiplied together. b^2 is b x b. Finally, it must be -9 and +9 to make -81, because when the signs are the same the result is a positive number
Answer:
(7b - 9)(7b + 9)
Step-by-step explanation:
49b2 - 81
49 - 7 x 7
b2 - b x b
81 - 9 x 9
(a + b) (a - b) = a2 - b2
(7b - 9)(7b + 9)
PLEASE HELPPPPPP FINDING CIRCUMFERENCE AND AREA OF A CIRCLE
Answer:
The circumference of the circle is 28.26 m.
The area of the circle is 63.585 [tex]m^{2}[/tex].
Step-by-step explanation:
To solve for the circumference of the circle, start by using the circumference formula of a circle, which is [tex]C= 2\pi r[/tex]. However, 3.14 will be used instead of [tex](\pi)[/tex] for this formula.
First, the radius of the circle needs to be found. To find the radius of the circle, divide the diameter by 2 because the radius equals half of the diameter. The radius is 9 m divided by 2, which equals 4.5 m.
Next, plug in the radius into the formula, and the formula will look like [tex]C=(2)(\pi )(4.5 m)[/tex]. Then, solve the equation, and the answer will be 28.26 m.
To solve for the area of the circle, start by using the area formula of a circle, which is [tex]A=\pi r^{2}[/tex]. However, 3.14 will be used instead of [tex](\pi)[/tex] for this formula.
For the area, plug the radius into the formula, and the formula will look like [tex]A= (3.14)(4.5m)^{2}[/tex]. Then, solve the equation, and the answer will be 63.585 [tex]m^{2}[/tex].
The area of a trapezoid is represented by the expression 12x2 + 7x – 10. The other dimensions are shown in the diagram below. Determine an expression for the height of the trapezoid.
Answer:
(24x^2 + 14x – 20) /(3x+5) = h
Step-by-step explanation:
The area of a trapezoid is given by
A =1/2 (b1+b2) h
12x^2 + 7x – 10 = 1/2 ( x+3+ 3x+2)h
Multiply each side by 2
24x^2 + 14x – 20 = ( x+3+ 3x+2)h
Combine like terms
24x^2 + 14x – 20 = ( 4x+5)h
Divide each side by (4x+5)
(24x^2 + 14x – 20) /(4x+5) = ( 4x+5)h/(4x+5)
(24x^2 + 14x – 20) /(4x+5) = h
Whats the measure of
Answer:
C. 80°
Step-by-step explanation:
Recall: SOH CAH TOA
Reference Angle = J
Opposite = 60
Adjacent = 11
Hypotenuse = 61
Apply trigonometric function, SOH, which is:
Sin J = Opp/Hyp
Sin J = 60/61
[tex] J = sin^{-}(\frac{60}{61}) [/tex]
J = 79.6111422°
J = 80° (nearest degree)
Marie made lasagna for dinner. She ate 1/6 of it, Morris ate 1/3 of it, and Larry ate 1/4 of it. How much of the lasagna was left?
Answer:
1/12 of the lasagna was left
Step-by-step explanation:
To find out how much of the lasagna has been eaten, you have to find the least common denominator (LCD) for the three fractions. The LCD of 1/3, 1/4, and 1/6 is 12 (3x4x6). Now convert all the fractions so that all of their denominators is equal to 72 (1/3=4/12, 1/4=3/12, 1/6=2/12), then add all of the fractions together (4/12 + 3/12 +2/12 = 3/4). 3/4 of the lasagna has been eaten and the remaining lasagna is 1/12 (1-3/4=4/4-3/4).
Answer:
[tex]\frac{1}{4}[/tex] of the lasagna
Step-by-step explanation:
[tex]\frac{1}{4} +\frac{1}{6}+ \frac{1}{3}[/tex]
4 = 2 × 2
3 = 3
6 = 2 × 3
LCM = 2 × 2 × 3
LCM = 12
4 × 3 × 6 = 72
[tex]\frac{18}{72} +\frac{12}{72}+ \frac{24}{72}[/tex]
[tex]\frac{18+12+24}{72}[/tex]
[tex]\frac{54}{72}[/tex]
54 = 2 × 3 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
GCF = 2 × 3 × 3
GCF = 18
[tex]\frac{\frac{54}{18} }{\frac{72}{18} }=\frac{3}{4}[/tex]
[tex]1-\frac{3}{4}[/tex]
[tex]\frac{4}{4} -\frac{3}{4}[/tex]
[tex]\frac{4}{4} -\frac{3}{4}=\frac{1}{4}[/tex]
What is the solution to the equation fraction 1 over 4 x = 5? (5 points) x = fraction 4 over 5 x = fraction 5 over 4 x = 20 x = 1
Answer:
your question was barely readable, but I'll try it anyways. hope it helps you to understand the concept.
[tex] \frac{1}{4} x = 5[/tex]
multiply each side of the equation by 4
[tex]x = 20[/tex]
sorry, the test really doesn't make much sense as a question. try to photograph the problem if possible. but take care not to photograph personal information
If one candy bar weighs 3 ounces, what is the weight of 11 candy bare
Answer: 3 times 11 would be 33 ounces.
Step-by-step explanation:
33 is the answer.
A small auditorium has 20 seats in the first row and each successive row contains 2
additional seats. If there are 12 rows in the auditorium, how many seats are in this
auditorium?
O 384
O 372
O 330
O 264
Answer:
330.
Step-by-step explanation:
Count all the way up. The first row is 20, then goes, 22,24,26,28,30,32,34,36,38,40. These are the number of seats for all 12 rows, since we added 2 each row. Add them all together including 20 to get 330 seats. The whole auditorium has 330 seats.
Hope this helps!
As per arithmetic Progression, there are 372 seats in the given auditorium.
What is an arithmetic progression?"Arithmetic Progression is a sequence of numbers in order, in which the difference between any two consecutive numbers is a constant value."
Given, the auditorium has 20 seats in the first row.
Then, each successive row contains 2.
We can assume it as an arithmetic progression.
Here, the first term(a) is 20.
The common difference(d) is 2.
Total number of terms(n) is 12.
Therefore, the sum of all the terms is
[tex]= \frac{n}{2}[2a + (n-1)d]\\= \frac{12}{2}[2(20) + (12-1)2]\\= 6[40+(11)2)]\\= 6(40+22)\\= 6(62)\\= 372[/tex]
Learn more about an arithmetic progression here: https://brainly.com/question/20733446
#SPJ2
Can someone help me please?
Step-by-step explanation:
Given that,
No. of heads = 40
No. of tails = 60
We know that,
Probability = (no. of favourable outcomes)/(total no. of outcomes)
Experimental probability of getting heads,
no. of favourable outcomes = 40
Total no. of outcomes = 40+60 = 100
So,
[tex]P=\dfrac{40}{100}[/tex]
She has taken 60 on denominator. She should have taken 100 instead of 60.
HELP WILL GIVE BRAINLIEST SHOW WORK LOOK AT IMAGE
Answer:
Step-by-step explanation:
What are the names of the segments in the figure
Answer:
C. The three segments are segments AB, CA, and AC
Find the equation of the line that passes through points A and B.
Answer:
y = 2x + 5
Step-by-step explanation:
Step 1 : Find slope:
[tex]slope , m = \frac{y_B - y_A}{x_B - x_A}[/tex]
[tex]=\frac{-1 - 7}{-3-1} \\\\= \frac{-8}{-4}\\\\ = 2[/tex]
Step 2 : Find the equation of the line :
[tex](y - y_A) = m(x - x_A) \ or \ (y - y_B) = m(x - x_B)\\\\we \ will \ consider \ points \ of \ A :\\\\[/tex]
[tex](y - 7) = 2(x -1)\\\\y - 7 = 2x - 2\\\\y = 2x - 2 + 7\\\\y = 2x + 5[/tex]
The graph of f(x) = x^2+ 3 is translated to produce the graph
of g(x) = (x + 2)^2+ 3. In which direction was the graph of f
translated?
left
right
up
down
Answer:
the graph of f(x) is translated 2 units to the LEFT
Step-by-step explanation:
The original function, f(x) = x^2 + 3, has its vertex at (0, 3). If we translate the graph h units to the right, this function becomes g(x) = (x - h)^2 + 3. The x-coordinate of the vertex appears h units to the right of the original vertex.
In this case g(x) = (x + 2)^2 + 3, which tells us that h = -2. The effect of inserting the "-2" is that the graph of f(x) is translated 2 units to the LEFT.
If, on the other hand, we went from f(x) = x^2 + 3 to g(x) = (x - 2)^2 + 3, the original graph would be translated 2 units to the right.
Help a bab out please?
Answer:
the answer is 55
Step-by-step explanation:
if you have a straight line each side equals 180 degrees so take 60+65 which equals 125 then do 180-125 and you get 55
What is the area of the triangle shown below?
(please help, im trying to bring my grades up)
Answer:
65 units²
Step-by-step explanation:
10 × 13 = 130
130 ÷ 2 = 65
Answer:
5²+x² =13²
x². =169-25
x² =144
x. =√144
x. =12
area of the triangle=1/2×10×12
=60 units²
What is point A on the coordinate plane
Answer:
4,1
Step-by-step explanation:
Answer:
(4,1)
Step-by-step explanation:
Ez
an architects cWhat is the domain of this relation?
(12, 5)
(20, 0)
(20, 20)
(–13, 0)
Answer:
Domain { -13,12,20 }
Step-by-step explanation:
The domain is the input values
Domain { -13,12,20 }
We list them in order from smallest to largest and do not list repeats
What is least common multiple of 15, 14, and 7
Answer:
210
Step-by-step explanation:
15 = 3 x 5
14 = 2 x 7
7 = 7
LCM = 3 x 5 x 2 x 7 = 210
Answer:
210
Explanation:
find the least common multiple of two numbers is to first list the prime factors of each number. Then multiply each factor the greatest number of times it occurs in either number. If the same factor occurs more than once in both numbers, you multiply the factor the greatest number of times it occurs.
Anyone.....................
Answer:
[tex] \frac{1}{p - q} [/tex]Step-by-step explanation:
[tex] \frac{ {p}^{2} + 2pq + q}{ {p}^{3} - p {q}^{2} + {p}^{2} q - {q}^{3} } [/tex][tex] \frac{ {p}^{2} +2 \times p \times q+ {q}^{2} }{p^2−pq^2+p^2q−q^3} [/tex][tex] \frac{(p + q {)}^{2} }{p^3−pq^2+p^2q−q^3} [/tex][tex] \frac{( p+ q {)}^{2} }{p(p^2−1q^2)+q(p^2−q^2)} [/tex][tex] \frac{ (p + q {)}^{2} }{ {p}^{3} - p {q}^{2} + {p}^{2} q - {q}^{3} } [/tex][tex] \frac{(p+q {)}^{2} }{(p+q)(p−q)(p+q)} [/tex][tex] \frac{(p + q {)}^{2} }{(p + q {)}^{2}(p - q) } [/tex] ( cancel common factors)
[tex] \frac{1}{p - q} [/tex]Hope it is helpful...Find the measures of angles 1, 2, & 3.
Answer:
1=68 (Vertically opposite angles are equal)
2= 112 (sum of angles on a straight line gives 180°)
3=112 (vertically opposite angles are equal)
Which refers to a method that relies on sound waves and is used by different animal species for navigation, communication, and finding food? echolocation analog signaling infrared detection digital location
Answer:
I believe echolocation
Answer:
echolocation
Step-by-step explanation:
The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism.
Answer:
I don't see the triangular prism.
Step-by-step explanation:
here is the problem if you want to help them
A 9 year old boy has $12 saved.
He decides to start saving on a regular basis because he selss aluminum
cans
He figures out that he can save $2.50 per day.
What is the total amount he will have saved after 1 day?
2 days?
3 days?
17days?
X days?
Organize the information however you think is best and find out the totals.
Do...
g
in
Answer:
.............................
a cell phone plan charges a base fee of $62 and an overage charges $30 per gigabyte of data that exceeds 2 GB
what is the correct answer
Answer:
We can solve this with the Pythagorean Theorem.
The Pythagorean theorem states that a2 + b2 = c2 in a right triangle where c is the longest side. You can use this equation to figure out the length of one side if you have the lengths of the other two.
Just square the sides, add them, and then take the square root. Here's an example:
We can solve it like this ~ [tex]30^2+60^2 = y[/tex]
= 2,500
y = [tex]\sqrt{2500}[/tex]
= 50
Therefore, the correct answer is 50.
Un deposito de agua tiene forma de un cubo de 10 metros de arista ¿cual es la capacidad del deposito?
Respuesta:
1000m³
Explicación paso a paso:
La capacidad del tanque viene dada por el volumen del cubo;
El volumen, V del cubo se da como: a³
V = a³
El borde del cubo mide 10 metros.
Por eso,
Volumen = 10³
Volumen = 10 * 10 * 10
Volumen = 1000 m³
Por lo tanto, la capacidad del tanque de agua es de 1000 m³.
An artist is preparing to open a gallery, but wants to have 35 finished works of
art before he opens. He creates 4 new works each week. If he already has 19
works prepared, how many weeks until he is ready to open?
Answer:
tic ishaan t,x Germany ruff hero
Which graph represents
y= -2x?
Answer:
The second one
Step-by-step explanation:
what is the length of BC?
A. 9 units
B. 11 units
C. 15 units
D. 16 units
Answer:
15units
Step-by-step explanation:
BC is: 5x=5×3=15 units. so,Length of BC=15 units
Analyze the diagram below and complete the instructions that follow.
Find the exact value of tan(M).
Explanation:
Recall that tangent = opposite/adjacent.
For reference angle M, the side ON = 5 is the opposite side and MN = 12 is the adjacent side. We don't need the hypotenuse.
Answer:
C or 5/12
Step-by-step explanation: