Answer:
remainder = 4
Step-by-step explanation:
using the remainder theorem
when f(x) is divided by (x - a) then the remainder is f(a)
so when f(x) is divided by (x - 7) the remainder is f(7) , that is
f(7) = 7³ - 13(7)² + 40(7) + 18
= 343 - 13(49) + 280 + 18
= 343 - 637 + 298
= 4
Hence, the remainder is [tex]4[/tex].
What is the remainder value?
The remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient.
Applying the remainder theorem
In general when [tex]f(x)[/tex] is divided by [tex](x - a)[/tex] then the remainder is [tex]f(a)[/tex].
So, here when [tex]f(x)[/tex] is divided by [tex](x - 7)[/tex] the remainder is [tex]f(7)[/tex], that is
[tex]f(7)=7^3-13(7)^3+40(7)+18\\=343-13(49)+280+18\\=343-637+298\\=4[/tex]
Hence, the remainder is [tex]4[/tex].
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i will ask alot of questions again sorry
Answer:
7.5 m = 0.0075 km (Correct)
0.31 = 310 mm (Correct)
46 m = 4,600 cm (Correct)
457 mm =4.57 cm (Incorrect)
0.6 km = 6,000 m (Incorrect)
Step-by-step explanation:
Tell me if something is wrong.
8. Resuelve los siguientes problemas:
a) Cinco trabajadores de una empresa reci-
ben salarios de $1 200, $1 500, $1 600,
$1 300 y $2 500. ¿Cuál es el promedio
salarial?
see the attachment photo!
Volume of a triangular prism with numbers 3 4 5 6
Answer:
Step-by-step explanation:
V=14h﹣a4+2(ab)2+2(ac)2﹣b4+2(bc)2﹣c4aBase sidebBase sidecBase sidehHeight
use the information given to answer the question. write your answer as a decimal rounded to the nearest tenth
Answer: The value of x is 3.5
Explanation:
Equation:
y = 2x - 7
When the equation's Line intersects the x-axis, the value of y shall be always 0
Insert y = 0, to find x intercept
⇒ 0 = 2x - 7
⇒ 2x - 7 = 0
⇒ 2x = 7
⇒ x = 3.5
So coordinates: (x, y) → (3.5, 0)
Question 1 of 10
The slope of the line below is - Write a point-slope equation of the line -1/7
using the coordinates of the labeled point.
10
610
(3, 3)
10
610
Step-by-step explanation:
A triangle cannot have one obutse angle and one right angle. True or flase?
Answer:
No
Step-by-step explanation:
Since an equilateral triangle has equal sides and angles, each angle measures 60°, which is acute. Therefore, an equilateral angle can never be obtuse-angled. A triangle cannot be right-angled and obtuse angled at the same time. Since a right-angled triangle has one right angle, the other two angles are acute.
Answer:
false
Step-by-step explanation:
What is a divided by a% of a?
Answer:
[tex]\frac{100}{a}[/tex]
Step-by-step explanation:
Hello!
a% is the same as [tex]\frac a{100}[/tex].
a% of a can be found by multiplying them both, giving us [tex]\frac {a^2}{100}[/tex]
Solve:[tex]\frac{a}{\frac{a^2}{100}}[/tex][tex]a * \frac{100}{a^2}[/tex][tex]\frac{100a}{a^2}[/tex][tex]\frac{100}{a}[/tex]The value of the expression is [tex]\frac{100}{a}[/tex]
Factor 6x¹ − 5x² + 12x² − 10 by grouping. What is the resulting expression?
(6x + 5)(x²-2)
(6x - 5)(x²+2)
(6x² + 5)(x-2)
(6x²-5)(x+2)
Answer:
[tex](6x-5)(x^2+2)[/tex]
Step-by-step explanation:
[tex]~~~6x^3 -5x^2 +12x -10\\\\=6x^3-5x^2+12x-10\\\\=x^2(6x-5) +2(6x-5)\\\\=(6x-5)(x^2+2)[/tex]
Which classification describes the following system of equations? inconsistent and dependent consistent and dependent consistent and independent inconsistent and independent.
The system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
What is a linear equation?It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.
The question is incomplete.
The complete question is in the picture, please refer to the attached picture.
We have three linear equations in three variables:
x - y - z = 0 ..(1)
2x - y + 2z = 1 ..(2)
x - y + z = -2 ..(3)
From the equation (1):
[tex]\rm x=y+z[/tex]
Plug this value in the equation (2) and (3):
[tex]\rm 2\left(y+z\right)-y+2z=1\\\\ y+z-y+z=-2[/tex]
After solving we get:
z = -1
y = 5
Plug the above two values in equation (1) we get:
x = 4
Thus, the system of equations is consistent and independent and the solutions are x = 4, y = 5, and z = -1 option third is correct.
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Which equation is showed in the graph above
Answer: A
It has a negative gradient.
Hope this helps :))
P.s. Can you mark me as the brainliest? <3
Answer:
Step-by-step explanation:
Remark
You can read the y intercept right off the graph. Follow the y axis upwards until the line intercepts the y axis. I think you will find it is at 0,5
So far what you know is
y = mx + 5
Finding m is a little harder. I would use 6,0 and 0,5 as the two points that will define m.
Givens
x1 = 6
x2 = 0
y1 = 0
y2 = 5
Equation
m = (y2 - y1) / (x2 - x1) Put the givens into this equation.
Solution
m = (5 - 0) / (0 - 6)
m = 5/-6
m = - 5/6
Answer
The line is
y = -5/6 x + 5
Match the tan R, cos R and sin R to the correct ratios
3. Twelve people work together: four of them are managers and eight of them are office workers. Two people are chosen at random from the twelve members of the group. Calculate the probability that one is a manager and one is an office worker.
Answer:
2/9
Step-by-step explanation:
8/12 you pick an office worker
4/12 chance you pick a manager
8/12 multiplied by 4/12 is 32/144
We can simplify this to 16/72
We can simplify this to 8/36
We can simplify this to 4/18
We can simplify this to 2/9
HELP ASAP
A timer is started and a few moments later a swimmer dives into the water and then comes back up. The swimmer's depth (in feet) as a function of time (in seconds after the timer was started) is given by the equation h(t)=t2−12t+27
Rewrite the formula in factored form and select each true statement below.
The swimmer is underwater for 12 seconds.
The swimmer dives into the water 3 seconds after the timer was started.
The swimmer comes back up 9 seconds after the timer was started.
The swimmer dives to a maximum depth of 27 feet.
The swimmer dives into the water 12 seconds after the timer was started.
The correct true statement is the swimmer comes back up 9 seconds after the timer was started.
Maximum height of a functionThe maximum height of a function is the point where the velocity the body is zero.
Given the function that represent the height of the swimmer as h(t)=t^2−12t+27
If the velocity of the function is zero, hence;
h'(t) = 2t - 12
0 = 2t - 12
2t = 12
t = 6secs
Substitute t = 6 into the function as shown:
h(6) = 6^2−12(6)+27
h(6) = 36 - 72 + 27
h(6) = -36 + 27
h(6) = -9 feet
Hence the correct true statement is the swimmer comes back up 9 seconds after the timer was started.
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ΔXYZ has angles with the following measurements:
m∠X=(10x-33)°
m∠Y=(4x-19)°
m∠Z=(100-2x)°
What are the measures of the three angles?
Answer:
Below in bold.
Step-by-step explanation:
The 3 angles add up to 180 degrees as they are in a triangle.
So 10x - 33 + 4x - 19 + 100 - 2x = 180
12x = 180 + 33 + 19 - 100
12x = 132
x = 11.
So the 3 angles are
10(11) - 33 = 110 - 33 = 77 degrees
4(11) - 19 = 25 degrees
100 - 2(11) = 78 degrees
Hi can anybody answer this please !
Answer:
7ft; 8 minutes
Step-by-step explanation:
a. to find the height the person boarded at, plug in t=0 since this is right when the person got on the Ferris wheel. we then get:
h(0) = -45 * cos ((pi/4)*0) + 52 = 7 ft
b. to find the period, we have pi/4 * t = 2*pi, solve for t to get t=8
question 2 help me please
Answer:
90π in²
Step-by-step explanation:
Surface area of cylinder:r = 3 in
h = 10 in
[tex]\sf \boxed{\text{\bf Surface area of cylinder =$\pi r^2h$}}[/tex]
[tex]= \pi 3*3*10\\\\= 90 \pi \ in^2[/tex]
In this question it is given that the radius of a cylinder is 3 inches. The height of the cylinder is 10 inches. We are asked to calculate the surface area of the cylinder in terms of π .
Radius = 3 inches
Height = 10 inches
We know,
[tex] \star \: \small \boxed{\rm{ Surface \: area \: of \: a \: cylinder = πr²h}}[/tex]
Substituting the values we get
[tex] \small\sf{ Surface \: area \: of \: a \: cylinder = π × 3² × 10}[/tex]
[tex] \small\rm{ Surface \: area \: of \: a \: cylinder = π × 3 \times 3 × 10}[/tex]
[tex] \small\rm Surface \: area \: of \: a \: cylinder = π × 90[/tex]
[tex] \small\sf{ Surface \: area \: of \: a \: cylinder = \bf{90 π \: inches²}}[/tex]
The demand function for a christmas music cd is given by q=0. 6(3800-p^2)
The expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have a demand function:
q=0. 6(3800-p²)
Differentiate with respect to p:
[tex]\rm \dfrac{dq}{dp} = -1.2p[/tex]
We know the elasticity:
[tex]\rm E(p) = \dfrac{dq}{dp}\times\dfrac{p}{q}[/tex]
[tex]\rm E(p) =-1.2p \times\dfrac{p}{0.6(3800-p^2)}[/tex]
[tex]\rm E(p) = -\dfrac{2p^2}{(3800-p^2)}[/tex]
Here the data for p and q are not given, but we can find any value using the above expression by putting the known data.
Thus, the expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.
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Determine whether triangles EFG and PQR are congruent
Plsss help
Answer:
B
Step-by-step explanation:
Because it flipped over the x axis
Spot the coordinates
E(-3,1)P(-3,-1)F(1,1)Q(1,-1)G(4,4)R(4,-4)Yes it's reflection along x axis
.(x,y)=(x,-y)Option B
It makes that every time we flip a fair the probability of flipping tails is
It makes that every time we flip a fair the probability of flipping tails is 50%.
What is the probability?Probability determines the chances that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0. If it is equally likely and unlikely that the event would happen, it would have a probability of 0.5
Probability of flipping tails = number of tails / number of sides
1/2 = 0.5 = 50%
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Which equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17)?
Answer: y - 17 = -2(x-7)
Step-by-step explanation:
point-slope form: y - y1 = m(x - x1)
m = y2-y1/x2-x1
= 9+17/-6-7
= 26/-13
= -2
y1 = -17
x1 = 7
y - 17 = -2(x-7)
The equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
What is the general equation of a straight line?The general equation of a straight line is-
y = mx + c
where, m is the gradient and is given by y₂ - y₁/x₂ - x₁
and, c is the value where the line cuts y-axis.
Now it is given that the line passes through points (−6,9) and (7,−17)
Therefore we have,
x₁ = -6, y₁ = 9, x₂ = 7, y₂ = -17
So, the slope m of the line is given as,
m = (y₂ - y₁)/(x₂ - x₁)
Put the values,
m = (-17 - 9)/(7 - (-6))
m = -26/7+6
m = -26/13
m = -2
Thus, the equation parallel to the line will be given as:
y - y₁ = m(x - x₁)
y - 9 = -2{x - (-6)}
y - 9 = -2(x + 6)
y = -2x - 12 + 9
y = -2x - 3
Thus, the equation represents a line that is parallel to the line that passes through the points (−6,9) and (7,−17) is y = -2x - 3
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Please help! This is reflections in geometry! Thank you.
If these coordinates reflected over y = -1, the resulting coordinate will be:
P = (-4, -6)
Q = (-2,-8)
R = (1, -4)
Reflection of coordinatesA reflected coordinates are mirror images of each other. From the given diagram, the coordinate points are;
P = (-4, -3)
Q = (-2,-4)
R = (1, -2)
If these coordinates reflected over y = -1, the resulting coordinate will be:
P = (-4, -6)
Q = (-2,-8)
R = (1, -4)
The y coordinates are multiplied by a factor of 2
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Hailey's laundry basket contains 777 socks. These 777 socks account for approximately 21\!!, percent of Hailey's socks. How many socks does Hailey have in total
The number of socks for Hailey will be 163.
What is the percentage?
The Percentage is defined as representing any number with respect to the 100. It is denoted by the sign %.
Given that:-
Hailey's laundry basket contains 777 socks. These 777 socks account for approximately 21, per cent of Hailey's socks.The number of Haley's socks will be calculated as=
Socks = 777 x 21/100
Socks = 777 x 0.21
Socks = 163
Therefore the number of socks for Hailey will be 163.
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these box plots show daily low temperatures for a sample of days in two different towns which statment is the most appropriate comparison of the centers
The correct statement about the center of both box plots is: the median for Town A, 30° is greater median for Town B, 25°
What is the correct statement?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. The two lines are known as whiskers. The end of the first line represents the minimum number and the end of the second line represents the maximum number.
On the box, the first line to the left represents the lower (first) quartile. The next line on the box represents the median. 50% of the score represents the median. The third line on the box represents the upper (third) quartile.
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Do ∠ABE and ∠DBC share a ray
Answer:
yes they do
Step-by-step explanation:
they share a ray
(x + 8/3)^2 + y^2 = 1 What is the center of the circle? what is the radius?
(x+8/3)²+y²=1
(x+8/3)²+y²+0²+2×0y=1
(x+8/3)²+(y+0)²=(V1)²
->center: C(8/3,0)
-> radius: V1
Sheryl makes $7 per pair of
earrings, e, and $13 per necklace,
n, she sells. What expression
represents her total income?
The expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.
What is an expression?It is defined as the combination of constants and variables with mathematical operators.
We have:
Sheryl makes $7 per a pair of earrings, e, and $13 per necklace, n, she sells.
Let's suppose the total income of Sherly is T:
Then,
T = 7e + 13n
Here e is the number of earrings she sells and n is the number of necklace she sells.
T is the total income and the expression T = 7e + 13n represents the total income of Sherly.
Thus, the expression T = 7e + 13n represents the total income of Sherly where e is the number of earrings she sells and n is the number of necklace she sells.
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Abrianna sold 20, 23, 18, 4, 17, 21, 15, and 56 boxes of cookies after different football games. Which data value(s) are outliers? Select all that apply.
The data values that are outliers are 4 and 56.
What is an outlier?
An outlier is a number that is way smaller or way larger than that of other numbers in a data set. An outlier distorts the mean and median of the dataset.
In this data, 4 is smaller than the average of the data set and 56 is larger than the average numbers. They are the outliers.
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Which set of values could be the side lengths of a 30-60-90 triangle?
OA. (6,6 2,12}
OB. (6,6√3, 12)
OC. (6, 12, 12√√3}
D. (6, 12, 12 √2)
The correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle are (6,6√3, 12).
What is the right-angled triangle?A triangle has three angles of 30-60 and 90 degrees in which the two sides are perpendicular to each other.
The three sides of the triangle will be calculated by applying the Pythagorean theorem:-
The sum of the square sides will be equal to the square of the third side.
For sides (6,6√3, 12)
12² = 6² + (6√3)²
144 = 36 + (36 x 3)
144 = 36 + 108
144 = 144
Therefore the correct answer is option B which is the set of values that could be the side lengths of a 30-60-90 triangle (6,6√3, 12).
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I need help with this problem, please explain
Answer:
v = 164.64
Step-by-step explanation:
Your friend forgot to divide 6.8 by two as 6.8 is the diameter not the radius. The volume equation needs the radius so you divide 6.8 by 2 which equals 3.4 thats what inputed into the volume equation
General Sherman, a tree located in Sequoia National Park, stands 275 feet tall. To see the top of the tree,
Carlos looks up at a 19° angle of elevation. If Carlos is 6 feet tall, how far is he from the base of the tree to the
nearest foot?
By using trigonometric relations, we will see that the distance between Carlos and the tree is:
D = 781.23 ft
How far is Carlos for the base of the tree?We can model this with a right triangle. We know that Carlos is 6ft tall, and the height of the tree is 275ft.
Then one of the cathetus of the triangle is equal to:
275ft - 6ft = 269ft.
That cathetus is the opposite cathetus to the angle of 19° (the elevation angle). And the adjacent cathetus is the distance between Carlos and the tree.
Then we can use the relation:
tan(a) = (opposite cathetus)/(adjacent cathetus).
Where:
a = 19°opposite cathetus = 269ftadjacent cathetus = D.Replacing that, we get:
tan(19°) = 269ft/D
Solving for D, we get:
D = 269ft/tan(19°) = 781.2ft
So we conclude that Carlos is at 781.23 ft of the tree.
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