Answer:
15,10
Step-by-step explanation:
let the numbers be 3x and 2x
3x-2x=5
x=5
∴ numbers are 3×5,2×5
or 15,10
AB = 3.2 cm
BC= 8.4 cm
The area of triangle ABC is 10 cm²
Calculate the perimeter of triangle ABC.
Give your answer correct to three significant figures.
Answer:
Therefore, perimeter of the given triangle is 18.300 cm.
Step-by-step explanation:
Area of the triangle ABC = [tex]\frac{1}{2}(\text{AB})(\text{BC})(\text{SinB})[/tex]
10 = [tex]\frac{1}{2}(3.2)(8.4)(\text{SinB})[/tex]
Sin(B) = [tex]\frac{10}{3.2\times 4.2}[/tex]
B = [tex]\text{Sin}^{-1}(0.74405)[/tex]
B = 48.08°
By applying Cosine rule in the given triangle,
(AC)² = (AB)² + (BC)²-2(AB)(BC)CosB
(AC)² = (3.2)² + (8.4)² - 2(3.2)(8.4)Cos(48.08)°
(AC)² = 10.24 + 70.56 - 35.9166
(AC)² = 44.88
AC = [tex]\sqrt{44.8833}[/tex]
AC = 6.6995 cm
Perimeter of the ΔABC = m(AB) + m(BC) + m(AC)
= 3.200 + 8.400 + 6.6995
= 18.2995
≈ 18.300 cm
Therefore, perimeter of the given triangle is 18.300 cm
Need help ! Help needed very much !
Answer:
x/2 > 5
Step-by-step explanation:
Quotient means division
x/2
is more than means greater
x/2 > 5
For the function f(x) = -12x + 7, find the
matching value for x when f(x) = 17. Write
your answer as a fraction.
Answer:
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
Step-by-step explanation:
f(x) is the same value as y. Therefore, y = 17. We can place this into slope intercept form (except with a defined value for y) and solve for x.
Start by subtracting 7 from both sides. Then, divide by -12 to solve for x. Finally, simplify the fraction.
17 = -12x + 7
10 = -12x
-10/12 = x
-5/6 = x
[tex]\large\boxed{x=-\frac{5}{6}}[/tex]
HELPPP PLZZZZ DUE SOONnnn
Answer:
x = 7, EF = 10, FG = 12
Step-by-step explanation:
EF = 4x - 18
FG = 3x - 9
EG = 22
EG = 22
EF + FG = 22
4x - 18 + 3x - 9 = 22
4x + 3x - 18 - 9 = 22
7x = 22 + 18 + 9
7x = 49
x = 7
EF = 4x - 18
EF = 4*7 - 18
EF = 28 - 18
EF = 10
FG = 3x - 9
FG = 3*7 - 9
FG = 21 - 9
FG = 12
Find the radius of a circle that has an area of 6.76 cm². Use it for pi.
Answer:
radius = 1.47 cmStep-by-step explanation:
Area of a circle = πr²
where
r is the radius
From the question
Area = 6.76 cm²
To find the radius substitute the value of the area into the above formula and solve for the radius
That's
[tex]6.76 = \pi \: {r}^{2} [/tex]
Divide both sides by π
We have
[tex] {r}^{2} = \frac{6.76}{\pi} \\ r = \sqrt{ \frac{6.76}{\pi} } [/tex]
r = 1.46689291
We have the final answer as
radius = 1.47 cm
Hope this helps you
what is the general form to find square roots
Answer:
see below (I hope this helps!)
Step-by-step explanation:
Square roots are usually in the form a√b where a and b are any rational number.
Solve logs (8 - 3x) = log20 for x.
A. X = 14
B. X = -13
C.x = -8
D. X= -4
Answer:
x = -4
Step-by-step explanation:
logs (8 - 3x) = log20
Since we are taking the log on each side
log a = log b then a = b
8 -3x = 20
Subtract 8 from each side
8 -3x-8 =20 -8
-3x = 12
Divide by -3
-3x/-3 = 12/-3
x = -4
Answer:
[tex] \boxed{\sf x = -4} [/tex]
Step-by-step explanation:
[tex] \sf Solve \: for \: x \: over \: the \: r eal \: numbers:[/tex]
[tex] \sf \implies log(8 - 3x) = log 20[/tex]
[tex] \sf Cancel \: logarithms \: by \: taking \: exp \: of \: both \: sides:[/tex]
[tex] \sf \implies 8 - 3x = 20[/tex]
[tex] \sf Subtract \: 8 \: from \: both \: sides:[/tex]
[tex] \sf \implies 8 - 3x - 8 = 20 - 8 [/tex]
[tex] \sf \implies - 3x = 12 [/tex]
[tex] \sf Divide \: both \: sides \: by \: - 3:[/tex]
[tex] \sf \implies \frac{-3x}{-3} = \frac{12}{-3} [/tex]
[tex] \sf \implies x = - 4[/tex]
Solve for x. 3x-91>-87 AND 17x-16>18
Answer & Step-by-step explanation:
For this problem, we have two inequalities to solve for x.
3x - 91 > -87
17x - 16 > 18
Now that we know what our inequalities are, we will solve them as if we are solving for the value of x.
3x - 91 > -87
Add 91 on both sides.
3x > 4
The solution for the first inequality is 3x > 4
Now let's do the second inequality.
17x - 16 > 18
Add 16 on both sides.
17x > 34
Divide by 17 on both sides.
x > 2
The soultion for the second inequality is x > 2
Answer:
The answer is x>2
Step-by-step explanation:
The coordinate grid shows the graph of four equations:
Which set of equations has (3, 1) as its solution?
A and B
C and D
B and D
A and D
Answer:
A and D
Step-by-step explanation:
All you need to do is locate the point (3,1) on the graph and figure out which two lines are intersecting it. In this case it is A and D so that is your solution.
Please help! Question is given below in form of image!
Answer:
c
Step-by-step explanation:
Answer:
None of the choices are correct.
Step-by-step explanation:
[tex] 9x^3 + 9x^2 - 4x - 4 = 0 [/tex]
The polynomial has 4 terms and no common factors. We can try factoring by grouping.
[tex] 9x^2(x + 1) - 4(x + 1) = 0 [/tex]
[tex] (x + 1)(9x^2 - 4) = 0 [/tex]
Now we factor the difference of squares.
[tex] (x + 1)(3x + 2)(3x - 2) = 0 [/tex]
[tex] x + 1 = 0~~or~~3x + 2 = 0~~or~~3x - 2 = 0 [/tex]
[tex]x = -1~~or~~x = -\dfrac{2}{3}~~or~~x = \dfrac{2}{3}[/tex]
None of the choices are correct.
16-32)
What is the equation of the line that is perpendicular to
the given line and passes through the point (3, 0)?
O 3x + 5y = -9
O 3x + 5y = 9
O 5x - 3y = -15
O 5x - 3y = 15
Answer:
the fourth option : 5x - 3y = 15
Step-by-step explanation:
the slope of the original line is given by the coordinate differences between the 2 points on the line.
remember, the slope is the factor of x in the line equation and is the ratio y/x indicating how many units y is changing, when x changes a certain number of units.
so, to go from (-3. 2) to (2, -1) x changes 5 units and y -3 units.
therefore, the slope is -3/5.
the slope of a perpendicular line simply switched x and y. and the sign of the slope.
therefore the slope of the perpendicular line is 5/3.
and the line equation is
y = (5/3)x + c
to get c we need the point on the line (3, 0).
0 = (5/3)×3 + c = 5 + c
c = -5
y = (5/3)x - 5
3y = 5x - 15
3y - 5x = -15 or (after multiplying both sides by -1)
5x - 3y = 15
What is the simplest form of 20 over 315?
Answer:
4/63
Step-by-step explanation:
20/315 = (20÷5)/(315÷5)
PLEASE HELP!!! The data set shows the ages of people riding a bus.
What is the mode for this data set?
18 16 11 45 33 11 33 14 18 11
A. 11, 18, and 33
B. 17
C. 21
D. 11
Step-by-step explanation:
The number which is repeated more times will be mode...
So...
11 is Answer
In right triangle ABC, AB = 3 and AC = 9. What is the measure of angle B to the nearest degree?
Answer:
90 degrees
Step-by-step explanation:
see image
make x A
y B
z C
AB=3 (given)
AC=9 (given)
measure of angel B or y, is 90
if
x= A
y= C
z= B
then the hypotenuse would be shorter than one of the legs
3<9
so B has to be the right angle (90 degrees)
Find an equation of the line: Through the point (2, −4) with a y-intercept of −2 Through the points (4,2) and (3,1) Through the point (3,2) with a slope of −2
Answer and Step-by-step explanation: Equations of line through points and slope can be determined by:
[tex]y-y_{0}=m(x-x_{0})[/tex]
m is slope
Point (2,-4) and y-intercept = -2Y-intercept is point (0,-2)
m = [tex]\frac{y_{a}-y_{b}}{x_{a}-x_{b}}[/tex]
m = [tex]\frac{-4-(-2)}{2-0}[/tex]
m = - 1
Equation:
[tex]y+2=-1(x-0)[/tex]
[tex]y=-x-2[/tex]
Points (4,2) and (3,1)m = [tex]\frac{2-1}{4-3}[/tex]
m = 1
Equation:
[tex]y-2=(x-4)[/tex]
[tex]y=x-2[/tex]
Point (3,2) and slope = -2m = -2
Equation:
[tex]y-2=-2(x-3)[/tex]
[tex]y=-2x+6+2[/tex]
[tex]y=-2x+8[/tex]
Plz solve it
Factorize: no w
Answer:
here we can go for two solution
Solve the following non-linear system of equations algebraically.
y = - 2x² - 4x + 5 and
y = 2x^2 + 4x + 5
Answer:
x = -2
Step-by-step explanation:
since y is common in both equations, you can equate them to be equal
-2x² - 4x + 5 = 2x² + 4x + 5
4x² + 8x = 0
factor out 4x
4x(x + 2) = 0
divide both sides by 4x
x + 2 = 0
x = -2
Joe is responsible for reserving hotel rooms for a company trip. His company changes plans and increases how many people are going on the trip, so they need at least 50 total rooms. Joe had already reserved and paid for 16 rooms, so he needs to reserve additional rooms. He can only reserve rooms in blocks, and each block contains 8 rooms and costs $900. Let B represent the number of additional blocks that Joe reserves. 1) Which inequality describes this scenario? 2)What is the least amount of money that Joe can spend to get the amount of rooms they need? Work not needed!
Answer:
The answer is below
Step-by-step explanation:
1) The number of rooms Joe company needs is 50. Let the number of rooms needed be n, this can be represented by the inequality:
n ≥ 50
Joe has already reserved 16 rooms, therefore the number of additional rooms needed to be reserved = 50 - 16 = 34 rooms. At least 34 rooms have to be reserved, if B is the number of additional blocks that Joe reserves, the inequality is:
B ≥ 34
2) Each block contains 8 rooms therefore the minimum number of block (a) needed to be reserved = 34/8 = 4.25 = 5 to the next whole number. Therefore the minimum number of blocks needed is given as:
a ≥ 5
Since each block cost $900, let c represent the minimum amount of money needed, therefore the least amount of money needed is given as:
c = $900(5) = $4500
c ≥ $4500
Here, we are required to determine which inequality describes the scenario in the question and the least amount of money that Joe can spend to get the amount of rooms they need.
(1) The inequality which best describes the scenario is; B ≥ 4.25.
(2) The least amount of money that Joe can spend to get the amount of rooms they need is; $4500
First, since they need at least 50 total rooms and Joe had already reserved 16 rooms.Therefore, Joe needs to reserve an additional 34 rooms to completely accomodate people who are going on the trip.And since, he can only reserve rooms in blocks with each block containing 8 rooms;The number of blocks he needs to reserve; B ≥ 4.25.
Therefore, since only whole blocks can be reserved, Joe needs to reserve 5 blocks.Therefore, since one block costs $900, then, 5 blocks will cost $900 × 5 = $4500.Read more:
https://brainly.com/question/19003099
11) MZHGF = 16x + 4, m EGF = 110°,
and MZHGE = 3x + 11. Find x.
G
H
F
E
=======================================================
Explanation:
The smaller angles HGE and EGF combine to form the largest angle HGF.
This is an example of the angle addition postulate.
(angle HGE) + (angle EGF) = angle HGF
(3x+11) + (110) = 16x+4
3x+121 = 16x+4
121-4 = 16x-3x
117 = 13x
13x = 117
x = 117/13
x = 9 which is the final answer
We can stop here.
--------------------
Extra info (optional section)
Use this x value to find each angle shown below
angle HGE = 3x+11 = 3*9+11 = 27+11 = 38 degreesangle HGF = 16x+4 = 16*9+4 = 144+4 = 148 degreesThen notice how,
(angle HGE)+(angle EGF) = 38+110 = 148
which is exactly the measure of angle HGF
This confirms that the equation
(angle HGE) + (angle EGF) = angle HGF
is true for that x value of x = 9. Therefore, the answer is confirmed.
9514 1404 393
Answer:
11) x = 9°
13) x = -12°
Step-by-step explanation:
11) ∠HGE +∠EGF = ∠HGF
(3x +11) +(110°) = (16x +4)
117° = 13x . . . . . . . . . . . . . . . subtract 3x+4, collect terms
9° = x . . . . . . . . . . . . divide by 13
__
13) ∠BCF +∠FCD = ∠BCD
(x +78) +(x +41) = 95°
2x = -24°
x = -12°
pls help me asap !!!!
Answer:
9--7
Step-by-step explanation:
plssss help i want it now
Find each of the following products
a) 6x * (-2y)
Answer ) -12xy
Step-by-step explanation:
6x × (-2y) = -12xy thank youHow do I find the Derivative of a Function where the x is a number?
If I was to find d/dx g(1) for example, would I first find the value of the function g(x) at x=1 and then find the derivative of that which becomes 0 because the result would probably be a constant. Or do I first find the derivative of g(x) and then plug in x=1 to calculate it?
Thanks
Given a function g(x), its derivative, if it exists, is equal to the limit
[tex]g'(x) = \displaystyle\lim_{h\to0}\frac{g(x+h)-g(x)}h[/tex]
The limit is some expression that is itself a function of x. Then the derivative of g(x) at x = 1 is obtained by just plugging x = 1. In other words, find g'(x) - and this can be done with or without taking a limit - then evaluate g' (1).
Alternatively, you can directly find the derivative at a point by computing the limit
[tex]g'(1) = \displaystyle\lim_{h\to0}\frac{g(1+h)-g(1)}h[/tex]
But this is essentially the same as the first method, we're just replacing x with 1.
Yet another way is to compute the limit
[tex]g'(1) = \displaystyle\lim_{x\to1}\frac{g(x)-g(1)}{x-1}[/tex]
but this is really the same limit with h = x - 1.
You do not compute g (1) first, because as you say, that's just a constant, so its derivative is zero. But you're not concerned with the derivative of some number, you care about the derivative of a function that depends on a variable.
(-6x)(½y)(-⅓z) what is the product?
Answer:
xyz
Step-by-step explanation:
[tex](-6x)(\frac{1}{2}y)(-\frac{1}{3}z) = (-6)*\frac{1}{2}*(-\frac{1}{3}) * xyz = \frac{6}{6} xyz = xyz[/tex]
"A die is rolled and a number less than 5 comes up"
Which letter from A to G best represents the probability of the event?
Answer:
4/6
Step-by-step explanation:
Im pretty sure***
but if a dice has 6 sides, and you have to get something less than 5, which is 1-4, which is 4 numbers, so 4 out of 6 total is 4/6
A random number generator chooses 2 numbers between 1 and 5. This table demonstrates all possible outcomes. 1 2 3 4 5 1, 1 1, 2 1, 3 1, 4 1, 5 2 2, 1 2, 2 2, 3 2, 4 2, 5 3 3, 1 3, 2 3, 3 3, 4 3, 5 4 4, 1 4, 2 4, 3 4, 4 4, 5 5 5, 1 5, 2 5, 3 5, 4 5, 5 What is the probability that the computer will pick two 5s?
Answer as a fraction = 1/25
Answer in decimal form = 0.04
Answer in percent form = 4%
Explanation:
There are 5*5 = 25 different outcomes, of which only one outcome has 5,5. The probability of picking two 5s is 1/25 = 0.04 = 4%
Answer:
4%
Step-by-step explanation:
You pay $10 to play the following game of chance. there is a bag containing 12 balls: three are red, five are green, and the rest are yellow. You are to draw one ball from the bag. You will win $15 if you draw a red ball, and you will win $10 if you draw a yellow ball. You win nothing for drawing a green ball. What is the expected value? Should you play?
Answer:
$ -2.08 expected to lose
Step-by-step explanation:
3 25.0% $15.00 $5.00 $1.25
5 41.7% $10.00 $- $-
4 33.3% $- $(10.00) $(3.33)
$(2.08) expected to lose
Question 20 of 33
What is the surface area of the sphere shown below with a radius of 7?
1.72
A. 495 sq. units
B. 65x sq, units
C. 457 sq. units
D. 1965 sq. units
SERNAT
Answer:
The surface area of the sphere 1s 615.75 sq. unit.
Step-by-step explanation:
The surface area of a sphere [tex]A_s[/tex] = 4·π·r²
Given that the radius of the sphere = 7, we have
The surface area of the sphere = 4 × π × 7^2 = 615.75 sq. unit
The surface area can also be derived from the volume of the sphere by differentiation as follows;
Volume of a sphere, V = 4/3·π·r³
(The volume of the sphere is 4/3·π·7³ = 1436.76 cube unit)
dV/dr = d(4/3·π·r³)/dr = 3×4/3·π·r² = 4·π·r²
The surface area of the sphere = 615.75 sq. unit.
how do you solve this?
Triangles ABC and LBM are similar. We know this because AL and LB have the same length, so that AB is twice as long as either AL or LB. The same goes for MC and BM, and BC. The angle B is the same for both tirangles ABC and LBM, so the side-angle-side postulate tells us the triangles are similar, and in particular that triangle ABC is twice as large as LBM.
All this to say that LM must be half as long as AC, so LM has length (B) 14 cm.
Which graph represents a function?
Answer:
The first one is the only function
Step-by-step explanation:
You cannot have points on the same y gridline
If it is a function is has to pass the pencil test
Answer:
[tex]\boxed{Graph A.}[/tex]
Step-by-step explanation:
Hey there!
Well graph A is correct because if you do the vertical line test which decides is the graph is a function or not you can see that all the graph expect A have the vertical line go through 2 points.
Hope this helps :)