Answer:
a=7
Step-by-step explanation:
3a+4=a+18
-1a -1a
2a+4=18
-4 -4
2a = 14
÷2 ÷2
a=7
Answer:
a = 7
Step-by-step explanation:
3a + 4 = a + 18
Add -a and -4 on both sides.
3a - a = 18 - 4
2a = 14
Divide 2 into both sides.
a = 14/2
a = 7
f(x) is a function.
A. True
B. False
Answer:
True, this is a function
Step-by-step explanation:
There is a 1 to one correspondence between x and y
Each x goes to one y, so this is a function
AWARDING FIRST CORRECT ANSWER WITH BRANLIEST
Answer:
[tex] \boxed{\sf (8x + y)(2x + 3y)} [/tex]
Step-by-step explanation:
[tex] \sf Factor \: the \: following: \\ \sf \implies {(5x + 2y)}^{2} - {( 3x - y)}^{2} \\ \\ \sf Factor \: the \: difference \: of \: two \: squares. \\ \sf {(5x + 2y)}^{2} - (3x - y)^{2} = ((5x + 2y) + (3x - y)) \\ \sf ((5x + 2y) - (3x - y)) : \\ \sf \implies ((5x + 2y) + (3x - y))((5x + 2y) - (3x - y)) \\ \\ \sf Grouping \: like \: terms, \: 5x + 2y + 3x - y = \\ \sf (5x +3x) + (2y - y) : \\ \sf \implies \boxed{ \sf( (5x +3x) + (2y - y))}((5x + 2y) - (3x - y) \\ \\ \sf 5x + 3x = 8x : \\ \sf \implies (\boxed{ \sf 8x} + (2y - y))((5x + 2y) - (3x - y)) \\ \\ \sf 2y - y = y : \\ \sf \implies (8x + \boxed{ \sf y})((5x + 2y) - (3x - y)) \\ \\ \sf - (3x-y)=y-3x: \\ \sf \implies (8x + y)(5x + 2y + \boxed{ \sf y - 3x}) \\ \\ \sf Grouping \: like \: terms, \: 5x + 2y + y - 3x = \\ \sf (5x - 3x)(2y + y) : \\ \sf \implies (8x + y) + \boxed{ \sf ((5x - 3x)(2y + y))} \\ \\ \sf 5x - 3x = 2x : \\ \sf \implies (8x + y)( \boxed{ \sf 2x} + (2y + y)) \\ \\ \sf 2y + y = 3y : \\ \sf \implies (8x + y)(2x + \boxed{ \sf 3y})[/tex]
Answer:
(8x+y)(2x+3y)
Step-by-step explanation:
see attached
In the diagram below, angle BAC = 34°.
Find the following angles, giving reasons for your answers.
a) angle ABC
b) angle BCA
Answer:
a) 90°
b) 56°
Step-by-step explanation:
If we connect O with B to get two isosceles triangles: ΔAOB and ΔBOC
∠BOC= is central angle ans is twice as ∠BAC, so equals to 2*34°= 68°
Then ∠BCA= (180°- 68°)/2= 56°
∠ABC= ∠ABO+∠CBO= 34°+56°= 90°
Find the missing side lengths. Answers are in simplest radical form with the denominator rationalized
Answer:
Option B.
Step-by-step explanation:
The given triangle is a right angle triangle.
In a right angle triangle,
[tex]\tan \theta=\dfrac{Perpendicular}{Base}[/tex]
In the given triangle,
[tex]\tan (45^{\circ})=\dfrac{v}{7}[/tex]
[tex]1=\dfrac{v}{7}[/tex]
[tex]7=v[/tex]
Using Pythagoras theorem, we get
[tex]hypotenuse^2=Perpendicular^2+Base^2[/tex]
[tex]u^2=v^2+7^2[/tex]
[tex]u^2=7^2+7^2[/tex]
[tex]u^2=2(7^2)[/tex]
Taking square root on both sides, we get
[tex]u=\sqrt{2(7^2)}[/tex]
[tex]u=7\sqrt{2}[/tex]
Therefore, the correct option is B.
Please help me match these formulas thank you :)
Answer:
Circle Circumference: 5
Triangle: 8
Circle Area: 3
Regular Polygon: 7
Parallelogram:6
Equilateral triangle: 1
Trapezoid:4
Rectangle:2
Step-by-step explanation:
I don't know how I would do a step by step explanation
Jason wants to build a ramp for a wheelchair at an angle of 10° with the ground. If the ramp has a horizontal length of 20 m, what is the maximum height of the ramp?
Answer:
12 mStep-by-step explanation:
Given data
θ= 10°
Horizontal length is equivalent to the adjacent= 20 m
the height of the ramp is equivalent to the opposite=?
Applying SOH CAH TOA we have
using TOA
Tan θ= opp/adj
Tan 10= opp/20
opp= Tan(10)* 20
opp= 0.64836*20
opp= 12.96
Approximately the maximum height of the ramp is 12 m
Which of the following is NOT a solution to the system of inequalities?
a. (0, 4)
b. (2, 1)
c. (1, 5)
d. (1, 2)
Answer:
(2,1)
Step-by-step explanation:
The point (2,1) is the only point that is not included in the shaded region so I would assume that it's not a solution to the system.
Need Help With this question
Answer:
Area of ΔDEF = 12 in²
Step-by-step explanation:
Since they are similar, we have to find the scale factor
Scale Factor = [tex]\frac{Side OfDilated Triangle}{Side of Original Triangle}[/tex]
Scale Factor = 4/2
Scale Factor = 2
This means The area of ΔABC is 2 times the area of ΔDEF
So,
ΔABC = 2(ΔDEF)
Where Area of ΔABC = 24 in²
24 = 2(ΔDEF)
Dividing both sides by 2
=> Area of ΔDEF = 12 in²
David and Amanda are trying to figure out how long they can live off their $12,350 savings if they spend $240 each month. They have each created an equation.
David’s Equation y = 12,350 – (240x)
Amanda’s Equation y = 12,350 + (240x)
Which person has the correct equation to model this linear relationship?
1. Amanda’s equation is correct because their spending will be multiplied by the number of months and then added to their savings.
2. Amanda’s equation is incorrect because their spending will increase the amount of their savings.
3. David’s equation is correct because their spending will be multiplied by the number of months and then subtracted from their savings.
4. David’s equation is incorrect because their spending should be a fixed amount and should not be multiplied.
Hey there! :)
Answer:
Choice 3: David's equation is correct because their spending will be multiplied by the number of months and then subtracted from their savings.
Step-by-step explanation:
In the question, $12,350 is given as the initial value and '240x' is the monthly spending in terms of x.. When writing the equation, we must subtract 240x because the money is being spent.
The correct equation for this situation would be:
y = 12,350 - (240x).
Thus, David's Equation is correct.
due in 5 min need help please ?
Answer:
x = 1
Step-by-step explanation:
This is a 30-60-90 triangle, which means that if the long leg is the square root of 3, the hypotenuse is 1.
Answer:
X=1
Step-by-step explanation:
2. In the diagram below, angle AOB = 66°
Find angle OAB, giving reasons for your answer.
Answer:
57°
Step-by-step explanation:
Δ AOB has 2 equal sides as radius of the circle, this is isosceles triangle
So the angles ∠OAB= ∠OBA
∠AOB= 66° and sum of 3 angles = 180°
So ∠OAB= (180° - 66°)/2= 57°
The function h(x) is a translation of the exponential function g(x) = 9(1∕6)x. What's h(x) if the translation is a vertical shrink by a factor of 1∕3 and horizontal shift to the left 4 units?
Answer: h(x) = 3*(1/6)^(x + 4)
Step-by-step explanation:
if we have a function g(x), and we want to create another function h(x) such that:
h(x) is a vertical contraction/dilation of factor a.
Then h(x) = a*g(x).
h(x) is a right shift of N units (N positive):
h(x) = g(x - N)
Then:
A vertical shink of factor 1/3 means that:
h(x) = (1/3)*g(x)
And a left shift of 4 units (or a right shift of -4 units) means that
h(x) = (1/3)g(x - (-4)) = (1/3)*g(x + 4)
and we know that:
g(x) = 9*(1/6)^x
Then:
h(x) = (1/3)*9*(1/6)^(x + 4) = 3*(1/6)^(x + 4)
Two boats leave port at noon. Boat 1 sails due east at 12 knots. Boat 2 sails due south at 8 knots. At 2 pm the wind diminishes and Boat 1 now sails at 9 knots. At 3 pm, the wind increases for Boat 2 and it now sails 7 knots faster. How fast (in knots) is the distance between the two ships changing at 5 pm. (Note: 1 knot is a speed of 1 nautical mile per hour.)
Answer:
14.86 knots.
Step-by-step explanation:
Given that:
The boats leave the port at noon.
Speed of boat 1 = 12 knots due east
Speed of boat 2 = 8 knots due south
At 2 pm:
Distance traveled by boat 1 = 24 units due east
Distance traveled by boat 2 = 16 units due south
Now, speed of boat 1 changes to 9 knots:
At 3 pm:
Distance traveled by boat 1 = 24 + 9= 33 units due east
Distance traveled by boat 2 = 16+8 = 24 units due south
Now, speed of boat 1 changes to 8+7 = 15 knots
At 5 pm:
Distance traveled by boat 1 = 33 + 2[tex]\times[/tex] 9= 51 units due east
Distance traveled by boat 2 = 24 + 2 [tex]\times[/tex] 15 = 54 units due south
Now, the situation of distance traveled can be seen by the attached right angled [tex]\triangle AOB[/tex].
O is the port and A is the location of boat 1
B is the location of boat 2.
Using pythagorean theorem:
[tex]\text{Hypotenuse}^{2} = \text{Base}^{2} + \text{Perpendicular}^{2}\\\Rightarrow AB^{2} = OA^{2} + OB^{2}\\\Rightarrow AB^{2} = 51^{2} + 54^{2}\\\Rightarrow AB^{2} = 2601+ 2916 = 5517\\\Rightarrow AB = 74.28\ units[/tex]
so, the total distance between the two boats is 74.28 units.
Change in distance per hour = [tex]\dfrac{Total\ distance}{Total\ time}[/tex]
[tex]\Rightarrow \dfrac{74.28}{5} = 14.86\ knots[/tex]
PRE CALC PLEASE HELP PLEASE
Answer:
The statement is true
Step-by-step explanation:
We have been given an equation of hyperbola
In the given equation of hyperbola center is located at h at -1 and k at 2. so:
C:(h,k) = (-1,2)
Coordinated of the foci of the hyperbola are given as:
Foci: (h, k ± c)
Substitute the values of h and k into the coordinated of foci of hyperbola.
Foci: (-1, 2 ± c)
Where c can be found by using the given formula
c = √(a²+b²)
c = √(16+144)
c = 4√10
So the the coordinates of the foci are:
Foci: (-1, 2 - 4√10) and (-1, 2 + 4√10)
Thus, the statement given is true
WILL AWARD BRAINLIEST PLEASE HELP!!!
Answer:
A
Step-by-step explanation:
Identify the lateral area and surface area of a right cone with radius 7 cm and slant height 15 cm a. L = 329.9 cm2 ; S = 373.9 cm2 b. L = 329.9 cm2 ; S = 483.8 cm2 c. L = 659.7 cm2 ; S = 483.8 cm2 d. L = 659.7 cm2 ; S = 813.6 cm2
Answer:
Step-by-step explanation:
a.
L
=
329.9
c
m
2
;
S
=
373.9
c
m
2
.
b.
L
=
659.7
c
m
2
;
S
=
483.8
c
m
2
.
c.
L
=
659.7
c
m
2
;
S
=
813.6
c
m
2
.
d.
L
=
329.9
c
m
2
;
S
=
483.8
c
m
2
.
Surface Area of a Cone:
In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.
The height of the cone is the length of a line segment that joins the base to the vertex of the cone.
The radius of the cone is the same as the radius of the base.
Surface area of a cone
(a) Lateral Surface Area
If
l
and
r
are the slant height and radius of a cone then its lateral surface area is given by the formula-
L
=
π
r
l
where
L
is the lateral surface area of the cone
(b) Total surface area
It is the sum of the area of the circular base and the lateral surface area of the cone.
S
=
L
+
π
r
2
S
=
π
r
l
+
π
r
2
Where
S
is the total surface area of the cone
Answer and Explanation:
Given that the radius and slant height of a right cone is
7
c
m
and
15
c
m
respectively
r
=
7
c
m
l
=
15
c
m
So the lateral surface area of the cone-
L
=
π
r
l
L
=
π
(
7
)
(
15
)
L
=
105
π
L
=
105
(
3.14159
)
L
=
329.866
L
≈
329.9
c
m
2
And the total surface area of the cone-
S
=
L
+
π
r
2
S
=
329.9
+
π
(
7
)
2
S
=
329.9
+
49
(
3.14159
)
S
=
329.9
+
153.937
S
=
483.83
c
m
2
So the lateral area and total area of a right cone are
329.9
c
m
2
and
483.8
c
m
2
respectively.
Answer:
Step-by-step explanation:
Step-by-step explanation:
a.
L
=
329.9
c
m
2
;
S
=
373.9
c
m
2
.
b.
L
=
659.7
c
m
2
;
S
=
483.8
c
m
2
.
c.
L
=
659.7
c
m
2
;
S
=
813.6
c
m
2
.
d.
L
=
329.9
c
m
2
;
S
=
483.8
c
m
2
.
Surface Area of a Cone:
In the three dimensional geometry, a cone is a shape that has a circular base and a lateral surface is associated with a vertex and the base.
The height of the cone is the length of a line segment that joins the base to the vertex of the cone.
The radius of the cone is the same as the radius of the base.
Surface area of a cone
(a) Lateral Surface Area
If
l
and
r
are the slant height and radius of a cone then its lateral surface area is given by the formula-
L
=
π
r
l
where
L
is the lateral surface area of the cone
(b) Total surface area
It is the sum of the area of the circular base and the lateral surface area of the cone.
S
=
L
+
π
r
2
S
=
π
r
l
+
π
r
2
Where
S
is the total surface area of the cone
Answer and Explanation:
Given that the radius and slant height of a right cone is
7
c
m
and
15
c
m
respectively
r
=
7
c
m
l
=
15
c
m
So the lateral surface area of the cone-
L
=
π
r
l
L
=
π
(
7
)
(
15
)
L
=
105
π
L
=
105
(
3.14159
)
L
=
329.866
L
≈
329.9
c
m
2
And the total surface area of the cone-
S
=
L
+
π
r
2
S
=
329.9
+
π
(
7
)
2
S
=
329.9
+
49
(
3.14159
)
S
=
329.9
+
153.937
S
=
483.83
c
m
2
So the lateral area and total area of a right cone are
329.9
c
m
2
and
483.8
c
m
2
respectively.
Find the volume, in cubic centimeters, of the solid shown
where h = 14 cm, s = 7 cm, and d = 10 cm. (Round to two
decimal places.)
Answer:
733.04
Step-by-step explanation:
Cylinder:
V=3.14x5x5x7
=549.78
Cone:
V=3.14x5x5x7/3
=183.26
TOTAL:
549.78+183.26=733.04
Given the following system of equations, solve it by using substitution and elimination. Do
you get the same answer? Why or why not? Explain using complete sentences.
2x+3y = -14
3x + y =-14
Step-by-step explanation:
2x+3y=-14------equation i ×1
3x+y=-14--------equation ii ×3
2x+3y=-14
9x+3y=-42
-7x =- 28
x=4
Substitute for x in equation ii
3x+y= -14
3(4)+y=-14
12+y=-14
y=-14-12
y=- 26
A science test, which is worth 100 points, consists of 24 questions. Each question is worth either 3 points or 5 points. If x is the number of 3-point questions and y is the number of 5-point questions, the system shown represents this situation.
x + y = 24
3x + 5y = 100
What does the solution of this system indicate about the questions on the test?
The test contains 4 three-point questions and 20 five-point questions.
The test contains 10 three-point questions and 14 five-point questions.
The test contains 14 three-point questions and 10 five-point questions.
The test contains 20 three-point questions and 8 five-point questions.
help will give brainliest
Answer: A. (-3,7)
Step-by-step explanation:
No work needed, you just need to look at the coordinate plane.
Coordinate II is x as a negative and y as a positive
Answer:
D, (5,-1)
5 is in the x axis
-1 is in the y axis
This point is it the second quadent
Hope this helps ( if incorrect try a)
how many real roots and how many complex roots are possible with a root of 9
Answer:
12
Step-by-step explanation:
because the more the root the faster the plant grows
Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel. please Show All Work! Thanks!!
Answer:
Here You Go! I'm not really sure about this one but i tried.
Step-by-step explanation:
Answer:
Step-by-step explanation:
To prove this we should first make a little representation to get an idea of how will proceed to work .
To solve it we should use vectors so the first step is to identify this vectors :
we have four points : A/B/C/DA(-2,-4)B(1,2)C(2,10)D(-1,4)VECTOR AB WITH VECTOR DC VECTOR AD WITH VECTOR BCNOW LET'S IDENTIFY THEIR COORDINATES :
VECTOR AB (1-(-2),2-(-4)) VECTOR DC (2-(-1),10-4)VECTOR AD (-1-(-2),4-(-4)) VECTOR BC (2-1,10-2)We get :
VECTOR AB (3,6) VECTOR DC (3,6)VECTOR AD (1,8) VECTOR BC (1,8)We notice that the opposite ones have the same coordinates so the edges are parallel .
If we want to check more we can calculate the lenghts :
AB=[tex]\sqrt{3^{2}+6^{2} }[/tex] DC=[tex]\sqrt{3^{2}+6^{2} }[/tex]So AB=DC
AD=[tex]\sqrt{1^{2}+8^{2} }[/tex] BC=[tex]\sqrt{1^{2}+8^{2} }[/tex]So AD=BC
SO ABCD IS A PARALLELOGRAM
Identify the two remote interior angles that correspond to angle 4.
Answer:
1 & 2
Step-by-step explanation:
Remote interior angles are the angles inside of a triangle but not on the same straight line as the exterior angle (4)
Answer:
<1 and <2 are the remote interior angles for angle 4
Step-by-step explanation:
The remote interior angles that correspond to angle 4 are the angles that are in the triangle that are not adjacent to angle 4
<1 and <2 are the remote interior angles
When converting a improper fraction into a mixed number how do you find the denominator for the mixed number?
answer: the denominator of the improper fraction is the sum of the numerator and the product of denominator and the whole number of the mixed fraction.
Answer:
It is the same denominator of the fraction.
Step-by-step explanation:
[tex]1\frac{1}{5} = \frac{x}{y}[/tex]
[tex]1\frac{1}{5} = \\1=\frac{5}{5}\\\frac{1}{5} = \frac{1}{5}\\\frac{5}{5} +\frac{1}{5} =\frac{6}{5}[/tex]
Work out the value of n 1/4 × √ 2 = 2 n | 1/4 is a fraction
Answer:
n = √2/8
Step-by-step explanation:
1/4 × √ 2 = 2n
√2/4 = 2n
√2 = 4×2n
8n = √2
n = √2/8
The value of n in
[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]
is n = √2 / 8
The given equation is:
[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]
Multiply through by 4
[tex] \sqrt{2} = 4(2n)[/tex]
This can be further simplified as
[tex] \sqrt{2} = 8n[/tex]
[tex] \frac{ \sqrt{2} }{8} = \frac{8n}{8} [/tex]
The like terms cancel out
[tex]n = \frac{ \sqrt{2} }{8} [/tex]
Therefore, the value of n in
[tex] \frac{1}{4} \times \sqrt{2} = 2n[/tex]
is
[tex]n = \frac{ \sqrt{2} }{8} [/tex]
Learn more here: https://brainly.com/question/2956399
Box A contains 5 dark chocolates and
10 milk chocolates. Box B contains 12
dark chocolates and 12 milk chocolates.
Craig picks a box at random and then
takes out one chocolate at random.
What is the probability he chooses box B?
%
Answer:
50 %
Step-by-step explanation:
WXY is congruent to CBA, If
Answer:
If they are opposite.
A factory can work its employees no more than 6 days a week, and no less than 2 days per
week. Create an inequality to represent the range of days an employee can work. Solve
the inequality to determine the range in hours if the work day is 6.5 hours. Show all of your
work and explain each of your steps. Explain your answer.
Answer:
13<x<39 (range of hours)
Step-by-step explanation:
2<x<6 (x is the range of days)
Since each workday is 6.5 hours, multiply everything by 6.5:
13<x<39 (the new x is the range of hours)
Solve the system of equations and choose the correct ordered pair. 6x-6y+11=17 and 9y=3x+15
Answer:
D is the correct answer
Step-by-step explanation:
according to the graph you can see that D should be correct.
Good luck! ^_^
how do I find the radius
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the SURFACE AREAS AND VOLUMES.
Since the given section is a Sector of a Circle with length as, 8πcm .
Thus then it's folded veltically at an axis to make a cone.
since we know that, The Curved surface area of a cone is given as formula,
C.S.A = πrl
where, r = radius and l = slant height.
also 2πr = circumference of a circle,
we get as, radius = 4 cm.
Answer:
r = 4 cm
Step-by-step explanation:
AB is actually the circumference of the circle
So,
Circumference = 8π cm
Whereas,
Circumference = 2πr
8π = 2πr
Dividing both sides by 2π
=> r = 4 cm