Answer:
An expression for the temperature on February 10 = -15F +42F = 27F
Step-by-step explanation:
the problem given is based on the algebra of simple addition : -
Addition of Algebraic Expressions : -
In addition of algebraic expressions while adding algebraic expressions we collect the like terms and add them. The sum of several like terms is the like term whose coefficient is the sum of the coefficients of these like terms.
Two ways to solve addition of algebraic expressions.
Horizontal Method: In this method, all expressions are written in a horizontal line and then the terms are arranged to collect all the groups of like terms and then added.
Column Method: In this method each expression is written in a separate row such that there like terms are arranged one below the other in a column. Then the addition of terms is done column wise.
so the question can be solved using Horizontal method :-
temperature on 9 Feb = -15F
temperature rose on 10th Feb = 42F
so the temperature on 10th Feb is :
-15F +42F = 27F
therefore, an expression for the temperature on February 10 is
-15F +42F = 27F (answer)
read more about Addition of Algebraic Expressions at
https://brainly.com/question/12109607
#SPJ10
What is the measure of the unknown angle?
straight angle divided into a one hundred thirty two degree angle and an unknown angle
48°
49°
51°
53°
Given a b and m/1 = 42°
What is m/6?
Enter your answer in the box.
A,B, C and D are the four corners of a rectangular plot marked out on level ground. Given that the bearing of B from A is 40 and the bearing of C from A is 90, Find the bearing B frOm C
Answer:
given - a rectangle ABCD
AB = 40
AC. = 90
BC = ?
in triangle ABC
using Pythagoras theorem
(AB) ² + (BC) ² = (AC) ²
(40)² + (BC) ² = (90)²
(BC) ² = (90)²- (40)²
(BC) ² = 8100 - 1600
(BC) ² = 6500
BC =
[tex]20 \sqrt{10} [/tex]
what is 25:28 in slimpelst from
Answer:
25:28 is the simplest form
Step-by-step explanation:
This is a ratio, think of it like a fraction. You can simplfy it by dividing by common factor.
25 and 28 have no common factors except for 1.
25: 1,5,25
28: 1,2,4,7,14,28
It will stay as 25:28
Answer:
it stays the exact same or 0.893
Step-by-step explanation:
Determine whether the given differential equation is exact. If it is exact, solve it. (tan(x)-sin(x)sin*y))dx+cos(x)cos(y)dy=0 g
The differential equation
[tex]M(x,y) \, dx + N(x,y) \, dy = 0[/tex]
is considered exact if [tex]M_y = N_x[/tex] (where subscripts denote partial derivatives). If it is exact, then its general solution is an implicit function [tex]f(x,y)=C[/tex] such that [tex]f_x=M[/tex] and [tex]f_y=N[/tex].
We have
[tex]M = \tan(x) - \sin(x) \sin(y) \implies M_y = -\sin(x) \cos(y)[/tex]
[tex]N = \cos(x) \cos(y) \implies N_x = -\sin(x) \cos(y)[/tex]
and [tex]M_y=N_x[/tex], so the equation is indeed exact.
Now, the solution [tex]f[/tex] satisfies
[tex]f_x = \tan(x) - \sin(x) \sin(y)[/tex]
Integrating with respect to [tex]x[/tex], we get
[tex]\displaystyle \int f_x \, dx = \int (\tan(x) - \sin(x) \sin(y)) \, dx[/tex]
[tex]\implies f(x,y) = -\ln|\cos(x)| + \cos(x) \sin(y) + g(y)[/tex]
and differentiating with respect to [tex]y[/tex], we get
[tex]f_y = \cos(x) \cos(y) = \cos(x) \cos(y) + \dfrac{dg}{dy}[/tex]
[tex]\implies \dfrac{dg}{dy} = 0 \implies g(y) = C[/tex]
Then the general solution to the exact equation is
[tex]f(x,y) = \boxed{-\ln|\cos(x)| + \cos(x) \sin(y) = C}[/tex]
Sylvia bought 4 bananas for 50 cents each and 1 apple for 80 cents. Write a numerical expression to represent this situation and then find the total cost.
Answer: 280
Step-by-step explanation:
50 cents for each banana so: 4* 50= 200
200+80
Answer is 280
The base of the pyramid is a rectangle that is not a
square. Which statements correctly describe the
symmetry of the pyramid? Check all that apply.
The pyramid has four planes of symmetry.
O The pyramid has two planes of symmetry.
An axis of symmetry passes through the vertex and
is perpendicular to the base.
An axis of symmetry passes through the vertex and
through one of the triangular faces of the pyramid.
An angle that measures 90° is an angle of rotation
for an axis of symmetry for the pyramid.
An angle that measures 45° is an angle of rotation
for an axis of symmetry for the pyramid.
An axis of symmetry passes through the vertex and is perpendicular to the base. Then the correct options are B, C, and E.
What is a rectangular pyramid?Take a rectangle. This is the base. Now take 4 triangles such that each of them are connected to one-one side of the base rectangle and when they're taken together, they form a closed object. That shape is called rectangular pyramid.
The base of the pyramid is a rectangle that is not a square.
The pyramid has two planes of symmetry.
An axis of symmetry passes through the vertex and is perpendicular to the base.
An angle that measures 90° is an angle of rotation for an axis of symmetry for the pyramid.
Then the correct options are B, C, and E.
Learn more about rectangular pyramid here:
https://brainly.com/question/16261758
#SPJ1
Solve for x in the equation
X
O x=-11±25
O x=-11+25
0 x--11+5√/5
Ox--11,5/5
2
x²+11x+121-125
4
=
Answer:
The answer for this question is c
The value of x from the quadratic term equation is x = ( -11/2 ) ± ( 5√5 ) / 2
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 11x + 121/4 = 125/4
Subtracting ( 125/4 ) on both sides , we get
x² + 11x + ( 121 - 125 ) / 4 = 0
x² + 11x - 1 = 0 be equation (1)
On simplifying , we get
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
So , x = [ -11 ± √ ( 11 )² - 4 ( 1 ) ( -1 ) ] / 2
On further simplification , we get
x = -11 ± √ ( 121 + 4 ) / 2
x = [ -11 ± √125 ] / 2
x = ( -11/2 ) ± ( 5√5 ) / 2
Therefore , the roots of the equation are x = ( -11/2 ) ± ( 5√5 ) / 2
Hence , the quadratic equations are solved
To learn more about quadratic equations click :
https://brainly.com/question/25652857
#SPJ5
A car travels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles pr
hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of
car for the whole trip?
O20.0 mph
37.5 mph
40.0 mph
O45.0 mph
O80.0 mph
Click Save and Submit to save and submit. Click Save All Answers to save all answers.
Answer:
Definition: The average speed over the course of mobion can be calculated using the formula Total Distance Traveled Average Speed = Time of Travel A car fravels a distance of 300 miles along a straight road from point A to point B. The car maintains a speed of 30 miles per hour (mph) during the first 150 miles and a speed of 50 mph during the remaining 150 miles. What is the average speed of the car for the whole trip? 20.0 mph 37.5 mph 40.0 mph 45.0 mph 80.0 mph QUESTION 13 Wriat is the height h, of the equilateral triangle shown below? Aak Sareend Sabmit ro save and submit. Click Save AlAnseers to save all ansuers Save
Average speed of the whole trip is equals to 37.5 mph.
What is average speed?
" Average speed is defined as the ratio of the total distance travelled to the total time taken."
Formula used
Average speed = [tex]\frac{Total distance travelled }{Total time taken}[/tex]
According to the question,
Total distance travelled = 300miles
Speed for first 150 miles = 30 miles per hour
For, 30 miles = 1hour
⇒150 miles = 5 hours
Speed for remaining 150 miles = 50 miles per hour
For, 50 miles = 1hour
⇒150 miles = 3 hours
Substitute the value in the formula to get average speed,
Average speed = [tex]\frac{300miles}{(5 + 3)hours}[/tex]
[tex]=\frac{300}{8}\\ \\= 37.5 miles per hour[/tex]
Hence, average speed of the whole trip is equals to 37.5 mph.
Learn more about average speed here
https://brainly.com/question/12322912
#SPJ2
Y = 4x -2 and y = x +3
Answer:
(0.5,2) and (-3,3)
Step-by-step explanation:
Answer:
Y = 4x -2 is (0.5,2)
y = x +3 is (-3,3)
Raya buys a van for £9500 plus VAT at 20%
Raya pays a deposit for the van.
She then pays the rest of the cost in 12 equal payments of £665 each month.
Find the ratio of the deposit Ray pays to the total of the 12 equal payments.
Give your answer in its simplest form.
Step-by-step explanation:
yo thara bhai joginder tu he ek bndr
Mark ran a mean distance of 13.2 km in five days. The next day, Mark ran 20 km.
Find the mean distance Mark ran in the six days.
Answer:
16.6
Step-by-step explanation:
Add the numbers together.
13.2+20=33.2
Now divide the number by 2.
33.2/2=16.6
Hope this helps!
If not, I am sorry.
Which currency is it
Answer:
pounds (£)
Step-by-step explanation:
pounds are used in countries such as the UK and South Georgia
Type a number for the types of journals that will be available to you in the new lma
Answer:
Step-by-step explanation:
What are the 6 types of journals?
There are various types of journals including:
academic/scholarly journals.
trade journals.
current affairs/opinion magazines.
popular magazines.
newspapers.
f(x) = x^2 + 5x - 1 is shifted 3 units left the result is g(x). What is g(x)?
Answer:
A. g(x)=x^2+5x+2
Step-by-step explanation:
f(x) = x^2 + 5x - 1 Shift 3 units to the left. k=3
g(x)=x^2+5x-1+3=x^2+5x+2
g(x)=x^2+5x+2
Hope this helps!
If not, I am sorry.
You are heading to a drive-in movie and will need exact cash at the entrance for everyone in your car to get in. The cost is $6.50 per person. Write an expression that represents the total cash needed for your car based on the number of people, p, in your car.
Answer:
Using the concept of equation of line, we find that the relationship will be
C = $6.5p.
Step-by-step explanation:
If the cost per head is $6.5 and there are p persons entering the car, then the total amount would be $6.5p.
The final equation would resemble the equation of line y = mx + c.
The expression for the total cost C, would be
C = 6.5p.
Here y = C, x = p, m = 6.5 and c = 0.
So, the expression for the total cost will be the equation of line C = 6.5p.
For more explanation, refer the following link:
https://brainly.com/question/11552995
#SPJ10
Which of the following are solutions to the equation below?
(2x+3)^2 = 10
Check all that apply.
Answer:
x = (√10 -3)/2 and (-√10 -3)/2
Step-by-step explanation:
(2x+3)^2 = 10
To solve the equation, take the square root of each side
sqrt((2x+3)^2) = ±√10
2x+3 = ±√10
Subtract 3 from each side
2x+3-3 = ±√10 -3
2x = ±√10 -3
Divide each side by 2
2x/2 = (±√10 -3)/2
x = (±√10 -3)/2
There are two solutions
x = (√10 -3)/2
and (-√10 -3)/2
Answer:
[tex]\large {\textsf{A and D}}\ \implies \sf \sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]
Step-by-step explanation:
Given: (2x + 3)² = 10
In order to find the solutions to the given equation, we can take the (square) roots of the equation to find the zeros, which are also known as the x-intercepts. This is where the zeros intersect the x-axis.
Note: when taking the square roots of a quadratic equation, remember to use both the positive and negative roots.
Step 1: Square both sides of the equation.
[tex]\sf \sqrt{(2x + 3)^2} = \sqrt{10}\\\\\Rightarrow 2x+3=\pm\sqrt{10}[/tex]
Step 2: Separate into possible cases.
[tex]\sf x_1 \implies 2x+3=-\sqrt{10}\\\\x_2 \implies 2x+3=\sqrt{10}[/tex]
Step 3: Solve for x in both cases.
[tex]\sf \bold{x_1} \implies 2x+3=-\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=-\sqrt{10}-3\\\\\Rightarrow 2x=-\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{-\sqrt{10}-3}{2}\\\\\Rightarrow x_1=\dfrac{-\sqrt{10}-3}{2}\\\\[/tex]
[tex]\sf \bold{x_2}\implies 2x+3=\sqrt{10}\ \ \textsf{[ Subtract 3 from both sides. ]}\\\\\Rightarrow 2x+3-3=\sqrt{10}-3\\\\\Rightarrow 2x=\sqrt{10}-3\ \ \textsf{[ Divide both sides by 2. ]}\\\\\Rightarrow \dfrac{2x}{2}=\dfrac{\sqrt{10}-3}{2}\\\\\Rightarrow x_2=\dfrac{\sqrt{10}-3}{2}[/tex]
Therefore, the solutions to this quadratic equation are: [tex]\sf \bold{x_1}=\dfrac{-\sqrt{10}-3}{2},\ \bold{x_2}=\dfrac{\sqrt{10}-3}{2}[/tex]
Learn more about quadratic equations here:
brainly.com/question/27031173
I need help for solving y in this problem 2x -y =1
Answer:
y = 2x - 1
Step-by-step explanation:
Given equation: 2x - y = 1
We're being asked to solve for y. This is also known as the Slope-Intercept Form. It is represented by the following formula:
y = mx + b
where:
m is the slopeb is the y-intercept (when x = 0)Steps:
1. Subtract 2x from both sides:
[tex]\sf 2x-2x - y = 1-2x\\\\\implies-y=-2x+1[/tex]
2. Divide both sides by -1:
[tex]\sf \dfrac{-y}{-1}=\dfrac{-2x+1}{-1}\\\\\implies y=2x-1[/tex]
This equation has a slope of 2, and a y-intercept of -1.
Learn more about the Slope-Intercept Form here:
brainly.com/question/27913326
brainly.com/question/27941697
An amusement park charges $7 for adults, $2 for youths, and $0.50 for children. if 150 people enter and pay a total of $100, find the numbers of adults, youths, and children. [hint: these numbers are nonnegative integers.]
The number of adults are 2 . the number of youths are 8
Given charge $7 for adults , $2 for youth and $0.50 for children
Let the number of adults , youths and children be x , y and z
Now it is given that there is total pay of 100
Therefore the equation formed is
7x + 2y +0.50 = 100
Now it is also given that 150 people enter
Therefore
x+y+z=150
x+y+z =150
14x+4y+z=200
Using argument matrix
[tex]\left[\begin{array}{ccc}1&1&1\\14&4&1\end{array}\right] \left[\begin{array}{ccc}150\\200\end{array}\right][/tex]
Corresponding system equation is
x+y+z=150
y+(13/10)z=190
Take z = m (arbitary)
y = 190 - 1.3 m
x = 150 - y
m = 140 x = 2 and y = 8
Hence The number of adults are 2 . the number of youths are 8
Learn more about argument matrix here:
https://brainly.com/question/1821869
#SPJ10
1. Given the points A (2, 14) and B (17, -6).
(a) Find the distance of the line AB.
(b) Find the midpoint of the line AB.
(c) Find the gradient of the line AB.
(d) Find the equation of the line AB.
(e) Find the equation of the line parallel to AB passing through the point (3,5).
(f) Find the equation of the line perpendicular to AB passing through point (4,-2).
(g) Draw the above 3 lines on a graph.
Answer:
Step-by-step explanation:
The work of a student to solve the equation 4(2x − 4) = 8 + 2x + 8 is shown below: Step 1: 4(2x − 4) = 8 + 2x + 8 Step 2: 6x − 8 = 16 + 2x Step 3: 6x − 2x = 16 + 8 Step 4: 4x = 24 Step 5: x = 6 In which step did the student first make an error and what is the correct step? (5 points) Step 2; 8x − 4 = 2(6 + x + 6) Step 2; 8x − 16 = 16 + 2x Step 3; 6x − 2x = 16 − 8 Step 3; 6x + 2x = 16 + 8
What is the equation of the directrix of the parabola given by the equation y2 = -24x?
The equation of the directrix of the parabola given is x = 6, Option D is the correct answer.
What is Directrix of a Parabola ?A parabola is a U shaped curve whose all point are at same distnace from a point called as focus and a line called as Directrix .
The equation of the parabola given is
y² = -24x
When the standard equation of parabola is
(y - k)² = 4p (x - h),
where the focus is (h + p, k) and the directrix is x = h - p.
here h = 0
p = -24/4 = -6
x = 0 - (-6)
x = 6
Therefore Option D is the correct answer.
To know more about Directrix
https://brainly.com/question/17376399
#SPJ1
PLS I REALLY NEED HELP I NEED TO PASS THIS ASAP
The volume of the cylinder is 1692.46dm³.
How to calculate the volume?It should be noted that the volume of a cylinder is calculated as:
= πr²h
r = radius = 7dm
h = height = 11dm
Volume = πr²h
Volume = 3.14 × 7² × 11
Volume = 3.14 × 49 × 11
Volume = 1692.46dm³
Learn more about volume on:
brainly.com/question/1972490
#SPJ1
??????????????????????????????????????????????????
Answer:
x=20
Step-by-step explanation:
The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees
so 4x +5x =9x
9x=180
x=20
4x=80
5x=100
m∠DFG=(2x+6)° and m∠EFG=(3x−11)°. Find the value of x.
The figure shows straight angle D F E that consists of two angles, D F G and E F G.
Answer:
x = 37
Step-by-step explanation:
A straight angle is 180 degrees. That means ∠DFG & ∠EFG have to add together to be 180.
2x + 6 + 3x - 11 = 180 Combine like terms
5x - 5 = 180 Add 5 to both sides
5x = 185 Divide by 5
x = 37
∠DFG = 80°
∠EFG = 100°
Find the solution:
3x + 2y = 12
-2x + 3y = 5
Answer:
x = 3
y = 2
Step-by-step explanation:
3x + 2y = 12
-2x + 3y = 5 to find the solution we will use elimination method and for that, multiply second equation with 3 and the first equation with 2
2 * 3x + 2y = 12
6x + 4y = 24
3 * -2x + 3y = 5
-6x + 9y = 15 now find the sum of both equation:
6x + 4y -6x + 9y = 24 + 15 add like terms
13y = 39 divide both sides by 13
y = 3 now that we found the value of y we can use this to calculate the value of x
3x + 2y = 12 replace y with 3
3x + 2*2 = 12
3x + 4 = 12 subtract 4 from both sides
3x = 9 divide both sides by 3
x = 3
a motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West what is the velocity of the wind.
The velocity of the wind will be 50 km per hour.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
A motorcyclist riding North along a straight road at 50 km per hour observes that the wind appeared to have a velocity of 50 km per hour from the direction North 60 degrees West.
Then the velocity of the wind will be
Let x be the speed of the wind. Then we have
x² = 50² + 50² - 2 x 50 x 50 x cos 60°
x² = 2500 + 2500 - 2500
x² = 2500
x = 50 km per hour
More about the vector link is given below.
https://brainly.com/question/13188123
#SPJ1
A solid right pyramid has a regular hexagonal base with an area of 7.4 units2. The pyramid has a height of 6 units.
It should be noted that the volume of the pyramid will be 14.8 unit³.
From the information given, the solid right pyramid has a regular hexagonal base with an area of 7.4 units².
The height of the pyramid is also 6 units.
Therefore, the volume of the pyramid will be
What is the formula for the area of the pyramid?= 1/3 × Area of the base × height
= 1/3 × 7.4 × 6
= 14.8 units³
In conclusion, the volume of the pyramid is 14.8 unit³.
To learn more about the pyramid visit:
brainly.com/question/218706
#SPJ1
(-3, 1)
-5-4-3
(-2,-4)
k
4
4
ob
1
2-
3+
(2/2)
What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
point (-3, 1)?
Oy-1= -2(x+3)
Oy-1=-(x+3)
Oy - 1 =
Oy-1 =
(x+3)
(x+3)
Answer:
What is the slope of the line represented by the equation y = y equals StartFraction 4 Over 5 EndFraction x minus 3.x – 3?
Step-by-step explanation:
The equation of line that is parallel to the given line having slope m = -1 and passes through the point ( -3 , 1 ) is y = -x - 2
What is an Equation of a line?The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept
And y - y₁ = m ( x - x₁ )
y = y-coordinate of second point
y₁ = y-coordinate of point one
m = slope
x = x-coordinate of second point
x₁ = x-coordinate of point one
The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given data ,
Let the equation of line be represented as A
Now , the value of A is
Let the first point be P ( -3 , 1 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
The slope of the line m = -1
Now , the line is parallel to the line passing through P
So , the slopes of the lines are equal
And , the equation of line is y - y₁ = m ( x - x₁ )
On simplifying , we get
y - 1 = -1 ( x - ( -3 ) )
y - 1 = -1 ( x + 3 )
Adding 1 on both sides , we get
y = -x - 3 + 1
y = -x - 2
Hence , the equation of line is y - 1 = -1 ( x + 3 )
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ5
Bookwork code: M29 Calculator allowed The circle below has centre U. BC and DE are tangents to this circle. Work out the size of angle 0. Give reasons for your answer. A 52° B O E Watch video D 27° 0 C Not drawn accurately A Bookwork code : M29 Calculator allowed The circle below has centre U. BC and DE are tangents to this circle . Work out the size of angle 0 . Give reasons for your answer . A 52 ° B O E Watch video D 27 ° 0 C Not drawn accurately A
1) [tex]OA=OB[/tex] (all radii of a circle are equal)
2) [tex]\angle OBA=52^{\circ}[/tex] (angles opposite equal sides in a triangle are equal)
3) [tex]\angle OAB+\angle OBA+\angle AOB=180^{\circ}[/tex] (angles in a triangle add to 180 degrees)
4) [tex]52^{\circ}+52^{\circ}+\angle AOB=180^{\circ}[/tex] (substitution)
5) [tex]\angle AOB=76^{\circ}[/tex] (subtraction)
6) [tex]\angle AOB+\angle BOD=180^{\circ}[/tex] (angles on a line add to 180 degrees)
7) [tex]76^{\circ}+\angle BOD=180^{\circ}[/tex] (substitution)
8) [tex]\angle BOD=104^{\circ}[/tex] (subtraction)
9) [tex]\angle ODE=\angle OBC=90^{\circ}[/tex] (tangents are perpendicular to the radius of a circle at the point of tangency)
10) [tex]\angle ODC=117^{\circ}[/tex] (angle addition postulate)
11) [tex]\angle BOD+\angle OBC+\angle ODC+\angle DCB=360^{\circ}[/tex] (angles in a quadrilateral add to 360 degrees)
12) [tex]104^{\circ}+90^{\circ}+117^{\circ}+\theta=360^{\circ}[/tex] (substitution)
13) [tex]\theta=49^{\circ}[/tex] (subtraction)
