Answer:
Step-by-step explanation:
Cost per unit of gas = 4.2 pence
Average units of gas used per week = 50.1 units
Total cost of gas per week = Cost per unit of gas × Average units of gas used per week
= 4.2 pence × 50.1
= 210.42 pence
= £ 2.1042
Amount ria pays for gas for 13 weeks = cost of gas per week × number of weeks
= 210.42 pence × 13
= 2,735.46 pence
2,735.46 pence = £ 27.3546
Anna, Bob and Chris are altogether 31 years old. How old will all three be altogether in three years time? (A)32 (B)34 (C)35 (D)37 (E)40
Answer:
40
Step-by-step explanation:
A+B+C = 31
Add 3 years to each age
A+3 +B+3 + C+3 = 31 +3+3+3
They will be
A+3 +B+3 + C+3 = 40
Answer:
it will be 40
Step-by-step explanation:
If they are altogether 31 years old now in 3 years we just add 9 thus it is 40
Use slope to determine if lines AB and CD are parallel, perpendicular, or neither. A(0,2), B(5,4), C(1,8), and D(3,3). What is the slope of line CD? Enter as a ratio in its lowest terms.
Answer:
Perpendicular, CD has a slope of -5/2
Step-by-step explanation:
Parallel lines have the same slope, perpendicular have slopes that are negative reciprocals, or in other words if one slope is m then the other's slope is -1/m and if it is neither fo those then it is neither parallel or perpendicular. Also, if two lines have the same slope you have to make sure they are not the same line.
Now, to find the slope when you have two points you use the formula (y2 - y1)/(x2 - x1), where the points are (x1, y1) and (x2, y2). You can make either point point 1 or point 2. Just make sure x1 and y1 are from one point and x2 and y2 are from the other point.
So the two lines are AB and CD. Since the question asks I will start with CD. The points are (1,8) and (3,3) So I will call C point 1 and D point 2.
(y2 - y1)/(x2 - x1)
(3 - 8)/(3 - 1)
-5/2
Thankfully this is lowest terms.
Now for AB. A will be point 1 and B will be point 2
(y2 - y1)/(x2 - x1)
(4-2)/(5-0)
2/5
So they are not the same, so what if you take negative 1 over one of the slopes.
well. -1/(2/5) = -5/2
So these are perpendicular.
If you would like an explanation for how to find the full equation of a line I can explain that.
Si "m" es el lado mayor de un triángulo, dos cuyos ángulos interiores miden 30° y 60°, entonces el perímetro del triángulo es
Answer:
[tex]perimetro = \dfrac{(3 + \sqrt{3})m}{2}[/tex]
Step-by-step explanation:
triángulo 30°-60°-90°
[tex] 1~:~\sqrt{3}~:~2 [/tex]
[tex] 1m~:~m\sqrt{3}~:~2m [/tex]
[tex] \dfrac{m}{2}~:~\dfrac{m\sqrt{3}}{2}~:~m [/tex]
[tex]perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + m[/tex]
[tex]perimetro = \dfrac{m}{2} + \dfrac{m\sqrt{3}}{2} + \dfrac{2m}{2}[/tex]
[tex]perimetro = \dfrac{m + m\sqrt{3} + 2m}{2}[/tex]
[tex]perimetro = \dfrac{3m + m\sqrt{3}}{2}[/tex]
[tex]perimetro = \dfrac{(3 + \sqrt{3})m}{2}[/tex]
5- Observá el cartel y resolvé calculando el m.C.M entre las cantidades. FRECUENCIA A Mar del Plata, cada 2 horas A Necochea , cada 4 horas A San Clemente, cada 6 horas a) Si acaba de partir un micro a cada destino, ¿cuántas horas pasarán para que vuelvan a salir tres micros al mismo tiempo?
Respuesta:
12 horas
Explicación paso a paso:
Dado que :
A Mar del Plata = cada 2 horas
A Necochea = cada 4 horas
A San Clemente = cada 6 horas
Número de horas que tardarán los 3 autobuses en salir al mismo tiempo, si ambos salieron ahora;
Tome el mínimo común múltiplo de los 3 autobuses:
Múltiplos de:
2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22
4: 4, 8, 12, 16, 20, 24, 28, 32
6: 6, 12, 18, 24, 30, 36, 42
El mínimo común múltiplo de 2 horas, 4 horas y 6 horas es 12;
Por lo tanto, los 3 autobuses saldrán a la misma hora en las próximas 12 horas:
maths questions on coordinate geomery
Answer:
:
Example Question #1:
Step-by-step explanation:
Which of the following is the equation of a line that is parallel to the line 4x – y = 22 and passes through the origin?
Possible Answers:
4x – y = 0
(1/4)x + y = 0
4x + 8y = 0
4x = 8y
y – 4x = 22
Correct answer:
4x – y = 0
Explanation:
We start by rearranging the equation into the form y = mx + b (where m is the slope and b is the y intercept); y = 4x – 22
Now we know the slope is 4 and so the equation we are looking for must have the m = 4 because the lines are parallel. We are also told that the equation must pass through the origin; this means that b = 0.
In 4x – y = 0 we can rearrange to get y = 4x. This fulfills both requirements.
', .
find the angles of the triangle if they are proportainal to 3, 4, 5. The angles are?
Answer:
Because it is a right triangle one angle is obviously 90°. The other two are approximately 36.87° and 53.13°.
hope it helps you
have a good day
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Complete the function for this graph.
Answer:
[tex]y=|x-(-2)|+2[/tex]
Step-by-step explanation:
Hope this is helpful.
The required absolute function is given as y = |x - 2| + 2.
Given that,
From the graph, y = |x - h| + k, values of h and k is to be determined,
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
In the graph and function, h represents the shift on the x-axis, which 2 units left so the value of h is 2, while k is given the shift of the function over the y-axis which 2 units up means that k = 2
Thus, The required absolute function is given as y = |x - 2| + 2.
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ASAP !!
If using the method of completing the square to solve the quadratic equation x^2+3x-17=0x
2
+3x−17=0, which number would have to be added to "complete the square"?
Answer:
17
Step-by-step explanation:
???????????????????????????
Answer: its 20 I think
Answer:
x = 50
I hope this help the side note also help me a lot as well
divide 3 divided by 2/5
Answer:
[tex]{ \tt{ = 3 \div \frac{2}{5} }} \\ = { \tt{3 \times \frac{5}{2} }} \\ = \frac{15}{2} [/tex]
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $20 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month
The question is incomplete. The complete question is :
Small Manufacturing Company has a standard overhead rate of $42 per hour. The labor rate is $15 per hour. Overhead is applied based on direct labor hours. Jobs B-1 and B-2 were completed during the month of March. Small incurred 140 hours of indirect labor during the month. Job B-1 used 82 direct labor hours and $3650 worth of direct material used. Job B-2 used 130 direct labor hours and $2,900 worth of direct material. What is the total cost of job B-2? Round to closest whole dollar (no cents).
Solution :
Particulars Job B-2
Direct material used $ 2,900
Add : Direct labor cost (130 hours x $15) $ 1,950
Add : overhead cost (130 hours x $ 42) $ 5,460
Total Cost of Job B-2 $ 10,310
Therefore, the total cost of the Job B-2 is $ 10,310.
Determine the dimensions of the rectangle of largest area that can be inscribed in a semicircle of radius 4
Answer:
The length and width that maximize the area are:
W = 2*√8
L = 2*√8
Step-by-step explanation:
We want to find the largest area of a rectangle inscribed in a semicircle of radius 4.
Remember that the area of a rectangle of length L and width W, is:
A = L*W
You can see the image below to see how i will define the length and the width:
L = 2*x'
W = 2*y'
Where we have the relation:
4 = √(x'^2 + y'^2)
16 = x'^2 + y'^2
Now we can isolate one of the variables, for example, x'
16 - y'^2 = x^'2
√(16 - y'^2) = x'
Then we can write:
W = 2*y'
L = 2*√(16 - y'^2)
Then the area equation is:
A = 2*y'*2*√(16 - y'^2)
A = 4*y'*√(16 - y'^2)
If A > 1, like in our case, maximizing A is the same as maximizing A^2
Then if que square both sides:
A^2 = (4*y'*√(16 - y'^2))^2
= 16*(y'^2)*(16 - y'^2)
= 16*(y'^2)*16 - 16*y'^4
= 256*(y'^2) - 16*y'^4
Now we can define:
u = y'^2
then the equation that we want to maximize is:
f(u) = 256*u - 16*u^2
to find the maximum, we need to evaluate in the zero of the derivative:
f'(u) = 256 - 2*16*u = 0
u = -256/(-2*16) = 8
Then we have:
u = y'^2 = 8
solving for y'
y' = √8
And we know that:
x' = √(16 - y'^2) = √(16 - (√8)^2) = √8
And the dimensions was:
W = 2*y' = 2*√8
L = 2*y' = 2*√8
These are the dimensions that maximize the area.
Someone tell me where everyone is going right please !!
Answer:
1) -4(3-5x) >= –6x+9
–12+20x >= -6x+9
The choose (D)
2 ) The choose (A)
3) The choose (A) step 1
4) 1/2(n-4)-3=3-(2n+3)
n=2
The choose ( B)
5) 2.5 (5x-4)=10+4(1.5+0.5x)
x=2
The choose (C)
1. -12 + 20 > -6x + 9
2. simplify by combining like terms
3. step 1
4. n=2
5. 2
When planning for a party, one caterer recommends the amount of meat be at least 2 pounds less than One-third the total number of guests. Which graph represents the overall equation represented by this scenario (all points may not apply to the scenario)?
Answer:
It's d or the 4th graph
Step-by-step explanation:
A graph which represents the overall equation (inequality) represented by this scenario.
What is a graph?A graph can be defined as a type of chart that is commonly used for the graphical representation of data points on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis).
Let the variable x represent the total number of guests.
Let the variable y represent the amount of meat
Next, we would write an inequality that represents an amount of meat that must be 2 pounds fewer than one-third (1/3) the total number of guests. Since the customer decides they want at least that amount of meat, the inequality symbol that must be used is greater than (>).
y > 1/3(x) + 2
y > x/3 + 2
In conclusion, the y-value for this inequality graph (see attachment) intersects the x-axis at 0 and 6 with the boundary line shaded upward and dashed to indicate that it is not part of the solution, which must be represented with a greater than (>) inequality symbol.
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which statement proves that polygon ABCD is not a rectangle
Answer:
ummm u did not add the statements to the question
Step-by-step explanation:
but a polygon ABCD might not be a rectangle if:
opposite sides of polygon ABCD are not of equal lengthsall angles of the polygon may not be right angles (90°)opposite sides may not be parallelFind the area
Help me please
Answer:
143
Step-by-step explanation:
to find the area we multiply half of the sum of the bases with height
(18+8)/2*11 = 143
Which of the following are exterior angles?
Answer:
3,4
Step-by-step explanation:
Isosceles trapezoid EFGH has area 80 cm ^2, height 20 cm and legs 22 cm. One of the bases is 5 cm. How long is the remaining base ?
Answer:
3
Step-by-step explanation:
A = [tex]\frac{base1 + base2}{2}[/tex] x h Formula
[tex]\frac{base1 + 5}{2}[/tex] x 20 = 80 Substitution
[tex]\frac{base1 + 5}{2}[/tex] = 4 Work (divide by 20, multiply by 2, subtract 5)
base1 + 5 = 8
base1 = 3 Solution
can anyone please explain this?
Find the equation of locus of a point A(-3,2) and B(0,4).....
what is locus actually?
Answer:
Solution given:
Let there be a point P(x, y) equidistant from
A(-3, 2) and B(0,4),
so PA = PB,
[tex]\sqrt{(x+3)²+(y-2)²}=\sqrt{(x-0)²+(y-4)²}[/tex]
squaring both side
[tex](\sqrt{(x+3)²+(y-2)²})^{2}=(\sqrt{(x-0)²+(y-4)²})²[/tex]
x²+6x+9+y²-4y+4=x²+y²-8y+16
x²+6x+y²-4y-x²-y²+8y=16-4-9
6x-4y+8y=3
6x-4y=3 is a required locus
Actually:
A locus is a curve or other figure formed by all the points satisfying a particular equation of the relation between coordinates, or by a point, line, or surface moving according to mathematically defined conditions.
Mrs.Carlyle bought a bag of peanuts for her children. When Phillip, Joy, Brent, abd Preston came home from school, they each took some peanuts from the bag.
If the point ((4,-2) what is included in a direct viration relationship which point also belongs and variation
Answer:
The answer is "This direct variant (-4,2) is part of it".
Step-by-step explanation:
The equation expresses its direct variation relation
[tex]y = mx ........ (1)[/tex]
Where x and y vary directly, and k vary continuously.
Now so the point (4,-2) is in the direct relation of variation, so from equation (1) we are given,[tex]-2 = 4m[/tex]
[tex]\to m=-\frac{1}{2}[/tex]
The equation (1) is therefore converted into
[tex]\to y=-\frac{1}{2}x \\\\\to x + 2y = 0 ......... (2)[/tex]
Then only the point (-4,2) satisfies the connection with the four possibilities (2). Therefore (-4,2) is a direct variant of this.
Given a circle with (4. -3) and (2, 1) as the endpoints of the diameter.
Complete question is;
Given a circle with (4. -3) and (2, 1) as the endpoints of the diameter. Write the equation of the circle.
Answer:
x² + y² - 6x + 2y + 5 = 0
Step-by-step explanation:
The end points of the diameter are;
(4. -3) and (2, 1).
Thus, the centre coordinates will be the midpoint of the diameter endpoints.
Thus;
Centre coordinates = ((4 + 2)/2), ((-3 + 1)/2) = (3, -1)
Diameter;
d = √(1 - (-3))² + (2 - 4)²)
d = √20
d = 2√5
Radius = ½ × diameter
Thus;
r = ½ × 2√5
r = √5
Equation of a circle is;
(x - a)² + (y - b)² = r²
Where;
(a, b) are coordinates of the centre of the circle
r is radius.
Thus;
(x - 3)² + (y - (-1))² = (√5)²
x² - 6x + 9 + y² + 2y + 1 = 5
x² + y² - 6x + 2y + 10 = 5
x² + y² - 6x + 2y + 10 - 5 = 0
x² + y² - 6x + 2y + 5 = 0
A sea turtle can swim 13 kilometers in 5 hours at this rate speed how far can it travel in 9 hours
Answer:
23.4 km
Step-by-step explanation:
We can use a ratio to solve
13 km x km
-------- = ---------------
5 hours 9 hours
Using cross products
13*9 = 5x
117 = 5x
Divide each side by 5
117/5 = 5x/5
23.4 =x
Answer:
It travel 23.4 km in 9 hours.
Step-by-step explanation:
Given :-
A sea turtle can swim 13 km in 5 hours at this rate speed .
To find :-
How far can it travel in 9 hours.
Solution :-
Sea turtle swim 13 km in 5 hours Then find the how far it can travel in 9 hours.
Let us assume that In 9 hours turtle swim x km.
Now, We solve by using ratio for x.
In 5 hours it swim = 13 km
And, In 9 hours it swim = x km
Calculate for x
5 hours = 13 km
9 hours = x km
Use cross multiplication method , we get
5 × x = 9 × 13
5x = 117
Divide both side by 5
5x / 5 = 117 / 5
x = 23.4
Hence, It can travel 23.4 km in 9 hours.
Please help me with this one
Answer:
2×5×7+2×5×2+2×7×2
70+20+28
108cm^2
[tex] \huge\boxed{\mathfrak{Answer}}[/tex]
[tex]l = 5 \: cm \\ w = 2 \: cm \\ h = 7 \: cm[/tex]
The formula to find SA => 2lh + 2lw + 2hw
[tex]SA => 2lh + 2lw + 2hw \\ = 2 \times 5 \times 7 + 2 \times 5 \times 2 + 2 \times 7 \times 2 \\ = 70 + 20 + 28 \\ = 118 \: \: cm {}^{2} [/tex]
=> The surface area of the rectangular prism is 118 cm².
Factorize
a⁴-3a²b²+b⁴
(a⁴-3a²b²+b⁴)/(a²-ab-b²)
Let me know if there is something wrong to my answer ^_^
Answer:
hope it will helpfulll to youuu
A committee that consists of five members are to be chosen from 6 boys and 5 girls. Find the number of different committees that can be formed if only two boys are selected
Answer:
150 different committees can be formed
Step-by-step explanation:
We have 6 boys and 5 girls and we want to select 5 members
Out of these 5 members, two boys are selected
Since two boys are selected, we are left with three girls
So, out of 6 boys, we select 2 boys and out of 5 girls, we select 3 girls
Mathematically, we know that the number of ways in which we can select r items from a total n follows the combinatorial formula;
nCr = n!/(n-r)!r!
With this, we have;
6C2 * 5C3
= (6!/(6-2)!2!) * (5!/(5-3)!3!) = 150 different committees can be formed
If “the notation arcsin x represents the inverse function to sine” is true or false.
If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].
What is the sin function?The sine function is one of the three primary functions in trigonometry, the others being cosine, and tan functions.
The confusion is compounded by the fact that we use the notation sin⁻¹(x) interchangeably with arcsin(x), and we call it the inverse sine.
Here is a counterexample disproving your given statement:
Let x = π.
The value π is in the domain of sin(x).
arcsin[sin(π)] = arcsin(0) = 0
arcsin[sin(π)] ≠ π
Therefore arcsin(x) is not the inverse of sin(x).
If you restrict the sine function to the interval [ -pi/2, pi/2 ]. Otherwise, arcsin will not be a function.
Hence, If “the notation arcsin x represents the inverse function to sine” is true when the sine function is to the interval [ -pi/2, pi/2 ].
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convert 1100111 into decimal numbers
Answer:
103 is my answer.
Step-by-step explanation:
hope it helps
Helpppppp and explain toooo thankyouuuu
Step 1: Distribute
5x + 10 - 3x > 7 - 4x + 12
Step 2: Combine like terms
2x + 10 > -4x + 19
Step 3: Move all variable terms to one side, and all constants to the other
6x + 10 > 19
6x > 9
Step 4: Divide
x > 9 / 6
x > 1.5
Hope this helps!
3. Find the equations of the lines that form the sides to the polygon shown below. What type of polygon is it? Explain your reasoning.
Answer: The question is not complete. the figure is attached below.
The polygon is a rectangle.
Step-by-step explanation:
Line 1 goes through (-2, 3)
hence the slope of line 1 = -3/2
Line 2 goes through (0, 3) (2, 0)
hence the slope of line 2 = -3/2
Line 3 goes through (0, 1) (-3, 1)
hence the slope of line 3 = 2/3
Line 4 goes through (3, 0) (0, -2)
Hence the slope of line 4 = 2/3
therefore -3/2 * 2/3 = -1
Line1 + Line3 Line1 + Line4 Line2 + Line3 Line2+Line4
because, the distance between Line1 and Line2 is not equal to that Line3 and Line4.
The polygon is a rectangle polygon.