The solution to the equations 2x + 3y = 3, x – 2y = 5 using substitution method is y = -1 and x = 3 respectively.
Simultaneous equation2x + 3y = 3
x – 2y = 5
from equation (2)
x = 5 + 2y
Substitute x = 5 + 2y into equation (1)
2x + 3y = 3
2(5 + 2y) + 3y = 3
10 + 4y + 3y = 3
10 + 7y = 3
7y = 3 - 10
7y = -7
y = -7/7
y = -1
Substitute y = -1 into (2)
x – 2y = 5
x - 2(-1) = 5
x + 2 = 5
x = 5 - 2
x = 3
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First, complete the sentence to show how the figure can be decomposed into triangles and rectangles with the fewest number of pieces Then find the area of the divisions.
The figure will have a triangle and a rectangle. The area of a triangle is 10 in² and the rectangle is 80 in². Therefore, the total area is 90 in².
Area of Compound ShapesThis question requires your knowledge about the area of compound shapes. For solving this, you should:
Identify the basic shapes; Calculate your individual areas; Sum each area found. STEP 1 - Identify the basic shapes.The figure is composed of a triangle and a rectangle.
Therefore, you should sum the area of these geometric figures for determining the area of the irregular figure.
STEP 2 - Find the area of the trinagle.Area of the triangle= [tex]\frac{b*h}{2}[/tex]. The figure shows that: the base = 10 in and the height =2 in
Thus, A_triangle=[tex]\frac{b*h}{2}=\frac{10*2}{2} =10 in^{2}[/tex]
STEP 3 - Find the area of the rectangle.Area of the rectangle = bh . The figure shows that: the base = 10 in and the height =8 in
Thus, A_rectangle=bh= 10*8=80 in²
STEP 4 - Find an expression for the total area of the figure.
A_total= A_triangle + A_rectangle
A_total= 10+80=90 in²
A_total= 90 in²
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The variables A, B, and C represent polynomials where A = x², B = 3x + 2, and C = x - 3. What is AB - C² in
simplest form?
3x³ + 2x²-x+ 3
O 3x³ + 2x²-x-3.
O 3x³ + x² - 6x +9
O 3x³ + x² + 6x-9
The polynomial in its simplest form is 3x³ + x² + 6x-9 , Option D is the correct answer.
What are Polynomials ?The algebraic expression that consists of variables and coefficients are called Polynomials.
It is given that
The variables A, B, and C represent polynomials
where
A = x²
B = 3x + 2
C = x - 3
The Polynomial AB -C² = ?
From the value given
AB -C² = x² (3x + 2) - (x - 3)²
= 3x³ + 2x² - x² - 9 + 6x
= 3x³ + x² + 6x-9
Therefore the polynomial in its simplest form is 3x³ + x² + 6x-9 , Option D is the correct answer.
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Determine the slope-intercept form (y = mx + b) of the equation of the line that contains the
points (3, 5) and (5, 6)
Hello,
We have A(3, 5) and B(5, 6)
[tex]m=\frac{y_{B}-y_{A}}{x_{B}-x_{A}} =\frac{6-5}{5-3} =\frac{1}{2}[/tex]
We know the line contain the point (3, 5)
y = 1/2x + b
⇔ 5 = 1/2 × 3 + b
⇔ 5 = 3/2 + b
⇔ 5 - 3/2 = b
⇔ b = 10/2 - 3/2
⇔ b = (10 - 3)/2
⇔ b = 7/2
[tex]\boxed{y = \frac{1}{2}x + \frac{7}{2} }[/tex]
4 mark please help me
Answer:
There are 4 red counters
Step-by-step explanation:
1. Add the known decimals
[tex]0.25+0.35+0.3=0.9[/tex]
2. Subtract that amount from one
[tex]1-0.9=0.1[/tex]
3. multiply the result by 40
[tex](40)(0.1)=4[/tex]
Hope this helps
Step-by-step explanation:
a probability is always desired cases / total cases.
from the table and given information we know :
there are 40 blue counters.
0.25 = 40/x
x being the total number of counters in the box.
x = 40 / 0.25 = 160
the sum of all probabilities must be 1 (the always true probability), as there are only counters in the box, and one of the 4 colors is always the result.
so,
1 = 0.25 + 0.35 + 0.3 + red-probability
1 = 0.9 + red-probability
red-probability = 1 - 0.9 = 0.1
0.1 = red counters / 160
red counters = 0.1 × 160 = 16
there are 16 red counters in the box.
Figure ABCD is transformed to figure A prime B prime C prime D prime, as shown: A coordinate grid is shown from negative 5 to 0 to 5 on both x- and y-axes. A polygon ABCD has A at ordered pair 2, 3, B at ordered pair 4, 4, C at ordered pair 3, 1, D at ordered pair 2, 1. A polygon A prime B prime C prime D prime has A prime at ordered pair negative 1, 3, B prime at ordered pair negative 3, 4, C prime at ordered pair negative 2, 1, D prime at ordered pair negative 1, 1. Which of the following sequences of transformations is used to obtain figure A prime B prime C prime D prime from figure ABCD? (1 point) Group of answer choices Counterclockwise rotation by 90 degrees about the origin followed by a translation to the right by 1 unit Counterclockwise rotation by 90 degrees about the origin followed by a translation to the left by 1 unit Reflection about the x-axis followed by a translation to the left by 1 unit Reflection about the y-axis followed by a translation to the right by 1 unit
Last option. The sequence that can be used to to get the figure A'B'C'D' is Reflection about the y-axis followed by a translation to the right by 1 unit.
How to get the reflection of the imageWe have an opposite orientation in this question. This based on the fact that (ABCD)' is counterclockwise. While its reflection ABCD is clockwise.
The reflection has to go over a vertical line given that (CD)' and CD are at the bottom. Hence this reflection has to go over a vertical line.
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4. (07.06)
Write a simplified polynomial expression in standard form to represent the area of the rectangle below. (2 points)
2x - 4
O 2x² + 6x-20
2x² - 4x-20
D
2x² + 6x + 20
2x² + 10x + 20
X+5
The expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.
What is a rectangle?A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but reverse statement may or may not be true.
The area of the rectangle is the product of its length and its width. Therefore, the area of the given rectangle is,
Area = (2x-4)(x+5)
= 2x² + 10x - 4x - 20
= 2x² +6x - 20
Hence, the expression that represents the area of the rectangle is 2x² + 6x − 20. Thus, the correct option is C.
The complete question is:
Write a simplified polynomial expression in standard form to represent the area of the rectangle below.
2x² + 10x + 202x² + 6x + 202x² + 6x − 202x² − 4x − 20The image of the rectangle is given below.
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What is the equation of the line that passes through the point (-5,4)(−5,4) and has a slope of 3/5?
Answer: y = 3/5x + 7
Explanation:What we know:
The final equation will be in the form y=mx+bThe slope (m) is 3/5The slope must go through the point (-5,4)How to solve:
By substituting the point the slope passes through into slope-intercept form, we can calculate the y-intercept (b.) From here, we can use our slope and y-intercept values to set up the final equation.
Process:
Finding the y-intercept
Set up equation y = mx + b
Substitute 4 = 3/5(-5) + b
Simplify 4 = -3 + b
Simplify +3 +3
Solve 7 = b
Creating final equation
Set up equation y = mx + b
Substitute y = (3/5)x + 7
Answer: y = 3/5x + 7Check:
If you graph this equation (a good tool to use is desmos graphing calculator,) then this equation creates a line that has a slope of 3/5 and passes through the point (-5,4)
Martha climbs 40 steps to reach the first floor of a building. If the vertical and horizontal distance of each step is 1.5 ft and 1 ft, find the distance between the start and end points of each step
The distance between the initial position and the final position is 72.1ft
How to get the distance?
The initial position is (0ft, 0ft). Where the notation used is:
(horizontal position, vertical position).
Martha climbs 40 steps, then the final position is:
(40*1ft, 40*1.5ft) = (40ft, 60ft)
The distance between the initial position and the final position is:
[tex]d = \sqrt{(40ft - 0ft)^2 + (60ft - 0ft)^2} = 72.1ft[/tex]
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The graphs below have the same shape. What is the equation of the blue
graph?
G(x) =
―
F(x)=x3
-6
O A. G(x) = (x+1)³
OB. G(x) = x³-1
OC. G(x) = (x-1)³
OD. G(x)= x³ +1
GX) = ?
Using translation concepts, it is found that the equation of the blue graph is given by:
C. G(x) = (x - 1)³.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the function G(x) is a shift of one unit right of F(x) = x³, hence it's equation is:
G(x) = F(x - 1) = (x - 1)³.
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Find a 10-digit number where the first digit is how many zeros in the number, the second digit is how many 1s in the number etc. until the tenth digit which is how many 9s in the number.
Answer:
9000000001
Step-by-step explanation:
.....................
Answer:
6210001000
Hope This Helps!!!
Factorise the following:
a) x² + 10x + 16 answer
Factoring polynomials is breaking them down to the products of other smaller polynomials. Identifying the greatest common divisor (GCF) is an important first step because it will reduce the number of factors in each term and thus make factoring easier. In addition to polynomials, it can be factored by decomposition of the intermediate term or by difference of squares. Then, the Zero Product Property can be applied to solve the equation.
x² + 10x + 16Use the sum-product pattern.
x² + 8x + 2x + 16Extract the common factors.
x (x + 8) + 2(x + 8)Rewrite factored
( x + 2 ) ( x + 8 ) ===> Answer{ Pisces04 }Answer:
(x+2)(x+8)
Step-by-step explanation:
two numbers that multiply to 16 and add up to 10 is 2 and 8. You just plug both numbers in this factored form (x+ n1)(x+n2). if you chech the answer by multiplying the binomials, you will find out that the answer is the original question (x^3 +10x+16).
There are 4 circles and 6 triangles. What is the simplest ratio of circles to triangles?
Answer:
2/3
Step-by-step explanation:
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be 4/6
4/6 when divided by two = 2/3 which is the simplest form of the fraction 4/6
The simplest ratio of circles to triangles would be; 2/3
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
We are given that there are 4 circles and 6 triangles.
Since there are 4 circles and 6 triangles, and they are asking for the ratio of circles to triangles, the fraction would be as given;
4/6
when divided by two we get;
2/3
This is the simplest form of the fraction 4/6
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Find the LCM of 10 and 25?
Does this graph represent a function? Why or why not?
C A. Yes, because it passes the vertical line
test.
B. No, because it is not a
straight line.
No, because it fails the vertical line test.
O D. Yes, because it passes the horizontal line test.
Answer:
A. Because it passed the y axis
gradients - pls help :)
The line which has a gradient of 6 is A. line A
To answer the question, we need to know what the gradient of a line is.
What is the gradient of a line?The gradient of a line is its slope. It is given by m = Δy/Δx where
Δy = change in y and Δx = change in x. How to find the line that has the gradient 6?Now, to find the line that has the gradient of 6, we see that the gradient
m ∝ Δy and m ∝ 1/Δx.So, for a high value of gradient, we need
a large change in y and a small change in x.Also, since 6 is positive, the gradient for the line will be positive.
The only line that meets these criteria is line A.
So, the line which has a gradient of 6 is A. line A
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Distance (feet)
2
14
12
10
20
5
4
2
2
4
6
garden
Distance (feet)
12 14 15
The diagram shows a garden plot. The area of the garden is
garden is … square feet.
square feet. The length of fencing required to completely enclose the garden is … feet.
The area of a 2D form is the amount of space within its perimeter. The area of the garden is 72 feet² and the perimeter of the garden is 36 feet.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The diagram for the given garden is given below.
1.) The area of the garden is,
The area of the garden = Area of rectangle + Area of triangle
= (6 x 8) + (0.5 x 6 x 8)
= 48 + 24
= 72 feet²
2.) The perimeter of the garden is,
The perimeter of the triangle = 12 + 8 + 6 + 10 = 36 feet
Hence, the area of the garden is 72 feet² and the perimeter of the garden is 36 feet.
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A tub contains red, yellow and blue counters. There is ten more yellow than red counters, and the ratio of red to blue counters is 3:4.If there are 20 blue counters, what is the probability of picking a yellow counter?
Answer:
5/12
Step-by-step explanation:
A ratio of 3:4 means that red counters make up 3/7 of the sum of red and blue counters and blue counters make up 4/7 of the total sum of red and blue counters.
If there is 20 blue counters, then 20 is 4/7 of the sum of the total red and blue counters.
So we need to solve for the total sum.
[tex] \frac{4}{7} x = 20[/tex]
[tex]4x = 140[/tex]
[tex]x = 35[/tex]
So the total amount of red and blue counters are 35,
So this means the amount of red counters is 15.
The amount of yellow counters is 25.
So the total number of counters are 60.
So P(Yellow counters)= 25/60= 5/12
Find m/CDU if m/CDE-154° and m/UDE = 108°.
U
E
D
C
Answer: [tex]46^{\circ}[/tex]
Step-by-step explanation:
[tex]m\angle CDE=m\angle UDE+m\angle CDU\\\\154^{\circ}=108^{\circ}+m\anlge CDU\\\\m\angle CDU=46^{\circ}[/tex]
Find value of x in the 45° - 45°-90° triangle. Give
answer rounded to the nearest tenth. Geometry!! pls helppp
Answer: X = 5.0
Step-by-step explanation:
- since these are right triangles you can use trigonometry to solve this pretty easily
- for this situation, you only have to use sine/sin
sine/sin is [tex]opposite/hypotenuse[/tex]__________________________________________________________
- to start you just need to identify which side is which:
the side that is labeled 10 is the hypotenusein this case, the shared side is the opposite since you're using sin- so, for this problem the equation is: [tex]10xSin(45) = 7.071067812[/tex]
__________________________________________________________
- so 7.071067812 is the hypotenuse of the smaller triangle so you just do the same thing again
- start with identifying which side is which:
as said, the side that is shared and 7.071067812 is the hypotenusethe side labeled x is the opposite- so for this part, the equation is: [tex]7.071067812xSin(45) = 5.0[/tex]
- so X = 5.0
__________________________________________________________
hope this helps :)
Answer:
x = 5
Step-by-step explanation:
Check the file for detailed solution.
This involves SOH-CAH-TOA method, always remember that the opposite of the 90 degree mark is always the hypotenuse. Meanwhile, the position of the given angle (theta) is dependent on which side it is placed. It give either an adjacent or opposite side.
Point Y is the circumcenter of triangle DEF.
Point Y is the circumcenter of triangle D E F. Lines are drawn from the points of the triangles to point Y. Lines are drawn from point Y to the sides of the triangle to form right angles and line segments Y L, Y M, and Y N. The line segments cut the sides of the triangles into 2 equal parts.
Which statement is true about point Y?
Point Y is the center of the circle that passes through points D, F, and N.
Point Y is the center of the circle that passes through points M, N, and E.
Point Y is the center of the circle that passes through points L, M, and N.
Point Y is the center of the circle that passes through points D, E, and F.
Point Y is the centre of the circle that passes through points D, E, and F.So option A is correct.
What is circumcircle?If we draw a circle through all the vertices of a triangle then the circle obtained is the circumcircle of the given triangle.
And the circumcenter is the centre point of the circumcircle which is obtained by the point of intersection of the perpendicular bisector of all the sides of the triangle.
Therefore, since Y is the circumcenter of the triangle DEF, so, point Y is the centre of the circle that passes through points D, E, and F.
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Answer:
A
Step-by-step explanation:
work out the volume of the cone,giving your answer to 3 significant figures
The volume of the cone is 1, 139. 49 cm³
How to determine the volumeHeight of cone = 17cm
Base of cone = 16cm
Diameter = 16cm
Radius = diameter/2 = 16/2 = 8cm
Formula for volume of a cone = [tex]\pi r^{2} \frac{h}{3}[/tex]
Substitute the values
Volume = [tex]3. 142[/tex] × [tex]8[/tex] × [tex]8[/tex] × [tex]\frac{17}{3}[/tex]
Volume = [tex]201. 088[/tex] × [tex]5. 67[/tex]
Volume = 1, 139. 49 cm³
Thus, the volume of the cone is 1, 139. 49 cm³
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Which ordered pair below is a solution to the following system of equations?
-x + 2y = 5
x + y = 1
Answer:
The correct option is OPTION (A) .
Where s is the distance traveled by an object (in meters) with an initial velocity u (in m/s) and final velocity v (in m/s), t
seconds later.
Find s when u is 6 m/s, v is 20 m/s, and t is 5 seconds.
B. 25 m
C. 130 m
= 1/2 (u + v) t
OD. 65 m
S=
The distance travelled by the object in meters is 65 meters.
How to find distance?using the formula,
s = 1 / 2 (u + v)t
where
u = initial velocityv = final velocitys = distancet = timeTherefore, the distance can be found as follows;
s = 1 / 2 (6 + 20)5
s = 1 / 2 (26)5
s = 13(5)
s = 65 m
Therefore, the distance travelled by the object in meters is 65 meters.
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Answer:
D.
Step-by-step explanation:
I had the same question
A body and tackle with a velocity ratio of 5 is used to raise a mass of 50kg through a vertical distance of 20n at a steady rate if the effort is equal to 80n. Determine (a) distance moved by effort (b)the workdone by the effort in lifting the load (c)the losses in energy involve the operating in machine
a. Distance moved by effort = 1 meter
b. Work done by effort = 80 Joules
c. Losses in energy = 18 Joules
How to determine the parametersa. Note that velocity ratio is defined as the ratio of a distance through which any part of a machine moves to the distance moved by its parts
Velocity ratio = distance moved by the effort/distance moved by the body
Where velocity ratio = 5
vertical distance = 20cm
Distance moved by effort = 5 × 0. 20 = 1 meter
b. Formula for work done is given as ;
Work done = Effort × distance moved by effort
Work done = 80 × 1
Work done = 80 Newtons
c. First, let's find the work output
Work output = m g h
Work output = 50 × 9.8 × 0. 20
Work output = 98 Joules
Losses in energy = Work output - work done
Losses in energy = 98 - 80
Losses in energy = 18 Joules
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Two similar triangles have areas 16 and 4. if a side of the smaller triangle measures 2, find the length of the corresponding side in the larger triangle.
Answer: 4
Step-by-step explanation:
The ratio of the areas of similar figures is the square of the side length.
Since the ratio of the areas is 16:4 = 4:1, the ratio of the side lengths is 2:1.
So, the length of the corresponding side is 2(2) = 4.
Point X is the incenter of ΔABC.
Triangle A B C has point X as its incenter. Lines are drawn from the points of the triangle to point X. Lines are drawn from point X to the sides of the triangle to form right angles. Line segments X F, X G, and X E are formed.
If EX = 4z + 1, XF = 2z + 7, and mABC = 44°, find the following measures.
GX =
mABX = °
The value of GX is 13 and m ∠ABX is 22°
How to determine the angles
With the information, we have
EX = 4z + 1 and XF = 2z + 7
It is important to note that EX = XF = GX are congruent, that is, they are equal
Equate EX = XF to determine z
4z + 1 = 2z + 7
Collect like terms
2z = 6
z = 3
We know that EX = XF = GX and x = 3, substitute into the value of any one
EX = 4(3) + 1
EX = 13
EX = GX
GX = 13
To determine m ∠ABX, we divide m ∠ABC by 2
We have
m ∠ABX = 44/2
m ∠ABX = 22°
Therefore, the value of GX is 13 and m ∠ABX is 22°
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Answer: 13, 22°
Step-by-step explanation: Trust Me!
Answer is correct on Edge. Good Luck! :)
GX = 13
mABX = 22°
There are 135 people in a sport centre. 73 people use the gym. 59 people use the swimming pool. 31 people use the track. 19 people use the gym and the pool. 9 people use the pool and the track. 16 people use the gym and the track. 4 people use all three facilities. A person is selected at random. What is the probability that the person uses exactly one of the facilities?
The probability that the person uses exactly one of the facilities is 0.64
What is probability?Probability is the likelihood of an event happening or an event not happening.
When it is certain an event would happen the probability is 1.
Probability can be independent or mutually exclusive.
Analysis:
Find analysis in the attached file.
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How do I find the formula for the nth term in a sequence? Like for example the sequence:4,9,14,19 what is the next term?
Answer:
Step-by-step explanation:
Arithmetic sequence:
a = first term = 4
d = common difference = second term - first term
= 9 - 4
d = 5
[tex]\sf t_n =a +(n -1)*d[/tex]
= 4 + (n - 1) *5
= 4 + 5n - 5
= 5n -1
Check; n= 1 , first term = 5*1 - 1 = 5 - 1 = 4
n = 2, second term = 5*2 - 1 = 10 -1 = 9
n = 3, third term = 5*3 - 1 = 15 - 1 = 1
The next term, fifth term = 5*5 - 1
= 25 - 1
= 24
A certain tranquilizer decays exponentially in the bloodstream and has a half-life of 47 hours. How long with it take for the drug to decay to 82% of the original dose?
This is a two-step problem.
The drug will decay to 82% of the initial dosage after 7.18 hours.
Finding the Decay constant(λ):
λ = 0.693 / (half-life)
we are given that the half-life is 47 hours
λ = 0.693 / (47)
λ = 0.01925 /hour
Time is taken for 82% decay:
How do find the decay?Since decay is first-order, we will use the formula:
[tex]t = \frac{2.303}{0.0192} log\frac{100}{82}[/tex]
Final amount = 100*82/100 = 82 mg
Replacing the values in the equation:
t = 2.303/ 0.0192 x 0.06
t = 7.18 hours
Therefore, the drug will decay to 82% of the initial dosage after 7.18 hours.
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Please Help!!!
Right triangle ABC is on a coordinate plane. Segment AB is on the line y = 2 and is 5 units long. Point C is on the line x = −2. If the area of ΔABC is 12.5 square units, then find a possible y-coordinate of point C.
5
6
7
8
Answer: its 7
Step-by-step explanation: hope it helps