The values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)
Simultaneous linear equationFrom the question, we are to determine the solution of the given system of equations
The given system of equations are
2 x + 3 y = 6 ------- (1)
x + 3 y = 12 ------- (2)
From equation (2)
x + 3y = 12
Then, we can write that
x = 12 - 3y --------- (3)
Substitute this into equation (1)
2x + 3y = 6
2(12 -3y) + 3y = 6
24 - 6y + 3y = 6
24 -3y = 6
24 - 6 = 3y
18 = 3y
∴ y = 18/3
y = 6
Substitute the value of y into equation (3) to get the value of x
x = 12 - 3y
x = 12 -3(6)
x = 12 - 18
x = -6
∴ x= -6 and y = 6 ; Thus, (-6, 6) is a solution
Hence, the values of x = -6 and y = 6 satisfy both the equations; therefore, (-6, 6) is the solution. The correct option is a)
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One Solution
No Solutions
Infinitely Many Solutions
2+y=3
−2x − y = −6
Answer:
it is -6. . . . . . . . . . . . . . . . .. ... . . . . . . .
This list shows the lengths in feet of the 25 longest bridges in the United States.
1010
1470
1600
2000
2800
1053
1495
1632
2150
3500
1200
1596
1750
2150
3800
1207
1600
1800
2300
4200
1380
1600
1850
2310
4260
Jamie made a frequency table of the bridge data.
U.S. Bridges
Length (ft)
Tally
Frequency
(first interval)
|||| ||
7
(last interval)
||
2
Based on the tallies and frequencies for the first and last intervals, how many intervals of what length did Jamie use?
a.
4 intervals of 1000 feet
c.
6 intervals of 500 feet
b.
5 intervals of 1000 feet
d.
7 intervals of 500 feet
Please select the best answer from the choices provided
A
B
C
D
The length of the intervals of the given frequency table is
500 ft.
The given list shows the lengths in feet of the 25 longest bridges in the United States.
we have to determine the median and mode of the bridge data.
The median is the middle number of the data set arranged in ascending order.
1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260.
The median is 1750.
Mode is the number that appears most often in the data set.
1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260
The mode is 1600.
Therefore the correct option is Median: 1750, Mode: 1600
So the length of the intervals of the given frequency table is
500 ft.
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How much will a sum of ¥4000 amount to in 1 1/2 yrs at 10% per annum compound interest,interest being paid half-yearly
Answer:
¥4630.50
Step-by-step explanation:
Compound Interest Formula
[tex]\large \text{$ \sf A=P(1+\frac{r}{n})^{nt} $}[/tex]
where:
A = final amountP = principal amountr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of time periods elapsedGiven:
P = 4000r = 10% = 0.1n = 2t = 1.5Substitute the given values into the formula and solve for A:
[tex]\implies \sf A=4000\left(1+\dfrac{0.1}{2}\right)^{2 \times 1.5}[/tex]
[tex]\implies \sf A=4000\left(1.05\right)^{3}[/tex]
[tex]\implies \sf A=4630.50[/tex]
Answer:
¥4630.50
Step-by-step explanation:
Here,
P = ¥4000n = 1 1/2 = 3/2 yearsr = 10% per annumATQ, as well,the interest is payable in half-yearly.
We know that,
[By this formula,it could easily solved][tex] \boxed{\rm \: A = P \bigg(1+ \cfrac{ \cfrac{r}{2} }{100} \bigg) {}^{2n} }[/tex]
Substitute the values
[tex]A = 4000 \bigg(1 + \cfrac{5}{100} \bigg) {}^{2 \times \frac{3}{2} } [/tex]
Now solve.
[tex]A = 4000 * (21/20)^3[/tex]
[tex] \implies \: A = 4000 \times \cfrac{21}{20} \times \cfrac{21}{20} \times \cfrac{21}{20} = \cfrac{21 \times 21 \times 21}{2} [/tex]
[tex] \implies \: A = \: \yen \: 4630.50[/tex]
Hence,the sum of ¥ 4000 will be amounted to ¥4630.50 in 1 1/2 years.
[tex] \rule{225pt}{2pt}[/tex]
This question arises:Why we used that formula?
Reason:
The compound interest is calculated half-yearly, the formula changes a little.In this case for r we write r/2 and for n we write 2n because a rate of r% per annum is r/2% half-yearly and n years = 2n half year So this is the reason.
A line that passes through the point (x,y), with a y-intercept of b and a slope of m, can be represented by the equation y = mx + b.
A line is drawn on the coordinate plane that passes through the point (3,-6) and has a slope of 4. The y-intercept of the line is .
Answer:
b= -18
Step-by-step explanation:
x=3, y= -6, m=4
y=mx+b
-6 = 4 x 3 + b Solve for b
-6 = 12 + b
-6-12 = b
b= -18
Answer:
b = -18
Step-by-step explanation:
Slope y-intercept form: y =mx +bSlope = m = 4
Plugin the value of slope in the above equation.
y = 4x + b
Now, the line passes through the point (3 , -6). Substitute x and y coordinates in the above equation.
-6 = 4*3 + b
-6 = 12 + b
b = -6 - 12
b = -18
[tex]\sf \boxed{\bf y-intercept = -18}[/tex]
What is the simple interest on N450 for 2 years at 3%?
Answer:
Simple Interest = PTR/100
P=450
T=2
R=3%
Simple Interest = PTR/100
=450×2×3\100
=27
Hence the interest is 27.
Graph the linear equation.
4x+6y=-12
Answer:
Step-by-step explanation:
To graph an equation using the slope and y-intercept, 1) Write the equation in the form y = mx + b to find the slope m and the y-intercept (0, b). 2) Next, plot the y-intercept. 3) From the y-intercept, move up or down and left or right, depending on whether the slope is positive or negative.
(URGENT) Madelina wants to make a prediction using a linear model with a correlation coefficient of 0.55. Which statement best describes how accurate she can expect her prediction to be? Her prediction will probably be close to the actual value. Her prediction will be unlikely to be close to the actual value. Her prediction will be somewhat likely to be close to the actual value. Her prediction will very likely be close to the actual value.
A correlation coefficient of 0.55 indicates that her prediction will probably be close to the actual value.
What is correlation coefficient?The correlation coefficient shows the relationship between two variables. It can be used to describe how to variables increase or decrease.
Thus, a correlation coefficient of 0.55 indicates that her prediction will probably be close to the actual value.
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Does anyone know how to do this I’m really confused
The size of the unknown angle "x"
Solution:The given polygon is a Pentagon so the sum of interior angle will be,
[tex]\large\boxed{Formula: ( n − 2 ) × 180}[/tex]
n means the number of sides
Let's substitute the values according to the formula.
[tex](5-2)×180[/tex]
[tex]=540°[/tex]
Now, we can find the sum of one interior angle.
[tex]\large\boxed{\frac{sum \: of \: interior \: angles}{n}}[/tex]
n means the number of sides.
Let's substitute the values according to the formula.
[tex]x=\frac{540}{5}[/tex]
[tex]\large\boxed{x= 108°}[/tex]
Therefore, the size of the unknown angle "x" is 108°
It cost a boy $13.50 to take a girl out for the evening. Sixty percent of this was for the theater tickets. What was the cost of each ticket ?
It cost a boy $13.50 to take a girl out for the evening. Sixty percent of this was for the theater tickets. What was the cost of each ticket?
Solution:60% of $13.50 is 0.6*13.50 = 8.10
Cut this figure in half to get 8.10/2 = 4.05
So the cost of each ticket was $4.05
Answer:The cost of each ticket is $4.05.
학습을 계속하다
Someone, please help! I really don't understand congruent triangles
Answer:
D. (CPCTC)
Step-by-step explanation:
Your proof that the triangles are congruent is complete at the 4th step. In Step 5, you are asked to draw a conclusion about corresponding angles in those congruent triangles.
__
what is congruence?Two geometric objects are congruent if they are identical in size and shape by any measure. If they are not labeled, you cannot tell them apart. Every measure of one is identical to the corresponding measure of the other. The location and orientation of congruent figures does not affect their congruence. You can move them, rotate them, flip them over, and they remain congruent.
This property, "corresponding parts of congruent triangles are congruent," is abbreviated "CPCTC." Once you have demonstrated objects are congruent, you can use this fact to relate measures of the objects that may not have been part of the demonstration.
proving congruencegeneral
We generally work with plane geometric figures that are polygons or have well-defined curved edges. Polygon figures are comprised of straight sides of fixed length. At each vertex, where sides meet, an angle is formed. Corresponding sides form corresponding angles.
The sides are generally named by the vertices at either end. The angles may be named by the vertex where it is located, or by the names of the sides that make it up.
In triangle ABC, for example, the vertices have labels A, B, and C. The sides are AB, AC, and BC. And the angles are A, B, and C, or BAC, ABC, ACB. (The vertex of the angle is the middle letter.)
To prove polygons are congruent, you must show corresponding angles are congruent, and corresponding sides are congruent. Generally, the number of sides will put constraints on the size of the angles. (A 6-sided polygon will have 6 angles that total 720°, for example.)
triangles
When the polygon is a triangle, the constraints on side lengths and angles generally mean there are shortcuts to proving congruence. The postulates that tell you what these are have been given mnemonic abbreviations. When we say, "angle" or "side" in this context, we are referring to congruent corresponding angles in the two triangles, or congruent corresponding sides.
AAS -- two consecutive angles and a side adjacent to one of them will prove congruenceASA -- two angles and the side between them will prove congruenceSAS -- two sides and the angle between them will prove congruenceSSS -- three sides will prove congruenceThese can also be applied to right triangles, where one angle is known to be 90°. In addition, there is a theorem that only applies to right triangles:
HL -- the hypotenuse and one leg will prove congruence. (Note that the hypotenuse is opposite the known 90° angle, so this is effectively an SSA congruence statement, only applicable to right triangles.)your proof
The triangles in your figure have a side marked with a single hash mark. This means those corresponding sides in the two triangles are congruent to each other.
There is an angle marked with two (2) arcs in each triangle. This marking means those corresponding angles are congruent. Likewise for the angles marked with three (3) arcs. You will notice the 3-arc angle, 2-arc angle, and 1-hash mark side are in the same order in the two triangles. This means the AAS congruence postulate applies, as is claimed on line 4 of your proof.
using congruenceAs you have seen, we only need to show some parts of a triangle are congruent in order to show all parts of the triangle are congruent. When we make a claim about corresponding parts that weren't an explicit part of the proof, we are essentially relying on the definition of congruent polygons. For triangles, that definition is summarized by the abbreviation CPCTC.
Line 5 of your 2-column proof is making a claim about corresponding angles of the triangle. That claim is supported by CPCTC.
_____
Additional comment
Choices A and C refer to congruence postulates, as discussed above. Those have no relation to the claim regarding angles ACB and XZY.
The "corresponding angles theorem" tells you corresponding angles are congruent where a transversal crosses parallel lines. It has no relation to the angles in this problem.
Saundra's credit has an APR of 18%, calculated on the previous monthly balance. Her credit card record for the last 7 months is hown in the table below. On what amount of money will Saundra be charged interest for month 8?
Answer:
I think the answer is $244.65 im not completely sure if this is the right answer so correct me if im wrong
The bearing
of P from Q is 0.60°. What is the bearing
of Q from P
Answer:
MMm mmm mmm mmm sh get wicked mmm mmm mm like what u saying mmm mmm mmm gla mmmm
Step-by-step explanation:
EASY POINTS
NEED HELL ASAP WIT THIS
Answer:
5
Step-by-step explanation:
You just multiply the indices by the power so 1/6 x 6 = 1 and 5 to the power of 1 is just 5.
Please show your work! I'll give you brainliest as well as a 5 star rating, thanks!
Answer:
281.3
Step-by-step explanation:
If the shapes are similar then the linear scale factor is :
15÷20 = 0.75
The area scale factor will be 0.75²
The area scale factor is 0.5625
500 × 0.5625 = Area of shaded rectangle
Area of shaded rectangle = 281.25
To the nearest tenth = 281.3
Hope you understood and brainliest please
Answer:
[tex]281.3 m^{2}[/tex]
Step-by-step explanation:
I've done this before I have the work attached below in a screenshot. Sorry that it's not much but I hope it helps!
Please feel free to comment, give feedback, ask questions, and correct me if I am wrong!
Have a great day
:)
A game decreased in price by 2/3. After the reduction it was priced at £13. What was the original price of the game?
Answer:
[tex]x = 39[/tex]
Step-by-step explanation:
Based on the given conditions, write: [tex]x=\frac{13}{1-\frac{2}{3}}[/tex]
Find common denominator and write numerators above common denominator: [tex]x=\frac{\frac{13}{3-2} }{3}[/tex]
Calculate the sum or difference: [tex]x=\frac{\frac{13}{1} }{3}[/tex]
Divide the fraction by multiplying its reciprocal: [tex]x=13*3[/tex]
Calculate the product or quotient: [tex]x=39[/tex]
Answer: [tex]x=39[/tex]
Answer:
£19.50
Step-by-step explanation:
let x be the original price , then
[tex]\frac{2}{3}[/tex] x = 13 ( multiply both sides by 3 to clear the fraction )
2x = 39 ( divide both sides by 2 )
x = 19.5
original price of game was £19.50
Suponga que los clientes demandarán 60 unidades de un producto cuando el precio es de $24 por unidad, y 40 unidades cuando el precio es de $20 cada una. suponiendo que es lineal. Determine el precio cuando se requiere 50 unidades.
Considerando la ecuación lineal, cuando se requiere 50 unidades, el precio será $22.
Qué es la ecuación linealUna ecuación lineal o línea se puede expresar en la forma y = mx + b.
dónde
x e y son coordenadas de un punto.m es la pendiente.b es la ordenada al origen y representa la coordenada del punto donde la línea cruza el eje y.Conociendo dos puntos (x1, y1) y (x2, y2) de una recta, se puede calcular la pendiente m de dicha recta mediante la siguiente expresión:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Sustituyendo el valor de la pendiente m y el valor de uno de los puntos en la expresión de una ecuación lineal, y = mx + b, se obtiene el valor de la ordenada al origen b.
Precio de 50 unidades de un productoEn este caso, siendo la ecuación lineal Precio=m× cantidad + b, sabes que los clientes demandarán 60 unidades de un producto cuando el precio es de $24 por unidad, y 40 unidades cuando el precio es de $20 cada una. Esto es:
(x1, y1)= (60, 24)(x2, y2)= (40, 20)Entonces, la pendiente m es calculada mediante la siguiente expresión:
[tex]m=\frac{20-24}{40-60}[/tex]
Resolviendo:
m= 0.2
Entonces, considerando el valor de la pendiente m y el punto 1, el valor de la ordenada al origen b se calcula como:
24 = 0.2× 60 + b
24 = 12 + b
24 -12= b
12= b
Entonces. la relación entre la cantidad de unidades y precio es Precio=0.2×cantidad + 12
Entonces, cuando se requiere 50 unidades, el precio será calculado como:
Precio=0.2×50 + 12
Resolviendo:
Precio= 22
Finalmente, cuando se requiere 50 unidades, el precio será $22.
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The data below show the expenditure of a housewife for a particular day
Item amount
Rice. 120
Yam. 100
Beans. 140
Vegetable 140
Meat. 180
Sugar. 40
Palm oil. 60
Display using a pie chart
The pie chart below depicts a housewife's expenditures for a certain day.
What is a pie chart?A map wherein the round is split into segments, each one representing a percentage of the total.
The data below show the expenditure of a housewife for a particular day
Item amount
Rice - 120
Yam - 100
Beans - 140
Vegetable - 140
Meat - 180
Sugar - 40
Palm oil - 60
The pie chart is given below.
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In how many years will $7000 yield an interest of $4620 at 22% simple interest?
Answer:
3 Years
Step-by-step explanation:
7000*22% = 1540
4620/1540 = 3
1540 = the yearly interest
so it will take 3 years of $1540 of interest to get $4620.
Normally you would also have to take into account the interest plus the base varible but since it specifically says 7000 it makes it a simple problem.
hope this helped
How many full 4 2/3 in. Sheets can be cut from 22 1/6 in. Stick
Answer:
4
Step-by-step explanation:
Because i divided 4 2/3 by 22 1/6 = 4.75 and for full sheets it would be 4
Hope This Helped
A line contains points F, G, H, I, J. The space between F G is 2. The space between H and I is 1. The space between F and I is 7.
If FG = 2 units, FI = 7 units, and HI = 1 unit, what is GH?
Based on the segment addition postulate, the length of GH is: 4 units.
What is the Segment Addition Postulate?The segment addition postulate states that if a line segment is divided into smaller parts, the sum of the length of the smaller parts equals the length of the line segment.
FG = 2 unitsFI = 7 unitsHI = 1 unitGH = ?FI = FG + HI + GH [segment addition postulate]
7 = 2 + 1 + GH
7 = 3 + GH
7 - 3 = GH
4 = GH
GH = 4 units.
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Answer:
B- 4 units
Step-by-step explanation:
CHARLES' LAW CALCULATION.
1.The temperature will be, T2= 169.8 K
2. The volume if the temperature is 318 K is 0.170 L
What is Charles Law?Charles's law, a statement that the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature, if the pressure remains constant.
Given: V1= 250 ml=0.25L
V2=150 ml= 0.15 L
T1= 10 °C=283 K, T2=?
Now using Charles law
V1/T1=V2/T2
0.25/283=0.15/T2
T2= 169.8 K
2. T1= 20 °C= 293 K
V1= 160 cm³
T2= 318 K
V2=?
Using Charles Law,
V1/T1=V2/T2
0.16/293=V2/313
0.170 L=V2
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EN=NG, which of the following statements CANNOT be true? F M E R NP Q A. MN is a perpendicular bisector. OB. FM = MG O C. Pis a midpoint. O D. MN is a midsegment. G
help dawg
Answer:A. MN is a perpendicular bisector.
Hope that helps
Step-by-step explanation:
I need help with this
Answer:
1. obtuse angle
2. Right angle
3. Adjacent angle
4. Supplementary angle
5. Acute angle
6. Straight line
7. Complementary angle
8. Vertical Angle
9. linear
10. Vertex
Step-by-step explanation:
1. Obtuse angle are angle that measures greater than 90 degree but less and 180 degree
2. Right angle are angle that measures exactly 90 degree
3. Adjacent angle are angles that has a common vertex and share a common side
4. Straight angle is a pair of angle whose sum is 180 degree.
5. Acute angle is an angle greater than 0 degree but less than 90 degree
6. straight line measure exactly 180 degree
7. Complementary angle is a pair of angle whose sum is 90 degree.
8. Vertical Angle is a pair of angle made by intercepting lines with congruent opposite side
9. Linear is a pair of adjacent, supplementary angles.
10. Vertex is an common end point that two rays meet to form an angle.
PLEASE HELP ITS DUE SOON IM SO CONFUSED! HELP NEEDED!!
Answer:
e
Step-by-step explanation:
According to Angle Sum Property :
∠A + ∠B + ∠C = 180°
============================================================
Given :
⇒ ∠A = 50°
⇒ ∠B = 32°
===========================================================
Solving :
⇒ 50° + 32° + ∠C = 180°
⇒ ∠C + 82° = 180°
⇒ ∠C = 98°
PLEASE HELP ASAP WILL MARK BRAINLY
Mark the lines
tanD=BC/BDPut the values
tanD=√38/√53Done
Answer:
[tex]\sf \tan(D)=\dfrac{\sqrt{38}}{\sqrt{53}}[/tex]
Step-by-step explanation:
Tangent trigonometric ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
[tex]\theta[/tex] is the angleO is the side opposite the angleA is the side adjacent the angleGiven:
[tex]\theta[/tex] = DO = √38A = √53Substituting the given values into the formula:
[tex]\implies \sf \tan(D)=\dfrac{\sqrt{38}}{\sqrt{53}}[/tex]
a circular garden has a diameter of 12 yards whag is the area of the garden use 3.14
Step-by-step explanation:
the area of a circle is
pi × r²
r is the radius (= half of the diameter) of the circle.
radius in our car is 12/2 = 6 yd
and we are to use 3.14 as pi.
so we get as area
3.14 × 6² = 3.14 × 36 = 113.04 yd²
rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Answer:
36 units²
Step-by-step explanation:
rectangle with area of 12 square units is dilated by a scale factor of 3. What is the area?
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
we use the inverse formula
12 * 3 =
36 units²
-----------------------
check
36 : 12 = 3
the answer is good
Find cos 20 if theta is in the first
quadrant and tan 0 = 40/9
If the value of the angle θ is 77.32°. Then the value of cos 2θ will be the negative 0.90.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric equation is given below.
tan θ = 40/9
tan θ = 4.444
Then the angle θ will be
θ = tan⁻¹(4.444)
θ = 77.32°
Then the value of cos 2θ will be
cos 2θ = cos (2 x 77.32°)
cos 2θ = cos 154.64°
cos 2θ = - 0.9036
cos 2θ ≅ - 0.90
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Dean started with 5 meters
of yarn. He used 300
millimeters of yarn each day
for 5 days. How many
meters of yarn does Dean
have left?
Answer:
3.5 meter is the answer.
Answer:
3.5 Meters
Step-by-step explanation:
5 Meters is equivalent to 5000 millimeters
1 day = 300mm
5 days = (300*5)
= 1500 mm
= 5000 mm - 1500 mm
Yarn left = 3500 mm
= 3.5 Meters
X =
(19) Find the values for X and Y, and then solve for the side lengths.