in the diagram below,RQ is parallel to ST. ST =4cm RP =10cm PT = 5cm a.find,. i.the scale factor. ii.|RQ|. b.if the area of ∆PRQ is 80 cm find the area of triangle ∆PST.
Answers
Answer:
us7e7eoeod8rr8r88rr8 fnddkdkiduduruScale factor is 1/2. and, Area of PST = 20cm^2
What is triangle?
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.
here, we have,
we get in the diagram below, RQ is parallel to ST.
ST =4cm
RP =10cm
PT = 5cm
Now, PRQ is larger than PTS
i.e. the scale factor = 5/10
=1/2
And, |RQ|= ST*2
=4*2
=8
Now, area of PRQ =80cm^2
so, area of PST = 80*1/2^2
=80*1/4
=20cm^2
Hence, Scale factor is 1/2., Area of PST = 20cm^2.
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Related Questions
In the adjoining parallelogram ABCD, A is joined to any point E on BC. AE and DC produced meet at E Prove that. area of ∆BEF = area of ∆ CDE
Answers
Answer:
In parallelogram ABCD any point E is taken on the side BC . AE and DC when produced to meet at a point M . Prove that ar(ADM) = ar(ABMC) .Question is in the photo*
Answers
Answer:
3x - y +5=0
Step-by-step explanation:
Slope:-
=> m = 2-8/-1-1 = -6/-2
=> m = 3
Using point slope form :-
=> y - 2 = 3 ( x - (-1))
=> y - 2 = 3x + 3
=> 3x - y +5 = 0
Answer:
y=3x+5
Step-by-step explanation:
first find the gradient
m=y2-y1/x2-x1
from the coordinates you are given x one is -1,x two is1,y one is 2,y two is 8
8-2/1-(-1)
=3
therefore the gradient is 3
after finding the gradient use the equation
y-y1=m(x-x1)
substitute x1,y1 and the gradient..y and x are constant
y-2=3(x-(-1))
y-2=3x+3
y=3x+3+2
y=3x+5
Which formulas can be used to find the surface area of a right prism where p is the perimeter of the base, h is the height of the prism, BA is the area of bases, and LA is the lateral area? Check all that apply.
A. SA = BA - LA
B. SA = p + LA
C. SA = BA + LA
D. SA = BA + ph
E. SA = 1 / BA + LA
Answers
Answer:
SA=BA+LA and SA=BA+ph
Step-by-step explanation:
I just looked it up
The correct formulas to find the surface area of a right prism are:
SA = BA + LA and SA = BA + ph.
Options (A), and (D) are the correct answer.
What is a prism?A prism is a three-dimensional object.
There are triangular prism and rectangular prism.
We have,
The correct formulas to find the surface area of a right prism are:
1)
SA = BA + LA, where SA is the total surface area, BA is the area of the two identical bases, and LA is the lateral area (the sum of the areas of all the rectangular sides).
2)
SA = BA + ph, where SA is the total surface area, B is the area of one base, p is the perimeter of the base, h is the height of the prism, and ph is the area of all the rectangular sides (the lateral area).
Therefore,
The correct formulas to find the surface area of a right prism are:
SA = BA + LA and SA = BA + ph.
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SA is the perpendicular bisector of TR . m
A) 45
B) 60
C) 39
D) 180
Answers
Answer:
if you are supposed to find m<STR, then the answer is B
Step-by-step explanation:
Answer:
i thinkits c
Step-by-step explanation:
based on the info given
Please decide !!!!!!
Answers
Starting from the top and going horizontally the missing numbers are:
18, 3, 1, 9, 7, 6, 2, 8, 16, 4, 15, 10
The sum of 1+2+3+...+18+19 = 190
There are 5 vertical lines (3,4,5,4,3 in each) so each line has to add to 190 / 5 = 38
Solve for X.
-3/2(x-2)=45/14
Please show work.
Answers
Answer:
-1/7
Step-by-step explanation:
-3/2(x-2)=45/14
x-2=(45/14)/(-3/2)
x-2=(45/14)(-2/3)
x-2=-90/42
simplify -90/42 into -15/7
x-2=-15/7
x=-15/7+2
x=-15/7+14/7
x=-1/7
x=-1/7
Decimal form:
-0.142857
Explanation:
You simplify both sides of the equation and then isolate the variable.
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.
Answers
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.
Kenneth ran a marathon (26.2) miles) in 5.5 hours. What was Kenneth’s average speed? (Round your answer to the nearest tenth.)
Answers
Answer:
4.8 miles per hour.
Step-by-step explanation:
Average speed=Total distance/Time taken
=26.2miles/5.5hour
=4.8 miles per hour
Si "m" es el lado mayor de un triángulo, dos cuyos ángulos interiores miden 30° y 60°, entonces el perímetro del triángulo es
Answers
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]
Determine the axis of symmetry of the parabola with x-intercepts at (4, 0) and (12, 0)
Answers
Step-by-step explanation:
hope it helps thank you❤
Helpppp someone please
Answers
Given:
The graph of system of inequalities.
To find:
The system of inequalities.
Solution:
From the given graph it is clear that the shaded region is lies below the line y=10 and the boundary line y=10 is a solid line. So, the sign of inequality must be [tex]\leq[/tex].
[tex]y\leq 10[/tex].
The shaded region lies on the right side of the y-axis. So, [tex]x\geq 0[/tex].
Another boundary line passes through the point (0,1) and (1,2). So, the equation of the line is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-1=\dfrac{2-1}{1-0}(x-0)[/tex]
[tex]y=1(x)+1[/tex]
[tex]y=x+1[/tex]
The boundary line [tex]y=x+1[/tex] is a dotted line and the shaded region lies above the boundary line, so the sign of inequality must be [tex]>[/tex].
[tex]y> x+1[/tex]
So, the required system of inequalities is:
[tex]y> x+1[/tex]
[tex]y\leq 10[/tex]
[tex]x\geq 0[/tex]
Therefore, the correct option is B.
i need help asap. rn
Answers
Answer:
4
Step-by-step explanation:
For this, you need to find the scale factor of two sides that are already given to you.
So, we will have to use the hypotenuse and one of the legs to make sure there is an accurate scale factor.
Hypotenuse:
15 / 5 = 3
Leg:
6 / 2 = 3
____________
So the scale factor is 3.
Using the leg (with the x) we need to divide 12 by the scale factor (3) to give us what x is equal to.
12 / 3 = 4
So, the answer is 4.
10 points!!!!!:)
Describe the graph of the function.
[tex]y = \sqrt{x + 3} [/tex]
a). the graph is a radical function y=sqrt(x) shifted 3 units right.
b). the graph is a radical function y=sqrt(x) 3 units left.
c). the graph is of exponential growth.
d). the graph is an absolute value function with vertex (-3,0).
pls help me:).
Answers
Answer:
b) y=sqrt(x) shifted 3 units left
Step-by-step explanation:
3rd line in the attached table:
f(x+3) = sqrt(x+3) horizontal translation left 3 units
5 positive integers are arranged in ascending order, as follows:
1,9, 9, 10, X
The mean and the median are equal.
Find X.
Answers
Answer:
x = 16
Step-by-step explanation:
Since the numbers are in ascending order, x is the number with the highest value here.
From the arrangement, we can see that the median (the middle number) is the third number which is 9
The mean is the sum of the numbers divided by their count. So we set up the mean and equate to the median
We have this as;
(1 + 9 + 9 + 10 + x)/5 = 9
29 + x = 5(9)
29 + x = 45
x = 45-29
x = 16
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?
Answers
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
Answers
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 m20. The diagram is not to scale.
R
689
33°
Select one:
O a. 79
O b. 101
O c.
89
O d. 112
Answers
180-101= 79.
79 is the answer
Find the area
Help me please
Answers
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
can anyone please explain this?
Find the equation of locus of a point A(-3,2) and B(0,4).....
what is locus actually?
Answers
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.
Someone tell me where everyone is going right please !!
Answers
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
Graph the line with slope -5 and y-intercept 1.
Answers
Answer:y=-5+1
Step-by-step explanation:
which algebraic expressions are polynomials
Answers
Answer:
last option
Step-by-step explanation:
3.9x3 -4.1x2+7.3
A rectangular tank 60 cm long and 50 cm wide is /5 full of water. When 24 liters of water are added, the water level rises to the brim of the tank. Find the height of the tank. (1 liter is 1000cm3 )
Answers
Answer:
The tank is 10cm high
Step-by-step explanation:
Given
[tex]L=60cm[/tex] -- length
[tex]W=60cm[/tex] -- width
[tex]x = \frac{1}{5}[/tex] --- water lever
[tex]Addition = 24L[/tex]
Required
The height of the tank
Let y represents the remaining fraction before water is added.
So:
[tex]y + x = 1[/tex]
Make y the subject
[tex]y = 1 - x[/tex]
[tex]y = 1 - \frac{1}{5}[/tex]
Solve
[tex]y = \frac{5 - 1}{5}[/tex]
[tex]y = \frac{4}{5}[/tex]
Represent the volume of the tank with v
So:
[tex]y * v = 24L[/tex]
Make v the subject
[tex]v = \frac{24L}{y}[/tex]
Substitute: [tex]y = \frac{4}{5}[/tex]
[tex]v = \frac{24L}{4/5}[/tex]
[tex]v = 30L[/tex]
Represent the height of the tank with h;
So, the volume of the tank is:
[tex]v = lwh[/tex]
Make h the subject
[tex]h = \frac{v}{lw}[/tex]
Substitute values for v, l and w
[tex]h = \frac{30L}{60cm * 50cm}[/tex]
Convert 30L to cm^3
[tex]h = \frac{30*1000cm^3}{60cm * 50cm}[/tex]
[tex]h = \frac{30000cm^3}{3000cm^2}[/tex]
[tex]h = 10cm[/tex]
What is the relationship between an angle of elevation and an angle of depression in a right triangle?
Answers
Answer: Angles of Elevation and Depression are used in measuring heights and distances in trigonometric applications using right triangles. These angles are made when we look up or down to view objects. Devices are available to measure angles of elevation and depression. These measured angles can be used in measuring heights and distance which are either tedious or impractical to measure, by modelling the situation into right triangles
Answer:
Angles of Elevation and Depression are used in measuring heights and distances in trigonometric applications using right triangles. These angles are made when we look up or down to view objects. Devices are available to measure angles of elevation and depression. These measured angles can be used in measuring heights and distance which are either tedious or impractical to measure, by modelling the situation into right triangles
Step-by-step explanation:
correct on EDGE2021
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.
Answers
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.
I just need to know how I would be able to find x
Answers
Answer:
[tex]x=15[/tex]°
Step-by-step explanation:
The sum of degree measures in a full angle (a circle) is (360) degrees. This means that the sum of all of the angles in this diagram is (360) degrees, as the angles form a full arc. Therefore, one can form an equation by adding up all of the angles and setting the equation equal to (360) degrees. Then one can substitute each angle value with the equation that is used to represent it, simplify, and use inverse operations to solve for the value of (x).
[tex](m<AMB)+(m<BMC)+(m<CMD)+(m<AMD)=(360)[/tex]
Substitute,
[tex](46)+(4x-2)+(9x+6)+(8x-5)=360[/tex]
Simplify,
[tex](46)+(4x-2)+(9x+6)+(8x-5)=360[/tex]
[tex]21x+45=360[/tex]
Inverse operations,
[tex]21x+45=360[/tex]
[tex]21x=315[/tex]
[tex]x=15[/tex]
Solve for x.
Help me please
Answers
Answer:
x = 24
Step-by-step explanation:
Mathematically, in a cyclic quadrilateral; two opposite angles are supplementary
what this mean is that the opposite angles add up to equal 180 degrees
mathematically, we have this as;
(4x + 9) + (3x + 3) = 180
4x + 3x + 3 + 9 = 180
7x + 12 = 180
7x = 180-12
7x = 168
x = 168/7
x = 24
increase 30 by 1/2
help please its urgent
Answers
Answer:
30.5 for decimal form and 30 1 /2 if mixed fraction needed
If “the notation arcsin x represents the inverse function to sine” is true or false.
Answers
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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Sal is trying to determine which cell phone and service plan to buy for his mother. The first phone costs $100 and $55 per month for unlimited usage. The second phone costs $150 and $51 per month for unlimited usage. How many months will it take for the second phone to be less expensive than the first phone?
The inequality that will determine the number of months, x, that are required for the second phone to be less expensive is
.
The solution to the inequality is
.
Sal’s mother would have to keep the second cell phone plan for at least
months in order for it to be less expensive.
Answers
Answer:
It will take 13 months for the second phone to be less expensive than the first phone.
Step-by-step explanation:
Since Sal is trying to determine which cell phone and service plan to buy for his mother, and the first phone costs $ 100 and $ 55 per month for unlimited usage, while the second phone costs $ 150 and $ 51 per month for unlimited usage, to determine how many months will it take for the second phone to be less expensive than the first phone, the following calculation must be performed:
100 + (55 x 10) = 100 + 550 = 650
150 + (51 x 10) = 150 + 510 = 660
100 + (55 x 12) = 100 + 660 = 760
150 + (51 x 12) = 150 + 612 = 762
100 + (55 x 13) = 100 + 715 = 815
100 + (51 x 13) = 150 + 663 = 813
Therefore, it will take 13 months for the second phone to be less expensive than the first phone.
Answer:
1) 100 + 55x > 150 + 51x
2) x > 12.5
3) 13
Step-by-step explanation:
Got it right on Edge :D