solve the following simultaneous equations using SUBTITUTION METHOD
m+3n=7 and 5m-n=3
To check:put value of m and n in both equations
Answer: n=2 and m=1
Step-by-step explanation:
m+3n=7 , 5m-n=3
m=7-3n => 5(7-3n)-n=3
=> 35-15n-n=3
=> -16n=-32
=> n=2
n=2 => 5m-2=3
=> m=1
Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match the rectangles formed by the sets of points to their corresponding areas.
A(-9, 8), B(-5,5), C(1, 13), D(-3, 16)
50 square units
E(30, 20), F(39, 29), G(49, 19), H(40, 10)
300 square units
I(-6, 2), J(2, 2), K(2, -8), L(-6, -8)
100 square units
M(5,5), N(11,5), O(11,-5), P(5,-5)
80 square units
Q(10, 0), R(15,5), S(25,-5), T(20,-10)
U(0,5), V(15, 20), W(25, 10), X(10,-5)
Answer:
A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16) → 50 square units
I(-6, 2), J(2, 2), K(2, -8), L(-6, -8) → 80 square units
Q(10, 0), R(15, 5), S(25, -5), T(20, -10) → 100 square units
U(0, 5), V(15, 20), W(25, 10), X(10, -5) → 300 square units
Step-by-step explanation:
The area of a rectangle, given the coordinates of the vertices is found as follows;
1) The vertices of the rectangle ABCD are; A(-9, 8), B(-5, 5), C(1, 13), and D(-3, 16)
The length of side AB = √((-9 - (-5))² + (8 - 5)²) = 5
The length of side BC = √((1 - (-5))² + (13 - 5)²) = 10
The length of side CD = √((1 - (-3))² + (13 - 16)²) = 5
The length of side DA = √(((-9) - (-3))² + (8 - 16)²) = 10
The area of rectangle ABCD = 5 × 10 = 50 square units
2) The vertices of the rectangle EFGH are; E(30, 20), F(39, 29), G(49, 19), and H(40, 10)
The length of side EF= √((39 - 30)² + (29 - 20)²) = 9·√2
The length of side FG = √((39 - 49)² + (29 - 19)²) = 10·√2
The length of side GH = √((40 - 49)² + (10 - 19)²) = 9·√2
The length of side HE = √((40 - 30)² + (10 - 20)²) = 10·√2
The area of rectangle EFGH = 9·√2 × 10·√2 = 180 square units
3) The vertices of the rectangle IJKL are; I(-6, 2), J(2, 2), K(2, -8), and L(-6, -8)
The length of side IJ= √((-6 - 2)² + (2 - 2)²) = 8
The length of side JK= √((2 - 2)² + ((-8) - 2)²) = 10
The area of rectangle IJKL = IJ × JK
∴ The area of rectangle IJKL = 8 × 10 = 80 square units
4) The vertices of the rectangle MNOP are; M(5, 5), N(11, 5), O(11, -5), and P(5, -5)
The length of side MN = √((5 - 11)² + (5 - 5)²) = 6
The length of side NO = √((11 - 11)² + ((-5) - 5)²) = 10
The area of rectangle MNOP = 6 × 10 = 60 square units
5) The vertices of the rectangle QRST are; Q(10, 0), R(15, 5), S(25, -5), and T(20, -10)
The length of side QR = √((10 - 15)² + (0 - 5)²) = 5·√2
The length of side RS = √((25 - 15)² + ((-5) - 5)²) = 10·√2
The area of rectangle QRST = 5·√2 × 10·√2 = 100 square units
6) The vertices of the rectangle UVWX are; U(0, 5), V(15, 20), W(25, 10), and X(10, -5)
The length of side UV = √((0 - 15)² + (5 - 20)²) = 15·√2
The length of side VW = √((25 - 15)² + (10 - 20)²) = 10·√2
The area of rectangle UVWX = 15·√2 × 10·√2 = 300 square units
Answer:
A(-9, 8), B(-5, 5), C(1, 13), D(-3, 16)—
(50 square units)
I(-6, 2), J(2, 2), K(2, -8), L(-6, -8)—
(80 square units)
Q(10, 0), R(15, 5), S(25, -5), T(20, -10)—(100 square units)
U(0, 5), V(15, 20), W(25, 10), X(10, -5)—(300 square units)
Step-by-step explanation:
got it right on test, hope I helped
60
What is the value of x in the equation x - y = 30, when y= 15?
O. 4
O. 8
O. 80
O. 200
Answer:
Step-by-step explanation:
x - y = 30
Substitute 15 for y.
x - (15) = 30
Add 15 to both sides.
x = 45
What is the value of the power? Negative StartFraction 9 Over 12 EndFraction Negative StartFraction 27 Over 64 EndFraction StartFraction 9 Over 12 EndFraction StartFraction 27 Over 64 EndFraction
Answer:
[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]
Step-by-step explanation:
Given
[tex](\frac{-3}{4})^3[/tex]
Required
Evaluate
The expression can be represented as:
[tex](\frac{-3}{4})^3 = (\frac{-3}{4})*(\frac{-3}{4})*(\frac{-3}{4})[/tex]
So, we have:
[tex](\frac{-3}{4})^3 = \frac{-3*-3*-3}{4*4*4}[/tex]
[tex](\frac{-3}{4})^3 = \frac{-27}{64}[/tex]
Rewrite as:
[tex](\frac{-3}{4})^3 = -\frac{27}{64}[/tex]
Answer:
B -27/64
Step-by-step explanation:
Five number have amean of 12,when one number is removed, the mean becomes 11,what is the removed number
Answer:
The removed number is 16
Step-by-step explanation:
Five numbers have a mean of 12.
Now;
Mean = Σx/x
Thus; Σx = 12 × 5 = 60
Now,we are told that if one number is removed, the mean is 11.
Thus;
(60 - x)/4 = 11
60 - x = (11 × 4)
60 - x = 44
x = 60 - 44
x = 16
Thus,the removed number is 16
Which of the following expressions represents the distance between -3.9 and -4.7
Answer:
None of the above
Step-by-step explanation:
Distance is the difference between two positions. That is x1- x2 Since both numbers were negative, you would want the absolute value of one plus the other, because subtracting a negative results in a positive. For this example the distance would look more like this:
| -4.7 - ( -3.9 ) | = .8
= (b) Use your calculator to determine the exact value of 35.23 x 3.02 Exactly Correct to 2 decimal place
Answer:
The exact value is 106.40
Step-by-step explanation:
The exact value of the given operation obtained with the calculator is:
[tex] 35.23 \times 3.02 = 106.3946 [/tex]
The result expressed in 2 decimal places is:
[tex] 106.3946 = 106.40 [/tex]
Therefore, the exact value is 106.40
I hope it helps you!
ANSWER THIS PLEASE !!
Answer:
B. point B
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
B(-1, -3)
y = 3x
When x = -1,
y = 3(-1) = -3
Answer: B.
17:56 Dawn is trying to find out how much weight she can push across the room. She is really trying to find her __________.
Integrate with respect to x
3√(2-5x)
It is a special kind of segment, ray, or line that intersects a given segment at a 90∘ 90 ∘ angle, and passes through the given segment's midpoint.
Answer:
Perpendicular bisector
Step-by-step explanation:
Given
The above statement
Required
What describes the given statement?
The term that describes the given statement is the perpendicular bisector.
This is so because:
- The perpendicular bisector passes through midpoints
- The point of intersection is at the [tex]90^o[/tex]
A coin is flipped five times. Find the number of possible sets of heads and tails that have at most 3 heads
Answer:
[tex]Sets = 27[/tex]
Step-by-step explanation:
Given
[tex]Coin = 1[/tex]
[tex]Toss = 5[/tex]
Required
Number of outcomes with at most 3 heads
First, we list out the sample space of a toss of coin 5 times
[tex](HHHHH)[/tex], [tex](HHHHT)[/tex], [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], [tex](THHHH)[/tex], [tex](HTHTH)[/tex], [tex](THTHT)[/tex], [tex](HHTHH)[/tex], [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](HHHTH)[/tex], [tex](TTTHT)[/tex]
Next, we list out all outcomes with at most 3 heads
, , [tex](HHHTT)[/tex], [tex](HHTTT)[/tex], [tex](HTTTT)[/tex], [tex](TTTTT)[/tex], [tex](TTTTH)[/tex], [tex](TTTHH)[/tex], [tex](TTHHH)[/tex], , [tex](HTHTH)[/tex], [tex](THTHT)[/tex], , [tex](TTHTT)[/tex], [tex](HTTHT)[/tex], [tex](THHTH)[/tex], [tex](THHHT)[/tex], [tex](HTTTH)[/tex], [tex](THHTT)[/tex], [tex](HTTHH)[/tex], [tex](HHTTH)[/tex], [tex](TTHHT)[/tex], [tex](TTHTH)[/tex], [tex](HHTHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](THTTH)[/tex], [tex](HTHHT)[/tex], [tex](HTHTT)[/tex], [tex](THTHH)[/tex], [tex](TTTHT)[/tex]
So, the number of set is:
[tex]Sets = 27[/tex]
How many solutions are there to the equation below? 9(x – 4) = 9x – 33
Answer:
no solution
Step-by-step explanation:
Can somebody answer this????
Answer:
x=46
Step-by-step explanation:
Isosceles triangle which means that the bottom two angles are equal. 180 degrees minus 88=92. Since there are two angles you divide 92/2 which gets 46.
Answer:
D
Step-by-step explanation:
two sides are equal.
so opposite angles are also equal.
x+x+88=180
2x=180-88=92
x=92/2=46°
does this table represent a function? why or why not 2,1 3,4 4,4 5,2 5,5
What is the value of Z?
Answer:
137
Step-by-step explanation:
Since angle Z and the angle of 43° are supplementary, the sum of them must equal 180. Therefore,
∠Z + 43 =180
∠Z = 137°
Answer:
137 degrees
Step-by-step explanation:
First thing, we know y is 43 because 43 degrees and y are vertical angles meaning they are congruent. (This is just a small part doesn't really do much though.)
Straight lines add up to 180 so simply just subtract 43 from 180.
180 - 43 = 137.
Therefore,
z = 137 degrees
line I is parallel to line m.if the maesure of angle 6 is 75 what is the measure of angle 3
Answer:
105
Step-by-step explanation:
l is parallel m so angle 3+angle 6=180
Someone please help me with this algebra problem
Answer:
$110
Step-by-step explanation:
We are looking for the decrease in money per desk purchased. Because the x-axis is the number of desks purchased, what we have to find is the (opposite) of the slope. The formula to represent slope can be written as:
[tex]\frac{y_{2} -y_{1} }{x_{2}- x_{1} }[/tex]
We can substitute the points given, (2, 480) and (5, 150) and simplify:
[tex]\frac{150-480}{5-2} =\frac{-330}{3} = -110[/tex]
We would multiply by -1 because we are asking for the decrease, and negative increase is decrease. -1 * -110, gives us $110
1). What is the equation of the line that is perpendicular to y= -3x+1 that passes through the point (9,0)?
2). What is the equation of the line that is parallel to y= -3x+1 that passes through the point (9,0)?
Answer:
Step-by-step explanation:
1) Slope of the given line = -3
slope of the perpendicular line = 1/3
y - 0 = 1/3(x-9)
y = 1/3x - 3
2) slope of the parallel line = -3
y - 0 = -3(x-9)
y = -3x + 27
Answer:
1). y = 1/3x - 3 2).y = -3x + 27
Step-by-step explanation:
1). y = 1/3x + b
0 = 1/3(9) + b
0 = 3 + b
-3 = b
y = 1/3x - 3
2)/ y = -3x + b
0 = -3(9) + b
0 = -27 + b
27 = b
y = -3x + 27
Which congruence theorem can be used to prove BDAS DBC?
Answer:
We know that the hypotenuse-leg theorem states that if the hypotenuse and one leg of a right triangle are congruent to hypotenuse and corresponding leg of another right triangle, then the triangles are congruent. hypotenuse(AB) of △BDA equals to hypotenuse (CD) of △DBC.
Answer:
A. HL
Step-by-step explanation:
A teacher asks students to determine the accuracy of this statement.
A reflection over the x-axis and then over the y-axis results in the same transformation as a 180degree rotation about the origin of the original figure.
Kwame’s explanation of the accuracy of the statement is shown below.
Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3).
Step 2: Reflect the pre-image over the x-axis: (1, –2), (1, –4), (2, –3).
Step 3: Reflect the figure from step 2 over the y-axis: (–1, 2), (–1, 4), (–2, 3).
Step 4: Rotate the pre-image 180degree: (–1, –2), (–1, –4), (–2, –3).
Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate.
Which best explains Kwame’s solution?
Kwame’s explanation and solution are incorrect. He reflected the image over the y-axis in step 2 and the x-axis in step 3, instead of the reverse.
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Kwame’s explanation and solution are incorrect. When reflecting over the x- and y-axes, he negated the incorrect coordinate in the ordered pair.
Kwame’s explanation and solution are incorrect. The coordinates of the rotated figure should be switched and negated, not just negated.
Answer:
B. Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Step-by-step explanation:
I just did it, and thankfully, all was well! :) :) :)
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
What is transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation. Rotation, translation and reflection produce congruent images.
The vertices of the pre-image is (1, 2), (1, 4), (2, 3). It is reflected over the x axis to get (1, –2), (1, –4), (2, –3)It is then reflected over the y axis to get (-1, 2), (-1, 4), (-2, 3) instead of (-1, –2), (-1, –4), (-2, –3).Rotating the vertices 180 degrees gives (-1, –2), (-1, –4), (-2, –3).
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Find out more on transformation at: https://brainly.com/question/1620969
What is the equation of the following line? Be sure to scroll down first to see
all answer options.
10-
(7.2)
- 10
(0,0)
10
- 10 -
A. y 1x
B. y = 7x
C. y = 2x
D. y = -7x
E. y= ²x
F. y= -2x
Answer:
[tex]y = \frac{2}{7} x[/tex]
Step-by-step explanation:
The slope is
[tex]slope = \frac{rise}{run} = \frac{2}{7} [/tex]
The y-intercept is 0
The equation of line between the points is y = ( 2/7 )x
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 ( 7 , 2 )
Let the second point be Q ( 0 , 0 )
Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values in the equation , we get
Slope m = ( 2/7 )
Now , the equation of line is y - y₁ = m ( x - x₁ )
y - 0 = ( 2/7 ) ( x - 0 )
y = ( 2/7 )x
Hence , the equation of line is y = ( 2/7 )x
To learn more about equation of line click :
https://brainly.com/question/14200719
#SPJ7
91.55
Which equation has the solutions -
5:27
3
1?
I
3x2 - 5x + 7 = 0
03x2 - 5x – 1 = 0
3x2 - 10x + 6 = 0
O 3x2 _ 10x + 1 = 0
Answer:
the answer is 3x2-10x+6=0
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
complete the table of values for y=x^2-2x+2
Nachelle went to the store to buy some almonds. The price per pound of the almonds is $6.50 per pound and she has a coupon for $4.75 off the final amount. With the coupon, how much would Nachelle have to pay to buy 5 pounds of almonds? Also, write an expression for the cost to buy pp pounds of almonds, assuming at least one pound is purchased.
Step-by-step explanation:
hope this will help you mark me as brinalist friend please
The amount paid for the 5 pound of almond by Nachelle is $27.75.
What is meant by the term equation?In its most basic form, an equation is a numerical declaration that demonstrates that two formulas are equal. 3x + 25 = 14, for example, is an equation whereby a 3x + 25 and 14 are 2 expressions separated by a 'equal' sign.Let 'p' be the number of pounds of almonds purchased by Nachelle.
Let 'c' be the total cost paid.
The cost of per pound of the almonds is $6.50 per pound.
The amount of the coupon is $4.75.
Thus, the equation will be ;
c = 6.50p - 4.75 ......equation.
For number of pounds p = 5.
c = 6.50×5 - 4.75
c = $27.75
Thus, the amount paid for the 5 pound of almond by Nachelle is $27.75.
To know more about equation, here
https://brainly.com/question/18831322
#SPJ2
use the substitution method to solve the system of equations
3x+2y=13
y=x-1
Answer:
[tex]x=3\\y=2[/tex]
Step-by-step explanation:
[tex]3x+2y=13\\y=x-1[/tex]
Solve for [tex]y=x-1[/tex] for y:
[tex]y=x-1[/tex]
Substitute [tex]x-1[/tex] for y in [tex]3x+2y=13[/tex]:
[tex]3x+2y=13[/tex]
[tex]3x+2(x-1)=13\\[/tex]
[tex]5x-2=13[/tex]
[tex]5x=13+2[/tex]
[tex]5x=15[/tex]
[tex]x=15/5[/tex]
[tex]x=3[/tex]
Substitute 3 for x in [tex]y=x-1[/tex]:
[tex]y=x-1[/tex]
[tex]y=(3)-1[/tex]
[tex]y=2[/tex]
[tex]x=3[/tex] and [tex]y=2[/tex]
hope this helps...
can you please help me with number 4 please?
what is the average cost of 7 articles if 3 of them cost 30k each and the rest cost 12.5k each
[tex] {\bold{\red{\huge{\mathbb{QUESTION}}}}} [/tex]
what is the average cost of 7 articles if 3 of them cost 30k each and the rest cost 12.5k each
[tex]\bold{ \red{\star{\blue{GIVEN }}}}[/tex]
TOTAL NUMBER OF ARTICLE= 7
ARTICLES FOR 30K = 3
ARTICLES FOR 12.5K = 7-3= 4
[tex]\bold{\blue{\star{\red{TO \: \: FIND}}}}[/tex]
Average cost of 7 articles
[tex] \bold{ \green{ \star{ \orange{FORMULA \: USED}}}}[/tex]
[tex] \red{AVERAGE = \frac{TOTAL \: COST}{ NUMBER \: OF\: ARTICLES }}[/tex]
[tex] \huge\mathbb{\red A \pink{N}\purple{S} \blue{W} \orange{ER}}[/tex]
[tex]Average \: cost \: of \: 7 \: articles - > \\ \frac{(3 \times 30k) + (12 .5k \times 4)}{7} \\ \frac{90k + 50k}{7} \\ \frac{140k}{7} \\ \blue {Average \: cost \: of \: 7 \: articles - >} \\ 20k[/tex]
For each calculation choose the correct answer written in standard form.
a) (7 * 10°) ~ (3 x 10?)
A
B
21 x 100 21 x 10
С
2.1 x 10"
D
2.1 x 10
b) (2 x 10°) = (4 x 102)
A
2 x 10
B
5 x 10
с
0.5 x 10
D
2 x 10
Answer:
Both the answers will be B
