we have the system
8x-4y=-12 -----> equation A
8x+y=-17 -----> y=-17-8x -----> equation B
substitute equation B in equation A
8x-4(-17-8x)=-12
solve for x
8x+68+32x=-12
40x=-12-68
40x=-80
x=-2
Find the value of y
y=-17-8(-2)
y=-17+16
y=-1
the solution is x=-2y=-1Example8x-4y=-12 -----> equation A8x+5y=-17 -----> equation B
isolate the variable y in equation B (or equation A)
5y=-17-8x
y=-(17/5)-(8/5)x
substitute in equation A
8x-4[-(17/5)-(8/5)x ]=-12
solve for x
Evaluate each expression.5. -36.97. 13 +-28. -12-8
7) 13 + -2 = 13 + (-2) = 13 - 2 = 11
8) -12 - 8 = - (12 + 8) = - (20) = -20
Describe how the graph of g (x) is related to the graph of the parent function
g(x) = -x-2
vertical translation:
horizontal translation
dilation:
reflection:
The graph of the function is reflected across the y-axis and vertically translation by 2 units downwards.
The parent function of the graph is f(x) = x
Now the first is the reflection along the y-axis.
Hence the graph of the function h(x) becomes h(x) = -x
Now there is a translation by 2 units downwards. or a vertical translation of 2 units downwards.
Hence the graph of f becomes g(x) = -x -2
In mathematics, a shape can be translated by moving up, down, left, or right. Since they seem to have the same proportions as the original shapes, the translated shapes are consistent with one another. Just a few more adjustments have been made to the instructions.
As we just saw, before translations are carried out, a shape is referred to as a "preimage," and when translations are complete, a shape is referred to as an "image."
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Determine if the proportion is true 1/2= 3/4 Proportion is true Proportion is not true
K:
1/2 and 3/4 are NOT equivalent.
If you divide 1 by 2, the result is 0.5
If you divide 3 by 4, the result is 0.75
Therefore, they are NOT equivalent
1/2 and 2/4 are equivalent:
If you divide 1 by 2, the result is 0.5
If you divide 2 by 4, the result is also 0.5
Now, you can answer the question.
the altitude of a triangle is increasing at a rate of 1 1 centimeters/minute while the area of the triangle is increasing at a rate of 4 4 square centimeters/minute. at what rate is the base of the triangle changing when the altitude is 10.5 10.5 centimeters and the area is 90 90 square centimeters?
Answer:
-128/147 cm/min
Step-by-step explanation:
[tex]A=\frac{1}{2}bh \\ \\ 90=\frac{1}{2}(10.5)b \\ \\ b=\frac{120}{7} \\ \\ \\ A=\frac{1}{2} bh \\ \\ \implies \frac{dA}{dt}=\frac{b}{2} \frac{dh}{dt}+\frac{h}{2} \frac{db}{dt} \\ \\ 4=\frac{21}{4}+\frac{db}{dt}+\frac{60}{7} \\ \\ \frac{db}{dt}=-\frac{128}{147}[/tex]
I dont really understand this. (10th grade math)
Answer:
Angle 1: 56 degrees
Angles 2: 56 degrees
Angles 3: 74 degrees
Step-by-step explanation:
triangles angles added up equal 180
So we add the 2 angles in the first triangle to find angle 1
58+66
124
Then subtract by 180
180-124
56
Angle 1 is 56 degrees
angles 2 is also 56 degrees since they are corresponding angles
Now we know 2 angles of the second triangle and to find angle 3 we add the 2 angles
56+50=106
And subtract by 180
180-106
74
Angles 3 is 74 degrees
Hopes this helps please mark brainliest
An item is regularly priced at $29. Jane bought it at a discount of 55% off the regular price.  how much did Jane pay?
Answer:
Jane payed $15.95 for the item.
Step-by-step explanation:
55% as a decimal is 0.55
You can multiply 0.55, or get 55%, of 29.
0.55x29 = 15.95
Now you have your answer!
29.What is the surface area of the cone?90 cm²1207 cm²12 cm5 cm
Given:
The cone with height(h) 12 cm and radius(r) 5 cm.
Required:
What is the surface area of the cone?
Explanation:
The formula required to calculate surface area of cone:
[tex]\begin{gathered} SA=\pi r(r+\sqrt{h^2+r^2}) \\ Where, \\ r(Radius) \\ h(Height) \end{gathered}[/tex]We have radius(r) = 5 cm and height(h) = 12 cm.
So,
[tex]\begin{gathered} SA=\pi\times5\times(5+\sqrt{12^2+5^2}) \\ SA=\pi\times5\times(5+\sqrt{169}) \\ SA=\pi\times5\times(5+13) \\ SA=\pi\times5\times18 \\ SA=90\pi cm^2 \end{gathered}[/tex]I kind of understand but what I'm having trouble with is when u simply it 6/5 ×5/6=6/5×40 how are they getting 48 i get 33.3
37 = -3 + 5(x + 6)
Distributing:
37 = -3 + 5(x) + 5(6)
37 = -3 + 5x + 30
Commuting:
37 = -3 + 30 + 5x
37 = 27 + 5x
27 is adding on the right, then it will subtract on the left.
37 - 27 = 5x
10 = 5x
5 is multiplying on the right, then it will divide on the left
10/5 = x
2 = x
A small television cost $120, the sales tax is 6.5%. What is the total cost of the television? * Your answer
∵ The cost of the television = 120 dollars
∵ The sale tax = 6.5%
→ Find at first the value of tax by multiplying 6.5% by 120
∵ 6.5% = 6.5/100 = 0.065
∴ The tax = 0.065 x 120 = 7.8 dollars
→ Add the tax to the cost to find the total cost
∵ The tota
please I need helpppppppppppp
The value of angle a will be = 50 degrees
Since the given figure has 4 sides hence it is a quadrilateral, we know that the sum of all 4 sides should be equal to 360 degrees so,
Sum of all 4 sides = 360 degrees
The sum of the given 3 sides = 100+100+110 = 310 degrees
Angle a = Sum of all 4 sides - the sum of the given 3 sides
Angle a = 360 - 310
Angle a = 50 degrees
Hence the value of the remaining angle a = 50 degrees
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In one country, approximately 193,200 of 920,000 residences are rentals. Determine the percentage of residences in the country that are rentals.The percentage of residences in the country that are rentals is %.
To find the percentage of the residences in the country that are rentals is calculated with this formula:
[tex]\begin{gathered} =\frac{\text{population of rental residence}}{total\text{ country population}}\times100\text{ \%} \\ \text{Given:} \\ \text{Population of rental reseidence = 193,200} \\ \text{Total country population = 920,000} \end{gathered}[/tex]Now substituting the given information, into the above percentage expression, we will have:
[tex]\begin{gathered} =\frac{193,200}{920,000}\times100\text{ \%} \\ =0.21\times100\text{ \%} \\ =21\text{ \%} \end{gathered}[/tex]The percentage of residences in the country that are rentals is 21 %.
What is the unit rate in price per ounce for choice A? Round your answer to the nearest hundredth.
Choice A: 25 ounces of potato chips for $3.49
Choice B: 45 ounces of potato chips for $4.79
a
$7.16 per ounce
b
$0.14 per ounce
c
$9.39 per ounce
d
$0.11 per ounce {jackpot points} {if you dont know DON'T ANSWER}
The unit rate in price per ounce for choice A is $0.1396, using arithmetic operation.
What is the arithmetic operation?
The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.
The given question, 25 ounces of potato chips cost $3.49
So for 1 ounce the price will be 3.49/25 = $0.1396
Hence, the unit rate in price per ounce for choice A is $0.1396
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Find the length of RP given the coordinates R (5,8) and P (3,6).m:Il m:Im:RP:
2nd Question)
1) Considering that this is a line segment R(5,8) and P(3,6). Let's find out the distance between those points using the distance formula, derived from the Pythagorean Theorem:
[tex]\begin{gathered} d=\sqrt[]{(x_2-x_1)^2+(y_2-y_1)} \\ d=\sqrt[]{(3-5)^2+(6-8)^2} \\ d=2\sqrt[]{2}\approx2.82 \end{gathered}[/tex]2) Let's now find the slope between those points, making use of the slope:
[tex]m=\frac{y_2-y_1}{x_2-x_1}=\frac{6-8}{3-5}=\frac{-2}{-2}=1[/tex]The next step is to fill in the table, so:
m: 1
Parallel slopes are identical so we can state:
║m = 1
Perpendicula
2.5x+6 find value of x
Answer:
I only got 8.5 but I could be wrong
Step-by-step explanation:
10. Wesley willed his estate to Margaret, Betty Jo, and Johnny. He gave Margaret $20,000. Betty Jo got 22 times as much as Margaret. Johnny got 32 times as much as Margaret. What was the total value of the estate? (1) $26,000 (2) $50,000 (3) $70,000 (4) $120,000 (5) $1,140,000
We were told that Wesley willed his estate to Margaret, Betty Jo, and Johnny.
Given that he gave Margaret $20,000. Betty Jo got 22 times as much as Margaret, it means that the amount the at Betty Jo got is 22 * 20000 = 440000
Given that Johnny got 32 times as much as Margaret, it means that the amount that Johnny got is
20000 * 32 = 640000
Therefore, the total value of the estate is
20000 + 440000 + 640000 = 1100000
The total value of the estate is $1,100000
WILL GIVE BRAINIEST!!!!!
The x-coordinates of the points of intersection of the given function graphs are;
1) x = 0 and x = 2
2) x = -1
3) x = 0
What is the point of intersection of the graph?The point of intersection of a graph is in simple terms explained as the point or coordinates where two lines or even curves intersect.
1) The first question gives us the functions as;
f(x) = -³/₄x² + 3x + 1
g(x) = 2ˣ
Therefore;
From the first graph, At f(x) = g(x), the coordinates of intersection is at (2,4 and (0, 1)
2) In the second question, we are given the functions as;
f(x) = x² + 4x + 2
g(x) = (¹/₂)ˣ + 1
Therefore;
From the first graph, At f(x) = g(x) the coordinates of intersection is at (-1. 3)
C) In the third question, we are given the functions as;
f(x) = -⁷/₃x - 3
g(x) = 2ˣ - 4
Thus;
From the graph, At f(x) = g(x), the coordinates of the point of intersection is at (0, -3)
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help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 19.6 feet
Step-by-step explanation:
Using the Pythagorean theorem,
[tex]x^2 +(x+6)^2 =48^2\\\\x^2 +x^2 +12x+36=2304\\\\2x^2 +12x-2268=0\\\\x^2 +6x-1134=0\\\\x=\frac{-6 \pm \sqrt{6^2 -4(1)(-1134)}}{2(1)}\\\\x \approx 30.8 \text{ } (x > 0)\\\\\implies x+(x+6) \approx 67.6\\\\\therefore (x+(x+6))-48 \approx 19.6[/tex]
Help QUick Help !!!! I beg you help now !!!!!!!!!!!!! 5 mins!!!!!!!
Brainliest!!!!!
Find the area of the triangle whose vertices are (−6,3), (5,3) and (8,7).
Answer:
Area of the triangle is 22 units²------------------------------
GivenTriangle with vertices (−6,3), (5,3) and (8,7)Two of the vertices are on horizontal line with same y-coordinate of 3.
These two vertices form the base of the triangle which is:
b = 5 - (-6) = 11 units longThe height is the difference of the y-coordinates of the third vertex with the first two:
h = 7 - 3 = 4Find the areaA = bh/2A = 11*4/2 = 22 units²11 1/2
+ 3 5/8
Write your answer as a mixed number with the fractional part in lowest terms
Answer:
Step-by-step explanation:
11 [tex]\frac{1}{2}[/tex] + [tex]\frac{5}{8}[/tex]
make all the fractions an improper fraction
(11×2)+1/2 = 23/2
(3x5)+5/8 = 29/8
you need to make sure both fractions have a common denominator
to make 23/2 common with 5/8 you multiply 23/2 by 4/4
wich will make 92/8
continiue with the question
92/8 + 29/8= 121/8
simplify by dividing by 8 to get a mixed number
15 1/8
four students write algebraic math expressions and equations on their whiteboard. Which of the following students wrote expressions?
The students who write expressions when the students write algebraic math expressions and equations on their whiteboard is student 1 and 4.
What is an expression?In mathematics, an algebraic expression is an expression composed of variables and constants as well as algebraic operations (addition, subtraction, etc.). Terms combine to form expressions. An expression or mathematical expression in mathematics is a finite combination of symbols that is well-formed according to context-dependent rules.
An algebraic expression is one that is composed of integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). 3x² 2xy + c, for example, is an algebraic expression.
In this case, student 1 wrote 1/2x + 6 and student 4 wrote 5 - x. It should be noted these are algebraic expressions as they don't have equal signs.
The diagram is attached.
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find the error & explain why it is wrong:
jon had to solve the equation below. what did he do wrong?
x^2 = x - 6
Answer:
Step A is incorrect.
[tex] {x}^{2} = x - 6[/tex]
[tex] {x}^{2} - x + 6 = 0[/tex]
Jon should have subtracted x from both sides and then added 6 to both sides.
Which of the following points are on the line given by the equation y=2x
A. (1,3)
B. (5,10)
C. (4,6)
D. (3,6)
E. (16,8)
F. (4,2)
Answer:
Step-by-step explanation:
The answer is B because if you multiply 5 by 2 it equals 10.
The answer could also be D because if you multiply 3 by 2 it equals 6.
Which is the correct equation needed to solve for x.
Responses
10x−10=8x
10x−10=90
and 8x=90
10x−10+8x=180
10x−10+8x=90
Answer:
(a) 10x -10 = 8x
Step-by-step explanation:
Given the lengths of corresponding sides in congruent triangles are 10x-10 and 8x, you want to know the correct equation needed to solve for x.
CPCTCCorresponding parts of congruent triangles are congruent, so the corresponding sides (10x -10) and (8x) are the same length. The equation that expresses this relationship is useful for finding the value of x:
10x -10 = 8x
__
Additional comment
The nature of the answer choices suggests that the values (10x-10) and (8x) could be considered to be the measures of the right angles. These two equations would give different values of x.
We interpret the figure as showing these expressions represent the lengths of the segments opposite the marked acute angles.
An architect makes a model of a new house. The model shows a tile patio in the backyard. In the model, each tile has length 2/3 in. and width 1/2. The actual tiles have length 1/2 ft and width 3/8 ft. What is the ratio of the length of a tile in the model to the length of an actual tile? What is the ratio of the area of a tile in the model to the area of an actual tile? Use pencil and paper. Describe two ways to find each ratio. The ratio of the length of a tile in the model to the length of an actual tile is?
The ratio of the length of an actual tile is 4/3, and the ratio of area is 16/9.
What is ratio?
A ratio is a comparison of two or more numbers that indicates their sizes in relation to each other. A ratio compares two quantities by division, with the dividend or number being divided termed the antecedent and the divisor or number that is dividing termed the consequent.
Given,
the length of tile is 2/3 and width = 1/2
The length of actual tile is 1/2 and width = 3/8
Therefore, the ratio of the actual length of tile = 2/3 ÷ 1/2
=2/3×2/1
=4/3
The area of the tile in the model to the area of tile in actual tile = 2/3×1/2÷(1/2×3/8)
=1/3÷3/16
=1/3×16/3
=16/9
And another method is property of dilation,
The ratio of the areas = (4/3)^2
=16/9
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Please help! I need explanation on why the answer is what it is.
Answer:
The answer is C.
Step-by-step explanation:
y=mx+b
m represents slope
b represents the y-intercept
In the problem, it is asking you to make an equation just plug it in!
y=3x-1
Hope this helps!
Find the equation of a straight line passing through the points (1, 1) and (2, -1)
The equation of a line with slope a and y-intercept b can be expressed in the for y = ax + b.
For a line passing through the points (1,1) and (2,-1), its slope is given by:
[tex]a=\frac{(-1)-1}{2-1}=-2[/tex]To find the intercept, we can just replace x and y by one of the given pairs of coordinates:
[tex]\begin{gathered} y=-2x+b \\ 1=(-2)\cdot1+b \\ b=1+2 \\ b=3 \end{gathered}[/tex]Therefore, the equation of the line is y = -2x + 3
Which condition would prove AJKL - AXYZ?
J
O A. JK
XY
OB.
O C. KL
=
JL
X 2/2 = 1/2
XZ
118
O D. JL
118
= 8
YZ
3=8
XZ
K
56
L
N
7
Y
X
ΔJKL and ΔXYZ are similar triangles with condition KL / YZ = 8
Two triangles are said to be Similar triangles if they have same shape but not necessarily the same size , ratio of all the corresponding sides are same and corresponding angles are equal to each other
In ΔJKL and ΔXYZ ,
1 . The shape of both triangles are same
2 . ∠KLJ = ∠YZX
3 . Ratio of corresponding sides KL / YZ = 56 / 7
= KL / YZ = 8
so , KL / YZ = 8 is condition to prove ΔJKL and ΔXYZ are similar triangles.
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Answer:
KL/YZ=8 have a nice day:)
If a box holds 540 balls, and each layer holds 18 balls. How many layers does the box have?
Does it have 30 layers because 540 divided
by 18=30
Answer:
You are absolutely correct!
Step-by-step explanation:
To find the area of a cube, we do length (l), times width (w), times height (h).
Let's say that the length is 6, while the width is 3. That would make the first layer 18, like in your problem.
18 × 10 = 180
18 × 20 = 360
18 × 30 = 540
So, yes! You are correct!
As each layer can hold 18 balls 540 balls can be placed in 30 layers.
What is a unitary method?A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.
Given, A box holds 540 balls, and each layer holds 18 balls.
∴ To determine no. of layers we have to divide the total no. of balls by no. of balls in one layers,
= (540/18) layers.
= 30 layers.
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Can someone please tell and show me the steps on how to do this I need help
Answer:
(2,3)
Step-by-step explanation:
-3x-2y=-12
y=5x-7
according to the second equation y is equal to 5x-7 so we enter that into the first equation for y
-3x-2(5x-7)= -12
-3x-10x+14= -12
-13x+14= -12
-14. -14
-13x= -26
/-13. /-13
x= 2
now we know x is 2 we fill in x in any of these equations to find y but i will use the second equation
y=5(2)-7
y=10-7
y=3
now we write it as an ordered pair (x,y)
(2,3)
hopes this helps please mark brainliest
Please help! Help is much appreciated. I think I already got a.
b.
To determine how many accounts will minimize the long run average cost.
Given the function;
[tex]C=576-48N+N^2[/tex]We need to plot a graph of the function and identify the lowest point on the graph ( since we are minimizing).
Above is a section of the graph of the function.
The lowest point on the graph is at;
[tex]\begin{gathered} N=24 \\ C=0 \end{gathered}[/tex]Therefore, the number of accounts that will minimize the long run average cost is 24 accounts.
Also, the minimum long run average cost is 0
c.
We want to determine whether the territories should be merged together.
To do this we will check their average long run cost when they merge and compare to their average long run cost when they are separate;
When the merge, the total number of accounts is;
[tex]N=16+19=35[/tex]So, the long run average cost is;
[tex]\begin{gathered} C=576-48N+N^2 \\ C=576-48(35)+35^2 \\ C=121 \end{gathered}[/tex]When they are separate, as calculated in a.
the long run average cost for both is;
[tex]\begin{gathered} C_1=576-48(16)+16^2 \\ C_1=64 \\ C_2=576-48(19)+19^2 \\ C_2=25 \\ C=C_1+C_2=64+25 \\ C=89 \end{gathered}[/tex]So, since the long run average cost for when they merge is greater that the total long run average cost when the are separate, then they should not merge the two territories because merging the two territories increases the long run average cost. And we all know the aim is to always try to reduce cost.
Therefore, they should not merge