Answer:
x = 2 , y = 11
Step-by-step explanation:
the diagonals of a parallelogram bisect each other , then
PT = TR , that is
y = 5x + 1 → (1)
QT = TS , that is
2y = 6x + 10 → (2)
substitute y = 5x + 1 into (2)
2(5x + 1) = 6x + 10
10x + 2 = 6x + 10 ( subtract 6x from both sides )
4x + 2 = 10 ( subtract 2 from both sides )
4x = 8 ( divide both sides by 4 )
x = 2
substitute x = 2 into either of the 2 equations for corresponding value of y
substituting into (1)
y = 5(2) + 1 = 10 + 1 = 11
TR=PT as diagonals bisect each other in parallelogram
y=5x+1--(1)Similarly
QT=TS
2y=6x+10-(2)Equate both equations in (2)
2(5x+1)=6x+1010x+2=6x+104x=8x=2Now
y=5(2)+1y=11the lowest common multiple of 8 and 15
If an item has an original price of $65, but is discounted 20%. What is the total cost after sales tax (.0825)?
Answer:56.29$
Step-by-step explanation:
65 x .80 = 52
52 x 1.0825 = 56.29
<Brainliest is appreciated!>
Answer:
$56.29
Step-by-step explanation:
Original price = $65
discount = 20%
hence discounted price = 100% - 20% = 80% of the original price
discounted price = 80% x $65 = $52
sales tax rate = 0.0825 (i.e 8.25%)
amount of sales tax paid
= 0.0825 x discounted price
= 0.0825 x $52
= $4.29
Final cost
= discounted price + sales tax
= $52 + $4.29
= $56.29
Find the measure of the indicated arc or angle.
Answer: Arc EG/GE = 135°
Step-by-step explanation:
Given:
∠EGF = 80°
Arc FG = 65°
Since ∠EGF = 80°, the value of Arc EF = 2(∠EGF)
Therefore, Arc EF = 2(80°) = 160°
The arc measure of an entire circle is 360°.
Therefore,
360° = EF + FG + GE
360° = 160° + 65° + GE
GE/EG = 135°
pla shop mathematics
The number of trees more than 10m tall but not more than 20m tall is 18 trees.
How many of the trees are more than 10m tall but not more than 20m tall?0 < h ≤ 5 = 5
height greater than 0m less than or equal to 5m
5 < h ≤ 10 = 9
height greater than 5m less than or equal to 10m
10 < h ≤ 15 = 13
height greater than 10m less than or equal to 15m
15 < h ≤ 20 = 5
height greater than 15m less than or equal to 20m
20 < h ≤ 25 = 1
height greater than 20m less than or equal to 25m
The number of trees that are more than 10m tall but not more than 20m tall are;
10 < h ≤ 15 = 13
15 < h ≤ 20 = 5
So,
13 + 5 = 18 trees
Therefore, the total number of trees which are 10m tall but not more than 20m tall is 18 trees.
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Garden Avenue Middle School has 23 boxes of math books delivered each box contains 12 books a group of four Math teachers divide the books of evenly amongst the cells for their students how many books did each math teacher receive
Step-by-step explanation:
this is very roughly converted from the original question, I bet. no punctuation marks and, and ...
what I understood of the important information is :
there are 23 boxes of books with 12 books in each.
there are 4 teachers dividing the books evenly among themselves for their cells (classes ?) of students.
so, we need to divide the books by 4 to distribute them evenly into 4 parts.
23×12/4 = 23×3 = 69
each teacher got 69 books.
solve the following inequalitie and fin x
5/( + 2)(4 − )< 1
Answer: -1 < x < 3
Step-by-step explanation:
\(\dfrac{5}{(x+2)(4-x)}<1\)
Step 1 The denominator cannot equal zero:
x + 2 ≠ 0 and 4 - x ≠ 0
x ≠ -2 4 ≠ x
Place these restrictive values on the number line with an OPEN dot:
<----------o-------------------o--------->
-2 4
Step 2 Find the zeros (subtract 1 from both sides and set equal to zero):
\(\dfrac{5}{(x+2)(4-x)}-1=0\\\\\\\dfrac{5}{(x+2)(4-x)}-\dfrac{(x+2)(4-x)}{(x+2)(4-x)}=0\\\\\\\dfrac{5-(-x^2+2x+8)}{(x+2)(4-x)}=0\\\\\\\dfrac{5+x^2-2x-8}{(x+2)(4-x)}=0\\\\\\\dfrac{x^2-2x-3}{(x+2)(4-x)}=0\\\\\\\text{Multiply both sides by (x+2)(4-x) to eliminate the denominator:}\\x^2-2x-3=0\\(x-3)(x+1)=0\\x-3=0\quad x+1=0\\x=3\quad x=-1\)
Add the zeros to the number line with an OPEN dot (since it is <):
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 3 Choose test points to the left, between, and to the right of the points plotted on the graph. Plug those values into (x - 3)(x + 1) to determine its sign (+ or -):
Left of -2: Test point x = -3: (-3 - 3)(-3 + 1) = Positive
Between -2 and -1: Test point x = -1.5: (-1.5 - 3)(-1.5 + 1) = Positive
Between -1 and 3: Test point x = 0: (0 - 3)(0 + 1) = Negative
Between 3 and 4: Test point x = 3.5: (3.5 - 3)(3.5 + 1) = Positive
Right of 4: Test point x = 5: (5 - 3)(5 + 1) = Positive
+ + - + +
<----------o-----o----------o----o--------->
-2 -1 3 4
Step 4 Determine the solution(s) based on the inequality symbol. Since the original inequality was LESS THAN, we want the solutions that are NEGATIVE.
Negative values only occur between -1 and 3
So the solution is: -1 < x < 3
I need help with this question
Answer:
-5,2
Step-by-step explanation:
it literally represents LM and Shows it on the graph
A surveyor measures the lengths of the sides of a triangular plot of land. what is the measure of the angle of the triangular plot at which the surveyor stands? approximate to the nearest degree. cosâ€""1(0.75) = 41° cosâ€""1(0.125) = 83° cosâ€""1(0.563) = 56° cosâ€""1(0.15) = 89°
The surveyor determines the angle of the triangular plot by using the inverse cosine function with a given value of cos⁻¹(0.15). The result of approximately 89° represents the approximate measure of the angle at which the surveyor stands in relation to the sides of the plot.
Among the given options for the inverse cosine values, the measure of the angle of the triangular plot at which the surveyor stands is determined by the value of cos⁻¹(0.15), which is approximately 89°.
Each result represents the measure of the angle at which the surveyor stands in relation to the sides of the triangular plot. It's important to note that these results are approximate values rounded to the nearest degree.
By using the given cosine values and applying the inverse cosine function, the surveyor can determine the approximate angle of the triangular plot.
Therefore, The approximate measure of the angle of the triangular plot at which the surveyor stands is 89°.
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Question-
A surveyor measures the lengths of the sides of a triangular plot of land. what is the measure of the angle of the triangular plot at which the surveyor stands? Approximate to the nearest degree.
cos^(-1)(0.75) ≈ 41°
cos^(-1)(0.125) ≈ 83°
cos^(-1)(0.563) ≈ 56°
cos^(-1)(0.15) ≈ 89°
Please someone answer this I’ll give 20 points
Calculate the gradient of the following line, please answer B with explanation
Answer:
2
Step-by-step explanation:
to find the gradient use the formula : y2 - y1 / x2 -x1some coordinates the line is intersecting are: (3,6) , ( 0,0)0-6 / 0 -3
2
20% of what number is 75?
Answer:
15
Step-by-step explanation:
Answer: 375
Step-by-step explanation:
how do you convert % into fractions?
Answer:
To convert a decimal to a fraction, place the decimal number over its place value. For example, in 0.6, the six is in the tenths place, so we place 6 over 10 to create the equivalent fraction, 6/10.
Step-by-step explanation:
Find the surface area. HELP PLEASE!!!!
Answer:
I think the answer is 792
Answer:
SA = 696cm^2
Step-by-step explanation:
First we need to identify the shapes
There are 3 rectangles and 2 triangles
Now the individual surface area for each shape
20 x 10 = 200 (1 rectangle)
1/2(12 x 8) = 48 (1 triangle)
Now we add them together
(200 x 3) + (48 x 2) = 696
describe the set (Sunday, Saturday)
Answer:
I don't really know what you mean but I guess my best description would be
it contains 2 elements it is a subset of a set containing all days of the weekHOPE IT HELPS
Find the values of x and y
A. X=34, y=17 √3
B. X=17 √3, y=34
C. X=34 √3, y=17
D. X=17, y=34 √3
Step-by-step explanation:
B
\( \tan(30) = \frac{17}{x} \\ x = \frac{17}{ \tan(30) } \\ x = \frac{17}{0.577} = 29.46\)
\( \sin(30) = \frac{17}{y} \\ y = \frac{17}{ \sin(30) } = 34\)
Chelsea has 0.90 pounds of meat. She uses 0.15 pound of meat to make one hamburger. How many hamburgers can Chelsea make with the meat she has?
Chelsea can make 6 hamburgers with the meat she has.
- To find out how many hamburgers Chelsea can make with 0.90 pounds of meat, we need to divide the total amount of meat by the amount of meat needed to make one hamburger.
- According to the problem, Chelsea uses 0.15 pound of meat to make one hamburger.
- So we need to divide 0.90 (the total amount of meat) by 0.15 (the amount of meat needed for one hamburger).
- When we do the division, we get 6.
- This means that Chelsea can make 6 hamburgers with the meat she has.
To calculate the number of hamburgers that Chelsea can make with 0.90 pounds of meat, we need to use the information given in the problem and perform a simple division calculation.
Firstly, we know that Chelsea has 0.90 pounds of meat. This is the total amount of meat that she has available to make the hamburgers.
Secondly, we know that it takes 0.15 pound of meat to make one hamburger. This is the amount of meat needed for each individual hamburger.
To find out how many hamburgers Chelsea can make with the meat she has, we need to divide the total amount of meat by the amount of meat needed for each hamburger.
So, the calculation looks like this:
0.90 ÷ 0.15 = 6
This means that Chelsea can make 6 hamburgers with the meat she has.
In conclusion, the answer to the problem is that Chelsea can make 6 hamburgers with the 0.90 pounds of meat that she has available.
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1400 people signed up for a bike sharing program. This represents 8% of the people who live in Divyas town. 75% of the people who signed up for the program also own cars.
Answer:
what is the question??????
i dont even know what to put
Answer:
first one (2*2*2*3*3)
Step-by-step explanation:
2*2*2*3*3=72
y = 4x + 2
on a graph
Use the graph of y=Ca to determine C and a.
C= 1
a=
CIT
Help me solve this View an example Get more help
[-10, 10] [-10, 10]
Xscl=1 Yscl=1
Aу
Clear all
Answer:
C = 1a = 4Step-by-step explanation:
You want the values of C and 'a', given the graph of y = C·a^x.
Values of yWhen x = 0, ...
y = C·a^0 = C·1 = C
The graph shows y = 1 when x = 0, so C = 1.
When x = 1, ...
y = C·a^1 = C·a = 1·a = a
The graph shows y = 4 when x = 1, so a = 4.
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The value of the variable are; C = 1 and a = 4
If we know that the function crosses the x axis at some point, then for some polynomial functions, we have those as roots of the polynomial.
We want the values of C and 'a', given the graph of y = C·a^x.
To find the Values of y
When x = 0, y = C·a^0 = C·1 = C
The graph shows that y = 1 when x = 0, so C = 1.
When x = 1, then y = C·a^1 = C·a = 1·a = a
The graph shows that y = 4 when x = 1, so a = 4.
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Sketch the graph of the function below, including correct signs, x-intercepts and y-
intercepts.
f(x) = (x + 5)(x + 3)(x - 2)2
Answer:
if you learned derivative:
f'x=(x+3)(x-2)²+(x+5)(x-2)²+2(x+5)(x+3)(x-2)
=4x³+12x²-26x-28=0
⇒x=2; =-0.84; =-4.16
⇒fx=0; =72.47; -36.97⇒fx contain (2;0); (-0.84;72.47); (-4.16;-36.97)
if x=0⇒f'x=-28<0⇒from -0.84 to 2, fx Decreasing
Step-by-step explanation:
A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:
Reason 2:
Reason 3:
Reason 4:
The table shows the multiplication of two linear expressions and the subsequent simplification and standard form conversion. The reasons given are the input expressions, Distributive property, Associative Property, simplification to standard form conversion. So, the correct option answer for reason 1, 2, 3 and 3 are B, C, A and D respectively.
The table shows the multiplication of two linear expressions is
Step Step
1 (1/4)x(5x-1)
2 (1/4)x(5x)+(1/4)x(-1)
3 (1/4)(5x^2)+(-1/4)x
4 (5/4)x^2+(-1/4)x
Reason 1: The multiplication of two linear expressions is given in the first column for each step.
Reason 2: The given linear expressions are rearranged in the second column for each step. It is Distributive Property.
Reason 3: The rearranged expressions in the second column are simplified using algebraic operations. It is Associative Property.
Reason 4: The simplified expressions in the second column are written in the standard form of a quadratic polynomial.
So, the correct order of options for reason 1, 2, 3 and 3 are B, C, A and D respectively.
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_____The given question is incomplete, the complete question is given below:
A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:
Reason 2:
Reason 3:
Reason 4:
(A)associative property of multiplication
(B)multiplication
(C)Distributive property
(D) simplify
8 is not more than m
Answer: It is the 2nd one
Step-by-step explanation: 8≤m
What is c?
1.5/1=c/10
Answer:
15
Step-by-step explanation:
1.5/1 = 1.5
1.5 x 10 = 15
Answer:
c=15
Step-by-step explanation:
You can use equivalent fractions for this. 1x10 is 10, so you do the same to 1.5. 1.5x10 is 15. So 15 takes the place of c.
Hope it helps!
£130 is divided between Dan, David & Mark so that Dan gets twice as much as David, and David gets three times as much as Mark. How much does Dan get?
Answer:
£78
Step-by-step explanation:
Given:
£130 is divided between Dan, David & Mark so that Dan gets twice as much as David, and David gets three times as much as Mark.
To find: How much does Dan get?
Solution:
Let D represents Dan, V represents David and M represents Mark.
Now we have given that Dan gets twice as much as David:
D = 2V .....(i)
David gets three times as much as Mark
V = 3M ......(ii)
The total sum of money is D + V + M = 130 ........(iii)
Putting (i), (ii) in (iii), we get:
2V + V + V/3 = 130
6V + 3V + V = 390
10V = 390
V = 39
Putting the value of V in (i), we get:
D = 2(39)
D = £78
Therefore, Dan gets £78
In ΔABC, m < B = 22°, m < C = 52° and a = 30. Find the length of b to the nearest tenth.
Answer:
The length of \(b\) is approximately 11.7.
Step-by-step explanation:
The sum of internal angles in triangles equals 180°, as we know the measures of angles B and C, we determine the measure of angle A by algebraic means:
\(A = 180^{\circ}-B-C\) (1)
(\(B = 22^{\circ}\), \(C = 52^{\circ}\))
\(A = 180^{\circ}-22^{\circ}-52^{\circ}\)
\(A = 106^{\circ}\)
The length of \(b\) is found by the Law of Sine:
\(\frac{b}{\sin B} = \frac{a}{\sin A}\)
\(b = a\cdot \left(\frac{\sin B}{\sin A} \right)\)
(\(a = 30\), \(A = 106^{\circ}\), \(B = 22^{\circ}\))
\(b = 30\cdot \left(\frac{\sin 22^{\circ}}{\sin 106^{\circ}} \right)\)
\(b \approx 11.7\)
The length of \(b\) is approximately 11.7.
factoring polynomials
3x^2 - 3xy - 2x + 2y
Answer:
( x - y ) ( 3x - 2 )Do the grouping 3x² - 3xy - 2x + 2y =
( 3x² - 3xy ) + ( -2 + 2y ) and factor out 3x in the first and -2 in the second group.
3x ( x-y ) -2 ( x-y)
Factor out common term x-y by using distributive property.
So the answer is ( x - y ) ( 3x - 2 )
Hope it's Help
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By using sum or difference formulas, cos(-a) can be written as OA. - sin(x) B. - cos(x) Oc.cos(x) D. sin(x) OE. All of the above OF. None of the above By using sum or difference formulas, cos(-a) can be written as OA. - sin(x) B. - cos(x) Oc.cos(x) D. sin(x) OE. All of the above OF. None of the above By using sum or difference formulas, cos(-a) can be written as OA. - sin(x) B. - cos(x) Oc.cos(x) D. sin(x) OE. All of the above OF. None of the above
By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)
This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)
This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).
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Why math is important for student like us?
Given: A statement, "Why math is important for students like us".
Required: To give the reason for the given statement.
Explanation: There are several reasons for the given statement. Maths is important for students as it is the basis of several other subjects such as Physics, Business Studies, Programming, etc. Practicing math is a critical part of developing good problem-solving skills. It helps students identify and solve problems. It teaches them how to arrive at a solution to a problem by considering different factors and approaching it from various perspectives.
Besides the academic aspect, maths is also an important factor in our daily problems.
Final Answer: The importance of math is at every step of a student's life.
jeans parents let her pour out the familys coin jar so she could record the number of each type of coin it cfontained
The relative frequency for dimes in the coin jar is approximately 19%.
To determine the relative frequency for dimes in the coin jar, we need to calculate the percentage of dimes out of the total number of coins. The table provided shows the frequencies for each type of coin:
Coin | Frequency
Penny | 124
Nickel | 52
Dime | 46
Quarter | 16
To calculate the relative frequency for dimes, we divide the frequency of dimes (46) by the total number of coins:
Relative Frequency of Dimes = Frequency of Dimes / Total Number of Coins
Total Number of Coins = Sum of all frequencies
Total Number of Coins = 124 + 52 + 46 + 16 = 238
Relative Frequency of Dimes = 46 / 238 ≈ 0.1933
To express this relative frequency as a percentage rounded to the nearest percent, we multiply by 100 and round:
Relative Frequency of Dimes ≈ 0.1933 * 100 ≈ 19%
Therefore, the relative frequency for dimes in the coin jar is approximately 19%.
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jeans parents let her pour out the family's coin jar so she could record the number of each type of coin it contained. The result are shown in the table
coin Penny Nickel Dime Quarter
Frequency 124 52 46 16
Drag and match the correct value to the given relative frequency rounded to the nearest percent
the relative frequency for dimes in the jar .....................
7% 19% 22% 24% 28%
Let x be a real number satisfying the condition : √x²-9 · √x²-1 = 2x+3
Calculate the expression value : Q = √x²-1 · √x^2-4 - 3x
Answer:
x= 2
1 =0.5
x=0
Step-by-step explanation: