Answer:
5. 18%
6. 5.25% o 5.3 o 5
7. 33.33%
8. 2005-2010
The lengths of the four sides of a quadrilateral (in meters) are consecutive even
integers. If the perimeter is 52 meters, find the value of the longest of the four side
lengths.
The lengths of the sides of the quadrilateral are 10, 12, 14, 16, respectively.
How to determine the lengths of the sides of quadrilateral
Quadrilaterals are figures with four sides, the statement indicates that such lengths are four consecutive even integers. Two even numbers are consecutive when their difference is equal to 2.The mathematical definition of the perimeter is shown below:
52 = x + (x + 2) + (x + 4) + (x + 6)
52 = 4 · x + 12
4 · x = 40
x = 10
Then, the lengths of the sides of the quadrilateral are 10, 12, 14, 16, respectively.
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Which equation has NO SOLUTION? Select all that apply.
a. -2x + 4 = 2x + 4
b. 12x-2x = 10x -8
C. 3x + 10 = 2x
d. 3x - 12 = 3(x-4) +1
The equation that has no solution will be:
a. -2x + 4 = 2x + 4
b. 12x-2x = 10x -8
d. 3x - 12 = 3(x-4) +1
How to calculate the values?It should be noted that -2x + 4 = 2x + 4
-2x - 2x = 4 - 4
-4x = 0
It has no solution
Also, 12x-2x = 10x -8 and 3x - 12 = 3(x-4) +1has no solution.
The only equation with solution will be:
3x + 10 = 2x
3x - 2x = -10
x = -10
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A lawn care company charges a base fee plus an hourly fee to mow lawns.
For small lawns, the company charges $15.95 plus $23 per hour. The total charge S (in dollars) to mow a small lawn for H hours is given by the function S = 23H + 15.95.
For large lawns, the company charges $20.35 plus $28 per hour. The total charge L (in dollars) to mow a large lawn for H hours is given by the function L = 28H + 20.35.
Let F represent the difference between the charge for large lawns and the charge for small lawns. Which equation best represents this scenario?
The difference [tex]f^{}[/tex] between the charge for large lawns and the charge for small lawns is given by the linear equation [tex]f^{}[/tex] = 5H +4.40, which is D option
For small lawns the company charge is given by the linear equation S = 23H + 15.95.
For large lawns, the company charge is given by the linear equation L = 28H + 20.35.
[tex]f^{}[/tex] represent the difference between the charge for large lawns and the charge for small lawns.
So, the equation can be written as [tex]f^{}[/tex] = (28H + 20.35) - (23H + 15.95)
this can be simplified as
[tex]f^{}[/tex] = 28H + 20.35 -23H - 15.95
[tex]f^{}[/tex] = 28H- 23H + 20.35 - 15.95
[tex]f^{}[/tex] = 5H + 4.40
Hence, the difference between the charge for large lawns and the charge for small lawns is given by the linear equation [tex]f^{}[/tex] = 5H +4.40, which is D option
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Each pair of values is from an inverse variation. Find the missing value. (3,7),(8, y)
the missing value (3,7),(8, y) is y = 21/8
What exactly is a function's inverse?Inverse functions are those that cancel one another out. In other words, if g(x) is f's inverse, then f(g(x)) = g(f(x)) = x. (x). Given an equation for which we want the inverse, we have a fantastic method we can utilize to do this.
Not every function has a counterpart. If f(x) has an inverse, it is clear to see that it will never again have the same value. We give this resource a special name.
Inverse variation is y = k. 1/x
given y = 7
x = 3
So, 7 = k. 1/3
So, the value of k = 21
We can conclude that the value of constant variation is 21
when x = 8, the value of y will be -
y = k.1/x
y = 21 . 1/8
y = 21/8
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Help!! I need help with equations
Answer:
[tex]Y=\frac{1}{2}x +2[/tex]
Step-by-step explanation:
When y=2,X=0
When Y =7,X=10
X coordinates come first
(0,2)(10,7)
(x1,y1)(x2,y2)
To find the slope(M)=y2 -y1/x2 -x1
M=7-2/10-0
M=5/10=1/2 (Simplest form)
The equation of a line is given by Y=Mx + C
Where c is the Y intercept which is 2
- The equation of the line = Y=[tex]\frac{1}{2} x +2[/tex]
The deli brought in a total of $580,800 last year. If they served approximately 200 customers each day over the 363 days that the deli was open, about how much did each customer spend on any given day?
$8.00
$10.31
$16.00
$29.04
Answer: 8
Explanation: Based on the given conditions, formulate: 580800 ÷ 363 ÷ 200
Reduce the fraction: 8
Answer: 8
Answer:
the ans is 8.00 the first one
Step-by-step explanation:
Chloe is deciding between two landscaping companies for her place of business. Company A charges $70 per hour and a $150 equipment fee. Company B charges $55 per hour and a $300 equipment fee. Let A A represent the amount Company A would charge for t t hours of landscaping, and let B B represent the amount Company B would charge for t t hours of landscaping. Write an equation for each situation, in terms of t , t, and determine the number hours, t , t, that would make the cost of each company the same.
Answer:
At 10 hours both companies charge the same rate. So Company A is cheaper if the time is less than 10 hours and after 10 hours, company B is cheaper.
Step-by-step explanation:
It is given that Chloe is deciding between two landscaping companies for her place of business. Company A charges $70 per hour and a $150 equipment fee. Company B charges $55 per hour and a $300 equipment fee. Let A A represent the amount Company A would charge for t t hours of landscaping, and let B B represent the amount Company B would charge for t t hours of landscaping.
Now, we need to write an equation for each situation, in terms of t , t, and determine the number hours, t , t, that would make the cost of each company the same.
Now,
Let A(t) = 70t + 150
Let B(t) = 55t + 300
Further, on equating both the equations at same rate to determine the time t;
=> 70t + 150 = 55t + 300
=> 15t = 150
=> t = 10
Therefore, at 10 hours both companies charge the same rate. So Company A is cheaper if the time is less than 10 hours and after 10 hours, company B is cheaper.
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Priya mows 1/6 yards in 1/4 hour. How many yards does Priya mow per hour?
Yo what up?, Answer:
2/3 yards.
Best Explanation Possible:
Nothing lol just do the math.
1/6 x 4 = 4/6 = 2/3 of a yard per hour
LOL have a good day hope you do good in school kiddo.
What is f(x)=3 x¹/₃ for x=1/125 ?
(F) 15 (G) 3/5 (H) ∛3/5 (I) 5∛3
The value of the given expression for x=1/1250is 3/5. The correct option is (G).
Given the expression is f(x)=[tex]3x^{\frac{1}{3}}[/tex].
The cube root of a number is the factor that we want multiply by itself three times to get that number. The symbol for the cube origin is 3 cube roots, the last cube root. Finding the cube root of any number is the opposite of cubing a number.
We will simplify the given expression by using substitution method and cube root.
Firstly, we will substitute x=1/125 in the given expression f(x)=[tex]3x^{\frac{1}{3}}[/tex], we get
f(x)=[tex]3\left(\frac{1}{125}\right)^{\frac{1}{3}}[/tex]
As we know that the cube root of √125 is 5.
Now, we want to simplify the above equation, we get
f(x)=3(1/5)
f(x)=3/5
Hence, the value of [tex]f(x)=3x^{\frac{1}{3}}[/tex] for x=1/125 is 3/5.
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if f (2) =-5, what does 5 represent
We can state that, 5 represents the output of the function at x = 2.
How to Interpret Functions?A function is a relation whereby each input gives only one possible output for the function.
For example, "f(x)" is the output of a typical function that is given by an input of "x".
Given the function statement, f(2) = -5, the input is x = 2, the output is -5. This means that, the function that has an input of 2, will give an output of -5.
-5, therefore, represents the output of the function when the input, x = 2, that is, f(-2) = -5.
Thus, we can state that, 5 represents the output of the function at x = 2.
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yo can somebody help me with this please i really need a good grade ill give crown to
Answer: 3/4
Step-by-step explanation:
You have to find one single number that goes into both the numerator and the denominator. In this case, it was 8.
24/8 = 3
32/8 = 4
Answer:
1st one is 3/4
second one is 32
I cant really see the third one
fourth one is $1.03
Step-by-step explanation:
Question 8A: Mr. Sowers wants to purchase expo markers for his classroom. He has a budget of $35. A four pack of markers costs $5.49, including tax. Write and solve an inequality, using x for the variable, to solve for the number of packs of markers Mr. Sowers can purchase.
Question 8B: Describe the graph of the solution for question 8A.
A. Place an open circle on 6 with shading to the left
B. Place a closed circle on 6 with shading to the left
C. Place an open circle on 6 with shading to the right
D. Place a closed circle on 6 with shading to the right
Answer
I think it should be
please help, this is due today.
The points for the ordered pairs of the linear function has been plotted in the graph shown in the image attached below.
How to Graph a Linear Function?A linear function is a straight line graph consisting of domain elements (x-values) and their corresponding range elements (y-values).
Given the function, y = 1/2x + 1 having the following domain elements (x-values):
D: {-8, -4, 0, 2, 6}
Find the corresponding y-value to each of the x-values by substitution
When x = -8, then:
y = 1/2(-8) + 1
y = -4 + 1
y = -3
(-8, -3)
When x = -4, then:
y = 1/2(-4) + 1
y = -2 + 1
y = -1
(-4, -1)
When x = 0, then:
y = 1/2(0) + 1
y = 0 + 1
y = 1
(0, 1)
When x = 2, then:
y = 1/2(2) + 1
y = 1 + 1
y = 2
(2, 2)
When x = 6, then:
y = 1/2(6) + 1
y = 3 + 1
y = 4
(6, 4)
Thus, the points for the ordered pairs of the linear function has been plotted in the graph shown in the image attached below.
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how many ordered pairs of positive integers (x, y) is 2x + y < 5?
( 0, 5) , ( 1, 3) , (2, 1) are the only ordered pair of positive integer(x, y) that satisfy Linear inequality 2x+ y ≤ 5
The given linear inequality is 2x + y ≤ 5
This is a question of linear inequality
Linear inequality is solved as linear equality and than the signs are taken care of
if x= o
2(0) + y = 5
y = 5
if x= 1
2(1) +y = 5
2 + y= 5
y =3
If x= 2
2( 2) + y = 5
y=1
Hence, ( 0, 5) , ( 1, 3) , (2, 1) are the only ordered pair of positive integer(x, y) that satisfy Linear inequality 2x+ y ≤ 5
The correct question is how many ordered pairs of positive integers (x, y) is 2x + y ≤ 5?
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6n - 12 = 3( 2n- 4 )
Answer:
0 = 0 (this equation is always true)Step-by-step explanation:
6n - 12 = 3( 2n- 4 )
6n - 12 = 6n - 12
0 = 0
this equation is always true
Which of the following is not a correct way to label the following angle?
→ x ↑w ↓y
a. ∠W
b. ∠X
c. ∠WXY
d. ∠YXW
Answer:
Angle W
Step-by-step explanation:
An angle can be identified by the order of points, with the vertex in the middle (like angle WXY and angle YXW) or by the vertex (angle X).
Someone help really need it
Answer:
first row is 11
2nd row is 16
3rd row is 34,41,25
Step-by-step explanation:
45-18-16=11
55-25-14=16
18+16=34
100-41-34=25
Here is a list of four fractions. 3/10 4/16 5/24 8/36 Only one of these fractions is equivalent to 1/4 which fractions ?
Answer: I think its 4/16
Step-by-step explanation:
please let me know if I'm wrong.
2/3 - (-1/12)
Very confused and need someone to explain very exact on how to solve it.
Sure I can help!!!!
Step by step explanation: - + - = -
2/3+1/2 (LCM is 6)
=2/3 (6) + 1/2 (6)
=4 + 3
=7
I really hope this helps!!!! have a great day!!!
In a sale, normal prices are reduced by 25%. Freddie bought a car in the sale. The sale price of the car was £7500. Work out the normal price of the car.
The normal price of the car on the basis that the sale price of the car was £7500 is £10,000.
What percentage of the normal price is the sales price?The fact that the normal prices are reduced by 25% means that the actual price paid eventually is 75%, which is 100% minus discount of 25%, hence, the actual price of £7500 paid eventually represents 75% of normal price
75% of normal price= £75001% of normal price=£100100% of normal price=£100*100100% of normal price=£10,000Find out more about normal price on: brainly.com/question/20532904
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1 2/3*1 1/5
you must show working
Answer: 2
Step-by-step explanation:
= Convert 1 2/3 to an improper fraction (which is 5/3)
= Convert 1 1/5 to an improper fraction (which is 6/5)
= Proceed to cancel out the common factor of 5 so your answer should start to look like this
1/3 * 6
= Now cancel the common factor which is three
Therefore your answer is 2
Hope it helps ^^
How is 6×1+5×(110)+2×(1100) written in standard form?
A
652
B
256
C
6.52
D
0.652
Answer:
The answer is C = 0.652 in standard form
Good Evening. Please I really need help for this Further Math Question. Thanks
You should be aware of the fundamental theorem of algebra (FTCoA). If a quadratic has roots at [tex]r_1[/tex] and [tex]r_2[/tex], then we can factorize it as
[tex](x - r_1) (x - r_2)[/tex]
Expanding, this is equivalent to
[tex]x^2 - (r_1 + r_2) x + r_1 r_2[/tex]
Now, if we can also write this
[tex]x^2 + bx + c[/tex]
then we must have
[tex]x^2 + bx + c = x^2 - (r_1 + r_2) x + r_1r_2 \\\\ ~~~~ \implies \begin{cases} b = -(r_1 + r_2) \\ c = r_1r_2 \end{cases}[/tex]
(By the way, these are known as Vieta's formulas.)
We're told that the quadratic,
[tex]p(x) = 3x^2 - 6x + 8,[/tex]
has roots [tex]x=\alpha[/tex] and [tex]x=\beta[/tex], so by the FTCoA, we can write
[tex]p(x) = 3 (x - \alpha) (x - \beta)[/tex]
Expanding this last form, we have the identity and exact values
[tex]3x^2 - 6x + 8 = 3 (x^2 - (\alpha + \beta) x + \alpha\beta) \\\\ ~~~~ \implies x^2 - 2x + \dfrac83 = x^2 - (\alpha + \beta) x + \alpha\beta \\\\ ~~~~ \implies \begin{cases} \boxed{\alpha + \beta = 2} \\\\ \boxed{\alpha\beta = \frac83} \end{cases}[/tex]
(i) We want to construct a new quadratic [tex]p_{\rm i}(x)[/tex] such that its roots are [tex]x=\alpha^2[/tex] and [tex]x=\beta^2[/tex]. By the FTCoA, we would have
[tex]p_{\rm i}(x) = (x - \alpha^2) (x - \beta^2)[/tex]
Expanding,
[tex]p_{\rm i}(x) = x^2 - (\alpha^2 + \beta^2) x + \alpha^2\beta^2[/tex]
Now, notice that
[tex]\alpha^2 + \beta^2 = (\alpha + \beta)^2 - 2\alpha\beta = 2^2 - 2\cdot\dfrac83 = -\dfrac43[/tex]
[tex]\alpha^2\beta^2 = (\alpha\beta)^2 = \left(\dfrac83\right)^2 = \dfrac{64}9[/tex]
It follows that
[tex]p_{\rm i}(x) = x^2 + \dfrac43 x + \dfrac{64}9[/tex]
which we can rewrite with integer coefficients by scaling each term by a factor of 9 to get
[tex]p_{\rm i}(x) = \boxed{9x^2 + 12x + 64}[/tex]
(ii) Now we want a quadratic [tex]p_{\rm ii}(x)[/tex] with roots at [tex]2\alpha[/tex] and [tex]2\beta[/tex]. This means
[tex]p_{\rm ii}(x) = (x - 2\alpha) (x - 2\beta) \\\\ ~~~~~~~~ = x^2 - 2 (\alpha + \beta)x + 4\alpha\beta[/tex]
[tex]\implies p_{\rm ii}(x) = x^2 - 4x + \dfrac{32}3[/tex]
or more cleanly, scaling by 3,
[tex]p_{\rm ii}(x) = \boxed{3x^2 - 12x + 32}[/tex]
(iii) Now the roots are [tex]x=\frac\alpha2[/tex] and [tex]x=\frac\beta2[/tex], which gives
[tex]p_{\rm iii}(x) = \left(x - \dfrac\alpha2\right) \left(x - \dfrac\beta2\right) \\\\ ~~~~~~~~ = x^2 - \dfrac{\alpha + \beta}2 x + \dfrac{\alpha\beta}4[/tex]
[tex]\implies p_{\rm iii}(x) = x^2 - x + \dfrac8{12}[/tex]
[tex]\implies p_{\rm iii}(x) = \boxed{12x^2 - 12x + 8}[/tex]
(iv) If the roots are [tex]x=\frac\alpha{\alpha+1}[/tex] and [tex]x=\frac\beta{\beta+1}[/tex], we have
[tex]p_{\rm iv}(x) = \left(x - \dfrac\alpha{\alpha+1}\right) \left(x - \dfrac\beta{\beta+1}\right) \\\\ ~~~~~~~~~= x^2 - \left(\dfrac\alpha{\alpha+1} + \dfrac\beta{\beta+1}\right) x + \dfrac{\alpha\beta}{(\alpha+1)(\beta+1)}[/tex]
Note that
[tex]\dfrac\alpha{\alpha+1} + \dfrac\beta{\beta+1} = \dfrac{\alpha(\beta+1) + \beta(\alpha+1)}{(\alpha+1)(\beta+1)} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{2\alpha\beta + \alpha + \beta}{\alpha\beta + \alpha + \beta + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{\frac{16}3 + 2}{\frac83 + 2 + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~ = \dfrac{22}{17}[/tex]
[tex]\dfrac{\alpha\beta}{(\alpha+1)(\beta+1)} = \dfrac{\alpha\beta}{\alpha\beta + \alpha + \beta + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \dfrac{\frac83}{\frac83 + 2 + 1} \\\\ ~~~~~~~~~~~~~~~~~~~~~ = \dfrac8{17}[/tex]
[tex]\implies p_{\rm iv}(x) = x^2 - \dfrac{22}{17}x + \dfrac8{17}[/tex]
[tex]\implies p_{\rm iv}(x) = \boxed{17x^2 - 22x + 8}[/tex]
Which equation is equivalent to 2^3x =10
log 3x = 2
10?
log 2 = 3x
log₂ 10 = 3x
log₂ 3x = 10
2^3x =10 //log
log(2^3x) = log(10)
3x*log(2) = log(10)
3x = log(10) / log(2)
3x = log₂ 10
Answer: log₂ 10 = 3x
If EG =85 and point F is 2/5 of the way between E and G find the value of FG.
Answer:
FG = 51
Step-by-step explanation:
2/5 of 85 = 34
The value of EF is 34
So the value of FG would be the value of EG - EF
85 - 34 = 51
there are 22 students in a 6th grade class. for the class field trip, they went to the local museum. admission to the museum was $7 a person. after going to the museum, they went to the art festival. admission to the art festival was $4 a person. each student paid $12 for the field trip and the bus. what is the total amount of money the teacher collected from the students? a. $12 b. $31 c. $242 d. $264
Answer: d. $264 hope this helps :)
Step-by-step explanation:12x22=264
Express in simplest radical form.
√17x
Answer:
this cant be simplified further
Step-by-step explanation:
17 is prime
A recipe for a punch call for 12 fluid ounces of orange juice. reyna needs to make 4 batches of punch for a party. how many quarts of orange juice will reyna need? need help fast!! please!
Reyna will need 0.048 quart of orange juice.
In this question, we have been given a recipe for a punch call for 12 fluid ounces of orange juice.
Reyna needs to make 4 batches of punch for a party.
We need to find number of quarts of orange juice Reyna will need.
From given conditions, we formulate:
= 4 × 12 ÷ 1000
= 12 ÷ 250 .................(Separate out the common factor)
= 6/125
= 0.048 quart
Therefore, Reyna will need 0.048 quart of orange juice.
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What would be different about the problem if we change the equation to Y equals 5X squared or what about
you don’t have a negative side to the graph and your number is completely different
10 points Please help!!!!
Question 15:
Option B is the correct answer
If the Patriots win their division, then they will go to the playoffs:
- Invalid conclusion was made.
Question 16:
Option D is the correct answer.
Conclusion: Ethan's boy scout dues are free:
- Drawn using the law of detachment.
What is the law of detachment?
The Law of Detachment states that we must detach ourselves from the outcome in order to allow what we desire to materialize in the physical universe.
Example:
If p equals q and p is also true. Then q is true.
We have,
- If the Patriots win their next game, then they will win their division.
- If the Patriots win their next game, then they will go to the playoffs.
Each statement's conclusion is drawn using the law of detachment.
Therefore, if the patriots win their division, then they will go to the playoffs is an invalid conclusion made.
Ethan sold $1000 worth of popcorn.
Conclusion: Ethan's boy scout dues are free.
This conclusion was drawn using the law of detachment.
Thus,
Therefore, if the patriots win their division, then they will go to the playoffs: - Invalid conclusion made.
Conclusion: Ethan's boy scout dues are free:
- Drawn using the law of detachment.
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