If B is collinear and between points A and C, then the value of x is 5 and the value of AC is 50.
Collinear points refers to the points that lies on the same straight line.
If B is collinear with points A and C, and lies between them, then the sum of the distance from A to B and the distance from B to C is equal to the distance from A to C.
AB + BC = AC
Given:
AB = 12
BC = 8x - 2
AC = 10x
Substitute the expressions given to the equation and solve for x.
AB + BC = AC
12 + 8x - 2 = 10x
8x - 10x = 2 - 12
-2x = -10
x = 5
Substitute the value of x in the expression for AC.
AC = 10x
AC = 10(5)
AC = 50
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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
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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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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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
10. Shade the models to show that 0.7 and
0.70 are equivalent.
In a figure we can see that 0.7 and0.70 are equivalent, we have shade in the figure.
Given that,
To illustrate that 0.7 and 0.70 are equivalent, shade the models.
We have 0.7
We can say 7/10
For example, take a square and divide it by 10 part in column and shade 7 column.
Draw horizontal lines connecting the model's dots using a ruler.
Now divide it into 100 equal pieces.
So,
70/100
Shade the 7 rows and column.
Shaded at 70 or 0.70.
Therefore, in a figure we can see that 0.7 and0.70 are equivalent.
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7
[tex]7 \sqrt{6 } - 4 \sqrt{6} = [/tex]
[tex] - 0.7 \sqrt{7} + 2.3 \sqrt{7} = [/tex]
[tex] \sqrt{45} + \sqrt{20} = [/tex]
What are answers to these formulas
The answer to the formula are-
7√6 - 4√6 = 3√6-0.7√7 + 2.3√7 = 1.6√7√45 + √20 = 5√5How to add square roots?Square roots, like "regular" numbers, can be added together. However, you may not be able to reduce the addition to a single number.Because the radical in each term is the same, these are "like" terms.Part 1: 7√6 - 4√6
As both the digits have the same value √6. It means they can simply be added with sign to solve.
= 7√6 - 4√6
Take √6 common from both;
= √6(7 - 4)
= 3√6
Thus, the simplification of the expression is 3√6.
Part 2: -0.7√7 + 2.3√7
Here, also the common term is √7.
= √7( -0.7 + 2.3)
Simply add the number with sign.
= 1.6√7.
Thus, the simplification of the number is 1.6√7.
Part 3: √45 + √20
In thus, first write the number in its prime factors;
= √3×3×5 + √2×2×5
Take the root of 3 and 2 from the first and second digits of expression.
= 3√5 + 2√5
Now, both have the same term √5.
= √5(3 + 2)
Do the addition;
= 2√5
Thus, the simplification of given expression is 2√5.
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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!!!
Express in simplest radical form.
√17x
Answer:
this cant be simplified further
Step-by-step explanation:
17 is prime
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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An audience of 482 people were at a concert.
How many people were in the audience, to the
a) nearest 100?
b) nearest 1000?
Answer
482 rounded off to nearest 100 is 500 and 482 rounded off to nearest 1000 is zero.
By maintaining a number's value while moving it closer to the next number, rounding off makes the number easier to understand. It is done for entire numbers as well as decimals at different places such as hundreds, tens, and tenths. To maintain the major figures, numbers are rounded off.
At a concert there were 482 people in the audience:
(a) With a number line, 482 was rounded to the nearest hundred.
Find the two consecutive 100-multiples that surround 482.Between 400 and 500 is 482.The halfway point between 400 and 500 is 450.482 is greater than the midway, as shown on the number line (450)The result is 500 when 482 is rounded to the nearest hundred.(b) Since 4 is the hundredth value of 482 and there is no previous thousand to 499. So when 499 is rounded to the nearest thousand, equals 0.
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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
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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help plssssssssssssss ty
Answer:
associative property
Step-by-step explanation:
because the variables match
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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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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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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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
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 the circumference of this circle? r = 2 km
Answer:
12.56 km
Step-by-step explanation:
C = 2πr
= 2 x 3.14 x 2
= 12.56 km
Answer:
12.56km or 12,560m
Step-by-step explanation:
c = 2πr
c = (2)(3.14)(2)
c = (6.28)(2)
c = 12.56
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
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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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:
Tyrone solved the equation 4x=2−4(2−3x).
Match the property with each of Tyrone's steps for solving the equation.
PLEASE I NEED A ANSWER FAST thank you
The property with each of Tyrone's steps for solving the equation is;
Multiplication property of equalitySubtraction property of equalitycombine like termsdivision property of equalityProperty of equality4x = 2 - 4(2 - 3x)
Apply Multiplication property of equality4x = 2 - 8 + 12x
Apply Subtraction property of equality4x = - 6 + 12x
Apply combine like terms4x - 12x = -6
-8x = - 6
Apply division property of equalityx = -6 / - 8
x = 3/4
Therefore, the solution to Tyrone's equation for x is 3/4
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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).
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
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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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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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.
SOS URGENT PLS HELP ASAP THANKS ILL GIVE BRAINLIEST DUE TOMORROW PLSSSS TYSM
Step-by-step explanation:
you can ask any questions for clarification
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]