A-
1 box --- 6 minutes
y boxes --- 1 minute
y = 1/6
B-
1 box --- 9 minutes
t boxes --- 1 minute
t = 1/9
So...
r - used time
r(1/9 + 1/6)=100
r=(100.18)/5
r= 360 minutes
1/6 . 360 = 60 boxes
answer: 60 boxes
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
Let's use the concept of the rate of work to solve this problem. The rate of work is the amount of work done per unit of time.
Machine A's rate of work is 1 box of nails every 6 minutes.
Machine B's rate of work is 1 box of nails every 9 minutes.
Let's assume that machine A filled x boxes, and machine B filled y boxes. Since they worked for the same amount of time, the total number of boxes filled by both machines is 100.
So, the equation representing the total work is:
x (boxes filled by A) + y (boxes filled by B) = 100
Now, let's use their rates of work to form two more equations:
Rate of work of A = 1 box every 6 minutes
Rate of work of B = 1 box every 9 minutes
Since work = rate × time, we can write two equations:
x (boxes filled by A) = (1/6) * t (time in minutes)
y (boxes filled by B) = (1/9) * t (time in minutes)
Since they both worked for the same time, we can set the time for both machines as equal:
t = t
Now, we have a system of equations:
x + y = 100
x/6 = y/9
t = t
Let's solve the system of equations. We can start by substituting the value of y from the second equation into the first equation:
x + (x/6)*3 = 100
x + (x/2) = 100
Multiply both sides by 2 to eliminate the fraction:
2x + x = 200
3x = 200
x = 200/3
Now, let's find the value of y using the second equation:
y = (x/6)*3
y = (200/3)/6 * 3
y = 200/3
So, machine A filled 200/3 boxes of nails, which is approximately 66.67 boxes.
Machine B filled 200/3 boxes of nails, which is also approximately 66.67 boxes.
Since they cannot fill a fraction of a box, we can distribute the remaining 2/3 box between machine A and machine B, giving one extra box to each.
In total, machine A filled 66 boxes, and machine B filled 66 boxes, resulting in a total of 100 boxes filled.
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Which numbers can be classified as rational? Select all that apply.
5/6
[tex] \sqrt{11} [/tex]
6.565656...
0.23
0.32416
-5 3/8
Answer:
5/6, 0.23, -5 3/8
Step-by-step explanation:
Phillip deposited $5,670 into a savings account 19 years ago. The account has an interest rate of 4.1% and the balance is currently $12,356.04. How often does the
interest compound?
Answer:
$12165.97
Step-by-step explanation:
100 + 4.1 = 104.1%
104.1% = 1.041
$5670 x 1.041^19 = $12165.97
Answer:
daily
Step-by-step explanation:
To answer this try plugging in each type of compund: daily, monthly, quarterly, and annually.
5670(1+0.041/365)^(365*19)
= 12356.04
365= daily
so your answer would be that the interest compounds daily.
Find the value of x.
Answer:
27
Step-by-step explanation:
By the theorem of intersecting secant and tangent out side of a circle, we have:
[tex] {60}^{2} = 48 \times (48 + x) \\ 3600 = 48 \times (48 + x) \\ \frac{3600}{48} = 48 + x \\ 75 = 48 + x \\ 75 - 48 = x \\ x = 27 \\ [/tex]
4. Multiple-Choice
1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What
is the measure of the smaller angle?
(1) 5°
(2) 42°
(3) 48°
(4) 90°
I already know that the answer is 42 but I don’t know how to get that! Please help.
Sry i couldn't find the answer
Answer:
(2) 42°
Step-by-step explanation:
Copy of the given problem:
4. Multiple-Choice
1. Two complementary angles measure (12r - 18)° and (5x + 23)°. What
is the measure of the smaller angle?
(1) 5°
(2) 42°
(3) 48°
(4) 90°
Solution:
The sum of the measures of complementary angles is 90 deg.
12r - 18 + 5x + 23 = 90
We have 1 equation with two different variables, so we cannot solve the equation to find unique values of the variables.
I assume the above is an error, and both variables should be the same.
12r - 18 + 5r + 23 = 90
Combine like terms on the left side. Terms with r are combined. Terms with no variable are combined.
12r + 5r - 18 + 23 = 90
17r + 5 = 90
Subtract 5 from both sides.
17r = 85
Divide both sides by 5.
r = 5
The measures of the angles are:
12r - 18 = 12(5) - 18 = 60 - 18 = 42
5r + 23 = 5(5) + 23 = 25 + 23 = 48
The measures of the two angles are 42° and 48°.
The smaller angle measures 42°
Answer: (2) 42°
35= -5(2k+5)?????? need help
Answer:
k=-6
Step-by-step explanation:
Answer:
[tex]\Large \boxed{k=-6}}[/tex]
Step-by-step explanation:
35 = -5(2k+5)
Expand brackets.
35 = -10k - 25
Add 25 on both sides.
60 = -10k
Divide both sides by -10.
-6 = k
Plzz help me I’ll mark brainliest
Answer:
The answer is option BStep-by-step explanation:
To find the side adjacent to the 50° angle we use tan
[tex] \tan( \alpha ) = \frac{opposite}{adjacent} [/tex]
From the question
The opposite is 6m
The adjacent is ?
So we have
[tex] \tan(50) = \frac{6}{?} [/tex]
[tex]? \tan(50) = 6[/tex]
[tex]? = 6 \times \frac{1}{ \tan(50) } [/tex]
But
[tex] \frac{1}{ \tan(x) } = \cot(x) [/tex]
So we have
[tex] \frac{1}{ \tan(50) } = \cot(50) [/tex]
Substitute it into the expression
That's
We have the final answer as
[tex]? = 6 \cot(50) [/tex]
Hope this helps you
=====================================================
Explanation:
We're given an opposite side and an adjacent side. The tangent rule ties these two sides together. "tangent" is nowhere to be found in any of the answer choices, but cotangent is. Recall that
cot = 1/tan
which means
tan = opposite/adjacent
cot = adjacent/opposite
one is the reciprocal of the other
-----------
This means
cot(angle) = adjacent/opposite
cot(50) = x/6
6*cot(50) = x
x = 6*cot(50)
for n prove by
[tex]3 + 3 {}^{2} + 3 {}^{3} ... + 3 {}^{n} = \frac{3(3 {}^{n} - 1) }{2} [/tex]
thank you
Answer:
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
Step-by-step explanation:
Given
[tex]3 + 3^2 + 3^3 ...+ 3^n[/tex]
Required
Show that the sum of the series is [tex]\frac{3(3^{n}-1)}{2}[/tex]
The above shows the sum of a geometric series and this will be calculated as shown below;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex]
Where
a = First term;
[tex]a = 3[/tex]
r = common ratio
[tex]r = \frac{3^2}{3} = \frac{3^3}{3^2}[/tex]
[tex]r = 3[/tex]
Substitute 3 for r and 3 for a in the formula above;
[tex]S_n = \frac{a(r^n - 1)}{r - 1}[/tex] becomes
[tex]S_n = \frac{3(3^n - 1)}{3 - 1}[/tex]
[tex]S_n = \frac{3(3^n - 1)}{2}[/tex]
Hence;
[tex]3 + 3^2 + 3^3 ...+ 3^n = \frac{3(3^n - 1)}{2}[/tex]
i need help please
260 units2 is the answer
which construction can you use to prove that the Pythagorean theorem based on similarity of triangles
The construction that you can use to prove the Pythagorean Theorem based on similarity of triangles is 2nd construction. Please see the attached file.
What are similar triangles?Two triangles are similar triangles of their corresponding angles are equal corresponding sides are in equal ratios.
The Pythagorean theorem, also known as Pythagoras's theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It mentions that the sum of the squares of the other two sides is equal to the square of the hypotenuse (the side opposite the right angle).
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help me plz can somewon help me
Answer:
4*10^6
Step-by-step explanation:
Answer:
4 × 10^6Step-by-step explanation:
[tex]\frac{8\times 10^2^4}{2\times 10^1^8}=\\\\\mathrm{Divide\:the\:numbers:}\:\frac{8}{2}=4\\\\=\frac{10^{24}\times \:4}{10^{18}}\\\\\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}\\\\\frac{10^{24}}{10^{18}}=10^{24-18}\\\\=4\times \:10^{24-18}\\\\\mathrm{Subtract\:the\:numbers:}\:24-18=6\\\\=10^6\times \:4\\\\10^6=1000000\\\\=1000000\times \:4\\\\=4000000\\\\= 4\times10^6[/tex]
Dilate line f by a scale factor of 3 with the center of dilation at the origin to create line f'. Where are points A' and B' located after dilation, and how are lines f and f' related?
Answer:
a 0,1 and b 1,0
Step-by-step explanation:
exam took
Answer:
The other answer is incorrect the answer is
D) The locations of A' and B' are A' (0, 6) and B' (6, 0); lines f and f' are parallel.
HELP!!! SHOW WORK PLEASE.
[tex]\dfrac{x}{4}=\dfrac{x+9}{4+12}\\\\16x=4(x+9)\\16x=4x+36\\12x=36\\x=3[/tex]
Given that F( x ) = x 2 + 2, evaluate F(1) + F(5).
Hi there! :)
Answer:
[tex]\huge\boxed{f(1) + f(5) = 30}[/tex]
Given:
[tex]f(x) = x^{2} + 2[/tex]
Evaluate [tex]f(1) + f(5)[/tex]
Solve for each:
[tex]f(1) = (1)^{2} + 2 = 3[/tex]
[tex]f(5) = (5)^{2} + 2 = 27[/tex]
[tex]27 + 3 = 30[/tex]
Answer:
30
Step-by-step explanation:
need help with these questions!!! please explain bc I don't really get it!
Answer:
1. b. 2. a. 3. a.
Step-by-step explanation:
1. (f + g)x = f(x) + g(x)
= x^2 + 2x + 4
(f + g)(-1) = (f + g)(x) where x = 1 so it is
(-1)^2 + 2(-1) + 4
= 1 - 2 + 4
= 3.
2. We find (f o g)(x) by replacing the x in f(x) by g(x):
= √(x + 1) and
(f o g)(3) = √(3 + 1)
= √4
= 2.
3. (f/g) c = f(x) / g(x)
= (x - 3)/(x + 1)
The domain is the values of x which give real values of (f/g).
x cannot be - 1 because the denominator x + 1 = -1+1 = 0 and dividing by zero is undefined. So x can be all real values of x except x = -1.
The domain is (-∞, -1) U (-1, ∞)
Find the measure of of RA. A. 24 B. 2 C. 12 D. 3
Answer: 24
Step-by-step explanation:
R= 3
You can find this using simple algebra
The measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.
What is the congruent triangle?Congruent triangles are those that are exactly the same size and shape. Congruent is represented by the symbol ≅ When the three sides and three angles of one triangle match the dimensions of the three sides and three angles of another triangle, they are said to be congruent.
We have a triangle shown in the picture.
It is required to find the measure of the RA
To find the measure of the RA we can apply the concept of congruent triangle:
In the triangle LRU and triangle LAU
LU = LU (common side)
LR = LA (equal sides)
Angle RLU = Angle ALU (equal)
The triangles are congruent.
RU = UA
18 - 2r = 4r
6r = 18
r = 18/6 = 3
The measure of the RA = 18 - 2r + 4r = 18 + 2r
The measure of the RA = 18 + 2(3) = 18+6 = 24 units
Thus, the measure of RA is 24 units after using the concept of congruent triangle option (A) 24 is correct.
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AB and CD intersect at point O, ∠ACO ≅ ∠DBO, and BO ≅ CO . Prove that △ACO ≅ △DBO. Plz Help Me... Thanks
Since ∠COA and ∠BOD are vertical angles, they are congruent.
You are also given that ∠ACO ≅ ∠DBO and BO ≅ CO.
By ASA (Angle-Side-Angle) congruency, you know that △ACO ≅ △DBO
The proof is shown below:
What is congruency of Triangles?If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.
In Δ PQR and ΔXYZ, as shown below, we can identify that PQ = XY, PR = XZ, and QR = YZ and ∠P = ∠X, ∠Q = ∠Y and ∠R = ∠Z. Then we can say that Δ PQR ≅ ΔXYZ.
What is ASA congruency criteria?ASA criterion stands for Angle-Side-Angle criterion. Under the ASA criterion, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.
Given:
∠ACO ≅ ∠DBO, and BO ≅ CO
as, ∠COA =∠BOD (vertically opposite angles)
∠ACO ≅ ∠DBO ( given)
BO ≅ CO ( given)
So, By ASA (Angle-Side-Angle) congruency, △ACO ≅ △DBO
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Laura has a step of 50cm She walks along by taking two steps forward and one step back. What is the least number of steps counting forward and backwards step, she takes to reach a step 20m away? ~Thanks - don't know how to solve :(
Answer:
The least number of steps she takes to reach 20 m is 118 steps
Step-by-step explanation:
For Laura, the length of a walking step = 50 cm = 0.5 m
The repeating number of steps she takes = Two steps forward one step backwards
The number of forward steps it would take for her to reach 20 m = (20 m)/(0.5 m) = 40 steps
Given that she always takes two steps forward and one step backwards, we have;
The number of steps forward every three steps = 2 step forward + (-1) step (backward)
The number of steps forward every three steps = 2 - 1 = 1 step forward
To reach 39 steps forward, she would need 39 × 3 = 117 steps
To get to the 40 steps she needs just a step forward, making the total number of steps to reach 40 steps = 117 + 1 = 118 steps
Therefore, the least number of steps she takes to reach 20 m = 118 steps.
9x^3-16x^2=0. Solve and show all steps.
Answer Step one x=16/9 =1.778
Last step is x²=0
Hope I helped you
Answer:
the roots are {0, 0, 16/9}
Step-by-step explanation:
The trick to solving this is to factor out x^2 from both terms on the left:
x^2*9*x - 16x^2=0, or
x^2(9x - 16) = 0
Then, either x^2 = 0 or (9x - 16) = 0.
Thus, the roots are {0, 0, 16/9}
There are 6 flowers in vases in your kitchen. You want to put 3 of them on the dining room table for dinner tonight. Order isn’t important. How many ways can you display the flowers for dinner?
The required ways of the combination to display the flowers on the dinner is 20.
There are 6 flowers in vases in your kitchen. You want to put 3 of them on the dining room table for dinner tonight. Order isn’t important. How many ways can you display the flowers for dinner to determiined.
What are permutation and combination?In arithmetic, combination and permutation are two different ways of grouping elements of a set into subsets. In a combination, the components of the subset can be recorded in any order. In a permutation, the components of the subset are listed in a distinctive order.
Examples of permutation and combination, Managing people, numbers, numerals, alphabets, letters , and colors are examples of permutations. Choosing of menu, foodstuffs, dresses, matters, and the group are examples of combinations.
Since, the total number of flower in vases is 6
3 of them to be selected for the dinner table tonight.
The combination is given as.
= C( 6 , 3)
= 6!/3!(6 - 3)!
= 6!/3!3!
= 20
Thus, the required ways of combination to display the flowers on dinner is 20.
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What is the value of i 20+1?
1
- т т .-
Solve for x: |3x + 12| = 18 (5 points) A. x = 2, x = −10 B. x = 2, x = −2 C. x = 10, x = −10 D. x = −2, x = 10
Answer:
The solution set is therefore {-10, 2}
Step-by-step explanation:
The absolute value equation |3x + 12| = 18 has two distinct solutions.
|3x + 12| = 18 may be rewritten as
3x + 12 = 18 and
-(3x + 12) = 18
The first equation immediately above becomes 3x = 6 after we subtract 12 from both sides. Therefore, x = 6/3, or x = 2.
Simplifying the second equation yields -3x - 12 = 18. To solve this for x, we add 12 to both sides, obtaining -3x = 30.
Dividing both sides by -3 yields x = -10.
The solution set is therefore {-10, 2}
11. Find the slope of the following coordinate points: (11,4)
and (5.-3)
Answer:
7/6
Step-by-step explanation:
We can find the slope by using the slope formula
m = (y2-y1)/(x2-x1)
= ( -3 -4)/(5 -11)
-7/-6
=7/6
Answer:
7/6
Step-by-step explanation:
m = (y2 - y1)/(x2 - x1)
m = (-3 - 4)/(5 - 11)
m = -7/(-6)
m = 7/6
in the figure above, pqrs is a parallelogram. What is the value of x?
Answer:
x = 162 degrees.
Step-by-step explanation:
m < RSP = 180 - 72
= 106 degrees (adjacent angles)
m < Q = m < RSP ( Opposite angles in a parallelogram are equal).
So m < Q = 180 degrees.
m < x = 360 - 90 - 108
= 360 - 198
= 162 degrees.
Using the appropriate angle theorems, the value of the angle, x in the parallelogram would be 162°
At angle S :
S + 72 = 180 (sum of straight line angles)
S = 180° - 72°
S = 108°
S = Q (opposite angles of a parallelogram)
Q = 108°
Hence,
Q + x + right angle = 360° (sum of angles at a point)108° + x + 90 = 360
x = 360 - (108 + 90)
x = 162°
Hence, the value of x is 162°
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Someone explain to me if this is correct?
Answer:
Yes, that is correct.
Step-by-step explanation:
W = x
L = ?
A = x^2 + 12x
(x^2 + 12x)/x = x + 12
L = x + 12
Subbing in 10 for each X, we get:
Perimeter: 64
2(10) + 2(10 + 12) = 20 + 44 = 64
Area: 220
10 * 22 = 220
Part A looks perfect. You've shown that x^2+12x factors into x(x+12) indicating that x is the width and x+12 is the length. Convention usually has the length be longer than the width, but to be honest, the order doesn't really matter (since we can multiply in any order we want).
----------------
Part B is a bit hazy. You show that 10 * 22 = 220 is the area, so you imply that the rectangle has width 10 and length 22. However, you don't directly mention the dimensions of the rectangle.
You can pick either x^2+12x or x(x+12). I prefer x(x+12) as its easier in my opinion. You don't need to do both.
All you really need to do is say that if x is the width and x = 10, then the width is 10. Furthermore, if x+12 is the length then x+12 = 10+12 = 22 is the length.
what is x? Please explain how you got it so I can understand for future questions.
Answer:
[tex]\boxed{x = 40}[/tex]
Step-by-step explanation:
Hey there!
Well angles like 142 and 2x + 22 equal each other because they are across from each other.
So we can set up the following,
142 = 3x + 22
Single out x
-22 to both sides
120 = 3x
Divide both sides by 3
x = 40
Hope this helps :)
Answer:
x=40
Step-by-step explanation:
142=3x+22
3x+22-22=142-22
3x=120
120/3=40
I have 31 stamps total. I have 4 more 1-cent stamps than 8-cent stamps and twice as many one cent stamps as 12 cent stamps. If my stamps are worth $1.78 altogether how many one cent stamps do I have?
Answer: 14 1-cent stamps (in case anyone else still needs)
Step-by-step explanation:
1-cent stamps=x
8-cent stamps=x-4
12-cent stamp=.5x
x+x-4+.5x=31
2.5x-4=31
2.5x=35
x=14
You can use the $1.78 to double check:
(1*14)+(8*10)+(12*7)
14+80+84=178 cents (or $1.78)
Abby and Katy are selling cheesecakes. There are apple and pecan cheesecakes. Abby sold 14 pecan and 3 apple cheesecakes for a total of $113. Katy sold 7 pecan and 8 apple cheesecakes for a total of $180. What's the cost of one pecan cheesecake and one apple cheesecake?
How would I set this up?
If you want to set up the equations:
let the cost of one apple cheesecake be [tex] a[/tex] and the cost of one pecan cheesecake be $p$
from Abby, $14p+3a=113$
and from Katy....?
then solve for both variables
can you take it from here?
If you're good at trigonometry please help meeeeeee
Answer:
Hey there!
What we know:
The three triangles (two smaller ones and one larger one, are all right triangles)Measure of angle A is 42 degrees.Measure of angle C is 58 degrees.AC is 65 m.What we would like to know:
ABBDFirst, let's find AB.
Sine 58= AB/65
Solving for AB, we see that it is about 55.12 m.
Next, let's find BD.
Sine 42= BD/55.12
Solving for BD, we see that it is about 36.88 m.
Let me know if this helps :)
When purchased, a beach ball is deflated and packaged flat. The package states that when inflated to its maximum capacity, the radius of the inflated ball is 7.6 inches. To the nearest hundredth of a cubic inch, how much air will occupy the space contained by the inflated beach ball? Use 3.14 for [tex]\pi[/tex]. In your final answer, include all of your calculations.
Step-by-step explanation:
V=(4/3) * πr^3
V=(4/3) * π * 7.6 ^3
V=(4/3) * π * 438.976
V= π * 585.301333
V = 1837.85 inch^3
3.14 for pi btw
8 w 4 + 10 w 3 − 12 w 2 Factor completely
Answer:
[tex] 2w^2(w + 2)(4w - 3) [/tex]
Step-by-step explanation:
[tex] 8w^4 + 10w^3 − 12w^2 = [/tex]
First, factor out the GCF of all terms, 2w^2:
[tex] = 2w^2(4w^2 + 5w - 6) [/tex]
Now we work on the trinomial.
Think of ax^2 + bx + c.
Multiply ac
ac = 4 * (-6) = -24
Now we need two numbers whose product is -24 and whose sum is 5.
They are -3 and 8.
We break up the middle term, 5w, into a sum using these two numbers.
5w = 8x - 3w
[tex] = 2w^2(4w^2 + 8w - 3w - 6) [/tex]
Now we factor by parts. We factor a common factor out of the first two terms, and we factor a common factor out of the last two terms.
[tex] = 2w^2[4w(w + 2) - 3(w + 2)] [/tex]
[tex] = 2w^2(w + 2)(4w - 3) [/tex]
