Answers
Answer:
Hello from MrBillDoesMath!
Answer:
p = 12
Discussion:
Assume we have a right trainload (looks like it but no angle indication given). By the Pythagorean Theorem
p^2 + 5^2 = (p+1) ^ 2 =>
p^2 + 25 = p^2 + 2p + 1 =>
25 = 2p + 1 => (subtract p^2 from both sides)
25 -1 = 2p => (subtract 1 from both sides)
24 = 2p =>
p = 24/2 = 12 => (divide both sides by 2)
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!
Related Questions
What is the simplified form of the complex fraction?
Answers
Answer:
[(x+3)(x+2)] /[(2x+3)(x-3)]
Step-by-step explanation:
[(2x²+x-6)/(x²-x-6)]/[(4x²-9)/(x²+5x+6)]
= (2x²+x-6)/(x²-x-6) × (x²+5x+6) /(4x²-9) Factor
= [(2x-3)(x+2)]/[(x-3)(x+2] × [(x+3)(x+2)] /[(2x+3)(2x-3)] Cancel terms
= (2x-3)/(x-3) × [(x+3)(x+2)] /[(2x+3)(2x-3)] Cancel terms
= [(x+3)(x+2)] /[(2x+3)(x-3)]
[tex]\dfrac{\frac{2x^2+x-6}{x^2-x-6}}{\frac{4x^2-9}{x^2+5x+6}}=(*)\\---------------------\\2x^2+x-6=2x^2+4x-3x-6=2x(x+2)-3(x+2)=(x+2)(2x-3)\\-----------\\x^2-x-6=x^2+2x-3x-6=x(x+2)-3(x+2)=(x+2)(x-3)\\-----------\\x^2+5x+6=x^2+2x+3x+6=x(x+2)+3(x+2)=(x+2)(x+3)\\-----------\\4x^2-9=(2x)^2-3^2=(2x-3)(2x+3)\\----------------------[/tex]
[tex](*)=\dfrac{(x+2)(2x-3)}{(x+2)(x-3)}\cdot\dfrac{(x+2)(x+3)}{(2x-3)(2x+3)}=(**)\\----------------------\\(x+2)-canceled\\(2x-3)-canceled\\----------------------\\(**)=\dfrac{(x+2)(x+3)}{(x-3)(2x+3)}\\\\Answer:\ \boxed{\boxed{\dfrac{(x+2)(x+3)}{(2x+3)(x-3)}}}[/tex]
Last one lol Thanks Bro...
The only solution of the equation x2 + bx + 16 = 0 is x = 4. What is the value of b?
b = –16
b = –8
b = 8
b = 16
Answers
[tex]\heartsuit[/tex] If x = 4 is the Only Solution of the Equation x² + bx + 16 = 0
[tex]\heartsuit[/tex] Then the Value x = 4 should satisfy the Given Equation
⇒ (4)² + b(4) + 16 = 0
⇒ 16 + 4b + 16 = 0
⇒ 4b + 32 = 0
⇒ 4b = -32
⇒ b = -8
PLEASE HELP ME WITH THIS PROBLEMS 1.
Answers
Answers: -4, 5
Step-by-step explanation:
[tex]e^{x^{2}}=e^{x}*e^{20}[/tex]
[tex]e^{x^{2}}=e^{x+20}[/tex]
x² = x + 20
x² - x - 20 = 0
(x + 4)(x - 5) = 0
x + 4 = 0 x - 5 = 0
x = -4 x = 5
**************************************************
Answers:
a. domain: (-∞,∞)b. range: (-∞, 0)c. y-intercept: [tex]-\dfrac{1}{8}[/tex]d. horizontal asymptote: y = 0e. graph: see attachmentStep-by-step explanation:
domain: there are no restrictions on the x-value so x = All Real Numbers
range: since the new graph has a reflection then y < 0
y-intercept is when x = 0:
y = -2⁰⁻³ = -2⁻³ = [tex]-\dfrac{1}{2^{3}}[/tex] = [tex]-\dfrac{1}{8}[/tex]horizontal asymptote: y ≠ 0 so the H.A. is y = 0
graph: The parent graph is: y = 2ˣ
The new graph of y = -2ˣ⁻³ has the following transformations:
reflection over the x-axishorizontal shift 3 units to the right***************************************************************************
graph: see attachment
(0, 0) and (-1/3, 1)
(-1, ∞)
x = -1
A tourist starts to walk up a mountain path that is 31 miles long at the rate of 4 miles per hour. After walking for a while, he gets tired and decides to get a taxi. The taxi gets him to the top travelling at a constant speed of 50 mph. If the tourist reaches the destination 2 hours after he started, what distance does he have to pay the cab driver for?
Answers
Let the Distance traveled by the tourist by walking be : D miles
Given : Tourist walks at a rate of 4 Miles per Hour
[tex]\mathsf{\implies Tourist\;travels\;D\;Miles\;in : \frac{D}{4}\;Hours}[/tex]
Given : The Total Distance of Mountain Path = 31 Miles
Distance traveled by the tourist by hiring a Taxi is : (31 - D) Miles
Given : The Taxi travels at a constant speed of 50 miles per hour
[tex]\mathsf{\implies Tourist\;travels\;(31 - D)\;Miles\;in : (\frac{31 - D}{50})\;Hours}[/tex]
Given : The Tourist reaches the destination 2 Hours after he started
Time taken by Walking + Time Taken by travelling in Taxi = 2 Hours
[tex]\mathsf{\implies \frac{D}{4} + \frac{31 - D}{50} = 2}[/tex]
[tex]\mathsf{\implies \frac{D}{2} + \frac{31 - D}{25} = 4}[/tex]
[tex]\mathsf{\implies (\frac{25D + 2(31 - D)}{50}) = 4}[/tex]
[tex]\mathsf{\implies (\frac{25D + 62 - 2D}{50}) = 4}[/tex]
[tex]\mathsf{\implies ({23D + 62}) = 200}[/tex]
[tex]\mathsf{\implies 23D = 200 - 62}[/tex]
[tex]\mathsf{\implies 23D = 138}[/tex]
[tex]\mathsf{\implies D = 6}[/tex]
⇒ Distance traveled by the tourist by walking = 6 Miles
⇒ Distance traveled by the tourist by hiring a taxi = (31 - 6) = 25 Miles
⇒ The Distance for which tourist has to pay for cab driver is 25 Miles
The distance traveled by taxi = 25 miles
Further explanationLinear motion consists of 2: constant velocity motion with constant velocity and uniformly accelerated motion with constant acceleration
• At constant velocity motion:
the speed of vo = v = constant
acceleration = a = 0
Δx = vt or x = xo + vtAn equation of constant velocity motion
[tex]\large {\boxed {\bold {x = v \times \: t}}}[/tex]
x = distance = m
v = speed = m / s
t = time = seconds
x1, x2 = distance traveled
t1, t2 = travel time
1 = tourist, 2 = taxi
[tex]\rm x1=v1.t1=4t1\\\\x2=v2.t2=50.t2\\\\t1+t2=2~hours\\\\t1=2-t2[/tex]
Total distance = x1 + x2
[tex]\rm 31~miles=4t1+50t2\\\\31=4(2-t2)+50t2\\\\31=8-4t2+50t2\\\\23=46t2\\\\t2=0.5[/tex]
then:
[tex]\rm x2=v2.t2\\\\x2=50\times 0.5\\\\x2=\boxed{\bold{25~miles}}[/tex]
Learn more
The distance of the elevator
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resultant velocity
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the average velocity
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Select all of the values that are solutions of x2 + 20 = 12x. x = -10 x = -2 x = 2 x = 10
Answers
Answer:
2, and 10
Step-by-step explanation:
Let's work through each one.
First, plug -10 into the equation:
-10² + 20 = 12 x -10?
-10² = 100
100 + 20 = 120
12 x -10 = -120
120 = -120? False!
But, using these same calculations, we can see that 10 is a correct answer.
Because everything's the same up to 12 x 10 = 120.
120 = 120
Same with 2 and -2
-2 does not work, but 2 does.
2² + 20 = 12 x 2?
4 + 20 = 24?
24 = 24? True!
The solution of the given quadratic equation is x = 2 and x = 10.
What is a quadratic equation?A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.
Given a quadratic equation, x²+20 = -12x
x²-12x+20 = 0
On factorizing the equation,
x²-10x-2x+20 = 0
x(x-10)-2(x-10) = 0
(x-10)(x-2) = 0
x = 10 or x = 2
Hence, the solution of the given quadratic equation is x = 2 and x = 10.
For more references on quadratic equation, click;
https://brainly.com/question/17177510
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He price of a shampoo, cut, and style at the hairstyling salon where you work is $18.00. You generally get a 20% tip from each customer, and the salon owner pays you 1/4 of each job's cost. On a typical day, you give shampoos, cuts, and styles to 8 customers. About how much can you expect to earn on such a day?
Answers
Answer:
total earning is $64.80
Step-by-step explanation:
Price of one work = $18.00
Payment by owner = 1/4 of $18.00
= 18/4
= $4.50
Earning by tip = 20% of $18.00 = 20/100 x18 = 3.60
Total earning from one work = $4.50+$3.60
= $ 8.10
Earning from 8 tips = 8x8.10
= $64.80
Classify the series as arithmetic or geometric then determine whether the series is convergent or divergent
Answers
Answer: Arithmetic , Divergent
Step-by-step explanation:
Given sequence is
{aₙ} = { 4 , 10/3 , 8/ 3 , 2 , . . . }
To check whether the sequence is geometric or not , we divide second term by first term to find the common ratio . Then we again divide third term by second term to get common ratio .
The common ratio we get would same , then it is geometric .
10/3 10 5
r₁ = ----------- = ------ = ------
4 12 6
8/3 8 3 4
r₂= ---------- = ---------- * ------------ = -----
10/ 3 3 10 5
Thus the common ratio are not same . So the sequence is not geometric .
Now we check for arithmetic .
We take difference of second and first term and then difference of third and second term . If it will be same then it is arithmetic . This is called common difference , d .
10 - 2
d₁ = ------ - 4 = -------
3 3
8 10 - 2
d₂ = ------ - -------- = ---------
3 3 3
Thus the common difference is same .
So the given sequence is arithmetic .
To find whether it is convergent or divergent , we need to write sum of n terms first .
Formula for finding sum of n terms of arithmetic sequence is
n
sₙ = ----- [ 2a + ( n - 1 ) d]
2
We have a = 4 , d = - 2/3 .
Plug in this formula we get
n n 2 2
sₙ = ------- [ 2 * 4 + ( n - 1 ) ( -2/3) ] = ------ [ 8 - ----- n + ------ ]
2 2 3 3
n 26 2
sₙ = ------ [ ------ - ------- n ]
2 3 3
To check whether it is convergent or divergent , we take limit sₙ approaches to infinity .
n 26 2
lim sₙ = lim { --- [ --- - ------ n ] } = - ∞
n → ∞ n→∞ 2 3 3
As the sequence diverge , thus the series is divergent .
Thus given series is arithmetic , divergent .
Second is the correct option .
Faye can sort 150 recyclable items in 3 minutes.How many recyclable items can Faye sort in 4 minutes?
Answers
Answer:
200
Step-by-step explanation:
150/3=50 so she sorts 50 items per minute, then 50*4=200
Answer:
Number of recyclable items sort in 4 minutes by Faye = 200
Step-by-step explanation:
Given that Faye can sort 150 recyclable items in 3 minutes.
Number of recyclable items sort in 3 minutes = 150
[tex]\texttt{ Number of recyclable items sort in 1 minute =}\frac{150}{3}=50[/tex]
Number of recyclable items sort in 4 minutes = 4 x Number of recyclable items sort in 1 minute
Number of recyclable items sort in 4 minutes = 4 x 50 = 200
Number of recyclable items sort in 4 minutes by Faye = 200
Sixteen students in a drama club want to attend a play . The ticket price is $35 for each student, and the transportation and meal for everyone will cost $960. To pay for the trip the students design sweatshirt to sell for a profit $19 per sweatshirt . If each student sells the same number of sweatshirt how may sweatshirts must each students sell so that there will be enough money to pay for the entire cost of the trip
Answers
16 • 35 = 560
add the 960
560 + 960 = 1520
then divide by 16
1520 / 16 = 95
then divide by 19
95 / 19 = 5
each student must sell 5
So firstly, we need to find how much the entire trip will cost. To do this, add the product of 16 and 35 (since tickets are 35 per student, and there are 16 students) with 960:
[tex](35*16)+960\\560+960\\\\\$ 1520[/tex]
The total cost of the trip is $1520. Next, we know that the sweatshirts will be making a profit of $19 per article sold so divide 1520 by 19:
[tex]1520\div 19=80[/tex]
The students need to sell 80 sweatshirts total to get enough money for the trip. Now, to know how many sweatshirts each student needs to sell individually, divide 80 by 16 (since there are 16 students):
[tex]80\div 16=5[/tex]
AnswerIn short, each student must sell 5 sweatshirts to pay for the entire trip.
What is the inverse of the function? g(x)=-4/3x+2
Answers
The correct answer is A.
The inverse function of your problem is [tex]g^{-1}[/tex] (x) = -[tex]\frac{3}{4}[/tex] x + [tex]\frac{3}{2}[/tex] .Hope this helps,
Davinia.
The inverse of the function g(x)=-4/3x+2 is
[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
The given function is:
[tex]g(x) = -\frac{4}{3}x + 2[/tex]
To find the inverse of the function g(x), follow the steps below
Make x the subject of the formula
[tex]g(x) = -\frac{4}{3}x+2\\\\ -\frac{4}{3}x = g(x) - 2\\\\-4x=3g(x)-6\\\\x = -\frac{3}{4}g(x)+\frac{6}{4} \\\\x = -\frac{3}{4}g(x)+\frac{3}{2}[/tex]
Replace x by [tex]g^{-1}(x)[/tex] and replace g(x) by x
The inverse function therefore becomes:
[tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
The inverse of the function g(x)=-4/3x+2 is [tex]g^{-1}(x) = -\frac{3}{4}x+\frac{3}{2}[/tex]
Learn more here: https://brainly.com/question/12220962
1 liter = 4.23 cups
1 cup = 8 ounces
Convert 2 liters to ounces (round to the nearest whole ounce).
A) 8 ounces
B) 34 ounces
C) 48 ounces
D) 68 ounces
Answers
Answer:
(D)68
Step-by-step explanation:
If 1 litre =4.23 cups
and 1 cup = 8 ounces
Therefore: 1 litre = 4.23 X 8 Ounces = 33.84 Ounces
2 litres = 2 x 33.84 Ounces
=67.68 Ounces
=68 Ounces (To the nearest whole number)
The number of ounces in 2 liters will be 68 ounces. Thus, the correct option is D.
Given that:
1 liter = 4.23 cups
1 cup = 8 ounces
Unit modification is the process of converting the measurement of a given amount between various units, often by multiplicative constants that alter the value of the calculated quantity without altering its impacts.
The number of cups in 2 liters is calculated as,
⇒ 2 x 4.23
⇒ 8.46 cups
The number of ounces in 8.46 cups is calculated as,
⇒ 8.46 x 8
⇒ 67.68 or 68 ounces
Thus, the correct option is D.
More about the conversion link is given below.
https://brainly.com/question/9414705
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Points S,U, and T are the midpoints of the sides of PQR. Which statements are correct ? 1/2QP=UT 1/2TS=RQ SU=PR SU||RP UT=RP
Answers
Answer:
A) 1/2QP=UT
D) SU II RP
Step-by-step explanation:
A & D ARE THE ANSWERS
The correct statements are 1/2QP=UT and SU||RP.
Explanation:In this question, we are given that points S, U, and T are the midpoints of the sides of triangle PQR. We need to determine which statements are correct.
1/2QP=UT: This statement is correct. Since S, U, and T are midpoints, we know that SU is parallel to PQ and UT is parallel to QR. Therefore, by the Midpoint Theorem, we have 1/2QP = UT.SU=PR: This statement is incorrect. Since S and U are midpoints, we know that SU is parallel to QR, not PR.SU||RP: This statement is correct. Since S and U are midpoints, we know that SU is parallel to QR. Therefore, SU is also parallel to RP.UT=RP: This statement is incorrect. Since U and T are midpoints, we know that UT is parallel to PQ, not RP.What is the solution to the system of equations? Use the substitution meathod to solve. 6=-4x+y and -5x-y=21
Answers
6+4x=y or y=4x+6
Plug in to second equation: -5x-(4x+6)=21
-9x-6=21
-9x=27
x=-3
Plugging in, you get that y=-12+6 or -6.
Therefore, the solution is (-3,-6)
Drew bout a chemistry book for $30. Later that book was marked down by 20%. By how much has the value been decreased
Answers
To find the answer, multiply 30 by 20% than divide by 100%. The answer is 6. So, subtract $6 from $30 which equals $24
I need help on this, please hurry and thank you!
Answers
Answer:
[tex]A.\ a_n=n^2+1[/tex]
Step-by-step explanation:
[tex]Check:[/tex]
[tex]a_n=n^2+1\\\\a_1=1^2+1=1+1=2\qquad CORRECT\\\\a_2=2^2+1=4+1=5\qquad CORRECT\\\\a_3=3^2+1=9+1=10\qquad CORRECT\\\\a_4=4^2+1=16+1=17\qquad CORRECT\\\\a_5=5^2+1=25+1=26\qquad CORRECT[/tex]
Used PEMDAS:
P Parentheses first
E Exponents (ie Powers and Square Roots, etc.)
MD Multiplication and Division (left-to-right)
AS Addition and Subtraction (left-to-right)
First Power, next Addition
Answer: A.
Step-by-step explanation:
2, 5, 10, 17, 26
First, check the difference between each term:
2 → 5 = +3
5 → 10 = +5
10 → 17 = +7
17 → 26 = +9
Since the difference (d) is not the same, this is not an arithmetic sequence.
Now, check the second tier {3, 5, 7, 9}
3 → 5 = 2
5 → 7 = 2
7 → 9 = 2
The difference (d) of the second tier is the same, so it is an exponential sequence.
--> the only option that is an exponential sequence is option A.
Stacy is attending music festival the tickets for the festival cost $87.96. Staci plans to purchase $30 T-shirts from the event for close friends. She's taking $200 to the festival. What is the maximum number of T-shirts Staci can purchase
Answers
The radius of a cylindrical construction pipe is 2ft. If the pipe is 19ft long, what is its volume?
Use the value 3.14 for π, and round your answer to the nearest whole number.
Be sure to include the correct unit in your answer.
Answers
Answer:
239 ft³
Step-by-step explanation:
Multiply the squared radius by π:
2*2*3.14=12.56 ft².
Multiplying the height:
12.56*19≅239 ft³.
Please answer this question! Thirty points and brainliest!
Answers
Answer:
d. 40
Step-by-step explanation:
x/4 - 7=3
Add 7 to both sides
x/4 - 7+7=3+7
x/4 = 10
Multiply by 4 on each side
x/4*4 = 10*4
x = 40
Answer:The Answer of this probelm is D 40.
Step-by-step explanation:
x/4 - 7=3
First you need to add 7 to both sides
x/4 - 7+7=3+7
x/4 = 10
second you need to multiply by 4 on each side
x/4*4 = 10*4
Once you finish this should be your final answer right here x = 40
Hope this helps
Consider the equation below. (if an answer does not exist, enter dne.) f(x) = 5 sin(x) + 5 cos(x), 0 ? x ? 2? (a) find the interval on which f is decreasing. (enter your answer using interval notation.)
Answers
Answer: [tex]\bold{[\dfrac{\pi}{4},\dfrac{5\pi}{4}]}[/tex]
Step-by-step explanation:
Step 1: Create a table
x | 5sinx + 5cosx = y
0 | 0 + 5 = 5
[tex]\frac{\pi}{2}[/tex] | 5 + 0 = 5
π | 0 + -5 = -5
[tex]\frac{3\pi}{2}[/tex] | -5 + 0 = -5
2π | 0 + 5 = 5
Notice that y = 5 at 0 and [tex]\frac{\pi}{2}[/tex] , so there will be a vertex at their midpoint. Similarly at y = -5.
Midpoint of 0 and [tex]\frac{\pi}{2}[/tex] is [tex]\dfrac{\pi}{4}[/tex] . Midpoint of π and [tex]\frac{3\pi}{2}[/tex] is [tex]\dfrac{5\pi}{4}[/tex]
(graph is attached to confirm interval)
Solve the linear equation.
7x+10=13(12x−3)+14x
Enter your answer in the box.
x =
Answers
[tex]7x+10=13(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=(13)(12x)+(13)(-3)+14x\\\\7x+10=156x-39+14x\\\\7x+10=170x-39\qquad\text{subtract 10 from both sides}\\\\7x=170x-49\qquad\text{subtract 170x from both sides}\\\\-163x=-49\qquad\text{divide both sides by (-163)}\\\\\boxed{x=\dfrac{49}{163}}[/tex]
In the process of proving that opposite sides of a parallelogram are congruent, Ross drew a diagonal of the parallelogram and determined that the two triangles formed are congruent. He then concluded that opposite sides must be congruent, because corresponding parts of congruent triangles are congruent.
Using his markings in the diagram, which postulate allowed him to determine that the two triangles formed are congruent?
A) AAS
B) ASA
C) SAS
D) SSS
Answers
Answer:
(B) ASA
Step-by-step explanation:
we will verify each options
option-A:
we can see that there is no consecutive two angles
so, this postulates can not be true
so, this is FALSE
option-B:
We can see that
one angle and then side and another angle are equivalents
so, this is TRUE
option-C:
We can see that
one side and two angles are equivalents
so, this is FALSE
option-D:
we can see that
one side and two angles are equivalents
so, this is FALSE
Answer:
B
Step-by-step explanation:
What is the value of X?
Enter your answer in the box.
Answers
[tex]180 - (71 + 90) = (6x + 4)[/tex]
Answer:
x = 5
Step-by-step explanation:
in ΔABC , AB = BC , hence triangle is isosceles, thus
∠A = ∠C = 73° ( base angles are equal )
the sum of the 3 angles in a triangle = 180°
subtract the sum of the base angles from 180 for ∠B
∠B = 180° - (73 + 73)° = 34°
⇒ 6x + 4 = 34 ( subtract 4 from both sides )
6x = 30 ( divide both sides by 6 )
x = 5
complex roots problem
Answers
Answer:
b^2-4ac >0 the roots are real
Step-by-step explanation:
b^2-4ac >0 the roots are real
b^2-4ac = 0 there is 1 root
b^2 -4ac <0 the root are complex
Identify the values of the variables. Give your answers in simplest radical form. PLEASE HELP!!
Answers
First question:
By definition of sine and cosine, we have
[tex]\sin30^\circ=\dfrac h{\sqrt5}\implies h=\dfrac{\sqrt5}2[/tex]
[tex]\cos30^\circ=\dfrac g{\sqrt5}\implies g=\dfrac{\sqrt{15}}2[/tex]
Second question:
By definition of tangent, we have
[tex]\tan60^\circ=\dfrac{5\sqrt2}x\implies x=\dfrac{5\sqrt2}{\sqrt3}=\dfrac{5\sqrt6}3[/tex]
Then by Pythagoras' theorem,
[tex](5\sqrt2)^2+x^2=y^2\implies y=\sqrt{(5\sqrt2)^2+\left(\dfrac{5\sqrt6}3\right)^2}=\sqrt{50+\dfrac{50}3}=\sqrt{\dfrac{200}3}=\dfrac{10\sqrt6}3[/tex]
Mrs. Gustafsson's English class is taking an exam that is made up of short-response questions and essay questions. There are 22 questions that are worth 100 points in total. Each short-response question is worth 4 points, and each essay question is worth 10 points. How many short-response question are on the exam? Select one: A. 14 B. 2 C. 18 D. 2
I need help with this ASAP, 99 points
Answers
Answer:
Short-response question = 20.
Step-by-step explanation:
Let x be number of short response questions and y be the number of essay questions.
We have been given that there are 22 questions that are worth 100 points in total. Each short-response question is worth 4 points, and each essay question is worth 10 points. Using our given information we can form a system of equations as:
[tex]x+y=22...(1)[/tex]
[tex]4x+10y=100...(2)[/tex]
Now we will solve our system of equations using substitution method.
From equation 1 we will get,
[tex]y=22-x[/tex]
Upon substituting [tex]y=22-x[/tex] in equation 2 we will get,
[tex]4x+10(22-x)=100[/tex]
[tex]4x+220-10x=100[/tex]
[tex]4x-10x=100-220[/tex]
[tex]-6x=-120[/tex]
[tex]x=\frac{-120}{-6}[/tex]
[tex]x=20[/tex]
Therefore, there are 20 short-response questions on the exam.
Answer:
D. 20
Step-by-step explanation:
I got it right on prepworks
Solve the linear equation.
7x+10=1/3(12x−3)+14x
Enter your answer in the box.
Answers
[tex]7x+10=\dfrac{1}{3}(12x-3)+14x\qquad\text{use distributive property}\\\\7x+10=\dfrac{1}{3}\cdot12x-\dfrac{1}{3}\cdot3+14x\\\\7x+10=4x-1+14x\\\\7x+10=18x-1\qquad\text{substitute 10 from both sides}\\\\7x=18x-11\qquad\text{subtract 18x from both sides}\\\\-11x=-11\qquad\text{divide both sides by (-11)}\\\\\boxed{x=1}[/tex]
Answer:
I believe the correct awnser is x=1 I took the test
what is 4/7*3/4??? NEED HELP
Answers
Answer
3/7 - three sevenths
Step-by-step explanation:
Multiply both numerators and both denominators
4*3=12 and 7*4=28
first one is your numerator
second one is your denominator
12/28
Then simplify
12/4=3 and 28/4=7
3/7
Find the following measure for this figure. Area of base= 6 square units, 8 square units. 12 square units
Answers
Answer:
8 square units
Step-by-step explanation:
Base area= Length* width
Base area= 4* 2
Base area= 8 square units
Answer:
8 square units
Step-by-step explanation:
Base area= Length* width
Base area= 4* 2
Base area= 8 square units
Both the football and volleyball teams have games today. The football team plays every 7 days. The volleyball team plays every 3 days. When will both teams have games on the same day again? A. in 14 days c. in 7 days b. in 21 days d. in 10 days
Answers
The least common multiple of 7 and 3 is 21, so both the football and volleyball teams will have games on the same day again in 21 days.
The question requires us to determine when the football and volleyball teams will have games on the same day again. Since the football team plays every 7 days and the volleyball team plays every 3 days, we are looking for the least common multiple (LCM) of 7 and 3, which represents the number of days until both teams will have games on the same day again.
To find the LCM of 7 and 3, we can list the multiples of each number until we find a common multiple:
Multiples of 7: 7, 14, 21, 28, ...
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, ...
The first common multiple we encounter is 21. Therefore, both teams will have games on the same day again in 21 days.
The art club at a school raised $248 at a car wash. They spent $206 to set up an art show, and raised $316 at the art show by selling artwork the members had made. How much money did the club have after the show?
Answers
Answer:
Money club have after the show is $358 .
Step-by-step explanation:
As given
The art club at a school raised $248 at a car wash.
They spent $206 to set up an art show, and raised $316 at the art show by selling artwork the members had made.
Than
Money club have after the show = school raised money at a car wash + Raised money at the art show - spent money to set up an art show.
Money club have after the show = 248 + 316 - 206
Money club have after the show = 564 - 206
Money club have after the show = $358
Therefore money club have after the show is $358 .
Answer:
It is 358.
Step-by-step explanation:
The club started with $248, and then spent $206.
248−206=42
The club had $42, left after they spent for the art show.
Then, they raised another $316, at the show.
42 + 316 = 358
Answer: 358