the square with a side length (x + 3) and an equilateral triangle with side lengths (3x-1) have the same perimeter what is the value of x?
Help please
Answers
Answer: x = 9/5 or \(1\frac{4}{5}\)
35 1/5 is the perimeter of the square and the triangle.
Step-by-step explanation:
The square has 4 sides, so the perimeter of the square is 4(x+3)
The triangle has 3 sides so the perimeter is 3(3x-1)
The perimeters are equal, so 4(x+3) = 3(3x-1)
Solve by distributing and then
4x +12 = 9x - 3 subtract 4x from both sides and add 3 to both sides
4x-4x +12 -3 = 9x-4x -3 +3 cancel the zero sums and combine similar terms.
9 = 5x divide both sides by 5
x = 9/5
Check: 4(9/5 +3) = 3[3(9/5) -1]
36/5 + 3 = [3( 27/5 -1 ] 27/5 -3 -3 equivalent -15/5 27/5 -15/5 = 12/5
36/5 = 3(12/5) = 36/5 TRUE! simplify to mixed numbers
35 1/5 is the perimeter of the square and the triangle.
Answer:
u,
Step-by-step explanation:
Related Questions
In western music, an octave is divided into 12 pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
Answers
Answer:
This should be a permutation
Step-by-step explanation:
P (n, r) = n!/(n-r)!
P (12,5) = 12!/(12-5)!
P (12,5) = 12!/7!
P(12,5) = 95040
please help me find these angles, i dont want a wrong answer.
Answers
Answer:
<EAC=75
<BAD=36
<ACD=75
<FAB=75
<CAD=69
<BDA=69
Step-by-step explanation:
EAC= 180-105=75
BAD= CDA
ACD= 75 opposite <s congruent
FAB= 75 vertical <s congruent
CAD=105-36=69
BDA=69 Opposite <s congruent.
Hope this helps! Should be right we just finished this unit.
Solve the following proportion. Round your answer to two decimal places.
Answers
Answer:
x = 2
Step-by-step explanation:
\(\frac{x+1}{x+3}\) = \(\frac{3}{5}\) ( cross- multiply )
5(x + 1) = 3(x + 3) ← distribute parenthesis on both sides
5x + 5 = 3x + 9 ( subtract 3x from both sides )
2x + 5 = 9 ( subtract 5 from both sides )
2x = 4 ( divide both sides by 2 )
x = 2
Students at Sunnyvale Middle School volunteered to work a 2-hour shift at a
car wash fundraiser. The table shows the number of people who worked each
shift and how many cars they washed.
Is the relationship between the number of
cars washed and the number of workers
proportional? Complete the statement.
The number of cars washed per person
?
of workers, so the relationship is
the same for each number
?
People Working
4
6
8
10
Cars Washed
8
12
20
25
Answers
The relationship in this problem is not proportional, as there are different ratios between the number of people and the number of cars washed.
What is a proportional relationship?A proportional relationship is a relationship in which a constant ratio between the output variable and the input variable is present.
The equation that defines the proportional relationship is a linear function with slope k and intercept zero given as follows:
y = kx.
The slope k is the constant of proportionality, representing the increase or decrease in the output variable y when the constant variable x is increased by one.
The ratios between the output and the inputs are given as follows:
8/4 = 2.12/6 = 2.20/8 = 2.5.25/10 = 2.5.Different ratios, hence the relationship is not proportional.
A similar problem, also featuring proportional relationships, is presented at https://brainly.com/question/7723640
#SPJ1
If Fran were to paint her living room alone, it would take 6 hours. Her sister Denise could do the job in 8 hours. How many hours would it take them working together? Express your answer as a fraction reduced to lowest terms, if needed.
Answers
It would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.
To solve this problem, we can use the concept of "work rates."
Let's find out how much work Fran and Denise can do individually in one hour.
If Fran takes 6 hours to paint the living room alone, her work rate is \(\frac{1}{6}\) of the room per hour \((\frac{1 room}{6 hours } = \frac{1}{6}room/hour )\).
Similarly, if Denise takes 8 hours to paint the living room alone, her work rate is \(\frac{1}{8}\) of the room per hour \((\frac{1 room}{8 hours } =\frac{1}{8}room/hour )\).
When they work together, their work rates are additive.
So, their combined work rate would be:
\(\frac{1}{6} room/hour+\frac{1}{8} room/hour\)
\(=(\frac{4}{24} )room/hour + (\frac{3}{24} )room/hour\)
\(=\frac{7}{24} room/hour\)
This means that working together, Fran and Denise can paint \(\frac{7}{24}\) of the living room in one hour.
To determine the total time required for them to paint the entire room, we can invert their combined work rate:
\(\frac{(1 room) }{(\frac{7}{24}room/hour) } =\frac{24}{7}hour\)
Therefore, it would take Fran and Denise (working together) approximately \(\frac{24}{7}\) hours to paint the living room.
For such more questions on living room
https://brainly.com/question/31126272
#SPJ8
multiply [4, 0, -1, 2, -3, -1]x[0, 1, -3, 1]
Please Help...
Answers
Multiplication of the given matrix is not possible by definition of matrix multiplication.
Since, To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.
We have to given that;
Expression for multiply,
⇒ [4, 0, -1, 2, -3, -1] x [0, 1, -3, 1]
Since, We can see that;
First matrix have order 1 x 6
And, Second matrix have order 1 x 4
We know that;
Matrix multiplication is possible when number of column in first matrix is same as number of rows in second matrix.
Hence, By given matrices we get;
Number of column in first matrix (6) ≠ number of rows in second matrix (1)
So, Multiplication of the given matrix is not possible by definition of matrix multiplication.
Learn more about the multiplication visit:
https://brainly.com/question/10873737
#SPJ1
Mr. Williams drove 440 miles in 8 hours, on the highway, at a steady speed. How far could he drive in five hours at the same average speed?
Answers
Answer:
275 miles
Step-by-step explanation:
Please help
will mark BRAINLIEST
Answers
The angle sum property of a triangle and the angle formed between a tangent and a radius of a circle indicates.
m∠ADC = 58°
What is a tangent to a circle?A tangent to a circle is a straight line which touches the circumference of a circle at only one point.
The vertical angles theorem indicates that we get;
∠1 ≅ ∠2
Therefore; m∠1 = m∠2
The tangent to a circle indicates that we get;
The angle formed at vertex B and Q are 90 degrees angles and the triangles ABP and AQP are right triangles, which indicates that the acute angles of each of the right triangles are complementary, therefore;
m∠1 + 26° = 90°
m∠1 = 90° - 26° = 64°
Therefore, m∠2 = m∠1 = 64°
m∠2 = m∠CAD = 64°
The segments AC and AD are radial lengths therefore, the triangle ΔACD is an isosceles triangle.
m∠ADC ≅ m∠ACD (Base angles of an isosceles triangle)
The angles ∠ADC and ∠ACD are therefore;
m∠CAD + m∠ADC + m∠ACD = 180° (Angle sum property of a triangle)
m∠CAD + m∠ADC + m∠ADC = 180°
m∠CAD + 2 × m∠ADC = 180°
64° + 2 × m∠ADC = 180°
m∠ADC = (180° - 64°)/2 = 58°
m∠ADC = 58°
Learn more on the angle sum property of a triangle here: https://brainly.com/question/22262639
#SPJ1
find the value for x y and z
Answers
Answer:
All triangles add up to 180 degrees so...
180 - 43 - 59 = 78 degrees.
So x - 78 degrees.
x and y are supplementary angles so...
180 - 78 = 102.
So y = 102.
180 - 102 - 49 = 29 degrees
So z = 29 degrees
Hope this helps!
Jane evaluates x2-3x+5 for x=-2 below.
Step 1: (-2)²-3(-2)+5
Step 2: -4+6+5
=
Step 3: = 7
What, if any, was Jane's mistake?
Jane made no mistakes.
O Jane incorrectly evaluated (-2)² in step 2.
Jane incorrectly added the terms in step 3.
O Jane incorrectly substituted in x=-2 in step 1.
K
Answers
Answer: Jane incorrectly evaluated (-2)² in step 2.
Step-by-step explanation:
\((-2)^{2}=4\), not -4.
a retailer makes a profit of 5% by selling a fan for Rs 735 at what price did he purchase the fan
Answers
\(\large\boxed{\pink{\sf \leadsto He \ purchased \ the \ fan \ for \ Rs 700. }}\)
Step-by-step explanation:Given that , a retailer makes a profit of 5% by selling a fan for Rs 735 . So let us take CP be x .
Now , here
\(\implies \red{\sf Profit \ made \ by \ retailer = 5\% }\)
Here we assumed CP to be x , and profit % is 5% . So , its SP will be
\(\implies SP = CP + 5\% \ of \ CP \\\\\implies Rs 735 = x + \dfrac{5}{100}x \\\\\implies \dfrac{100x+5x}{100}= Rs 735 \\\\\implies \dfrac{105x }{100}= Rs 735 \\\\\implies x = \dfrac{735\times 100}{105} \\\\\underline{\boxed{\orange{\tt \implies x = Rs 700 }}}\)
Hence the CP of the fan was Rs 700 .Cindy has decided to lease a car. the lease includes a money factor of 0.00354. what interest rate is cindy being charged in her lease? a. 0.85% b. 8.5% c. 1.475% d. 14.75% please select the best answer from the choices provided a b c d
Answers
The interest rate Cindy will be charged with money factor 0.00354 is approximately 8.5% which is option b.
Given The factor included in lease is 0.00354.
Interest is the amount that a bank or person who gives loan charges from loan taker.
Money factor is a method for finding the financing charges on a lease with monthly payments. The money factor can be translated into the annual percentage rate by multiplying the money factor by 2400.
Money factor=0.00354.
So the interest rate that Cindy will charge is equal to 2400*0.00354
The interest rate Cindy will be charged =8.496%
=8.5%
Hence the interest rate charged is approximately 8.5%.
Learn more about interest at https://brainly.com/question/2151013
#SPJ4
Please help thank you
Answers
Answer:
(-2)
Step-by-step explanation:
just do -2 x-3 x than + 13 and than you will get - 2
Morganton Company makes one product and it provided the following information to help prepare the master budget:
The budgeted selling price per unit is $60. Budgeted unit sales for June, July, August, and September are 8,600, 17,000, 19,000, and 20,000 units, respectively. All sales are on credit.
Thirty percent of credit sales are collected in the month of the sale and 70% in the following month.
The ending finished goods inventory equals 25% of the following month’s unit sales.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Each unit of finished goods requires 5 pounds of raw materials. The raw materials cost $2.40 per pound.
Thirty five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
The direct labor wage rate is $14 per hour. Each unit of finished goods requires two direct labor-hours.
The variable selling and administrative expense per unit sold is $1.80. The fixed selling and administrative expense per month is $67,000.
5. If 96,250 pounds of raw materials are needed to meet production in August, how many pounds of raw materials should be purchased in July?
Answers
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
To determine the number of pounds of raw materials that should be purchased in July, we need to calculate the raw materials production needs for August and then consider the inventory policies given in the information provided.
Each unit of finished goods requires 5 pounds of raw materials. The budgeted unit sales for August are 19,000 units. Therefore, the raw materials production needs for August would be 19,000 units multiplied by 5 pounds per unit, which equals 95,000 pounds.
The ending raw materials inventory equals 10% of the following month’s raw materials production needs. Therefore, the desired ending raw materials inventory for July would be 10% of 95,000 pounds, which is 9,500 pounds.
To calculate the raw materials purchases for July, we need to consider the payment terms provided. Thirty-five percent of raw materials purchases are paid for in the month of purchase and 65% in the following month.
Let's assume the raw materials purchases for July are X pounds. Then the payment for 35% of X pounds will be made in July, and the payment for 65% of X pounds will be made in August.
The payment for raw materials purchases in July (35% of X pounds) will be:
0.35 * X pounds
The payment for raw materials purchases in August (65% of X pounds) will be:
0.65 * X pounds
Since the raw materials purchases for July should cover the desired ending raw materials inventory for July (9,500 pounds), we can set up the following equation:
Raw materials purchases in July - Payment for raw materials purchases in July = Desired ending raw materials inventory for July
X pounds - 0.35 * X pounds = 9,500 pounds
Solving this equation will give us the value of X, which represents the pounds of raw materials that should be purchased in July.
for such more question on equation
#SPJ8
You visit the tallest building in a city and drop a penny off the edge of the observation deck. The distance the penny will fall is 16 feet the first second, 48 feet the next second, 80 feet the third second, and then it will continue falling at the same rate. How many feet will the penny fall during the 8th second?
384 feet
272 feet
256 feet
240 feet
Answers
The distance that an object falls due to gravity is given by the equation:
d = 1/2 * g * t^2
where d is the distance fallen, g is the acceleration due to gravity, and t is the time elapsed.
In this case, we are given that the penny falls 16 feet during the first second, 48 feet during the second second, and 80 feet during the third second. From this, we can see that the penny is falling with a constant acceleration of 32 feet per second per second (since the distance is increasing by 32 feet each second).
To find the distance that the penny falls during the eighth second, we can use the same equation as before, but with a value of t equal to 8 seconds:
d = 1/2 * g * t^2
d = 1/2 * 32 * 8^2
d = 1/2 * 32 * 64
d = 1024 feet
Therefore, the penny will fall 1024 feet during the eighth second.
if f(x) = 4^x - 8 and g(x) = 5 + 6, find (f + g)(x)
Answers
The solution to the composite function operation is: (f + g)(x) = 4ˣ + 5x - 2
How to solve composite functions?Composite functions are defined as functions that occur when the output of one of the functions is used as the input of another of the functions. If we have a function f and then another function g, the function “ f of g of x”, is the composition form of the two functions.
The functions we are given are:
f(x) = 4^x - 8 and g(x) = 5x + 6
Thus:
(f + g)(x) = 4^x - 8 + 5x + 6
= 4ˣ + 5x - 2
Read more about Composite functions at: https://brainly.com/question/29103939
#SPJ1
Complete question is:
if f(x) = 4^x - 8 and g(x) = 5x + 6, find (f + g)(x)
a deli employee can make a sandwhich in 6 minutes.she works for 84 minutes.how many sandwhiches can she make
Answers
Answer:
14
Step-by-step explanation:
84/6
Explanation: all you have to do is divide 84 by 6
Which inequality has the graph shown below?
Oy > 2x – 3
O y < 2x - 3
oy > 2x - 3
O y < 3x + 1
Answers
Answer:
The answer is y < 2x -3
Step-by-step explanation:
You can read this as all values on the graph will be the value of x times 2 minus 3..
For example, if we wanted to know what the value of y would be if x =2, we would plug in 2 and get 2(2) - 3 or just 1. We can see at the graph that when x = 2 y does equal 1. **In this situation we are pretending that the < symbol is the equal symbol..
To actually find the answer you can graph each equation until you find it or do it this way:
1) Find the slope and determine if it it works for the given graph.
We can see that the slope of the given graph is positive and if we look closer we can see that the slope is 2 over and that we have a y-intercept of (0,-3).
2) We know that it is Option 2 instead of the first option because o the < sign. If it was option 1, then the shaded part of the graph would be on the other side of the line.
The inequality has the graph shown in the question. is to be considered as the y < 2x -3.
Calculation of an inequality function:Since
First determine the slope
So we can see that the slope of the given graph should be positive and then the slope should be 2 over and there is y-intercept of (0,-3).
So based on this, we can say that The inequality has the graph shown in the question. is to be considered as the y < 2x -3.
Learn more about y-intercept here: https://brainly.com/question/15587122
WILL GIVE 30 POINTS AND BRAINLIEST
Calculate in the smartest way: (2^5 * 5^22 - 2 * 5 ^ 21) / 25^10.
Answers
The simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.
To simplify the expression (2⁵ x 5²² - 2 x 5²¹) / 25¹⁰.
we can use the properties of exponents and the fact that 25 = 5².
First, let's simplify the numerator:
(2⁵ x 5²² - 2 x 5²¹)
Using the distributive property, we can factor out 5²¹ from both terms:
= 5²¹ x (2⁵ x 5 -2)
= 5²¹ (32 x 5- 2)
= 5²¹ (160-2)
= 5²¹ x 158
Now, let's simplify the denominator: 25¹⁰
Since 25 = 5², we can rewrite it as (5²)¹⁰, which gives us:
= (5²)¹⁰
= 5²⁰
Using the quotient rule of exponents \((a^m / a^n = a^{(m-n)})\), we can simplify further:
= 5²¹ x 158 / 5²⁰
= 5²¹⁻²⁰ x 158
= 5 x 158
= 790
Therefore, the simplified value of the expression ((2⁵ x 5²² - 2 x 5²¹) / 25¹⁰ is 790.
Learn more about exponents and power here:
https://brainly.com/question/28515493
#SPJ1
Need help with question
Answers
Answer:
f(2) = 1
x = 0
Step-by-step explanation:
f(2) = 1 since y=1 when x=2.
f(0) = -3 since x=0 when y=-3
PLEASE HELP THIS IS VERY IMPORTANT I'LL GIVE YOU BRAIN THING IF ITS CORRECT!! <3 NO LINKS PLEASEE.
Answers
Answer:
a is 23 1/24 or 553/24 and b is 109 43/87
Step-by-step explanation:
What kind of transformation is illustrated in this figure?
Answers
The transformation illustrated in the figure is translation.
What is Translation?Translation is a Transformation process in which the size or shape of a figure is not changed rather it only changes the coordinates of the vertices that make up that shape by moving them from one point to another.
Analysis:
Both shapes are congruent, since all the vertices remain in their respective positions even though they were moved and no change in the shape or size, then the transformation process is Translation.
Learn more about Translation: brainly.com/question/12861087
#SPJ1
Chris completes a word search in 3 minutes. Oliver takes
20 seconds longer. How long did Oliver take?
seconds
Answers
Answer: 200 seconds
Okay - so then Oliver would take 3 minutes and 20 seconds. There are 60 seconds in a minute so it would be 30 times 60 = 180 + 20 = 200
i
dont
get
this
help
rn
Answers
Answer:
6 first box. 12 second box. 21 third box. 10 fourth box. 4 fifth box.
Step-by-step explanation:
Look for common denominaters, that will show you what to multiply the equation by to get rid of fractions.
Use the function below to find F(3).
Answers
Answer: B
Step-by-step explanation:
Plug in x for 3. Then solve.
4*(1/3)^3
4*1/9
4/9
plug in x for 3
4*(1/3)^3
4*(1/27)
4/27
solve the following system of equations. 1/x-1/3y=-12. -4/5x+7y=-1/5
Answers
The value of
x = 1/9
y = 1/63
We have given two equations :
1/x - 1/3y = -12 ... eq. (1)
- 4/5x + 7y = -1/5 ... eq. (2)
First we will multiply the 1st equation by 4/5,
We get, 4/5x - 4/15y = -48/5 ... eq. (3)
Now, we will add the equation 3 and equation 2
4/5x - 4/15y = -48/5
- 4/5x + 7y = -1/5
____________________
7y - 4/15y = -49/5
(105y - 4)/15y = -49/5
105y - 4 = (-49/5) × 15y
105y - 4 = -49 × 3y = -147y
105y + 147y = 4
y = 4/252
y = 1/63
We get the value of y which is 1/63,
Now, we will solve the eq. 1 by putting is equal to 1/63.
1/x - 1/3y = -12
1/x - (1 × 63/3 × 1) = -12
1/x -21 = -12
1/x = 21 - 12 = 9
x = 1/9
Hence, we get the value of x and y as 1/9 and 1/63 respectively.
To learn more about Algebra visit :
https://brainly.com/question/24875240
#SPJ9
Please look at the graphs in the photo. Thank you!
Answers
(a). The graph of y = -f(x) is shown in the image below.
(b). The graph of y = g(-x) is shown in the image below.
How to draw the graph of the transformed functions?By reflecting the parent absolute value function g(x) = |x + 2| - 4 over the x-axis, the transformed absolute value function can be written as follows;
y = -f(x)
y = -|x + 2| - 4
Part b.
In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
x and y represent the data points.m represent the slope.First of all, we would determine the slope of this line;
Slope (m) = rise/run
Slope (m) = -2/4
Slope (m) = -1/2
At data point (0, 5) and a slope of -1/2, a linear equation for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 5 = -1/2(x - 0)
g(x) = -x/2 + 5, -4 ≤ x ≤ 4.
y = g(-x)
y = x/2 + 5, -4 ≤ x ≤ 4.
Read more on reflection here: brainly.com/question/27912791
#SPJ1
Is the number 1.13 greater than, less than or equal to 1
Answers
Solve
5x + 20 ≤ 60
(x= ?)
Answers
Answer:
x ≤ 8
Step-by-step explanation:
5x + 20 ≤ 60
5x ≤ 40
x ≤ 8
Answer:
x = (-infinity, 8], or x <_ 8
Step-by-step explanation:
Just like with equalities, we can add or subtract anything from both sides of an inequality, and it will still be true. So, our first step is:
5x + 20 ≤ 60
becomes
5x ≤ 40
Next, we can divide both sides by 5 to isolate the variable on the left hand side of the inequality. So,
5x ≤ 40
becomes
x ≤ 8
This means that x can be any number less than or equal to 8.
x ≤ 8
x = (-infinity, 8]
Tell whether b = 12 is a solution of b - 7 = 5
Answers
Answer:
Yeah, \( \sf b = 12 \)
Step-by-step explanation:
Given equation,
→ b - 7 = 5
Now the value of b will be,
→ b - 7 = 5
→ b = 7 + 5
→ [ b = 12 ]
Hence, the value of b is 12.
Answer: Yes
Step-by-step explanation: If you plug 12 into b, you will get the equation 12 - 7 = 5.
Try solving 12-7. It is 5.
Make me brainliest! Have a nice day :)