Randy and two of his friends have rectangular desks of the exact same size. The sum of the perimeters of the 3 desks is 324 inches.
If the width of each of the desks is 30 inches, what is the length of each desk?
The length of each desk when the width of each of the desks is 30 inches is A. 24 inches.
How to calculate the length?From the information, Randy and two of his friends have rectangular desks of the exact same size and the sum of the perimeters of the 3 desks is 324 inches.
The perimeter for each desk will be:
= 324 / 3
= 108
The perimeter is calculated as:
= 2(length + width)
This will be
2(length + width) = 108
2(length + 30) = 108
2l + 60 = 108
Collect like terms
2l = 108 - 60
2l = 48
Divide
l = 48/2
l = 24
The length is 24 inches.
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what if n is negative what is the value of the equation below n(2)+8 divided by 4 = 11
If n is negative the value of the equation that we have below would be -18
How to solve the equationWe have to rewrite the equation in a way that it would be easier to understand first.
[tex]\frac{-2n+8}{4} =11[/tex]
Next we would have to cross multiply
this would give us
-2n + 8 = 11 * 4
-2n + 8 = 44
take the like terms
-2n = 44 - 8
-2n = 36
divide through by -2 from the above
-2n / -2 = 36 / -2
n = - 18
Therefore given that we have that the value of the equation after n is negative is -18.
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The ratio of the number of beads collected by Jane to the number of beads collected by Jill is 7: 3. Jane gave some beads to Jill. Is it possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill? Explain why you think so
yes , it is possible for both Jane and Jill to have the same number of beads after Jane gave some beads to Jill and The number of beads Jane has is 7t/4 and Jill has 3t/4 bead's
The ratio of Jane's beads to Jill's beads is 7: 3
Let x be the number of beads Jane has
y be the number of beads Jill has
x/y = 7/3
When Jane's gives t of her beads away both will have the same number of beads so
x - t = y
substituting in the first equation
x/ ( x- t) =7/3
3x= 7x-7t
4x= 7t
x= 7t/4
y= 7t/4 -t
= 3t/4
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What are the missing segment lengths shown in the image?
The length of the missing ,line segments show in the image are AC = CD = 10√2 and AB = BC = 10 .
In the question ,
a figure is given , we have to find the length of the missing line segments .
From the given figure
the Δ ACD is a right triangle ,
given that ∠A and ∠D are equal
so , their corresponding length AC and CD will be equal , that is AC = CD
So , By Pythagoras Theorem
AC² + CD² = AD²
2*AC² = AD²
2*AC² = (20)²
2*AC² = 400
AC² = 400/2 = 200
AC = √200
AC = CD = 10√2
The triangle ABC is also right triangle
and ∠A and ∠C are equal
so , their corresponding length AB and BC will be equal , that is AB = BC
So , By Pythagoras Theorem
AB + BC = AC
2*AB² = AC²
2*AB² = (10√2)²
2*AB² = 200
AB² = 200/2 = 100
AB = √100
AB = 10 = BC
Therefore , The length of the missing line segments show in the image are AC = CD = 10√2 and AB = BC = 10 .
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. suppose the sides of a rectangle are changing with respect to time. the first side is changing at a rate of 2 in./sec whereas the second side is changing at the rate of 4 in/sec. how fast is the diagonal of the rectangle changing when the first side measures 16 in. and the second side measures 20 in.? (round answer to three decimal places.)
Diagonal of rectangle is changing by the rate of 4.373 in. /sec.
What is rate of change ?Rate of change (ROC) is the rate at which a variable changes over a particular period of time
To find the average rate of change, divide the change in the y-values by the change in the x-values . Finding the average rate of change is especially useful for identifying changes in measurable values such as average speed or average velocity.
A ratio is a special ratio in which the two terms have different units.
Calculationthe calculation part is shown in the below picture attached .
so after seeing the solution we come to an answer of = 4.373 in./sec
therefore diagonal of rectangle is changing by the rate of 4.373 in. /sec
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one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches. what is the area of the parallelogram? express your answer in simplest radical form.
The area of parallelogram with "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches" is 60√3 inch².
What is parallelogram?A quadrilateral with the opposing sides parallel is called a parallelogram (and therefore opposite angles equal). A parallelogram with all right angles is known as a rectangle, and a quadrilateral with equal sides is known as a rhombus. A parallelogram is a geometric shape with sides that are parallel to one another in two dimensions. It is a type of polygon with four sides (also known as a quadrilateral) in which each parallel pair of sides is the same length.
Here,
A parallelogram has adjacent angles that add up to 180 degrees.
Since one angle of parallelogram is 120°.
240+2x=360
2x=120
x=60
The other will be 60°
The area of parallelogram= lh
l=15 inch
h=b(sin 60°)
=8*√3/2
h=4√3 inch
area of parallelogram= 15*4√3
= 60√3 inch²
The parallelogram's area is 60√3 inch² when "one angle of a parallelogram is 120 degrees, and two consecutive sides have lengths of 8 inches and 15 inches."
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Caroline can make eleven lassis out of two mangoes. How many lassis can she make out of twelve mangoes?
Answer
Step-By-Step-Explanation
2 mangoes=eleven lassis
×6 ×6
12 mangoes=66 lassis
Answer=66 lassis
Which postulate can be used to prove the two triangles are congruent?
Answer:
SAS
Step-by-step explanation:
If two sides and the included and the included angle of one triangle are congruent to two sides and the included angle of another triangle , then the triangles are congruent. The included angle is the angle formed by the two sides.
EF = BC
∠ F = ∠ C
DF = AC
then the two triangles are congruent by the SAS postulate.
Answer:
SAS
Step-by-step explanation:
On triangle one and two, they both start by having a congruent side, then a congruent angle, then another congruent side, thus making these triangles congruent by Side Angle Side.
It can't be AAS because there is only one angle, we know is congruent.
It can't be SSS because there are only two sides, we know are congruent.
It can't be HL because there is no right angle, meaning these aren't right triangles.
7(x+4)-2[x-3(5+x)]=2/3(x-6)
With detailed workings
the profit y (in dollars) for a business from selling x games is represented by y=33x graph the equation
THIS IS URGENT!!! SOMEONE PLEASE RESPOND!!!!
ty!
Answer: check the image attached
Step-by-step explanation:
Hope this helps
Answer:
Just point the graph on Y=33x+0
Step-by-step explanation:
There's no B or starting point, so you would just plant the point on 0,33
WILL GIVE BRAINLIST TO BEST ANSWER! EASY POINTS
write the point slope form of the equation of the line through the given points.
through (-1, -5) and (-5, 3)
LOTS OF POINTS coordinate proof explaining how the midsegment of a triangle forms a triangle with 1/4 of area
The coordinate geometry, the midsegment theorem shows that the midsegment of a triangle is 1/4 area of the triangle.
How to show that the midsegment of a triangle is 1/4 area?
The midsegment if a triangle is defined as a line that joins two midpoints of two opposite sides of a triangle.
The midsegment theory of a triangle states that in a triangle, the midsegments of 2 sides is parallel to, and half the length of the 3rd side.
The 3 midsegments of a triangle forms a small triangle within the larger triangle.
This therefore, forms 4 triangles.
Area of a triangle =base x height
Hence 4 triangles are formed,
The area of the larger triangle is [tex]\frac{bh}{4}[/tex] =1/4(bh)
Therefore; Area =1/4 of area.
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asking help for a friend again
To find the parallel line of y =3z+6 passing through the slope intercept points (-2,5).
For a line to be parallel to another line, by definition it must have the same slope.
Because the equation is in the slope-intercept form we can use the slope of the line.
The slope- intercept form of a linear equation is :
y=mx+b
Where m is the slope and b is the y− intercept value.
Therefore, for the given equation, the slope is 3.
Now we can use the point slope formula to determine the equation for the parallel line.
The point - slope formula states: (y−y1)=m(x−x1)
Where m is the slope and (x1,y1) is a point the line passes through.
Substituting the slope from the given line and the given point gives:
y−5=3(x+2)
Transforming this to the slope-intercept form by solving for y gives:
y−5=3x+6
y−5+5=3x+6+5
y=3x+11
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Tanks are used to deliver liquid fuel to a factory. each tank holds 22.5 cubic yards of fuel. the weight of 1 cubic yard of fuel is 0.74 tons. the fuel will be stored in containers that each holds 7.4 tons of fuel. how many containers of this size are needed to hold all the fuel from 12 tanks?
27 containers are needed to hold all the fuel from 12 tanks.
How do you prove that?We are given that each tank holds 22.5 cubic yard of fuel, the weight of 1 yd³ (cubic yard) of fuel is equal to .74 tons, and each container holds 7.4 tons of fuel. Solving this problem would involve converting units.
In order to find out how many containers of the size are needed to hold all the fuel from 12 tanks, first we need to find how much fuel is delivered by 12 tanks. Since 12 x 22.5 = 270, 12 tanks are used to deliver 270 yd³ of fuel.
Next we convert it to tons. Recall that 1 yd³ of fuel is equal to .74 tons. Therefore, 270 yd³ = 270 x .74 = 199.8 tons.
A container holds 7.4 tons of fuel. 199.8 ÷ 7.4 = 27, hence 27 containers are needed to hold all the fuel.
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The linear functions f(x) and g(x) are represented on the graph, where g(x) is a transformation of f(x): Part A: Describe two types of transformations that can be used to transform f(x) to g(x). (Choose from: shift up, shift down, shift right, shift left). Part B: Solve for k in each type of transformation. (This means tell me how many units you are shifting for each transformation you picked in part A). Part C: Write an equation for each type of transformation that can be used to transform f(x) to g(x). (This would be f(x) + k, f(x) - k, f(x -k), or f(x+k) but replace k with the values from part B).
A. The translations used in the transformation of f(x) to g(x) can be given as follows:
Left 6 units.Up 18 units.B. The solutions for k are given as follows:
Left 6 units: k = 6.Up 18 units: k = 18.C. The rules are given as follows:
Left 6 units: g(x) = f(x + 6).Up 18 units: g(x) = f(x) + 18.What are the translations to an image?There are four cases for the translation of an image, and they can be represented as follows:
Translation left a units: f(x + a).Translation right a units: f(x - a).Translation up a units: f(x) + a.Translation down a units: f(x) - a.From the graph of the linear functions shown at the end of the answer, two translations are possible, listed as follows:
Left 6 units: As the x-intercept of g(x) is of -6 and the x-intercept of f(x) is of x = 0.Up 18 units, as the y-intercept of g(x) is of 17 and of f(x) is of -1, 17 - (-1) = 18.The values of k are equivalent to the values of a in the bullet points listing the translations above, and the equations were also built from those bullet points.
Missing InformationThe lines are shown by the image at the end of the answer.
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if f(x) = 2x - 4 find f(3x)
Answer: the answer would be 2
Step-by-step explanation: f(x) means that for every x you are going to multiply it by the value it gives you in this case it is 3.
2x3=6-4=2
need help on this !!!!!!!!!!!
Using the Triangle Inequality Theorem we can state that the range of z is 4 < z < 20.
What is the Triangle Inequality Theorem?The above theorem states that The length of any two sides of a triangle must sum to more than the length of the third side. That is:
12 + 8 > z.............1
12 + z > 8;.............2
8 + z > 12.............3
Solving for (1)
20 > z...............4
Solving for (2)
we have- 12 + z > 8
remove 8 from both sides and we have
4 + z > 0 or z > -4 ...............5
Solving for (3) we have
8 + z > 12
remove 8 from both sides
z > 4 .....................6
Since we can't have a negative value on a triangle, we must deal with expressions 4 and 6 which state:
20 > z; and
z > 4
Another way to write this is:
20 > z > 4; or
4 < z < 20
Hence the range of the unknown side that will form a triangle is:
4 < z < 20
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Write an absolute value equation representing all numbers x whose distance 7 is 3 units
Answer:
|x-7|=3
Step-by-step explanation:
x is 3 units away from 7
x-3=7
x-7=3
x+3=7
3=7-x
|x-7|=3
Which inequality has like variable terms on each side of the inequality symbol?
Inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
As given in the question,
Inequality which have like variables term on each side of the given inequality symbol is :
a. 15c + 25 ≤ 115
In the given inequality, on left hand side we have variable c and constant term while on the right hand side of the inequality only constant.
Not correct option.
b. 0.75r - 6.25 > 10
In the given inequality, on left hand side we have variable r and constant term while on the right hand side of the inequality only constant.
Not correct option.
c. 16 - 2x > x + 16
In the given inequality, on left hand side we have variable x and constant term while on the right hand side of the inequality also variable x and constant term.
Correct option.
d. 12.25h -175 < 5,000
In the given inequality, on left hand side we have variable h and constant term while on the right hand side of the inequality only constant.
Not correct option.
Therefore, inequality which have like variables term on each side of the given inequality symbol is given by 16 - 2x > x + 16.
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The toy store created a display of s shelves of remote control cars. Each shelf contains 16 cars. Write an expression that shows how many cars are on the display.
The expression that shows number of remote control cars on the display self is 16s.
Mathematical expressions are formed using at least two numbers, variables, and there must be one arithmetic operation, and a statement. If there are x items are given in one self and there are n number of self and we have to find total number of items in all self, then we have to multiply x by n.
Here, there are 16 remote control cars on a display self. The number of display shelves is s.
So, the total number of cars will be 16 times of s.
Number of cars on display = 16s
Therefore, the expression that shows the number of cars on display is 16s.
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Answer:
It is 16s
Step-by-step explanation:
Use the distributive property to remove the parentheses.
3c³(7c8 +8c+7)
Simplify your answer as much as possible.
Answer: 21 c^16 + 24c^9+ 21 c^8
Step-by-step explanation: To multiply exponents with the same base, add them.
Answer:
3c^3(7c^8+8c+7)
=(3c^3)(7c^8+8c+7)
=(3c^3)(7c^8)+(3c^3)(8c)+(3c^3)(7)
=21c^11 + 24c^4 + 21c^3
Step-by-step explanation:
Remember.... ^ is for power
Ahmad decided to increase his homework time of 8 hours per week by 15%,
Calculate his new homework time.
Give your answer in hours and minutes.
Answer:
it's a answer done bro
A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100shares at 50 per share was $33. 77 (AAII Journal, February 2006). The survey is conducted annually. With the historical data available, assume a known population standard deviation of $15.
a. Using the sample data, what is the margin of error associated with a 95% confidence interval?
b. Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share
a) The margin of error associated with a 95% confidence interval is 4.
b) The 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
a) We are given with the information that the mean for 54 discount brokers is $50 for 100 shares is $33.77 Also the population standard deviation is $15.
The formula for margin of error is Z = zα/2 σ √ n
Now we know from our z-table that value of zα/2 for 95% confidence interval is 1.96
So, the value of error margin is zα/2 σ √ n =1.96 (15/√54) = 1.96 x 2.04
= 4
b) We know from part a that margin of error is 4.
Also, the mean price charged for a trade of 100shares at 50 per share was $33. 77
The value of confidence interval for population mean is,
x ± zα/2 σ √ n = 33.77 ± 4 = (29.77,37.77)
Thus, the 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share is ($29.77,$37.77)
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a box contains tiles. each tile has certain properties: each tile is made of wood or plastic. each tile is red, yellow, or blue. each tile is a triangle, square, pentagon, or circle. there is exactly one tile for each combination of properties. for example, there is one red circle that is made of wood. steve chooses one tile, and ellen chooses a different tile. what is the probability that the two chosen tiles differ with respect to all three properties?
1/24 is the probability that the two chosen tiles differ with respect to all three properties
1/2 chance that the tiles materials will be different (wood or plastic). 1/3 chance exists that the tiles will have different colors (r, y or b) 1/4 chance where the tile shapes will change (t, s, p or c)the probability that all three attributes of the two tiles will be different.1/2 * 1/3 * 1/4 = 1/24 The probability of an event occurring is a measure of its likelihood. It assesses the likelihood of an event. P(E) = Number of Favourable Outcomes/Total Outcomes is the probability formula.
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help for the rest pls
Answer :
9 girls and 18 boys don't have a voucher
Step-by-step explanation :
There are 38 boys and 22 girls. The total number of children is 60. We know that 33 children have a voucher. 27 children don't have a voucher. ( 60 - 33 = 27 ) .
"Twice as many boys as girls do not have a voucher."
We can now make an equation.
The girls who do not have a voucher will be x, boys who don't have a voucher will be 2x, since it says twice as many boys.
We can now make our equation.
x + 2x = 27
Add x and 2x
3x = 27
Divide both sides by 3
x = 9
We know now that girls who don't have a voucher is 9.
The boys who don't have a voucher is 2x, so we plug 9 instead of x.
2(9) = 18.
18 boys do not have a voucher.
If you would like the rest for the frequency tree...
Total students : 60
Boys : 38
Boys who don't have a voucher : 18
Boys who have a voucher : 20
Girls : 22
Girls who don't have a voucher : 9
Girls who have a voucher : 13
Hope this helped.
Este gráfico circular resume las especializaciones de los 450 miembros de una sororidad universitaria. El ángulo central el sector correspondiente a la especialización de ingeniería mide 50.4°. ¿Qué porcentaje de los miembros de la sororidad se especializan en ingeniería? No redondear.
Los miembros de la sororidad tiene un porcentaje de 14 % de estudiantes procedentes de la especialización de ingeniería.
¿Cuál es el porcentaje de estudiantes de la sororidad que pertenecen a la especialización de ingeniería?
El enunciado describe las características de un diagrama circula, en donde el 100 % de los miembros de la sororidad representan a los 360° del ángulo central del círculo, esto es, una revolución completa del círculo.
El porcentaje de los miembros que se especializan en ingeniería mediante la siguiente fórmula:
e = (E / 360°) × 100 %
Donde E es el ángulo asociado a la cantidad de estudiantes de la especialización de ingeniería, en grados sexagesimales.
e = (50.4° / 360°) × 100 %
e = 14 %
Los estudiantes que especializan en ingeniería corresponden a un porcentaje de 14 % de los miembros de la sororidad.
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Which of the following would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years? Question content area bottom Part 1 Select all that apply. A. $80 at 75% for 18 months B. $200 at 5% for 8 years C. $225 at 10% for 4 years D. $300 at 2% for 2 years E. $250 at 10% for 2 years
The option that would earn the same amount of interest as a $600 principal with 2.5% interest for 6 years include:
A. $80 at 75% for 18 months
C. $225 at 10% for 4 years
How to calculate the interest?It's important to note that the simple interest can be calculated thus:
= Principal × Rate × Time
Therefore, the amount of interest as a $600 principal with 2.5% interest for 6 years will be:
= PRT
= (600 × 0.025 × 6)
= $90
The interest on $80 at 75% for 18 months will be:
= $80 × 0.75 × 1.5
= $90
The interest on $225 at 10% for 4 years will be:
= $225 × 0.1 × 4
= $90
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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equation that can be used to find the price of one tire patch is 22.20 - 4x = 1.90 and 4x + 1.90 = 22.20
What is an equation?An equation is an expression showing the relationship between two or more numbers and variables.
Rhyan paid using a gift card that had $22.20 on it.
Let x represent the cost of each tire patch needed for the mountain biking trip. Rhyan bought four tire patches and had $1.90 remaining. Hence:
22.20 - 4x = 1.90
4x + 1.90 = 22.20
The equation is 22.20 - 4x = 1.90
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i will literally do ANYTHING for doordash mcdonalds literally Anything for 20 dollars
Answer: Nice
Step-by-step explanation:
If the area of the rectangle is 42 square units, what is the area of the shaded part?
Answer: 16
Step-by-step explanation:
The first triangle has an area of [tex]\frac{1}{2}(7)(2)=7[/tex].
The second triangle has an area of [tex]\frac{1}{2}(6)(3)=9[/tex].
Adding these areas together yields an area of 16.
