Answer:
The length of the rectangle = 20
The width of the rectangle = 8
Step-by-step explanation:
Step(l):-
let 'W' be the width of the rectangle
Given the length of a rectangle is 4 more than 2 times its width
length of a rectangle(L) = 4+2W
Given the Area of rectangle = 160
Step(ii):-
we know that the area of the triangle = length ×width
(4+2w)w= 160
[tex]2w^{2} +4w-160=0[/tex]
[tex]2(w^{2} +2w- 80)=0[/tex]
[tex]w^{2} +10w-8w- 80=0[/tex]
[tex]w(w +10)-8(w+10)=0[/tex]
[tex](w+10)(w-8) =0[/tex]
[tex]w+10=0 , w-8=0[/tex]
w = -10 and w =8
Step(lll)
we can choose the width is 'w' = 8
now the length of the rectangle = 4+2(8) = 20
The width of the rectangle is '8'
Conclusion:-
The length of the rectangle = 20
The width of the rectangle = 8
what is the standard form of y=6(x-3)²-2
Answer:
B
Step-by-step explanation:
y = 6(x^2-6x+9)-2
y = 6x^2-36x+54-2
y = 6x^2-36x+52
The standard form of the given quadratic equation y=6(x-3)²-2 is y = 6x² - 36x + 52 after expanding the squared binomial and simplifying.
Explanation:The student has asked for the standard form of the quadratic equation y=6(x-3)²-2. The standard form of a quadratic equation is ax² + bx + c = 0. To rewrite the given equation in standard form, expand the squared binomial and simplify:
Expand the binomial: y = 6(x² - 6x + 9) - 2.Distribute the 6: y = 6x² - 36x + 54 - 2.Simplify the constants: y = 6x² - 36x + 52.So, the standard form of the given equation is y = 6x² - 36x + 52.
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The common ratio in a geometric series is 4 and the first term is 3.
Find the sum of the first 8 terms in the series.
Show Calculator
Answer:
The sum of the first 8 terms in the series is 65535.
Step-by-step explanation:
We have,
The common ratio in a geometric series, r = 4
First term of GP is, a = 3
It is required to find the sum of the first 8 terms in the series. The sum of first n terms of a GP is given by :
[tex]S_n=\dfrac{a(r^n-1)}{r-1}, r>1[/tex]
Here, n = 8
[tex]S_8=\dfrac{3\times ((4)^8-1)}{4-1}\\\\S_8=65535[/tex]
So, the sum of the first 8 terms in the series is 65535.
Simplify -3xy 3 + 7xy 3 + (-xy 3) + (-3xy 3
(−3x)(y3)+7xy3+(−x)(y3)+(−3x)(y3) = 0
Pleaseeeeeeee help me
Answer:
x = 24
Step-by-step explanation:
10:8
10(3) = x(3)
x = 8
30 : 24
¿Cuántas personas encuestadas se comunican más de 77 minutos?
AYUDA POR FAVOR ES DE APRENDO EN CASA
Respuesta:
se comunican 27 personas 9 +14+4=27 personas
Explicación paso a paso:
para resolver vean los datos en la tabla de frecuencia que van a desarrollar
observamos el intervalo [77; 81[ a partir de el determinamos la cantidad de personas que se comunican 77 minutos o mas minutos
In order to answer the following question, please use the following image down below:
Find the value of x.
X=(Blank)
What is the value of X? Please show all the work on how you got your answer.
(If you can't explain your work, then it's fine. The only thing that I'm asking for is for you to show the work alongside your answer)
Answer:
23
Step-by-step explanation:
(x-3)(9) = (10)(18)
9x - 27 = 180
9x = 207
x = 23
Evaluate the following:
ln ex + 1
A) x-2
B) y+1
C) x+1
Pls help, I don't understand this :(
Answer:
I believe the answer is C, x+1 :)
Use technology or a z-score table to answer the question.
The number of baby carrots in a bag is normally distributed with a mean of 94 carrots and a standard deviation of 8.2 carrots.
Approximately what percent of the bags of baby carrots have between 90 and 100 carrots?
Answer: 46%
Step-by-step explanation:
Since the number of baby carrots in a bag is normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the number of baby carrots in the bag.
µ = mean
σ = standard deviation
From the information given,
µ = 94 carrots
σ = 8.2 carrots
The probability that a bag of baby carrots have between 90 and 100 carrots is expressed as
P(90 ≤ x ≤ 100)
For x = 90,
z = (90 - 94)/8.2 = - 0.49
Looking at the normal distribution table, the probability corresponding to the z score is 0.31
For x = 100,
z = (100 - 94)/8.2 = 0.73
Looking at the normal distribution table, the probability corresponding to the z score is 0.77
Therefore,
P(90 ≤ x ≤ 100) = 0.77 - 0.31 = 0.46
The percent of the bags of baby carrots that have between 90 and 100 carrots is
0.46 × 100 = 46%
3. Given that (5,12, 13) is a Pythagorean triple, which of the following isn't a Pythagorcan
triple?
(1) (10, 24, 26)
(3) (50,120,130)
(2) (10, 17, 18)
(4) (15, 36, 39)
Answer:
(2) (10,17,18)
Step-by-step explanation:
Answer:
2
Step-by-step explanation:
Well, let’s use a cancelling technique.
We know that 10, 24, 26 is just 5, 12, 13 multiplied by 2. So that works! And 50, 120, 130 is just 5, 12, 13 multiplied by 10. So that also works! And 15, 36, 39 is just 5, 12, 14 multiplied by 3. Therefore 2 is our answer...
The difference of a number and 8
Answer:8
Step-by-step explanation:
Only the ones that are circle. I NEED THEM QUICK PLEASE
Answer:
10
Step-by-step explanation:
183.35
Help asap please due tomorrow
Answer:
The first one is 15.75 lbs or 15 3/4. The second one is 28 years old. The third one is$9.90 each t-shirt
Step-by-step explanation:
For the first one you multiply 18 by 14 and you get 252. Then there is 16 ounces in a pound so you divide by 16. Then you get 15.75. So that is your answer. The 2nd one you take 84 and multiply it by 1/6 then since she is twice the age of her sister you multiply by 2. so it would look like: 84 times 1/6= 14
14 times 2 = 28. So she is 28 years old. The third one you take 32 and subtract it by 12.20. You will be left with 19.8. Then both t-shirts cost the same so you would divide 19.8 by 2. You are left with 9.9. So the answer is $9.90. Sorry this took 10 minutes.
Answer:
15.75lb of hotdogs
Amy is 28 years old
she paid $9.90 for each shirt.
Step-by-step explanation:
1) we multiply the number of packages by how much each package weighs. which gives us 252ounces we can then convert ounces to pounds by multiplying by 0.0625pounds/1ounce which gives us 15.75lb
2) amy's age is her fathers age devided by 6 which gives us fourteen. we know Hannah's age is twice Amy's age, so we multiply 14 by two, 14X2=28
3) we subtract the money Rose spent on the poster from the overall amount rose spent. $32.00-$12.20=$19.80. so we know Rose spent $19.80 on t-shirts, since we also know she bought two equaly priced t-shirts we can devide $19.80 by 2, $19.80/2=$9.90, therfore, she spent $9.90 on each shirt.
At barlow school 4/9 of the 873 students are boys at willow school 2/3 of the 630 students are girls which school has the greater number of boys and by how many
Answer:
There are 178 more boys in Barlow school as compared to Willow school.
Step-by-step explanation:
We are given the following in the question:
Barlow school:
Total number of students = 873
Number of boys =
[tex]=\dfrac{4}{9}\times 873 = 388[/tex]
Willow school:
Total number of students = 630
Number of girls =
[tex]=\dfrac{2}{3}\times 630 = 420[/tex]
Number of boys =
Total number of students - total number of girls
[tex]=630-420 = 210[/tex]
Thus, Barlow school has greater number of boys than Willow school.
Difference between the number of boys =
[tex]=388-210\\=178[/tex]
Thus, there are 178 more boys in Barlow school as compared to Willow school.
A group of students auditioned for a theater performance and 3/4 of the group less six students made up the cast of 42 students. Write an equation to represent the total number of students who auditioned, t.
Answer:
3/4x-6=42
x=64
Step-by-step explanation:
Let the number of students be x hence 3/4 of this number will be 3/4x
Since the number was 42 if they were 3/4x less six, it means minus six hence
3/4x-6=42
Therefore, the equation will be
3/4x-6=42
Solving the equation
3/4 x=42+6=48
3/4x=48
X=62
Find the value of this expression.
2(4+1)-3x6
A) -9
B) -8
C) 8
D) 36
E) 42
Answer:
B) -8
Step-by-step explanation:
2*5-18=10-18=-8
Answer:
B
Step-by-step explanation:
4+1 = 5
2*5 = 10
3*6 = 18
10-18=-8
Which function has an initial value of 0.2?
Group of answer choices
Function Three
Function Four
Function Two
Function One
PICTURE IS BELOW
Answer:
Function Four
Step-by-step explanation:
Put x=0 into each of the functions and see what you get.
1. 3
2. 2
3. 1
4. 0.2 . . . . function 4 is the one you want
5. 0
_____
Anything with an exponent of 0 has a value of 1. (except 0^0 is indeterminate)
There are 16 baseball games per day at Lansing's annual baseball tournament, which lasts 10 days. Estimate the number of baseball games during the tournament by rounding the larger number to the nearest ten.
To estimate the total number of games during the baseball tournament, round the daily games (16) to the nearest ten (20) and multiply by the number of days (10), resulting in an estimated 200 games.
To estimate the number of baseball games during Lansing's annual baseball tournament, we can round the larger number to the nearest ten and then multiply it by the number of days in the tournament. The larger number, representing the number of games per day, is 16. Rounding 16 to the nearest ten gives us 20. As the tournament lasts 10 days, we calculate the total by multiplying these two numbers.
Estimated total number of games = Rounded number of games per day x Number of days in the tournament
Estimated total number of games = 20 x 10
Estimated total number of games = 200 games.
If the zeros of a quadratic function are 3 and 8, what are the factors of the function?
Answer:
(x-3)(x-8)
Step-by-step explanation:
the zero are what cancel out the factors.
Answer:
(x-8) and (x - 3)
Step-by-step explanation:
Enjoy your day:)
A spinner travels around a circle. The radius is 3 inches. Mike spins the spinner and it travels completely around the circle 5 times. About how far did the tip of the spinner travel?
Answer:
The spinner travelled 94.2 inches.
Step-by-step explanation:
In order to solve this question we first need to calculate the length of the circle, that is given by the following formula:
length = 2*pi*r
length = 2*3.14*3 = 18.84 inches
Since the spinner revolved around the circle 5 times, the distance travelled by the tip is the length of the circle multiplied by 5, as shown below:
distance = length*5
distance = 18.84*5 = 94.2 inches
The spinner travelled 94.2 inches.
Answer:
94.2 inches.
Step-by-step explanation:
The length of the circle can be determined by
length 'l'= 2πr
l = 2 x 3.14 x 3 = 18.84 inches
As the spinner and it travels completely around the circle 5 times, therefore, we'll have the distance of
distance = l x 5
distance = 18.84 x 5 => 94.2 inches
Thus, the tip of the spinner traveled 94.2 inches.
Grace and her dad are planning to attend the state fair. An adult ticket is $15.00. The price of an adult ticket is one half the price of a student ticket plus $8.00. Write an equation to determine how much Grace will pay for a student ticket.
Answer:
(1/2)x + 8 = 15
Step-by-step explanation:
A _____________________________ has a constant change in the x values and a constant ratio in the y values.
A 'directly proportional' has a constant change in the x values and a constant ratio in the y values' is filled by the term .
A directly proportional relationship between two variables means that there is a constant change in the x values and a constant ratio in the y values. In mathematical terms, we say that y is directly proportional to x if y = kx, where k is known as the proportionality constant. This implies that for any constant increment in x, there will be a proportional constant change in y.
If we plot a graph of two variables that are directly proportional, the result is a straight line that passes through the origin (0, 0). This is because the ratio y/x remains constant at the value of k. The slope of this line represents the constant rate of change between y and x, and the slope is equal to the proportionality constant k.
Which statements about square roots are true? Check all that apply.
The square root of a positive number cannot be negative.
All positive numbers have two square roots.
18 = 9 because 9(2) = 18.
149 = 7 because 7(7) = 49.
25 = 5 because 52= 25.
The square root of a positive number cannot be negative, all positive numbers have two square roots, and 25 = 5 because 52 = 25.
Explanation:The statements that are true about square roots are:
The square root of a positive number cannot be negative.All positive numbers have two square roots.25 = 5 because 52 = 25.These statements are correct because the square root of a positive number will always be positive, every positive number has two square roots (one positive and one negative), and the square root of 25 is 5 because 5 multiplied by itself is equal to 25.
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I need help with transversals!’
Answer:
∠ TWV = 106°
Step-by-step explanation:
∠ TWV and ∠ SVW are same- side interior angles and are supplementary, thus
∠ TWV + ∠ SVW = 180°, that is
3x - 5 + 2x = 180
5x - 5 = 180 ( add 5 to both sides )
5x = 185 ( divide both sides by 5 )
x = 37
Thus
∠ TWV = 3x - 5 = 3(37) - 5 = 111 - 5 = 106°
subtract 7/9 from 4 / 9
Answer:
3/9
Step-by-step explanation:
You just substract the numerator :) So, 7-4= 3
What is the first step in solving the equation
x^2-16/25=0
What is the second step in solving the equation?
Answer:
First Step: separate x^2 from -16
Second Step: add -16/25 to the other side.
Step-by-step explanation:
x^2 - 16/25 = 0
^^ this might be easier if you separate x^2 and -16
First Step-
so rewrite the problem as x^2/25 -16/25 = 0
then...
Second Step-
add -16/25 to the other side. This makes it: x^2/25 = 16/25
Continuation-
Now, you can multiply 25 on both sides to cancel it out.
so you have x^2 = -16
Message me if you want to solve for x.
What does V= If V/13 =14
Answer:
182
Step-by-step explanation:
Reverse the problem,
13 x 14 = ?
13 x 14 is 182
182/13=14
I need help ASAP please (radical expressions)
Answer:
D
Step-by-step explanation:
Using the rule of radicals
[tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex] = [tex]\sqrt{\frac{a}{b} }[/tex]
Given
[tex]\frac{14\sqrt{14} }{7\sqrt{2} }[/tex] ← cancel 14 and 7
= 2 × [tex]\sqrt{\frac{14}{2} }[/tex]
= 2[tex]\sqrt{7}[/tex] → D
What is the slope of (2,4) and (6,7) ?
Answer:
(7-4)/(6-2)= 3/4
Step-by-step explanation:
Answer:
3/4
Step-by-step explanation:
Rise/ Run = (7-4)/(6-2) = 3/4
A square root of paper 150 millimeters on a side is folded in half along a diagonal. The result is a 45° -45° -90° triangle. What is the length of the hypotenuse of this triangle in millimeters? Write your answer in simplified radical form, if necessary.
Answer:
The length of the hypotenuse of this triangle is 150√2 mm.
Step-by-step explanation:
Consider the square ABCD shown in the image below.
The sides are 150 mm each.
All the angles of a square are 90°.
Now The square is folded in half along the diagonal BD.
The angles A, B and D are: 45°, 45° and 90°.
The hypotenuse of the right angled triangle is BD.
Compute the length of BD using the pythagoras theorem as follows:
[tex]BD^{2}=AB^{2}+AD^{2}\\=150^{2}+150^{2}\\=2\times 150^{2}\\BD=\sqrt{2\times 150^{2}}\\=150\sqrt{2}[/tex]
Thus, the length of the hypotenuse of this triangle is 150√2 mm.
A cylindrical drinking glass can hold 56.52 cubic inches of
water. The diameter of the glass is 3 in. How tall is the glass?
Use 3.14 for T.
A. 4 inches
B. 6 inches
CC. 7 inches
D. 8 inches
Answer:
The answer is
D. 8 inches
Step-by-step explanation:
This problem bothers on the mensuration of solid shapes, a cylinder this time.
Given data
Volume of cylindrical shape v=
56.52 inch³
Diameter of cylindrical glass d= 3
inch
But raduis r =diameter/2=3/2= 1.5
inch
We know that the the expression for the volume of a cylinder is given as
v= πr²h
Substituting our given data to solve for the height h
56.52= 3.14*(1.5)²*h
56.52= 7.065h
h= 56.52/7.065
h= 8 inches
To calculate the height of the cylindrical glass, use the volume formula with the radius from the diameter, and solve for the height. The final calculation shows that the glass is 8 inches tall, corresponding to option D.
Explanation:To find the height of a cylindrical drinking glass given its volume and diameter, we can use the formula for the volume of a cylinder: V = πr²h, where V is the volume, π (pi) is a constant approximated as 3.14, r is the radius of the cylinder, and h is the height of the cylinder.
Since the diameter is given as 3 inches, the radius r is half of that, which is 1.5 inches. By substituting the values into the formula and solving for h, we get:
V = πr²h
56.52 = 3.14 × (1.5)² × h
56.52 = 3.14 × 2.25 × h
56.52 = 7.065 × h
h = 56.52 / 7.065
h = 8 inches
Therefore, the height of the drinking glass is 8 inches, which corresponds to choice D.