Answer:
Freedom is any case,
is only possible
by constantly
struggling for it.
Albert Einstein
jim buys a calculator that is marked 30% off. If he paid $35, what was the original price?
Answer:
x = 50
Step-by-step explanation:
Let x be the original price.
He got 30% off
The discount is .30x
Subtract this from the original price to get the price he paid
x - .30x = price he paid
.70x = price he paid
.70x = 35
Divide each side by .7
.70x/.7 = 35/.7
x=50
A daycare facility is enclosing a rectangular area along the side of their building for the children to play outdoors. They need to maximize the area using 180ft of fencing on three sides of the yard. The quadratic equation A=−2x2+180x gives the area, A, of the yard for the length, x, of the building that will border the yard. Find the length of the building that should border the yard to maximize the area, and then find the maximum area.
Answer:
a) length x = 45ftb) maximum area = 4050 ft²Step-by-step explanation:
Given the quadratic equation A=−2x2+180x that gives the area A of the yard for the length x, to maximize the area of the yard then dA/dx must be equal to zero i.e dA/dx = 0
If A=−2x²+180x
dA/dx = -4x + 180 = 0
-4x + 180 = 0
Add 4x to both sides
-4x + 180 + 4x = 0 + 4x
180 = 4x
x = 180/4
x = 45
Hence the length of the building that should border the yard to maximize the area is 45 ft
To find the maximum area, we will substitute x = 45 into the modelled equation of the area i.e A=−2x²+180x
A = -2(45)²+180(45)
A = -2(2025)+8100
A = -4050 + 8100
A = 4050 ft²
Hence the maximum area of the yard is equal to 4050 ft²
A man gave his 8000$ as pocket money and his son 1000$ less.Express the girls money as a percentage of the total sum of money.
Answer:
About 89%
Step-by-step explanation:
8000 + 1000 = 9000.
To find the girls money as a percentage of the total sum of money, you must take 8000 and divide it by 9000.
8000/9000 = .8888 = 88.88 = 88.9% or about 89%.
Please answer question now
Answer:
90
Step-by-step explanation:
Tangents drawn to a circle from an external point are equal, thus
IH = IJ = 7
ON = OH = 19 - 7 = 12
MN = ML = 26 - 7 = 19
Summing the 4 sides for perimeter (P)
P = 26 + 19 + 7 + 7 + 12 + 19 = 90
Which recrusive formula can be used to generate the sequence shown, where f(1)=5 and n>=1 5,-1,-7,-13,-19
Answer:
a_n = 11 - 6n
Step-by-step explanation:
you can observe every next element is smaller then the previous one by 6
a_n = 5 - 6*(n-1)
a_n = 5 - 6n + 6
a_n = 11 - 6n
Matrix multiplication is not commutative. Why?
Answer:
For matrix multiplication to work, the columns of the second matrix have to have the same number of entries as do the rows of the first matrix. ... In particular, matrix multiplication is not "commutative"; you cannot switch the order of the factors and expect to end up with the same result.
"All the religions are equal,the difference is their name ".Justify.
Complete the square.
3x^2-12x=96
Answer:
x = 8 and -4
Step-by-step explanation:
3x² - 12x = 96
3(x² - 4x + 4 = 32 + 4)
3[(x - 2)² = 6²]
x - 2 = +/- 6
x = 8
x = -4
Answer the question below. Type your response in the space provided. Then compare your answer to the sample answer.
Point B(-2,4) lies on a circle centered at A(1, 3). Write a paragraph proof to determine whether C(4, 2) also lies on the circle.
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Characters used: 0/15000
Submit
Answer: see proof below
Step-by-step explanation:
The standard equation of a circle is (x - h)² + (y - k)² = r² where (h. k) is the center of the circle and r is the radius. It is given that A (h, k) = (1, 3) and point B (x, y) = (-2,4) is on the circle. Substitute the center (h, k) and point B(x, y) = (-2,4) into the standard equation of a circle to get r² = 10. To prove that C(x, y) = (4, 2) is also a point on the circle, substitute the center (h, k) and the point C(x, y) = (4, 2) into the standard equation of a circle to get r² = 10. Since the radius is the same for both point B and point C and it is given that point B is on the circle, then we must conclude that point C is also on the circle.
Answer:
I am given that the center of a circle is at A(1, 3) and that point B(-2, 4) lies on the circle. Applying the distance formula to A and B, I get the following:
AB=Square Root ( (-2 - 1 )^2 + (4 - 3 )^2 ) = Square root ( 9 + 1 )
AB = Square root (10)
Since B lies on the circle, this length is the length of the radius of the circle. Applying the distance formula to A and C(4, 2), I get the following:
AC = Square Root ( ( 4 - 1 )^2 + (2 - 3 )^2 ) = Square root ( 9 + 1 )
AC = Square root (10)
Thus, the distance to C from the center A is equal to the length of the radius of the circle. Any point whose distance from the center is equal to the length of the radius lies on the circle. Therefore, point C lies on the circle.
Step-by-step explanation:
What is the area of triangle BCD to the nearest tenth of a square centimeter? Use special right triangles to
help find the height. Show your work.
Answer:
21.7 cm²
Step-by-step explanation:
Given:
Right ∆BCD,
<D = 60°
adjacent length = 5 cm
Required:
Area of ∆BCD
SOLUTION:
Step 1: find the height (opposite side length) of ∆BCD
[tex] tan(D) = \frac{opp}{adj} [/tex]
[tex] tan(60) = \frac{h}{5} [/tex]
Multiply both sides by 5
[tex] tan(60)*5 = \frac{h}{5}*5 [/tex]
[tex] tan(60)*5 = 8.7 cm [/tex] (approximated)
Step 2: find the area of ∆BCD
Area = ½*base*height
Area = ½*5*8.7 = 21.7 cm² (nearest tenth)
how do you find the surface area of this triangular prism?
To find the area of a triangular prism you have to do A 1/2 bh or A bh/2 which means you have to multiply those two fractions and reduce them
Answer:
Find the area of the 2 triangle faces first and then find the area of the 3 rectangle faces and add them together to get [tex]159cm^{2}\\[/tex]
Step-by-step explanation:Step 1: Find the surface area of the 2 triangles
[tex]\frac{(6)(5.5)}{2}[/tex] x2 = [tex]33cm^2\\[/tex]
Step 2: Find the surface area of the 3 rectangles
(6x7) x 3 = [tex]126cm^2[/tex]
Step 3: Add the 2 surface areas together
[tex]33cm^2\\[/tex] + [tex]126cm^2[/tex] = [tex]159cm^2[/tex]
Therefore the surface area of the prism is [tex]159cm^{2}[/tex]
Which expressions are equivalent to -3(2w+6)-4−3(2w+6)−4minus, 3, left parenthesis, 2, w, plus, 6, right parenthesis, minus, 4 ? Choose all answers that apply: Choose all answers that apply: (Choice A) A 6w-146w−146, w, minus, 14 (Choice B) B 2(-3w+(-11))2(−3w+(−11))2, left parenthesis, minus, 3, w, plus, left parenthesis, minus, 11, right parenthesis, right parenthesis (Choice C) C None of the above
Answer:
B. 2{-3w+(-11)}Step-by-step explanation:
Given the expression, -3(2w+6)-4, we are to look for an equivalent expression for the equation.This is as shown:
Step 1: Open the parenthesis
= -3(2w+6)-4
= -3(2w)-3(6)-4
= -6w-18-4
Step 2: Simplify the resulting expression in step 1
= -6w-18-4
= -6w - 22
Step 3: factor out the common values from each term. Since the common value is 2, on factoring we will have;
2{-3w+(-11)}
Hence the equivalent expression is 2{-3w+(-11)}
Answer:
a and b
Step-by-step explanation:
no.
The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}
This Question is incomplete
Complete Question:
The data represents the number of runs allowed by 8 college softball pitchers. {18, 49, 38, 41, 33, 44, 42, 22}
What is the five number summary:
a) Minimum
b) Q₁
c) Median
d) Q₃
e) Maximum
Answer:
a) Minimum = 18
b) Q₁ = 27.5
c) Median = 39.5
d) Q₃ = 43
e) Maximum = 49
Step-by-step explanation:
From the above diagram, we were given the following set of data.
{18, 49, 38, 41, 33, 44, 42, 22}
Before answering any of the questions, we have to rearrange the data from the lowest to the highest (ascending order). Hence, we have:
{18, 22, 33, 38, 41, 42, 44, 49}
a) Minimum
{18, 22, 33, 38, 41, 42, 44, 49}
Looking at this set of arranged data, the minimum number is the least or lowest number.
This number is 18
b) Q₁
{18, 22, 33, 38, 41, 42, 44, 49}
Q₁ means First Quartile. The formula is = ¼(n + 1)th value
n = Number of terms in the data set = 8
= ¼(8 + 1)th value
= ¼(9)th value
= 2 1/4 value
= 2.25 value
In the above Question, the 2.25 value is the value between the second and third number.
Hence:
22+33/2 = 55/2 = 27.5
Therefore, Q₁ = 27.5
c) Median
{18, 22, 33, 38, 41, 42, 44, 49}
The median of the number is the number in the middle
For this data, we have 8 number, Hence the median is the sum of the 4th and 5th term divided by 2
4th term = 38
5th term = 41
= 38 + 41/ 2 = 79/2
= 39.5
Hence, the median = 39.5
d) Q₃
{18, 22, 33, 38, 41, 42, 44, 49}
Q₃ means Third Quartile. The formula is = ¾(n + 1)th value
n = Number of terms in the data set = 8
= ¾(8 + 1)th value
= ¾(9)th value
= 6 3/4 value
= 6.75 value
In the above Question, the 6.75 value is the value between the sixth and seventh number.
Hence:
42+44/2 = 86/2 = 43
Therefore, Q₃ = 43
e) Maximum
{18, 22, 33, 38, 41, 42, 44, 49}
Looking at this set of arranged data, the Maximum number is the highest number.
This number is 49
Half the marbles in a bag are red, 1/6 of the marbles are blue, and the remaining 8 marbles are white how many total marbles are in the bag
Hey there! I'm happy to help!
Let's represent the total number of marbles with the variable t. We have the following information.
1/2t+1/6t+8=t (1/2 of total are red, 1/6 of total are blue, 8 are white, add them up to get total)
Now, we solve for t.
1/2t+1/6t+8=t
We combine like terms.
2/3t+8=t
We subtract t from both sides.
-1/3t+8=0
We subtract 8 from both sides.
-1/3t=-8
We divide both sides by -1/3.
t=24
Therefore, there ae 24 total marbles in the bag.
Have a wonderful day! :D
The total number of marbles will be 7/2.
What is Addition?
A process of combining two or more numbers is called addition.
Given that;
Half the marbles in a bag are red, 1/6 of the marbles are blue, and the remaining 8 marbles are white.
Now,
Since, Half the marbles in a bag are red, 1/6 of the marbles are blue, and the remaining 8 marbles are white.
Hence, Total number of marbles = 1/2 + 1/6 + 8
= 8 / 12 + 8
= 4 / 3 + 8
= 28/8
= 7/2
Thus, The total number of marbles will be 7/2.
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The area of a trapezium is 31.5 cm². If the parallel sides are of length 7.5 cm and 5.3 cm, calculate the perpendicular distance between them
Answer:
The answer is 4.9cmStep-by-step explanation:
To find the perpendicular distance between them that's the height we use the formula
[tex]Area \: \: of \: \: a \: \: trapezium = \frac{1}{2} (a + b) \times h[/tex]
where
a and b are the parallel sides of the trapezium
h is the perpendicular distance
From the question
Area = 31.5cm²
a = 7.5 cm
b = 5.3 cm
Substituting the values into the above formula we have
[tex]31 .5 = \frac{1}{2} (7.5 + 5.3) \times h[/tex]
[tex]31.5 = \frac{1}{2} \times 12.8h[/tex]
[tex]31.5 = 6.4h[/tex]
Divide both sides by 6.4
[tex]h = \frac{31.5}{6.4} [/tex]
h = 4.921875
We have the final answer
h = 4.9cmHope this helps you
Solve 8
Gisele has $5.90 in quarters and nickels. If Gisele has 16 more nickels than quarters, how many quarters does she have? [I don't want the answer I just want to know how to set the problem up please]
Answer:
See below
Step-by-step explanation:
Quarters= 25(x)
Nickels =5(x+16)
25x+5(x+16)=590 (no decimal)
If you solve for x, you’ll get the number of quarters.
The following expression is a polynomial: 4x + 5y True False
Answer: False. This expression is a monomial!
Answer:
false
Step-by-step explanation:
it is molonomial
Which of the following functions is neither even nor odd? A. f(x)=x6−3x4−4x2 B. f(x)=2x3−3x2−4x+4 C. f(x)=x5−2x3−3x D. f(x)=6x5−x3
even function : [tex] f(x)=f(-x)[/tex] , odd function: $f(x)=-f(-x)$
it is neither odd nor event when both condition don't hold.
See option B.
$f(x)=2x^3-3x^2-4x+4$
$f(-x)=-2x^3-3x^2+4x+4=-(2x^3+3x^2-4x-4)$
clearly, it is neither odd nor even.
Becky is buying fabric to make new pillows for her couch. She spends $71.50 on striped fabric and $52.25 on checkered fabric. If both fabrics cost $5.50 per yard, how many total yards of fabric does she buy?
Answer:
22.5
Step-by-step explanation:
im smart
Beaky bought 13 yards of striped fabric and 9.5 yards of checkered fabric.
Given that,
Becky is buying fabric to make new pillows for her couch. She spends $71.50 on striped fabric and $52.25 on checkered fabric.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
Both fabrics cost $5.50 per yard, how many total yards of fabric she buys is to be determined so,
Divide the total cost of the fabric by the cost per yard of $5.50,
Striped fabric = 71.50 / 5.50 = 13 yards
checkered fabric = 52.25/71.50 = 9.5 yards
Thus, beaky bought 13 yards of striped fabric and 9.5 yards of checkered fabric.
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8) There are 2116 students in a school .In how many equal rows and columns can they be arranged for a drill display?
Answer:
46
Explanation:
root of 2116
=46×46
Therefore 46 columns and 46 rows
Answer:
46 rows, 46 columns.
Step-by-step explanation:
First factor 2116:
2) 2116
2 } 2058
23 ) 529
23
2116 = 2*2*23*23
= 46 * 46
Dos secretarias deben escribir el mismo número de cartas. La primera escribe 2 cartas por hora y la otra, 5 cartas por hora. Si la primera ha empezado 6 horas antes que la segunda. ¿Cuántas horas
trabajó la primera?
Ayuden!!
Answer:
El número de horas que trabajó la primera secretaria es de 10 horas
Step-by-step explanation:
Los parámetros dados son;
El número de letras que la primera secretaria puede escribir por hora = 2 letras
El número de letras que el segundo secretario puede escribir por hora = 5 letras
Dado que la primera secretaria comenzó 6 horas antes que la segunda secretaria, tenemos;
Sea el tiempo en horas en que ambas secretarias habrán escrito el mismo número de letras = [tex]t_e[/tex]
2 × [tex]t_e[/tex] + 2 × 6 = 5 × [tex]t_e[/tex]
2 × [tex]t_e[/tex] + 12 = 5 × [tex]t_e[/tex]
12 = 5 × [tex]t_e[/tex] - 2 × [tex]t_e[/tex] = 3 × [tex]t_e[/tex]
12 = 3 × [tex]t_e[/tex]
3 × [tex]t_e[/tex] = 12
[tex]t_e[/tex] = 12/3 = 4 horas
El número de horas que trabajó la primera secretaria = Tiempo de inicio anticipado + Tiempo que le toma a la segunda secretaria que comenzó 6 horas más tarde y a la primera secretaria que había estado escribiendo durante 6 horas (inicio anticipado) escribir la misma cantidad de cartas
El número de horas que trabajó la primera secretaria = 6 + 4 = 10 horas.
Por lo tanto, el número de horas que trabajó la primera secretaria = 10 horas.
At a potluck, Agatha brings four dishes, Bertha brings three dishes, and five other friends bring no dishes but instead money to help pay for the food. If all the dishes are eaten up, and everyone eats the same amount, what fraction of the money should go to Bertha?
Answer:
3/7
Step-by-step explanation:
Agatha brings four dishes, Bertha brings three dishes. The total number of dishes brought = dishes brought by Agatha + dishes brought by Bertha.
Total dishes = 4 + 3 = 7 dishes
The remaining five friends brought money for the dishes. Therefore the fraction of money going to Bertha is the ratio of dishes brought to Bertha to the total number of dishes multiplied by the money. Therefore:
Fraction of the money should go to Bertha = dishes brought by Bertha/total dishes
Fraction of the money should go to Bertha = 3/7 × money
what is the correct symbol?
Answer:
Since 10/9 is greater than 1, multiplying by 10/9 makes the value larger
Step-by-step explanation:
Step 1: Solve the fraction
10/9 = 1.1112
Therefore 10/9 > 1
Step 2: Multiple the fraction by itself
10/9 x 10/9 = 100/81
Convert fraction to decimals
100/81 = 1.2345678901.....
1.234567901 > 1.1112
Therefore 10/9 x 10/9 is bigger than 10/9
how many are 8 raised to 2 ???
Answer:
The correct answer would be 64 because 8 times 8 would be 64 therefore the answer is 64
Step-by-step explanation:
ast week, the Vargas family drove 30 miles in their car and 15 miles in their truck. The letter m stands for the total number of miles they drove. Which equation can you use to find m?
Answer:
m = 30 + 15
Step-by-step explanation:
The distance traveled by the Vargas family in their car is 30 miles while the distance traveled when using their truck is 15 miles. To get the total distance traveled, we need to add the distance traveled by the truck and the distance traveled by the car. Since m stands for the total number of miles they drove, the equation needed to find the total distance traveled (m) is given as:
m = 30 + 15
m = 45 miles
1 point
Which point represents -(-10) on the number
line?
E
B
C D
-1 0 1 2 3 4 5 6 7 8 9 10
Answer:
E is the answer because the two negative becomes positive
Fogoh!! Plz HELPi suck at math haha
Answer:
f(g(h(x))) = (sqrt(x) - 1)^4 + 4
Step-by-step explanation:
f(x) = x^4 + 4
g(x) = x - 1
h(x) = sqrt(x)
g(h(x)) = sqrt(x) - 1
f(g(h(x))) = (sqrt(x) - 1)^4 + 4
sandra is playing a trivia game.on her first turn she lost 75 points. on her second turn,she lost 35 points. on her third turn,she scored 100 points. What is sandras score after three turns?
Answer: -10 points
Step-by-step explanation:
She lost 110,so that loss -the gain(100) is the total score at the end of three games
I need 51-55 Thanks You :D no
Answer:
Below
Step-by-step explanation:
All figures are squares. The area of a square is the side times itself
Let A be the area of the big square and A' the area of the small one in all the 5 exercices
51)
● (a) = A - A'
A = c^2 and A' = d^2
● (a) = c^2 - d^2
We can express this expression as a product.
● (b) = (c-d) (c+d)
■■■■■■■■■■■■■■■■■■■■■■■■■■
52)
● (a) = A-A'
A = (2x)^2 = 4x^2 and A'= y^2
● (a) = 4x^2 - y^2
● (b) = (2x-y) ( 2x+y)
■■■■■■■■■■■■■■■■■■■■■■■■■■
53)
● (a) = A-A'
A = x^2 and A' = y^2
● (a) = x^2-y^2
● (b) = (x+y) (x-y)
■■■■■■■■■■■■■■■■■■■■■■■■■■
54)
● (a) = A-A'
A = (5a)^2 = 25a^2 and A' =(2b)^2= 4b^2
● (a) = 25a^2 - 4b^2
● (a) = (5a-2b) (5a+2b)
■■■■■■■■■■■■■■■■■■■■■■■■■■
55)
● (a) = A - 4A'
A = (3x)^2 = 9x^2 and A'= (2y)^2 = 4y^2
● (a) = 9x^2 - 4 × 4y^2
● (a) = 9x^2 - 16y^2
● (a) = (3x - 4y) (3x + 4y)
