Answer:
The scale is [tex]\frac{1}{60}[/tex]
Step-by-step explanation:
The correct question is
An artist is making a mural by reproducing a painting at a different scale. the original painting is 10 1/2 inches long and 4 inches wide. the mural will cover an entire wall that is 52.5 feet long and 20 feet wide. what will be the scale that relates to the original painting to the mural?
we know that
To find out the scale divide the measure of the original painting by the measure of the mural
so
Long
[tex]\frac{10.5}{52.5}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{10.5}{52.5*12}=\frac{10.5}{630}\ \frac{in}{in}=\frac{10.5}{630}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural
Verify the scale with the wide (both scale must be equals)
wide
[tex]\frac{4}{20}\ \frac{in}{ft}[/tex]
Remember that
[tex]1\ ft=12\ in[/tex]
Convert feet to inches
[tex]\frac{4}{20*12}=\frac{4}{240}\ \frac{in}{in}=\frac{4}{240}[/tex]
simplify
[tex]\frac{1}{60}[/tex]
That means ----> 1 unit in the original painting represent 60 units in the mural
Find
HCF of
(726, 255).
Good evening ,
Answer:
3Step-by-step explanation:
255 = 3×5×17
726 = 2×3×11^2
Then HCF(255,726) = 3.
:)
Find each unit cost rounded to the nearest cent. Then determine the better buy.
3 cans of corn for $1.68; 5 cans of corn for $2.45
Answers:
$5.04 per can; $12.25 per can; 3 cans for $1.68
$5.04 per can; $12.25 per can; 5 cans for $2.45
$.56 per can; $.49 per can; 3 cans for $1.68
$.56 per can; $.49 per can; 5 cans for $2.45
Answer:
$.56 per can; $.49 per can; 5 cans for $2.45
Step-by-step explanation:
If it were a dollar for two cans, it's pretty easy to figure out each can is 50 cents. So you use the same idea. if you have x cans for y dollars, if you divide both numbers by x you get the price of 1 can.
3 cans for 1.68 is 1 can for 1.68/3 = .56 so 56 cents
5 cans for 2.45 is 1 can for 2.45/5 = .49 so 49 cents.
You could use this trick dividing by the price and find how many cans you need to but to pay 1 dollar.
3 cans for 1.68 is 3/1.68 for 1 dollar or 1.786 cans for 1 dollar. Doesn't make a lot of sense since you can't but part of a can, but I wanted to show you how you could use the logic for other things.
What is the equation of the line in the slope-interception form that passes through (3,-1) and (-1,5)
Answer:
y+1=-3/2(x-3)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(5-(-1))/(-1-3)
m=(5+1)/-4
m=6/-4
simplify
m=-3/2
y-y1=m(x-x1)
y-(-1)=-3/2(x-3)
y+1=-3/2(x-3)
width of a rectangle is 7 meters greater than its length
Answer:
[tex]x^{2} +7x-170=0[/tex]
Step-by-step explanation:
Here is the complete question: The width of a rectangle is 7 meters greater than its length . If the area of the rectangle is 170 m², write the quadratic equation in standard form for the equation that would represent the area of the rectangle. Let x equal to the length of the rectangle.
Given: Width of rectangle is 7 meter greater than length
Length of rectangle is x.
Area of rectangle= 170 m²
Now as given, length is x meter and width is (x+7) meter
we know that, area of rectangle= [tex]length\times width[/tex]
∴ substitute the values to get correction equation.
⇒170= [tex]x\times (x+7)[/tex]
now distributing x into (x+7).
⇒ [tex]170= x^{2} +7x[/tex]
subtracting 170 both side.
[tex]x^{2} +7x-170=0[/tex]
∴ [tex]x^{2} +7x-170=0[/tex] is the quadratic equation in standard form for the equation that would represent the area of the rectangle.
Grant is trying to make money to help pay for college by taking a job with Brian’s bike taxis if Baltimore. He has an agreement with Brian to rent the bike for $35.00 a night. He charges customers $3.75 for every mile he transports them. If grant needs to make at least $15.00 a day, how many miles would he need to ride?
Grant needs to ride at least 13.33 miles to male at least $ 15.00 a day
Solution:
Given that Grant has an agreement with Brian to rent the bike for $35.00 a night
He charges customers $3.75 for every mile he transports them
Grant needs to make at least $15.00 a day
To find: miles needed to ride
From given question, He charges customers $3.75 for every mile he transports them
So if he transports for "x" miles he would get,
[tex]\$ 3.75 \times x = \$ 3.75x[/tex]
So the profit he gets is $ 3.75 and initial cost invested to rent bike is $ 35. Also, Grant needs to make at least $15.00 a day
So we can frame a inequality as:
[tex]3.75x - 35 \geq 15\\\\3.75x\geq 35 + 15\\\\3.75x\geq 50\\\\x \geq 13.33[/tex]
So he needs to ride atleast 13.33 miles to male atleast $ 15.00 a day
Solve /x-5/=3
A. x=2, x=8
B. x=-8, x=8
C. x=-2, x=2
D. x=-8, x=-2
Answer:
A) x=2, 8
Step-by-step explanation:
abs(x-5)=3
x-5=3, x-5=-3
x=3+5=8,
x=-3+5=2
Final answer:
option A. x=2, x=8
Explanation:
To solve the equation |x-5|=3, we need to consider both cases regarding the absolute value function. The absolute value of an expression is equal to 3 if the expression itself is 3 or -3. Therefore, we have two equations to solve:
x - 5 = 3x - 5 = -3Solving the first equation:
x = 3 + 5x = 8Solving the second equation:
x = -3 + 5x = 2Thus, the solutions for the equation |x-5|=3 are x=2 and x=8, which corresponds to option A.
Solve 13 - 2x > 21
x>-4
x > -17
x< -17
x<-4
Answer:
x>-4
Step-by-step explanation:
13-2x > 21
-13 -13
-2x >8
(-2x)/(-2) >(8)/(-2)
x>-4
A Six Flags theme park charges $30 for adults and $15 for kids. How many adult tickets and kid tickets were sold, if a total of 1,644 tickets were sold for a total of $11,250?
Answer:
The number of adult tickets sold is 894 and the number of kid tickets is 750.
Step-by-step explanation:
Given:
A Six Flags theme park charges $30 for adults and $15 for kids.
Total of 1,644 tickets were sold.
Total amount of tickets $11,250.
Now, to find the number of adult tickets and kid tickets.
Let the number of kid tickets be [tex]x.[/tex]
And the number of adult tickets be [tex]y.[/tex]
So, the total number of tickets:
[tex]x+y=1644.[/tex].....(1)
Solving the equation we get the value of [tex]x[/tex]:
[tex]x=1644-y.[/tex]
Now, the total amount of tickets of adult and kids:
[tex]15x+30y=11250.[/tex]
So, by putting the value of [tex]x[/tex] we get:
[tex]15(1644-y)+30y=11250[/tex]
[tex]24660-15y+30y=11250[/tex]
[tex]24660+15y=11250[/tex]
Subtracting both sides by 24660 we get:
[tex]15y=-13410[/tex]
Dividing both sides by -15 we get:
[tex]y=894[/tex]
Thus number of adult tickets = 894.
Now, putting the value of [tex]y[/tex] in equation (1):
[tex]x+894=1644[/tex]
On solving we get:
[tex]x=1644-894[/tex]
[tex]x=750.[/tex]
So. the number of kid tickets = 750.
Therefore, the number of adult tickets sold is 894 and the number of kid tickets is 750.
Answer: 750
Step-by-step explanation:
Paul wants to write equations in the form y=mx + b for the lines passing through
point D that are parallel and perpendicular to line h. First he finds the slopes of these
two lines. What could he do next to find the y-intercepts?
Answer:
Substitute the slope and the coordinates of point D in the equation of the line y=mx+b and then solve for b in each equation
Step-by-step explanation:
we know that
The first step is calculate the slopes of these two lines. Remember that if two lines are parallel then the slopes are the same (m1=m2) and if two lines are perpendicular then the slopes is equal to m1*m2=-1
The second step is substitute the slope m2 and the coordinates of point D in the equation of the line in slope-intercept form y=mx+b and then solve for b in each equation
A clothing factory makes 7,200 t shirts in one week on average there are 45 employees at the factory if each employee makes the same number of t shirts how many t shirts does each employee make in one week
Answer:
160Step-by-step explanation:
Divide 7,200 by 45
The number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
A clothing factory makes 7,200 t-shirts in one week on average there are 45 employees at the factory.
Let x be the number of t-shirts each employee make in one week
The value of x can be calculated as follows:
x = 7,200/45
x = 160
Thus, the number of t-shirts each employee make in one week is 160 if the clothing factory makes 7,200 t-shirts in one week.
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A company makes and sells headphones. The
function R= - 5x² +65x + 700 gives the amount
of money the company expects to make when the
price of the headphones is x dollars. When this
function is graphed, the vertex is 6.5, 911.25).
What does the x-value 6.5 represent?
Final answer:
The x-value 6.5 in the quadratic function's vertex represents the price of the headphones in dollars at which the company's expected revenue is maximized, according to the revenue function [tex]R= - 5x^2 +65x + 700[/tex].
Explanation:
The question involves understanding the meaning of the x-value in the vertex form of a quadratic function, which in this context represents the price of the headphones for which the company expects to make the maximum revenue. The given function is [tex]R= - 5x^2 +65x + 700[/tex], and the vertex of the graph of this function is given as (6.5, 911.25). The x-value, 6.5, therefore represents the price in dollars at which the revenue of the company is maximized. This is because, in the context of a quadratic revenue model, the vertex represents the maximum point when the parabola opens downwards (which it does, since the coefficient of x² is negative), meaning that increasing or decreasing the price from this point will lead to a decrease in the total revenue.
Solve for x and y in the given the 45° - 45° - 90° triangle shown above. When applicable, simplify all radicals and show your work.
Answer:
Therefore,
[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]
Step-by-step explanation:
Given:
Consider In Right Angle Triangle ABC
∠B = 90°
∠C = ∠A = 45°
AB = y
BC = x = adjacent side
AC = 8 = hypotenuse
To Find:
x = ?
y = ?
Solution:
In Right Angle Triangle ABC by Cosine Identity we have
[tex]\cos C = \dfrac{\textrm{side adjacent to angle C}}{Hypotenuse}\\[/tex]
substituting the above given values we get
[tex]\cos 45 = \dfrac{BC}{AC}=\dfrac{x}{8}[/tex]
[tex]\dfrac{1}{\sqrt{2} } =\dfrac{x}{8}\\\therefore x=\dfrac{8}{\sqrt{2} } \\Rationalizing\ we\ get\\\therefore x=\dfrac{8}{\sqrt{2}}\times \dfrac{\sqrt{2} }{\sqrt{2}}}\\\therefore x=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]
As The triangle is 45 - 45 - 90
It is an Isosceles Right triangle
[tex]x=y[/tex]..... Isosceles Triangle property
[tex]\therefore y=4\sqrt{2}=4\times 1.4142=5.6568\ units[/tex]
Therefore,
[tex]x=y= 4\sqrt{2}=5.6568\ units[/tex]
Solve for w, x, y, z
x + 2y - z = 3
2x - y + z - w = -3
y + 2z - w = -7
x + 3y + 2z + 2w = 3
Answer:
x= 1; y= 0; z= -2 and w= 3.
Step-by-step explanation:
Given that,
1) x + 2y - z = 3
2) 2x - y + z - w = -3
3) y + 2z - w = -7
4) x + 3y + 2z + 2w = 3
now, from 1) z = x + 2y -3 →→(5)
from 2) w = 2x -y + z +3
⇒w = 2x -y + x + 2y -3 +3 (from (5))
w = 3x + y →→(6)
Now substitute (5) and (6) in 3), we get
y +2(x + 2y -3) - (3x + y) = -7
⇒ 4y - x = -1 →→→(7)
Now substitute (5) and (6) in 4), we get
x + 3y + 2(x + 2y -3) + 2(3x + y) = 3
⇒ 9x +9y = 9
⇒ x + y =1 →→→(8)
⇒ x= 1-y , substituting this in (7) gives 5y -1 = -1
⇒ y = 0 and x = 1
substituting these values in
(5) and (6) gives, z = -2 and w = 3
⇒ x= 1; y= 0; z= -2 and w= 3.
Solve this system of linear equations. Separate
the x- and y-values with a comma.
- 19x = 26 - 9
9x = 54 - 9y
HELP!!
Answer:
x=-17/19, y=131/19. (-17/19, 131/19).
Step-by-step explanation:
-19x=26-9
-19x=17
x=-17/19
9(-17/19)=54-9y
-153/19=54-9y
9y=54-(-153/19)
9y=54+153/19
9y=1026/19+153/19
9y=1179/19
y=(1179/19)/9
y=(1179/19)(1/9)
y=1179/171
y=131/19
If a certain cannon is fired from a height of 8.8 meters above the ground, at a certain angle, the height of the cannonball above the ground, h, in meters, at time, t, in seconds, is found by the function h left parenthesis t right parenthesis equals negative 4.9 t squared plus 30.5 t plus 8.8. Find the time it takes for the cannonball to strike the ground.
Answer:
It would take approximately 6.50 second for the cannonball to strike the ground.
Step-by-step explanation:
Consider the provided function.
[tex]h(t)=-4.9t^2+30.5t+8.8[/tex]
We need to find the time takes for the cannonball to strike the ground.
Substitute h(t) = 0 in above function.
[tex]-4.9t^2+30.5t+8.8=0[/tex]
Multiply both sides by 10.
[tex]-49t^2+305t+88=0[/tex]
For a quadratic equation of the form [tex]ax^2+bx+c=0[/tex] the solutions are: [tex]x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
Substitute a = -49, b = 305 and c=88
[tex]t=\frac{-305+\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}=-\frac{-305+\sqrt{110273}}{98}\\t = \frac{-305-\sqrt{305^2-4\left(-49\right)88}}{2\left(-49\right)}= \frac{305+\sqrt{110273}}{98}[/tex]
Ignore the negative value of t as time can't be a negative number.
Thus,
[tex]t=\frac{305+\sqrt{110273}}{98}\approx6.50[/tex]
Hence, it would take approximately 6.50 second for the cannonball to strike the ground.
find x and y
2x+3y=80
Answer:
x = 40 + -1.5y
Step-by-step explanation:
Simplifying
2x + 3y = 80
Solving
2x + 3y = 80
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-3y' to each side of the equation.
2x + 3y + -3y = 80 + -3y
Combine like terms: 3y + -3y = 0
2x + 0 = 80 + -3y
2x = 80 + -3y
Divide each side by '2'.
x = 40 + -1.5y
Simplifying
x = 40 + -1.5y
A cube has a volume of 343 cubic cm. What is the area of the base
Answer:
49 cm²
Step-by-step explanation:
The volume (V) of a cube is calculated as
V = s³ ← s is the length of the side, thus
s³ = 343 ( take the cube root of both sides )
s = [tex]\sqrt[3]{343}[/tex] = 7, thus
area of base = s² = 7² = 49 cm²
A square pyramid is 6 feet on each side. The height of the pyramid is 6 feet. What is the total area of the pyramid?
Answer:
It is B. (36√5 + 36) ft^2.
Step-by-step explanation:
Total area = area of the base + 4 * area of the triangular side.
The slant height of a triangular side = √(6^2 + 3^2)
= √45
= 3√5
The area of this side = 3 * 3 √5
= 9√5.
Therefore the total area of the pyramid
= 6^2 + 4*9√5
= (36 + 36√5) ft^2.
7.
What is the solution to the equation shown below?
2/3x+5=1
[tex] \frac{2}{3} x + 5 = 1[/tex]
[tex] \frac{2}{3} x = 1 - 5[/tex]
[tex] \frac{2}{3} x = ( - 4)[/tex]
[tex]x = ( - 4) \div \frac{2}{3} [/tex]
[tex]x = ( - 4) \times \frac{3}{2} [/tex]
[tex]x = \frac{ - 12}{ \: \: \: 2} [/tex]
[tex]x = ( - 6)[/tex]
[tex]∴ \frac{2}{3} \times ( - 6) + 5 = 1[/tex]
given the following formula solve for a
s = a+b+c/2
Answer:
[tex]a=2s-b-c[/tex]
Step-by-step explanation:
Given formula:
[tex]s=\frac{a+b+c}{2}[/tex]
To solve for [tex]a[/tex]
In order to solve for [tex]a[/tex] we will try to isolate [tex]a[/tex] on one side of the equation.
Steps to isolate [tex]a[/tex].
1) Multiplying both sides by [tex]2[/tex] to remove fractions.
[tex]2\times s=2\times \frac{a+b+c}{2}[/tex]
[tex]2s=a+b+c[/tex]
2) Subtracting both sides by [tex]b[/tex]
[tex]2s-b=a+b-b+c[/tex]
[tex]2s-b=a+c[/tex]
3) Subtracting both sides by [tex]c[/tex]
[tex]2s-b-c=a+c-c[/tex]
[tex]2s-b-c=a[/tex]
Thus, we successfully isolated [tex]a[/tex] on one side. The formula for [tex]a[/tex] can be given as:
∴ [tex]a=2s-b-c[/tex]
i do not get this i'm so dumb
Answer:
The answer is B. 6 and 8.
Answer:
B) 6 and 8
Step-by-step explanation:
[tex]3 \times 8 = 24[/tex]
[tex]4 \times 6 = 24[/tex]
[tex]2 \times 12 = 24[/tex]
Evaluate the expression 9 P 4
Answer:
The answer is 3024
Step-by-step explanation:
you do 9!/(9-4)! which comes out to 3024
Given the function f(x) = 4(x − 11) − 9, determine the value of x such that f(x) = -13.
Answer:
For x = 10, the value of the given function f(x)= 4(x − 11) − 9 is -13.
Step-by-step explanation:
Here, the given expression is:
f(x) = 4(x − 11) − 9
Now, given: f(x) = -13
⇒ -13 = 4(x − 11) − 9
Now, solving for the value of x, we get:
-13 = 4(x-11) -9
⇒ -13 = 4 x - 44 - 9
or, -13 + 44 + 9 = 4x
or, 4 x = 40
or, x = 40/4 = 10
or, x = 10
Hence, for x = 10, the value of the given function f(x)= 4(x − 11) − 9 is -13.
Rajeev buys good worth Rs 6650.He gets a rebate of 6% on it.After getting the rebate, he pays sales tax @10%. Find the amount he will have to pay for the goods.
Rajeev will pay Rs 6876.10 for the goods.
Step-by-step explanation:
Given,
Worth of goods = Rs 6650
Rebate = 6%
Amount of rebate = 6% of worth of goods
Amount of rebate = [tex]\frac{6}{100}*6650=0.06*6650[/tex]
Amount of rebate = Rs 399
Amount after rebate = 6650 - 399 = Rs 6251
Sales tax = 10%
Amount of sales tax = 10% of amount after rebate
Amount of sales tax = [tex]\frac{10}{100}*6251=0.1*6251[/tex]
Amount of sales tax = Rs 625.10
Total amount of goods paid = Amount after rebate + sales tax
Total amount of goods paid = 6251+625.10 = Rs 6876.10
Rajeev will pay Rs 6876.10 for the goods.
Keywords: addition, percentage
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7<-(-k-3)+2 solve inequality
Answer:
7<k+3+2
7<k+5
2<k
which is same as k>2
A $50.00 pair of shoes is discounted 20%. If sales tax is 8%, what is the amount of tax paid?
A) $0.32
B) $0.40
C) $3.20
D) $4.00
Answer:
The amount of tax paid is C. $3.20
Step-by-step explanation:
If we take $50.00 and give a 20% discount, we're taking 20% of 50 and then subtracting it from the origional price (50) which brings us down to 40, because 20% of 50 is 10 and we subtract.
Now that we have $40.00, sales tax comes in at a whopping 8%. To calculate the solution of a price with sales tax, we need to find what 8% of $40 is, which after calculations will be 3.20.
Since this question is asking on tax only, our answer is $3.200, C.
a store buys hirts for $18 and marks them up by 49% for retail sale. What is the retail price of each shirt.
Answer:
26.82
Step-by-step explanation:
Answer:
$26.82
Step-by-step explanation:
Product Cost: $18
Markup: 49%
Selling Price = (49% / 100% * $18) + $18 = $8.82 + $18 = $26.82
This gives you a price markup of $26.82.
this is my first answer and it could very well be wrong, sorry ;(
Inequalities and variables
Answer:
[tex]a - 6 \leqslant 15 + 8a[/tex]
[tex] - 7a \leqslant 21[/tex]
[tex]a \geqslant - 3[/tex]
A sports shop has 84 employees. 25% of the employees work part-time. How many part-time employees does the sports shop have?
Answer:
The sports shop has 21 part-time employees.
Step-by-step explanation:
Solution:
What is 25% of 84?
.Y is 25% of 84
Equation: Y = P% * X
Solving our equation for Y
Y = P% * X
Y = 25% * 84
Converting percent to decimal:
p = 25%/100 = 0.25
Y = 0.25 * 84
Y = 21
Or another quicker way....
50% is half of the whole, and 25 is half of 50.
84/2/2
equals 21 too, I don't recommend to use it as row form.
The sports shop has 21 part-time employees, found by calculating 25% of 84.
The question asks how many part-time employees a sports shop with 84 employees has if 25% of them work part-time. To find the answer, we need to calculate 25% of 84 employees. The calculation is done as follows:
First, convert the percentage to a decimal by dividing it by 100: 25% = 0.25.
Then, multiply the total number of employees by this decimal: 84 times 0.25 = 21.
Therefore, the sports shop has 21 part-time employees.
How do you rewrite an equation in slope-intercept form
Answer:
y = mx + b
Step-by-step explanation:
m is slope
b is y-intercept