[tex]3x-\dfrac{1}{5}(10x+5)=6\qquad\text{use distributive property}\\\\3x-\left(\dfrac{1}{5}\right)(10x)-\left(\dfrac{1}{5}\right)(5)=6\\\\3x-2x-1=6\qquad\text{add 1 to both sides}\\\\\boxed{x=7}[/tex]
A company makes traffic signs.One of their signs can be modeled by an equilateral triangle with a perimeter of 144 inches. The company makes a similar sign with perimeter that is 1.25 times the one shown. What is the height in inches of the larger sign?
Answer:
The perimeter of the larger sign : 144*1,25= 180 inches
Side of the triangle= 180/3= 60 inches
square of the height= 60^(2) - 30^(2)= 2700 ( Pythagoras' theorem)
height= square root ( 2700)= 51,96
Step-by-step explanation:
To find the height of the larger sign, determine the scale factor between the two signs and use the formula for the height of an equilateral triangle.
Explanation:To find the height of the larger sign, we need to determine the scale factor between the two signs. The perimeter of the original sign is 144 inches, and the new sign has a perimeter that is 1.25 times the original. This means the perimeter of the new sign is 144 x 1.25 = 180 inches.
Since the original sign is an equilateral triangle, each side has a length of 144/3 = 48 inches. The larger sign will have sides that are 180/3 = 60 inches in length.
Since the larger sign is also an equilateral triangle, we can use the formula h = (√3/2) x s, where h is the height and s is the length of a side. Therefore, the height of the larger sign is h = (√3/2) x 60 = 51.96 inches (rounded to two decimal places).
You are making a poster to support your friend for homecoming. Your original photo is 3 inches by 5 inches. You want the photo on the poster to be 2 1/2 feet by 4 1/6 feet. What is the scale factor of this dilation?
Answer:
9
Step-by-step explanation:
We have been given that dimensions of original photo are 4 inches by 6 inches. We want the photo on the poster to be of dimensions 3 feet by 4 1/2 feet.
First of all we will convert dimensions of poster from feet to inches.
3ft = 3x12 in = 36ft
4 1/2 ft = 4.5x 12in = 54in
Now let us compare sides of our original photo with corresponding sides of poster.
frac{36}{4} = 9
Now let us compare the second pair of corresponding sides.
\frac{54}{6} =9
We have seen that sides of poster are 9 times the sides of our original photo, therefore, the scale factor of this dilation is 9.
To find the scale factor for enlarging a photo from 3 inches by 5 inches to 2 1/2 feet by 4 1/6 feet, first convert feet to inches and then compare the dimensions of both photos. The scale factor is 10, as both width and height are enlarged by a factor of 10.
Explanation:You are making a poster and need to determine the scale factor for resizing a photo from 3 inches by 5 inches to 2 1/2 feet by 4 1/6 feet. To find the scale factor, you compare the dimensions of the enlarged photo to the original photo.
First, convert the measurements of the larger photo from feet to inches, since the original photo is in inches (1 foot = 12 inches):
2 1/2 feet = 2.5 * 12 inches = 30 inches
4 1/6 feet = (4 + 1/6) * 12 inches = (4 * 12) + (1/6 * 12) inches = 48 + 2 inches = 50 inches.
Next, calculate the scale factor for each dimension separately and check that they are consistent:
Scale factor for width = 30 inches / 3 inches = 10
Scale factor for height = 50 inches / 5 inches = 10
Since both width and height have the same scale factor of 10, the overall scale factor for the dilation is 10.
Brenda deposits $500 in a savings account that pays a simple interest rate of 2.5% per year. How much internet will Brenda earn after 18 months
Final answer:
Brenda will earn $18.75 in simple interest after 18 months on her $500 deposit at a 2.5% annual simple interest rate.
Explanation:
To calculate the simple interest Brenda will earn after 18 months on a $500 deposit at a simple interest rate of 2.5% per year, we can use the simple interest formula:
I = P * r * t, where:
I represents the interest earned,
P is the principal amount (the initial amount of money),
r is the annual interest rate (in decimal form), and
t is the time in years.
First, convert the interest rate from a percentage to a decimal by dividing by 100:
2.5% = 2.5 / 100 = 0.025
Next, since the time is given in months, convert it to years:
18 months = 18 / 12 = 1.5 years
Now, plug the values into the formula:
I = $500 * 0.025 * 1.5
I = $18.75
Therefore, Brenda will earn $18.75 in simple interest after 18 months.
Joshua is going to mow lawns during his summer break. The graph in the figure shows a linear relationship between the number of weeks he will be mowing and the number of lawns he will mow. If he earns $25 for each lawn he mows, how much money will he earn after mowing lawns for 5 weeks?
Final answer:
To determine Joshua's earnings after mowing lawns for 5 weeks, multiply the total number of lawns mowed in 5 weeks by the rate of $25 per lawn.
Explanation:
To calculate the money Joshua will earn after mowing lawns for 5 weeks:
Identify the rate: $25 per lawnCalculate the total number of lawns mowed in 5 weeks using the linear relationship graphMultiply the total lawns by the rate to find the earningsTherefore, Joshua will earn $X after mowing lawns for 5 weeks.
Danny buys 4 pizzas and some pretzels for his baseball team. The cost of each pizza is $8.99, and the cost of each pretzel is $0.99. Danny spends a total of $50.81 on the pizzas and pretzels.
Answer:
Step-by-step explanation: The answer to your question is 15 pretzels.To figure this out, you first multiply 8.99 by 4 since he did buy 4 pizzas and each pizza is 8.99. Then once you do that, you should come up with 35.96. Then subtract 50.81 from 35.96,which should give you 14.85. Then just divide 14.85 by 0.99 to figure out the amount of pretzels he bought.It should give you 15.Hope this helps!!!!
Please give brainliest!!!☺
Answer:
15
Step-by-step explanation:
Danny buys 4 pizzas and some pretzels for his baseball team.
The cost of each pizza is $8.99
Total cost of 4 pizza = 4 × 8.99
= $35.96
Let buy p numbers of pretzels whose cost $0.99 each.
Total cost for p pretzels = 0.99p
Total spend by Danny on pizzas and pretzels = $50.81
35.96 + 0.99p = 50.81
0.99p = 50.81 - 35.96
0.99p = 14.85
p = 15
Hence, Danny bought 15 pretzels for baseball team.
The table below shows the distance d(t) in feet that an object travels in t seconds: t (seconds) d(t) (feet) 2 64 4 256 6 576 8 1024 What is the average rate of change of d(t) between 2 seconds and 6 seconds, and what does it represent? 128 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds 80 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds 128 ft/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds 80 ft/s; it represents the average distance traveled by the object between 2 seconds and 6 seconds
Answer:
128 ft/s; it represents the average speed of the object between 2 seconds and 6 seconds
Step-by-step explanation:
The average rate of change is another way to say slope.
slope = (y2-y1)/(x2-x1)
= (576-64)/(6-2)
= (512/4)
=128 ft/s
This represents the change in ft per second, or the average speed the object is going during the time period.
Answer:
it's A
Step-by-step explanation:
Which car can travel at the slowest rate? Plz help fast
A) 300 miles in 4 hours
B) 450 miles in 6 hours
C) 750 miles in 10 hours
D) 800 miles in 12 hours
Answer:
D
Step-by-step explanation:
Let's find unit rate of each (number of miles traveled in 1 hour). For that we will divide the distance by time to get the unit rate.
Note: [tex]rate=\frac{Distance}{Time}[/tex]
(A)
rate = [tex]\frac{300}{4}=75[/tex] mph (miles per hour)
(B)
rate = [tex]\frac{450}{6}=75[/tex] mph
(C)
rate = [tex]\frac{750}{10}=75[/tex] mph
(D)
rate = [tex]\frac{800}{12}=66\frac{2}{3}[/tex] mph
As we can see, the first 3 rates are same, 75 mph, and the last one is [tex]66\frac{2}{3}[/tex] mph. So clearly, the last rate is the slowest.
D is the right answer.
Answer:
D) 800 miles in 12 hours
Step-by-step explanation:
300/4=75
450/6=75
750/10=75
800/12=66.6666667
evaluate the expression 4!×3!
If you mean 4 x |3| =12
If it's 4 = 3x => 0.75
I'm sorry if I didn't help, I don't understand what you mean with " ! "
Answer is 144
4! = 4*3*2*1 = 24
3! = 3*2*1 = 6
6*24 = 144
Jaden is in charge of building a dance floor for the school dance. He wants to build the largest dance floor that he can while staying within the budget. His plan is to buy wooden planks and lay them side by side on the grass just outside the gym. A plank that 2 inches thick, 4 inches wide, and 8 feet long costs $3.25. How large of a dance floor, in square yards, can he build with $526.50?
Jaden can build a dance floor measuring 48 square yards with his budget of $526.50, based on the cost of $3.25 per wooden plank.
To calculate the size of the dance floor Jaden can build with his budget, we first need to determine how many wooden planks he can purchase. Each plank costs $3.25 and he has $526.50 to spend.
Number of planks = Total budget / Cost per plank
= $526.50 / $3.25
= 162 planks
Next, we need to find out the area that each plank covers. Since each plank is 8 feet long and 4 inches (or 1/3 feet) wide, its area in square feet is:
Area per plank = Length * Width
= 8 feet * 1/3 feet
= 8/3 square feet
Now, let's calculate the total area covered by 162 planks:
Total area in square feet = 162 planks * [tex]\frac{8}{3}[/tex] square feet/plank
= 432 square feet
Since 1 square yard is equivalent to 9 square feet, we convert the total area to square yards:
Total area in square yards = Total area in square feet / 9
= 432 square feet / 9
= 48 square yards
Therefore, Jaden can build a dance floor measuring 48 square yards within his budget.
Jenny's Knitting Corner had a profit of $298 in January and a loss of $370 in February. What was the total loss for the two months?
A.) -$75
B.) -$668
C.) $72
B.) $668
-72, I don't see any of that over there
Is the equation y=3x in slope-intercept form? Explain.
Answer:
y = 3x is in slope intercept form.
Step-by-step explanation:
The slope intercept form of an equation is y =mx+b where m is the slope and b is the y intercept.
y =3x can be written as
y = 3x+0
where 3 is the slope and has a y intercept of 0
y = 3x is in slope intercept form.
The transformation (x, y) to (x + 5, y + 7) is a what??
Answer: Translation
More specifically, it is a translation shifting every point 5 units to the right and 7 units down.
In geometry, "translation" is a special term to basically mean "shift the point left, right, up or down". You can think of the point sliding across the page in some manner.
Answer:
translation
Step-by-step explanation:
the point is moved 5 units to the right and 7 units up
What is the degree of x^5-4x+2
Answer:
degree 5
Step-by-step explanation:
the degree of a polynomial is determined by the term with the largest exponent and is the value of the exponent.
[tex]x^{5}[/tex] is the term with the largest exponent of 5
degree of polynomial is 5
The school play started at 2:10pm and ended at 3:22pm. How long did the play last?
Answer:
The play lasted 1 hour and 12 minutes.
Step-by-step explanation:
Start: 2:10 pm. End: 3:22 pm.
3 hours - 2 hours = 1 hour
Start: 2:10 pm. End: 3:22 pm.
22 minutes - 10 minutes = 12 minutes
The play lasted 1 hour and 12 minutes.
Which system of inequalities is shown in the graph?
The system of the inequalities is y ≥ 2x - 2, y ≥ x - 3x. Option B
How to determine the inequalitiesTo determine a system of inequalities graphically, plot each inequality on the same coordinate plane.
Represent each inequality as a boundary line (dashed or solid, depending on the inequality sign) and shade the region that satisfies the inequality. The solution area is the overlapping shaded region where all inequalities intersect.
The points within this shared region satisfy all the given inequalities simultaneously. If there is no intersection or common shaded area, the system has no solution that satisfies all the inequalities simultaneously.
So, we have that;
y ≥ 2x - 2
y ≥ x - 3x
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Please help.
Write the linear inequality shown in the graph.
Please explain how you got your answer.
A. y > or = 3x +4
B. y < or = 3x + 4
C. y < or = 3x - 4
D. y > or = 3x - 4
Answer:
D. y > or = 3x - 4
Step-by-step explanation:
Looking at the graph, we know the y intercept, or where the graph crosses the y axis, is -4.
We can find the slope of the line from 2 points (0,-4) and (2,2)
The slope is given by
m = (y2-y1)/(x2-x1)
= (2--4)/(2-0)
= (2+4)/(2-0)
=6/2
=3
Using the slope intercept form for the line, y=mx+b
y = 3x+-4
y = 3x-4
The graph is shaded above the line so y is greater than the line, and the line is solid so y is also equal to the line
y ≥3x-4
Kendra bought a magazine for $3 and 4 paperback books for $5 each. The expression 3+4*5 represents the total cost on dollars of her purchases. What are the terms in this expression?
The total cost for the magazine and 4 paperback books is $23.
What is an Algebraic expression?An algebraic expression can be obtained by doing mathematical operations on the variable and constant terms.
The variable part of an algebraic expression can never be added or subtracted from the constant part.
Given that,
The cost of a magazine is $3.
And, the cost of each of 4 paperback books is $5.
Then, the cost of 4 paperback books is 4 × 5 = 20
Thus, the expression for the total cost is given as,
3 + 4 × 5
= 23
Hence, the total cost is given as $23 and the terms in the expression 3 + 4 × 5 represent the cost of magazine and that of 4 books respectively.
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tina has 50 coins, all dimes and quarters. the value of the coins is $7.10. write a system of equations to determine how many dimes and how many quarters tina has
Answer:
A) D + Q = 50
B) .10D + .25Q = 7.10
We multiply A) by -.10
A) -.10D - .10Q = -5 then adding this to B)
B) .10D + .25Q = 7.10
.15Q = 2.10
Quarters = 14 = 3.50
Dimes = 36 = 3.60
Step-by-step explanation:
Mya takes a drive from a springboard at a swimming pool. The board is 3 1/2 feet above the surface of the water. The total length of her dive is 8 3/4 feet. How far below the surface of the water is mya at the end of the dive
Answer:
dive below = 5 1/4 ft
Step-by-step explanation:
Dive above water + dive below water = total dive
We know the dive above water is 3 1/2 ft
The total length of the dive is 8 3/4 ft
Substitute in what we know
3 1/2 + dive below = 8 3/4
get a common denominator of 4
3 1/2*2/2 +dive below = 8 3/4
3 2/4 +dive below = 8 3/4
Subtract 3 2/4 from each side
3 2/4 - 3 2/4 +dive below = 8 3/4 - 3 2/4
dive below = 5 1/4 ft
Final answer:
To find out how far below the surface of the water Mya is at the end of her dive, subtract the diving board's height from the total dive length. Convert mixed numbers to improper fractions for easy subtraction, and after calculation, you find that Mya is 5 1/4 feet below the water's surface.
Explanation:
To determine how far below the surface of the water Mya is at the end of the dive, we need to subtract the height of the diving board from the total length of the dive. Mya's dive board is 3 1/2 feet above the water, and the total length of her dive is 8 3/4 feet.
First, convert the mixed numbers to improper fractions to make the subtraction easier. For 3 1/2, multiply 3 (the whole number) by 2 (the denominator) and add 1 (the numerator) to get 7/2. For 8 3/4, multiply 8 by 4 and add 3 to get 35/4.
The fractions are now 7/2 and 35/4. Before subtracting, find a common denominator, which is 4 in this case.
Convert 7/2 to 14/4, so we can subtract it from 35/4.
Subtract 14/4 from 35/4 to find the distance below the water's surface: 35/4 - 14/4 = 21/4.
Finally, convert the improper fraction back to a mixed number. The mixed number for 21/4 is 5 1/4, which means Mya is 5 1/4 feet below the surface of the water at the end of her dive.
Estimate the square root of 4.92+2.18x7.31
Answer:
4.36
Step-by-step explanation:
The given expression is
[tex]\sqrt{4.98+2.18\times 7.31}[/tex]
We need to estimate the value of given expression.
First approximate each term of the given expression.
First term : [tex]4.92\approx 5[/tex]
Second term : [tex]2.18\approx 2[/tex]
Third term : [tex]7.31\approx 7[/tex]
The value of given expression after approximation is
[tex]\sqrt{5+2\times 7}[/tex]
[tex]\sqrt{5+14}[/tex]
[tex]\sqrt{19}[/tex]
The approximate value of [tex]\sqrt{19}[/tex] is 4.36.
Therefore, the estimated value of given expression is 4.36.
The estimated square root of 4.92 + 2.18 x 7.31 is between 4 and 5.
To estimate the square root of 4.92 + 2.18 x 7.31, we first calculate the value inside the square root:
4.92 + 2.18 x 7.31 = 4.92 + 15.8678 = 20.7878
Next, we estimate the square root of 20.7878:
Since the square root of 16 is 4, and the square root of 25 is 5, we can estimate that the square root of 20.7878 is between 4 and 5.
Therefore, the estimated square root of 4.92 + 2.18 x 7.31 is between 4 and 5.
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The price of a Barry bonds baseball card in 2001 was $50. It is now being sold for $30. Find the percent decrease in the cost of the card
Final answer:
The percent decrease in the cost of the Barry Bonds baseball card is 40%.
Explanation:
To calculate the percent decrease in the cost of the card, we can use the formula:
Percent decrease = ((original value - new value) / original value) * 100
In this case, the original value of the card was $50 and the new value is $30. Plugging in these values into the formula:
Percent decrease = ((50 - 30) / 50) * 100 = (20 / 50) * 100 = 0.4 * 100 = 40%
Therefore, the percent decrease in the cost of the card is 40%.
what is a real life example for exponential parent functions
Answer:
Putting money into a savings account
Step-by-step explanation:
Answer:
Each year, a law firm gains 20% more clients. This continues on a regular basis. The number of clients that the law firm has will be about 1.2 times the amount from the past year.
Step-by-step explanation:
Evaluate the expressions.
Answer:
- 1 and 1
Step-by-step explanation:
using the rule of exponents
• [tex]a^{0}[/tex] = 1
- ([tex]2^{0}[/tex]) = - 1
( - [tex]\frac{4}{9}[/tex])^0 = 1
For this case we have that by definition, any number raised to zero gives 1.
Knowing that:
[tex]\frac {a ^ 2} {a ^ 2} = 1[/tex] and by power properties of the same base we have that: [tex]\frac {a ^ 2} {a ^ 2} = a ^ {2-2} = a ^ 0[/tex]
So:
[tex]a ^ 0 = 1[/tex]
So, if we have:
[tex]- (2) ^ 0 = - (1) = - 1\\(- \frac {4} {9}) ^ 0 = 1[/tex]
Answer:
[tex]- (2) ^ 0 = - (1) = - 1\\(- \frac {4} {9}) ^ 0 = 1[/tex]
James swam 3 and 1/3 miles. For 2/6 of his swim he did the backstroke. How many miles did he swim the backstroke?
Answer:i believe thats only a third of a mile
Step-by-step explanation:
if you have the both take on the same denominator the 3 miles would be 3/3 and then it would be 6/6 and the 1/3 mile would become 2/6 hope i helped
Answer: yes its 1/3 of a mile
Step-by-step explanation:
A group of 40 people went to the theme park. While there, each person bought popcorn. Regular bags of popcorn sold for $6 per bag. Super size sold for $8 per bag
Each person in the group could have either bought a regular bag of popcorn for $6 or a super size bag for $8. The total costs would be $240 and $320 respectively.
Explanation:In this scenario, we have a group of 40 people each buying popcorn at a theme park. The prices available were the regular bag for $6 each or the super size for $8 each. Depending on their choice, the total amount spent will vary. For example, if every person in the group purchased a regular bag, the total would be 40 * $6 = $240. And if everyone decided to get a super size bag, it would end up being 40 * $8 = $320
.
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ou work at the Peacock Blue store 40 hours/week over five days at a rate of $10.25/hour. Deductions are FICA (7.65%), federal withholding (15%), and state withholding (10%). Your expenses are transportation at $5.25/day, lunch at $3.85/day, and black slacks required for work at $19.95. How much is your discretionary income for one week?
Answer:
$210.69
Step-by-step explanation:
Firstly, just calculate how much money you earn:
40 * 10.25 = $410
Your transportation expenses = 5.25 * 5 = $26.25
Your lunch expenses = 3.85 * 5 = $19.25
Expenses for black slacks = $19.95
FICA = 7.65/100 * 410 (money you earned) = $31.365
Federal withholding = 15/100 * 410 = $61.5
State withholding = 10/100 * 410 = $41
Your discretionary income = 410 - (26.25 + 19.25 + 19.95 + 31.365 + 61.5 + 41) = $210.69
Solve using substitution
y=1/2x
x+4y=18
Answer:
The solution set is (6,3)
Step-by-step explanation:
Begin by multiplying equation 1 by 2. You'll see why in a moment
2y = 2*(1/2) x
2y = x
Substitute this value into equation 2.
2y + 4y = 18 Combine like terms on the left
6y = 18 Divide both sides by 6
6y/6 = 18/6 Do the division
y = 3
To solve for x just use the top equation
y = 1/2x
3 = 1/2x Multiply by 2
3*2 = x
x = 6
rebecca is given two triangles, ABC and DEF. at first glance, she thinks that the triangles are congruent l. how can she use what she knows about rotations and triangle congruence to prove the triangle congruence?
Answer:
She can use rotation and overlap the two triangles, and if they overlap perfectly/identically, that means they are surely congruent.
Rebecca can prove triangle congruence by applying the rotation property. If she can rotate one triangle to align with the other, maintaining the same shape and size, then the triangles are congruent. Additionally, she can compare corresponding angles and sides to confirm congruence.
Rebecca can use rotations to prove triangle congruence by performing a sequence of rotations, translations, and reflections on one triangle to align it with the other. If she can manipulate one triangle to superimpose it exactly onto the other triangle without changing its shape or size, then they are congruent. She can also use the properties of triangle congruence, such as side-angle-side (SAS), angle-side-angle (ASA), side-side-side (SSS), or angle-angle-side (AAS), to verify their congruence. By demonstrating that the corresponding sides and angles of the two triangles are congruent based on these properties, she can conclusively prove their congruence. This approach ensures that both triangles share identical measurements and configurations, providing geometric evidence for their congruence.
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which fact would help Estelle prove that the measure of angle KNQ is equal to the measure of MNS
To demonstrate that the measure of angle KNQ is equal to the measure of angle MNS, one should use geometric principles to show congruency or similarity between the angles, which could involve establishing congruent triangles or proportional relationships.
Explanation:To prove that the measure of angle KNQ is equal to the measure of angle MNS, one would need to establish a relationship between the two angles based on geometric principles or congruent triangles. This could involve demonstrating that the angles are corresponding angles of similar triangles, alternate interior angles of a transversal crossing parallel lines, or possibly vertical angles resulting from intersecting lines. Given the information provided, it seems that if one could show that triangles KNQ and MNS are congruent, then by the Corresponding Parts of Congruent Triangles are Congruent (CPCTC) theorem, it would follow that the angles in question are equal.
Applying trigonometry in proving congruency or similarity might be necessary, especially if an equivalence can be drawn from given proportional relationships or if one can establish that angles are congruent through right triangles and the definition of trigonometric ratios.
A dripping faucet loses about 2.5×10^−4 liters of water each minute. There are approximately 3×10^5 minutes in a month. About how many liters of water are lost because of the dripping faucet in a month?
Answer:
750 liters are lost.
Step-by-step explanation:
This question can be solved with multiplication.
Its important that when multiplying scientific forms of number together, always remember to add the exponents. -5+4=-1
-25 x -30= 750
750 liters are lost in a month.
Hope this helps!
Answer:
The answer should be 7.5*10 ^1 and that equalls 75
Step-by-step explanation: