Final answer:
The integers that satisfy the given condition of the equation x^2 + 2 = 10x - 7 are 1 and 9. To find these integers, the quadratic equation x^2 - 10x + 9 = 0 was factored and solved.
Explanation:
To find the integer(s) that satisfies the given condition, we need to set up an equation based on the description. The condition states: if 2 is added to the square of an integer x, the result equals 10 times that integer minus 7. Mathematically, this can be expressed as x2 + 2 = 10x - 7. To solve this, first rearrange the terms to one side to form a quadratic equation:
x2 - 10x + 9 = 0
Now we factor the quadratic equation:
(x - 1)(x - 9) = 0
Setting each factor equal to zero gives us the solutions:
x - 1 = 0 ⇒ x = 1
x - 9 = 0 ⇒ x = 9
The integers that satisfy the given condition are 1 and 9.
Simplify 14^15 over 14^5
A. 1^3
B. 1^10
C.14^3
D.14^10
Simply just subtract 5 from 15 to get 14^10, or D.
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.
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
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.
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
Can anyone help me with this question?
You don't need to help me with number 10 because i got it now help with the other's please.
Answer:
10)C 18,000
11) B 130.83
12)B or C not for sure
13) D the domain is 1 < f<7 the range is 24 < c(f)<168
Step-by-step explanation:
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:
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.
Reyesburg Corporation is contemplating using a new, more expensive glue in the construction of its laminated veneer lumber. Of importance to the company is the carrying load of the lumber. The company has tested 24 beams using the new glue, recording for each beam the pressure (in pounds per square foot) at which the beam breaks. The data collected are presented in the following histogram.
Answer:
The correct answer is 904.1 pounds per square foot
Step-by-step explanation:
(mcgraw)
What does y=-1/2x-4
Answer:
[tex]y = -1/2x - 4[/tex]
From this, you can tell it's in slope-intercept form, has a slope of -1/2, and a y-intercept of -4.
I've included a picture of what this equation looks like.
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:
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.
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
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).
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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Write a number in which the value of the 3 is 10 times the value of the digit 3 in 156.32
Answer:
1563.2
Step-by-step explanation:
If you just multiply 0.3 by 10 you will get 3
Now all you need to do is write 3 or have a number which has unit place value of 3
Answer: The number in which the value of the 3 is 10 times the value of the digit 3 in 156.32 = 3
Step-by-step explanation:
The given number = 156.32
The place value of 3 in 156.32 is 3 tenth [since it the left most number after the decimal].
3 tenth can be written as [tex]\frac{3}{10}[/tex]
The number 10 times [tex]\frac{3}{10}[/tex]= [tex]10\times\frac{3}{10}[/tex]
Therefore, The number 10 times [tex]\frac{3}{10}[/tex]=3
Hence, the number in which the value of the 3 is 10 times the value of the digit 3 in 156.32 = 3
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.
Alicia uses 3/4 gallon of paint to paint her room. Becca uses for 4/5 gallon more than Alicia to paint her room. How many gallons of paint do they use together
Answer:
23/10 gallons
Step-by-step explanation:
Alicia uses 3/4 gallon of paint to paint her room.
Alicia use = 3/4 gallon of paint
Becca uses for 4/5 gallon more than Alicia to paint her room.
Becca uses = Alicia (3/4 gallons ) + 4/5
Becca uses = [tex]\frac{3}{4} + \frac{4}{5}[/tex]
Total paint used together = Aliccia used + Becca used
[tex]\frac{3}{4}+\frac{3}{4} + \frac{4}{5}[/tex]
Add like fractions 3/4 + 3/4 becomes 6/4
[tex]\frac{6}{4} + \frac{4}{5}[/tex]
Make the denominators same
[tex]\frac{6*5}{4*5} + \frac{4*4}{5*4}[/tex]
[tex]\frac{30}{20} + \frac{16}{20}[/tex]
[tex]\frac{46}{20}[/tex]
Divide top and bottom by 2
[tex]\frac{23}{10}[/tex] gallons
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
Solve using double substitution
y=2x+5
6x-3y=6
Substitute y = 2x + 5 to the second equation 6x - 3y = 6:
6x - 3(2x + 5) = 6 use distributive property
6x - (3)(2x) - (3)(5) = 6
6x - 6x - 15 = 6
-15 = 6 FALSE
Answer: NO SOLUTION
If f(x) = 8x^2 - 5 what is f(-1)
Answer:
Step-by-step explanation:
f(-1)=8(-1)^2-5
f(-1)=8(1)-5
f(-1)=8-5
f(-1)=3
Answer:
3
Step-by-step explanation:
In this problem you substitute x for -1
8(-1)^2-5
the perimeter is at least 18 feet. Write and solve inequality that represents x
The inequality that represents x is [tex]$x \geq 6$[/tex]. This means that the total length of all the sides of the shape must be at least 6 feet.
Let's say the total length of all the sides of the shape is represented by the variable x. We are given that the perimeter is at least 18 feet. This can be written as an inequality: [tex]$x \geq 18$[/tex]
Since the sides of the triangle measure 3 feet, 5 feet and x-2 feet, we can express the perimeter inequality in terms of x as: [tex]$x+ 3 + 5 +x-2 \geq 18$[/tex]
Simplifying the left side of the inequality, we get: [tex]$2x + 6 \geq 18$[/tex]
Subtracting 6 from both sides, we obtain: [tex]$2x \geq 12$[/tex]
Dividing both sides by 2, we get: [tex]x \geq 6$.[/tex]
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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What’s 22.5 as a fraction in simplest form
Answer:
22.5% = 9/40 as a fraction
Step by Step Solution
To convert 22.5 percent to a fraction follow these steps:
Step 1: Write down the percent divided by 100 like this:
22.5% = 22.5/100
Step 2: Multiply both top and bottom by 10 for every number after the decimal point:
As we have 1 digit after the decimal point, we multiply both numerator and denominator by 10, or, simply shift 1 decimal place to the right. So,
22.5/100 = (22.5 x 10)/(100 x 10) = 225/1000.
Step 3: Simplify (or reduce) the above fraction by dividing both numerator and denominator by the GCD (Greatest Common Divisor) between them. In this case, GCD(225,1000) = 25. So,
(225÷25)/(1000÷25) = 9/40 when reduced to the simplest form.
Step-by-step explanation:
Answer:
9/4, or 2 1/4 is your answer
Step-by-step explanation:
Note that 22 is a whole number, and that 5 is a decimal.
Change the decimal into a fraction. To do so, move the decimal point to the right two place values and set the number over 100
22.5 = 225/100
Simplify.
(225/100)/(25/25) = 9/4
9/4, or 2 1/4 is your answer
~
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]
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
Can someone show me what I need to do here
Answer:
A) 25/75
C) 1/3
F) 0.3333333(repeated decimal)
Step-by-step explanation:
He started out with 75 planners, and has 25 planners left, meaning he have 25/75 (or 1/3) of the planners left.
25/75 = 1/3 = 0.333333(repeated decimal)
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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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 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%.