x + (x + 2) = 50
Combine like terms.
2x + 2 = 50
Subtract 2 from both sides.
2x = 48
Divide both sides by 2.
x = 24
Now that we have the value of x, we can find the value of the 2nd integer by adding 1 to the value of x.
24 + 1 = 25
The middle integer is equal to 25.Sears sells a sweater for $69 and has a 60% markup on the selling price what is the cost of the sweater to Sears
Answer:
$43.13
Step-by-step explanation:
The original price plus the markup = selling price
The markup = original price * percent markup
So
selling price = original price + original price* percent markup
Factoring out the original price
selling price = original price (1+ percent markup)
Substituting what we know)
69 = original price (1+.60)
69 = original price(1.6)
Divide both sides by 1.6
69/1.6 = original price
43.125 = original price
We round money to the nearest cent
$43.13
To find the cost of the sweater to Sears, divide the selling price by 1.6.
Explanation:To calculate the cost of the sweater to Sears, we need to first find the selling price. A 60% markup on the selling price means that the selling price is 160% of the cost price. Let's say the cost price of the sweater to Sears is C.
So, the selling price of the sweater is 160% of C. In equation form, this can be expressed as: 1.6C = $69.
To find the cost price, we can divide both sides of the equation by 1.6: C = $69/1.6 = $43.125.
The cost of the sweater to Sears is $43.125.
The recursive equation for t(n)=4.5n-8
Answer:
t(1) = -3.5, Recursive equation is t(n) = t(n-1) + 4.5
Step-by-step explanation:
t(n)=4.5n-8
Let find the sequence
Plug in n=1,2,3,4.....
n=1 t(1)=4.5(1) -8= -3.5
n=2 t(2)=4.5(2) -8= 1
n=3 t(3)=4.5(3) -8= 5.5
n=4 t(4)=4.5(4) -8= 10
so sequence is -3.5, 1, 5.5, 10................
Now we find the common difference
1 - (-3.5) = 4.5
5.5-1 = 4.5
10 - 5.5 = 4.5
common difference d = 4.5
Formula for recursive function is
t(n) = t(n-1) + d
We got d= 4.5
t(n) = t(n-1) + 4.5 , also t(1) = -3.5
Final answer:
The student seems confused between a linear and a quadratic equation. The provided equation is linear (t(n) = 4.5n - 8), while the supporting information describes how to solve a quadratic equation using the quadratic formula with specified coefficients.
Explanation:
The question posed by the student pertains to a recursive equation, which is a formula that defines each term of a sequence using preceding terms. However, the recursive equation mentioned (t(n) = 4.5n - 8) seems to be a simple linear equation rather than a recursive one. The student may be asking for a recursive form, but has provided a linear formula instead.
The additional information provided references a quadratic equation where the coefficients a, b, and c are given as 4.90, ±14.3, and ±20.0, respectively. The general form of a quadratic equation is at² + bt + c = 0. The solutions to this quadratic equation can be found using the quadratic formula, which is x = (-b ± √(b² - 4ac)) / (2a). To find the solutions to the given quadratic equation, the values of a, b, and c would be substituted into the quadratic formula and the resulting expression solved.
For clarity, it seems there might be some confusion in the question as it mixes linear and quadratic equations. It is important to correctly identify the type of equation and its coefficients to proceed with finding a solution.
What is the function for the arithmetic sequence 7,9,11,13,15,17
Answer:
Step-by-step explanation: I would say y=x+2 or 2 because every number that you add 2 to, it gives you the solution which is the second number
Hope this helps!!!!
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Find the sum or difference.
20/21. - 5/21. HELP ME PLEASE
A.2/3
B.5/7
C.16/21.
Answer:
It would be B. because if you subtract them you would have 15/21. divide both by three and you get 5/7. Hope this helps
Step-by-step explanation:
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Looking at the graph When X is at 2 meals, the total cost is at Y = 3
Dividing the total coat of the mean by the number of means: 3 / 2 = 1.50
This means Fiona pays $1.50 per meal, which is less than the $1.75 Frank pays.
The answer is: Fiona's meals are less expensive.
6+6-1+45*7= ???????????
HELP
Following PEDMAS ( order of operations, multiplication comes before addition:
6+6-1+45*7=
6 +6 -1 + 315 =
Now do the addition and subtraction from left to right:
6+6 = 12 - 1 = 11 + 315 = 326
The answer is 326.
A school is contemplating purchasing new computers for its computer lab. Each computer costs $1125. The school has a budget of $8,000. What are the possible numbers of computers that the school can buy?
A 0, 1, 2, 3, 4, 5, or 6 computers
B 0, 1, 2, 3, 4, 5, 6, or 7 computers
C 7 computers
D 1, 2, 3, 4, 5, or 6 computers
Answer:
C
Step-by-step explanation:
divide budget by the cost of one computer
An archaeologist at a dig sets up a coordinate system using string. Two similar artifacts are found—one at position (1,4) and the other at (5,2). How far apart were the two artifacts? Round to the nearest tenth of a unit if necessary
Answer:
The distance between both positions are 4.5
Step-by-step explanation:
we are given
Two similar artifacts are found—one at position (1,4) and the other at (5,2)
First point is (1,4)
x1=1
y1=4
Second point is (5,2)
x2=5
y2=2
now, we can use distance formula
[tex]D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
now, we can plug values
[tex]D=\sqrt{(5-1)^2+(4-2)^2}[/tex]
[tex]D=\sqrt{20}[/tex]
[tex]D=4.5[/tex]
Answer:
Step-by-step explanation:
Answer:
The distance between both positions are 4.5
Step-by-step explanation:
we are given
Two similar artifacts are found—one at position (1,4) and the other at (5,2)
First point is (1,4)
x1=1
y1=4
Second point is (5,2)
x2=5
y2=2
now, we can use distance formula
now, we can plug values
Y=-4x y=x^2-12 solve the system of equations
Answer:
-4x = x² - 12
x² + 4x - 12 = 0
(x - 2)(x + 6)
x = -6, 2
{(-6, 24), (2, -8)}
Adele is 5 years older than Timothy. In three years, Timothy will be  of Adele’s age. What is Adele’s current age?
Answer:
Adele's current age is 12
Step-by-step explanation:
Let a = Adele's current age
Let t = Timothy's current age
Adele is 5 years older than Timothy:
a = t + 5 {equation 1}
In 3 years Timothy will be 2/3 of Adele's age:
(2/3)(a + 3) = t + 3 {equation 2}
Since we are looking for Adele's age, let's rearrange equation 1 to:
t = a - 5
Substitute that into equation 2 and solve for a.
(2/3)(a+3) = a - 5 + 3
(2/3)(a + 3) = a - 2
Multiply through by 3 to clear the fraction
2(a+3) = 3a - 6
2a + 6 = 3a - 6
Add 6 to both sides, subtract 2a from both sides
12 = a
Adele is 12 years old
This means Timothy is 7 years old.
Check equation 2 to verify:
(2/3)(a + 3) = t + 3
(2/3)(12+3) = 7 + 3
(2/3)(15) = 10
10 = 10
Answer:
Adele is 12 years old
Step-by-step explanation:
Help me understand this problem please
Answer: 49
==============================================
Explanation:
HI is parallel to KL, so this means that the two triangles can be proven similar through the AA (angle angle) similarity theorem.
Consequently, that means we can set up the proportion below
JH/JK = HI/KL
noticed how the left slant sides JH and JK pair up together on one side; the horizontal sides HI and KL pair up on the other side. I have the larger triangle's side lengths as the numerator for each side
Plug in the given values. Solve for HI
JH/JK = HI/KL
35/15 = HI/21
7/3 = HI/21
21*7 = 3*HI
3*HI = 147
HI = 147/3
HI = 49
This means that 35/15 = HI/21 turns into 35/15 = 49/21
Note: to check the answer that the last equation mentioned is true, we can subtract the fraction 49/21 from both sides to end up with 35/15 - 49/21 = 0. If you type "35/15 - 49/21" into your calculator, you should get 0, which will help confirm we have the right answer.
Solve: 7-5x= -5x - 6x +7
Answer:
actually it is x=0
Step-by-step explanation:
what is the value of
[tex] \sqrt{9 + 16} [/tex]
9 + 16
Answer:
I think it's maybe 5
Step-by-step explanation:
First, you would do 16+9, which is 25
Second, you would figure out the square root of 25, which would be 5
So, 5 would be your answer I guess
Hope this helps :)
Holly, Maria and Johnny went to a fair over Spring Break. Holly paid $12.50 and went on one ride. Maria paid $15.00 and went on two rides. Johnny paid $20.00 and went on 4 rides. With x being the number of rides and y being the total amount paid, is the situation linear and why?
No. Between Holly and Maria there is an increase of $2.50 and between Maria and Johnny there is an increase of $5.00.
Yes. The y-intercept can be determined to be $10.00.
Yes. There is a constant rate of increase of $2.50 for each ride.
No. We are not given the initial cost if they went on no rides.
Answer:
Yes. There is a constant rate of increase of $2.50 for each ride.
Step-by-step explanation:
Lets write each persons cost and rides in the form y =mx+b
y being the total cost and x is the number of rides
Holly
(1 , 12.50)
Maria
(2,15)
Johnny
(4,20)
Lets calculate the slope
m = (y2-y1)/(x2-x1)
= (20-15)/ (4-2)
= 5/2
We can use the point slope form to determine b
y-y1 = m(x-x1)
y-20 = 5/2 (x-4)
Distribute
y-20 = 5/2x -20/2
Add 20 to each side
y-20+20 = 5/2x -10 +20
y = 5/2x +10
The slope or cost per ride is 2.50 and the y intercept is 10
If lines m and n are parallel, and < 2 measures 45°, which is the measure of <3?
a. 30°
b. 45°
c. 90°
d. 180°
Answer:
B
Step-by-step explanation:
The meal costs $52.95 for 5 people. Jenna ordered a dessert for $2.50 if she deducts this amount from the total, how much will each of the other people pay for their meal?
Answer:
10.09
Step-by-step explanation:
52.95-2.50=50.45
divided by 5 = 10.09
How much would your total cost be for a $153.99 item with a 10% discount?
Jade has $10, Julio has $100, and Anna has $1,000. How many Japanese yen would each person get in exchange for their dollars?
Answer:
Jade has 1,124.41 Yen. Julio has 11,244.15 Yen. Anna has 112,445.39 Yen.
Step-by-step explanation:
I know this because I went to an exchange website.
The question was about converting US dollars to Japanese yen. The conversion is based on the exchange rate, last known to be 103 yen per US dollar. Jade with $10 would have 1,030 yen, Julio with $100 would have 10,300 yen and Anna with $1,000 would have 103,000 yen.
Explanation:The value of each individual's dollars in Japanese yen would be determined by the current exchange rate. As of the last known rate, it was approximately 103 yen per US dollar. Therefore:
Jade with $10 would have about 1,030 yen (10 multiplied by 103).Julio with $100 would have approximately 10,300 yen (100 multiplied by 103).Anna with $1,000 would have approximately 103,000 yen (1,000 multiplied by 103).These calculations can change depending on the fluctuations in the exchange rate.
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what is the answer to this math question 4×(-9+12)÷(2×3) I keep getting 14
Answer:
2
Step-by-step explanation:
Answer:
2. Hope this helps.
PS
Can I get brainliest?
Can someone give me the answer for this
Answer:
perpendicular
IF F , G and H are the midpoints of the sides of triangleJKL, FG = 37 , KL = 48 , and GH = 30, find each measure
Answer: The measure of JK is 60 and the correct option is d.
Explanation:
It is given that the points F, G, and H are the midpoints of the sides of triangle JKL , FG = 37, KL = 48, and GH = 30.
The point F is midpoint of JK, point G is midpoint of KL and the point H is midpoint of LJ as shown in figure .
According to the midpoint theorem, the line connecting the midpoints of two sides is parallel to the third and its length is half of the third side.
By midpoint theorem,
Therefore the measure of JK is 60 and the correct option is d
The measure of FH = 24 units, measure of JL = 74, measure of KJ = 60
and, measure of FJ = 30.
What is coordinate geometry?
A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.
As given in the question,
F, G, and H are the midpoints of the sides of ΔJKL.
F is the midpoint of KJ, G is the midpoint KL, H is the midpoint of JL
Measure of the required sides are as follow:
FH = (KL / 2) (by midpoint theorem)
= (48/2)
= 24
JL = 2 x FG (by midpoint theorem)
= 2 x 37
= 74
KJ = 2 x GH (by midpoint theorem)
= 2 x 30
= 60
FJ = GH = 30 (by midpoint theorem)
Therefore, measure of FH = 24, measure of JL = 74, measure of KJ = 60 and measure of FJ = 30.
Learn more about midpoints here :
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In a parking lot of 240 red and blue cars, the ratio of red cars to blue cars is 3 : 5
How many red cars are in the parking lot?
Answer:
Step-by-step explanation:
Given:
240 red and blue cars
3:5 ratio of red cars to blue cars
3 + 5 = 8
red cars: 3/8 * 240 = 90
blue cars: 5/8 * 240 = 150
ratio of red cars to blue cars: 90:150
simplify:
90 ÷ 30 = 3
150 ÷ 30 = 5
Thus: 90:150 = 3:5
Answer:
Imagine math : 90, because 38 of the cars are red
Step-by-step explanation:
Using what you know about percents, explain why a commercial that says "80% of dentists recommend this toothpaste" might be misleading.
Final answer:
The commercial's claim that '80% of dentists recommend this toothpaste' might be misleading because it lacks context and does not specify the criteria or sample size used in the recommendation survey.
Explanation:
The commercial that says "80% of dentists recommend this toothpaste" might be misleading because the 80% figure does not provide the full context of the recommendation. It does not specify whether the recommendation is based on a survey of all dentists or a specific group of dentists. For example, if the survey only included a small sample of dentists who were given incentives to recommend the toothpaste, the result may not accurately represent the entire dentist population. Additionally, the commercial does not provide information about the criteria used for the recommendation. It is possible that the toothpaste is recommended for a specific condition or age group, but not necessarily for everyone. Therefore, it is important to critically evaluate such claims and look for more detailed information before making a decision based solely on the statistic provided in the commercial.
Joel's family has four more pets than Brian's family. Together the two families have at least 7 pets. Let x represent the number of pets Brian's family has. Which inequality can be used to find the possible numbers of pets Brian's family has?
Answer: 2x + 4 ≥ 7
Step-by-step explanation: If Brian = x then Joel = x + 4. Sum up the expressions that represent the amount of pets they have and it has to be greater than or equal to 7 since that is the smallest amount of total pets the two families have. Therefore, the correct answer is 2x + 4 ≥ 7
which statement is true? A)4[3(5+2)]=95-4×3 B)4[3(5+2)] not equal 95-4×3
Answer:
B) 4[3(5+2)] not equal 95-4×3
Step-by-step explanation:
4[3(5+2)]=95-4×3
84=95-4x3
84=83
So since they are not equal B. is the correct answer!
Answer:
Option B.
Step-by-step explanation:
The given expression is
4[3(5 + 2)] = 95 - 4×3
We will solve the left side of the expression first
4[ 3(5 + 2)] = 4[ 3(7) ]
= 4 × 21
= 84
Now we take the right side of the expression
95 - 4×3
= 95 - 12
= 83
Now it's clear that right side of the expression is not equal to the left side of the expression.
Therefore, Option B is the correct option.
Mr. Blaine pays Ron,Nan, and Lin $45 to mow and clean up his yard. If the children share the money equally how much will each person get
Answer:
$15 each
Step-by-step explanation:
$45/3 children= $15 each
Chloe lives in an area where she runs the air conditioned runs for 7 hours per day at a cost of 21 cents per hour. How much does spend per year on utility bills for the air conditioner?( assume there are 30 days in each month)
a. $ 705.60
b. $ 588.00
c. $216.09
d. $176.40
Answer:
$529.20
Step-by-step explanation:
If there are 30 days in a month and there are 12 months in a year,
30*12 = 360
then there are 360 days in a year
Assuming we run at 7 hours per day
7 hrs/ day * 360 days = 2520 hours
We will run 2520 hours in a year
At $.21 per hour,
.21* 2520 = 529.20
It will cost $529.20 to run the air conditioner for the year
None of the choices
Determine which of the following terms is a function: a. (1,2) (2,4) (3,5) c. (1,2) (2,4) (2,6) b. (1,2) (2,3) (1,5) d. (1,2) (3,5) (3,7) Please select the best answer from the choices provided
Final answer:
Only the set of ordered pairs listed in option a. (1,2), (2,4), (3,5) represents a function because each element of the domain is mapped to a unique element of the range.
Explanation:
To determine which of the given terms is a function, we recall that a function is a relation where each element of the domain (the first member of an ordered pair) is mapped to a single, unique element of the range (the second member of the ordered pair).
Option a - (1,2), (2,4), (3,5) has no repeated domain elements, so it is a function.
Option b - (1,2), (2,3), (1,5) has the domain element '1' mapped to two different range elements (2 and 5), so it is not a function.
Option c - (1,2), (2,4), (2,6) has the domain element '2' mapped to two different range elements (4 and 6), so it is not a function.
Option d - (1,2), (3,5), (3,7) has the domain element '3' mapped to two different range elements (5 and 7), so it is not a function.
Therefore, the correct answer is: a. Function 1 only.
Please help with 25
I need this plz
Find the center and the radius of the circle x^2+y^2+6x-4y-12=0 show your work
Answer:
see explanation
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
To obtain this form use the method of completing the square on both the x and y terms
rearranging
x² + 6x + y² - 4y = 12
x² + 2(3)x + 9 + y² + 2(- 2)y + 4 = 12 + 9 + 4
(x + 3)² + (y - 2)² = 25 ← in standard form
with centre = (- 3, 2) and r = [tex]\sqrt{25}[/tex] = 5