Answer:
[tex]\large\boxed{x=\dfrac{17}{7}}[/tex]
Step-by-step explanation:
[tex]\text{A geometric mean of}\ x\ \text{and}\ y:\\\\\sqrt{xy}\\\\\text{Let}\ x-\text{the number}.\\\\\text{Substitute:}\\\\\sqrt{17}=\sqrt{(7)(x)}\iff17=7x\qquad\text{divide both sides by 7}\\\\\dfrac{17}{7}=\dfrac{7x}{7}\to x=\dfrac{17}{7}[/tex]
The running back for the Bulldogs football team carried the ball 5 times for a total loss of 11 1/4 yards. Find the average change in field position on each run. Enter the average change as a simplified mixed number.
Answer:
[tex]\displaystyle 2\ \frac{1}{4}[/tex]
Step-by-step explanation:
Fractions
They can be expressed as proper fractions, improper fractions or mixed numbers. Proper fractions are such that the numerator is less than the denominator, like 2/5, 7/11, -9/10. Improper fractions are those whose numerators are greater than the denominator, such as 5/3, 10/9, -21/8.
Mixed numbers are expressions made of whole numbers and a proper fraction, like 4 3/5, 1 1/2, -5 4/9. Mixed numbers can be transformed to improper fractions and vice-versa.
The question requires us to find the average change in field position on each run of the running back for the Bulldogs football team which carried the ball 5 times for a total loss of 11 1/4 yards.
The number 11 1/4 is mixed, to express it as an improper fraction, we add the numbers like
[tex]\displaystyle 11+\frac{1}{4}=\frac{45}{4}[/tex]
This improper fraction will now be divided by 5 to find the average of 5 runs:
[tex]\displaystyle \frac{\frac{45}{4}}{5}=\frac{9}{4}[/tex]
We now need to separate the improper fraction to a mixed number, let's just divide 9 by 4 to get 2 as the quotient and 1 for the remainder, thus
[tex]\boxed{\displaystyle \frac{9}{4}=2\ \frac{1}{4}}[/tex]
What are the angle measurements of 6x + 1° = 3x + 11°
Answer:
[tex]x=3\frac{1}{3}^\°[/tex]
Step-by-step explanation:
Given equation:
[tex]6x+1\°=3x+11\°[/tex]
To find the angle measure of [tex]x[/tex]
Solution:
In order to find the angle measure [tex]x[/tex] , we will isolate [tex]x[/tex] on left side by carrying out math operations on both sides.
We have:
[tex]6x+1\°=3x+11\°[/tex]
Subtracting both sides by [tex]3x[/tex]
[tex]6x-3x+1\°=3x-3x+11\°[/tex]
[tex]3x+1\°=11\°[/tex]
Subtracting both sides by 1°.
[tex]3x+1\°-1\°=11\°-1\°[/tex]
[tex]3x=10\°[/tex]
Dividing both sides by 3.
[tex]\frac{3x}{3}=\frac{10\°}{3}[/tex]
[tex]x=\frac{10}3}^\°[/tex]
Converting fraction to mixed number by dividing and writing the quotient as whole number and the remainder as numerator.
∴ [tex]x=3\frac{1}{3}^\°[/tex] (Answer)
consider the functions given below
f(x) + -3x-5
g(x) + f(x)+9
what is the y intercept of g
The y-intercept of the function g(x), defined as g(x) = f(x) + 9 where f(x) = -3x - 5, is 4. This is determined by evaluating g(0), resulting in a y-intercept at the point (0, 4).
Explanation:The question asks about finding the y-intercept of the function g(x), which is defined in terms of another function f(x). Given that f(x) is equal to -3x - 5 and g(x) equals f(x) + 9, to find the y-intercept of g(x), we substitute x with 0 in the function f(x) and then add 9. The y-intercept is the point where the function crosses the y-axis, which is when x = 0.
First, we find the value of f(0):
f(0) = -3(0) - 5 = -5Next, we determine g(0) by adding 9 to the value of f(0):
g(0) = f(0) + 9 = -5 + 9 = 4Therefore, the y-intercept of g(x) is 4, which means the line representing g(x) crosses the y-axis at the point (0, 4).
Kayla takes 3 quizzes each week. How many weeks of school will Kayla have to attend his quarter before she will have taken a total of 9 quizzes
Answer:3 weeks
Step-by-step explanation:The reason for that is because if Kayla is taking 3 tests each week then 3 times 3 is 9 so three weeks.
Which expression is equivalent to 5(2x + 10)?
A. 2x + 15
B. 2x + 50
C. 7x + 15
D. 10x + 10
E. 10x + 50
Will mark as brainliest
Help trigonometry ( angles of evaluation and depression)
Answer:
y ≈ 242.4 ft
Step-by-step explanation:
The lower angle in the triangle is 29° ( alternate angles )
Using the sine ratio in the right triangle
sin29° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{y}{500}[/tex]
Multiply both sides by 500
500 × sin29° = y, thus
y ≈ 242.4 ft ( to the nearest tenth )
Kwesi is putting on sunscreen. He uses 3\text{ ml}3 ml3, start text, space, m, l, end text to cover 45 \text{ cm}^245 cm
2
45, start text, space, c, m, end text, squared of his skin. He wants to know how many milliliters of sunscreen (g)(g)left parenthesis, g, right parenthesis he needs to cover 240\text{ cm}^2240 cm
2
240, start text, space, c, m, end text, squared of his skin. He assumes the relationship between milliliters of sunscreen and area is proportional.
How many milliliters of sunscreen does Kwesi need to cover 240 \text{ cm}^2240 cm
2
240, start text, space, c, m, end text, squared of his skin?
Answer:
16 mL
Step-by-step explanation:
The ratio of areas is (245 cm²)/(45 cm²) = 16/3, so Kwesi expects the ratio of volumes to be the same:
(needed volume)/(3 mL) = 16/3
needed volume = (16/3)×(3 mL) = 16 mL
Kwesi expects to need 16 mL of sunscreen to cover 240 cm² of skin.
Joanna buys a table and 2 chairs. She receives a 25% discount for being a preferred customer and then pays 6% sales tax on the discounted purchase price. If the table costs $250 and each chair costs $100, what is the total purchase price?
The total purchase price is $ 357.75
Solution:
Joanna buys a table and 2 chairs
Cost of table = $ 250
Cost of 1 chair = $ 100
Therefore, cost of a table and 2 chairs = 250 + 2(100) = 450
Thus, cost price = $ 450
She receives a 25% discount for being a preferred customer
Therefore, discount = 25 % of cost price
[tex]discount = 25 \% \times 450\\\\discount = \frac{25}{100} \times 450\\\\discount = 0.25 \times 450 = 112.5[/tex]
Thus, amount after discount = cost price - discount
amount after discount = 450 - 112.5 = 337.5
Thus, amount after discount is $ 337.5
Then pays 6% sales tax on the discounted purchase price
Sales tax = 6 % of 337.5
[tex]sales\ tax = 6 \% \times 337.5\\\\sales\ tax = \frac{6}{100} \times 337.5\\\\sales\ tax = 20.25[/tex]
Thus, total purchase price is given as:
total purchase price = Amount after discount + sales tax
total purchase price = 337.5 + 20.25 = 357.75
Thus total purchase price is $ 357.75
The perimeter of an equilateral triangle is directly proportional to the length of one of its sides. The perimeter is 17.7
when the length of a side is 5.29. What is the constant of proportionality
Answer: 3.35 in 3 significant figures.
Step-by-step explanation:
According to question,
Perimeter ∝ length
Here, ∝ means directly proportional.
To remove symbol, introduce a constant. Let the constant be k.
Perimeter ∝ length
Perimeter = k × length
Now, perimeter = 17.7 and length = 5.29
Perimeter = k × length
k = perimeter / length
k = 17.7 / 5.29
k = 3.35 in 3 significant figures.
Answer:
3
Step-by-step explanation:
k=y/x
k=17.75/5.29
k= 3.345
=3
On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3). What is the rule for the reflection? rx-axis(x, y) → (–x, y) ry-axis(x, y) → (–x, y) rx-axis(x, y) → (x, –y) ry-axis(x, y) → (x, –y)
The reflection transformation of the triangles is C) [tex]( rx-axis(x, y) \rightarrow (x, -y) )[/tex].
The points of the original triangle are:
M (-5, 4) N (-2, 3) L (-4, 2)The points for the reflected triangle are:
L' (-4, -2) M' (-5, -4) N' (-2, -3)Identify the transformation
From the pairs of coordinates, we can observe how each point has changed from the original triangle to the reflected triangle:
M (−5, 4) was reflected to M' (−5, −4). N (−2, 3) was reflected to N' (−2, −3). L (−4, 2) was reflected to L' (−4, −2).Analyze the change in coordinates
We see that for each point, the x-coordinates remain unchanged while the y-coordinates change sign from positive to negative. This indicates that the reflection is across the x-axis.
Reflection rule
The general rule for reflection across the x-axis can be stated as follows:
If a point is given by (x, y), then the reflected point will be (x, -y).
Reflection across the x-axis :
[tex]( rx-axis(x, y) \rightarrow (x, -y) )[/tex]
Complete question
On a coordinate plane, 2 triangles are shown. The first triangle has points M (negative 5, 4), N (negative 2, 3), and L (negative 4, 2). The second triangle has points L prime (negative 4, negative 2), M prime (negative 5, negative 4), and N prime (negative 2, negative 3). What is the rule for the reflection?
a. rx-axis(x, y) → (–x, y)
b. ry-axis(x, y) → (–x, y)
c. rx-axis(x, y) → (x, –y)
d. ry-axis(x, y) → (x, –y)
what is the answer to x over 7 = 89
Answer: x = 623
Step-by-step explanation: In this problem, notice that x is being divided by 7 so to get x by itself,
we need to multiply both sides of the equation by 7.
Notice that on the left side, the 7 and 7 cancel each other out so we're just left with x. On the right side we have
89 x 7 which is 623 so x = 623.
Finally, we can check our answer by plugging a 623 back into the original equation. So we have [tex]\frac{(623)}{7} = 89[/tex] or 89 = 89. Since this is true, our answer checks.
use an identity to find the value of expression. sin 40° csc 40°
Answer:
Step-by-step explanation:
1. sin37xcsc37
For this use the recipricol identity. csc37 = 1/sin37
sin37x(1/sin37) = (sin37)/(sin37) = 1
2. sec^2(23) - tan^2(23)
For this one use the pythagorean identity
sec^2(23) = 1+tan^2(23)
1+tan^2(23) - tan^2(23) = 1
Give two ways to write the algebraic expression 13 ÷ y in words
Answer:
thirteen divided by y
Step-by-step explanation:
Solve this 8x-6(3-2x)
Answer:
20x−18
Step-by-step explanation:
Apply the distributive property.
8x−6⋅3−6(−2x)8x-6⋅3-6(-2x)
Multiply −6-6 by 33.
8x−18−6(−2x)8x-18-6(-2x)
Multiply −2-2 by −6-6.
8x−18+12x
Add 8x8x and 12x12x.
20x−18
The given expression 8x - 6(3 - 2x) simplifies to 20x - 18.
The expression is given as follows:
8x - 6(3 - 2x)
As we know that algebraic expressions are mathematical statements that comprise at least two variables or integers.
Start by distributing the -6 to the terms inside the parentheses:
⇒ 8x - 6 × 3 + 6 × 2x
Simplify the above expression to get:
⇒ 8x - 18 + 12x
Combine like terms in the above expression to get:
⇒ 20x - 18
Therefore, the given expression 8x - 6(3 - 2x) simplifies to 20x - 18.
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Which expression is equivalent to (2x^2+4-7)(x-3)
Answer:
0
Step-by-step explanation:
Claire wants to solve the equation -1/4(x-1)=2/3x+2. Which step would not be an appropriate first step for Claire to take to solve for x?
A. Multiply both sides by -4.
B. Use the distributive property to distribute -1/4
C. Add 1 to both sides.
D. Multiply both sides by 3/2.
Answer:
A
Step-by-step explanation:
The answer is A because it says -4 and not -1/4.
Final answer:
Option C, adding 1 to both sides, is not an appropriate first step in solving the equation -1/4(x-1)=2/3x+2. Claire should instead focus on simplifying the equation, such as using distributive property or eliminating fractions.
Explanation:
To solve the equation -1/4(x-1)=2/3x+2, there are several steps that Claire can take. However, answer option C, which suggests adding 1 to both sides, is not an appropriate first step for solving for x. Instead, Claire might consider other steps like using the distributive property or getting rid of the fractions by multiplying both sides of the equation by a common denominator.
When solving linear equations, it is generally more logical to start by simplifying each side of the equation by using distribution or by eliminating fractions. This makes further manipulation of the equation simpler and more straightforward. The inappropriate step of adding 1 would create an extra unnecessary step, not simplifying the equation in a beneficial way.
If m^2 + 8 = 39, then m^2-7=?
Answer:
24
Step-by-step explanation:
Subtract 15 from both sides of the equation:
m^2 +8 -15 = 39 -15
m^2 -7 = 24
Determined if the sequence is geometric if it is find the common ratio : -1,1,4,8
The given sequence is not geometric because they don't have a common ratio.
What is geometeric sequence?
A geometric sequence is set of numbers which have a common ratio. The next number in a geometirc sequence is the multiple of the previous number.
Ratios of the numbers in the sequence-1/1 = -1
4/1 = 4
8/4 = 2
The numbers don't have a common ratio.
Thus, we can conclude that the given sequence is not geometric because they don't have a common ratio.
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The common ratio is not the same for all pairs of consecutive terms, so the sequence is not geometric.
To determine if a sequence is geometric, we need to check if there is a common ratio between consecutive terms.
In a geometric sequence, each term is obtained by multiplying the previous term by a constant value called the common ratio.
Let's check the given sequence: -1, 1, 4, 8.
To find out if it is geometric, we need to check if the ratio of consecutive terms is constant:
Common Ratio (r) = (Second Term) / (First Term)
= 1 / (-1)
= -1
Now, let's check if the common ratio is the same for the other pairs:
1st and 2nd terms: 1 / (-1) = -1
2nd and 3rd terms: 4 / 1 = 4
3rd and 4th terms: 8 / 4 = 2
The common ratio is not the same for all pairs of consecutive terms. Since the common ratio is not constant, the given sequence (-1, 1, 4, 8) is not a geometric sequence.
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jake ordered 275 large pizzas for a party. when the party was over he had 250 large pizzas remaining. estimate the percent decrease in the number of large pizzas.
Answer:
9% decrease
Step-by-step explanation:
Owen and his friend kayden are going to a carnival that has games and rides . Owen played 5 games and went on 6 rides and spent a total of 28.75 kayden played 4 games and went on 3 rides and spent a total of 16.25. Determine the cost of each game and the cost of each ride
Each game costs 1.25 and each ride costs 3.75
Step-by-step explanation:
Let,
Cost of each game = x
Cost of each ride = y
According to given statement;
5x+6y=28.75 Eqn 1
4x+3y=16.25 Eqn 2
Multiplying Eqn 2 by 2
[tex]2(4x+3y=16.25)\\8x+6y=32.50\ \ \ Eqn\ 3[/tex]
Subtracting Eqn 1 from Eqn 3
[tex](8x+6y)-(5x+6y)=32.50-28.75\\8x+6y-5x-6y=3.75\\3x=3.75[/tex]
Dividing both sides by 3
[tex]\frac{3x}{3}=\frac{3.75}{3}\\x=1.25[/tex]
Putting x=1.25 in Eqn 1
[tex]5(1.25)+6y=28.75\\6.25+6y=28.75\\6y=28.75-6.25\\6y=22.50[/tex]
Dividing both sides by 6
[tex]\frac{6y}{6}=\frac{22.50}{6}\\y=3.75[/tex]
Each game costs 1.25 and each ride costs 3.75
Keywords: linear equation, elimination method
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Final answer:
The cost of one game is 1.25 dollars and the cost of one ride is 3.75 dollars at the carnival. This was determined by setting up and solving a system of equations based on the expenses of Owen and Kayden.
Explanation:
To determine the cost of each game and each ride at the carnival, we can set up a system of equations based on Owen and Kayden's expenses. Let x represent the cost of one game and y represent the cost of one ride.
Owen played 5 games and went on 6 rides for a total cost of 28.75 dollars. This can be represented by the equation:
5x + 6y = 28.75
Kayden played 4 games and went on 3 rides for a total cost of 16.25 dollars. This can be represented by the equation:
4x + 3y = 16.25
We now have a system of linear equations:
5x + 6y = 28.75
4x + 3y = 16.25
To solve the system, we can multiply the second equation by 2 to align the y-terms:
5x + 6y = 28.75
8x + 6y = 32.50
Subtracting the first equation from the multiplied second equation, we get:
3x = 3.75
Dividing both sides by 3, we find that x = 1.25, which is the cost of one game.
To find the cost of one ride, we substitute x = 1.25 into either of the original equations. If we use the second equation 4(1.25) + 3y = 16.25, we get:
3y = 16.25 - 5
3y = 11.25
y = 3.75
Therefore, the cost of one ride is 3.75 dollars.
HELPPPPPP!!!
Rule: y=x-1/4
Step-by-step explanation:
if x=1/4 then y=1/4-1/4=0
if x=13/4 then y=13/4-1/4=12/4=3
if x=2 then y=2-1/4=8/4-1/4=7/4=1 3/4
How many solutions does this system have? x- y = - 4. 3 x + y = 8.
Answer:
one solution (1,5)
Step-by-step explanation:
if you graph the equations on a graph the line would intersect.
intersect = one solution
overlap = infinite solutions
parallel = no solution
a college graduates by a factor of 1.045 every year since 1999. in 1999 924 student graduated approximately how many students will graduate in 2014
Answer:
1788
Step-by-step explanation:
The number of students who graduates from college is multiplied by a factor of 1.045 every year since 1999.
So, the number of students graduated every year can be modeled as
[tex]G(x) = 924(1.045)^{x}[/tex] where x is the number of the year since 1999.
Now, in 2014, the x value is (14 + 1) = 15 years.
So, the number of students who will graduate in 2014 is given by
[tex]G(15) = 924(1.045)^{15} = 1788.2[/tex] ≈ 1788. (Answer)
area of irregular shapes
Answer:
To find area of irregular shapes you need to divide the irregular shape to get a new shape (for instance: rectangle); then you have to find the area of that particular shape using its formula (for instance: area of square = side*side)
In Mr. Martinez’s class there are 8 boys and 12 girls. What is the probability of randomly selecting a girl?
Answer:
3/5
Step-by-step explanation:
there are 20 people altogether in the class (12 plus 8)
since 12 of them are girls the probability it 12/20
but to simplify it we divide both sides of the fraction by 4 (as that's the largest whole number they will both divide by) and we get 3/5
5x + 2y = 29 and 8x - 8y = 80
Answer:
both of The answers are equal to Zero
At bright minds learning , 75% of employees work as instructors . If there are 300 employees at bright mind Learning , how many of them work as instructors
Answer:
Number of instructors are 225.
Step-by-step explanation:
Given:
Total number of employees at bright mind learning = 300
Number of instructors = 75%
We have to convert this percentage and find the number.
So,
[tex]75\%[/tex] can be written as [tex]\frac{75}{100}=0.75[/tex]
Now 75% of 300 employees are the instructors at Bright mind learning.
Can be written as [tex]0.75*300=225[/tex]
Number of instructors at Bright mind learning =225
7-4+6=7 Complete the equation to make it equal
Answer:
7-4+6=7 + 2
Step-by-step explanation:
The original equation 7-4+6=7 is incorrect because it simplifies to 9, not 7. There is no simple way to adjust the equation with the given numbers to make the equation balance correctly. It's crucial to check your work and make sure the equation balances, just like ensuring a chemical equation has equal numbers of atoms on both sides.
To complete the equation 7-4+6=7 to make it equal, we need to perform the operations on the left side of the equation and see if the result is indeed 7, the same as the right side. Let's solve it step by step:
First, subtract 4 from 7, which gives us 3.Next, add 6 to this result, which gives us 3 + 6 = 9.So, the left side of the equation is actually 7-4+6, which calculates to 9.Since 9 does not equal 7, there seems to be an error in the equation as presented.The original equation 7-4+6=7 is incorrect because 7-4+6 equals 9, not 7. To make the equation correct, we would need to change a number or an operation. One possible solution could be adding parentheses: (7-4)+6=7+2, which simplifies to 3+6=9, but again that does not equal 7. Therefore, there is no simple way to correct the equation using basic operations without changing the numbers given.
To make sure the charge and atoms on both sides of an equation balance or to ensure the correctness of a mathematical operation, eliminating terms where possible to simplify the algebra and checking the answer to see if it’s reasonable are important steps.
When balancing equations, whether they are chemical equations or mathematical ones, it's essential to make sure each side is equal to maintain the balance, as seen in the example: 7 carbon atoms, 16 hydrogen atoms, and 22 oxygen atoms on each side of a balanced chemical equation.
Is the expression 3(x+ 1 1/2)-3 equivalent to 3x+ 1 1/2?
Answer:
No, because 3x+9/2 isn't equivalent to 3x+3/2.
Step-by-step explanation:
1 1/2=3/2
3(x+3/2)=3x+9/2