the larger of two numbers is 7 less than three times the smaller number. if the sum of the numbers is 61, find the numbers

(2, 2 ), (- 2, 18 ), (0, 10 )

substitute the x-coordinate of each point into f(x) and if the value is equal to the y-coordinate then it is on the graph of f(x)

(- 18, 2 ) ⇒ y = 10 + 72= 82 ≠ 2

(- 10, 0 ) ⇔ y = 10 + 40 = 50 ≠ 0

(- 2, - 2 )⇒ y = 10 + 8 = 18 ≠ 2

(18, - 2 ) ⇒ y = 10 - 72 = - 62 ≠ - 2

(2, 2 ) ⇒ y = 10 - 8 = 2 ⇒ (2, 2 ) is on graph

(- 2, 18 ) ⇒ y = 10 + 8 = 18 ⇒ (- 2, 18 ) is on graph

(0, 10 )⇒ y = 10 - 0 = 10 ⇒ (0, 10 ) is on graph

(2, - 18 ) ⇒ y = 10 - 8 ≠ - 18

Final answer:

To find the missing term in the proportion 72:24 = 15:__, you divide 72 by 24 to find the common ratio, which is 3. Then, you set 15/x = 3 and solve for x, giving you the missing term 5, making the proportion 72:24 = 15:5.

Explanation:

To find the missing term in the proportional relationship 72:24 = 15:__, we can set up a proportion where both ratios are equal. We know that 72 divided by 24 equals 3, so the missing term, which we'll call x, needs to satisfy the equation 15/x = 3.

By cross-multiplying, we get:

15 * 1 = 3 * x

15 = 3x

x = 15 / 3

x = 5

Therefore, the missing term is 5, and the proportion correctly reads 72:24 = 15:5.

x = 6

given f(x) = 310, we obtain the equation

10 + 50x = 310 ( subtract 10 from both sides )

50x = 300 ( divide both sides by 50 )

x = [tex]\frac{300}{50}[/tex] = 6

Let n = the unknown number.

Six times a number =  6 * n = 6n

20 more than number = n + 20

Greater than = >

Put it all together:

6n > n + 20

Subtract n from both sides to get constants on one side and variables on the other:

6n - n > 20

5n > 20

Divide both sides by 5 to isolate variable N

n > 4

or (4, ∞)

slope intercept form: y = mx + b

Note the equal sign. what you do to one side, you do to the other. First, subtract 4x from both sides

4x - 3y = 15

4x (-4x) - 3y = 15 (-4x)

-3y = -4x + 15

Next, divide -3 from both sides to isolate the y.

(-3y)/-3 = (-4x + 15)/-3

y = (4/3)x - 5

y = (4/3)x - 5 is your answer

hope this helps

The correct option is Brianna's equation [tex]\dfrac{1}{p^5q^0}[/tex].

To find the correct simplification of given expression we have to apply negative exponent rule.

Given:

The given expression is [tex]\dfrac{p^{-5}}{q^0}[/tex].

The negative exponent can be change in to positive by writing same in denominator and 1 in numerator.

Simplify the given expression.

[tex]\dfrac{p^{-5}}{q^0}=\dfrac{1}{p^5q^0}[/tex]

Thus, the correct option is Brianna's equation [tex]\dfrac{1}{p^5q^0}[/tex].

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Answer: 32

Step-by-step explanation:

Complete solution is attached below.

Answer: -3< 0

Step-by-step explanation: this means -3 is less than 0.

As on number line -3 and 0 are marked. We know 0 is origin if we go rightward i .e towards the positive number all numbers are greater than zero.

But if we move leftward on number line the numbers are less than zero.

To solve this problem we propose the following equation:

1) [tex]b*h =45\\[/tex]  This is the equation of the area of a rectangle.

Where a and b are the sides of the rectangle

If b is the longest side, then

b is 80% longer than h.

2) [tex]b= h+0.8h\\[/tex]

Now we have 2 equations and two unknowns.

Therefore we solve the following equations

[tex]45=b*\frac{b}{1+0.8}\\[/tex]

[tex]b^2=45(1+0.8)[/tex]

[tex]b =\sqrt{45(1+0.8)}\\[/tex]

b = 9 feet

The length of the longest side is 9 feet.

The area of a rectangle is 45 ft^2

If the length of the long side of the rectangle is 80% greater than the short side of the rectangle.

Let the shortest side be the width (x)

Length of rectangle L = 80% greater than x

So length = 0.8 x + x

Length = 1.8 x

Area of the rectangle = Length * width

45 = 1.8x * x

[tex]45= 1.8x^2[/tex]

Divide by 1.8 from both sides'

[tex]25= x^2[/tex]

Take square root on both sides

x=5

so width of the rectangle = 5 feet

Length of the rectangle (longer side) = 1.8x = 1.8 * 5 = 9 feet

Answer:

y = 7x/5 - 5

Step-by-step explanation:

m = 7/5

y - 2 = 7/5(x - 5)

y - 2 = 7x/5 - 7

y = 7x/5 - 5

Your answer is C. Y= -4x-12

Answer:

NOT the graph A and the graph B.

Step-by-step explanation:

y = mx + b

m - slope

b - y-integer

If m > 0 then the function is increasing.

if m < 0 then the function is decreasing.

We have y = -2x + 3

m = -2 < 0 the function is decreasing

b = 3 y-intercept = 3

The x-intercept: y = 0. Substitute

0 = -2x + 3     add 2x to both sides

2x = 3    divide both sides by 2

x = 1.5

Therefore your answer is C or D (look at the picture)

First, model it out in an equation, and lets say x is the amount carrie walked

x+2x+3x=15

Then, combine like terms

6x=15

then divide

2.5

So now we have carries walk speed, then we go by the question, multiply 3 by 2.5 for amy, and 2 by 2.5 for marcus

carrie walked 2.5 miles

marcus walked 5 miles

amy  walked 7.5

To find out how many miles Amy, Marcus, and Carrie each walked, algebra is used. Carrie walked 2.5 miles, Marcus walked twice as much (5 miles), and Amy walked three times as much as Carrie (7.5 miles), totaling 15 miles.

The student is asking how many miles Amy, Marcus, and Carrie each walked if together they walked a total of 15 miles in the Wilbur School Walkathon, with Marcus walking twice as far as Carrie, and Amy walking three times as far as Carrie. To solve this problem, we can use algebra. Let's denote the number of miles Carrie walked as c. According to the problem, Marcus walked twice as far as Carrie, so Marcus walked 2c miles. Amy walked three times as far as Carrie, therefore Amy walked 3c miles.

Total distance walked by all three together is 15 miles.

Carrie walked c miles.

Marcus walked 2c miles.

Amy walked 3c miles.

The sum of their distances is equal to the total distance, so we can write the equation c + 2c + 3c = 15. When we add up the left side, we get 6c = 15. To find out how many miles Carrie walked, we divide both sides of the equation by 6, resulting in c = 15 / 6, which simplifies to c = 2.5. Carrie walked 2.5 miles.

Since Marcus walked twice as much, Marcus walked 5 miles (2 times 2.5). And since Amy walked three times as much as Carrie, Amy walked 7.5 miles (3 times 2.5).

The correct way to write the number 3.405 in expanded form is 3×1 + 4×1/10 + 5×1/1,000.

The weight of Darrin's phone is given as 3.405 ounces. You are asked to write this decimal number in expanded form. The concept of expanded form is a way to break down numbers to show how each digit in a number has a value based on its position or place. In the case of 3.405, the 3 is in the ones place, the 4 is in the tenths place, and the 5 is in the thousandths place. As such, when we expand the number, we multiply each digit by the place it represents: 3×1 + 4×1/10 + 5×1/1,000 , option A is the correct one for representing the number 3.405 in expanded form.

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[tex]5(2q-8)\geq7\\10q-40\geq7\\10q\geq47\\q\geq4.7[/tex]

so the solution is not really a single number but a range, depending on how q is defined. I am assuming q is defined in domain of Real numbers, and then the solution to the inequality will be "all real numbers larger or equal to 4.7"

C) X also increases to y7 times its original value

To estimate the number of bottles Margaret can fill, multiply the daily milk production (21.7 liters) by the number of production days (280) to get the total milk produced, then divide this by the volume of one bottle (0.5 liters) to determine the number of bottles (12152).

Estimating Number of Bottles from Milk Production

Margaret has goats that produce an average of 21.7 liters of milk a day for 280 days. The key task here is to estimate how many half-liter bottles could be filled with this amount of milk. Since each bottle holds half a liter, we need to calculate the total volume of milk and then divide it by the volume of one bottle, which is 0.5 liters.

Therefore, Margaret would be able to fill an estimated 12152 half-liter bottles with the milk produced.

Answer:

Team A= 2b-5

Team B= b

Team C= b+80

The equation representing this scenario is (2b-5)+ b + (b+80)= 983

Step-by-step explanation:

Solving the equation b + (2b - 5) + (b + 80) = 983, we found that Team B scored 227 points. Therefore, Team A scored 449 points and Team C scored 307 points.

To represent the scenario mathematically, let's define the variable b as the total points scored by Team B. Then, we can express the points scored by the other two teams in terms of b:

The combined score for all three teams was 983 points. Thus, we can write the equation:

Simplify the equation step-by-step:

So, Team B scored 227 points.

Answer:

20 2/5

Step-by-step explanation:

25 1/2

  1 1/4

1 1/4 times 4 is 5

5 times 5 is 25

Hello!

[tex]\frac{3}{10}*\frac{8}{9}[/tex]

Explanation:

↓↓↓↓↓↓↓↓↓↓

First you had to multiply by the fractions.

[tex]\frac{3*8}{10*9}[/tex]

Then you can multiply by the numbers.

[tex]\frac{24}{10*9}[/tex]

Next you can also multiply by the numbers again.

[tex]\frac{24}{90}[/tex]

You can also can the common factor of 6.

[tex]\frac{4}{15}[/tex]

Answer⇒⇒⇒⇒⇒4/15

Hope this helps!

Thank you for posting your question at here on Brainly.

Have a great day!

-Charlie

Not for just 5 points...

1.There are 167960 different ways the list of starting players could be formed.

2. The number of ways to write the batting order is 362880.

3. 42,758,676 different ways the group of interviewees can be made.

4. The total number of ways the students can win first, second, or third place is 144 ways.

5. The total number of different answer keys possible is 4096 ways.

1. **Varsity Baseball Team:**

  There are 20 students on the team, and 9 will be chosen for the starting lineup. The number of ways to choose 9 out of 20 students is calculated by the binomial coefficient formula, also known as "20 choose 9":

 [tex]\[ \binom{20}{9} = \frac{20!}{9!(20-9)!} = 167960. \][/tex]

2. **Batting Order:**

  Once the starting lineup is selected, there are 9 players. The first position can be any of the 9 players, the second position can be any of the remaining 8 players, and so on. So, the number of ways to write the batting order is [tex]\(9! = 362880\) (9 factorial).[/tex]

3. **Jury Duty:**

  There are 42 citizens, and 11 need to be chosen. The number of ways to choose 11 out of 42 is given by the binomial coefficient [tex]\(\binom{42}{11} = \frac{42!}{11!(42-11)!}\).[/tex] Calculating this gives [tex]\(42,758,676\)[/tex] different ways the group of interviewees can be made.

4. **Spelling Bee:**

  There are 24 students competing for first, second, and third place. For the first place, there are 24 choices, for the second place, there are 23 choices (as one student has already won the first place), and for the third place, there are 22 choices left. So, the total number of ways the students can win first, second, or third place is [tex]\(24 \times 23 \times 22 = 12,144\)[/tex] ways.

5. **Multiple Choice Test:**

  Each of the 6 questions has 4 possible answers. For each question, there are 4 choices. Since there are 6 questions, the total number of different answer keys possible is [tex]\(4^6 = 4096\)[/tex] ways.

For more such questions on number of ways

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Answer:

Your answer would be 7.

Step-by-step explanation:

9 - 8/s first you divide 8 and s which in this case is 4.

8/4 is 2.

9 - 2 = 7

Therefore, your answer is 7

The required value of 9 -8/s when x = 4 is 7.

Given that,
to determine the value of the expression 9- 8/s when s=4.

Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.

The procedure in mathematics to perform and solve the expression to make expression simple or more understandable called simplify and the process is called simplification.

Here,
Let the given expression is equal to x
x = 9 - 8/s
here, s = 4
x = 9 - 8 /4
x = 9 - 2
x = 7

Thus, the required value of 9 -8/s when x = 4 is 7.

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The coordinates of the entrance to the new city park on this map should be (-5, -3).

In Mathematics and Geometry, a reflection over or across the y-axis or the line y = 0 is represented by this transformation rule .

This ultimately implies that, a reflection over or across the y-axis would maintain the same y-coordinate while the sign of the x-coordinate changes from positive to negative or negative to positive.

By applying a reflection over the y-axis to the coordinates of the point for the school entrance (5, -3), we have the following coordinates of its image;

(x, y)         →              (-x, y)

(5, -3)        →         (-5, -3)

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Courage.

Heros often take risks, you must have courage to take risks.

Answer:

Courage

Step-by-step explanation:

Hero has some special characteristics which makes him hero

one of those characteristics of a hero is that a hero always shows courage and never fall down or run out from the situations instead he faces all the challenges with courage and never pocks down even in tricky situations.

a hero is that which helps the other when they need him in any situation or at any mode  of life.a real hero does not care for his life .To save others he put his life in danger and shows courage.

all these qualities make a person a real hero.

B because 30% of 1000 is 300

Answer:

Option B) $1000 would be correct.

Step-by-step explanation:

Jacklyn's employer matches 30% of Jacklyn's contributions to her 401(k) plan.

Let Jacklyn's contribution = x

Her employer's contribution = 30% of x = 300

= [tex]\frac{30x}{100}[/tex] = 300

= 30x = 300 × 100

= x = 30000 ÷ 30 = $1000

Jacklyn contributed $1000 to the 401(k) plan last year.

d(4) = 64

substitute n = 2, 3, 4 into d(n) = d(n - 1) + 17

d(2) = d(1) + 17 = 13 + 17 = 30

d(3) = d(2) + 17 = 30 + 17 = 47

d(4) = d(3) + 17 = 47 + 17 = 64

If it's $2.70 now, the cost would be $4.45 in 1995.

To find the 1995 cost of a movie ticket that was $2.70 in 1980, divide the 1995 CPI by the 1980 CPI and multiply by the 1980 price. The calculation yields a cost of approximately $4.99 for a movie ticket in 1995.

To calculate the cost of a movie ticket in 1995 using the Consumer Price Index (CPI) from 1980 to 1995, we can use the formula to adjust prices based on inflation:

Let's assume the cost of a movie ticket in 1980 was $2.70. The CPI for 1980 is 82.4, and for 1995 it is 152.4. We calculate the ratio as 152.4 / 82.4 = 1.8495.

Multiplying the 1980 ticket price by this ratio gives us:

$2.70 * 1.8495 = $4.99 approximately.

Therefore, the cost of a movie ticket in 1995, adjusted for inflation, would be about $4.99.