solve the system of linear equations by substitution.

4x−2y=14
y=12x−1

Final answer:

Michelle used 70 beads to make her 14-inch long necklace, as determined by solving the equation 1/7b + 4 = 14 and isolating the variable b.

Explanation:

The question asks us to solve for the number of beads, b, in a necklace that is 14 inches long. The equation given is 1/7b + 4 = 14. We need to solve for b.

To solve for b, we first subtract 4 from both sides of the equation to get 1/7b = 10. Next, we multiply both sides by 7 to isolate b on one side of the equation, which gives us b = 70. Therefore, Michelle used 70 beads for her necklace.

The real-world problem involves maintaining a minimum safe temperature in an animal shelter that can be represented by the inequality r + 32 ≥ 56, which simplifies to r ≥ 24 after subtracting 32 from both sides.

Consider a situation where r represents the room temperature in degrees Fahrenheit without accounting for wind chill or humidity, and the inequality r + 32 ≥ 56 represents the minimum safe temperature that must be maintained in an animal shelter to keep the animals comfortable during winter months.

To solve the inequality for r, we would subtract 32 from both sides:

So, the shelter must keep the room temperature at 24 degrees Fahrenheit or higher to ensure the animals' safety.

If we were to compare this with mathematical rules presented in LibreTexts, subtracting the same number from both sides of an inequality does not change the relationship, which is a standard procedure for solving inequalities.

Answer:

Do the one that looks like this

here is also a really cute pic

Final answer:

The ratios 10/20 and 30/60 both simplify to 1/2, showing they form a proportion as they equal the same value when reduced to simplest form.

Explanation:

Proportion is a mathematical concept where two ratios are equivalent.

For example, the ratios 10/20 and 30/60 form a proportion.

We can show this by finding a common multiplier and simplifying the ratios.

10/20 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 10.

This yields:

10 ÷ 10 = 1 and 20 ÷ 10 = 2. So, 10/20 simplifies to 1/2.

Similarly, 30/60 can be simplified by dividing both the numerator and denominator by 30, resulting in:

30 ÷ 30 = 1 and 60 ÷ 30 = 2. This simplifies to 1/2, the same as the first ratio.

Since both ratios simplify to 1/2, we can say that 10/20 and 30/60 form a proportion because they both equal the same value when reduced to simplest form.

Answer: 3.055 feet

Step-by-step explanation:

Given : The statue of liberty is 305.5 feet tall from the foundation of its pedestal to the top of its torch.

Its model will be one hundredth times as tall as the actual statue.

Now , One hundredth = [tex]\dfrac{1}{100}=0.01[/tex]

According to the statement,

The height of the model will be = [tex]\dfrac{1}{100}\times\text{Height of original statue}[/tex]

[tex]=\dfrac{1}{100}\times305.5=3.055\text{ feet}[/tex]

Hence, the height of the model will be 3.055 feet.

Victoria would have paid $4.25 for 8.5 pounds of carrots if they were $0.50 less per pound.

To find out how much Victoria would have paid for 8.5 pounds of carrots if they were $0.50 less per pound, we need to subtract $0.50 from the original price per pound and then multiply it by 8.5.

Let's say the original price per pound of carrots is $1.00. Subtracting $0.50 from it gives us $0.50. Multiplying $0.50 by 8.5 gives us $4.25.

Therefore, Victoria would have paid $4.25 for 8.5 pounds of carrots if they were $0.50 less per pound.

Answer:

11

Step-by-step explanation:

The product of the missing number (4,230) is 2,115,000

Therefore let the missing number be X

Hence,

X = 42300 ÷ 10

X = 42300 / 10

X = 4,230

Therefore the missing number is 4230.

Recall, we are to find the product 4230 and 500. This process require that we multiply 4230 and 500.

Therefore, let the product of 4,230 and 500 be P

P = 4230 x 500

P = 2,115,000

Hence, the product of the missing number (4230) and 500 is 2,115,000.

The above math problem deals with numbers, and was solved with the aid of division and multiplication, which are functions of an order of operations known as BODMAS.  

Division deals with splitting or dividing numerical values into different equal parts or groups. Multiplication on its part is the repeated adding of several numbers to derive a final numerical value.

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The factored form of the expression 16a + 10 is 2(8a + 5).

To factor the expression 16a + 10, we can divide each term by the greatest common factor (GCF) of the expression.

The GCF of 16a and 10 is 2, so we can divide each term by 2 to get:

16a + 10 = 2(8a + 5)

Therefore, the factored form of the expression 16a + 10 is 2(8a + 5).

Answer:

80 total candy bars

Step-by-step explanation;

set up proportion

24

30/100

24 x 100=2400 divided by 30

=80

The total number of candy bars that he has sold is 80 candy bars.

Using this formula

Total sold candy bars=Number of candy bars sold/Percentage of candy bar sold

Where:

Number of candy bars sold=24 candy bars

Percentage of candy bar sold=30%

Let plug in the formula

Total sold candy bars =24/0.30

Total sold candy bars=80 candy bars

Inconclusion the total number of candy bars that he has sold is 80 candy bars.

Learn more here:

https://brainly.com/question/3598503

Answer:

Step-by-step explanation:

Answer:

To sum 37+58 mentally, we could first sum 30+50=80 and then sum the units, 80+7+8= 95.

But, if we have to show properties, we could separate first the numbers:

30 + 7 + 50 + 8.

Then, we apply commutative property to position like numbers aside:

30+50+7+8

Then, we apply associate property, to have a better order of the operation, which is easier to the mind:

(30+50) + (7+8)

Then, we sum each group:

80 + 15

At last, we sum again and have the result:

80+15=95.