By using equations to represent the relationship between Kevin and Daniel's ages, we can determine that Kevin is 24 years old.
Kevin is 3 times as old as Daniel. Let's denote Kevin's age as K and Daniel's age as D. From the information given, we can form two equations:
K = 3D
K - 4 = 5(D - 4)
3D - 4= 5D -20
16 = 2D
D = 8
K = 24
Solving these equations simultaneously gives the age of Kevin, therefore, Kevin is 24 years old.
-6 + (-5) + 7
what do I need to do first?
-6 + (-5) +7
just add from left to right:
1st step:
-6 + (-5) = -11
2nd step:
-11 +7 = -4
-4 1/2, -5.6, -2 3/8, 2.35 from least to greatest
If triangle JKL s congruent to triangle RST which congruences are true by CPCTC
the true statements by CPCTC are options A, B, and C. [tex]\( \overline{KL} \cong \overline{ST} \)[/tex] ,[tex]\( \overline{JK} \cong \overline{RS} \)[/tex], [tex]\( \angle K \cong \angle S \)[/tex].
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It means that if two triangles are congruent, then their corresponding parts are also congruent.
Given that △ JKL ≌ △ RST, let's examine each option:
A. [tex]\( \overline{KL} \cong \overline{ST} \)[/tex] - True by CPCTC, corresponding sides of congruent triangles are congruent.
B. [tex]\( \overline{JK} \cong \overline{RS} \)[/tex] - True by CPCTC, corresponding sides of congruent triangles are congruent.
C. [tex]\( \angle K \cong \angle S \)[/tex] - True by CPCTC, corresponding angles of congruent triangles are congruent.
D. [tex]\( \angle L \cong \angle R \)[/tex] - This statement cannot be determined solely from the fact that △ JKL ≌ △ RST. The corresponding angles may or may not be congruent, depending on the specific congruent triangles.
E. [tex]\( \overline{JL} \cong \overline{RS} \)[/tex] - This statement cannot be determined solely from the fact that △ JKL ≌ △ RST. The corresponding sides may or may not be congruent, depending on the specific congruent triangles.
F. [tex]\( \angle J \cong \angle S \)[/tex] - This statement cannot be determined solely from the fact that △ JKL ≌ △ RST. The corresponding angles may or may not be congruent, depending on the specific congruent triangles.
Therefore, the true statements by CPCTC are options A, B, and C.
The complete question is:
If △ JKL≌ △ RST, which congruences are true by CPCTC? Check all that apply.
A. [tex]\( \overline{KL} \cong \overline{ST} \)[/tex]
B. [tex]\( \overline{JK} \cong \overline{RS} \)[/tex]
C. ∠ K≌ ∠ S
D. ∠ L≌ ∠ R
E. [tex]\( \overline{JL} \cong \overline{RS} \)[/tex]
F. ∠ J≌ ∠ S
What is the APR of a payday loan for $1460 due in 15 days that charges a $90 fee?
Answer:
The answer is 150%
Step-by-step explanation:
Amount of pay day loan = $1460
Also given is that the payday loan for $1460 due in 15 days that charges a $90 fee.
Per day it will charge = [tex]\frac{90}{15}=6[/tex] dollars
For a year it will charge = [tex]365\times6=2190[/tex]
Thus for the due amount of $1460, it will be charged on a rate of =
[tex]\frac{2190}{1460} \times100[/tex] = 150%
Therefore, the APR is 150%.
A candle is 6 inches tall and burns at a rate of one half an inch per hour. Write an equation to represent the situation.
Answer: [tex]y=6-0.5x[/tex]
Step-by-step explanation:
Given : The initial height of candle = 6 inches
Amount of candle burn each hour = one half an inch per hour.
[tex]=\dfrac{1}{2}\text{ inch per hour}[/tex]
Now , the height of candle = ( initial height ) -( Rate of burning) (Numb er of hours)
Let y be the height of the candle after x hours.
Then, the equation to represent the situation will be :
[tex]y=6-\dfrac{1}{2}x\\\\\Rightarrow\ y=6-0.5x[/tex]
The equation to represent the situation will be, [tex]y=6-\frac{1}{2} \times x[/tex].
Given A candle is 6 inches tall.
The candle burns at a rate of one half an inch per hour.
Let [tex]x[/tex] be the number of hours candle burn and [tex]y[/tex] be the height of the candle after [tex]x[/tex] hours.
Now , the height of candle = ( initial height ) -( Rate of burning) (Number of hours)
So, the equation to represent the situation will be, [tex]y=6-\frac{1}{2} \times x[/tex].
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Which of the angles are congruent, select all that apply
A students work to solve 2 6/7 / 2/7 is shown below.
Which of the following statements do you agree with.
2 6/7 / 2/7 =
19/7 / 2/7 =
7/19 x 2/7 =
1/19 x 2/1 = 2/19
A. The only mistake is changing the mixed number to an improper fraction.
B. There's a mistake with the multiplicative inverse 2/7 .
C. The problem looks correct.
D. There's a problem with changing the mixed number to an improper fraction, as well as changing the division problem to multiplication.
Answer:
D. There's a problem with changing the mixed number to an improper fraction, as well as changing the division problem to multiplication.
Step-by-step explanation:
We have shown work of a student to solve a division of fractions. We are asked to check student's work.
Let us check
[tex]2\frac{6}{7}\div\frac{2}{7}[/tex]
Convert mixed fraction into improper fraction:
[tex]2\frac{6}{7}\Rightarrow \frac{2\times 7+6}{7}=\frac{14+6}{7}=\frac{20}{7}[/tex]
[tex]\frac{20}{7}\div\frac{2}{7}[/tex]
Convert division problem to multiplication problem by flipping the 2nd fraction:
[tex]\frac{20}{7}\times\frac{7}{2}[/tex]
[tex]\frac{20}{1}\times\frac{1}{2}[/tex]
[tex]\frac{20}{2}[/tex]
[tex]10[/tex]
Therefore, the student made two mistakes and option D is the correct choice.
W = 3x + 7y solve for y
Please solve this equation 2/5h +g =d for h
why is iron usually made into alloy for commercial uses?
A iron is too lightweight of a metal
B iron is a scare natural resource
C iron reacts easily with air and water
D iron by itself is to hard
answer fast please
Iron is typically alloyed for commercial uses because it reacts easily with air and water, leading to corrosion. By creating alloys such as steel with added elements like carbon and chromium, iron becomes more robust and rust-resistant, lending itself to a wider range of applications.
The reason iron is usually made into an alloy for commercial uses is that iron reacts easily with air and water, which is option C. Commercial alloys of iron, like steel, are produced by adding elements such as carbon and metals like manganese, chromium, nickel, tungsten, molybdenum, and vanadium. These elements create an alloy that is more resistant to corrosion (rusting), and they can be engineered to have different properties suitable for specific applications. For example, stainless steel contains chromium which helps in forming a protective oxide layer on the surface, thereby protecting the base iron from rusting.
While wrought iron, which is a commercially pure iron containing less than 0.2% carbon, is quite resistant to rust and is malleable and ductile, it has largely been replaced by mild steel. Mild steel, though not as corrosion-resistant as true wrought iron, is more cost-effective and widely available. Therefore, the commercial use of iron predominantly involves its transformation into alloys that benefit from enhanced strength, durability, and corrosion resistance.
what is the distributive property of the GCF of 36 and 45
i am a fraction in the simplest form. i am greater than 4/5. the sum of my terms is 25. what fraction am i?
A scuba diver's vertical position in relation to the surface of the water changes by -90 ft in 3 min. What is the average change in the diver's vertical position each minute?
What is, 901x1041 pls help dont have a calculator
If 4/5 of a population of a certain town is considered to be middle class and the population of the town is 2000 how many people are considered middle class
A salt mixture has 8 parts water and 2 parts salt. Suppose one part of each is added. What is the new ratio of salt to water?
The rates for a long distance telephone call are $0.70 for the first 5 minutes and $0.40 for each additional minute. How much would a 4-minute call cost?
is it true that Kilogram is a unit of volume.
a new television set was recently purchased for the common room in a Residence Hall for $492.20 including tax. If the tax rate is 7% ,find the price of the television before taxes
PLEASE HELP. Which is the best interpretation of the solution set for the compound inequality? 3/2x-1<2x + 4 or 3(2/3x + 1) < 11 A. no solution B. x > -10 C. x<4 D. all real numbers.
Answer:
D
Step-by-step explanation:
Just did it
passes through (-1,4) and m=4
To find the equation of the line passing through the point (-1, 4) with slope 4, we use the point-slope form. Substituting the values into the formula, we find the equation to be y = 4x + 8.
Explanation:In the given question, we have a line that passes through the point (-1, 4) and has a slope of 4.
To find the equation of this line, we can use the point-slope form, which is given by y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope.
Substituting the values into the formula, we get y - 4 = 4(x - (-1)). Simplifying further, we have y - 4 = 4x + 4. Rearranging the equation, we find the equation of the line to be y = 4x + 8.
Next year, four elementary schools will each send 126 students to Bedford Middle School. What is the total number of students the elementary schools wil send to the middle school?
Write a division problem that will have a two digit quotient and another division problem that will have a 3 digit quotient. Explain how you chose the divisors and dividends
The sum of 225 can be expressed as 200 + 25. Use the Distributive Property and GCF to rewrite the sum
wrote a doubles fact. It has a sum less than 10 and greater than 4. The addends are each less than 5. What fact might she have written?
40 is 160% of what number?
writing this in equation form you have 160% times X = 40
so 160% * x =40
160% as a decimal = 1.60
so 1.60 * x = 40
to find x divide both sides by 1.6
40 /1.6 = 25
the number is 25
what is the area of a rectangle with a length of 6 2/5 feet and width of 4 1/6 feet
Mr. Rodriguez is packing bags of snacks for his children’s lunchboxes. If he has 20 blueberries and 30 grapes, what is the maximum number of bags of snacks that he can pack so that each bag has the same number of blueberries and grapes?
With equal distribution of blueberries and grapes, Mr. Rodriguez can pack maximum of 10 bags of snacks.
What is ratio?Ratio is a quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
Given is that Mr. Rodriguez is packing bags of snacks for his children’s lunchboxes and for that he has 20 blueberries and 30 grapes.
Now, we have -
Number of blueberries = n[b] = 20 blueberries
Number of grapes = n[g] = 30
For equal distribution, there should be a ratio of → n[b]/n[g] = 20/30 = 2/3
Or we can write it as 2 : 3. This means that in each box there should be 2 blueberries and 3 grapes.
The maximum number of bags [x] that Mr. Rodriguez can pack can be calculated as -
2x + 3x = 20 + 30
5x = 50
x = 10
Therefore, with equal distribution of blueberries and grapes, Mr. Rodriguez can pack 10 bags of snacks.
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In solving the inequality -3x < 9, you would divide both sides of the inequality by -3 and flip over the inequality symbol. true or false
Answer: true.
Step-by-step explanation: do you really want an explanation?
1.2 divided by .3 in the model
The solution for the division of 1.2 by .3 is 4. This can be visualized by considering how many times .3 fits into 1.2, or by dividing equivalent decimals.
Explanation:To solve the problem 1.2 divided by .3, simply divide the numbers as you would normally. For this problem, 1.2 divided by .3 equals 4. This is because the fundamental basis of division is how many times one number fits into another. In this case, .3 'fits' into 1.2, four times.
Alternatively, you can think of this process in three steps: First, convert 1.2 to an equivalent decimal of 12 tenths. Then, divide that by .3 (or 3 tenths). The result is 4 because 3 tenths 'fits' into 12 tenths, four times.
Another way to cross-verify your result is by multiplying the divisor (.3) by the quotient (4). The product should be equal to the dividend (1.2). Here, .3 multiplied by 4 equals 1.2, hence confirming the correctness of the answer.
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Final answer:
To divide 1.2 by 0.3 in a model, first convert the decimal numbers to fractions. Then, divide the numerator by the denominator to get the answer, which is 4.
Explanation:
To divide 1.2 by 0.3 in a model, we can use a similar approach to the example given. Let's first convert the decimal numbers into fractions by using the place value of the decimal places. 1.2 is equivalent to 12/10 and 0.3 is equivalent to 3/10.
Next, we can set up a division problem where the numerator is 12 and the denominator is 3, giving us 12 ÷ 3. This can be simplified to 4, so 1.2 divided by 0.3 in the model is equal to 4.
Therefore, the answer to 1.2 divided by 0.3 in the model is 4.