The measure of angle S is [tex]38^\circ[/tex] and the measure of angle T is [tex]111^\circ[/tex] and this can be determined by using the property of sum of interior angles.
Given :
[tex]\rm \angle R = 31^\circ[/tex][tex]\rm \angle S = (x + 4)^\circ[/tex][tex]\rm \angle T = (3x+9)^\circ[/tex]Apply the property of the sum of the interior angles of the triangle in order to determine the angles R, S, and T.
[tex]\rm \rm \angle R +\rm \angle S+\rm \angle T = 180^\circ[/tex]
31 + (x + 4) + (3x + 9) = 180
Simplify the above equation in order to determine the value of 'x'.
4x + 13 = 149
4x = 136
[tex]\rm x = 34^\circ[/tex]
Now, the measure of angle S is:
[tex]\rm \angle S = x + 4 = 34 + 4 = 38^\circ[/tex]
[tex]\rm \angle T = 3x + 9 = 3(34) + 9= 111^\circ[/tex]
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About 24.8 million people live in Texas. About 0.6 million people live in Vermont. How many times as many people live in Texas than in Vermont?
To find out how many times more people live in Texas than in Vermont, calculate the ratio of their populations, resulting in 41.33 times more people live in Texas than in Vermont.
To find out how many times more people live in Texas than in Vermont, we can calculate the ratio of the populations of Texas and Vermont. Given that about 24.8 million people live in Texas while about 0.6 million people live in Vermont, the ratio would be 24.8 million / 0.6 million = 41.33 times as many people live in Texas than in Vermont.
Nine people come to a party and shake hands with each other. If each person shakes the hand of every other person, how many handshakes occur?
Final answer:
There will be 36 handshakes among the nine people at the party, as determined by the combination formula 9C2.
Explanation:
Calculating Handshakes
To determine the number of handshakes that occur when nine people shake hands with each other, we can use the concept of combinations. In a handshake situation, the order in which the handshakes occur does not matter; what matters is which two people are shaking hands. Therefore, we can use the formula for combinations without repetition, which is nCk = n! / (k!(n-k)!), where n is the total number of items, and k is the number of items to choose at a time.
In this case, there are 9 people (n=9) and the handshake involves 2 people at a time (k=2). So, the calculation would look like this:
9C2 = 9! / (2!(9-2)!) = 9! / (2!7!) = (9 × 8) / (2 × 1) = 36 handshakes
Therefore, there would be a total of 36 handshakes among nine people at the party.
The committee is planning a party and 150 guests are expected. Each package of plastic spoons contains 24 spoons. How many packages of spoons will be needed to so that each guest gets 1 spoon? 5 6 7 124
divide the number of guests by the number of spoons in a package
150/24 = 6.25 so they need to buy 7 packages
The packages of spoons will be needed to so that each guest gets 1 spoon is 7.
It is required to find the packages of spoons.
What is arithmetic?Arithmetic is the branch of mathematics that deals with the study of numbers using various operations on them. Basic operations of math are addition, subtraction, multiplication and division. These operations are denoted by the given symbols.
Given:
The committee is planning a party = 150 guests
package of plastic =24 spoons.
According to given question we have
The packages of spoons will be needed to so that each guest gets 1 spoon
150/24
= 6.25 ≈7
Therefore, the packages of spoons will be needed to so that each guest gets 1 spoon is 7.
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7x-4d use x = 8 and d = have (simplify algebraic exression)
What is the reason for each step in the solution of the inequality?
−2(x+3)−4>4x+30
Select the reason for each step from the drop-down menus.
−2(x+3)−4>4x+30 Given
−2x−6−4>4x+30
−2x−10>4x+30
−6x−10>30 Subtraction Property of Order
−6x>40
x<−203 Division Property of Order
The correct answers are:
Distributive property; subtraction; addition property of equality.
Explanation:
To get from the first step to the second step, the terms inside parentheses have been multiplied by -2. The property that allows us to multiply through parentheses, or distribute through parentheses, is the distributive property.
To get from the second step to the third step, the -6 and 4 have been subtracted; this means the reason for this is subtraction.
To get from the fourth step to the fifth step, 10 has been added to each side. The addition property of equality allows us to do this.
Inequalities help us to compare two unequal expressions. The given inequality can be solved as shown below.
What are inequalities?Inequalities help us to compare two unequal expressions. Also, it helps us to compare the non-equal expressions so that an equation can be formed. It is mostly denoted by the symbol <, >, ≤, and ≥.
The given inequality can be solved as shown below.
−2(x+3)−4>4x+30 → Given
−2x−6−4>4x+30 → Solving the parenthesis using the distributive property
−2x−10>4x+30 → Subtract 4x from both the sides of the inequality, Subtraction property of order
−6x−10>30 → Subtraction Property of Order
−6x>40 → Division property of order
x<−203 → Division Property of Order
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This is scrambled words what is number 8 9 10 11 12 13
In 2008 election there was 28 blue states and 22 red states express the red and blue states as fractions in lowest terms of the total number of states and also as decimals
Is this a funtion? Explain.
Which of the following is a multiple of 2?
A. 847
B. 75
C. 2,461
D. 1,000
what is y=-3x+4 and y=3x-2
by using transitive property
There are 8 students on the minibus.five of students are boy. What fraction of the students are boys?
3 pizzas for $ 16.50 what is the unit rate for one pizza
4.625 as a fraction in simplest form
4.625 as a fraction in the simplest form can be written as 37/8.
Given is a decimal number 4.625.
Here the decimal point is 3 units to the left.
So any decimal number can be written as a fraction with powers of 10 as the denominator.
Here since the decimal point is 3 units to the left divide by 1000.
So,
4.625 = 4625 / 1000
Both 4625 and 1000 are multiples of 25.
So this can be written as :
4625 / 1000 = 4625 ÷ 25/ 1000 ÷ 25
= 185 / 40
= 37/8
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When is the sum to two negative mixed numbers an integer?
A recipe for apple cake needs 10 mL of baking powder, 70 mL of butter, 190 mL of sugar and 420 mL of flour. This is enough to make a cake for 8 people. How much of each ingredient would be needed to make a cake for 20 people?
20/8 = 2.5
multiply all the ingredients by 2.5
10 ml * 2.5 = 25 ml of baking powder
70 *2.5 = 175 ml of butter
190 * 2.5 = 475 ml of sugar
420 * 2.5 = 1050 ml of flour
A refrigerator magnet uses 5/8 inch of magnetic tape. How many refrigerator magnets can you make with 10 inches of magnetic tape. Explain
Mrs.D. gives 13 % of her salary to a charity. Last year she donated to the charity $6500.00. How much money did Mrs.D. earn last year?
GCF and Distributive property of 55 + 88
Final answer:
The GCF of 55 and 88 is 11. Applying the distributive property, 55 + 88 is equal to 143.
Explanation:
The student is asking about the greatest common factor (GCF) and the distributive property of the expression 55 + 88.
To find the GCF, we need to break down the numbers 55 and 88 into their prime factors. The prime factorization of 55 is 5 × 11, and the prime factorization of 88 is 2² × 11. The GCF is the highest common factor between the two prime factorizations, which is 11.
The distributive property states that a × (b + c) = a × b + a × c. Applying this property to the expression 55 + 88, we get 11 × 5 + 11 × 8 = 55 + 88 = 143.
Final answer:
The GCF of 55 and 88 is 11. When we apply the distributive property to 55 and 88, the expression simplifies to 143.
Explanation:
To find the Greatest Common Factor (GCF) of 55 and 88, we can first list the factors of each number:
Factors of 55: 1, 5, 11, 55
Factors of 88: 1, 2, 4, 8, 11, 22, 44, 88
The GCF is the largest factor that both numbers have in common, which in this case is 11.
Now, let's apply the distributive property to the numbers 55 and 88:
55 + 88 = (5 * 11) + (8 * 11)
Using the distributive property, we can simplify this to:
55 + 88 = (5 + 8) * 11
Therefore, the expression 55 + 88 is equal to 13 * 11, which is 143.
Which answer is the correct form of bar notation for this decimal number: 4.676767…
4.67
4.67
4.67
4.67
Answer:
4.67 with the bar notation above the 67
Step-by-step explanation:
To solve this correctly you need to recall the rules repeating decimal numbers and what bar notation looks like. but i forgot my answer so its not above 6
At 0°C, the volume of a gas is 22 liters. For each degree the temperature T (in degrees Celsius) increases, the volume V (in liters) of the gas increases by 2/25. Write an equation that represents the volume of the gas in terms of the temperature.
How many times can 10 go to 20
Write the product as a single power
Manuela has two boxes. The larger of the two boxes has dimensions of 15cm by 25cm by 29 cm. The smaller of the two boxes is a cube with sides that are 10 cm long. If she were to put the smaller box inside the larger, what would be the remaining volume of the larger box?
This has really gotten confuzzing for me. SOS
let number of hours = x
1st equation is 15.54+0.11x
2nd equation is 16.14-0.09x
now calulate x so the 2 equations are equal:
15.54+0.11x=16.04-0.09x
mutiply evrything by 100 to get rid of the decimal points andmake the calculations a little easier
1554+11x=1604-9x
add 9 x to both sides:
1554+20x=1604
subtract 1554 from both sides:
20x=50
divide 50 by 20 for x
x=50/20 = 2.5
x = 2.5
so they were the same after 2.5 hours
In the diagram to the right three lines intersect at n.The measure of < GNF is 60, and the measure of < MNL is 47. What is the measure of < HNK?
Measure of ∠HNK is equals to 73°.
What are linear pair angles?
" Linear angles are formed when the sum of pairs of adjacent angles is equals to 180°."
According to the question,
Measure of ∠GNF = 60°
Measure of ∠MNL = 47°
As per the linear pair angles definition ,
∠GNF, ∠FNM, ∠MNL forms linear pair angles .
Therefore,
∠GNF + ∠FNM + ∠MNL = 180°
Substitute the given values we get,
60° + ∠FNM + 47° = 180°
⇒ ∠FNM = 180° - 107
= 73°
As given three lines intersect at 'N'
∠FNM and ∠HNK are vertically opposite angles and are congruent.
Therefore,
Measure of ∠HNK = 73°
Hence, measure of ∠HNK is equals to 73°.
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Earth diameter is 12,756 kilometers.How many meters is this?
What is .04 as a mixed number
Find the equation of the line (3,-2) and parralel to the line containing the points (-2,4) and (-4,-2).
Deniz tried to subtract two polynomials. Her work is shown below.
Solve the equation 3x+6y=18 for x
Answer:
x=6-2y
Step-by-step explanation: