Suppose m<3 = 105. find m<6
To find the measure of angle 6, we can use the fact that angles 3 and 6 are vertical angles (opposite angles formed by the intersection of two lines). Therefore, their measures are equal.
Given that[tex]\( m\angle 3 = 105^\circ \), we have \( m\angle 6 = m\angle 3 = 105^\circ \).So, the measure of angle 6 is \( \boxed{105^\circ} \).[/tex]
The measure of angle 6 is 105 degrees. This is because angles 3 and 6 are vertical angles, meaning they are formed by intersecting lines and are opposite each other. According to the Vertical Angles Theorem, vertical angles are congruent, meaning they have the same measure. Therefore, if angle 3 measures 105 degrees, angle 6, being its vertical angle, also measures 105 degrees. This principle holds true regardless of the specific configuration of lines or shapes, as long as the angles are formed by intersecting lines. Hence, in this case, the measure of angle 6 directly corresponds to the measure of angle 3 due to their relationship as vertical angles, resulting in both having a measure of 105 degrees.
What are the factors of the trinomial x^2+6x-7
Divide 300 in a ratio of 3:7
To divide 300 by a ratio of 3:7, calculate the value of each part by dividing 300 by the sum of the ratio parts (10) and then multiply by each part of the ratio to get 90 and 210, respectively.
Explanation:To divide 300 in a ratio of 3:7, first add the parts of the ratio together to determine how many parts you will split 300 into.
In this case, 3 + 7 equals 10 parts.
Then, you divide 300 by 10 to find out how much one part is worth.
This gives 300 ÷ 10 = 30. Now, to find the amounts corresponding to the ratio, multiply the single part value by the numbers in the ratio. For the first part (ratio 3), multiply 30 by 3 to get 90.
For the second part (ratio 7), multiply 30 by 7 to get 210.
So, 300 divided in a ratio of 3:7 gives us 90 and 210, respectively.
Please need help to solve this
How do I find slope?
how long would it take a ball dropped from a 100 ft building to hit the ground
Final answer:
To find the time it takes for a ball to fall from a 100 ft building, convert the height to meters and use the free fall motion formula. Solving s = (1/2)gt² for time, it takes approximately 2.5 seconds for the ball to hit the ground.
Explanation:
To determine how long it would take for a ball dropped from a 100 ft building to hit the ground, we can use the formula for the free fall motion under the influence of gravity, assuming air resistance is negligible. The formula is s = (1/2)gt², where s is the distance fallen, g is the acceleration due to gravity (approximately 9.8 m/s², but we will need to convert it to feet per second squared for this problem), and t is the time in seconds.
First, convert 100 feet to meters because the standard unit of gravity is in meters per second squared. There are approximately 3.281 feet in a meter, so 100 feet is roughly 30.48 meters.
Now apply the formula and solve for t:
Convert acceleration due to gravity to feet: 9.8 m/s² is approximately 32.2 ft/s².
Use the formula: 100 = (1/2)(32.2)t².
Solve for t: t² = 100 / 16.1.
Find t: t = √(100 / 16.1).
Calculate t: t ≈ 2.49 seconds.
Therefore, it would take approximately 2.5 seconds for the ball to hit the ground.
Tasha believes that she can rewrite the difference 120 - 36 as a product of the greatest common factor of the two numbers and other difference is she correct explain your answer
Terrance is 3.5 years older than Stephanie. Stephanie is 22.5 years old. If the equation t – 3.5 = 22.5 models the situation, find the value for t, Terrance’s age.
Answer:
T= 3.5+22.5
T=26
Hope I helped!!
Step-by-step explanation:
The Age of Terrance is 26 years.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
Model Equation : t – 3.5 = 22.5
where t is Terrance’s age.
Now, solving the equation for t we get
t - 3.5 = 22.5
Add 3.5 on both side
t -3.5+ 3.5 = 22.5 + 3.5
t = 26
Hence, Terrance age is 26 years.
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three numbers are in the ratio 2:3:4 if the sum of the largest and the smallest equals the sum of the third and 33 find the numbers
the vega family has a cell phone plan that costs $75 per month including taxes and fees. the plan lets the 5 members of the vega family share 1000 minutes of talk time per month and 400 text messages per month. any minutes over 1000 cost $1 per minutes and any text over 400 cost $2 per text. because of a family emergency the family uses 1050 minutes and 415 texts in march. write an expression you could use to find the amount of the vega cell phone bill for march. evaluate the expression show the work
A turtle walks 7/8 mile in 50 minutes. What is the unit rate in miles per hour? (Hint: 50 minutes=5/6 of an hour.)
We can use the right outside diagonal of the empty Lacsap's triangle as the coefficients of a polynomial: $$t^3 + 6t^2 + 12t + 8.$$ If we replace every $t$ with $t-1,$ we get $$(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8.$$Expand and simplify this polynomial. Enter the polynomial as your answer.
To expand the given polynomial $(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8$, we can apply the binomial theorem to each term and then combine like terms.
Explanation:To expand the polynomial $$(t-1)^3 + 6(t-1)^2 + 12(t-1) + 8,$$ we can start by applying the binomial theorem to each term:
$$(t-1)^3 = t^3 - 3t^2 + 3t - 1$$
$$6(t-1)^2 = 6(t^2 - 2t + 1) = 6t^2 - 12t + 6$$
$$12(t-1) = 12t - 12$$
$$8$$
Now, we can combine like terms:
$$t^3 - 3t^2 + 3t - 1 + 6t^2 - 12t + 6 + 12t - 12 + 8$$
Cancelling out terms that add up to zero, we are left with:
$$t^3 + 6t^2 + 12t + 8$$
Find all values of x in the interval [0, 2π] that satisfy the equation. (enter your answers as a comma-separated list.) 3|tan(x)| = 3 g study
The values of x in the interval [0, 2π] that satisfy the equation 3|tan(x)| = 3 are π/4, 3π/4, 5π/4, and 7π/4.
Explanation:The given equation is 3|tan(x)| = 3. This means the absolute value of the tangent of x times 3 is equal to 3. We can remove the 3 from both sides to simplify to |tan(x)| = 1. The absolute value operator denotes the non-negative value of a number. So, we need to find the values of x such that tan(x) equals 1 or -1.
The solutions for tan(x) = 1 in the interval [0, 2π] are π/4 and 5π/4. The solutions for tan(x) = -1 in the same interval are 3π/4 and 7π/4.
Thus, the values of x that satisfy the equation are π/4, 3π/4, 5π/4, and 7π/4.
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Question
There are 30 students in an art class. Fourteen of the students are girls.
What is the ratio of boys to girls?
due by now
30 total students
14 are girls
so 30-14 = 16 are boys
16 boys to 14 girls = 16/14 reduced to 8/7
If x denotes the length of a side of an equilateral triangle, express the area of the triangle as a function of x.
Using the concept of an equilateral triangle, it is found that it's area is given by:
[tex]A = \frac{\sqrt{3}}{4}x^2[/tex]
In an equilateral triangle, all sides have the same length.The area of a triangle is one half of the base multiplied by the height.For the equilateral triangle in this problem, the base is x, that is, [tex]b = x[/tex]The height is one side of a right triangle, in which the other side is half the base and the other is the base, thus, applying the Pythagorean Theorem:
[tex]h^2 + (\frac{x}{2})^2 = x^2[/tex]
[tex]h^2 + \frac{x^2}{4} = x^2[/tex]
[tex]h^2 = \frac{3x^2}{4}[/tex]
[tex]h = \sqrt{\frac{3x^2}{4}}[/tex]
[tex]h = \frac{\sqrt{3}}{2}x[/tex]
Then, the area is:
[tex]A = \frac{bh}{2} = \frac{1}{2} \times x \times \frac{\sqrt{3}}{2}x = \frac{\sqrt{3}}{4}x^2[/tex]
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Thirty-eight fifth graders at Vernon Elementary are going on the field trip to the art museum. They are riding in vans that each hold 9 students. How many vans will they need for everyone to get to the art museum?
The division is a process of splitting a specific amount into equal parts.
The number of vans they will need for everyone to get to the art museum is 5.
What is division?The division is a process of splitting a specific amount into equal parts.
We have,
Number of five grader students = 38
One van can hold = 9 students.
The number of vans needed to hold 38 students:
= 38 / 9
= 4.2 vans
This means we need 5 vans to accommodate all 38 students because in 4 vans only 36 students will be accommodated and 2 students remaining will need a van.
Thus the number of vans they will need for everyone to get to the art museum is 5.
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Which of the following is equivalent to the expression (9x^2y^3)(12x^-3y^5)( 2xy)? 23x^-5y^8 216^9 -x^-6y^8
Final answer:
The expression (9x^2y^3)(12x^-3y^5)(2xy) simplifies to 216y^9 by multiplying the coefficients and adding the exponents of like bases.
Explanation:
The student's question involves simplifying an algebraic expression by using the properties of exponents. When we multiply expressions with the same base, we add the exponents. The given expression (9x2y3)(12x-3y5)(2xy) can be simplified by multiplying the coefficients (numerical values) and adding the exponents of like bases separately.
Multiply the coefficients: 9 * 12 * 2 = 216
Add the exponents for x: 2 + (-3) + 1 = 0 (x's cancel out because x0 = 1)
Add the exponents for y: 3 + 5 + 1 = 9
Thus, the simplified expression is 216y9.
The movement of the progress bar may be uneven because questions more on your answer. The price of a CD decreased from $15 to $12. What is the percent of decrease? 3% 20% 33% 75%
15 -12 = 3
3/15 = 0.2 = 20% decrease
The distance between the two islands shown on the map is 210 miles. A ruler measures the distance on the map is three 1/2 inches how many miles would be represented by one 3/4 inches on the map?
What is 763 thousandths in scientific notation?
Answer: [tex]7.63\times10^{-1}[/tex]
Step-by-step explanation:
The scientific notation is a technique to express a very large or a very small number in the product of a decimal form of number [commonly between 1 and 10] and powers of ten.We know that one thousandth is written as :
[tex]\text{One thousandth}=\frac{1}{1000}[/tex]
Therefore, 763 thousandths can be written as :
[tex]\text{ 763 thousandths}=\frac{763}{1000}=\frac{7.63}{10}[/tex]
In Scientific notation:
[tex]\frac{7.63}{100}=763\times10^{-1}......[\text{ By law of exponents }](\frac{1}{a^n}=a^{-n})[/tex]
The number [tex]763\text{ thousandths}[/tex] in scientific notation is [tex]\boxed{\bf 7.63\times 10^{-1}}[/tex].
Further Explanation:
The scientific notation is a technique which is used to express a very large or a very small number in the product of a decimal form of number [commonly between 1 and 10] and a power of ten.
It can easily simplify an arithmetic operation and in a scientific calculator it is known as SCI display mode.
In scientific notation, all the numbers can be written as follows:
[tex]\boxed{x\times 10^{y}}[/tex]
Here, [tex]y[/tex] is an exponent integer and [tex]x[/tex] is the real number. The integer [tex]y[/tex] is the order of the magnitude and [tex]x[/tex] is called the mantissa (fractional part of the number).
As we know that one thousandths in mathematical form can be written as follows:
[tex]\boxed{1\text{ thousandths}=\dfrac{1}{1000}}[/tex]
Therefore, the number [tex]763\text{ thousandths}[/tex] in mathematical form is written as follows:
[tex]\boxed{\begin{aligned}763\text{ thousandths}&=\dfrac{763}{1000}\\&=\dfrac{7.63}{10}\end{aligned}}[/tex]
So, in scientific notation the number [tex]763\text{ thousandths}[/tex] is written as follows:
[tex]\boxed{\dfrac{7.63}{10}=7.63\times 10^{-1}}[/tex]
Therefore, the number [tex]763\text{ thousandths}[/tex] in scientific notation is expressed as [tex]\boxed{\bf 7.63\times 10^{-1}}[/tex].
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Answer details:
Grade: Middle school
Subject: Mathematics
Chapter: Number system
Keywords: scientific notation, 763 thousandths, multiplication, division, exponent power, real number, integers, power of ten, scientific calculator, decimal form.
A punch bowl that holds 150 cups of jungle ounch is to he used at a birthday party. Each plastic cup hols 1 1/2 cups of punch. How many plastic cups can be filled?
Consider the following incomplete deposit slip: Description Amount ($) Cash, including coins 150 75 Check 1 564 81 Check 2 2192 43 Check 3 4864 01 Subtotal ???? ?? Less cash received ???? ?? Total 7050 50 How much cash did the person who filled out this deposit slip receive? a. $849.25 b. $715.56 c. $7,621.53 d. $721.50
The amount of cash did the person who filled out this deposit slip receive [tex]\boxed{\$ 721.50}.[/tex] Option (d) is correct.
Further explanation:
Given:
The options are as follows,
(a). [tex]\$ 849.25[/tex]
(b). [tex]\$ 715.56[/tex]
(c). [tex]\$ 7621.53[/tex]
(d). [tex]\$ 721.50[/tex]
Explanation:
The deposit slip can be expressed as follows,
Cash in the form of coins is [tex]\$ 150.75.[/tex]
The amount of check 1 is [tex]\$ 564.81[/tex], the amount of check 2 is [tex]\$ 2192.43[/tex] and the amount of check 3 is [tex]\$ 4864.01.[/tex]
The less cash received is [tex]\$ 7050.50.[/tex]
The total amount is [tex]\$ 7772.00.[/tex]
The amount of cash did the person who filled out this deposit slip receive can be calculated as follows,
[tex]\begin{aligned}{\text{Amount}} &= 7772.00 - 7050.50\\&= \$ 721.50\\\end{aligned}[/tex]
The amount of cash did the person who filled out this deposit slip receive [tex]\boxed{\$ 721.50}[/tex]. Option (d) is correct.
Option (a) is not correct.
Option (b) is not correct.
Option (c) is not correct.
Option (d) is correct.
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Answer details:
Grade: Middle School
Subject: Mathematics
Chapter: Interest rate
Keywords: Incomplete deposit slip, description amount, cash, including coins, check, person, less cash receives.
In the solution to this system, what is the value of y?
x+y+z=1x+y+z=1
2x+y−z=82x+y-z=8
x−y+z=−5
When does the proportion form of newton's second law take the form of an equation?
Which is 10^-5 written in standard form?
A. 0.00001
B. 0.0001
C. 10.000
D. 100.000
URGENT!: Which property justifies this statement?
If x + y = z and z = x + 4, then x + y = x + 4.
A.
symmetric
B.
distributive
C.
transitive
D.
associative
Through any three noncollinear points, there is exactly one plane containing them. Points W, X, and Y are noncollinear.
Answer:
There is exactly one plane containing points W, X, and Y
Step-by-step explanation:
Estimate the square root to the nearest integer. Square root of 48
Which sign makes this number sentence true? |78| __ |-222|
6,000 is 10 time as much as