the second angel im a triangle is 2° less the 3 times the first angle the third Angle is 14° more than twice the first angle find the measure of all three angles I'm the triangle (plz show step by step)
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:
A 1-ounce serving of cream cheese contains 7.8
grams of saturated fat. How much saturated fat is in 12
ounces of cream cheese?
To find the total grams of saturated fat in 12 ounces of cream cheese, multiply the grams per ounce (7.8) by the total ounces (12), which equals 93.6 grams.
Explanation:To answer this question, we need to multiply the amount of saturated fat in one ounce of cream cheese by the total number of ounces you have. Since one ounce of cream cheese contains 7.8 grams of saturated fat, you would multiply 7.8 by 12 (the total number of ounces) to get the total amount of saturated fat.
7.8 grams of saturated fat per ounce × 12 ounces = 93.6 grams
So, 12 ounces of cream cheese contains 93.6 grams of saturated fat.
Learn more about multiplication here:https://brainly.com/question/5992872
#SPJ2
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
Simplify 13 + 2 - 5 - 15
13 +2 = 15 -5= 10 -15 = -5
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:
$$t^3 + 6t^2 + 12t + 8$$
What is the lateral area of a pyramid with base edges 5 ft and surface area 55 ft2?
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.
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
For what values of r does the function y = erx satisfy the differential equation y'' − 6y' + 2y = 0? (enter your answers as a comma-separated list.)
The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]
Further explanation:
Given:
The function is [tex]y = {e^{rx}}.[/tex]
The differential equation is [tex]y'' - 6y' + 2y = 0\,\,\,\,\,or\,\,\,\,\dfrac{{{d^2}y}}{{d{x^2}}} - 6\dfrac{{dy}}{{dx}} + 2y = 0[/tex]
Explanation:
The given function can be expressed as follows,
[tex]y = {e^{rx}}[/tex]
Differentiate the above equation with respect to [tex]x[/tex].
[tex]\begin{aligned}\frac{{dy}}{{dx}} &= \frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&= {e^{rx}} \times \frac{d}{{dx}}\left( {rx} \right)\\&= {e^{rx}} \times r\\&= r{e^{rx}}\\\end{aligned}[/tex]
Again differentiate with respect to [tex]x[/tex].
[tex]\begin{aligned}\frac{{{d^2}y}}{{d{x^2}}} &= \frac{d}{{dx}}\left( {r{e^{rx}}} \right)\\&= r\frac{d}{{dx}}\left( {{e^{rx}}} \right)\\&=r\times {e^{rx}} \times\frac{d}{{dx}}\left( {rx} \right)\\&= {r^2}{e^{rx}}\\\end{aligned}[/tex]
Now solve the differential equation.
[tex]\begin{aligned}y'' - 6y' + 2y &= 0\\{r^2}{e^{rx}} - 6r{e^{rx}} + 2{e^{rx}} &= 0\\{e^{rx}}\left( {{r^2} - 6r + 2} \right) &= 0\\{r^2} - 6r + 2 &= 0\\\end{aligned}[/tex]
Solve the quadratic equation [tex]{r^2} - 6r + 2 = 0.[/tex]
[tex]\begin{aligned}D&= {b^2} - 4ac\\&={\left( { - 6} \right)^2} - 4\left( 1 \right)\left( 2 \right)\\&= 36 - 8\\&= 28\\\end{aligned}[/tex]
The value of [tex]r[/tex] can be obtained as follows,
[tex]\begin{aligned}r&= \frac{{ - b \pm \sqrt D }}{{2a}}\\r&=\frac{{ - \left( { - 6} \right) \pm \sqrt {28} }}{{2 \times 1}} \\ r &= \frac{{6 \pm 2\sqrt7 }}{2}\\r&= 3 \pm \sqrt7\\r&= 3 - \sqrt 7 \,\,\,\,\,\,\,or\,\,\,\,\,\,\,r = 3 + \sqrt7 \\\end{aligned}[/tex]
The values of [tex]r[/tex] is [tex]\boxed{r = 3 - \sqrt7 }[/tex] and [tex]\boxed{r = 3 + \sqrt 7 }.[/tex]
Learn more:
1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.
2. Learn more about equation of circle brainly.com/question/1506955.
3. Learn more about range and domain of the function https://brainly.com/question/3412497
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Derivatives
Keywords: Derivative, value of x, function, differentiate, minimum value, dy, compute, given value of [tex]x, y=6x, x=4, x=1[/tex]
The equation y = 6.3x + 67.4 is the equation of a linear model in a scatter plot comparing the ages of boys between 2 and 10 years old open (x) and their average heights in centimeters open (y).
What is the average height of a 5-year-old boy?
98.9 cm
78.7 cm
67.4 cm
62.4 cm
The average height of a 5 year old baby can be obtained by substituting the x and y values into the regression equation ; Hence, the average height of the baby is 98.9 cm
Given the linear regression equation :
y = 6.3x + 67.4 x = age of baby = 5 ; y = height of babyThe average height of a 5 year old baby is thus :
y = 6.3(5) + 67.4
y = 31.5 + 67.4
y = 98.9
Hence, the average height a 5 year old baby will be 98.9cm
Learn more :https://brainly.com/question/18405415
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
theses two questions are together
How do I find slope?
Estimate the square root to the nearest integer. Square root of 48
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.
Learn more about Trigonometry here:https://brainly.com/question/31896723
#SPJ2
The line contains the point (-7,0) and is parallel to the line defined by 4x=3y. What is the equation of the line
Daniela finds the sum of two addenda. The sum is odd. Which statement is true about the addenda
6,000 is 10 time as much as
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.)
A student is trying to remember some formulas from geometry. in what follows, assume a is area, v is volume, and all other variables are lengths. determine which formulas are dimensionally consistent.
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 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].
Learn more
1. Learn more about the division: https://brainly.com/question/545132
2. Learn more about the simplification https://brainly.com/question/894273
3. Learn more about the percentage https://brainly.com/question/928382
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.
Curly used a shovel to dig his own swimming pool. He figured he needed a pool because digging it was hard work, and he could use it to cool off after working on it all day. He also planned to build a rectangular concrete deck around the pool that would be 6 feet wide at all points. The pool is rectangular and measures 14 feet by 40 feet. What is the area of the deck?
The area of the deck that is built around the pool is 1352 ft².
What is the area of the deck?A rectangle is a 2-dimensional quadrilateral with four right angles.
Area of a rectangle = length x width
Length = 14 + 6 + 6 = 26 Width = 40 + 6 + 6 = 52Area = 26 x 52 = 1352 ft²
To learn more about how to calculate the area of a rectangle, please check: https://brainly.com/question/16595449
#SPJ2
Which sign makes this number sentence true? |78| __ |-222|
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?
Which is 10^-5 written in standard form?
A. 0.00001
B. 0.0001
C. 10.000
D. 100.000
What are the factors of the trinomial x^2+6x-7
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.