The angle of elevation of the ramp to the nearest degree will be 5.71°.
What is trigonometry?The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as a circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.
Given that a ramp goes from a doorway of a building to the ground. The end of the ramp connected to the doorway is 1 foot above the ground. The horizontal distance from the bottom of the ramp to the building is 10 feet.
The angle of elevation will be calculated as,
tanθ = ( 1 / 10)
θ = tan⁻¹(1/10)
θ = 5.7°
Therefore, the angle of elevation of the ramp to the nearest degree will be 5.71°.
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If 3x – y = 5 and 2x + y = 15, evaluate x^2 + 2y
If 3x – y = 5 and 2x + y = 15 then evaluation of x^2 + 2y is equal to 72.
What is evaluation ?
Finding the value of an algebraic expression when a given number is used to replace a variable is known as evaluating the expression. When evaluating an expression, we change the variable in the expression to the given number and then use the order of operations to simplify the expression.
3x-y=5 and 2x+y= 15
Add the two equations together to eliminate y
3x-y=5
2x+y= 15
---------------------
5x = 20
Divide by 5
5x/5 = 20/5
x = 4
Now we can find y
2x+y = 15
2(4) +y = 15
8+y =15
Subtract 8 from each side
8+y-8 = 15-8
y =7
We want to find
x^2+2xy
(4)^2 +2(4)(7)
16+56
72
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Determine the number of imaginary zeros of the function with the given degree and graph. Explain your reasoning.
Answer:
1
Step-by-step explanation:
Number of roots = number of real roots + number of non-real roots
The graph intersects the x-axis 3 times
4 = 3 + x
x = 1
Why were goods planned to become obsolete?
A. So that the company would become known for quality goods
B. So that people would keep buying new things
C. So that companies could protect their brand
D. So that people could save as much money as possible
Answer: B
Step-by-step explanation: B. So that people would keep buying new things
Goods are often planned to become obsolete in order to encourage people to continue buying new things. This can be done by intentionally designing products with a limited lifespan or by using materials that are prone to wear and tear. Companies may also release new versions of products or discontinue support for older models in order to encourage consumers to upgrade to the latest version. By making their products become obsolete, companies can create a sense of urgency for consumers to keep buying new things and maintain their sales.
Owen paid a landscaping company $108 for an initial lawn treatment,
then $74 per month thereafter.
The function p(t) = 108 + 74t represents the total amount of money he will
have paid after t months.
Find p(12).
The value of p(12) is $996
What is an equation?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated.
"Find p(24)" also means "Find the amount of money Owen pays for lawn service after 12 months" as we're given 12 for t. As such, rewrite the given function as p(12) = 108 + 74(12)
p(12) = 108 + 74(12)
p(12) = 108 + 888
p(12) = $996
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help please and thanks so much
Answer:
Option 2
Step-by-step explanation:
The greater than sign with the line under it means greater than/less than or equal to. So -2.4 is less than or equal to -2.40.
-Hope this helped
how many 3/4 cups serving aare in 5 1/2 cups of yogurt
Answer:
Below
Step-by-step explanation:
5 1/2 = 11 / 2
11/2 ÷ 3/4 = 11/2 x 4/3 = 44/6 = 7 1/3
Find the sum
5. 1/4+ 1/28+ 1/70+ ,.....
The sum is 9/28
What is sum ?
The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million.
The end result of addition is a sum. For instance, the sum 10, written, is obtained by adding 1, 2, 3, and 4. (1) The sum of the numbers is known as the sum of the addends, or summands occasionally.
1/4 + 1/28 + 1/70 + 1/30 + ............ 1/700
Multiply and divide by 3 in whole series
⇒ 1/3 X [3/4 + 3/28 + 3/70 + 3/130 + ......... 3/700]
⇒1/3 X [1-1/4+1/4-1/7+1/7-1/10+1/10-1/13+..........1/25-1/28]
⇒1/3 x [1 - 1/28]
⇒1/3 * 27/28
⇒ 9 / 28
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i only need 12 and 17, first good response i will give brainliest please i’m desperate
Answer:
[tex]\textsf{12.} \quad y = 6x - 5[/tex]
[tex]\textsf{17.} \quad y=-\dfrac{1}{4}x-2[/tex]
Step-by-step explanation:
Question 12Find the slope of the line by substituting two points from the given table into the slope formula.
Define the points:
Let (x₁, y₁) = (2, 7)Let (x₂, y₂) = (3, 13)[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{13-7}{3-2}=\dfrac{6}{1}=6[/tex]
Substitute the found slope and point (2, 7) into the point-slope formula to create an equation of the line:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-7=6(x-2)[/tex]
[tex]\implies y-7=6x-12[/tex]
[tex]\implies y=6x-5[/tex]
Question 17Given:
f(4) = 3f(0) = -2Therefore, two points on the line are:
(4, -3)(0, -2)The y-intercept is the y-value when x = 0.
Therefore, the y-intercept of the line is -2.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
Substitute the y-intercept and the point (4, 3) into the slope-intercept formula and solve for m to find the slope:
[tex]\implies y=mx+b[/tex]
[tex]\implies -3=m(4)-2[/tex]
[tex]\implies -1=4m[/tex]
[tex]\implies m=-\dfrac{1}{4}[/tex]
Therefore, the equation of the line is:
[tex]y=-\dfrac{1}{4}x-2[/tex]
What is the equation in point-slope form of the line that passes through the points (-3, -1) and (2, 9)?
y-1 = 2(x+3)
y-9=2(x-2)
y+9=2(x-2)
y-1= 2(x-3)
Answer:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{9cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Given points:
(-3, -1)(2, 9)Substitute the given points into the slope formula to find the slope of the line:
[tex]\implies m=\dfrac{9-(-1)}{2-(-3)}=\dfrac{10}{5}=2[/tex]
[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]
Substitute the found slope and point (-3, -1) into the point-slope formula:
[tex]\implies y-(-1)=2(x-(-3))[/tex]
[tex]\implies y+1=2(x+3)[/tex]
Substitute the found slope and point (2, 9) into the point-slope formula:
[tex]\implies y-9=2(x-2)[/tex]
Therefore, the correct answer option is:
[tex]\textsf{B)} \quad y-9=2(x-2)[/tex]
Which equation is equivalent to the given equation?
x² - 6x = 8
Answer:
(x-3)^2=17
Step-by-step explanation:
i took dis test b4
Bobby and Garnetta thought of four consecutive odd intergers such as five times the sum of the first and the third was 22 greater than the product of 8 and the sum of the second and the fourth. Find the numbers.
An integer is a whole number x=-11.
What are Integers?The Latin term "Integer," which implies whole or intact, is the source of the English word "integer." A particular category of numbers called integers includes zero, positive numbers, and negative numbers.SymbolThe symbol "Z" stands for an integer.
Z= {……-8,-7,-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7, 8,……}
Example :Let the numbers be x, x + 2, x + 4, x + 6...
5(x+x+4)=8(x+2+x+6)+22
5(2x+4)=8(2x+8)+22
10x+20=16x+64+22
The integers are -11,-9,-7,-5,
10x-16x=64+22-20 -6x=66/-6
x=-11.
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Find the value of the polynomial x2–3xy+ 1/2 y2 if x= 1/2 and y= 2/3 .
The value of the given polynomial x² - 3xy + 1/2y² if x = 12 and y = 2/3 is; -19 / 36.
What is the value of the polynomial for the given variable values?It follows from the task content that the value of the polynomial be determined for the given polynomial expression.
As evident in the task content; the given expression is;
x² - 3xy + 1/2 y².
Hence, since the given values of x and y are: 1/2 and 2/3 respectively.
On this note, we have that;
( 1/2 )² - ( 3 × 1 / 2 × 2 / 3 ) + ( 1 / 2 × (2 / 3)² )
= 1/4 - 1 + ( 2 / 9 )
= -3 / 4 + 2 / 9
= -19 / 36
On this note, the value of the given polynomial is; -19 / 36.
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What is the probability of obtaining five tails in a row when flipping a coin?
Answer:
1/32
Step-by-step explanation:
There are 2^5 outcomes from flipping 5 times = 32
only ONE is T T T T T 1 OUT OF 32 = 1/32
At the local bunny-hop, Mr. Meyering jumps 20 inches on his first jump and then 10 inches with his second jump. If the distances form a geometric sequence, what is the total distance Mr. Meyering jumps if he completes infinitely many jumps?
Hint: Use S = a1/ 1-r and remember that |r| must be less than 1.
If the distances form a geometric sequence, the total distance Mr. Meyering jumps if he completes infinitely many jumps is equal to 40 inches.
What is a geometric sequence?In Mathematics, a geometric sequence can be defined as a series of real and natural numbers that are calculated by multiplying the next number by the same number (common ratio) each time.
Mathematically, the sum of an infinite geometric sequence can be calculated by using this mathematical expression:
S = a₁/(1 - r)
Where:
S represents the sum of an infinite geometric sequence.r represents the common ratio or constant ratio.a is the first term of a geometric sequence.How to determine the total distance Mr. Meyering jumps?First of all, we would determine the common ratio between the distances he jumped as follows;
Common ratio, r = a₂/a₁
Common ratio, r = 10/20
Common ratio, r = 0.5.
For the total distance, we have;
S = a₁/(1 - r)
S = 20/(1 - 0.5)
S = 20/0.5
S = 40 inches.
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What is the sum? 8 + (negative 12) Group of answer choices –4 20 4 –20
PLS HELP THANK YOU SO MUCH
As we know that, while finding any angles on a line, the full angle is 360°.
Now we have three angles in the image and their sum will be 360°, and the angles are :
68° 90° yNow, 68° + 90° + y = 360°
=> 158° + y = 360°
=> y = 360° - 158°
=> y = 202°
Hence, y = 202° is the answer.
any help on this question
Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)
Given that,
We have to simplify the equation that is
36y / (y²- 2y+1) ÷ 12y² / (y²-1)
We know that,
We have to divide the equations,
36y / (y²- 2y+1) ÷ 12y² / (y²-1)
We can write in multiplication form that is
36y / (y²- 2y+1) × (y²-1) / 12y²
Now we can divide the 36y by 12 y² we get 3/y
3(y²-1)/ y(y²- 2y+1)
We can write the y²-1 as (y-1)(y+1) and by formula y²-2y+1 as (y-1)²
3(y-1) (y+1)/ y (y-1)²
Now we can divide
3(y+1)/ y(y-1)
So we can see in the options
Therefore, Option A satisfy the equation after simplification that is y(y-1) / 3(y+1) when the equation that is 36y / (y²- 2y+1) ÷ 12y² / (y²-1)
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How do you solve 12-8x=-5x-5x??
Please help me!!
Answer:
-6
Step-by-step explanation:
12-8x= -5x-5x
Combine like terms
12-8x= -10x
Add 8x to both sides
12-8x= -10x
+8x. +8x
12= -2x
Divide both sides by -2
12= -2x
/-2. ;-2
-6=x
Hopes this helps please mark brainliest
Please help, this is geometry and I need to find the measure of the missing angle
The measure of missing angle is 145°.
Define linear pair theorem.When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°. The linear pair postulate or linear pair theorem in mathematics states the same thing mathematically. The sum of the measurements of two angles that make up a linear pair is 180°.
Given
Missing angle = x°
Opposite angle = 100°
Exterior angle = 35°
x and exterior angle are linear pair
Sum of linear pair is 180
x + 35 = 180
x = 180 - 35
x = 145
The measure of missing angle is 145°.
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Rewrite the following scientific notation numbers into standard form. (Be sure to use commas)
a. 3.23x10 -3
b. 7.45x10 5 =
Answer:
a. 0.00,323
b. 745,000
Step-by-step explanation:
a) move the decimal 3 places to the left
b) move the decimal 5 places to the right.
If my math teacher asked me what's 5÷10+2-9 what would the answer be ??
Answer:-6.5
Step-by-step explanation:
Answer:
Step-by-step explanation
Use pemdas.
P- Parenthesis
e- Exponents
m- Multiplication
d- Division
a- Additon
s-Subtraction
5÷10+2-9
=5÷12-9
=5÷3
=1.666666666667
5+5p=5p +5 is what property
Answer:
Commutative Property Addition
I’m needing some help with this
Answer: place points at (0,3) and (5,5)
Step-by-step explanation: the formula for a line is y = mx + b, where m is the slope and b is the y-intercept (the point where the line meets the y-axis). Since b is positive 3, place a point at (0,3).
m = 2/5, and since slope is rise over run (distance traveled in y axis over distance traveled in x axis) and it is positive, your next point is 2 up and 5 right, which is (5,5). You could also place a point at (-2,-2).
Answer:
Step-by-step explanation:
Fill in the blanks. (Enter the domain in interval notation.) Function Alternative Notation Domain Range 2. -12 points LarPCakcCC3 4.7002 Fill in the blanks. (Enter the range in interval notation.) Function Alternative Notation Domain Range y cos-1x -1 s x s 1 3. -3 points LarPCakcc3 4.7.003 Fill in the blanks. (Enter the domain and the range in interval notation.) Function Alternative Notation Domain Range y-arctan x y-
The interval notation of domain and range is (-∞, ∞).
Interval notation:
In algebra, interval notation refers the way to describe continuous sets of real numbers by the numbers that bound them.
Given,
Here we need to write the interval notation of domain and range.
In order to find the interval notation, first we have to know the definition of domain and range.
In math domain refers the domain of a function is the set of values that we are allowed to plug into our function. Basically, this set is the x values in a function such as f(x).
And where as the range of a function is the set of values that the function assumes. And it is the values that the function shoots out after we plug an x value in.
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30 POINTS // A spinner is divided into six equal parts numbered 1, 2, 3, 4, 5, and 6. In a repeated experiment, Ryan spun the spinner twice. The theoretical probability of both spins being even numbers is 9 over 36.
If the experiment is repeated 200 times, predict the number of times both spins will be even numbers.
36
50
100
200
The number of times both spins will be even numbers in 200 spins is (b) 50
How to predict the number of times both spins will be even numbers.From the question, we have the following parameters that can be used in our computation:
Sections on the spinner = 1, 2, 3, 4, 5, and 6
Also, from the question;
We have the following statement
The theoretical probability of both spins being even numbers is 9 over 36.
This means that
P(Both even) = 9/36
Lastly, we have
Times of experiment = 200
So, we have
Outcomes of both even = P(Both even) * Times of experiment
Substitute the known values in the above equation, so, we have the following representation
Outcomes of both odd =9/36 * 200
Evaluate
Outcomes of both odd = 50
Hence, the outcomes is (b) 50
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10. The table represents the relationship between the base length and the height of some parallelograms, Both measurements are in inches. What is the relationship between the base length and height of these parallelograms?
The relation between base length and height is: f(x) = 48/x
What is parallelogram?
A parallelogram is a straightforward quadrilateral in Euclidean geometry that has two pairs of parallel sides. A parallelogram has opposite sides that are facing one another and opposite angles that are of equal size.
By the values given in the table, for base length and height of the parallelograms, you can notice that base length increases 1 units, so you have 1, 2, 3, 4, 5.
For height you can notice that while base length increase 1 unit, height decreases by a factor of 1/x, just as follow:
1 - 48
2 - 24
3 - 16
4 - 12
5 - 8
The relation between base length and height is:
f(x) = 48/x
where f(x) is the height and x is the base length. In fact, you have:
f(1) = 48/1 = 48
f(2) = 48/2 = 24
f(3) = 48/3 = 16
f(4) = 48/4 = 12
Hence, the relation between base length and height is: f(x) = 48/x.
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Casey inherited $70000, and decided to invest some of the money in a savings account earning 1% interest per year, and the rest in a certificate of deposit earning 2% interest per year. If the interest from the certificate of deposit was $800 more than the interest from the savings account, how much did Casey invest in each account?
Savings:
Certificate of Deposit:
The amount that Casey invested in the savings account is $10,000 and the amount Casey invested in the certificate of deposit is $60,000.
How much was invested in the savings account and the certificate of deposit?0.01c - 0.02s = $800 equation 1
c + s = $70,000 equation 2
Where:
c = amount invested in the certificate of deposit s = amount invested in the savings accountMultiply equation 2 by 0.01:
0.01c + 0.01s = 700 equation 3
Subtract equation 3 from equation 1:
0.01s = 100
Divide both sides of the equation by 0.01:
s = 100 / 0.01
s = 10,000
Substitute for s in equation 2:
c + 10,000 = 70,000
c = 70,000 - 10,000
c = 60,000
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A textbook store sold a combined total of 429 chemistry and biology textbooks in a week. The number of chemistry textbooks sold was 51 more than the number of biology textbooks sold. How many textbooks of each type were sold?
Using system of linear equation, the store sold 240 chemistry books and 189 biology books
System of Linear EquationA system of equations is a set or collection of equations that you deal with all together at once. The general representation of linear equations are given as y = mx + c
m = slopec = y-interceptLet set our variables as;
chemistry = x biology = yx + y = 429 ...eq(i)
x = 51 + y ...eq(ii)
Put eq(ii) into (i)
(51 + y) + y = 429
51 + 2y = 429
2y = 429
y = 189
x = 51 + 189
x = 240
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Quadra, PQRS is dilated by scale factor of 1/2 with point or as the center of dilation resulting in the image PQRS which statement is true about line Ps
The statement that is true about line segment P'S' is (c) Segment P'S' s 4 units long and lies on a different segment.
How to determine the true statement?
The complete question is in the attached image
From the image, we have:
PS = 8 units
This means that:
P'S' = 1/2 * PS
So, we have:
P'S' = 1/2 * 8
Evaluate
P'S' = 4
Also, the segment PS and P'S' do not lie on the same segment
Hence, the true statement is (c)
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i’ll give brainliest!!!!
Answer:
Lyric ran faster.
Step-by-step explanation:
When you plot y = 5x, you can trace a certain point to see which value is higher. When I plotted y = 5x and chose the point when x = 8, y = 40 for Kira, and for Lyric, at x = 8, y = 80. Since the y coordinate (distance) is higher, Lyric ran faster.
Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.
Step-by-step explanation:You may use the following logic to analyze this situation. Theoretically, the faster runner will have traveled a longer distance at any given point in time different than 0 when comparing to the other runner. Therefore, let's randomly pick a point in time to see who had traveled the longer distance.
The time we'll evaluate will be 4 seconds.
1. Evaluating the function to find Kira's traveled distance at 4 seconds.
For this, simply substitute the "x" by the number "4" in the given equation for Kira:
[tex]y=5(4)\\ \\y=20[/tex]
Conclusion: Kira had traveled a total distance of 20 yards, 4 seconds after starting the race.
2. Evaluating the function to find Lyric's traveled distance at 4 seconds.
To evaluate the graph, we'll have to draw a line where x=4 sits and then find the value of "y" the function returns. Check the attached images in order to see this process.
Conclusion: Lyric had traveled a total distance of 40 yards, 4 seconds after starting the race.
3. General conclusion.
After 4 seconds Kira traveled 20 yards;
After 4 seconds Lyric traveled 40 yards.
Conclusion: Lyric ran faster than Kira, since they were travelling a longer distance when comparing to Kira in the same period of time.