Answer:
⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex] is the required relationship.
Step-by-step explanation:
Let us assume, the given right angled triangle is ΔPQR.
Here. PQ = Perpendicular of the triangle.
QR = Base of the triangle.
PR = Hypotenuse of the triangle.
Now, PYTHAGORAS THEOREM states:
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“
⇒[tex](Base)^2 + ( Perpendicular)^2 = (Hypotenuse)^2[/tex]
Hence in ΔPQR: [tex](QR)^2 + ( PQ)^2 = (PR)^2[/tex]
And the above expression is the required relationship between the sides of a right triangle.
The sides of a right triangle have a specific relationship given by the Pythagorean Theorem, which states a² + b² = c², where a and b refer to the lengths of the sides and c refers to the length of the hypotenuse. Additionally, the sides have relationships to the angles of the triangle expressed through trigonometric functions.
Explanation:The relationship between the sides of a right triangle is given by the Pythagorean Theorem which was demonstrated by the ancient Greek philosopher, Pythagoras. This theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In mathematical terms, if the lengths of the sides are a, b, and c (where c represents the length of the hypotenuse), then the relationship can be represented as a² + b² = c².
Moreover, the sides of a right triangle also have specific relationships to the measures of the angles of the triangle, which are expressed through the trigonometric functions sine, cosine, and tangent. For example, for an angle in a right triangle, the sine is the length of the opposite side divided by the length of the hypotenuse, the cosine is the length of the adjacent side divided by the hypotenuse, and the tangent is the length of the opposite side divided by the adjacent side.
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Write an equation in slope intercept form for a line through the following: through (5,2). with a slope of -1/2
good evening ,
Answer:
let D represent the line
D : y = (-1/2)x + 4.5
Step-by-step explanation:
The equation for the line D is y=mx+p
now let’s find m and p
m is the slope then m= (-1/2)
A(5,2)∈D ⇌ 2=(-1/2)×5+p ⇌ p=9/2=4.5.
that’s it.
Look at the photo below for more info.
:)
3. Sherri bought a package of pens that contained 15 pens. How many packages should she
buy if she needs 240 pens?
Answer:
16 packages
Step-by-step explanation:
240 / 15 = 16 packs
Bevo has $5000 to invest. Bank A offers a savings account that has an APR of 1.15% and compounds monthly. Which equation will determine how much money Bevo will have in his account after 9 years?
The equation [tex]A=5000(1.000958333)^{108}[/tex] will determine how much money Bevo will have in his account after 9 years
Step-by-step explanation:
The formula for compound interest, including principal sum is
[tex]A=P(1+\frac{r}{n})^{nt}[/tex] , where:
A is the future value of the investment/loan, including interestP is the principal investment amount (the initial deposit or loan amount)r is the annual interest rate (decimal)n is the number of times that interest is compounded per unit tt is the time the money is invested or borrowed forBevo has $5000 to invest. Bank A offers a savings account that has an APR of 1.15% and compounds monthly
We need to find Which equation will determine how much money Bevo will have in his account after 9 years
Because there is no choices we will write the equation
∵ Bevo has $5000 to invest
∴ P = 5000
∵ Bank A offers a savings account that has an APR of 1.15%
and compounds monthly
∴ r = 1.15% = 1.15 ÷ 100 = 0.0115
∴ n = 12 ⇒ compounds monthly
∵ t = 9
- Substitute all of theses values in the formula below
∵ [tex]A=P(1+\frac{r}{n})^{nt}[/tex]
∴ [tex]A=5000(1+\frac{0.0115}{12})^{(12)(9)}[/tex]
∴ [tex]A=5000(1.000958333)^{108}[/tex]
The equation [tex]A=5000(1.000958333)^{108}[/tex] will determine how much money Bevo will have in his account after 9 years
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The equation to find out how much Bevo will have in his account after 9 years by investing $5000 in a saving account at Bank A which offers an APR of 1.15% compounding monthly is given by the future value formula of compound interest: FV = P(1 + r/n)^(nt). By plugging the values into this formula, Bevo can determine his future balance.
Explanation:The subject of this question is about understanding compound interest. Specifically, it is about interpreting how Bevo's financial investment would grow over a certain period at a specific rate of interest in a savings account. The equation to calculate the future value (FV) of Bevo's investment, compounded monthly, is given by the compound interest formula:
FV = P(1 + r/n)^(nt)
Where:
P is the principal amount (the initial amount of money Bevo has to invest, in this case $5000).r is the annual interest rate in decimal form (the APR divided by 100, for Bank A this would be 1.15/100 = 0.0115).n is the number of times that interest is compounded per unit t, in this case, this value is 12 (as it is compounded monthly).t is the time the money is invested for in years (specified in the question as 9 years).This gives a better understanding of how savings accounts and compounded interest work.
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What is 3z+3/4-2z equal
The simplified expression of 3z + (3/4) - 2z is z + (3/4).
Explanation:The expression 3z + (3/4) - 2z can be simplified by combining like terms. Like terms have the same variable and exponent. In this case, the like terms are the 3z and the -2z. When you combine them, you get z. So the simplified expression is z + (3/4).
8+5y=(8y-6)-7 how to work it out
the solution is y = 7
Step-by-step explanation:
Given equation is
[tex]8+5y=(8y-6)-7[/tex]
The equation has to be solved for y
So,
Opening brackets first
[tex]8+5y=8y-6-7\\8+5y=8y-13[/tex]
Subtracting 8 from both sides
[tex]8+5y-8=8y-13-8\\5y=8y-21[/tex]
subtracting 8y from both sides
[tex]5y-8y = 8y-21-8y\\-3y=-21y[/tex]
Dividing both sides by -3
[tex]\frac{-3y}{-3} = \frac{-21}{-3}\\y = 7[/tex]
so,
the solution is y = 7
Keywords: Linear equation, variables
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Which pair of angles are same side exterior angles?
2 and 8
1 and 8
2 and 4
3 and 7
Answer:
Exterior angles are the ones on the outside and same side means they sit on the same side of the bisector so your answer is 1 and 8
Step-by-step explanation:
∠1 and ∠8 are same side exterior angles
If a transversal line intersect 2 parallel lines, then same sides exterior angles
are supplementary.
This means same side exterior angles sum up to 180 degrees. Therefore,
∠1 and ∠8 are same side exterior angles.
This means ∠1 and ∠8 are supplementary angles . They sum up to 180 degrees.
∠1 + ∠8 = 180°
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For the basic function f(x) = x, what conclusions can you make about fix) and
f(x) - 5? Select all that apply.
a. They intercepts are the same.
b. The function () - 5 has a greater rate
of change
c. They are parallel lines:
d. The graph of the function(x) is translated
down 5 units to produce fix) - 5.
Answer:
c, d
Step-by-step explanation:
If f(x) = x, then f(x) - 5 = x - 5.
The two functions in slope-intercept form (y = mx+ b) are:
[1] y = x and [2] y = x - 5
In equation [1], the slope is 1 and the y-intercept is 0.
In equation [2], the slope is 1 and the y-intercept is -5.
a. The y-intercepts are not the same. 0 ≠ -5
b. The rates of change, or the slopes, are the same, neither are greater than the other. 1 = 1
c. They are parallel lines. Lines are parallel when they have the same slope. 1 = 1.
d. The (-5) indicates that the new function is translated down (-) by 5 units (5) from the parent function f(x) = x.
c and d are correct.
find the coordinates of point P along the directed line segment AB so that AP to PB is the given ratio. A(-4,-8), B(0,0) ; 3 to 1
To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we use the section formula. Substituting the values into the formula, we find that the coordinates of point P are (-1, -2).
Explanation:To find the coordinates of point P along the directed line segment AB so that AP to PB is in the ratio 3 to 1, we can use the concept of section formula.
The section formula states that if we have two points A(x1, y1) and B(x2, y2), and we want to find a point P along the line segment AB such that AP to PB is in the ratio m to n, then the coordinates of P can be found using the following formulas:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
In this case, A(-4, -8) and B(0, 0).
Let's substitute the values into the formula:
x = (3 * 0 + 1 * -4) / (3 + 1) = -4/4 = -1
y = (3 * 0 + 1 * -8) / (3 + 1) = -8/4 = -2
Therefore, the coordinates of point P are (-1, -2).
Final answer:
To find point P on line segment AB where AP:PB = 3:1, we use section formula to get P's coordinates as (-1,-2). This method applies interpolation of the endpoints' coordinates, A(-4,-8) and B(0,0), by their respective weights in the given ratio.
Explanation:
To find the coordinates of point P on the directed line segment AB such that the ratio of AP to PB is 3 to 1, we can use the section formula which combines the x and y coordinates of A and B weighted by the given ratio, since P divides AB internally in the ratio 3:1.
The coordinates of A are (-4, -8) and the coordinates of B are (0, 0). Using the section formula, we can find the coordinates of P as follows:
Let x and y be the coordinates of P.
The x-coordinate of P is given by ((3 * 0) + (1 * (-4))) / (3 + 1) = -1.
The y-coordinate of P is given by ((3 * 0) + (1 * (-8))) / (3 + 1) = -2.
Therefore, the coordinates of P are (-1, -2).
This process involves interpolation of the given points in the specific ratio to find the required coordinates.
Mrs. Jones ordered 5 cheese pizzas and 1 pepperoni pizza. She ordered a total of 6 pizzas. What fraction of pizzas are cheese?
Answer:
5/6
Step-by-step explanation:
5 is the amount of cheese pizzas Mrs. Jones ordered out of the 6 pizzas in total. 5 is a prime number, so the fraction cannot be simplified.
In which of the tables below x and y are inversely proportional? Find the constant of variation. If there is one. (a) x:y, 3:8, 4:6, 5:4.8, 5.5:4
(b) x:y, 0.1:300, 0.5:60 75:0.4, 100:0.3
Answer:
The table B represent an inverse variation
The constant of variation k is 30
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Verify table A
For x=3, y=8 ----> [tex]k=y*x[/tex] ----> [tex]k=8*3=24[/tex]
For x=4, y=6 ----> [tex]k=y*x[/tex] ----> [tex]k=6*4=24[/tex]
For x=5, y=4.8 ----> [tex]k=y*x[/tex] ----> [tex]k=4.8*5=24[/tex]
For x=5.5, y=4 ----> [tex]k=y*x[/tex] ----> [tex]k=5.5*4=22[/tex]
The values of k are different
therefore
The table A not represent an inverse variation
Verify table B
For x=0.1, y=300 ----> [tex]k=y*x[/tex] ----> [tex]k=300*0.1=30[/tex]
For x=0.5, y=60 ----> [tex]k=y*x[/tex] ----> [tex]k=60*0.5=30[/tex]
For x=75, y=0.4 ----> [tex]k=y*x[/tex] ----> [tex]k=75*0.4=30[/tex]
For x=100, y=0.3 ----> [tex]k=y*x[/tex] ----> [tex]k=100*0.30=30[/tex]
All the values of k are the same
therefore
The table B represent an inverse variation
The equation is equal to
[tex]y*x=30[/tex]
Answer: Only (A)
If you go RSM this the Answer.
What is cos θ when sin θ = 2/5? Rationalize the denominator if necessary.
Answer:
[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]
Step-by-step explanation:
we have that
The angle [tex]\theta[/tex] belong the the First Quadrant (see the figure)
so
[tex]cos(\theta)\ and\ sin(\theta)[/tex] are positive values
we know that
[tex]sin^2(\theta)+cos^2(\theta)=1[/tex] ----> trigonometric identity
we have
[tex]sin(\theta)=\frac{2}{5}[/tex]
substitute in the identity
[tex](\frac{2}{5})^2+cos^2(\theta)=1[/tex]
[tex]cos^2(\theta)=1-\frac{4}{25}[/tex]
[tex]cos^2(\theta)=\frac{21}{25}[/tex]
square root both sides
[tex]cos(\theta)=\frac{\sqrt{21}}{5}[/tex]
The figure shows two parallel lines KL and NO cut by the transversals KO and LN:
Which statement best explains the relationship between AKLM and AONM?
AKLM - AONM because mx3 = m_4 and m_1= m25
AKLM - AONM because m23 = m26 and mZ1=m24
AKLM E AONM because mZ3 =m24 and m_1=m25
AKLM = AONM because m23 =mZ6 and mZ1=m24
Answer:
the first answer posted is wrong
Step-by-step explanation:i put it in my exam and it was wrong and i think the right answermight be
AKLM = AONM because m23 =mZ6 and mZ1=m24
I will mark as brainiest who ever get this right
You are preparing cookies using a recipe that serves 240 people. However, you only want to make enough for 60 people. The original recipe is as follows:
9 cups all-purpose flour
4 teaspoons baking soda
4 teaspoons salt
4 cups butter
3 cups granulated sugar
3 cups packed brown sugar
4 teaspoons vanilla extract
8 large eggs
8 cups Semi-Sweet Chocolate Morsels
How much of each ingredient should you use to make a batch of these cookies for 60 people?
Answer:
2.25 cups of flour
1 teaspoon of baking soda
1 teaspoon of salt
1 cup of butter
0.75 cups of granulated sugar
1 teaspoon of vanilla extract
2 large eggs
2 cups of Semi-Sweet Chocolate Morsels
Step-by-step explanation:
The ingredients should be 4 times less than the original ones because 240:4=60
yan is running on a track that is of a km long. She can run 4 laps in 12
minutes. What is her speed in km per minute?
Answer:
3 km per minute
Step-by-step explanation:
12/4=3 laps
3 km per minute
simplify
-4(11+4n)-3(-2n+9)
Answer:
-71-10n
Step-by-step explanation:
-4(11+4n)-3(-2n+9)
-44-16n+6n-27
-44-27-10n
-71-10n
2+2+2+2x1=What I have no clue please help
Answer:
8
Step-by-step explanation:
Im guessing that the x means multiplication
so PEMDAS
so 2 times 1 is 2 so basically it is now
2+2+2+2= 8
Answer:
Your answer is 8 :)
Step-by-step explanation:
2+2 is 4
4+2 is 6
6+2 is 8
Then 8 times 1 is 8, because anything times 1 is that number!
Hope it helps!!
If 1 inch represents 10 miles on a map, then how many inches will represent 120 miles?
Answer:
12
Step-by-step explanation:
120 divide by 10
Answer:
12
Step-by-step explanation:
120/10
Which situation is best modeled by the equation
7-x=3?
CLEAR
CHECK
You spend $7 to enter a theme park, and then $3 per ride.
Three friends each get an equal share of the $7 they
earned.
You have some money left after you spend $7 and $3.
The price of a book, $7, was lowered by some amount to
$3.
Answer:
Step-by-step explanation:
The last one
The equation 7 - x = 3 is best modeled by the situation where the original price of a book at $7 is lowered by an amount of $4 to reach the final price of $3.
The given equation 7 - x = 3 can be used to model a situation where the price of a book, originally $7, is reduced by some amount to $3. After solving the equation by subtracting 7 from both sides and then multiplying by -1, we get x = 4. This means the amount reduced from the original price is $4, which is consistent with a price reduction scenario: the book's original price was $7, and it was reduced by $4, bringing the final price to $3.
Blaine buys 2 books and the total cost is $24.18. What is the constant of proportionality that relates the cost in dollars, y, to the number of books, x?
Answer:
$ 12.09
Step-by-step explanation:
formula Y = KX
Where; y = $ 24.18
x = 2 books
k = constant of proportionality
Step 1. Do the equation based on the formula
Y = kx
$24.18 = k2
Step 2. Divide by 2
$24.18/2 = k2/2
k = $12.09 (answer)
27/22 as a decimal rounded to the nearest tenth
The fraction 27/22, when converted into a decimal and rounded to the nearest tenth, is approximately 1.2.
To convert a fraction to a decimal, divide the numerator by the denominator. In this case, divide 27 by 22.
Explanation:The question asks to convert the fraction 27/22 into a decimal, rounded to the nearest tenth. First off, we calculate the division of 27 by 22, which gives us approximately 1.227. However, we need to round this figure to the nearest tenth, which results in the value of 1.2. Be sure to understand that when we say 'rounded to the nearest tenth', we refer to the first digit after the decimal point.
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Factor the expression.
3x2 + 7x-6
Answer:
this answer is. _48 am I right
the factored form of the expression [tex]\(3x^2 + 7x - 6\) is \((3x - 2)(x + 3)\).[/tex]
To factor the expression [tex]\(3x^2 + 7x - 6\),[/tex] we need to find two numbers that multiply to give [tex]\(3 \times (-6) = -18\)[/tex] and add to give the middle coefficient, (7)
The two numbers that meet these criteria are [tex]\(9\) and \(-2\).[/tex]
Now, we can rewrite the middle term \(7x\) as the sum of these two terms:
[tex]\[3x^2 + 9x - 2x - 6\][/tex]
Next, we group the terms and factor by grouping:
[tex]\[3x(x + 3) - 2(x + 3)\][/tex]
Now, we can factor out the common factor [tex]\(x + 3\):[/tex]
[tex]\[(3x - 2)(x + 3)\][/tex]
So, the factored form of the expression [tex]\(3x^2 + 7x - 6\) is \((3x - 2)(x + 3)\).[/tex]
A gallon of chevron gas is currently $3.75 per gallon. If your car's tank holds 12.25 gallons, about how much will it cost to fill the tank
Multiply the number of gallons by the price per gallon:
12.25 gallons x 3.75 per gallon = $45.94 total.
(02.01)The ratio of X's to O's is 12 over 9. . Use the image below to determine another ratio for X's to O's: Image with 12 Xs and 9 circles. The 12 Xs are broken down so that there are 4 Xs 3 times and the circles are broken down so that there are 3 circles 3 times.
3 over 4.
9 over 12.
4 over 3.
9 over 4.
Answer:
4 over 3 or 4 : 3.
Step-by-step explanation:
See the diagram attached.
Now, The ratio of X's to O's is 12 : 9.
Now, we have to determine another ration for X's to O's.
The image will help us to do that.
There are 12 numbers of X and that can be broken into 3 sets of X with 4 X in each set. Hence, 12 = 3 × 4
Again, there are 9 numbers of O and that can be broken into 3 sets of O with 3 O in each set. Hence, 9 = 3 × 3
Therefore, the ratio of X's to O's is 12 : 9 ≡ (3 × 4) : (3 × 3) ≡ 4 : 3
{Cancelling 3 from each term} (Answer)
Answer:
The answer is 4 over 3.
Step-by-step explanation:
if you look at the image all you have to do is count the X's on the top, and that's the top of your fraction, then count the bottom number, that's the bottom of your fraction.
4 on the top three on the bottom so your fraction/ratio is 4 over 3!
hope this helped!!!
write (-3, 5) and (-2, -6) standard form
Answer:The numbers are already in standard form
Step-by-step explanation:
2 and 1/7 :(15a)= 5/14 :(0.8)
Answer:
a = 0.32Explanation:
This question requires that you find the value of [tex]a[/tex] given that:
[tex]2\frac{1}{7}:(15a)=(5/14)/(0.8)[/tex]That is you have to solve the equation for a.
1. Rewrite the equation in form of fractions, convert the mixed number into an improper fraction, and convert the decimal number into fraction too.
[tex]2\frac{1}{7}:(15a)=(5/14)/(0.8)\\ \\ \frac{2+\frac{1}{7} }{15a} =\frac{5/14}{8/10}\\ \\\frac{(14+1)/7}{15a} =\frac{5\times 10}{8\times 14}\\ \\ \frac{15}{7\times 15a} =\frac{50}{112}[/tex]
2. Cross multiply to leave a alone:
[tex]a=15\times 112/(7\times 15\times 50)\\ \\a=1680/5250\\ \\a=0.32[/tex]
what is the mode of this data?
1.7 8.9 3 5.9 3.2 4.1 6.6 0.7
Answer:
The value of Mode is 2.43
Step-by-step explanation:
To find the mode of the given data first we have to arrange it in a increasing order then find out mean and median of the given data 0.7,1.7,3,3.2,4.1,5.9,6.6,8.9 is in increasing order For finding the median we need to take the average of 4th and 5th terms because we have the no of terms in the sequence is even not odd so we need to take the average the 4th term=3.2 and the 5th term =4.1so average =(3.2+4.1)/2=3.65so the median is equal to 3.65For mean we have to take the average of the data so mean= sum of all data /no of data mean =(0.7+1.7+3+3.2+4.1+5.9+6.6+8.9)/8=4.26so by using the formula we can get modeMode=3×Median-2×MeanMode=3×3.65-2×4.26=2.43∴The value of Mode is given as 2.43Let g(x) be the reflection of f(x) = x² + 3 in the y-axis. What is a function rule for g(x)?
It's [tex]g(x)=f(-x)=f(x)[/tex].
Reflection over y-axis is the same as original function.
Hope this helps.
(-5, -20), (9,9)
Slope
Answer:
m=29/14
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(9-(-20))/(9-(-5))
m=(9+20)/(9+5)
m=29/14
The required slope is [tex]\dfrac{29}{14}[/tex].
Given:
The two points are [tex](-5,-20)[/tex] and [tex](9,9)[/tex].
To find:
The slope of the line.
Explanation:
Slope formula:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Using the slope formula, we get
[tex]m=\dfrac{9-(-20)}{9-(-5)}[/tex]
[tex]m=\dfrac{9+20}{9+5}[/tex]
[tex]m=\dfrac{29}{14}[/tex]
Therefore, the slope of the line is [tex]\dfrac{29}{14}[/tex].
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Find the number of roots for each equation.
5. 5x4 + 12x3 – x2 + 3x + 5 = 0
Answer:
The number of roots for equation [tex]5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex] is 4 .
Step-by-step explanation:
Here, the given function polynomial is :
[tex]P(x) : 5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex]
The Fundamental Theorem of Algebra says that a polynomial of degree n will have exactly n roots (counting multiplicity).
Now here, the degree if the polynomial is 4 (highest power of variable x).
So, according to the Fundamental Theorem, the given polynomial can have AT MOST 4 roots, counting Multiplicity.
Hence, the number of roots for equation [tex]5x^4 + 12x^3 – x^2 + 3x + 5 = 0[/tex] is 4 .
Find the 15th term of the geometric sequence 3, -6, 12, ...
Answer:
49152
Step-by-step explanation:
To find the 15th term of the geometric sequence 3, -6, 12, ..., we identify the common ratio as -2 and use the formula for the nth term of a geometric sequence. By calculating 3 * (-2)^14, we find that the 15th term is 49152.
Explanation:To find the 15th term of the geometric sequence 3, -6, 12, ... we first need to determine the common ratio. By dividing the second term by the first term, we find that the common ratio is -2.
Formula for the nth term of a geometric sequence:
an = a1 × r(n-1), where an is the nth term, a1 is the first term, r is the common ratio, and n is the term number.
Finding the 15th term:
Plugging in the values, we get: a15 = 3 × (-2)(15-1) = 3 × (-2)14. Since (-2)14 is positive (because any even power of a negative number is positive), the 15th term will be positive. Calculating the value, a15 = 3 × 16384 = 49152.
Therefore, the 15th term of the geometric sequence is 49152.
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