It is true that the graph contains the point (0, 0).
The following three assertions regarding the function and its graph are true:
The function's graph resembles a parabola.
The graph begins at the bottom.
The point is shown in the graph (0,0).
Explanation:
A second-degree polynomial function, the quadratic function f(x) = x2 - 5x + 12 has a parabola as its graph.
The parabola widens downward because the coefficient of x2 is positive (1 in this instance).
When we replace x with -10 in the given function, we obtain the value of f(-10) as (-10)2 - 5(-10) + 12 = 82. Hence, "f(-10) = 82" is true.
We substitute x = 20 in the given function, resulting in f(20) = 202 - 5(20) + 12 = 212, to see if the point (20, -8) is on the function's graph. The claim "The graph contains the point (20, -8)" is untrue since the point's y-coordinate is -8, which is not equivalent to f(20).
We substitute x = 0 in the given function to get f(0) = 02 - 5(0) + 12 = 12 to determine if the point (0, 0) is on the function's graph. The assertion "The graph contains the point (0, 0)" is true because the y-coordinate of the point (0, 0) is 0, which is equivalent to f(0).
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A shop employs one man and one woman as shop assistants. The man works for 10 hours per day and the woman for 8 hours per day, and their wages per hour are in the ratio 7:5. If the woman receives $24 per day, find the man's daily wage.
The man's daily wage is given as follows:
$42.
How to obtain the man's daily wage?The wages are obtained applying the proportions in the context of the problem.
The woman receives $24 for 8 hours of work, hence her hourly wage is given as follows:
24/8 = $3 per hour.
(Hourly wage = Total wages/total hours).
Their wages per hour are in the ratio 7:5, hence the man's hourly wage is obtained multiplying the woman's hourly wage by 7/5, hence:
7/5 x 3 = 21/5 = $4.2 per hour.
The man works 10 hours a day, hence the daily wage is given as follows, multiplying the hourly wage by 10:
10 x 4.2 = $42.
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1. Decode the following ASCII code: [2 marks] 1010011 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011
Answer:
The decoded message is: "Steve Jobs".
Step-by-step explanation:
The given code is a sequence of binary digits, which represents the ASCII code of a message in binary form. To decode the message, we need to convert each 8-bit binary sequence into its corresponding ASCII character.
1010011 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011
To decode this message, we split it into 8-bit sequences:
01010011 --> 'S'
01110100 --> 't'
01100101 --> 'e'
01110110 --> 'v'
01100101 --> 'e'
00100000 --> ' '
01001010 --> 'J'
01101111 --> 'o'
01100010 --> 'b'
01110011 --> 's'
Therefore, the decoded message is: "Steve Jobs".
Answer:
The decoded message is: "Steve Jobs"
Step-by-step explanation:
Converting the binary code to ASCII, we get:
01010011 = S
1110100 = t
1100101 = e
1110110 = v
1100101 = e
0100000 = (space)
1001010 = J
1101111 = o
1100010 = b
1110011 = s
So the decoded message is: "Steve Jobs"
----------------
Here are the steps to decode the given binary code:
Break the binary code into groups of 8 digits, as each group represents a single ASCII character.
Convert each group of 8 digits into its corresponding ASCII character using a binary-to-text converter or an ASCII code chart.
Write down the decoded ASCII characters in the order in which they appear in the original binary code.
Let's follow these steps to decode the given binary code:
The given binary code is: 1010011 1110100 1100101 1110110 1100101 0100000 1001010 1101111 1100010 1110011
We break this binary code into groups of 8 digits:
1010011 = 53
1110100 = 74
1100101 = 65
1110110 = 76
1100101 = 65
0100000 = 32
1001010 = 74
1101111 = 111
1100010 = 98
1110011 = 115
We convert each group of 8 digits into its corresponding ASCII character using an ASCII code chart:
53 = S
74 = t
65 = e
76 = v
65 = e
32 = (space)
74 = J
111 = o
98 = b
115 = s
We write down the decoded ASCII characters in the order in which they appear in the original binary code:
Decoded message: "Steve Jobs"
ASCII mean?
ASCII stands for American Standard Code for Information Interchange. It is a character encoding standard that assigns unique numeric codes to represent text characters. The ASCII standard includes codes for uppercase and lowercase letters, digits, punctuation marks, and various other symbols. Each ASCII character is represented by a unique 7-bit binary code, allowing computers and other devices to communicate and display text in a consistent manner. The ASCII standard was first published in 1963 and has since been expanded and updated to include additional characters and support for different languages.
Ms. Curtis Basham grows pears and plums on her
urban homestead. Two years ago she gathered 40
pounds of pears and 12 pounds of plums. The next
year the
pears declined by 25% and the plums
declined by 20%. By what percentage did the total
yield, by weight, of her fruit harvest decline?
A. 22.5%
B. 24%
C. 45%
D. 76%
The percentage did the total yield, by weight, of her fruit harvest declined by approximately 24%, which is option B.
what is percentage ?
Percentage is a way of expressing a number or quantity as a fraction of 100. It is often denoted by the symbol % (percent). For example, 50% means 50 out of 100, or 50/100, or the equivalent fraction 1/2.
Percentages are commonly used in many real-world situations, such as in finance, statistics, and everyday life. They are often used to express changes, differences, or ratios between two values.
According to the question:
To solve this problem, we need to calculate the total weight of fruit harvested in the first year and the total weight of fruit harvested in the second year, and then calculate the percentage decline.
Total weight of fruit harvested in the first year = 40 + 12 = 52 pounds
After a 25% decline, the weight of pears in the second year = 40 - 0.25(40) = 30 pounds
After a 20% decline, the weight of plums in the second year = 12 - 0.20(12) = 9.6 pounds
Total weight of fruit harvested in the second year = 30 + 9.6 = 39.6 pounds
Percentage decline in the total yield of fruit harvest = [(52 - 39.6)/52] x 100% = 23.8%
Therefore, the answer is approximately 24%, which is option B.
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the rectangle repersents the base of a right rectangular prism. The height of the prism is 6 inches. What is the volume of this prism
Given- The rectangle that represents the base of right rectangular prism
To find - The volume of the prism.
Explanation- we know that the volume of the right rectangular prism is product of area of rectangle and the height
Area of rectangle is [tex](lb)[/tex]
length (l) = 4.2
breadth = 3
area = 4.2×3=12.6
Volume of prism = 12.6 × height =12.6×6=75.6
Hence the volume of the prism is 75.6 in^3
Final answer - The correct option is D.
How many solutions does the system of linear equations graphed below have?
A. No solution
B. 1 solution
B. Infinitely Many Solutions
A circular walking path is modeled by (x + 3)2 + (y − 4)2 = 64, where all measurements are in meters. Center at (−3, 4); r = 8 Center at (−3, 4); r = 64 Center at (3, −4); r = 8 Center at (3, −4); r = 64
To find the circle with center (3, -4) and radius 64, we again replace 64 with 64² in the equation, and get:
(x - 3)² + (y + 4)² = 4096
What would be a circular example?Several everyday items, such as turning ceiling fans, turning car wheels, spinning windmill blades, and turning gas turbine gears, exhibit circular motion. Another is an earth-orbiting satellite that was built by people.
The equation (x + 3)² + (y - 4)² = 64 represents a circle with center (-3, 4) and radius 8.
To find the circle with center (-3, 4) and radius 64, we replace 64 with 64² in the equation and get:
(x + 3)² + (y - 4)² = 4096
This circle has center (-3, 4) and radius 64.
To find the circle with center (3, -4) and radius 8, we replace (x + 3) with (x - 3) and (y - 4) with (y + 4) in the equation, and get:
(x - 3)² + (y + 4)² = 64
This circle has center (3, -4) and radius 8.
To find the circle with center (3, -4) and radius 64, we again replace 64 with 64² in the equation, and get:
(x - 3)² + (y + 4)² = 4096
This circle has center (3, -4) and radius 64.
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I swear mom write the ratio in lowest terms in order to decide whether the proportion is true or false 100/210 = 290/340
False, the given two proportions are not equal.
What are ratios and proportions?In this section, the terms ratio and percentage are defined. Both ideas play a significant role in mathematics. Many examples where the notion of the ratio is highlighted may be found in daily life, such as the rate of speed (distance/time) or price (rupees/meter) of a substance.
An equation known as proportion shows that the two ratios presented are equal to one another.
The two given proportions are:
100/210 = 290/340
Simplifying the two we have:
100/210 = 10/21
290/340 = 29/34
We see that the simplified form of the two proportions are different.
Hence, False, the two proportions are not equal.
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conver 121 pounds into kilograms use 1kg=2.2Ib
round you answer to nearest tenth
Answer:
55 KG
Step-by-step explanation:
To convert pounds to kilograms, we can use the conversion factor 1 kg = 2.2 lbs.So,121 lbs = (121 lbs) * (1 kg/2.2 lbs)Simplifying the expression, we have121 lbs ≈ 55.0 kgRounding to the nearest tenth, we get the final answer:121 lbs ≈ 55.0 kg
Answer:
To convert 121 pounds into kilograms, we can use the conversion factor:
1 kg = 2.2 lb
Dividing both sides of this equation by 2.2, we get:
1 lb = 0.454545 kg (rounded to the nearest tenth, this is 0.5 kg)
Therefore, we can convert 121 pounds to kilograms by multiplying by 0.454545:
121 lb * 0.454545 kg/lb = 54.884545 kg
Rounding this to the nearest tenth gives:
54.9 kg
Therefore, 121 pounds is approximately equal to 54.9 kilograms when rounded to the nearest tenth.
You would like to retire 25 years from now and have a retirement fund from which you can draw an income of $50,000 per year – forever! How can you do it? Assume a constant APR of 7%. (What balance do you need to earn $50,000 from interest? How can you get to that balance?)
We need a retirement fund balance of $714,285.71 in 25 years to generate an annual income of $50,000 at a constant APR of 7%.
What is Percentage?percentage, a relative value indicating hundredth parts of any quantity.
To generate an income of $50,000 per year forever, we need to create a retirement fund that can generate this income through interest and not deplete the principal amount.
We can use the following formula to calculate the required balance in the retirement fund:
Balance = Annual income / Annual interest rate
The annual income we need is $50,000, and the annual interest rate is 7%, so we can calculate the required balance as:
Balance = $50,000 / 0.07
= $714,285.71
Therefore, we need a retirement fund balance of $714,285.71 in 25 years to generate an annual income of $50,000 at a constant APR of 7%.
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Does singing to plants help them grow? You decide to test the effectiveness of your singing prowess on plant growth by singing to six different plants each day for 3 months (it would seem you have nothing better to do with your time). You start each plant with a seed and then count the number of leaves produced at the end of the 3 months. You data looks like this: 1, 2, 4, 5, 7, 11 1.
1. What scale of measurement was used by the researcher?
2. Calculate the mean, median, mode.
3. Calculate the range, variance and standard deviation for the data set using the formula for sample variance and SD.
4. Based on your sample, what is the number of leaves associated with +2SD?
5. What number of leaves are associated with 68% of the sample?
Answer:
The scale of measurement used by the researcher is interval scale as the data is continuous and there are equal intervals between the values.
Mean = (1+2+4+5+7+11)/6 = 5
Median = (4+5)/2 = 4.5
Mode = There is no mode in the data set as none of the numbers are repeated.
Range = maximum value - minimum value = 11 - 1 = 10
Sample Variance = ((1-5)^2 + (2-5)^2 + (4-5)^2 + (5-5)^2 + (7-5)^2 + (11-5)^2)/(6-1) = 14.67
Standard Deviation = sqrt(sample variance) = sqrt(14.67) = 3.83
Mean + 2SD = 5 + 2*3.83 = 12.66, rounded to the nearest integer = 13.
According to the Empirical Rule, 68% of the sample lies within 1 standard deviation of the mean. Therefore, we need to find the values that are 1 standard deviation away from the mean:
Lower limit = Mean - SD = 5 - 3.83 = 1.17, rounded to the nearest integer = 1.
Upper limit = Mean + SD = 5 + 3.83 = 8.83, rounded to the nearest integer = 9.
So the number of leaves associated with 68% of the sample is between 1 and 9.
Step-by-step explanation:
the domain of discourse is set of male patients in a clinical study. define the following predicates: p(x): x was given the placebo
(a) One patient did not receive the medication.
(b) One patient did not get either the medicine or the placebo.
(c) None of the patients took the drug or experienced migraines (or both).
(d) One patient who received a placebo experienced no migraines.
what is variable?A variable in algebra is an alphabet that is used to symbolize the unknowable integer. It stands in for the value. An amount that can fluctuate depending on the mathematical issue is referred to as a variable. The generic letters x, y, and z are frequently employed in mathematical expressions and equations. A variable, then, is a symbol denoting a number whose value is unknown.
from the question:
(a)
Logical expression: ∀x D(x)
Negation: ¬(∀x D(x))
Applying De Morgan's law: ∃x ¬D(x)
One patient did not receive the medication.
(b)
Logical expression: ∀x (D(x) ∨ P(x))
Negation: ¬(∀x (D(x) ∨ P(x)))
Applying De Morgan's law: ∃x ¬(D(x) ∨ P(x))
Applying De Morgan's law: ∃x (¬D(x) ∧ ¬P(x))
One patient did not get either the medicine or the placebo.
(c)
Logical expression: ∃x (D(x) ∧ M(x))
Negation: ¬∃x (D(x) ∧ M(x))
Applying De Morgan's law: ∀x ¬(D(x) ∧ M(x))
Applying De Morgan's law: ∀x (¬D(x) ∨ ¬M(x))
None of the patients took the drug or experienced migraines (or both)
(d)
Logical expression: ∀x (P(x) → M(x))
Using the conditional identity: ∀x (¬P(x) ∨ M(x))
Negation: ¬∀x (¬P(x) ∨ M(x))
Applying De Morgan's law: ∃x ¬(¬P(x) ∨ M(x))
Applying De Morgan's law: ∃x (P(x) ∧ ¬M(x))
One patient who received a placebo experienced no migraines.
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complete question;
In the following question, the domain of discourse is a set of male patients in a clinical study. Define the following predicates:
P(x): x was given the placebo
D(x): x was given the medication
M(x): x had migraines
Translate each statement into a logical expression. Then negate the expression by adding a negation operation to the beginning of the expression. Apply De Morgan's law until each negation operation applies directly to a predicate and then translate the logical expression back into English.
Sample question: Some patient was given the placebo and the medication.
∃x (P(x) ∧ D(x))
Negation: ¬∃x (P(x) ∧ D(x))
Applying De Morgan's law: ∀x (¬P(x) ∨ ¬D(x))
English: Every patient was either not given the placebo or not given the medication (or both).
(a)Every patient was given the medication.
(b)Every patient was given the medication or the placebo or both.
(c)There is a patient who took the medication and had migraines.
(d)Every patient who took the placebo had migraines. (Hint: you will need to apply the conditional identity, p → q ≡ ¬p ∨ q.)
Find the value of each expression for a=1/3 b=9 c=5
Answer: Provide the picture if you have one or write out the whole problem
Step-by-step explanation:
Unit 5 Day 4 - Exit Ticket 5.3 - Dividing Polynomials
Perform the operation shown below.
Hint: Shift 6 for exponents and put remainders in (),
Ex. 2x^2+(4/x+2)
(x3+10x2+13x+36)÷(x+9)
We can state that the polynomial [tex]x^3 + 10x^2 + 13x + 36[/tex] is
factored by (x + 9).
the remainder is 0, and the quotient is [tex]x^2 + 9x + 4[/tex]. The outcome can be expressed as
[tex]x^3 + 10x^2 + 13x + 36 = (x^2 + 9x + 4)(x + 9)[/tex]
What are polynomials?Algebraic expressions called polynomials include coefficients and variables. Indeterminates are another name for variables. For polynomial expressions, we can do mathematical operations like addition, subtraction, multiplication, and positive integer exponents but not division by variables.
Poly (which means "many") and Nominal (which means "terms") are the two terms that make up polynomials. An expression that consists of variables, constants, and exponents that are combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable)
From the question:
We use the long division method to divide polynomials.
[tex]x^2 + 9x + 4[/tex]
_____________________________
[tex]x + 9 | x^3 + 10x^2 + 13x + 36 - (x^3 + 9x^2)[/tex]
_________________
[tex]x^2 + 13x - (x^2 + 9x)[/tex]
___________
[tex]4x + 36 - (4x + 36)[/tex]
__________
0
the remainder is 0, and the quotient is [tex]x^2 + 9x + 4[/tex]. The outcome can be expressed as
[tex]x^3 + 10x^2 + 13x + 36 = (x^2 + 9x + 4)(x + 9)[/tex]
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Solve the inequality 9> n-2
Answer:
n < 11
Step-by-step explanation:
We must solve for n, first we will rearrange the inequality
n - 2 < 9
n < 9 + 2
n < 11
Answer:
n < 11
Step-by-step explanation:
The length of a wall in a computer classroom is 15 metres. How many computer desks can be placed side-by-side along the wall if the desk has a length of 70cm and a breadth of 40cm
There will be 21 computer workstations that may be arranged side by side along the wall.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The number of computer desks that can be placed side-by-side along the wall is calculated as,
⇒ (15 x 100) / 70
⇒ 1500 / 70
⇒ 21.42
There will be 21 computer workstations that may be arranged side by side along the wall.
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Please help!!! see image below!!
Answer:
onomatopoeia
Step-by-step explanation:
A sales director for an educational curriculum company shares information about reading proficiency with several regional school districts to inform them of new policies and assist in sales of a new product.
What region and grade should the sales director target as most likely to want a new reading product based on low reading scores and trending?
West region, 8th grade
Northeast region, 8th grade
West region, 4th grade
Northeast region, 12th grade
According to the information, it can be inferred that the region and grade that the sales director should target to offer a new reading product based on low reading scores is West region, 4th grade.
How to select the right conclusion?To select the correct conclusion we must carefully look at the graphs and identify in which regions and grades the reading score rates are low. Based on this information, we can infer that the region and grade with the lowest rates in this area is West region, 4th grade.
Due to the above, the sales manager should focus his sales strategy on new products in this population because there is a high probability that they will buy the products to improve the rates they have.
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Mary's mom gave her $100.00 to go shopping. She spent $22.65 on a shirt and 3
$33.31 on a skirt. She had a coupon for 10% off. How much change did the cashier give back to her?
The clerk did not give Mary any change, so that is the correct response.
How does discount work?A price decrease from the normal or list amount or a proportional deduction from such a debt account, typically applied in exchange for on-time or cash payments.
The total cost of the shirt and three skirts before the coupon is:
$22.65 + 3($33.31) = $122.58
With the 10% discount, the total cost becomes:
$122.58 - 0.1($122.58) = $110.32
To find out how much change the cashier gave back to Mary, we need to subtract the total cost from the amount of money Mary's mom gave her:
$100.00 - $110.32 = -$10.32
Since the result is negative, it means Mary did not have enough money to pay for her purchases and would have to give the cashier an additional $10.32 to cover the full cost of her shopping.
Therefore, the answer is that Mary did not receive any change from the cashier.
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Find the length of the third side. If necessary, write in simplest radical form.
The length of the third side is 9.
Describe Right Angled Triangle?A right-angled triangle is a triangle in which one of its angles is a right angle, meaning it measures exactly 90 degrees (π/2 radians). The other two angles are acute angles, meaning they measure less than 90 degrees.
In a right-angled triangle, the side opposite the right angle is called the hypotenuse. The other two sides are called the legs. The leg opposite to an acute angle is called the opposite side, and the leg adjacent to that angle is called the adjacent side.
The Pythagorean theorem is a fundamental concept in right-angled triangles. It states that the sum of the squares of the lengths of the legs of a right-angled triangle is equal to the square of the length of its hypotenuse. This theorem is often used to calculate the length of one side of a right-angled triangle when the lengths of the other two sides are known.
Let's call the missing side of the right triangle "x". We can use the Pythagorean theorem to solve for x, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the length of the longest side (hypotenuse).
So, we have:
x² + 7² = (√130)²
Simplifying:
x² + 49 = 130
x² = 81
Taking the square root of both sides, we get:
x = 9
Therefore, the length of the third side is 9.
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Answer:
The length of the third side of the given right triangle is 9 units.
Step-by-step explanation:
We can use Pythagoras Theorem to find the length of the third side of the given right triangle.
[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]
From inspection of the given right triangle:
[tex]a = 7[/tex][tex]c = \sqrt{130}[/tex]Substitute these values into the formula and solve for the third side, b:
[tex]\implies 7^2+b^2=\left(\sqrt{130}\right)^2[/tex]
[tex]\implies 49+b^2=130[/tex]
[tex]\implies 49+b^2-49=130-49[/tex]
[tex]\implies b^2=81[/tex]
[tex]\implies \sqrt{b^2}=\sqrt{81}[/tex]
[tex]\implies b=9[/tex]
Therefore, the length of the third side of the given right triangle is 9 units.
what is the diameter of a circle with a circumference of 132ft ? Use 22/7 for pie
Answer:
Step-by-step explanation:
The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter.
Given that the circumference is 132ft and π is 22/7, we can write:
132 = (22/7)d
To solve for d, we can multiply both sides by 7/22:
132 × 7/22 = d
Simplifying the left side:
42 = d
Therefore, the diameter of the circle is 42 feet.
Answer:
D = 42
Step-by-step explanation:
Formula to find Diameter = [tex]\frac{C}{\pi }[/tex]
D = 132 ÷ [tex]\frac{22}{7}[/tex]
[tex]D = \frac{132}{1}[/tex] × [tex]\frac{7}{22}[/tex]
132 divide 22 = 6
D = 6 × 7
D = 42
A construction company is building a retaining wall. It has a 12-inch piece of stone and then
bricks are stacked on top. Each brick measures 1.5 inches in height and the entire wall must
be at least 60 inches tall. How many rows of bricks will the retaining wall have?
The retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The wall needs to be at least 60 inches tall, and we already have a 12-inch piece of stone, so we need to stack enough rows of bricks to reach a height of:
60 inches - 12 inches = 48 inches
Each row of bricks adds 1.5 inches to the height
we can divide the remaining height of 48 inches by the height of each row:
48/1.5 = 32 rows
Therefore, the retaining wall will need to have at least 32 rows of bricks to reach a height of at least 60 inches, not counting the initial 12-inch piece of stone.
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The peaches are priced at three for $2. How much does one dozen cost? Write an equivalent ratio to find the answer. Show your work.
Answer:
12:8
Step-by-step explanation:
3:2
12:x
12÷3=4
2×4=8
12:8
question is in the picture
A customer at a Mexican diner placed an order for burrito
bowls at $6.50 each. The customer also ordered a plate
of corn tacos at $12.96 and was billed a total of $32.46.
How many burrito bowls did the customer order?
Answer:
x=3
Step-by-step explanation:
Let's assume that the customer ordered x burrito bowls.
The cost of x burrito bowls at $6.50 each is 6.50x.
The cost of the plate of corn tacos is $12.96.
The total cost of the order is $32.46.
So we can set up the equation:
6.50x + 12.96 = 32.46
Subtracting 12.96 from both sides, we get:
6.50x = 19.50
Dividing both sides by 6.50, we get:
x = 3
Therefore, the customer ordered 3 burrito bowls.
2x-y=-22
y=7x+67
Help me it might be simple but I need an explanation
The solution to the system of linear equations,
2x - y = - 22 and - 7x + y = 67 is x = - 9 and y = 4.
What are the three types of solutions for a system of linear equations?If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.
Given, Two linear equations 2x - y = 22 and y = 7x + 67 in two variable 'x' and 'y'.
Arranging the equation in a similar pattern we have,
2x - y = - 22 and - 7x + y = 67.
Now, Adding these two equations +y and -y will cancel out,
So, We have - 5x = 45.
x = - 9, and 2(-9) - y = - 22 ⇒ y = 4.
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1.The angles above are examples of___________ angles. (SUPPLEMENTARY OR COMPLEMENTARY)
The value of the missing angle is _____
75
105
90
15
please please help
Therefore , the solution of the given problem of angle comes out to be x = 15° option d is correct.
What does an angle mean?In Euclidean geometry, an angle is a shape made up of two rays, or circular sides, that split at the wall's apex and the wall's apex, which is located at the centre. Two rays can combine at their points to create an angle. Another result of two things interacting is an angle. Dihedral angles are what they are called. Two line beams can be arranged at their edges in a number of ways to form a curve through two dimensions.
Here,
Given :
It is an right angle or we can say 90° angle.
So,
In order to find the value of x :
We can,
=> x + 75 = 90
=> x =90 -75
=> x = 15°
Therefore , the solution of the given problem of angle comes out to be x = 15° option d is correct.
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2.
The x-intercept is where:
The graph crosses the x-axis
Aaron Rodgers throws interceptions
The graph crosses the y-axis
The x-axis and y-axis intersect
intercept - means to cross through
answer = a - the graph crosses the x=axis
A right triangle has side lengths 5, 12, and 13 as shown below.
Use these lengths to find tanB, sin B, and cos B.
In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side, the sine of an acute angle is the ratio of the length of the opposite side to the length of the hypotenuse, and the cosine of an acute angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
Using the side lengths given in the problem, we can identify that angle B is the acute angle opposite the side with length 5.
So, we have:
tanB = opposite/adjacent = 12/5
sinB = opposite/hypotenuse = 12/13
cosB = adjacent/hypotenuse = 5/13
Therefore, the values of the trigonometric functions for angle B in this right triangle are:
tanB = 12/5
sinB = 12/13
cosB = 5/13
You are interested in buying a car that costs $10,000. The bank offers you an installment loan
with an interest rate of 17% over a 60-month term. What do you expect your monthly payments
to be? How much will you pay in total? How much will you pay in interest?
The monthly payments are $248.53.
The total amount that he will pay $14911.8.
The amount of interest is $4911.8
What is the interest rate?
The amount of interest due each period expressed as a percentage of the amount lent, deposited, or borrowed is known as an interest rate. The total interest on a loaned or borrowed sum is determined by the principal amount, the interest rate, the frequency of compounding, and the period of time the loan, deposit, or borrowing took place.
The formula of monthly payment is
P = [tex]\frac{r (PV)}{1-(1-r)^{-n}}[/tex]
r is the rate of interest.
PV is the present value
n is the number of terms.
The bank offers you an installment loan with an interest rate of 17% over a 60-month term. The cost of the car is $10,000.
PV = $10,000
n = 60
r = 17%/12 = 0.17/12
The monthly installment is
P = [tex]\frac{ \frac{0.17}{12}\times 10000}{1-(1- \frac{0.17}{12})^{-60}}[/tex]
P = 248.53
The monthly installment is $248.53.
Total payment is (60 ×$248.53) = $14911.8
The interest is $(14911.8 - 10000) = $4911.8
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I NEED HELP RIGHT NOW!!!!!!
For the triangle shown, what are the values of x and y?
a 30-60-90 triangle with a long leg length of 6, a short leg length of x, and a hypotenuse length of y
As a consequence, in a triangle with angles 30-60-90 and legs 6 long and x short, x is equal to 2√3 and y is equal to 12.
what is triangle ?Three-sided polygons, which are closed plane figures with straight edges, include triangles. One of the most fundamental and significant geometric and mathematical shapes, triangles have a wide range of useful characteristics and applications. Typically, a, b, and c are used to denote the triangle's three edges, and A, B, and C are used to denote the triangle's three angles. A triangle's inner angles are always added up to 180 degrees.
given
The percentage of the side lengths in a triangle with sides of 30-60-90 is:
Hypotenuse Means 1: Long leg: Short leg: 3: 2
In this quadrilateral, we have the following:
Hypotenuse = y; short limb = x; long leg = 6.
With the number mentioned above, we can write:
x : 6 : y = 1 : √3 : 2
For x and y, we can use cross-multiplication to get the following result:
x/1 = 6/√3
y/2 = 6/1
When we simplify these formulae, we obtain:
x = 6/√3 = 2√3
y = 12
As a consequence, in a triangle with angles 30-60-90 and legs 6 long and x short, x is equal to 2√3 and y is equal to 12.
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