What is the length of BC, rounded to the nearest tenth?
A. 13.0 units
B. 28.8 units
C. 31.2 units
D. 33.8 units
Answer:
Option C. [tex]BC=31.2\ units[/tex]
Step-by-step explanation:
step 1
In the right triangle ABD find the length side AB
Applying the Pythagoras Theorem
[tex]AB^{2}=5^{2}+12^{2}[/tex]
[tex]AB^{2}=169[/tex]
[tex]AB=13\ units[/tex]
step 2
In the right triangle ABD
we know that
[tex]m<ABD=m<BCD[/tex]
[tex]sin(<ABD)=\frac{5}{13}[/tex] -------> equation A
step 3
In the right triangle ABC
[tex]sin(<BCD)=\frac{13}{5+DC}[/tex] ------> equation B
Remember that
[tex]m<ABD=m<BCD[/tex]
so equate equation A and equation B solve for DC
[tex]\frac{5}{13}=\frac{13}{5+DC}[/tex]
[tex]5(5+DC)=13*13[/tex]
[tex]25+5DC=169[/tex]
[tex]5DC=169-25[/tex]
[tex]5DC=144[/tex]
[tex]DC=144/5=28.8\ units[/tex]
step 4
In the right triangle BDC find the length side BC
Applying the Pythagoras Theorem
[tex]BC^{2}=28.8^{2}+12^{2}[/tex]
[tex]BC^{2}=973.44[/tex]
[tex]BC=31.2\ units[/tex]
Algebra 2 Will give brainiest
If Maria earned $60 in interest over a 4-year period at a 4% simple annual interest rate, how much did she originally deposit in savings?
A.
$160
B.
$320
C.
$375
D.
$800
Answer:
the answer is c} 375
Write an equation of the line that has a slope of 3 and contains the point (2,5) in point-slope form.
If twenty-four is subtracted from a number, the result is the same as the number divided by nine. What is the number?
The required number is 27.
What are linear equation?A linear equation only has one or two variables. No variables in a linear equation is raised to power greater than 1 or used as denominator of a fraction.
Let x be the number,
Then
Twenty-four is subtracted from a number = x - 24
and number divided by nine = x/9
Now according to the question,
x - 24 = x/9
Multiplying whole equation by 9 we get,
9x - 216 = x
Adding 216 both the sides we get
9x = x + 216
Substracting x both the side we get
8x = 216
Dividing whole equation by 8 we get
x = 27
which is the required number.
Hence,the required Number is 27.
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Daphne paid $68a month for 2 years for internet service. How much did she pay in total?
1.What is the value of x?
2.What is the value of x?
Enter your answer as a decimal.
3.What is the value of x?
4.What is the value of x?
5.The area of a right triangle is 210 in². The height of the right triangle is 35 in.
What is the length of the hypotenuse of the right triangle?
Enter your answer in the box.
The base of the triangle is calculated to be 12 inches using the area and height. Then, through the Pythagorean theorem, the hypotenuse is found to be approximately 36.06 inches.
Explanation:The subject of the question is related to the calculation of a triangle's hypotenuse using the area and height of a right triangle. Given that the area of a triangle is calculated by halving the product of the base and the height (Area = 1/2 * base * height), we can use the given area to find the base of the right triangle.
First, we call the base of the triangle 'x'. The area is 210 square inches and the height is 35 inches.
We rearrange the formula for the area of a triangle to find 'x' as follows: base = (2*Area) / height.
Our calculation then becomes x = (2*210) / 35. This simplifies to x = 12 inches.
Next, we use the Pythagorean Theorem, that states: a² + b² = c², where 'c' represents the hypotenuse. Here, 'a' is the base found (12 inches), 'b' is the height (35 inches), and 'c' is the hypotenuse we're seeking.
Plugging the values into the theorem, we get c = √(12² + 35²). Hence, the hypotenuse of the right triangle is approximately 36.06 inches.
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How to factor 81y^2 -4
Solve for x 3(2x-1)=9
A math class containing 57 students was divided into two sections one section has three more students than the other how many students were in each section
Help Needed xD
What is the value of X?
Remember to show calculations and formulas used for credit.
Question 1 options:
Save
Question 2 (3 points)
What is the measure of one of the exterior angles of a regular octagon?
Make sure to show your calculation and formulas used for credit.
Question 2 options:
Find each product by factoring the tens.
6 x 2, 6 x 20, 6 x 200
_________________
_________________
P.S those lines are for the answer
12 x 10 = 120
12 X 100 = 1200
Take for instance in 6 x 2, 6 x 20 and 6 x 200. Find the factors and these are the computations. We can also say:
6 x 20 = 6 x 2 x 10 = 12 x 10 = 120
60 x 20 = 6 x 10 x 2 x 10 = 12 x 10 x 10 = 1200
It must be remembered that in the commutative and associative properties of multiplication, the order of the factors does not matter when solving this kind of problem
enter the coordinates of the point (−5, 1) after a 180° rotation about the origin. ( , )
(5,-1) because it would turn the points to their opposite "charge" and turn the positive to a negative and a negative to a positive
35.7 divided by 11.4
What was the name of Jupiter’s big pet dog
Jupiter, the Roman king of the gods, has no mythical records signifying that he had a pet dog. He is mostly associated with the eagle and the bull.
Explanation:Jupiter, the Roman king of the gods, The question you're asking seems to be based on the mythology of the Roman god Jupiter. However, there is no record in Roman mythology of any pet dog belonging to Jupiter. Jupiter, also known as Jove, was the king of the gods and the god of the sky and thunder in Ancient Rome. Animals often associated with him are the eagle and the bull, but not a dog.
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if f (x) =15x-7 then f^-1(x)=
For the function f (x) = 15x - 7, the value of f ⁻¹ (x) is,
⇒ f ⁻¹ (x) = (x + 7) / 15
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = 15x - 7
Now, We can find the inverse of f (x) as;
⇒ f (x) = 15x - 7
Substitute y = f (x),
⇒ y = 15x - 7
Solve for x;
⇒ y + 7 = 15x
⇒ x = (y + 7) / 15
Hence, We get;
⇒ f ⁻¹ (x) = (x + 7) / 15
Thus, The inverse function is,
⇒ f ⁻¹ (x) = (x + 7) / 15
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Find the value of x in the equation 9-4x=57
Is the square root of 7 an irrational number
The square root of 7 is an irrational number because it cannot be expressed as a ratio of two integers and its decimal form is infinite and non-repeating.
The square root of 7 is indeed an irrational number. An irrational number is one that cannot be expressed as the ratio of two integers, or as a predictable or repeating decimal. Unlike the square roots of perfect squares like 4 or 25, which are 2 and 5 respectively, the square root of 7 does not result in a whole number or a rational fraction. Additionally, this number cannot be exactly represented by a finite or repeating decimal sequence, which means it continues infinitely without repetition.
When we use a calculator to determine the square root of 7, we might see a value such as 2.646, but this is only an approximation because the actual decimal expansion goes on infinitely without repeating. Furthermore, the square root of a number like 7 does not solve a polynomial with rational coefficients, which further proves its irrationality.
Rational numbers, on the other hand, include integers and fractions where the numerator and the denominator are both integers. Numbers like 2/3 are rational because they have a clear ratio. However, roots of numbers that are not perfect squares, such as √7, cannot be expressed in such a ratio and are therefore irrational.
If you flip a coin three times what is the probability of getting three tails in a row
The magnitude, M, of an earthquake is defined to be M=log I/S, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and S is the intensity of a “standard” earthquake, which is barely detectable. What is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? Use a calculator. Round your answer to the nearest tenth.
log(35) = 1.544
rounded to nearest tenth = 1.5
Answer: The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5
Step-by-step explanation:
Given : The magnitude M of an earthquake is defined to be [tex]M=\log \frac{I}{S}[/tex]---(1)
, where I is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and
S is the intensity of a “standard” earthquake, which is barely detectable.
If the magnitude of an earthquake that is 35 times more intense than a standard earthquake
⇒Intensity of earthquake I=35 S
Substitute the value of I in (1), we get [tex]M=\log(\frac{35S}{S})=\log(35)=\log(5\times7)=1.544068[/tex] [tex]\approx1.5[/tex]
∴ The magnitude of the earthquake that is 35 times more intense than a standard earthquake=1.5
Graph y = −x2 − 2. Identify the vertex of the graph. Tell whether it is a minimum or maximum.
(0, –2); minimum
(–2, 0); minimum
(–2, 0); maximum
(0, –2); maximum
Answer:
(0, –2); maximum
Step-by-step explanation:
[tex]y = -x^2 - 2[/tex]
WE are given with the quadratic equation.
Vertex form of quadratic equation is in the form of [tex]y=a(x-h)^2+k[/tex]
where (h,k) is the vertex
[tex]y = -(x-0)^2 - 2[/tex]
The value of a=-1
when the value of 'a' is negative, then the vertex is maximum
To find the vertex we look at the value of h and k
h=0 and k= -2
Vertex is (0,-2)
(0, –2); maximum
−3 1/3 ÷ 9..........help
Which choice (s) when rounded to the nearest hundred thousand will result in 600,000?
is dilated by a scale factor of 3 to form . Point O is the center of dilation, and point O lies on . If the slope of is 3, what can be said about line ?
a.The slope of is 6, but does not pass through O.
b.The slope of is 9, and passes through O.
c.The slope of is 9, but does not pass through O.
d.The slope of is 3, and passes through O.
e.The slope of is 3, but does not pass through O.
Please help!! Evaluate the piece wise function at x=-4 and x=4.
x = -4, so use the first equation, x^2 = -4^2 = -16
x = 4, use 3rd equation, sqrt(x) = sqrt(4) = 2
Michael made 4 dozen chocolate chip cookies he is bringing 75% of them to school for a party how many cookies does he bring to chool
Michael made 48 cookies and is bringing 75% of them to a school party. To calculate this, multiply 48 (the total number of cookies) by 0.75, resulting in 36 cookies that he will bring to school.
Explanation:Michael made 4 dozen chocolate chip cookies. He wants to bring 75% of them to school for a party. To find out how many cookies he will bring, we need to calculate 75% of 4 dozen cookies. Since each dozen is 12 cookies, 4 dozen would be 4 times 12, which equals to 48 cookies.
To find 75% of 48, you can either multiply 48 by 0.75 or calculate 75/100 of 48:
48 × 0.75 = 36 (75/100) × 48 = 36
Therefore, Michael will bring 36 cookies to the school for the party.
Michael brings 36 cookies to school for the party.
Explanation:To find out how many cookies Michael brings to school, we need to calculate 75% of the total number of cookies he made.
Michael made 4 dozen cookies, and a dozen is equal to 12, so he made a total of 4 x 12 = 48 cookies.
75% of 48 is calculated by multiplying 48 by 0.75. 48 x 0.75 = 36.
Therefore, Michael brings 36 cookies to school for the party.
Error analysis a studinet write the word phrase the quotient of n and 5" to describe the expression 5/n describe and correct the students error
Final answer:
The student made an error in describing the expression 5/n as "the quotient of n and 5." The correct phrase to describe this expression would be "the quotient of 5 and n."
Explanation:
The student made an error in describing the expression 5/n as "the quotient of n and 5." The correct phrase to describe this expression would be "the quotient of 5 and n."
When describing division, it is important to remember that the dividend (the number being divided) comes before the divisor (the number dividing the dividend).
Can someone solve this?
greg score = x
kara score = 3/4x-1
x + 3/4x-1 = 153
1 3/4x -1 = 153
1 3/4x = 154
x = 154 / 1 3/4 = 88
gregs score was 88
kara s score was 153 -88 = 65
An elephant can run one over four mile in 36 seconds. Which of the following correctly shows this rate as miles per hour?
Evaluate 3x+y3x+y when x=13x=13 and y=−74y=−74. write your answer as a fractionin simplest form.