Answers
Answer:
Option B
Step-by-step explanation:
step 1
Find the measure of angle A
Remember that the sum of the interior angles of a triangle must be equal to 180 degrees
∠A+∠B+∠C=180°
substitute the given values
∠A+23.4°+90°=180°
∠A+23.4°+90°=180°-113.4°=66.6°
step 2
Find the length of side BC (a)
Applying the law of sines
c/sin(C)=a/sin(A)
3.3/sin(90)=a/sin(66.6)
a=3.3*sin(66.6)/sin(90)
a=3.0 mm
step 3
Find the length side AC (b)
Applying the law of sines
c/sin(C)=b/sin(B)
3.3/sin(90)=b/sin(23.4)
b=3.3*sin(23.4)/sin(90)
b=1.3 mm
Related Questions
HELP ASAP
What is the area of the triangle?
A)24 square units
B)32 square units
C)48 square units
D)96 square units
Answers
Answer:
A. 24 square units
Step-by-step explanation:
length is 8 and height is 6
gets you 48 but you need to divide by 2 because its a triangle so you get 24
Answer:
a
Step-by-step explanation:
sin30°=1/2 and cos30°=(sqrt3)/2
true or false?
Answers
Answer:
True.
Step-by-step explanation:
It's true.
The sin of 30 in degrees equals 1/2 and the cos of 30 degrees equals sqrt(3)/2.
I am attaching a table that can be useful for remembering the values of the cosine and sine of some angles.
Answer:
True
Step-by-step explanation:
TanX= sinX/cosX. Therefore, tan(90-A)= . (All angle measurements are in degrees.)
1/tan(90-A)
1/sin A
1/cos(90-A)
1/tan A
Answers
Answer:
tan(90 - A) = 1/tan(A) ⇒ last answer
Step-by-step explanation:
* Lets revise some important information for the right triangle
- In any right triangle
# The side opposite to the right angle is called the hypotenuse
# The other two sides are called the legs of the right angle
* If the name of the triangle is ABC, where B is the right angle
∴ The hypotenuse is AC
∴ AB and BC are the legs of the right angle
- ∠A and ∠C are two acute angles
∵ The sum of the interior angles of any triangle is 180°
∵ m∠B = 90°
∴ m∠A + m∠C = 180° - 90° = 90°
- If the measure of angle A is x°
∴ The measure of angle C = 90° - x°
- tan(A) = opposite/adjacent
∵ The opposite to ∠A is BC
∵ The adjacent to ∠A is AB
∴ tan(A) = BC/AB ⇒(1)
- tan(C) = opposite/adjacent
∵ The opposite to ∠C is AB
∵ The adjacent to ∠C is BC
∴ tan(C) = AB/BC ⇒ (2)
- From (1) and (2)
∴ tan(A) = 1/tan(C)
∵ m∠A = A , m∠C = (90 - A)
∴ tan(A) = 1/tan(90 - A)
OR
∴ tan(90 - A) = 1/tan(A)
Answer:
LAST OPTION.
Step-by-step explanation:
Remember that:
[tex]tan(x)=\frac{sin(x)}{cos(x)}[/tex]
[tex]\frac{cos(x)}{sin(x)}=cot(x)=\frac{1}{tan(x)}[/tex]
[tex]sin(x\±y) = sin(x)cos(y)\±cos(x)sin(y)\\\\cos(x\±y) =cos(x)cos(y)\± sin(x)sin (y) [/tex]
[tex]sin(90\°)=1\\cos(90\°)=0[/tex]
Then, you need to rewrite [tex]tan(90-A)[/tex]:
[tex]tan(90-A)=\frac{sin(90-A)}{cos(90-A)}[/tex]
Applying the identities, you get:
[tex]tan(90\°-A)=\frac{sin(90\°)cos(A)-cos(90\°)sin(A)}{cos(90\°)cos(A)-sin(90\°)sin(A))}[/tex]
Finally, you must simplify. Then:
[tex]tan(90\°-A)=\frac{(1)cos(A)-(0)sin(A)}{(0)cos(A)-(1)sin(A))}\\\\tan(90\°-A)=\frac{cos(A)}{sin(A)}\\\\tan(90\°-A)=\frac{1}{tan(A)}[/tex]
What is the distance between the points (-4,2) and (1,-3) on the coordinate points? WILL GIVE BRAINIEST ANSWER HELP ASAP
Answers
For this case we have that by definition, the distance between two points is given by:
[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+(y_ {2} -y_ {1}) ^ 2}[/tex]
We have the following points:
[tex](x_ {1}, y_ {1}) = (- 4,2)\\(x_ {2}, y_ {2}) = (1, -3)[/tex]
Substituting we have:
[tex]d = \sqrt {(1 - (- 4)) ^ 2+(-3-2) ^ 2}\\d = \sqrt {(1 + 4) ^ 2+(-5) ^ 2}\\d = \sqrt {(5) ^ 2+(-5) ^ 2}\\d = \sqrt {25 + 25}\\d = \sqrt {50}\\d = 7.07units[/tex]
Answer:
Option B
Answer: Option B
[tex]d=7.07[/tex]
Step-by-step explanation:
The distance between two points is calculated using the following formula
[tex]d=\sqrt{(x_1-x_0)^2+(y_1-y_0)^2}[/tex]
In this problem we have the following points
(-4,2) and (1,-3)
Therefore
[tex]x_0=-4\\y_0 = 2\\x_1=1\\y_1=-3[/tex]
Then the distance d is:
[tex]d=\sqrt{(1-(-4))^2+((-3)-2)^2}[/tex]
[tex]d=\sqrt{(1+4)^2+(-3-2)^2}[/tex]
[tex]d=\sqrt{(5)^2+(-5)^2}[/tex]
[tex]d=\sqrt{50}[/tex]
[tex]d=5\sqrt{2}[/tex]
[tex]d=7.07[/tex]
what is the differences between 2^8 and 8^2?
Answers
Answer:
The answer is 192
Step-by-step explanation:
2^8 = 256
8^2 = 64
256 - 64 = 192
Remember:
2^8 is really 2*2*2*2*2*2*2*2
Remember:
8^2 is really 8*8
To find the difference, you must subtract the smaller product from the larger product.
<Hope this helps!>
Answer:
192
Step-by-step explanation:
Method 1:
2^8 - 8^2 = 2^8 - 2^6 = 2^6(2^2 - 1) = 64(3) = 192
Method 2:
2^8 - 8^2 = 256 - 64 = 192
XYZ is a dilation of triangle ABC by a scale factor of 5. Which of the following proportions verified that triangle ABC and XYZ are similar?
Answers
Answer:
C. AB/XY = AC/XZ
Step-by-step explanation:
Dilation:
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. The original figure either stretches or shrinks by a certain factor.
In the problem, the dilation is by a factor of 5 and we can see that ABC shrinks to form XYZ.
So, ABC and XYZ are similar triangles which means that the ratio of their corresponding sides will be equal:
AB/XY = AC/XZ = BC/YZ = 5
Answer with explanation:
When ΔABC is dilated by a Scale factor of 5 we will get ΔX Y Z.
Pre-Image = ΔABC
Image = ΔX Y Z
When a triangle is dilated , then the two Triangles that is Original ΔABC and Triangle after dilation ΔX Y Z will be Similar.
⇒Similar triangles has Corresponding sides proportional as well as Corresponding Angles are congruent.
≡Corresponding congruent Angles are
→∠A=∠X
→∠B=∠Y
→∠C=∠Z
≡Corresponding congruent Sides are
[tex]\frac{AB}{XY}=\frac{AC}{XZ}=\frac{BC}{YZ}[/tex]
The Proportionality statement which proves two triangles are Similar
Option B
[tex]\frac{AB}{XY}=\frac{AC}{XZ}[/tex]
Identify the values of a, b, and c that would be used in the quadratic
formula to solve the equation
- x2 + 5x = 7.
A) a = -1, b = 5, c = 0
B) a = 1, b = 5, c = 7
C) a = -1, b = 5, c = -7
D) a = 1, b = -5, c = 0
Answers
Answer:
C) a= -1, b=5, c= -7
Step-by-step explanation:
To get the values of a, b and c we must first write the equation in the form
ax²+bx+c=0 where a b and c are the coefficients.
Therefore, -x² +5x=7 can also be written as:
-x²+5x-7=0
a= -1 ( coefficient of x²)
b=5 (coefficient of x)
c= -7 ( the constant in the equation)
Answer:
a=-1, b=5 and c=-7
Step-by-step explanation:
We have the following equation:
[tex]-x^{2} + 5x = 7[/tex] → [tex]-x^{2} + 5x - 7 = 0[/tex]
Given the equation of a parabola: [tex]ax^{2} +bx + c = 0[/tex]. By comparison, we know that:
a=-1, b=5 and c=-7
So the correct option is Option C.
Lorena took a survey of the students in her honors science class to determine how many are going to college. She found that 85% of the students plan to go to college.
Can Lorena make the inference that 85% of all the seniors at her school are going to college?
Answers
Answer:
No, Lorena cannot make the inference about all the seniors going to college.
Step-by-step explanation:
We are given that Lorena took a survey of students in her science class to determine how many of them were going to college.
From the survey results, she found that 85% of the students from her science class were going to the college but with these results she cannot infer that 85% of all the seniors at her school were going to college.
This is because the survey was biased as it was not taken from the entire school but only Lorena's science class.
Answer:
No, Lorena’s sample was biased because it was taken only from an honors class.
No, Lorena’s sample was not a random sample of the entire school.
those are the two correct answers, i took the test!
Simplify by dividing -5/8 and -3/4
Answers
Answer:
Step-by-step explanation:
-5 -3 ×2 /8
-11/8
Hence the answer is,
-11/8
Hope this helps!
HELPP SOS!!!!! THANK YOU SO MUCH WHOEVER ANSWERS WITH ACCURACY
•The parent function of the graph of f(x) is the square root function, which was reflected across the x-axis. Which of the following is the equation of f(x)?
Answers
The equation of f(x) is B. F(x) = -√x. Therefore , B. F(x) = -√x is correct.
Here's why:
The parent function of the graph is the square root function, which means the original equation is f(x) = √x.
The graph is reflected across the x-axis.
This means that the y-values are multiplied by -1. In other words, if the original point was (x, √x), the reflected point would be (x, -√x).
Therefore, the equation of the reflected function is f(x) = -√x.
The other options are incorrect because:
A. F(x) = √x is the original equation, not the reflected equation.
C. F(x) = √x - 1 shifts the graph down one unit, but it does not reflect it across the x-axis.
D. F(x) = √x + 1 shifts the graph up one unit, but it does not reflect it across the x-axis.
If g(x) = x2 + 2, find g(3). (2 points) 9 8 11 6
Answers
For this case we have a function of the form [tex]y = g (x)[/tex]
Where:
[tex]g (x) = x ^ 2 + 2[/tex]
We must find the value of the function when x = 3. Then we substitute:
[tex]g (3) = 3 ^ 2 + 2\\g (3) = 9 + 2\\g (3) = 11[/tex]
Thus, the value of the function when [tex]x = 3[/tex] is [tex]y = 11[/tex]
Answer:
[tex]g (3) = 11[/tex]
Option C
Answer: Third Option
[tex]g(3) = 11[/tex]
Step-by-step explanation:
We have the function [tex]g(x) = x^2 + 2[/tex] and we must find the value of g(3).
To find g (3) we must evaluate the function g(x) for x = 3. That is, we must replace x = 3 in the function
Then
[tex]g(x) = x^2 + 2[/tex]
[tex]g(3) = (3)^2 + 2[/tex]
[tex]g(3) = 9 + 2[/tex]
[tex]g(3) = 11[/tex]
Finally the correct answer is the third option
What is 1.2 to the tenth power
Answers
Answer:
Step-by-step explanation:
that would be written as 1.2^10, and the end result would be the same as you'd get if you use 1.2 as a factor 10 times: 1.2*1.2*1.2* .......1.2
You could use a calculator to evaluate 1.2^10:
Typing in 1.2^10, you'll get 6.191736422.
This is not an exact answer; there are more digits following the ones shown.
Another way in which you could do this problem would be to use logs:
Let y = 1.2^10. Then log y = 10*log 1.2, or log y = 10(0.07918) = 0.791812.
Finding the antilog, we get y = 6.19174
which sequences are arithmetic? select three options
Answers
Answer:
The sequences are arithmetic
1).-8.6, -5.0, -1.4, 2.2, 5.8
2). 5, 1, -3, -7, -11
3). -3, 3, 9, 15, 21
Step-by-step explanation:
If a sequence is a an AP then there is a common difference d.
1) Check sequence 1
-8.6, -5.0, -1.4, 2.2, 5.8
-5.0 - - 8.6 = 3.6
-1.4 - -5.4 = 3.6 It is an AP
2) Check sequence 2
2, -2.2,2.42, -2.662, 2.9282
-2.2 - 2 = -4.2
-2.662 - 2.42 = -5.082 Not AP
Similarly AP sequences are
5, 1, -3, -7, -11
-3, 3, 9, 15, 21
The sequence that are arithmetic are as follows:
5, 1, -3, -7, -11.
-3, 3, 9, 15, 21
-8.6, - 5.0, -1.4, 2.2, 5.8
What is arithmetic sequence?Arithmetic sequence is a list of numbers with a definite pattern. Therefore, let's find the sequence with a definite pattern.
5, 1, -3, -7, -11.
This is a sequence as it as a definite pattern. The value are reduced by 4. Therefore, the common difference is 4.
1 - 4 = 4-3 - (-1) = 4...-3, 3, 9, 15, 21
This is a sequence because it has a common difference of 6.
3 - (-3) = 69 - 3 = 615 - 9 = 6...-8.6, - 5.0, -1.4, 2.2, 5.8
This is a sequence because it has a common difference of 3.6.
-5.0 - (-8.6) = 3.6-1.4 - (-5.0) = 3.6learn more on sequence here: https://brainly.com/question/17627016
classify the system of equations 2x=-3-y 4+y=-2x-2
intersecting
parallel
coincident
please hurry!
Answers
Answer:
parallel
Step-by-step explanation:
we have
2x=-3-y
isolate the variable y
y=-2x-3 ----> equation A
4+y=-2x-2
isolate the variable y
y=-2x-2-4
y=-2x-6 -----> equation B
Remember that
If two lines are parallel, then their slopes are the same
Line A and Line B have the same slope m=-2 and different y-intercept
therefore
The lines are parallel
Answer:
Second option: Parallel.
Step-by-step explanation:
The equation of the line in Slope-Intercept form is:
[tex]y=mx+b[/tex]
Where "m" is the slope and "b" is the y-intercept.
Solve for "y" in each equation:
Equation 1
[tex]2x=-3-y \\\\2x+y=-3\\\\y=-2x-3[/tex]
Equation 2
[tex]4+y=-2x-2\\\\y=-2x-2-4\\\\y=-2x-6[/tex]
You can notice that the slope of the Equation 1 is:
[tex]m_1=-2[/tex]
And the slope of the Equation 2 is:
[tex]m_2=-2[/tex]
Observe that [tex]m_1=m_2[/tex], then you can conclude that the lines are: Parallel.
Solve 3^(x+1) = 15 for x using the change of base formula
Answers
[tex]\bf \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \\\\\\ \textit{Logarithm Change of Base Rule} \\\\ \log_a b\implies \cfrac{\log_c b}{\log_c a}\qquad \qquad c= \begin{array}{llll} \textit{common base for }\\ \textit{numerator and}\\ denominator \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf 3^{x+1}=15\implies \log_{10}(3^{x+1})=\log_{10}(15)\implies (x+1)\log_{10}(3)=\log_{10}(15) \\\\\\ x+1=\cfrac{\log_{10}(15)}{\log_{10}(3)}\implies \stackrel{\textit{change of base rule}}{x=\cfrac{\log_{e}(15)}{\log_{e}(3)}-1}\implies x\approx 1.47[/tex]
Answer:
[tex]x=\frac{log(15)}{log(3)}-1[/tex]
Step-by-step explanation:
[tex]3^{x+1} = 15[/tex]
LEts convert exponential form to log form
[tex]b^x=a[/tex] can be written as [tex]log_b(a)=x[/tex]
WE apply the same rule to convert the given exponential form to log form
[tex]3^{x+1} = 15[/tex]
[tex]log_3{15} = x+1[/tex]
HEre the base of log is 3. Lets apply change of base formula
[tex]log_b(a)=\frac{log(a)}{log(b)}[/tex]
[tex]log_3{15} = x+1[/tex]
[tex]\frac{log(15)}{log(3)} = x+1[/tex]
Now subtract 1 from both sides
[tex]x=\frac{log(15)}{log(3)}-1[/tex]
The table and graph both represent the same relationship. Which
equation also represents that relationship?
Answers
Answer:
A
Step-by-step explanation:
Just try to label the data in a table for every choice. It is clearly A. If you tried to solve it you will find that =
(-2)² = 4
(-1)² = 1
1² = 1
2² = 4
classify the following triangle
Answers
Answer:
Obtuse and Scalene
Step-by-step explanation:
Obtuse means that it is over 90 degrees, in which there is an angle of 102 degrees.
Scalene means that all three side lengths are different.
Answer:
A. Obtuse
C. Scalene
Which relationship in the triangle must be true?
sin(B) = sin(a)
sin(B) = cos(90 -B)
cos(B) = sin(180-B)
cos(B) cos(A)
Answers
Answer:
sin(B)=cos(90°-B)
Step-by-step explanation:
we know that
In the right triangle of the figure
sin(B)=b/c -----> The sine of angle B is equal to divide the opposite side to angle B by the hypotenuse
cos(A)=b/c -----> The cosine of angle A is equal to divide the adjacent side to angle A by the hypotenuse
we have that
sin(B)=cos(A)
Remember that
A+B=90° -----> by complementary angles
so
A=90°-B
therefore
sin(B)=cos(A)
sin(B)=cos(90°-B)
Answer:
sin(B) = cos(90 -B)
Step-by-step explanation:
In triangle ABC by using angle sum property, ∠A + ∠B + ∠C= 180°
∠A + ∠B + 90°= 180°
∠A + ∠B= 180°-90°
∠A + ∠B = 90°
∠A = 90°- ∠B
sin B = b/a.
cos A = b/a.
Hence, sin B = cos A
put the value of ∠A = 90°- ∠B in cos A
sin (B) = cos (90°-B)
Thus, the correct answer is option (2).
What is the sum of the measures of the interior angles of a 13-sided polygon?
Answers
The correct answer is 1980 or A:)
A point has coordinates (0, 3). Where is it located in the coordinate plane?
Choose the best answer from the options below:
A x-axis
B y-axis
C quadrant 3
D quadrant 4
Answers
Answer:
A: x-axis
I did a quiz and got it wrong when I choose B: y-axis.
Final answer:
The point with coordinates (0, 3) is on the y-axis, above the origin by 3 units. Therefore, the correct answer is B, the y-axis.
Explanation:
A point with the coordinates (0, 3) is located where the x-coordinate is 0 and the y-coordinate is 3. In the context of a two-dimensional Cartesian coordinate system, this means the point does not move left or right from the origin on the horizontal axis, but it moves up by 3 units on the vertical axis.
Therefore, the correct answer to the question is B, the point is located on the y-axis. It is neither on the x-axis nor in any of the four quadrants since its x-coordinate is zero. Hence, it lies directly above the origin on the y-axis.
Least common multiple (3,10)
Answers
Answer: 30
Step-by-step explanation: Start off by multiplying the two numbers.
3 x 10 = 30.
30 is a common multiple. Find any multiples below 30. Let’s start off using the biggest number of the two, which is 10, to see what other numbers can be multiples. 10, 20, and 30 can be. 3 can’t be divided into 10 or 20, so your least common multiple is 30.
What is the radius and diameter of the following circle?
Answers
Answer:
The radius of the circle is already there, 11cm, and the diameter is 2 times the radius, which is 22
Step-by-step explanation:
First, you look at the radius (which is half of the circle) which is 11, then you multiply that times two to get the diameter. :)
Diameter-22cm
Brody can fill a bowl with candy in 3 minutes. While Brody fills the bowl, Hudson takes the candy out of the bowl. With Hudson taking candy out of the
bowl, it takes 5 minutes for Brody to fill the bowl.
Which of the following can be used to determine the amount of time it takes for Hudson to empty the bowl if Brody does not add candy?
Answers
Answer:
1/3 - 1/x=1/5
Step-by-step explanation:
Let the total work be "1"
Brody Hudson Brody+Hudson
Time 3 mins x min 5 min
Efficiency 1/3 -1/x 1/5
The efficiency of Hudson is negative as he is taking out the candies out of the bowl, since efficiency of Brody + efficiency of Hudson = efficiency of both, which means,
1/3 - 1/x = 1/5....
What is 6 more than 5 times the measure number of mn , what is m np
Answers
Answer:
6 more than 5 times the measure of mn is (5mn + 6)
Step-by-step explanation:
What’s the answer help???
Answers
Answer:
a = 5 cm, b = 2 cm.Step-by-step explanation:
[tex]\text{We have:}\\\\A_{PQRS}=45\ cm^2\\\\A_{PQRS}=a(7+b)\\\\A_{PXYS}=10\ cm^2\\\\A_{PXYS}=ab\\\\\text{Therefore we have the system of equations:}\\\\\left\{\begin{array}{ccc}a(7+b)=45&\text{use the distributive property}\\ab=10\end{array}\right\\\left\{\begin{array}{ccc}7a+ab=45&(1)\\ab=10&(2)\end{array}\right\\\\\text{Substitute (2) to (1):}\\7a+10=45\qquad\text{subtract 10 from both sides}\\7a=35\qquad\text{divide both sides by 7}\\a=5\\\text{Put it to (2):}\\5b=10\qquad\text{divide both sides by 5}\\b=2[/tex]
what would the answer be
Solve the system of equations.
5x + y = 9
3x + 2y = 4
Answers
Answer:
(x,y) (2,-1)
Step-by-step explanation:
Answer:
the first one is 2 the second one is 3
Step-by-step explanation:
solve the equation 53=-6-17x
Answers
Answer:
-59/17 =x
Step-by-step explanation:
53=-6-17x
Add 6 to each side
53+6=-6+6-17x
59 = -17x
Divide each side by -17
59/-17 = -17x/-17
59/-17 = x
-59/17 =x
Akira and tori Chang received a total of $48,000 from an estate. They decided to put $9,600 in a trust and divide the remainder. Tori received 3/8 of the remainder. How much did Akira receive?
Answers
Answer:
$24,000
Step-by-step explanation:
After putting in trust they have left:
48000 - 9600 = $38,400
If Tori gets 3/8, Akira will get the remaining (1 - 3/8 = 5/8). So Akira will get:
[tex]\frac{5}{8}*38,400=24,000[/tex]
Hence akira will get $24,000
PLEASEEEE I NEED HELPP
Answers
Answer:
∠C = 143°
Step-by-step explanation:
For the quadrilateral to be a parallelogram
Then ∠C = ∠A
Given ∠B = ∠D then consecutive angles are supplementary, that is
∠C + ∠D = 180
∠C + 37 = 180 ( subtract 37 from both sides )
∠C = 143°
Given the functions, fx) = x^2-4 and g(x) = x+ 2, perform the indicated operation. When applicable, state the domain
restriction.
F(g(x))
Answers
To perform F(g(x)), substitute g(x) into F(x) by squaring g(x) and subtracting 4. The domain of F(g(x)) is all real numbers.
Explanation:The question asks us to perform the composition of two functions - f(x) and g(x). Composition is denoted by (f ∘ g)(x) and involves substituting the output of the inner function (g(x)) into the input of the outer function (f(x)). In this case, we have f(g(x)), which means we need to substitute g(x) into f(x).
First, substitute g(x) into f(x) to get f(g(x)):
f(g(x)) = (g(x))^2 - 4 = (x+2)^2 -4 = x^2 + 4x + 4 - 4 = x^2 + 4x.
The domain restriction is the set of all values that x can take. Since there are no restrictions mentioned in the question, the domain is all real numbers.
Learn more about Composition of Functions here:https://brainly.com/question/30143914
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