In triangle abc, ac=10, bc=8, angle b =90 degrees and angle bda = 90. how long is line bd
Name the property of real numbers illustrated by the equation 16(3t + 4v) = 48t + 64v.
If x is 6, then 7x = _____. 13 42 42x 76
Answer: 42
Step-by-step explanation:
x = 6 now that you know what x represents switch it out the x by the 7 with a 6 like this 7(x)- 7(6) seven times six is 42 in other words x
=42
The length of a rectangle is represented by the function L(x) = 6x. The width of that same rectangle is represented by the function W(x) = 4x2 − 3x + 8. Which of the following shows the area of the rectangle in terms of x?
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Write x^2 − 2x − 3 = 0 in the form (x − a)^2 = b, where a and b are integers.
(x − 4)^2 = 3
(x − 3)^2 = 2
(x − 2)^2 = 1
(x − 1)^2 = 4
The coordinates of the vertices of / are G(–2, 3), H(–1, 2), and I(–3, 1). If / is reflected across the x-axis to create /, find the coordinates of the vertex located at point W.
Answer:
A. (–2, –3)
that is the answer
Which statement justifies that angle XAB is congruent to angle ABC?
A. Corresponding angles of parallel lines cut by a transversal are congruent.
B. Vertical angles are congruent.
C. Same-side interior angles of parallel lines cut by a transversal are supplementary.
D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Given: m || CB
Prove: m∠ABC + m∠BAC + m∠ACB = 180°
Answer: D. Alternate interior angles of parallel lines cut by a transversal are congruent.
Step-by-step explanation:
In the given picture m is parallel to CB .
Since m is a straight line and the angle of straight line is 180° .
Therefore, m∠XAB+m∠BAC+m∠YAC=180° ........................ (a)
Also, m is parallel to CB and AB is a transversal and because Alternate interior angles of parallel lines cut by a transversal are congruent.
⇒m∠XAB=m∠ABC and m∠YAC=m∠ACB
Put the values of m∠XAB and m∠YAC in equation (a), we get
m∠ABC + m∠BAC + m∠ACB = 180°.
Hence proved.
Statement D Alternate interior angles of parallel lines cut by a transversal are congruent is the most relevant to the congruence of XAB and ABC.
It is proved that m∠ABC + m∠BAC + m∠ACB = 180°.
For angle XAB being congruent to angle ABC, and then prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Parallel lines m and CB.
Points X, A, and Y are on line m.
To prove that angle XAB is congruent to angle ABC.
Justification for Congruence:
In this context, use the Alternate Interior Angles Theorem,
which states that when a transversal intersects two parallel lines, the alternate interior angles formed are congruent.
Here's the reasoning:
Line m is parallel to line CB.
The line XY is a transversal line that intersects m and CB.
Therefore, the alternate interior angles formed by this setup are congruent.
This means that angle XAB and angle ABC are congruent.
Now, let's prove the equation m∠ABC + m∠BAC + m∠ACB = 180°.
Angle XAB is congruent to angle ABC (justified by the Alternate Interior Angles Theorem).
Now, let's consider the triangle ABC. By the angle sum property of triangles, the sum of the angles in a triangle is always 180°. Therefore:
m∠ABC + m∠BAC + m∠ACB = 180°
Since angle XAB is congruent to angle ABC, replace angle ABC with angle XAB:
m∠XAB + m∠BAC + m∠ACB = 180°
Now, the equation holds true, and you have successfully proven that m∠ABC + m∠BAC + m∠ACB = 180°.
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please help asap! 14 points
The sum of three consecutive odd integers is − 105 . find the numbers.
PLEASE HELP ME ON THIS
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Combine and simplify these radicals. square root of 8 times square root of 20
Answer:
√8 * √20 = 4√10
Step-by-step explanation:
√8 * √20= √(4*2) * √(4*5)
√8 * √20 = (√4)(√2)*(√4)(√5)
√8 * √20 = (2)(√2)*(2)(√5)
√8 *√20 = (2*2)(√2*√5)
√8 * √20 = (4)(√(2*5)
√8 * √20 = 4√10
Create an equation to model an investment of 5000 dollars which increases 15% each year. Set up an equation to solve for how long it would take for the investment to double. ( you do not need to solve this problem)
A(-5,-4) ——> A’ is a glide reflection where the translation is (x,y)—->(x+6,y), and the line of reflection is y=3. What are the coordinates of A’?
A. (1,-4)
B. (-5,2)
C. (1,10)
D. (11,2)
Solution:
The Point in the coordinate plane is A(-5,-4).
Perpendicular or shortest Distance from line y=3 that is (-5,3) to point (-5,-4) is
[tex]=\sqrt{(-5+5)^2+(3+4)^2}\\\\=7[/tex]
When it is reflected through the line, y=3, the coordinate of point A (-5,-4) changes to (-5,3+7)= B(-5,10).
Now, the Point B is translated by the rule , (x,y)—->(x+6,y),
So,the point B is translated to, (-5+6,10)=(1,10)
Option C: (1,10) is the glide reflection of point A(-5,-4).
The coordinates of A' after the glide reflection (translation and reflection over y = 3) from A(-5, -4) are (1, -4), so the answer is A.
In a glide reflection, first apply a translation and then a reflection. Let's follow the given transformations step by step:
Translation: (x, y) → (x + 6, y)
This means you move the point A(-5, -4) six units to the right and keep the same y-coordinate. Applying the translation:
A' = (-5 + 6, -4)
= (1, -4)
Reflection over the line y = 3:
In this reflection, points above the line will move below it and vice versa, while points on the line will remain unchanged.
Since the original point A(-5, -4) is below the line y = 3, its reflection A' will be above the line.
Therefore, the coordinates of A' are (1, -4) ,the correct option is A. (1, -4).
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Which of the following expression expressions is equivalent to cos3x/sinxcosx?
A.) cscxcos2x-secxsin2x
B.) secxcos2x-cscxsin2x
C.) secxcosx-cscxsinx
D.) cscxcosx-secxsinx
Answer:
A.) cscxcos2x-secxsin2x
Step-by-step explanation:
I'm sorry I really do not know how to solve this but I just did the quiz and b was not correct.
Final answer:
To find an expression equivalent to cos3x/sinxcosx, we use trigonometric identities and simplification to arrive at cscx - secx. Option D, cscx cosx - secx sinx, when expanded and simplified, is equivalent to cscx - secx, thus it is the correct answer.
Explanation:
The question asks us to find an expression equivalent to cos3x/sinxcosx. To start, let's simplify the given expression using trigonometric identities.
We can write cos3x as cos(2x+x), which by using the angle addition formula for cosine gives us cos(2x+x) = cos2x cosx - sin2x sinx. Now our expression looks like this: (cos2x cosx - sin2x sinx) / (sinx cosx).
The next step is to split the numerator to have two separate fractions: cos2x/sinx - sin2x/cosx. We can then recognize that cos2x/sinx is equivalent to 1/sinx or cscx, and -sin2x/cosx is equivalent to -1/cosx or -secx. Therefore, the equivalent expression is cscx - secx.
Comparing this result to the options given, option D, cscx cosx - secx sinx, expands to 1/sinx × 1 - 1/cosx × sinx, which can be simplified to cscx - secx. Thus, option D is the correct answer.
How do I solve this problem?
Which expression gives the area of the triangle shown below?
The expression gives the area of the triangle shown below 1/2cx is the answer.
The reason this is the answer is because to find the area of a triangle you will find half of the base times the height.
What is the formula of the triangle?
The formula of a triangle
A=1/2bh.
In this picture, the base is the length of the bottom part of the triangle (c).
It is the distance of the solid line only.
The height is represented as the straight line that is perpendicular to the base (forms a right/90-degree angle).
X is the height of the triangle.
Therefore, 1/2cx is the answer.
So option D is correct.
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Two trains leave the station at the same time, one heading west and the other east. The westbound train travels at
90
miles per hour. The eastbound train travels at
80
miles per hour. How long will it take for the two trains to be
272
miles apart?
Do not do any rounding.
Find the equation of the axis of symmetry for the parabola y = x2 + 4x – 5 .
make w the subject of the formula y-aw=2w-1
To make w the subject of the formula y-aw=2w-1, rearrange the equation as follows: add aw to both sides, factor out w on the right side, add 1 to both sides, and then divide by (a+2). The final equation is w=(y+1)/(a+2).
Explanation:The question is asking to rearrange the given formula y-aw=2w-1 to solve for the variable w. We can follow these steps:
Add aw to both sides of the equation to eliminate it on the left side. This gives us y=aw+2w-1. Factor out w from the right side. This gives us y=w(a+2)-1. Add 1 to both sides of the equation to eliminate it on the right side. This gives us y+1=w(a+2). Divide both sides of the equation by (a+2) to isolate w. This gives us w=(y+1)/(a+2).
Therefore, in the formula y-aw=2w-1, w=(y+1)/(a+2) when solved for w.
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Carl puts 1.10 in his penny bank every day in the month of July. His total savings was 55at the end of June. What’s the best estimate for Carl’s savings at the end of July
Answer:
About 85 is the answer
Match each problem (term) with its sum or difference (definition).
Term Definition
4.23 + 16.21 A) 26.09
42.3 + 1.621 B) 2.609
4.23 − 1.621 C) 20.44
42.3 − 16.21 D) 43.921
GET THIS RIGHT ILL GIVE U BRAINLIEST!!!!!!!
Each mathematical term has been calculated and the correct sum or difference matched with its definition: 4.23 + 16.21 matches with C) 20.44, 42.3 + 1.621 with D) 43.921, 4.23 - 1.621 with B) 2.609, and 42.3 - 16.21 with A) 26.09.
To match each mathematical term with its correct sum or difference, we simply perform the addition or subtraction:
4.23 − 1.621 = 2.609, so this term matches with definition B)
Each problem has been matched with its corresponding definition based on the results of the arithmetic operations.
Please help simple math problem
URGENT!!!! You must create a 6-character password using the letters A-Z and the numbers 0-9. Characters may be repeated. How many possible passwords are there?
Which number system BEST describes this set? {-10, 0, 28 7 , 102.9} A) integers B) natural numbers C) rational numbers D) irrational numbers
Bianca has 3:5 The ratio of the number of books Bianca has to the number books Chrissy has 10:11 If amy has 36 books how many books does Bianca have
Compare the numbers in the following sequence and try to determine what the next number should be.
6, 9, 18, 21, 42, 45, ?
Now When i did the math I thought it might be 54 but I'm not sure can someone help me or tell me if I'm right!
Help!! Would the answer be c??
The steps below show the incomplete solution to find the value of x for the equation 7x − 3x − 4 = −1 + 21:
Step 1: 7x − 3x − 4 = −1 + 21
Step 2: 7x − 3x − 4 = 20
Step 3: 4x − 4 = 20
Which of these is most likely the next step? (4 points)
Select one:
a. 4x = 24
b. 4x = 16
c. 4x = 5
d. 4x = 80
Answer: is a
Step-by-step explanation:
Please help asap!!! 19 pts
The top of a rectangular table has an area of 100 square feet and width of 5 feet. What is the length in feet of the surface
The length of the surface of the rectangular table that has an area of 100 sq. ft is: 20 ft.
What is the Area of a Rectangle?Area of rectangle = (length)(width).
The table given has a rectangular surface.
Area of the rectangular table = 100 square feetWidth of the rectangular table = 5 feet(length)(5) = 100
Length = 100/5
Length of the rectangular table = 20 feet.
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What is the quotient of 78.3 ÷ 3.48?