Mathematics High School

Write a congruency statement for the pair of triangles.

Answers

Answer 1

Answer:

ΔABP is congruent to ΔBAQ

ΔABP ≡ ΔBAQ

Explanation:

We are given two triangles; ΔABP and ΔABQ

In these two triangles, we have:

AB as a common side

∠ABP = ∠BAQ

AQ = BP

We can conclude that these two triangles are congruent by SAS (side-angle-side) postulate which states that:

"When two sides and the included angle between them in the first triangle are congruent to the corresponding two sides and the included angle between them in the second triangle, then the two triangles are congruent"

Note that when writing congruency statements, the order of the letters is critical as each angle/side in the first triangle must be congruent to its corresponding angle/side in the second triangle.

Based on the above, the congruency statement would be:

ΔABP is congruent to ΔBAQ

Hope this helps :)

Related Questions

A carnival ride is in the shape of a wheel with a radius of 20 feet. The wheel has 16 cars attached to the center of the wheel. What is the central angle, arc length, and area of a sector between any two cars? Round answers to the nearest hundredth if applicable. You must show all work and calculations to receive credit.

Answers

Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.

The total central angle around the wheel is 2π.
Therefore the central angle between two cars is
(2π)/16 = π/8 = 0.39 radians (nearest hundredth)

The arc length between two cars is
s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)

The area of a sector formed by two cars is
(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)

Answers: (to the nearest hundredth)
Between two cars,
Central angle = 0.39 radians (or 71.4°)
Arc length = 7.85 ft
Area of a sector = 78.54 ft²

Refer to the diagram shown below, which shows two of 16 equally-spaced cars attached to the center of the wheel.

The total central angle around the wheel is 2π.

Therefore the central angle between two cars is

(2π)/16 = π/8 = 0.39 radians (nearest hundredth)

The arc length between two cars is

s = (20 ft)*(π/8 radians) = 2.5π = 7.85 ft (nearest hundredth)

The area of a sector formed by two cars is

(1/16)*(π*20²) = 78.54 ft² (nearest hundredth)

Answers: (to the nearest hundredth)

Between two cars,

Central angle = 0.39 radians (or 71.4°)

Arc length = 7.85 ft

Area of a sector = 78.54 ft²

A particular metal alloy a has 20% iron and another alloy b contains 60% iron. how many kilograms of each alloy should be combined to create 80 kg of a 52% iron alloy?

Answers

Let t and s represent the masses of 20% and 60% alloys respectively.

t+s=80, s=80-t

(0.2t+0.6s)/80=0.52 multiply both sides by 80

0.2t+0.6s=41.6, now using s=80-t in this equation gives us:

0.2t+0.6(80-t)=41.6 perform indicated multiplication on left side

0.2t+48-0.6t=41.6 combine like terms on left side

-0.4t+48=41.6 subtract 48 from both sides

-0.4t=-6.4 divide both sides by -0.4

t=16, since s=80-t

s=64

So 16kg of 20% alloy is mixed with 64kg of 60% allow to make 80kg of a 52% alloy.

Peter bought an antique piece of furniture in 2000 for $10,000. Experts estimate that its value will increase by 12.12% each year. Identify the function that represents its value. Does the function represent growth or decay?
A) V(t) = 10000(1.1212)t; growth
B) V(t) = 10000(0.8788)t; decay
C) V(t) = 10000(1.1212)t; decay
D) V(t) = 10000(0.8788)t; growth

Answers

values increases so we have growth

the exponent will be 1.1212

The answer of it is 1.1212

4n-3<12 solve and please don't give me the answer just the equation

Answers

just as with an equation with an = sign, we want to isolate the variable, n.
So first bring -3 to the right hand side:

4n-3<12 => 4n < 12+3 => 4n < 15

Then divide by 4

4n/4 < 15/4 => n < 15/4

You can't simplify it beyond that.

Write log(x^2-9)-log(x+3) as a single logarithm.

Answers

One way: log(A)-log(B) = log(A/B) right?

So, log( x^2-9/(x+3))

Now x^2-9 = (x+3)*(x-3), and x^2-9/(x+3) = x-3,

so log(x^2-9)-log(x+3) = log(x-3),

Indeed for all x but for x = -3, but probably no one asks you about that detail?

Answer:

b edge

Step-by-step explanation:

Select the assumption necessary to start an indirect proof of the statement. If 3a+7 < 28, then a<7.

Answers

When applying indirect proofs, we assume the negation of the conclusion is true, and show that this assumption would lead to nonsense, or contradiction.

In our case we assume a is not smaller than 7, that is we assume a≥7.

a≥7 then, multiplying both sides by 3:
3a≥21, then, adding both sides 7:

3a+7≥28,

which is a contradiction because 3a+7 is smaller than 28.

So our assumption is wrong, which means the opposite of it is correct.

Answer: assume a≥7

a number diminished by 2 is 6

Answers

n-2=6 add 2 to both sides

n=8

x-2=6

x=8

hope that helps

if you subtract 23.47 km from 560.589 km, how many significant digits would your answer have?

Answers

560.589 - 23.47 is hmm 537.119 <---- 6 significant digits

alrite... looks good, however, when it comes to dealing with significant digits, for addition/subtraction, we go with the lowest significant amount for decimals, in this case,

560.589 <--- has 6 significant digits, accurate to the 1000th place
23.47 <--- has 4 significant digits, and is accurate to the 100th place

thus, our answer will have to be rounded up in 2 significant decimals, or 537.12
and that only has 5 significant digits, since is rounded up to the 100th place.

Find the area under the standard normal curve between z = -1.5 and z = 2.5

Answers

Final answer:

To area under the standard normal curve between z = -1.5 and z = 2.5 is 0.927

Explanation:

A standard normal curve, also known as the standard normal distribution, is a bell-shaped, symmetrical probability distribution with a mean of 0 and a standard deviation of 1. It serves as a reference for many statistical analyses and is often denoted as the Z-distribution.

To find the area under the standard normal curve between z = -1.5 and z = 2.5, we need to use the z-table. The z-score of -1.5 corresponds to an area of 0.0668 and the z-score of 2.5 corresponds to an area of 0.9938. To find the area between these two z-scores, we subtract the smaller area from the larger area:

= 0.9938 - 0.0668

= 0.927

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The area between these z-scores is 0.9270.

The area under the standard normal curve between z = -1.5 and z = 2.5 can be found using the z-table.

First, find the area to the left of

z = -1.5, which is 0.0668.

Next, find the area to the left of

z = 2.5, which is 0.9938.

Subtract these two values to get the area between z = -1.5 and z = 2.5 :

0.9938 - 0.0668

= 0.9270.

Which of the following relations represent a function? {(1,-3),(-2,0),(1,4)} {(-2,0),(3,0),(-2,1)} {(3,-8),(-2,0),(4,1)} {(4,12),(4,13),(-4,14)}

Answers

that means no x repeats with a different y

example
(1,2) and (1,4) would not be a function

but (1,2) and (3,2) is

no firs tnumber repeats

first one, 1 repeats with -3 and 4
2nd one, -2 repeatts with 0 and 1
3rd one, no repeats
4th one, 4 repeats with 12, 13, 14

answer is 3rd one or
{(3,-8),(-2,0),(4,1)}

Final answer:

To determine if a relation is a function, check for repeated x-values. The relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.

Explanation:

In order for a relation to represent a function, each input (x-value) must correspond to exactly one output (y-value). We can determine if a relation is a function by checking for any repeated x-values. If there are no repeated x-values, then the relation is a function. Let's apply this to the given relations:

The relation {(1,-3),(-2,0),(1,4)} represents a function because each x-value is unique.

The relation {(-2,0),(3,0),(-2,1)} does not represent a function because there is a repeated x-value (-2).

The relation {(3,-8),(-2,0),(4,1)} represents a function because each x-value is unique.

The relation {(4,12),(4,13),(-4,14)} does not represent a function because there is a repeated x-value (4).

So, the relations that represent a function are {(1,-3),(-2,0),(1,4)} and {(3,-8),(-2,0),(4,1)}.

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In two or more complete sentences, compare the number of x-intercepts in the graph of f(x) = x2 to the number of x-intercepts in the graph of g(x) = -x2 -6. Be sure to include the transformations that occurred between the parent function f(x) and its image g(x).

Answers

f(x) has only one x-intercept when x=0

g(x)=-x^2-6

g(x)=-(x^2+6) so g(x) will have no x-intercepts as its maximum value will be -6.

g(x) is f(x) reflected about the x axis and shifted downwards by 6 units.

The vertical ______ of the function secant are determined by the points that are not in the domain.

Answers

The word that goes in the blank is asymptote.

The population of a type of local frog can be found using an infinite geometric series where a one equals 84 and the common ratio is one over five find the sum of the infinite series that will be the upper limit of this population. 87,105,425, or this series is divergent

Answers

a=84 and r=1/5

Since r, the common ratio squared is less than one, the sum will converge to a limit. Rule: if r^2<1 infinite series converges, otherwise it diverges.

Since the sum of any geometric sequence is:

s(n)=a(1-r^n)/(1-r)

And if r^2<1, (1-r^n) becomes 1-0=1 as n approaches infinity.

So whenever r^2<1 the sum of the infinite series is just:

s(n)=a/(1-r)

Since a=84 and r=1/5 this infinite series has a sum of:

s(n)=84/(1-1/5)

s(n)=84/(4/5)

s(n)=5(84)/4

s(n)=105

Yana is using an indirect method to prove that segment DE is not parallel to segment BC in the triangle ABC shown below: A triangle ABC is shown. D is a point on side AB and E is a point on side AC. Points D and E are joined using a straight line. The length of AD is equal to 4, the length of DB is equal to 5, the length of AE is equal to 6 and the length of EC is equal to 7. She starts with the assumption that segment DE is parallel to segment BC. Which inequality will she use to contradict the assumption? 4:9 ≠ 6:13 4:9 ≠ 6:7 4:13 ≠ 6:9 4:5 ≠ 6:13

Answers

Please see attached file for the triangle’s figure:

Going with the image attached, if DE is parallel to BC
then
4: (4 + 5) = 6 : (6 + 7).

Therefore, the inequality that she will use to contradict the assumption is 4:9 ≠ 6:13.

To add, a relation that holds between two values when they are different in mathematics is called an inequality. A is not equal to b also means the notation a ≠ b.

Inequalities are governed by the following properties:

Transitivity
Converse
Addition and subtraction
Multiplication and division
Additive inverse
Multiplicative inverse
Applying a function to both sides

Answer:

4:9 ≠ 6:13.

Step-by-step explanation:

3!3! = 362,880 81 36

Answers

3! = 3*2*1

3!3! = 3*2*1*3*2*1 = 6*6 = 36

The answers 36. Hope this helps.
3! ----) 3 . 2 . 1 ----------) 3!3! = 36

if the trapezoid below is reflected across the x axis what are the coordinates of B

Answers

reflected across the x axis , coordinates of B will be (5, -9)

answer is B. (5,-9)

If the coordinate B is reflected over x-axis, the resulting coordinate will be (5, -9)

Reflection of image

If an image is reflected over the x-axis, the resulting coordinate will be (x, -y). The reflections shows the mirror image of a figure.

Given the coordinate B before reflection as (5, 9)> If the coordinate is reflected over x-axis, the resulting coordinate will be (5, -9)

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The cosine of the angle is 4/5

Answers

The cotangent of the angle is [tex]$\frac{4}{3}$.[/tex]

In triangle ABC, where angle ABC is a right angle (90 degrees) and sides AB, BC, and AC are given as 6, 8, and 10 units respectively, we can use the cosine and cotangent functions to find the cotangent of angle ABC.

The cosine of an angle in a right-angled triangle is defined as the ratio of the adjacent side to the hypotenuse.

In this case,[tex]$\cos(\angle ABC) = \frac{BC}{AC} = \frac{8}{10} = \frac{4}{5}$.[/tex]

The cotangent [tex]($\cot$)[/tex] of an angle is the reciprocal of the tangent (tan).

The tangent is the ratio of the opposite side to the adjacent side.

Therefore,[tex]$\cot(\angle ABC) = \frac{1}{\tan(\angle ABC)}$.[/tex]

Since [tex]$\tan(\angle ABC) = \frac{AB}{BC} = \frac{6}{8} = \frac{3}{4}$[/tex], we can find the cotangent:

[tex]\[ \cot(\angle ABC) = \frac{1}{\tan(\angle ABC)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \][/tex]

Therefore, the cotangent of the angle is [tex]$\frac{4}{3}$.[/tex]

The probable question may be:

The cosine of a certain angle is 4/5. What is the cotangent of the angle?

In triangle ABC , Angle ABC=90 degree, AB=6, BC=8 AC=10

Final answer:

The cosine of an angle being 4/5 means that the ratio of the adjacent side to the hypotenuse in a right triangle is 4/5.

Explanation:

The given question states that the cosine of an angle is 4/5. In trigonometry, the cosine function is defined as the ratio of the adjacent side to the hypotenuse in a right triangle. So, if we have a right triangle with an angle A, and the cosine of A is 4/5, it means that the ratio of the length of the adjacent side to the hypotenuse is 4/5.

Thus, we can say that if the length of the adjacent side is 4 units, then the length of the hypotenuse would be 5 units, assuming the units are consistent. This relationship holds true for any right triangle with an angle whose cosine is 4/5.

For example, if we have a right triangle with an adjacent side of 8 units, then the hypotenuse would be 10 units.

7+2[3(x+1) -2 (3x-1)]

Answers

7+2[3(x+1) -2 (3x-1)]

= 7 + 2(3x + 3 - 6x + 2) ...expand by using distributive property
= 7 + 2(-3x + 5) .....combine like terms
= 7 - 6x + 10...expand by using distributive property
= -6x + 17 ...simplify

hope it helps

Given a soda can with a volume of 21 and a diameter of 6, what is the volume of a cone that fits perfectly inside the soda can? (Hint: only enter numerals in the answer blank).

Answers

if the soda can is a cylinder, which is most likely, than that means we need to find the height of the cone. The formula for volume of a cylinder is V= пr^2h (look at the pic for clearer formula) and we know the diameter of the soda can is 6, we know the radius is 3 because diameter is a line reaching from one point of the circle to the other. Radius is a line reaching from the center of the circle to the outside as shown in the image. We divide pi (you can put in the calculator 3.14) from 21, then we get 6.688 (if we round up) and then you must look at the formula now

it looks like
6.688=r^2h

that means we must find 3^2
that basically means 3x3 which is 9

then you have to divide that from 6.688

then you get 0.743

that is your height.

now we must find the volume of the cone. The formula for that is

V=пr^2(h/3)

now lets plug in our info

V=(3.14)(9)(0.743/3)

you get 6.999

Answer:

Volume of the cone = 7 unit³

Step-by-step explanation:

Soda can has the shape of a cylinder.

Volume of soda can = πr²h

where r = [tex]\frac{6}{2}=3[/tex] units

and volume = 21 unit³

We put the values in the formula to get the value of h.

21 = πr²h

[tex]h=\frac{21}{\pi r^{2} }[/tex]

Now If we fit a cone inside the can, radius of the cone will be equal to the radius of the cylinder and height of the cylinder will be equal to the height of the cone fit inside.

By the formula of volume of cone

Volume = [tex]\frac{1}{3}\pi r^{2}h[/tex]

= [tex]\frac{1}{3}\pi r^{2}( \frac{21}{\pi r^{2} })[/tex]

= [tex]\frac{21}{3}=7[/tex] units³

Volume of the cone is 7 unit³

Point r is located at (3,0). point s is located at (0,-4). what is the equation of the line through these two points

Answers

(3,0)(0,-4)
slope = (-4 - 0) / (0 - 3) = -4/-3 = 4/3

y = mx + b
slope(m) = 4/3
(0,-4)....x = 0 and y = -4
now we sub and find b, the y int
-4 = 4/3(0) + b
-4 = b
so ur equation is : y = 4/3x - 4....or 4x - 3y = 12 <==

There are 6 performers who will present their comedy acts this weekend at a comedy club. one of the performers insists on being the last? stand-up comic of the evening. if this? performer's request is? granted, how many different ways are there to schedule the? appearances

Answers

since the 6th comic will be last you need to know how many different ways to schedule 5 comics

5x4x3x2 = 120

there are 120 different ways.

If BC = 5 and CD = 26, find AC.

Answers

Answer:

[tex]AC=\sqrt{130}[/tex]

Step-by-step explanation:

AC is the geometric mean. Solve it using this proportion:

[tex]\frac{BC}{AC}=\frac{AC}{CD}[/tex]

Now fill in the values we know:

[tex]\frac{5}{AC}=\frac{AC}{26}[/tex]

Cross multiply to get

[tex](AC)^2=130[/tex]

That means that

AC = [tex]\sqrt{130}[/tex], which, in decimal form is

AC = 11.40175425

what is larger 0.0013 or 0.02

Answers

.02 because there are less 0's after the decimal place.

0.02>0.0013 because if we compare the hundredth place of these two numbers, we could see that 0.02>0.00... As a result, 0.02 is larger than 0.0013. Hope it help!

How many cans of paint are needed to cover an area of 2,200 square units if one can of paint covers an area of 400 square units? 4 5 6 8?

Answers

In this case, one can of paint can covers an area of 400 square units. You are asked how much cans needed to cover an area of 2,200 square units.

Then you just need to divide 2,200 square units with 400 square units.
The equation will be : (2,200 square units / 400 square units) x 1 can= 4.5 cans
After you round up the result it would be 5 cans.

Answer: 5 cans

Which translation will change figure ABCD to figure A'B'C'D'?

A. 7 units left and 6 units up
B. 6 units left and 7 units up
C. 7 units left and 5 units up
D. 5 units left and 7 units up

Answers

answer is A. 7 units left and 6 units up

7 units left, 6 units up

Are the lines parallel, perpendicular, or neither?

5x + 2y = 10
15x + 4y = -4

Answers

5x+2y=10, 2y=-5x+10, y=-2.5x+5

15x+4y=-4, 4y=-15x-4, y=-3.75x-1

-2.5 != -3.75

And -2.5m=-1, m=0.4, 0.4 !=-3.75

So the slopes are not equal and they are also not negative reciprocals of one another.

Thus the lines are neither parallel nor perpendicular.

How do I set up this equation and solve ?

Answers

angles in a triangle need to equal 180 degrees

so x = 180 - 47 - 58

x = 180-105

x= 75 degrees

PLEASE HELP!! IMAGE ATTACHED find the measure of angle 2

Answers

the figure is an equilateral triangle, which all angles are 60 degrees

angle 3 divides a 60 degree angle in half so angle 3 = 30 degrees

the base is a right triangle which is 90 degrees

90+30 = 120

180-120 = 60

Angle 2 is 60 degrees

Write a possible function rule for the following sequence.

11, 15, 19, 23, 27, ...

a(n)=?

Answers

a(n) = 4(n - 1) + 11 is the equation because a(1) = 11 and the common difference (d) = 4. Then you just plug it into the arithmetic sequence formula which is a(n) = d(n - 1) + a(1). I hope this was helpful.

This is an arithmetic sequence because a common difference exists. The common difference is a constant found when taking any term and subtracting the previous term from it. In this case the common difference is 4, meaning that each term is 4 units greater than the previous term. Any arithmetic sequence can be expressed as:

a(n)=a+d(n-1), a=initial term, d=common difference, n=term number

In this case we know a=11 and d=4 so

a(n)=11+4(n-1) which can be simplified...

a(n)=11+4n-4

a(n)=4n+7

I NEED THIS ANSWER

Which linear inequality is represented by the graph?

y > 2x + 3
y < 2x + 3
y > −2x + 3
y < −2x + 3

Answers

It's y<-2x+3 since the y-intercept is positive 3 and the shade is below the line which means it's less than

Since there is a point (0,3) on the line we can say:

y=mx+3, using any other point we can find the slope, m

-1=m(2)+3

-4=2m

-2=m

So the line is:

y=-2x+3

Since the shaded region is below the line:

y<-2x+3

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