Apply the Distributive Property and simplify.
- 8(x + 3) = 24
- 8x +
= 24

Answer:

Option (2)

Step-by-step explanation:

Given:

AC is an angle bisector of ∠DAB and ∠DAB

m∠BCA ≅ m∠DCA

m∠BAC ≅ m∠DAC

To Prove:

ΔABC ≅ ΔADC

Solution:

               Statements                                  Reasons

1). m∠BCA ≅ m∠DCA                            1). Given

2). m∠BAC ≅ m∠DAC                           2). Given

3). AC ≅ AC                                            3). Reflexive property

4). ΔABC ≅ ΔADC                                 4). ASA property of congruence

Therefore, Option (2) will be the correct option.

Answer:

The answer is below

Step-by-step explanation:

1) A triangle is a polygon with three sides and three angles. There are different types of triangles such as obtuse, scalene, right angle, equilateral and isosceles triangle.

Given that triangle ABC is right angled and AC = 25 cm = hypotenuse and BC = 15 cm. Using Pythagoras:

AC² = BC² + AB²

25² = AB² + 15²

AB² = 25² - 15²

AB² = 400

AB = √400

AB = 20 cm

Using sine rule:

[tex]\frac{sin(B)}{AC}=\frac{sin(A)}{BC}=\frac{sin(C)}{AB}\\\\But\ \angle B= 90^o(right\ angle)\ hence:\\\\ \frac{sin(B)}{AC}=\frac{sin(A)}{BC}\\\\\frac{sin(90)}{25}=\frac{sin(A)}{15}\\\\sin(A)=\frac{sin(90)}{25}*15\\\\sin(A)=0.6\\\\A=sin^{-1}(0.6)\\\\A=36.87^o[/tex]

2)

Using Pythagoras:

hypotenuse² = 8² + 6²

hypotenuse² = 100

hypotenuse = √100

hypotenuse = 10

Using sine rule:

[tex]\frac{sin(x)}{8}=\frac{sin(90)}{10}\\\\sin(x)=\frac{sin(90)}{10}*8\\\\sin(x)=0.8\\\\x=sin^{-1}(0.8)\\\\x=53.13 ^o[/tex]

Answer:

h(x) = (1/4)x - 2 which is choice A

Step-by-step explanation:

Replace f(x) with y. Then swap x and y. Lastly, solve for y to get the inverse.

f(x) = 4x+8

y = 4x+8

x = 4y+8

x-8 = 4y

4y = x-8

y = (x-8)/4

y = x/4 - 8/4

y = (1/4)x - 2

h(x) = (1/4)x - 2

Given :

Heather spend 2/7 of her money buying presents.

She then had €48.65 left.

To Find :

The initial amount of money she had.

Solution :

Let, initial amount she had is €x.

So,

[tex]x - \dfrac{2x}{7} = 48.65\\\\\dfrac{5x}{7} = 48.65 \\\\x = \dfrac{48.65\times 7}{5}[/tex]

x = €68.11

Therefore, initially he had €68.11 .

Answer:

32.8

Step-by-step explanation:

you divide 8 1/5 by 1/4 to find the unit rate.

Answer:0.60 is a parameter .

Step-by-step explanation:

In statistics, a parameter is a number that summarize the data for a whole population.

On the other hand , statistic gives a measure for sample of population.

Given: We have a population in which 60% of the people approve of gambling.

60% = 0.60

Since it is a measure for the population , it is denoted as population parameter.

Hence, 0.60 is a parameter not statistic.

Answer:

-7

Step-by-step explanation:

you cant change the numerator if you cant change the denominator

Answer:

(3,7)

Step-by-step explanation:

Answer:

(a,m=(-1499/1812, 1/2)

Step-by-step explanation:

hope this helps!

Answer:

that is simple, use the graph and put parenthesis around say 1 and 2 then graph it then keep doing that throughout the graph if you want further explanation just ask

Step-by-step explanation:

Answer:

Hello, for the second question, you can actually form a triangle from the line. From there, you can see the height (aka y) will be easier to solve. I hope this helps!

Ans: 1) 47.5

2) 3.4

Step-by-step explanation:

Answer:

The mean squares has d.f (n-1)

Step-by-step explanation:

The total number of degrees of freedom is n-1 as there is only one restriction of computing the grand mean. The d.f for k samples is k-1 beacuase the mean of the sample means must equal the grand mean. Similarly , the d.f for within SS is n-k , due to the k restrictions of computing the k sample means. Hence we find that

Total df= Within df + Between df

n-1=  (n-k)+(k-1)

Between SS has (k-1) d.f

Within SS has (n-k) d.f

These two quantities are known as mean squares and has d.f (n-1)

Answer:

it is A, the first one

Step-by-step explanation:

bc +6 and then -10 it ends up on -4

Answer: y=-3/4x

Step-by-step explanation:

The slope intercept form is when you use the equation y=mx+b (m is the slope and b is the y-intercept). First, let's find the y intercept. The y intercept is what y would be if x is 0. here, you can see that this particular line passes through the origin. So, the y-intercept is zero because when x passes through zero, y is also zero. Next, let's find the slope. The formula for slope is change in y/change in x. Let's randomly choose 2 points off this line. To make this a thousand times easier for us, let's choose the points (-4, 3) and (4, -3). Now, to find the change in y, let's find the difference between the 2 y coordinates we have chosen. To do this we just need to do -3-3, which gives us -6. Now let's find the change in x. To do this we will do the same thing we did to find the change in y but this time we'll use the x coordinates. We will do 4-(-4), which simplifies to 8. Now, we're almost done. Just divide the change in y by the change in x. You will get -6/8. This can be simplified to -3/4. So now we know our slope is -3/4 and our y-intercept is 0. Let's insert them into the equation. y=-3/4x+0. We know that we can just get rid of that 0 because 0 literally means nothing. So our final answer is y=-3/4x. Hope this helps!

Answer:

The answer is below

Step-by-step explanation:

From the question,

Statement                                           Reason

ΔWZX and ΔYZX are                         Given

right angled triangles

WX = YX                                              Given

XZ ≅ XZ                                               Reflexive property. The reflexive  

                                                            property of congruence states that              

                                                            any shape is congruent to itself.

∠XZW = ∠XZY                                     Definition of right angle.

∠XWZ = ∠XYZ                                     Definition of isosceles triangle.

                                                             Triangle XYW forms a right angled  

                                                             triangle since YX = WX

∠XWZ + ∠WXZ + ∠XZW = 180°           Sum of angles in triangle WZX

∠XZY + ∠XYZ + ∠YXZ = 180°            Sum of angles in triangle YZX

∠XWZ + ∠WXZ + ∠XZW =                 Substitution

∠XZY + ∠XYZ + ∠YXZ

∠XYZ + ∠WXZ + ∠XZY =                 Substitution

∠XZY + ∠XYZ + ∠YXZ

∠WXZ = ∠YXZ                                  Simplification

Answer:

6 1/2

Step-by-step explanation:

4 1/2+2 1/2

= 9/2+5/2

=14/2

=7

Hope This Helps, BadAtMath99

Answer:

180

Step-by-step explanation:

Answer:5n+10d=365.7 pennies

Step-by-step explanation:

Answer:

[tex]tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)[/tex]

Option A is correct.

Step-by-step explanation:

We need to find equivalent of [tex]tan\:\left(\frac{5\pi }{6}\right)[/tex]

First we solve [tex]tan\:\left(\frac{5\pi }{6}\right)[/tex]

We get [tex]-\frac{1}{\sqrt{3} }[/tex]

Now checking all the options.

Option A: [tex]tan\:(-\frac{\pi}{6} )[/tex]

Solving [tex]tan\left(-\frac{\pi }{6}\right)\: we\: get\: \mathbf{ -\frac{1}{\sqrt{3} }}[/tex]

Option B: [tex]tan\left(\frac{7\pi }{6}\right)[/tex]

Solving [tex]tan\left(\frac{7\pi }{6}\right)\: we\: get\: \mathbf{\frac{1}{\sqrt{3} }}[/tex]

Option C: [tex]cot\left(\frac{5\pi }{6}\right)[/tex]

Solving [tex]cot\left(\frac{5\pi }{6}\right)\:we\:get\:\mathbf{-\sqrt{3} }[/tex]

Option D : [tex]tan\left(-\frac{5\pi }{6}\right)[/tex]

Solving [tex]tan\left(-\frac{5\pi }{6}\right) \:we\:get:\mathbf{\frac{1}{\sqrt{3} } }[/tex]

So, looking at the options, only Option A has the same result as given question

So, [tex]tan\:\left(\frac{5\pi }{6}\right)=tan\left(-\frac{\pi }{6}\right)[/tex]

Option A is correct.

Answer:

21/3 i think

Step-by-step explanation:

uh-

well 2+2 is 4 and 7/3x=2/3 is 2/7

Answer: If you see my picture and you will see my answer

Step-by-step explanation: Hope this help

Answer:

Step-by-step explanation:

The proportional relationship is:

In the given case we have:

This is a linear function but not proportional relationship because it has y-intercept, different than zero

Answer:

58% of 250 is 145.

Step-by-step explanation:

145 * 100/58

= 250

Answer:

250

Step-by-step explanation:

Answer:

c < 8

Step-by-step explanation:

Answer:

Josh charges $5 more than Lindsay

Step-by-step explanation:

Answer:

b

Step-by-step explanation:

lindsay's equation is y=6x+15.

you compare the first row and second row to find the cost per dog and then subtract from the total to find the initial cost.

Answer:

244 ft²

Step-by-step explanation:

Rectangle Base Area: 6•4=24

Rectangle Side Area: 8•10=80; 80•2(sides) = 160

Triangle Sides Area: (10•6=60); 60/2(area of triangle) = 30; 30•2(sides)=60*

*Technically can skip the divide by two and then multiply by two, since they cancel out*

(Area of Triangle Formula= 1/2bh)

Add areas together: 24+160+60= 244 ft²

Answer: part a: area = bh part b: split it on its diagonals

Step-by-step explanation: