Are the triangles similar if so what postulate or Theorem proves their Similarity

[tex]x=y^2-1\implies y=\pm\sqrt{x+1}[/tex]

We want to find [tex]a[/tex] such that

[tex]\displaystyle\int_{-1}^a2\sqrt{x+1}\,\mathrm dx=\int_a^02\sqrt{x+1}\,\mathrm dx[/tex]

On the left,

[tex]\displaystyle\int_{-1}^a2\sqrt{x+1}\,\mathrm dx=4(x+1)^{3/2}\bigg|_{x=-1}^{x=a}=4(a+1)^{3/2}[/tex]

and on the right,

[tex]\displaystyle\int_a^02\sqrt{x+1}\,\mathrm dx=4(x+1)^{3/2}\bigg|_{x=a}^{x=0}=4-4(a+1)^{3/2}[/tex]

For the areas to be equal, we need

[tex]4(a+1)^{3/2}=4-4(a+1)^{3/2}\implies(a+1)^{3/2}=\dfrac12[/tex]

[tex]\implies a=\dfrac1{2^{2/3}}-1\approx-0.370[/tex]

To find the value of 'a' for which the line x = a splits the region into two equal areas, integrate the curve starting from -sqrt(a+1) to sqrt(a+1) and set it equal to the area of the region between the curve and the y-axis.

This question pertains to the concept of finding the area under curves in Calculus. To solve this problem, we need to set up an equation that represents the given situation and solve for 'a'. The line 'x = a' splits the region into two equal areas, meaning the area on the right of the line is equal to the area on the left of the line.

Starting from the x-axis, the curve 'x = y^2 - 1' intersects the line at y = sqrt(a+1) and y = -sqrt(a+1). Thus, we want the integral from -sqrt(a+1) to sqrt(a+1) of the curve to be equal to the area of the region between the curve and the y-axis. Formulate and solve the intergral problem to get the desired value of 'a'.

Additionally, this problem might involve the use of numerical methods like the Simpson's rule or midpoint rule to get an accurate result.

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The correct answer is (D) because 3 multiple 1/3, the 3 go with 3 and we get the 1. And 9 multiple 1/3, the 9 go with 3 and we will go 3 multiple 1 and we will get 3.

Decrease in the temperature: 5.4×5=27°C

Final temperature: 12-27=-15°C

To find out how long it would take Petra to jog 13 miles at the same rate, we can set up a proportion and solve for the unknown variable. The answer is approximately 156 minutes.

To find out how long it would take Petra to jog 13 miles at the same rate, we can set up a proportion using the given information. Since Petra jogs 2 miles in 24 minutes, the rate at which she jogs is 2 miles / 24 minutes. We can use this rate to find out the time it would take her to jog 13 miles.

Set up the proportion: 2 miles / 24 minutes = 13 miles / x minutes. Cross multiply and solve for x to find the answer.

2 miles / 24 minutes = 13 miles / x minutes
2x = 24 × 13
2x = 312
x = 156

So, it would take Petra approximately 156 minutes to jog 13 miles at the same rate.

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Answer:

y²+4y+2x+xy+4

Answer:

xy+y^2+2x+4y+4

Step-by-step explanation:

simplify by multiplying variable in the first parentheses set with the ones in the second parentheses set:

(x+y+2)(y+2)

=(x)(y)+(x)(2)+(y)(y)+(y)(2)+(2)(y)+(2)(2)

=xy+2x+y^2+2y+2y+4

=xy+y^2+2x+4y+4

hope this helps!

Answer:

You have walked [tex]\frac{17}{24}[/tex] miles

Step-by-step explanation:

In order to add these two fractions, we must find a common denominator. In this case, I used 24

[tex]\frac{3}{8} +\frac{1}{3} \\\\\frac{9}{24} +\frac{8}{24} =\frac{17}{24}[/tex]

Answer:

3/8 + 1/3 = 9/24 + 8/24 = 17/24

Step-by-step explanation:

Answer:

Praiseworthy is a main character in Sid Fleischman's 'By the Great Horn Spoon!' Praiseworthy is an incredibly likable guy who is able to help his fellow travel partner - Jack - out of some pretty sticky situations.

Step-by-step explanation:

Praiseworthy is a main character in Sid Fleischman's 'By the Great Horn Spoon!' Praiseworthy is an incredibly likable guy who is able to help his fellow travel partner - Jack - out of some pretty sticky situations.

Answer:

d) The maximum number of footballs the team can purchase is 44.

Step-by-step explanation:

975+34f≤ 2500

Subtract 975 from both sides: 975-975+34f≤ 2500-975

34f≤ 1525

Divide both sides by 34: 34f/34≤ 1525/34

f≤ 44.853

You can't purchase 0.853 of a helmet so the maximum you can buy is 44

The maximum number of footballs the team can purchase is 44.

Inequality directs to the phenomenon of unequal and/or unjust distribution of resources and possibilities among members of a given society. The word inequality may mean different things to various people and in different contexts.

A declaration of an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.

Given

975+34f≤ 2500

Subtracting 975 from both sides: 975-975+34f≤ 2500-975

34f≤ 1525

Dividing both sides by 34: 34f/34≤ 1525/34

f≤ 44.853

so the maximum you can buy is 44

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Answer:

The answer is D.

Step-by-step explanation:

A. 8^3 x 8^2 < 8^4

8^3 = 512    8^2 = 64       512 x 64 = 32768

8^4 = 4096                  32,768 < 4096 is NOT true

B. 4^4 x 4^4 = 4^16

4^4 = 256       256 x 256 = 65536

4^16 = 4294967296

256 = 4294967296   is NOT true

C. 2^2 • 2^6 < 2^8

2^2 = 4     2^6 = 64    64*4 = 256

2^8 = 256             256 < 256   is NOT true

D. 3^3 • 3^3 > 3^5​

3^3 = 27    27*27 = 729

3^5 = 243

729 > 243 IS true

Answer:

                 [tex]\bold{\dfrac{\,351\,}{275}}[/tex]

Step-by-step explanation:

[tex]\left(\dfrac9{10}+\dfrac25\right)\div\left(\dfrac{11}{6}\cdot\dfrac59\right)\ =\ \left(\dfrac9{10}+\dfrac4{10}\right)\div\dfrac{55}{54}=\\\\\\ =\ \dfrac{13}{10}\times\dfrac{54}{55}\ =\ \dfrac{13}{5}\times\dfrac{27}{55}\ =\ \dfrac{351}{275}[/tex]

The correct steps are:

start with

[tex]x^2+8x+15=0[/tex]

Add 1 to both sides:

[tex]x^2+8x+16=1[/tex]

The left hand side is a perfect square:

[tex](x+4)^2=1[/tex]

Answer:

Option D

Step-by-step explanation:

The given expression is x² + 8x + 15 = 0

We have to solve it further to transform into the form ( x - p )² = q

x² + 8x + 15 = 0

[ x² + 8x + 15 ] + 1 = 0 + 1

x² + 8x + 16 = 1

( x + 4 )² = 1

Option D is the answer.

Answer:

[tex]4c^{7}d^{13}[/tex]

Step-by-step explanation:

[tex](2cd^{4} )^{2} *(cd)^{5}[/tex]

[tex]4c^{2}d^{8} *c^{5} d^{5}[/tex]

[tex]4c^{7}d^{13}[/tex]

Answer:

The correct answer is option C.   16√2

Step-by-step explanation:

Points to remember

If the angles of a right angled triangle are 45°, 45° and 90° then the sides of the triangles are in the ratio 1 : 1: √2

To find the length of each leg of triangle

From the figure we can see that a right angled triangle with angles 45°, 45°, 90° and hypotenuse = 32

Therefore the sides are in the ratio 1 : 1 :√2

Leg1 : Leg2 : hypotenuse = 1 : 1 : √2 = x : x : 32

Therefore x = 32/√2 = 16√2

So the correct answer is option C.   16√2

- "Let's see how many packs of each item we can make and what's left over. That's the remainder.

287 = 6(287/6) = 6(47) + 5

143 = 3(143/3) = 3(47) + 2

341 = 7(341/7) = 7(48) + 5

So on that 48th pack we have 5 people markers so need 1 more and 2 dice, so we need one more. We have enough teleport markers for the 48th pack.

Choice A."

Answer:

Step-by-step explanation:

I think 33 : this i got by multiplying 75 by 45%

or 166: i got this by dividing 75 by 45%

The total points for 75 positive behaviors points are 33.45.

We have given that,

n order to go on the field trip, you must accrue 75 positive behavior points. You found out that you have 45% of the points necessary to go.

We have to determine the points.

Positive behavior strategies are evidence-based, proactive approaches to changing challenging student behavior.

We have 75 are the positive points so we have,

[tex]75\times 0.45=33.75[/tex]

Therefore we get the total points are 33.45.

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Final answer:

The problem involves finding the values of x and y in a parallelogram, using given segment lengths. Without an additional equation, we can only express one variable in terms of the other, resulting in the equation 4 = 3x + 2y.

Explanation:

The question is asking us to find the values of x and y in a parallelogram DEFG, where we know the lengths of some segments inside the parallelogram, specifically DH, HF, GH, and HE. As properties of a parallelogram dictate that opposite sides are equal in length, and segments DH and HF form one side, while segments GH and HE form the opposite side, we conclude that DH + HF must equal GH + HE.

Setting up the equation (x + 2) + (2y) = (4x - 3) + (4y + 1), we combine like terms, which gives us x + 2y + 2 = 4x + 4y - 2. Upon further simplification, by subtracting x and 2y from both sides, we get 4 = 3x + 2y. This equation allows us to express one variable in terms of the other.

Finding a specific value for x and y would require additional information, such as another equation involving x and y to solve this system of equations. Without this, we are limited to only expressing one variable in terms of the other.

Answer:

1= 115

2=45

3=110

4=115

5=115

Step-by-step explanation:

Answer:

1:

[tex]180-(70+45)=65[/tex] degrees(3rd angle of triangle)

Angle 1 is [tex]180-65=115[/tex] degrees.

2:

Angle 2 is 45 degrees as vertically opposite is also 45 degrees.

3:

[tex]180-(65+45)=70[/tex] degrees(third angle of lower triangle)

Its opposite will also be 70 degrees.

So, 3rd can be found as : [tex]360-(70+110+70)=110[/tex] degrees

You can also say that 3 is vertically opposite of 110 degrees.

4:

[tex]180-65=115[/tex] degrees

5:

This is also 115 degrees as its vertically opposite angle to 4.

Answer: Option C

Step-by-step explanation:

Given the quadratic equation [tex]y = x^2 - 13x[/tex], substitute [tex]y=0[/tex]:

 [tex]0 = x^2 - 13x[/tex]

In this case, to find the solutions of the given quadratic equation, you must factor out the variable "x". Then:

[tex]0=x(x-13)[/tex]

Therefore, you get that the solutions of this equation are the following:

[tex]x=0\\\\\\x-13=0\\x=13[/tex]

Then, the answer is:

[tex]x = 0\ or\ x = 13[/tex]

This matches with the option C.

Answer:

FIRST OPTION: (-4, -2)

Step-by-step explanation:

Given the inequality [tex]y + x < -5[/tex], substitute each solution given in the options:

1) For (-4, -2) :

[tex](-2)+ (-4) < -5[/tex]

[tex]-6 < -5[/tex] (This is true)

2) For (-3, -2):

[tex](-2)+ (-3) < -5[/tex]

[tex]-5 < -5[/tex] (This is not true)

3) For (-2, -3):

[tex](-3)+ (-2) < -5[/tex]

[tex]-5 < -5[/tex] (This is not true)

4) For (-1, -3):

[tex](-3)+ (-1) < -5[/tex]

[tex]-4 < -5[/tex] (This is not true)

You can observe that (-4, -2) is a solution of [tex]y + x < -5[/tex]

The answer is A.

Hope this helps :)

(a+3)(a-2)

a^2-2a+3a-6

a^2+a-6

Answer is a^2+a-6

You must FOIL (first, outside, inside, last)

First (The first number/variable of each parentheses must be multiplied together)

(a + 3)(a - 2)

[tex]a^{2}[/tex]

Outside (The outside number/variable of each parentheses must be multiplied together)

(a + 3)( a - 2)

-2a

Inside (The inside number/variable of each parentheses must be multiplied together)

(a + 3)(a - 2)

3a

Last (The last number/variable of each parentheses must be multiplied together)

(a + 3)( a - 2)

-6

Now add/subtract each FOIL answer according to its sign

[tex]a^{2}[/tex] - 2a + 3a - 6

Combine like terms

[tex]a^{2}[/tex] + a - 6

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

85000/100*10.5 = $8925

Step-by-step explanation:

N/A

Answer:

$24.4

Step-by-step explanation:

We are given that a discount store promises that all items it sells are 40% of their normal asking retail price.

If a shoes have a retail price of $60.99, we are to find the expected price of the shoes at this store.

Expected price of shoes = 40% of $60.99 = [tex] \frac { 4 0 } { 1 0 0 } \times 6 0 . 9 9 [/tex] = $24.4

Step-by-step explanation:

Cir=30π=2πr , thus r=15 , Area=π(r^2)=225 pie meters

The area of circle is 225π m².

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

Given that,

Circumference of the circle = 30π m

Let r be the radius of circle.

Since we know that,

circumference of the circle = 2πr

Therefore,

⇒  2πr = 30π

⇒       r = 15 m

Area of circle = πr²

                      = (15)²π

                      = 225π

Hence required area is 225π square meter.

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Answer: OPTION D

Step-by-step explanation:

We know that the function [tex]y=log(x)[/tex] is not defined for values of x less or equal than zero, therefore its domain is [tex](x|x>0)[/tex] and the range is all real numbers.

In this case we have the function [tex]y=log(x-2)+1[/tex], then [tex]x-2[/tex] must be greater than zero.

Then:

[tex]x-2>0\\\\x>2[/tex]

Therefore, the domain of the function is:

[tex]x>2[/tex] or [tex](2, \infty)[/tex]

And the range is:

All real numbers.

Answer:

the answer is D the other guy was right i just tried it.

Step-by-step explanation:

[tex]\bf \begin{array}{llllll} -2a(a+b-5)&+&3(-5a+2b)&+&b(6a+b-8)\\\\ -2a^2-2ab+10a&+&-15a+6b&+&6ab+b^2-8b \end{array} \\\\[-0.35em] ~\dotfill\\\\ (-2a^2-2ab+10a)+(-15a+6b)+(6ab+b^2-8b) \\\\\\ -2a^2-2ab+10a-15a+6b+6ab+b^2-8b \\\\\\ -2a^2-2ab+6ab+10a-15a+6b-8b+b^2 \\\\\\ \boxed{-2} a^2\boxed{+4} ab-5a\boxed{-2} b+b^2[/tex]

The answer is 16

The Pythagorean theorem is a^2+b^2=c^2

You already have one side and the hypotenuse (c)

15^2+b^2=17^2

15^2= 225

17^2= 289

Now you have 225+b^2= 289

Subtract 225 from both sides and you get

b^2=64

Then take the square root of both sides to get b alone

b=8

Now, since the base of the inner triangle is half of the base of the pyramid, multiply your answer by 2

You will get 16

Answer:

- 4 + 7i

Step-by-step explanation:

Solving (3+5i) - (7-2i)

= 3 + 5i - 7 + 2i

=3 - 7 + 5i + 2i

= - 4 + 7i

So, (3+5i) - (7-2i) is equivalent to - 4 + 7i

Answer:

92 squre feeeet you willllll paintttttttttttttttttttttt

Step-by-step explanation:

The probability that Chloe is awarded a blue ribbon in both January and February is 0.1421 or  14.21%.

To calculate this, we simply multiply the probabilities of Chloe being awarded a blue ribbon in January and February:

Probability in January = 0.29

Probability in February = 0.49

Probability in January and February = 0.29 * 0.49 = 0.1421

Explanation:

1. Given probabilities:

  - Probability of Chloe being awarded a blue ribbon in January = 29% = 0.29

  - Probability of Chloe being awarded a blue ribbon in February = 49% = 0.49

2. To find the probability of Chloe being awarded a blue ribbon in both January and February, we multiply the probabilities together:

  - Probability in January and February = 0.29 * 0.49 = 0.1421

Therefore, the probability that Chloe is awarded a blue ribbon in both January and February is approximately 14.21%.

Complete question:

Each month a retail store awards a blue ribbon to its employee of the month. The probability that Chloe is the employee of the month is 29% in January and 49% in February. What is the probability that she is awarded a blue ribbon in both January and February?

Answer:

4 ounces of flour will make 1 cake.

Step-by-step explanation:

16 ounces = 1 pound

16 ounces divided by 4 cakes = 4 ounces for 1 cake

Jesse needs ⅔ pound or 0.125 pounds (2 ounces) of flour to make one cake, calculated by dividing the half-pound bag of flour by the number of cakes it can produce (4 cakes).

Jesse is baking cakes for a bake sale and needs to know how much flour is needed for one cake.

From the information provided, we know that a ½ pound bag of flour is enough to make 4 cakes.

To determine how much flour is needed for one cake, we use a simple division.

To find the amount of flour per cake, we divide the total amount of flour by the number of cakes that can be made from it. That gives us:

½ pound flour ÷ 4 cakes = ⅔ pound flour per cake.

Therefore, Jesse needs ⅔ pound (which is 0.125 pounds or 2 ounces) of flour to make one cake.