which similarity postulate or theorem can be used to verify that the two triangles shown below are similar?​

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}

Step-by-step explanation:

we have

[tex]f(x)=-x^{2}-2x+15[/tex]

This is a the equation of a vertical parabola open downward

The vertex is a maximum

The vertex is the point (-1,16)

see the attached figure

therefore

The domain of the function is all real numbers ----> interval (-∞,∞)

Te range of the function is

[tex]y\leq 16[/tex]

All real numbers less than or equal to 16 ----> interval  (-∞,16]

Answer:b

Step-by-step explanation:

-75 = -8b - 7b

To solve for "b"  you must isolate it, meaning that "b" must be the only thing on the right side of the equation.

First you must combine like terms. Like terms are numbers that have matching variables OR are numbers with out variables. In this case the like terms are -8b and -7b, since they both have the variables "b" attached.

-8b + (-7b) = -15b

so...

-75 = -15b

Next, to completely isolate b, divide -15 to both sides. Since -15 is being multiplied by b, division (the opposite of multiplication) will cancel -15 out (in this case it will make -15 one) from the right side and bring it over to the left side.

-75/-15 = -15b/-15

5 = 1b

b = 5

Check:

-75 = -8(5) - 7(5)

-75 = -40 - 35

-75 = -75

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

8b is the answer to this question.

Step-by-step explanation:

Answer:

1961

Step-by-step explanation:

replace x with 8

25(8)^2-28(8)+585

25(64)-28(8)+585

1600-224+585

1961

f(8) = 1961.

The quadratic function given is: f(x) = 25x2 - 28x + 585

To predict f(x) when x = 8:

Substitute x = 8 into the function:

f(8) = 25(8)2 - 28(8) + 585

f(8) = 25(64) - 224 + 585

f(8) = 1600 - 224 + 585

f(8) = 1961

Therefore, f(8) equals 1961.

Answer:

8 inches

Step-by-step explanation:

Surface area of a prism is:

S = 2A + Ph

where A is the area of the base, P is the perimeter of the base, and h is the height of the prism.

The base is a square, so A = s² and P = 4s:

S = 2s² + 4sh

Given that S = 512 and h = 12:

512 = 2s² + 4s(12)

512 = 2s² + 48s

256 = s² + 24s

0 = s² + 24s - 256

0 = (s + 32) (s - 8)

s = -32, s = 8

Since s must be positive, s = 8 inches.

Follow below steps;

To find the length of the square base of the right prism:

First, calculate the lateral surface area: 512 in² = 4s * 12 where s is the side length of the square base.

Then, solve for s: 512 = 48s, s = 512 / 48 = 10.67 in.

Therefore, the length of the square base is 10.67 inches.

The answer is -65

X+(-13)=-5

x=13*-5

13 * -5= -65

x=65

An equation is formed when two equal expressions. The solution of the equation x+(-13) = -5 is 8.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

The solution of the equation x+(-13) = -5 is,

x + (-13) = -5

x - 13 = -5

x = -5 + 13

x = 8

Hence, The solution of the equation x+(-13) = -5 is 8.

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1 hour = 60 minutes

1 minute = 60 seconds

therefore 2.07 hours = (2.07*60*60) seconds

=7452 seconds

Answer:

7452

Step-by-step explanation:

There are 3600 seconds per hour

60*60= 3600

To find how many seconds are in 2.07 hours you need to multiply 3600 by 2.07

2.07* 3600 = 7452 seconds

Hope This helps

Answer:

x = 5 + √3,  5 - √3

which is 6.73 , 3.27 to the nearest hundredth.

Step-by-step explanation:

(x - 5)^2 = 3

Take the square root of both sides:

x - 5 = +/- √3

x = 5 + √3, 5 - √3

Answer:

x = 5 + √3 or x = 5 - √3

Step-by-step explanation:

Equation: (x - 5)² = 3

Square root: x - 5 = ±√3 <-- the square root of a number can be positive or negative.

Subtract: x = 5 + √3 or x = 5 - √3

Answer: x=8.5 y=1.5

Step-by-step explanation:

Use the second problem and get X by itself. X= 5y+1. Now plug that equation into the 1st equation.

-(5y+1) +9y =-5.

-5y-1+9y=-5.

-5y+9y= 1+5

4y= 6

Y=1.5

Now that you know what is the value of Y you can plug that into any equation.

5(1.5) +1

7.5+1

X=8.5

For this case we have the following system of equations:

[tex]-x + 9y = -5\\x-5y = 1[/tex]

We clear "x" from the second equation and replace it in the first:

[tex]x = 1 + 5y[/tex]

Substituting in the first equation:

[tex]- (1 + 5y) + 9y = -5\\-1-5y + 9y = -5[/tex]

We have similar terms:

[tex]-1 + 4y = -5[/tex]

Adding 1 to both sides of the equation:

[tex]4y = -5 + 1\\4y = -4\\y = \frac {-4} {4}\\y = -1[/tex]

We look for the value of "x":

[tex]x = 1 + 5 (-1)\\x = 1-5\\x = -4[/tex]

Answer:

[tex](x, y): (- 4, -1)[/tex]

Answer:

A, C and D are continuous

Step-by-step explanation:

A is a set of any number x which 30 < x <=45

B is a set that contains only 3 and 7

C is a set of any number x which 60 <= x < 100

D is a set of any number x which -infinity < x < + infinity

E is a set that contains only even whole numbers

A continuous data set is a quantitative data set representing a scale of measurement that can consist of numbers other than whole number, like decimals and fractions.

Answer: Option C

h = 6 or h= -7

Step-by-step explanation:

We have the expression

[tex]h^2-42 = -h[/tex]

To solve add h on both sides of the equality

[tex]h^2+h-42 = -h+h[/tex]

[tex]h^2+h-42 = 0[/tex]

For an equation of the form [tex]ah^2 +bh +c[/tex]  the quadratic formula is

[tex]h=\frac{-b \± \sqrt{b^2 -4ac}}{2a}[/tex]

In this case

[tex]a = 1\\b= 1\\c =-42[/tex]

[tex]h=\frac{-1 \± \sqrt{1^2 -4(1)(-42)}}{2(1)}[/tex]

[tex]h_1=6[/tex]

[tex]h_2=-7[/tex]

The answer is the option C

Answer:

Commutative Property because it only switched the numbers around.

The property represented by the equation 3x(4x5)=(3x4)x5 is the Associative Property of Multiplication, which indicates that numbers' grouping does not influence the outcome of multiplication.

The property represented by the equation 3x(4x5)=(3x4)x5 is called the Associative Property of Multiplication. This property states that the way in which numbers are grouped when being multiplied does not change the product. In your equation, whether you multiply 4 and 5 first (in the expression 3x(4x5)) or 3 and 4 first (in the expression (3x4)x5), the result is the same.

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Answer:

200 miles were driven

Step-by-step explanation:

We know that [tex]C (m) = 0.50m + 30[/tex] represents the cost of renting a car

Where m represents the number of miles driven

If we know that the cost was $ 130 then we can equal C(m) to 130 and solve for m.

[tex]C(m) =0.50m + 30=130[/tex]

[tex]0.50m + 30=130[/tex]

[tex]0.50m=130-30[/tex]

[tex]0.50m=100[/tex]

[tex]m=\frac{100}{0.50}[/tex]

[tex]m=200\ miles[/tex]

Answer: a lower annual interest fee is better than a low annual fee if you expect to pay your balance in full during most months

Final answer:

A lower annual interest fee is generally better than a low annual fee when it leads to significant savings over time, especially with large amounts or long-term financial products. Interest rates dictate the overall cost of borrowing more than annual fees, particularly for longer terms or larger sums. However, for small, short-term borrowing, a low annual fee might be more beneficial.

Explanation:

When comparing a lower annual interest rate versus a low annual fee, it is essential to consider the specific financial situation and the amount of money involved. As a general rule, a lower interest rate is beneficial when it leads to significant savings on the overall interest paid throughout the loan or credit product term. This is often the case for larger amounts or longer terms where the interest accumulates considerably over time.

For example, financial investors who choose a Certificate of Deposit (CD) earn a higher interest rate compared to savings accounts, as they agree to leave the money deposited for a fixed period, forgoing liquidity. However, if interest rates rise after a loan is made, the existing loan with the lower interest rates becomes less attractive. On the other hand, if the economy experiences a fall in interest rates, the value of the loan with the previously fixed lower rate increases.

Therefore, while a low annual fee can seem attractive, it's the annual interest that ultimately has a more significant impact on the cost of borrowing, especially over longer periods or with larger sums of money. Conversely, for small short-term loans or when the outstanding balance is frequently paid off, a low annual fee might be more advantageous than a lower interest rate, as the interest charges could be minimal.

Answer:

[tex]7+\sqrt{x+3}[/tex]

Step-by-step explanation:

The conjugate of a radical expression is obtained by changing the sign of the middle term.

The conjugate of [tex]a+\sqrt{b}[/tex] is simply [tex]a-\sqrt{b}[/tex]

Therefore, to obtain the conjugate of the given expression we simply shall be  changing the negative sign to positive;

The conjugate of [tex]7-\sqrt{x+3}[/tex] is simply;

[tex]7+\sqrt{x+3}[/tex]

Answer:

-14336

Step-by-step explanation:

We are given the first term (a) = 14, the common ratio (r) = -2 and the number of term (n) = 11 that we are to find for a geometric sequence.

We know that the formula of nth term for a geometric sequence is given by:

[tex]n^{th}term = ar^{n-1}[/tex]

Substituting the given values in the above formula to find the 11th term:

11th term = [tex] 14 \times 2^{11-1}[/tex] = -14336

It is 24 yards long.

Let the width = x

Given that the rectangular field is 3 times as long as it is wide.

So, the length = 3x.

So area = Length * width = [tex](3x)*(x) = 3x^2[/tex].

Given:  it has an area of 192 square yards.

So,

[tex]3x^2=192\\x^2=64\\x=\sqrt{64}\\x=8[/tex]

So length = 3x = 3(8) = 24.

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Answer:

2×2×2×7=56

Step-by-step explanation:

Find the multiples that goes into 56

Each number that goes into 56 put then from least to greatest and you got your prime numbers

Answer:

The set of equations has an infinite number of solutions

Step-by-step explanation:

The system of linear equations represented by the following equations:

Line A: 4x + 4y = 16 and Line B: x + y = 4 are dependent.

This is because both equations represent the same line;

if we divide both sides of the equation of line A by 4, we would obtain

x + y = 4, which is basically the equation of line B

If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line.

Answer:

The length of a leg of the triangle = 59.83 cm

Step-by-step explanation:

Points to remember

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

It is given a right angled triangle with  45°, 45° and 90° and hypotenuse = 84.6 cm

To find the length of a leg

Let 'x' be the length of each leg,

From the figure we can write,

1: 1 :  √2 = x : x : 84.6

Therefore x = 84.6/√2

 = 59.83 cm

Therefore the length of a leg of the triangle = 59.83 cm

ANSWER

59.82

EXPLANATION

The given right angle is an isosceles right triangle.

Let the length of a leg be x cm.

Then by the Pythagoras Theorem,

[tex] {x}^{2} + {x}^{2} = 84.6 ^{2} [/tex]

[tex]2 {x}^{2} = 7157.16[/tex]

Divide both sides by 2.

[tex]{x}^{2} = \frac{7157.16}{2} [/tex]

[tex]{x}^{2} = 3578.58[/tex]

Take positive square root of both sides to get,

[tex]x = 59.82123369[/tex]

Hence the length of a leg is 59.82 to the nearest hundredth.

Answer:

-6

Step-by-step explanation:

Let x =1

F(x)=-x^3-2x^2+7x-10

F(1) = - (1)^3 -2(1)^2 +7(1) -10

     = -1 -2 +7-10

    = -3+7-10

   =-6

The output of the given function F(x)=-x^3-2x^2+7x-10 when x equals 1 is -6. We substituted x=1 into each term to calculate this.

The given function is F(x)=-x^3-2x^2+7x-10. To find the output of the function when x equals 1, you substitute '1' in place of 'x' in the equation. So let's calculate:

Now, add all the results together: -1 - 2 + 7 - 10 = -6. Therefore, when x equals 1, the output of the function F(x) is -6.

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Answer:

At 10 hours there will be 10 milligrams

Step-by-step explanation:

On a graph your slope would be y= -1x+20 because there where 20 mill at 0 hours and 12 mill at 8 hours. 20-8=12 meaning 1 mill would be deluded every hour. Hope this helps.

Final answer:

Using the exponential decay formula, we can find the half-life of the medication from the initial and given 8-hour amounts and then use it to calculate the amount of medication remaining after 10 hours.

Explanation:

To determine the remaining medication after a given number of hours, we will apply the exponential decay formula which accounts for substances with a half-life. Thus, given that there are initially 20 milligrams of the medication and that it decreases to 12 milligrams after 8 hours, we need to calculate the half-life and then use it to predict the amount remaining after 10 hours.

First, finding the half-life 't1/2' can be done using the formula A = A0×2−t/t1/2, where A is the remaining amount (12 mg), A0 is the initial amount (20 mg), and t is the time elapsed (8 hours). Solving for the half-life gives us t1/2 as the unknown in this equation.

12 mg = 20 mg ×2−(8 hours)/t1/2
Reducing this equation, we find that:
t1/2 = 8 hours / (log2(20 mg/12 mg))

After finding 't1/2', we can then determine the amount remaining after 10 hours. The calculation would be as follows:
A = 20 mg ×2−(10 hours)/t1/2

This will give us the final amount of medication left in the system at the 10-hour mark, rounded to the nearest hundredth.

Answer:

6

Step-by-step explanation:

You are given the radius, 3

The diameter is twice the radius, so 6.

Answer:

Half a block ( 0.5 or 1/2 )

Step-by-step explanation:

8 1/2  blocks can also be written as 8.5 blocks.

If Kira walks 8.5 blocks in 17 minutes [and continues to walk at this steady pace], divide 8.5 by 17.

8.5/17 = 0.5

So, Kira walked 0.5 or 1/2 blocks in a minute.

I hope this helps! :)

Kira walks at a rate of 0.5 blocks per minute when she walks 8 and a half blocks in 17 minutes.

Kira walks 8 and a half blocks in 17 minutes. To find out how many blocks she will walk each minute, we need to calculate the rate by dividing the total number of blocks by the total number of minutes:

Rate = Total Blocks Walked / Total Minutes

Rate = 8.5 blocks / 17 minutes

Rate = 0.5 blocks per minute.

Therefore, at a steady pace, Kira will walk half a block every minute.

ANSWER

The choice is correct.

[tex]y = {(x -1)}^{2} + 2[/tex]

EXPLANATION

The equation of a parabola in vertex form is given by:

[tex]y = a {(x -h)}^{2} + k[/tex]

where (h,k) is vertex of the parabola and 'a' is the leading coefficient of the parabola.

From the given options, the leading coefficient must be a=1.

We also have the vertex of the parabola at (1,2). This implies that h=1 and k=2.

We substitute these values into the formula to get,

[tex]y = {(x -1)}^{2} + 2[/tex]

The second option is correct.

Answer:

108,000 females

Step-by-step explanation:

12% of 900,000 is 108,000.

Therefore, there are 108,000 female officers in the U.S.

Answer: 108,000

Step-by-step explanation:

In 2014, 900,000 sworn law enforcement officers who were serving in the United States and 12% of those officers were female. To find the number of females that were law enforcement officers, we multiply the percentage of females by the total number of law enforcement officers. This will be:

= 12% of 900000

= 12/100 × 900000

= 0.12 × 900000

= 108,000

There were 108,000 females as law enforcement officers serving in the United States.

Answer:

480 mm³

Step-by-step explanation:

The volume (V) of a pyramid is

V = [tex]\frac{1}{3}[/tex] area of base × height, hence

V = [tex]\frac{1}{3}[/tex] × 96 × 15 = 32 × 15 = 480

Note that [tex]\sqrt[2]{x}=x^{\frac{1}{2}}[/tex]

[tex]\sqrt[2]{16x^{36}}=\sqrt[2]{4^2x^{18\cdot2}}[/tex]

[tex]4^{2\cdot\frac{1}{2}}x^{18\cdot2\cdot\frac{1}{2}}=4^{\frac{2}{2}}x^{\frac{18\cdot2}{2}}[/tex]

[tex]\boxed{4x^{18}}[/tex]

Hope this helps.

r3t40

Answer:

x is in the element of all real numbers.

Step-by-step explanation:

Simplify the equation.

[tex]y=x+6-7[/tex]

[tex]y=x-1[/tex]

This means that the equation [tex]y=x[/tex] has just been moved down one.

Since the equation can be any number on the x axis, the domain is all real numbers.

Answer: X is all numbers I think.

Step-by-step explanation:

Answer:

15

Step-by-step explanation:

First add 20 to both sides to get x/3 = 5

Then multiply both sides by 3 to get 15.

You can check it by substituting it into the equation

15/3 - 20 = -15

5 - 20 = -15

-15 = -15

Step-by-step explanation:

x/3 - 20 = -15

x/3 = -15 + 20

x/3 = 5

x = 15