assume a*b means a+b-1. what is 5*3

The triangle that seems to be congruent to the given one is triangle EFA.

Here's why:

Both triangles have three straight sides.
Both triangles have the same angles at corresponding vertices. For example, the angle at vertex E in triangle EFA is congruent to the angle at vertex A in the given triangle, and the angle at vertex F in triangle EFA is congruent to the angle at vertex C in the given triangle.
The corresponding sides of the triangles have the same lengths. For example, side EF in triangle EFA is congruent to side AC in the given triangle, and side FA in triangle EFA is congruent to side CB in the given triangle.
Therefore, based on the properties of congruence, triangle EFA is congruent to the given triangle.

Answer:

[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3

Step-by-step explanation:

The given sequence is; 3, –6, 12, –24, 48, …

The first term of this sequence is

[tex]f(1)=3[/tex]

There is a common ratio of [tex]r=\frac{-6}{3}=-2[/tex]

We can actually use any other two consecutive terms in the sequence to obtain the common ratio.

The recursive formula is given by:

[tex]f(n)=r\cdot f(n-1)[/tex]

We plug in the common ratio to get:

[tex]f(n)=-2\cdot f(n-1)[/tex], where f(1)=3

Answer:

The answer is C

Step-by-step explanation:

Answer:

4 is your answer.

Step-by-step explanation:

You would break down both numbers into their factors.

28 is divisible by 1,2,4,7,14,and 28

60 is divisible by 1,2,3,4,5,6,10,12,15,20,30, and 60

find the common pairs: (1,1), (2,2), (4,4) Both numbers have these as factors, so find the largest one.  

The greatest common factor (GCF) of 28 and 60 is 4.

To find the Greatest Common Factor GCF of two numbers, we need to determine the largest number that divides both numbers without leaving a remainder. One way to find the GCF of 28 and 60 is to list the factors of each number and identify the largest factor that they have in common.

The factors of 28 are 1, 2, 4, 7, 14, and 28.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

The largest factor that 28 and 60 have in common is 4.

Therefore, the GCF of 28 and 60 is 4.

Another way to find the GCF of two numbers is to use prime factorization. To do this, we need to express each number as a product of its prime factors.

The prime factorization of 28 is 2² x 7, and the prime factorization of 60 is 2² x 3 x 5. To find the GCF, we take the product of the common prime factors with the smallest exponents, which in this case is 2². Therefore, the GCF of 28 and 60 is 2², which is equal to 4.

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Answer:

sin(-50°) is not equal to sin(-230°)

Step-by-step explanation:

You will be required to use a scientific calculator for this.

Step 1 : Find out the value of sin(-230°)

sin(-230°) = 0.766

Step 2 : Find out all the other values and see if they are 0.766 or not.

sin(130°) = 0.766 (It is equal to sin(-230°))

-sin(-50°) = 0.766 (It is equal to sin(-230°))

sin(50°) = 0.766 (It is equal to sin(-230°))

sin(-50°) = -0.766 (It is not equal to sin(-230°))

!!

Answer:

sin⁡(-230°) =sin(50°)

Step-by-step explanation:

1) sin(-a) = -sina

note : 2)  sina = sinb :   a=b   or a+b =180°

in this exercice :  

sin⁡(-230°) = - sin⁡(230°)  = - sin(-50°)=- (-sin(50°)) =sin(50°)  because :

sin⁡(230°) = sin(-50°)  because ; 230°+(-50°) =180°

           sin⁡(230°)    = -sin(50°)

Answer:

Step-by-step explanation:

false

Answer: [tex]h(-2)=-1[/tex]

Step-by-step explanation:

We need to find [tex]f(g(x))[/tex]. Substitute the function [tex]g(x)[/tex] into the function [tex]f(x)[/tex]:

[tex]f(g(x)) = (x+ 2)^2- 1[/tex]

Now, we know that the function [tex]h(x)[/tex] is [tex]h(x)=f(g(x))[/tex], then:

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

In order to find the value of [tex]h(-2)[/tex], we must substitute [tex]x=-2[/tex] into the function  [tex]h(x)=(x+ 2)^2- 1[/tex].

Therefore, the value of  [tex]h(-2)[/tex] is:

[tex]h(x)=(x+ 2)^2- 1\\\\h(-2)=(-2+ 2)^2- 1\\\\h(-2)=(0)^2- 1\\\\h(-2)=0-1\\\\h(-2)=-1[/tex]

Answer:

[tex]\sqrt{2^5}[/tex]

Step-by-step explanation:

[tex]2^{1/2}[/tex] × [tex]2^{3/4}[/tex] = [tex]2^{5/4}[/tex]

([tex]2^{5/4}[/tex])² = [tex]2^{5/2}[/tex] = [tex]\sqrt{2^5}[/tex]

Answer:

[tex]\large\boxed{\sqrt{2^5}}[/tex]

Step-by-step explanation:

[tex]\bigg(2^\frac{1}{2}\cdot2^\frac{3}{4}\bigg)^2\qquad\text{use}\ a^n\cdot a^m\\\\=\bigg(2^{\frac{1}{2}+\frac{3}{4}}\bigg)^2\qquad\left/\dfrac{1}{2}+\dfrac{3}{4}=\dfrac{1\cdot2}{2\cdot2}+\dfrac{3}{4}=\dfrac{2}{4}+\dfrac{3}{4}=\dfrac{5}{4}\right/\\\\=\bigg(2^\frac{5}{4}\bigg)^2\qquad\text{use}\ (a^n)^m=a^{nm}\\\\=2^{\frac{5}{4}\cdot2}\\\\=2^{\frac{5}{2}}\qquad\text{use}\ a^\frac{m}{n}=\sqrt[n]{a^m}\\\\=\sqrt{2^5}[/tex]

Answer:

( -3√5)

Step-by-step explanation:

√45 - √20 - 4√5 = √5*3*3 - √2*2*5 - 4√5

                            = 3√5 - 2√5 - 4√5

                            = √5 (3 - 2 - 4)

                            =  ( -3√5)

The correct answer is: B) 5x √3x

I just did the test, trust me it is B.

The solution for the following expression is,[tex]5x\sqrt{3x}[/tex].None of the options are correct.

Simplifying is making something easier to do or comprehend, as well as making something less difficult.

The following expression is given ;

[tex]3\sqrt{27x^3}-2\sqrt{12x^3}[/tex]

Simplify the given expression;

[tex]3\sqrt{27x^3}-2\sqrt{12x^3} \\\\ 3 \times 3x \sqrt {3x} -2 \times 2x \sqrt{3x}\\\\ 9x \sqrt {3x}-4x\sqrt{3x}\\\\\ 5x\sqrt{3x}[/tex]

The solution for the following expression is,[tex]5x\sqrt{3x}[/tex].

Hence one of the options is correct.

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Answer:

144 in^2

Step-by-step explanation:

There are four triangular sides to this square pyramid.  According to the area-of-a-triangle formula, A = (1/2)(b)(h), which here is A = (1/2)(8 in)(5 in) = 20 in^2.

Thus, the total lateral (side) area is 4(20 in^2) = 80 in^2.

The area of the bottom is (8 in)^2, or 64 in^2.

Thus, the total surface area is 80 in^2 + 64 in^2, or 144 in^2.

Answer:

144

Step-by-step explanation:

For this case we have the following equation:

[tex]24-3x = -27[/tex]

To solve we follow the steps below:

We subtract 24 from both sides of the equation:

[tex]-3x = -27-24\\-3x = -51[/tex]

We divide between -3 on both sides of the equation:

[tex]x = \frac {-51} {- 3}\\x = 17[/tex]

The value of x is 17

Answer:

[tex]x = 17[/tex]

Answer:

[tex]\boxed{x=17}[/tex]

Step-by-step explanation:

Subtract by 24 from both sides.

[tex]24-3x-24=-27-24[/tex]

Simplify

[tex]-27-24=-51[/tex]

[tex]-3x=-51[/tex]

Divide by -3 from both sides.

[tex]\frac{-3x}{-3}=\frac{-51}{-3}[/tex]

Simplify to find the answer.

[tex]-51\div-3=17[/tex]

[tex]x=17[/tex], is the correct answer.

sales tax alone = 0.99, 2.06, 16.5, 1237.5 for the items

[tex](f-g)(x)=4x-3-(x+4)=4x-3-x-4=3x-7[/tex]

Answer:

Step-by-step explanation:

[tex]x^2-25=x^2-5^2\qquad\text{use}\ a^2-b^2=(a-b)(a+b)\\\\=(x-5)(x+5)\\\\x^2-25=0\to(x-5)(x+5)=0\iff x-5=0\ \vee\ x+5=0\\\\x-5=0\qquad\text{add 5 to both sides}\\x=5\\\\x+5=0\qquad\text{subtract 5 from both sides}\\x=-5[/tex]

Answer:

The value of m is 3

Step-by-step explanation:

we have

[tex]x^{2}+mx+n=0[/tex]

step 1

Find the value of n

For x=0

[tex]0^{2}+m(0)+n=0[/tex]

[tex]n=0[/tex]

step 2

Find the value of m

For x=-3

substitute

[tex]x^{2}+mx=0[/tex]

[tex](-3)^{2}+m(-3)=0[/tex]

[tex]9-3m=0[/tex]

[tex]3m=9[/tex]

[tex]m=3[/tex]

Answer:

The slope is the percentage of test score per number of days absent

Step-by-step explanation:

we know that

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

we have

y -----> is the percentage of test score

x ----> is the number of days absent

so

That means -----> The slope is the percentage of test score per number of days absent

In this problem the slope is negative

so

If the percentage test score increases----> the number of days decreases

If the percentage test score decreases----> the number of days increases

Answer:

two

Step-by-step explanation:

Two

x - 1 = 0

x = 1

x + 3 = 0

x = - 3

You can see them for your self. The roots are the points where the graph cuts the x axis.

(1,0) and

(-3,0)

Answer:

m = 19

Step-by-step explanation:

With a rate of change of -8

27 - 8 = 19

16 - 8 = 11

so m = 19

Answer:

Third option: [tex]m=19[/tex]

Step-by-step explanation:

The rate of change is the slope of the line.

The formula for calculate the slope is:

[tex]slope=\frac{y_2-y_1}{x_2-x_1}[/tex]

You know that:

[tex]slope=-8\\y_2=m\\y_1=27\\x_2=11\\x_1=10[/tex]

Then, you can substitute them into the formula:

[tex]-8=\frac{m-27}{11-10}[/tex]

Finally, you must solve for "m":

[tex]-8=\frac{m-27}{11-10}\\\\-8(1)=m-27\\\\-8+27\\\\m=19[/tex]

Answer:

1

Step-by-step explanation:

[tex] ln4x = 2 ln8 \div 2 \\ ln4x = ln4 \\ x = 1[/tex]

Hope it helps you...☺

Answer:

x = 2

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ n logx

• log x = log y ⇒ x = y

Given

2 ln 4x = 2 ln 8

ln (4x)² = ln 8²

ln 16x² = ln 64, hence

16x² = 64 ( divide both sides by 16 )

x² = 4 ( take the square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

4 ft or 5 ft

i think thats right

Answer:

The width can be 5 ft   or the width can be 4 ft

Step-by-step explanation:

Perimeter = 2 (l+w)  for a rectangle

Area = l*w for a rectangle

Using perimeter

18 = 2(l+w)

Divide by 2

18/2 = 2/2 (l+w)

9 = l+w

Solving for l

9-w = l

Using area

20 = l*w

Substituing for l

20 = (9-w) * w

20 = 9w - w^2

Subtract 20 from each side

20-20 =-w^2 +9w -20

0 = -w^2 +9w -20

Multiply by -1

0 = w^2 -9w+20

Factor

0 = (w-5) (w-4)

Using the zero product property

w-5 = 0   w-4 = 0

w= 5   w=4

The width can be 5 ft   or the width can be 4 ft

Answer:

B if you mean log_7 (1)*log_ 5 (25)

Step-by-step explanation:

I think you mean 7 and 5 as bases... like

log_7(1)*log_5(25)

log_7(1)=0 because 7^0=1

log_5(25)=2 because 5^2=25

So you have to perform the following operation 0*2=0

so 0 is definitely one answer

1  and 5*7 are definitely not equal to 0

let's look at last choice now

log_7(7)=1 because 7^1=7

so D is equivalent to saying 2*1 which is 2 not 0

so only one choice works and it is B

The answer would be...

1/3n + 3/4n = n + 1

^^^That would be the last option

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The correct answer is last option

1/3n + n 3/4= n + 1

Step-by-step explanation:

It is given that,the sum of one-third of a number and three-fourths of the number exceeds that number by one

To find the correct option

Let 'n' be the number, one- third of the number = 1/3(n)

three - fourths of the number = 3/(4n)

Therefore the equation becomes,

1/(n) + 3/4(n)  = n + 1

Therefore the correct answer is last option

Answer:

Oak tree is 33 ft tall.

Step-by-step explanation:

We know that Irene places a mirror on the ground and walks backwards such that the mirror is in between her and the oak tree (as shown in the attached picture).

Given the distance of Irene's eyes from ground, distance between oak tree and mirror and distance between mirror and Irene, we are to find the height of the tree.

For this, we will use the ratio method:

[tex]\frac{T}{24} =\frac{5.5}{4}[/tex]

T = 33 ft

To find the answer, we can use the method of finding x- intercepts by solving the equation.

To solve the equation:

x^2 + x -12> 0

by using cross method,

we can find that 3 x -4 = -12

(x-3)(x+4) = 0

Therefore, x = 3 or x=-4

Hope it helps!

graph C represents the solutions for x^2+x-12>0​

Inequality is a statement of an order relationship—greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.

The given inequality is :

x^2+x-12>0​

Now factorizing the expression we get,

(x-3)(x+4)>0

⇒ x>3 and x<-4

Clearly graph C represents the solutions.

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Answer:

(f-g)(x) = 9x + 2

Step-by-step explanation:

(f-g)(x) = (3x+10x) - (4x-2)

          = 3x + 10x - 4x + 2

          = 9x + 2

Step-by-step explanation: would be the other answer for APEX as of 9/13/19

The domain of a function is all the x-values which it passes through.  The function is a continuous exponential function, and therefore, it will contain every x value.  The answer is:

The domain of the function is negative infinity to positive infinity.

Hope this helps!!

The domain of a function is the set of input values, the function can take.

The domain of the function is negative infinity to positive infinity,

The function is given as:

[tex]\mathbf{y = 4^x}[/tex]

The function is an exponential function, and there are no restriction as to the input values of an exponential function.

i.e: [tex]\mathbf{(-\infty, \infty)}[/tex]

Hence, the domain of the function is negative infinity to positive infinity,

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Answer:

Option 2 - Approximately 24–36 pounds

Step-by-step explanation:

Given : A standard American Eskimo dog has a mean weight of 30 pounds with a standard deviation of 2 pounds. Assuming the weights of standard Eskimo dogs are normally distributed.

To find : What range of weights would 99.7% of the dogs have?

Solution :

The range of 99.7% will lie between the mean ± 3 standard deviations.

We have given,

Mean weight of Eskimo dogs is [tex]\mu=30[/tex]

Standard deviation of Eskimo dogs is [tex]\sigma=2[/tex]

The range of weights would 99.7% of the dogs have,

[tex]R=\mu\pm3\sigma[/tex]

[tex]R=30\pm3(2)[/tex]

[tex]R=30\pm6[/tex]

[tex]R=30+6,30-6[/tex]

[tex]R=36,24[/tex]

Therefore, The range is approximately, 24 - 36 pounds.

So, Option 2 is correct.

Answer:

B: Approximately 24–36 pounds

Step-by-step explanation:

Answer:

960

Step-by-step explanation:

We can find the number of unique combinations by

Multiplying 4*5*6*8

960

There are 960 possible choices  by picking 1 from each group

Answer:

$[tex]4f[/tex]

Step-by-step explanation:

Let's assume [tex]f[/tex] represents the number of pounds of fruit.

We need to multiply the number of pounds of fruit by the cost per pound.

This is $[tex]f * 4[/tex], or in a simpler form, $[tex]4f[/tex].

In this context, the variable 'f' represents the number of pounds of fruit. In the expression '4f', it means that for every pound of fruit, which costs $4, you multiply the number of pounds by that price to get the total cost.

The problem is asking us to provide an equation for the total cost of fruit based on the cost per pound, which is $4. As you identified the variable 'f' in the previous question, let's use that to stand for the number of pounds of fruit.

The written expression for the total cost would then be 4f. This expression says that the total cost is four times the number of fruit pounds ('f') purchased

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