(Pictures included, pls help)

Carlos draws a transversal, t, on two parallel lines AB and CD, as shown below:

He makes the following table to prove that the alternate interior angles are equal:

Which is The missing justification?

A) Opposite Interior Angles Are congruent when parallel lines are intersecting by a transversal

B) Vertical Angles Formed By Two Intersecting Segments Are Congruent

C) Adjacent Angles Formed By Two Interesting Segments Are Supplementary

D) Opposite Exterior Angles Are Congruent When Parallel Lines Are Intersected By A transversal​

Answer:

the answer is D

Step-by-step explanation:

if you look on the graph and compare the statements you'll see none of them correlate except for the last one. 7 erasers cost 3.50, since the point on the graph is (7, 3.50)

Answer:

The correct option is D) Seven eraser cost $3.50

Step-by-step explanation:

Consider the provided graph.

The graph shows the relationship between the total cost and the number of erasers bought at the student store.

Here the x-axis represents the number of erasers bought and the y-axis represents the total cost.

Now consider the provided options.

Options (A) Each eraser cost $1.00

This option is incorrect because when x = 1 the value of y = 0.5, that means the cost of each eraser is $0.5

Options (B) Each eraser cost $1.50

This option is incorrect as the cost of each eraser is $0.5

Options (C) Three eraser cost $6

This option is incorrect because when x = 3 the value of y = 1.5, that means the cost of 3 eraser is $1.5

Options (D) Seven eraser cost $3.50

This option is correct because when x = 7 the value of y = 3.5, that means the cost of 7 eraser is $3.5

Answer:

XY=10 cm

Step-by-step explanation:

The sum of three positive integers given their product is 7, analyze the factors of the product and sum them up.

The sum of three positive integers whose product is 8 can be found by analyzing the factors of 8.

Given that the product of three different positive integers is 8, the three integers are 1, 2, and 4. Therefore, the sum of these integers is 1 + 2 + 4 = 7.

1st one

Step-by-step explanation:

I have answered ur question

Answer:

A

Step-by-step explanation:

Given

x² - 8x = 3

To complete the square

add (half the coefficient of the x- term)² to both sides

x² + 2(- 4)x + 16 = 3 + 16

(x - 4)² = 19 ( take the square root of both sides )

x - 4 = ± [tex]\sqrt{19}[/tex] ( add 4 to both sides )

x = 4 ± [tex]\sqrt{19}[/tex]

Solution set is (4 - [tex]\sqrt{19}[/tex], 4 + [tex]\sqrt{19}[/tex] )

Answer:

=3501 yards.

Step-by-step explanation:

The three ships form a triangle.  From the Voyager the angle between the Norman and the Gladstone=180-(55+48)=77°

Let the position of the Voyager be V that of Norman be N and that of the Gladstone be G

Then, the distance between Norman and voyager is g

g/sin G=v/ Sin V

4590/Sin 77=g/Sin 48

g=(4590 Sin 48)/Sin 77

=3500.8 yards

The distance between the Norman and the voyager= 3501 yards.

[tex]3\sqrt5-2\sqrt7+\sqrt{45}-\sqrt{28}=\\3\sqrt5-2\sqrt7+\sqrt{9\cdot5}-\sqrt{4\cdot7}=\\3\sqrt5-2\sqrt7+3\sqrt{5}-2\sqrt{7}=\\6\sqrt5-4\sqrt7[/tex]

[tex]\large\boxed{\text{C}).\,15\,\text{cm}}[/tex]

In this question, we're trying to find what the radius of the circular pie is.

In this question, we know that the area of the pie is 706.5 cm²

We can use the area to find our radius.

We would use the formula [tex]r=\sqrt\frac{A}{\pi}[/tex] to find the radius.

R= radius

A = Area

Your equation should look like this:

[tex]r=\sqrt\frac{706.5}{\pi}[/tex]

Now, you will solve.

[tex]r=\sqrt\frac{706.5}{\pi}\\\\\text{You can make it simpler by turning}\, \pi\,\text{into} 3.14\\\\r=\sqrt\frac{706.5}{3.14}\\\\\text{Divide 706.5 by 3.14}\\\\r=\sqrt225\\\\\text{Now, get the square root of 225}\\\\r=15[/tex]

When you're done solving, you should get 15.

This means that the radius of the pie is 15 cm.

Final answer:

To find the radius of the pie given its area of 706.5 cm², we use the formula A = πr² and solve for r, yielding an approximate radius of 15 cm. This corresponds to option C) on the given list.

Explanation:

To find the radius of the pie given its area, we can use the area formula for a circle: A = πr². Since the area of the pie is given as 706.5 cm², we can rearrange the formula to solve for the radius (r).

The rearranged formula to solve for the radius is: r = √(A/π).

Substituting the given area, we have:
r = √(706.5 cm²/π)
r = √(706.5/3.14159265359)
r ≈ √(225)
r ≈ 15 cm

Therefore, the radius of the pie is approximately 15 cm, making option C) the correct answer.

[tex]-1=\dfrac{5+x}{6}\\\\-6=5+x\\\\x=-11[/tex]

"Solve for x" means get an equation that says " X = something ".  It has nothing but X all alone on one side, and the other side tells exactly what X is equal to.

How do you get such an equation ?  

-- Take what they gave you in the question.

-- Do anything you want on one side of it, to get X all by itself on that side.

BUT . . .

-- Whatever you do to one side, you must immediately do the same thing on the other side.

Here's how that goes:

Given in the question:  -1 = (5 + X) / 6

Multiply each side by 6 :  -6 = 5 + X

Subtract 5 from each side:  -11 = X

And there you are.  It's over almost as soon as it started.

Answer:

278.9 units^3 to the nearest tenth.

Step-by-step explanation:

This is a cylinder on the bottom . resting on the cylinder is a prism.

Volume of the cylinder = π r^2 h  where r = 1/2 * 7 = 3.5 and h = 6.

V = π * 3.5^2 * 6 = 230.907 units^3.

Volume of the prism = l*w*h

= 4*4*3 = 48 units^3.

Volume of the composite figure = 230.907 + 48

= 278.9.

Answer:it’s the number that appears most often,so the answer would be 2,4,and 0.

Step-by-step explanation:

The modes of the data set are 0, 2, and 4

In this question, it is asking you to find the mode of the given data set.

We would be using the data set in the question in order to find out what the mode is.

The mode would be the number that "occurs" the most. In other words, the number(s) that are more "frequent."

Data set:

2, 2, 1, 4, 4, 2, 3, 0, 0, 4, 1, 0, 4, 0, 2

Now, we could count how many of each numbers there are.

0 = 4 (Most)

1 = 2  

2 = 4 (Most)

3 = 1

4 = 4 (Most)

When you're done counting the numbers, you would notice that 0, 2, and 4 have the highest number of occurrence in the data set.

This means that the modes of the data set are 0, 2, and 4

Answer:

a is the only true one if you meant 6 times 5!

Step-by-step explanation:

Before we being

n!=n*(n-1)*(n-2)*...(3)(2)(1)

Example: 5!=5(4)(3)(2)(1) and 10!=10(9)(8)(7)(6)(5)(4)(3)(2)(1)

Yes that operation is multiplication.

a) Does 6!=6*5!

Let's see

6!=6*5*4*3*2*1

5!=5*4*3*2*1

So 6*5!=6(5*4*3*2*1)=6*5*4*3*2*1=6!

So true!

b) Does 4!+2!=6! ?

4!=4(3)(2)(1)

2!=2(1)

6!=6(5)(4)(3)(2)(1)

Does

4(3)(2)(1)+2(1)=6(5)(4)(3)(2)(1)

24          +2  =720

26=720 (this is not true)

So 4!+2! is not 6!

c) Does 6!/3!=2! ?

6!=6(5)(4)(3)(2)(1)

3!=3(2)(1)

If you divide 6! by 3!, then the factors 3 and 2 and 1 cancel and you are left with 6(5)(4).

So the question becomes is 6(5)(4)=2!

2!=2(1)=2

6(5)(4)=2?

No way! That is saying 120=2 which is not true.

The evaluations of the statements are: (a) false because non-integer factorials are not defined, (b) false because the sum of 4! and 2! does not equal 6!, and (c) false because 6! divided by 3! is 120, not 2!.

Let's evaluate each statement one by one.

This statement is false. The factorial function is defined for non-negative integers. Since there is no definition for non-integer factorial such as 6.5!, this comparison is invalid. A correct statement may involve only integer factorials.

This statement is also false. To show this, let's calculate each factorial:

Adding 4! and 2! gives 24 + 2 = 26, which is not equal to 6! (720). This statement could be corrected by finding two factorials that add up to another factorial, if such a pair exists.

This statement is false. By calculating the factorials, we have:

Therefore, 6!/3! is equal to 720/6, which simplifies to 120, not 2 (which is the value of 2!). The correct statement is 6!/3! = 120.

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Answer:

3                     sqrt(3)

-----------    or  -----------

2 sqrt(3)            2

Step-by-step explanation:

3 sqrt(8)

-----------------

4 sqrt(6)

3 sqrt(4*2)

-----------------

4 sqrt(3*2)

We know that sqrt(ab) = sqrt(a) sqrt(b)

3 sqrt(4) sqrt(2)

------------------------

4 sqrt(3) sqrt(2)

Canceling the sqrt(2) and sqrt(4) is 2

3*2

----------

4 sqrt(3)

3

-----------

2 sqrt(3)

We can simplify the answer be multiplying by sqrt(3)/sqrt(3)

3                 sqrt(3)

----------- * ----------

2 sqrt(3)     sqrt(3)

3 sqrt(3)

-----------

2 *3

sqrt(3)

-----------

2

Answer:

6

Step-by-step explanation:

60% of 40 = 24

25% of 24 = 6

Therefore, 6 girls in  the class wear glasses.

Answer:

b

Step-by-step explanation:

I would use b.

Why?

[tex]2 \csc(2x)[/tex]

[tex]2 \frac{1}{\sin(2x)}[/tex]

[tex]\frac{2}{\sin(2x)}[/tex]

[tex]\frac{2}{2\sin(x)\cos(x)}[/tex]

[tex]\frac{1}{\sin(x)\cos(x)}{/tex]

[tex]\frac{1}{\sin(x)\frac{1}{\cos(x)}[/tex]

[tex]\csc(x) \sec(x)[/tex]

I applied the identity sin(2x)=2sin(x)cos(x) in line 3 to 4.

Answer: OPTION B.

Step-by-step explanation:

It is important to remember these identities:

[tex]csc(x)=\frac{1}{sin(x)}\\\\sec(x)=\frac{1}{cos(x)}[/tex]

Knowing this, we can say that:

[tex]csc(x) sec(x)=\frac{1}{sin(x)}*\frac{1}{cos(x)}=\frac{1}{sin(x)*cos(x)}[/tex]

Now we need to use the following Double angle identity :

[tex]sin(2x)=2sin(x)cos(x)[/tex]

And solve for [tex]sin(x)cos(x)[/tex]:

[tex]\frac{sin(2x)}{2}=sin(x)cos(x)[/tex]

The next step is to make the substitution into [tex]\frac{1}{sin(x)*cos(x)}[/tex] and finally simplify:

[tex]\frac{1}{\frac{sin(2x)}{2}}=\frac{\frac{1}{1}}{\frac{sin(2x)}{2}}=\frac{2}{sin(2x)}=2csc(2x)[/tex]

Answer:

1/12 of a gallon of water in each container

Step-by-step explanation:

Answer = [tex]\frac{Water}{Containers}[/tex] = 1/12

Answer:

Oliver poured [tex]\frac{1}{12}[/tex] gallons of water in each container.

Step-by-step explanation:

Oliver has the amount of water = 0.5 gallons.

He pours all of the water into 6 containers.

So amount of water in each container will be = [tex]\frac{\text{Total amount of water}}{\text{Number of containers}}[/tex]

= [tex]\frac{0.5}{6}[/tex]

= [tex]\frac{\frac{1}{2} }{6}[/tex]

= [tex]\frac{1}{12}[/tex] gallons of water.

Therefore, in each container amount of water poured will be [tex]\frac{1}{12}[/tex] gallons.

This is a linear equation in standard form [tex]\( Ax + By = C \).[/tex] None of the options provided in the multiple-choice question exactly match this equation in standard form

To find the equation of a line perpendicular to the given line and passing through a specific point, follow these steps:

1. Identify the slope of the original line.

  The line given is [tex]\( y = -10x + 1 \)[/tex]. The slope (m) of this line is -10.

2. Find the perpendicular slope:

  The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. Therefore, the perpendicular slope [tex]\( m_{\perp} \) is \( \frac{1}{10} \)[/tex]  because [tex]\( m_{\perp} = -\frac{1}{m} \).[/tex]

3. Use the point-slope form to find the equation:

  The point-slope form is [tex]\( y - y_1 = m_{\perp}(x - x_1) \)[/tex], where [tex]\( (x_1, y_1) \)[/tex] is the point the line passes through, which is (5,7) in this case.

4. Plug in the point and the perpendicular slope:

  [tex]\( y - 7 = \frac{1}{10}(x - 5) \)[/tex].

5. Simplify the equation to get it into slope-intercept form  [tex](\( y = mx + b \))[/tex]:

  [tex]\( y = \frac{1}{10}x - \frac{1}{10}(5) + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x - \frac{1}{2} + 7 \)[/tex].

  [tex]\( y = \frac{1}{10}x + \frac{13}{2} \)[/tex] after combining like terms.

The equation in slope-intercept form is [tex]\( y = \frac{1}{10}x + \frac{13}{2} \),[/tex]which corresponds to one of the choices given in the multiple-choice question. Let's identify which one it is.

The equation that represents a line which is perpendicular to the line [tex]\( y = -10x + 1 \)[/tex] , passing through the point (5,7), is:

[tex]\[ y = \frac{1}{10}x + \frac{13}{2} \][/tex]

This can be simplified to:

[tex]\[ 10y = x + 65 \][/tex]

Or:

[tex]\[ x - 10y = -65 \][/tex]

This is a linear equation in standard form \( Ax + By = C \). None of the options provided in the multiple-choice question exactly match this equation in standard form

Answer:

[tex]\large\boxed{\dfrac{4}{x}+6}[/tex]

Step-by-step explanation:

Six more than the quotient of four and a number x:

[tex]\dfrac{4}{x}+6[/tex]

Answer:

[tex]\frac{4}{x}+6[/tex]

Step-by-step explanation:

We have been given a  word phrase. We are supposed to represent our given word phrase into an algebraic expression.

The quotient of four and a number x will be 4 divided by x. We can represent this information in an expression as:

[tex]\text{Quotient of four and a number }x=\frac{4}{x}[/tex]

Six more than the quotient of four and a number x would be [tex]\frac{4}{x}+6[/tex]

Therefore, our required expression would be [tex]\frac{4}{x}+6[/tex].

Answer:

Option A

Step-by-step explanation:

Given:

Center of circle = (h,k)= (3,8)

Radius = r = 5

The standard form of equation of circle with center and radius is:

[tex](x-h)^2+(y-k)^2=r^2\\Putting\ the\ values\\(x-3)^2+(y-8)^2=(5)^2\\Simplifying\\x^2+9-6x+y^2+64-16y=25\\x^2+y^2-6x-16y+9+64=25\\x^2+y^2-6x-16y+73=25\\x^2+y^2-6x-16y+73-25=0\\x^2+y^2-6x-16y+48=0[/tex]

Therefore, the general form of the equation of circle given is:

[tex]x^2+y^2-6x-16y+48=0[/tex]

Hence, option A is correct ..

Answer:

2/7

Step-by-step explanation:

If two events A and B are independent, then P(A and B)=P(A)P(B).

So since Q and R are independent, then P(Q and R)=P(Q)P(R).

Let's substitute and evaluate:

[tex]P(Q\text{ and }R)=P(Q)\cdot P(R)=\frac{4}{7} \cdot \frac{1}{2}=\frac{4}{14}[/tex].

Both 2 and 14 are divisible by 2, so to reduce 4/14 we could divide top and bottom by 2:

4/14=(4/2)/(14/2)=2/7

Answer:

nope its not. You should  count it like this  (8 / 2) * (2 + 2)

Step-by-step explanation:

(8 / 2) * (2 + 2)

4 * 4

16

[tex]\text{Hey there!}[/tex]

[tex]\text{PEMDAS means: Parentheses, Exponents, Multiplication, Division, Addition}\\\text{, \& Subtraction}[/tex]

[tex]\text{\underline{No}, it is \underline{NOT} correct because you had to work with the parentheses first}[/tex]

[tex]\dfrac{8}{2}(2 + 2) = \ ? \\ \\ (2 + 2) = 4 \\ \\ \dfrac{8}{2}(4) = \ ? \\ \\ \dfrac{8}{2}= 4 \\ \\ \text{4(4)\ = 16} \\ \\ \boxed{\boxed{\huge\text{Answer should be: 16 }}}[/tex]

[tex]\text{You had to do what was inside the parentheses first, then}\text{ divsion}[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

√135

Step-by-step explanation:

3^2+b^2=12^2

9+b^2=144

9-9+b^2=144-9

b^2=135

√135=b

[tex]\large\boxed{12\,\text{apples}}[/tex]

In this question, we're trying to find how many apples Jenson picked from the basket.

Lets gather information that can help us.

Important information:

With the information above, we can solve the question.

We know that he picked up a fruit 40 times, but we need to find how many apples he picked up during the 40 times.

The probability of picking an apple is 0.3, which is equivalent to 30%

This means that 30% of the 40 times he picked an apple.

We would multiply 40 by 0.3 to get our answer.

[tex]40*0.3=12[/tex]

This means that Jenson picked 12 apples.

Answer:    B.12

Step-by-step explanation:

7v(4v2-8v+1)+8(4v2-8v+1)

28v3-56v2+7v+32v2-64v+8

Answer= 28v3 -24v2 -57v +8

Answer:

x-intercept (-8,0)

y-intercept (0,2)

Step-by-step explanation:

To find the x-intercept, you set y equal to 0.

Like this:

-2(0)+x=2(0)-8

  0  +x=0    -8

        x=   -8

So the x-intercept is (-8,0).

To find the y-intercept, you set x equal to 0.

Like this:

-2y+0=2y-8

  -2y =2y-8

Subtract 2y on both sides

 -4y=-8

Divide both sides by -4

   y=2

So the y-intercept is (0,2)

Answer:

O 30, 24, and 18

Step-by-step explanation:

18^2+24^2=30^2

324+576=900

Final answer:

Using the Pythagorean theorem, only the set of lengths 24, 7, and 26 satisfy the condition for a right triangle, as 24² + 7² equals 26².

Explanation:

The question seeks to determine which set of lengths can form a right triangle. When assessing whether a given set of three lengths can form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two shorter sides (the legs) is equal to the square of the length of the longest side (the hypotenuse). The formula for the Pythagorean theorem is a² + b² = c², where a and b are the lengths of the legs, and c is the length of the hypotenuse.

We will check each set of given lengths:

Therefore, the lengths that would form a right triangle are 24, 7, and 26.

ANSWER

alternate interior angles theorem

EXPLANATION

According to the alternate interior angles theorem, when two parallel lines are are intercepted by a straight line (transversal) the angles in the interior corners of a Z-shape pattern are congruent.

From the above diagram line r is parallel to line s, therefore

[tex] \angle \: 3 \cong \angle6[/tex]

and

[tex] \angle \: 4\cong \angle5[/tex]

because they are alternate interior angles.

See attachment for how to spot alternate interior angles.

Question:

Given that r||s and q is a transversal, we know that  by the [________].

Answer:

alternate interior angles theorem

Answer:

Step-by-step explanation:

1/5 + 1/5^-2

1/5 + 1/25

1/5 = 5*1 / 5*5

5/25 + 1/25

6/25 which cannot be reduced or changed.

Answer:

[tex]y=3x+8[/tex]

Step-by-step explanation:

Slope-intercept form is as follows:

[tex]y=mx+b[/tex]

In this equation, "m" represents your slope and "b" represents your y-intercept.

To convert your equation into slope-intercept form, distribute your 3 across your parentheses and then add 5 to both sides to isolate for y.

[tex]y-5=3(x+1)\\y-5=3x+3\\y=3x+8[/tex]

The correct equation for the given graph will be option A that is

y=[tex]x^{2} +9x+18[/tex]

It is a relationship between two variables and having a equal to sign in between.

Firstly we need to find the points of the respective equations.

y=[tex]x^{2} +9x+18[/tex]

y=[tex]x^{2}[/tex]+6x+3x+18

y=x(x+6)+3(x+6)

y=(x+3)(x+6)

Put  this equal to 0 and we get x=-3 and x=-6

y=[tex]x^{2} -2x+4[/tex]

It is a wrong equation.

y=(x-3)(x-6)

put this equal to 0 we get x=3 and x=6

Now we have to check in the graph whether points (-3,0)(-6,0) satisfies or (3,0)(6,0)

We can easily see that (-3,0)(-6,0) satisfies the graph.

Hence the correct equation is y=x2+9x+18

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