Name the property of equality or congruence that justifies going from the first statement to the second statement.

3x+x+7=23

4x+7=23

Answer:

transitive property

Step-by-step explanation:

Generally proofs flow naturally from one step to the next.  Consequently, each step usually follows from the previous step, and the Reason given justifies why that change is valid.

From statement 8, note that [tex]90^{o}=m\angle{ABD}[/tex]

For statement 9, the proof asserts that [tex]m\angle{ABC}=m\angle{ABD}[/tex]

What changed between line 8 and 9?  The left side of the equation lost it's 90 degrees, and it became the measure of angle ABC.

So, what justifies changing the 90degrees into a measure of an angle (specifically, the measure of angle ABC)?

Recall from statement 3, that [tex]m\angle{ABC}=90^{o}[/tex].

The "substitution property" would be a valid reason for step 9, (but of the given options, that isn't one, so we must look for another valid reason).

Recall that the transitive property states:

[tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

There are three parts,

1. the first part needs a=b

2. the second part needs b=c

3. the third part produces a=c

Notice that in the second part, b=c, and then for the third part, on the left side, the "b" disappears, and the "a" sort of appears out of nowhere.

Statement 8 is like the second part, and statement 9 is like the third part.

Replacing "a" with [tex]m\angle{ABC}[/tex], replacing "b" with [tex]90^{o}[/tex], and replacing "c" with [tex]m\angle{ABD}[/tex], we can update the transitive property and see how it applies to our situation:

Original transitive property:  [tex]\text{If }a=b\text{ and }b=c, \text{then }a=c[/tex]

Updated transitive property:  [tex]\text{If }m\angle{ABC}=90^{o}\text{ and }90^{o}=m\angle{ABD}, \text{then }m\angle{ABC}=m\angle{ABD}[/tex]

In order to use the transitive property, we need the first part and the second part to be true, and then it will be a valid reason for the last part to be true.  The first part was already proven back in statement 3, the second part was just proven in statement 8, so the conclusion (the third part) is valid and can be statement 9, because of the transitive property.

cranberry juice = 350 ml

blueberry juice = 2 liters = 2000 ml

Ratio of cranberry juice : blueberry juice = 350 : 2000 = 7 : 40

The simplest ratio is 7 : 40    or    7/40

Answer:

4x55x2

Step-by-step explanation:

4 kids 55trys 50 50 odds

Answer:

Answer:

(3*6) - (6/2) = 15

Step-by-step explanation:

3 and 6 are being multiplied by them selves, and then subtracted by the answer of 6/2.

The answer of the equation is 15.

Answer:

to be honest i don't know

Step-by-step explanation:

uh

Answer: its all

Step-by-step explanation:

it does not matter which one you pic, you just have to pick one.

Answer:

[tex]\mathrm{Slope=== > 0}[/tex]

Step-by-step explanation:

Hi student, let me help you out!

.............................................................................................................

First, let's recall the slope formula: [tex]\boxed{\mathrm{\cfrac{y2-y1}{x2-x1}}}}[/tex], where y2 and y1 are y-coordinates; x2 and x1 are x-coordinates.

Plugin the values: [tex]\mathrm{\cfrac{0-0}{-17-(-9)}}[/tex].

Upon simplifying, we obtain [tex]\mathrm{\cfrac{0}{-17+9}}[/tex].

Upon simplifying this further, we obtain [tex]\mathrm{\cfrac{0}{-9}}[/tex].

0 divided by anything results in 0.

✨ ∴, the slope of this particular line is 0, and this line looks something like this: [tex]\rule{200}{1}[/tex].

See, it's a horizontal line, with a rise of 0, meaning that it goes up 0 units.

Hope this helped you out! Ask in comments if even the slightest queries arise.

Best Wishes!

[tex]\star\bigstar\underline{\underline{\overline{\overline{\textsf{Reach far. Aim high. Dream big.}}}}}\bigstar\star[/tex]

[tex]\underline{\rule{300}{5}}[/tex]

The point F lies on 4.5 in the number line.

Number line is a One dimensional representation of point referring by a number only.

We know that if a point divides a line joining the points at x,y in the number line respectively in m:n ratio then that point lies on = (my+nx)/(m+n) in the number line.

Here in the give problem that,

Point D lies on -6 in number line

Point E lies on 8 in number line

And F lies between D and E points and DE:EF = 3:1

So the point F clearly divides the staright line DE joining the point D at -6 and E at 8 in 3:1 ratio.

So the point F lies on = (1*(-6)+3*8)/(3+1) = (-6+24)/4 = 18/4 = 4.5

Hence the point F lies on 4.5 in the number line.

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Answer: 4.5

Step-by-step explanation:

Answer:

y = (5/3)x + 4

Step-by-step explanation:

The general equation for slope-intercept form is:

y = mx + b

In this form, "m" represents the slope and "b" represents the y-intercept. Since you have been given both of these values, you can plug them into the formula to find your answer.

slope (m) = 5/3

y-intercept (b) = 4

y = mx + b

y = (5/3)x + 4

Answer:

no they did not make enough money

Step-by-step explanation:

Glass: 35 ×0.50 = 17.5

plastic: 50 × 0.25 = 12.5

aluminum: 22 × 0.75 = 16.5

17.5 + 12.5 + 16.5 = $46.5

The equation of the function is  F(x) = -3(x-4)² +4 , the correct answer is Option D

The missing graph is attached with the answer

A function is a law that relate the independent variable and the dependent variable.

It is given that

The graph of F(x), shown below, resembles the graph of G(x)= x², but it has been changed

From the graph, it is seen that,

G(x) when shifted by -4 on the negative x axis.

and graph shifted by +4 on the positive y axis.

F(x) is scaled by a factor of -⅓ of G(x)

it is reflected across the x-axis.

So the equation of the function is

F(x) = -3(x-4)² +4

Therefore ,  the correct answer is Option D.

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Answer:

B. Similar discs

Step-by-step explanation:

Definitions

Cone: A three-dimensional solid figure that has a circle at one end (the "base"), a point at the other end (the [tex]\sf a\:\!pex[/tex]), and a curved side.

Right Cone:  A cone where the [tex]\sf a\:\!pex[/tex] is aligned on the center of the base.

Oblique Cone:  A cone where the [tex]\sf a\:\!pex[/tex] is not centered over the base.

Horizontal Cross-section: The intersecting plane parallel to the base of the solid figure.

Congruent:  The same shape and size.

Similar:  When one shape can become the other after being resized, reflected, translated or rotated.

Disc: The region in a plane bounded by a circle.

Polygon: A two-dimensional closed shape with a minimum of 3 straight sides.

Therefore, the horizontal cross-sections of an oblique cone are similar discs.

12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.

An equation is an expression that shows the relationship between two or more variables and numbers.

It took 4 days for 4 butterflies to give birth to 4 larvae. After 4 days, each butterfly produces a larvae

Hence for 12 butterflies in 12 days:

number of larvae = 12 butterflies * (12 days /4 days per larvae) = 36 larvae

12 butterflies would give birth to 36 larvae in 12 days, if It took 4 days for 4 butterflies to give birth to 4 larvae.

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Answer: (0,1)

Step-by-step explanation:

If (x,y) lies on the graph of the original function, then (y,x) lies on the graph of the inverse.

Since (1,0) lies on the graph of h(x), (0,1) lies on the graph of its inverse.

(0, 1) point is on the graph of the inverse function h-¹(x).

Two functions f(x) and g(x) are inverses if their composition is equal to the identity.

Equation of line will be

y = -2x + 2 = h(x)

h⁻¹(x) will be calculated as:

x = -2y + 2

x - 2 = -2y

y = (2 - x)/2

So, y = h⁻¹(x) = (2 - x)/2

put x = 0 in the equation y = (2 - x)/2

y = 1

(0, 1) = (0, 1)

This, (0, 1) is the point on h⁻¹(x).

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Answer:

3/5x + 3 = 6

3/5x = 6 - 5

3/5x = 1

3/5x (5x) = 1* 5x

3 = 5x

3/5 = X

Answer:

0.00305 (rounded)

Step-by-step explanation:

this is a geometric sequence so the formula is

an=a×r×n-1

Answer:

all I know is the second on about world population in 2014 which was c

7•10⁹

Answer:

B

B

Step-by-step explanation:

there are 9 steps for the second question so it 10^9

and if you times the 1st population size by 20 you get very close to the second population size.

Step-by-step explanation:

Let simplify the identity

[tex] \frac{ \csc {}^{2} (x) - \sec {}^{2} (x) }{ \csc {}^{2} (x) + \sec {}^{2} (x) } [/tex]

[tex] \frac{ \frac{1}{ \sin {}^{2} (x) } - \frac{1}{ \cos {}^{2} (x) } }{ \frac{1}{ \sin {}^{2} (x) } + \frac{1}{ \cos {}^{2} (x) } } [/tex]

Combine Like Fractions

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

Multiply by reciprocals.

[tex] \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \sin {}^{2} (x) \cos {}^{2} (x) } \times \frac{ \cos {}^{2} (x) \sin {}^{2} (x) }{ \sin {}^{2} (x) + \cos {}^{2} (x) } [/tex]

Pythagorean Identity

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

Double Angle Identity

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

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

Now, we need to find cos 2x. Given that we have tan x.

Note that

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

So let find cos x and tan x.

We know that

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

We know that

[tex] \tan(x) = \frac{o}{a} [/tex]

[tex] \sin(x) = \frac{o}{h} [/tex]

[tex] \cos(x) = \frac{a}{h} [/tex]

So naturally,

[tex] \tan(x) = \frac{ \frac{o}{h} }{ \frac{a}{h} } = \frac{o}{a} [/tex]

So we need to find the hypotenuse,

remember Pythagorean theorem.

[tex]h {}^{2} = {o}^{2} + {a}^{2} [/tex]

Here o is 1

h is root of 5.

So

[tex] {h}^{2} = {1}^{2} + ( \sqrt{5} ) {}^{2} [/tex]

[tex] {h}^{2} = 1 + 5[/tex]

[tex] {h}^{2} = 6[/tex]

[tex]h = \sqrt{6} [/tex]

Now, we know h, let plug in to find sin x and cos x.

[tex] \sin(x) = \frac{1}{ \sqrt{6} } [/tex]

[tex] \cos(x) = \frac{ \sqrt{5} }{ \sqrt{6} } [/tex]

Let's find these values squared

[tex] \sin {}^{2} (x) = \frac{1}{6} [/tex]

[tex] \cos {}^{2} (x) = \frac{5}{6} [/tex]

Finally, use the trig identity

[tex] \frac{5}{6} - \frac{1}{6} = \frac{2}{3} [/tex]

So part I.= 2/3

ii. Use the definition of sine and cosine and Pythagorean theorem

Let sin x= o/h

Let cos x= a/h.

So

sin x squared is

[tex] \sin {}^{2} (x) = \frac{o {}^{2} }{h {}^{2} } [/tex]

[tex] \cos {}^{2} (x) = \frac{ {a}^{2} }{h {}^{2} } [/tex]

By definition,

[tex] \frac{ {o}^{2} }{ {h}^{2} } + \frac{ {a}^{2} }{h {}^{2} } = 1[/tex]

[tex] \frac{ {o}^{2} + a {}^{2} }{h {}^{2} } = 1[/tex]

Remember that

[tex]{ {o}^{2} + {a}^{2} } = {h}^{2} [/tex]

So

[tex] \frac{ {h}^{2} }{h {}^{2} } = 1[/tex]

[tex]1 = 1[/tex]

Answer:

it’s correct

Step-by-step explanation:

Answer:

[tex]\fbox {See below} \downarrow[/tex]

Step-by-step explanation:

When taking the perpendicular of the line, it should be done at the midpoint of the line. Hence, by taking arcs from both endpoints, it should be done. This is why this is incorrect.

Answer:

A. All squares are rectangles because both are quadrilaterals, have 90-degree angles and the opposite sides are parallel.

Step-by-step explanation:

This is the only true statement because all squares are rectangles just with equal sides, the angles will always be 90-degrees.

Hope this helps!

If not, I am sorry.

Answer:

x=12

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

12-1 is 11 and than 9 times 1 is 9

Answer:

0.4 bottles can be filled

Step-by-step explanation:

divide the amount that is present by the max amount

the bottle can only hold 5.55 millimeters; therefore the max amount would be 5.55 millimeters.

the amount that is present is 2.22 millimeters.

[tex]\frac{222 millimeters}{555 millimeters} = 0.4[/tex]

0.4 bottles

if the given values are 555 and 222 then the answer is still .4

Answer:

0.4 bottles can be filled

Answer:

103mm or 53mm

Step-by-step explanation:

--A------B------C--

AB=78mm BC=25mm AC=AB+BC=103mm

--A----C---B---

AB=78mm BC=25mm AC=AB-BC=53mm

-B---A---C-

is impossible because BA<BC but 78mm>25mm

Answer:

-2x³ - 7x².

Step-by-step explanation:

- (4x³ + x²) + 2(x³ - 3x²)

= - 4x³ - x² + 2x³ - 6x²    Simplifying like terms:

= -2x³ - 7x².

Answer:

The last option that starts with (1,-1)

Answer:

The shelter can house 17 cats because

17 < 28.

Step-by-step explanation:

We cannot have fractions of cats, and we cannot have a negative number of cats. So the third statement is reasonable because c < 28.

Answer:

[tex]\frac{13}{33}[/tex]

Step-by-step explanation:

we require 2 equations with the repeating digits placed after the decimal point.

let x = 0.3939.... (1) ← multiply both sides by 100

100x = 39.3939... (2)

subtract (1) from (2) thus eliminating the repeating digits

99x = 39 ( divide both sides by 99 )

x = [tex]\frac{39}{99}[/tex] = [tex]\frac{13}{33}[/tex] ← in simplest form

Step-by-step explanation:

0.39 repeating as a fraction

= 13/33

Answer:

is it radius or diameter?

Answer:

Basically find the unit rate by doing 3.99/24 = $0.16625/1oz

1 quart = 32 ounces so 4.8/32 = $0.15/1oz

1 gallon = 153.722 ounces so 11/153.722 = 0.07

49.6/768.61 = 0.06

Step-by-step explanation:
D.