Drag a statement or reason to each box to complete this proof.



If −3(x+8)=−21, then x=−1.

(Please refer to attached image for more info.)

Answer:

See below

Step-by-step explanation:

Next step is to gather 'like' terms

-x2 - 4x -3 = 2x + 5.

x^2 + (4x + 2x)   + (3+5)    = 0       then simplify

x^2 + 6x + 8     = 0        then factor

(x+4)(x+2) = 0  

so either of these terms = 0

x+4 = 0    means   x = -4

x+ 2 = 0 means  x = - 2          

Answer:

d

Step-by-step explanation:

Combine like terms onto one side of the equation.

Answer:

x = 34

Step-by-step explanation:

A straight line is 180 degrees

We can sum angles to form a straight line

x+12 + 100 +x = 180

Combine like terms

2x+112 = 180

2x+112-112 = 180-112

2x = 68

Divide each side by 2

2x/2 = 68/2

x = 34

answer:

=x+12+100+x =180

=x+x+12+100=180

=2x+112=180

=2x=180-112

=2x=68

=2/2x=68/2

=x=34

The area of victor's storage space is 28 square inches

A polygon is a plane shape with at least three sides.

Analysis:

Area of storage = area of triangle + area of rectangle

Height of triangle = 5 - 3 = 2 inches

Base of triangle = 12 - 4 = 8 inches

length of rectangle = 5 inches

width of rectangle = 4 inches

Area of storage = 5 x 4 + 1/2 x 8 x 2 = 28 square inches

In conclusion, the area of the storage space is 28 square inches.

Learn more about polygon: brainly.com/question/1592456

#SPJ1

Answer:

25

Step-by-step explanation:

Because 100 25+25+25+25 or 25/1/4

Answer:

A 3 and 8

Step-by-step explanation:

if a/b=c/d, the extremes are "a" and "d". The means would then be "b" and "c"

The extremes of the proportion are 3 and 8.

To find the extremes of a proportion, we need to identify the numbers that are positioned at the far ends of the proportion. In the given proportion:

3/4 = 6/8

The numerator of the first fraction, 3, and the denominator of the second fraction, 8, are the extremes. These numbers form the far ends of the proportion.

Therefore, the extremes of the proportion are 3 and 8.

Learn more about proportion click;

https://brainly.com/question/31548894

#SPJ7

Answer:

-11 < x < 7

(first option listed)

Step-by-step explanation:

we know that x² + 4x < 77

first, we should rewrite our expression in standard

x² + 4x - 77 < 0

factor {find two numbers that multiply to c (77) and add to b (4)  }

(x - 7) (x + 11) < 0

set both roots to 0:

x - 7 < 0

  + 7  + 7

x < 7

x + 11 < 0

x > -11

so, x will be < 7 and > -11

which can be expressed as

-11 < x < 7

So, -11 < x < 7

Answer:

-11 < x < 7

Step-by-step explanation:

1st option;

Answer:

B. $5.20

Step-by-step explanation:

18 decrease 20% =

18 × (1 - 20%) = 18 × (1 - 0.2) = 14.4

14.4 increase 8.25% =

14.4 × (1 + 8.25%) = 14.4 × (1 + 0.0825) = 15.588

15.588/3 = 5.196

Answer:

DEF

Step-by-step explanation:

it is mathematically similar as the sides have a scale factor of 4

Answer:

The size of the angle is between 180 and 360*. I cannot say the exact angle but my guess is correct and the correct answer is in between the 2 numbers.

Step-by-step explanation:

Answer:

0.5774

Step-by-step explanation:

1) Input tan(30) into a calculator to get 0.5773502692...

2) To count 4 decimal places, we start after the decimal point. This means that we end it at the first 3. Additionally, we round 3 up to 4 because of the digit after it which is 5.

[tex]\Large\maltese\underline{\textsf{Our problem:}}[/tex]

What is the tangent of 30, rounded to 4 decimal places?

.

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

First, let's focus on this phrase - "tan 30"

.

What in the world could that possibly mean?

"tan" is the tangent, which is one of the six trig ratios.

.

The simplest way to find the tangent of 30 degrees is ... with a calculator!

[tex]\bf tan\quad 30 \approx 0.5774[/tex]

The answer has been rounded to 4 decimal places, like you asked.

Since the fifth decimal place was more than 5, I added 1 to the fourth decimal place - 0.5774, and not 0.5773.

[tex]\rule{300}{1.7}[/tex]

[tex]\bf tan 30\approx 0.5574. \quad Hope\;you\;will\;have\;a\;fantabulous\;day![/tex]

~ [tex]\boxed{\bf aesthetic\;\not{101}}[/tex]~

Answer:

6/- 3

Step-by-step explanation:

Answer: In between the red and yellow ribbons

Step-by-step explanation:

When something is rotated 180 degrees, you basically just mirror it. Since this pinwheel has an uneven amount of ribbons, there isn't a ribbon opposite of it, so it would be between red and yellow.

Answer:

15 (second option listed)

y = 15

x = 30

Step-by-step explanation:

setting up this statement algebraically:

[where x = one of our numbers, y = other number]

x + y = 48

x = (2y + 3)

x = 2y + 3

plug x [now in terms of y] into the original equation

(2y + 3) + y = 48

3y  + 3 = 48

  - 3        - 3

3 y = 45

÷3       ÷3

y = 15

from this value, we can plug it back into the y-value of the original equation to find our x-value

x + y = 48

x + 15 = 48

  - 15    - 15

x = 33

{to check: 33 is 2y + 3}

we know that y = 15 (smaller number) and that x = 33 (larger number)

so, the solution to the question of which is the smaller number is 15

Answer:

2 times a number more than 4

Answer:B

Step-by-step explanation:

Step-by-step explanation:

eq of a circle is

(x-h)^2+(y-k)^2=r^2

h is 0

k=3

r is 1.5 this is radius of the circle

x^2+(y-3)^2=1.5^2

The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.

The triangle is having three sides in an isosceles triangle the two opposite sides are equal and the two adjacent angles with similar sides are equal.

The isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent.

Therefore the isosceles triangle theorem states that if two sides of a triangle are congruent then the angles opposite those sides are congruent. The correct answer is option c.

To know more about the Isosceles triangle follow

https://brainly.com/question/1475130

#SPJ1

Refer to the figure given below while reading the solution.

Suppose the dog reaches position A when traveled 10 m diagonally towards the opposite side.

And then position B when traveled 5 m towards the right turning 90°.

We can observe that APC is a right triangle with legs of equal length AC. And the coordinates of the point A is (AC, AC).

Also we can observe that APB is a right triangle with legs of equal length AD. Then the coordinates of the point D is (AC, AC-AD).
Hence, the coordinates of B will be (AC+AD, AC-AD).

Now, we since we have the coordinates we can calculate the shortest distances of B from each of the sides.

So, the average of the shortest distances of B from each side is [tex]\frac{(AC-AD)+44-(AC-AD)+(AC+AD)+44-(AC+AD)}{4}=\frac{44+44}{4}=22[/tex]

Hence, the average of the shortest distance of B from each side is 22 m

Learn more about average here-

brainly.com/question/24057012

#SPJ10

Answer:

can you write these in proper way

A linear inequality that is represented by the graph include the following: C. y > 2/3(x) + 3.

In Mathematics, there are two (2) main rules that are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph and these include the following:

here, we have,

The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).

The line on a graph should be a dashed (dotted) line when the inequality symbol is (> or <).

The line on a graph should be shaded above the line when the inequality symbol is (>).

Since the line on this graph was shaded above the line and it passes through the point (0, 3), it ultimately implies that 3 is part of its solution and as such, it is represented by this inequality equation:

y > 2x/3 + 3.

Read more on inequality here:

brainly.com/question/27976143

#SPJ5

The interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

The complete question is

A survey conducted by Conquest Communications Group randomly sampled 700 registered voters in the U.S. 258 of the 700 sampled voters correctly answered that fourth graders in the U.S. are above average for overall education compared to other countries.

Choose a number between 80 and 96. This is the level of confidence you will use for this section of problems. What is your number?

It is defined as the margin by which the values calculated will differ from the real values .

Let the chosen number is 95  %

95% Confidence Interval ,

[tex]\rm p = p \pm \dfrac{Z_{0.05}}{2} \sqrt \dfrac{p(1-p)}{n}}\\\\= \dfrac{258}{700} \pm 1.96 \sqrt \dfrac{\dfrac{258}{700}(1-\dfrac{258}{700})}{700}}\\[/tex]

Therefore p at 95% Confidence Interval is given by 0.3329 , 0.4043

The margin of error is given by  0.4043-0.3329

= 0.0357

Therefore the interval of probability at the confidence interval is 95% is 0.3329 , 0.4043 and the margin of error is 0.0357.

To know more about Margin of Error

https://brainly.com/question/10501147

#SPJ1

Answer:

1:(1/6) where n = 1/6

The equation formed by the given condition is 960.5 + 35.75p ≤ 1818.50 and the number of players they can bring is a maximum of 24.

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

Given that,

The total amount that can be spent = $1818.50

Rent of bus = $960.50

Cost per player = $35.75/player

So,

Cost of bus + Cost per player × number of players ≤ The total amount that can be spent

960.50 + 35.75p ≤ 1818.50

35.75p ≤ 858

p ≤ 24

Hence "The equation formed by the given condition is 960.5 + 35.75p ≤ 1818.50 and the number of players they can bring is a maximum of 24".

For more about the equation,

https://brainly.com/question/10413253

#SPJ2

Equation:

Step-by-step explanation:

No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.

The equivalent is the expressions that are in different forms but are equal to the same value.

Then the equation is given below.

-11(x - 2) = 8

By simplifying, we have

x - 2 = - 8 / 11

No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.

More about the equivalent link is given below.

https://brainly.com/question/889935

#SPJ1

The last  equation h(x) = 2x+4/x+1.

The pictorial representation of quantities and how the increase or decrease in one affects the other.

Analysis:

The graph cuts the x-axis and y-axis at (-2, 0) and(0, -4) respectively.

gradient of the curve = y2 - y1/x2 - x1 = -4-0/0--2 = -4/2 = -2.

The equation with a gradient equal to -2 is, h(x) = 2x+4/x+1

differentiating the equation by quotient rule,

u = 2x+4, du/dx = 2, v = x+1 dv/dx = 1

dy/dx = [tex]\frac{(x+1)(2) - (2x+4)(1)}{(x+1)^{2} }[/tex] = [tex]\frac{-2}{(x+1)^{2} }[/tex]

When x = -2, dy/dx = -2

In conclusion, 2x+4/x+1 is the equation for the curve above.

Learn more about parabolic curves: brainly.com/question/12896871

#SPJ1

Answer:

julie

Step-by-step explanation:

12 x 4 +=48

19x 6 = 114

Answer:

Un= 1 + (n-1)4

Step-by-step explanation:

a=1

d=5-1=9-5=4

using the formula Un=a+(n-1)d

8.46 be located between 8.45 and 8.47 on a number line.

A number line is a horizontal line that has equally unfolded range increments. The numbers protected on the line will determine how the wide variety on the road may be responded to. The query that goes with the wide variety determines how it will likely be used, as an instance, in plotting a point.

Numbers on various lines include all sets of numbers namely natural and complete numbers. An instance of a fixed of entire numbers is:(0, 1, 2, 3,5,6 …….) while the natural numbers consist of:1, 2, 3, four, five, 6…. a number of lines consists of 3 basic elements. within the center, the starting place is commonly plotted with 0.

Learn more about the number line here: https://brainly.com/question/24644930

#SPJ10

Answer:

33.3333%

Step-by-step explanation:

Total number of kg- 2+3=5

Total money- (2×8)=16

(3×6)=18

16+18=34

$34=5000g

=250g

(250×$34)÷5000=$1.7

profit-2.55-1.7=0.85

(0.85/2.55)×100=33.333%

Answer:

x ≈ 12.182

Step-by-step explanation:

1 - 2lnx = - 4 ( subtract 1 from both sides )

- 2lnx = - 5 ( divide both sides by - 2 )

lnx = 2.5

x = [tex]e^{2.5}[/tex] ≈ 12.182 ( to the nearest thousandth )

Answer:

x = 12.182  (nearest thousandth)

Step-by-step explanation:

Given equation:

[tex]1-2 \ln x=-4[/tex]

Subtract 1 from both sides:

[tex]\implies 1-1 -2 \ln x =-4-1[/tex]

[tex]\implies -2 \ln x=-5[/tex]

Divide both sides by -2:

[tex]\implies \dfrac{-2 \ln x}{-2}=\dfrac{-5}{-2}[/tex]

[tex]\implies \ln x = \dfrac{5}{2}[/tex]

[tex]\textsf{As }\: \ln x=\log_ex \:\:\textsf{}[/tex], the natural logarithm can be canceled by giving both sides a base of e (Euler's number):

[tex]\implies e^{\ln x}= e^{\frac{5}{2}[/tex]

[tex]\implies x= e^{\frac{5}{2}[/tex]

[tex]\implies x=12.182\:\: \sf (nearest\:thousandth)[/tex]