For what value of x do expressions 2x+3 and 3x-6 have the same value?

Answer:

Step-by-step explanation:

Problems like these are aided immensely by your knowledge of multiplication tables.

1) 36 = 1·36 = 2·18 = 3·12 = 4·9 = 6·6

  27 = 1·27 = 3·9

The greatest common factor is 9, so the sum can be written as 9(4+3).

__

2) 45 = 1·45 = 3·15 = 5·9

  25 = 1·25 = 5·5

The greatest common factor is 5, so the sum can be written as 5(9+5).

__

3) 16 = 1·16 = 2·8 = 4·4

  72 = 1·72 = 2·36 = 3·24 = 4·18 = 6·12 = 8·9

The greatest common factor is 8, so the sum can be written as 8(2+9).

Answer:

1/2

Step-by-step explanation:

The y-intercept is [tex]\frac{1}{2}[/tex].

Given that f(x) = 4x-2.

To find the inverse function:

1) Write f(x) = y

2) Switch x and y.

3) Solve for y.

4) Write [tex]y=f^{-1}\left(x\right)[/tex].

So,

[tex]f(x) = 4x - 2\\y=4x-2\\x=4y-2\\4y=x+2\\y=\frac{\left(x+2\right)}{4}\\y=\frac{1}{4}x+\frac{2}{4}\\y=\frac{1}{4}x+\frac{1}{2}\\f^{-1}\left(x\right)=\frac{1}{4}x+\frac{1}{2}[/tex]

Comparing this with y=mx+b,

b = y-intercept = [tex]\frac{1}{2}[/tex]

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Answer:

80

Step-by-step explanation:

50*2= b  b/2=40 40+10=50

Answer: 20 pencils and 80 cards

Step-by-step explanation:

Answer:

-1/3

Step-by-step explanation:

it goes down one and over three

Answer: your slope would be -[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

The solution of given inequality is: [tex]x>-3[/tex]

Solution:

Given inequality is:

[tex]7(x+1)>-14[/tex]

We have to find the value of "x"

Let us solve the given inequality

Divide both sides of inequality by 7

[tex]\frac{7\left(x+1\right)}{7}>\frac{-14}{7}\\[/tex]

Simplify the above expression

[tex](x+1)>-2[/tex]

[tex]x+1>-2[/tex]

[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides\: of\: inequality}[/tex]

[tex]x+1-1>-2-1\\\\x>-3[/tex]

Thus the value of x is [tex]x>-3[/tex]

The height of the branch is 9.54 ft

Step-by-step explanation:

Apply Pythagorean relationship in this question where the length of the ladder is the hypotenuse, and the distance from the tree base is the shortest side.Finding the height will be;

a²+b²=c²

a²+3²=10²

a²=10²-3²

a²=100-9

a²=91

a=√91=9.54 ft

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Keywords: cat, stuck, tree. rescue,base, ladder, height , branch

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Answer:

-4

Step-by-step explanation:

6 times 4 equals 24

24 minus 12 equals 12

12 divided by 3 equals 4

4 minus 8 equals -4

(btw i did this in the order from the question and not BIDMAS )

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Answer:

53/50

Step-by-step explanation:

The ratio of males to females is 53:50.

A ratio is a comparison between two amounts that is calculated by dividing one amount by the other. The quotient a/b is referred to as the ratio between a and b if a and b are two values of the same kind and with the same units, such that b is not equal to 0. Ratios are represented by the colon symbol (:). As a result, the ratio a/b has no units and is represented by the notation a: b.

Given:

Number of baby boys = 106

Number of baby girls = 100

So, the ratio of males to females

= 106/100

= 53/50

Hence, the ratio of males to females is 53:50.

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Answer:

B. SSS

Step-by-step explanation:

All of the sides are the same

SSS postulate proves that the two triangles are congruent.

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

Given:

From the figure we have two triangles named as FED and CBA

Now, In triangles FED and CBA

FE = AC

ED = BA

FD = BC

So, by SSS Congruency Criteria triangles FED and CBA are Congruent.

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The factors of given expression are: -5 and 3/4

Step-by-step explanation:

Given equation is:

[tex]4x^2+17x-15[/tex]

Making pairs for the mid-term 17x by factoring the product of co-efficient of 4x^2 and 15

[tex]4x^2+20x-3x-15[/tex]

[tex]= 4x(x+5) - 3(x+5)[/tex]

[tex]=(4x-3)(x+5)[/tex]

Now

[tex]4x-3 = 0\\4x = 3\\x = \frac{3}{4}[/tex]

[tex]x+5 = 0\\x = -5[/tex]

Hence,

The factors of given expression are: -5 and 3/4

Keywords: Quadratic equation, factors

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Answer:

  480

Step-by-step explanation:

Let h represent the number of high-quality downloads. Then the total download size is ...

  4.1h +2.7(1130-h) = 3723

  1.4h = 672 . . . . . . . . . . . . . . subtract 2.7·1130 = 3051

  h = 480 . . . . . . . divide by 1.4

There were 480 downloads of the high-quality version.

The complete question is:

A geometric sequence is defined recursively by

    [tex]a_{(1)}=40\text{ and }a_n=(-1/2)a_{(n-1)}[/tex]

(a) Write out the first four terms of this sequence.

(b) Is the 9th term of this sequence larger or smaller than 1/10? Show the calculation that you use to determine your answer.

Answer:

Explanation:

You are given the first term,    [tex]a_(1)=40[/tex] , and the recursive formula

   [tex]a_{(n)}=(-1/2)a_{(n-1}[/tex]

Thus, you can find the sequence of terms by multiplying each term by the constant ratio, (-1/2).

(a) First four terms of the sequence

[tex]a_{(1)}=40\\ \\ a_{(2)}=40\times (-1/2)=-20\\ \\ a_{(3)}=-20\times (-1/2)=10\\\\ a_{(4)}=10\times (-1/2)=-5[/tex]

Those are the first four terms.

(b) 9th term

You can write the explicit formula of the sequence as:

[tex]a_{(n)}=a_{(1)}\times r^{(n-1)}\\ \\ a_{(n)}=40(-1/2)^{(n-1)}[/tex]

Thus, for the 9th term, n = 9, and the term is:

[tex]a_{(9)}=40\times (-1/2)^{(9-1)}\\ \\ a_{(9)}=40\times(-1/2)^8\\ \\ a_{(9)}=40\times(1/256)=0.1526[/tex]

Since 1/10 = 0.1, and 0.1 < 0.1526, the 9th term is larger than 1/10.

Answer:

36

Step-by-step explanation:

If you see this kind of problem do this two steps:

1. Multiply the numerator and the multiplier.

2. Divide the result with the denominator.

[tex]\frac{3}{10}[/tex] × 120

3 × 120 = 360 (STEP 1)

360 ÷ 10 = 36 (STEP 2)

Answer:

36

Step-by-step explanation:

Final answer:

Calculating the least common multiple (LCM) of 3 and 5 to determine that 6 students will receive both a medal and a ribbon at a swim meet of 100 students.

Explanation:

To find the number of students at the swim meet who will receive both a medal and a ribbon, we need to look for the common multiples of 3 and 5, as medals are given to every 3rd finisher and ribbons to every 5th finisher. The least common multiple (LCM) of 3 and 5 is 15, which means every 15th student will receive both a medal and a ribbon. Since there are 100 students, we simply divide 100 by 15 and then take the integer part of the result, because we can't have a fraction of a person.

100 ÷ 15 equals approximately 6.66. The integer part is 6, which means 6 students will receive both a medal and a ribbon.

See the graph below

We need to remember the following rules:

[tex]For \ any \ function \ f(x) \ we have: \\ \\ \\ \bullet \ g(x)=f(x-k) \ Translation \ k \ units \ to \ the \ right \\ \\ \bullet \ g(x)=f(x+k) \ Translation \ k \ units \ to \ the \ left \\ \\ \bullet \ g(x)=f(x)+c \ Translation \ c \ units \ up \\ \\ \bullet \ g(x)=f(x)-c \ Translation \ c \ units \ down \\ \\ With \ c>0 \ and \ k>0[/tex]

Here we know that The function y = log (x) is translated 1 unit right and 2 units down, so:

[tex]k=1 \\ \\ c=2 \\ \\ \\ Finally: \\ \\ g(x)=log(x-1)-2[/tex]

Below you can see the graph. The red one is the original function while the blue one is the translated one.

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Answer:

B

Step-by-step explanation:

Took test on edge

Answer:

[tex]z=12[/tex]

Step-by-step explanation:

The lines a and b intersect at point D. Angles with measures [tex](5z+8)^{\circ}[/tex] and [tex](4z+20)^{\circ}[/tex] are vertical angles.

Vertical angles theorem states that vertical angles, angles that are opposite each other and formed by two intersecting straight lines, are congruent.

Congruent angles have equal measures.

Hence,

[tex]5z+8=4z+20\\ \\5z-4z=20-8\\ \\z=12[/tex]

Answer:

12

Step-by-step explanation:

Answer:

0,1 is greater because...

Answer:0,1

Step-by-step explanation:

Answer:

The percent (relative) change is 7.14 percent (%).

Step-by-step explanation:

We are given that the original support value is at 42%.

Then the support increased by 3%, to reach 45%.

We want the Percentage Change (i.e. relative) change of this increase, which can be computed as:

[tex]\frac{X_{F}-X_{O}}{X_{O}}*100[/tex]

where [tex]X_{F}[/tex] is the final value reached

           [tex]X_{O}[/tex] is the original value

So plugging in our known values and computing we have:

[tex]\frac{45-42}{42}*100= \frac{3}{42}*100 = 0.071428*100=7.14[/tex] percent increase.

Now lets go back and check if we are correct.

[tex]42+42\frac{7.14}{100}=42+2.9988=42+3=45[/tex]

So it works!

Answer:

11.5

Step-by-step explanation:

(11+12)/2=11.5

Answer: 8/5 or 1 ⅗ acres

Step-by-step explanation:

Answer:

[tex]AB=\sqrt{3}\ in[/tex]

Step-by-step explanation:

The correct question is

The diagonal of rectangle ABCD measures 2 inches in length.

What is the length of line segment AB?

The picture of the question in the attached figure

we know that

In the right triangle ABD

[tex]cos(30^o)=\frac{AB}{BD}[/tex] ----> by CAH (adjacent side divided by the hypotenuse)

substitute the given values

[tex]cos(30^o)=\frac{AB}{2}[/tex]

Remember that

[tex]cos(30^o)=\frac{\sqrt{3}}{2}[/tex]

so

[tex]\frac{AB}{2}=\frac{\sqrt{3}}{2}[/tex]

[tex]AB=\sqrt{3}\ in[/tex]

Answer:

B

Step-by-step explanation:

the answer is B on edge.

Answer:

π = a/(r²) = a÷(r²)

Answer:

pie is equal to the square root of A divided by r

Step-by-step explanation:

Set the equation first...a=pie times r squared. Then u need to get rid of everything to make pie by itself. U square both sides or all the equation. the square cancels out and on the other side, it will be the square root of a. Next, divide by r on each sides. The r cancels out. Then it's gonna be pie =the square root of a all over r. It can't be a/r square because in the original...pie is being multiplied by r which is squared so that means both variables are squared. U cant find pie if the square is stopping it so u square for the very first step

Answer:

2.339×10^3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10

If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

2.339×10^3

Answer:

So she need [tex]\frac{5}{36}\ cups[/tex] more to put in.

Step-by-step explanation:

Given:

Recipe for cookies calls for 3 1/4 cups of sugar.

Amy has already put three and one nine cups.

Now, to find the number of cups she need to put in.

Number of cups of sugar for recipe calls = [tex]3\frac{1}{4} =\frac{13}{4}\ cups.[/tex]

Amy has already put = [tex]3\frac{1}{9} =\frac{28}{9}\ cups.[/tex]

So, to get the number of cups she need to put in we subtract number of cups of sugar for recipe calls from number of cups of sugar for recipe calls:

[tex]\frac{13}{4} -\frac{28}{9}[/tex]

Subtracting by taking the same denominator:

[tex]=\frac{117-112}{36}[/tex]

[tex]=\frac{5}{36}[/tex]

Therefore, so she need [tex]\frac{5}{36}\ cups[/tex] more to put in.

the graphs picture is not provided (incomplete question. explanation:

Answer:bar graphs and pie charts

Step-by-step explanation:

edge 2021

Answer:

-50/7

Step-by-step explanation:

-7 1/7=-50/7

Because 7*7+1=49+1=50, and don't forget the negative sign.

Since you know the value of n = 3, plug in 3 for n in the equation

4(n + 1)

4(3 + 1)      

4(4)

= 16

Answer:

B. right

Step-by-step explanation:

In the bottom left corner there is a square. The square represents a 90 degree angle. A 90 degree angle is named a right angle.