By what percent will the product of two numbers decrease if one of them is decreased by 20% and the other is decreased by 60%?

Answer:

height = 5

Step-by-step explanation:

If area = (1/2)bh, the equation would be 25 = (1/2)10h.

The first step I'd do is multiply both sides by 2 to get rid of the (1/2). So, now the equation is 50 = 10h.

Divide both sides by 10, and you get h = 5! :D

Answer:

Step-by-step explanation:

Given:

A= 25

b=10

Find the height:-

[tex]\sf A=0.5\:bh[/tex]

[tex]\sf 25=0.5(10)h[/tex]

[tex]\sf 25=5h[/tex]

[tex]\sf 5h=25[/tex]

[tex]\sf \cfrac{5h}{5}=\cfrac{25}{5}[/tex]

[tex]\sf h=5[/tex]

Hope it helps!

Answer:

I think its -120m

Step-by-step explanation:

Coz negatives are less than positives

Answer:

2

Step-by-step explanation:

Since the 3's are the same on either side, you need to find a number that, when multiplied by 9, yields 18. The only number that satisfies that is 2, which is the answer. Hope this helps!

Answer:

Below.

Step-by-step explanation:

The y-intercept of the graph is at (0, 8)

Plugging in x = 0 we get  y = -4/3 * 0 + 8 = 8.

So we can mark 2 points on the graph paper.

One is at (0, 8).

If we let x = 3 then y = -4/3 * 3 + 8

y = -4 + 8

y = 4.

So our second point is at (3, 4)

We draw a line through these 2 points to get our graph.

Answer:

See below in bold.

Step-by-step explanation:

(x - 1)(x^2 + 1)

= x(x^2 + 1) - 1(x^2 + 1)

= x^3 + x - x^2 - 1

= x^3 - x^2 - x - 1.

Leading coefficient = 1.

Constant term = -1.

Degree = 3.   (because of the x^3).

If the algebraic expression is (x - 1)(x² + 1). The leading coefficient is 1, the constant term is -1 and the degree is 3. Option A is correct.

It is defined as the combination of constants and variables with mathematical operators.

It is given that the expression is,

(x - 1)(x² + 1)

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

=(x - 1)(x²+ 1)

= x(x² + 1) - 1(x² + 1)

= x³ + x - x² - 1

= x³ - x² - x - 1.

From the expression the obtained result is,

Leading coefficient = 1

Constant term: -1

Degree: 3

Thus, if the algebraic expression is (x - 1)(x² + 1). The leading coefficient is 1, the constant term is -1 and the degree is 3. Option A is correct.

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Answer:

Ernie has a greater range

The statement "the medians are equal" is true for the given table of data about playing a game by Ernie and Lori. This is obtained by calculating the mean, median, mode, and range of the data elements of each.

Given data sets for Ernie and Lori as follows:

Ernie: {18, 24, 17, 19, 17} and Lori: {16, 22, 18, 14, 18}

The number of elements in both the data sets is equal and it is 5

Calculating Mean:

For Ernie: {18, 24, 17, 19, 17}

Mean=(18+24+17+19+17)/2

        =19

For Lori: {16, 22, 18, 14, 18}

Mean=(16+22+18+14+18)/2

        =17.6

Thus, their "means are not equal". (3rd statement is false)

Calculating Median:

For Ernie: {18, 24, 17, 19, 17}

Re-arranging the data - 17, 17, 18, 19, 24

Since n=5 (odd), then the median is at (5+1)/2 th term i.e., 3rd term

So, the median is 18

For Lori: {16, 22, 18, 14, 18}

Re-arranging the data - 14, 16, 18, 18, 22

Since n=5 (odd), then the median is at (5+1)/2 th term i.e., 3rd term

So, the median is 18

Thus, their "medians are equal". (first statement is true)

Calculating Mode:

The most occurring number in Ernie: {18, 24, 17, 19, 17} is 17 and

The most occurring number in Lori: {16, 22, 18, 14, 18} is 18

Thus, their modes are not equal, and "Lori has the greater mode".

(4th statement is false)

Calculating Range:

The range for Ernie's data set is 24 - 17=7

The range for Lori's data set is 22 - 14=8

Thus, their ranges are also not equal but "Lori has the greater range".

(2nd statement is false).

Therefore, 1st statement - " the medians are equal" is true.

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Answer:

<ADC = 131

Step-by-step explanation:

< ADC = <ADB + < BDC

The large angle is the sum of the two smaller angles.

<ADC = 89+42

          =131

Answer:

131 degrees

Step-by-step explanation:

The reason for, is since <ADC is equal to < ADB + <BDC and that we already know the values of <ADB and <BDC, we can simply do

89 + 42 = 131.

So, <ADC is 131 degrees.

:)

Answer:

7.38

Step-by-step explanation:

Answer:

A) Median: 7

Mode: 8

Range: 5

B) Tyler is wrong, the greater the MAD value, the greater the variability

Step-by-step explanation:

A) Given the data set: 4,6,6,7,7,8,8,8,9

The median is 7 (the middle point in the ordered list)

The mode is 8 (the most repeated number)

The range is 5 (the difference between the highest and lowest values)

A set of data will not always have a mode.

A mode is defined as the value that appears the most often in a set.

For instance, a set of 1, 2, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 6 would have a mode of 4, as it appears more often than any other number in the set.

However, a set of 1, 2, 3, 4, 5, 6 has no mode as there is no number that appears more than other numbers in the set.

Answer:

(x + y)(x² - xy + y²)(x + 1)

Step-by-step explanation:

Given

[tex]x^{4}[/tex] + xy³ + x³ + y³ ( factor out x from the first 2 terms )

= x(x³ + y³) + 1(x³ + y³) ← factor out (x³ + y³) from each term

= (x³ + y³)(x + 1)

x³ + y³ is a sum of cubes and factors as (x + y)(x² - xy + y²)

Thus

[tex]x^{4}[/tex] + xy³ + x³ + y³ = (x + y)(x² - xy + y²)(x + 1)

Answer:

Length of the other side of the backyard is 80.4 feet.

Step-by-step explanation:

Let the dimensions of the Liam's rectangular backyard = 85 feet × a feet

Diagonal of the rectangle, AD = 117 feet

When we apply Pythagoras theorem in ΔABD,

AD² = AB² + BD²

(117)² = (85)² + BD²

a² = 13689 - 7225

a = √6464

  = 80.399 feet

a ≈ 80.4 feet

Therefore, length of the other side of the backyard is 80.4 feet.

Answer:

+30 + -25

Savings is positive

Buying is negative

Step-by-step explanation:

We save 30 dollars

+30

We buy a game for 25

-25

+30 -25

Savings is positive

Buying is negative

Answer:

Option D

Step-by-step explanation:

Given: set of inequalities

To find: Points which do not satisfy all the inequalities

Solution:

For point [tex](15,0)[/tex]:

[tex]15\leq 30-3(0)=30\\15\geq 15-0=15\\15\leq 25-0=25\\15\geq 0\\0\geq 0[/tex]

So, (15, 0) satisfies all the inequalities

For point [tex](7.5,7.5)[/tex]:

[tex]7.5\leq 30-3(7.5)=30-22.5=7.5\\7.5\geq 15-7.5=7.5\\7.5\leq 25-7.5=17.5\\7.5\geq 0\\7.5\geq 0[/tex]

So, (7.5, 7.5) satisfies all the inequalities

For point (22.5,2.5):

[tex]22.5\leq 30-3(2.5)=30-7.5=22.5\\22.5\geq 15-2.5=12.5\\22.5\leq 25-2.5=22.5\\22.5\geq 0\\2.5\geq 0\\[/tex]

So, (22.5,2.5) satisfies all the inequalities

For point (7.5 ,0):

Put s = 7.5 and t = 0 in [tex]s\geq 15-t[/tex]

[tex]7.5\geq 15-0=15[/tex] which is false

So, [tex](s,t)\neq (7.5,0)[/tex]

Answer:

D.

Step-by-step explanation:

Answer:

i think it would be 28.26

Step-by-step explanation:

because C=2 pie r and D=2 r (solving for C=pie d =pie . 9 = 28.27433 then just round and thats how you get 28.27 (sorry if its confusing) (im not good at explaining but i am smart)

Answer:

[tex]x=7[/tex]

[tex]y=3[/tex]

Step-by-step explanation:

Considering the system of equations:

[tex]$\left \{ {{-2x + 3y = -5} \atop {2x + 4y = 26}} \right. $[/tex]

[tex]$\left \{ {{ 3y = -5} \atop {4y = 26}} \right. $[/tex]

[tex]7y=21\\y=3[/tex]

[tex]2x + 4(3) = 26\\2x + 12 = 26\\2x=14\\x=7[/tex]

Answer:

J'(2, 1)

K'(0, 3)

Step-by-step explanation:

On a coordinate plane, coordinates of the points J, K and L are (-2, 1), (0, 3) and (2, -1) respectively.

If we reflect these points over the line x = 0 or y-axis, rule to be followed is

(x, y) → (-x, y)

Only sign of x coordinates get changed while y coordinates remain the same.

Following this rule coordinates of the images of J' and K' will be

J(-2, 1) → J'(2, 1)

and K(0, 3) → K'(0, 3)

Answer:

j = 2, 1

k = 0, 3

Step-by-step explanation:

i got it right on edg

Answer:

x = -4

Step-by-step explanation:

x - 8 = 3x

First, subtract x from both sides:

x - 8 = 3x

-x        - x

________

-8 = 2x

Then, divide both sides by 2:

-8 = 2x

-4 = x

Answer:

Area =  

b1 + b2  ×h

2

=  

10 + 10  × 10

2

=  100 feet2

Step-by-step explanation:

Answer:

second option

Step-by-step explanation:

Given

x² - 6x - 33 = 0 ( add 33 to both sides )

x² - 6x = 33

To complete the square

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

x² + 2(- 3)x + 9 = 33 + 9

(x - 3)² = 42 → second option

Answer:

b = 9

Step-by-step explanation:

A= 30°      a = 3[tex]\sqrt{3x}[/tex]

B =            b =

C = 90°     c =

find B first

90 + 30 = 120

180 - 120 = 60

B = 60°

Now, let's find b

use the Law of Sines

[tex]\frac{sin A}{a} = \frac{sin B}{b} \\\frac{sin 30}{3\sqrt{3} } = \frac{sin 60}{b}\\b = \frac{3\sqrt{3} sin 60 }{sin 30}\\b = 9[/tex]

Answer: 16384

Step-by-step explanation:

The 15th term of the geometric sequence 4,-8, 16, -32, 64... is 131072. The term is obtained by using the formula for the nth term of a geometric sequence.

The sequence given is a geometric sequence. This means every term is obtained by multiplying the previous term by a constant. In this case, the constant is -2 (since -8 = 4*-2, 16 = -8*-2, -32 = 16*-2, etc).

The formula for the nth term of a geometric sequence is a*r^(n-1), where a is the first term, r is the ratio (constant), and n is the position of the term in the sequence. In this case, the first term a is 4 and the ratio r is -2. Substituting these values and n=15 into the formula, we get the 15th term as 4*(-2)^(15-1) = 131072.

Therefore, the 15th term of the sequence 4,-8, 16, -32, 64... is 131072. This can be found by applying the formula for the nth term of a geometric sequence and substituting the given values.

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Answer:

1,000,000,000 as a power of 10, is: 10^12

Step-by-step Solution:

We can expand 1,000,000,000, and write this number as a multiplication sentence using only the number 10. By doing this, we can count the number of tens needed to be multiplied to get to his answer:

1,000,000,000 = 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10  

Since 10 is multiplied by itself 12 times, we can therefore say that 10^12 is equal to 1,000,000,000

Answer:

10^12 (10 to the 12th power)

Step-by-step explanation:

10 to the twelth power would basically be 10x10x10x10x10x10x10x10x10x10x10x10

This equals 1,000,000,000,000, which is one trillion.

Answer:

m<A = 20

Step-by-step explanation:

6y plus 3y = 9y

180 divided by 9 = 20

20x6=120

20x2=40

120+40=160

a triangle is equal to 180 so..

180-160=20

i did 6y + 3y because that line is 180 degrees ( half of a circle)

Answer:

C = 12 pi

Step-by-step explanation:

The area of a circle is given by

A = pi r^2

36 pi = pi r^2

Divide each side by pi

36 = r^2

Take the square root of each side

sqrt(36) = sqrt (r^2)

6 =r

We can find the circumference

C = 2 * pi *r

C = 2* pi *6

C = 12 pi

Answer:

first option

Step-by-step explanation:

In order to find the area of composite figures and trapezoids, you should decompose the figure into simple shapes, calculate each of their areas, and then sum these areas up. For trapezoids, use the formula 1/2 (sum of the bases) x height.

The question provides a complex description of a figure, but it seems this is a mathematical problem dealing with areas of trapezoids and composite figures. It can be inferred that you need to maneuver pieces to cover the shaded area of a figure. Here's a general way to approach it:

For the trapezoids, remember that the area of a trapezoid is given by 1/2 (sum of the bases) x (height).

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Answer:

the answer is C

Step-by-step explanation:

Answer:

A = 3

B = -7

C = -12

Step-by-step explanation:

3x^2−7x=12.

The standard form for a quadratic equation is

Ax^2 +Bx +C =0

Subtract 12 from each side

3x^2−7x-12=12-12

3x^2−7x-12=0

A = 3

B = -7

C = -12

Answer:

a = 3

b = -7

c = -12

Step-by-step explanation:

General form of a quadratic:

ax² + bx + c

Given:

3x² − 7x = 12

3x² - 7x - 12 = 0

Comparing the two:

a = 3

b = -7

c = -12