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andreyandreev [35.5K]

3 years ago

6

Which statements are true about the ordered pair (10, 5) and the system of equations? {2x−5y=−5 x+2y=11 Select each correct answ

er. The ordered pair (10, 5) is a solution to the first equation because it makes the first equation true. The ordered pair (10, 5) is a solution to the second equation because it makes the second equation true. The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false. The ordered pair (10, 5) is a solution to the system because it makes both equations true.

1 answer:

sleet_krkn [62]3 years ago

3 0

Answer:

The ordered pair (10, 5) is not a solution to the system because it makes at least one of the equations false.

Step-by-step explanation:

2x−5y=−5

x+2y=11

In equation (1), substitution of (10,5)

2x−5y=2(10)-5(5)=20-25=-5

However in equation (2), on substitution of (10,5)

x+2y=10+2(5)=10+10=20 ≠11.

However, the solutions of the simultaneous equations

2x−5y=−5

x+2y=11

are (5,3)

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The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 20 per cent.Find the single reduction the

Evgen [1.6K]

Answer:

40% . The single reduction together is 40%.

Step-by-step explanation:

Let the bicycle cost is x before reduced price.

First 25% is reduced and again 20% further reduced.

Let the single reduction is y% if the two reduction together are equal.

Solution,

Case .1

reduction cost $=x\times 25%$ %

$=x\times 25/100$

$=x/4$

The cost of bicycle after reduction of 25% is

$=x-x/4=3x/4$

cost of reduction further reduction of 20% $=3x/4\times 20$ %

$=3x\times 20/(4\times 100)$

$=3x/20$

The new cost of bicycle is further reduction of 20% is

$=3x/4-3x/20$

$=\left ( 15x-3x \right )/20$

$=12x/20=3x/5$

Case.2

if single reduction is done new cost of cycle is equal

$x-x\times y$ %= $3x/5$

$x\left ( 1-y/100 \right )=3x/5$

$\left ( 100-y \right )/100=3/5$

$100-y=60$

$y=40$ %

single reduction of a cycle is 40%

8 0

3 years ago

NEED MATH HELP QUICK!

Korolek [52]

Answer:

Minimum = 14

$Q_1=23$

Median = 32

$Q_3=49$

Maximum = 65

Step-by-step explanation:

<u>Step 1: </u>Put your numbers in ascending order (from smallest to largest). For this particular data set, the order is

14, 18, 28, 29, 32, 44, 48, 50, 65

<u>Step 2:</u> Find the minimum and maximum for your data set. Now that your numbers are in order, this should be easy to spot.

Minimum = 14

Maximum = 65

<u>Step 3: </u>Find the median. The median is the middle number. The middle number in your list is 32, so

Median = 32

<u>Step 4: </u>Place parentheses around the numbers above and below the median.

(14, 18, 28, 29), 32, (44, 48, 50, 65)

<u>Step 5: </u>Find Q1 and Q3. Q1 can be thought of as a median in the lower half of the data, and Q3 can be thought of as a median for the upper half of data.

First quartile

$\bf{Q_1=\dfrac{18+28}{2}=\dfrac{46}{2}=23}$

Third quartile

$\bf{Q_3=\dfrac{48+50}{2}=\dfrac{98}{2}=49}$

<u>Step 6:</u> Write down your summary found in the above steps.

Minimum = 14

$Q_1=23$

Median = 32

$Q_3=49$

Maximum = 65

5 0

4 years ago

IRISSAK [1]

Answer:

Step-by-step explanation:

Given f(x) = 2x²+16

g(x) = √5x³

First is to get the composite function f(g(x))

f(g(x)) = f(√5x³)

To get f(√5x³), we will replace x in f(x) with √5x³ as shown:

f(√5x³) = 2(√5x³)²+16

f(√5x³) = 2(5x³)+16

f(√5x³) = 10x³+16

Hence f(g(x)) = 10x³+16

f(g(x)) will be the function of amount earned by Raul for the total number hour he works

6 0

3 years ago

Find an equation for the perpendicular bisector of the line segment whose endpoints are (5, -9) and (-9, -5).

GrogVix [38]

Answer:

y = x - 9

Step-by-step explanation:

Find the slope of the first line.

(-9 + 5)/(5 + 9)

-1

Lines perpendicular have opposite reciprocal slopes

1

Find the middle point of the first line, this is where it will intersect with the bisector.

5 + - 9/2 = 2

-5 + -9/2 = -7

(2,-7) is the midpoint

Use Point Slope Form to reduce it to Standard Form

y + 7 = 1(x - 2)

y + 7 = x - 2

y = x - 9

5 0

3 years ago

an enrollment of 200 students and this year enrollment has increased by 118%. What is this year's enrollment ?

Airida [17]

Answer:

436 students

Step-by-step explanation:

Original number of students enrolled = 200students

% increase = 118%

Increment = 118% of 200

Increment = 1.18 * 200

Increment = 236

The year enrollment = 200 + 236

The year enrollment = 436 students

8 0

3 years ago