The sum of two numbers is 23. The larger number y is 1 less than twice the smaller number x. Write and solve a system of linear equations to find the two numbers.

Answer:

Step-by-step explanation:

For a quadratic equation to have 2 equal root, the discriminant value must be equal to zero.

Discriminant D = b² - 4ac = 0

Given the equation

x^2 − 2(2k + 1)x + (k + 2) = 0

From the equation, a  = 1, b = -2(2k+1), c = k+2

a = 1, b = -4k - 2, c = k+2

Substitute into the discriminant formula;

Recall that: b² - 4ac = 0

(-4k - 2)²-4(1)(k+2) = 0

16k²+16k + 4 - 4k - 8  =0

16k²+12k - 4 = 0

16k²+16k - 4k - 4 = 0

16k(k+1)-4(k+1) = 0

16k - 4 = 0 and k+1 = 0

16k = 4 and k = -1

k = 4/16 and k = -1

k = 1/4 and -1

Hence the required value of k is 1/4 and  -1

Answer:

The fraction of the beads that are red is

Step-by-step explanation:

Algebraic Expressions

A bag contains red (r), yellow (y), and blue (b) beads. We are given the following ratios:

r:y = 2:3

y:b = 5:4

We are required to find r:s, where s is the total of beads in the bag, or

s = r + y + b

Thus, we need to calculate:

[tex]\displaystyle \frac{r}{r+y+b} \qquad\qquad [1][/tex]

Knowing that:

[tex]\displaystyle \frac{r}{y}=\frac{2}{3} \qquad\qquad [2][/tex]

[tex]\displaystyle \frac{y}{b}=\frac{5}{4}[/tex]

Multiplying the equations above:

[tex]\displaystyle \frac{r}{y}\frac{y}{b}=\frac{2}{3}\frac{5}{4}[/tex]

Simplifying:

[tex]\displaystyle \frac{r}{b}=\frac{5}{6} \qquad\qquad [3][/tex]

Dividing [1] by r:

[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+y/r+b/r}[/tex]

Substituting from [2] and [3]:

[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{1+3/2+6/5}[/tex]

Operating:

[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{1}{\frac{10+3*5+6*2}{10}}[/tex]

[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{10+15+12}[/tex]

[tex]\displaystyle \frac{r}{r+y+b}=\displaystyle \frac{10}{37}[/tex]

The fraction of the beads that are red is [tex]\mathbf{\frac{10}{37}}[/tex]

Answer:

The distance would be (5,-3)

Answer:

sss and sas both work

Step-by-step explanation:

Answer:

Step-by-step explanation:

We can see two congruent sides as per marks and one shared side which is congruent to itself

So the correct option is SSS

Answer:

17

Step-by-step explanation:

To find how many notes of Rs. 500 he has, we need to find out the total value of all the Rs. 500 notes.

Total value of Rs. 20 notes = 20 × 40

                                             = 800

Total value of Rs. 1000 notes = 1000 × 20

                                                 = 20 000

Total value of Rs. 500 notes = 29 300 - 800 - 20 000

                                                = 8500

No. of Rs. 500 notes = 8500 ÷ 500

                                   = 17

Rohit has total 17 notes of Rs.500

" Unitary method is the process of finding value of one unit using which we can find the value of other units."

According to the question,

Number of Rs.20 notes = 40

Total amount of Rs.20 = 20 × 40

                                     = Rs.800

Number of Rs.1000 notes = 20

Total amount of Rs.1000 = 20 × 1000

                                         = Rs.20,000

Total amount of Rs.20 and Rs.1000 notes = 20,000 +800

                                                                      = Rs.20,800

Made a payment of Rs.29,300

Left amount of Rs.500 notes = 29,300 -20,800

                                                = Rs.8500

Number of Rs.500 notes = 8500 ÷ 500

                                          = 17 notes of Rs.500

Hence, Rohit has total 17 notes of Rs.500.

Learn more about unitary method here

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Answer:

hope it helps

Step-by-step explanation:

1: 4

2:2

3:1

4:3

GIVE ME BRAINIEST!!!!!

thanks!

Answer:

D

x is less than or equal to -3

Step-by-step explanation:

I hope I was fast enough ^^

Answer:

Step-by-step explanation:

No problem

Answer:

$100,000

Step-by-step explanation:

Let the total income of the store = [tex]\$x[/tex]

Total spends on salaries = [tex]\frac{1}{4}[/tex] of total income

Total spends on advertising = [tex]\frac{1}{6}[/tex] of total income

Also, we are given that:

Total money paid as salaries = $150,000

To find:

Total spends on advertising ?

Solution:

As per question statement, we can write the following equation:

[tex]\dfrac{1}{4}x =\$150000\\\Rightarrow x =\$150000\times 4\\\Rightarrow x = \$600000[/tex]

Now, as per the given statement, total spends on advertising are:

[tex]\dfrac{1}{6}x =\dfrac{1}{6}\times 600000 = \bold{\$100,000 }[/tex]

Therefore, the answer is $100,000

Answer:

8

Step-by-step explanation:

32/4=8

Answer: 8 minutes

Step-by-step explanation: You can use a proportion to calculate.

[tex]\frac{32}{4} = \frac{x}{1}[/tex]

32 x 1 / 4 = 8

8 minutes = 1 mile

Answer:

Please check the attached graph.

Step-by-step explanation:

Note: You did not add the graph; so I am taking a sample graph to clear the concept anyway. Please check the referred graph attached below.

The slope on the graph basically tells us the time rate of change.

The slope can also be termed as:

From the attached graph, taking twp points

Finding the slope between (0, 3) and (-1, 0) using the formula

[tex]\left(x_1,\:y_1\right)=\left(0,\:3\right),\:\left(x_2,\:y_2\right)=\left(-1,\:0\right)[/tex]

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]m=\frac{0-3}{-1-0}[/tex]

[tex]m=3[/tex]

Thus, the slope of the given line on the graph = m = 3

Answer:

Step-by-step explanation:

Answer:

I believe the answer is D)

Step-by-step explanation:

I really hope this helps

UwU

Answer:

slope intercept form:

y=mx+b where m is the slope and b is the y intercept.

The y intercept is where the line crosses the y axis which in this example is at (0, 2). The y intercept is 2. The slope can be found by plugging in the x and y values of any 2 points on the line into the equation: y2 - y1 / x2- x1:

y2 - y1 / x2- x1

4-2 / 5-0

2/5 is the slope

therefore, y=2/5x+2 is the equation

D is correct

Step-by-step explanation:

Answer:

Step-by-step explanation:

Option 1

Use point (0, 11)

Option 2

Option 3

Use point (2, -1)

Option 4

Use point (3, -7)

Answer:

$2,400

Step-by-step explanation:

3 tons equals 6000 pounds

6000*0.40= $2,400

Answer:

1.5% x 412 = 618?

Step-by-step explanation:

Answer:

103/50

Step-by-step explanation:

Simplify

1/2

100

(412)

Answer:

B

Step-by-step explanation:

it is

Answer:

834*3 + 1058*4 = ___

2,502 + 4,232 = 6,734 feet of wood

Step-by-step explanation:

Answer:

6734 is the answer.

Step-by-step explanation:

834 x 3 = 2502.

1058 x 4 = 4232.

2502 + 4232 = 6734.

Answer:

your answer is $42

Step-by-step explanation:

for $42 you could get 6 tickets for 42 you could get 6 tickets so your answer is letter c

Answer:15

Step-by-step explanation: So we have this triangle but it's not a right triangle right so we can't just Pythagorean theorem our way out. So we have to treat the sizes as ratios.  2:12 is the ratio of the smaller triangle. 12 increases to 78 which means side 2 has to increase as well by the same ratio so 78/12 = 6.5 and 6.5*2=13 so PQ is 13 and to find NQ just add NP and PQ or 2+13 = 15

Hope it helps :)

Answer:

D.20

Step-by-step explanation:

4*5=20

Answer:

x = 21

y = 114

Step-by-step explanation:

Here, we are to find the values of x and y

Mathematically;

3x - 15 + 6x + 6 = 180

reason for this is that opposite interior angles are supplementary, they add up to 180

9x-9 = 180

9x = 180 + 9

9x = 189

x = 189/9

x = 21

Also;

3x-15 + y + 18 = 180

Reason for this is that angles on a straight line are supplementary

Recall, x = 21

3(21)-15 + y + 18 = 180

63-15 + y + 18 = 180

y = 180-66

y = 114 degrees

Answer:

904.32 cubic ft

Step-by-step explanation:

To find the volume of a sphere, the formula is [tex]4\pi\frac{r^3}{3}[/tex]

First, 3.14 * 4 for 12.56.

The radius is 6, and that cubed is 216.

After that, divide 216 by 3 for 72

Then, 12.56 times 72, which gets you the final answer of  904.32 cubic ft.

(10 * 72) + (2 * 72) + (0.5 * 72) + (0.06 * 72)

720 + 144 = 864

864 + 36 = 900

900 + 4.32 = 904.32

Your answer is D, I took the test.

Answer:

1

Step-by-step explanation:

1/4 every 1/2

so 1/2 every 1 cup

so 1 every 2 cups

Answer:

m = undef

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

Point (2, 3)

Point (2, -6)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Answer:

wELL.. Im no expert BUTTTTTTTTT....that would mean that there is no cherry pies (i think)

Step-by-step explanation:

Answer:

Buddy should have given Trudy c +3 apple pies and c cherry pies

Step-by-step explanation:

Trudy orders 3 more apple pies than c cherry pies

which means that Trudy orders:

c cherry pies

and c+3 apple pies

But Buddy gives him c cherry and c-3 apple