Which ordered pair is the solution to the system of linear equations -5x+y=26 and 2x-7y=16?
(–4, 6)
(6, –4)
(–4, –6)
(–6, –4)

[tex]A.\\\\\dfrac{y}{a}-b=\dfrac{y}{b}-a\qquad\text{multiply both sides by }\ ab\neq0\\\\by-ab^2=ay-a^2b\qquad\text{add}\ ab^2\ \text{to both sides}\\\\by=ay+ab^2-a^2b\qquad\text{subtract}\ ay\ \text{from both sides}\\\\by-ay=ab^2-a^2b\qquad\text{distributive}\\\\(b-a)y=ab^2-a^2b\qquad\text{divide both sides by}\ (b-a)\\\\\boxed{y=\dfrac{ab^2-a^2b}{b-a}}\to y=\dfrac{ab(b-a)}{b-a}\to\boxed{y=ab}[/tex]

[tex]B.\\t+\dfrac{b^2}{a}=\dfrac{bt}{a}+a\qquad\text{multiply both sides by}\ a\neq0\\\\at+b^2=bt+a^2\qquad\text{subtract}\ b^2\ \text{from both sides}\\\\at=bt+a^2-b^2\qquad\text{subtract}\ bt\ \text{from both sides}\\\\at-bt=a^2-b^2\qquad\text{distributive}\\\\(a-b)t=a^2-b^2\qquad\text{divide both sides by}\ (a-b)\neq0\\\\\boxed{t=\dfrac{a^2-b^2}{a-b}}\to t=\dfrac{(a-b)(a+b)}{a-b}\to\boxed{t=a+b}[/tex]

Answer:

Where are y and t?

Step-by-step explanation:

Answer:

8 cm

Step-by-step explanation:

We can use ratio's to solve this problem

4 cm = 5 km

We need to know how many cm = 10 km

4 cm             x cm

---------- = --------------

5 km             10 km

Using cross products

4* 10 = 5* x

40 = 5x

Divide each side by 5

40/5 = 5x/5

8=x

On the map it is 8 cm.

Answer:

The probability that exactly 2 of the rolls is a sum of 7 will is 0.296

Step-by-step explanation:

The probability of rolling a sum of 7 when rolling two dice simultaneously is 0.167.

Let us assume that, A be the event that the sum is 7. So,

[tex]P(A)=0.167[/tex]

Binomial probability represents the probability that a binomial experiment results (i.e either success or failure or only two results) in exactly x successes.

[tex]b(x;\ n, p) =\ ^nC_x \cdot p^x \cdot (1-p)^{n - x}[/tex]

So the probability that exactly 2 of the rolls is a sum of 7 will be,

[tex]P(2) =\ ^{12}C_2 \cdot (0.167)^2 \cdot (1-0.167)^{12 - 2}[/tex]

[tex]=\ ^{12}C_2 \cdot (0.167)^2 \cdot (0.833)^{10}[/tex]

[tex]=66 \cdot (0.167)^2 \cdot (0.833)^{10}[/tex]

[tex]=0.296[/tex]

Answer:

Step-by-step explanation:420÷24=20, so 2 sides are 20, and 2 sides are 24. 20+20+24+24=88 feet of fencing

Answer:

Ruth is  x+4=7/3+4,   esmerelda  is  5x+4=35/3+4

Step-by-step explanation:

if Ruth is x, esmerelda is 5x,

four years ago,

Ruth is x+4,  esmerelda is 5x+4,  depend on the sum, we get:

x+4+5x+4=22, x=7/3

so:

Ruth is  x+4=7/3+4,   esmerelda  is  5x+4=35/3+4

Answer:

The original price of the  bracelet before tax is $12.

Step-by-step explanation:

Let us assume that the original price of the  bracelet be x.

As given

Casey buys a bracelet.

She pays for the bracelet and pays $0.72 in sales tax .

The sales tax rate is 6% .

6% is written in the decimal form.

[tex]= \frac{6}{100}[/tex]

= 0.06

Than the equation becomes

x × 0.06 = 0.72

0.06x = 0.72

[tex]x = \frac{0.72}{0.06}[/tex]

x = $12

Therefore the original price of the  bracelet before tax is $12.

Answer:

Alternative C

Step-by-step explanation:

x² + 10x + 24 = 0

∆ = 10² - 4.1.24

∆ = 100 - 96

∆ = 4

[tex]x' = \frac{- 10 + 2}{2} \\\\\ x' = - 4 \\\ x" = \frac{- 10 - 2}{2} \\\\\ x" = - 6[/tex]

I hope I helped you.

Answer: C

Step-by-step explanation:

x² + 10x + 24 = 0

                ∧

               1 + 24 = 25

               2 + 12 = 14

               3 + 8 = 11

                4 + 6 = 10  ← THIS WORKS!

(x + 4)(x + 6) = 0

x + 4 = 0       x + 6 = 0

 x = -4             x = -6

Answer:

cos C = 9/41

Step-by-step explanation:

cos C = adjacent side/ hypotenuse

cos C = 9/41

Answer:

cos C = 9/41

Step-by-step explanation:

The given triangle is right angle triangle.

Cos C = Adjacent/Hypotenuse

Here, Adjacent = 9 and Hypotenuse = 41

cos C = 9/41

Thank you.

The Synthetic Division form of Given Division Problem is :

✿   [tex]-5\;\arrowvert\overline{\;4\;\;\;\;\;-13\;\;\;\;\;\;8}[/tex]

Option C is the Answer

In synthetic division for [tex]\( \frac{4x^2 - 13x + 8}{x + 5} \)[/tex], option C (-5 | 4 -13 8) correctly represents the coefficients, showcasing the division process with a remainder of 8.

The synthetic division problem given is [tex]\( \frac{4x^2 - 13x + 8}{x + 5} \)[/tex]. Synthetic division is a method used to divide polynomials, particularly when dividing by a linear factor of the form (x - c) . The correct representation in synthetic division form would be:

**C.  -------------

 -  5 | 4   - 13  8**

Here's the breakdown of the synthetic division:

1. The divisor x + 5 corresponds to c = -5, so the root is x = -5.

2. Write down the coefficients of the dividend 4x^2 - 13x + 8 in the synthetic division box.

3. Bring down the leading coefficient, which is 4 in this case.

4. Multiply the root (-5) by the leading coefficient (4) and write the result below the second column. Add the result to the second column.

5. Multiply the root by the result from step 4 and write the result below the third column. Add the result to the third column.

The final result in the bottom row represents the coefficients of the quotient, and the last number (8) is the remainder. The synthetic division in option C accurately reflects this process.

Answer:

The store will sell it for $58.50

Step-by-step explanation:

To find this amount, start by multiplying the cost by the mark up percentage.

$45 * 30% = $13.50

Now that we have the markup amount, we can add it to the original cost to get the store price.

$45.00 + $13.50 = $58.50

Answer:

65

Step-by-step explanation:

Hi,

I think you mean red or blue.

Number which are red or blue = 12 + 14

= 26% or 0.26

The number of red and blue = 0.26 * 250

=  65 marbles

Answer:

B.5.6g

Step-by-step explanation: Density of object=mass/volume

Therefore, Mass=density of object X volume

                           =0.7 X 8

                           =5.6g

Answer:

Mass of an object is:

B. 5.6 g

Step-by-step explanation:

Mass of an object= Density × Volume

An object that has a density of 0.7 g/cm³

and a volume of 8 cm³

Mass= 0.7 g/cm³ × 8 cm³

       = 5.6 g

Hence, Correct option is:

B. 5.6 g

x = -2 - it's a vertical line with undefined slope.

The line parallel to the vertical line is vertical.

Answer:

1

Step-by-step explanation:

We are given the two bases of the trapezium:

[tex] ED = 5,\qquad AB = 9 [/tex]

The formula for the area of the trapezium is

[tex] A = \dfrac{(B+b)h}{2} [/tex]

So, we only need to figure out the length of the height EF.

We know that FA+EF = 11. Also, we're given that the perimeter of ABCF is 28, which means

[tex] 2AB+2FA = 28 \iff 2\cdot 9 + 2FA = 28 \iff 2FA = 10 \iff FA = 5 [/tex]

So, we can deduce

[tex] EF = 11-FA = 11-5=6 [/tex]

And so we're ready to use the solving formula:

[tex] A = \dfrac{(5+9)\cdot 6}{2} = \dfrac{14\cdot 6}{2} = 7\cdot 6 = 42 [/tex]

G = number of green = 7

S = number of striped = 8

T = number total = 10+7+8 = 25

probability of picking green = P(G) = G/T = 7/25

probability of picking striped = P(S) = S/T = 8/25

P(green and striped) = P(G)*P(S)  ... events are independent

P(green and striped) = (7/25)*(8/25)

P(green and striped) = (7*8)/(25*25)

P(green and striped) = 56/625

P(green and striped) = 0.0896

--------------------------------

In summary, the answer as a fraction is 56/625

In decimal form, the answer is 0.0896

The value 0.0896 can be converted to percent form to get 8.96%

Final answer:

The probability of picking a green marble and then a striped marble from a bag with replacement is the product of the probability of picking a green marble (7/25) and a striped marble (8/25), which is 56/625.

Explanation:

The student is asking about the probability of selecting a green marble followed by a striped marble when drawing from a bag that contains red, green, and striped marbles with replacement. To calculate this probability, we will use the basic principle that the probability of two independent events happening in sequence is the product of their individual probabilities.

First, we determine the probability of choosing a green marble, which we'll call P(G). Since the bag contains 7 green marbles out of a total of 25 (10 + 7 + 8), the probability P(G) is 7/25. Next, since the marble is replaced, the probability of choosing a striped marble, P(S), remains the same at 8/25. Therefore, the probability of choosing a green marble and then a striped marble is P(G and S) = P(G) x P(S) = (7/25) x (8/25).

To find the combined probability, simply multiply the two individual probabilities:

P(G and S) = (7/25) x (8/25) = 56/625.

The probability of drawing a green and then a striped marble is 56/625.

Answer:

RX = 12 and XU = 6

Step-by-step explanation:

Given :  In ΔTRV , TW ,RU and VS are the medians .

             X is the centroid

To Find : RX and XU

Solution:

Since we know that the centroid divides each median in a ratio of 2:1.

Since X is the centroid so RX : XU = 2:1

So, let RX = 2x and XU = x

And we are given that RU = 18

⇒RX +XU=18

⇒2x+x=18

⇒3x=18

⇒[tex]x=\frac{18}{3}[/tex]

⇒[tex]x=6[/tex]

Thus,  RX = 2x = 2*6 =12

          XU = x =6

Hence length of RX = 12 and XU = 6

Answer : No, levi's reasoning is incorrect. The correct answer is, [tex]2.63\times 10^{11}[/tex]

Step-by-step explanation :

Scientific notation : It is the representation of expressing the numbers that are too big or too small and are represented in the decimal form with one digit before the decimal point times 10 raise to the power.  The numerical digit lies between 0.1.... to 9.9.....

For example :

5000 is written as [tex]5.0\times 10^3[/tex]

889.9 is written as [tex]8.899\times 10^{-2}[/tex]

In this examples, 5000 and 889.9 are written in the standard notation and [tex]5.0\times 10^3[/tex]  and [tex]8.899\times 10^{-2}[/tex]  are written in the scientific notation.

If the decimal is shifting to right side, the power of 10 is negative and if the decimal is shifting to left side, the power of 10 is positive.

As we are given the 263,000,700,000 in standard notation.

Now converting this into scientific notation, we get:

[tex]\Rightarrow 263,000,700,000=2.63\times 10^{11}[/tex]

As, the decimal point is shifting to left side, thus the power of 10 is positive.

Hence, the correct answer is, [tex]2.63\times 10^{11}[/tex]

Answer:

No. He answered incorrectly. The correct scientific notation of the number will be [tex]2.630007\times10^{11}[/tex].

Step-by-step explanation:

Levi wants to write 263,000,700,000 in the scientific notation.

In scientific notation, the number is represented by a numerical value between 1 and 9.99...., multiplied by power of 10.

The given number can be written as,

[tex]263,000,700,000=2.630007\times100,000,000,000\\263,000,700,000=2.630007\times10^{11}[/tex]

Thus, in scientific notation, the given number can be written as [tex]2.630007\times10^{11}[/tex].

Here, the numerical value is 2.630007 and power of 10 is [tex]10^{11}[/tex].

Now, the power of 10 is 11 which is positive. So, Levi has answered incorrectly.

For more details, refer the link:

https://brainly.com/question/1705769?referrer=searchResults

Answer:

a

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

19-10=9

Answer: (A) If it is a bib, then it is a bab

Step-by-step explanation:

p: The bib is a bub.

Rewrite it as: If it is a bib, then it is a bub.

q: The bub is a bab.

Rewrite it as: If it is a bub, then it is a bab

The conclusion of p equals the hypothesis of q so the Law of Syllogism can be applied  --> hypothesis of p → conclusion of q

Answer:

(1)

option-B

(2)

f(x) is continuous at a=4

Step-by-step explanation:

(1)

we are given

[tex]\lim_{x \to 0} \frac{sin(2x)}{x}[/tex]

Since, we are suppose to find limit x-->0

so, we always choose value of x that is  close to 0

At x=-0.03:

[tex]\frac{sin(2\times (-0.03))}{(-0.03)}=1.99880[/tex]

At x=-0.02:

[tex]\frac{sin(2\times (-0.02))}{(-0.02)}=1.99947[/tex]

At x=-0.01:

[tex]\frac{sin(2\times (-0.01))}{(-0.01)}=1.99987[/tex]

At x=0.01:

[tex]\frac{sin(2\times (0.01))}{(0.01)}=1.99987[/tex]

At x=0.02:

[tex]\frac{sin(2\times (0.02))}{(0.02)}=1.99947[/tex]

At x=0.03:

[tex]\frac{sin(2\times (0.03))}{(0.03)}=1.99880[/tex]

(2)

we are given

[tex]f(x)=\frac{x-4}{x+5}[/tex]

Since, we have to check continuity at a=4

So, firstly we will find limit value and then functional value

Limit value:

[tex]\lim_{x \to a}  f(x)=\lim_{x \to a}\frac{x-4}{x+5}[/tex]

now, we can plug a=4

[tex]\lim_{x \to 4}  f(x)=\lim_{x \to 4}\frac{4-4}{4+5}[/tex]

[tex]\lim_{x \to 4}  f(x)=0[/tex]

Functional value:

We can plug x=4 into f(x)

[tex]f(4)=\frac{4-4}{4+5}[/tex]

[tex]f(4)=0[/tex]

So, we can see that

[tex]\lim_{x \to 4}  f(x)=f(4)=0[/tex]

So, limit value is equal to function value

so, f(x) is continuous at a=4.............Answer

Answer:The years vary

Step-by-step explanation:

If you are them all and divide, it could solve your equation.

I hoped I helped :)

Answer: y = 5.5

Step-by-step explanation:

[tex]y=\dfrac{1}{2}x^2+6x+24[/tex]

Step 1: find the vertex

axis of symmetry: [tex]x = \dfrac{-b}{2a} = \dfrac{-6}{2(\frac{1}{2})} =\dfrac{-6}{1} = -6[/tex]

y-coordinate of vertex: [tex]y=\dfrac{1}{2}(-6)^2+6(-6)+24[/tex]

= 18 - 36 + 24

= 6

Vertex: (-6, 6)

Step 2: find p (the distance from the vertex to the focus): [tex]\dfrac{1}{4p} =a[/tex]

[tex]\dfrac{1}{4p} =\dfrac{1}{2}[/tex]

cross multiply to get: 2 = 4p

divide both sides by 4 to get: [tex]p =\dfrac{1}{2}[/tex]

Step 3: find the directrix

Since the parabola opens up, the focus will be above the vertex.

focus: (-6, 6 + [tex]\dfrac{1}{2}[/tex]) = (-6, 6.5)

and the directrix will be below the vertex.

directrix: y = 6 - [tex]\dfrac{1}{2}[/tex] ⇒ y = 5.5

The directrix also gets shiftd toward right.  Then the equation of the directrix of the parabola will be y = 11/2.

The equation of a parabola function is given as,

y² = 4ax

x² = 4ay

Where a is the coordinate of the focus.

The equation of a parabola is given.

y = (1/2) x² + 6x + 24

Simplify the equation, we have

2y = x² + 12x + 48

2y = x² + 12x + 36 + 12

2y = (x + 6)² + 12

Then the equation can be written as,

4(1/2)y = (x + 6)² + 12

Compare with standard equation, we have

a = (-1/2, 0)

The parabola is gets shifted toward right.

Then the directrix also gets shiftd toward right.

Then the equation the directrix will be

y = -1/2 + 6

y = 11/2

More about the parabola link is given below.

https://brainly.com/question/8495504

#SPJ2

Answer: It has one solution. The solution is (x,y) = (-4,-3)

Add up the equations doing so straight down

x + -x = 0x = 0 so the x terms go away

2y + 2y = 4y

-10 + (-2) = -12

We end up with 4y = -12 so y = -3 after you divide both sides by 4. Use this y value to find the value of x

x+2y = -10

x + 2(-3) = -10

x - 6 = -10

x = -10+6

x = -4

The single solution is (x,y) = (-4,-3)

As a check, plug this solution into each equation to see if you get a true statement or not. Let's do so with the first equation

x+2y = -10

-4 + 2(-3) = -10

-4 - 6 = -10

-10 = -10 .... true

and then the second equation

-x+2y = -2

-(-4) + 2(-3) = -2

4 - 6 = -2

-2 = -2 .... true

both equations are true, so the solution is confirmed

Answer:

325 miles

Step-by-step explanation:

65=0.20x

x=65/0.2

x=325 miles