How can you decide which variable to solve for the first when you are solving a linear system by substitution

the answer is 0.5531 (✿◠‿◠)

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances and find the corresponding probabilities using a standard normal distribution table or calculator.

To find the probability that the car will travel a maximum distance between 125 and 135 miles, we need to calculate the z-scores for these distances using the formula: z = (x - mean) / standard deviation.

For 125 miles: z = (125 - 134) / 4.8 = -1.875.

For 135 miles: z = (135 - 134) / 4.8 = 0.208.

Next, we need to find the corresponding probabilities for these z-scores using a standard normal distribution table or calculator. The probability of a z-score less than -1.875 is approximately 0.0301, and the probability of a z-score less than 0.208 is approximately 0.5829.

To find the probability between 125 and 135 miles, we subtract the probability of a z-score less than 125 from the probability of a z-score less than 135: 0.5829 - 0.0301 = 0.5528.

Therefore, the probability that the car will travel a maximum distance between 125 and 135 miles is approximately 0.5528 or 55.28%.

Answer:

two real different roots

Step-by-step explanation:

Consider polynomial function

[tex]M(x)=-4x^2+x+1.[/tex]

The discriminant is

[tex]D=b^2-4ac=1^2-4\cdot (-4)\cdot 1=1+16=17.[/tex]

Since [tex]D>0,[/tex] the polynomial function [tex]M(x)[/tex] has two real different roots.

Answer:

see explanation

Step-by-step explanation:

Check the value of the discriminant

Δ = b² - 4ac

• If b² - 4ac > 0 then roots are real

• If b² - 4ac = 0 roots are real and equal

• If b² - 4ac < 0 then roots are not real

given (x - a)(x - b) = k² ( expand factors )

x² - bx - ax - k² = 0 ( in standard form )

x² + x(- a - b) - k² = 0

with a = 1, b = (- a - b), c = -k²

b² - 4ac = (- a - b)² + 4k²

For a, b, k ∈ R then (- a - b)² ≥ 0 and 4k² ≥ 0

Hence roots of the equation are always real for a, b, k ∈ R

Answer:

put the sum on 0, put 1.4 4 spaces away from the positive 1 and put k four spaces away from the negative 1

Step-by-step explanation:

Answer: ($4.19 x 1) + ($6.95 x 4) = $31.99

Step-by-step explanation: 4.19 is the price of the loaf of bread, so the first part of the equation ($4.19x), in this case the x is 1 since she bought only one loaf.

6.95 is the price of the turkey per pound, so our second part to the equation, ($6.95y), in this case y is 4 since the turkey weighed 4 pounds.

The complete equation is the combined cost of the turkey and bread so ($4.19x) + ($6.95y) = $?

The we replace the letters, ($4.19 x 1) + ($6.95 x 4) = $?

And then we add and multiply, ($4.19 x 1) + ($6.95 x 4) = $31.99

Answer:

a

Step-by-step explanation:

Answer:

The store has 100 cans of soup

Step-by-step explanation:

20x5=100

Answer: 100 cans

Step-by-step explanation:

20 times 5 = 100

To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, factor the equation and set each factor equal to zero. The real solutions are x=2, x=1, and x=5.

To find the real solutions of the equation x^3-8x^2+17x-10=0 using the x-intercept method, we need to find the x-values where the graph of the equation intersects the x-axis. This is done by factoring the equation and setting each factor equal to zero.

Step 1: Factor the equation: (x-2)(x-1)(x-5)=0

Step 2: Set each factor equal to zero and solve for x:

Therefore, the x-intercepts or real solutions of the equation are x=2, x=1, and x=5.

Answer:

(3 1/2, 7 1/4)

Step-by-step explanation:

A 1:3 ratio means we want 4 equal parts  (1+3 = 4)

Find the distance of the segment and divide by 4

(x2+x1)/4,  (y2+y1)/4

(8-2)/4 , (5-8)/4

6/4, -3/4

Since the first part is of ratio 1, we multiply by 1

Now add this to the starting point

(2 + 6/4, 8+ -3/4)

Getting a common denominator of 4

2*4/4 = 8/4

8 *4/4 = -3/4

(8/4 + 6/4, 32/4 -3/4)

(14/4, 29/4)

Now change back to a mixed number

(3 2/4 , 7 1/4)

(3 1/2, 7 1/4)

Answer:

1

Step-by-step explanation:

Answer:

1   (plus 1/6 cup of the original 2/3 cup left over)

Step-by-step explanation:

The LCD of 1/2 and 2/3 is 6.  Thus, 1/2 and 2/3 are equivalent to 3/6 and 4/6.  3/6 divides into 4/6 once, with a remainder of 1/6 (cup).

Answer:  just one 1/2 cup serving can be made from 2/3 cup of cole slaw, with 1/6 cup of the original 2/3 cup of slaw left over.

Answer:

Step-by-step explanation:

If you lose cash and someone finds it, you've lost it without recourse. If you lose a credit card, usually the issuer of the card can cancel it after your last verified purchase and replace the card for you. That is the main advantage.

You also have a record of what you've spent with a credit card. Sometimes you get a receipt and some sometimes you don't when you use cash.

Cash forces you to carry around coins, especially if you make a lot of small purchases in different places. Getting change for 2.22 cents from a 20 can be a little awkward and soon the big bills turn into many more little ones. Credit cards don't have that disadvantage.

Answer:

There are online services that will help someone monitor their credit and make a note of any changes in their credit score. Credit card monitoring keeps track of all open accounts and monitors hard inquiries. That way, if someone did not make the purchase, they can immediately tell the lender that the card has been compromised.

Step-by-step explanation:

This is an altered version of the information from the website given. I got a 100% on edgenunity.

8 = 2 · 2 · 2

22 = 2 · 11

GCF(8, 22) = 2

Answer: x = 7.2

=============================

Explanation:

As shown in the diagram (see attached image below), the red interior angles are

180-10x

180-15x

180-20x

180-5x

Each of those expressions is in the form 180-E, with E as the exterior angle. Add up the interior angles. Set the sum equal to 360 and solve for x. For any quadrilateral, the four interior angles always add to 360.

(angle1)+(angle2)+(angle3)+(angle4) = 360

(180-10x) + (180-15x) + (180-20x) + (180-5x) = 360

(180+180+180+180)+(-10x-15x-20x-5x) = 360

720-50x = 360

-50x = 360-720

-50x = -360

x = -360/(-50)

x = 36/5

x = 7.2

Answer:

±sqrt(7) = r

Step-by-step explanation:

21 = 3r^2

Divide each side by 3

21/3 = 3r^2/3

7 = r^2

Take the square root of each side

±sqrt(7) = sqrt(r^2)

±sqrt(7) = r

Answer:

The square root of 84 is 9.1651...etc, so in a shorter form, 9.

Answer: [tex]\sqrt[2]{21}[/tex]

Explanation: Work is provided in the image attached.

Answer:

f(x) = -60 is your answer

Step-by-step explanation:

Plug in 3 for x

f(x) = 5x² - 7(4x + 3)

f(x) = 5(3²) - 7(4(3) + 3)

Follow PEMDAS. First, solve the parenthesis

3² = 9

4(3) + 3 = 12 + 3 = 15

f(x) = 5(9) - 7(15)

Multiply

f(x) = 45 - 105

Simplify. Subtract

f(x) = 45 - 105

f(x) = -60

f(x) = -60 is your answer

~

The value of f(3) in the function f(x) = 5x² - 7(4x+3) is -60.

To find the value of f(3), we need to substitute x = 3 into the given function f(x) = 5x² - 7(4x+3). First, let's simplify the expression inside the parentheses: f(x) = 5x² - 28x - 21. Now substitute x = 3: f(3) = 5(3)² - 28(3) - 21. Simplifying further, we get: f(3) = 45 - 84 - 21 = -60.

To find the value of f(3) for the given function f(x) = 5x² - 7(4x+3), we need to substitute 3 in place of x:

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Answer:

x = 12        and    x = -4

Step-by-step explanation:

abs (x-4) = 8

When we have absolute value equations, we get two solutions, one positive and one negative

x-4 = 8        and   x-4 = -8

Add 4 to both sides

x-4+4 = 8+4       x-4+4=-8+4

x = 12        and    x = -4

[tex]|x-4|=8\iff x-4=8\ \vee\ x-4=-8\qquad\text{add 4 to both sides}\\\\\boxed{x=12\ \vee\ x=-4}[/tex]

Answer:

p = 12+5n

Step-by-step explanation:

For every added triangle, the perimeter only increases by 5.

For n=1, the perimeter is 6+6+5 = 17

For n=2, the perimeter is 6+6+5+5 = 22

So in general, the perimeter is 12 + 5n

Answer:

Q12. p = 5n + 12

Q13. See below.

Q14. y-intercept = (0, -3); x-intercept = (-3/2, 0).

Step-by-step explanations:

Question 12. Perimeter

      One triangle: p₁ = 2×6 + 1×5

    Two triangles: p₂ = 2×6 + 2×5

Three triangles : p₃ = 2×6 + 3×5

         n triangles: pₙ = 2×6 + n×5

General formula: p = 5n + 12

===============

Question 13. Modelling a function

Here's one possible table of values.

x   y

-3    3

-2    1

-1   -1

0  -3

1   -5

You can see the graph of the function in Fig. 1 below.

===============

Question 14. x- and y-intercepts

y- intercept

y = -2x – 3     Set x = 0

y = -2×0 – 3

y = 0 – 3

y = -3

The y-intercept is at (0, -3).

=====

x-intercept

y = -2x – 3      Set y = 0

0 = -2x – 3     Add 3 to each side

3 = -2x            Divide each side by -2

x = -3/2

The x-intercept is at (-3/2, 0).

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have the points (5, 2) and (0, -13). Substitute:

[tex]m=\dfrac{-13-2}{0-5}=\dfrac{-15}{-5}=3[/tex]

Answer:

3

Step-by-step explanation:

We are to find the slope of a line which passes through the two given points: (5, 2) and (0, -13).

We know the formula of the slope (m):

[tex]Slope[/tex][tex](m)[/tex]=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

So putting in the values of the coordinates of the given points in the formula to get:

Slope = [tex]\frac{-13-2}{0-5} =\frac{-15}{-5}[/tex] = 3

Therefore, the slope slope of a line which passes through the two given points: (5, 2) and (0, -13) is 3.

Answer:

x=9, y=-4

C (9,-4)

Step-by-step explanation:

−4y − 3x = −11

x − 2y = 17

WE are using substitution, so solve the second equation for x

Add 2y to each side

x -2y+2y = 17+2y

x = 17+2y

Substitute this into the first equation

-4y -3x = -11

-4y -3(17+2y) = -11

Distribute the 3

-4y -3*17 -3*2y = -11

-4y -51 -6y = -11

Combine like terms

-10y-51=-11

Add 51 to each side

-10y-51+51=-11+51

-10y = 40

Divide by -10

-10y/-10 = 40/-10

y = -4

Now we need to find x

x= 17+2y

x = 17+ 2(-4)

x =17-8

x=9

By solving the second equation for x, substituting into the first equation, and simplifying, we find the solution to the system is (9, -4), which corresponds to Option C.

In order to find the solution of the system using substitution, we first solve one of the equations for x or y. Looking at the second equation x - 2y = 17, we can solve for x to get x = 2y + 17. Now we substitute this expression for x into the first equation - 4y - 3x = - 11, which gives us:

- 4y - 3(2y + 17) = - 11

Simplifying this equation, we obtain:

- 4y - 6y - 51 = - 11

Combine like terms:

- 10y - 51 = - 11

Add 51 to both sides:

- 10y = 40

Now, divide both sides by - 10 to find y:

y = - 4

After obtaining the value for y, we substitute it back into the equation we derived for x (x = 2y + 17):

x = 2( - 4) + 17

Which simplifies to:

x = - 8 + 17

Finally, we get x = 9.

The solution for the system is therefore (9, - 4), which corresponds to Option C.

Answer:

The y intercept is -2

Step-by-step explanation:

To find the y intercept, set x = 0 and solve for y

2x-5y=10

0  -5y = 10

Divide each side by -5

-5y/-5 = 10/-5

y = -2

The  number sentence that  is not true is |-20| < 20 , option A

Let us consider each of the options;

Option A;

|-20| < 20

20<20

This statement is wrong because 20 is not less than 20

Option B

|9|=9

9=9

This statement is correct mathematically, hence the correct statement

Option C

|-20|>|9|

20>9

This statement is correct mathematically, hence the correct statement

Option D

|9|<|20|

9<20

This statement is correct mathematically, hence the correct statement

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Answer: y = 0.4

Step-by-step explanation: Using the distributive property, first by distributing the numbers outside the bracket to the ones inside.

( - 3 * 2 ) (- 3 *-0.4y) +5.6 = (0.4*3y) (0.4*1)

   - 6     +       1.2y  +   5.6  =  1.2y  +   0.4

Next step is to collect like terms :

(- 6 + 5.6) +1.2y  =  1.2y +0.4

- 0.4 +1.2y =1.2y +0.4

Next step is to get rid of of the 0.4 :

- 0.4 +1.2y =1.2y +0.4

+0.4                     +0.4

= 1.2y=1.2y+0.4

=1.2y-1.2y=0.4

y=0.4.

Answer:

The equation of  line is shown below.

Step-by-step explanation:

The equation of line is

[tex]y+1=\frac{-3}{5}(x-4)[/tex]

It is the point slope form of a line, therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the line passing through (4,-1).

Rewrite the above equation in slope intercept form.

[tex]y=\frac{-3}{5}x+\frac{12}{5}-1[/tex]

[tex]y=\frac{-3}{5}x+\frac{12-5}{5}[/tex]

[tex]y=\frac{-3}{5}x+\frac{7}{5}[/tex]

The point slope form of a line is

[tex]y=mx+b[/tex]

Where m is the slope and b is y-intercept.

Therefore the slope of the line is [tex]\frac{-3}{5}[/tex] and the y-intercept of the line is [tex]\frac{7}{5}[/tex].

Slope is defined as

[tex]m=\frac{Rise}{Run}[/tex]

Since the slope is negative, therefore the run of the line is considered on the left side. The line rise by 3 and run by 5, therefore we will add 7 in y and subtract 5 from x.

The y-intercept is [tex](0,\frac{7}{5})[/tex].

[tex](0-5,\frac{7}{5}+3)=(-5,\frac{22}{5})=(-5,4.4)[/tex]

Therefore we have three points (4,-1), (-5,4.4) and (0,1.4). Plot the point on the coordinate plane and connect them be a straight line.

The graph line for y+1 = -3/5(x-4)

Plot the y-intercept at (0, 7/5).

From that point, move 5 units to the right and 3 units down to find another point on the line. This gives you the point (5, 4/5).

You can continue this pattern, moving 5 units to the right and 3 units down from the previous point to find more points on the line.

To graph the line with the equation y + 1 = -3/5(x - 4), we can first rearrange it into the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

Starting with your equation:

y + 1 = -3/5(x - 4)

Let's isolate y:

y = -3/5(x - 4) - 1

Now, we can distribute the -3/5 to both terms inside the parentheses:

y = (-3/5)x + (12/5) - 1

y = (-3/5)x + 12/5 - 5/5

y = (-3/5)x + 7/5

Now that we have the equation in slope-intercept form (y = mx + b), we can see that the slope (m) is -3/5, and the y-intercept (b) is 7/5.

Now, we can plot this line on the coordinate plane. Start by plotting the y-intercept, which is the point (0, 7/5), and then use the slope to find additional points on the line. The slope of -3/5 means that for every 5 units to the right, you go 3 units down.

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Answer:

1. (h + p)(x) = 2x^2 - 11x + 16

2. It is the same problem as #1.

3. (k - f)(x) = 5x^3 + x^2 - 17x + 2

4. (q - g)(x) = 4x^2 + 7x - 14

Step-by-step explanation:

We are given that the values of h(x) = 2x^2 - 5x + 15 and p(x) = -6x + 1. Using these values you can substitute them into (h + p)(x).

(2x^2 - 5x + 15) + (-6x + 1)

Start by combining like terms. -5x and -6x will combine; 15 and 1 will also combine. 2x^2 will stay the same since there is no other term for it to combine with.

2x^2 - 11x + 16

Combine like terms. We will be adding since h(x) and p(x) are being added together.

We are given that k(x) = 8x^3 - 12x + 2 and f(x) = 3x^3 - x^2 + 5x. Knowing these values we can substitute k(x) and f(x) into (k - f)(x). This will look like:

(8x^3 - 12x + 2) - (3x^3 - x^2 + 5x)

Start by combining like terms. The terms to the same power can be combined (keep in mind we are finding the difference, in other words: subtracting). The terms with "x" can be combined as well. After doing so, your evaluated expression will look like:

5x^3 + x^2 - 17x + 2

q(x) = 4x^2 + 9x - 10 and g(x) = 2x + 4. Substitute q(x) and g(x) into (q - g)(x).

(4x^2 + 9x - 10) - (2x + 4)

Use the same rules I said above. The simplified expression will look like:

4x^2 + 7x - 14

The ascending order of the provided numbers is 4.045, 4.054, 4.405, 4.4005, and 4.504. This was achieved by comparing each decimal place from left to right.

The numbers 4.054, 4.045, 4.405, 4.504 and 4.4005 can be arranged in increasing order (from less to greater) by comparing each place value from left to right. When we compare these numbers, the arrangement from less to greater would be 4.045, 4.054, 4.405, 4.4005, and 4.504.

To do this, we first compare the numbers at each decimal place (tenths, hundredths, thousandths etc.), and arrange accordingly. We continue this process until we have the complete list in ascending order.

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Answer:

4.4

Step-by-step explanation:

The answer is 4.4 because if you know that 5*4 equal 20 so 4 can go each of the 5 groups so 24-20 leaves you with 4 so your answer is 4 remainder 4

Answer:

The value of y is 6.

Step-by-step explanation:

To find the value of y, start by using the known information we have in the equation for slope. The equation is below.

m(slope) = (y2 - y1)/(x2 - x1)

In this equation, the first ordered pair would be (x1, y1) and the second would be (x2 , y2). So we put the values in for these variables and we get.

1/2 = (7 - y)/(2 - 0)

1/2 = (7 - y)/2

Now we can use cross multiplication to solve for y.

1/2 = (7 - y)/2

1*2 = 2(7 - y)

2 = 14 - 2y

-12 = -2y

6 = y

It is closer to 1/4.

Hope this helps.

-TheOneandOnly003