Show that the equations x^2-7x+6=0 and y^2-14y+40=0 form a rectangle.Also find the joint equations of diagonals.

Answer:

11 yd

Step-by-step explanation:

To find the volume of a rectangular prism, we multiply the width, length and height.

We already know the length, 18, and the height, 11, and the volume, 2178, so we can easily solve for y.

[tex]18\cdot y\cdot11=2178\\192y=2178\\y = 11[/tex]

Hope this helped!

Answer:

Option B.

Step-by-step explanation:

Consider the correct question is "Which statement correctly compares

1. -201  and  151

-201 = 151

-201 < 51

-201 > 151"

The given numbers are -201 and 151. We need to compare these numbers.

We know that all negative numbers are less than positive numbers.

So,

-201 < 151

If both numbers are negative, then the larger negative number is the smaller number.

Therefore, the correct option is B.

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

Work Shown:

[tex]33^{-1} \equiv 77 \text{ (mod 508)}\\\\(3*11)^{-1} \equiv 77 \text{ (mod 508)}\\\\3^{-1}*11^{-1} \equiv 77 \text{ (mod 508)}\\\\3*3^{-1}*11^{-1} \equiv 3*77 \text{ (mod 508)}\\\\11^{-1} \equiv 231 \text{ (mod 508)}\\\\[/tex]

Notice how 33*77 = 2541 and 11*231 = 2541

[tex]2541 \equiv 1 \text{ (mod 508)}[/tex] since 2541/508 has a remainder of 1.

So effectively [tex]33*77 \equiv 1 \text{ (mod 508)}[/tex] and [tex]11*231 \equiv 1 \text{ (mod 508)}[/tex]

Answer:

d. -4

Step-by-step explanation:

Let's plug in g

8 - |2(-3.5) - 5|

8 - |-7-5|

8 - |-12|

The absolute value is always positive of any number,

8 - 12

= -4

Answer:

D. -4

Step-by-step explanation:

We are given this expression:

[tex]8-|2g-5|[/tex]

and asked to evaluate when g= -3.5 Therefore, we must substitute -3.5 in for g.

[tex]8-|2(-3.5)-5|[/tex]

First, multiply 2 and -3.5

2 * -3.5 = -7

[tex]8-|-7-5|[/tex]

Next, subtract 5 from -7.

-7-5= -12

[tex]8-|-12|[/tex]

Next, evaluate the absolute value of -12. The absolute value is how far away a number is from 0, and it is always positive. The absolute value of -12 is 12.

[tex]8-12[/tex]

Subtract 12 from 8.

[tex]-4[/tex]

The value of the expression is -4 and D is the correct answer.

Answer:

Step-by-step explanation:

Cost price of three machines with repairment charge ( CP ) = 5400 × 3 + 4000

= Rs 20200

Selling price of 1 machine = Rs 7000

Selling price of 3 machines ( S.P )= Rs 7000 × 3

= Rs 21000

Since , SP > CP , he made a profit

Profit = SP - CP

= Rs 21000 - Rs 20200

= Rs 800

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

Further more explanation

Profit and loss

In any business , owners have intension to have profit by selling articles. The price at which an article is purchased is called it's Cost price ( C.P ) and the price at which it is sold is called Selling price ( S.P ).

If the selling price is less than cost price of an article then there is a loss.

[tex] \mathrm{Loss \: = \: Cost \: Price \: (C.P) - Selling \: Price \: (S.P)}[/tex]

If the selling price is more than cost price of an article then there is a profit ( gain )

[tex] \mathrm{Profit = Selling \: Price \: (S.P) - Cost \: Price \: (C.P)}[/tex]

So, If S.P > C.P, there is profit in dealing.

If C.P > SP , there is loss in dealing.

Hope I helped!

Best regards!!

Answer:

Step-by-step explanation:

A matrix is a set of numbers organized in rows and columns to represent the variables in a situation, and the determinant is used to find the inverse of a matrix which helps you solve for different variable values.

Answer: A matrix or matrices is a rectangular grid of numbers or symbols that is represented in a row and column format. A determinant is a component of a square matrix and it cannot be found in any other type of matrix. ... A determinant is a number that is associated with a square matrix.

Step-by-step explanation:

Answer:

x = -0.4

x = -(2/5)

Answer:

x = ± √5

Step-by-step explanation:

Please indicate exponentiation by using the symbol " ^ ":

5x^2 + 25x = 0

Divide all three terms by 5.  We get:

x^2 + 5 = 0, or x^2 = -5

Then x = ± √5

Answer: C) similar, SAS similarity, triangle LQR

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

Explanation:

The vertical angles KLJ and QLR are congruent. This forms the "A" in "SAS". The angles in question are between the marked sides.

KL = 18 is twice that of QL = 9, or put another way, KL/QL = 18/9 = 2. The ratio of the sides is 2. Also, JL/RL = 16/8 = 2 is the same ratio. Because both pairs of sides have the same ratio, the sides are in proportion. This helps form the two "S" letters of "SAS".

The original triangle has LKJ mentioned at the top. Note the order as its important. We start with L and move to K, so LK is the first segment mentioned. LK = 18 pairs up with LQ = 9, meaning that LQ must be the first segment mentioned of the answer triangle. Therefore LQR is the correct letter sequence if we start with point L. Writing QLR is not correct because Q is the first letter here but Q does not pair up with L.

Answer:

3250

Step-by-step explanation:

so for the first and 2nd show, the attendance is 2580 and 2920.

The average of both these numbers is 2750

the if the third show had 3000 people, the average attendance would only be 2875.

We need the average number to be 3000.

2750 is 250 less than 3000, so the other number must be 250 more.

3250 is how many people should go to the last show.

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

Explanation:

We have 2580 people attend the first show and 2920 attend the second. So far, that's 2580+2920 = 5500 people. Add on another x people to get 5500+x, which represents the sum of all three days attendance figures. Divide this sum by 3 to get the average attendance

average attendance = (sum of individual attendance values)/(number of days)

average attendance = (5500+x)/3

So that's why (5500+x)/3 goes in the first box. The parenthesis are important to ensure that you divide all of "5500+x" over 3. If you just wrote 5500+x/3, then the computer would think you just want to divide x only over 3.

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

We set (5500+x)/3 equal to 3000 as we want the average of the three days to be 3000

(5500+x)/3 = 3000

5500+x = 3*3000

5500+x = 9000

x = 9000-5500

x = 3500

We need 3500 people to show up on day 3 so that the average of all three days is 3000.

3500 goes in the second box.

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

Check:

The figures for the three days are 2580, 2920, and 3500

They add to 2580+2920+3500 = 9000

Which divides to 9000/3 = 3000, which is the average we're after. So the answer is confirmed.

Answer:

  C)  y ≥ 3

Step-by-step explanation:

The answer choices suggest that you're interested in the range of the function. x^2 cannot be negative, so its value will be 0 or greater. Adding 3 to x^2 ensures that the value of f(x) will be 3 or greater.

  y ≥ 3 . . . . matches C

Answer:

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos es de $13.90

Step-by-step explanation:

La información dada son;

El valor de la máscara = $ 1.25

El valor del paquete de jabones = $ 2.00

El valor del gel de alcohol = $ 3.00

La cantidad que le quedaba después de pagar = $ 7.65

Por lo tanto, tenemos;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = La cantidad que le quedaba después de pagar + El valor del gel de alcohol + El valor del paquete de jabones + El valor de la mascarilla

Por lo tanto;

La cantidad inicial que tenía la madre de Rosita antes, comprando los artículos = $ 7.65 + $ 3.00 + $ 2.00 + $ 1.25 = $ 13.90.

Answer:

p= 25/100 = 180/x

Step-by-step explanation:

In order to find the computer's original price, you must use the equation p= 25/100 = 180/x and solve for x.

Answer:

0.75p=p-180

Step-by-step explanation:

0.75p=p-180 is your answer

Part (a)

BC = opposite side (furthest leg from the reference angle)

AB = adjacent side (closest leg from the reference angle)

AC = hypotenuse (always opposite the 90 degree angle)

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

Part (b)

i. False. Angle B is 90 degrees as shown by the square angle marker.

ii. False. Side AB is opposite angle C. Note how "C" is part of "BC", so that means we cannot have BC be opposite C.

iii. True. Leg AB is the closer leg to angle A. We have "A" in "AB" to see this without having to draw the diagram. Refer to part (a) above.

iv. False. The longest side of any right triangle is always the hypotenuse. The longest side of any triangle is always opposite the largest angle.

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

Part (c)

cos(theta) = adjacent/hypotenuse = AB/AC

tan(theta) = opposite/adjacent = BC/AB

Refer back to part (a) to determine the opposite,adjacent and hypotenuse side lengths.

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

Part (d)

The reference angle has changed, so the opposite and adjacent sides swap. The hypotenuse remains the same regardless of what reference angle you pick.

sin(C) = opposite/hypotenuse = AB/AC

cos(C) = adjacent/hypotenuse = BC/AC

tan(C) = opposite/adjacent = AB/BC

Note the tangent ratio is the reciprocal of what we found back in part (c).

Answer & Step-by-step explanation:

(a)

The hypotenuse is on line CA (the hypotenuse is always opposite the 90° angle (marked by a little square))

The adjacent is on the line BA (adjacent is next to the given angle, but NOT the hypotenuse)

The opposite is on the line CB (this is opposite the given angle)

(b)

i.   false (b is a right angle)

ii.  false (the side opposite C is BA)

iii. true

iv. false (the side opposite B is the hypotenuse, and the hypotenuse is always the longest side in a triangle)

(c)

cosine ratio: [tex]cos=\frac{adjacent}{hypotenuse}[/tex]

tangent ratio: [tex]tan=\frac{opposite}{adjacent}[/tex]

The cosine and tangent ratios of the given angle:

[tex]cos0=\frac{AB}{CA} \\\\tan0=\frac{CB}{AB}[/tex]

(d)

Remember SOH-CAH-TOA:

Sine=Opposite/Hypotenuse

Cosine=Adjacent/Hypotenuse

Tangent=Opposite/Adjacent

Using the angle C, plug in the appropriate sides:

[tex]sinC=\frac{BA}{CA}\\\\ cosC=\frac{CB}{CA}\\\\ tanC=\frac{BA}{CB}[/tex]

:Done

Answer:

I hope this helps!

Answer D

Step-by-step explanation:

Step-by-step explanation:

salary per day =$140

bonus on sales =14%

sales on Saturday =$600

bonus on Saturday sales=14/100*$600

=$84

sales on Sunday =$1200

bonus on Sunday sales=14/100*$1200

=$168

total amount she earned over the two days=$140+$84+$168

=$532

Answer:

a21 = -61

Step-by-step explanation:

[tex]a_{n}=a_{1}+(n-1)d[/tex]

[tex]-19=a_{1}+(7-1)d[/tex]

[tex]-28=a_{1}+(10-1)d[/tex] (subtract to eliminate a₁)

9 = -3d

d = -3

-19 = a₁ + (6)(-3)

-1 = a

a21 = -1 + (21 - 1)(-3)

= -61

Answer:

-61 (Answer D)

Step-by-step explanation:

The general formula for an arithmetic sequence with common difference d and first term a(1) is

a(n) = a(1) + d(n - 1)

Therefore, a(7) = -19 = a(1) + d(7 - 1), or a(7) = a(1) + d(6) = -19

and a(10) = a(1) + d(10 - 1) = -28, or a(1) + d(10 - 1) = -28

Solving the first equation a(1) + d(6) = -19 for a(1) yields a(1) = -19 - 6d.  We substitute this result for a(1) in the second equation:

-19 - 6d + 9d = -28.  Grouping like terms together, we get:

3d = -9, and so d = -3.

Going back to an earlier result:  a(1) = -19 - 6d.

Here, a(1) = -19 - 6(-3), or a(1) = -1.

Then the formula specifically for this case is a(n) = -1 - 3(n - 1)

and so a(21) = -1 - 3(20) = -61 (Answer D)

Answer:

h = 10

Step-by-step explanation:

Given

[tex]\frac{3}{7}[/tex] = [tex]\frac{h}{14}[/tex] - [tex]\frac{2}{7}[/tex]

Multiply through by 14 to clear the fractions

6 = h - 4 ( add 4 to both sides )

10 = h

Answer:

10

Step-by-step explanation:

We start out with 3/7 = h/14 - 2/7

add 2/7 to both sides:

(5/7) = h/14

Multiply both sides by 14 to get rid of the fraction:

h = 10

Answer:

(7,-4) ; 12

Step-by-step explanation:

Basically, three corners of a rectangle are already on the graph. If you put a dot at (7,-4), that is the last corner(vertex) that finishes the rectangle

Then to find base of the rectangle, you find the length of the longer side, (the distance between the x coordinates). So you would subtract -5 from 7 and get 12, and 12 is the length of your base.

Answer:

B. 1/2

Step-by-step explanation:

y = ax^2 + bx + c

14 = a(0)^2 + b(0) + c

c = 14

10.5 = a(1)^2 + b(1) + 14

10.5 = a + b + 14 ____(i)

8 = a(2)^2 + b(2) + 14

8 = 4a + 2b + 14

4 = 2a + b + 7 ___ (ii)

i - ii

10.5 - 4 = -a + 7

6.5 = -a + 7

a = 7- 6.5

a = 0.5

Value of a in the quadratic function is 0.5

In algebra, a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic, is a polynomial function with one or more variables in which the highest-degree term is of the second degree

Given,

Quadratic function

y = [tex]ax^{2}+bx+c[/tex]

Consider values in the table x= 0 and  y =14

[tex]14=a(0)^{2}+b(0)+c\\ c=14[/tex]

Consider x=1 and y = 10.5

[tex]10.5=a(1^{2})+b(1)+c\\ a+b=10.5-14\\a+b=-3.5[/tex]

Consider x=2 and y =8

[tex]8=a(2^{2})+b(2)+c\\ a\\8=4a+2b+14\\4a+2b=-6\\2a+b=-3[/tex]

Subtract a + b= -3.5 from 2a + b= -3

a=-3--3.5=0.5

Hence, the Value of a in the quadratic function is 0.5

Learn more about Quadratic function here

https://brainly.com/question/5975436

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Answer:

Step-by-step explanation:

a:b = 3:2    ⇒   a = 3x  and  b = 2x

a - b = 5

3x - 2x = 5

x = 5

a = 3•5 = 15

b = 2•5 = 10

Answer:

The critical value of F for this situation is 2.975.

Step-by-step explanation:

A test is being performed to determine if a particular drug, smartozine, affects maze learning in rats.

The groups are divided as follows:

So, there were in total k = 4 groups with n = 30 rats.

The significance level of the test is, α = 0.05.

Compute the critical value of F as follows:

[tex]F_{\alpha, (k-1, n-k)}=F_{0.05, (4-1, 30-4)}=F_{0.05, (3,26)}=2.975[/tex]

*Use the F-table.

Thus, the critical value of F for this situation is 2.975.

The critical value of F for this situation has been 2.975.

The F value has been the statistical factor that has been used for the determination of the significance of the test.

The high F value has been the representation of the rejected null hypothesis, while the low  F value represents the accepted hypothesis. The study that has been performed with the rats has:

Number of groups of rats = k = 4

Total number of rats = n = 30

The 0.05 significance test has been performed, thus the value of α has been 0.05.

The value of F can be given as:

Critical value = [tex]\rm F_\alpha_\;_,(_k_-_1,_n_-_k_)[/tex]

Substituting the values:

Critical value = [tex]\rm F_0._0_5,_(_4_-_1,_3_0_-_4_)[/tex]

Critical value = 2.975

Thus, the critical value of F for this situation has been 2.975.

For more information about the F value, refer to the link:

https://brainly.com/question/11566053

Answer:

10800

Step-by-step explanation:

1 trimesters cost = 1450 + 350  $

2 year -> 6 trimester

1800$ x 6 = 10800 $

Estimate:

2.3 rounds down to 2

So after multiplying by 2, the area is estimated to be 4 cm squared.

Actual Area:

2.3 x 2 = 4.6

The actual area of the shape is 4.6 cm squared.

Hope this helped!

Answer:

4.6

Step-by-step explanation:

Answer:

f(x) = - 3x + 4

Step-by-step explanation:

Note that y = f(x)

Rearrange making y the subject

9x + 3y = 12 ( subtract 9x from both sides )

3y = - 9x + 12 ( divide all terms by 3 )

y = - 3x + 4 , that is

f(x) = - 3x + 4

Step-by-step explanation:

why did u add the 5 in the question?.

Answer:

Each slice of pizza cost:

$1.63

Step-by-step explanation:

4.89/3 = 1.63

Answer:

$1.63

Step-by-step explanation:

We want to find the cost per slice of pizza. Therefore, we must divide the total cost by the number of slices of pizza.

cost / slices

It costs $4.89 for 3 slices.

$4.89 / 3 slices

Divide 4.89 by 3 (4.89/3=1.63)

$1.63 / slice

The cost of each slice of pizza is $1.63

Answer:

D. zero

Step-by-step explanation:

Since the graphs do not intersect, there are zero solutions.

The number of solutions on the graph is zero

The graph shows a linear equation (the straight line) and a non linear equation (the curve)

From the graph, we can see that the straight line and the curve do not intersect

This means that the graph do not have any solution

Hence, the number of solutions on the graph is zero

Read more about non-linear graphs at:

https://brainly.com/question/16274644

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Answer:

-i

Step-by-step explanation:

(-i)^0 = 1

(-i)^1 = -i

(-i)^2 = -1

(-i)^3 = -i

(-i)^4 = 1

(-i)^5 = -i

etc.

From this pattern, you see that when the exponent is a multiple of 4, you get 1. When the exponent is a multiple of 4 plus 1, you get -i, etc.

213 = 4 * 53 + 1

213 is 1 more than a multiple of 4.

(-i)^213 = (-i)^1 = -i

Answer:

18 inches by 36 inches.

Step-by-step explanation:

Since we have given that

The generic version was basedOn the brand name and was 2/3

And given Dimensions of generic version is given by 12inches ×24inches

If we use the first dimensions of 12inches we have

12=2/3 × brand

12×3/2 = brand

=18inches= brand

we use the first dimensions of 24 inches we have

24=2/3 × brand

24×3/2 = brand

=36 inches= brand

brand= 36 inches

Therefore,the dimensions of brand name will be 18 inches by 36 inches.

[tex]t=\sqrt{\dfrac{ab-s}{r+ak}}\\\\t^2=\dfrac{ab-s}{r+ak}\\\\rt^2+akt^2=ab-s\\\\akt^2-ab=-rt^2-s\\\\a(kt^2-b)=-(rt^2+s)\\\\a=-\dfrac{rt^2+s}{kt^2-b}\\\\a=-\dfrac{rt^2+s}{-(b-kt^2)}\\\\a=\dfrac{rt^2+s}{b-kt^2}[/tex]

Answer:

Amplitude = 2

Step-by-step explanation:

The amplitude of this sine wave is 2 denoted by the coefficient -2 in front of the sin(x).  The negative of the coefficient denotes that the sine wave is the opposite of the standard sine wave.

Cheers.