A system of linear equations has infinitely many solutions. Does that mean any ordered pair in the coordinate plane is a solution?

Answer:

[tex]\large\boxed{\left\{\begin{array}{ccc}3x-2y-7=0\\10x+2y-6=0\end{array}\right}[/tex]

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}3x-2y-7=0\\5x+y-3=0&\text{multiply both sides by 2}\end{array}\right\\\\\boxed{\underline{+\left\{\begin{array}{ccc}3x-2y-7=0\\10x+2y-6=0\end{array}\right}}\qquad\text{add both sides of the equations}\\.\qquad\qquad13x-13=0\qquad\text{add 13 to both sides}\\.\qquad\qquad 13x=13\qquad\text{divide both sides by 13}\\.\qquad\qquad x=1\\\\\text{put the value of x to the second equation:}\\\\5(1)+y-3=0\\(5-3)+y=0\\2+y=0\qquad\text{subtract 2 from both sides}\\y=-2\\\\\boxed{x=1,\ y=-2}[/tex]

Answer:

It takes 1 hour to travel 90 miles.

The point (1,90) represents a specific location on the graph based on its coordinates.

The point (1,90) represents a specific location on the graph. In this case, the x-coordinate is 1, which means it is 1 unit to the right from the origin on the horizontal axis. The y-coordinate is 90, which means it is 90 units above the origin on the vertical axis. So, the point (1,90) is plotted on the graph at the intersection of the x-coordinate 1 and the y-coordinate 90.

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Step-by-step explanation:

if f = c/lambda

then c = f × lambda

Answer:

B. c = fλ

Step-by-step explanation:

Given formula,

f equals c over lambda,

[tex]\implies f=\frac{c}{ \lambda}[/tex]

Where, f = frequency,

c = wave speed,

λ = wavelength,

By the above formula,

[tex]f\times \lambda = c[/tex]   ( By cross multiplication ),

Hence, the required formula for c,

[tex]c=f\lambda[/tex]

Option 'B' is correct.

Answer:

Im pretty sure its answer d hope that helped

Step-by-step explanation:

D. f(x) = 5*.

The derivative of a function may be used to determine whether the function is increasing or decreasing at any intervals in its domain. If f′(x) > 0 at each point in an interval I, then the function is said to be increasing on I. f′(x) < 0 at each point in an interval I, then the function is said to be decreasing on I.

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The mode is the number that appears most often in a data set.

For number two you have the numbers 100, 83, 97, 63, 83

The number 83 is listed two times and the other numbers are only listed once.

The mode would be 83

Answer:

Square with side length 25/4 m

Step-by-step explanation:

The area is always going to be largest for a rectangle when the two dimensions are equal.  You are looking for a square. What square has perimeter 25? 4s=25 so the side length of this rectangle (Square) is 25/4 m.

Answer:

It's a square  6.25 * 6.25 m.

Step-by-step explanation:

We can do this using calculus.

Let the  length of the  rectangle be x m.

2x + 2w = 25   where w = the width.

2w = 25 - 2x

w = 12.5 - x

So the area A = x(12.5 - x) = 12.5x - x^2.

Finding the derivative:

dA /dx = 12.5 - 2x

For a maximum area this = zero

12.5 - 2x = 0

x = 6.25m.

and w = 25 - 12.5  = 6.25m.

(For any rectangle the  maximum area is always a square).

Answer:

The variance of the data is 49.

The median is 64.

The data point 50 is tow standard deviations away for the mean.

The correct statements are true about the curve are as follows;

The variance of the data set is 49.

The median is 64.

The data point 50 is two standard deviations away from the mean.

The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance.

The correct statements are true about the curve are as follows;

1. The variance of the data set is;

[tex]\rm \sigma ^2=7^2\\ \\ \sigma ^2=49[/tex]

The variance of the data set is 49.

2. The median is the middle value of the data set.

The median is 64.

3. The data point 50 is two standard deviations away from the mean.

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Answer:

A

Step-by-step explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 4, 2) and (x₂, y₂ ) = (3, 9)

m = [tex]\frac{9-2}{3+4}[/tex] = [tex]\frac{7}{7}[/tex] = 1 → A

Answer:

The variance is 8732.24 and the standard deviation is 93.45

Step-by-step explanation:

* Lets explain how to find variance and the standard deviation

# Step 1: find the mean of the data set

∵ The mean = the sum of the data ÷ the number of the data

∵ The data set is 3832 , 3779 , 3655 , 3642 , 3579

∵ Their sum = 3832 + 3779 + 3655 + 3642 + 3579 = 18487

∵ They are five numbers

∴ The mean = 18487 ÷ 5 = 3697.4

# Step 2: subtract the mean from each data and square the answer

∴ (3832 - 3697.4)² = 18117.16

∴ (3779 - 3697.4)² = 6658.56

∴ (3655 - 3697.4)² = 1797.76

∴ (3642 - 3697.4)² = 3069.16

∴ (3579 - 3697.4)² = 14018.56

# Step 3: calculate the Variance (σ²) , by adding the square difference,

  and divide it by the number of the data

∵ Variance = sum of the square difference ÷ number of the data

∵ The sum = 18117.16 + 6658.56 + 1797.76 + 3069.16 + 14018.56  

∴ The sum = 43661.2

∴ σ² = 43661.2 ÷ 5 = 8732.24

# Step 4: the standard deviation (σ) is the square root of variance

∴ The standard deviation = √(8732.24) = 93.446455 ≅ 93.45

* The variance is 8732.24 and the standard deviation is 93.45

Answer:

try the third table

Step-by-step explanation:

try the third table because the others would end up nonlinear

Answer:

A

Step-by-step explanation:

2y=3x-4

4=3x-2y

3x-2y=4

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}-5x=y-5&\text{subtract y from both sides}\\-2y=-x-21&\text{add x to both sides}\end{array}\right\\\left\{\begin{array}{ccc}-5x-y=-5&\text{multiply both sides by (-2)}\\x-2y=-21\end{array}\right\\\underline{+\left\{\begin{array}{ccc}10x+2y=10\\x-2y=-21\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad11x=-11\qquad\text{divide both sides by 11}\\.\qquad x=-1\\\\\text{put the value of x to the first equation:}\\\\10(-1)+2y=10\\-10+2y=10\qquad\text{add 10 to both sides}\\2y=20\qquad\text{divide both sides by 2}\\y=10[/tex]

Answer:The person above is right

Step-by-step explanation:

Let's say that the coordinates of the squirrel are: (x, y)

Since the coordinates of the acorn is halfway, between the tree and the squirrel, that means the acorn is the midpoint.

To work out the midpoint you do:

(sum of x-coordinates) divided by 2,  (sum of y coordinates) divided by 2.

We can use this to form an equation .

So the sum of the x coordinates of the tree and the squirrel = -1   :

x-coordinates of the squirrel:

[tex]\frac{-3+x}{2}=-1[/tex]                   (now solve for x)

[tex]-3+x = -2[/tex]

[tex]x=1[/tex]

y-coordinates:

[tex]\frac{8+y}{2}=5[/tex]                   (now solve for y)

[tex]8+y=10[/tex]

[tex]y = 2[/tex]

So the coordinates of the squirrel are: (1, 2)

____________________

Answer:

(1, 2)

Answer:

(1,2)

Step-by-step explanation:

By the information given in the problem, we know that the midpoint of the squirrel's coordinates and the tree's coordinates are the coordinates of the acorn on the tree.

Let the squirrel's coordinates be $(x,y)$ so we have $$\left(\frac{-3+x}{2},\frac{8+y}{2}\right)=(-1,5).$$Solving $\frac{-3+x}{2}=-1$ and $\frac{8+y}{2} = 5$, we find that the squirrel's coordinates are $\boxed{(1,2)}$.

Answer:

yes

Step-by-step explanation:

connect dc to <abc and you have a triangle

connect bc to <ebc and you have the same triangle just reflected over the y axis

Congruent triangles are the exact same triangles, but they might be placed at different positions. The correct option is B.

Congruent triangles are the exact same triangles, but they might be placed at different positions.

Suppose it is given that two triangles ΔABC ≅ ΔDEF

Then that means ΔABC and ΔDEF are congruent.

The order in which the congruency is written matters.

For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.

Thus, we get:

[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D \angle B = \angle E\\\\\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E \\\\\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F \\\\\rm |AB| = |DE| \: \: or \: \: AB \cong DE\\\\\rm |AC| = |DF| \: \: or \: \: AC \cong DF\\\\\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex]

(|AB| denotes length of line segment AB, and so on for others).

In the two of the given triangle, therefore, ΔADC and ΔEBC,

∠CAD = ∠CEB {Already given in the triangle}

∠ACD = ∠ ECB {It is the common angle between two triangles}

CD = CB {Already given in the triangle}

Since in the two triangles, two angles are equal and a side is equal as well, therefore, the two triangles are congruent using the AAS (Angle-Angle-Side) postulate.

Hence, the correct option is B.

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Check the picture below.

let's recall Cavalieri's principle, that solids with equal altitudes and identitical cross-sectional areas at each part all the way up, have the same volume.

so, for a prism like this that is not oblique, with rhombic bases of area 600 and a height/altitude of 24, the volume will simply be the base * height, 600 * 24 = 14400.

well, based on Cavalieri's principle, an oblique one will also have the same volume.

Answer:

The volume of the prism is 14400 units³.

Step-by-step explanation:

It is given that an oblique prism is created using rhombuses with edge lengths of 25 units.

The volume of a prism is

[tex]V=B\times h[/tex]                   ..... (1)

Where, B is base area and h is height of the prism.

It is given that the area of one rhombus is 600 sq units. The perpendicular distance between the bases is 24 units.

Substitute B=600 and h=24 in equation (1) to find the volume of the prism.

[tex]V=600\times 24[/tex]

[tex]V=14400[/tex]

Therefore the volume of the prism is 14400 units³.

Answer:

15

Step-by-step explanation:

f(x)=5x+40

f(x)=5(-5)+40

f(x)=-25+40

f(x)=15

You must replace x with -5 and solve using the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction) REMEMBER: IF NOT APPLICABLE TO THE EQUATION YOU MAY SKIP THAT STEP IN PEMDAS .

5(-5) + 40

Multiplication...

5 * -5 = -25

-25 + 40

Addition...

When adding a positive number with a negative number you will act as if you are subtracting the two numbers, then take the sign of the largest number. In this case the largest number is 40 and its sign is positive. Your answer will  have a posititve sign.

-25 + 40 ----> 40 - 25 = 15

-25 + 40 = 15

15

Hope this helped!

~Just a girl in love with Shawn Mendes

the angles are supplementary meaning they equal 180 degrees so 100-x=180

x=80

ANSWER

[tex]m \angle ACE = 80 \degree[/tex]

EXPLANATION

Recall that adjacent angles on a straight line will add up to 180°

From the diagram, m<ACD and m<ACE are adjacent angles on a straight line because they have a common vertex at C.

We sum the two angles and equate them to 180°

[tex] m \angle \: ACD + m \angle ACE = 180 \degree[/tex]

From the diagram

[tex]m\angle ACD= 100 \degree[/tex]

We substitute the known angle to obtain:

[tex]100 \degree + m \angle ACE = 180 \degree[/tex]

[tex]m \angle ACE = 180 \degree - 100 \degree[/tex]

[tex] \therefore \: m \angle ACE = 80 \degree[/tex]

Answer:

Step-by-step explanation:

n²+2n+1 = (n+1)(n+1)

n²-8n-9 = (n+1)(n-9)

the least common denominator for these two rational expressions is :

(n+1)(n-9)

Answer:

The measure of the angles are

m∠1=128°

m∠2=52°

m∠3=52°

m∠4=128°

m∠5=128°

m∠6=128°

m∠7=52°

m∠8=52°

Step-by-step explanation:

see the attached figure with numbers to better understand the problem

step 1

Find the measure of angle 5  

we know that

m∠5+52°=180° ----> by consecutive interior angles

m∠5=180°-52°=128°

step 2

Find the measure of angle 8

we know that

m∠8=52° ----> by vertical angles

step 3  

Find the measure of angle 7

we know that

m∠7=m∠8 ----> by corresponding angles

we have

m∠8=52°

therefore

m∠7=52°

step 4

Find the measure of angle 6

we know that

m∠6+m∠7=180° ----> by supplementary angles

we have

m∠7=52°

therefore

m∠6+52°=180°

m∠6=180°-52°=128°

step 5

Find the measure of angle 3

we know that

m∠3+m∠6=180° ----> by consecutive interior angles

we have

m∠6=128°

m∠3=180°-128°=52°

step 6

Find the measure of angle 2

we know that

m∠2=m∠3 ----> by vertical angles

we have

m∠3=52°

therefore

m∠2=52°

step 7

Find the measure of angle 1

we know that

m∠1+m∠3=180° ----> by supplementary angles

we have

m∠3=52°

therefore

m∠1+52°=180°

m∠1=180°-52°=128°

step 8

Find the measure of angle 4

we know that

m∠4=m∠1 ----> by vertical angles

we have

m∠1=128°

therefore

m∠4=128°

Answer: The Answer Is 9

Step-by-step explanation:

If 4x - 12 = 24, add 12 to 24, and divide 36 by 4.

Answer: B.9

Step-by-step explanation:

You know that [tex]\angle A[/tex]≅[tex]\angle B[/tex], this means that the measure of the angle A and the measure of the angle B are equal. Then:

[tex]m\angle A=m\angle B[/tex]

You know that:

[tex]m\angle A=4x-12[/tex] and [tex]m\angle B=24[/tex]

Therefore, you can substitute them into [tex]m\angle A=m\angle B[/tex] :

[tex]4x-12=24[/tex]

Now you can solve for the variable "x":

[tex]4x=24+12\\\\4x=36\\\\x=\frac{36}{4}\\\\x=9[/tex]

You can observe that this value of "x" matches with the option B.

Answer:

the answer is 181 2/4 OR 181 1/2 hours a month.

Step-by-step explanation:

you multiply the days per month=22

by the hours they work per day=8 1/4

(optional) You turn 1/4 into .25

then: 22 × 8.25= 181.5/181 1/2

Based on the number of days worked per month and the hours worked, the number of hours worked per month is 181.5 hours.

First convert the mixed fraction to a decimal:

1/4 = 0.25

8¹/₄ = 8.25

If they work 8.25 hours a day and work for 22 days, the number of hours worked per month is:

= 8.25 x 22 days

= 181.5 hours

In conclusion, they would work for 181.5 hours.

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[tex]\frac{4}{7}/\frac{-3}{8}[/tex]

With division when using fraction the first fraction stays the same, but you will switch the division sign to multiplication and you will take the reciprocale (flip the numerator and denominator) of the second fraction like so...

[tex]\frac{4}{7}*\frac{-8}{3}[/tex]

Now you can multiply normally:

[tex]\frac{4*(-8)}{7*3}[/tex]

[tex]\frac{-32}{21}[/tex] <<<This is your answer

Hope this helped!

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Answer:

Commutative property

Answer:

No, because it does not have a constant rate of change.

Step-by-step explanation:

On the x side of the table, there is a constant rate of change (+1). However, on the y side, it is not. The first change is +7, the next +5, and the last +6. The rate of change has to be constant on both sides for the table to be considered linear.

Step-by-step explanation:

0.89 = 1 - 1/(k²)

Start by subtracting 1 from both sides:

0.89 - 1 = -1/(k²)

-0.11 = -1/(k²)

Multiply both sides by -1:

0.11 = 1/(k²)

Multiply both sides by k²:

0.11 k² = 1

Divide both sides by 0.11:

k² = 1 / 0.11

Take the square root:

k = √(1 / 0.11)

Answer:

+/- 3.015 to the nearest thousandth.

Step-by-step explanation:

0.89 = 1 - 1 / k^2

Multiply through by k^2

0.89k^2 = k^2 - 1

k^2 - 0.89k^2 = 1

0.11 k^2 = 1

k^2 = 1/0.11 = 9.091

k = +/- √0.091

= +/-3.015.

Answer:

The mixed number, can be written as the improper fraction, . The reciprocal of is found by interchanging (“flipping”) the numerator and denominator. When you divide by a whole number, you multiply by the reciprocal of the divisor.

Step-by-step explanation:

To get the reciprocal of a fraction, swap the numerator and denominator; if the original fraction's numerator is divisible by the denominator, the reciprocal will be a whole number. Multiplying by a fraction is the same as dividing by its reciprocal.

To find the reciprocal of a fraction, you simply swap the numerator and the denominator.

For example, the reciprocal of ⅔ (which is 2/8) is 8/2.

However, if you have a fraction and you want to get a reciprocal that is a whole number, you must ensure that the numerator of the original fraction is divisible by the denominator.

If we consider the fraction ⅕ (which is 1/5), its reciprocal is 5/1, or simply 5, which is a whole number.

In essence, finding a reciprocal involves flipping the fraction: turning the top number (numerator) into the bottom number (denominator), and the bottom number into the top number.

This process is akin to multiplying or dividing by the fraction.

For instance, when you multiply a value by a fraction, you are effectively dividing by its reciprocal, and vice versa.

Multiplying fractions involves multiplying the numerators together and the denominators together, and simplifying where possible.

Answer:

[tex]\large\boxed{x=-1\pm3\sqrt2}[/tex]

Step-by-step explanation:

[tex]x^2+2x=17\\\\x^2+2(x)(1)=17\qquad\text{add}\ 1^2=1\ \text{to both sides}\\\\x^2+2(x)(1)+1^2=17+1\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1)^2=18\Rightarrow x+1=\pm\sqrt{18}\\\\x+1=\pm\sqrt{9\cdot2}\\\\x+1=\pm\sqrt9\cdot\sqrt2\\\\x+1=\pm3\sqrt2\qquad\text{subtract 1 from both sides}\\\\x=-1\pm3\sqrt2[/tex]

Answer:

D

Step-by-step explanation:

The ratios of corresponding sides are equal, that is

[tex]\frac{BD}{CD}[/tex] = [tex]\frac{AD}{BD}[/tex]

Substitute values

[tex]\frac{h}{16}[/tex] = [tex]\frac{9}{h}[/tex] ( cross- multiply )

h² = 16 × 9 = 144 ( take the square root of both sides )

h = [tex]\sqrt{144}[/tex] = 12 → D

Answer:

(-2,  3).

Step-by-step explanation:

x + 3y = 7

2x + 4y = 8

1 .   x = 7 - 3y.

2.  2(7 - 3y) + 4y = 8

3.  14 - 6y + 4y = 8

   -2y = -6

    y = 3

4.  Substitute y in the second equation:

    2x + 4(3) = 8

    2x = -14

      x = -2..

The solution to the system of equations is: (-2, 3).

Given the system of equations:

x + 3y = 7 --> eqn. 1

2x + 4y = 8 --> eqn. 2

First, isolate x in equation 1:

x = 7 - 3y

Plug in the value of x into eqn. 2 to solve for y.

2(7 - 3y) + 4y = 8

14 - 6y + 4y = 8

14 - 2y = 8

14 - 8 = 2y

6 = 2y

3 = y

y = 3

Find the value of x by substituting y = 3 into eqn. 1.

x + 3(3) = 7

x + 9 = 7

x = 7 - 9

x = -2

Therefore, the solution to the system of equations is: (-2, 3).

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