Solve the system of equations using elimination: -x+3y=-24− and -4x+2y=4

1) Isosceles [tex]\triangle ABC[/tex] with [tex]\overline{AC} \cong \overline{BC}[/tex], [tex]\overline{DE} \perp \overline{AC}[/tex], [tex]\overline{DF} \perp \overline{BC}[/tex], [tex]\overline{DE} \cong \overline{DF}[/tex] (given)

2) [tex]\angle CAB \cong \angle CBA[/tex] (angles opposite congruent sides in a triangle are congruent)

3) [tex]\angle AED[/tex] and [tex]\angle DFB[/tex] are right angles (perpendicular lines form right angles)

4) [tex]\angle AED \cong \angle DFB[/tex] (all right angles are congruent)

5) [tex]\triangle DEA \cong \triangle DFB[/tex] (AAS)

6) [tex]D[/tex] is the midpoint of [tex]\overline{AB}[/tex] (if a point splits a segment into two congruent parts, it is a midpoint)

The value of 32 in the equation will serve as the time taken by the driver to travel

If Alice fills up the gas tank of her car before going for a long drive, and the equation that shows the amount of gas in gallons in Alice's car when she has driven m (miles). is given as:

g = 15 - m/32

The value of 32 in the equation will serve as the time taken by the driver to travel

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Answer:

Step-by-step explanation:

What line segment is equal to AC - BC?

A_____B_____C -

             B_____C =

A_____B

The correct answer is option B: there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

The practice or science of organizing and interpreting numerical data in big quantities, particularly for the objective of concluding proportions in a whole from those in an expected sample.

From the dot plot attached, we can find the average number of students per class for each school.

For Poplar Middle School;

Total number of students = (20 × 3) + (21 × 5) + (22 × 7) + (23 × 4) + (24 × 1) = 435 students.

There are 20 classes.

Thus;

Average number of students per class = 435/20 = 21.75

For Oak Middle School;

Total number of students = (20 × 1) + (21 × 2) + (22 × 2) + (23 × 4) + (24 × 3) + (25 × 2) + (26 × 2) + (27 × 2) + (28 × 1) + (29 × 1) = 483

The average number of students per class; 483/20 = 24.15

Difference in average = 24.15 - 21.75 = 2.40

This implies that there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

Therefore the correct answer is option B: there are about 2 more students in each class at Oak Middle School than at Poplar Middle School.

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The gas exerts a pressure of 218.75 kPa when its volume is reduced to 2.0 L, following the behavior of an ideal gas.

Ideal gas behavior:

Suppose the initial volume of carbon dioxide gas is V = 3.5l

Initial pressure is P = 125 kPa

Since the volume is reduced to 2.0l, the final volume is shown as V'= Will be done. 2L

The final pressure of the gas is P'.

We consider the behavior of gas to be ideal. From the ideal gas equation, it becomes as follows.

PV = P'V'

125 × 3.5 = P'× 2

P'= 218.75 kPa

Therefore, the final pressure is 218.5 kPa.

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Answer:

First part: 219 kPa (option D)

Second part: 2.3 L (option A)

Step-by-step explanation: just got asked the question

Answer:

domain of the sine and cosine functions is all real numbers

Step-by-step explanation:

range of both the sine and cosine functions is [−1,1]

graph can go left and right to infinity

graph goes up and down between 1 and -1

graph looks like a wave or

like U letters next to each other

UUUU

sine and cosine of an angle have the same absolute value as the sine and cosine of its reference angle.

mathlibretextsorg

The dependent events are:

Two events are dependent when the outcome of the first event affects the probabilities for the outcomes of the second event.

The first pair:

"choosing 2 socks from a drawer, without replacement"

Is a pair of dependent events. Because the first pair chosen can't be chosen on the second event. Then, the outcome of the first event affects the second event.

The third option:

"picking 4 cards from a deck, one after the other"

Again, here we have dependent events, because the cards already picked can't appear in the next events.

The other 3 options are sets of independent events.

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Answer:

option OE. 8i

Step-by-step explanation:

[tex] \sqrt{64 } \: is \: equal \: to \: 8[/tex]

[tex]i \: = 1[/tex]

[tex]8 \times 1 = 8[/tex]

[tex]therefore \: \sqrt{64} \: is \: equivalent \: to \: 8i[/tex]

Answer:

Constant: A numerical value

Coefficient: The constant preceding the variables in a product

Variable: a letter or symbol used to represent and unknown

Expression: A mathematical phrase that cannot be determined by true or false

Algebraic expression: A mathematical expression containing one or more variables

Step-by-step explanation:

The proof that quadrilateral WXYZ, having vertices W(-5, 6), X(-1, 10), Y(1, 4), and Z(-2, -3) is a trapezoid is given below.

Mathematical proof is a set of logical statements that are sequentially indicated to guaranty that a stated position is indeed accurate.

It is to be noted that with parallelograms, the diagonals intersect at the midpoints. (See the attached image).

The Diagonals are  WY  and  XZ; Where

WY :  (-4, -3) to  (6, -2); and

Midpoint is  [ (0 + 2)/2 ,  (-1 + -4)/2 ]  

= (1, -5/2)

The diagonals are bisectors of each other.

It is to be noted that the diagonals are not congruent. For if they were congruent, then the above would not be a trapezoid.

The Length of WY  = √((-4 - 6)²  +  (-3 - (-2))²)

WY = √(100 + 1)

WY = √101

The Length of XZ =    √((0 - 2)²  +  ( -1 - -4)²)

XZ = √(4+9)

XZ = √13

From the above, it is clear that both diagonals are unequal. Hence, given the first and second proof, we can state that quadrilateral WXYZ is a Trapezoid.

QED

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Answer:

B

Step-by-step explanation:

i took the test

The correlation is a negative correlation, because weights and city MPG do not increase at the same time

To graph of the table of values, we plot

See attachment for graph

The correlation is a negative correlation, because weights and city MPG do not increase at the same time

To do this, we make use of a graphing calculator.

From the graphing calculator, we have the following summary:

The line of best fit equation is

y = bx + a

Where

b = SP/SSX = -857.75/862.94 = -0.99

a = MY - bMX = 24.25 - (-0.99*28.94) = 53.0

So, we have:

y = -0.99x + 53

Hence, the equation of the line of best fit is y = -0.99x + 53

This means that y = 30

So, we have:

-0.99x + 53 = 30

Subtract 53 from both sides

-0.99x = -23

Divide by -0.99

x =23

Hence, the predicted weight is 23 pounds

This means that x = 1500

So, we have:

y = -0.99 * 1500 + 53

Evaluate

y = -1432

Hence, the city MPG for 1500 pounds is -1432

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Answer:

x = 2

Only 1 solution

Step-by-step explanation:

6 - 3x = 12 - 6x

3x = 6

x = 2

The second statement is the inverse statement of the first conditional statement.

If x and y are two propositions, then:

x ⇒ y

Is a conditional statement:

"If x, then y".

The other statement is:

¬x ⇒ ¬y

Where:

¬x means "not x"

So the statement is:

"If not x, then not y".

That would be the inverse statement of the given conditional statement.

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Answer:

B. x < -1

Step-by-step explanation:

Hello!

Let's put them in order from greatest to least:

Given our possible inequalities, we need to find the inequality that contains all of these values.

The inequality that works is x < -1, as all values are less than -1.

Therefore, the answer is B. x < -1.

Yes, the horizontal line test is important when finding the inverse of a function because without the intersection of the line, they would be no inverse.

The steps include;

A property of horizontal line is that if it intersects the graph of a function more that on way, then 'f' does not have an inverse.

If no horizontal line intersects the graph , 'then f' does have an inverse.

Thus, the horizontal line test is important when finding the inverse of a function because without the intersection of the line, they would be no inverse.

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The answer choice in which case the equation has no solution are; Choice A ; 40x+40=40x+20 and Choice C; -20x+40=-20x+20.

A system of linear equations is determined to have no solutions when the variable coefficients diminish upon evaluation and hence, the value of the variable can not be determined.

Hence, Choices A and C; in which case; the coefficients of variable X amount to 0 upon evaluation are equations with no solution.

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Answer:

There are no solutions.

Step-by-step explanation:

Hope this helped! :D

The force required to move the object by 15 feet will be 48 lbs.

The effort or an external agent responsible for moving or stopping any object is called a force. It is given that the force required to move the object at the distance of 9 feet is 80 lbs we need to calculate the force required to move the object by 15 feet.

The force will be calculated. We can make an equation from the given data in the question:-

[F1/F2] = [d2/d1]

F2 = [F1 x d1 ] / [d2]

F2 = [ 80 x 9 ] / [ 15 ]

F2 = a

Therefore the force required to move the object by 15 feet will be 48 lbs.

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The correct option is B. Yes, SSS congruency

Yes, more than one triangle can be made using the given measurements

The appropriate triangle congruence postulate is the SSS congruence which states that If all the three sides of one triangle are equivalent to that of the second triangle, then the two triangles are said to be congruent.

Thus, the option  B is correct

The complete question is ;

The measurements of a triangle are given. Is there exactly one triangle that can be formed using the given measurements? If so, identify the appropriate triangle congruence postulate.

∆ABC : m ∠A = 90°, AB = 15, AC = 15

A)No, More than one triangle could be made with these measures

B)Yes, SSS congruency

C)Yes, ASA congruency

D)Yes, SAS congruency

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The reciprocal relationship of the graph is graph (a)

The reciprocal relationship implies that:

The x and the y axes are swapped.

When the x and the y axes are swapped, the value on both axes swap their positions

For the given graph, the reciprocal relationship is graph (a)

This is shown in the attached graph

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Based on the given population function, the population of the town can be said to be increasing.

The population of the town is increasing because the value of "b" is positive and greater than one.

"b" which in this case is 0.87, is the rate at which the population is growing overtime. If it is a positive figure, then the population is expanding.

The question is:

Is the town's population increasing or decreasing?

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Pound is the unit of measure of passengers car weight

According the statement

The weight of passengers car is 4.5 times 10 superscript 3 units.

from this it is clear that the in simple terms the weight become 4.5 * 10^3

AND

the term 10^3 is used when we measure the weight in pounds.

So, Pound is the unit of measure of passengers car weight.

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The correct property of equality to solve each equation is x=24.

We have given that,

Identify the correct property of equality to solve each equation.

3+x=27

The multiplication property of equality states that when we multiply both sides of an equation by the same number, the two sides remain equal.

For this case, we must solve the following equation

3+x=27

Subtracting 3 on both sides of the equation we have

3+x-3=27-3

x=24

We observe the property of equality of subtraction.

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Therefore, the equation of circle is: [tex](x+3)^{2}+(y+5)^{2} = 100[/tex]

Here we know that[tex](h,k) = (-3,5)[/tex]but we are not given the radius.

However, we can find the radius by using the distance formula.

[tex]\sqrt{x^{2} +y^{2} }[/tex], where [tex]x=x_{1} -x_{2}[/tex] and [tex]y=y_{1} -y_{2}[/tex]

Putting the values, we get:

[tex]\sqrt{8^{2} +6^{2} }[/tex]

The radius comes out to be:

[tex]r=10[/tex]

An equation of the circle with center [tex](h,k)[/tex] and radius r is

[tex](x-h)^{2} +(y-k)^{2} = r^{2}[/tex]

Now, substituting the values, we get:

[tex](x--3)^{2} +(y-5)^{2} = 10^{2}[/tex]

Therefore, the equation of circle is:

[tex](x+3)^{2}+(y+5)^{2} = 100[/tex]

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The equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2

The standard vertex of a function is given as shown below

y = a(x - h)² + k

where (h, k) is the vertex of the function

Given the vertex of a function at (-3, 2). On substituting, we will have:

y = a(x - (-3))² + 2

y = a(x + 3)² + 2

Hence the equation represents a graph with a vertex at (–3, 2) is y = a(x + 3)² + 2

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The result of the evaluation as demanded in the task content is; -40 - 80√3.

The expression; a² - b² can be evaluated by means of difference of two squares as follows;

a² - b² = (a+b)(a-b)

Therefore, we have;

= ((√3 +5√3 -5) + (√3 -5√3 -5)) ((√3 +5√3 -5) - (√3 -5√3 -5))

= (2√3 -10)(10√3 +10)

= 60 - 80√3 -100

= -40 - 80√3.

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