(08.03)A set of equations is given below:

Equation H: y = −x + 2
Equation J: y = 3x − 4

Which of the following steps can be used to find the solution to the set of equations?
−x = 3x − 4
−x +2 = 3x
−x + 2 = 3x − 4
−x + 1 = 3x + 2

6km in 30 min so he traveled at a speed of 12km per hour;

In 2 hours he will travel 24km;

12km in 60 min

9km in ? min

?=9x60/12=45 minutes will take to travel 9 km at the speed of 12km/h

Answer:

12km/h.

Step-by-step explanation:

Answer:

Step-by-step explanation:

The triangles are similar. Therefore the corresponding sides are in proportion:

[tex]\dfrac{x}{40}=\dfrac{4}{32}[/tex]               cross multiply

[tex]32x=(40)(4)[/tex]

[tex]32x=160[/tex]             divide both sides by 32

[tex]x=5[/tex]

Answer:

Answer:

1.25 cups or 1 1/4 cups

Step-by-step explanation:

Note that half of 12 muffins is 6 muffins.

If making 12 muffins requires 2.5 cups of flour, then halving both measurements results in       1.25 cups of flour per 6 muffins.

Answer:

the last one

Linear functions are straight lines. The first two go up and down when graphing and the third one is an exponential.

Answer:

D.

Step-by-step explanation:

The main difference is that a Bimodal Histogram has two peaks representing the most frequent data values, whereas a Symmetric Histogram has one peak and its data is evenly distributed around a central value. In a symmetric histogram, mean, median, and mode coincide, unlike in a bimodal distribution, where the modes are different from the mean and median.

The difference between a Bimodal Histogram and a Symmetric Histogram relates to the distribution of data within the histogram.

A Bimodal Histogram has two distinct peaks or modes, indicating two prevalent data values within the dataset.

In contrast, a Symmetric Histogram is characterized by a single peak, with the data points arranged evenly around a central value such that it creates a mirror image on either side of the peak.

Symmetric histograms often indicate that the mean, median, and mode of the dataset coincide at the center of the distribution.

However, in a symmetric distribution with bimodality, the modes will differ from the mean and median.

When data is skewed to the left or right, it is not symmetric, and the mean, median, and mode do not align, with the mean being pulled towards the tail of the distribution in skewed datasets.

To visualize these concepts, one may create a histogram by plotting the frequency of data points against specified ranges.

Bimodal histograms will show two high-frequency areas, while symmetric histograms will show a single, central peak, indicating where the bulk of the data lies.

Answer:

a = 12 ft, b = 12 ft

Step-by-step explanation:

The triangle is 45 45 90 right triangle

so a = b

Ratio of leg : hypo. = a : a√2

Given hypo = 12√2, so legs a = b = 12

Answer

a = 12 ft, b = 12 ft

Answer:

Reasonable domain is [1.375,3].

Step-by-step explanation:

Given function is [tex]f\left(t\right)=-16t^2+44t+12[/tex].

Now we need to find about what is the reasonable domain of the graph of the function [tex]f\left(t\right)=-16t^2+44t+12[/tex] when the basketball falls from its maximum height to the ground.

Compare with [tex]at^2+bt+c[/tex], we get a=-16 and b=44

then t-coordinate of vertex [tex]t=-\frac{b}{2a}=-\frac{44}{2\left(-16\right)}=1.375[/tex]

Then that means maximum height of the ball occurs when time t=1.375 seconds.

Now let's find time when ball falls on ground so set f(t)=0

[tex]f\left(t\right)=-16t^2+44t+12[/tex]

[tex]-16t^2+44t+12=0[/tex]

[tex]4t^2-11t-3=0[/tex]

[tex]\left(4t+1\right)\left(t-3\right)=0[/tex]

[tex]4t+1=0[/tex] or [tex]t-3=0[/tex]

[tex]4t=-1[/tex] or [tex]t=3[/tex]

[tex]t=-0.25[/tex] or [tex]t=3[/tex]

Time can't be negative so we use t=3 only

Hence reasonable domain is [1.375,3].

Answer:

(4+3)x(7-1)=42

The correct position of the brackets is [tex](4+3)*(7-1)=42[/tex].

The given equation is:

               [tex]4+3*7-1=42[/tex]

          ⇒[tex](4+3)*(7-1)=42[/tex]

Let us consider LHS,

[tex](4+3)*(7-1)[/tex]

[tex]=7*(7-1)[/tex]

[tex]=7*6[/tex]

[tex]=42[/tex]

[tex]=RHS[/tex]

Hence, the above position of the bracket in the given statement is making it true.

Therefore, the correct position of the bracket is [tex](4+3)*(7-1)=42[/tex].

Brackets, in math, are a set of marks like parentheses that are used to enclose a set of terms. These terms may be within an algebraic expression, and in this case, the brackets are used to separate terms and denote the order of operations.

Square brackets (also called brackets, especially in American English) are mainly used to enclose words added by someone other than the original writer or speaker, typically in order to clarify the situation: He [the police officer] can't prove they did it.

Different symbols like these: (, ), [, ], {, and } in your math books. These symbols are called brackets. Brackets in mathematics serve a very important purpose; these symbols help us group different expressions or numbers together.

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Answer:

36

Step-by-step explanation:

Answer:

The correct answer is area of given circle = 36π inches²

Step-by-step explanation:

Formula:-

Area of circle = πr²

Where r is the radius of circle

To find the area of circle

Here radius r = 6 inches

Area = πr²

 = π * 6²

 = 36π inches²

Therefore area of  a circle with a radius of 6 inches = 36π inches²

We can only sum matrices with equal order, so we can't sum matrices A and B in the first exercise.

As for the second exercise, we have:

All of these answers depend on the fact that the sum/difference of two matrices is simply the sum/difference of the correspondent elements. So, if the element in the i-th row and the j-th column of A is [tex]a_{ij}[/tex] and the element in the i-th row and the j-th column of B is [tex]b_{ij}[/tex], we have

[tex]C=A+B\implies c_{ij} = a_{ij}+b_{ij}[/tex]

So, the sum between matrices inherits the properties of the sum between numbers: the order matters when you subtract (which is why a and f are false), the sum is commutative (which is why b, c, d are true) and associative (which is why e is true).

Subtracting vectors is akin to adding their opposites, and the operations are commutative and associative. Graphically, vector subtraction involves reversing a vector's direction before adding. Straight-line vector addition or subtraction simply depends on magnitudes and directions.

When dealing with adding and subtracting matrices or vector addition and subtraction, it's important to understand that these operations have straightforward rules. In particular, subtracting vectors can be interpreted as adding vectors in the opposite direction - this is analogous to scalar subtraction, such as how 5 - 2 can be thought of as 5 + (-2). Graphically, this means that when subtracting vectors, you essentially reverse the direction of the vector being subtracted and then perform vector addition as you would normally.

Mathematically, the vector addition is associative and commutative, and these properties extend to matrix addition as well. Likewise, multiplying vectors or matrices by scalars follows the distributive property. In a practical sense, when vectors are aligned on a straight line, adding or subtracting them is simplified since you only need to consider their magnitudes and directions along that line.

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[tex]

l_t=200m \\

s=20\frac{m}{s} \\

t=2\times60+30=150s \\

l=? \\

s=\frac{l}{t}\Longrightarrow l=st \\

l=20\frac{m}{s}\times150s=3000m=\boxed{3km}

[/tex]

The length of the tunnel is 2.8 kilometers.

Let's first convert the time taken to pass through the tunnel from minutes and seconds to seconds only.

2 minutes is equal to 2 * 60 = 120 seconds.

Adding the 30 seconds, the total time is 120 + 30 = 150 seconds.

We can calculate the speed of the train in meters per second using the formula:

Speed = Distance / Time

Given that the average speed of the train is 20 m/s, we can set up the equation as:

20 = (200 + L) / 150

Where L is the length of the tunnel in meters.

To find the length of the tunnel, we can solve this equation for L.

Multiplying both sides of the equation by 150, we get:

150 * 20 = 200 + L

3000 = 200 + L

Subtracting 200 from both sides, we have:

L = 3000 - 200

L = 2800 meters

Finally, to convert the length of the tunnel from meters to kilometers, we divide by 1000:

Length of the tunnel = 2800 / 1000 = 2.8 kilometers.

Therefore, the length of the tunnel is 2.8 kilometers.

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Answer:

14.1 in³

Step-by-step explanation:

Your expression for the volume was correct, except that it lacked units of measurement.

The volume is V = (1/3)π(1.5 in)²(6 in) = 14.1 in³

The volume of the cup will be 14.1 cubic inches. Thus, the correct option is B.

Let h be the height of the cone and A be the base area of the cone. Then the volume of the cone will be given as,

V = 1/3 × πr²h

A paper cup in the shape of an inverted cone is 6 inches tall and 3 inches in diameter.

The volume of the cup is calculated as,

V = 1/3 × π(1.5)²(6)

V = 14.1 cubic inches

Thus, the correct option is B.

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Answer:

130 yards equals 118. 8 meters and 120 meters equals 131 .2 yards so not only are they different measurement types but they also do not equal the same.

Step-by-step explanation:

Follow below steps:

To find the difference in feet between 130 yards and 120 meters:

Convert 130 yards to feet: 130 yards x 3 feet/yard = 390 feet

Convert 120 meters to feet: 120 meters x 3.281 feet/meter = 393.72 feet

Difference in feet = 393.72 feet - 390 feet = 3.72 feet

Answer:

90%

Step-by-step explanation:

If you are going to find out the percent of the car that do not have 4 wheel drive, you take the total amount of car that passed though the stoplight which is 100% . You take this 100% and then subtract the 10% to get the final answer 90%. 90% of the cars do not have 4 wheel drive.

To find the percentage of cars without four-wheel drive, subtract the percentage of cars with four-wheel drive from the total. Since 10% of cars have four-wheel drive, 90% do not.

If 10% of the cars have four-wheel drive, then the percentage of cars without four-wheel drive is the remainder when the total percentage (100%) is reduced by the percentage of those that do have four-wheel drive.

To calculate this, we subtract the percentage of cars with four-wheel drive from the total percentage:

100% - 10% = 90%

Therefore, 90% of the cars do not have four-wheel drive.

Answer:

The range here is the set {8, -10, -4, 20, 32}.

Step-by-step explanation:

Please use " ^ " to denote exponentiation.  Thanks.   f(x)=x^2 + 5x - 4

f(-4)=(-4)^2 + 5(-4) - 4  =  8

f(-2)=(-2)^2 + 5(-1) - 4   = -10

f(0)=0^2 + 5(0) - 4 = -4

f(3) =3^2 + 5(3) - 4      =   20

f(4)=4^2 + 5(4) - 4       = 32

In this problem we have to calculate the actual function values for the given domain (input values).  The range here is the set {8, -10, -4, 20, 32}.

Answer:

The answer is the attached figure

Step-by-step explanation:

* Lets revise the equation of the circle

- The center-radius form of the circle equation is

  (x – h)² + (y – k)2 = r², where the center is the point (h, k)

  and the radius is r.

- This form of the equation is helpful, since you can easily find the

  center and the radius.

* Now lets solve the problem

- The equation of the circle is (x + 2)² + (y - 0.5)² = 16

* Lets compare it with form above

∵ (x - h)² = (x + 2)²

∴ -h = 2 ⇒ × -1

∴ h = -2

∵ (y - k)² = (y - 0.5)²

∴ -k = -0.5 ⇒ × -1

∴ k = 0.5

∴ The center of the circle is (-2 , 0.5)

∵ r² = 16 ⇒ take √ for both sides

∴ r = √16 = 4

∴ The radius of the circle is 4 units

* Now lets look to the answer to find the circle whose center is

 (-2 , 0.5) and radius 4 units

∴ The answer is the attached figure

* From the graph:

- The center of the circle is (-2 , 0.5)

- The horizontal diameter is between -6 and 2, then the length

 of the diameter = 2 - -6 = 8

∵ The radius = 1/2 the diameter

∴ The raduis = 1/2 × 8 = 4 units

ANSWER

The image is located at (5,-6)

EXPLANATION

The rule for reflection over the y-axis is to negate the x-coordinates.

This implies that,

[tex](x,y)\to (-x,y)[/tex]

If the point located at (-5, -6) is reflected over the y-axis, the coordinates of the image is obtained by negating the x-coordinate.

Therefore

[tex]( - 5, - 6)\to (5, - 6)[/tex]

The image is located at (5,-6)

Answer:

The correct answer option is (5, -6).

Step-by-step explanation:

We are given the following coordinates of a point:

[tex] ( - 5 , - 6 ) [/tex]

If this point is reflected through y axis, what will be the coordinates of its image?

Reflection through y-axis means that the sign of the x coordinate will be changed so we get:

[tex] ( - 5 , -6 ) [/tex] [tex] \implies [/tex] (5, -6)

Answer:

B:  c²/9

Step-by-step explanation:

                                    c²

(c/3)² is the same as ------'

                                     9

Answer:

Step-by-step explanation:

[tex]\text{Use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\\\\\left(\dfrac{c}{3}\right)^2=\dfrac{c^2}{3^2}=\dfrac{c^2}{9}[/tex]

Answer:

The number of faces is 29

Step-by-step explanation:

we know that

The Euler's formula state that, the number of vertices, minus the number of edges, plus the number of faces, is equal to two

[tex]V- E + F= 2[/tex]    

we have

[tex]V=16[/tex]

[tex]E=43[/tex]

substitute and solve for F

[tex]16- 43 + F= 2[/tex]

[tex]-27+F= 2[/tex]

[tex]F= 2+27[/tex]

[tex]F= 29[/tex]

This is least to greatest

2 2/5 or 2.40

2.45

2 2/3

2 2/5 , 2.45 , 2 2/3

Answer:

2 2/3

Step-by-step explanation:

2 2/3 = 2.666...

2.45 = 2.45

2 2/5 = 2.4

From least to greatest:

2 2/5, 2.45, 2 2/3

The greatest of the three numbers is 2 2/3

Answer:

A unit rate describes how many units of the first type of quantity corresponds to one unit of the second type of quantity.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Common examples of "unit rate" follow:

miles per hour (mph).  How many miles are covered in 1 hour of driving?

25 cents/pen:  each pen costs 25 cents each.

Suppose I know I can pack 1/4 box in 20 minutes.  How many boxes can I pack in 1 hour?  That would be a unit rate.  To find it, write out the ratio

1/4 box                                                                                 60 min

-------------   and multiply this by the conversion factor    ---------------

 20 min                                                                                  1 hour

... which results in  3/4 box per hour (a unit rate)

Answer:

I would say d bit I'm not 100% sure

Choice A. It is the only answer that makes sense.

Answer:74

Step-by-step explanation:

Answer: 74

Step-by-step explanation:

185 divided by 2.50 is 74.

Answer:

20 cm

Step-by-step explanation:

If the scale says that the building uses the scale or 1 cm: 6 meters. You pretty much just take 120 and divide by 6. You take that answer and turn the units in cm.  

Answer:

Step-by-step explanation:

We write only the coefficients of the given equation inside the upside down symbol of division.

We first do synthetic substitution and then verify the result by putting g(4) and g(-5) in the original equation. Both should have the same result.

The questions are solved on the image attached.

Answer:

709, 1,708

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

to find the surface area, you need to find the area of all 6 sides using the dimensions given. each visible side has an opposite side that has the same dimensions.

1) 6*2=12

2) 6*2=12

3) 9*2=18

4) 9*2=18

5) 9*6=54

6) 9*6=54

then, you have to add all 6 sides together.

12+12+18+18+54+54

24+36+108

60+108

168 cm squared is the surface area

Answer:

Step-by-step explanation: its b

First, you'd have to decompose the shape. The way I decomposed it was by splitting the shape into a small rectangle and a large one. The formula for the rectangles is 6 times 3 and 6 by 9. You multiply 6 by 3 and get 18; then you multiply  6 by 9 and get 54. Lastly, you simply add 18 and 54. This gives you an answer; 72.

Let m be the no of trucks and n be the no of passenger vehicles...

Then m + n = 600

and 100m + 45n = 29200

Multiplying 1st equation by 45, we have 45m+45n=27000

then subtracting from 2nd eqn we have, 55m = 2200 that is m=40.Then n=560

So we have 40 trucks and 560 passenger vehicle