Graph this line:
y + 5 = 2(x + 7)

The number of scores by the Eagles is 45.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Cowboys scores = x

Eagles scores = y

y = 2x - 7 _____(1)

Now,

x + y = 71 ______(2)

From (1) and (2) we get,

x + 2x - 7 = 71

3x - 7 = 71

3x = 71 + 7

3x = 78

x = 26

Now,

y = 2x - 7

y = 2 x 26 - 7

y = 52 - 7

y = 45

Thus,

The eagles scored 45.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

The image point which results from the transformation R180° of the point (-6, -1) is; (6, 1).

It follows from the task content that the image point of the point (-6, -1) is to be determined after a transformation R180°.

Recall that a rotation of 180° in the clockwise or anticlockwise direction is such that;

( x, y ) =====>. ( -x, -y )

On this note, since the pre-image point is; ( -6, -1 ), it therefore follows that the image point which corresponds to the given transformation is; (6, 1).

Ultimately, the required image point is; (6,1).

Read more on transformations;

https://brainly.com/question/5020733

#SPJ1

Yes, a triangle can have three equal angles. The term "equilateral triangle" is used to describe this.

A 60-degree equilateral triangle has the same length for all three angles. This is due to the fact that all three angles in a triangle have to add up to 180 degrees, and when three angles are equal, the sum is divided equally between them.

An equiangular triangle is another name for an equilateral triangle. An equilateral triangle takes on the form of an equilateral triangle because all of its sides are equally angled. The term "congruent" refers to the fact that all three sides of the triangle are the same length.

Numerous mathematical disciplines, including geometry and trigonometry, make use of equilateral triangles. They are often used to show how other shapes, like parallelograms and rhombi, work. Additionally, they are utilized in the process of determining the perimeter, angles, and area of a triangle.

Learn more about Equilateral Triangles here:

https://brainly.com/question/17264112

#SPJ4

The number of weeks that it will take for Aaliyah yo have enough money is 13.4 weeks.

The equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.

It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.

The number of weeks will be calculated thus:

25 + 8.25w = 135.75

where w = number of weeks.

Collect the like terms

8.25w = 135.75 - 25

8.25w = 110.75.

Divide

w = 110.75 / 8.25

w = 13.4 weeks

Learn more about equations on:

brainly.com/question/2972832

#SPJ1

The property states that when two vectors a and b are multiplied together, the result is equal to the negative of b multiplied by a. This can be shown by multiplying the components of both vectors and then multiplying the result by -1.

a×b = (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)

= (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)

= (−1) * (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1)

= (−1) * (b2*a3 - b3*a2, b3*a1 - b1*a3, b1*a2 - b2*a1)

= − b × a.

The property a × b = − b × a states that when two vectors a and b are multiplied, the result is equal to the negative of b multiplied by a. This can be proven by first expanding the components of both vectors. For a vector a=(a1,a2,a3) and b=(b1,b2,b3), the expanded form of a×b is (a2*b3 - a3*b2, a3*b1 - a1*b3, a1*b2 - a2*b1). This can then be multiplied by -1 to get the expanded form of -b×a, which is (b2*a3 - b3*a2, b3*a1 - b1*a3, b1*a2 - b2*a1). Since this is equal to the original form of a×b, this proves the property.

Learn more about vector here

https://brainly.com/question/15709504

$SPJ4

Answer: $14.84

Step-by-step explanation: 14 + 6% = 14.84

Answer:-32

Step-by-step explanation:

p=-32

7Answer:

-7

-Step-by-step explanation:

It is less likely to randomly meet someone who obtained a SAT score of over 1150.

Z score or standard score is defined as the number of standard deviations by which the observed value is above or below the mean value.

The formula for calculating z score is,

z = (x - μ) / σ

where x is the observed value, μ is the population mean and σ is the population standard deviation.

For IQ scores,

z = (80 - 100) / 16 = -1.25

For SAT scores,

z = (1150 - 1000) / 100 = 150/100 = 1.5

z score is closer to 0 for IQ scores and far to 0 for SAT scores.

Hence it is less likely to meet someone who obtained a SAT score of over 1150.

Learn more about Z score here :

https://brainly.com/question/15016913

#SPJ1

Answer:

140 square meters

Step-by-step explanation:

A= lw

A= 10 times 14 = 140

A dot plot that corresponds to the values in the table include the following: dot plot B.

In Mathematics, a dot plot can be defined as a type of line plot that is typically used for the graphical representation of a data set above a number line, especially through the use of dots.

Based on the values contained in the table, the high school students' essays score on a scale of 0 to 10 should be plotted on a dot plot as follows:

An essay score of 3 would have 1 dot.

An essay score of 4 would have 1 dot.

An essay score of 5 would have 2 dots.

An essay score of 6 would have 5 dots.

An essay score of 7 would have 4 dots.

An essay score of 8 would have 7 dots.

An essay score of 9 would have 3 dots.

An essay score of 10 would have 2 dots.

Read more on dot plots here: brainly.com/question/18466974

#SPJ1

The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.

To find the average value of a function f(x) on an interval [a, b], we need to evaluate the definite integral of the function over that interval and divide it by the length of the interval.

The definite integral of f(x) = 8x sec^2(x) over the interval [0, π/4] is given by:

∫[0,π/4] 8x sec^2(x) dx

This integral can be evaluated by substitution. Let u = sec(x) and du = sec(x)tan(x)dxmthen the integral becomes:

∫[0,π/4] 8x sec^2(x) dx = ∫[1,sec(π/4)] 8xu^2du

= 8/3u^3 evaluated at u = sec(π/4) - 8/3u^3 evaluated at u = 1

= 8/3sec^3(π/4) - 8/3 = 8/3(1/cos^3(π/4)) - 8/3 = 8/3*(1/1/2) - 8/3 = 4/3 - 8/3 = -4/3

Thus, The average value of f(x) = 8x sec^2(x) on the interval [0, π/4] is -4/3.

To learn more about definite integrals,

Visit; brainly.com/question/29974649

#SPJ4

Looking at the triangles in the figure, the difference in the x coordinates of points Q and R is 10

This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent

Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions

Examining the figure shows that pair of equivalent sides are

ST and QR, UT and SR.

The solution is worked out using sides ST and QR, UT and SR.

ST / QR = UT / SR

5 / QR = 3 / (4 - (-2))

5 / QR = 3 / 6

cross multiplying

3 * QR = 30

QR = 10

hence  QR = 10

Learn more about similar triangles here:

https://brainly.com/question/29333623

#SPJ1

The resultant vector on the car would be a vector pointing north with a magnitude of 2 miles per hour.

The resultant vector is the net effect of two or more individual vectors on an object. It is the overall force or movement that is produced when all the individual vectors are combined. To find the resultant vector, you would add together all of the individual vectors using vector addition. The resultant vector would be represented by a single vector with a certain magnitude and direction.

If a car is rolling south at 8 miles per hour, and a man pushes the car north at 10 miles per hour, subtract the southward velocity from the northward velocity.

10 mph northward - 8 mph southward= 2 mph northward

Therefore, the resultant vector on the car is 2 mph northward.

Learn more about resultant vector here: https://brainly.com/question/11558676

#SPJ4

Answer:

<2 = 45

< 7 = 135

< 3 = 135

< 5 = 135

<8  = 45

< 6 = 45

Step-by-step explanation:

Angles 2 and 7 are supplemental angles.  This means that together they add to 180.

x + 3x = 180  Combine like terms

4x = 180  Divide both sides by 4

x = 45

<2 = 45

Angle 7

3x   Substitute 45 for x

3(45)

135

Angle 3

Corresponding angle to 7.  Corresponding angles are congruent (equal).

Angle 5

Vertical to angle 7.  Vertical angles are congruent.

Angle 8

Alternate exterior angle to 7.  Alternate exterior angels are congruent.

Angle 6

Vertical angle to 8.  Vertical angles are congruent.

Answer:

To mow the lawn once, it takes 1/12 gallon.

She can mow the lawn 12 times with 1 gallon.

Step-by-step explanation:

Answer:

Step-by-step explanation:

write k for the divisor

write the coefficients of the dividend.

Bring the leading coefficient down.

Multiply the leading coefficient by k.

Add the terms of the second column.

Multiply the result by k.

Repeat steps 5 and 6 for the remaining columns

The vertex and equation of the line of symmetry will be (1, 3) and x = 1.

It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.

Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.

Then the equation of the parabola will be given as,

y = a(x - h)² + k

The lowest points of the parabola from the table represent the vertex of the parabola. Then we have

Vertex = (1, 3)

The axis of symmetry is parallel to the y-axis. Then the equation of the axis of symmetry will be given as,

x = 1

The vertex and equation of the line of symmetry will be (1, 3) and x = 1.

More about the equation of the parabola link is given below.

https://brainly.com/question/20333425

#SPJ1

Answer:

Step-by-step explanation:

8g=9.6

Divide both sides by 8 to isolate the variable

g=1.2

Answer:

[tex] \sf \: g = 1.2[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of g.

The equation is,

→ 8g = 9.6

Then the value of g will be,

→ 8g = 9.6

→ g = 9.6 ÷ 8

→ [ g = 1.2 ]

Hence, the value of g is 1.2.

Answer:

Range: 20.

Step-by-step explanation:

Put in order:

12, 13, 13, 15, 16, 19, 32

Subtract smallest number from largest number

32 - 12 =20

The length of the missing side is 19 units

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

In the given triangle there is a bisector which is bisecting on hypotenuse of length 25.

The length of opposite side will be 25-9=16

From pythagoras theorem we can find the length x

x²+16²=25²

x²=25²-16²

=625-256

=369

x=19

Hence, the length of the missing side is 19 units

To learn more on trigonometry click:

https://brainly.com/question/25122835

#SPJ1

If the value of x is greater than 0.01, then Tanya finished the race first.

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the inequality sign if you multiply or divide either side by a negative number.

Given:

Tanya ran the 200-meter race in 24 +(6x) seconds.

Cecella ran the same race in 24 and 6 hundredths seconds.

That means,

Cecella ran the same race in 24 and 6/100 seconds.

Cecella ran the same race in 24 and 0.06 seconds.

Cecella ran the same race in 24.06 seconds.

And if,

Then, 6x = 0.06

x = 0.01 seconds.

If the value of x is greater than 0.01.

x > 0.01

Then Tanya finished the race first.

Therefore, if x > 0.01, then Tanya finished the race first.

To learn more about the inequality;

brainly.com/question/28823603

#SPJ1

A logarithmic graph has a curved shape, with its vertical axis increasing exponentially, and its horizontal axis increasing in a logarithmic scale. The graph is useful for plotting data with a wide range of values, as it can be used to compress the data into a smaller range.

A logarithmic graph is a type of graph that is used to represent data with a wide range of values. It has a curved shape, with its vertical axis increasing exponentially and its horizontal axis increasing in a logarithmic scale. This scale compresses the data into a smaller range, which makes it easier to visualize and compare values that span a large range. It is useful for plotting data that grows or decreases exponentially, such as population growth or exponential decay. Logarithmic graphs are also used to graph values that have a very large range, such as the size of galaxies. The graph helps to compress the data into a smaller range, making it easier to visualize and compare values.

Learn more about logarithmic here

https://brainly.com/question/30085872

#SPJ4

The length of the third side of the triangle is 10 units long.

       (base)² + (perpendicular)² = (hypotenuse)²

Given is a right angle triangle.

We can write -

(base)² + (perpendicular)² = (hypotenuse)²

(√51)² + (7)² = (hypotenuse)²

(hypotenuse)² = 49 + 51

(hypotenuse)² = 100

(hypotenuse) = 10

Therefore, the length of the third side of the triangle is 10 units long.

To solve more questions on right angled triangle, visit the link below -

https://brainly.com/question/3772264

#SPJ1

The solution to the given IVP is.[tex]$i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$[/tex]

Initial value problems describe a type of problem in calculus. Initial value problems in calculus concern differential equations with a known initial condition that specifies the value of the function at some point. The purpose of these problems is to find the function that describes the system, which can be done by integrating the differential equation.

Consider the initial value problem,

L [tex]\frac{d i}{d t}+R i=E \text {. }[/tex]

The initial condition is. [tex]$i(0)=i_0$[/tex]

Rewrite the DE as,

[tex]\begin{gathered}L \frac{d i}{d t}+R i=E \\\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}\end{gathered}$$[/tex]

This is a linear DE.

Compare the DE  [tex]\frac{d i}{d t}+\frac{R}{L} i=\frac{E}{L}$[/tex] with the general DE [tex]\frac{d i}{d t}+P(t) i=Q(t)$[/tex]. Then [tex]$P(t)=\frac{R}{L}$[/tex] and [tex]$Q(t)=\frac{E}{L}$[/tex].

Find the integrating factor (IF).

                                     [tex]$$\begin{aligned}I F & =e^{\int P(t) \vec{t}} \\& =e^{\int\left(\frac{\pi}{\mathrm{I}}\right) \mathrm{A}} \\& =e^{\frac{\pi}{l^2}}\end{aligned}$$[/tex]

Thus, the integrating factor is [tex]$I F=e^{\frac{R^2}{2^2}}$[/tex].

Now multiply both sides of the DE with the IF.

                                   [tex]$$\begin{array}{r}e^{\frac{R}{\bar{L}^t}}\left(\frac{d i}{d t}+\frac{R}{L} i\right)=\frac{E}{L} e^{\frac{R}{L^t}} \\\frac{d i}{d t} e^{\frac{\pi}{L^t}}+\frac{R}{L} e^{\frac{R}{\bar{L}^t}} i=\frac{E}{L} e^{\frac{\pi}{\bar{L}^t}} \\{\left[i e^{\frac{R}{L^2}}\right]=\frac{E}{L} e^{\frac{R^L}{L^t}}}\end{array}$$[/tex]

Integrate on both sides.

        [tex]$$\begin{aligned}& \int\left[i e^{\frac{R}{L}}\right] d t=\int \frac{E}{L} e^{\frac{R}{L^t}} d t \\& i e^{\frac{R}{L^{\mathrm{r}}}}=\frac{E}{L} \int e^{\frac{\pi}{L^t}} d t \\& i e^{\frac{R}{\perp} r}=\frac{E}{L}\left[\frac{e^{\frac{R}{2}}}{\frac{R}{L}}\right]+C \\& i e^{\frac{R}{\Gamma}+}=\frac{E}{R} e^{\frac{R^2}{I^{+}}}+C \\& i(t)=\frac{\frac{E}{R} e^{\frac{R}{L^2}}+C}{e^{\frac{R}{D^2}}} \\& t(t)=\frac{E}{R}+C e^{-\frac{R}{L^t}} \\&\end{aligned}$$[/tex]

Thus, the general solution to the [tex]\mathrm{DE}[/tex] is [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{t^*}}$[/tex].

Use the initial condition. [tex]$i(0)=i_0$[/tex]

Substitute [tex]$t=0$[/tex] and [tex]$i(0)=i_0$[/tex] in [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{I^t}}$[/tex].

[tex]$$\begin{aligned}& i(0)=\frac{E}{R}+C e^{-\frac{R}{I}(0)} \\& i_0=\frac{E}{R}+C e^0 \\& i_0=\frac{E}{R}+C \quad \text { use } e^0=1 \\& C=i_0-\frac{E}{R}\end{aligned}$$[/tex]

Substitute  [tex]$C=i_0-\frac{E}{R}$[/tex] in [tex]$i(t)=\frac{E}{R}+C e^{-\frac{R}{L^1}}$[/tex].

[tex]$$\begin{aligned}& i(t)=\frac{E}{R}+C e^{-\frac{R}{I}} \\& i(t)=\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{\pi}{t^t}}\end{aligned}$$[/tex]

Therefore, the solution to the given IVP is. [tex]$i(t)-\frac{E}{R}+\left(i_0-\frac{E}{R}\right) e^{-\frac{R}{L}}$[/tex].

For more such questions on Initial-value problems:

https://brainly.com/question/8736446

#SPJ4

As a result, you are turning the entire trapezium figure 90 degrees clockwise in order to change the trapezoid LMNQ into L′M′NQ′.

In American and Canadian English, a trapezoid is a quadrilateral with at least one set of parallel sides. In British and other versions of English, the word is a trapezium. A trapezoid is always a convex quadrilateral in Euclidean geometry. The parallel sides of the trapezoid are referred to as its bases.

Given: When (-7,-2) to L, L becomes L' (-2,7)

You will often obtain a rotation of 90 degrees clockwise or 270 degrees counterclockwise around the origin (0,0), as well as a reflection across the x-axis and across the line of symmetry of the image, if you have (x,y) and it becomes (y,-x).

The entire graphic is therefore rotated 90 degrees in a clockwise orientation.

To know more about trapezoid visit -

brainly.com/question/8643562

#SPJ1

Answer: Divide

Step-by-step explanation: (Don't look at this if you are taking a test) :)

Hello! What you do to answer this question is divide 5100 grams by 2.5 grams.  You would do this because you want to divide the weight of all the pennies by the weight of a single penny to find the number of pennies.  This is because number of pennies multiplied by 2.5 grams (weight of a penny) = 5100 grams (weight of all pennies).  You will be able to figure out what the answer is by dividing 5100 by 2.5.  

I will give you an example problem if you need help dividing decimals:

3000/1.5

Move the decimal space over one to get 3000/15

15 √3000

30 divided by 15 is 2

        2

15√3000

15 x 2 = 30

       200

15 √3000

      - 30      bring down two zeroes
__________________

       000
Since there are two extra zeroes that you took, down your answer is 200. Since you already moved the decimal space one space to the right, move it to the right again and you will get 2000.  Your answer for the example problem is 2000.

ΔQRS, r = 10.32 cm.

Solved by using the concept of triangle.

Three straight sides and three angles make up a triangle, a two-dimensional form. Three vertices, three angles, and three sides define a triangle. In a triangle, the lengths of its two longest sides are always bigger than its third side's length.

A triangle seems to be a three-sided polygon with three vertices. There is a 180-degree angle created inside the triangle. In other words, a triangle's internal angles add up to 180 degrees.

Triangles can be categorized into one of three groups, namely Scalene, Isosceles, or Equilateral, depending on how long their sides are.

In ΔQRS,

given that,

s = 4.2 cm

∠R = 160°

∠S = 8°

From, ΔQRS

As we know,

r / sin A = s / sin B

∠Q = 180° - 160° - 8°

∠Q = 12°

now, putting the values we get -

r = 10.32 cm

To know more about triangles refer to:

https://brainly.com/question/1058720

#SPJ1

Change in Paula's elevation/altitude per minute is 8.4m.

There are numerous variations of altitude.

Now,

Given Change in Paula's elevation in 4.5 minutes=-37 4/5 m or -189/5m

- shows decrease in elevation.

so, for change in one minute = 189/5*4.5=189/22.5=8.4m

To know more about altitude visit the link

brainly.com/question/12336236

#SPJ1