Evaluate each expression for the given values of the variables: |a−b| − |c+d| , if a=−5; b=4; c=1; d=−3

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Explanation:

Subtract straight down. The x terms subtract to 5x-2x = 3x. The y terms subtract to 3y-3y = 0y = 0, so the y terms go away and are eliminated. The terms on the right hand side subtract to 31-25 = 6.

After all that subtraction, we end up with the equation 3x = 6 which solves to x = 2 after dividing both sides by 3.

Use x = 2 to find the value of y

5x+3y = 31

5(2)+3y = 31

10+3y = 31

3y = 31-10

3y = 21

y = 21/3

y = 7

or

2x+3y = 25

2(2)+3y = 25

4+3y = 25

3y = 25-4

3y = 21

y = 21/3

y = 7

Using either equation has x = 2 lead to y = 7.

Therefore, the solution is (x,y) = (2,7)

If you were to graph the two original equations, then they would intersect at (2,7).

Hi there! :)

Answer:

Choice D. (y - 4) = 3(x + 2)

Step-by-step explanation:

An equation in point-slope form is:

(y - y1) = m(x - x1)

Where:

y1 = y-coordinate of a point

m = slope

x1 = x-coordinate of a point

In this instance, the point given is (-2, 4) with a slope of 3. Therefore, the equation in point-slope form would be Choice D. (y - 4) = 3(x + 2)

Answer:

Step-by-step explanation:

answer is C

Because formula of equation of slop is

Y-y1=m(x-x1)

Answer:

x = 6

Step-by-step explanation:

The x-intercept of the equation is where the graph crosses the x-axis when y = 0. So, we simply plug in 0 for y:

2(0) - x = -6

0 - x = -6

-x = -6

x = 6

Alternatively, you can graph the equation into a graphing calc and analyze where the graph crosses the x-axis.

Answer:

x=3

Step-by-step explanation:

We want to find the value of x where the two graphs intersect

The graphs intersect at ( 3,8)

The value of x is 3

Answer:

paying $7.25 per sq feet

Step-by-step explanation:

So we can start off by solving the area:

12*13=156

so the total area is 156 feet sq

the first deal:

156/7.25= about $21.52

the second deal:

156/6.75= about $23.11, however with the installation fee, it will cost even more.

Answer:

t > 212

Step-by-step explanation:

Given

Boiling point = 212°F

Required

Inequality that shows temperature greater than the boiling point

From the question, temperature is represented with t.

The inequality "greater than" is represented with >

So, temperature greater than the boiling point implies that t > 212

Answer: t > 212

Step-by-step explanation:

The question says "Write an inequality that is true only for temperatures that are higher than the boiling point of water."

This means t has to be higher than 212 since it says only for temperatures that are higher than the boiling point.

But since we have to write an inequality the answer would be: t > 212.

I know I did this very late and you probably don't need it but i was bored

Answer:

b) tiene la mayor frecuencia

Step-by-step explanation:

Las medidas de tendencia central se refieren a un centro alrededor del cual se encuentran todos los datos y estas medidas son: la media, la moda y la mediana. La media es el valor promedio de un grupo de datos, la moda es el dato que se repite más veces y la mediana es el valor que se encuentra en el centro cuando los datos se ubican de menor a mayor. De acuerdo a esto, la respuesta es que la moda es una medida de tendencia central que tiene la mayor frecuencia.

Los otras opciones no son correctas porque el tamaño del conjunto de datos no depende de las medidas de tendencia central, esto depende de cada situación y pueden ser muchos o pocos datos. Además la opción "al ordenar los datos de menor a mayor es el dato que se ubica en el centro" se refiere a la mediana.

Answer:

Amount of car in 2012 = $1,242.55 (Approx)

Step-by-step explanation:

Given:

Rate of depreciation(d) = 18% = 0.18

Amount of car in 1998 = $19,995

Find:

Amount of car in 2012

Computation:

Number of year(n) = 14 year

[tex]Amount\ of\ car\ in\ 2012 = Amount\ of\ car\ in\ 2012 [1-d]^n[/tex]

Amount of car in 2012 = 19,995[1-0.18]¹⁴

Amount of car in 2012 = 19,995[0.82]¹⁴

Amount of car in 2012 = 19,995[0.0621432458]

Amount of car in 2012 = 1,242.5542

Amount of car in 2012 = $1,242.55 (Approx)

Answer:

8.3miles

Step-by-step explanation:

Here Jeff's sister drives 14 miles

his brother only drives 57/10 miles then the question is only asking the difference between their distance of driving to school knowing fully well that Jeff's sister drive farther than his brother, then we find the difference between their drives which is done bow

14miles -57/10 miles

= 83/10

= 8.3miles

Therefore, Jeff's sister drive 8.3miles farther than his brother

Answer:

158

Step-by-step explanation:

The sequence is 3, 8, 13, ..., 253.

Going backwards, it's 253, 248, 243, ..., 3.

First term is 253, common difference is -5.

The nth term is:

a = 253 − 5(n − 1)

The 20th term is:

a = 253 − 5(20 − 1)

a = 158

Answer:

Correct answer is option D. 96.4 yd.

Step-by-step explanation:

Please refer to the attached figure for labeling of the given diagram.

ABC is a triangle with the following labeling:

A is the hole, B is the Tee and C is the point where the ball is.

Sides are labeled as:

[tex]a =255\ yd\\c = 305\ yd\\\angle B =17^\circ[/tex]

To find:

Side [tex]b = ?[/tex]

Solution:

Here, we have one angle and two sides . Third side of the triangle is to be found opposite to the given angle.

We can use cosine formula here to find the value of the unknown side.

[tex]cos B = \dfrac{a^{2}+c^{2}-b^{2}}{2ac}[/tex]

Putting all the values:

[tex]cos 17 = \dfrac{255^{2}+305^{2}-b^{2}}{2\times 255\times 305}\\\Rightarrow 0.956 = \dfrac{65025+93025-b^{2}}{155550}\\\Rightarrow 148753.2= 158050-b^{2}\\\Rightarrow b^{2}= 158050-148753.2\\\Rightarrow b^{2}= 9296.795\\\Rightarrow b= 96.42\ yd[/tex]

So, the distance between the Ball and hole is 96.42 yd

Correct answer is option D. 96.4 yd.

Answer:

D.) 96.4 yd

Step-by-step explanation:

I got it correct on founders edtell

Answer:

first one

Step-by-step explanation:

Answer

5.85

Step-by-step explanation:

$0.05 x 1.5 = 0,075 x 1 hour (60) = 4,5

$0.03 x 1.5 = 0,045 x half an hour (30) = 1,35

So 4.5 + 1.35 = 5.85

Answer:

Step-by-step explanation:

Cost of the conference call before 8 pm =0.15 * 0.05 = $ 0.075

Cost of the conference call after 8 pm   = 0.15 * 0.03 = $ 0. 045

Cost of the conference call from 7pm to 8pm that last  60 minutes= 0.075 * 60

= $ 4.50

Cost of the conference call 8pm to 8:30pm =0.045 * 30 = $ 1.35

Cost of the conference call 7 pm to 8:30 pm = 4.50 + 1.35 = $ 5.85

Answer:

Step-by-step explanation:

let the parabola be y=a(x+5)²+0

or y=a(x+5)²

∵ it passes through (-3,1)

1=a(-3+5)²

4a=1

a=1/4

so parabola is y=1/4(x+5)²

Answer:

1. x=40

2. x=15

3. x=197

4. x=39

Step-by-step explanation:

pythagorean theorem: a^2 + b^2 = c^2

c= hypotenuse

Answer:

1 is 40, 2 is 15, 3 is 197, and 4 is 89

Step-by-step explanation:

Answer:

V = 200

Step-by-step explanation:

Cylinder

V = pi r^2 h

150 = pi r^2 h

We know that h = r

150 = pi r^2 r

150 = pi r^3

Divide each side by pi

150 /pi = r^3

Take the cube root of each side

( 150 / pi ) ^ 1/3 = r

3.627831679 = r

Rounding to 3.63

Now find the volume of the sphere

V = 4/3 pi  r^3

Replacing r^3 with 150 /pi

V = 4/3 * pi ( 150/pi)

V = 4*150 /3

V = 200

Subtract the monthly fee:

10.58 -5 = 5.58

Divide the remaining amount by cost per minute:

5.58/ 0.09 = 62

He was billed for 62 minutes.

Answer:

2 / 5.

Step-by-step explanation:

The slope is the rise over the run.

In this case, the rise is 2 - (-6) = 2 + 6 = 8.

The run is 4 - (-16) = 4 + 16 = 20.

So, the slope is 8 / 20 = 4 / 10 = 2 / 5.

Hope this helps!

Answer:

the slope of the line that goes through (4,2) and (-16,-6) is 2/5

m= 2/5

Step-by-step explanation:

in order to find the slope we use the ∆y/∆x which is really the change in y over the change in x.

so all you have to do is find your y's and X's.

your y's are -6 and 2

your X's are -16 and 4

now in order to find the change in y and x you subtract your y's and x'x

the formula for this is:

∆y/∆x = y1-y2/x1-x2= (m aka the slope)

y1 is -6

and y2 is 2

-6 - 2 = -8

now do the X's

X1 is -16

and X2 is 4

-16 - 4 = -20

put that in fraction form and it's -8/-20

simplify that you get 2/5

Answer:

Y= -1/5x + 1

Step-by-step explanation:

Just type it on a graphing calculator an click graph

Answer:

Step-by-step explanation:

a. Given,

v = 34 , a = 5 , t = 3

[tex]v = u + at[/tex]

plugging the values:

[tex]34 = u + 5 \times 3[/tex]

Calculate the product

[tex]34 = u + 15[/tex]

Move 'u' to L.H.S and change its sign

[tex] - u + 34 = 15[/tex]

Move constant to RHS and change its sign

[tex] - u = 15 - 34[/tex]

Calculate

[tex] - u = - 19[/tex]

The difference sign (-) will be cancelled in both sides:

[tex]u = 19[/tex]

b. Given,

v = 50 , u = 20 , a = 5

[tex]v = u + at[/tex]

plugging the values

[tex]50 = 20 + 5 \times t[/tex]

[tex]50 = 20 + 5t[/tex]

Move 5t to L.H.S and change its sign.

Similarly, Move 50 to R.H.S and change its sign

[tex] - 5t = 20 - 50[/tex]

Calculate

[tex] - 5t = - 30[/tex]

The difference sign (-) will be cancelled in both sides

[tex]5t = 30[/tex]

Divide both sides of the equation by 5

[tex] \frac{5t}{5} = \frac{30}{5} [/tex]

Calculate

[tex]t = 6[/tex]

c. Given,

v = 22 , u = 8 , t = 7

[tex]v = u + at[/tex]

plugging the values

[tex]22 = 8 + a \times 7[/tex]

[tex]22 = 8 + 7a[/tex]

Move 7a to LHS and change its sign

Similarly, Move constant to R.H.S and change its sign

[tex] - 7a = 8 - 22[/tex]

Calculate

[tex] - 7a = - 14[/tex]

The difference sign (-) will be cancelled in both sides

[tex]7a = 14[/tex]

Divide both sides of the equation by 7

[tex] \frac{7a}{7} = \frac{14}{7} [/tex]

Calculate

[tex]a = 2[/tex]

Hope this helps...

Good luck on your assignment..

5.23 m

in cm 523 cm

nearest tenth 520cm

Step-by-step explanation:

60 / 360 × 2 ×22/7 × 5

110/ 21

5.23m

Answer:

5,2(3) meters

Step-by-step explanation:

Formula

arc length = 2π·r (x°/360°)

= 2π·5m(60°/360°)

= 2·3,14·5m·1/6

= 31,4m/6

= 5,2(3) meters

Answer:

D

Step-by-step explanation:

the inscribed angle intersects an arc that twice the measure of the arc interested by the central angle. The inscribed angle's arc measures 144° and the central angle's arc measures 72°

>central angle and the arc the intersected arc are equal i.e they are both 72°

>the inscribed angle is half of the measure of the intersected arc i.e since the inscribed angle is 72° the arc interested is 144°

Answer:

1,675.516

Step-by-step explanation:

The formula for a cone is V = pi r^2 h/3.

Plugging in the values of the radius and height, V = pi 10^2 16/3

Solving, you get:

V = pi 100 5.3333333

V = 1,675.516

Answer:

266.67 feet^2.

Step-by-step explanation:

The scale is 1:40.

That means that if the scale has a width of 4 inches, the room will have a width of 4 * 40 = 160 inches. 160 / 12 = 80 / 6 = 40 / 3 feet.

The length in the model is 6 inches, so the room has a length of 6 * 40 = 240 inches. 240 / 12 = 120 / 6 = 60 / 3 = 20 feet.

The area will then be (40 / 3) * 20 = 800 / 3 = 266.67 feet^2.

Hope this helps!

Answer: A. Factor 2 => 4x greater

                   Factor 3 => 9x greater

                   Factor 5 => 25x greater

Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

[tex]A_{1}[/tex] = 2πrh

If multiply both dimensions by a factor of 2:

[tex]A_{2}[/tex] = 2.π.2r.2h

[tex]A_{2}[/tex] = 8πrh

Comparing [tex]A_{1}[/tex] to [tex]A_{2}[/tex] :

[tex]\frac{A_{2}}{A_{1}}[/tex] = [tex]\frac{8.\pi.rh}{2.\pi.rh}[/tex] = 4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

By factor 3:

[tex]A_{3} = 2.\pi.3r.3h[/tex]

[tex]A_{3} = 18.\pi.r.h[/tex]

Comparing areas:

[tex]\frac{A_{3}}{A_{1}}[/tex] = [tex]\frac{18.\pi.r.h}{2.\pi.r.h}[/tex] = 9

Multiplying by 3, gives an area 9 times bigger.

By factor 5:

[tex]A_{5} = 2.\pi.5r.5h[/tex]

[tex]A_{5} = 50.\pi.r.h[/tex]

Comparing:

[tex]\frac{A_{5}}{A_{1}}[/tex] = [tex]\frac{50.\pi.r.h}{2.\pi.r.h}[/tex] = 25

The new area is 25 times greater.

B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.

Answer:

2x^2+4x+11

Step-by-step explanation:

Answer:

-∞ < x< -∞

Step-by-step explanation:

The domain is the values that x takes

The values that x can take is all real values of x

-∞ < x< -∞

Answer:

B. Triangles A B C and A Y C are congruent and share common side A C. Triangle A B C is reflected across line A C to form triangle A Y C.

Step-by-step explanation:

Translation and reflection are examples of methods of rigid transformation. Translation ensure that each point on a given figure is moved the same distance with respect to the reference plane. Reflection involves the flipping of a given figure across a given line.

From the question, both reflection and transformation would map the triangles into one another. Since the reference line contains AB, then the two triangles are congruent and would share a common side.

Thus, the triangle pairs that can be mapped into each other is that of option B.

Based on the information given, the triangle pairs that can be mapped to each other using both a translation and a reflection across the line containing AB will be A. Triangles X Y Z and A B C are congruent. Triangle X Y Z is reflected across a line to form triangle A.

The triangle pair that can be mapped to each other using both translation and reflection across line containing AB is the first triangle pair.

The first figure consists of ΔXYZ and ΔABC that are a reflection of each other across the line AB and a translation.

Learn more about triangles on:

https://brainly.com/question/12261308

Answer:

Step-by-step explanation:

Given,

[tex] - \frac{2}{3} [/tex]

Now, let's find the value of 9x + 6

[tex]9x + 6[/tex]

plug the value of X

[tex] = 9 \times (- \frac{2}{3} ) + 6[/tex]

Multiplying a positive and negative equals a negative

[tex]( + ) \times ( - ) = ( - )[/tex]

[tex] = - 9 \times \frac{2}{3} + 6[/tex]

Reduce the number with Greatest Common Factor 3

[tex] = - 3 \times 2 + 6[/tex]

Multiply the numbers

[tex] = - 6 + 6[/tex]

The sum of two opposites equals 0

[tex] = 0[/tex]

Hope this helps..

best regards!!

Answer:

The value of M₁₁ is -6.

Step-by-step explanation:

The minor, [tex]M_{ij}[/tex] is the determinant of a square matrix, say P, formed by removing the ith row and jth column from the original square matrix, P.

The matrix provided is as follows:

[tex]A=\left[\begin{array}{ccc}7&9&-3\\3&-6&5\\4&0&1\end{array}\right][/tex]

The matrix M₁₁ is:

Remove the 1st row and 1st column to form M₁₁,

[tex]M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|[/tex]

Compute the value of M₁₁ as follows:

[tex]M_{11}=\left|\begin{array}{cc}-6&5\\4&0\end{array}\right|[/tex]

       [tex]=(-6\times 1)-(5\times 0)\\\\=-6-0\\=-6[/tex]

Thus, the value of M₁₁ is -6.