Lines a and b are perpendicular. The slope of line a is −2. What is the slope of line b?

Substitute y = x + 2 into y = 3x - 2

x + 2 = 3x - 2

Solve for x in x + 2 = 3x - 2

x = 2

Substitute x = 2 into y = x + 2

y = 4

Therefore,

x = 2

y = 4

The answer is C

Explanation; there are 2 triangles and 3 rectangles

The statement that describes the net of the prism is:

       C. Two triangular bases and three rectangular lateral faces

Net of a solid--

A net is a two dimensional figure which can be folded to get a three dimensional figure.

or we may say it is a pattern which is made when we scatter out different faces of the solid or three dimensional figure.

Step-by-step explanation:

12/3.48= cost of 1 book

cost of 20 books = 12/3.48×20 =68.95

To find the cost of 20 pens when 12 pens cost $3.48, divide $3.48 by 12 to get the cost per pen and then multiply by 20. The cost for 20 pens would be $5.80.

To calculate the cost of 20 pens when 12 pens cost $3.48, first, we need to find the cost of one pen. We do this by dividing the total cost of 12 pens by the number of pens:

$3.48 / 12 pens = $0.29 per pen.

Now that we know the cost of one pen, we can calculate the cost of 20 pens by multiplying the cost per pen by 20:

$0.29 / pen x 20 pens = $5.80.

So, 20 pens would cost $5.80.

1.5 × 10 to the 1 st power

Answer:

0.00002

2*10^-5 = 2*00001 = 0.00002

Answer:

Google says 9?

Step-by-step explanation:

Answer:

92 more miles

Step-by-step explanation:

60 mph is 1 mile per min so in 42 min they traveled 42 miles and 134 miles minus 42 miles is 92 miles

Answer:

Refer to step-by-step.

Step-by-step explanation:

To find the LCD of the different fractions, we first need to follow the steps of finding the LCD of algebraic fractions.

1st step: Factor

You need to factor out the expressions if they do not have a difference of two squares.

2nd step: Find the LCD of the coefficients.

You need to find the LCD of the coefficients before moving onto the variables.

3rd step: The variable part of the LCD will be every single variable you see, with the highest exponent.

So let's begin, since all the given denominators are already factored out, we can proceed straight to step 2.

[tex]\dfrac{5}{9m^{2}n}and\dfrac{5}{16mn^{3}}[/tex]

Now since we're dealing with the denominators, let's focus on them alone.

The LCD of 9 and 16 is 144

The LCD of variables m² and m is m²

The LCD of variables n and n³ is n²

So the LCD of the algebraic fractions [tex]\dfrac{5}{9m^{2}n}and\dfrac{5}{16mn^{3}}[/tex] is:

144m²n³

Now to the next one.

[tex]\dfrac{5+m}{8m^{4} n^{2} }and\dfrac{5+n}{18m^{2} n^{4} }[/tex]

The LCD of 8 and 18 is 72

The LCD of variables [tex]m^{4}[/tex] and m² is [tex]m^{4}[/tex]

The LCD of variable n² and [tex]n^{4}[/tex] is [tex]n^{4}[/tex]

So the LCD of the algebraic fractions [tex]\dfrac{5+m}{8m^{4} n^{2} }and\dfrac{5+n}{18m^{2} n^{4} }[/tex]is:

[tex]72m^{4} n^{4}[/tex]

Next one we have:

[tex]\dfrac{m+n}{12mn}and\dfrac{n+m}{18m^{3}n }[/tex]

The LCD of 12 and 18 is 36

The LCD of m and m³ is m³

The LCD of n and n is n

So the LCD of the algebraic fractions [tex]\dfrac{m+n}{12mn}and\dfrac{n+m}{18m^{3}n }[/tex] is:

36m³n

Last but not the least.

[tex]\dfrac{m-n}{24mn^{4}}and\dfrac{m-n}{16m^{4}n }[/tex]

The LCD of 24 and 16 is 48

The LCD of m and [tex]m^{4}[/tex] is [tex]m^{4}[/tex]

The LCD of [tex]n^{4}[/tex] and n is [tex]n^{4}[/tex]

So the LCD of the algebraic fractions [tex]\dfrac{m-n}{24mn^{4}}and\dfrac{m-n}{16m^{4}n }[/tex] is:

[tex]48m^{4} n^{4}[/tex]

Answer:

20

Step-by-step explanation:

But you should know this already...

The answer is:

[tex]sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75[/tex]

[tex]cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15[/tex]

Since we are working with a right triangle, we can use the Pythagorean Theorem to know the missing side size (Opposite Side).

Pythagorean Theorem formula:

[tex]c^{2}=a^{2} +b^{2}[/tex]

Where:

[tex]c=hypotenuse=73\\a=AdjacentSide=48\\b=OppositeSide[/tex]

So, the opposite side will be:

[tex]OppositeSide=\sqrt{c^{2}-a^{2}}=\sqrt{73^{2}-48^{2}}=\sqrt{5329-2304} \\OppositeSide=\sqrt{3025}=55[/tex]

Then:

[tex]sin(F)=\frac{OppositeSide}{Hypotenuse}=\frac{55}{73}=0.75[/tex]

[tex]cos(F)=\frac{AdjacentSide}{Hypotenuse}=\frac{48}{73}=0.66\\\\tan(F)=\frac{OppositeSide}{AdjacentSide}=\frac{55}{48}=1.15[/tex]

Have a nice day!

Answer:

Sin F  = 0.7534

Cos F = 0.6575

Tan F= 1.145

Step-by-step explanation:

From the given figure we can see that,

triangle DEF is right angled triangle

Base = DF = 48

Hypotenuse = EF = 73

Height = ED

To find ED

We have ,

Hypotenuse² = Base² + Height²

EF² = DF² + ED²

ED² = EF² - DF² = 73² - 482

ED² = 3025

ED = √3025 = 55

To find Sin (F)

Sin ∅ =Opposite side /Hypotenuse

Sin F = ED/EF = 55/73 = 0.7534

To find Sin (F)

Cos ∅ =Adjacent side /Hypotenuse

Cos F =DF/EF = 48/73 = 0.6575

To find Sin (F)

Tan ∅ =Opposite side /Adjacent side

Tan F = ED/DF = 55/48 = 1.145

Answer:

Mike = m pencils

Jen  = m + 3 pencils

Total = Mike + Jen

   = m+m+3

= 2m+3

Step-by-step explanation:

x squared and -9 are both square numbers.

the square root of x^2 is x

the square root of -9 is 3. so you just need to write (x+3)(x-3)

you can check by expanding the brackets and the middle x terms should cancel out

Answer:

(x-3)(x+3)

Step-by-step explanation:

Here we have to represent our algebraic expression as difference of square.

In order to do so we have use the formula given under.

[tex](x^2-a^2)=(x-a)(x+a)[/tex]

Hence first we have to guess the square root of the 9 , which is 3 and represent our numeric term in our expression as square of it.

Hence

[tex](x^2-9)\\= (x^2-3^2)[/tex]

Now we apply the formula

[tex](x^2-3^2)=(x-3)(x+3)[/tex]

Hence the above expression is our answer.

Answer:

The perimeter of rectangle is [tex]18\ cm[/tex]

Step-by-step explanation:

Let

x-----> the length of the rectangle

y----> the width of the rectangle

we know that

[tex]x=y+5[/tex] ----> equation A

[tex]120=xy+2x^{2}+2y^{2}[/tex] ---> equation B (area of the constructed figure)

substitute the equation A in equation B

[tex]120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=(y+5)y+2(y+5)^{2}+2y^{2}\\ 120=y^{2}+5y+2(y^{2}+10y+25)+2y^{2}\\ 120=y^{2}+5y+2y^{2}+20y+50+2y^{2}\\120=5y^{2}+25y+50\\5y^{2}+25y-70=0[/tex]

using a graphing calculator -----> solve the quadratic equation

The solution is

[tex]y=2\ cm[/tex]

Find the value of x

[tex]x=y+5 ----> x=2+5=7\ cm[/tex]

Find the perimeter of rectangle

[tex]P=2(x+y)=2(7+2)=18\ cm[/tex]

Answer:

Perimeter of rectangle = 38 cm

Step-by-step explanation:

It is given that, Length of a rectangle is 5 cm longer than the width.

Let 'x' be the width then length = x + 5

Area of of rectangle = x(x + 5)

One side of square = ( x+ 5)/4

Area of all squares = [(x +5)/4]² * 4 = (x + 5)²/4

To find the value of x

Total area = 120 cm²

Area of of rectangle + Area of all squares  = 120

x(x + 5) + (x + 5)²/4 = 120

x² + 5x + (x² + 10x + 25)/4 = 120

4x² + 20x + x² + 10x + 25 = 120 * 4

x² + 6x + 5  = 24 * 4

x² + 6x - 96 =0

x = 7

To find the perimeter of rectangle

width = x = 7

Length = x + 5 = 7 + 5 = 12

Perimeter = 2(length + width) = 2(7 + 12) = 38 cm

The question involves predicting the temperature of water after six intervals using an exponential decay function. Without the exact values to form the function, we can infer that the temperature will likely be around option (b) 101°F after six intervals based on the pattern of decrease shown in the provided intervals.

The student's question is about using an exponential function to model the temperature decrease of water as it cools at room temperature.

To solve this problem, one would generally apply the formula for an exponential decay function, which is of the form w(t) = [tex]a * e^{(kt)[/tex], where w(t) is the temperature at time t, a is the initial temperature, e is the base of the natural logarithm, and k is the decay constant. Given the temperatures at specific intervals, one could use these to estimate the constants a and k.

However, without the necessary values to develop an equation, we instead look for the pattern in the temperature's decrease to predict the sixth interval's approximate temperature.

Examining the table provided:

We can see that the temperature is decreasing less with each interval. While it is not explicitly stated, it's reasonable to assume that an exponential decay function would fit this scenario. Without the exact function, we can make an educated guess based on the trend that after six intervals, the temperature will be less than 121°F and likely close to option (b) 101°F.

Answer:

The correct options are 1, 2, 3 and 4.

Step-by-step explanation:

The given function is

[tex]f(x)=2^x[/tex]

The above function is defined for all the values of x.

⇒ Therefore the domain is all real numbers x because the exponent of 2 can be any real number.

⇒ The x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.

Put x=0, to find the y-intercept.

[tex]f(x)=2^=1[/tex]

⇒The y-intercept is (0, 1).

The value of f(x) is always greater than 0 because powers of 2 are never negative.

[tex]f(x)>0[/tex]

⇒The graph never goes below the x-axis because powers of 2 are never negative.

⇒Therefore the range of the function is all positive real numbers.

Therefore the correct options are 1, 2, 3 and 4.

The True statements about the graph of the function [tex]y =2^x[/tex] are option a), b), c) and d). Refer the below solution for better understanding.

Given :

[tex]y = 2^x[/tex]

Solution :

Domain is all real numbers x because the exponent of 2 can be any real number.

x is exponent of 2, therefore the x-values increases by 1 unit, the y-value multiplies by 2.

At [tex]x=0[/tex],

[tex]y=2^0=1[/tex]

y intercept -- (0 , 1).

y is always greater than zero because power of 2 never be negative.

Graph never goes below the x-axis because powers of 2 are never be negative.

The range of the function is all positive real numbers.

Therefore all the options are correct.

For more information, refer the link given below

https://brainly.com/question/14418346

step 2: Chris added the exponents when he should have multiplied them

Answer:

Step 2

Step-by-step explanation:

Answer:

x = -3, x= 0, and x = 1.5

Step-by-step explanation:

The zeros of a function f(x) refers to the x-values for which f(x) = 0.

We simply graph the function and determine the points where the graph crosses the x-axis. Thus, we shall be solving the problem graphically;

From the attachment below, the graph of f(x) crosses the x-axis at;

x = -3, x= 0, and x = 1.5

Answer:

= 8.9 units

Step-by-step explanation:

When a chord intersects with a tangent outside a circle then we use the relationship;

X ² = AO × BO, Where A and are the points of intersection of the chord an the circle, while O is the point of intersection between the chord and the tangent.

Therefore;

x² = 4 × 20 or 8 × 10

x² = 80

x = √80

= 8.944

 ≈ 8.9

Answer: 8.9

Step-by-step explanation:

x² = 4 × 20 or 8 × 10

x² = 80

x = √80

= 8.944

≈ 8.9

Your answer is A) 1/2 inch per foot

Multiply the given info by 2 to get the answer.

Please mark brainliest if this helps you! :)

Answer:

The theoretical probability of rolling a number smaller than a 3 is __1/3_____because this is what__we expect to happen____ . The experimental probability of rolling a number smaller than a 3 is __1/4____ because this is what___actually happened____

Step-by-step explanation:

The experimental probability is

P (<3) = (  getting a one or 2)/ number of times that he rolled

        He rolled a one or a two 2 times of the 8 times rolled

          = 2/8 = 1/4

Theoretical probability is what we expect  happen

P (<3) = (getting a one or two) / 6

         = 2/6 = 1/3

The theoretical probability of rolling a number smaller than a 3 is __1/3_____because this is what__we expect to happen____ . The experimental probability of rolling a number smaller than a 3 is __1/4____ because this is what___actually happened____

Answer:

The answer is 50

Step-by-step explanation:

You add up all the numbers and divide the numbers by how many numbers there are.

The answer would be 50!

Answer:

B. 6,700 m

Step-by-step explanation:

Mr. Gephart is traveling from his house to the history museum = 6.7 km

1 km = 1,000 m

so

6.7 x 1,000 = 6,700 m

Answer is B. 6,700 m

Answer:

Step-by-step explanation:

B. 6,700m

Answer:

The length is 22 and the width is 18.

Step-by-step explanation:

You can solve for the length by using the perimeter formula.

P = 2l + 2w.

You know P = 80. You also know the length is l and the width is w = l - 4.

80 = 2l + 2(l - 4)

80 = 2l + 2l - 8

80 = 4l - 8

88 = 4l

22 = l

This means the width which is 4 meters less is 22 - 4 = 18.

Answer:

A. 1/5

C. 2/3

Step-by-step explanation:

30x^2 - 26x + 4=0

2(15x^2 - 13x + 2) = 0

2(15x^2 - 10x - 3x  + 2) = 0

2[(5x(3x - 2)  - 1(3x - 2)] = 0

2(5x - 1)(3x - 2) = 0

5x - 1 = 0; x = 1/5

3x - 2 = 0; x = 2/3

Answer:

x = 1/5, x = 2/3.

Step-by-step explanation:

30x^2 - 26x + 4 = 0

15x^2 - 13x +2 = 0

(5x - 1 )(3x  - 2) = 0

5x - 1 = 0  or 3x - 2 = 0

x =  1/5,  2/3.

Answer:

the word is viewpoint

Step-by-step explanation:

Answer:

Step-by-step explanation:

Viewpoint refers to a particular and individual way to see the world. It's the personal perspective in a specific context, it's people's point of view. For example, in a situation like an accident between a motorcycle and a bus, some people would say that the fault is no the bus drives, other would say that it's on the motorcycle driver, but at the end, those just are different viewpoint.

In this case, a writer's opinion or way of seeing an issue, it's referring to a point of view, or viewpoint, because involves an individual opinion about something.

Answer:

YL=130 (PWP)

m<YPL=65 (Inscribed < th)

Step-by-step explanation:

Answer:

[tex]m\angle YPL=65^{\circ}[/tex]

Step-by-step explanation:

We have been given an image of a circle and we are asked to find the measure of angle YPL.

Since the degree measure of circumference of a circle is 360 degrees, so we can set an equation to find the measure of arc LY as:  

[tex]m\widehat{LY}+m\widehat{PL}+m\widehat{PY}=360^{\circ}[/tex]

Upon substituting our given values in above equation we will get,

[tex]m\widehat{LY}+80^{\circ}+150^{\circ}=360^{\circ}[/tex]

[tex]m\widehat{LY}+230^{\circ}-230^{\circ}=360^{\circ}-230^{\circ}[/tex]

[tex]m\widehat{LY}=130^{\circ}[/tex]

We can see that angle YPL is inscribed angle of arc LY, so the measure of angle YPL will be half the measure of arc LY.

[tex]m\angle YPL=\frac{1}{2}m\widehat{LY}[/tex]

[tex]m\angle YPL=\frac{1}{2}\times130^{\circ}[/tex]

[tex]m\angle YPL=65^{\circ}[/tex]

Therefore, the measure of angle YPL is 65 degrees.

Randy caught quails at a slower rate

Answer:

rate change: -8

Equation: y = 232 -8x

After 5 hours: 192

Step-by-step explanation:

8 are destroyed every hour, so there are 8 less every hour, so the rate of change is -8

It starts with 232 and loses 8 per hour, so the formula is

y = 232 - 8x

After 5 hours:

y = 232 - 8(5)

    y = 232 - 40

         y = 192

Answer:

Step-by-step explanation:

The rate of change in this case is -8, since the amount is decreasing.

The equation is:

y=232-8x.

After 5 hours, he will have 192 rews.

Answer:

I am not sure that this is a solvable equation.

Answer:

CBX and FBC

Step-by-step explanation:

because they both are supplememntary

Adjacent angles share a common vertex and side, and do not overlap. Without a diagram, specific adjacent angles cannot be identified. Angle BAB' being equal to the angle of incidence is relevant to the geometry but does not determine adjacency.

Adjacent angles are two angles that have a common vertex and a common side, but do not overlap. By definition, they are next to each other on a plane and their shared side is called the ray. In the given question, we should look for two angles that meet this criteria.

The answer is not directly provided since it seems to be referencing a diagram that we do not have. However, in general, to determine adjacent angles in a diagram, you would look for angles that share a vertex and a common side. For example, if angle GMB and angle FBC shared a side and a vertex, they would be considered adjacent angles.

Given the information that the segment AB' is shared by triangles in two different mediums, and that angle BAB' is equal to the angle of incidence, this does not directly relate to the angles being adjacent but gives insight into the geometry of the situation.