. Let f(x) = x2 and g(x) = x − 3. Evaluate (g ∘ f)(−2). 1 7 20 −20

Answer:

The number of cutters is 7

The number of screw drivers is 22

Step-by-step explanation:

Let

x-----> the number of cutters

y----> the number of screw drivers

we know that

x+y=29 ----> equation A

15.2x+2y=150.40 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (7,22)

see the attached figure

therefore

The number of cutters is 7

The number of screw drivers is 22

Answer:

The answer is 2

Step-by-step explanation:

we know that

step 1

Estimate each coefficient:      

1.81 ≈ 2

1.2 ≈ 1

step 2

Write the product:

[tex](2*10^{4})(1*10^{2})=(2*1)*10^{4+2}=2*10^{6}[/tex]  pairs of shoes in 10 years.

Answer:

the answer is two 2

Step-by-step explanation:

Answer:

D. (2, 6)

Step-by-step explanation:

Look at the picture.

Check:

(2, 6) → x = 2, y = 6

Put the coordinates of the point to the inequalities:

y < x² + 6

6 < 2² + 6

6 < 4 + 6

6 < 10    TRUE

y > x² - 4

6 > 2² - 4

6 > 4 - 4

6 > 0   TRUE

Final answer:

The correct solution to the system of inequalities is point D (2,6), as it satisfies both inequalities y < x^2 +6 and y > x^2 -4 when x=2 and y=6 are substituted into them.

Explanation:

The student is asked to select the point that is a solution to the system of inequalities.

The two inequalities given are:

< x^2 +6

y > x^2 -4

To solve this, we need to check which point(s) satisfy both inequalities. Let's evaluate the options given:

A. (0,8): Substituting x=0 into both inequalities gives 8 < 6 (false) and 8 > -4 (true), so point A does not satisfy both inequalities.

B. (-2,-4): Substituting x=-2 into both inequalities gives -4 < 10 (true) and -4 > 0 (false), so point B does not satisfy both inequalities.

C. (4,2): Substituting x=4 into both inequalities gives 2 < 22 (true) and 2 > 12 (false), so point C does not satisfy both inequalities.

D. (2,6): Substituting x=2 into both inequalities gives 6 < 10 (true) and 6 > 0 (true), so point D satisfies both inequalities and is the correct solution.

Therefore, the solution to the system of inequalities is point D (2,6).

The width of the border around the stained glass window is approximately 1.15 feet, calculated by subtracting the stained glass area from the total area including the border.

To find the width of the border, we need to subtract the area of the stained glass window from the total area including the border.

Given:

- Length of stained glass window = 4 feet

- Width of stained glass window = 2 feet

- Area of stained glass window = [tex]\(4 \times 2 = 8\)[/tex] square feet

- Total area including the border = Area of stained glass window + Area of border = 8 + 7 = 15 square feet

Let's denote the width of the border as x feet.

The total length including the border is 4 + 2x feet, and the total width including the border is 2 + 2x feet.

The area of the total window with the border is the product of its length and width:

(4 + 2x)(2 + 2x) = 15

Expanding this equation:

8 + 4x + 4x + 4x^2 = 15

8 + 8x + 4x^2 = 15

4x^2 + 8x - 7 = 0

Now, let's solve this quadratic equation using the quadratic formula:

[tex]\[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}\][/tex]

Where a = 4, b = 8, and c = -7.

[tex]\[x = \frac{{-8 \pm \sqrt{{8^2 - 4 \times 4 \times (-7)}}}}{{2 \times 4}}\][/tex]

[tex]\[x = \frac{{-8 \pm \sqrt{{64 + 112}}}}{8}\][/tex]

[tex]\[x = \frac{{-8 \pm \sqrt{{176}}}}{8}\][/tex]

[tex]\[x = \frac{{-8 \pm 4\sqrt{{11}}}}{8}\][/tex]

[tex]\[x = \frac{{-2 \pm \sqrt{{11}}}}{2}\][/tex]

Since the width cannot be negative, we take the positive root:

[tex]\[x = \frac{{-2 + \sqrt{{11}}}}{2} \approx 1.15 \text{ feet}\][/tex]

Therefore, the width of the border is approximately 1.15 feet.

Answer:

[tex]AC=\frac{11\sqrt{3}}{3}[/tex]

Step-by-step explanation:

Given that triangle ABC is a right angle triangle. Where angle C is a right angle. Also we have been given that BC = 11, B = 30°. Now we need to find the value of AC.

Apply formula:

[tex]\tan\left(\theta\right)=\frac{opposite}{adjacent}[/tex]

[tex]\tan\left(B\right)=\frac{AC}{BC}[/tex]

[tex]\tan\left(30^o\right)=\frac{AC}{11}[/tex]

[tex]\frac{1}{\sqrt{3}}=\frac{AC}{11}[/tex]

[tex]\frac{11}{\sqrt{3}}=AC[/tex]

[tex]AC=\frac{11}{\sqrt{3}}[/tex]

or

[tex]AC=\frac{11}{\sqrt{3}}\cdot\frac{\sqrt{3}}{\sqrt{3}}[/tex]

or

[tex]AC=\frac{11\sqrt{3}}{3}[/tex]

Hence final answer is [tex]AC=\frac{11\sqrt{3}}{3}[/tex].

The value of F in terms of K is (9K - 2298.67)/5.

An expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Here, given function:

                     K = 5/9 (F + 459.67)

                   9K = 5(F + 459.67)

                   9K = 5F + 2298.67

                   9K - 2298.67 = 5F

                   F =(9K - 2298.67)/5

Thus, the value of F in terms of K is (9K - 2298.67)/5.

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To solve for F in terms of K, you can use the equation F = (9/5)(K) - 459.67.

To solve for F in terms of K, we need to isolate F on one side of the equation.

Step 1: Start with the given equation:

K = (5/9)(F + 459.67)

Step 2: Multiply both sides of the equation by 9/5 to undo the multiplication on the right side:

(9/5)(K) = F + 459.67

Step 3: Simplify the left side:

(9/5)(K) = F + 459.67

Step 4: Subtract 459.67 from both sides to isolate F:

(9/5)(K) - 459.67 = F

Therefore, F in terms of K is given by the equation F = (9/5)(K) - 459.67.

Answer:

it is 33,699

Step-by-step explanation:

you add the MSRP, then the other charges

The sticker price of the car is $33,699.

The sticker price of the car can be calculated by adding the MSRP, premium package, navigation package, and destination charge. The MSRP is $29,999, the premium package is $2500, the navigation package is $500, and the destination charge is $700.

The sticker price is calculated as follows:

Therefore, the sticker price of the car is $33,699.

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[tex]\bf \textit{Law of sines} \\\\ \cfrac{sin(\measuredangle A)}{a}=\cfrac{sin(\measuredangle B)}{b}=\cfrac{sin(\measuredangle C)}{c} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{sin(75^o)}{17}=\cfrac{sin(D)}{10}\implies \cfrac{10sin(75^o)}{17}=sin(D) \\\\\\ sin^{-1}\left[ \cfrac{10sin(75^o)}{17} \right]=D\implies 34.6\approx D[/tex]

since all interior angles in a triangle must be 180°, that means that C = 180 - 75 - 34.6 = 70.4.  Let's find AD, which is the other sides pair length.

[tex]\bf \cfrac{sin(75^o)}{17}=\cfrac{sin(70.4^o)}{AD}\implies ADsin(75^o)=17sin(70.4^o) \\\\\\ AD=\cfrac{17sin(70.4^o)}{sin(75^o)}\implies AD\approx 16.58[/tex]

now, check the picture below, let's find the altitude of the parallelogram.

[tex]\bf sin(34.6^o)=\cfrac{\stackrel{opposite}{h}}{\stackrel{hypotenuse}{16.58}}\implies 16.58sin(34.6^o)=h\implies 9.4\approx h \\\\[-0.35em] ~\dotfill\\\\ \textit{area of a parallelogram}\\\\ A=bh~~ \begin{cases} b=base\\ h=height\\ \cline{1-1} b=17\\ h=9.4 \end{cases}\implies A=(17)(9.4)\implies A=159.8[/tex]

17k−25 is the answer.

Expressions are equal if they may be simplified to the same 0.33 expression or if one of the expressions can be written just like the other. similarly, you can additionally determine if two expressions are equal when values are substituted in for the variable and both arrive at an equal solution.

Algebraic expressions are equal in the event that they constantly lead to the same result whilst you evaluate them, irrespective of what values you substitute for the variables. For instance, if x = three, then x + x + 4 = three + three + 4 = 10 and 2x + 4 = 2(3) + four = 10 additionally.

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Answer:

120 cm^3

Step-by-step explanation:

volume = lwh

I = 4 centimeters  

w = 5 centimeters  

h = 6 centimeters

volume = (4 cm)(5 cm)(6 cm)

volume = 120 cm^3

Answer:

2/3

Step-by-step explanation:

The cube has the following numbers written on its faces;

1, 2, 3, 4, 5, 6

Among these numbers, the multiples of 2 and 3 are;

2, 3, 4, 6 .

The probability of rolling a multiple of 2 or 3 is thus;

4/6 = 2/3

Which is the required probability

Answer:

C [tex]11+13+15+17+...[/tex]

Step-by-step explanation:

Consider the series

[tex]\sum\limits_{n=3}^{\infty}(2n+5)[/tex]

The nth term of series is [tex]a_n=2n+5[/tex]

The bottom index tells you that n starts changing from 3, so

[tex]a_3=2\cdor 3+5=11\\ \\a_4=2\cdot 4+5=13\\ \\a_5=2\cdot 5+5=15\\ \\a_6=2\cdot 6+5=17\\ \\...[/tex]

Thus, the sum of all terms is

[tex]11+13+15+17+...[/tex]

Answer:

[tex]\$6,087.75[/tex]  

Step-by-step explanation:

we know that    

The compound interest formula is equal to  

[tex]A=P(1+\frac{r}{n})^{nt}[/tex]  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

[tex]t=5\ years\\ P=\$5,400\\ r=0.024\\n=12[/tex]  

substitute in the formula above  

[tex]A=\$5,400(1+\frac{0.024}{12})^{12*5}[/tex]  

[tex]A=\$5,400(1.002)^{60}=\$6,087.75[/tex]  

Answer:

a)zw  = 44.295 cos(1.924) +isin(1.924))

b) z/w= 4.921 cos(-0.936) + isin(-0.936)

Step-by-step explanation:

Given:

z=13+7i

w=3(cos(1.43)+isin(1.43)  

a. convert zw using De Moivre's theorem  

First coverting z into  polar form:

13^2 + 7^2  = 14.765

[tex]\sqrt{14.765}[/tex] =r

θ= arctan (7/13)

 = 0.49394                            (28.301 in degrees)

z= 14.765(cos(0.49394)+isin(0.49394)  )

Now finding zw

zw= 14.765(cos(.494)+isin(.494))×3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be multiplied

14.765 x 3=44.295

whereas the angles will be added

.494+1.43=1.924

Thus:

zw  = 44.295 cos(1.924) +isin(1.924))

b)

finding z/w

z/w= 14.765(cos(.494)+isin(.494)) / 3(cos(1.43)+isin(1.43))

Using De Moivre's theorem, the modulus will be divided

14.765 / 3 = 4.921

whereas the angles will be subtracted:

.494-1.43=-0.936

Thus:

z/w= 4.921 cos(-0.936) + isin(-0.936) !

Answer:

b

Step-by-step explanation:

yes

Answer:

B

Step-by-step explanation:

If we draw another vertical line on the other side, we can split this into a rectangle and two triangles.  The width of the rectangle is 5 m, so the base of the triangle on the left is 1 m, just like the triangle on the right.

The area is therefore the sum of the areas of each shape:

A = Arectangle + 2Atriangle

A = (5 m)(3 m) + 2(½ (1 m)(3 m))

A = 18 m²

Answer:

32

Step-by-step explanation:

put the numbers in order from less to greatest

3,13,14,16,27,37,42,64,95,97

the middle numbers are 27 and 37

27+37 is 64

64 divided by 2 is 32

First put the numbers in order from least to greatest

3, 13, 14, 16, 27, 37, 42, 64, 95, 97

Median means middle so find the middle number by deleting the least and greatest number in each "layer"

3, 13, 14, 16, 27, 37, 42, 64, 95, 97

   13, 14, 16, 27, 37, 42, 64, 95

         14, 16, 27, 37, 42, 64

               16, 27, 37, 42

                     27, 37

You have two numbers left. To find the middle take the mean of these two numbers, by adding them together then dividing the sum by two

27 + 37 = 64

64 / 2 = 32

32 is the median!!!

Hope this helped!

Answer:

perpendicular is the opposite, so -3

Answer:

FIRST OPTION: -3

Step-by-step explanation:

By definition, if two lines are perpendicular to each other, then their slopes are negative reciprocals.

In this case you can observe that that the slope of the line is [tex]\frac{1}{3}[/tex] and you know that the other line is perpendicular to this line. Therefore, their slopes are negative reciprocals.

This means that:

If [tex]slope_1=\frac{1}{3}[/tex] ,then  [tex]slope_2=-3[/tex]

This matches with the first option.

Answer

1) [tex]b=101\degree[/tex]

2) [tex]m=50\degree[/tex]

3) [tex]h=79\degree[/tex]

4) [tex]g=101\degree[/tex]

5) [tex]i=51\degree[/tex]

6) [tex]j=130\degree[/tex]

Explanation

From the diagram,

[tex]b=101\degree[/tex], corresponding angles are equal.

From the diagram, m=k, corresponding angles are equal.

But k+130=180, angles on a straight line sum up to 180 degrees.

This implies that k=180-130=50

[tex]\therefore m=50\degree[/tex]

From the diagram ; [tex]h+101=180\degree[/tex],angles on a straight line sum up to 180 degrees.

[tex]\implies h=180-101\degree[/tex]

[tex]\implies h=79\degree[/tex]

From the diagram, [tex]g=101\degree[/tex] vertically opposite angles are equal.

From the triangular portion;

i+h+m=180. sum of interior angles of a triangle.

This implies that:

i+79+50=180

i+129=180

i=180-129

[tex]i=51\degree[/tex]

Finally

[tex]j=130\degree[/tex], vertically opposite angles are equal.

Answer:

Part 1) ∠b=101°

Part 2) ∠m=50°

Part 3) ∠h=79°

Part 4) ∠g=101°

Part 5) ∠i=51°

Part 6) ∠j=130°

Step-by-step explanation:

Part 1) ∠b

we know that

∠b=101° ------> by corresponding angles

Part 2) ∠m

we know that

∠m=∠k ------> by corresponding angles

and

∠k+130°=180° -----> by supplementary angles

∠k=180°-130°=50°

therefore

∠m=50°

Part 3) ∠h

we know that

∠h+101°=180° -----> by supplementary angles

∠h=180°-101°=79°

Part 4) ∠g

we know that

∠g=101° -----> by vertical angles

Part 5) ∠i

we know that

The sum of internal angles of a triangle must be equal to 180 degrees

so

∠h+∠m+∠i=180°

substitute the values and solve for ∠i

79°+50°+∠i=180°

∠i=180°-129°=51°

Part 6) ∠j

we know that

∠j=130° -----> by vertical angles

Answer:

y = 37/36

Step-by-step explanation:

let's take a peek at the denominators hmmmm 5, 9, 8   hmmmm we can get an LCD of simply their product, well, that'd be 360, so then, let's multiply both sides by the LCD of 360 to do away with the denominators and proceed.

[tex]\bf \cfrac{3}{5}y+\cfrac{2}{9}=\cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8}\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{360}}{360\left( \cfrac{3}{5}y+\cfrac{2}{9} \right)=360\left( \cfrac{5}{8}-\cfrac{2}{5}y+\cfrac{5}{8} \right)} \\\\\\ 72(3y)+40(2)=45(5)-72(2y)+45(5) \\\\\\ 216y+80=225-144y+225\implies 216y+80=450-144y \\\\\\ 216y=370-144y\implies 360y=370\implies y=\cfrac{370}{360}\implies y=\cfrac{37}{36}[/tex]

Answer:

Step-by-step explanation:

Sample space {1,2,3,4,5,6}

3 to 6: {3,4,5,6}

My punctuation may not be the same as yours, but that is what they are asking for.

Answer:

128

Step-by-step explanation:

To create 128 different hamburgers with multiple combinations of condiments, you would need 7 different condiments. This is due to the fact that each condiment presents 2 possibilities, on the burger or not, and 2 to the power of 7 equals 128.

In this scenario, each condiment represents an option that can be either included or excluded. This means that, for each condiment, there are 2 possibilities (it's either on the burger, or it's not). The question implies that the number of possible combinations equals 128, which is 2 to the power of 7.

So, to create 128 different hamburgers, the restaurant must offer 7 different condiments. This is because 2 (possibilities for each condiment) to the power of 7 (condiments) equals 128.

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Answer:

80

Step-by-step explanation:

Answer:

I think it is C. I am not sure

The correct equation that has solutions of 3 ± √5 is (x - 3)² = 5.

The solutions of the equation are given as 3 ± √5 To find an equation that has these solutions, we would look for an equation in the form (x - a)^2 = b, where the solutions to x can be found using the square root property x = √b + a or x = -√b + a. In this case, we are looking for an equation where a is 3 and b is 5 to fit the solutions provided.

Examining the options provided:

Therefore, the equation with solutions of 3 ± √5 is (x - 3)² = 5.

ANSWER

C. 33 units^2

EXPLANATION

The area of a kite is half times product of the diagonals.

The diagonals are

3+3=6 units

and

9+2 =11 units.

The area of the kite is

[tex] = \frac{1}{2} \times 11 \times 6[/tex]

[tex] = 11 \times 3[/tex]

[tex] = 33 {units}^{2} [/tex]

The correct choice is C

x+5/30 = 50/75

x+5/10 = 2

x+5 = 20

x = 15

Answer:

Step-by-step explanation:

The sample space should show all the possible outcomes.

The first option includes all 4 colors and both head and tails.

The second option is missing tails as an outcome.

The third option is missing blue.

The fourth option is missing tails.

So it must be the first one.

As we know distance equals speed multiplied by time

118*2.25=265.5

Therefore the car can travel 265.5km in 2 hours 15 minutes with the speed of 118km/h

The van can travel approximately 265.5 kilometers in 2 hours and 15 minutes.

To find out how far the van can travel in 2 hours and 15 minutes, we need to use the formula:

Distance = Speed × Time

Given:

- Speed of the van = 118 km/h

- Time = 2 hours 15 minutes

First, let's convert the time to hours:

2 hours 15 minutes = 2 + 15/60 hours

= 2.25 hours

Now, we can use the formula to calculate the distance:

Distance = 118 km/h × 2.25 hours

Distance ≈ 265.5 km

Therefore, the van can travel approximately 265.5 kilometers in 2 hours 15 minutes.

Well it depends. If your radical is wrapped around the entire expression, then your answer would be 3xy²z²√10xz, but if your radical is ONLY wrapped around 90, then your answer would be 3√10x³y⁴z⁵ [radical wrapped ONLY around 10]. So, with the way this is written, although it is simple to figure this out, it is difficult to find the answer you are looking for.

Answer:

48984 m^2

Step-by-step explanation:

The height(h) of cone is given by: 50 m.

Diameter of cone is: 240 m.

Also radius(r) of cone is:240/2=120 m.

The lateral surface(S) area is given by:

The lateral area of the cone comes out to be 48984 m^2.

What is lateral area?

The formula of the lateral area of cone is given by, area = pi×r×L

The amount of territory occupied by the curved surface area of a cone is known as the lateral surface area.

The lateral surface area of a cone is also in the three-dimensional plane because it is a three-dimensional form. The shape of a cone is created by stacking and rotating several triangles around an axis. Since a cone has a flat base so it has curved surafce area as well as total surface area.  A cone's lateral area is measured in square units, such as cm2, m2, in2, and so on.

Given,

Height of cone : 50m

Diameter of cone: 240m

so,it's radius will be 120m

L = [tex]\sqrt{r^{2}+h^{2}}[/tex]

L = [tex]\sqrt{120^{2} +50^{2} }[/tex]

L = 130

since,Area = pi×r×L

=3.14×120×130

=48984m^2

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true

any given point in a circle is equal distance from the center

Answer: TRUE.

Step-by-step explanation:

It knows that the distance "d" between any two points is equal to [tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex].

In a circle the distance between a point that belongs to the circumference and the center ([tex]x_0,y_0[/tex]) is always the same. Then:

[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}[/tex] is always equal to a constant called "r".

This is:

[tex]\sqrt{(x-x_0)^2-(y-y_0)^2}=r[/tex]

Square both sides of the equality:

[tex](\sqrt{(x-x_0)^2-(y-y_0)^2})^2=r^2[/tex]

[tex](x-x_0)^2-(y-y_0)^2=r^2[/tex]

Note that we obtain the General equation of a circle.

This prove that if the distance between a given point in the plane and a collection of points is equal, then the equation of a circle is obtained.

Therefore, the statement "A circle is the collection of points in a plane that are the same distance from a given point in the plane." is true.