Which of these tables represents a function

The exponential equation that represent the graph is y = 2(4)^x

The standard exponential function is expressed as

y = ab^x

Given the coordinate points (1, 8) and (0,2), the equivalent equations are;

8 = ab^1

2 = ab^0

from equation 2, a = 2

8 = 2b

b = 4

Hence the exponential equation that represent the graph is y = 2(4)^x

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The line plot shown C in the figure is correct.

Given that the recorded lengths of ribbon pieces which is used in project is [tex]11\frac{1}{4},11\frac{1}{4},10\frac{3}{4},10\frac{1}{2},10\frac{7}{8},10\frac{5}{8},9\frac{7}{8},11\frac{1}{4}[/tex].

Frequency refers to the number of times an event or  value occurs. A frequency table is a table that lists items and shows how many times those items occurred.

A line plot displays the data using a no. line.

Firstly, we will fimd the frequency of each value

Values                               Frequency

9 (7/8)                                        1

10(4/8)=10(1/2)                           1

10(5/8)                                       1

10(6/8)=10(3/4)                          1

10(7/8)                                       1

11(2/8)=11(1/4)                             3

Option A is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)

Option B is incorrect because 11(2/8) has no data values in the line plot (i.e. frequency = 0)

Option C is correct because the frequency distribution of the data is represented correctly in the line plot.

Option D is incorrect because 11(2/8) has 2 data values in the line plot (i.e., frequency = 2)

Hence, the line plot which correct shows the data is third line plot.

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Answer: x=5.6 or 5 3/5

Step-by-step explanation:

Cross multiplication is when you have two fractions (ratios) that are equivalent and you can multiply the numerator of the first one by the denominator of the second one, and the denominator of the first one by the numerator of the first one. The answers to these two are equivalent.

So, 5x/8 = 7/2

10x=56

x=5.6

x= 5 3/5

Answer:

The answer is X=3/4 or -1/2

Answer:

slope = [tex]-\frac{1}{2}[/tex]     if it were in an

Step-by-step explanation:

the graph is a negative and will therefore have a negative slope. to find the slope, pick a point on the graph and find the [tex]\frac{rise}{run}[/tex].

for instance, start with the point (0,1). Then go down 1 and left 2 to get to the next point on the graph (2,0). 1 is the "rise" and 2 is the "run" hence -1/2 being the slope.

you could also use the slope formula: [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]

point 1: (0,1)    (x₁ ,y₁)

point 2: (2,0)    (x₂ , y₂)

[tex]\frac{0-1}{2-0} =-\frac{1}{2}[/tex]

Answer:

96

Step-by-step explanation:

(2^22-2^20) (3^24-3^22) (4^26-4^24)

=[(2^2-1)2^20][(3^3-1)3^22][(4^2-1)4^24]

=3*2^20*8*3^22*15*4^24

=2^23*3^23*4^24*15

=2^23*3^23*2^48*3*5

=2^71*3^24*5.

∵(2^22-2^20) (3^24-3^22) (4^26-4^24)=2^x × 3^y × 5^z，

∴x=71, y=24, z=1,

∴x+y+z=71+24+1=96.

Answer:

[tex](f-g)(x)=x^2-6x+5[/tex]  dom: (-∞,∞)

[tex](\frac{f}{g})(x)=x-7+\frac{7}{x+2}[/tex] dom: (–∞,–2)u(–2,∞)

Step-by-step explanation:

[tex](f-g)(x)=f(x)-g(x)=(x^2-5x+7)-(x+2)[/tex] *distribute the negative sign into (x+2)!

[tex]x^2-5x+7-x-2\\x^2-6x+5[/tex]

a parabola (anything that begins with [tex]x^2[/tex]) will have a domain of (-∞,∞) or all real numbers!!

[tex](\frac{f}{g} )(x)= \frac{x^2-5x+7}{x+2}[/tex]      use synthetic division to divide (the attached picture)

domain: Because the graph is not continuous, you have to write the domains on both sides of the asymptote which is (-∞,-2)u(-2,∞)

synthetic division:

1. take the divisor (x+2) and solve for x.    x= –2 this goes in the top left corner

2. write the numbers AND their signs on the top row. if there is no number and just the variable (like [tex]x^2[/tex] ) just write 1.

3. the first number gets pulled down

4. multiply -2 by 1 and subtract it from –5. (-5-2= -7)

multiply -2 by -7 and add that to the next number in the top row which is -7. (-7 + 14=7)

5. the first number in the bottom row of numbers is the first number in the answer but with one less exponent than the dividend. **write 1 as x**

6. the last number in the bottom row, if it is not 0, is a remainder. write it as that number over the divisor. in this case the remainder is 7. so write it as [tex]\frac{7}{x+2}[/tex]

In a two-tailed hypothesis test the null hypothesis is rejected.

According to the statement

The test statistic is 3.06 and the critical values are /-2.086.

If we find the value of t by using the formula the then it comes with Negative sign and it lies under the critical region.

That's why In a two-tailed hypothesis test the null hypothesis is rejected.

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(a) The scale used in the analysis is qualitative as the data is not assigned any numeric value.

The daily performance is an ordinal variable, as the values assigned are ranked according to an order of the delivery time.

(b) The frequency table of the given data is:

Variable Frequency

Early  23

On-time  65

Late            9

Lost            3

Total 100.

(c) The relative frequency table for the given data is:

Variable Frequency Relative frequency

Early  23           23/100 = 0.23 = 23%

On-time  65           65/100 = 0.65 = 65%

Late            9             9/100 = 0.09 = 9%

Lost            3             3/100 = 0.03 = 3%

(a) The scale used in the analysis is qualitative as the data is not assigned any numeric value.

The daily performance is an ordinal variable, as the values assigned are ranked according to an order of the delivery time.

(b) The frequency table is a table showing frequency of each variable for the number of times they appear in the data.

The frequency table of the given data is:

Variable Frequency

Early  23

On-time  65

Late            9

Lost            3

Total 100.

(c) The relative frequency for a variable is the ratio of its frequency to the total frequency.

The relative frequency table for the given data is:

Variable Frequency Relative frequency

Early  23           23/100 = 0.23 = 23%

On-time  65           65/100 = 0.65 = 65%

Late            9             9/100 = 0.09 = 9%

Lost            3             3/100 = 0.03 = 3%

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Answer:

C.

Step-by-step explanation:

The equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

In accordance with the statement, car travels in a straight line at constant speed. The distance traveled (d), in miles, is equal to the product of the speed (v), in miles per hour, and time (t), in hours:

d(t) = v · t     (1)

If we know that v = 60 mi/h, then the equation of distance traveled by the car is d(t) = 60 · t, for t ≥ 0.

The statement is incomplete and complete form cannot be found. Then, we decided to complete the statement by asking for the equation that describes the distance of the car.

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Answer:

x=27.80

Step-by-step explanation:

we know that cosA=base/hypotaneous

so,

[tex]cos44 = \frac{20}{x} \\ x = \frac{20}{cos(44)} \\ = \frac{20}{0.7193...} \\ = 27.80 [/tex]

The coterminal angles are given as follows:

a) 0º.

b) 120º.

The coterminal angle of a negative angle between 0 and -360º = -2pi is found adding 360º = 2pi to the angle, hence:

-2pi + 2pi = 0, which is the answer to item a.

The coterminal angle is found taking the remainder of the division of the angle by 360º.

The remainder of the division of 480º by 360º is of 120º, hence the coterminal angle of 480º is of 120º.

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The charges of entrance fee for a bus containing 30 people is $98

let

Charges For 2 people = mx + y

14 = 2x + y

Charges For 4 people = mx + y

20 = 4x + y

14 = 2x + y

20 = 4x + y

20 - 14 = 4x - 2x

6 = 2x

x = 6/2

x = 3

Substitute x = 3 into

14 = 2x + y

14 = 2(3) + y

14 = 6 + y

14 - 6 = y

8 = y

Charges For 8 people = mx + y

= 8(3) + 8

= 24 + 8

= $32

Therefore,

Charges For 30 people = mx + y

= 30(3) + y

= 90 + 8

= $98

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Answer: y = -2x + 1.

Step-by-step explanation:

From (-1, 3) follow the line to go 1 to the right and 2 down (because the slope is -2). That takes you to (0, 1). So the y-intercept is 1 and the equation is y = -2x + 1.

Question 6

1) [tex]\overline{AB} \cong \overline{BD}[/tex], [tex]\overline{CD} \perp \overline{BD}[/tex], O is the midpoint of [tex]\overline{BD}[/tex], [tex]\overline{AB} \cong \overline{CD}[/tex] (given)

2) [tex]\angle ABO, \angle ODC[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle ABO, \triangle CDO[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\overline{BO} \cong \overline{OD}[/tex] (a midpoint splits a segment into two congruent parts)

5) [tex]\triangle ABO \cong \triangle CDO[/tex] (LL)

Question 7

1) [tex]\angle ADC, \angle BDC[/tex] are right angles), [tex]\overline{AD} \cong \overline{BD}[/tex]

2) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)

3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)

5) [tex]\overline{AC} \cong \overline{BC}[/tex] (CPCTC)

Question 8

1) [tex]\overline{CD} \perp \overline{AB}[/tex], point D bisects [tex]\overline{AB}[/tex] (given)

2) [tex]\angle CDA, \angle CDB[/tex] are right angles (perpendicular lines form right angles)

3) [tex]\triangle CDA, \triangle CDB[/tex] are right triangles (a triangle with a right angle is a right triangle)

4) [tex]\overline{AD} \cong \overline{DB}[/tex] (definition of a bisector)

5) [tex]\overline{CD} \cong \overline{CD}[/tex] (reflexive property)

6)  [tex]\triangle ADC \cong \triangle BDC[/tex] (LL)

7) [tex]\angle ACD \cong \angle BCD[/tex] (CPCTC)

This exercise involves the construction of a blueprint. To do so, we need to solve for angles using the Cos Rule. See the step by steps procedure below.

A blueprint is a masterplan that highlights how a structure will be look like when it is completed.

From the above, see attached the first simple quadrilateral QRST (Draft I) that is indicates the above information.

Next Step

We have to derive ∠T, ∠ S, and ∠R.
In order to achieve the above, we must split the quadrilateral into two triangles.

As noted in the image, the quadrilateral is bisected from R to T.

∠R and ∠T are also divided into R1 R2 and T1, T2 respectively.

Next step - Derive ∠T1 and ∠R1 .

To do the above,  we must deploy the Pythagoras Theorem. (PT)

PT requires:

TR² = QT² + QR²

TR² = (210)² + (515)²

TR² = 44,100 + 265,225

TR² =  309,325

TR = √309,325

TR = 556.17

Next step, Derive T1

We can derive T1 using the cos rule:

Cos T1 = QR/QT

= 515/556.17

Cos T1 = 0.926

Therefore

T1 = Cos⁻¹(0.926)

T1  = 22.18°

Next we derive R1

R1 = 180° - (90° + 22.18°)
R1 = 67.82°

In ΔTRS, by using Cosine Rule,

Cos T2 = [TS² + QR² - RS²]/2(TS) * (TR)

Cos T2 = [(232)² + (556.16)² - (542)²]/ 2 * (232) x (556.16)

Cost T2 = 69,373.945/258,058

Cost T2 ≈ 0.269

Therefore,

T2 = Cos⁻¹(0.269)

T2 ≈ 74.4°

Applying the same process, we can derive R2

Cos R2 = TR² + RS² - TS²

Cos R2 = [(556.16)² + (542)² - (232)²] / 2 (556.16) * (542)

Cost R2 = 0.911

R2 = Cos ⁻1 (0.911)

R2 = 24.34°

From the above, we can execute the following iterations:

∠S = 180° - (R2 + T2)

= 180 ° - (24.34 + 74.4)
∠C = 81.26°

Likewise:

∠R = R1 + R2
= 67.82 + 24.34
∠B = 92.16°

Lastly:

∠T = T1 + T2

= 22.18 + 74.40

∠T = 96.48°

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Full Question:

A client has just inherited a property. The deed is quite old, but she knows where the front two corners of the property are and that the distance between them is 210 feet. The shape is an irregular quadrilateral and the other three sides have a distance of 515 feet, 232 feet, and 542 feet in a clockwise direction from the front left corner. More importantly, it is known that the front left corner of the property is a right angle.

-Construct a blueprint of the property labeling the measures of all sides and angle of the property.

Answer:

[tex]\huge\boxed{\sf x = 55\°}[/tex]

Step-by-step explanation:

Given that,

x° + 35° = 90° (complementary angles)

Subtract 35 to  both sides

x = 90 - 35

x = 55°

[tex]\rule[225]{225}{2}[/tex]

Answer:

300

Step-by-step explanation:

25 choose 2 (exactly how it sounds like)

= (25*24)/(2*1)=600/2=300

To make x² + 6x = 7 a perfect square, we add 16 to the equation.

In the question, we are asked for the term that must be added to the equation x² + 6x = 7, to make it into a perfect square.

The given equation can be shown as:

x² + 6x = 7,

or, x² + 6x - 7 = 0.

To make it a perfect square, we need to find the b² term as per the 2ab term for the formula, (a + b)² = a² + 2ab + b², where a is x.

This can be shown as:

x² + 6x - 7 = 0,

or, x² + 2(x)(3) - 7 = 0, where we get b = 3.

Thus, b² = 3² = 9, can be obtained by adding 16 to the equation, as -7 + 16 = 9.

Thus, we add 16 to both sides of the equation, to get:

x² + 2(x)(3) - 7 + 16 = 16,

or, x² + 2(x)(3) + 9 = 16,

or, (x + 3)² = 16, which gives us the required perfect square.

Thus, to make x² + 6x = 7 a perfect square, we add 16 to the equation.

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Answer:

Step-by-step explanation:

Add 4% food tax:

Total amount of purchase is:

Subtract $30 paid in cash:

Answer:

$5.25

Step-by-step explanation:

Cost of gasoline

⇒ 9.25 × $3.15 = $29.1375

Cost of gum

$1.10 plus 4% food tax:

⇒ $1.10 × 1.04 = $1.144

Total cost of purchases

Gasoline + gum + Windshield wiper fluid

⇒ $29.1375 + $1.144 + $4.97 = $35.2515 = $35.25 (nearest cent)

If $30.00 was paid by cash and the rest was paid for by debit card:

Debit card charge = $35.25 - $30.00 = $5.25

Answer:

4a²*(9a + 3)

Step-by-step explanation:

Prime factorize 32 and 12. Then find GCF.

 32a³ = 2 * 2 * 2 * 2 * 2  * a³

12a²  = 2 * 2 *  3 * a²

GCF = 2 * 2 * a² = 4a²

32a³ + 12a² = (4a²*9a) + (4a²*3)

                   =4a²*(9a + 3)

Answer:

23 there will be 100 paperclips leftover

the value of 'x' is 0. 9

For the given triangle, we have the;

We want to find the value of x

Using the tangent ratio

Tan θ = opposite/adjacent

Let's substitute the value of theta, opposite and adjacent

Tan 60 = 13 + x / 7

1. 73 = 13+ x/ 7

cross multiply

1. 73 × 7 = 13 + x

12. 1 = 13 + x

x = 13 - 12. 1

x = 0. 9

We can see that the value of x is 0. 9

Thus, the value of 'x' is 0. 9

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1a. 10. 24

1b. 125/243

2a. 0. 0048

2b. 32/3125

3a. 0. 64

3b. 0. 0031

4a. 2/5

4b. 48. 735

5a. 2. 36

5b. 1. 39

1a. Given the values

(2/5)^2/(1/2)^6

Multiply both the numerator and denominator by the powers

⇒ [tex]\frac{\frac{4}{25} }{\frac{1}{64} }[/tex]

To find the common ration, multiply thus;

⇒ [tex]\frac{4}{25}[/tex] × [tex]\frac{64}{1}[/tex]

⇒ [tex]\frac{256}{25}[/tex]

= 10. 24

1b. (5/7)^2 × (5/7)^1

= [tex]\frac{25}{49}[/tex] × [tex]\frac{5}{7}[/tex]

= [tex]\frac{125}{343}[/tex]

= 125/243

2a. 0. 6^1  × 0. 2^3

= 0. 6 × 0. 008

= 0. 0048

2b. (2/5)^3 × (2/5)^2

= [tex]\frac{8}{125}[/tex] × [tex]\frac{4}{25}[/tex]

= [tex]\frac{32}{3125}[/tex]

= 32/ 3125

3a. 1^99 - 0. 6^2

= 1 - 0. 36

= 0. 64

3b. (0. 2 ) ^1 × (1/8)^2

= 0. 2 × 1/64

= 0. 2 × 0. 016

= 0. 0031

4a. (1/2)^2/ (5/8)^1

= [tex]\frac{\frac{1}{4} }{\frac{5}{8} }[/tex]

Take the inverse of the denominator

= [tex]\frac{1}{4}[/tex] × [tex]\frac{8}{5}[/tex]

= 2/5

4b. 7^2 - 0. 5^3

= 49 - 0. 125

= 48. 875

5a. 3^1 - 0. 8 ^2

= 3 - 0. 64

= 2. 36

5b. 0. 7^2 + 0. 9^1

= 0. 49 + 0. 9

= 1. 39

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The missing fraction is 7/9

The given equation is:

[tex]\frac{3}{4}+\frac{1}{2}+\frac{2}{9}+x=\frac{9}{4}[/tex]

This can be simplified as:

[tex]\frac{27+18+8+36x}{36} =\frac{9}{4} \\\\\frac{53+36x}{36} =\frac{9}{4}[/tex]

Cross multiply

[tex]9(36)=4(53+36x)\\\\324=212+144x\\\\144x=324-212\\\\144x=112\\\\x=\frac{112}{144} \\\\x=\frac{7}{9}[/tex]

Therefore, the missing value is [tex]\frac{7}{9}[/tex]

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The volume of the cone based on the figure illustrated wil be 196cm³.

The information is incomplete and the complete question wast found online. An overview will be given.

Let's assume that the height is 4cm and the radius of the cone is 7cm. The volume of the cone will be:

= 1/3πr²h

= 1/3 × 3.14 × 7² × 4

= 196cm³

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Answer:

a) 10, 20, 30, ...
b) 2, 4, 6, ...
c) 10, 20, 30, ...
d) 61, 66, 71, 76, ...
e) 180, 280, 380, ...

i dont know if this is correct but hope it helps

Answer:

3.959797975

Step-by-step explanation:

1. Find the square root of 98 which is 9.899494937

2. Divide 9.899494937 by 2.5 which is 3.959797975

(sorry if it's wrong, but I think it's correct)

The length of the side of the octagon is 4.142 inches.

Let the length of the congruent sides of the isosceles triangle be x.

The hypotenuse of the triangle is given by:

√x+x = √2x

This is also the length of the sides of the octagon. It is given that the sides of the octagon are equal.

It is also given that the length of the square side is 10 inches.

This means that:

x + √2x + x = 10

2x + √2x = 10

(2 + √2)x = 10

(2 + 1.414)x = 10

3.414x = 10

x = 10/3.414

x = 2.929 inches.

The side of the octagon is given by:

√2 × 2.929 = 4.142 inches

Therefore, we have found that the length of the sides of the octagon is 4.142 inches.

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