Question 1 (Essay Worth 10 points)
(06.02 MC)

Part A: Write an algebraic expression for 6 more than 7 times a number. (5 points)

Part B: Write a verbal expression for 3(n + 8). (5 points)

Answer:

5

Step-by-step explanation:

seven has 5 letters

Answer:

its 93.4

Step-by-step explanation:

just multiply 46.7 by 2

Answer:

20

h(x) = 2x - 20

Step-by-step explanation:

f(x) = ¹/₂ x + 10

First, isolate x, like so:

f(x) - 10 = ¹/₂ x

x = 2(f(x) - 10)

x = 2f(x) - 20

Now, simply switch f(x) with x and x with h(x), like so:

h(x) = 2x - 20

Answer:

the answer is 20

Step-by-step explanation:

took the test on edge

Answer:

The first number is 138.

Step-by-step explanation:

Let the first number be x.

Then since they are consecutive numbers, the second number will be (x + 1), the third (x + 2), the fourth (x + 3) and the fifth being (x + 4).

We are given that their sum is 700. Therefore:

[tex]x+(x+1)+(x+2)+(x+3)+(x+4)=700[/tex]

Solve for x. Combine like terms:

[tex]5x+10=700[/tex]

Subtract 10 from both sides:

[tex]5x=690[/tex]

Divide both sides by five. Therefore:

[tex]x=138[/tex]

The first number is 138.

Answer:

138

Step-by-step explanation:

(n) + (n+1) + (n+2) + (n+3) + (n+4) = 700

5n + 10 = 700

5n = 690

n = 138

Answer:

[tex]8\%[/tex]

Step-by-step explanation:

Since question already gives the number of dollars she will tip, I'm assuming it's asking for percent tipped.

Because the total is $75 and Theresa is tipping $6, she is tipping [tex]\frac{6}{75}=0.08[/tex] of the total. To convert this to a percentage, multiply by 100: [tex]0.08\implies 0.08\cdot 100=\boxed{8\%}[/tex]

Answer:

2.82

Step-by-step explanation:

Answer: Unlock code = 76

==========================================================

Explanation:

Use a factor tree to find the prime factorization of each value

22 = 2*11

30 = 2*3*5

Both values have '2' in common and this is the largest such value. Therefore, the GCF of 22 and 30 is 2.

So E = 2

----------------------------

Since 3 and 8 have no factors in common (other than 1), this means the LCM is 3*8 = 24

We can say that F = 24.

If the numbers had some larger number in common, then we'd have to do a bit more work to find the LCM.

----------------------------

As the hint suggests, we'll use the distributive property to show that

3*(7+10) = G + 30

3*7 + 3*10 = G + 30

21 + 30 = G + 30

21 = G .... subtract 30 from both sides; they cancel and go away

G = 21

----------------------------

Use the same idea for the other equation as well

5*(3 + H) = 15 + 45

5*3 + 5*H = 15 + 45

15 + 5H = 45

5H = 45 ............ subtract 15 from both sides; they go away

H = 45/5 ......... divide both sides by 5

H = 9

------------------------------

The unlock code is

E+F+G+H = 2+24+21+29 = 76

Answer:

Step-by-step explanation:

let the other angle be x

in complementary angle sum of two angle is 9 degree.so,

73.9+x=90 degree

x=90-73.9

x=16.1 degree

Answer:

Y = -1/4x + 5

Step-by-step explanation:

Answer:

C. 1

Step-by-step explanation:

angle L and angle N are equal so the length of ML and MN should be equal too (isosceles triangle)

4x = x + 3 subtract x from both sides

3x = 3 divide both sides by 3

x = 1

Answer:

2 -cups

Step-by-step explanation:

-cup = 1/2 cup

-cup =1/2 cup

1/2 + 1/2 = 1 cup

Answer: x=45

Step-by-step explanation:

2x+6=96

2x=90

x=45

Answer:

36 cuz they are congruent

Step-by-step explanation:

Answer:

The hypotenuse is sqrt ( 2x^2)

Step-by-step explanation:

Given a right angled triangle, we can find the hypotenuse of a triangle using the Pythagorean theorem which says that c^2 = a^2 + b^2, where a is the length, b is the perpendicular height and c is the hypotenuse. The length of the triangle (l) is x and the height of the triangle is also x. By substituting the values,

c^2 = x^2 + x^2 = 2x^ 2

There are two possible answers to c but the hypotenuse cannot be negative.

Hence,

c = Sqrt (2x^2)

Answer:

8 / 17

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as acute, isosceles, obtuse, scalene, equilateral and right angled triangle.

Trigonometric identities are used in a right angled triangle to show the relationship between the sides and the angles. They are:

sinθ = opposite / hypotenuse, cosθ = adjacent / hypotenuse, tanθ = opposite / adjacent

From the triangle attached:

sin(H) = opposite / hypotenuse

sin(H) = 8 / 17

Answer:

hope this helps

Step-by-step explanation:

what do you have to do

Step-by-step explanation:

Hey there!

The equation of line which passes through the point (1,2) is (y-2) = m1(x-1)............(i)

The another given equation is y= 2x + 3.........(ii)

Comparing the equation (ii) with y= mx+c we get;

Slope (m2)= 2.

As per the condition of perpendicular lines, m1*m2 = -1.

m1*2 = -1

Therefore, m1 = -1/2.

Keeping the value of m1 in equation (i) we get;

(y-2) = -1/2(x-1)

y - 2 = -1/2x +1/2

y = -1/2 X + 1/2 + 2

Therefore, the required equation is y = -1/2 X + 5/2.

Hope it helps!

Answer:

49a^7

Step-by-step explanation:

Combine like terms (30+19 = 49)

Answer:

[tex]{ \bf{30 {a}^{7} + {19a}^{7} }} \\ = (30 + 19) {a}^{7} \\ = 49 {a}^{7} [/tex]

Answer:

comment if u have questions

Step-by-step explanation:

a)

10x-6=24

10x=30

x=3

b.

10x+5=50

10x=45

x= 45/10 (9/2)

Answer:

this is the correct answer

Answer:

312

Step-by-step explanation:

13 x 24 = 312

Answer:

3.33 hours

Step-by-step explanation:

Take the total bill minus the flat charge. ($300 - $50 = $250)

Then take that amount and divide by the charge per hour.

($250/$75) = 3.33 hours

Answer:

x = 3 1/3 so approximately 3 hrs

Step-by-step explanation:

50 + 75x = 300

75x = 250

x = 3 1/3

Answer:

x = -6

Step-by-step explanation:

8 + 4x = -16

4x = -16 - 8

4x = -24

x = -24/4

x = -6

[tex]\implies {\blue {\boxed {\boxed {\purple {\sf { \: x = - 6}}}}}}[/tex]

[tex]\sf \bf {\boxed {\mathbb {Step-by-step\:explanation:}}}[/tex]

[tex]\:8 + 4x = - 16[/tex]

➺[tex] \: 4x = - 16 - 8[/tex]

➺[tex] \: 4x = - 24[/tex]

➺[tex] \: x = \frac{ - 24}{4} [/tex]

➺[tex] \: x = - 6[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\blue{To\:verify}}{\blue{:}}}}}[/tex]

[tex]\:8 + 4x = - 16[/tex]

➼[tex] \: 8 + 4( - 6) = - 16[/tex]

➼[tex] \: 8 - 24 = - 16[/tex]

➼[tex] \: - 16 = - 16[/tex]

➼[tex] \: L.H.S.=R. H. S[/tex]

Hence verified.

[tex]\large\mathfrak{{\pmb{\underline{\orange{Mystique35 }}{\orange{❦}}}}}[/tex]

Answer:

1/10

Step-by-step explanation:

7 is one number in a 10 sided die

Answer:

16) r = C/(2·π)

17)  [tex]r^2 = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]

18) x = (9 - 3·y)/2

19) Please find attached the required graph of the inequality x ≤ 4 created with MS Excel

20) z ≥ 1

Solve each inequality and graph the solution

21) n ≤ 1

22) p > -5

23) -3 ≤ q ≤ 2/5

24) x > 1/5

25) x < -11

26) 7

Step-by-step explanation:

Solving for the indicated variable

16) C = 2·π·r for r

Dividing both sides by 2·π gives;

C/(2·π)  = 2·π·r/(2·π)  = r

∴ r = C/(2·π)

17) [tex]V = \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h \ for \ r^2[/tex]

Dividing both sides by [tex]\left( \dfrac{1}{3} \cdot \pi \cdot h \right)[/tex] gives;

[tex]\dfrac{V}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)} = \dfrac{ \dfrac{1}{3} \cdot \pi \cdot r^2 \cdot h}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)}[/tex]

[tex]\therefore r^2 = \dfrac{V}{\left( \dfrac{1}{3} \cdot \pi \cdot h \right)} = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]

[tex]r^2 = \dfrac{3 \ \cdot V}{\pi \cdot h}[/tex]

18) 2·x + 3·y = 9 for x, gives;

x = (9 - 3·y)/2

19) Please find attached the required graph of the inequality x ≤ 4 created with MS Excel

20) Solve each inequality

z - 3 ≥ -2

z ≥ -2 + 3 = 1

∴ z ≥ 1

Solve each inequality and graph the solution

21) 3·n  + 5 ≤ 2·n + 6

n ≤ 1

22) 10·p + 20 - p > p + 3 - 23

9·p + 20  > p - 20

8·p > -40

p > -5

23) -1 ≤ 1 - 5·q ≤ 16

∴ 2/5 ≥ q ≥ -3

-3 ≤ q ≤ 2/5

Solve each word problem

24) Let x represent the number, we have;

2·x + 3·(x + 2) > 17

5·x + 6 > 7

∴ x > 1/5

The numbers are numbers larger than (1/5)

Solve each inequality

25) 2·(x - 5) + 3·x < 4·(x - 6) + 3

2·x - 10 + 3·x < 4·x - 24 + 3

x < -11

26) -2 - [-4 - (3 - 2)] = -2 + 4 + 3 - 2 = 7

Answer:

perimeter of the garden=2(length+width)

=2(7√13+√13)

=2(8√13)

=16√13

Answer:

1/6=6

Step-by-step explanation:

Conversion a mixed number 2 1/

4

to a improper fraction: 2 1/4 = 2 1/

4

= 2 · 4 + 1/

4

= 8 + 1/

4

= 9/

4

To find new numerator:

a) Multiply the whole number 2 by the denominator 4. Whole number 2 equally 2 * 4/

4

= 8/

4

b) Add the answer from previous step 8 to the numerator 1. New numerator is 8 + 1 = 9

c) Write a previous answer (new numerator 9) over the denominator 4.

Two and one quarter is nine quarters

Divide: 9/

4

: 3/

8

= 9/

4

· 8/

3

= 9 · 8/

4 · 3

= 72/

12

= 12 · 6/

12 · 1

= 6

Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 3/

8

is 8/

3

) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 12 gives 6/

1

.

In words - nine quarters divided by three eighths = six.

Answer:

180 -110 = 70

c =70

Step-by-step explanation:

Answer: 4th week

Step-by-step explanation:

You just keep adding 150 to 250 for Sarah and subtract 200 from 1,650 for Felicia until they both have the same amount which would be 850.

At the end of 4th week Sarah and Felicia have same amount of money equals to $850.

"Amount is defined as representation of total of two or more quantities."

According to the question,

Amount with Sarah at the beginning of the week = $250

Amount save per week by Sarah = $150

Amount with Felicia at the beginning of the week = $1650

Amount save per week by Felicia = $200

As per the given conditions,

Sarah amount for different weeks:

At the end first week = $250 + $150

                                   = $400

At the end second week = $400 + $150

                                         = $550

At the end third week = $550 + $150

                                    = $700

At the end fourth week = $700 + $150

                                       = $850

Felicia amount for different weeks:

At the end first week = $1650 - $200

                                   = $1450

At the end second week = $1450- $200

                                         = $1250

At the end third week = $1250 - $200

                                    = $1050

At the end fourth week = $1050- $200

                                       = $850

Hence, at the end of 4th week Sarah and Felicia have same amount of money equals to $850.

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