Jenny planned to solve 2/3 of her homework problems on Saturday. However, she got home late and had less time than planned. As a result, she solved only 7/8 of the problems she planned to solve. How many problems were in Jenny's homework if she solved 28 on Saturday?

Answer:

z > -4/5

Step-by-step explanation:

-9 - (2z - 7) > -2z - 6 - 5z

Get rid of the parenthesis

-9 - 2z + 7 > -2z - 6 - 5z

Combine like terms:

       -2 - 2z > -7z - 6

       +2       >       +2

Add 2 to both sides.

 -2z > -7z - 4

 +7z > +7z

Add 7 to both sides.

5z > -4

Divide both sides by 5 to get z.

z > -4/5

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

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Based on the information, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

It should be noted that to prove the commutativity of the logical connectives ∧ (conjunction) and ∨ (disjunction), we need to show that they satisfy the commutative property

From the truth table, both P ∧ Q and Q ∧ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∧ Q ≡ Q ∧ P, and ∧ (conjunction) is commutative.

In order to prove P ∨ Q ≡ Q ∨ P, we construct a truth table for both expressions. Both P ∨ Q and Q ∨ P have the same truth values for all combinations of truth values of P and Q. Therefore, we can conclude that P ∨ Q ≡ Q ∨ P, and ∨ (disjunction) is commutative.

Hence, both ∧ (conjunction) and ∨ (disjunction) satisfy the commutative property.

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According to the information we can infer that the total yardage traveled from 0 to 120 seconds is 140 yards.

To calculate the total yardage traveled we have to consider the movement of the O'Connor Panthers. In this case we have to consider that the movement in the y axis.

In this case we can conclude that the total yardage traveled was 140 yards because:

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Using word problems and equations, Sarah worked for 10 hours and Penelope worked for 5 hours

This is a word problem and in order to solve this, we need to translate mathematical statements in form of word problems into mathematical equations.

Let's assume that Sarah worked x hours.

Given that Sarah can iron 30 shirts per hour, the total number of shirts she ironed is 30x.

Since Penelope worked half the hours of Sarah, Penelope worked x/2 hours.

Given that Penelope can iron 35 shirts per hour, the total number of shirts she ironed is 35 * (x/2) = (35/2)x.

The total number of shirts ironed by both Sarah and Penelope is 475 shirts.

So, we can write the equation: 30x + (35/2)x = 475.

To solve this equation, we can simplify it: (60/2)x + (35/2)x = 475, which becomes (95/2)x = 475.

Now, we can solve for x: x = (475 * 2) / 95 = 10.

Therefore, Sarah worked 10 hours and Penelope worked half of that, which is 5 hours.

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Answer:

Step-by-step explanation:

I think thats how its done, sorry for messy handwriting

Step-by-step explanation:

2x - y = 5

-y = 5 - 2x

.........

The value of the inverse function f-¹ (3) is (e) 11

From the question, we have the following parameters that can be used in our computation:

f(x) = x - 8

To calculate the inverse value at f-¹ (3)

We set the value to 3

using the above as a guide, we have the following:

x - 8 = 3

Evaluate the like terms

x = 11

Hence, the value of the inverse function is (e) 11

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Complete question

if f(x) = x - 8, what is the value of f-¹ (3)?

Answer:

that answer is 17x

Step-by-step explanation:

Given System of equation has multiple solution.

Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.

There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.

Given a system of equation:

-1 = 2x - y and  8x - 4y = -4​

From equation 1

-1 = 2x - y

y = 2x + 1

Substitute this value on equation 2

8x - 4y = -4​

8x - 4(2x + 1) = -4

-4 = -4

An equation can have infinitely many solutions when it should satisfy some conditions. The system of an equation has infinitely many solutions when the lines are coincident, and they have the same y-intercept. If the two lines have the same y-intercept and the slope, they are actually in the same exact line.

Thus, Given System of equation has multiple solution.

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Answer:

5.44 meters

Step-by-step explanation:

We Know

0.3048 meter = 1 ft

How many ft makes a height of 1.66m?

We Take

1.66 ÷ 0.3048 ≈ 5.44 meters

So, the answer is 5.44 meters.

Answer:

(8,-43)

(4,-22)

Step-by-step explanation:

In order for the ordered pair to be a solution of the inequality, you must be able to plug in the y-value of the ordered pair and it must be less than or equal to 0.

For example:

(4,-22)

x=4 ; y=-22

Plug y into the inequality

y≤0

-22≤0

Since the statement is true, I know that (4,-22) must be a solution to the inequality.

Another way to solve this problem is by graphing. If an ordered pair is in the shaded region, it is a solution to the inequality. Attached is a graph of both the inequality and ordered pairs plotted.

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Answer:

Step-by-step explanation:

To determine whether each ordered pair is a solution to the inequality y ≤ 0, we need to check if the y-coordinate of each pair is less than or equal to zero.

Let's check each ordered pair:

(8, -43):

The y-coordinate is -43. Since -43 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(4, -22):

The y-coordinate is -22. Since -22 is less than zero, this ordered pair is a solution to the inequality y ≤ 0.

(-3, 25):

The y-coordinate is 25. Since 25 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

(-7, 45):

The y-coordinate is 45. Since 45 is greater than zero, this ordered pair is not a solution to the inequality y ≤ 0.

So, the solutions to the inequality y ≤ 0 are:

(8, -43) and (4, -22).

Answer:

Whats your question?

Step-by-step explanation:

Answer:

1/2( x+16)

Step-by-step explanation:

1/2x + 8

Factor out 1/2

1/2*x + 1/2 *16

1/2( x+16)

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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The number of pretzels and hot dog sales will be 33 and 48.

The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.

Let x be the number of pretzels and y be the number of hot dogs.

Joanie runs the concession stand for the school's baseball games.

At each game, the best-selling items are pretzels and hot dogs.

Pretzels are $3 each, and hot dogs are $2 each.

Today she sold 15 more hot dogs than pretzels and made $195 in total sales. Then the equations will be

y = x + 15    ....1

3x +2y = 195    ...2

From equations 1 and 2, then we have

3x + 2(x + 15) = 195

3x + 2x + 30 = 195

5x = 165

x = 33

Then the value of y will be

y = 33 + 15

y = 48

Then the number of pretzels and hot dog sales will be 33 and 48.

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The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range.

By factoring the numerator and denominator and setting them both to zero, the domain of a fraction function can be determined. The domain's values are the roots of the ensuing equation. Using the algebraic method of factoring is another method for determining the domain of a fraction function.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

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The answer is: 15 ft

Answer:

The central angle measure of the sector is 150º.

Step-by-step explanation:

A sector of a circle is the portion of a circle enclosed by two radii and an arc.

When you know the central angle the area of a sector is given by

                                              \(A=\pi r^2(\frac{C}{360} )\)

where

r is the radius of the circle of which the sector is part.

C is the central angle in degrees.

We know that the area of the sector is \(60\pi \:cm^2\) and the radius is 12 cm. Applying the above formula and solving for the central angle we get that

\(60\pi =\pi (12)^2(\frac{C}{360}) \\\\\pi \left(12\right)^2\left(\frac{C}{360}\right)=60\pi \\\\\frac{\pi 12^2\cdot \frac{C}{360}}{144\pi }=\frac{60\pi }{144\pi }\\\\\frac{C}{360}=\frac{5}{12}\\\\C=150\)

Answer:5pi/6

Step-by-step explanation:

Solve for x:

ANSWER:

The answer is x equals 2

Answer:

21 questions

Step-by-step explanation:

0.84 times 25 = 21

Answer:

James got 21 questions correct.

Step-by-step explanation:

100% = 25 questions

84% = \(\frac{84}{100}\) × 25

       = 21 questions

Answer: 40 pupils

Step-by-step explanation:

 35           14

-------   =   --------

100             ?

find the denominator.

multiply 14 and 100:

14 x 100 = 1400

divide 1400 by 35

1400/35 = 40

Therefore there are 40 students

To answer this questions we need to remember the order of operations:

• Parentheses (simplify inside 'em)

• Exponents

• Multiplication and Division (from left to right)

• Addition and Subtraction (from left to right)

With this in mind we have:

Therefore the answer is 205.

The 2 : 5 scaled version of the deck Sam plans to build and the dimensions of the original deck indicates;

Part A; Base length of the new deck = 7.2 feet

Height of the new deck = 2.8 feet

Part B; The area of the original deck is 63 square feet

The area of the new deck is 10.08 square feet

Part C; The ratio of the areas is the square of the scale factor

A scale factor is a number or factor that is used to enlarge or reduce the dimensions a shape or size of a figure.

The base length of the triangular deck = 18 feet

The height of the triangular deck = 7 feet

The scale factor for the scaled version Sam intends to build = 2 : 5

Part A; The dimensions of the new deck are;

Base length of the new deck using the the 2 : 5 ratio is; (2/5) × 18 = 7.2 feet

The height of the new deck = (2/5) × 7 = 2.8 feet

Part B; The area of the original deck = (1/2) × 18 × 7 = 63 square feet

Area of the new dec = (1/2) × 7.2 × 2.8 = 10.08 square feet

Part C; The ratio of the areas is; 10.08/63

Ratio of the area = 10.08/63 = 4/25 = 4 : 25

The scale factor is; 2 : 5

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Given :

An infinite series :

\(a_1=26\)

\(r=\dfrac{1}{2}\)

To Find :

The sum of the infinite series .

Solution :

The sum of infinite series of G.P is given by :

\(S=\dfrac{a_1}{1-r}\\\\S=\dfrac{26}{\dfrac{1}{2}}\\\\\\S=52\)

Therefore , the sum of the infinite series is 52 .

Hence , this is the required solution .

We have the following:

solving for y:

To calculate the y-intercept, x must be equal to 0 and to calculate the x-intercept, y must be 0, therefore

y-intercept

x-intercept