I don’t understand these three algebra 1 problems. They are in the topic of solving multi-step inequalities and I also don’t get the adding like terms portion.
Thank you for answering this!

Answer: The smallest two-digit prime number such that reversing the digits of the number produces a composite number is 19

Step-by-step explanation:

11, which is the smallest two-digit prime number, 11 remains the same number when the digits are reversed, and it is a prime number, of course.

The next two-digit prime number is 13. 13 becomes the prime number 31 when the digits are reversed.

17 is the following two-digit prime number. The result of flipping the digits of 17 is 71, a prime number.

19 is the following two-digit prime number. Reversing the digits of 19 results in 91, which is composite because 7*13= 91

Thus, 19 is the answer.

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solve 1/3 x= -4/5

1/3 * -4/5 = -4/15

-2 2/5

4/15

2 2/5

-4/15

Answer:

first option

Step-by-step explanation:

[tex]\frac{1}{3}[/tex] x = - [tex]\frac{4}{5}[/tex]

multiply both sides by 15 ( the LCM of 3 and 5 ) to clear the fractions

5x = - 12 ( divide both sides by 5 )

x = - [tex]\frac{12}{5}[/tex] = - 2 [tex]\frac{2}{5}[/tex]

The system of equation for each condition will be; 2a + 3c = 325.94 and

2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and

c = $46.99

A linear equation is an algebraic equation of the form y = mx+b. involving only a constant and a first-order term, where m is the slope and b is the y-intercept.

At an amusement park, the cost for an adult admission is a and for a child the cost is c. For a group of six that included two children, the cost was $325.94. For a group of five that included three children, the cost was $256.95 and all ticket prices include tax.

According to question,

2a + 3c = $325.94

4a + 2c = $256.95

2a + c = $162.97

Solving the equation by using elimination method, we get,

a = $57.99 and c = $46.99

Hence, The system of equation for each condition will be; 2a + 3c = 325.94 and 2a + c = 162.97 and exact cost of each type of ticket is a = $57.99 and c = $46.99

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Answer:

below

Step-by-step explanation:

y = 3 * 2^x          plug in the values of x (first column) to get the values in the second column

The answer to the given question is -4/3 or 1/2

The product of 6 and the square of a number is increased by 5 times the number, the result is 4.

Firstly, let's write the algebraic expression for the above statement and represent the number as x.

The algebraic expression can be written as:

(6 x x²) + 5x = 4

6x² + 5x = 4

The other expression can also be written as:

6x² + 5x - 4 = 0

Secondly, we must factorize the algebraic expression to solve for x.

6x² - 3x + 8x - 4 = 0

3x (2x - 1) + 4 (2x + 1) = 0

(3x + 4)(2x - 1) = 0

Thirdly, we need to solve for x.

3x + 4 = 0

3x = -4

Now, we need to divide both sides by 3.

3x/3 = -4/3

x = -4/3

or

2x - 1 = 0

2x = 1

Now, we need to divide both sides by 2.

2x/2 = 1/2

x = 1/2

Hence, the values that the number could be is -4/3 or 1/2.

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Answer:

Let x = # of magazines , $23.65=$5.95+$2.95x , x = 6

Step-by-step explanation:

$23.65=$5.95+$2.95x

this is equation for this one because we know that 23.65 is the total money they have total and 5.95 cost for book and 2.95 dollar what each magazine. however, this equation needs to be solved to find x

23.65=5.65+2.95x

23.65-5.95=-5.95+2.95x

17.70=2.95x

17.70/2.95=

6=x

He can buy 6 magazines with his money.

Answer:

65

Step-by-step explanation:

Since 39 is 60%, 100/60= 1 2/3

39*1 2/3 is 65

Answer:

Step-by-step explanation:

2

The consecutive integers such 4 that times the smaller integer is 50 less than 6 times the larger integer are 22 and 23.

Let the consecutive integers be x and x + 1.

In this case, the integers are such 4 that times the smaller integer is 50 less than 6 times the larger integer.

This will be:

4(x) = 6(x + 1) - 50

4x = 6x + 6 - 50

Collect like terms

4x - 6x = -44

-2x = -44

Divide

x = 44/2

x = 22

Also, x + 1 = 22 + 1 = 23

The numbers are 22 and 23.

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The expression for tension in the string is T = [(L/2)×(m1×g) + (x)×(m2×g)]/d.

We are a diagram that shows two blocks with masses m1 and m2.There are two strings, A and B. Everything is in equilibrium. Equilibrium is a condition of rest or balance caused by opposing forces acting equally. We need to find the tension in string A. Let the tension in the strings A and B be denoted by the variables "Ta" and "Tb", respectively. The net torque at point B must be zero as everything is in equilibrium. The diagram is attached below.

Στ(B) = 0

τ(a) + τ(b) + τ(m1) + τ(m2) = 0

τ = r×F×sin(θ)

d×(Ta)×sin(90°) + 0 - (L/2)×(m1×g)×sin(90°) - (x)×(m2×g)×sin(90°) = 0

d×(Ta) - (L/2)×(m1×g) - (x)×(m2×g) = 0

Ta = [(L/2)×(m1×g) + (x)×(m2×g)]/d

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If the null hypothesis that two means are equal is true, 97% of the computed z values lie between 2.17.

Any variation between the selected characteristics that you observe in a set of data is thought to be the result of chance, according to the null hypothesis. For instance, any difference between the average earnings in the data and zero is caused by chance if the expected earnings for the gambling game are actually equal to zero. An assertion that there is no correlation between two population parameters is referred to as a null hypothesis. To prepare the ground for additional experimentation or research that explains the position of interest, researchers reject or refute the null hypothesis.

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The value of the digit 2 in 23,876 is 100 times greater than value of digit 2 in 3,254. This result is obtained by paying attention to the place value of the number in the number.

These are the specified parameters:

Numbers 23,876 and 3,254.

The value of the digit 2 in 23,876 is 20,000

The value of the digit 2 in 3,254 is 200

Magnification the value of the digit 2

= 20,000 ÷ 200

= 100

So the value of the number 2 at 23,876 is 100 times greater than the value of the number 2 at 3,254.

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Answer:

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

Given is the right triangle.

The two angles are complementary, so their sum is 90°:

The angles are:

Answer:

Step-by-step explanation:

Now we have to,

→ find the value of each angle.

Forming the equation,

→ 90° + (p - 10°) + (p + 50°) = 180°

Now the value of p will be,

→ 90° + (p - 10°) + (p + 50°) = 180°

→ (90° - 10° + 50°) + (p + p) = 180°

→ 130° + 2p = 180°

→ 2p = 180° - 130°

→ p = 50°/2

→ [ p = 25° ]

Then the value of other angle is,

→ p - 10° || → p + 50°

→ 25° - 10° || → 25° + 50°

→ 15° || → 75°

Hence, these are the angles.

The value of x in the given equation is 1 or 8.

First, let us understand the equation:

An equation is a mathematical expression that includes the equals sign. Algebra is frequently used in equations.

We are given;

x / (x + 8) + 1 / (x - 8) = 2x / (x^2 - 64)

x (x - 8) + 1 (x + 8) / (x^2 - 64) = 2x / (x^2 - 64)

x^2 - 8x + x + 8 = 2x

x^2 - 8x - 2x + x + 8 = 0

x^2 - 9x + 8 = 0

x^2 - 8x - x + 8 = 0

x(x - 8) - 1 (x - 8) = 0

(x - 1) (x - 8) = 0

(x - 1) = 0 or (x - 8) = 0

x = 1 or x = 8

So, the value of x = 1 or 8.

Thus, the value of x in the given equation is 1 or 8.

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140.23 liters are in 37 gallons

We have been given you can convert gallons to liters by using a factor of 3.79

That is, 1 gallon = 3.79 liters.

We need to find the amount of liters in 37 gallons.

Let 37 gallons = x liters

As we know 1 gallon = 3.79 liters.

So, by Unitary method,

x = 37 * 3.79

x = 140.23 liters

Therefore, 140.23 liters are in 37 gallons

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If the perimeter of XYZ is 26 then the answer will be 6.5.

What is composition of transformation?

A composition of transformations combines two or more transformations that were separately applied to the prior image. The result of a composition of reflections along parallel lines is identical to that of a translation (twice the distance between the parallel lines).

What is Perimeter?

The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.

Given;

The composition of transformations Ry=-5 r (90,A) maps ABC to XYZ .

the perimeter of XYZ is 26

ΔABC is the reflection of ΔXYZ which is transformed with angle 90°.

So,the answer will be [tex]26\div 4 = 6.5[/tex].

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Percentage Change = (ΔV/IV₁I) × 100

Constant rate of Change = (y₂ - y₁)/ (x₂ - x₁)

Constant Percentage Change:

This means that after t period the something has grown to [tex]g^{t} = 1.10^{t}[/tex] it original value .

percentage change formula equals the change in value divided by the absolute value of the original value multiplied by 100.

Constant rate of Change:

In which the rate does not change between different points in the function. in short, constant rate of change refers to the comparison of the way two quantities changes. in equation, the constant rate of change can be seen as a slope.

An exponential function is a function that changes at a constant percentage rate.

An exponential function y of t is characterized by the following property:

when t increases by 1 to find the new value of y the current value by the base.

                 y- value for t +1 = Base of y - value for t

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The sentence, using the rational root theorem, is completed as follows:

If a polynomial function f has integer coefficients, then every rational solution of f(x) = 0 has the format p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

The rational root theorem states that a polynomial with integer coefficients will have every rational solution following the format p/q.

The variables p and q are defined as follows:

Hence the blanks in this problem are completed, respectively, by:

Constant term and leading coefficent.

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The Answer is Han will cover 2.5 miles distance

What is distance ?

Distance is the total path covered by a object or person. As its name implies, any distance formula outputs the distance (the length of the line segment). In coordinate geometry, there is a number of formulas for finding distances, such as the separation between two points, the separation between two parallel lines, the separation between two parallel planes, etc.

Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river.

We need to find the distance run by Han after a half hour.

Han will cover a distance in 12 minutes=1 mile

Han will cover a distance in 1 minute= 1/12mile

Han runs distance in 30 minutes=30*1/12 miles

Hence, Han runs 2.5 miles after half hour.

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1/2x + 3/4x + 1/4x + 4

2/4 x + 3/4x + 1/4x + 4

1.5x + 4 or 3/2x + 4

(Both are the same, depends on if you need decimal or fractional answer)

Answer:

Step-by-step explanation:

The area of the quilt is:

The area of each block:

Number of blocks:

Correct choice is [A]

Dimensions of the quilt excluding borders on each side:

Area of the quilt:

Area of each block with side 9 in:

Number of blocks:

Correct choice is [D]

The subsets of the given set are {-2}, {1}, {-2, 1}, and ∅.

From the question, we are to list all the subsets of the given set.

Given two sets A and B; set A is a subset of set B if all elements of A are also elements of B.

Therefore, we will find all possible sets that have the element(s) of the given set.

The given set is {-2, 1}

The subsets of this set are {-2}, {1}, {-2, 1}, and ∅

Hence,

The subsets are {-2}, {1}, {-2, 1}, and ∅

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For the given ordered pairs, function f(x)= 13(2)ˣ models f(x). Therefore, option B is the correct answer.

From the given table, the ordered pairs are (0, 13), (3, 104) and (5, 416).

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

Substitute (0, 13), (3, 104) and (5, 416) in the given functions and simplify

A) f(x)=2x+13

With x=0, we get f(x)=13

With x=3, we get f(x)=19

With x=5, we get f(x)=23

B) f(x)= 13(2)ˣ

With x=0, we get f(x)=13

With x=3, we get f(x)=104

With x=5, we get f(x)=416

For the given ordered pairs, function f(x)= 13(2)ˣ models f(x). Therefore, option B is the correct answer.

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The amount that will be spent on the cupcakes is $48.

From the information, Luisa plans to prepare cupcakes for her daughter's birthday and spends $15 on 25 units.

Let the amount spent on 80 cupcakes be x.

This will be illustrated as:

25/80 = 15/x

Cross multiply

25x = 15 × 80

25x = 1200

Divide

x = 1200/25

x = 48

The amount will be $48.

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Answer:

11?

Step-by-step explanation:

since 8+3 = 11 won't each student get 11 because they equally share it and in total 11 x 8 = 88 so they have to share 11 blocks of clay.

Answer:

convert the fractions to a common denominator of 90

5 1/6 , 5 13/30 , 5 68/90

The expression that represents the total amount of discount in dollars is; (48d - 0.18 x 48d)

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

The Numbers constants, variables, operations, functions, brackets, punctuation, and grouping can all be represented by the mathematical symbol; which can b used to indicate the logical syntax's order of operations and other features.

We are given that the reseller has a budget of $800 to purchase desks. Each desk costs an equal amount and is available at a fixed discounted percent.

The expression 800 (48d - 0.18 x 48d) represents the amount of the budget, left after buying d desks.

Therefore, the expression that represents the total amount of discount in dollars are;

(48d - 0.18 x 48d)

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the probablilty of p and k is 82.6%.

Given:

key club P(k) = 2.3%

physics P(p) = 8.6%

(p∩k) = 1.9%

formula:

P(p/k) = P(p∩k)/P(k)

putting the value,

P(p/k) = 1,9%/2.3%

= 0.019/0.023

= 0.826 = 82.6%

hence the probability of p given k is 82.6%.

#123

The probability of P given K is 0.826.

Given information;

The guidance department has stated that of the senior class, 2.3% are members of key club, K, 8.6% are enrolled in AP physics, P, and 1.9% are enrolled in both. This information is supplied in the question.

To get the probability of P given K [P(A)];

P(K) = 2.3

P(P) = 8.6

P(P ∩ K) = 1.9

P(A) = P(P ∩ K) / P(K)

       = 1.9/2.3

       = 0.826

Hence, the probability of P given K is 0.826.

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As per the given ratio, the four numbers are 27, 33, 81 and 99.

Ratio:

Ratio means a mathematical expression written in the form of a:b, where a and b are any integers. It expresses a fraction.

Give,

Here we have the ratio 9: 11.

And the difference is 6.

And we need to find the four numbers to it.

Let us consider both the number be 9x, 11x since their ratio is 9:11

And we have assume that our expected answer to be positive (since we are dealing with ratios)

So, their difference can be written as,

=> 11x-9x = 6

When we simplify it, then we get,

=> 2x = 6

Here we need the value of x,

=> x= 3

Now that we know the value of ‘x’ is, we can find required numbers through it,

=> 9x = 9 * 3= 27

=> 11x = 11*3 = 33

=> 27x = 27*3 = 81

=> 33x = 33*3 = 99

Thus, the four numbers are 27, 33, 81, 99.

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The statements (b) and (d) are true concerning the measurements of a circle.

What is a circle?

A circle is a reconstructed by all elements in a plane that lie at a particular separation from the center. It is the curve sketched out by a point moving in a surface so that its radius from a particular point remains constant. The radius describes the distance either between two points on a circle and the center. Ordinarily, the radius must be a greater than 0. A circle, in particular, is a basic closed curve that splits the plane into two regions: inner and exterior. A circle can alternatively be described as a kind of ellipse with two coincident foci, zero eccentricity, and equal semi-major and semi-minor axes.

The statements:

(b) The area of a circle with a diameter of 1 unit is equal to pi square units and

(d) The circumference of a circle with a diameter of 1 unit is equal to pi units are true concerning the measurements of a circle.

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