Answer:
-4
Step-by-step explanation:
Simplifying
8(x + 12) = 64
Reorder the terms:
8(12 + x) = 64 (12 * 8 + x * 8) = 64 (96 + 8x) = 64
Solving
96 + 8x = 64
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-96' to each side of the equation.
96 + -96 + 8x = 64 + -96
Combine like terms: 96 + -96 = 0
0 + 8x = 64 + -96
8x = 64 + -96
Combine like terms:
64 + -96 = -32
8x = -32
Divide each side by '8'.
x = -4
Simplifying
x = -4
Answer:
x = 19/2 (or) 9.5
Step-by-step explanation:
The equation is,
→ (8x - 12) = 64
Now the value of x will be,
→ (8x - 12) = 64
→ 8x = 64 + 12
→ x = 76/8
→ x = 19/2
→ [ x = 9.5 ]
Hence, the value of x is 9.5.
When the product of 6 and the square of a number is increased by 5 times the number, the result is 4. Select all of the values that the number could be. 2.
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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List all subsets for the following set: {-2,1}
The subsets of the given set are {-2}, {1}, {-2, 1}, and ∅.
Determining the subsets of a given setFrom 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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find 4 numbers if their ratio is 9 11 and their difference is 6
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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Luisa plans to prepare cupcakes for her daughter's birthday. If you spend S/15 on 25 units, how much money do you need to make 80 cupcakes?
The amount that will be spent on the cupcakes is $48.
How to calculate the amount?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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Nick's mark on a test was 39.
This mark was 60%.
What was the total possible mark?
Answer:
65
Step-by-step explanation:
Since 39 is 60%, 100/60= 1 2/3
39*1 2/3 is 65
2) Select all of the statements that are true concerning the measures of a circle.
a. The circumference of a circle with a radius of 1 unit is equal to pi square units.
b. The area of a circle with a diameter of 1 unit is equal to pi square units.
c. The circumference of a circle with a radius of 1 unit is equal to pi units.
d. The circumference of a circle with a diameter of 1 unit is equal to pi units.
e. The value pi represents the constant of proportionality that gives the circumference of a
circle, if you know its diameter.
f. The value pi represents the constant of proportionality that gives the area of a circle, if
you know its diameter.
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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What function is represented in the table? HELP!!!!
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
if the null hypothesis that two means are equal is true, where will 97% of the computed z values lie between?
If the null hypothesis that two means are equal is true, 97% of the computed z values lie between 2.17.
What is null hypothesis?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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Three students share 8 blocks of clay equally How much clay does each student get? 8+3= Each student's share is blocks of clay
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.
A 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-0.18.48d) represents the amount of the budget, in dollars, left
after buying d desks.
The expression that represents the total amount of discount in dollars is; (48d - 0.18 x 48d)
What is an expression?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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write an explanation comparing constant percentage change to constant rate of change. 2. what are some key words in a verbal description that indicate an exponential function can be used to model the situation? what is meant by such words?'
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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Find two consecutive integers such 4 that times the smaller integer is 50 less than 6
times the larger integer.
The consecutive integers such 4 that times the smaller integer is 50 less than 6 times the larger integer are 22 and 23.
How to calculate the value?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 screen of a tablet is shaped like
a rectangle. Find the area of the screen by
A = bh, when b = 7 in and
A h = 11 in.
The screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.
What is the area of a rectangle?
If the length of the rectangle is 'l' and the breadth of the rectangle is 'b', then the area of the rectangle can be calculated as
Area = Length * Breadth
The length of the screen is 11 in. and the breadth of the screen is 7 in.
Then the area of the screen,
Area = length * breadth
= 11 * 7
= 77 square inches.
Hence, the screen of a tablet is shaped like a rectangle. then the area of the screen is 77 square inches.
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Find the value of each angle
Answer:
15° and 75°----------------------------
Given is the right triangle.
The two angles are complementary, so their sum is 90°:
p - 10 + p + 50 = 902p + 40 = 902p = 50p = 25The angles are:
p - 10 = 25 - 10 = 15°p + 50 = 25 + 50 = 75°Answer:
p - 10° = 15° p + 50° = 75°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.
John has $23.65 to spend on a book and magazines. The book costs $5.95. the magazine cost 2.95 each
Make let statements and equation than solve the equation you made
Unit-Solving equations
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.
Am I right or wrong?
Answer:
Step-by-step explanation:
right i think?
solve 1/3 x= -4/5
-2 2/5
4/15
2 2/5
-4/15
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]
It's a small sentence word problem, I don't understand it though...
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.
What is stated by the rational root theorem?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:
Variable p: factor of the constant term, which is the last coefficient of the polynomial function.Variable q: factor of the leading coefficient, which is the first coefficient of the polynomial function.Hence the blanks in this problem are completed, respectively, by:
Constant term and leading coefficent.
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Which set of coordinates represents Figure MNOP reflected across the x-axis?
The set of coordinates after the reflection is (c) M' = (-3, -4) N' = (2, -3) O' = (1, -1) P' = (-2, -2)
How to determine the coordinates after the reflection?The graph represents the given parameter
On the graph, we have the following coordinate points
M = (-3, 4)
N = (2, 3)
O = (1, 1)
P = (-2, 2)
The rule of the reflection is given as:
Reflection across the x-axis
Mathematically, this is represented as
(x, y) ⇒ (x, -y)
When this is applied to the points, we have the following representation
M' = (-3, -4)
N' = (2, -3)
O' = (1, -1)
P' = (-2, -2)
Hence, the set of coordinates is (c)
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Find the area (in cm) of the rectangle shown.
7
3
Write each equation in slope-intercept form.
9.-10x + 2y = 12
12. 6x-3y=-18
10. 4y + 12x = 16
13.-2x-8y = 24
11. -5x + 15y = -30
14. -4x-10y = -7
Answer:
Step-by-step explanation:
2
At 10:00 am Han and Tyler both started running toward each other from opposite ends of a 10 mile path along a river. Han runs at a pace of 12 minutes per mile. Tyler runs at a apce of 15 minuttes per mile
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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You can convert gallons to liters by using a factor of 3.79. That is, 1 gallon is about 3.79 liters. About how many liters are in 37 gallons? Is your answer an underestimate or overestimate? Explain.
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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1/2x + 3/4x + 1/4x + 4
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)
Multiply. Write your answer as a fraction or as a whole or mixed number.
7 ×
5
6
Answer:210
Step-by-step explanation:
find ta , the tension in string a. express the tension in string a in terms of g , m1 , l , d , m2 , and x .
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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Chitchat wireless charges $0. 30 per minute plus a monthly base fee. In september, maggie used 120 minutes and her bill was $51. Write and solve an equation that best represents the scenario.
The equation is 51 = x + 120 × 0.30 that can find the monthly base fee charged by Chitchat wireless.
The equation representing the scenario will be formed through following components.
Total bill = monthly base fee + number of minutes × cost per minute
In the above mentioned equation, let us assume the monthly base fee to be x. Now, keep the values in formula to find the value of x.
51 = x + 120 × 0.30
Performing multiplication on Right Hand Side of the equation
51 = x + 36
Rewriting the equation according to x
x = 51 - 36
Performing subtraction on Right Hand Side of the equation
x = 15
Thus, the monthly base fee is $15.
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4. 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. All ticket prices include tax. Write a system of equations, in terms of a and c, that models this
situation. Use a system of equations to determine the exact cost of each type of ticket algebraically.
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
What is linear equation?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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Part A
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Choose the system of equations that models the situation.
A. 2x + 3y = 7.20
2x + 4y = 8.80
B. 3x + 2y = 7.20
4x + 2y = 8.80
C. 2x + 3y = 7.20
4x + 2y = 8.80
D. 2x + 3y = 8.80
4x + 2y = 7.20
Part B
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80. Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges. Use the system of equations from Part A to find the price per pound for oranges.
price: $ ____ per pound
System of equations that models the situation is Option C . 2x+3y = 7.20 , 4x+3y = 8.80 and the price per pound for oranges is $1.40.
Given:
Part A
Steve buys 2 lb of grapefruit and 3 lb of oranges for $7.20. Kennedy buys 4 lb of grapefruit and 2 lb of oranges for $8.80.
Let x represent the price per pound for grapefruit, and let y represent the price per pound for oranges.
2x + 3y = 7.20
4x + 2y = 8.80
Part B
on solving two equations:
2x + 3y = 7.20 and 4x + 2y = 8.80
2(2x + 3y) - 4x - 2y = 2*7.20 - 8.80
4x + 6y - 4x - 2y = 14.40 - 8.80
4y = 5.60
y = 5.60/4
= $1.40
hence price of oranges per pound is $1.40.
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g a pair of fair dice is rolled. what is the probability of getting a total on the two dice greater than 10
The probability of getting a sum greater than 10 is 1/12.
From the question, we have
total outcomes = 6 ×6 = 36
Number of events of sum greater than 10: {5, 6}, {6, 5}, {6, 6} = 3
Probability = 3/36
=1/12
The probability of getting a sum greater than 10 is 1/12.
Probability:
Probability refers to possibility. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is.
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