MATH HELP PLEASE ---->
#13 - 16 Solve for x
16.) -31 < 3x – 7 < 14
17.) xy – ab = cd ; solve for b
18.) 3(a – b) = 9mn ; solve for a
#19 – 28 Factor Each Expression (If possible)
19.) 3x2 (y – 2) – 5(y – 2)
20.) kmfd – 3jkm
21.) 49x2– 9
22.) 64x2+ y2
23.) x2+ 7x – 35
24.) 2x2+ 11x + 14
25.) x2- 2x – 63
26.) 3x2– 2x + 7
Answers
Answer:
16.) The solution to this inequality is x < -4 or x > -3.
17.) To solve for b, we need to isolate b on one side of the equation. To do this, we can subtract ab from both sides of the equation, which gives us xy = cd - ab. Then, we can divide both sides of the equation by xy, which gives us b = (cd - ab)/xy.
18.) To solve for a, we need to isolate a on one side of the equation. To do this, we can divide both sides of the equation by 3, which gives us a - b = 3mn. Then, we can add b to both sides of the equation, which gives us a = b + 3mn.
19.) To factor this expression, we first distribute the 3x2 to get 3x2y - 6x2. Then, we notice that the 3x2 and the -6x2 have a common factor of -3x2, so we can factor them out to get -3x2(y - 2) - 5(y - 2). Finally, we notice that the -3x2(y - 2) and the -5(y - 2) have a common factor of -(y - 2), so we can factor them out to get -(y - 2)(3x2 - 5).
20.) To factor this expression, we notice that the kmfd and the -3jkm have a common factor of -jkm, so we can factor them out to get -jkm(f - 3).
21.) To factor this expression, we notice that 49 is a perfect square, so we can write 49 as 72. Then, we can factor out the x from the x2 to get 7x(x - 9).
22.) To factor this expression, we notice that 64 is a perfect square, so we can write 64 as 82. Then, we can factor out the x from the x2 to get 8x(x + y).
23.) To factor this expression, we notice that the x2 and the -35 have a common factor of x - 5, so we can factor them out to get (x - 5)(x + 7).
24.) To factor this expression, we notice that the 2x2 and the 14 have a common factor of 2, so we can factor them out to get 2(x2 + 11x + 7). Then, we notice that the x2 and the 7 have a common factor of x + 1, so we can factor them out to get 2(x + 1)(x + 7).
25.) To factor this expression, we notice that the x2 and the -63 have a common factor of x + 9, so we can factor them out to get (x + 9)(x - 7).
26.) To factor this expression, we notice that the 3x2 and the 7 have a common factor of 3x + 7, so we can factor them out to get 3(x + 1)(x - 2).
Related Questions
What is the value of this expression when c= -4 and d= 10
1/4 (c^3 + d^2)
А. 2
B. 9
C. 21
D. 41
Answers
Answer:
9
Step-by-step explanation:
\( \frac{1}{4} ( {c}^{3} + {d}^{2} ) \: when \: c = - 4 \: and \: d = 10 \\ = \frac{1}{4}[ {( - 4)}^{3} + ( {10}^{2} )] \\ = \frac{1}{4}( - 64 + 100) \\ = \frac{1}{4} \times 36 \\ = \frac{36}{4} \\ = 9\)
find the value of x. PLEASE HELP
The answer is 14, teacher gave us the answer, but I need to show my work
Answers
Answer:
14*
Step-by-step explanation:
5x+4*=74*
-4 -4
5x=70*
x=14*
*dont mind the asterisks they are my temporary degree signs
hope this helps
brainliest?
please give a step by step explanation please
Answers
The radius of a sphere whose surface area is 324*pi cm² is:
R = 9 cm.
What is the radius of the sphere in the image?We know that the surface of a sphere of radius R is given by:
S = 4*pi*R^2
Where pi = 3.14
Here we know that a sphere has a surface of 324*pi cm², then we can write the equation:
S = 324*pi cm² = 4*pi*R^2
We can divide both sides by pi, so we get:
324 cm^2 = 4*R^2
Now we can solve that equation for R, we will get:
R^2= (324 cm^2)/4 = 81cm^2
R = √(81 cm^2)
R = 9cm
The radius of the sphere is 9cm.
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solve: 2x+p/q = 2x+q/p If p=q, if p cannot equal to q
Answers
Answer:
p= -q
Step-by-step explanation:
(2xq+p)/q= (2xp+q)/p
After cross multiplying,
2xpq+p²= 2xpq+q²
p²=q²
p²-q²=0
(p+q)(p-q)=0
either p+q=0 : p= -q
or p-q=0 : p=q which is not possible because of the given condition
Thus, the only solution of this equation is:
p= -q
For p = \(\pm q\), the LHS of equation is equal to RHS.
We have the following equation -
2x + p/q = 2x + q/p
We have to solve this equation.
If f(p) = 2p + 1 and g(p) = 3p -3, then for what value of p is f(p) = g(p) ?f(p) = g(p)
2p + 1 = 3p - 3
3p - 2p = 1 + 3
p = 4
According to question, we have -
⇒ 2x + p/q = 2x + q/p
⇒ \($\frac{p}{q} =\frac{q}{p}\)
⇒ \(p^{2} =q^{2}\)
⇒ p = \(\pm q\)
Hence, for p = \(\pm q\), the LHS of equation is equal to RHS.
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A typical red blood cell in human blood has a diameter of approximately 0.007 mm. Enter this diameter in scientific notation.
In scientific notation, this diameter is × 10 mm.
What is the answer?

Answers
Using scientific notation it is found that the diameter of a red blood cell in human blood is of:
\(7 \times 10^{-3}\) mm.
What is scientific notation?A number in scientific notation is given by:
\(a \times 10^b\)
With the base being \(a \in [1, 10)\).
In this problem, the diameter is of 0.007 mm, hence:
\(0.007 = 0.07 \times 10^{-1} = 0.7 \times 10^{-2} = 7 \times 10^{-3}\)
Hence in scientific notation, the diameter is:
\(7 \times 10^{-3}\) mm.
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Use the figure below to complete the following problem.Given:R, S, T are midpoints of AC, AB, and CB.RS =½CB½RT½AB
Answers
The answer is 1/2 CB , because CB is the segment parallel to RS. And since the midpoints are joined it must be half
to factorize the following algebraic expression: 3x² + 6x + 4x + 8 Provide a three-step guide on how to factorize the expression.
Answers
Answer:
Check below:
Step-by-step explanation:
To factorize the algebraic expression 3x² + 6x + 4x + 8, you can follow these three steps:
Step 1: Grouping
Group the terms in pairs so that you can factor out a common factor from each pair.
3x² + 6x + 4x + 8
(3x² + 6x) + (4x + 8)
Step 2: Factoring out the common factors
Factor out the common factors from each pair separately.
3x(x + 2) + 4(x + 2)
Step 3: Factoring out the common factor from the resulting expression
Notice that we have a common factor, (x + 2), in both terms.
(x + 2)(3x + 4)
Therefore, the factored form of the expression 3x² + 6x + 4x + 8 is (x + 2)(3x + 4).
Mark me brainliest!
Write x² + 8x + 6 in the form (x + a)² + b, where a and b are constants.
Answers
The quadratic equation x² + 8x + 6 written in the form (x + a)² + b, is:
(x + 4)² - 10. where a and b are constant.
What is defined as making perfect square?A perfect square is a number that may be expressed as the product of two integers or as an integer's second exponent.A perfect square is indeed a positive integer formed by multiplying one integer by itself. In layman's terms, perfect squares have been numbers that are products of integers by themself. In general, a perfect square can be expressed as x², in which x is an integer and also the value of x² is a perfect square.Consider the given equation;
x² + 8x + 6 .......equation 1
Let,
8x = 2ax
x will get cancelled,
a = 4
a² = 16
Add and subtract 16 from equation 1.
x² + 8x + 6 + 16 - 16
Rearranging.
x² + 8x + 16 + 6 - 16
This can be written as;
(x + 4)² - 10
The result expression is in the form of (x + a)² + b, in which a and b are the constant whose values are 4 and -10 respectively.
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Can someone tell me the answer?
Answers
Answer:
5
Step-by-step explanation:
16÷3=5r1. Hope this helps
Find the equation of the line that
is perpendicular to y = 4x + 5 and
contains the point (8,-4).
Answers
The equation of the line that is perpendicular to y = 4x + 5, in slope-intercept form is: y = -1/4x - 2.
What is the Equation of Perpendicular Lines?Lines that are perpendicular to each other have slope that are negative reciprocal to each other.
Slope of y = 4x + 5 is 4.
Negative reciprocal of 4 is -1/4.
Substitute m = -1/4 and (a, b) = (8, -4) into y - b = m(x - a):
y - (-4) = -1/4(x - 8)
y + 4 = -1/4x + 2
y = -1/4x + 2 - 4
y = -1/4x - 2
Equation of the perpendicular line is: y = -1/4x - 2.
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The arc length x = True O False 4(3 + y)² on the interval [1, 4] is approximately 131 units.
Answers
The statement is false. The arc length of the curve defined by x = 4(3 + y)² on the interval [1, 4] is not approximately 131 units.
To find the arc length of a curve, we use the formula ∫ √(1 + (dx/dy)²) dy, where the integral is taken over the given interval.
In this case, the equation x = 4(3 + y)² represents a parabolic curve. By differentiating x with respect to y and substituting it into the arc length formula, we can calculate the exact arc length over the interval [1, 4].
However, it is clear that the arc length of the curve defined by x = 4(3 + y)² cannot be approximately 131 units, as this would require a specific calculation using the precise integral formula mentioned above.
Therefore, the statement is false, and without further calculations, we cannot determine the exact arc length of the given curve on the interval [1, 4].
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could the table of x y pairs be generated by a linear function. yes or no
Answers
Question: Could the table of x y pairs be generated by a linear function?
Answer: Yes
hope it helps...
have a great day.
It asks "plot the next two points but I do not understand because the table only shows until 9 years not until 10 years
https://gyazo.com/33f5ff104f60eca987633cce6d4a0347
Answers
There are 10 children.
Which statement can john use this figure to prove?
Answers
Answer:
Can you post a picture of the figure?
Help me please I am having trouble figuring out the answer. Help me find the ratio.
Answers
Answer:
not equivalent to meteorologists ratio
Step-by-step explanation:
meteorologists ratio is
rainy days : sunny days = 2 : 5
last months weather is
rainy days : sunny days
= 10 : 20 ( divide both parts by LCM of 10 )
= 1 : 2 ← not equivalent to 2 : 5
a computer is programmed to generate a sequence of three digits, where each digit is either 0 or 1, and each of these is equally likely to occur. construct a sample space that shows all possible three-digit sequences of 0s and 1s and then find the probability that a sequence will contain at least one 0.
Answers
Answer:
Sample space:
000
001
010
011
100
101
110
111
From the sample space, total = 8
At least one 0, there are 7 with at least one 0
Probability = Possible outcome / Total = 7/8
i need your helpppppppp
Answers
Answer: 1.9 or 90%
Step-by-step explanation: it’s worth it x
first interpret the slope. select the correct choice below and, if necessary, fill in the answer box to complete your choice.
Answers
An essential concept in mathematics and can be applied to a variety of fields such as physics, economics, and engineering.
The slope of a line in a Cartesian plane is a numerical representation of its steepness and inclination relative to the x-axis.
The slope of a straight line refers to the rise or fall of the y-coordinate as it moves from left to right along the x-axis.
There are a few different ways to interpret the slope of a line, but generally it can be thought of as the rate at which the dependent variable changes with respect to the independent variable.
When the slope is positive, the line rises from left to right, indicating that the dependent variable is increasing as the independent variable increases.
In other words, there is a direct relationship between the two variables.
Conversely, when the slope is negative, the line falls from left to right, indicating that the dependent variable is decreasing as the independent variable increases.
This means that there is an inverse relationship between the two variables.
The magnitude of the slope can also provide information about the relationship between the variables.
If the slope is close to zero, then the relationship between the two variables is weak or nonexistent.
However, if the slope is large in magnitude (i.e. close to 1 or -1), then there is a strong relationship between the variables.
A slope of zero indicates that there is no change in the dependent variable as the independent variable changes, while a slope of undefined means that the line is vertical and has no slope.
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How many subjects were examined based on the following: t(29) = 2.001, p < 0.05?
Answers
Based on the provided information, the number of subjects examined is not explicitly mentioned. However, the given t-value (t(29) = 2.001) suggests that the study involved a sample size of 30 participants, as denoted by the degrees of freedom (df) in parentheses.
The notation t(29) = 2.001 represents a t-test, a statistical test used to determine if there is a significant difference between the means of two groups. In this case, the subscript "29" in t(29) denotes the degrees of freedom (df), which is calculated by subtracting 1 from the sample size. Therefore, df = 30 - 1 = 29.
Since the degrees of freedom are 29, it indicates that the sample size used in the study was 30 participants. The t-value of 2.001 represents the magnitude of the t-statistic, which measures the difference between the means of the two groups being compared.
The critical value for significance is not provided, but the statement "p < 0.05" suggests that the obtained p-value is less than 0.05, indicating statistical significance. However, the exact p-value is not given, so the level of significance cannot be precisely determined.
Overall, the information provided implies that the study involved a sample of 30 subjects, and the t-value and p-value suggest a significant result.
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Solve: 72x + 436= -96x + 1108 X=?
Answers
72x + 436= -96x + 1108x
72x+436=1012x
436=1012x−72x
436=940x
436/940=x
109/235=x
x=109/235
Hope this helps have a blessed and wonderful day!
Answer:
x=4
Step-by-step explanation:
72x+436=-96x+1108
or,72x+96x=1108-436
or,168x=672
x=672/168
x=4
PLZ help meeeee.... srry if it's not clear
Answers
need help with the inverse temperature calculations. please show
how you solved them, thanks!
Part B, table 2: Average temperature calculation in kelvin and inverse temperature calculation Taverage (°C) Unrounded 18.90 28.95 38.80 48.95 58.90 ------- Unrounded 292.05 302.10 311.95 322.10 5. T
Answers
To calculate the inverse temperature, follow these three steps:
Step 1: Convert the average temperature from Celsius to Kelvin.
Step 2: Divide 1 by the converted temperature.
Step 3: Round the inverse temperature to the desired precision.
Step 1: The given average temperatures are in Celsius. To convert them to Kelvin, we need to add 273.15 to each temperature value. For example, the first average temperature of 18.90°C in Kelvin would be (18.90 + 273.15) = 292.05 K.
Step 2: Once we have the average temperature in Kelvin, we calculate the inverse temperature by dividing 1 by the Kelvin value. Using the first average temperature as an example, the inverse temperature would be 1/292.05 = 0.0034247.
Step 3: Finally, we round the inverse temperature to the desired precision. In this case, the inverse temperature values are provided as unrounded values, so we do not need to perform any rounding at this step.
By following these three steps, you can calculate the inverse temperature for each average temperature value in Kelvin.
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In a game, players roll a number cube. the faces of the cube are numbered from 1 to 6. for the player to win a prize, the number cube must land with the top face showing the number 3. what is the probability of the complement of this event occurring?
Answers
The probability of the complement of this event occurring is 5/6.
What is probability?
Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.
The likelihood that a population parameter will be less than a given value when the null hypothesis is true is expressed as the p-value, also known as a probability value or a measure of significance, for a particular statistical model.
Sample space: {1,2,3,4,5,6}
Total number of outcomes=6
Complement of an Event: All outcomes that are NOT the event
In this case:
So, possible outcomes in the complement event:{1,2,4,5,6}
Number of possible outcomes=5
Formula:
Probability = (Number of possible outcomes)/(Total number of outcomes)
= 5/6
So, the probability of the complement of this event occurring is 5/6.
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PQ= RQ and PS= RS a=?
Answers
The measure of angle a is 15 degrees and this can be determined by using the properties of the isosceles triangle.
What are interior angles?In geometry, interior angles are formed in two ways. One is inside a polygon, and the other is when parallel lines cut by a transversal. Angles are categorized into different types based on their measurements.
Given:
The length of the segment PQ is equal to the length of the segment RQ.The length of the segment PS is equal to the length of the segment RS.The following steps can be used in order to determine the measure of angle a:
Step 1 - According to the given data, it can be concluded that triangle PQR and triangle PSR are isosceles triangles.
Step 2 - Apply the sum of interior angle property on triangle PQR.
\(\angle\text{Q}+\angle\text{P}+\angle\text{R}=180\)
\(\angle\text{Q}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-60\)
\(\angle\text{R}=60^\circ\)
Step 3 - Now, apply the sum of interior angle property on triangle PSR.
\(\angle\text{P}+\angle\text{S}+\angle\text{R}=180\)
\(\angle\text{S}+2\angle\text{R}=180\)
\(2\angle\text{R}=180-90\)
\(\angle\text{R}=45^\circ\)
Step 4 - Now, the measure of angle a is calculated as:
\(\angle\text{a}=60-45\)
\(\angle\text{a}=15\)
The measure of angle a is 15 degrees.
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Graph this line using the slope and y-intercept: y= 1/5x + 8
Answers
The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.
What is the slope?The slope is the ratio of the vertical changes to the horizontal changes between two points of the line.
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
where (x₁, y₁) and (x₂, y₂) are the two points that you are trying to find the slope between.
According to the given information line using the slope and y-intercept is; y= 1/5x + 8
thus, the slope of this line is:
m = 1/5
And its y-intercept is: c= 8
The graph of this line using the slope and y-intercept: y= 1/5x + 8 is attached below.
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Match a recursive formula for the graph and identify the sequence as arithmetic or geometric.
Graph of a sequence
Arithmetic, t0=15
and tn=2.8+tn−1
where n≥1
.
Geometric, t0=15
and tn=2.8⋅tn−1
where n≥1
.
Arithmetic, t0=15
and tn=2.8⋅tn−1
where n≥1
.
Geometric, t0=15
and tn=2.8+tn−1
where n≥1
.
Answers
The recursive formula in this case is;
Arithmetic, t0=15
and tn=2.8+tn−1
where n≥1
Option A
What is a recursive formula?A recursive formula is a formula that defines a sequence of values in terms of its previous values. It provides a way of defining a sequence in a compact form, with each term of the sequence depending on one or more preceding terms.
In mathematics, recursive formulas are often used to define sequences. We can see that in this sequence, the first term is 15 and the common difference is obtained by simple subtraction .
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Becca earns money mowing her neighbors lawns.
What is p(x)?
Answers
The function of p(x) is p(x) = 13x - 20
How to find function?The revenue for mowing x lawn is r(x) = 18x
Her cost for gas and mower rental is c(x) = 5x + 20
Profit for mowing is p(x) = (r - c)(x)
p(x) = r(x) - c(x)
p(x) = 18x - (5x + 20)
p(x) = 18x - 5x - 20
p(x) = 13x - 20
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Karmyn is using vinegar for a salad dressing recipe. She has 3 1/2 cups of vinegar. She knows there are 16 tablespoons in one cup. How many tablespoons are in her 3 1/2 cups of vinegar?
Answers
Karmyn has 56 tablespoons of vinegar for a salad dressing recipe.
What is the Multiplication operation?In mathematics, Multiplication operations perform Multiplying values on either side of the operator.
For example 4×2 = 8
Karmyn is making a salad dressing using vinegar. She has three and a half glasses of vinegar. She understands that one cup contains 16 tablespoons.
First, we need to convert the 3 1/2 cups of vinegar to tablespoons.
We know that there are 16 tablespoons in 1 cup, so we can multiply the number of cups by the number of tablespoons per cup to convert the measurement.
3 1/2 cups × 16 tablespoons/cup = 56 tablespoons.
Therefore, she has 56 tablespoons of vinegar.
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Copy and complete the table below for the graph of
y = 2x + 1.
What values should replace A and B?
X
Y
-1
-1
-
0
A
1
3
23
B
3
7
Answers
Answer:
A is 1
B is 5
Step-by-step explanation:
0 times 2 is 0 plus 1 is 1 that gives the answer to A
2 times 2 is 4 plus 1 is 5 which gives you B
Show whether each logical expression is a tautology, contradiction or neither.
(a) (p ⨠q) ⨠(q â p)
(b) (p â q) â (p ⧠¬q)
(c) (p â q) â p
(d) (p â q) ⨠p
(e) (¬p ⨠q) â (p ⧠¬q)
(f) (¬p ⨠q) â (¬p ⧠q)
Answers
The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.
(a) Neither - This expression can be written as ¬(p ∨ q) ∧ (q ∨ ¬p), which is neither a tautology nor a contradiction.
(b) Contradiction - This expression can be written as (p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.
(c) Tautology - This expression can be written as (p ∨ q) ∧ p, which is a tautology because it is equivalent to p, which is always true.
(d) Contradiction - This expression can be written as (p ∨ q) ∧ ¬p, which is a contradiction because it is equivalent to (p ∨ q) ∧ (¬p), which is a false statement.
(e) Contradiction - This expression can be written as (¬p ∨ q) ∧ (p ∧ ¬q), which is a contradiction because it is equivalent to (¬p ∨ q) ∧ (¬p), which is a false statement.
(f) Tautology - This expression can be written as (¬p ∨ q) ∧ (¬p ∨ q), which is a tautology because it is equivalent to (¬p ∨ q), which is always true.
The expressions (a), (b), (c), (d), (e), and (f) are respectively neither, contradiction, tautology, contradiction, contradiction, and tautology.
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