Answer: We know that in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Using the triangle inequality theorem, we can set up the following inequality:
BD + BC > CD
7x - 10 + 4x - 29 > 5x - 9
Simplifying, we get:
11x - 39 > 5x - 9
Subtracting 5x from both sides, we get:
6x - 39 > -9
Adding 39 to both sides, we get:
6x > 30
Dividing by 6 from both sides, we get:
x > 5
So x must be greater than 5.
To find the value of BD, we can substitute the value of x in the equation:
BD = 7x - 10
BD = 7(5) - 10 = 25 - 10 = 15
To find the value of BC, we can substitute the value of x in the equation:
BC = 4x - 29
BC = 4(5) - 29 = 20 - 29 = -9
To find the value of CD, we can substitute the value of x in the equation:
CD = 5x - 9
CD = 5(5) - 9 = 25 - 9 = 16
So, BD = 15, BC = -9, CD = 16
Step-by-step explanation:
Expand and simplify
a) x(x + 2)(x + 3)
The required expression is x³ + 5x² + 6x as an expanded form.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
The expression is given in the question, as follows:
x(x + 2)(x + 3)
We have to expand and simplify the given factors.
As per the question, we have
⇒ x(x + 2)(x + 3)
Open the first parentheses, and distributes
⇒ (x² + 2x)(x + 3)
⇒ x²(x + 3) + + 2x(x + 3)
Combine the likewise terms in the above expression,
⇒ x³ + 3x² +2x² + 6x
⇒ x³ + 5x² + 6x
Thus, the required expression is x³ + 5x² + 6x.
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Find the perimeter of the image below: (4 points)
37 units
38 units
39 units
40 units
38, 39, 40, 37, 38, and so forth. The perimeter of the supplied figure must be determined. = 38.97 units. As a result, 38.97 units make up the perimeter.
How do you find the perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter.
The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length: The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)\x^{2} }[/tex] ≤ b r/≥ d=[tex]\sqrt{(8-(-2)^{2})+(7-11)^{2} }[/tex] ≤b r/≥
d=[tex]\sqrt{116}[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length:
P = (-2, 11)
T = (8, 7)
The length of PT is [tex]\sqrt{116}[/tex]
The other 4 sides are handled in the same way, and the results are as follows:
TS = [tex]\sqrt{49}[/tex]
SR = [tex]\sqrt{50}[/tex]
RQ = [tex]\sqrt{61}[/tex]
QP = [tex]\sqrt{40}[/tex]
You may calculate the perimeter by adding all the sides:[tex]\sqrt{116}[/tex]+[tex]\sqrt{49}[/tex]+[tex]\sqrt{50}[/tex]+[tex]\sqrt{61}[/tex]+[tex]\sqrt{40}[/tex] = 38.97
The solution is 39 units if you round off.
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Jenny buys candy that costs $7 per pound. She will spend more than $70 on candy. What are the possible numbers of pounds she will buy?
Use p for the number of pounds Jenny will buy.
Write your answer as an inequality solved for p.
Answer: p > 10
Step-by-step explanation:
If one pound of candy is $7, then ten pounds of candy would be $70. If Jenny plans on spending more that $70, this means that she plans on buying more that ten pounds of candy, which shows that p (the number of pounds of candy she will buy) is greater than ten.
I hope this helps!!
fully factor (x^2 + 4)(x -3)
Answer: x³ - 3x² + 4x - 12
Step-by-step explanation:
Using FOIL:
x³ - 3x² + 4x - 12
Answer:
x=1
Step-by-step explanation:
(x^2+4)(x-3)
"x^2=x*x=x"
(x+4)(x-3)
x+1
x/x/
x=1
Expressed as a single fraction, 3/4x - 2/5x is equal to
The single fraction is 7x/20
What is a fraction?A fraction can be defined as the part of a whole variable, number or element.
The different types of fractions are;
Simple fractionsMixed fractionsProper fractionsComplex fractionsImproper fractionsWhat are algebraic expressions?Algebraic expressions are mathematical expressions consisting of terms, coefficients, variables, factors and constants.
They are made of operations such as multiplication, addition, subtraction, division, etc
Given the expression;
3/4x - 2/5x
Find the LCM
15x - 8x/20
7x/20
Thus, the value is 7x/20
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you can perform 6 push ups in 24 seconds. wrote and graph an equation that represent the relationship between time and number of push up. at this rate how many pushups can you perform in 2 minutes
At the given rate, I can perform 480 pushups.
Your goal should be to complete 100 push-ups in 2 minutes (this is a standard for elite soldiers).
White defines that as 10 to 20 push-ups if your max is 25 reps, 2 sets of 10 to 20 if your max is 25 to 50 reps, and 2 to 3 sets of 10 to 20 if your max is greater than 50 push-ups. "If you're doing a lot of sets and hitting a lot of volume, I'd try to do them every other day.
24/6 = 4
meaning they are doing 4 push ups per second, this is your slope
the equation of your line is y = 4x, you can graph this using a table of values
2 minutes = 120s
y = 4(120)
y = 480 push ups
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What is the equation of the midline of the sinusoidal function
Answer: y = 0
Step-by-step explanation:
A midline of a sinusoidal function is the horizontal center line about which the function oscillates above and below. For y = sin x, the midline is y = 0 (the x-axis). The midline is parallel to the x-axis and is located halfway between the graph's maximum and minimum values.
Assume a total current of 2 amperes flows in a circuit with three resistorsR1 has a value of 1400 ohms, R2 has a value of 200 ohms and R3 has a value of 100 ohms , producing a total resistance of 80 ohms for the circuit. What is the amount of the current flow through resistor R3?
Answers:
(A)0.114
(B)0.800
(C)1.600
(D)0.228
1.600 amps of current flow through resistor r3 are measured.
Describe the resistor.A resistor is a passive, two-terminal electrical component used in circuits to apply electrical resistance.
Resistors are employed in electronic circuits for a variety of purposes, including reducing current flow, adjusting signal levels, dividing voltages, biassing active devices, and terminating transmission lines.
The parameters are determined by the query:
total current = 2 amperes
Total resistance = 80 ohms
Total current = voltage * Resistance
Total current = 2* 80
= 160V.
Consequently, the current passing through resistor R3 will be
V= IR (Ohms law)
where I (current)= V/R
current = 160/ 100
Current flowing through R3 =1.600 amperes.
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What is the equation of this line? y>1/2x−3 y<1/2x−3 y>2x−3 y<2x−3
Answer:
The equation of this line is y>1/2x-3
Step-by-step explanation:
This is an inequality equation that represents a line that is greater than 1/2x-3. The inequality symbol ">" indicates that all the y-coordinates that are on the same side of the line as the y-axis are greater than 1/2x-3.
In other words, all the points that lie above the line will satisfy the inequality, while all the points that lie below the line will not.
It's worth noting that the line y<1/2x-3 represents the same line but the inequality symbol "<" indicates that all the y-coordinates that are on the same side of the line as the x-axis are less than 1/2x-3.
y>2x-3 and y<2x-3 represent different lines, the first one represents a line with a slope of 2 and the second one represents a line with a slope of -2.
Calculate the combinations of 5 things 3 at a time
Answer:
5 combination 3
5 fictorial divided by (5-3)! 3!
by using the above method 10 will be your answer
A new van is priced at $19,500. If the buyer chooses to finance, they will pay $5,000 as a down payment and $375 per month. After how many months will the buyer have paid more that $10,000 toward the van?
A. 19,500 — 375x < 10,000
B. 5,000x + 375 > 10,000
C. 19,500 — 5000x > 10,000
D. 5,000 + 375 > 10,000
The inequality that represents the situation is . 5,000x + 375 > 10,000
(option b)
What is the the inequality?
The inequality that can be used to determine after how many months he would have paid more than $10,000 has this form:
down payment + (monthly payment x number of months) > $10,000
$5,000 + ($375 x m) > $10,000
$5,000 + $375m > $10,000
In order to determine the value of m, take the following steps:
Combine similar terms together:
375m > 10,000 - 5,000
Add similar terms together:
375m > $5000
Divide both sides of the equation by 375
m > 5000 / 375
m > 13.3 days
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Statistics and probability
When a number cube with faces labeled from 1 to 6 will be rolled once. The number rolled will be recorded as the outcome.
The sample space describing all possible outcomes is {1, 2, 3, 4, 5, 6}
Then outcomes for the event of rolling an even number. {2, 4, 6}
What is probability in math?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has included probability to foretell the likelihood of many events.
In probability, sample space refers to the list of all potential outcomes of an experiment. Regardless of the number of ways an event could occur, each potential result is represented by a single point in the sample space.
The sample space is the numbers from 1 to 6 while event of rolling an even number is 3/6 = 1/2
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find the value of x in both examples
For 1, since the exponential decay formula is a*(1-r)^x, a is still the same as the base value and r would replace 1-r with r being the decay rate, so r would be 1-the decay rate.
For 2, applying that formula, getting 52500*(1-2.5%)^10 (because it's for 10 years and compounded annually). Since 100% is 1, 2.5% is 0.025, and
1-0.025=0.975. Putting that in, we get 52500*(0.975)^10=around 40757 people.
For inverse functions, what we do is have y=2x+1, so we switch x and y and solve for y, so in x=2y+1 we subtract one from both sides to get x-1=2y. Next, dividing both sides by 2, we get (x-1)/2=y as our inverse. Since we want positive integers less than 10, (x-1) has to be even and therefore x has to be odd. Hence, we get that x can be 9 while y can be 4 for (9, 4)
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Can someone help me with this math problem? The answer is 7/2, but does anyone know how to get that answer?
The value of 3x₁ + x₂ is 7/2
How to find the value of 3x₁ + x₂?
A quadratic equation is an equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants.
5/x - 2/x² = 2
The LCM of x and x² is x². So we have:
(5x - 2)/x² = 2
Cross multiply:
5x - 2 = 2x²
2x² - 5x + 2 = 0
Factorize:
(2x - 1)(x - 2) = 0
2x - 1 = 0 or x - 2 = 0
2x = 1 or x = 2
x = 1/2 or x = 2
Thus, x₁ = 1/2 and x₂ = 2
Therefore, the value of 3x₁ + x₂ will be:
3x₁ + x₂ = 3×(1/2) + 2 = 3/2 + 2 = 7/2
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On Sunday a local hamburger shop sold a combined total of 309 hamburgers and cheeseburgers. The number of cheeseburgers sold was two times the number of hamburgers sold. How many hamburgers were sold on Sunday
Answer: 103
Step-by-step explanation: 309/3 = 103
write a function g(x) that transforms the function f(x)=4 square root x +1 such that f(x) is horizontally stretched by a factor of 5, reflected across the x-axis, then translated down 5.
Answer:
[tex]g(x)=-4\sqrt{\dfrac{x}{5}}-6[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=4\sqrt{x}+1[/tex]
1. Horizontal stretch
[tex]f\left(\dfrac{1}{a}x\right) \implies f(x) \: \textsf{stretched parallel to the $x$-axis (horizontally) by a factor of $a$}.[/tex]
Therefore, if f(x) is horizontally stretched by a factor of 5:
[tex]\implies f\left(\dfrac{1}{5}x\right)=4\sqrt{\dfrac{x}{5}}+1[/tex]
2. Reflection across the x-axis
[tex]-f(x)\implies f(x) \: \textsf{reflected in the $x$-axis}.[/tex]
Therefore, if f(x/5) is reflected in the x-axis:
[tex]\begin{aligned}\implies -f\left(\dfrac{1}{5}x\right)&=-\left(4\sqrt{\dfrac{x}{5}}+1\right)\\\\&=-4\sqrt{\dfrac{x}{5}}-1 \end{aligned}[/tex]
3. Translation
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
Therefore, if -f(x/5) is translated 5 units down:
[tex]\begin{aligned}\implies -f\left(\dfrac{1}{5}x\right)-5&=-4\sqrt{\dfrac{x}{5}}-1 -5\\\\&=-4\sqrt{\dfrac{x}{5}}-6\end{aligned}[/tex]
Therefore:
[tex]g(x)=-4\sqrt{\dfrac{x}{5}}-6[/tex]
Find the sum of the first 5 terms of a G.P whose first term is 3 and its common ration ¼ to four Significant figure.
Answer:85
Step-by-step explanation:
PLS HELP TANK YOUUUUU
Answer:
Step-by-step explanation:
a. 47 men
b. 24 men like soda
c. 23 men do not like soda
d. 61 women
e. 26 women like soda
f. 35 women do not like soda
what's th y intercept of y=6(x-1/2)(x+3)
to get the y-intercept of any equation we can simply set x = 0 and solve for "y", so let's do so
[tex]y=6\left( x-\cfrac{1}{2} \right)(x+3)\implies \stackrel{\textit{setting x = 0}}{y=6\left( 0-\cfrac{1}{2} \right)(0+3)}\implies y=6\left( -\cfrac{1}{2} \right)(3) \\\\\\ y=(-3)(3)\implies y=-9\hspace{12em} {\Large \begin{array}{llll} \stackrel{y-intercept}{(0~~,~~-9)} \end{array}}[/tex]
Polynominal 2x ^ 2 - 2 3x - 9 Name Using Degree Name Using Number of Terms - 3i ^ 2 - 6i + 9
Given polynomials are Binomial and Trinomial.
What are polynomials?
Polynomials are algebraic expressions that consist of variables and coefficients. Variables are also sometimes called indeterminates. We can perform arithmetic operations such as addition, subtraction, multiplication, and also positive integer exponents for polynomial expressions but not division by variable. An example of a polynomial with one variable is x^2+x-12. In this example, there are three terms: x^2, x and -12.
Based on the number of terms present in the expression, it is classified as
Monomial:-A monomial is an expression which contains only one term. For an expression to be a monomial, the single term should be a non-zero term. A Examples of monomials are: 5x,3.
Binomial:-A binomial is a polynomial expression which contains exactly two terms. A binomial can be considered as a sum or difference between two or more monomials. Examples of binomials are:
– 5x+3, 6a^4 + 17x.
Trinomial:-A trinomial is an expression which is composed of exactly three terms. A Examples of trinomial expressions are:
– 8a^4+2x+7, 4x^2 + 9x + 7.
Now,
Given polynomials are 2x ^ 2 - 2, 3x - 9, - 3i ^ 2 - 6i + 9.
As the number of terms in first two polynomials is 2, they are binomial.
and the number of terms in third polynomial is 3, it is trinomial.
hence,
Given polynomials are Binomial and Trinomial.
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Write an equation to represent the following: the product of the quantity
eight times a number x plus 4 and is equal to 17. Lesson 5-1
Answer:
8x+4=17
Step-by-step explanation:
Grayson can spend a maximum of 3 hours,h, watching television on the weekend
Grayson can spend a maximum of 3 hours, h, watching television on the weekend, and is shown in the number line.
What is number line?Numbers on a straight line are represented graphically as a number line. For comparing and sorting numbers, it serves as a reference. Including all whole numbers and natural numbers, it can be used to represent any real number.
Just to refresh your memory, the natural number is the collection of all counting numbers, i.e. 1, 2, 3, 4, 5, 6, while the whole number is a set of numbers that includes both zero (0) and all counting numbers.
Compare numbers more easily by writing them on a number line. The integers in the above figure are smaller on the left than they are on the right, as can be seen.
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Grayson is only permitted to watch television for a total of three hours on the weekends. 8-10. 5-5, 5-6 7.5-6
How do you calculate time in an hour?[Time = Distance Speed] is the formula for calculating time. The time formula can be changed to [Distance = Speed Time] to compute distance. Find the vertex of the parabola given a generalised quadratic function. Find a, b, and c. By changing a and b into h=-b2a, you can determine h, the vertex's x-coordinate. By evaluating k=f(h)=f(b2a), you may determine k, the vertex's y-coordinate.
In order to get the vertex (h, k) of the given quadratic y = ax2 + bx + c, one must first compute h= b 2 a h=2ab 2a, and then one must evaluate y at h in order to determine k. The speed equation is speed=distance*time. According to the currently accepted definition of the kilogramme, it reads as follows: "The kilogramme is defined by considering the fixed numerical value of h to be 6.62607015 unit Js,"
The fact is [tex]$3 \geqslant h \geqslant 0$[/tex]
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Find the distance between the two points (5, -4) and (3 , 6). Give an exact answer in terms of a square root.
Answer:
√104.
Step-by-step explanation:
To find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, we can use the distance formula:
d = √((x2 - x1)² + (y2 - y1)²)
So, for the given points (5, -4) and (3, 6), the distance is:
d = √((3 - 5)² + (6 - (-4))²)
d = √((-2)² + (10)²)
d = √(4 + 100)
d = √104
Therefore, the distance between the two points (5, -4) and (3, 6) is √104.
HELPP PLSSS
factor by grouping
The required factors of the polynomial by grouping are (x-3)(x^2 + 2).
What is grouping to solve cubic polynomial?To factor polynomial equations, a specialized approach is called grouping. It can be applied to polynomials with four terms as well as quadratic equations. Although they differ significantly, the two approaches are comparable.The first two terms and the final two terms are combined: p(x)=(x3 - 4x2) + (3x - 12), and we then identify the shared
factors as follows: p(x) = x2(x - 4) + 3(x - 4). (x - 4).
According to question:x^3 - 3x^2 + 2x -6
(x-3)(x^2 + 2)
Thus, required factors are (x-3)(x^2 + 2).
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If P = 4s represents the square’s perimeter in terms of the square’s side length (in inches), write a formula that represents the perimeter’s side length 's' in terms of the square’s perimeter 'P.'
The side of the square in terms of the perimeter is P/4.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
P = 4s
Where s is the side of the square and P is the perimeter of the square.
Now,
The side of the square.
P = 4s
Divide 4 into both sides.
s = P/4
Thus,
The side of the square is P/4.
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Is 6 inches in 10 seconds proportional to 12 inches in 60 seconds?
Answer: No
Step-by-step explanation:
to be proportional, both numbers have to increase by the same number
because if u multiply 6 by 2 you get 12, but when you multiply 10 by 2 you get 20, not 60 it would be proportional if you said 6 and 10 in to 12 and 20 in
if a^2 = 3a + 1, find the value of (a+1/a)^2
Answer:First, we can simplify the equation a^2 = 3a + 1 by subtracting 3a and 1 from both sides, to get:
a^2 - 3a - 1 = 0
Now we can factor the left side:
(a-1)(a+1) = 0
This equation tells us that either a-1 = 0 or a+1 = 0. So, a = 1 or a = -1.
Next, we can substitute these values into the expression (a+1/a)^2
For a = 1, (1+1/1)^2 = 2^2 = 4
For a = -1, (-1+1/(-1))^2 = 0^2 = 0
So, the value of (a+1/a)^2 is 4 when a = 1, and 0 when a = -1
Step-by-step explanation:
The distribution of hourly rates of registered nurses in a large city has mean $31 and standard deviation $5.
a) What is the distribution of the sample mean based on a random sample of 100 registered nurses in the city?
b) Find the probability that the average hourly rate of the 100 nurse sample exceeds $31.50.
a) The distribution of sample means of 100 registered nurses in the city is approximately normal, with mean $31 and standard deviation of $0.5.
b) The probability that the average hourly rate of the 100 nurse sample exceeds $31.50 is of: 0.1587 = 15.87%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n is approximately normal and has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 31, \sigma = 5, n = 100, s = \frac{5}{\sqrt{100}} = 0.5[/tex]
The probability that the average hourly rate of the 100 nurse sample exceeds $31.50 is one subtracted by the p-value of Z when X = 31.5, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (31.5 - 31)/0.5
Z = 1
Z = 1 has a p-value of 0.8413.
1 - 0.8413 = 0.1587 = 15.87%.
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How many unit angles does the smaller angle 30° of a small pattern block go through
Answer:
30 unit angles
Step-by-step explanation:
A unit angle is defined as an angle that measures 1 degree. To find the number of unit angles that the smaller angle 30° of a small pattern block goes through, we can divide the measure of the angle by the measure of a unit angle.
30° ÷ 1° = 30 unit angles
So, the smaller angle 30° of a small pattern block goes through 30 unit angles.
The probability of getting heads on a single coin flip is ;
2
The probability of getting nothing but heads
on a series of coin flips decreases by
2
for each additional coin flip. Enter an exponential function for the
probability p(n) of getting all heads in a series of n coin flips. Give your answer in the form a (b)'. In the
event that a = 1, give your answer in the form (b)'.
