Step-by-step explanation:
we have the 2 numbers x and (x+2).
x × (x + 2) = 143
x² + 2x = 143
x² + 2x - 143 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case this is
x = (-2 ± sqrt(2² - 4×1×-143))/(2×1) =
= (-2 ± sqrt(4 + 572))/2 = (-2 ± sqrt(576))/2 =
= (-2 ± 24)/2 = (-1 ± 12)
x1 = -1 + 12 = 11
x2 = -1 - 12 = -13
so, we have 2 solutions : 11 and 13, -13 and -11
11× 13 = 143
-11×-13 = 143
The graph shows the first four ordered pairs formed by the corresponding terms of two patterns. Which ordered pair would be the fifth point on this graph? (4,12) (12,4) (12,8) (10, 4) Q1 6 7 8 9 10 11 12
As shown in the graph:
There are four points:
(0,0) , (3, 1) , ( 6, 2) and ( 9, 3)
The points represent a proportion relation between x and y
The relation will be:
[tex]y=\frac{1}{3}x[/tex]So, the fifth point will be: ( 12, 4)
find the x value (6x+9)° (4x-19)°
In this problem m and n are parallel lines, and the first angle is an exteriar angle an the secon is a interior angle.
this two condition give us that the two angles are complementary anlges so the sum of them should be 180 so:
[tex]6x+9+4x-19=180[/tex]and we can solve for x so:
[tex]\begin{gathered} 10x-10=180 \\ 10x=180+10 \\ x=\frac{190}{10} \\ x=19 \end{gathered}[/tex]The number of microbes in a tissue sample is given by the functionN (t) = 34.8 + In(1 + 1.2t)where N(t) is the number of microbes (in thousands) in the sample after thours.a.) How many microbes are present initially?b.) How fast are the microbes increasing after 10 hours?
Explanation
[tex]N(t)=34.8+\ln (1+1.2t)[/tex]we have a function where the number of microbes ( N) depends on the time(t)
hence
Step 1
a.) How many microbes are present initially?
to know this, we need replace time I= t = zero, because it was "initially"
so
when t=0
replace.
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(0)=34.8+\ln (1+1.2\cdot0) \\ N(0)=34.8+\ln (1) \\ N(0)=34.8+0 \\ N(0)=34.8 \end{gathered}[/tex]so, initially there were 34.8 microbes
Step 2
b)How fast are the microbes increasing after 10 hours?
to know this, let t=10
so
[tex]\begin{gathered} N(t)=34.8+\ln (1+1.2t) \\ N(10)=34.8+\ln (1+1.2\cdot10) \\ N(10)=34.8+\ln (1+12) \\ N(10)=34.8+\ln (13) \\ N(10)=34.8+2.56 \\ N(10)=37.36 \end{gathered}[/tex]therefore , after 10 hours the number of microbes is 37.36
I hope this helps you
linear equation in deletion method2x + y − 3z = 13x − y − 4z = 75x + 2y − 6z = 5
The given system is:
[tex]\begin{gathered} 2x+y-3z=1\ldots(i) \\ 3x-y-4z=7\ldots(ii) \\ 5x+2y-6z=5\ldots(iii) \end{gathered}[/tex]Add (i) and (ii) to get:
[tex]\begin{gathered} 2x+y-3z=1 \\ + \\ 3x-y-4z=7 \\ 5x-7z=8\ldots(iv) \end{gathered}[/tex]Multiply (ii) by 2 to get:
[tex]6x-2y-8z=14\ldots(v)[/tex]Add (iii) and (v) to get:
[tex]\begin{gathered} 6x-2y-8z=14 \\ + \\ 5x+2y-6z=5 \\ 11x-14z=19\ldots(vi) \end{gathered}[/tex]Multiply (iv) by 2 to get:
[tex]10x-14z=16\ldots(vii)[/tex]Subtract (vii) from (vi) to get:
[tex]\begin{gathered} 11x-14z=19 \\ - \\ 10x-14z=16 \\ x=3 \end{gathered}[/tex]Put x=3 in (iv) to get:
[tex]\begin{gathered} 5\times3-7z=8 \\ -7z=8-15 \\ -7z=-7 \\ z=1 \end{gathered}[/tex]Put x=3 and z=1 in (i) to get:
[tex]\begin{gathered} 2(3)+y-3(1)=1 \\ 6+y-3=1 \\ y+3=1 \\ y=-2 \end{gathered}[/tex]So the values are x=3,y=-2 and z=1.
Compare f(0) and g(0)f(0) is <, =, or > to g(0)
From the graph of f(x), it can be obseved that function f(x) value at x = 0 is -3, which means that f(0) = -3.
From the graph of g(x), it can be observed that g(0) = 0.
As value 0 is greater than -3. So f(0) is lesser than g(0).
Answer: f(0) < g(0)
Hi, can you help me answer this question please, thank you!
Let x be a random variable representing the blood pressures of adults in the USA. Since it is normally distributed, we would apply the formula for determining z score which is expressed as
z = (mean - population mean)/standard deviation
From the information given,
population mean = 121
Standard deviation = 16
For stage 2 high blood pressure, the probability is
P(x greater than or equal to 160). It is also equal to 1 - P(x < 160)
Thus, for x = 160, we have
z = (160 - 121)/16 = 2.4375
From the standard normal distribution table, the probability value corresponding to a z score of 2.4375 is 0.9927
P(x < 160) = 0.9927
P(x greater than or equal to 160) = 1 - 0.9927 = 0.0073
Converting to percentage, it is 0.0073 * 100 = 0.73%
b) If 2000 peaople were sampled, the number of people with stage 2 high blood pressure would be
0.73/100 * 2000 14.6
To the nearest person, it is 15 people
c) For stage 1, the probability is
P(140 < x < 160)
For x = 140,
z = (140 - 121)/16 = 1.1875
From the standard normal distribution table, the probability value corresponding to a z score of 1.1875 is 0.883
Recall, for x = 160, the probaility is 0.9927
Thus,
P(140 < x < 160) = 0.9927 - 0.883 = 0.1097
Converting to percentage, it is
0.1097 * 100 = 10.97%
d) The 30th percentile refers to all values of blood pressure below k, where k is the 30th percentile. This means that we would find
P(x < k) = 0.3
The z score corresponding to a probability value of 0.3 is - 0.52
Thus,
(k - 121)/16 = - 0.52
k - 121 = - 0.52 * 16 = - 8.32
k = - 8.32 + 121
k = 112.68
The pressure for the 30th percentile is 112.68
What’s the total of all the present values of the payments? $320,640 $787,116 $878,611 $987,116
The total of all the present values of the payments is $2,973,483.
What is the present value?The present value is the future cash flows discounted to the present day's values.
The present value can be determined using an online finance calculator that inputs the future cash flows, the interest rate, and the period.
How is the total present value determined?The total present value is a function of the summation of the four present values.
Since the present values are given, computing the total involves the mathematical operation of addition.
Present Values:1st payment $320,640
2nd payment $787,116
3rd payment $878,611
4th payment $987,116
Total PV $2,973,483
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Answer:
The correct answer is $878,611 for plato users
Step-by-step explanation:
solve 2x^2+5x-3>0 quadratic inequalities
The solution set of the inequality 2 · x² + 5 · x - 3 > 0 is (- ∞, - 3) ∪ (1 / 2, + ∞).
How to solve a quadratic inequality
Herein we find a quadratic inequality, whose solution set can be found by factoring the expression and determine the interval where the expression is greater than zero. Initially, we use the quadratic formula to determine the roots of the quadratic function:
2 · x² + 5 · x - 3 = 0
x₁₂ = [- 5 ± √[5² - 4 · 2 · (- 3)]] / (2 · 2)
x₁₂ = (- 5 ± 7) / 4
x₁ = 1 / 2, x₂ = - 3
Then, the factored form of the inequality is:
(x - 1 / 2) · (x + 3) > 0
In accordance with the law of signs, we must look for that intervals such that: (i) (x - 1 / 2) > 0, (ii) (x + 3) > 0, (ii) (x - 1 / 2) < 0, (x + 3) < 0. Then, the solution set of the quadratic inequality is:
Inequality form - x > 1 / 2 ∨ x < - 3
Interval form - (- ∞, - 3) ∪ (1 / 2, + ∞)
The solution set of the inequality is (- ∞, - 3) ∪ (1 / 2, + ∞).
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4. Driving on the highway, you can safely drive 65 miles per hour. How far can you drive in ‘h’ hours? What is the domain of the function which defines this situation?A) 65B) the number of hours you driveC) the distance you driveD)the amount of gas you use
Answer:
[tex]\text{ The number of hours you drive.}[/tex]Step-by-step explanation:
For distance, we can apply the following equation:
[tex]\begin{gathered} d=s*h \\ where, \\ s=\text{ speed} \\ h=\text{ hours} \end{gathered}[/tex]Since we know that we can safely drive 65 miles per hour, the domain will be defined by the number of hours you drive:
[tex]d=65h[/tex]At 3:00 PM a man 138 cm tall casts a shadow 145 cm long. At the same time, a tall building nearby casts a shadow 188 m long. How tall is the building? Give your answer in meters. (You may need the fact that 100 cm = 1 m.)
A tall man(138cm) casts a shadow of 145cm
A building nearby casts a shadow of 188m
Using the information you have to determine the height of the building.
First step is to convert the units of the height of the man and the length of his shadow from cm to meters:
100cm=1m
So 145cm=1.45m
And 138co=1.38m
Now that the measurements are expressed in the same units you can determine the height shadow ratio of the man and use it to calculate the height of the bulding.
[tex]\frac{\text{height}}{\text{shadow}}=\frac{1.38}{1.45}[/tex]Compare this ratio with the ratio between the heigth/shadow ratio of the building to determine the heigth of the building.
Said height will be symbolized as "x"
[tex]\begin{gathered} \frac{1.38}{1.45}=\frac{x}{188} \\ x=(\frac{1.38}{1.45})188 \\ x=178.92m \end{gathered}[/tex]The building is 178.92m
24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas Choose the correct letter
Since 24 miles is to 1 gallon of gas as 60 miles is to 2.5 gallons of gas
These are 2 equal ratios, then
They will be 2 equal fractions
[tex]\frac{24\text{ miles}}{1\text{ gallon}}=\frac{60\text{ miles}}{2.5\text{ gallons}}[/tex]The correct answer is D
At a carry-out pizza restaurant, an order of 3 slices of pizza, 4 breadsticks, and 2 juice drinks costs $12. A second order of 5 slices of pizza, 2 breadsticks, and 3 juice drinks costs $15. If four breadsticks and a juice drink cost $.30 more than a slice of pizza, write a system that represents these statements. p: slices of pizza b: bread sticks d: juice drinks Choose the correct verbal expressions for problems into a system of equations or inequalities.
p = slices of pizza
b = bread sticks
d = juice drinks
Equation 1
3p + 4b + 2d = 12
Equation 2
5p + 2b + 3d = 15
Equation 3
4b + 1d = 1p + 0.3
That's all
A saw blade is rotating at 2700 revolutions per minute. Find theangular speed in radians per second.
The rule of the angular speed is
[tex]\omega=No\text{ of revolution per min }\times\frac{2\pi}{60}[/tex]Since the number of revolutions is 2700 per min, then
[tex]\begin{gathered} \omega=2700\times\frac{2\pi}{60} \\ \\ \omega=90\pi\text{ rad per sec} \end{gathered}[/tex]The answer is 90pi rad per second
The answer is the 3rd answer
For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 35 N acts on a certain object, the acceleration of the object is 5 m/s^2. If the force is changed to 49 N what will be the acceleration of the object?
Answer:The acceleration that an objects gains is given by the mass of the object.
If the acceleration of the object becomes 5 m/s² the force is 15 N.
Reason:
The given parameters are;
The acting force ∝ The acceleration of the object.
The acceleration given by an amount of force, F, of 18 N = 6 m/s²
Required:
The force acting on the object acceleration, a, is 5 m/s².
Solution:
According to Newton's Second Law of motion, we have;
F = m·a
Where;
m = The mass of the object
Therefore, we have;
From the conditions, F = 18 N, when a = 6 m/s², we have, the mass of the
given object is given as follows;
The force acting when the the acceleration, a = 5 m/s², is therefore;
F = 3 kg × 5 m/s² = 15 N
If the acceleration of the object becomes 5 m/s² the force is 15 N.
Step-by-step explanation:
need two column proof I'm not understanding how the process with a midpoint and difference with a bisect
we have that
GJ=JL -------> given
so
1) HJ=JK ------> by GL bisects HK
2) m by vertical angles
3) triangle GJH is congruent with triangle LJK ------> by SAS theorem
You have 1/4 of a quiche left over from lunch. If you sent 4/6 of the leftover quiche home with your brother, how much of the quiche do you have left in the dish?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
If the brother took home 4/6, that means that you still have 2/6.
[tex]\frac{1}{4}[/tex] x [tex]\frac{2}{6}[/tex] = [tex]\frac{2}{24}[/tex] which is the same as 1/12
Some airlines charge a fee for each checked luggage item that weighs more than 21,000 grams. How many kilograms is this?
The value of 21,000 grams to kilograms is 21 kilograms
How to convert kilograms to grams ?1000 grams = 1kg
The first step is to convert 21,000 grams to kilograms
It can be calculated as follows;
= 21000/1000
= 21
Hence the value of 21,000 grams in kilograms is 21 kilograms
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In a cricket match, you have a squad of 15 players and you need to select 11 for a game. The two opening batsmans are fixed and the rest of the players are flexible. How many batting orders are possible for the game?
The number of batting orders that are possible for the game is 1365 orders.
What are combination?Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.
Combination formula
ⁿCr = n! / ((n – r)! r!
n = the number of items.
r = how many items are taken at a time.
This will be:
15! / 11! (15 - 11)!
= 15! / 11! 4!
= 15 × 14 × 13 × 12 / 4 × 3 × 2
= 1365 orders
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I need you to make a problem and solve it on the side and explain how explain it I’m making a practice test and I can show you examples of how I did the others This are the topics you can choose fromTopic 1: is the relation a function- domain and range Topic 2: zero is of a function
For topic (1), we have the following question:
Which of the following is a function: y=x² or x=y²?
Identify domain and range of each equation.
We can identify a given relation if it is a function or not by identifying the number of possible values of y.
The equations below are both relations.
[tex]y=x^2\text{ and }x=y^2[/tex]However, only one of them is a function.
For the first equation, note that for each value of x, there is only one value of y. Some of the points on the equation are as follows.
[tex]\begin{gathered} x=-2 \\ y=x^2^{} \\ y=(-2)^2=4 \\ \\ x=0 \\ y=x^2 \\ y=0^2=0 \\ \\ x=2 \\ y=x^2 \\ y=2^2 \\ y=4 \end{gathered}[/tex]Thus, the equation passes through the following points.
[tex](-2,4),(0,0),(2,4)[/tex]Notice that no value of x is repeated. Therefore, the given relation is a function.
We can also determine it using graphs. The image below is the graph of the first equation.
If we test it using the vertical line test, no vertical line can pass through the graph twice. Therefore, it shows that the equation is a function.
On the otherhand, the other equation is not a function. This is because when we substitute -2 and 2 to the value of y, we will have the same value of x, which is equal to 4.
[tex]\begin{gathered} y=-2^{} \\ x=y^2 \\ x=(-2)^2=4 \\ \\ y=2 \\ x=y^2^{} \\ x=2^2=4 \end{gathered}[/tex]Since there are two values of y for only one value of x, the equation must not be a function.
To illustrate this using its graph, we can notice that the vertical line below passes through two points on the graph when x=4.
Therefore, the second equation is not a function.
As for the domain and range, we can obtain it from both graphs.
The domain the set of all possible values of x. Thus, for the first equation, since it extends indefinitely to the left and right, the domain must be from negative infinity to positive infinity.
[tex]D_1\colon(-\infty,\infty)[/tex]On the otherhand, since the second equation extends indefinitely to the right from 0, the domain must be from 0 to positive infinity, inclusive.
[tex]D_2\colon\lbrack0,\infty)[/tex]As for the range, it is the set of all possible values of y.
Thus, for the first equation, since the graph extends indefinitely upwards from 0, the range must be from 0 to positive infinity, inclusive.
[tex]R_1\colon\lbrack0,\infty)[/tex]On the otherhand, the graph of the second equation extends indefinitely upwards and downwards. Thus, its range must be from negative infinity to positive infinity.
[tex]R_2\colon(-\infty,\infty)[/tex]To summarize, here are the questions and the answers for each question.
Which of the following is a function: y=x² or x=y²?
Answer: y=x²
Identify domain and range of each equation.
Answer:
For y=x²:
[tex]\begin{gathered} D\colon\text{ (-}\infty,\infty\text{)} \\ R\colon\lbrack0,\infty) \end{gathered}[/tex]For x=y²:
[tex]\begin{gathered} D\colon\lbrack0,\infty) \\ R\colon(-\infty,\infty) \end{gathered}[/tex]what is x^4 − 14x2 + 45 as factored
Answer: B=3
Step-by-step explanation:
how do I solve (4w+3x+5)-(4w-3x+2)
Answer:
6x + 3
Explanation:
To solve the initial expression, we need to write it without the parenthesis as:
( 4w + 3x + 5 ) - ( 4w - 3x + 2)
4w + 3x + 5 - 4w + 3x - 2
Then, we need to identify the like terms as:
4w and -4w are like terms
3x and 3x are like terms
5 and -2 are like terms
Now, we can organize the terms as:
4w - 4w + 3x + 3x + 5 - 2
Adding like terms, we get:
(4w - 4w) + (3x + 3x) + (5 - 2)
0 + 6x + 3
6x + 3
Therefore, the answer is 6x + 3
The expression (222)(x?) is equivalent to z What is the value of p?
SOLUTION;
Step 1:
[tex]undefined[/tex]If f(x) = 8x2 - 18x + 5, find when f(x) = -4
Setting the given equation equals -4 we get:
[tex]\begin{gathered} 8x^2-18x+5=-4 \\ 8x^2-18x+5+4=0 \\ 8x^2-18x+9=0 \end{gathered}[/tex]Notice that:
[tex]8x^2-18x+9=8(x^2-\frac{9}{4}x+\frac{9}{8})=8(x-\frac{3}{2})(x-\frac{3}{4})[/tex]Therefore, f(x)=-4 when x=3/2 or x=3/4.
Sheldon is painting a wall in his house and is using a paint roller.The paint roller had a radius of 1 inch and a height of 8 inches.How many square inches of space Sheldon paint with one revolution of paint roller?Round to nearest tenths
The information we have about the paint roller:
Radius: r=1in
Height: h=8in
To find the answer to how many square inches of space he can paint with one revolution, it is useful to visualize the surface area of a cylinder:
The circles are the top and bottom of the cylinder, and the rectangle is the body of the cylinder (the paint roller). The area of this rectangle is the area that the paint roller will paint with one revolution.
Calculate the area of the rectangle:
To find the area, first, we need to find the length "L":
This length L is equal to the circumference of the circle defined as follows:
[tex]L=2\pi r[/tex]So to find L we substitute r=1in and pi=3.1416:
[tex]\begin{gathered} L=2(3.14216)(1\text{ in)} \\ L=6.2832in \end{gathered}[/tex]And finally, to find the area of the rectangle and thus, the area that the paint roller covers with one revolution, we multiply the length by the height:
[tex]A=h\times L[/tex]Where "A" is area.
Substituting h and L:
[tex]\begin{gathered} A=8in\times6.2832in \\ A=50.2656in^2 \end{gathered}[/tex]Rounding our answer to the nearest tenths:
[tex]50.2656\approx50.3[/tex]Answer: 50.3 square inches
What is the slope of the line that passes through the points (2,8) and (12,20)?
The slope of the line with that passes through the coordinates (2,8) and (12,20) is 6/5.
What is the slope of the line with the given coordinates?Slope is simply expressed as change in y over the change in x.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Given the data in the question;
Point 1( 2,8 )
x₁ = 2y₁ = 8Point 2( 12,20 )
x₂ = 12y₂ = 20Slope m = ?
To find the slope m, plug the given x and y values into the slope formula and simplify.
Slope m = ( y₂ - y₁ )/( x₂ - x₁ )
Slope m = ( 20 - 8 )/( 12 - 2 )
Slope m = ( 12 )/( 10 )
Slope m = 12/10
Slope m = 6/5
Therefore, the slope of the line is 6/5.
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make a conjecture about each value or geometric relationship.
The relationship between the angles of a triangle with all sides congruent.
Congruence of all sides implies congruence of all angles. All of the angles line up.
What is geometric conjecture?
According to Thurston's geometrization conjecture in mathematics, each of a select group of three-dimensional topological spaces has a distinctive geometric structure that can be connected to it.
How do the angles of a triangle with congruent sides relate to one another?
We refer to a triangle as being equilateral when its three sides are congruent. We add a slash mark to the sides that are congruent. An equilateral triangle always has 60° angles.Learn more about congruent
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what is 0.09 as a percentage?
15.) In the accompanying diagram, ABC is a straight line and BE bisects 4DBC. If m4ABD = 2x and m4DBE = 2x + 15, find m&ABD.
Using bisection, the measure of angle ABD is of m<ABD = 50º.
What is the bisection of an angle?The bisection of an angle is when the angle is divided into two angles of equal measure.
In the context of this problem, we have that the angle BE bisects the angle DBC, hence the measures of these angles are given as follows:
mDBE = mEBC = 2x + 15.
As shown in the diagram, the entire line forms a ray, meaning that the sum of the measures of the angles is of 180º, hence we can solve for x as follows:
2x + 2(2x + 15) = 180º
2x + 4x + 30 = 180º
6x = 150º
x = 150º/6
x = 25º.
Then the measure of angle ABD is found as follows:
m<ABD = 2x = 2(25) = 50º.
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Please help thank you sm it would be very helpful and very much appreciated ♥️‼️
2. Write the formula for the circumference of a circle.
a. Calculate the circumference of circle B if the diameter is 8 inches.
b. Calculate the radius of circle B if the circumference is 94.2 square centimeters.
Step-by-step explanation:
2. C = [tex] 2 \pi r [/tex]
a. to find radius from diameter in order to calculate the value of the circumference we have to divide the diameter by 2
d/2 = 8/2 = 4
Next, Find the circumference
C = [tex] 2 \pi r [/tex]
C = [tex] 2 \cdot 3.142 \cdot 4 [/tex]
C = 25.13
b. Rearrange formula for circumference to find the value of the radius
Where, C = [tex] 2 \pi r [/tex]
Make r the subject of formula
C/[tex] 2 \pi [/tex] = [tex] 2 \pi r [/tex] /[tex] 2 \pi [/tex]
94.2/2 × 3.142 = r
94.2/6.3 = r
r = 14.95 ≈ 15
2.circumference= pi×diameter
a)25.136 inches
b)14.99 cm
Step-by-step explanation:
a) pi × 8
3.142× 8= 25.136
b) diameter = radius × 2
circumference = pi × diameter OR pi × radius×2
because we are trying to find the radius we will use the pi × 2 radius.
94.2= 3.142 × 2 radius
94.2 ÷ 3.142= 2 radius
29.981 = 2 radius
29.981 ÷ 2 = radius
14.99 = radius
Please help me solve this math problemRewrite in exponential form Ln3=y
1) Let's rewrite it as a logarithmic expression of the following exponential one. Let's do it step by step.
[tex]\begin{gathered} e^6=x \\ \ln e^6=\ln x \\ \ln(x)=6 \end{gathered}[/tex]Note that when we apply the natural log on both sides, we use one of those properties that tell us that we can eliminate the log since the base of a natural log is "e", as well as, "e" is the base of that power.
2) To rewrite in the exponential form we can do the following:
[tex]\ln(3)=y\Leftrightarrow e^y=3[/tex]Note that in this case, we have used the definition of logarithms.
