By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
Given,
In the question:
To solve the equation:
x² + 5x - 14 = 0
Now, According to the question:
x² + 5x - 14 = 0
Split the middle term into two terms :
x² - 2x + 7x - 14 = 0
Factor the first two terms and the last two terms separately
x(x - 2) + 7 (x -2) = 0
Factor out
(x - 2) (x + 7) = 0
Apply Zero Product Property
x - 2 = 0 or x + 7 = 0
x = 2 or x = -7
Hence, By solving the equation x² + 5x - 14 = 0 get the value of x is 2 or -7.
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The table of ordered pairs (x, y) gives an exponential function.
Write an equation for the function.
X
-1
0
1
2
y
1
3
2
12
72
Answer:
y=2·6^2
Step-by-step explanation:
Use formula y=a[tex]b^x[/tex], plug in two different points.
72=ab^2
12=ab^1
isolate one so that a is on one side
a=[tex]\frac{12}{b}[/tex]
plug in a into the other equation
72=[tex]\frac{12}{b}[/tex][tex]b^2[/tex]
72=[tex]\frac{12b^2}{b}[/tex]
72=12b
b=6
complete solving for a now
a=2
now put it back into [tex]y=ab^x[/tex]
y=2·6^2
Simplify the following expressions by adding the like terms: 3a² - 2a - 7 + 3a + 4 - 2a² + 9a x² + 6xy + 5y² - 6xy + 2y² 1 2
can the sum X to the power of two plus X to the power of three be written in simpler form? explain.
The sum X to the power of two plus X to the power of three be written in simpler form is X² + X³.
What is an exponent?The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number.
For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.
Based on the information given, this will be illustrated as X² + X³. In this case, it illustrate the addition of exponents.
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solve for n. 15n<580.5 ill give 30 points. i need it fast asap
Answer: K 35
Step-by-step explanation:
We're given the inequality : 15n < 580.5
Divide both sides by 15.
-> 15n : 15 < 580.5 : 15
-> n < 38.7
Therefore, the final inequality is : n < 38.7
what condition or conditions must hold true for the sampling distribution of the sample mean to be normal when the sample size is less than 30?
When the sample size is smaller than 30, the following requirements must be met for the sampling distribution of the sample mean to be considered normal:
The data values should be symmetrical in the sample.No outliers should be in sample data .If these conditions are satisfied then the sampling distribution of the sample mean to be normal when sample size is less than 30.
A statistic's sampling distribution is a form of probability distribution produced by selecting several random samples of a predetermined size from the same population. You may better comprehend the variations in a sample statistic by using these distributions.
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A store owner bought dog bowls for $6 and sold them for $8.10. What is the mark-up, as a percentage?
Answer:I am not fully going to do it for you, but here is the best way i can explain, it if not i am sorry.
Step-by-step explanation: Simply take the sales price minus the unit cost, and divide that number by the unit cost. Then, multiply by 100 to determine the markup percentage. For example, if your product costs $50 to make and the selling price is $75, then the markup percentage would be 50%: ( $75 – $50) / $50 = . 50 x 100 = 50%.
if the slope of a line 4/9 the slope of a line perpendicular to this would be
Answer:Use the slope-intercept form to find the slope.
m=4
The equation of a perpendicular line to
y
=
4
x
−
9
must have a slope that is the negative reciprocal of the original slope.
m
perpendicular
=
-1/4
Step-by-step explanation:
hii lily how are u
Given f(x) = -11x² + 5, what is the value of f(4)?
Answer: f(4) = -171
Step-by-step explanation:
To answer this question, we will solve the function for 4. In other words, we will input 4 into the function and simplify. Don't forget the order of PEMDAS when simplifying.
Given:
f(x) = -11x² + 5
Input of 4:
f(4) = -11(4)² + 5
Raise to the power of 2:
f(4) = -11(16) + 5
Multiply:
f(4) = -176 + 5
Add:
f(4) = -171
AB= 8x+2y
BC= 4x+18
encuentra AC
Answer:
Step-by-step explanation:
Thevalueof theAC segmentknown asthe AB and BC segmentsis:
AC = 12x + 2y + 18
What is a segment?
It is the distance or vector obtained from the sum of the differences of the coordinates of the ends of that segment.
AB = B - A
What are mathematical operations?
They are those such as addition, subtraction, multiplication and division, being the most basic and also have the roots, exponents, among others ...
Thesumis addition to one number to another.
Subtraction is subtractingone number from another.
Multiplicationis adding the same number as many times as the multiplier indicates.
Divisionis the decomposition or separation of one number from another.
What is the value of AC?
Assume that AC is the length of the segment containing AB and BC.
AC = AB + BC
Being;
AB= 8x + 2y
BC = 4x + 18
Replace
AC = 8x +2y + 4x + 18
AC = 12x + 2y + 18
solve for x: 4x-3=2x+7
Answer:
x=5
Step-by-step explanation:
Follow the steps in the image.
-Hope this helped
This shows a triangle.
What is the value of x?
43
62
105
115
Answer:
105 degrees
Step-by-step explanation:
Find angle F:
the sum of angles of triangle =180
62+43+y=180
105+y=180
y=75
straight line = 180 degrees
75+x=180
x=105 degrees
What is the slope of the line created by this equation?
Round your answer out to the two nearest decimal places
6x + 9y = 1
Answer:
-0.67
Step-by-step explanation:
What is the slope of the line created by this equation? Round your answer out to the two nearest decimal places. 6x + 9y = 1
_____________________________________________
Slope intercept form solves for y:
y = mx + b when m = slope and b = y-intercept
First, solve for y:
6x + 9y = 1
subtract 6x from both sides:
6x + 9y - 6x = 1 - 6x
9y = 1 - 6x
divide both sides by 9:
9y/9 = (1 - 6x)/9
y = 1/9 - 6/9x
reduce right side:
y = 1/9 - 2/3x
rearrange right side:
y = - 2/3x + 1/9
Back to the equation: y = mx + b when m = slope and b = y-intercept
your slope is -2/3
in decimal form, rounded to two digits: -0.67
probabilities of a part need to be painted and galvanized are 0.20 and 0.30, respectively. what is the probability of the part needs both painted and galvanized?
The probability that the component requires both painting and galvanizing is 0.06.
Considering the values provided in the question,
P(Painted) = 0.20
P(Galvanized) = 0.30
Both the events are independent of each other.
The probability of the part needs both painted and galvanized is
= P(Painted and Galvanized)
= P(Painted) × P(Galvanized)
= 0.20 × 0.30
= 0.06
Therefore, The probability of the part needs both painted and galvanized is 0.06.
The possibility of an event happening is determined by probability. We may need to forecast an event's result in a variety of real-world circumstances. The outcomes of an event may be certain or uncertain to us. In these circumstances, we say if there is a chance the event will happen or not.
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What is -900+16-2^3 ?
Answer: -893
Step-by-step explanation: -900 -(+16) = 884 +(-8) = -893
Answer:
-892
-900+16-2^3=-900+16-8=-900+8=-892
Express as a trinomial.
(2x-8)(2x-2)
Answer:
Step-by-step explanation:
:
The answer is 4x^{2}+12x-16. correct me if im not ty!
Answer:
4x^2 - 20x + 16
Step-by-step explanation:
4x^2 - 4x - 16x + 16
4x^2 - 20x + 16
the price of a 2 liter bottle of sprite holds 67.6 oz and costs $3.38. what is the unit price per oz
The unit of price per oz = 114.2
What is unitary method?The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units. What can be values and units.Let's say you go to the store to buy six apples. You are informed by the shopkeeper that he is offering 10 apples for Rs 100. In this instance, the value and the units are the price of the apples.Recognizing the units and values is crucial when using the unitary technique to a problem.Always write the items that need to be computed on the right side and the things that are known on the left side to simplify things.We are aware of the quantity of apples and the amount of money in the aforesaid problem.According to our question-
the price of a 2 liter bottle of sprite holds 67.6 oz
and costs $3.38.
2 = 67.6
67.6/2= 33.8
33.8*3.38= 114.24
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What is the constant term of h(x) if h(x) = f(x) · g(x)
when f(x) = x - 7 and g(x) = (2x + 3)²?
Main Answer:
The constant term of h(x) is 4x^3 - 16x^2 - 75x - 63\
Supportive Question and Answer:
What is an Algebraic Expression?
An expression that includes variables, constants, and algebraic operations is an algebraic expression in mathematics (addition, subtraction, etc.). Terms combine to form expressions.
Solution Explained:
Given,
h(x) = f(x).g(x)
h(x) = (x-7)(2x+3)^2
now, simplify,
(x-7)(2x +3) Expand the expression
(x-7)((2x)^2+2 X 2x X 3+3^2) Simplify the expression
(x-7)(2^2 X x^2 +2 X 2x X 3+3^2) Calculate
(x-7)(4x^2+2 X 2x X 3 + 9) Mutiply
(x-7)(4x^2 + 12x + 9) Expand the expression
x X 4x^2 + x X 12x + x X 9 - 7 X 4x^2 - 7 X 12x -7 X 9 Mutiply
4x^3 + 12x^2 + 9x - 28x^2 84x - 7 X 9 Calculate
4x^3 + 12x^2 + 9x - 28x^2 - 84x - 63 Combine like terms
Hence, the constant term for h(x) is 4x-16x-75x 63.
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match to form complementary angle pairs. sin(14) cos(37) sin(49) cos(66) sin(41) cos(24)
cos(76) —>
sin(66)—>
sin(53)—>
cos(49)—>
Answer:
see explanation
Step-by-step explanation:
using the cofunction identities
cos x = sin(90 - x)
sin x = cos(90 - x)
then
cos76° = sin(90 - 76)° = sin14°
sin66° = cos(90 - 66)° = cos24°
sin53° = cos(90 - 53)° = cos37°
cos49° = sin(90 - 49)° = sin41°
The Matched values are
cos(76) —> sin (14)
sin(66)—> cos (24)
sin(53)—> cos (37)
cos(49)—> sin (41)
What is Trigonometry?One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.
For complementary angle,
a+ b= 90
So, sin (14)
= cos (90 - 76)
= cos 76
and, cos (37)
=sin (90 - 53)
= sin (53)
and, sin (49)
= cos (90- 41)
= cos 41
and, cos (66)
= sin (90 - 24)
= sin 24
Then, the Matched values are
cos(76) —> sin (14)
sin(66)—> cos (24)
sin(53)—> cos (37)
cos(49)—> sin (41)
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Salem and Eugene, Oregon, are 65 miles apart.If the distance on the map is 31 inches, find the scale of the map.
The scale on the map is of 1 mile: 0.477 inches.
From the question, we have
65 miles - 31 inches
1 mile - x inches
Applying cross multiplication:
65x = 31
x = 31/65
x=0.477
The ratio of inches on a map to feet, miles, or another unit of measurement on the ground is known as the scale.
Scale (map):
The ratio between a distance on a map and its actual distance on the ground is known as the map's scale. Since scale must vary across a map due to the curvature of the Earth's surface, this straightforward idea is made more difficult. This change makes the idea of scale significant in two different ways.
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1. prior to cellular radio, mobile radio and telephone services required: a. a high-power transmitter/receiver b. multiple transmitters/receivers c. only one or two dedicated channels d. that many channels be used, which exceed the frequency capacity
Prior to cellular radio, mobile radio and telephone services required
a. high-power transmitter/receiver.
A radio transmitter, also known as a transmitter, is an electronic device that generates radio waves using an antenna in electronics and telecommunications. The transmitter generates alternating current with a radio frequency that is applied to the antenna. The antenna emits radio waves when it is excited by this alternating current.
Typically, the term transmitter refers to equipment that generates radio waves for communication or radiolocation, such as radar and navigational transmitters. Even though they frequently use similar circuits, radio wave generators for heating or industrial purposes, such as microwave ovens or diathermy equipment, are not typically referred to as transmitters.
Transmitters are required components of all radio-communication devices, including radio and television broadcasting stations, cell phones, walkie-talkies, wireless computer networks, and Bluetooth-enabled devices.
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overbooking: a boeing 767-300 a boeing 767-300 aircraft has 213 seats. when someone buys a ticket for a flight, there is a 0.0995 probability that the person will not show up for the flight (based on data from an ibm research paper by lawrence, hong, and cherrier). how many reservations could be accepted for a boeing 767-300 for there to be at least a 0.95 probability that all reservation holders who show will be accommodated?
7.82 % is probability that all reservation holders who show will be accommodated.
What is probability in math?
Probability refers to potential. The subject of this area of mathematics is the occurrence of random events.The range of the value is 0 to 1. To forecast how likely events are to occur, probability has been introduced in mathematics.If 236 are booked.
and there is only room of 213.
if 214 or 215 or 216 ............ etc
all the way to 236
there won't be enough seats.
P( X = 214 ) = ²³⁶C₂₁₄ * ( 0.9005 ) ²¹⁴ * ( 0.995 )²²
P( X = 214 ) = 0.08439109
= 8.44 %
P( X = 215 ) = ²³⁶C₂₁₅ * ( 0.9005 ) ²¹⁵ * ( 0.995 )²¹
= 0.0781522
= 7.82 %
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3 exponet 4 x (20.3 - 9) + 14.5
The solution to the expression is given as 3 exponent 4 x (20.3 - 9) + 14.5 is 929.8
How to determine solution to the expression?From the question, the expression is given as
3 exponent 4 x (20.3 - 9) + 14.5
When the expression is rewritten, we have the following representation
3⁴ x (20.3 - 9) + 14.5
Evaluate the exponent
So, we have
3⁴ x (20.3 - 9) + 14.5 = 81 x (20.3 - 9) + 14.5
Evaluate the expression in the bracket
3⁴ x (20.3 - 9) + 14.5 = 81 x 11.3 + 14.5
Solving further, we have
3⁴ x (20.3 - 9) + 14.5 = 915.3 + 14.5
Lastly, we have
3⁴ x (20.3 - 9) + 14.5 = 929.8
Hence, the solution is 929.8
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What is the area of the parallelogram shown?
A= In^2
The area of the parallelogram shown is 6.6 square inches.
According to the question,
We have the following information:
We have a parallelogram with base 2.2 inches and height 3 inches.
We know that the following formula is used to find the area of parallelogram:
Area of parallelogram = Base*height
Area of parallelogram = 2.2*3
Area of parallelogram = 6.6 square inches
(Please note that area of any object or figure is always given in square units. For example, it may be square meters, square inches, square feet, etc.)
Hence, the area of the parallelogram shown is 6.6 square inches.
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suppose a sample of a certain substance decayed to 67.8% of its original amount after 300 days. (round your answers to two decimal places.) (a) what is the half-life (in days) of this substance? days
The half-life of this sample is 535.1 days.
Half-life is defined as the time it will took a substance to reduce to half of its initial amount. The half-life of a substance is determined with respect to the rate of the reaction. It can be calculated using the formula below.
N(t) = N₀(1/2)^(t/T)
where N(t) = amount of substance remaining after time t
N₀ = initial amount of substance
t = time
T = half-life
If a sample of a certain substance decayed to 67.8% of its original amount after 300 days, then N(300) = 0.678N₀.
Plug in the given values to the equation.
N(t) = N₀(1/2)^(t/T)
0.678N₀ = N₀(1/2)^(300/T)
0.678 = (1/2)^(300/T)
T = 535.1 days
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Write the following numbers in words form 1. 126.042 2. 64.1027 3. 67,421.004 4. 621.4021 5. 2.4826 6. 372.6218 7. 87.1648 8. 0.4806 9. 1.2761
Find the length and the width.
Answer:
Length would be 6ft
Width would be 4ft
Step-by-step explanation:
24ft^2 is the area as we know 6x4 = 24 and 4 is two less than 6, therefor your answer is 4 and 6.
3 math questions for 50 points.
sophie's favorite number is a two-digit number. if she reverses the digits, the result is $45$ less than her favorite number. the sum of the digits in her favorite number is $11$. what is sophie's favorite number?
Sophie's favorite number is 83
We have that;
A two-digit number is Sophie's preferred number. Her favorite number is 45 less when the digits are in reverse. Her favorite number has digits that add out to 11 in total.
To get Sophie's favorite number, we need to assume the case as;
Let,
⇒10x + y = 10y + x + 45
x + y = 11
y = 11-x
⇒10x + 11 - x = 10(11 - x) + x + 45
10x + 11 - x = 110 - 10x + x + 45
9x + 11 = 155 - 9x
18x + 11 = 155
18x = 144
x = 8
Therefore, y = 11 - 8
y = 3
Sum = x + y = 8 + 3 = 11
Hence, the given condition is satisfied.
Sophie's favorite number is 83.
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a set of bivariate data was used to create a least-squares regression line. which of the following is minimized by the line? responses the sum of the residuals the sum of the residuals the sum of the squared residuals the sum of the squared residuals the sum of the absolute values of the residuals the sum of the absolute values of the residuals the influence of outliers the influence of outliers the slope
The only correct option that is minimized by the least squares regression line is. Option B the sum of the squared residuals.
lets check all the option -
Option A - This claim is untrue because the residuals' summation would provide a value of 0.
Option B - Because error must be kept to a minimum, the residuals must sum to zero and the line must be as close to the points as possible. Prior to summing them, we must first square the residuals, which will always result in a positive value. This option is accurate since the Least Square Regression Line minimizes the total of residuals.
Option C - This choice is incorrect because the least squares regression line cannot be created by adding the absolute values of the residuals.
Option D - This alternative is incorrect since the influence of outliers has nothing to do with the subject at hand.
Option E - Due to slope's lack of relevance to the subject at hand, this choice is also incorrect.
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4 friends want to take a vacation together. Each person has 8 weeks to save $720 for the vacation. Analyze the 4 individual plans below and decide which of the 4 people will reach his or her goal.
a) Friend A: Works 6 hours per week at $13.90 per hour
b) Friend B: Works 7.5 hours per week at $11.70 per hour
c) Friend C: Works 9 hours per week at $10.50 per hour
d) Friend D: Works 5.5 hours per week at $15.60 per hour
The person from the 4 people that will reach his or her goal is Friend C.
How to calculate the amount?Friend A: Works 6 hours per week at $13.90 per hour. The amount in 8 weeks will be:
= 6 × $13.90 × 8
= $667.2
b) Friend B: Works 7.5 hours per week at $11.70 per hour. The amount in 8 weeks will be:
= 7.5 × 11.70 × 8
= $702
c) Friend C: Works 9 hours per week at $10.50 per hour. The amount in 8 weeks will be:
= 9 × $10.50 × 8
= $756
d) Friend D: Works 5.5 hours per week at $15.60 per hour. The amount in 8 weeks will be:
= 5.5 × $15.60 × 8
= $686.40
In this case, C had $756 which is above the amount needed.
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