Answer:
a = ± [tex]\sqrt{\frac{2d-2c}{b} }[/tex]
Step-by-step explanation:
c + [tex]\frac{1}{2}[/tex] a²b = d ( multiply through by 2 to clear the fraction )
2c + a²b = 2d ( subtract 2c from both sides )
a²b = 2d - 2c ( divide both sides by b )
a² = [tex]\frac{2d-2c}{b}[/tex] ( take square root of both sides )
a = ± [tex]\sqrt{\frac{2d-2c}{b} }[/tex]
Determine the smallest integer value of x in the solution of the following inequality.
-4x - 1 ≤ 13
Answer:
-3.5
Step-by-step explanation:
-4x-1+1≤ 13+1
-4x/-4 ≤ 14/-4
x≤ -3.5
Sylvia Okumbe is trying to break her national record of 14 minutes 35 seconds
for running 5000 m (12 1/2 laps of the track). Her average time per lap for the
first 5 laps is 1 minute 13 seconds. What average lap time does she need for
the remaining 7 1/2 laps?
Enter your answer as a number in seconds. Only type the number of seconds -
no spaces or words
Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
What is Time, Speed and Distance?Time is the duratiοn between twο events, speed is the rate at which distance is cοvered per unit time, and distance is the amοunt οf space between twο οbjects οr pοints.
Sylvia has cοmpleted the first 5 laps in a tοtal time οf 5 x 73 secοnds = 365 secοnds.
Tο break the natiοnal recοrd οf 14 minutes 35 secοnds (οr 875 secοnds) fοr running 5000m, Sylvia has 5000m - 5 laps (οf 400m each) = 3000m remaining tο run, which is equivalent tο 7.5 laps (since each lap is 400m).
Let's say Sylvia needs tο cοmplete the remaining 7.5 laps in x secοnds.
Tο break the natiοnal recοrd, the tοtal time fοr running 12.5 laps (οr 5000m) shοuld be 875 secοnds οr less. Sο, we can set up the fοllοwing equatiοn tο find the required average lap time fοr the remaining 7.5 laps:
365 secοnds + 7.5x secοnds ≤ 875 secοnds
Subtracting 365 secοnds frοm bοth sides gives:
7.5x secοnds ≤ 510 secοnds
Dividing bοth sides by 7.5 gives:
x secοnds ≤ 68 secοnds
Sο, Sylvia needs tο cοmplete the remaining 7.5 laps in an average time οf 68 secοnds οr less tο break the natiοnal recοrd.
Therefοre, the answer is 68 secοnds.
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How do i solve this equation? 4x - 2y > 12
As per the given equation in form of inequality 4x - 2y > 12 gives the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.
As given in the question,
Given equation in inequality form is :
4x - 2y > 12
Simplify the given equation in intercept form we get,
2y < 4x -12
⇒ y < 2x -6
If we write this inequality in equation form we have,
y = 2x -6
slope of the line is 2
x -intercept is x = 3
y - intercept is y = -6
And in inequality form x > 3 and y < -6.
Therefore, for the given equation in form of inequality 4x - 2y > 12 gives the solution in intercept form as y < 2x -6, and for the given inequality x-intercept is x > 3 and y-intercept is y <-6 with slope equal to 2.
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Verify experimentally that the diagonals of a square are equal to each other.
The diagonals of a square are equal to each other
Let ABCD be a square.
We need to prove that the diagonals are equal to each other
AC=BD and AC and BD bisect each other at right angles
(i) Considering the ΔABC and ΔBAD,
AB=AB ( common line)
BC=AD ( opppsite sides of a square)
∠ABC=∠BAD ( = 90° )
ΔABC≅ΔBAD( By SideAngleSide property)
AC=BD ( by CPCT).
(ii) Now in triangles ΔOAD and ΔOCB,
AD=CB ( opposite sides of a square)
∠OAD=∠OCB ( transversal AC )
∠ODA=∠OBC ( transversal BD )
ΔOAD≅ΔOCB (ASA property)
OA=OC ---------(i)
Similarly OB=OD ----------(ii)
From (i) and (ii) we can conclude that AC and BD bisect each other.
Now in a ΔOBA and ΔODA,
OB=OD ( from (ii) )
BA=DA
OA=OA ( common line )
ΔAOB=ΔAOD----(iii) ( by CPCT
∠AOB+∠AOD=180° (linear pair)
2∠AOB=180°
∠AOB=∠AOD=90°
Therefore, it is proved that AC and BD bisect each other at right angles.
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Can someone please help with five?
Answer:
-3,-2,-1,0,1
Step-by-step explanation:
Just replace x with the x value to find the y value
y=x-1
y=-2-1
y=-3
Y=-1-1
y=-2
y=0-1
y=-1
y=1-1
y=0
y=2-1
y=1
hopes this helps please mark brainliest
Justify each of the following manipulations to multiply two binomials by filling in the blanks with the associative property the commutative property or the distribution (3x+5)(2x+7)=2x(3x+5)+7(3x+5) helpppp!!
The property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
In this question we have been given an expression.
We need to identify the property that is used to multiply two binomials.
(3x+5)(2x+7)=2x(3x+5)+7(3x+5)
Consider two binomials,
(3x+5)(2x+7)
= (2x+7)(3x+5) ...............(commutative property)
= 2x(3x+5)+7(3x+5) ................(distributive property)
Therefore, the property that is used to multiply two binomials (3x+5)(2x+7)=2x(3x+5)+7(3x+5) is distributive property.
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What are some ways we have learned to solve percent increase or percent decrease problems? How are these ways related to one another?
The different ways of solving percent increase or percent decrease problems has been described below
What is percentage?
Suppose there is a number and the number has to be expressed as a fraction of 100. The fraction is called percentage.
One way to solve the percentage increase or decrease problem is by multiplying the original number by the percentage given and then adding the result with the original number.
Another method is by multiplier method
Here, the original number is taken as 1 and the given percentage has to be converted to decimal and then 1 and the percentage obtained as decimal is added or subtracted. The result obtained has to be multiplied by the original number to get the required number after increase or decrease
For the first method
Suppose the number is n and it is increased by p%
Required result is
[tex]n + \frac{p}{100}\times n\\n( 1 + \frac{p}{100})[/tex]
For the second method
Suppose the number is n and it is increased by p%
Here n is taken as 1 and p% is converted to decimal
then 1 and p% in decimal form is added
we get (1 + 0._p)
Now the result is obtained is multiplied by n
Required result is
n(1 + 0._p)
[tex]n(1 + \frac{p}{100})[/tex]
In this way the two methods are related
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find the median of the following: 14.8, 16.2, 4.8, 12.1, and 6.9. if needed, round your answer to the nearest tenth.
The mean will be the middle number or 12.1.
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.According to our question-
The median is the middle number in the data set when the data set is written from least to greatest.
least to greatest 4.8, 6.9, 12.1, 14.8, 16.2
Hence, The mean will be the middle number or 12.1.
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the mayor of a town has proposed a plan for the construction of an adjoining community. a political study took a sample of 1600 voters in the town and found that 34% of the residents favored construction. using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is over 31%. find the value of the test statistic. round your answer to two decimal places.
The value of the test statistic is 2.59.
What is Test Statistics?A number derived from a statistical test of a hypothesis is the test statistic. It displays how closely your actual data fit the distribution predicted by the statistical test's null hypothesis.
Here, the percentage of residents favored construction is 34%.
[tex]p\leq 0.31\\p > 0.31[/tex]
The test statistics is given by,
[tex]Z=P-\frac{p}{\sqrt{p(1-p)n} }[/tex]
Here n=1600, P=0.34 and p=0.31,
Putting the values,
[tex]Z=0.34-\frac{0.31}{\sqrt{0.31(1-0.31)1600} }\\=2.59[/tex]
Test Statistics = 2.59
Therefore, the value of test statistics is 2.59.
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PLEASE HELP 69 POINTS
Triangle A has vertices (−2, 1), (1, 1), and (1, 0).
Which triangle is similar to triangle A?
Responses
Triangle Y with vertices (−4, 3), (2, 3), and (2, 2)
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)
Triangle X with vertices (−2, 2), (1, 2), and (1, 0)
Triangle Z with vertices (−4, −1), (2, −1), and (2, −2)
The triangle with vertices (−2, 1), (1, 1), and (1, 0) is similar to
Triangle W with vertices (−4, 2), (2, 2), and (2, 0)What are similar triangles?This is a term used in geometry to mean that the respective sides of the triangles are proportional and the corresponding angles of the triangles are congruent
Hence assuming the corresponding angles of the triangle are congruent then the side should be in proportions.
Examining the vertices shows that; Triangle W with vertices (−4, 2), (2, 2), and (2, 0) is in proportion to the given vertices (−2, 1), (1, 1), and (1, 0)
The difference is a scale factor of 2
(−2, 1) * 2 = (−4, 2)
(1, 1) * 2 = (2, 2)
(1, 0) * 2 = (2, 0)
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determine if line AB and line CD are parallel, perpendicular or neither
Answer:
Line 1 is considered perpendicular
Line 2 is considered parallel
Line 3 is also parallel
Step-by-step explanation:
This should be right if this is the rest to your problem:
1. Line AB formed by A(-1,3) and B(1,5); Line CD formed by C(2,3) and D(-2,7)
2. Line AB formed by A(3,8) and B(-6,5); Line CD formed by C(-6,7) and D(-3,8)
3. Line AB formed by A(2,-7) and B(2,3); Line CD formed by C(-4,0) and D(-4,-5)
the difference between two numbers is 8. The lesser number is a. Write an expression for the greater number.
The expression is x - a = 8.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Difference between two numbers is 8.
The lesser number is a.
let the another number be 'x'.
So, Difference between two numbers
x - a = 8
Hence, the expression is x - a = 8.
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the food and drug administration (fda) is a u.s. government agency that regulates (you guessed it) food and drugs for consumer safety. one thing the fda regulates is the allowable insect parts in various foods. you may be surprised to know that much of the processed food we eat contains insect parts. an example is flour. when wheat is ground into flour, insects that were in the wheat are ground up as well. the mean number of insect parts allowed in 100 grams (about 3 ounces) of wheat flour is 75. if the fda finds more than this number, they conduct further tests to determine if the flour is too contaminated by insect parts to be fit for human consumption. the fda takes a random sample of 35 bags of flour for evaluation and finds that they contain an average of 80 insect parts per 100 grams, with a standard deviation of 6.3. which hypothesis test should be used to determine whether the sample contains more than the allowed 75 insect parts per 100 grams?
From the information, observe that the food and drug Administration is a US government agency that regulates food and drugs for customer safety.
One thing the FDA regulates is the allowable insect parts in various foods.
When wheat is ground into the flour, insects that were in the wheat are ground up as well.
The mean number of insect parts allowed in 100 grams of wheat flour is 75
The FDA takes a random sample of 35 bags of floor for evaluation and finds that their average of 80 insect parts per 100 grams with a standard deviation of 6.3
In this situation use t test for population mean because the population standard deviation is not known.
Hence, the correct option is (2).
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= y = 3x - 4? help me pls
Answer:
Step-by-step explanation: add 4 to cancel out, dive both sides by 3, y=1.3 repeating
Write an equation perpendicular to y =− 3x + 2 and passes through the point (0, 8).
Answer:
y = [tex]\frac{1}{3}[/tex] x + 8
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 2 ← is in slope- intercept form
with slope m = - 3
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-3}[/tex] = [tex]\frac{1}{3}[/tex]
the line crosses the y- axis at (0, 8 ) ⇒ c = 8
y = [tex]\frac{1}{3}[/tex] x + 8 ← equation of perpendicular line
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeee pleaseeeee rn rnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The number of bicycles that must be manufactured to minimize the cost of 250 and the minimum cost is $11,500.
In the given question,
The cost C in dollars of manufacturing x bicyles at a production plant is given by the function shown below;
C(x) = 3x^2-1500x+199,000
(a) In the given question we have to find the number of bicyles that must be manufactured to minimize the cost.
The given function is
C(x) = 3x^2-1500x+199,000
To find the maximum or minimum value we firstly find the value of f'(x).
C'(x) = 6x-1500
Now put f'(x)=0
6x-1500=0
Add 1500 on both side, we get
6x=1500
Divide by 6 on both side we get
x=250
Hence, the number of bicycles that must be manufactured to minimize the cost of 250.
(b) Now finding the value of function at x=250
C(250) = 3(250)^2-1500*250+199,000
C(250) = 3*62,500-375,000+199,000
C(250) = 187,500-375,000+199,000
C(250) = 11,500
The minimum cost is $11,500.
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A plane has a cruising speed of 200 miles per hour when there is no wind. At this speed, the plane flew 500 miles with the wind in the same
amount of time it flew 300 miles against the wind. Find the speed of the wind.
The speed of the wind is 50 mile per hour .
In the question ,
it is given that
the speed of the plane is [tex]=[/tex] 200 miles per hour .
let the speed of the wind is = "w"
So ,the speed of the plane with wind is [tex]=[/tex] 200 + w
and the speed of the plane against wind is [tex]=[/tex] 200 - w
we know that , distance [tex]=[/tex] speed × time
the plane flew "500 miles" with wind ,
which means ,
500 [tex]=[/tex] (200 + w) × t .....(1)
and the plane flew 300 miles against the wind ,
which means ,
300 [tex]=[/tex] (200 - w) × t ......(2)
adding both the equations ,
we get
800 [tex]=[/tex] t ( 200 [tex]+[/tex] w [tex]+[/tex] 200 - w)
800 = t × 400
t = 2
Substituting , t = 2 in 500 [tex]=[/tex] (200 + w) × t
we get
500 = (200 + w) × 2
500/2 = 200 + w
250 = 200 + w
w = 250 - 200
w = 50
Therefore , The speed of the wind is 50 mile per hour .
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Determine the next three terms in the following sequence:
2, 3, 5, 8, ____, ____, ____,...
a.
13, 19, 26
b.
12, 17, 23
c.
12, 16, 20
d.
13, 17, 23
Answer:
b. 12, 17, 23
Step-by-step explanation:
Look at the differences between the numbers.
Number Difference
2
3 1
5 2
8 3 The difference increase by 1 at each step. The next 3 increase would be:
4
5
6
The next three numbers are:
12 4
17 5
23 6
Answer:
b.
12, 17, 23
Step-by-step explanation:
Como puedo Terminar la sucesion asta el decimo termino 3.8 +2.7
The addition of the decimals given as 3.8 and 2.7 will be 6.5.
What are decimals?Decimals simply means the numbers that are not whole numbers. They consist of whole numbers and fractions. Examples include 3.6, 2.1 eyc.
In this case, we want to find the value of 3.8 and the addition to 2.7. This will be:
= 3.8 + 2.7
= 6.5
Therefore, the value is 6.5.
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A car originally is worth $3000. It is decreasing in value by 3% every year. How much is it worth in 3 years.
(Round to the nearest cent)
Answer: $2738.02
Step-by-step explanation:
1) (3000x0.97) = 2910 } Year 1
2) (2910x0.97) = 2822.7 } Year 2
3) (2822.7x0.97) = 2738.019 } Year 3
in a two-factor anova, if there is a significant interaction effect, what should be your interpretation for the main effects of factor a and factor b?
In two - factor ANOVA , if there is significant interaction effect then Not necessary that main effects of both factors a and b is significant.
A two- way ANOVA (analysis of variance) is a statistical test used to analyze the difference in means of three or more groups.
Two-Way ANOVA is used to estimate how the mean of a quantitative variable varies according to the levels of two categorical variables. Use two-way ANOVA when you want to know how the combination of two independent variables affects the dependent variable.
Interaction effects occur when the effect of one variable depends on the value of another variable. Interaction effects are common in ANOVA and designed experiments.
We see that interaction effect in ANOVA test is significant . but interaction effect significant is not implies the significance of main effects of factors a and b. So, we conclude that main effects of factor a and b need not be significant.
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PLEASE HELP ME!!!!!!!!!!!!!!
The equivalents of the functions are f(x)+g(x) = -2x²-x+6, g(x) - f(x) = -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6
How to match the function operation with its equivalent value?A function is a relationship between inputs where each input is related to exactly one output. Every function has a domain and codomain or range. A function is generally denoted by f(x) where x is the input
Given: f(x) = 3x + 2, g(x) = -2x²-2x+4 and h(x) = 3x²-4x
To solve this problem, just substitute the value of the function and perform the necessary operations on them.
f(x)+g(x) = (3x+2) + (-2x²-2x+4)
= 3x+2-2x²-2x+4
= -2x²-x+6
g(x) - f(x) = (-2x²-2x+4) - (3x+2)
= -2x²-2x+4-3x-2
= -2x²-5x+2
f(x).g(x) = (3x+2)(-2x²-2x+4)
= -6x³-6x²+12x -4x²-4x+8
= -6x³-10x²+8x+8
h(x) - f(x) = (3x²-4x) - (3x + 2)
= 3x²-4x-3x-2
= 3x²-7x-2
f( x) . h(x) = (3x + 2)(3x²-4x)
= 9x³-12x²+6x²-8x
= 9x³-6x²-8x
f(x)+g(x)+h(x) = (3x + 2) + (-2x²-2x+4) + (3x²-4x)
= 3x+2-2x²-2x+4+3x²-4x
= x²-3x+6
Therefore, the equivalents are f(x)+g(x) = -2x²-x+6, g(x) - f(x) = -2x²-5x+2, f(x).g(x) = -6x³-10x²+8x+8, h(x)-f(x) = 3x²-7x-2, f(x).h(x) = 9x³-6x²-8x and f(x)+g(x)+h(x) = x²-3x+6. You should match them accordingly
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A pot of soup, currently 74°C above room temperature, is left out to cool. If that temperature
difference decreases by 5% per minute, then what will the difference be in 14 minutes?
If necessary, round your answer to the nearest tenth.
°C
Answer:36.1
Step-by-step explanation:
ixl
students and courses have ....... relationship: a. one to one b. one to many c. many to many d. none. mcq answer
The students and courses have one to many relationship.
A one to many relationship is such kind of relation which exist when a particular function is linked to many other functions. It means that many elements of the set A is related to a single element of the set B.
In this case, the course is only one but the students studying the course are more in number. The same course is studied by many student but in different manner but the course is same. This is why we conclude that the relationship between the students and the course is one to many.
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Simplify negative 1 and 2 over 3 minus 9 and 2 over 5.
11 and 1 over 15
negative 10 and 4 over 8
negative 16 over 15
negative 166 over 15
The simplified form of the given expression; negative 1 and 2 over 3 minus 9 and 2 over 5 as required is; -166/15 (negative 166 over 15).
What is the simplified form of the expression?It follows from the task content that the simplified form of the given expression is to be determined.
Since the given expression is; -1 ⅔ - 9 ⅖.
First, the mixed numbers as in the task content must be converted to fractions so that we have;
- 1 ⅔ = -5/3 and
9 ⅖ = 47/5
Therefore, the required evaluation is; -5/3 - 47/5
= -25/15 - 141/15
= (-25 - 141) / 15
= -166/15
Therefore, the required simplified form of the expression is; negative 166 over 15.
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Add/Subtract Rational Numbers :
Add ; -1/2 + 2/3 (Simplify)
Evaluate ; -1/8 - (-5/6) (Simplify)
Can someone help I don’t understand??
Answer:
What you need to do is match with one is a regular, irregular, and or not a polygon.
Each shape has a label like A is a triangle and so on
Put the Label of the shape where it belongs inside the chart
Answer:
If all the sides and interior angles of the polygons are equal, they are known as regular polygons.
C and E are regular polygons.
Irregular polygons are those types of polygons that do not have equal sides and equal angles.
A, B and F are irregular polygons.
3D shapes are irregular polygons.
D is an irregular polygon.
Step-by-step explanation:
L, M and N are points on a circle, centre O.
QMT is the tangent at M
(1) find LNOM
(2) find LNMQ
Please help me guys it urgent it would really make my day.
The size if the angle NOM is 54.
What is angle?
An angle is formed when two straight lines or rays meet at a common endpoint. The common point of contact is called the vertex of an angle.
What is tangent of circle?
A Tangent of a Circle is a line that touches the circle’s boundary at exactly one point. The tangential point is the place where the line and the circle meet.
Given,
M and N are points on a circle.
QMT is the tangent
O is the center.
angle NOM = 2 angle NLM
NOM = 2(27)
= 54.
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PLEASE ANSWER THE QUESTIONS BELOW.. A PICTURE WILL BE PROVIDED ABOVE^^^^^
1: RADIUS FOR NEW TANK?
2. EXISTING VOLUME?
3.SPHERE VOLUME?
4. TOTAL VOLUME?
5. NEW TANK VOLUME?
6. TRIAL OF VALUES FOR R?
1) Radius of the standard tank = 3 feet
2) Existing volume for the tank is 126[tex]\pi[/tex] cubic feet.
3) Sphere volume for the tank is 36[tex]\pi[/tex] cubic feet.
4)Total volume of the tank is 36[tex]\pi[/tex] + 126[tex]\pi[/tex] = 162[tex]\pi[/tex] cubic feet
5) New volume for the tank is 252[tex]\pi[/tex] cubic feet.
6)Trails of values for r is 4 feet.
What do you mean by Volume?
A three-dimensional object's volume, expressed in cubic units (such as inches, quarts, or centimeters): cubic volume. the volume that a material takes up in a given space.
What is radius?
A line segment connecting the circumference or boundary surface of a circle or sphere to its center.
Given that;
Volume of the standard tank [tex]= \pi r^2h + \frac{4}{3} \pir^3[/tex]
[tex]= \pi 3^2h + \frac{4}{3} \pi3^3\\= 90\pi +36\pi\\= 126\pi \ cubic \ feet[/tex]
Volume of new tank = 2 x Volume of standard tank
= 2 x 126π
= 252π
But according to formula, volume of new tank will be;
[tex]V = \pi r^2h + \frac{4}{3}\pir^3[/tex]
where r = radius of new tank
[tex]\pi r^2 \times 10 + \frac{4}{3} \pi r^3 = 252 \pi\\30r^2 +4 r^3 = 756\\2r^3 + 15r^2-378 = 0\\r = 4.04591\\r \approx 4 feet[/tex]
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Please Help Me, I need an answer ASAP.
The measure of < BAP in the figure of the circle is 30 degrees
How to find < BAP< ACB covers same angle as < APB
therefore
< ACB = < BAP = 120
complete the line PB to form another radius. since radius of a circle are equal, an isosceles triangle is created
Isosceles triangle has a unique property of 2 equal equal sides and equal base angles. one of the angles of the isosceles triangle is < BAP
solving with the new triangle APB
< BAP = < PBA (base angles of isosceles triangle)
< BAP + < PBA + 120 = 180
2 < BAP = 180 - 120
2 < BAP = 60
< BAP = 30 degrees
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