Step-by-step explanation:
[tex]4 {x}^{2} -5x-6=0 [/tex]
Solve using quadratic formula
Solution:
We know that
[tex] \rm \: Quadratic \: Formula = \cfrac{ - b± \sqrt{ {b}^{2} - 4(ac) } }{2a} [/tex]
ATQ,here,
a = 4b = -5c = -6Substitute the values into the quadratic formula.
[Let Quadratic Formula = x][tex]\rm\implies x = \cfrac{5 ± \sqrt{( - 5) {}^{2} - 4 \times (4 \times - 6) } }{2 \times 4} [/tex]
[tex]\rm\implies{x} = \cfrac{5 ± \sqrt{25 - 4 \times (24) } }{2 \times 4} [/tex]
[tex] \implies \rm \: x = \cfrac{5 ± \sqrt{25 - 96} }{8} [/tex]
[tex] \implies \rm \: x = \cfrac{5± \sqrt{121} }{8} [/tex]
[tex] \implies \rm \: x = \cfrac{5± \sqrt{11 \times 11} }{8} [/tex]
[tex] \implies \rm \: \: x = \cfrac{5±11}{8} [/tex]
The answer will be the combination of both solutions[tex]\boxed{x = 2}[/tex]
OR
[tex]x = \boxed{- \cfrac{3}{4}} [/tex]
A population of beavers decreases exponentially at a rate of 7.5% per year. What is the equivalent monthly rate to the nearest hundredth of a percent
Answer:
0.65%
Step-by-step explanation:
i took the test
Which represents the value of c?
C=
(3) sin(40%)
sin (45°)
c=
(3) sin(45°)
sin (40%)
c=
sin(40%)
(3) sin(45°)
c=
sin(45°)
(3) sin(40%)
Calculate the area of the following composite figure. (Please i need help with this)
The area of the composite shape in the diagram given is: 100 square inches.
How to Find the Area of a Composite Figure?Area of a composite figure = sum of the areas of the shapes that make up the figure.
Area of the composite shape = 2(area of triangle) = 2(1/2bh)
Area of the composite shape = 2(1/2×10×10)
Area of the composite shape = 100 square inches.
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Q: Sam challenges Tom to a race. If Sam can run 6 meters per second and Tom can run at 7 meters per
second. After a minute and a half how far apart will they be?
Answer:
90 meters
Step-by-step explanation:
so, what we know is that there are 90 seconds in one minute and a half.
Sam can run 6 meters per second. which means after 90 seconds, he should have run 540 meters.
Tom can run 7 meters per second. This means after 90 seconds, he should have run 630 meters.
630-540 = 90
give brainliest please!
hope this helps :)
The sum of the lengths of any two sides of a triangle is greater than the length of the third side. What can you conclude about AC in ABC?
BC + AC = 22; AB + BC = 12
Answer:
ab<6 units
Step-by-step explanation:
One of the basic property of any triangle is that the sum of the length of any two sides of a triangle is always greater than the length of the third side. Here we are given a triangle abc, in whicn bc=4ac= 8-abIf have to make some conclusion about ab.As per the property discussed above ab<ac+bcab<8-ab+42ab<12ab<6Hence the length of ab must be less than 6 units
The following cone has a height of 12 cm and a slant height of 16 cm. A right angle is formed between the height and radius of the cone
what is the length of the radius
Step-by-step explanation:
[tex]\pink{\large{\underline{\underline{\sf Given:-}}}}[/tex]
[tex] \sf Height_{\blue{cone}}=12 \: cm [/tex][tex] \sf Slant \: height_{\blue{cone}}=16\: cm [/tex][tex]\pink{\large{\underline{\underline{\sf To \: find:-}}}}[/tex]
[tex] \sf Radius_{\blue{cone}}=? [/tex][tex]\pink{\large{\underline{\underline{\sf Solution:-}}}}[/tex]
We know that,
[tex]\underline{\boxed{\sf (Radius)^2= (Slant height)^2-(height)^2}}[/tex]
[tex] \sf (Radius)^2 = (16)^2-(12)^2[/tex]
[tex] \sf (Radius)^2 = 256-144=112[/tex]
[tex] \longmapsto \sf Radius = \sqrt{112}≈10.6\:cm[/tex]
A craftsperson must attach a lead strip around all four sides of a stained glass window that is
6 4/5 in. by
15 14/25 in. before it is installed. find the length of lead stripping needed.
Answer: 37.9 inch the length of lead stripping .
Step-by-step explanation:
Given ,
Sides of windows are [tex]6\frac{4}{5}[/tex] and [tex]15\frac{14}{25}[/tex]
[tex]= (6\frac{4}{5} + 15 \frac{14}{25} ) * 2\\ \\=\frac{34}{5} + \frac{389}{25} * 2\\\\ \frac{170}{25} + \frac{389}{25}* 2 \\\\= \frac{559}{25} * 2\\\\= \frac{948}{25} \\\\= 37.9 inch[/tex]
So , the answer is 37.9 inch
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The equation in Question 4 shows a relationship between the length of arc EF in circle AB and the radius of circle AB. So, for a given central angle, what does the length of the arc it intersects depend on?
For a given central angle, the length of the arc it intersects depends on the radius of the circle and the central angle.
What is the Length of an Arc?Any smooth curve connecting two points is called an arc. The arc length is the measurement of how long an arc is. The length of an arc is given by the formula,
Length of an Arc = 2π×R×(θ°/360°)
where
θ is the angle, that which arc creates at the center of the circle in degree.
The measurement of the length of an arc formed by a central angle that intersects the circle at two points is given as,
[tex]\rm {Length\ of\ the\ arc} = 2\pi \times \text{Radius of the circle}\times \dfrac{\text{(Measurement of central angle)}}{360^o}[/tex]
Now, the length of the arc EF will be,
Arc EF = 2π × (AB) × (θ/360°)
Where θ is the measurement of the central angle.
Hence, For a given central angle, the length of the arc it intersects depends on the radius of the circle and the central angle.
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Answer: Plato/edmentum sample answer
Step-by-step explanation:
For a given central angle, the length of the arc it intersects depends only on the radius of the associated circle.
The base of a triangular prism is a right triangle with a base of 6 inches, a height of 8 inches, and a third side length of 10 inches. the height of the prism is 14 inches. find the surface area of the prism.
The surface area of the rectangular prism with the dimensions that are stated is: 384 in.²
What is the Surface Area of a Triangular Prism?Surface area = perimeter of base × height of prism + 2(base area)
= (s1 + s2 + s3)L + 2(1/2bh)
Given the following:
side of base (s1) = 6 in.side of base (s2) = 8 in.side of base (s3) = 10 in.Length of prism (L) = 14 in.Triangular base length (b) = 6 in.h = 8 in.Surface area = (6 + 8 + 10)14 + 2(1/2 × 6 × 8)
Surface area = 384 in.²
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the perimeter of a rectangle is 20 cm and it's area is 24cm^2 find the length and breath of the rectangle
Answer:
length = 6cm , breadth = 4cm
Step-by-step explanation:
Let's assume length = l
breadth = b
Given perimeter of a rectangle = 20 cm
2(l+b) = 20
l+b = 20/2
l+b = 10
l = 10 - b____(1)
Given area of rectangle = 24 cm²
l×b = 24____(2)
(1) in (2) => l × b = 24
(10-b) × b = 24
10b - b² = 24
10b = 24 + b²
0 = b² - 10b + 24
b² - 10b + 24 = 0
b² + 6b + 4b + 24 = 0
b(b+6) +4(b+6) = 0
(b+4)(b+6) = 0
b+4 = 0. &. b+6 = 0
b = -4. b = -6
breadth must be less than length and it should be positive
So b = 4 cm
b=4 in (1)
(1)=> l = 10 - b
l = 10 - 4
l = 6
Please help! Giving brainlist!
Evaluate 5(x - 1) - 2 when x = 3
Answer:
8
Step-by-step explanation:
Given algebraic expression:
5(x - 1) - 2
To:
Evaluate this expression using x = 3
Solution:
5(x - 1) - 2Evaluate by plugging x = 3 to this expression:
5(3-1)-2Simplify using PEMDAS.
5(2)-210-28We can conclude:
By evaluating x = 3 to the given expression,the answer will be 8.
Solve for x in the equation x squared 4 x minus 4 = 8.
Answer:
±2√3
Step-by-step explanation:
Equation :
x² -4 = 8
x² -12 = 0
Using the quadratic formula then simplifying gives you :
±2√3
I know this lacks explanation but please brainliest
Answer:
x=2 or -6
Step-by-step explanation:
×^2+4×-4=8
8 will enter inside and become -8
x^2+4x-4-8=0
x^2+4x-12
(x^2+6x)(-2x-12)
x(x+6)-2(x+6)
(x-2)(x+6)
x=2 or x=-6
One day Maria spends 6/20 of the day asleep. Calculate in hours and minutes the amount of time she spends asleep.
Answer:
7 hours and 12 minutes
Step-by-step explanation:
there are 24 hours in a day, so multiply 6/20 by 24 to find the number of hours:
6*24/20 = 36/5 = 7 1/5 hours
we now know maria sleeps for 7 whole hours
next, there are 60 minutes in an hour, so multiply 1/5 by 60 to get 12 minutes
When written in factored form, 4w² -11w-3 is equivalent to
When written in factored form, 4w² -11w-3 is equivalent to (4w+1)(w−3).
What is the factored form of an expression?When an expression is written as a result of the multiplication of some terms, then that multiplication form is called the factored form of that expression.
Example: 6 = 3 x 2 is a factored way of writing 6.
Given expression as
4w² -11w-3
4w²- 12 w− 1w − 3
(4w+1)(w−3)
Thus, the factored form of 4w² -11w-3 is (4w+1)(w−3).
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True or false? The graph represents a function
Answer:
true
Step-by-step explanation:
The statement is true because every graph associated a unique x-value for each y - value
This table shows input and output values for a linear function f(x)
What is the difference of outputs for any two inputs that are three values apart.
Express your answer as a decimal.
The answer is 0.75 because I took the test and that's what the answer was :)
help please and I'll mark you brainiest.
The probability will include:
P(A and 1) = 1/24P(C and 2) = 1/12.P(B and 3) = 1/12.P(A and 4) = 1/12How to calculate the probability?The probability of P(A and 1) will be:
= 1/4 × 1/6
= 1/24
The probability of P(C and 2) will be:
= 1/4 × 2/6
= 1/12
The probability of P(B and 3) will be:
= 2/4 × 1/6
= 1/12
The probability of P(A and 4) will be:
= 1/4 × 2/6
= 1/12
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14 friends go out for dinner and the bill for food and drink comes to £130. The friends decided to add a 5% tip on the top of this total. If they divide this expense equally between them, How much does each friend pay?
The amount each friend does pay is £9.75
How to calculate the pay of each friend using fractions and arithmetic operations?We are going to find 5% of the total amount paid and divide it by the numbers of all the friends to determine the amount paid by each one of them.
From the given information:
The 5% of 130 = £6.5Total amount paid = £130 + £6.5 = £136.5Therefore, the cost of each friend is = [tex]\dfrac{136.5}{14}[/tex]
The cost of each friend = £9.75
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the ratio of Â, B and C in triangle ABC is 2:3:4. calculate the size of each angle
Answer:
40°, 60°, 80°
Step-by-step explanation:
sum the parts of the ratio , 2 + 3 + 4 = 9 parts
the sum of the 3 angles in a triangle = 180° , then
180° ÷ 9 = 20° ← value of 1 part of the ratio , then
2 parts = 2 × 20° - 40° = ∠ A
3 parts = 3 × 20° = 60° = ∠ B
4 parts = 4 × 20° = 80° = ∠ C
so i have 56 8 year old kids in my basement and i auction off 25 of them how many kids do i have left?
Answer:
none because i boiled them all
Step-by-step explanation:
Answer:
31 kids
Step-by-step explanation:
56-25=31
Find a fraction equivalent to 5/7 whose squared terms add up to 1184.
The system of equations of two unknowns is formulated and solved.
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}[/tex]
[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20 } \end{gathered}$}[/tex]
The fraction that satisfies the request is [tex]\bf{\dfrac{20}{28}}[/tex] , since in [tex]\bf{\dfrac{-20}{-28}}[/tex] the negative signs are canceled and the first fraction is obtained.
If ten rolls of tape cost $30, how much will 12 rolls cost?
Answer:
Step-by-step explanation:
10 rolls = $30
12 rolls = ...
Because $3 for each roll of tape, so 3 x 10 = 30. All we have to do is multiply 3 by 12 to get how much for 12 rolls.
36.
I need help
30 POINTS!!!!
Answer:
A. Upward
B. (-2, -1)
C. X= -3, -1 ||| Y= 3
D. X=-2
Step-by-step explanation:
Write the equation of the line that passes through the points (-3,3) and (4, -1).
put your answer in fully reduced point-slope form, unless it is a vertical or horizontal
line,
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{-1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-1}-\stackrel{y1}{3}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}} \implies \cfrac{-4}{4 +3} \implies \cfrac{ -4 }{ 7 }[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{-\cfrac{4}{7}}(x-\stackrel{x_1}{(-3)})\implies y-3=-\cfrac{4}{7}(x+3)[/tex]
A lake near the Arctic Circle is covered by a thick sheet of ice during the cold winter months. When spring arrives, the warm air gradually melts the ice, causing its thickness to decrease at a rate of 0.2 meters per week. After 7 weeks, the sheet is only 2.4 meters thick.
Let y represent the ice sheet's thickness (in meters) after x weeks.
Complete the equation for the relationship between the thickness and number of weeks.
y=_____
The equation for the relationship between the thickness and number of weeks is y = 3.8 - 0.2x
How to write equation?Ice lost per week = 0.2 metersIce remaining after 7 weeks = 2.4 metersNumber of weeks = xRelationship between the thickness and number of weeks = yIce lost at 7 weeks = 7(0.2) = 1.4 meters
Total thickness of ice before loss = Ice remaining after 7 weeks + Ice lost at 7 weeks
= 2.4 + 1.4
= 3.8 meters
The equation:
y = Total thickness of ice before loss - (Ice lost per week × Number of weeks)
= 3.8 - (0.2 × x)
y = 3.8 - 0.2x
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the average wieght of three children a b and c is 60 lbs if another child D is included in the grouo in the place of C the average weight of the group becomes 54 lb what is
The weight of the last child is 36 lbs.
How to calculate the mean?The average weight of the three children is 60 lbs. The total weight will be:
= 60 × 3
= 180 lbs.
When another child is added, the weight is 54lb. The total weight will be:
= 54 × 4
= 216 lbs
The weight of the last child will be:
= 216 - 180
= 36 lbs.
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Sofia's audio player has 15,000 songs. the play time for the songs is skewed to the right, with a mean of 255 seconds and a standard deviation of 30 seconds. part a: can you accurately calculate the probability that the mean play time is more than 260 seconds for an srs of 15 songs? explain. (4 points) part b: if you take a random sample of 40 songs instead of 15, explain how the central limit theorem allows you to find the probability that the mean play time is more than 260 seconds. calculate this probability and show your work. (6 points)
Using the normal distribution and the central limit theorem, it is found that:
a) Since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.
b) There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.
Normal Probability DistributionThe z-score of a measure X of a normally distributed variable with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex] is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score measures how many standard deviations the measure is above or below the mean. Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex], as long as the underlying distribution is normal and the sample size is at least 30.The mean and the standard deviation are given by, respectively:
[tex]\mu = 255, \sigma = 30[/tex]
In item a, according to the Central Limit Theorem, since the distribution is skewed and the sample size is less than 30, the probability cannot be calculated.
For item b, we have that n = 40 > 15, hence the standard error is given by:
[tex]s = \frac{30}{\sqrt{40}} = 4.74[/tex]
The probability is one subtracted by the p-value of Z when X = 260, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{260 - 255}{4.74}[/tex]
Z = 1.05
Z = 1.05 has a p-value of 0.8531.
1 - 0.8531 = 0.1469.
There is a 0.1469 = 14.69% probability that the mean play time is more than 260 seconds.
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Yuson must complete 15 hours of community sevice. She does 3 hours each day. Which linear equation represents the hours Yuson still has to work after x days?
A. Y=3x + 15
B. Y= -3x - 15
C. Y= -3x + 15
D. Y= 3x - 15
Answer:
C) y = -3x + 15
Step-by-step explanation:
Let's start with the hours required, 15. For each day worked we can subtract 3 hours. X days would mean 3x hours. Subtract that from the goal of 15 hours:
15 - 3x
The time remaining, y, is given by the equation 15 - 3x.
Rearrange the equation to match the format in the options,
y = 15 - 3x
y = -3x + 15
Option C
If y=2x-1 is changed to y = x+ 2,
how would the graph of the new
function compare with the first one in terms of steepness and shift?
The graph of the function y = x+2 is steeper than the graph y = 2x-1.
What is a graph?A graph is the representation of the data on the vertical and horizontal coordinates so we can see the trend of the data.
Given functions are:-
y=2x-1y = x+2The graph of the functions is attached with the answer below. In the graph, we can see that the slope of the graph y = x+2 is steeper than the graph of y = 2x - 1.
The two graphs intersect at the point ( 3,5 ) so it is the solution of the two linear equations.
Hence the graph of the function y = x+2 is steeper than the graph y = 2x-1.
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