The solutions of the given quadratic equation are:
[tex]x = \frac{-7 + \sqrt{17} }{2} \\\\x = \frac{-7 - \sqrt{17} }{2}[/tex]
How to get the solutions of the quadratic equation?
Here we have the quadratic equation:
[tex]x^2 = -7x - 8[/tex]
To solve it, we can rewrite it as:
[tex]x^2 + 7x + 8 = 0[/tex]
Now if we use Bhaskara's formula, we get the solutions:
[tex]x = \frac{-7 \pm \sqrt{(7)^2 - 4*1*(8)} }{2} \\\\x = \frac{-7 \pm \sqrt{17} }{2}[/tex]
Then the two solutions are:
[tex]x = \frac{-7 + \sqrt{17} }{2} \\\\x = \frac{-7 - \sqrt{17} }{2}[/tex]
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a group of students is collecting books to add to their library. the table shows the number of books in the library after 1, 3, and 5 days. if the relationship between days and books continues to be linear, which ordered pairs could appear in the table? check all that apply.
The options B and E are the correct answer.
We have given that,
A group of students is collecting books to add to their library.
The table shows the number of books in the library after 1, 3, and 5 days. if the relationship between days and books continues to be linear
We have to determine which ordered pairs could appear in the table.
What is the linear points?
The graph of the linear equation is a set of points in the coordinate plane that all are solutions to the equation.
If all variables represent real numbers one can graph the equation by plotting enough points to recognize a pattern and then connect the points to include all points.
B and E are the correct answer. Because (2,23) and (7,48) are linear.
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What is the value of f(x) when x=3?
Which polynomial are in standard form
Answer:
A and C
Step-by-step explanation:
Exponent from biggest to lowest
The manager at Jessica's Furniture Store is trying to figure out how much to charge for a couch that just arrived. The couch was bought at a wholesale price of \$113.00$113.00dollar sign, 113, point, 00, and Jessica's Furniture Store marks up all furniture by 45%, percent.
Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.
How much should the manager charge for the couch that just arrived?Given that;
Purchase price = $113.00 marks up = 45%Selling price = ?First, we determine the mark price.
Since the Furniture Store marks up all furniture by 45%.
Mark up price = mark up × purchase price
Mark up price = 45% × $113.00
Mark up price = 0.45 × $113.00
Mark up price = $50.85
Now, the selling price will be;
Selling price = Purchase price + mark up price
Selling price = $113.00 + $50.85
Selling price = $163.85
Given the mark up of all furniture in the store, the price that the manager should charge for the couch that just arrived is $163.85.
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The slope of a line is 7/8 The y-intercept of the same line is 4
Complete the slope-intercept form equation
Answer:
y = -7/8x + 4
Step-by-step explanation:
Slope-intercept form :
y = mx + b
m = slopeb = y-interceptHence, the equation formed is :
y = -7/8x + 4A parallelogram has a base of 16 centimeters and a height of 12 centimeters. What is the area of the parallelogram?
I think it's 192, am I correct?
Answer:
Correct (192)
Step-by-step explanation:
The formula for a parallelogram's area is just base times height. 16x12 is equal to 192, so you are correct.
A parallelogram can be:
The square, which has all its sides of equal length, and all its angles are right angles. The rhombus, which has all sides of equal length, and only two pairs of congruent angles. The rectangle, which has only its opposite sides of equal length, and all its angles are right angles.Therefore we calculate the rectangle of a square, which is a parallelogram.
To start solving, we obtain the following data:
Area = 16cmHeight = 12cmArea = ? ===> (It is the result that we are going to obtain)The formula to calculate the area is:
[tex]\bf{a=b*h }[/tex]
To calculate the area, multiply the base by the height (which is represented in "h")
We clear formula, calculate the area:
[tex]\bf{A=(16 \ cm)(12 \ cm) \ \ \ ==== > \ Multiply }[/tex]
[tex]\bf{A=192 \ cm^{2} }[/tex]
Answer: The area of the parallelogram is 192 cm2. So if you're right, it was a rectangle.
Slope of (-9,-2) and (-9,-6)
Answer:
Slope is undefined.
Step-by-step explanation:
A company has a budget of $1,700 for a banquet. A banquet hall charges $150 to rent a room, plus $30 per guest. What is the maxiumum number of guests that can attend the banquet for the costs to remain under the budget?
Answer:
51 guests
Step-by-step explanation:
150+30x
1700=150+30x
1550=30x
x=1550/30=51
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I NEED THE ANSWER STEP BY STEP.
find the smallest number by which 1323 must be divided so as to get a perfect square number. Also, find the square root of the square number so obtained.
Answer:
It is 49. You will know it is right down here:
Step-by-step explanation:
1323 when factorised = 3 *3*3*7*7
Therefore it is to be divided by 7*7 = 49
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What is the phenotypic ratio of the offspring? 1:1:1:1:2:2:2:2:4 1:3:3:9 1:4 4:12
The phenotypic ratio of the offspring as shown in the given Punnett square is: 1:3:3:9.
What is Phenotypic Ratio?Phenotypic ratio is quantitative relation of the number of offspring of a cross that manifest a certain combination of traits or characteristic.
From the Punnett square given, there are:
9 round and yellow individuals3 round and green individuals3 wrinkled and yellow individuals1 wrinkled and green individualsTherefore, the phenotypic ratio would be: 1:3:3:9.
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Answer:
B it the answer 1:3:3:9
Step-by-step explanation:
In a statistics activity, students are asked to determine the proportion of times that a spinning penny will land with tails up. the students are instructed to spin the penny 10 times and record the number of times the penny lands tails up. for one student, it lands tails side up six times. the student will construct a 90% confidence interval for the true proportion of tails up. are the conditions for inference met?
Using the Central Limit Theorem, it is found that the conditions for inference are not met, as there are less than 10 successes and less than 10 failures.
What does the Central Limit Theorem state?It states that for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].
In this problem, we have that np = 6 < 10, n(1-p) = 4 < 10, hence the conditions for inference are not met.
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a five question multiple choice quiz has five choices for each answer. use the random number table provided, with 0's representing incorrect answers, and 1's representing correct answers to answer the following question: what is the experimental probability of correctly guessing at random exactly zero correct answers?
The experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵
What is Probability?Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.
Here, total multiple choice quiz = 5 questions
Each question contains 5 choices in which 1 choice is correct and remaining 4 are incorrect.
Possibility of first wrong choice = 4/5
Possibility of second wrong choice = 4/5
Possibility of third wrong choice = 4/5
Possibility of fourth wrong choice = 4/5
Possibility of fifth wrong choice = 4/5
Overall probability for Zero correct answer=(4X4X4X4X4)/(5X5X5X5X5)
= (4/5)⁵
Thus, the experimental probability of correctly guessing at random exactly zero correct answers is (4/5)⁵
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When θ = 0, cos θ = 1. What is the next radian value that will result in cos θ = 1?
A coffee table is on sale for 20% off the original price of $115. If there is 7.5% sales tax, what is the final price of the coffee table?
Answer:
The final price for the coffee table is $98.9.
Step-by-step explanation:
1. First, is to convert the percentage to decimal form
We can do this by changing 7.5% to decimal number by dividing 7.5 by 100, we get:
\frac{7.5}{100}
100
7.5
= 0.0750.075
2. Then multiply 0.075 to the original price of $115
0.075(115) = 8.625
Then, add 8.625 to the original price of $115, we get:
115 + 8.625 = $123.625
3. After this, we subtract the 20% discount to $123.625
We can do this by converting 20% to decimal form, we get:
\frac{20}{100}
100
20
= 0.20.2
Then, multiply $123.625 by 0.2, we get:
123.625(0.2) = $24.725
4. Then subtract 24.725 from $123.625, we get:
123.625 -123.625−24.725 = $98.9
Final price of the table coffee which is on sale by 20% with a sales tax of 7.5% is $98.9.
Find the length of PC , the distance between San Cristobal and Panama. Show your work. Remember to scale the distance up by a factor of 10.
Answer:
Step-by-step explanation:
what is 1/10 as a decimal does it equal 0.1
represent the sum of 3/4 and -5/8 is ???
3/4 + -5/8
---Find a common denominator
6/8 + -5/8
---Simplify
1/8
Hope this helps!
Answer:
3/4 + -5/8 = 1/8
Step-by-step explanation:
When adding fractions, you always need to find a common denominator. 4 and 8 share a common denominator of 8.
You multiply 3/4 by 2/2 and get 6/8.
When adding negative numbers, it is the same as subtracting.
6/8 + (-5/8) =
6/8 - 5/8 = 1/8
So 1/8 is the answer.
I hope this helps!
the diagram shows a sector of a circle radius 10cm
calculate the perimeter of the sector
give answer to 1 decimal place
Answer:
[tex]\text{Perimeter of sector = 43.6 (Rounded to the nearest tenth.)}[/tex]
Step-by-step explanation:
[tex]\text{Perimeter of the sector = Radius + arc length + radius}[/tex]
[tex]\text{Radius = 10 cm}[/tex]
[tex]\text{Perimeter of the sector = 10 + arc length + 10 }[/tex]
[tex]\text{Perimeter of the sector = 20 + arc length }[/tex]
[tex]\text{arc length = (sector angle/ 360 ) * perimeter of the circle}[/tex]
[tex]\text{Perimeter of a circle }=2\pi r[/tex]
[tex]\text{sector angle} = 135[/tex]
[tex]\text{arc length} = (135/ 360 ) * 2\pi (10)[/tex]
[tex]= (3/8) 20\pi[/tex]
[tex]= 15\pi /2[/tex]
[tex]\text{Using }\pi =3.14[/tex]
[tex]= 15 * 3.14 /2[/tex]
[tex]= 23.55[/tex]
[tex]\text{Perimeter of the sector = 20 + 23.55}[/tex]
[tex]= 43.55[/tex]
[tex]= 43.6 cm[/tex]
[tex]\text{perimeter of the sector = 43.6 cm }[/tex]
Factorise completely 12 x³y - 18 xy²
Answer:
6xy(2x²-3y)
Step-by-step explanation:
factorized completely
Which of the following expressions is equivalent to (x5 y3 z2) (x4 y3 z6) for all real values of x y, and z ?
a. x9y6z8
b. x9y9z8
c. x20y6z8
d. x20y9z12
e. x21y6z12
The product of the expressions (x⁵y³z²) and (x⁴y³z⁶) is equivalent to the expression option is A x⁹y⁶z⁸. Hence, the correct option is A.
What is a simplification of an expression?Usually, simplification involves proceeding with the pending operations in the expression.
Simplification usually involves making the expression simple and easy to use later.
The expression is given as
(x⁵y³z²) and (x⁴y³z⁶)
Then, the product of the expression will be
= (x⁵y³z²) (x⁴y³z⁶)
= x⁵x⁴y³y³z²z⁶
= x⁵⁺⁴y³⁺³z²⁺⁶
= x⁹y⁶z⁸
Hence, the correct option is A x⁹y⁶z⁸.
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5. Hunter deposited $750 into a certificate of deposit that earns 4.35% annual simple interest for 3
years. How much interest will Hunter earn?
Answer:
$97.875
Step-by-step explanation:
interest = 750 * 4.35% * 3
= $97.875
Please help me thanks!
Part 1
V = pi*r^2*h .... volume of a cylinder
250 = pi*r^2*h
h = 250/(pi*r^2)
Plug this into the surface area of a cylinder equation
SA = 2*pi*r^2 + 2*pi*r*h
SA = 2*pi*r^2 + 2*pi*r*( 250/(pi*r^2) )
SA = 2*pi*r^2 + 500/r
Now replace every copy of r with x to get this function
f(x) = 2*pi*x^2 + 500/x
x = radius
y = f(x) = surface area
Next we'll use Desmos to graph this function. See the screenshot below. It produces some kind of curve that has two pieces to it. We'll only focus on the curve where x > 0 and y > 0. It makes no sense to have a negative radius, and we cannot have a negative surface area either.
Click on the lowest point of the parabolic looking shaped piece (it's not really a parabola, but we'll imagine that it is for the sake of simplicity).
The coordinates of that local min point will show up and they are (3.414, 219.689)
We have (x,y) = (3.414, 219.689) lead to r = 3.414 and SA = 219.689
This means that a radius of approximately r = 3.414 cm leads to the smallest surface area of approximately 219.689 square cm. This is when the amount of material is minimized.
Use this value of r to find h
h = 250/(pi*r^2)
h = 250/(pi*3.414^2)
h = 6.828
Desmos not only graphs, but it is also a standard calculator. The calculation is also shown in the screenshot.
Answer: This can has a radius of roughly 3.414 cm and height 6.828 cm.=============================================================
Part 2
Find the three side lengths of each triangle. So you should have 6 sides total. Then divide the corresponding sides to see if you get the same ratio. If so, then the triangles are similar by the side side side (SSS) similarity theorem. Another method is to find the angle between two sides and use the SAS (side angle side) similarity theorem. This is when the two pairs of sides form the same ratio, and the angles mentioned are congruent to each other. The angles must be between the sides used.A proportion can be used to solve equations based on similar polygons. For example, we could have the proportion x/2 = 30/10 which solves to x = 6.The first step is to multiply the two numbers. Then apply the square root to them. Example: The geometric mean of 4 and 9 is 6 because [tex]\sqrt{4*9} = \sqrt{36} = 6[/tex]The volume of air in a balloon is represented by the function v(r)=4/3 pi ^3, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.
A number cube is rolled 15 times how many times would you expect a number less than 3 to be rolled
Answer:
45
Step-by-step explanation:
how many number you rolled 3 times how many times its rolled 15 x 3 +45
Therefore,the answer would be 45
Which is true about the functional relationship shown in the graph?
Simplify 7x²-x²
how to simplify this maths question
Hi student, let me help you out! :)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
We are asked to simplify the expression [tex]\large\pmb{7x^2-x^2}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
Combine like terms! :)That's exactly what we need to do - combine like terms.
So, we subtract:
[tex]\star~\large\pmb{7x^2-x^2}[/tex]
Which gives us:
[tex]\star~\large\pmb{6x^2}[/tex]
Hope it helps you out! :D
Ask in comments if any queries arise.
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Quadrilaterals are angles that has 4 sides and angles. The measure of the angle m<SPQ is 110 degrees
Angles in a quadrilateralQuadrilaterals are angles that has 4 sides and angles. The given quadrilateral is a rhombus with equal opposite sides.
Given the following angles
m<SPR = 2x + 15
m<QPR = 3x - 5
From the figure
m<SPR = m<QPR
Substitute
2x+ 15 = 3x - 5
2x - 3x = -5 - 15
x = 20
Determine the measure of <SPQ
m<SPQ = 3x - 5 +2x +15
m<SPQ = 5x + 10
m<SPQ =5(20) + 10
m<SPQ = 110 degrees
Hence the measure of the angle m<SPQ is 110 degrees
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One ball is selected at random from a bag containing 12 balls of which x are white
a) what is the probability of selecting a white ball?
when a further 6 were white balls were added the probability of selecting a white ball is doubled
b) Find x
Answer:
a) 12/18
b) 6
Step-by-step explanation:
If adding 6 white balls doubles the probability then the original amount of balls is 6 and with the new amount of 18, the likelihood of picking a white ball becomes 12/18.
Kelly made fruit punch to serve at a party for her chess team. She mixed 1
2/5
liters of cranberry juice and 1
3/5
liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each glass?
Answer:
1/3 liters. or 33.33333 ml
Step-by-step explanation:
1 2/5 + 1 3/5 = 3
3 liters of juice is there.
3 liters of juice/9 glasses.
1/3 liters of juice is in every glass
If a baseball player hits 10 home runs in the first 45 game, at the same rate how many home runs can he expect to hit during the 162 game season
Using proportions, it is found that he can be expected to hit 36 home runs during the 162 game season.
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
In this problem, the player hits 10 home runs in 45 games, hence the proportion is:
p = 10/45.
Then, in 162 games, the amount is:
HR = 10/45 x 162 = 36.
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