Answer:
The roots are 0.5 and 4.
Step-by-step explanation:
-2x^2+9x=4
Rearrange:
-2x^2 + 9x - 4 = 0
x = [-b +/- √(b)^2 - 4ac)] / 2a
Using this quadratic formula the solution is:
x = [-9 +/- √(9)^2 - 4*(-2)*(-4)] / (2*-2)
= (-9 +/- √49) / -4
= 9/4 +/- (-7/4)
= 9/4 - 7/4 = 0.5
and 9/4 + 7/4 = 4
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.
Please help me thank you :3
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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A 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.
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
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
When θ = 0, cos θ = 1. What is the next radian value that will result in cos θ = 1?
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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how can i find area of abd triangle. .............
Answer:
6 square units
Step-by-step explanation:
The attachment shows the figure redrawn to scale, along with helpful semicircle O with diameter EB. Trig relations can be used to find the area of triangle ADB. The relation between an inscribed angle and its corresponding central angle is also helpful.
__
anglesAny right triangle can be inscribed in a semicircle whose diameter is the hypotenuse. Accordingly, we have constructed semicircle O whose center is the midpoint of EB. Hence its radius is EB/2 = 4/2 = 2.
Then angle EBD is an inscribed angle, hence half the measure of central angle EOD. Since ∠EOD is double the measure of ∠EBD, it is congruent to ∠EBC, which is also double the measure of ∠EBD. We have called the measure of this double angle θ. Its complement is the angle marked β.
segmentsThe fact that angles EOD and EBC are congruent means that segments OD and BC are parallel. Segment BC is the altitude of ΔADB with respect to base AD.
The tangent ratio is ...
Tan = Opposite/Adjacent
Applying that to angle β, we have
tan(β) = OD/AD [eqn 1]
tan(β) = BC/AC [eqn 2]
These two relations can be solved for the measures of AD and BC, which we need in order to find the area of ΔADB.
areaEquation [eqn 1] tells us ...
AD = OD/tan(β)
Equation [eqn 2] tells us ...
BC = AC·tan(β)
The area of ΔADB is ...
Area = 1/2bh
Area = 1/2(AD)(BC) = 1/2(OD/tan(β))·(AC·tan(β))
Area = 1/2(OD)(AC) . . . . . . factors tan(β) cancel
The length of AC is given as 6, and we know OD = 2, so the area is ...
Area = 1/2(2)(6) = 6
The area of triangle ADB is 6 square units.
The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was
Day 8.
(a) Determine C(5), C(6), and C(7). Explain how you determined these amounts.
(b) Estimate C(1), C(2), and C(3). Explain how you determined these amounts.
(c) The stage manager said that the amount of money taken out of the account each day between Day 8
and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4.
Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could
you show the stage manager was incorrect?
Answer:
The answer is c, hope this helps
Step-by-step explanation:
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]
Help!! Also the questions says “Which of the following shows JUST a variable?”
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:
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.
Which point is one fourth of the way between point A and point B on the line segment AB shown on the coordinate plane below?
The coordinate of the point between point A and point B on the line segment AB is [tex](\frac 92, -\frac{19}4)[/tex]
How to determine the point?The points are given as:
A = (4,-5)
B = (6,-4)
m : n = 1 : 3
The coordinate of the point is then calculated using:
[tex]P = \frac{1}{m + n}(mx_2 + nx_1,my_2 + ny_1)[/tex]
So, we have:
[tex]P = \frac{1}{1 + 3}(1 * 6 + 3 * 4, 1 * -4 + 3 * -5)[/tex]
Evaluate the sum of product
[tex]P = \frac{1}{4}(18, -19)[/tex]
Evaluate the product
[tex]P = (\frac 92, -\frac{19}4)[/tex]
Hence, the coordinate of the point is [tex](\frac 92, -\frac{19}4)[/tex]
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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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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!
Quadrilateral ABCD has the following coordinates: A(-6,3) B(-4,5) C(-1,6) and D(-3,2) and
maps onto A"B"C"D". It will undergo transformations that will consist of a reflection over
the y-axis followed by a translation. Point D" is shown plotted in the plane after the
transformation.
A) Write the translation rule that maps point D' to point D".
B) Write the coordinates of point A"
The translation rule that maps point D' to D" is (x + 3, y) and the coordinate of point A" is (9,3)
How to determine the translation rule?The coordinates are given as:
A(-6,3) B(-4,5) C(-1,6) and D(-3,2)
When reflected across the y-axis, the transformation rule is:
(x,y) -> (-x,y)
So, we have:
A' = (6,3)
D' = (3,2)
Point D" on the grid is (6,2).
This means that the translation rule that maps both point is (x + 3, y)
The coordinates of point AIn (a), we have:
A' = (6,3)
Using the translation rule (x + 3, y), we have:
A" = (6 + 3,3)
A" = (9,3)
Hence, the coordinate of point A" is (9,3)
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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:
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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What is the value of f(x) when x=3?
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 + 4The diagram shows a regular polygon.
x
What is the value of x?
Write your answer as an integer or as a decimal rounded to the nearest tenth.
Answer:
To find the value of x, use the formula
(n-2) x 180, where n is the number of sides.
In this case, we have a TRIangle, which has THREE sides.
So, n=3
(3-2) x 180
1 x 180
180
If the total sum of the angles is 180, then the measure of one angle would be 180 divided by 3, which is 60.
Let me know if this helps, or if you got any more questions
Points a and b lie on a circle centered at point o. if oa = 5 and what is the area of sector aob? use the value π = 3.14, and choose the closest answer. a. 19.6 square units b. 39.3 square units c. 7.85 square units d. 15.7 square units
The area of sector AOB whose radius OA 5 units is 19.6 sq. units.
What is the Sector?A sector is a portion of a circle which is enclosed between its two radii and the arc adjoining them. The most common sector of a circle is a semi-circle which represents half of a circle.
Here, Radius of Circle = 5 units
length of arc AB / circumference = 1/4
So, Area of Sector AOB = one fourth of area of circle
= 1/4 X π X r²
= 0.25 X 3.14 X 5²
= 0.25 X 3.14 X 25
= 19.625 sq. units
Thus, the area of sector AOB whose radius OA 5 units is 19.6 sq. units.
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Answer:
19.6
Step-by-step explanation:
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.
what is the distance from (7,0)- (-5,5)
Answer:
[tex]\frac{5}{-12}[/tex]
Step-by-step explanation:
If you use the formula [tex]m = \frac{y2 - y1} {x2 - x1}[/tex] with x1 being 7, y1 being 0, -5 being x2 and 5 being y2, then you can subtract. 5(y2) minus 0(y1) is 5, and -5(x2) minus 7(x1) is -12. The formula would look like this: [tex]m = \frac{5 - 0}{-5 - 7} \frac{5}{-12}[/tex].
(tip: you need to do rise over run, aka y over x, shown as [tex]\frac{y}{x}[/tex] or [tex]\frac{rise}{run}[/tex])
I hope I helped you answer your question, and helped better understand it as well
Factorise completely 12 x³y - 18 xy²
Answer:
6xy(2x²-3y)
Step-by-step explanation:
factorized completely
Which is true about the functional relationship shown in the graph?
A rectangle is 21 meters long and 11 meters wide. what is the perimeter of this rectangle?
Step-by-step explanation:
the perimeter is simply the distance you would have to walk when going around the whole object once.
so, you would go a length, a width, another length and another width, until you are finally arriving back at the starting point.
so, the perimeter of a rectangle is
2×length + 2×width = 2×21 × 2×11 = 42 + 22 = 64 m
Slope of (-9,-2) and (-9,-6)
Answer:
Slope is undefined.
Step-by-step explanation:
find the altitude of a kite where 120 feet of string makes a 64 degree angle to the ground
Answer:
107.86 to 2 d.p.
Step-by-step explanation:
makes a triangle. 120 feet is the hypotenuse.
we want to find the opposite so we will use sine.
sin(x) = opp/hyp which means opp = sin(x)hyp.
opp = sin(64)120
opp = 107.86 to 2d.p.