Answer:
25(1+2)
Step-by-step explanation:
25 goes into 25 once and 50 twice.
Complete the square and graph: 9y²−x − 18y +10=0
Answer:
See below ~
Step-by-step explanation:
Completing the square :
9y² - x - 18y + 10 = 09y² - 18y + 9 - 9 - x + 10 = 0(3y - 3)² - x + 1 = 0Graph :
Answer:
x = 9(y - 1)² + 1
see attached for graph
Step-by-step explanation:
Completing the squareGiven equation:
9y² - x - 18y + 10 = 0
As there is a y² in the equation, this implies it is a sideways parabola.
To complete the square for a sideways parabola, collect the y variable terms on the left and everything else on the right:
⇒ 9y² - 18y = x - 10
Factor out the leading coefficient from the left side:
⇒ 9(y² - 2y) = x - 10
Take the coefficient of y, half it, then square it: (-2 ÷ 2)² = 1
Add this inside the parentheses, and add the distributed value of this to the right side:
⇒ 9(y² - 2y + 1) = x - 10 + 9
Factor the parentheses and simplify the right side:
⇒ 9(y - 1)² = x - 1
Add 1 to both sides to make x the subject:
⇒ x = 9(y - 1)² + 1
Graphing the parabolaConic form of a sideways parabola with a horizontal axis of symmetry:
x = a(y - k)² + h
(where (h, k) is the vertex and y = k is the axis of symmetry)
If a > 0, the parabola opens to the right, and if a < 0, the parabola opens to the left.
Therefore, for x = 9(y - 1)² + 1
vertex = (1, 1)axis of symmetry: y = 1a > 0 ⇒ the parabola opens to the rightTo find the x-intercept, set y = 0 and solve for x:
⇒ x = 9(0 - 1)² + 1
⇒ x = 9(-1)² + 1
⇒ x = 9(1) + 1
⇒ x = 10
Therefore, the y-intercept is (10, 0)
As the axis of symmetry is y = 1, the other value of y when x = 10 is y = 2
Plot the vertex and points. Add an axis of symmetry to help draw the curve. Draw the parabola opening to the right.
**graph attached**
in fgh, m f=60 degrees g= 68 degrees. which side of fgh is the shortest
Answer:
h=52 and h is the shortest
Step-by-step explanation:
180-f-g=h step 1. -f from 180
180-60=120 step 2. -g from 120
120-68= 52
h=52 degrees
describe full the graph that has the equation x^2 + y^2=9
Answer:
see explanation
Step-by-step explanation:
the equation of a circle centred at the origin is
x² + y² = r² ( r is the radius )
x² + y² = 9 ← is in this form
with centre (0, 0 ) and r = [tex]\sqrt{9}[/tex] = 3
this then is the equation of a circle whose centre is (0, 0 ) with radius 3
Answer:
Step-by-step explanation:
Discussion
First of all, the graph is of a circle. Anytime you see x^2 + y^2 = r^2, you are dealing with a circleThe center is at 0,0. If it was anything else then x or y or both would be modified. (x+4)^2 + ( y - 3)^2 = 25 does not have it's center at 0,0Third, the radius of the circle is the square root of r^2. In this case, r^2 = 9 so r = sqrt(9) or r = 3Which of the following can be the third side of a triangle whose other two sides measure 8 inches and 10 inches
A) 17inches
B) 18inches
C) 19 inches
D) 20 inches
-3(x + 9) = 15
Enter value for x
Answer:
x = -14
Step-by-step explanation:
-3(x + 9) = 15Divide each side by -3.
-3(x + 9)/-3 = 15/-3x + 9 = -5Subtract 9 from each side.
x + 9 - 9 = -5 - 9x = -14Answer:
x = -14
Step-by-step explanation:
-3(x + 9) = 15
-3 × x + -3 × 9 = 15-3x + (-27) = 15+27 on both sides-3x = 42[tex] \frac{ - 3x}{ - 3} = \frac{42}{ - 3} [/tex]x = -14Given circle O lies perfectly within square ABCD. If side BC = 6.84, then what is the area of the orange region?
What we get to know by looking at picture :
There are two figures: 1. square 2. circle inside it touching all square's wall.As O is center of circle (given) ∴ OP is radius of circleAs the sides are of square , therefore AB = BC = DC = AD[tex] \\ \\\\ [/tex]
To find :
Area of orange region[tex] \\ \\ \\ [/tex]
Given:
O is the center of the circle.ABCD is squareLength of BC is equal to 6.84.[tex] \\ \\ \\ [/tex]
Concept:
So as we can orange doesn't lies inside circle. And the wall of circle touches all four sides of circle. So first we have to find area of circle and then Area of square. And then we will subtract the ares. The result will be Area of orange part.
[tex] \\\\ \\ [/tex]
Solution:[tex] \\ \\\\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of circle: }}}[/tex]
[tex] \\ [/tex]
To find area of circle we need radius of it i.e Length of OP.
As BC = AB
∴AB = 6.84
As O is the center of square ∴it's center of circle too
Therefore:
AB = 2 OP6.84 = 2 OPOP = 6.84/2OP = 684/2 × 10OP = 342/10OP = 3.42[tex] \\\\ [/tex]
Now Let's find area :
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~circle = \pi {r}^{2} }[/tex]
here :
r is the radius of circle.[tex] \\ [/tex]
[tex]: \implies\sf Area~of~circle = \pi {r}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times {3.42}^{2} \\ \\ \\ : \implies\sf Area~of~circle = \dfrac{22}{7} \times11.7\\\\\\: \implies\sf Area~of~circle = \dfrac{257.4}{7} \\ \\ \\ : \implies \boxed{ \orange{\tt{ Area~of~circle = 36.6 \{approx \}}}} \bf \dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of square: }}}[/tex]
[tex] \\\\ [/tex]
[tex] \star \boxed{ \rm Area~of~square = {side}^{2} }[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area~of~square = {side}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84}^{2} \\ \\ \\ : \implies\sf Area~of~square = {6.84} \times 6.84 \\ \\ \\ : \implies \boxed{\tt{ \orange{Area~of~square = 46.8 \{aprox \}}}}\bf\dag[/tex]
[tex] \\ \\ [/tex]
[tex] \red{ \textsf{ \textbf{Area of orange \: part: }}}[/tex]
[tex] \\ [/tex]
[tex] \star\sf \boxed{ \rm Area_{(orange \: part)} = Area_{(square)} - Area_{(circle)}}[/tex]
[tex] \\ \\ [/tex]
[tex]: \implies\sf Area_{(orange \: part)} = 46.8 - 36.6 \\ \\ \\ : \implies \boxed{ \blue{\tt{Area_{(orange \: part)} = 10.2}}}\bf\dag[/tex]
Q5. the population of an island has decreased by 40% over 50 years.
the population in 2018 was 360
what was the population in 1968?
Answer:
The population was 600 in 1968
Step-by-step explanation:
The population of an island decreased by 40% over 50 years, so the population in 1968 will be equal to 600.
What is the Percentage?The Latin term "per centum," which signifies "by the hundredth," was the source of the English word "percentage." Segments with a denominator of 100 are considered percentages. In other terms, it is a relationship where the worth of the entire is always considered to be 100.
As per the data provided by the question,
The current population in 2018 = is 360
which is 40% less than the population in 1968.
So, 60% of the total population will be equal to 360.
Let the total population is x.
60% × x = 360
x = (360 × 100)/60
x = 600
Therefore, the population at that time was 600.
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A simple random sample from an infinite population is a sample selected such that.
A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.
What is Simple Random Sampling?Simple random sampling is known to be a types of sampling where there are no laws, rules etc., on how to select the samples.
Note that it is seen easiest way of sampling and as such, A simple random sample from an infinite population is a sample selected such that each element is selected independently and from the same population.
See full question below
A simple random sample from an infinite population is a sample selected such that:
a. each element is selected independently and from the same population
b. each element has a 0.5 probability of being selected
c. each element has a probability of at least 0.5 of being selected
d. the probability of being selected changes
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Trina is trying to decide which lunch combination to order at a sandwich shop: 4, 5, 6, or
7. Each combination comes with the choice of an apple, an orange, or a pear. How many
possible outcomes are there for a lunch combination and a piece of fruit?
apple
orange
pear
apple
5
orange
pear
apple
orange
pear
apple
orange
pear
Type the answer in the box.
10
HELP HELP HELP PLEASE PLEASE
Answer:
Fourth one
Step-by-step explanation:
You can find the x coordinate of the vertex (which is the axis of symmetry)
by calculating x = - b/ 2a
( when equation is arranged into y = a x^2 + bx + c form )
first one - -2/4 = 1/2
second one -2/ -4 = 1/2
third one - -2 / 4 = 1/2
fourth one - 2 / 4 = - 1/2 BINGO !
Need some help, thanks in advance!
Answer: = 3 acres per day
Showing Work
This is a fraction equal to
3 acres ÷ 1 days
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 1
3 acres ÷ 1
__________
1 days ÷ 1
=
3 acres
_____
1 day
=
3 acres
______
day
= 3 acres per day
80 volunteers take a meningitis test to help doctors see how accurate this test is at identifying whether someone has meningitis or not. a positive result means the test has identified you as having meningitis. of the volunteers, only 17 people have meningitis. the results show 5 people who have meningitis gets a negative result and 7 people who don't have meningitis get a positive result. what was the accuracy of the test?
Using it's formula, it is found that the accuracy of the test was of 0.85 = 85%.
What is the accuracy of a test?The accuracy of a test is given by the number of correct results divided by the number of results.
In this problem, there are 80 tests, and of those, 5 + 7 = 12 had incorrect results, hence 68 had correct results.
Hence the accuracy of the test is given by:
a = 68/80 = 0.85 = 85%.
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11 gallons of water are used to completely fill 5 fish tanks. if each tank holds the same amount of water, how many gallons will each tank hold? solve on paper and check your work on zearn. express your answer as a mixed number
Answer:
[tex]2\frac{1}{5}[/tex]
Step-by-step explanation:
The 11 gals of water are equally split up into 5 tanks, so divide 11 by 5.
[tex]\frac{11}{5}[/tex] then simplifies into [tex]2\frac{1}{5}[/tex]
writing fractions with common denominators to add or subtract(Aleks)
Answer:
3/5+1/3= 9/15+5/15= 14/15
Step-by-step explanation:
Hi there!
To make fractions have a common denominator, multiply both the numerator and the denominator by a number. In this case, 3/5= 9/15, because both the numerator and denominator are multiplied by 3. 1/3= 5/15, using the same rule. 9/15+5/15=14/15
Hope this helped! If it did, pls press the heart :)
How to work out the mode
Answer:
mode
is the most common frequent value
How many layers of 1 inch cubes fill the carton
Answer:
3
Step-by-step explanation:
4 layers 15 cubes
the total amount of cubes =5*3*4
Please awnser my other question
Answer:
S = (-6, -1)
T = (-7, 4)
U = (-6, 9)
V = (-4, 4)
alia is shopping for school clothes she want to buy 5 T-shirts for 6 each and pair of shoes for 20 she thinks that she will spend about 30 is the answer reasonable
Answer:
it's not reasonable because the t-shirts alone cost 30 and the shoes cost 20 so it would cost 50 altogether.
in a group of 70 people, 37 like tea, 52 like milk and each people likes at least one of the two drinks.
1)how many people like both tea and milk ?
2) how many people like tea only ?
3)how many people like milk only ?
4)show the above information in a Venn diagram.
Step-by-step explanation:
got the answer see in the image :)
Please help with this problem about circles and tangents. solve for X.
As tangents from a single point to the circle are equal in measure
AC=BCABC is isosceles
<A=60°
We know the radius hits any tangent on right angles
So
<PAC=90°<PAD=90-60=30°Now
cosØ=Base/Hypotenusecos30=6/x√3/2=6/x√3x=12x=12/√3accurate value
x=6.9Answer:
[tex]x=4\sqrt{3}[/tex]
Step-by-step explanation:
If two tangents to a circle meet at one exterior point, the tangent segments are congruent. Therefore, AC = BC
This means that ΔABC is an isosceles triangle and so
∠ABC = ∠BAC = 60°
The tangent of a circle is always perpendicular to the radius.
Therefore, ∠PAC = 90°
With this information, we can calculate ∠PAD:
⇒ ∠PAD + ∠BAC = ∠PAC
⇒ ∠PAD + 60° = 90°
⇒ ∠PAD = 90° - 60°
⇒ ∠PAD = 30°
We now have a side length and an angle of ΔPAD (shown in orange on the attached diagram). So using the cos trig ratio, we can calculate [tex]x[/tex]:
[tex]\sf \cos(\theta)=\dfrac{A}{H}[/tex]
where:
[tex]\theta[/tex] is the angleA is the side adjacent the angleH is the hypotenuse (the side opposite the right angle)Given:
[tex]\theta[/tex] = ∠PAD = 30°A = AD = 6H = AP = [tex]x[/tex][tex]\implies \cos(30^{\circ})=\dfrac{6}{x}[/tex]
[tex]\implies x=\dfrac{6}{\cos(30^{\circ})}[/tex]
[tex]\implies x=\dfrac{6}{\frac{\sqrt{3}}{2}}[/tex]
[tex]\implies x=4\sqrt{3}[/tex]
3
————
i need help!!
math geniuses pls help me!
—-
—————
Answer:
the answer is A. sorry for dirty handwriting
Can you use Third Angles Theorem to prove that two
are congruent? Explain your reasoning.
triangles
Answer:
The Third Angle theorem is not enough to prove that two triangles are congruent.
Step-by-step explanation:
It establishes that if two angles of one triangle are congruent with two angles of another triangle, then the third angles are also congruent. This indicates that the two triangles are similar but not identical.
A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a club or a red king?
Answer:
1/2
Step-by-step explanation:
number of required outcome ÷number of possible outcomes
1/2
A triangle has sides with lengths of 17 feet, 31 feet, and 36 feet. Is it a right triangle?
yes
no
I HAVE A CYLINDER AND cone WITH THE
Same Dimensions (RADIUS AND HEIGHT OF
BOTH ARE THE SAme). The volume OF THE
cone is 33 CUBIC INCHES. WHAT IS THE
Volume OF THE CYLINDER IN CUBIC
inches?
125 Sunny
Answer:
99 in³
Step-by-step explanation:
Let the radius and height of each be r and h in. respectively.
Write an equation for the volume of cone.
Volume of cone= ⅓πr²h
⅓πr²h= 33
Multiply both sides by 3:
πr²h= 99
Volume of cylinder= πr²h
We have found the value of πr²h previously, which is 99.
Thus, the volume of the cylinder is 99 in³.
graph the following features ( need this fast by the next 2 hours please help !! )
Y-intercept = -3
Slope = 2
Find the surface area of the space figure represented by the net.
A) 264 in.2
B) 290 in.2
C) 145 in.2
D) 242 in.2
Answer:
290 in^2.
Step-by-step explanation:
Adding all the areas of rectangles:
= 11*8 + 11*3 + 11*8 + 11*3 + 3*8 + 3*8
= 290 in^2.
Answer:
B) 290 in²
Step-by-step explanation:
Area of a rectangle = length × width
⇒ SA of the net = 2(11 × 8) + 2(11 × 3) + 2(8 ×3)
= 176 + 66 + 48
= 290 in²
If P Is inversely proportional to the square of q and p is 22 when a is 8 determine p when Q is equal to 4
The value of p is equal to 76 when q is equal to 4
Given :
If p is inversely proportional to the square of q
when y is inversely proportional to x then [tex]y=\frac{k}{x}[/tex]
given that p is inversely proportional to the square of q. the equation becomes
[tex]p=\frac{k}{q^2}[/tex]
when p is 19 the value of a is 8
Replace the values and find out q
[tex]p=\frac{k}{q^2}[/tex]
[tex]22=\frac{k}{8^2}[/tex]
[tex]22=\frac{k}{64}[/tex]
Multiply both sides by 64
k=1216
Now we find out p when q is 4
Replace k value and q value to find out p
[tex]p=\frac{k}{q^2}[/tex]
[tex]p=\frac{1216}{4^2}[/tex][tex]p=76[/tex]
The value of p is equal to 76 when q is equal to 4
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Answer:
P = 88.
Step-by-step explanation:
P = k/q^2
22 = k/ 8^2
k = 22 * 64 = 1408.
So P = 1408/q^2
When q = 4:
P = 1408/4^2
q = 88
Pls answer this asap
Answer:
9.5 feet
Step-by-step explanation:
Area of square garden = side length²
⇒ 90 = l²
⇒ l = √90
⇒ l = 3√10
⇒ l = 9.5 feet (nearest tenth)
The length of one side lies between the whole numbers 9 and 10.
Answer:
9 and 10
side length = 9.5 ft (nearest tenth)
Step-by-step explanation:
Area of a square = s² (where s is the side length)
Therefore, if the square garden measures 90 ft², the length of one side will be √90.
To find the two whole numbers that √90 lies between, find the perfect square either side of 90.
Perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, ...
Therefore, 90 lies between 81 and 100:
⇒ 81 < 90 < 100
Square root the numbers:
⇒ √81 < √90 < √100
⇒ 9 < √90 < 10
Therefore, the length of one side of Grandma's garden is between 9 and 10.
To estimate √90 to the nearest tenth, find the difference between the three numbers:
[tex]81 \overset{+9}{\longrightarrow} 90 \overset{+10}{\longrightarrow} 100[/tex]
As 90 is almost in the middle of 81 and 100,
⇒ √90 = 9.5 (nearest tenth)
According to the calculator, √90 = 9.486832981... = 9.5 (nearest tenth)
which verifies the estimation.
A prism with a length of 4 inches, height of 4 inches, and width of 3 inches. How many more 1 in. cubes does the container need to be completely filled?
There are 10 number of 1 cubic inches box required to fill the container completely.
What is a cuboid?
It is defined as the six-faced shape, a type of hexahedron in geometry.
It is a three-dimensional shape.
We have:
A prism with a length of 4 inches, height of 4 inches, and width of 3 inches.
The volume of the prism box = 4×4×3 = 48 cubic inches
Here some data are missing.
We are assuming there are 38 1 cubic inches box already in the big box.
So,
= 48 - 38
= 10
Thus, there are 10 number of 1 cubic inches box required to fill the container completely.
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