Answer:
downwards
Step-by-step explanation:
the equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k ) are the coordinates of the vertex and a is a multiplier
• if a > 0 then parabola opens upwards
• if a < 0 then parabola opens downwards
for
f(x) = - 4(x - 3)² + 9 with a = - 4 < 0 , then
the parabola opens downwards
In the diagram, points D and E are marked by drawing arcs of equal size centered at B such that the arcs intersect and . Then, intersecting arcs of equal size are drawn centered at points D and E. Point P is located at the intersection of these arcs.
Based on this construction, m∠ABP is
°, and m∠ABC is
Based on this construction, the value of m∠ABC is 64°.
How to find the angle?From the point, E and D, two arcs are made which are intersecting each other at point P.
It means, that line BP is the bisector of angle ABC. ABC will be:
= 2 * 32=64
Therefore, based on this construction, the value of m∠ABC is 64°.
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find the area of the shaded regions. give your answer as a completely simplified exact value in terms of π
20 POINTS!!!
WILL MARK BRAINLIEST!!!!!!!!!!!!!!!!!!!!!!!!!
Mitra created a mosaic design using square 2x2 cm white tiles and 2x3 cm rectangular centimeter black tiles. She used twice as many white tiles as black tiles. The finished pattern was 1092 square centimeters in area. How many rectangular tiles did she use?
Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the number of white tiles and y represent the number of black tiles.
Area of white tiles = 2 cm * 2 cm = 4 cm²
Area of black tiles = 2 cm * 3 cm = 6 cm²
She used twice as many white tiles as black tiles. Hence:
x = 2y (1)
Also, the finished pattern was 1092 square centimeters in area. Hence:
4x + 6y = 1092 (2)
From both equations:
x = 156, y = 78
Mitra used 156 white tiles of 2x2 cm and 76 black tiles of 2x3 cm to form a pattern with an area of 1092 cm²
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x − y = 12
x + 2y = 21
Answer: x=15, y=3
Step-by-step explanation:
Subtracting the two equations, we get -3y=-9, meaning y=3.
Substituting this into the first equation, we get that x-3=12, and thus, x=15.
Find the sum of the first n terms
using the formula:
a(1-rn)
1-r
85 +85(.9) +85(.9)² + ...
. (5 terms)
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
What is the sum of terms of a geometric sequence?Let's suppose its initial term is a , multiplication factor is r and let it has total n terms,
then, its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
(sum till nth term)
Given geometric sequence;
85 +85(.9) +85(.9)² + ...
a = 85
r = 0.9
its sum is given as:
[tex]S_n = \dfra[/tex][tex]\dfrac{a(r^n-1)}{r-1}[/tex]
[tex]S_n = \dfrac{85(0.9^5-1)}{0.9-1}\\\\S_n = \dfrac{85(0.5904-1)}{-0.1}\\\\\\S_n = \dfrac{85(-0.4095)}{-0.1}\\\\S_n = 348.08[/tex]
Thus,
The sum of the first n terms of sequence 85 +85(.9) +85(.9)² + ... would be 348.08.
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A. Saving money at the grocery store by using unit pricing.
a. Toilet paper A is 6 mega rolls for $4.59.
b. Toilet paper B is 12 mega rolls for $9.02.
In order to save money, the person should buy Toilet paper B.
Which option is cheaper?In order to determine the unit price of each option, divide the total cost by the number of rolls. The option that would save money is the cheaper option.
Unit cost = total cost / number of rolls
$4.59 / 6 = $0.77
$9.02 / 12 = $0.75
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Please help me with this question!
Step-by-step explanation:
Yes it is .
7x+9 _> 7•3
7x+9_> 21
7x_> 21 - 9
7x _> 12 divide both side with 7 to find x
then x _> 1.4
which mean x can be any number that is greater than or equal to 1.4 so 2 is correct .
Hi Student!
Looking at the problem statement, we can see that they are asking for us to determine whether x = 2 is a solution of the expression provided or not. The first step that we take is plugging in all the values which means that we take 2 and plug it into all of the x's that we have in the expression that we provided. Then we simplify that expression down on both sides. If the expression in the end results to true then x = 2 is a solution of the expression but if it defaults to false than x = 2 isn't a solution.
Plug in the values
[tex]7x + 9 \ge 7 * 3[/tex][tex]7(2) + 9 \ge 7 * 3[/tex]Simplify both sides
[tex]14 + 9 \ge 7 * 3[/tex][tex]23 \ge 21[/tex]The final expression states that 23 is greater than or equal to 21 which is true. Therefore, x = 2 is a solution of the expression that was provided in the problem statement.
3) Find an estimated product.
59 x 42 = ?
Oa.) 50 x 40 = 2500
Ob.) 60 x 50 = 3500
Oc.) 60 x 40 = 2400
Answer:
c.
Step-by-step explanation:
we estimate by rounding the factors to "easy numbers". that means numbers we can easily calculate even in our heads, and we get at just a ballpark number as result for orientation.
59 is much closer to 60 than to 50.
42 is much closer to 40 than to 50.
of course, we round to the closest "round numbers", so that the loss of precision through the rounding is as little as possible, so that the estimation still gives a much value as possible.
and the sum of the differences of the factors should be as close to 0 as possible.
so, 60×40 is the closest and therefore best estimation.
the sum of the factor differences is (+1 - 2) = -1.
compare to the real result :
59×42 = 2,478
answer a and b are by the way not correct :
50×40 = 2000 (and not 2500)
60×50 = 3000 (and not 3500)
FYI - in this case 50×50 = 2500 would be the closest estimation.
and the sum of the factor differences would be (-9 + 8) = -1.
normally, this wide "jumping" (-9 to +8) would make it only second choice.
3/x=2
How do you solve this without get a loop
Answer:
x= 3/2
Step-by-step explanation:
3/x=2
Multiply x both sides so,
3 =2x
Divide 2 to get the value of x so,
x= 3/2
4. The diameter of a circle is 10 in. What is the approximate circumference? Show your work to receive
full credit. **You must include the units of measurement to receive full credit.**
Show work :))
Answer:
31.4 in
Step-by-step explanation:
The circumference of of a circle given the diameter is πd :
C = π×d = 10π = 31.4159....
C ≈ 31.4
The units will still be in as this is a length not an area .
Hope this helped and brainliest please
Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant. So, what is the highest possible number of inhabitants in that little town?
The highest possible number of inhabitants in that little town are 743.
What are inhabitant?A person or animal that lives in a place is called as the inhabitant.
Suppose there is this little town with a finite number of people: (1) No two inhabitants have exactly the same number of hairs. (2) No inhabitant has exactly 743 hairs or no hairs at all. (3) There are more inhabitants than there are hairs on the head of any inhabitant.
Let say there are 519 people in the town. and make them stand in a line with increasing number of hairs on their heads. This way, there will be a person on the last, who has no hair.
There are more number of people than the hairs. From bald to 742 hairs, 743 is the limit.
Thus, the highest possible number of inhabitants in that little town are 743.
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Your answer should be an expanded polynomial in standard form.
(7a³-2a-2) + (-5a + 3) =
Answer:
7a^3-7a+1
Step-by-step explanation:
(7a³-2a-2) + (-5a + 3) =
Combine like terms
7a^3-2a-5a-2+3
7a^3-7a+1
Help please…………………..
Find the surface area of the prism. 8 4 14
Answer:
4 8 1 4 0,683 the (783)-213=509
can you please help me with this two questions
Answer:
2) d. 60°
3) a. AB
Step-by-step explanation:
Question 2
ΔABC and ΔCDA are congruent because:
they are both right trianglesthey share one side (AC)their hypotenuse are parallel (marked by the arrows)This means the corresponding side lengths and angles are equal.
Therefore,
∠CDA = ∠ABC
⇒ x = 60°
Question 3
The hypotenuse is the longest side of a right triangle - the side opposite the right angle (the right angle is shown as a small square).
Therefore, the hypotenuse of ΔABC is the line AB.
please help meeeee will mark them brain
from biggest to smallest
Factor out the GCF from the given polynomial. 38x-8
Answer:
2(19x - 1)
Step-by-step explanation:
The GCF of 38 and 8 is 2 :
Now we take a common factor of 2 :
2(19x - 1)
Hope this helped and have a good day
Answer:
2(19x-4)
The gcf of 38 and 8 is 2 so factor it out.
Find the volume (to the nearest cubic foot) of a cone with base radius 4 ft. and height 8 ft.
Answer:
135 ft^3
Step-by-step explanation:
The volume of a cone is [tex]\frac{1}{3} \pi r^{2}h[/tex]. The radius is 4 and the height is 8, so these values can be plugged in:
[tex]V = \frac{1}{3} \pi \times 4^{2} \times 8[/tex]
[tex]V = \frac{128\pi }{3}[/tex]
This is about 134.041286553 which rounds to 135 ft^3.
1) Which is the first INCORRECT step in the
solution of the inequality shown below?
2(x+1)-(3-x) ≤ -4:
Step 1: 2x + 2-3+x≤-4;
Step 2: 3x - 1≤-4;
Step 3: 3x
-3;
Step 4: x>-1
(a) Step 1
(b) Step 2
(c) Step 3
(d) Step 4
Step-by-step explanation:
we are missing the inequality sign in step 3.
step 1 and step 2 are correct.
step 4 is wrong.
the correct step 3 looks like
3x <= -3
if your original step 3 says the same, then the first wrong step is step 4.
if your original step 3 does not say the same, then the first wrong step is step 3.
If y = 9 inches, z = 14 inches, h = 5 inches, and w = 4 inches, what is the area of the object?
Answer:
126
Step-by-step explanation:
Consider the halfpipe with a diameter of 7 cm and a height of 20 cm.
Find its volume, rounding to 2 decimal places.
Answer: 384.85
Step-by-step explanation
Caroline is looking for a tool to measure the mass of a dictionary. Which tool should she use?
A.
ruler
B.
pan balance
C.
stopwatch
D.
1‐liter container
[tex]\bold{Q:}[/tex]
Caroline is looking for a tool to measure the mass of a dictionary. Which tool should she use?[tex]\bold{Ans:}[/tex]
B. pan balanceA balance or scale is an instrument used to measure mass.
Hope it helps.
[tex]\bold{Feel \: free \: to \: correct \: me}[/tex]~
Alejandro and Emila ordered a pizza. Alejandro at 1/3 of the pizza and Emila ate 2/5 of the pizza. How much did they eat together? Was there any pizza left? How much?
Answer: [tex]\frac{4}{15}[/tex] of the pizza was left
Step-by-step explanation:
lets first get the denominators the same..
[tex]\frac{1}{3} = \frac{5}{15}[/tex]
[tex]\frac{2}{5} = \frac{6}{15}[/tex]
To find the total pizza eaten we add these two fractions
[tex]\frac{5}{15} +\frac{6}{15} =\frac{11}{15}[/tex]
we can think of [tex]\frac{15}{15}[/tex] as 1 pizza because it simplifies to 1
[tex]\frac{15}{15} -\frac{11}{15} =\frac{4}{15}[/tex]
Therefore, [tex]\frac{4}{15}[/tex] of the pizza was left
Answer:Amount left=4/15
Step-by-step explanation:
The solution is in the image
I paid $8000 to burrow $50000 for 2 years. What was the rate of simple interest charged?
[make brainliest if got correct and 20pts]
[tex]~~~~~~ \textit{Simple Interest Earned Amount} \\\\ A=P(1+rt)\qquad \begin{cases} A=\textit{accumulated amount}\dotfill & \$8000\\ P=\textit{original amount deposited}\dotfill & \$5000\\ r=rate\to r\%\to \frac{r}{100}\\ t=years\dotfill &2 \end{cases} \\\\\\ 8000=5000[1+(\frac{r}{100})(2)]\implies \cfrac{8000}{5000}=1+\cfrac{r}{50}\implies \cfrac{8}{5}=1+\cfrac{r}{50} \\\\\\ \cfrac{8}{5}-1=\cfrac{r}{50}\implies \cfrac{3}{5}=\cfrac{r}{50}\implies \cfrac{3(50)}{5}=r\implies 30=r[/tex]
What is the area of the parallelogram?
Answer:
Area = 120 in²Step-by-step explanation:
follow the formula in the picture
Area = b * h
Area = 15 * 8
Area = 120 in²
Simplify the following expression:
(3i + 4) - i + 4(6 + 2i)
A. 27 + 11i
B. 28 + 10i
C. 14 + 8i
D. 14 + 4i
The simplified form of this expression is 28 + 10i
This question is an expression of imaginary numbersImaginary numbers are numbers that are composed of a real number and an imaginary part.
< To resolve this issue, let's remove the first parenthesis:
(3i + 4) - i + 4(6 + 2i)
3i + 4 - i + 4(6 + 2i)
< In the second parentheses, let's apply the distributive property:
3i + 4 - i + 4(6 + 2i)
3i + 4 - i + 4 . 6 + 4 . 2i
3i + 4 - i + 24 + 8i
< Finally, let's just sum the like terms, along with the real terms:
3i + 4 - i + 24 + 8i
10i + 4 + 24
10i + 28
28 + 10i
Therefore, the correct value will be 28 + 10i
What is the solution to the following system of equations? (2 points) y = x2 + 10x + 11 y = x2 + x − 7
Answer:
y=x^(2)+10x+11,y=x^(2)+x-7
Step-by-step explanation:
I think so bro
Step-by-step explanation:
I assume you mean
y = x² + 10x + 11
y = x² + x - 7
well, I subtract equation 2 from equation 1 :
0 = 9x + 18
9x = -18
x = -2
y = x² + x - 7 = (-2)² - 2 - 7 = 4 - 2 - 7 = -5
the solution (the intersection point of both graphs) is the point (-2, -5).
A triangle has side lengths 9 cm, 12 cm, and 16 cm.
Answer:
https://www.calculator.net/triangle-calculator.html?vc=&vx=16&vy=9&va=&vz=12&vb=&angleunits=d&x=54&y=24
Step-by-step explanation:
I went to this website
https://www.calculator.net/triangle-calculator.html
put in what I knew of the triangle and got all the information you may need.
Which equation can be used to solve for c?
Triangle A B C is shown. Angle A C B is 90 degrees and angle A B C is 35 degrees. The length of C B is 5 inches, the length of A C is b, and the length of B A is c.
The equation which is used to find the value of c will be c = 5/Cos 35
What is trigonometry?The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry.
We are given the following
m<ACB = 90degrees
m<ABC = 35degrees
The side opposite to m<ABC is AC
BA = hypotenuse
CB = adjacent = 5inches
Required
The equation to solve BA which is c
Using the Pythagoras theorem;
Cos Ф = Adjacent/Hypotenuse
Cos m<ABC = CB/BA
Cos m<ABC = 5/c
c = 5/cosm<ABC
c = 5/Cos 35
Hence the equation that can be used to solve for c is c = 5/Cos 35
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Angles in circles
How many degrees are in a half of a full turn?
Answer:
180 degrees
Step-by-step explanation:
Because 360 is i full turn around and you can divide 360 by 2 and you will get 180
Hope This Helped