Answer:
[tex](x - \frac{\sqrt{209} - 1}{8} )(x - \frac{-1 - \sqrt{209} }{8} )[/tex]
Step-by-step explanation:
FACTS TO KNOW BEFORE SOLVING :-
Quadratic Formula :-
Lets say , there's an equation ax² + bx + c.
[tex]=> x = \frac{-b + \sqrt{b^2 - 4ac} }{2a} \: or \: \frac{-b - \sqrt{b^2 - 4ac} }{2a}[/tex]
SOLUTION :-
According to the question ,
a (Coefficient of x²) = 4b (Coefficient of x) = 1c (constant) = -13By using quadratic formula ,
[tex]x = \frac{-1 + \sqrt{1^2 - 4 \times 4 \times (-13)} }{2 \times 4} \: or \: \frac{-1 - \sqrt{1^2 - 4 \times 4 \times (-13)} }{2 \times 4}[/tex]
[tex]=> x = \frac{-1 + \sqrt{209} }{8} \: or \: \frac{-1 - \sqrt{209} }{8}[/tex]
[tex]=> (x - \frac{\sqrt{209} - 1}{8} ) \: and \: (x - \frac{-1 - \sqrt{209} }{8} )[/tex] are the factors of 4x² + x - 13.
Ms. Edwards can spend, at most, $250 on new books for the school library. She will buy a reference book on birds for $30 and a reference book on the planets for $14.95. Let x represent the amount of money Ms. Edwards can spend on other books. Write an inequality that correctly describes this situation.
Answer:
x ≤ 205.05
Step-by-step explanation:
x = dollar amt remaining for other books
30 + 14.95 + x ≤ 250
44.95 + x ≤ 250
x ≤ 205.05
x ≤ $205.05 is an inequality that correctly describes this situation.
What is algebraic Expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Let's use x to represent the amount of money Ms. Edwards can spend on other books.
We know that Ms. Edwards can spend at most $250 in total and that she will already spend $30 + $14.95 = $44.95 on the reference books on birds and planets.
Therefore, the amount she has left to spend on other books is:
x = $250 - $44.95
x = $205.05
Ms. Edwards can spend up to $205.05 on other books.
To write this as an inequality, we can use the less than or equal symbol since Ms. Edwards cannot spend more than $205.05:
x ≤ $205.05
Therefore, the inequality that correctly describes this situation is:
x ≤ $205.05
Learn more about algebraic Expression here:
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PLEASE HELP WITH ANSWER ITS DUE TOMORROW
Answer:
A: 46 meters at 3 seconds
B: 0 meters at 6.033 seconds
C. It depends where the tree is
D. 6.033 seconds
Step-by-step explanation:
A. To find max height, we need to find the vertex.
We can do this by using vertex from y=a(x-h)+k for y=a^2+b^2+c^2
h(t) = -5t^2+30t+1
h(t)+45 = - 5x^2+30x+45+1
h(t)+45= -5(x^2-6x-9)+1
h(t)+45 = -5(x-3)^2+1
h(t) = -5(x-3)^2+46
Hence, the max height is 46 at 3 seconds
B. The minimum height is 0 meters because of the problem
C. It depends because the parabola intersects x=10 in 2 places meaning that you need the tree to be in either of these two places to intercept the horseshoe
D. -5x^2+30x+1=0
5x^2-30x-1=0
x= (30+-sqrt(30^2-4*5*-1))/2*5
x=(30+-sqrt920)/10
x=3+-2sqrt230/10
x=3+-sqrt230/5
This means that x = -0.033 or 6.033. Negative value doesn't make sense so it's 6.033 seconds
solve by substitution y=-2x y=8x-10
find the surface area. round to the nearest hundredth when necessary.
Answer:
The surface area of the cuboid is 648 m^2
Step-by-step explanation:
What we have here is cuboidal in outlook
By using the formula for the surface area of a cuboid, we can get the surface area of the shape
mathematically, we have the surface area of a cuboid as follows;
2(lb + lh + bh)
where l is the length, b is the breadth (width) and h is the height
We can have the length as 9 m, the width as 9 m and the height as 13.5 m
Substituting these values, we have the surface area of the cuboid as;
A = 2(9(9) + 9(13.5) + 9(13.5))
A = 2(81 + 243)
A= 2(324)
A = 648 m^2
Nico dropped the brand new bottle of dog shampoo and 3 ounces spilled out. He measures
14
oun
ounces. Which is the correct
shampoos his dog and the bottle of shampoo originally contained 30-1
value of x, the number of times Nico can bathe his dog using this one bottle?
O 12x-3 - 302x- 22 times
o 1x
14x+3 - 302; x = 27 times
14x+3-30,
o 14x-3- 30-31 x - 27 times
X-22 times
Answer:
22 times
Step-by-step explanation:
C
On a coordinate plane, a square has points A (negative 5, 2), B (1, 2), C (negative 4, 1), and D (negative 5, negative 4).
If a translation of is applied to square ABCD, what is the y-coordinate of B'?
Answer:
-2
Step-by-step explanation:
Answer:
its -8
Step-by-step explanation:
i got it rigth on edge
What type of angle is shown on the protractor below?
Protractor with an angle that's greater than 90°, but less than 180°.
reflex
acute
obtuse
right
Answer:
obtuse
Step-by-step explanation:
The angle on the protractor is 113 degrees, which makes it an obtuse angle.
Obtuse angle is any angle greater than 90° and the angle shown is 133°
The angle of inclination from the base of skyscraper A to the top of skyscraper B is approximately 10.9 degrees. If skyscraper B is 1425 feet tall, how far apart are the two skyscrapers? Assume the bases of the two buildings are at the same elevation.
Answer:
269.46
Step-by-step explanation:
sin(theta) = opposite / adjacent
adjacent = opposite / sin(theta)
adjacent = 1425*sin(10.9)
adjacent = 269.4610063
The test scores of five students for the first two test of the semester are shown in the table below.
Answer:
A
Step-by-step explanation:
Take test score from Test 1 and add them all together and divide by the number of test
ex) 77+82+69+85+93=406
406/5= 81.2
Then repeat with Test 2
ex) 75+76+71+68+72=362
362/5= 72.4
Therefore the MAD of Test 1 > MAD of Test 2
the answer is A.
Step-by-step explanation:
Add the test scores of the first test together then add the test scores of the second test together then compare and contrast.
The boys kept adding sand, and ten minutes later the volume of the sand cone had increased by 30%. What is the exact volume of the sand cone now? (Show your work. Remember you can draw a picture to help you solve the problem.)
Answer:
a) 84π b) 109.2π
Step-by-step explanation:
The formula to find this is v=πr^2h/3
r=d/2. so the radius (r) is 6 because you have to divide the diameter (12) by 2. and the height is 7. so, 6^2=36 and 36x7=252.
252/3=84
and because the question is asking for the EXACT value, you need to just put the pi symbol next to it. Final answer for a is 84π
B) you need to find 30% of 84, which is 25.2 and add it to 84, and you will get 109.2! Final answer is 109.2π.
A silverware drawer contains 9 forks, 12 spoons, and 7 knives. One piece of silverware is selected at random from the drawer.
What is the probability that a spoon is selected?
Enter your answer as a decimal to the nearest hundredth in the box.
Answer:
The answer is 0.42
Step-by-step explanation:
First we add all the item counts
9 + 12 + 7 = 28
then we divide the number of spoons by 28
12/28 = 0.42
Hope this helps :)
The probability that the selected silverware from the drawer is a spoon is 12/28 or 0.42.
What is probability?Probability of an event is the ratio of number of favorable outcome to the total number of outcome of that event.
A silverware drawer contains 9 forks, 12 spoons, and 7 knives. The total number of items present in the drawer is,
[tex]n=9+12+7\\n=28[/tex]
One piece of silverware is selected at random from the drawer. The drawer contains 12 spoons.
Thus, the probability that a spoon is selected from the drawer which contains 28 silverware is,
[tex]P=\dfrac{12}{28}\\P=0.42[/tex]
Hence, the probability that the selected silverware from the drawer is a spoon is 12/28 or 0.42.
Learn more about the probability here;
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Determine whether the sequence is arithmetic or geometric.
Sequence 1: 32, 16, 0, –16, ...
Sequence 2: 32, 16, 8, 4, ...
Which of the following statements are true regarding Sequence 1 and Sequence 2.
Answer:
Sequence 1 is arithmetic, sequence 2 is geometric.
Step-by-step explanation:
Sequence 1 is being subtracted by 16 each time, so it is arithmetic.
Sequence 2 is being divided by 2 each time, so it is geometric.
Both, sequence 1 and 2, have terms 32 and 16.
Mateyo is building a rectangular prism with a volume of 1000 cubic units. The height of the prism is 10 units. Mateyo claims that the base of the prism must be a square. Draw a base for th rectangular prism that shows that Mateyo is not correct. Remember to label the units.
Answer:
See attachment for drawing
Step-by-step explanation:
Given
[tex]Volume = 1000[/tex]
[tex]Height = 10[/tex]
Required
Drawing that proves Mateyo wrong
First, calculate the base area
[tex]Volume = Base\ Area * Height[/tex]
This gives:
[tex]1000= Base\ Area * 10[/tex]
Divide both sides by 10
[tex]100= Base\ Area[/tex]
Rewrite as:
[tex]Base\ Area = 100[/tex]
The base area is calculated as:
[tex]Base\ Area = Length * Width[/tex]
So, we have:
[tex]Length * Width = 100[/tex]
Mateyo's claim can be interpreted as:
[tex]Length = Width = 10[/tex]
However, there are other possible cases such that:
[tex]Length \ne Width[/tex]
For instance:
[tex]Length = 20[/tex]
[tex]Width = 5[/tex]
See attachment for drawing
what are 2 reasons why people should wear masks for school report.
Answer:
-decreases the chance of contracting any type of virus
-decreases the chance of other people contracting the virus
Step-by-step explanation:
Answer: It keeps people safe, and it keeps you safe as well.
Step-by-step explanation: You're keeping other people safe by wearing a mask,since youre limiting or even entirely preventing particles and germs from reaching other people,and protecting yourself because a mask prevents germs entering your nose and mouth.
What does the P equal in P-17=33
Answer:
Hello! answer: 50
Step-by-step explanation:
33 + 17 = 50 50 - 17 = 33 Hope that helps!
Answer:
P equals 50
Step-by-step explanation:
33 plus 17 equals 50
ILL GIVE BRAILY!!!
If ABCD is dilated by a factor of 1/2 the
coordinate of A would be:
A = ([?],[ ]
Answer:
Step-by-step explanation:
here A(-3,-2)
-3 is x and -2 is y
so use this formula to find A'
p(x,y)=p'kx,ky)
here k is a scale factor which is 1/2
A(-3,-2)=A'(1/2*-3.1/2*-2)
A'(-3/2,-1)
If the circumference of the circle below is 90, what is the length of the minor arc)? 609 A. 90 B. 15 C. 30 D. 10
Answer:
arc XY = 15 units
Step-by-step explanation:
GIVEN :-
Angle subtended by arc XY at center = 60°Circumference of the circle = 90 units.TO FIND :-
Length of XYFACTS TO KNOW BEFORE SOLVING :-
Length of arc of the sector = [tex]\frac{\theta}{360} \times (Circumference \: of \: the \: circle)[/tex] where θ is the angle subtended by arc of the sector at the center of the circle.
SOLUTION :-
[tex]XY = \frac{60}{360} \times 90 = \frac{90}{6} = 15[/tex]
Make a box-and-whisker plot for the data.
Quiz scores: 6,6,7,8,8,8,9,10
Answer:
6-----7{8}9-----10
Step-by-step explanation:
I can't upload a photo but the lower extreme is 6, the lower quartile is 7, the median is 8, the upper quartile is 9, and the upper extreme is 10
Hope this helped :)
on the map the scale shown is 1 inch:20 miles if a city is 900 square miles what is the area of the city on the map
Answer:
45 square inches
Step-by-step explanation:
[tex]\frac{1}{20} = \frac{x}{900}[/tex]
to find x you need to divide 900 by 20
[tex]\frac{1}{20} = \frac{45}{900}[/tex]
The two identical rectangular doors of a barn have
glass panes in the top half, and each bottom half is
made of solid wood, as shown below.
Which of the following measurements is closest to
x, the length of the diagonal brace on the bottom
half of each door?
A. 6 1/2 ft.
B. 11 ft.
C. 8 ft.
D. 5/12 ft
Answer:
C
Step-by-step explanation:
The height of the door is given as 10 feet. The bottom 1/2 has a height of 5 feet.
The width of one door = 12/2 = 6 feet.
The value for x^2 = 5^2 + 6^2
x^2 = 25 + 36
x^2 = 61
sqrt(x^2) = sqrt(61)
x = 7.81
The closest value = 8
Help and explanation
Answer: do 8-10 = 2 the do 8+10= 18 then 18+2=20 so your answer is 20
Step-by-step explanation:
Find the area of the figure.
Answer:
132
Step-by-step explanation:
4*7 + (7+19)/2 * 8 = 28 + 104 = 132
what is the sum of the interior angles ?
Answer:The sum of interior angles in a triangle is 180°. To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is ( n − 2 ) × 180 ∘ where is the number of sides. All the interior angles in a regular polygon are equal.
Step-by-step explanation:
If the graph is reflected across the y-axis, what will be the equation of the new graph?
a) y=-3^-x+1
b) y=3^-x+1
c) y=-3^x-1
d) y=-3^x+1
Answer:
[tex] \displaystyle b)y = { 3}^{ - x} + 1[/tex]
Step-by-step explanation:
we are given a exponential function
[tex] \displaystyle y = {3}^{x} + 1[/tex]
we want to figure out the equation of the new graph reflected across the y-axis
remember that,
[tex] \rm\displaystyle (x,y) \xrightarrow{ \text{ reflection over y - axis}}( - x,y)[/tex]
let y be [tex]3^x+1[/tex] so,
[tex] \rm\displaystyle (x,y) \xrightarrow{ \text{ reflection over y - axis}}( - x, {3}^{ - x} + 1 )[/tex]
hence,
the equation of the new graph
[tex] \displaystyle y = { 3}^{ - x} + 1[/tex]
Please help, I'm behind
Help !!!!!pla for 20 point s
Answer:
look at the picture i have sent
Answer:
Hey mate......
Step-by-step explanation:
This is ur answer.....
Solution :-
= x + 40 + 67 = 180
= x + 107 = 180
= x = 180 - 107
= x = 73
40 + 67 + 73 = 180Hope it helps!
Brainliest pls!
Follow me! :)
PLEASE HELP FAST 30 POINTS! For Trancescient
c = 22.3 km
Step-by-step explanation:
You can solve this problem using cosine law:
[tex] {c}^{2} = {a}^{2} + {b}^{2} - 2ab \cos( \gamma ) [/tex]
where a and b are the legs of the triangle, c is the unknown length and the angle gamma is the angle opposite length c. We know that
a = 50 km
b= 52.4 km
gamma = 25°
c^2 = (50 km)^2 + (52.4 km)^2 -2(50)(52.4)cos25°
= 496.707 km^2
or
c = 22.3 km
Can someone help me with this it is for mathh.
Answer: it would be P=4n
An athlete jumps these 4 distances in a long jump competition.which jump does not round to 4.7 meters
Answer:
sadadacvfbrdgsdzf
Step-by-step explanation:
pls help me apparently its easy
Answer:
The answer should be 10c - 4d
Step-by-step explanation:
3c + 7c - 9d + 5d = 10c - 4d
Step-by-step explanation:
First you add up 3c and 7c as they have the same parameter. That makes 10c. Then calculate 5d-9d which equals -4d. You can change the order of 5d-9d in a way that you would reduce the larger number from the smaller number so that you could calculate it easily like that. The final Ander 2ould be 10c-4d