Answer:
Correct option: First one -> real and distinct.
Step-by-step explanation:
To evaluate the roots of the equation 7x^2 + x - 1 = 0, lets find the discriminant Delta using the Bhaskara's formula:
[tex]\Delta = b^{2} - 4ac[/tex]
Where a, b and c are coefficients of the quadratic equation (in this case, a = 7, b = 1 and c = -1)
So we have that:
[tex]\Delta = 1^{2} - 4*7*(-1) = 29[/tex]
To evaluate the roots of the equation, we have the following cases:
[tex]\Delta > 0[/tex] : Two roots real and distinct
[tex]\Delta = 0[/tex] : Two roots real and equal
[tex]\Delta < 0[/tex] : Two roots not real
In our case, we have [tex]\Delta > 0[/tex], so the roots are real and distinct.
Correct option: First one
Ava and Sara both started getting an allowance 12 weeks ago, and they haven't spent a cent! They get $1 for each year of their age. Sara is 8 and gets $8 per week. Ava has $24 more than Sara. How old is Ava?
Answer:
Ava is 10 years old
Step-by-step explanation:
Sara is 8
Sara=$8 per week for 12 weeks
$8×12 weeks=$96
Ava has $24 more than Sara
x*12=96$+$24
12x=120
x=120/12
x=10
Ava's age is 10
solve for x. 7(x-3)+3(4-x)=-8
Answer:
x=1/4
Step-by-step explanation:
1.distribute the 7 and 3 into parentheses
2. combine like terms
3. add 9 on both sides
4. divide both sides by 4
x=1/4
hope this helped!
Answer:
x = [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
7(x-3)+3(4-x)= -8
Expand 7(x-3) and 3(4-x)
i.e. 7x-21+12-3x= -8
4x-9=-8
Collect like terms
4x= -8+9
4x= 1
x = [tex]\frac{1}{4}[/tex]
Hope this helps!!!
what is the side length of a cube with a volume of 166 yd^3
Answer: 5.5 yd
Step-by-step explanation:
To find the side length of the cube, the volume is a clue. We know that all sides of a square are equal, and the volume of a cube is length×width×height. Since the length, width and height are all the same, we know it is V=x³. Since we know the volume, we can plug in and solve for x.
166=x³
In order to get x alone, we have to cube root both sides.
x≈5.5 yd
Last year, there were “x” students in the Math Club, but this year, there was a 40% increase in membership. Represent this year’s membership in terms of “x”.
Answer:
(x)1.4=Y
Step-by-step explanation:
40% increase of memeber so ita 140% of X
A hummingbird’s nest is 6 meters high in a tree. A flower is on the ground 14 meters away from the base of the tree. How far will the hummingbird need to fly to get from its nest to the flower if it takes a direct path?
Answer:
15.23 m
Step-by-step explanation:
The problem given describes the shape of a right angled triangle.
From the diagram below:
The height of the tree is the opposite = 6 m
The distance of the flower from the base of the tree = adjacent = 14 m
The distance the bird must fly to get from the nest to the flower = hypotenuse = h
According to Pythagoras rule:
[tex]hyp^2 = opp^2 + adj^2[/tex]
Therefore:
[tex]h^2 = 6^2 + 14^2\\\\h^2 = 36 + 196\\\\h^2 = 232\\\\h = \sqrt{232} \\\\h = 15.23 m[/tex]
The bird will have to fly 15.23 m to get from its nest to the flower in a direct path.
HELP ME!!! Find the y intercept of the line y=2x-11
Answer:
It would intercept the y-axis at y = -11
Step-by-step explanation:
Here is the work
Answer:
Step-by-step explanation:
the y interception is -11
Y=mx+b formula the b is for the y intercept and the m is the slope.
help..................
Answer:
D
Step-by-step explanation:
Let's say we're translating the origin, (0, 0) left 6 units and up 4 units. We would get ( -6, 4), which is (x - 6, y + 4), which is D
what is the slope of the equation y= 5/4c- 7/4
Answer:
5/4 is the slope
Step-by-step explanation:
y= 5/4c- 7/4
This is in the slope intercept form
y = mx+b where m is the slope and b is the y intercept
5/4 is the slope and -7/4 is the y intercept
Answer:
5/4
Step-by-step explanation:
This equation is in slope intercept form (y=mx=b) so when interpreting the information we see that the slope is 5/4.
y = y
m = slope
x = x or in this case they use c
b = y intercept
This equation represents a line that intercepts at -7/4 and has a slope of 5/4. This can be checked by plugging in any point on the line for x and y.
Hope this helps!
Which data set could be represented by the box plot shown below?
A horizontal boxplot is plotted along a horizontal axis marked from 0 to 20, in increments of 1. A left whisker extends from 1 to 6. The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12. The right whisker extends from 16 to 19. All values estimated.
Answer:
Any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.
Step-by-step explanation:
Interpreting Box Plots
A box plot is used to present the 5-Number summary of a set of data.
The 5-Number summary consists of the following in their order of appearance on the box plot.
Minimum ValueFirst Quartile, [tex]Q_1[/tex]Median, [tex]Q_2[/tex]Third Quartile, [tex]Q_3[/tex]Maximum ValueIn the box plot, the following rules applies
The whisker starts from the minimum value and ends at the first quartile.The box starts at the first quartile and ends at the third quartile. There is a vertical line inside the box which shows the median. The end whisker starts at the third quartile and ends at the maximum value.Using these, we interpret the given box plot
A left whisker extends from 1 to 6.
Minimum Value=1First Quartile =6The box extends from 6 to 16 and is divided into 2 parts by a vertical line segment at 12.
Median=12Thrid Quartile=16The right whisker extends from 16 to 19.
Maximum Value =19Therefore any set of data that satisfies the 5-Number summary: 1,6,12,16 and 19 can be represented with the box plot.
The distance between Joshua's home and school is 800 m. Joshua takes 5 min to walk
the first 100 m to a Convenient Store nearby. He would spend 10 min in the store to
complete his purchase. Finally, he takes another 20 min to reach school. What is his
average speed in m/s?
Answer:
= 0.38 m/s
Step-by-step explanation:
▪Total distance = 800 m
5 min = 100 m
▪Remaining distance = 800 - 100 = 700 m
20 min = 700 m
▪Total time taken = 20 + 10 + 5 = 35 min
If 1 min = 60 sec
What about 35 min = ?
= 35 x 60
= 2100 sec
▪Average speed = TD ÷ TT
= 800 ÷ 2100
= 0.38 m/s
Find the value of x in the isosceles triangle shown below
Thank you!
What’s the answer ??
Answer:
-5^x-3x-6
Step-by-step explanation:
(-5^x - 4 + g(x) ) (x)
(-5^x - 4 - 3x -2) simplified -5^x-3x-6
Answer:
-5^x -3x -6 = A[tex]f(x) = - {5}^{x} - 4 \\ g(x) = - 3x - 2 \\ (f + g)(x) = \\ ( - {5}^{x} - 4) + ( - 3x - 2)[/tex]
[tex]( - {5}^{x} - 4) + ( - 3x - 2) \\ - {5}^{x} - 4 - 3x - 2 \\ collect \: like \: terms \: \\ - {5}^{x} - 3x - 4 - 2 \\ [/tex]
[tex] - {5}^{x} - 3x - 6[/tex]
a cookie recipe calls for 10 cups of milk. Magdahas already put in 7.3 cups. How many more cups does she need to put in?
HELP! Which of the following are interior angles in the figure below? PLEASEEE!!!!! URGENT dont need to explain
Work out the value of x
Ps I would appreciate if you showed me how to work it out
Thank you
Answer:
x = 67.5°
Step-by-step explanation:
A circle's angles add up to 360°
So,
x+3x+90 = 360
4x+90 = 360
4x = 360-90
4x = 270
Dividing both sides by 4
x = 67.5°
I can’t find the area can you please help me with it. It’s the question with the question mark
Answer:
1947 units^2
Step-by-step explanation:
you can split it up into different sections of rectangles.
the first one is 25x39= 975
The second section is the connector which you do
43-25=18
and you do 39-27=12 and then
you multiple 18x12 which equals 216
and the final section you do 24+12=36
and 36x21=756
and finally you add them all up to equal 1947 units^2
A farmer has a 100 ft by 200 ft rectangular field that he wants to increase by 15.5% by cultivating a strip of uniform width around the current field. How wide of a strip should he cultivate around the edge of his field to do this? The strip around the outside is _ feet wide
Answer:
(a) The strip should be 5ft wide
(b) The strip around the outside field is 10ft wide.
Step-by-step explanation:
Given:
Length of the rectangular field, L= 200 ft
width of the rectangular field, w = 100 ft
Area of the rectangular field, A = 200ft x 100ft = 20000 ft^2
let the width of the strip = x
The strip around the outside field = 2x
If the field is increased by 15.5%
New area of the field = 1.155 x 20000 = 23,100 ft^2
The increase in area of the field = 3,100 ft
3,100 = New area of field - old area of the field
3100 = (200 + 2x)(100 + 2x) - 20000
3100 = 20000 + 400x 200x + 4x^2 - 20000
3100 = 600x + 4x^2
Divide through by 4
775 = 150x + x^2
x^2 + 150x - 775 = 0
Factorize
(x + 155)(x-5) = 0
x = 5 ft
The strip should be 5ft wide.
The strip around the outside field = 2 x 5 ft = 10 ft
Thus, the strip around the outside field is 10ft wide.
13. Jane buys a set of 17 spiral notebooks. Each notebook has 95 pages. What is total number of pages?
Multiply number of notebooks by number of pages in each one.
17 x 95 = 1615
The answer is 1,615 total pages
Answer:
A. 1615
Step-by-step explanation:
Solve as shown:
17 books that each have 95 pages equals the total pages.
17(95)=?
17(95)=1615
What is the equation of the following line? Be sure to scroll down first to see all answer options.
Answer:
y = 9x
Step-by-step explanation:
The y intercept is zero since it goes through the point (0,0)
We need to find the slope
m = (y2-y1)/(x2-x1)
= (9-0)/(1-0)
= 9/1
Putting this into slope intercept form y = mx+b
y = 9x +0
y = 9x
If you are asked to graph y = 3x + 1, or y = x2 - x - 6, or y = x3 - 3, do you think it is a good idea to start by plugging in zeros? That is, to let x = 0 and then let y = 0? Why or why not?
Answer:
I think you should start with a table and then write all your points for x then in the next column your answers for y.
Then take your medium and start drawing.
I suggest your x's should start from 0 and increase by 1 or 2
Then when you reach a certain point then go back to 0 and start doing your negatives.
For example if y = 2x
x | y
0|0
1 | 2
2| 4
3|6
4|8
....
then
16|32
0|0
-1|-2
-2|-4
Thanks for this question. I am working my way up to brainliest answer and Master Answerer. This answer took a lot of time to type so I hope I get good review.
:)
:)
Step-by-step explanation:
What is the image of the point (-5, 2) under the translation T3,-4?
Answer: (5,7)
Step-by-step explanation:
We want to find the image of a point after a given translation.
The image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)
First, we can define how a general translation T(a, b) affects a general point (x, y).
It will add a units to the x-value and b units to the y-value, then we have:
T(a,b)[(x, y)] = (x + a, y + b).
Now we just need to apply the translation:
T(3, -4) to the point (-5, 2)
It gives:
T(3, -4)[(-5, 2)] = (-5 + 3, 2 + (-4)) = (-2, -2)
So the image of the point (-5, 2) under the translation T(3, -4) is the point (-2, -2)
If you want to learn more, you can read:
https://brainly.com/question/16874971
What are the domain and range of f(x) = |x + 6|?
Answer:
The domain is (-∞,∞)
The range is [0,∞)
Step-by-step explanation:
The graph will be a V shape facing upwards with a vertex of (-6,0)
Answer:
Domain = (-∞,∞)
Range = [0,∞)
Step-by-step explanation:
1. When simplified, 17a - 14b - 20a - 2b is equal to
Answer:
- 3a -16b
Step-by-step explanation:
CAn someone please help
no. of squares=90
no. of toothpicks=(89*3)+4
=271
rule of patern = 4+3+3...
no. of toothpicks=1000
no. of squares= (996÷3)+1
= 333
Please help with these questions :(
In the Pythagorean theorem, a squared minim b squared equals c squared. If you apply that formule to question 2.
17^2-8^2 = 289 - 64 = 225 = 15^2.
Therefore, the answer to first question is yes
Then, for question 2, you do the same thing.
41^2 - 40^2 = 51
Here, 51 is not a square number. Most importantly it is not the square of9,
So this triangle is not right angled
Combine the like terms to create am equivalent expression y-(-3y)
Answer:
[tex]=4y[/tex]
Step-by-step explanation:
[tex]y-\left(-3y\right)\\\mathrm{Apply\:rule}\:-\left(-a\right)=a\\=y+3y\\\mathrm{Add\:similar\:elements:}\:y+3y=4y\\=4y[/tex]
Answer:
[tex] = 4y[/tex]
Step-by-step explanation:
[tex]y - ( - 3y)[/tex]
we know that,
[tex]( - ) \times ( - ) = ( + )[/tex]
so,
[tex]y - ( - 3y) \\ y + 3y \\ = 4y[/tex]
hope this helps
brainliest appreciated
good luck! have a nice day!
Find the surface area of the polyhedra
pls!! show how you got the surface area
Answer:
960cm^2
Step-by-step explanation:
surface area = sum of area of one sides
front + back = 336cm^2
side x 2 = 336cm^2
base + top = 288cm^2
sum = 960cm^2
Mark Brainiest, please
Deon has to buy all the butter she needs to make 60 biscuits. She buys the butter in 250 g packs. (b) How many packs of butter does Deon need to buy?
Answer:
200g of sugar, 600g of flour, 400g of butter
Step-by-step explanation:
50g sugar = 15 biscuits
3 x 50g = flour --) 150g = flour
2 x 50g = butter --) 100g = butter
60/15 = 4; 4 times as much
4 x 50g = 200g of sugar
4 x 150g = 600g of flour
4 x 100g = 400g of butter
pleaseee help me w dis!!! marking brainiest!!!
Answer:
x = -8 x=1
Step-by-step explanation:
x^2 +7x = 8
Subtract 8 from each side
x^2 +7x -8 =0
Factor
What 2 numbers multiply to -8 and add to 7
8*-1 = -8
8+-1 = 7
(x+8)(x-1) =0
Using the zero product property
x+8 =0 x-1 =0
x = -8 x=1
Mike built a sand castle that measured 484 centimetres by 386 centimetres, and dug a moat around it.Afterward, he decided to change the castle size, making it 725 centimetres by 314 centimetres.How much longer will the newer moat be than the older one?
Answer:
the newer moat is 169 cm longer than the older one
Step-by-step explanation:
in order to find the difference in length of the two castles, we will first find the perimeters of the two castles then calculate the difference in the perimeters:
old castle:
dimension = 484cm by 386cm
perimeter = 484 + 386 = 870 cm
new castle:
dimension = 725cm by 314cm
perimeter = 725 + 314 = 1039 cm
difference = 1039 - 870 = 169 cm
The total length of the moats used is equals to the perimeter of the sand castles, therefore, the newer moat is 169 cm longer than the older one.
Answer:
Look I know I'm about 2 1/2 years late but the answer is not 169 or whatever the person above me said, it's 660 I answered this before.