According to the discriminant of the quadratic equation, it will have equal roots for p = -16.
What is the discriminant of a quadratic equation and how does it influence the solutions?A quadratic equation is modeled by:
[tex]y = ax^2 + bx + c[/tex]
The discriminant is:
[tex]\Delta = b^2 - 4ac[/tex]
The solutions are as follows:
If [tex]\mathbf{\Delta > 0}[/tex], and it is a perfect square, it has 2 rational solutions.If [tex]\mathbf{\Delta > 0}[/tex], and it is not a perfect square, it has 2 irrational solutions.If [tex]\mathbf{\Delta = 0}[/tex], it has equal roots.If [tex]\mathbf{\Delta < 0}[/tex], it has 2 complex solutions.In this problem, the equation is:
[tex]f(x) = -x^2 + 8x + p[/tex]
Hence the coefficients are a = -1, b = 8, c = p.
It has equal roots if [tex]\Delta = 0[/tex], hence:
[tex]b^2 - 4ac = 0[/tex]
[tex]8^2 + 4p = 0[/tex]
[tex]4p = -64[/tex]
[tex]p = -16[/tex]
More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811
Can someone help me with one of these? Factor using the X method please!
Answer:
Step-by-step explanation:
6. x² + 8x + 7
= x² + 7x + x + 7
= x (x + 7) + 1 (x + 7)
= (x + 1) (x + 7)
Option D is the answer.
7. x² - x - 72
= x² - 9x + 8x - 72
= x(x - 9) + 8(x - 9)
Option B is the answer.
8. x² - 49
= (x - 7) (x + 7) [formula used a² - b² = (a-b)]
Option D is the answer.
9. 9x² - 54x + 72
= 9(x² - 6x + 8)
= 9(x² - 4x - 2x + 8)
= 9[x(x-4) -2 (x-4)]
= 9[(x - 2) (x - 4)]
= Option A is the answer.
10. x⁴ - 3x³ - 10x²
= x² (x² - 3x - 10)
= x² (x² - 5x + 2x - 10)
= x² [x (x-5) + 2 (x-5)]
= x² (x+2) (x-5)
Option A is the answer.
ridiculous a s s s questions
Can anyone help me with this question please ?
I’ll mark you as a brainliest.
Answer:
0.5
Step-by-step explanation:
Don't know if i did it right very sorry if wrong make sure to down vote if wrong have good day good luck on test ;)
If anyone is really good at math please help
Answer:
248 + 7x = 360
Step-by-step explanation:
x = 16
Pls help pls pls pls pls URGENT!!!!!!!!
PLS SOMEONEEEEE
Answer:
1. 51
2. 30
Step-by-step explanation:
Stephanie puts 30 cubes in a box. The cubes are inch on each side. The box holds 2 layers
with 15 cubes in each layer. What is the volume of the box?
Answer:
[tex] 11.25\: {in}^{3} [/tex]
Step-by-step explanation:
Since, box contains two layers of cubes and each layer has 15 cubes.
So, length = 15*1/2 in = 7.5 in,
width = 3*1/2 in = 1.5 in
height = (1/2 + 1/2) = 1 inch
Volume of box = lbh
= 7.5* 1.5 *1
= 11.25 cubic inches
A number b is increased by 6, and then the sum is doubled.
Answer:
2(b+6)
Step-by-step explanation:
The average area of a bedroom in a home is 219 square feet with a standard deviation of 32.5 square feet. What is the largest a bedroom can be and be among the smallest 25% of bedrooms in a home?
Answer:
197.095
Step-by-step explanation:
Mean, m = 219 ft²
Standard deviation, s = 32.5 ft²
For a bedroom to be among the smallest 25%
P(x < Z) = 0.25
From Z probability calculator, this corresponds to a Zscore of - 0.674
Recall :
Zscore = (x - m) / s
x = bedroom size
-0.674 = (x - 219) / 32.5
-0.674 * 32.5 = x - 219
-21.905 = x - 219
x = - 21.905 + 219
x = 197.095
Hence, the largest a bedroom can be and still be among the smallest 25% is 197.095
We wish to analyze the temperature during summer months for the northeaster part of the US proportion or mean
Answer:That would be mean
The mean is the average number. To get the average number you add up all of the numbers, then divide by how many numbers there are.
x2 - 2x
Factorise this pleasee
Answer:
x(x-2)
Step-by-step explanation:
the common multiple here is the x, notice how it appears in both both terms. thus, we can factor it out of the equation going from x²-2x to x(x-2)
x(x-2)
Im assuming you meant x² - 2x but correct me if i'm wrong!
so x is common in both terms so you can take it out and factorise it.
Hope this helps!
need help ASAP !!!
[tex] \sqrt{684 \times 684} [/tex]
Answer:
√(684×684)=√684²=±684
consider the image that shows a tower anchored by a guy with the guy wire is attached at point b on the tower 119 feet above the ground and then anchored to the ground at point a 120 feet from the base of the tower.
Options are: A) sin0= 119/120, B) sin0= 120/119, C) sin0= 119/169, and D) sin0= 120/169
Answer:
C
Step-by-step explanation:
You have to find the area
*Can I get brainliest*
Subtract 1 from the product of 4 and 2. what is this in fraction form? please help? A 4 ÷ 2 − 1 B 4 × 2 − 1 C 4 × (1 − 2) D 1 − (4 × 2)
Answer:
D.) 1 - (4 * 2)
Step-by-step explanation:
Given :
Product of 4 and 2 is written as : 4 * 2
Subtracting 1 from the product above : 1 - (4 *2)
Hence, the fractional form of the question above is simply written as :
1 - (4 * 2)
find the median 60,62,64,54,56,28
Answer:
58
Step-by-step explanation:
you need to order all the numbers together:
28, 54, 56, 60, 62, 64
since the middle 2 are 56 and 60 you need to find the average of those.
(56 + 60)/2 = 58
rolling two number dice and tossing one coin
Find the value or measure. Round answers to the nearest tenth, as needed.
Answer:
26
Step-by-step explanation:
Solve 9x-1 = 41-5x
9x-1 = 41-5x
+1 +1
9x = 42-5x
+5x +5x
14x = 42
/14 /14
x = 3
Plug in X for EF
41-5(3)
41-15
=26
I didn't pay attention in class for a few days and now I'm lost. if somebody could at least explain proportions I would be very thankful.
Answer:
A proportion is a comparison of two numbers that each represent the parts of a whole. Essentially, a proportion says that two fractions are the same, even if the amount is different. For example, 1/2 of 10 marbles is the same proportion as 1/2 of 50 marbles.
Step-by-step explanation:
Giving brainliest pleeeaaasssse help!
If heat transfers from hot to cold, and stops when two objects reach the same temperature, explain why it is possible for the inside of your car to be hotter than the air outside on a hot summer day.
Does a gas give off or absorb energy when it turns into a solid? Explain your answer.
You dont have to answer both just helping me with one would help me out!!! :)
also robot scammers stop giving me random links
Answer:
1. Consider a hot pot taken off the stove and placed on a tile countertop. At first it cools quickly. As it cools, the difference in temperature between the pot and the room air becomes less, and so it takes a long time for the pot to lose enough heat to match room temperature. Two objects at the same temperature are said to be in equilibrium.
2. When a liquid changes into a gas it absorbs energy. When it changes into a solid it gives off energy...If a solid (dry ice for example) is allowed to sublimate into a gas, it absorbs heat - that's why it feels cold when you touch ice. So, if a gas changes into a liquid, it give off heat as an opposite effect. Anytime you compress a gas, it gets warmer.
Sierra has enough fencing to make three chicken coops shown each has the same perimeter which has the greatest area?
Answer:
Top left triangle has the greatest area
Step-by-step explanation:
Area of a triangle:
area = base × height / 2
a = bh/2
Top Left Triangle:
a = 6 × 5.2 / 2
a = 31.2 / 2
a = 15.6
Top Right Triangle:
a = 8 × 2.9 / 2
a = 23.2 / 2
a = 11.6
Bottom Left Triangle:
a = 2 × 7.9 / 2
a = 15.8 / 2
a = 7.9
Compare areas:
15.6 > 11.6 > 7.9
What is the volume of the rectangular prism?
3 cm
8 cm
2 cm
Answer:
54 centimeters
Step-by-step explanation:
Find the points of intersection of the circles.
Answer:
D. (5,0) and (5,10)
Step-by-step explanation:
please use the image to solve it
Answer:
C, D and E are the correct statement
The triangles are congruent by SSS or HL.
Triangles M N Q and P Q N are connected at side Q N. Triangle M N Q is rotated about point N and then is shifted to the left to form triangle P Q N.
Which transformation(s) can map TriangleMNQ onto TrianglePQN?
translation only
reflection only
rotation, then reflection
rotation, then translation
Answer:
rotation, then translation
Step-by-step explanation:
The transformation that map triangle MNQ onto triangle PQN is rotation, then translation.
The given triangles;
Triangle MNQ Triangle PQNA translation of a triangle occurs when the triangle shifts up, or down, of left or right on the coordinate plane.
The reflection of a triangle occurs when the vertices of the triangle is flipped over the opposite side.
Since the triangle MNQ is rotated then shifted to the left to form the new triangle PQN, we can conclude that the transformation that map triangle MNQ onto triangle PQN is rotation, then translation.
Learn more about rotation and translation of triangles here: https://brainly.com/question/1616371
If you could answer all parts to this problem it’ll make my day . please
Answer: 40x25=1,000 and 64x40=2,560! Does this help
?
The net of a rectangular prism is shown below. Each square represents 1 square unit.
What is the total surface area of the net shown?
Answer:
56 units²Step-by-step explanation:
There are two bases of 3x4 and 4 sides of 2x4
Total surface area is:
2(3*4) +4(2*4) = 56 units²A cargo plane flew from the US across the Atlantic at 280 mph, and flew back to the US at 300
mph. Given that the first trip took two hours longer, how long was the return trip?
Answer:
Step-by-step explanation:
300t=280(t+2)
300t=280t+560
20t=560
t=28
11. What is the value of x?
X
X-
2
x + 5
x + 1
da - x+5
Explicación
cualquier expresión multiplicada por 1 es igual a si mismo
x-2x+s
agrupe los términos semejantes
-x+5
One jar has 13 pennies, a second jar has 7 pennies, a 3rd jar has 10 pennies, and a 4th jar has 30 pennies. On average how many pennies does each
jar have?
Answer:
60
Step-by-step explanation:
13+7=20 20=10=30 30+30= 60
Hope this helps!
Answer:15
Step-by-step explanation:
A quadrilateral has two angles that measure 290° and 20°. The other two angles are in a
ratio of 2:3. What are the measures of those two angles?
Answer:
Step-by-step explanation:
The remains two angles are 2x and 3x.
2x+3x = 360-290-20 = 50°
x= 10°
One angle is 20°. The last angle is 30°
I need help I'm confused