the discriminant of x2 + 6x + 9 = 0
Answer:
D = 0
Step-by-step explanation:
D = b^2 - 4ac =
= 6^2 - (4*1*9) =
= 36 - 36 = 0
Final answer:
The discriminant of the quadratic equation x² + 6x + 9 = 0 is 0, which means there is one real root, and the graph of the equation is tangent to the x-axis at one point.
Explanation:
The discriminant of a quadratic equation is the part of the formula b² - 4ac that determines the nature of the roots of the equation. For the quadratic equation x² + 6x + 9 = 0, we can identify a = 1, b = 6, and c = 9. Using the discriminant formula, we get:
• Discriminant, D = b² - 4ac
• D = (6)² - 4(1)(9)
• D = 36 - 36
• D = 0
Since the discriminant is zero, it indicates that the quadratic equation has one real root, and the graph of the equation touches the x-axis at one point (the vertex of the parabola).
Amanda surveyed 13 students in her class about their heights in inches. Her data are listed below.
52, 53, 55, 55, 56, 57, 58, 58, 59, 59, 59, 62, 65 Which box plot correctly displays her data?
Answer: The answer is A
Step-by-step explanation:
because you have to take your lowest number 52 and put a line the your highest number 65 and put a line then 55, 58 and 59 are being repeated so therefor you do a like box thing to get your answer dont really know how to explain hope this helps
You are measuring the height of a lamppost. You stand 40 inches from the base
of the lamppost. You measure the angle of elevation from the ground to the top!
of the lamppost to be 70°. Find the height h of the lamppost to the nearest inch.
Answer:
110in
Step-by-step explanation:
The horizontal distance from where you stand to the lamp post is 40 inches.
Let the height of the lamp post be y inches.
The angle of elevation from the ground to the top!
of the lamppost to be 70°.
The height , y and the horizontal distance, form the legs of a right triangle .
We can use the tangent ratio, to calculate the height of the lamp post .
[tex] \tan(70 \degree) = \frac{y}{40} [/tex]
[tex]y = 40 \tan(70) [/tex]
[tex]y = 109.9[/tex]
To the nearest inch, the height is 110 inches
The height of the lamppost is approximately 110 inches, calculated using the tangent of a 70° angle with a base distance of 40 inches.
To find the height ( h ) of the lamppost, we can use trigonometric relationships. Given that we stand 40 inches from the base of the lamppost and measure the angle of elevation to be 70°, we can use the tangent function:
[tex]\[\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\][/tex]
In this scenario:
- The angle [tex]\(\theta = 70^\circ\)[/tex]
- The adjacent side (distance from the base) is 40 inches
- The opposite side is the height \( h \) of the lamppost
Using the tangent function, we have:
[tex]\[\tan(70^\circ) = \frac{h}{40}\][/tex]
To solve for ( h ), we rearrange the equation:
[tex]\[h = 40 \cdot \tan(70^\circ)\][/tex]
Now we need to calculate [tex]\( \tan(70^\circ) \):[/tex]
[tex]\[\tan(70^\circ) \approx 2.747\][/tex]
Multiplying this by 40 inches:
[tex]\[h = 40 \cdot 2.747 \approx 109.88\][/tex]
Rounding to the nearest inch:
[tex]\[h \approx 110 \text{ inches}\][/tex]
Therefore, the height of the lamppost is approximately 110 inches.
An artist creates a cone-shaped sculpture for an art exhibit. If the sculpture is 6 feet long and has a base with a circumference of 28.260 feet, what is the volume of the sculpture? Use 3.14 for piπ HELP Me PLZ :(
Answer: The volume of the sculpture is 64.11 ft3
Hope this helps :)
Answer:
125.8983 ft^3
Step-by-step explanation:
Circumference of the circle is 28.260
Formula for the circumference of a circle is 2Πr
2*3.14 is 6.28
28.26/6.28=4.5
r is 4.5
Formula for the volume of a cone is 1/3*pi*r^2*h
1/3*3.14*4.5^2*6 = 125.8983
What are the foci of the hyperbola whose equation is (x-6)^2/16-(y+7)^2/9= 1?
The foci of the hyperbola is (0,3) and (0,-3).
Step-by-step explanation:
Given,
The equation of the hyperbola: [tex]\frac{(x-6)^{2} }{16} -\frac{(y+7)^{2} }{9} =1[/tex]
To find the foci of the given parabola
Formula
If the equation of the hyperbola: [tex]\frac{(x-h)^{2} }{a^{2} } -\frac{(y-k)^{2} }{b^{2} } =1[/tex]
The focus will be (0,±c) where c² = a²+b²
Now,
Here, a=3 and b=4
c² = 3²+4² = 25
or, c = ±5
Hence,
The foci of the hyperbola is (0,3) and (0,-3)
Answer:
(1, -7) and (11, -7)
or A on edge
Step-by-step explanation:
took the quiz
The table represents the function f(x) and g(x).
Which input value produces the same output value for the two functions.
A. x = -3
B.x = -1
C. x = 0
D. x =1
D. x =1 input value produces the same output value for the two functions.
What is F x and G x?Composition of a function is done by substituting one function into another function. For example, f [g (x)] is the composite function of f (x) and g (x). The composite function f [g (x)] is read as “f of g of x”. The function g (x) is called an inner function and the function f (x) is called an outer function.
What is the sum of G x and f x?Suppose we have two functions, f(x) and g(x). We can define the sum of these two functions by, (f + g)(x) = f(x) + g(x), where x is in the domain of both f and g.
How do you find the intersection of FX and GX?When the graphs of y = f(x) and y = g(x) intersect , both graphs have exactly the same x and y values. So we can find the point or points of intersection by solving the equation f(x) = g(x). The solution of this equation will give us the x value(s) of the point(s) of intersection.
Learn more about function f(x) and g(x), refer
https://brainly.com/question/4397150
#SPJ2
Help me with this please so I can finish this class and move on to the others
Answer:
20x
Step-by-step explanation:
1 do the work 2 dont ask brianly
Answer:C
Step-by-step explanation: 42 is bigger than 40 but I’m really not sure
1. - 4 = 7(1-n) =
2. -5x + 3(6 + 7x)
3.- 2b - (9 - 105) =
4. 10+ 5(9x - 9) =
5.-9(6x - 3) + 6(1 +4x) =
6.-10(2 - 9x) + 6(x - 10) =
7. 5(-2n+4) + 2(n + 3) =
8. - 7(n+3) - 8(3 +8n) =
Hope this will help u...
The perimeter of a rectangular shop in the mall is 34 m the area is 70 m² what are the dimensions of the shop
Answer:7 x 10
1) Can be done by trail and error
Or
2) setting and slowing two equations
Step-by-step explanation:
If a and b are sides of rectangle
(1). 2a + 2b = 34
(2). ab = 70
From 1
a= 17-b
Substitute above a to (2)
(17-b)b = 70
17b - b^2 = 70
-b^2 + 17b -70 = 0
Multiple above by -1
b^2 - 17b + 70 = 0
Solving quadratic equation by factorising
(b-7)(b-10)=0
b=7 or b=10
If b= 7. a =10
If b=10. a=7
The dimensions of the rectangular shop that satisfies the given condition of having a perimeter of 34 m and an area of 70 m² are length=20 m and width=7 m.
Explanation:The question is about finding the dimensions of a rectangular shop, given its perimeter and area. The perimeter and area of a rectangle can be expressed using the formulas Perimeter = 2*(length + width) and Area = length * width. In the problem, we are given that the perimeter is 34 m and the area is 70 m².
Let's denote the length as 'l', and the width as 'w'. To solve this, we can setup and solve a system of equations based on our formulas:
2*(l + w) = 34
l * w = 70
From these equations we can find that the dimensions of the rectangular shop that fit the conditions are length=20 m and width=7 m.
Learn more about Perimeter and Area here:https://brainly.com/question/11957651
#SPJ12
Select the correct answer.
What is the justification for step 3 in the solution process?
10d − 5 = 4d − 15 − 3d
Step 1: 10d − 5 = d − 15
Step 2: 9d − 5 = -15
Step 3: 9d = -10
Answer: subtraction property of equality
Step-by-step explanation:
subtracting d from both sides is the subtraction property of equality
Answer:
subtraction property of equality
Step-by-step explanation:
f(x)=x^2 what is g(x)
Answer:
Step-by-step explanation:
when x=2,g(x)=1
from B when x=2
g(x)=1/4×2²=1
which is true .
so B
If the center of the circle were moved from the origin to the
point (h, k) and point P at (x, y) remains on the edge of the
circle, which could represent the equation of the new
circle?
O (h + x)2 + (k + y)2 = 22
0 (x – n)2 + (y – k)2 = p2
O (k + x)2 + (h + y)2 = 22
0 (x – k)2 + (y – 5)2 = 12
Answer:(x-h)^2+(y-k)^2=r^2
Step-by-step explanation:
I just answered it and it’s correct
The equation of the new circle will be,
⇒ (x - h)² + (y - k)² = r².
What is mean by Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
Now, If the center of the circle were moved from the origin to the point (h, k) and point P at (x, y) remains on the edge of the circle.
Then, Equation of the new circle,
(x - h)² + (y - k)² = r²
Where center = (h, k)
radius = r
Hence, the equation of the new circle will be,
⇒ (x - h)² + (y - k)² = r².
Learn more about the circle visit:
https://brainly.com/question/24810873
#SPJ7
a coin is flipped and a number cube is rolled what is the sample space for this experiment
Answer:
h1,h2,h3,h4,h5,h6,t1,t2,t3,t4,t5,t6
Step-by-step explanation:
h or t is the coin, the number is the die
Final answer:
The sample space for flipping a coin and rolling a number cube consists of 12 possible outcomes. The probability of event A occurring is 1/6. Events A and B are mutually exclusive as they cannot occur at the same time.
Explanation:
A coin is flipped and a number cube is rolled; the sample space for this experiment can be listed by combining each possible outcome of the coin flip with each possible outcome of the number cube roll. The coin can either be heads (H) or tails (T), and the number cube, which is a six-sided die, can land on any number from 1 to 6.
H1
H2
H3
H4
H5
H6
T1
T2
T3
T4
T5
T6
Therefore, the sample space consists of 12 possible outcomes.
For part b, event A is "either a three or a four is rolled first, followed by landing a head on the coin toss." The favorable outcomes for event A are H3 and H4. Since there are 12 possible outcomes, and 2 of them are favorable, the probability P(A) is 2/12, which simplifies to 1/6.
For part c, event B is "the first and second tosses land on heads," which is not possible since the first "toss" is actually a roll of a die. Therefore, events A and B are mutually exclusive, as they cannot occur simultaneously. The occurrence of event A does not involve a second toss of the coin and event B is not possible within the context of this experiment.
Part A picture above
Part B. What are the coordinates of the point D after a dilation with a scale factor of 5, centered at the origin?
A. D’(0,2)
B. D’(0,5)
C. D’(0,10)
D. D’(10,0)
Answer:
Part A C = (10,5) Part B C. D'(0,10)
Step-by-step explanation:
Part A
Since c is at the point (2,1) in relation to the origin, we can multiply those distances by our scale factor of 5
(2,1) * 5 = (10,5)
The new point C is going to be (10,5)
Part B
If you dilate with a factor of 5 -- relative to the origin -- you have to multiply the distance from the origin by 5.
In this case, point D is already on the y axis, so it's x value wouldn't be affected. Point D is currently 2 units away from (0,0), so we can multiply 2*5 to get 10 -- our ending point is (0,10)
One more than three-eighths of a number is eleven. Just write out equation do not solve please
Answer:
Let's just call the number x. 3/8ths of x and 1 more equals 11.
As an equation, this basically means
[tex]\frac{3}{8} x+1=11[/tex]
The equation derived from the given statement "One more than three-eighths of a number is eleven" is 3/8 * X + 1 = 11.
Explanation:In mathematics, especially in algebra, we often have to deal with problems where a certain relationship is given between a number and its fraction, and the task is to find the number. In the problem you presented, "One more than three-eighths of a number is eleven", we are required to express this problem as an equation.
The three-eighths of a number can be represented as 3/8 * X (where X is the unknown number we're seeking), and 'one more than' simply means we're adding 1 to this fraction. The given relationship states that this result is eleven.
So, the equation can be written as: 3/8 * X + 1 = 11.
Learn more about Equation Formation here:https://brainly.com/question/30167556
#SPJ3
Please help asap please i will mark branlist
Answer:
B. (-3,3)
Step-by-step explanation:
We want to know the solution to the equations, which just means where the two lines intersect.
If we just count the spaces, we can see that they touch at (-3,3). Remember that coordinates are (x,y), so we go left 3 (-3,3) and up 3 (-3,3).
Answer: the answer to this question is B
Step-by-step explanation:
Daniel bought a computer and paid $50.94 in
sales tax. The sales tax was 11% of the
purchase price. What was the cost of the
computer before tax?
Answer:
Daniel bought a computer and paid $50.94 in sales tax. The sales tax was 11% of the purchase price. What was the cost of the computer before tax?
11/100 x 50.94= $5.60
Tax= $5.60
Cost of the computer before tax= $50.94- $5.60
Cost of computer= $45.34 before tax
Step-by-step explanation:
Please Help me !! Really I don’t know
100 points!!!!!!!!!!!!!!!!!!!!What should the numerator of the second fraction be so that the fractions are equivalent?
[tex]\frac{2}{3} =\frac{?}{14}[/tex] =
Answer:
28/3 or 9⅓
Step-by-step explanation:
2/3 = x/14
x = 2×14/3
x = 28/3
Answer:
28/3 =x
Step-by-step explanation:
2/3 = x/14
We can solve using cross products
2*14 = 3x
28 = 3x
Divide each side by 3
28/3 = 3x/3
28/3 =x
MATH EASY POINTS: the volume of water y (in cubic meters) that flows over niagara falls during peak daytime tourist hours in x minutes can be approximated by the equation y=168,000x. Approximately how many cubic meters of water flow over the falls in one hour
Answer:
10,080,000 cubic meters is the answer.
Step-by-step explanation:
For every minute (x), 168,000 cubic meters (y) of water are added. 1 hour has 60 minutes, so 60 x 168,000. That gives 10,080,000.
3 children share 6 crayons equally
How many pencils will each child get?
Answer:
2
Step-by-step explanation:
=6/3
=2
Answer: 2crayons
Step-by-step explanation:
3 children share 6crayons equally
Looking at this
We have 3 children
We have 6crayons
How many does each one of them get
Let the each child's crayon represent p
I child to p crayon
3children to 6crayon
Cross multiply
1 ----- p
3 -----6
So we have
6×1=3×p
6=3p
P=6/3
P=2
So 1 child is entitle to 2crayons
Therefore, each child has 2crayons to themselves.
Which graph represents the function given by the table of values? A) A B) B C) C D) D
Answer:
a
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
Pumpkins are being sold for $1.30 at the local farmers market. How much would a pumpkin be weighing 6lb 9oz
Answer:
$8.53
Step-by-step explanation:
The first thing you do is convert the oz into pounds. There is 16 oz in a pound so our fraction is 9/16 which is 0.5625 . Then adding to the pounds it becomes 6.5625 pounds. Then multiply by 1.3.
Find the area of the square in inches and enter your answer below. Do not
include units in your answer.
Given:
Side length of square = 2 in
To find:
The area of the square
Solution:
Area of the square:
Area = side × side
= 2 in × 2 in
Area = 4 in²
Therefore, the area of the square is 4 inches².
Angles A and B are two acute angles in a triangle. If sin A equals cosine B, what can you conclude about the triangle?
Answer:
It's a right angle triangle with 90° at C
Step-by-step explanation:
sin A = cosB when
A + B = 90
The condition that sin A equals cosine B, with A and B being acute angles, indicates that both angles are complementary and add up to 90 degrees, suggesting a right-angled triangle.
Explanation:When given the condition that sin A equals cosine B in a triangle, and both angles A and B are acute, we can determine that triangle A and B are complementary, which means they add up to 90 degrees.
This is due to the co-function identity, where sin(90° - θ) = cos(θ) and cos(90° - θ) = sin(θ) for acute angles in right-angled triangles.
If A and B are in the same triangle, and given it is a right triangle (since they are acute and the sine of one equals the cosine of the other), we can conclude that A + B = 90°, and thus, the third angle will also be 90 degrees, making the triangle a right-angled one.
What is
The lines graphed below are parallel. The slope of the red line is
the slope of the green line?
Answer:
2/5
Step-by-step explanation:
The lines are parallel, so they have the same slope.
The red lines has a slope of 2/5
The green line has a slope of 2/5
Answer: 2/5
Step-by-step explanation:
if they did not have the same slope, they would not be parallel
A. 18 is 20 percent of what number? B. 15 is 25 percent of what number? C. 12 is 30 percent of what number? D. 24 is 40 percent of what number? E. 39 is 60 percent of what number? F. 78 is 30 percent of what number? Question: Represent each as an equation with x as the unknown number, and solve.
A. 18 is 20% of 90
B. 15 is 25% of 60
C. 12 is 30% of 40
D. 24 is 40% of 60
E. 39 is 60% of 65
F. 78 is 30% of 234
(Sorry I have to go, but hopefully I helped you)
Choose all of the problems that result in an answer of 8.5.
A) 0.85 × 101
B) 85 × 101
C) 85 ÷ 101
D) 0.85 ÷ 102
E) 0.085 × 102
Answer:E
Step-by-step explanation:
Type it all into a calculator
Based on your results in Question 1, how is the volume of the cone related to the volume of the cylinder, given that their bases and heights are the same? (Keep in mind that the volumes you recorded were rounded, not exact values.)
Answer:
in a similar way,the volume of a cone and a cylinder that have identical bases and height are proportional. if a cone and a cylinder have bases (shown in color) with equal areas and both have identical heights, the the volume of a cone is one-third that volume of a cylinder is V=πr2h
Step-by-step explanation:
Answer:
If the base dimensions and the heights are the same, the volume of the pyramid is approximately 1/3 the volume of the cube.
Step-by-step explanation:
awnser for plato math
Please help me solve this ASAP
Answer:
x = (164 - y)/5
y = 165 - 5x
Step-by-step explanation:
A whole rotation is 360° (All the angles together = 360°)
148 + 2x + 47 + y + 3x = 360
195 + 5x + y = 360
165 = 5x + y
y = 165 - 5x
5x = 165 - y
x = (164 - y)/5