Answer:
The graphs do intersect at two values of x;
x = 1
and
x = -1
Step-by-step explanation:
We have the two equations:
y = 2*x - 9
y = -(x - 1)^2 - 7
We know that when we graph these equations, the graphs do intersect.
if the graphs intersect, then we must have at least one point (x, y) that is a solution for both equations.
because in this point y is the same for both equations, then we can write:
2*x - 9 = y = -(x - 1)^2 - 7
this leads to the equation:
2*x - 9 = -(x - 1)^2 - 7
now we can solve this for x.
2*x - 9 + (x - 1)^2 + 7 = 0
2*x + x^2 - 2*x + 1 + 7 - 9 = 0
x^2 - 1 = 0
x^2 = 1
x = √1
Then we have two possible solutions:
x = 1, and x = -1
For what value of k is the expression x^4 + kx^2 + 49 a perfect square?
Answer:
[tex]k=14[/tex]
Step-by-step explanation:
Completing the square gives
[tex]x^4 + kx^2 + 49\\= (x^2+7)^2 - 14x^2 + kx^2[/tex]
So we have to cancel the latter two terms out for the expression to always become a square (otherwise we are dealing with a square plus something else, which doesn't always result in a square), giving us our answer directly.
Answer:
k=± 14
Step-by-step explanation:
[tex]x^4+kx^2+49\\Disc.=b^2-4ac=k^2-4*1*49\\it ~ is ~a ~ perfect ~ square.\\k^2-196=0\\k^2=196\\k= \pm 14[/tex]
TWVU is a trapezoid with midsgment FG find the value of x please help
Answer:
Find each measure.
1.
SOLUTION:
The trapezoid ABCD is an isosceles trapezoid. So,
each pair of base angles is congruent. Therefore,
ANSWER:
101
2. WT, if ZX = 20 and TY = 15
SOLUTION:
The trapezoid WXYZ is an isosceles trapezoid. So, the
diagonals are congruent. Therefore, WY = ZX.
WT + TY = ZX
WT + 15 = 20
WT = 5
ANSWER:
5
COORDINATE GEOMETRY Quadrilateral
ABCD has vertices A(–4, –1), B(–2, 3), C(3, 3),
and D(5, –1).
3. Verify that ABCD is a trapezoid.
SOLUTION:
First graph the points on a coordinate grid and draw
the trapezoid.
Use the slope formula to find the slope of the sides of
the trapezoid.
The slopes of exactly one pair of opposite sides are
equal. So, they are parallel. Therefore, the
quadrilateral ABCD is a trapezoid.
ANSWER:
ABCD is a trapezoid.
4. Determine whether ABCD is an isosceles trapezoid.
Explain.
SOLUTION:
Refer to the graph of the trapezoid.
Use the slope formula to find the slope of the sides of
the quadrilateral.
The slopes of exactly one pair of opposite sides are
equal. So, they are parallel. Therefore, the
quadrilateral ABCD is a trapezoid.
Use the Distance Formula to find the lengths of the
legs of the trapezoid.
The lengths of the legs are equal. Therefore, ABCD
is an isosceles trapezoid.
ANSWER:
isosceles;
5. GRIDDED REPSONSE In the figure, is the
midsegment of trapezoid TWRV. Determine the value
of x.
SOLUTION:
By the Trapezoid Midsegment Theorem, the
midsegment of a trapezoid is parallel to each base
and its measure is one half the sum of the lengths of
the bases.
are the bases and is the
midsegment. So,
Solve for x.
16 = 14.8 + x
1.2 = x
ANSWER:
1.2
CCSS SENSE-MAKING If ABCD is a kite, find
each measure.
6. AB
SOLUTION
what is the answer to this problem
Answer:
-11/12
Step-by-step explanation:
Answer:
-11
12
Step-by-step explanation:
You have to add the numbers, multiply them, subtract them and then finally divide.
please help(: ( 8th grade lesson)
Step-by-step explanation:
Since angle 1 is on a straight line and we know that angle 4 is 160, and a straight line has a sum of 180 degrees, simply subtract 160 from 180 to get angle 1.
Angle one would be 180-160 = 20
Since the sum of angles in a triangle is 180 and we already know 2 of them, angle 1 is 20 and angle 3 is 30, just add them together and then subtract that from 180. 20 + 30 = 50, and 180 - 50 = 130.
So in conclusion:
Angle 1 is: 20
Angle 2 is: 130
15
Evaluate
T
1 when T-5.
Answer:
T= 6
Step-by-step explanation:
T-5=1
find T
+5 to both sides
T= 6
In a game show, players play multiple rounds to score points. Each round has 3 times as many points available as the previous round.
Round 0 1 2 3 n
Points 25 75 225 675
Which equation shows the number of points available, p, in round n of the game show?
Answer:
[tex]p = 25(3)^n[/tex]
Step-by-step explanation:
Given
Round 0 1 2 3
Points 25 75 225 675
Required
Determine the equation
Let n = rounds and p = points.
So, we have:
[tex](n_1,p_1) = (0,25)[/tex]
[tex](n_2,p_2) = (1,75)[/tex]
[tex](n_2,p_2) = (3,225)[/tex]
The above shows a geometric progression.
So, we solve using
[tex]p = ab^n[/tex]
In [tex](n_1,p_1) = (0,25)[/tex]
n = 0 and p = 25
Substitute these values in [tex]p = ab^n[/tex]
[tex]25 = ab^0[/tex]
[tex]25 = a*1[/tex]
[tex]25 = a[/tex]
[tex]a = 25[/tex]
In [tex](n_2,p_2) = (1,75)[/tex]
n = 1 and p = 75
Substitute these values in [tex]p = ab^n[/tex]
[tex]75 = ab^1[/tex]
[tex]75 = ab[/tex]
Substitute 25 for a
[tex]75 = 25*b[/tex]
Make b the subject
[tex]b = \frac{75}{25}[/tex]
[tex]b = 3[/tex]
So, we have:
[tex]a = 25[/tex] and [tex]b = 3[/tex]
The equation [tex]p = ab^n[/tex] becomes
[tex]p = 25(3)^n[/tex]
Equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].
Explicit formula of the Geometric sequence:a, ar, ar², ar³........arⁿ
There is a common ratio of 'r' in each successive term to the
previous term.
Therefore, it's a geometric sequence.
Explicit formula of a geometric sequence is given by,[tex]T_n=ar^{n-1}[/tex] (For n ≥ 1)
Here, [tex]a=[/tex] First term
[tex]r=[/tex] Common ratio
[tex]n=[/tex] nth term
Given in the table,
Common ratio (r) of any successive term to the previous term,[tex]r=\frac{75}{25}=3[/tex]
First term of the sequence 'a' = 25Explicit formula of the sequence will be,
[tex]P=25(3)^{n}[/tex] [For n ≥ 0]
Therefore, equation representing the number of points 'P' in 'n' games will be [tex]P=25(3)^{n}[/tex].
Learn more about the geometric sequence here,
https://brainly.com/question/11385300?referrer=searchResults
Please help answer correctly !!!!!!!!!!!! Will mark Brianliest !!!!!!!!!!!!!!!!!!!!
Answer:
i think its 360.......
Step-by-step explanation:
i hope it helps
Is (3,8) a solution to this system of equations? How do you know?
y=7x + 8
y=x + 1
Answer:
yes it is
Step-by-step explanation:
The point (3,8) is not a solution of system of equation. Explanation given below.
What is the system of equation?Simultaneous equations are any equations with the same number of unknowns that may be solved at the same time. The system of equations is a simultaneous equation.
Given system of equation,
y=7x + 8
y=x + 1
To find that the point (3,8) is a solution of system of equation,
we substitute the point to both of these equation and verify if that point is satisfying the equation or not.
In the first equation, x=3 and y =8
we get, 8 = 29
which is contradiction.
In the second equation ;
we get, 8 = 4.
Which is also contradiction.
Therefore, the equations do not have the solution (3 , 8).
To learn more about the system of equation;
brainly.com/question/13729904
#SPJ2
Describe the transformation from y= x + 4 to y= .5x + 4 Group of answer choices compresses stretches shifts right 4 shifts left 4
Answer:
This type of transformation is a horizontal stretch.
Step-by-step explanation:
Given
[tex]y = x + 4[/tex]
[tex]y = .5x + 4[/tex]
Required
Determine the type of transformation
The first function can be expressed as:
[tex]f(x) = x + 4[/tex]
While the second function is:
[tex]g(x) = f(0.5x)[/tex]
Solving f(0.5x), we have to substitute 0.5x for x in [tex]f(x) = x + 4[/tex]
[tex]f(0.5x) = 0.5x + 4[/tex]
So:
The second function is:
[tex]g(x) = 0.5x + 4[/tex]
This type of transformation is a horizontal stretch.
i.e. f(x) stretched to g(x)
1. A storage trunk is 3 feet long and 1 foot wide. The height of the trunk is 2 feet. What is the volume of the trunk?
Solve - 12x ≤ 72 and then plot the solution set on the number line.
Answer:
(6,0)
Step-by-step explanation:
Used Desmos Scientific calculator.
The discriminant of a quadratic equation is 0. Which statement is true?
a. there are two real solution
b. there are no real solution
c. there is one real solution
Answer:
A
Step-by-step explanation:
two real solutions! hope this helped!!
Express and simplest radical form.
Answer:
4 square root 5 is the answer
root(20*4)
2 × root(5×4)
4×root(5)
what does 2(3x − 7) + 18 = 10 equal
Answer:
x = 1
Step-by-step explanation:
We have an expression and are asked to find x perhaps?
2(3x - 7) + 18 = 10
To solve this, we need to get x alone.
Distribute :
(2(3x) - 2(7)) + 18 = 10
6x - 14 + 18
Add like terms :
6x + 4 = 10
Subtract 4 from both sides :
6x = 6
Divide 6 from both sides :
x = 1
Answer:
First you do 2x3 and then 2x7 that would be 6x and 14 so add 18 to 14 and that woukd be 32 so Try 32+6x... I would thnk i'm correct Can I also get Branliest..?
Ms. Myrie gave her class 20 minutes to read. Carrie read 5 1/2
pages in that time. At what rate, in pages per hour, did Carrie read?
Answer:
16.5
Step-by-step explanation:
60 minutes = 1 hour
20 minutes * 3 = 60.
That means, by multiplying by a factor of 3, we can see exactly what Carrier's pg/hr speed is.
5.5 * 3 = 16.5
Answer:3.63 pagers per hour
Step-by-step explanation:
5 1/2 is the same as 5.5
20/5.5=3.63
Write each phrase as an algebraic expression
1. Jenny is 5 times as old
2. Brandon spent 10 dollars more
Answer:
1. "5 times as" means multiply by 5.
Jenny = x * 5
2. "10 dollars more" means add 10
Brandon = x + 10
Please help...it due ASAP
Show workings please
Answer:
36.5 i believe.
Step-by-step explanation:
you divide 986 by 27 and it equals 36.5.
hope you get it right!
if this is wrong then you can report me i guess. ='(
pls help how many terms r there?
Answer:
3
Step-by-step explanation:
60% of ___ =39
I NEED AN ANSWER ASAP PLEASE HELP
Answer:
The answer is 65
Step-by-step explanation:
The length of a rectangle is 1 foot less than 3 times the width. The area is 310 ft². Find the dimensions of the rectangle.
A total of 150 tickets were sold for the annual concert. Student tickets were $4 and non-students $8. If the total revenue was $840, how many tickets of each type were sold ?
Answer:
x = 90
y = 60
Step-by-step explanation:
Let x = student
Let y = non-student
x + y = 150
4x + 8y = 840 <—— Use elimination/addition ethos for both equations
8 (x + y = 150)
-1 (4x + 8y = 840) <—— Let’s eliminate y
8x + 8y = 1200
+ -4x - 8y = -840
—————————————
4x = 360
x = 90
x + y = 150 <— substitute for x from above
90 + y = 150
- 90 = - 90 <— subtract from both sides
y = 60
Need help pleaseeeee!!
Answer: z 1/2
Step-by-step
:) 100%
jack is making a triangle shaped deck,one side is 5ft and the other is 7ft. he is going to make the third length 14ft. is jack correct about his third length?
Answer:
no
Step-by-step explanation:
In EFG, L is the centroid. If LJ=9 find EL.
Answer:
LG=LE=LF since it is the centroid. So I think it would also be 9.
What is the slope of the line that passes through the points (-4,5) and (0, -5)? Choose the BEST answer!
m = -10/4
m = -5/2
m= 0
m = 5/2
Answer:
m= -5/2
Step-by-step explanation:
formula for slope(m) : ΔY/ΔX (change in y coordinates - change in x coordinates)
change in y coordinates: 5-(-5) = 10
change in x coordinates: -4-(0) = -4
10/-4 = -5/2= -2.5
mark invested 125 he earned a simple interest of 3% per year on the initial investment if no money was added or removed from the investment what was the amount of interest mark received at the end of two years
Answer:
$7.50
Step-by-step explanation:
formula for simple interest:
I = prt
I = ($125)(0.03)(2)
I = $7.50
Answer:
You time 125 by 1.03 twice subtract 125 from that awnser to get the amount of money from interest 7.6125 is the awnser
Step-by-step explanation:
Which fraction divided by 3/6 is equal to -9/10? A-9/20. B9/20. C-3/2. D9/40
Answer: -9/20 is equal to -9/10 when divided by 3/6 (1/2)
Step-by-step explanation:
Begin by reducing the fraction you're dividing with. In this case 3/6 can be reduced to 1.2, also known as 0.5 Beginning with -9/20, as it is the first answer option, we can put the problem into the following equation: -9/20 * 2/1 = -9/10.It is always good to verify all of your answer options are not possible answers. However, in a question like this, the math evenly works out in most cases, eliminating any other possible answer options.
By submitting this answer and referring to the work and resources given I trust you're in accordance with the Brainly Honor Code and I take no responsibility for any laws or rules broken with you using this platform.
5*4 3/10 pls answer I will mark you as brainliest
Answer:
5x4 x 3 /10
20x 3 /10
60/10
6
Answer:
Step-by-step explanation:
[tex]5* 4 \frac{3}{10}=5* \frac{(4*10)+3}{10}\\\\= 5*\frac{43}{10}\\\\= \frac{43}{2}\\\\= 21 \frac{1}{2}[/tex]
Plz look at the photo for geometry
Answer: m<C = 45, m<M = 50, m< B = 85.
Step-by-step explanation:
Adjacent angles on a line sum to 180 degrees.
m<C + m<M + m<B = 180. 45 + (8x+10) + (12x+25) = 180. Combine like terms. 80+ 20x =180. Subtract 89 from both sides. 20x = 100. Divide both sides by 20. X = 5. Substitute x back into the angle measures. m<C = 45, m<M = 50, m< B = 85.
pls Help I hate math
Answer:
C
Step-by-step explanation:
Remark
There are three rectangles all the same size.
There are two triangles both the same size
Triangles.
Givens
b = 7.5 cm
h = 6.5
Solution
Area 1 triangle = 1/2 * 7.5 * 6.5
Area 1 triangle = 24.375
Area 2 triangles = 2*24.375 = 48.75
Rectangles
Givens
L = 13.5
w = 7.5
Solution
Area one rectangle = L*w
Area one rectangle = 13.5*7.5
Area one rectangle = 101.25
Area three rectangles = 3*101.25
Area three rectangles = 303.75 Add
Total Area = 352.5