Given:
The equation are
[tex]y=3x+2[/tex]
[tex]y=2x^2+7x-11[/tex]
To find:
The coordinates of intersection points.
Solution:
We have,
[tex]y=3x+2[/tex] ...(i)
[tex]y=2x^2+7x-11[/tex] ...(ii)
From (i) and (ii), we get
[tex]3x+2=2x^2+7x-11[/tex]
[tex]0=2x^2+7x-11-3x-2[/tex]
[tex]0=2x^2+4x-13[/tex]
If a quadratic equation is [tex]ax^2+bx+c=0[/tex], then by quadratic formula:
[tex]x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
In the equation [tex]0=2x^2+4x-13[/tex], we have [tex]a=2,b=4,c=-13[/tex].
Using quadratic formula, we get
[tex]x=\dfrac{-4\pm \sqrt{4^2-4(2)(-13)}}{2(2)}[/tex]
[tex]x=\dfrac{-4\pm \sqrt{16+104}}{4}[/tex]
[tex]x=\dfrac{-4\pm \sqrt{120}}{4}[/tex]
Now,
[tex]x=\dfrac{-4+\sqrt{120}}{4}[/tex] and [tex]x=\dfrac{-4-\sqrt{120}}{4}[/tex]
[tex]x=1.7386[/tex] and [tex]x=-3.7386[/tex]
[tex]x\approx 1.74[/tex] and [tex]x\approx -3.74[/tex]
Putting x=1.74 in (i), we get
[tex]y=3(1.74)+2[/tex]
[tex]y=5.22+2[/tex]
[tex]y=7.22[/tex]
Putting x=-3.74 in (i), we get
[tex]y=3(-3.74)+2[/tex]
[tex]y=-11.22+2[/tex]
[tex]y=-9.22[/tex]
Therefore, the coordinates of the intersection points are (1.74, 7.22) and (-3.74,-9.22).
Factor Trinomials:
1) 2x^2 + 14x + 20
2) 8x^2 + 64x +128
(Please show work)
I give out brainliest
Answer:
1. [tex]2(x+2)(x+5)[/tex]
2. [tex]8(x+4)^{2}[/tex]
Step-by-step explanation:
Problem #1:
1. Find the GCF (Greatest Common Factor)
[tex]GCF = 2[/tex]
2. Factor out the GCF and simplify.
[tex]2(x^{2} +7x+10)[/tex]
3. Factor [tex]x^{2} +7x+10[/tex]
Which two numbers add up to 7 and multiply to 10?
2 and 5
Rewrite the expression using the above.
[tex](x+2)(x+5)[/tex]
4. Done!
[tex]2(x+2)(x+5)[/tex]
Problem #2:
1. Find the GCF (Greatest Common Factor)
[tex]GCF=8[/tex]
2. Factor out the GCF and simplify.
[tex]8(x^{2} +8x+16)[/tex]
3. Use the perfect square formula. [tex]a^{2} +2ab+b^{2} =(a+b)^{2}[/tex]
[tex]a = x\\b=4[/tex]
[tex](x+4)^{2}[/tex]
4. Done!
[tex]8(x+4)^{2}[/tex]
EXIT TICKET
Ahmad constructed the composition of dilations shown. Figure 2 is 1/2 the
size of Figure 1, and Figure 3 is 2/3 the size of Figure 2.
What is the scale factor from Figure 1 to Figure 3?
Circle the best choice: What is the center of dilation that maps Figure 1 to Figure 3?
Point A
Point B
Point C
Point D
Answer:
Step-by-step explanation:
Point A
10. Sonia paid $ 19.55 for 3.4 pounds of salmon. What is the price per pound of the salmon?
The average grade Jared received on 4 tests was 94. If he drops his lowest test grade of 85, what will his new average be?
A.72.75
B.76
C.89.5
D.97
Pls help TT
Answer:
total points on the 4 tests- 94x4= 376
376- 85= 291
291/3= D. 97
Answer:
D. 97
Step-by-step explanation:
x = sum of 4 test grades Jared received
[tex]\frac{x}{4} = 94[/tex]
x = 376
If he drops lowest test grade of 85, then subtract 85 from Jared's sum of all test grades:
x - 85 --> 376 - 85
= 291
Now that one of his test grades are not considered, this means there are only 3 test grades to consider.
291 must be divided by 3 to get the average:
[tex]\frac{291}{3}[/tex] = 97
The answer is D) 97
write an equation in slope intercept form for the line passing through (2, 6) with a slope of -3
Answer:
y=-3x+12
Step-by-step explanation:
y-y1=m(x-x1)
y-6=-3(x-2)
y-6=-3x+6
y=-3x+6+6
y=-3x+12
Anyone help ASAP pls!!!
Answer:
my answer is B
Which expression shows 56x+40y-48z written as a product of the greatest common factor and one other factor
Answer:
Step-by-step explanation:
You have not provided the choices.
Factor each term into powers of primes and variables:
56x = 2³·7x
40y = 2³·5y
48z = 2⁴·3z
Greatest common factor = 2³ = 8
56x + 40y - 48z = 8(7x + 5y - 6z)
Plzz help!!!!!!!!!!!!!!!!!
Answer:
so far i got A and C
Step-by-step explanation:
if its incorrect im sorry
find the value of given expression
[tex]0 \times \sqrt{5} [/tex]
Answer and Step-by-step explanation:
The answer to this expression is 0.
This is because 0 times any number is 0.
#teamtrees #PAW (Plant And Water)
Answer:
0 because anything times 0 equals 0
Step-by-step explanation:
MEASUREMENT Write an expression in simplest form for the perimeter of each figure.
Answer:
I think it's 10...
Step-by-step explanation:
I'm sorry if I'm wrong. let me know if I am and if it's right please give brainliest I'm trying to rank up. ❤️
The length of a shadow of a building is 30 m. The distance from the top of the building to the tip of the shadow is 36 m.
Find the height of the building. If necessary, round your answer to the nearest tenth.
Answer:
the answer is 19.89
Step-by-step explanation:
round it
1) If Susie puts her pennies in piles of 4 she has 2 pennies left over. If she puts h
pennies in piles of 5 she has 3 pennies left over. What is the least amount of
pennies Susie can have?
Answer:
The least ammount of pennies would be 18 I belive.
Step-by-step explanation:
solve the equation -2|5w-7|+9=-7
Answer:
w = 3, w = -⅕
Step-by-step explanation:
See attached image
Find cuberoot of 27000*(-42875)
ANSWER:
35
DID YOU COPY MY ANSWER THAT IS CORRECT
Step-by-step explanation:
125=5*5*527=3*3*33√125=53√125*27= 3√5*5*5*3*3*35*315-1286250pls I need help please :D its math and you'll get 30 points
Its a picture
Answer:
5,750
Step-by-step explanation:
if he has 10 of each then you can multiply each bag by 10 and then multiply the amount of bags to the amount the coin is worth
help me please !!!!!!
Help please I will be marking brainliest!!!
A. 46.1
B. 50.1
C. 76
D. 54.2
Show work, if possible. Thanks❤️
Answer:
76 I think
Step-by-step explanation:
2x²-24x+64=0 How do you solve my factoring this
Find the solution to the following system using substitution or elimination:
y = 3x + 2
y=-2x - 8
A. (-2,-4)
O B. (-ş; – 34)
O C. (-9,-)
D. (1, -6)
Answer:
A. (-2,-4)
x = -2,
y = -4
thats the only way ik how to explain but its the correct answer
3x = 4x - 12 हे समीकरण सामान्य रूपात लिहा
Answer:
x=12
Step-by-step explanation:
Here,
3x =4x - 12
12= 4x - 3x
12= x
first to answer please be correct asap !!! giving brainleist and 10 pts.
Answer:
The third one
Step-by-step explanation:
Are these two lines parallel, perpendicular or neither
I am confused Help me.
about what there is no question here....?
You told your friend that you could eat 5/8 of a large pizza. If you only ate 1/2 of what you said you could eat, what fraction of a large pizza did you eat?
Answer:
5/16
Step-by-step explanation:
Given that:
Fraction of claim = 5/8
Amount actually eaten = 1/2 of claim
Amount actually eaten = 1/2 * 5/8 = 5/16
Fraction of large pizza actually eaten is 5 /16
Hence, he ate, 5/16 of large pizza
Answer:
Step-by-step explanation:
5/6
The regular price of a video game is $59.,95. This week it is on sale for 15% off. What does the game cost this week (before taxes)
Answer: $50.96
Step-by-step explanation:
The regular price of a video game is $59.95 and we are told that this week it is on sale for 15% off.
The game cost this week before taxes will be:
= 59.95 - (15% × 59.95)
= 59.95 - (0.15 × 59.95)
= 59.95 - 8.9925
= $50.9575
= $50.96
The amount this week is $50.96
if it takes you one hour and thirty minutes to drive 87 miles, find your average speed
Answer:
How to calculate average speed. Speed is distance divided by time. Simply put, if you drove 60 kilometres for one hour, it would look like this: Speed = distance (60 km) / time (1 hour) = 60km/h.
HELP ASAP PLSSS 10 POINTS
Answer:
true both
Step-by-step explanation:
i did math
Answer:
False
True
Step-by-step explanation:
because comparing one side it's 2:5
I need help pleaseee
Answer:
Step-by-step explanation:
20 (8+5+4+3)
A triangular-shaped sign has a base of 15 ft, and a height of 8 ft. What is the area of the sign?
Answer:
60ft²
Step-by-step explanation:
Area of a triangle = 1/2×base×height
=1/2×15×8
=60
3 divided by 12 in percentages and fractions
Answer: fraction: 1/4 decimal: .25 percentage: 25%
Step-by-step explanation:
Answer:
3 is 1/4 of 12 so there is ur fraction and that is 25.00%
Step-by-step explanation: