Solve the system of equations.
y = x2 + 3x - 4
y= 2x - 4
Answer:
The two solutions are
(0,-4) and (-1,-6)
Step-by-step explanation:
The ys have to be equal so you can equate the right hand side.
x^2 + 3x - 4 = 2x - 4 Add 4 to both sides
x^2 + 3x = 2x Subtract 2x from both sides
x^2 + 3x - 2x = 0 Combine
x^2 + x = 0 Factor
x(x + 1) =0
Just to show you that these two points really are the solutions, you can see the graph below
x has 2 values
x + 1 = 0
x = - 1
or
x = 0
Now solve for y
y = 2x - 4
Let x = 0
y = - 4
Let x = - 1
y = 2x - 4
y = -2 - 4
y = - 6
The blue is y = x^2 + 3x - 4
The green line is y = 2x - 4
the perimeter of a city rectangular park is 1428 feet. the length is 78 feet more than twice the width. Find the length and width of the park
ASAP!! PLEASE HELP
Max deposited P20,000 in an investment that will give him P1,750-gain for every year that his money stays in the account. How much money will he have in his account by the end of year 8?
Answer:
Step-by-step explanation:
8*1750=14000
Amount=14000+20000
=34000
(85^4 - 75^4)/(85^3 + 85*75^2 + 75*85^2 + 75^3).=
Answer:
10
Step-by-step explanation:
(85^4 - 75^4)/(85^3 + 85*75^2 + 75*85^2 + 75^3)=10
PLEASE HELP WILL MARK BRAINLIEST
Answer:
C
Step-by-step explanation:
Its the only answer where the y intercept is 16.
We know its 16 because the line crosses the y axis at 16
13. A map has a scale of 2 cm to 3 km.
(iii) If the actual area of a lake is 81 km?, calculate
its area on the map.
Scale = 1cm:3km
Therefore area of lake = 81Km
1:3 = x:81
= 27:81
Therefore the area on map is 27cm
Must click thanks and mark brainliest
Answer:
121.5 is answer.
Step-by-step explanation:
81 / 2 = 40.540.5 *3 = 121.5the quotient of a number and -9 is increased by 10 the result is 11 what is the number?
Answer:
so the division of a number and -9 or
x/-9+10=11 or
(x/-9)+10=11
subtract 10 from both sides
x/-9=1
multiply both sides by -9
x=-9
Can anyone tell me why by direct substitution of x, the equation (circled ones) equals to the indeterminate form, 0/0? When you can do x²-k=6 something like that
Answer:
See explanation and hopefully it answers your question.
Basically because the expression has a hole at x=3.
Step-by-step explanation:
Let h(x)=( x^2-k ) / ( hx-15 )
This function, h, has a hole in the curve at hx-15=0 if it also makes the numerator 0 for the same x value.
Solving for x in that equation:
Adding 15 on both sides:
hx=15
Dividing both sides by h:
x=15/h
For it be a hole, you also must have the numerator is zero at x=15/h.
x^2-k=0 at x=15/h gives:
(15/h)^2-k=0
225/h^2-k=0
k=225/h^2
So if we wanted to evaluate the following limit:
Lim x->15/h ( x^2-k ) / ( hx-15 )
Or
Lim x->15/h ( x^2-(225/h^2) ) / ( hx-15 ) you couldn't use direct substitution because of the hole at x=15/h.
We were ask to evaluate
Lim x->3 ( x^2-k ) / ( hx-15 )
Comparing the two limits h=5 and k=225/h^2=225/25=9.
I'LL GIVE BRAINLIEST !!! FASTERR
please provide explaination !
Answer:
x=50
y=75
Step-by-step explanation:
The explanation is in the picture!
Diana and Dulce were selling tickets for their upcoming
softball game. Dulce sold 20% more than Diana. If they
sold 55 tickets total, how many tickets did each of them
sell?
Answer:
Diana sold 25 tickets and Dulce sold 30 tickets
Step-by-step explanation:
Let us assume that Diana sold x number of tickets, dulce sold 20% more x or 1.2x. ATQ, x+1.2x=55. x=25. So Diana sold 25 tickets and Dulce sold 30 tickets
What is an equation of the line that passes through the points (-6, -8) and (-3,-3)?
Answer:
y = 5/3x+2
Step-by-step explanation:
First find the slope
m = ( y2-y1)/(x2-x1)
= ( -3 - -8)/( -3 - -6)
= ( -3+8) / (-3+6)
= 5/3
The slope intercept form of a line is
y = mx+b where m is the slope and b is the y intercept
Substituting the point (-3,-3)
-3 = 5/3(-3) + b
-3 = -5+b
-3+5 = b
2 = b
y = 5/3x+2
Given points
(-6,-8)(-3,-3)First find the slope
[tex]\boxed{\sf m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{-3+8}{-3+6}[/tex]
[tex]\\ \sf\longmapsto m=\dfrac{5}{3}[/tex]
Now
[tex]\boxed{\sf y=mx+b}[/tex]
[tex]\\ \sf\longmapsto -3=\dfrac{5}{3}(-3)+b[/tex]
[tex]\\ \sf\longmapsto b=2[/tex]
Hence the equation will be
[tex]\\ \sf\longmapsto y=\dfrac{5}{3}x+2[/tex]
Find the smallest natural number that has a remainder 3 when divided by 5, a remainder 5 when divided by 7, and a remainder 8 when divided by 10.
Answer:
68
Step-by-step explanation:
"a remainder 3 when divided by 5": The number must be 3 more than a multiple of 5.
"a remainder 5 when divided by 7": The number must be 5 more than a multiple of 7.
"a remainder 8 when divided by 10": The number must be 8 more than a multiple of 10.
List some number that are 8 more than a multiple of 10:
18, 28, 38, 48, 58, 68, 78, 88, 98
List some number that are 5 more than a multiple of 7:
12, 19, 26, 33, 40, 47, 54, 61, 68, 75
We see 68 as a the lowest common multiple.
68/5 = 13 remainder 3
Answer: 68
factorize. xy^2-y(x-z) -z
Answer:
The equation x The equation x 2The equation x 2 +xy+xz+yz can be factorised as follows:The equation x 2 +xy+xz+yz can be factorised as follows:x The equation x 2 +xy+xz+yz can be factorised as follows:x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x 2The equation x 2 +xy+xz+yz can be factorised as follows:x 2 +xy+xz+yz=(x 2 +xy)+(xz+yz)=x(x+y)+z(x+y)=(x+z)(x+y)Hence, x 2 +xy+xz+yz=(x+z)(x+y)Answer:
= (y-1) (xy-z)
Step-by-step explanation:
First we expand them -
= xy^2 - xy - yz - z
= xy(y-1)-z(y-1)
= (y-1) (xy-z)
Hope this helped
The mean of 14 numbers is 49. Removing one of the numbers causes the mean to decrease to 43. What number was removed?
Answer:
126 was removed.
Step-by-step explanation:
The total before division took place was
Total = mean * 14
mean = 49
Total = 49 * 14
Total = 685
Now you subtract x from the total
685 - x
And divide by 13 [one number is missing]
(685 - x)/13
and the result = 43
(685 - x ) / 13 = 43 Multiply both sides by 13
685 - x = 43 * 13
685 - x = 559 Subtract 685 from both sides
- x = - 126 Multiply by - 1
x = 126
please answer this!!
Answer:
You can not solve it because Side P does not exist
Step-by-step explanation:
Lydia Gomez has $185 deducted from her semimonthly pay for her group health insurance. Her employer
pays 65% of the cost. What is the annual premium amount for Lydia's group health insurance?
Answer:
$12,685.71
Step-by-step explanation:
35% is what she pays
Semimonthly is 24 because monthly is 12
0.35a
--------- = 185
24
Multiply both sides by 24
0.35a=4,440
divide by 0.35
a=$12,685.71
A net is a two-dimensional pattern that can be folded to form a three-dimensional surface. T/F
Answer: True
Explanation:
Consider a 3D cardboard box that you can unfold. It would unfold into a 2D net that you can then re-fold back into its 3D form. The 2D net is useful to help visualize and calculate the surface area. The surface area is simply the total area of all the external faces.
The side measurement of the wall of the Green House is 9m. Find the cost of the glass required for the walls of the Green House, if the cost of 1m2 glass is AED 12.
Answer:
AED 972
Step-by-step explanation:
Area of the wall = 9² = 81 m²
each m² costs AED 12
so 81 m² will cost 12×81 = AED 972
your village community group is putting a new fence around the park .you offer to help and measure the distance around the park as 337 metres. each fence panel is 550cm across .how many fence panels do you need
Explanation:
Perimeter of the park
= 337 m
= 33700 cm
Length of each fence panel
= 550 cm
Number of fence panel required
= Perimeter of the park/Length of each fence panel
= 33700 cm/550 cm
= 33700/550
= 3370/55
= 674/11
= 61 3/11
So, we will need 61 3/11 fence panels.
P.S. — 61 3/11 means 61 whole and 3/11. I have attached its picture, so that you understand.
PLEASE HURRY I HAVE 3 mins left Which relationship could be the one shown on the graph?
10fx
9
8+
7
6
5
4.
3
2+
1
1 2 3 4 5 6 7 8 9 X
Option A
Must click thanks and mark brainliest
Sorry if i am wrong
A pattern for a skirt calls for 1 7/8 yd of fabric. If Mary
Kate wants to make one skirt for herself and one for her
twin, how much fabric will she need?
Answer:
Mary Kate will need 3 6/8 yd of fabric.
Step-by-step explanation:
If Mary wants to make one skirt for herself AND her twin, that is equal to 2 skirts.
So if one skirt calls for 1 7/8 yd of fabric, multiply it by 2:
1 7/8 x 2
Convert 1 7/8 to an improper fraction and add 1 as a denominator for 2:
15/8 x 2/1 = 30/8
30/8 simplified is 3 6/8
Brainliest please?
HEEEEEEEEEEELLLLLLLLLLPPPPPPP!!!!!!!!! QUICK!!!!!!
Find the coordinates of the image of M(−1, 5) after the translation (x, y)→(x+3, y−2).
Thank you!!
Answer:
To find a translation image of a shape, you can use the following rule or formula. Suppose you want to translate or slide point P a units horizontally and b units vertically. Then, change the x-values and y-values of the coordinates of P. The points of the triangle of are A(-3, 1), B(-4, 3), and C(-2, 4).
whats the differnce in (5x+4)-(x+2)
Answer:
4x+2
Step-by-step explanation:
(5x+4)-(x+2)=(5-1)*x+(4-2)=4x+2
Value of the boat after 3 years?
after each year it's 83% of it's value from last year (100%-17%=83%)
the function in 19000 * (0.83) ^x
3 will be filled in for x
19000 * (0.83) ^3= 10863.953
$10863.95
Answer:
$10,863.95
Step-by-step explanation:
y = 19,000[tex](.83)^{t}[/tex]
y = 19,000[tex](.83)^{3}[/tex]
y =$10,863.95
What are the roots of the equation x2 + 6x - 4 = 0?
A6+2V13
B.-6+2V13
C.3V13
D.-3V13
Answer:
The answer is D
Step-by-step explanation:
use the quadratic formula, plug and chug, and voila!
Determine the slope of the line that has the following coordinates: (-2, 5) (4, -2)
Answer:
slope= -1 1/6
Step-by-step explanation:
x1 y1 x2 y2
-2 5 4 -2
(Y2-Y1) (-2)-(5)= -7 ΔY -7
(X2-X1) (4)-(-2)= 6 ΔX 6
slope= -1 1/6
B= 2 2/3
1+-2/3--m where m=9/2
Answer:
-25/9
Step-by-step explanation:
1 + (-2/3) - m
Plug in:
1 + (-2/3) - 9/2
1 + 2/3 - 9/2
1/3 - 9/2
-25/9
Hope this helped.
Answer:
4 5/6
Step-by-step explanation:
1+-2/3--m
Subtracting a negative is like adding
1-2/3 +m
1/3+m
m = 9/2
1/3 +9/2
Get a common denominator of 6
1/3 *2/2 +9/2*3/3
2/6 + 27/6
29/6
Changing to a mixed number
4 5/6
Use the quadratic formula to find the solution to the quadratic equation given
below.
x2-3x+
3x + = 0
Answer:
Is E
explanation:
Y+y+y+y rewrite in multiplication
Answer:
4y
Step-by-step explanation:
y+y+y+y
= (1+1+1+1) y
= 4y
Answer:
4y
Step-by-step explanation:
Y+y+y+y
Combine like terms
4y
Can someone helpp pls
Answer:
Step-by-step explanation:
You have to solve this as a system. We have 3 coordinates given; the first 2 are given as zeros of the quadratic, the 3rd one is given as a regular coordinate. The zeros of a quadratic are where the y values of a coordinate are 0's because the x-intercepts of a quadratic (aka zeros) exist where y = 0. We use each of those points in the standard form of a quadratic to solve for a, b, and c. First, (0, 0):
[tex]0 = a(0)^2+b(0)+c[/tex] which gives us that c = 0. We'll use that value of c as we move forward with the problem. Next we'll use (3, 0):
[tex]0=a(3)^2+b(3)+0\\0 =9a+3b[/tex]Hold that thought for a minute or 2. Next we'll use the coordinate (1, 6):
[tex]6=a(1)^2+b(1)+0\\\\6=a+b[/tex] Now we have a system that we can solve using either substitution or elimination for a and b. I used elimination:
6 = a + b
0 = 9a + 3b and multiply the top equation by -3:
-18 = -3a - 3b
0 = 9a + 3b
so
-18 = 6a and
a = -3. Now back solve for b:
6 = -3 + b so
b = 9 and our quadratic is
[tex]y=-3x^2+9x+0[/tex] or just
[tex]y=-3x^2+9x[/tex]
