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astraxan [27]
2 years ago
8

Solve the following system of equations algebraically and check. y=x^2+3x+4 y-x=7

Mathematics
1 answer:
FinnZ [79.3K]2 years ago
5 0
Y=x^2+3x+4
y-x=7

x^2+3x+4-x=7
x^2+2x+4=7
(factor) x^2+2x-3=0
(x+3)(x-1)=0
X= -3 and X=1
(Plug x in for y)
Y= 1^2+3(1)+4
Y=8
(Check your answer on the second equation)
8-1=7
7=7 (Which is the solution)
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Pls do it fast
galina1969 [7]

Answer:

solution :

in the given figure AB=10.2cm, AC=14cm, AD=DC and AD perpendicular to BC.

now ,

in rt angle tirangle ADC,

angleACD=45 degree, angle DAC=45 degree now,

in triangle ABD,

angle BAD+angleABD+angleADB=180 DEGREE (sum of the sngle of triangle)

angle BAD+75+30=180

angle BAD=180-165      therefore,angle BAD=15

angle BAC =15+45=60

Area of triangle ABC=1/2×AB×AC×SIN 60

=1/2×10.2×14×√3/2

=61.83cm³ ans

3 0
2 years ago
Consider the following data points.
Hoochie [10]

Answer:

the equation of the least-squares line for the data is: \hat Y=9.3+1.3x

Step-by-step explanation:

In a simple linear regression model, such as, \hat Y=b_0+b_1x, the coefficients bo and b1 are estimated through the method of least squares by the use of the equations:

b_1=\frac{S{xy}}{S_x^2}\\\\b_0=\bar{y}+b_1 \bar{x}

For the data provided you have to:

S_{xy}=\frac{\sum {(x_i-\bar x)(y_i-\bar y)}}{n-1}=3.25\\\\S_x^2=\frac{\sum {(x_i-\bar x)^2}}{n-1}=2.5\\\\\bar y=5.4, thus:

b_1=\frac{3.25}{2,5}=1.3\\\\b_0=5.4+1.3(3.0)=9.3

the equation of the least-squares line for the data is:

Y=9.3+1.3x

8 0
3 years ago
Read 2 more answers
Help as soon as possible!
8090 [49]

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a 2 − b 2 = ( a + b ) ( a − b ) where a = 7 and b = a + x . − ( 7 + a + x ) ( a + x − 7 )

7 0
2 years ago
Someone please help with this asap!! I will mark brainliest if it's right! Serious answers only !!!
Arlecino [84]

Answer:

1) given

2) given

3) definition of vertical angles

4) AAS

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Plz help me.
Vlad [161]
Assuming you want to find x?
You know that the angles at C and B have to be the same (6x) because it’s an isosceles triangle (as indicated by the lines going through AC and AB), and angles in a triangle add to 180*

So 3x + 6x + 6x = 180*
15x = 180*
x = 180*/15
x = 12*
4 0
2 years ago
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