Use the discriminant to determine the number of real solutions to the equation,
10n^2 = 10 - 8n
Answer:
2 real solutions
Step-by-step explanation:
Get all the terms to one side
10n^2 = 10 - 8n
10n^2 +8n -10 =0
ax^2 +bx+c =0
The discriminant is
b^2 -4ac
8^2 - 4(10)(-10)
64 +400
464
If the discriminant is greater than 0 we have 2 real solutions
Can someone help me on this please
What are the x- and y-intercepts of g(x) = 4 - X2?
Answer:
g(x) = 4 - x^2
at x-intercept, y=0
0=4-x^2
x^2=4
x = ± 2
=> two x- intercepts, (-2,0) and (2,0)
at y-intercept, x = 0
g(x) = y = 4 - 0 = 4
y-intercept = (0,4)
The x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).
What is an intercept?A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis.
This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.
g(x) = 4 - x²
At x-intercept, y = 0
0=4-x²
x² = 4
x = ± 2
Two x- intercepts, (-2,0) and (2,0)
at y-intercept, x = 0
g(x) = y = 4 - 0 = 4
y-intercept = (0,4)
Therefore, the x-intercept is ( ±2 , 0 ) and y- intercerpt is (0,4).
To know more about an intercept follow
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.......plz answer it plz
Answer:
a: x=90 b: x=45 y=45 c: y=68 x=68
HElp Please its Pre-Calculus Matrix
The determinant is C. -541.
Using a cofactor expansion along the first row:
[tex]\begin{vmatrix}-8&-4&-1\\1&7&-3\\8&9&9\end{vmatrix} = -8\begin{vmatrix}7&-3\\9&9\end{vmatrix} + 4\begin{vmatrix}1&-3\\8&9\end{vmatrix} - \begin{vmatrix}1&7\\8&9\end{vmatrix} \\\\= -8(7\times9-(-3)\times9) + 4(1\times9-(-3)\times8) - (1\times9-7\times8) \\\\ = -8(63+27) + 4(9+24) - (9-56)\\\\= \boxed{-541}[/tex]
Find all complex numbers z such that z^4 = -4.
Note: All solutions should be expressed in the form a+bi, where a and b are real numbers.
Simplify each numerical expression.
1) 6 + 2 x 8 - 12 + 9 - 3
Answer:
16
Step-by-step explanation:
using BODMAS rule
6 + 16 - 12 + 9 - 3............step 1
22 - 3 - 3....…...................step 2
16
Help ASAP I’ll mark you as brainlister
Answer: Try 2. This is my best guess
find x giving your answer to 1 decimal place
Step-by-step explanation:
[tex] \frac{ \sin(81) }{x} = \frac{ \sin(40) }{7} \\ x \times \sin(40) = 7 \times \sin(81) \\ x = \frac{7 \times \sin(81) }{ \sin(40) } = 10.75 = 10.8 \: cm[/tex]
Answer:
x is 10.8 cm
Step-by-step explanation:
from Lami's theorem:
[tex] \frac{7}{ \sin(40 \degree) } = \frac{x}{ \sin(81 \degree) } \\ \\ x = \frac{7 \sin(81 \degree) }{ \sin(40 \degree) } \\ \\ x = 10.8 \: cm[/tex]
no calculator needed! been stuck for a while. how do I solve this style of question?
Answer:
- [tex]\sqrt{3}[/tex] and 0
Step-by-step explanation:
tan(2x)
= tan(2 × [tex]\frac{\pi }{3}[/tex] ) = tan([tex]\frac{2\pi }{3}[/tex] ) = - tan([tex]\frac{\pi }{3}[/tex] ) = - [tex]\sqrt{3}[/tex]
cos(3x) = cos(3 × [tex]\frac{\pi }{6}[/tex] ) = cos([tex]\frac{\pi }{2}[/tex] ) = 0
Warren is on vacation and needs to arrange transportation. A rental car costs 40 dollars per day plus a one-time cost of 14 dollars for insurance. Construct a function C(x) that gives the total cost of renting a car for x days. C(x)=________.
If Warren has budgeted 254 dollars for the rental, how many days can he afford?
Answer:
C(x)=40x+14, 6 days
Step-by-step explanation:
C(x)= payment per day*x + initial payment. the payment per day is $40 while the initial payment is $14. so C(x)=40x+14.
C(x)=254=40x+14, 40x=240, x=6
For a positive integer n, if the difference between all neighbouring digits are all greater than 3 (e.g. 150),
it is defined as a “good number”. How many three-digit “good number(s)” is/are there?
Answer:
166 numbersStep-by-step explanation:
Let n = abc is the 3-digit number
b = 0 - 9, total 10 options
If b = 0, a= 4 to 9, c = 4 to 9, so 6 options each 6*6 = 36 good numbersIf b = 1, a= 5 to 9, c = 5 to 9, so 5 options each 5*5 = 25 good numbersIf b = 2, a= 6 to 9, c = 6 to 9, so 4 options each 4*4 = 16 good numbersIf b = 3, a= 7 to 9, c = 7 to 9, so 3 options each 3*3 = 9 good numbersIf b = 4, a = 8, 9, c = 0, 8, 9, so 2*3 = 6 good numbersIf b = 5, a = 1, 9, c = 0, 1, 9, so 2*3 = 6 good numbersIf b = 6, a = 1, 2, c = 0, 1, 2, so 2*3 = 6 good numbersIf b = 7, a = 1, 2, 3, c = 0, 1,2,3, so 3*4 = 12 good numbersIf b = 8, a = 1, 2, 3, 4, c = 0, 1, 2, 3, 4, so 4*5 = 20 good numbersIf b = 9, a = 1,2,3,4,5, c = 0, 1, 2, 3, 4, 5, so 5*6 = 30 good numbersTotal good 3-digit numbers:
36 + 25 + 16 + 9 + 6 + 6 + 6 + 12 + 20 + 30 = 166find the following ratios right triangle. PLS HURRY and disregard my answers.
Answer:
sinA= 5/13; cosB= 5/13
Step-by-step explanation:
sine is opposite over hypotenuse so 5/13. cosine is adjacent over hypotenuse so 5/13
A rectangle field is 10m longer than its width. If the perimeter is 300cm, find;
i) Its width
ii) the area if the rectangular field
Answer:
w = 70 cm
A = 5600cm^2
Step-by-step explanation:
P = 2(l+w) where l is the length and w is the width
300 = 2(l+w)
We know the length is 10 longer than the width
l = w+10
300 = 2(w+10+w)
Divide each side by 2
300/2 = (w+10+w)
150 = (2w+10)
Subtract 10 from each side
150-10 = 2w
140 = 2w
Divide by 2
140/2 = w
70 = w
Now find the area
A = l*w
A = (w+10) * w
= (70+10) *70
= 80*70
5600
Find the perimeter of the figure.
31 cm
18 cm
25 cm
Drawing not to scale
C.
b. 80 cm
68 cm
d.
87 cm
a.
74 cm
I need help!
Its a triangle
[tex]\\ \sf\longmapsto Perimeter=31+18+25[/tex]
[tex]\\ \sf\longmapsto Perimeter=48+25[/tex]
[tex]\\ \sf\longmapsto Perimeter=73cm[/tex]
42:-Its rectangle
[tex]\\ \sf\longmapsto Perimeter=2(L+B)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(15+10)[/tex]
[tex]\\ \sf\longmapsto Perimeter=2(25)[/tex]
[tex]\\ \sf\longmapsto Perimeter=50ft[/tex]
Answer:
a and c
Step-by-step explanation:
The perimeter is the sum of the 3 sides, that is
perimeter = 25 + 18 + 31 = 74 cm → a
-------------------------------------------------------------------
The opposite sides of a rectangle are equal, so
perimeter = (2 × 10) + (2× 15) = 20 + 30 = 50 ft → c
6. Alex and Brian park their bikes side-by-side. Alex leaves to visit friends, and Brian leaves 30 minutes later,
headed for the same destination. Alex pedals 5 miles per hour slower than Brian. After 1 hour, Brian passes Alex. At
what speed are they each pedaling?
Answer:
See below.
Step-by-step explanation:
When Brian passes Alex they both have travelled the same distance.
Call this distance d.
Let the speed that Brian passes = x miles/hour.
Distance = speed * time so:
For Alex:
d = (x - 5) * 1.5 ( Alex cycles for 1 + 30 minutes = 1.5 hours)
For Brian:
d = x * 1
So substituting d = x in Alex's equation:
x = 1.5(x - 5)
x = 1.5x - 7.5
7.5 = 0.5x
7/5 / 0.5 = x
15 = x.
ANSWER:
Brian's speed is 15 miles/hour.
Alex's speed is 15 - 5 = 10 miles/hour.
Will Mark Brainlest Help Please ,,,,
[tex]\\ \sf\longmapsto 2x+y=2[/tex]
[tex]\\ \sf\longmapsto 2x=2-y[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}\dots(1)[/tex]
And
[tex]\\ \sf\longmapsto x+1=y+2[/tex]
[tex]\\ \sf\longmapsto x=y+2-1[/tex]
[tex]\\ \sf\longmapsto x=y+1[/tex]
Put the value[tex]\\ \sf\longmapsto \dfrac{2-y}{2}=y+1[/tex]
[tex]\\ \sf\longmapsto 2-y=2(y+1)[/tex]
[tex]\\ \sf\longmapsto 2-y=2y+2[/tex]
[tex]\\ \sf\longmapsto 2-2=2y+y[/tex]
[tex]\\ \sf\longmapsto 3y=0[/tex]
[tex]\\ \sf\longmapsto y=\dfrac{0}{3}[/tex]
[tex]\\ \sf\longmapsto y=\infty[/tex]
Put in eq(1)[tex]\\ \sf\longmapsto x=\dfrac{2-y}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2-\infty}{2}[/tex]
[tex]\\ \sf\longmapsto x=\dfrac{2}{2}[/tex]
[tex]\\ \sf\longmapsto x=1[/tex]
Answer:
x=1 , y=0
Step-by-step explanation:
2x+y=2.......1
x+1=y+2
x-y=2-1
x-y=1...... 2
from equation 2 we get ,
x-y=1
x=1+y
putting the value of x in equation 1 we get,
2*(1+y) +y=2
2+2y+y=2
2+3y=2
3y=2-2
3y=0
y=0/3
y=0
putting the value of y in equation 2 we get,
x-0=1
x=1+0
x=1
hence x=1 , y=0
Please help please with geometry
Answer:
33
Step-by-step explanation:
HJ = HI + IJ
HJ = 3x - 9, HI = x and IJ = x + 5
So 3x - 9 = x + x + 5
Solve for x
Combine like terms
3x - 9 = 2x + 5
Add 9 to both sides
3x = 2x + 14
Subtract 2x from both sides
x = 14
Find HJ
HJ = 3x - 9
We have found that x = 14
HJ = 3(14) - 9
Multiply 3 and 14
HJ = 42 - 9
Subtract
HJ = 33
Please help me to solve this question
Answer:
x = 64°, y = 32°
Step-by-step explanation:
The sum of the angles on a straight line = 180° , then angles on PS are
2x + y + 20 = 180 ( subtract 20 from both sides )
2x + y = 160 → (1)
Angles on QT are
x + 3y + 20 = 180 ( subtract 20 from both sides )
x + 3y = 160 → (2)
Solve (1) and (2) simultaneously
Rearrange (1) expressing y in terms of x by subtracting 2x from both sides
y = 160 - 2x → (3)
Substitute y = 160 - 2x into (2)
x + 3(160 - 2x) = 160 ← distribute and simplify left side
x + 480 - 6x = 160
- 5x + 480 = 160 ( subtract 480 from both sides )
- 5x = - 320 ( divide both sides by - 5 )
x = 64
Substitute x = 64 into (3)
y = 160 - 2(64) = 160 - 128 = 32
Then
x = 64°, y = 32°
Pls help will give brainliest
Answer:
[tex] \frac{3}{2} + 2(x - 1) = 3 - 2x \\ \frac{3}{2} + 2x - 2 = 3 - 2x \\ 2x + 2x = 3 - \frac{3}{2} + 2 \\ 4x = 3 - \frac{3}{2} + 2 \\ 4x = \frac{6 - 3 + 4}{2} \\ 4x = \frac{7}{2} \\ x = \frac{7}{2} \div 4 \\ x = \frac{7}{8} [/tex]
Step-by-step explanation:
it was helpful to you ♫︎♫︎♫︎♫︎
3% of what number is 1.86
Answer:
62
Step-by-step explanation:
Of means multiply and is means equals
.03 * n = 1.86
Divide each side by .03
.03n/.03 = 1.86/.03
n =62
what is the value of |-403|×|-3|
Answer:
1209
Step-by-step explanation:
| - 403 | × | - 3 |
= | 403 | × | 3 |
= 403 × 3
= 1209
Sz – [32 – (10z + 2)]
Please help asap! Will give brainly
=========================================================
Work Shown:
The notation f(4) means we want to find f(x) when x = 4.
If x = 4, then we go for the middle definition since 4 makes [tex]3 \le x \le 10[/tex] to be true (ie, 4 is between 3 and 10)
Therefore,
f(x) = x^2 - 7 when [tex]3 \le x \le 10[/tex]
f(4) = 4^2 - 7
f(4) = 16 - 7
f(4) = 9
Answer:
f(4) = 9
Step-by-step explanation:
4 is between 3 and 10 so we use the middle function
f(4) = x^2 -7
= 4^2 -7
= 16 -7
= 9
Find the common ratio for the geometric sequence
Answer:
1/4
Step-by-step explanation:
Phoebe took a survey of her classmates' favorite sport. The results are in the table below:
The relative frequency for football is the number of people who like football divided by total people:
4/28 = 0.14
Answer: 0.14
Once upon a time there was a farmer whose family raised pigs and chickens. If you counted 24 heads and 80 feet, how many chickens were there? How many pigs were there?
Answer:
Number of chickens = 8
Number of pigs = 16
Step-by-step explanation:
Let the pigs = p
Let the number of chickens = c
Number of heads = 24
p + c = 24 ----------------(I)
p= 24 - c
Number of feet = 80
Chicken has 2 legs and pig has 4 legs
4p + 2c = 80 --------------(II)
Substitute p = 24 - c in equation (II)
4*(24 - c) + 2c = 80
4*24 - 4*c + 2c = 80
96 - 4c + 2c = 80 {Combine like terms}
96 - 2c = 80 {subtract 96 from both sides}
-2c = 80 - 96
-2c = -16 {Divide both sides by (-2)}
c = -16/-2
c = 8
Plugin c = 8 in equation (I)
p + 8 = 24
p = 24 - 8
p = 16
An airplane landed at a point 100 km east and 420 km south from where it took off. If the airplane flew in a straight line from where it took off to where it lands, how many kilometers did it fly? Enter only the number rounded to the nearest kilometer.
Answer:
[tex]\sqrt{100^2 + 420^2}[/tex]
[tex]\sqrt{100^2+420^2}=20\sqrt{466}\quad \left(\mathrm{Decimal:\quad }\:431.74066\dots \right)[/tex]
Step-by-step explanation:
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
At the Scott wedding, 12 guests sat on the groom's side and 10 guests sat on the bride's side. At the Smith wedding, 13 guests sat on the bride's side and 18 guests sat on the groom's side. Which wedding had a lower ratio of guests of the groom to guests of the bride?
A. not enough information
B. the Smith wedding
C. neither, the ratios are equivalent
D. the Scott wedding
Answer:
D. The Scott Wedding
Step-by-step explanation:
Scott: 12 guests on the groom's side and 10 guests on the bride's side
Smith: 18 guests on the the groom's side and 13 guests on the bride's side
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER!! Determine the Value of K in the diagram ( secant lines to circles).
Answer:
6
Step-by-step explanation:
5
Answer:
k = 10
Step-by-step explanation:
Given 2 secants from an external point to the circle, then
The product of the external part and the whole of one secant is equal to the product of the external part and the whole of the other secant, that is
2x(2x + kx) = 3x(3x + 5x)
4x² + 2kx² = 3x × 8x = 24x² ( subtract 4x² from both sides )
2kx² = 20x² ( divide both sides by 2x² )
k = 10
