Answer:
FH is the smallest angle since it is lesser than all the other ones.
What are the solutions of this quadratic equation? X2 − 10x = -34 A. X= -8, -2 B. X= 5 + 3i C. X= -5 + 3i D. X= -5 + square root of 59
Answer:
B. X= 5 + 3i
5 + 3i
Step-by-step explanation:
We are given the quadratic equation
x² - 10x = -34
x² - 10x + 34 = 0
Using Almighty formula
x = -b ± √b² - 4ac/2a
When given equation: ax² + bx + c
Where: a = 1, b = -10 , c = 34
x = -10 ± √-10² - 4 × 1 × 34/2 × 1
x = 10 ± √100 - 136/2
x = 10 ± √-36 /2
x = 10/2 ±. √-36/2
x = 5 ± 6i /2
x = 5 ± 3i
Hence: the roots of the equation are:
x = 5 - 3i , x = 5 + 3i
The expression 2 - x-1/x+2
is equivalent to
A. 1 - 3/x+2
B. 1 + 3/x+2
C. 1 - 1/x+2
D. 1 + 1/x+2
The expression [tex]2- \dfrac{x-1}{x+2}[/tex] is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].
We have to find, which equation is equivalent to the given expression.
The given expression is,
[tex]= 2- \dfrac{x-1}{x+2}[/tex]
To determine the equivalent expression following all the steps given below.
Step1; Taking LCM in the equation,[tex]\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\[/tex]
Step2; Solving the equation,[tex]= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\[/tex]
Step3; rewrite the equation in the small factors,[tex]=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\[/tex]
Step4; By using partial fraction rewrite the equation,[tex]= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}[/tex]
Hence, The expression [tex]2- \dfrac{x-1}{x+2}[/tex] is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].
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Question 1:
Solve this system of equations using any method.
4x – y = 5
3x + y = 16
a. (3, 5)
b. (4, 11)
c. (4, 4)
d. (3, 7)
Question 2:
Solve the following system of equations.
d + e = 6
d – e = 4
a. no solution
b. (5, 1)
c. (3, –1)
d. infinite number of solutions
Question 3:
Solve the following system of equations by linear combination:
4x + 3y = 12
y = x – 10
a. (3, –7)
b. (6, –4)
c. (–7, 3)
d. (–4, 6)
Answer:
Question 1: d. (3, 7)
Question 2: b. (5, 1)
Question 3: b. (6, –4)
Step-by-step explanation:
Question 1:
Solve this system of equations using any method.
4x – y = 5
3x + y = 16
Add the equations.
7x = 21
x = 3
4(3) - y = 5
-y = -7
y = 7
d. (3, 7)
Question 2:
Solve the following system of equations.
d + e = 6
d – e = 4
Add the equations.
2d = 10
d = 5
5 + e = 6
e = 1
b. (5, 1)
Question 3:
Solve the following system of equations by linear combination:
4x + 3y = 12
y = x – 10
4x + 3y = 12
-x + y = -10
Multiply the second equation by 4 and add to the first equation.
4x + 3y = 12
(+) -4x + 4y = -40
----------------------------
7y = -28
y = -4
-4 = x - 10
x = 6
b. (6, –4)
Please help. Thank you. (30 points included) (Shown work)
Answer:
True
Step-by-step explanation:
Supplementary angles are angles that add up to 180 degrees (straight line). *5 degrees + x create a straight line.
the top says for the first box : Part A Explain how Mrs. Soto could apply the
following theorem to the problem of restoring
the gate to its original rectangular shape.
Answer:
The given theorem proves that the door is not a rectangle right now since, the door came out of shape, it can be proved by the Pythagorean theorem. If the length is set to a certain shape, and the width is set to a certain shape, and drawn to diagonals. If solved by the Pythagorean Theorem, if the length of two diagonals are similar then and only then the door would be a rectangle.
Hope this helps!
Aaron as 3 times as many sweets as Bola Aaron gives Bola 6 sweets and now he has twice as many as her new total How many sweets did they each begin with
Answer:
Aaron = 54
Bola = 18
Step-by-step explanation:
Let
[tex]A \to Aaron[/tex]
[tex]B \to Bola[/tex]
From the first statement, we have:
[tex]A = 3B[/tex]
After given Bola 6 sweets,
[tex]A - 6 = 2(B + 6)[/tex]
Required
The initial number of sweets each has
Substitute [tex]A = 3B[/tex] in [tex]A - 6 = 2(B + 6)[/tex]
[tex]3B - 6 = 2(B + 6)[/tex]
Open bracket
[tex]3B - 6 = 2B + 12[/tex]
Collect like terms
[tex]3B -2B = 12+6[/tex]
[tex]B = 18[/tex]
Substitute [tex]B = 18[/tex] in [tex]A = 3B[/tex]
[tex]A = 3 * 18[/tex]
[tex]A = 54[/tex]
B E
400
(51)
А
C D
3t
Find the measure of ZF if mZD=88º.
A. 8°
B. 40°
C. 52°
D. 90°
the answer is c because you have to take the zf an time it by the zd
Answer:
C
Step-by-step explanation:
for the top of the triangle it has to be 40 and angle d has been declared as 88
so it is 40+88 = 128 now 180 -128 = 52 so the answer is C
Product of additive identity and multiplicative identity of -1/2 is
Answer:
1
Step-by-step explanation:
additive identity =1/2
multiplicative =2
Product = 1/2*2
So the answer is 1
If you deposit $350 in an account that compounds interest continuously at 6.3%, how long will ittake to double your money?
Answer:
11 years
Step-by-step explanation:
Double of the amount deposited = $350 × 2 = $700
First, convert R as a percent to r as a decimal
r = R/100
R = 6.3%
Hence,
r = 6.3/100
r = 0.063 per year,
Then, solve the equation for t = time, the formula is given as:
t = ln(A/P) / r
A = Doubled amount = $700
P = Principal = Initial amount = $350
t = ln(700.00/350.00) / 0.063
t = 11.002 years
Approximately , t = 11 years
Therefore, it will take 11 years for your money to double.
If k = -18 and m = 7, what is m - k?
Submit
Answer:
5
Step-by-step explanation:
Evaluate and substitute:
Sqrt of 7 - (-18)
Sqrt of 7 + 18 = 25
Sqrt of 25 = 5
Therefore, our answer!
Hope this helps, best of luck! :p
Really need help ?????pls
Answer:
34,833.21 ft³
Step-by-step explanation:
Volume of a cylinder = πr²h
r is the radius
h is the height
Given
height h = 19 3/4 ft
d = 1 1/5h
d = 6/5 * h
d = 6/5 * 19 3/4
d = 6/5 * 79/4
d = 474/20
radius r = 474/20 * 1/2
radius r = 474/40
radus r = 11 34/40
radus r = 11 17/20 ft
Get the volume
V = 3.14 * (474/40)² * 79/4
V = 3.14 * 561.69 * 19.75
V = 34,833.20535
Hence the volume of the cylinder to the nearest hundredth is 34,833.21 ft³
Write as a single power: (x^4)(x^10)/(x^3)^5
The solution of the expression as a single power is X²⁹.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given expression is (x⁴)(x¹⁰)/(x³)⁵. The equation will be solved by the property of exponents.
E = (x⁴)(x¹⁰)/(x³)⁵
Add all the powers of the same base x.
E = (x⁴)(x¹⁰)/(x¹⁵)
E = x⁽⁴⁺¹⁰⁺¹⁵⁾
E = x²⁹
Therefore, the solution of the expression as a single power is X²⁹.
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I really help on this question
Answer:
jojo reference
Step-by-step explanation:
(ii) Using a calculator, or otherwise, determine the exact value, to one decimal place, of 8792-6886 12 X 9
Answer: I did it in the explanation thingy-
Step-by-step explanation:
Step 1. 8792 - 6886 = 1906
Step 2. 12 x 9 108
That... OR the answer is 205848X
which is a solution of the equation y=2x+8
To find the y-intercept, plug in 0 for x and you solve to get 8
y=−2x+8
y=−2(0)+8
y=0+8
y=0
To find the x-intercept, plug in 0 for y and you solve to get 4
y=−2x+8
0=−2x+8
2x=8
x=0
Algebra Mary decided to travel from home to school which is 600 metres away. She started by walking “x” metres, then ran for twice the distance she walked. Mary then decided to take the bus for the rest of the journey which 65 metres more than the distance she ran. a) State an expression in terms of x for; i) the distance Mary ran [1 mark] ii) the distance Mary travelled by bus . [2 marks] iii) the total distance travelled [ 2 marks] b) Using the balancing method, solve the equation, hence state the distance Mary walked. [4 marks]
Answer:
Step-by-step explanation:
Distance traveled by walking = x
i) The distance Mary run = 2 *x = 2x
ii) Distance traveled by bus = 65 m more than the distance she ran
= 65 m more than 2x
Distance traveled by bus = 2x + 65
Total distance traveled = 600 m
x + 2x + 2x +65 = 600
5x + 65 = 600
5x = 600 - 65
5x = 535
x = 535/5
x = 107
Distance Mary walked = 107 m
A camera and a case cost 100 dollars. If the camera cost 90 more dollars than the case. How much does the case cost.
Answer:
Cost of case = $5
Step-by-step explanation:
x = cost of camera and y = cost of case
x = y + 90
x + y = 100
y + 90 + y = 100
2y = 10
y = 5
x = y + 90
x = 5 + 90
x = 95
Therefore, the cost of the camera is $95 and the cost of the case is $5.
The cost of case is 5 dollars.
What is the equation?The equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
Let,
Cost of camera = a and
Cost of case = b
Given that, camera and a case cost 100 dollars
a + b = 100
Since, the camera cost 90 more dollars than the case
So, a = b + 90
Substitute the value in the equation a + b = 100
b + 90 + b = 100
2b = 10
Divided by 2 both the sides
b = 5
Substitute the value of b in equation
a = b+ 90
a = 5 + 90
a = 95
So, the cost of the camera is $95 and the cost of the case is $5.
Hence, the cost of the case is 5 dollars.
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can someone please explain to me how to do this?
Answer:
The fourth coefficient is 4.
Step-by-step explanation:
Pascal's Triangle in this case has 5 rows of coefficients because the highest power in (y + w)^4 is 4. 4 plus 1 is 5.
Here's the appropriate Pascal's Triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1 Use this row when expanding the 4th power of (v + w).
Notice that in the given expansion, the coefficients are
1, 4, 6, 4 1
This corresponds to the last (5th) row of Pascal's Triangle (above).
So the correct coefficient to be placed in the box is 4.
simple interest 34,100 at 4% for 3 years
Answer:
Step-by-step explanation:
.....
MARKING BRAINLIEST
PLS HELP
Answer:
25
Step-by-step explanation:
Moving it down does not change the length.
Lexon is standing 7.05 meters away from the statue off the Merlin mp at Merlin park Singapore the height of her eyes from her feet is 1.55 meters given that the angle of elevation of the top of the statue from her eyes is 42゚ find the height of the statue
Answer:
7.9m
Step-by-step explanation:
We solve using the Trigonometric function of Tangent
tan θ = Opposite/Adjacent
Opposite = x
Adjacent = 7.05m
We solve for x
tan 42 = x /7.05m
Cross Multiply
tan 42 × 7.05 = x
x = 6.3478485123m
Approximately = 6.35m
Height of the statue = x + 1.55
Hence, = 6.35m + 1.55m
= 7.9m
The height of the statue = 7.9 meters
At a sale on winter clothing, Cody bought four pairs of gloves and four hats for $36.00. Tori bought three pairs of gloves and four hats for $31.00. What were the prices for the gloves and hats?
Answer:
gloves cost $5
hats cost $4
Step-by-step explanation:
four pairs of gloves and four hats for $36.00
4g + 4h = 36
three pairs of gloves and four hats for $31.00
3g + 4h = 31
-------------------------
Subtract the second equation from the first
4g + 4h = 36
-( 3g + 4h = 31 )
––––––––––––
g = 5
gloves cost $5
substitute for g = 5 into either equation
4(5) + 4h = 36
20 + 4h = 36
Subtract 20 from both sides
4h = 16
Divide both sides by 4
h = 4
hats cost $4
4,570= 3thousands+___hundreds+ 7 tens
Answer: 4 thousands, 5 hundreds, 7 tens
Step-by-step explanation: 4,570 is pretty easy to break down. The first place value is 0 so nothing for that. As you have it there the tens place values has 7. Next is hundreds and there's a 5 there so 5 hundreds. If the number is 4,570 then it should be 4 thousands not three.
you save 2/5 of your allowance every week. if you receive $40 per week
how much money will you have after 8 weeks
Answer:
$128
Step-by-step explanation:
2/5 × $40= $16
$16×8= $128
What is the remainder when 19x^2+15x+12 is divided by x-2?
Answer:
118
Step-by-step explanation:
Please answer these tree questions in detail...
Will give Brainliest for the best...
Want answer in detail ASAP
Answer:
Step-by-step explanation:
14.
A.
x = 5.0081818181..
10x = 50.08181818181....
100x = 500.81818181818...
100x - x = 500.8181818... - 5. 008181818....
99x = 495.81
[tex]x = \frac{495.81}{99} = \frac{495.81 \times 100}{99 \times 100} \\\\\\x= \frac{49581}{9900}[/tex]
[tex]x = \frac{5509}{1100}[/tex]
14.
B.
[tex]\sqrt{50} - \sqrt{98} + \sqrt{162} \\\\\sqrt{ 2 \times 25} - \sqrt{ 2 \times 49} + \sqrt{2 \times 81}\\\\\sqrt{ 2 \times 5^2} - \sqrt{ 2 \times 7^2} + \sqrt{2 \times 9^2}\\\\5\sqrt2 - 7 \sqrt 2 - 9 \sqrt 2\\\\\sqrt{2} ( 5 - 7 + 9 ) \\\\7\sqrt2[/tex]
15.
[tex]\frac{3 + \sqrt5}{4 - 2\sqrt 5} \\\\= \frac{3 + \sqrt5}{4 - 2\sqrt 5} \times \frac{4 + 2\sqrt5}{4 + 2\sqrt5}\\\\[/tex] [tex][ \ rationalizing \ the \ denominator \ ][/tex]
[tex]=\frac{(3 + \sqrt5)(4 + 2\sqrt5)}{(4 -2 \sqrt5)(4 + 2\sqrt5)}\\\\=\frac{12 + 6 \sqrt5 + 4\sqrt5 + 2(\sqrt5)^2}{(4)^2 - (2\sqrt5)^2}[/tex] [tex][ \ (a - b)(a +b) = a^2 - b^2 \ ][/tex]
[tex]=\frac{12 + 10 + 10\sqrt5}{16 - (4 \times 5)}\\\\=\frac{22 + 10\sqrt5}{16 - 20 }\\\\=\frac{22+ 10 \sqrt5 }{-4}[/tex]
[tex]= \frac{11}{-2} + \frac{5 \sqrt5}{-2}\\\\= -\frac{11}{2} + \frac{-5 }{2} \sqrt5\\\\[/tex]
[tex]a = - \frac{11}{2} , \ b = -\frac{5}{2}[/tex]
16
[tex]\frac{\sqrt7 + 1 }{\sqrt7 - 1} - \frac{\sqrt7 - 1}{\sqrt7 + 1}\\\\[/tex]
[tex]\frac{(\sqrt 7 + 1 )( \sqrt7 + 1)}{(\sqrt7 - 1 )(\sqrt7 + 1)} - \frac{(\sqrt7 - 1)(\sqrt 7 - 1)}{(\sqrt7 + 1)(\sqrt7 - 1)}[/tex] [tex][ \ LCM \ of \ denominators : (\sqrt7 -1)(\sqrt7 + 1) \ ][/tex]
[tex]\frac{(\sqrt 7 + 1 )^2 -( \sqrt7 - 1)^2}{(\sqrt7)^2 - 1^2}[/tex] [tex][ \ (a \pm b)(a \pm b) = (a \pm b)^2 \ (a-b)(a+b) = a^2 - b^2 \ ][/tex]
[tex]=\frac{(7 + 1 + 2\sqrt7) - ( 7 + 1 - 2\sqrt7)}{7 - 1}\\\\=\frac{8 + 2\sqrt7 - 8 + 2\sqrt7}{6}\\\\= \frac{4 \sqrt7}{6}\\\\= \frac{2 \sqrt 7}{3}[/tex]
Nvm, I know it's KM for this one y'all.
Answer:
If the question is asking which line is the radius then yes
Step-by-step explanation:
Solve the given portion 4/x=3/6 x=?
Answer:
8
Step-by-step explanation:
4/x=3/6
4=3/6x
4*6=3x
24/3=x
8=x
Please mark me as brainliest
What is parallel to y=-5+4.2x
Please help I’ll give brainliest
Answer:
R = 13%
Step-by-step explanation:
P = $4000
I = $780
T = 18 months = 18/12 years
[tex]I = \frac{PRT}{100} \\\\780 = \frac{ 4000 \times R \times \frac{18}{12}}{100}\\\\780 = \frac{6000 \times R }{100}\\\\780 = 60R\\\\R = \frac{780}{60} = 13 \%[/tex]