Answer:
h = 504, k = 65, t = -1
Step-by-step explanation:
56 = h/9
h = 56 x 9
h = 504
k/5 - 10 = 3
k/5 = 3 + 10
k/5 = 13
k = 13 x 5
k = 65
3t + 5 = 2
3t = 2 - 5
3t = -3
t = -3/3
t = -1
Why can't x^2+9 be factored? And is there a way to tell if a problem can be factored or not just by looking at it?
Answer:
There are no like terms
Step-by-step explanation:
×^2+9
=ײ+9
Someone help asappppp
Answer:
all have "bases" less than one which is a decay...
only "C" is greater than 1 (1.01)
"C" is the answer
Step-by-step explanation:
X^4+x^3-6x^2-14x-12=0 Make a list of possible rational roots. Test the possible roots until you find one that produces a remainder of 0 Write the resulting cubic function. Use synthetic division to find a second root that will reduce the cubic expression to a quadratic expression
Step-by-step explanation:
The Rational Roots Test states that for a polynomial with integer coefficients, the factors of the constant / the factors of the leading coefficient are the possible rational roots.
Here, the constant (the value without an x attached to it) is -12 and the leading coefficient (the value that the x to the highest degree is multiplied by) is 1 as x⁴ is multiplied by 1. The factors of -12 are
±(1, 2, 3, 4, 6, 12), so the possible rational roots are ±(1, 2, 3, 4, 6, 12)/1 (as 1 is the only factor of 1).
Trying out a few roots until we get one that works using synthetic division, we can try
x+1 (the root is x=-1)
-1 | 1 1 -6 -14 -12
| -1 0 6 8
__________________________
1 0 -6 -8 -4
the remainder is -4, so this does not work
x+2 (the root is x=-2)
-2 | 1 1 -6 -14 -12
| -2 2 8 12
__________________________
1 -1 -4 -6 0
Therefore, x=-2 is a root and x+2 is a factor of the polynomial. The quotient of the polynomial and x+2 is
-6 + (-4)x + (-1)* x² + 1 * x³ = x³-x²-4x-6
Using the rational roots theorem, the possible roots of x³-x²-4x-6 are
±(1,2,3,6)
Starting with
x-1 (root is x=1), we have
1 | 1 -1 -4 -6
| 1 0 -4
_____________________
1 0 -4 -10
there is a remainder, so this is not a root
next, x-2 (root is x=2)
2 | 1 -1 -4 -6
| 2 2 -4
_____________________
1 1 -2 -10
there is a remainder, so this is not a root
next, x-3 (root is x=3)
3| 1 -1 -4 -6
| 3 6 6
_____________________
1 2 2 0
x-3 is a factor and 3 is a root. the quotient of (x³-x²-4x-6)/(x-3) is x²+2x+2
What is the equation of the line that passes through (-12,6) and (-6,1)?
Utilize graphing to find the solution to
the following system of equations.
4x + 3y = 25 AND y = -5x + 1
([?], [])
Answer:
you guess any value of x and then you substitute any three values for example for the first equation you can guess the value of x to be 1 or 2 or 3
Instructions: Find the angle measures given the figure is a rhombus.
Answer:
m <1 = 147
m <2 = 90
Step-by-step explanation:
In rhombus diagonals are perpendicular to each other so
m <2 = 90
m < 1 = 180- 33
= 147
Answered by Gauthmath
The required angle of the rhombus m∠1 = 57° and m∠2 = 90°.
Given that,
A figure of a rhombus is shown,
An angle of 33° is given,
m∠1 and m∠2 is to be determined.
The triangle is a geometric shape that includes 3 sides and sum of the interior angle should not greater than 180°.
The angle can be defined as the one line inclined over another line.
Here, the rhombus has been shown with an angle of 33° of the side with one of the diagonal.
Since the diagonal of the rhombus bisect each other at an angle of 90 so the angle m∠2 = 90 and the sum of the interior angle of a triangle is 180. So,
m∠1 + 33 + 90 = 180
m∠1 = 180 - 123
m∠1 = 57
Thus, the required angle of the rhombus m∠1 = 57° and m∠2 = 90°.
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=X square there is written at the end
Answer:
see explanation
Step-by-step explanation:
[tex]\frac{pq+1}{9}[/tex]
= [tex]\frac{(3x+1)(3x-1)+1}{9}[/tex]
= [tex]\frac{9x^2- 1+1}{9}[/tex]
= [tex]\frac{9x^2}{9}[/tex]
= x²
Answer:
Hello,
Step-by-step explanation:
[tex]Using\ the\ formula\ (a+b)(a-b)=a^2-b^2\\p=3x+1\\q=3x-1\\\\p*q=(3x+1)*(3x-1)=9x²-1\\\\p*q+1=9x^2\\\\x^2=\dfrac{p*q+1}{9} \\[/tex]
Which of the following is(are) the solution(s) to |15x + 2 |= 8 ?
Hi!
[tex]|15x+2|=8\\\\\\15x+2=8\\15x=8-2\\15x=6 \ \ |:15\\\boxed{x_1=0,4}\\\\\\15x+2=-8\\15x=-8-2\\15x=-10 \ \ |:15\\\boxed{x_2=-\frac{2}{3}}[/tex]
Answer:
x = 2/5 x = -2/3
Step-by-step explanation:
|15x + 2 |= 8
There are two solutions, one positive and one negative
15x + 2 = 8 and 15x + 2 = -8
Subtract 2 from each side
15x + 2-2 = 8-2 and 15x + 2-2 = -8-2
15x = 6 15x = -10
Divide by 15
15x/15 = 6/15 15x /15 = -10/15
x = 2/5 x = -2/3
The exchange rate between dollars ($) and pounds (£) is $1 = £0.65 . The exchange rate between euros (€) and pounds is €1 = £0.74 . Khan changes €520 into pounds. He spends £260 and then changes the rest into dollars. Work out how many dollars he receives
Answer:
€520=£442.83
=£442.83-£260
=£182.83 into dollars=$251.52
Therefore he receives $251.52
AB←→||CD←→. Find the measure of ∠BFG.
Answer:
Value of ∠ BFG = 135°
Step-by-step explanation:
Given:
AB || CD
∠ AFG = (3x + 15)°
∠ FGD = (5x - 5)°
Find:
∠ BFG
Computation:
We know that;
∠ AFG = ∠ FGD
3x + 15 = 5x - 5
3x - 5x = - 5 - 15
- 2x = - 20
2x = 20
x = 10
Value of ∠ AFG = 3x + 15
Value of ∠ AFG = 3(10) + 15
Value of ∠ AFG = 45°
∠ BFG = 180° - Value of ∠ AFG
∠ BFG = 180° - 45°
∠ BFG = 135°
Value of ∠ BFG = 135°
4. Find the height, x, of the building
Urgent please help
Answer:
D
Step-by-step explanation:
The function you need to use is the Tan(39).
Tan(x) = opposite / adjacent.
The opposite side does not make up the reference angle.
In this case, the opposite side = x
The adjacent side is not the hypotenuse and does make up the reference angle (which is not the right angle).
opposite = x
adjacent = 68
Tan(39) = x / 68 Multiply by 68
68*Tan(39) = x Divide by Tan(39)
Tan(39) = 0.9098
68*.9098 = x
x = 55.07
After getting RM24 from his mother, Samuel had 3 times as much as he had previously. How much did he have previously?
Answer:
Samuel had RM8 previously
Step-by-step explanation:
24÷3=8
How do you calculate an antilog?
eg: antilog 2.1423
9514 1404 393
Answer:
138.77
Step-by-step explanation:
Your scientific or graphing calculator will have exponential functions for bases 10 and e. On the calculator shown in the first attachment, they are shifted (2nd) functions on the log and ln keys. Consult your calculator manual for the use of these functions.
The value can be found using Desmos, the Go.ogle calculator, or any spreadsheet by typing 10^2.1423 as input. (In a spreadsheet, that will need to be =10^2.1423.) The result using the Go.ogle calculator is shown in the second attachment.
You can also use the y^x key or the ^ key (shown to the left of the log key in the first attachment). Again, you would calculate 10^2.1423.
__
We have assumed your log is to the base 10. If it is base e (a natural logarithm), then you use the e^x key instead. Desmos, and most spreadsheets, will make use of the EXP( ) function for the purpose of computing e^( ). You can type e^2.1423 into the Go.ogle calculator.
_____
Additional comment
There are also printed logarithm tables available that you can use to look up the number whose log is 0.1423. You may have to do some interpolation of table values. You should get a value of 1.3877 as the antilog. The characteristic of 2 tells you this value is multiplied by 10^2 = 100 to get the final antilog value.
The logarithm 2.1423 has a "characteristic" (integer part) of 2, and a "mantissa" (fractional part) of 0.1423.
Evaluate C=5/9(F−32) for F = 77 degrees.
Answer:
b:25
Step-by-step explanation:
77 degrees Fahrenheit is 25 degrees Celsius. So, the correct answer for the given equation is the second option.
An equation is a combination of two or more expressions separated by an equal sign(=), indicating that the expressions are equal to each other. The expressions, though, are a group of numbers, variables, mathematical operations, etcetera. An equation can be represented on the Cartesian plane.
The relation between Celsius and Fahrenheit is given by the following equation:
[tex]C =\dfrac{5}{9}(F-32)[/tex],
Substitute F = 77 to convert 77 degrees Fahrenheit to Celsius.
[tex]C =\dfrac{5}{9}(77-32)[/tex]
[tex]=\dfrac{5}{9}(77-32)\\=\dfrac{5}{9}\times45\\= 25[/tex]
Thus, the second option is correct.
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3x + ky = 8
X – 2ky = 5
are simultaneous equations where k is a constant.
b) Given that y = 1/2 determine the value of k.
Answer:
(a): x is 3 and ky is -1
(b): k is -2
Step-by-step explanation:
Let: 3x + ky = 8 be equation (a)
x - 2 ky = 5 be equation (b)
Then multiply equation (a) by 2:
→ 6x + 2ky = 16, let it be equation (c)
Then equation (c) + equation (b):
[tex] { \sf{(6 + 1)x + (2 - 2)ky = (16 + 5)}} \\ { \sf{7x = 21}} \\ { \sf{x = 3}}[/tex]
Then ky :
[tex]{ \sf{2ky = 3 - 5}} \\ { \sf{ky = - 1}}[/tex]
[tex]{ \bf{y = \frac{1}{2} }} \\ { \sf{ky = - 1}} \\ { \sf{k = - 2}}[/tex]
Simultaneous equations are used to represent a system of related equations.
The value of k when [tex]y = \frac 12[/tex] is -2
Given that:
[tex]3x + ky = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]y = \frac 12[/tex]
Substitute [tex]y = \frac 12[/tex] in both equations
[tex]3x + ky = 8[/tex]
[tex]3x + k \times \frac 12 = 8[/tex]
[tex]3x + \frac k2 = 8[/tex]
[tex]x - 2ky = 5[/tex]
[tex]x - 2k \times \frac 12 = 5[/tex]
[tex]x - k = 5[/tex]
Make x the subject in [tex]x - k = 5[/tex]
[tex]x = 5 + k[/tex]
Substitute [tex]x = 5 + k[/tex] in [tex]3x + \frac k2 = 8[/tex]
[tex]3(5 + k) + \frac k2 = 8[/tex]
Open bracket
[tex]15 + 3k + \frac k2 = 8[/tex]
Multiply through by 2
[tex]30 + 6k + k = 16[/tex]
[tex]30 + 7k = 16[/tex]
Collect like terms
[tex]7k = 16 - 30[/tex]
[tex]7k = - 14[/tex]
Divide both sides by 7
[tex]k = -2[/tex]
Hence, the value of constant k is -2.
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If a sine curve has a vertical shift down 19 units with an amplitude of 21, what will the minimum and maximum values be? (i.e. how high and low will the graph go?)
Min Value:
Max Value:
Given:
Amplitude = 21
Vertical shift = 19 units down
To find:
The maximum and the minimum value.
Solution:
The general form of sine function is:
[tex]y=A\sin (Bx+C)+D[/tex]
Where, |A| is amplitude, [tex]\dfrac{2\pi}{B}[/tex] is period, [tex]-\dfrac{C}{B}[/tex] is phase shift and D is the vertical shift.
Here,
[tex]Maximum=D+A[/tex]
[tex]Minimum=D-A[/tex]
We have,
Amplitude: [tex]A = 21[/tex]
Vertical shift: [tex]D=-19[/tex]
Negative sign means shifts downwards.
Now,
[tex]Maximum=D+A[/tex]
[tex]Maximum=-19+21[/tex]
[tex]Maximum=2[/tex]
And,
[tex]Minimum=D-A[/tex]
[tex]Minimum=-19-21[/tex]
[tex]Minimum=-40[/tex]
Therefore, the minimum value is -40 and the maximum value is 2.
If ? A² + b² = 7b and b² + (2b-a) ²= 7², what is (a - b) ²?
Answer:
7^2+2ab - 4b^2
Step-by-step explanation:
A² + b² = 7b
b² + (2b-a) ²= 7²
FOIL
b^2 +4b^2-4ba+a^2= 7^2
Rewriting
a^2 -2ab + b^2 +4b^2 -2ab = 7^2
Add 2ab and subtract 4b^2 from each side
a^2 -2ab + b^2 +4b^2 - 4b^2 -2ab+2ab = 7^2+2ab - 4b^2
a^2 -2ab + b^2 = 7^2+2ab - 4b^2
(a-b)^2 = 7^2+2ab - 4b^2
Which of the following best describes when a relation is a function?
O A. Each element in the domain is the same as each element in the
range.
O B. Each element in the domain is twice the size of each element in
the range.
C. Each element in the domain is paired with just one element in the
range.
O D. Each element in the domain is paired with at least one element in
the range.
Answer:
Step-by-step explanation:
The answer is C.
That's another way of using the vertical line test. Put a ruler perpendicular to the x axis and going through a point. If the ruler hits only one point, then then if all the points plotted do the same thing, then the points make a function.
C says the same thing. Only 1 element in the domain (x) can be associated with 1 y value (the range). If there is more than 1 y value, then you do not have a function.
Which of the following characteristics best describes the given function of f(x) = 3x - 6?
A) exponential function, always increasing, linear
B) linear absolute value function, always increasing, linear, maximum
C) linear function, always increasing, straight lines, no maximum or minimum
D) exponential function, always decreasing, linear
Answer:
C
Step-by-step explanation:
degree 1 ( linear function
A whole number has the first four odd prime numbers as its factors. What is the smallest value this whole number could be?
a. 1 155
b. 945
c. 105
d. 210
Answer:
3×5×7×11=1155
a.1155 the answer
3×5×7×11=1155
What are prime factors?A natural number other than 1 whose only factors are 1 and itself is said to have a prime factor. In actuality, the first few prime numbers are 2, 3, 5, 7, 11, and so forth.
Given
3×5×7×11=1155
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Help please !!!!!!!!!
Answer: (a): Good course, (b): Bad course
Step-by-step explanation:
Firstly, because the standard deviation of the good course results is lower, there is less variation so he performs more consistently there.
Secondly, the trick with the second question is that while the mean of the bad course is slightly less, the standard deviation is quite a lot higher than that of the good course, so it's more likely that the highest single test score belongs to the bad course.
Find the value of x in the triangle shown below.
Answer:
x ≈ 55.5°
Step-by-step explanation:
Using the Sine rule in the triangle
[tex]\frac{5}{sinx}[/tex] = [tex]\frac{5.7}{sin70}[/tex] ( cross- multiply )
5.7 sinx = 5 sin70° ( divide both sides by 5.7 )
sin x = [tex]\frac{5sin70}{5.7}[/tex] , then
x = [tex]sin^{-1}[/tex] ([tex]\frac{5sin70}{5.7}[/tex] ) ≈ 55.5° ( to the nearest tenth )
Answer:
[tex]x =55[/tex]°
Step-by-step explanation:
An isosceles triangle is a triangle with two congruent sides. One can see that the given triangle is an isosceles triangle, as two sides have a side length of (5) units. One property of an isosceles triangle is the base angles theorem. This theorem states that the angles opposite the congruent sides of an isosceles triangle are congruent. In this situation, this means that two angles have a measure of (x) degrees. As a given, the sum of angles in any triangle is (180) degrees. Thus, one can form an equation, and solve for the unknown, (x):
[tex]x + x + 70 = 180[/tex]
Simplify,
[tex]2x + 70 =180[/tex]
Inverse operations,
[tex]2x + 70 =180[/tex]
[tex]2x = 110[/tex]
[tex]x =55[/tex]
Daphne borrows $2500 from a financial institution that charges 6% annual interest, compounded monthly, for 2 years. The amount that Daphne will need to pay back at the end of the term is
What are the solutions to the system of equations?
{y=x²−4x+8
y=2x+3
Answer:
x = 1, y = 5
x = 5, y = 13
Step-by-step explanation:
y = x² − 4x + 8 .......(1)
y = 2x + 3 .......(2)
Substitute the value of y in equation 2 into equation 1
y = x² − 4x + 8
y = 2x + 3
x² − 4x + 8 = 2x + 3
Rearrange
x² − 4x − 2x + 8 − 3 = 0
x² − 6x + 5 = 0
Solve by factorization
Find the product you x² and 5. The result is 5x²
Find the factors of 5x² such that their sum will result in −6x. The factors are −x and −5x.
Replace −6x in the equation above with −x and −5x. This is illustrated below:
x² − x − 5x + 5 = 0
x(x − 1) − 5(x − 1) = 0
(x − 1)(x − 5) = 0
x − 1 = 0 or x − 5 = 0
x = 1 or x = 5
Substitute the value of x into equation 2 to obtain the value of y.
y = 2x + 3
x = 1
y = 2(1) + 3
y = 2 + 3
y = 5
x = 5
y = 2x + 3
y = 2(5) + 3
y = 10 + 3
y = 13
SUMMARY:
x = 1, y = 5
x = 5, y = 13
Cuantos años hay que tener un capital de 8500 euros a un redito de 3,75% para que produzca un interes de 2868,75 euros?
Respuesta:
9 años
Explicación paso a paso:
Dado :
Capital = Principal, P = 8500 €
Rendimiento, tasa, r = 3,75%
Intereses, i = 2868,75 €
Para obtener el plazo, número de años que se necesitarán para devengar un interés de 2868,75 € sobre un capital de 8500 € al tipo del 3,75%;
Interés = principal * tasa * tiempo
2868,75 € = 8500 € * 0,0375 * t
2868,75 € = 318,75 billones €
t = 2868,75 € / 318,75 €
t = 9
Por lo tanto, tomará un período de 9 años.
Y = 2x - 4
(0, 4)
(3, -1)
(-1, -5)
(-4, 9)
Answer:
Y = 2x - 4
(2,-4)
gradient= 2
y-intersept = -4
Ао
D
B
120°
Angle A =
degrees.
Answer:
A = 120
Step-by-step explanation:
Angle A is a vertical angle to 120 and vertical angles are equal
A = 120
[tex]\Large\rm\underbrace{{\green{ \: Angle \: A \: = \: 120 \degree}}}[/tex]
Because vertically opposite angles are always equal.
30 cm . A rectangular baking tray has dimensions as shown. 18 cm 30 cm a) Calculate the area of the tray on which balls of biscuit dough can be placed. b) The baked biscuits are circular. Each has a radius of 3 cm.
i) Determine the area covered by one biscuit.
ii) The dough balls are placed in straight rows and columns on the baking tray. What is the maximum number of biscuits that can be baked in the pan at a time?
1 - 580squaredcm
2 - 540
Find the measure of the indicated angle.
Answer:
i think it the measured of the indicated angle is 55
Write an equation that represents the statement "the
product of a number, x, and the number 7 is 42."
Answer:
7x = 42
Step-by-step explanation:
"Product" refers to multiplication and "is" refers to equal to.
Hi! I'm happy to help!
This equation will be written like this
x×7=42
To make this easier to solve, we can use the inverse operation, division.
42÷7=x
42 divided by 7 is 6, so the answer is 6.
I hope this was helpful, keep learning! :D
