Answer: -10
Step-by-step explanation:
Simplifying
-3(y + 5) = 15
Reorder the terms:
-3(5 + y) = 15
(5 * -3 + y * -3) = 15
(-15 + -3y) = 15
Solving
-15 + -3y = 15
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '15' to each side of the equation.
-15 + 15 + -3y = 15 + 15
Combine like terms: -15 + 15 = 0
0 + -3y = 15 + 15
-3y = 15 + 15
Combine like terms: 15 + 15 = 30
-3y = 30
Divide each side by '-3'.
y = -10
Simplifying
Luis dispone de una cantidad de dinero de 25,000 RD$ para ponerlos en el banco a plazo fijo con un interés de un 1.7% al cabo de 8 meses, ¿Cuánto dinero posee Luis si no ha gastado nada? *
Answer:
Luis's balance = $25,283.33
Step-by-step explanation:
Given the following data;
Principal = $25,000Interest rate, R = 1.7 %Time = 8 monthsTo find how much money Luis will have;
First of all, we would have to convert the value of time in months to a year.
Conversion:
12 months = 1 year
8 months = X year
Cross-multiplying, we have;
12 * X = 8
X = 8/12
X = 2/3 years
To find the simple interest, we would use the formula;
[tex] S.I = \frac {PRT}{100} [/tex]
Where;
S.I is the simple interest.P is the principal.R is the interest rate.T is the time measured in years.Substituting the values into the formula, we have;
[tex] S.I = \frac {25,000 * 1.7 * \frac {2}{3}}{100} [/tex]
[tex] S.I = \frac {28333.33}{100} [/tex]
S.I = $283.33
Luis's balance = S.I + Principal
Luis's balance = 283.33 + 25000
Luis's balance = $25,283.33
HELP PLS!! ILL GIVE POINTS !! :(( m
Find the product of the complex numbers. Express your answer in
trigonometric form.
Z1 =5(cos15° + i sin 15°)
Z2=3(cos70° + i sin 70°)
A. 8(cos85° + isin85°)
B. 2 (cos(-55°) + i sin(-55°))
C. 2 (cos305° + i sin 305°)
D. 15(cos85° + i sin85°)
Answer: Choice D
15(cos85° + i sin85°)
===========================================================
Explanation:
Let's say we had these two general complex numbers, which are in polar form.
[tex]z_1 = r_1*\left(\cos(\theta_1)+i*\sin(\theta_1)\right)\\\\z_2 = r_2*\left(\cos(\theta_2)+i*\sin(\theta_2)\right)\\\\[/tex]
We can abbreviate them into the shorthand form
[tex]z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\[/tex]
The notation "cis" stands for "cosine i sine".
Now that we have those complex numbers set up, multiplying them is as simple as saying this:
[tex]z_1*z_2 = (r_1*r_2)*\text{cis}(\theta_1+\theta_2)[/tex]
We do two basic things:
Multiply the r values out frontAdd the theta values inside the the cis function---------------------------------------
With all that in mind, let's tackle the problem your teacher gave you.
The given complex numbers
[tex]z_1 = 5*\left(\cos(15^{\circ})+i*\sin(15^{\circ})\right)\\\\z_2 = 3*\left(\cos(70^{\circ})+i*\sin(70^{\circ})\right)\\\\[/tex]
abbreviate into
[tex]z_1 = 5*\text{cis}(15^{\circ})\\\\z_2 = 3*\text{cis}(70^{\circ})\\\\[/tex]
then those multiply to
[tex]z_1*z_2 = (r_1*r_2)*\text{cis}(\theta_1+\theta_2)\\\\z_1*z_2 = (5*3)*\text{cis}(15+70)\\\\z_1*z_2 = 15\text{cis}(85^{\circ})\\\\z_1*z_2 = 15\left(\cos(85^{\circ})+i\sin(85^{\circ})\right)\\\\[/tex]
which is why choice D is the final answer.
f(x) = x2 – 12x – 29
f(3) = (x+ ?)+ ?
Answer:
-6 and - 65
Step-by-step explanation:
X-12x-29, by completing the square we get (x-6)^2-65
A rectangular drawing is enlarged by 30%. The original dimensions of this drawing are 16cm x 24cm.
Determine the scale factor, as a fraction that represents this enlargement. What are the new, enlarged
dimensions?
Answer:
Step-by-step explanation: Scale [tex]\frac{130}{100} = \frac{13}{10}[/tex]
New dimensions [tex]16 * 1.3 --- 24*1.3 =20.8 cm * 31.2 cm[/tex]
the height of an equivalent triangle is 15cm and it's perimeter is 36cm find the area of the triangle
Answer:
The area is 72 cm².
Step-by-step explanation:
Since it is equivalent triangle
h = b
so,
b + b + b (since all sides are equal)= 36 cm
3b = 36 cm
or, b = 36/3
so, b = 12 cm
so
area of triangle = (1/2)×b×h
= (1/2)×12cm×12cm
= 6cm × 12cm
= 72 cm²
Will Mark Brainlest helpppp
Answer:
R = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]
Step-by-step explanation:
P - Q + R = I ( I is the identity matrix )
[tex]\left[\begin{array}{ccc}2&4\\3&5\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}-2&2\\4&1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( subtract corresponding elements )
[tex]\left[\begin{array}{ccc}2-(-2)&4-2\\3-4&5-1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]
x= 3/4 , y= - 2/5 then x+ y =
Step-by-step explanation:
Given
x = 3/4
y = -2/5
Now
X + y = 3/4 - 2/5
[tex] \frac{3 \times 5 - 2 \times 4}{20} [/tex]
[tex] = \frac{15 - 8}{20} [/tex]
[tex] = \frac{7}{20} [/tex]
Answer:
7/20
Step-by-step explanation:
x=3/4
y= -2/5
x+y=?
to get the sum, plug in x=3/4 into the x and y= -2/5 into the y
1. x + y = ?
2. 3/4 + (- 2/5) = ?
3. 3/4 - 2/5 =?
4. find the lcm of 4 and 5 to get the common denominator (in this case, the lcm of 4 and 5 is 20)
5. multiply 3/4 by 5 (numerator and denominator) and 2/5 by 4 (numerator and denominator)
6. 15/20 - 8/20 = 7/20
the answer is 7/20
what is the approximate shadow in feet of the tree in the figure below.
Answer:
224 ft
Step-by-step explanation:
The tree makes a 90° angle with the ground, so we have a right triangle.
For the 32° angle, the height of the tree is the opposite leg. The length of the shadow on the ground is the adjacent leg.
The trig ratio that relates the opposite leg to the adjacent leg is the tangent.
Let the length of the shadow of the tree on the ground be x.
tan A = opp/adj
tan 32° = 140 ft/x
x = 140 ft/tan 32°
x = 224 ft
Answer: 224 ft
a party of 7 comes into your restaurant and says they want to split the bill evenly 7 ways their total is $247.79 what does each customer owe ?
Answer:
each costumer owe $35.40
Step-by-step explanation:
so, u get 247.79÷7 (cuz it is 7 people)
u get 35.40.
to check just get 35.40×7 and u will revice their total.
find the measure of one exterior angle for the following regular polygon
Answer:
36 degrees
Step-by-step explanation:
10 corners/sides.
the sum of all exterior angles in a polygon is always 360 degrees.
so, one exterior angle here is 360/10 = 36 degrees
toán 9 nha mọi người
Answer:
Thamkhao
Step-by-step explanation:
please help with math!! geometry explain if you can :)
Answer:
Step-by-step explanation:
Applying the midpoint formula to the points (a, 0) and (0, a) looks like this:
[tex]M=(\frac{a+0}{2},\frac{0+a}{2})[/tex] which simplifies to
[tex]M=(\frac{a}{2},\frac{a}{2})[/tex]
Given m
11
n, find the value of x.
N
820
20
Answer: =
Submit Answer
CAN SOMEONE PLS HELP I keep getting it wrong
Answer:
x = 98
Step-by-step explanation:
x and 82 are adjacent angles on a straight line and sum to 180° , then
x + 82 = 180 ( subtract 82 from both sides )
x = 98
please help don’t understand question!
Answer:
[tex]{ \sf{ - 2 {a}^{5} + 4 {a}^{4} + 5 {a}^{3} + \frac{2}{3}a }}[/tex]
Answer:
D
Step-by-step explanation:
A polynomial is in standard equation when the degree of the polynomial are in descending order.
please help, I'm so confused how to-do this
Answer:
Step-by-step explanation:
use the quadratic formula : [tex]x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{2a}[/tex], where ax^2+bx+c=0
[tex]y = \frac{ -(-20) \pm \sqrt{(-20)^2 - 4(1)(50)}}{2(1)}[/tex]
[tex]y = \frac{ 20 \pm \sqrt{400 - 200}}{2}[/tex]
[tex]y = \frac{ 20 \pm \sqrt{200}}{2}[/tex]
y = 17.07106~ or 2.928932~
The diagram shows the floor of a room. The carpet used to
cover the floor costs $5.25 per square foot. How much will
it cost to carpet the entire floor?
Answer:
3rd option, $672
Step-by-step explanation:
The area is,
(4×12)+(8×10)
= 128
per square foot it costs $5.25, so the total cost will be,
128×$5.25
= $672
Answered by GAUTHMATH
Will mark brainlest helppppppp
Answer:
6
Step-by-step explanation:
again ?
7 = (3x - 4)/2
14 = 3x - 4
18 = 3x
x = 6
can you find the answer for m
Answer:
m∠LMK = 50°
Step-by-step explanation:
This is an isosceles triangle. Isosceles triangles have two sides of equal length and two equal angles. This means ∠K and ∠M will have the same degrees.
The sum of the angles of a triangle is 180°. The following equation can be arranged and solved for the missing angles:
[tex]x+x+80=180\\2x+80=180\\2x=100\\x=50[/tex]
Therefore, m∠LMK = 50°.
4² − 7 + 55 − 74 + 3 (Ascending with respect to n):
Answer:
If its supposed to be simplify it will be -7 . If your finding the derivative it is 0.
Step-by-step explanation:
Based on the markings of the two triangles, what statement could be made about ΔABC and ΔA′B′C′? Question 1 options: A) The corresponding pairs of sides and angles of ΔABC and ΔA′B′C′ aren't congruent. B) ΔABC and ΔA′B′C′ are congruent. C) ΔABC and ΔA′B′C′ are irregular polygons. D) ΔABC and ΔA′B′C′ aBased on the markings of the two triangles, what statement could be made about ΔABC and ΔA′B′C′? Question 1 options: A) The corresponding pairs of sides and angles of ΔABC and ΔA′B′C′ aren't congruent. B) ΔABC and ΔA′B′C′ are congruent. C) ΔABC and ΔA′B′C′ are irregular polygons. D) ΔABC and ΔA′B′C′ are similar but not congruent.re similar but not congruent.
Answer:
B) ΔABC and ΔA′B′C′ are congruent.
Step-by-step explanation:
Given
See attachment for [tex]\triangle ABC[/tex] and [tex]\triangle A'B'C'[/tex]
Required
Determine the relationship between both triangles
The single line on all sides of both triangles implies that the sides of the triangles are equal
i.e.
[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- sides
Similarly, the same mark on the three angles of both triangles means that the angles of the both triangles are equal
i.e.
[tex]\triangle ABC \cong \triangle A'B'C'[/tex] --- angles
Hence, both triangles are congruent
Answer:
B) ΔABC and ΔA′B′C′ are congruent.
Step-by-step explanation:
how to convert base two to base three
Consider this example: say we want to convert x = 11 0101 1001₂ to base 3.
The binary expansion of x is
x = 1×2⁹ + 1×2⁸ + 1×2⁶ + 1×2⁴ + 1×2³ + 1×2⁰
which in base 10 reduces to
x = 512 + 256 + 64 + 16 + 8 + 1 = 857
Recall the first several powers of 3:
3⁰ = 1; 3¹ = 3; 3² = 9; 3³ = 27; 3⁴ = 81; 3⁵ = 243; 3⁶ = 729
Now it's a matter of computing quotients and remainders. Pick the largest power of 3 that fits into the target number, then check the remainder and repeat.
• How many times does the 729 go into 857? 1 time, and it leaves a remainder of 128, or
857 = 1×729 + 128 = 1×3⁶ + 128
• How many times does 81 go into 128? Also 1 time, so
128 = 1×81 + 47 = 1×3⁴ + 47
• How many times does 27 go into 47? Also 1 time,
47 = 1×27 + 20 = 1×3³ + 20
• How many times does 9 go into 20? 2 times,
20 = 18 + 2 = 2×9 + 2 = 2×3² + 2
• How many times does 1 go into 2? Also 2 times,
2 = 2 + 1 = 2×1 + 0 = 2×3⁰
So we found
857 = 1×3⁶ + 1×3⁴ + 1×3³ + 2×3² + 2×3⁰
which is the ternary expansion of x,
x = 1 011 202₃
Multiply the polynomial by distribution. Show your work and explain the steps you used to solve.
- 8x(x^2 – 8x + 3)
Answer:
-8x^3 + 64x^2 - 24x
Step-by-step explanation:
To distribute, we must multiple -8x to each term:
-8x(x^2) - 8x(-8x) - 8x(3)
-8x^3 + 64x^2 - 24x
Step-by-step explanation:
[tex] - 8x( {x}^{2} - 8x + 3) \\ = ( - 8x \times {x}^{2}) - ( - 8x \times 8x) + ( - 8x \times 3) \\ = - 8 {x}^{3} + 64 {x}^{2} - 24x[/tex]
distribute -8x to each term in the perenthesis i.e. multiply each term by -8x
A garden is rectangular with a width of 8 feet and a length of 10 feet. If it is surrounded by a walkway 2 feet wide, how many square feet of area does the walkway cover?
Answer:
The rea of walk way is 32 ft^2.
Step-by-step explanation:
width, w = 8 feet
length, L = 10 feet
width of walkway, d = 2 feet
length of outer, L' = 10 + 2 + 2 = 14 feet
Area of outer, A' = L' x w = 14 x 8 = 112 ft^2
Area of inner, A = L x w = 10 x 8 = 80 ft^2
The area of walkway = A' - A = 112 - 80 = 32 ft^2
The rea of walk way is 32 ft^2.
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.
rearrange the formula to make x the subject : 5( a - 2x) = 9(x + 1)
Answer:
x = [tex]\frac{5a-9}{19}[/tex]
Step-by-step explanation:
Given
5(a - 2x) = 9(x + 1) ← distribute parenthesis on both sides
5a - 10x = 9x + 9 ( add 10x to both sides )
5a = 19x + 9 ( subtract 9 from both sides )
5a - 9 = 19x ( divide both sides by 19 )
[tex]\frac{5a-9}{19}[/tex] = x
I need help to find w =
Answer:
The answer is 12.
Step-by-step explanation:
Since one of the sides on the smaller polygon is two and on the other one is six that must mean the scale is multiply by 3 because 2x3=6. So 4 times 3 is 12.
So, w = 12
f The difference of 8 and 3 is multiplied by one-quarter of the sum of 7 and 5 37 vedanta Excel in Mathematics
Answer:
15
Step-by-step explanation:
first find f which is (8-3) × ( 1/4 × 7 + 5)
simplify
5 × (1/4 ×12)
5 × 3
15 is thw answer
Which linear inequality is represented by the graph?
Answer:
Wow
Step-by-step explanation:
I love the question pls i also want to know the answer to it
If Sin x = -¼, where π < x < 3π∕2 , find the value of Cos 2x
Answer: 7/8
Cos2x has 3 formulas, Sinx is given in the question, we should use the formula with sinus. I guess that's the solution.
HELP ME !! find the value of x
Answer:
ERROR
Step-by-step explanation:
