Answer:
f(3) = [tex]\frac{64}{3}[/tex]
Step-by-step explanation
f(3) = [tex]\frac{1}{3}[/tex] x [tex]4^{3}[/tex]
f(3) = [tex]\frac{1}{3}[/tex] x 64
f(3) = [tex]\frac{64}{3}[/tex]
3a+5b+2c=?
a+b=15
b+c=14
5b=3b,2b
Step-by-step explanation:
please check you typing 5b = 3b, 2b
?????
Answer:
73
Step-by-step explanation:
3a + 5b + 2c = ?
Given:
a + b = 15
b + c = 14
now express in terms of b
a = 15 - b equation (i)
c = 14 - b equation (ii)
3a + 5b + 2c
substitute the values
3(15 - b) + 5b + 2(14 - b)
45 - 3b + 5b + 28 - 2b
add or subtract like terms
73 + 5b - 5b
plus 5b and minus 5b gets cancel
73
Escribe un número de tres cifras digamos a1b1c1, en el cual a1 sea distinto de c1; ahora invierte los dígitos a1 y c1, (obtendrás el número c1b1a1 ); resta el número menor al número mayor, es decir a1b1c1 - c1b1a1 o bien c1b1a1 - a1b1c1, obtendrás como resultado un número de tres cifras, digamos a2b2c2 (es posible que a_2=0 ); invierte los dígitos a_2 y c_2. Finalmente suma los números a2b2c2 y c2b2a2 . ¿Qué número obtuviste?
Answer:
El número obtenido es:
1089.Step-by-step explanation:
Vamos a escoger tres números sencillos para cada variable como:
a1 = 1b1 = 2c1 = 3Por lo tanto, nuestro número de tres cifras es:
123 (la única pauta es que a1 sea diferente a c1 y con este número la cumplimos)Ahora, nos dice que invirtamos los números a1 y c1, por lo tanto, nuestro nuevo número de tres cifras sería:
321A continuación, nos menciona que restemos el menor del mayor, en este caso, nuestro número menor es 123 y el mayor es 321, por lo tanto:
321 - 123 = 198 (Este resultado será el mismo sin importar cuáles números elijas para el ejercicio)Como obtuvimos el número 198, se podría decir que:
a2 = 1b2 = 9c2 = 8Ahora nos piden que invirtamos a2 y c2, por lo tanto nuestro nuevo número sería:
891Y por último, nos solicita que sumemos los dos últimos números obtenidos, entonces tenemos:
891 + 198 = 1089Por lo tanto, el número obtenido al final es 1089, el cual obtendrás sin importar qué número de tres cifras elijas al inicio, siempre y cuando no se repitan el primero y el tercer dígito.
Write an equation of a line that passes through (3, -1) and is perpendicular to y = 6x - 4. Show work.
I NEED THIS FAST
Answer:
y = -1/6x - 1/2
Step-by-step explanation:
y = -1/6x + b
-1 = -1/6(3) + b
-1 = -1/2 + b
-1/2 = b
What am I doing wrong? I've tried every conceivable answer, I thought I knew this type of math well, but this program keeps telling me I'm wrong.
Answer:
15.0 units
Step-by-step explanation:
Here, we want to get the distance between the two points as follows;
CD = √(x2-x1)^2 + (y2-y1)^2
So we have;
CD = √(7+8)^2 + (-5+4)^2
CD = √225+ 1 =
CD = √(226
CD = 15.0 units
Help please!!!!!!!!!!!!!!!!!!!!
9514 1404 393
Answer:
(c) The solution -6 is an extraneous solution
Step-by-step explanation:
If you solve the equation graphically, you can avoid extraneous solutions. The true solution is x = -1.
You can tell from the equation that the domain will be restricted to values of x that make the radical non-negative:
x+4 ≥ 0 ⇒ x ≥ -4
Then x=-6 must be an extraneous solution. It arises when the negative square root is used.
__
The conventional solution method has you square both sides and solve the resulting quadratic.
(x +4)² = x +10
x² +7x +6 = 0
(x +6)(x +1) = 0 ⇒ x = -6 or -1
The solution x=-6 is not in the domain, so is extraneous.
__
Additional comment
Graphical solution is often easier if the equation is in the form f(x) = 0. That form can be had by subtracting one side of the equation from both sides. In the attached, we subtracted √(x+10) from both sides. (We added the negative branch of the square root function to show where the extraneous root comes from.)
A cube of sides 10cm was cut across to obtain a prism. Calculate the surface area of the prism and the volume of the prism
[tex] \frac{1}{2} bh \times h[/tex]
Answer:
Part A
The volume of the triangular prism is 500 cm³
Part B
The total surface area of the prism is approximately 441.42 cm²
Step-by-step explanation:
The given details are;
The dimensions of the side length of the cube, s = 10 cm
The shape the cube was cut across to obtain = A prism
Part A
Whereby the prism obtained is a triangular prism, we have;
The cube can be cut in half to form a triangular prism
The volume of each triangular prism obtained = (1/2) × The volume of the cube
∴ The volume of the triangular prism = (1/2) × (10 cm)³ = 500 cm³
Part B
The height of the prism, h = 10 cm × sin(45°) = 5·√2 cm = (1/2) × The base width of the prism
The triangular cross sectional area of the prism, A₁ = 5·√2 × 5·√2 = 50
The square cross sectional area, A₂ = 10 × 10 = 100
The cross sectional area of the base, A₃ = 10·√2 × 10 = 100·√2
The total surface area of the prism, A = 2·A₁ + 2·A₂ + A₃
∴ A = 2×50 + 2×100 + 100·√2 = 300 + 100·√2 ≈ 441.42
The total surface area of the prism, A ≈ 441.42 cm²
Using the net below, find the surface area of the pyramid. 6 cm 7 cm Surface Area - [?] cm2
Answer:
120 cm²
Step-by-step explanation:
Surface area of the pyramid = area of the 4 triangles + area of the square
✔️Area of the 4 triangles = 4(½*b*h)
b = 6 cm
h = 7 cm
Area = 4(½*6*7)
= 4(3*7)
= 4(21)
= 84 cm²
✔️Area of the square = s²
s = 6 cm
Area = 6² = 36 cm²
✅Surface area of the pyramid = 84 + 36 = 120 cm²
Q.No.1: A subset of {2, b} is:
Answer:
{2}
or
{b}
a subset is a part of the whole set.
Answer:
hope it helps...
Use the three steps to solve the problem.
Betty has 10 more dimes than quarters. If she has $3.45, how many quarters and dimes does she have?
Answer:
17
Step-by-step explanation:
Let d be dimes
q represent quarters
d = q + 10
10d + 25q = 345 cents
Substitute for "d" and solve for "q";
10(q+10) + 25q = 345
35q + 100 = 345
35q = 245
q = 7
Since d = q+10, d = 17
find the value of x and y
Answer:
x = 58
y = 39
Step-by-step explanation:
x = 58 (Vertically opposite angles)
x + 2y + (x-14) = 180 (Angles in a straight line)
=> x + 2y + x - 14 = 180
=> 2x + 2y = 180 + 14
=> 2(58) + 2y = 194
=> 116 + 2y = 194
=> 2y = 194 - 116
=> 2y = 78
=> y = 78/2
=> y = 39
The measurement of a rectangular room on a scale drawing are 8cm x 6cm. If the scale use is 1 : 400, calculate the actual area of the room in m².
Answer:
768 m²
Step-by-step explanation:
8 x 400 = 3200 cm = 32 m
6 x 400 = 2400 cm = 24m
32 x 24 = 768 m²
can someone help me I don't understand
Answer:
(a) 165 m/min
(b) 107.14m/min
Step-by-step explanation:
The slope of the distance time graph gives speed.
Here, the speed of the segment A is
[tex]v_A= \frac{900-0}{4-0}=225 m/min[/tex]
The speed of segment B is
[tex]v_B= \frac{1500- 900}{14-4}= 60 m/min[/tex]
(a) The change in speed is
= 225 - 60 = 165 m/min
(b) The average speed is defined as the ratio of total distance to the total time.
So, the average speed is
[tex]= \frac{1500}{14}= 107.14 m/min[/tex]
If the cos of an angle is .75, what is the csc?
A. 1/√(5)
B. 9/√(6)
C. 6/√(2)
D. 3/√(9)
E. 4/√(7)
F. 2/√(3)
Answer: Choice E. 4/sqrt(7)
This is the same as writing [tex]\frac{4}{\sqrt{7}}[/tex]
=================================================
Explanation:
0.75 = 3/4
Recall that cosine is the ratio of adjacent over hypotenuse.
That means if cos(theta) = 3/4, then the adjacent is 3 units and the hypotenuse is 4 units.
Through the pythagorean theorem, we would then find that
a^2+b^2 = c^2
a = sqrt(c^2 - b^2)
a = sqrt(4^2 - 3^2)
a = sqrt(7)
This is the opposite side of reference angle theta.
From here, we can say
csc(angle) = hypotenuse/opposite
csc(theta) = 4/sqrt(7)
which points to choice E as the final answer.
For the given functions f(x) and g(x), find (f + g)(x) or (f – g)(x) as
indicated.
f(x) = 8x – 7,8(x) = 6x – 4
Find (f + g) (x)
Answer:
(f + g) (x) = 14x-11
Step-by-step explanation:
From the question, what we have to do is to add the two given polynomials
We have this as;
(8x-7) + (6x-4) = 8x + 6x -7-4 = 14x -11
what is the vertex of x^2
Answer:
The vertex is (0,0)
Step-by-step explanation:
To find the x coordinate of the vertex
x = -b/2a where ax^2 +bx +c
a=1 b=0 c=0
x = -0/2(1) = 0
The y value is found by substituting into the equation
y = (0)^2 =0
The vertex is (0,0)
Find the odd one out, and explain why
26..325..226..49..50
a) 325
b) 226
c) 50
d) 49
Answer:
B.226
Step-by-step explanation:
I HOPE ITS HELP PO
What's the area of the entire shape?
Answer:
30
Step-by-step explanation:
you need to multiply its length by its with
By writing each number correct to 1 significant figure, estimate the value of
37.8 x 13.2
28,5 + 22.1
You must show all your working.
Answer:
37.8 x 13.2 =4988.6
28,5 + 22.1 = 50.6
Find the value of x. Round to
the nearest tenth.
27°
х
34°
11
X = [ ?
Answer:
[tex]{ \tt{from \: sine \: rule : }} \\ { \bf{ \frac{ \sin(A) }{A} = \frac{ \sin(B) }{B} }} \\ \\ { \bf{ \frac{ \sin(34 \degree) }{x} = \frac{ \sin(27 \degree) }{11} }} \\ \\ { \bf{x = \frac{11 \times \sin(34 \degree) }{ \sin(27 \degree) } }} \\ \\ { \tt{x = 13.5}}[/tex]
The ages of five children in a family are 6, 1, 3, 10, and 17. Which statement is true for this group of data?
mode>mean
median>mean
median=mode
mean>median
Answer:D - mean>median
Step-by-step explanation:
There are no repeating variables to have a mode so median and mean are the only options. The mean of this data set is 7.4 and the median is 6. Therefore mean greater than median
Can someone help me solve this? I will need the x and y and will also need to solve for angles 1, 2, 3, and 4.
Answer:
x = 20,
y = 15
m<1 = 75°
m<2 = 75°
m<3 = 75°
m<4 = 105°
Step-by-step explanation:
m<1 = 3x + 15
m<2 = 4x - 5
m<3 = 5y
✔️m<1 = m<2 (corresponding angles are congruent)
3x + 15 = 4x - 5 (substitution)
Collect like terms
3x - 4x = -15 - 5
-x = -20
Divide both sides by -1
x = 20
✔️m<3 = m<2 (corresponding angles are congruent)
5y = 4x - 5 (substitution)
Plug in the value of x and solve for y
5y = 4(20) - 5
5y = 80 - 5
5y = 75
5y/5 = 75/5
y = 15
✔️Find the measure of each labelled angle:
x = 20, y = 15
Thus:
m<1 = 3x + 15 = 3(20) + 15
m<1 = 75°
m<2 = 4x - 5 = 4(20) - 5
m<2 = 75°
m<3 = 5y = 5(15)
m<3 = 75°
m<4 + m<3 = 180° (same side interior angles are supplementary)
m<4 + 75° = 180° (substitution)
m<4 = 180° - 75° (subtraction property of equality)
m<4 = 105°
In Byron's class, there are 2 boys for every 3 girls. Today 7 new boys were added making the number of boys and girls the same. How many boys and girls were there originally?
Answer:
12
Step-by-step explanation:
2+3=5+7=12
Có 10 bạn mua cùng một loại vở hết tất ả 60 000 tính giá tiền của mỗi quyển vở biết rằng mỗi bạn mua 2 quyển vở
Answer:
Giá một cuốn sách là $ 1000
Step-by-step explanation:
Được
Tổng chi phí sách = 60000
Tổng số bạn bè = 10
Sách do mỗi người bạn mua = 2
Như vậy, tổng số sách mua của cả 10 bạn = 10 * 2 = 20
Giá của một cuốn sách = Tổng giá / tổng số sách đã mua
Giá một cuốn sách = 20000/20 = 1000
Giá một cuốn sách là $ 1000
In the diagram below, ΔPQR ≅ ΔSTR. Complete the statement ∠Q ≅ ___
Answer: Choice A. [tex]\angle T[/tex]
Explanation:
Notice how letters Q and T are in the middle of the sequences of PQR and STR respectively. This means the angles correspond.
Because the triangles are congruent, this means the corresponding pieces are congruent. Therefore, angle Q and angle T are the same measure.
As you can see, the order matters when it comes to forming congruence statements. Something like [tex]\triangle PQR \cong \triangle STR[/tex] is slightly different from [tex]\triangle PQR \cong \triangle SRT[/tex]
Congruent triangles have all corresponding measurements like angles and side lengths congruent. The completed statement would be ∠Q ≅ ∠T (Option A: ∠T)
What are congruent triangles?Suppose it is given that two triangles ΔABC ≅ ΔDEF
Then that means ΔABC and ΔDEF are congruent. Congruent triangles are exact same triangles, but they might be placed at different positions.
The order in which the congruency is written matters.
For ΔABC ≅ ΔDEF, we have all of their corresponding elements like angle and sides congruent.
Thus, we get:
[tex]\rm m\angle A = m\angle D \: or \: \: \angle A \cong \angle D[/tex] (small m shows we're taking about measurement) (both the statements are equivalent)[tex]\rm m\angle B = m\angle E \: or \: \: \angle B \cong \angle E[/tex][tex]\rm m\angle C = m\angle F \: or \: \: \angle C \cong \angle F[/tex][tex]\rm |AB| = |DE| \: \: or \: \: AB \cong DE[/tex][tex]\rm |AC| = |DF| \: \: or \: \: AC \cong DF[/tex][tex]\rm |BC| = |EF| \: \: or \: \: BC \cong EF[/tex](|AB| denotes length of line segment AB, and so on for others).
For this case, we have: ΔPQR ≅ ΔSTR
Thus, we have:
[tex]\angle Q = \angle T[/tex]
Thus, the completed statement would be ∠Q ≅ ∠T. (Option A: ∠T)
Learn more about congruent triangles here:
https://brainly.com/question/16921692
SOMEONE HELP ME LOL IM SO OVERWHELMED
Answer:
1) [tex]\frac{12.2}{sin(54)}[/tex] which rounds to 15.1
2) [tex]\frac{12.2}{cos(54)}[/tex] which rounds to 20.8
Step-by-step explanation:
1) We're going to have to use the trig ratios for this. We know that sin(x) = [tex]\frac{opposite}{hypotenuse}[/tex] (opposite side over the hypotenuse). In this case, we know that angle h = 54 and the side opposite to angle h = 12.2, and we're trying to find the hypotenuse. If we label the hypotenuse as x, then we can say that sin(H) = [tex]\frac{MI}{HI}[/tex]. We can plug in the values we know to get sin(54) = [tex]\frac{12.2}{x}[/tex]. From there, we multiply by x on both sides to get x out of the denominator, and then we divide by sin(54). So, we end up with x = [tex]\frac{12.2}{sin(54)}[/tex] which, if you put it in your calculator (and make sure the calculator is in degree mode) we get approximately 15.1 mi.
2) Follow the same steps that are described in 1), but instead of sin, we're using cos.
Hope this helps! Let me know if you have any further questions!
Trong mặt phẳng tọa độ Oxy , cho vectơ a = ( -3;4) . Độ dài vectơ a bằng bao nhiêu
Answer:
Step-by-step explanation:
Độ dài vecto a= căn bậc hai của (-3)*(-3)+4*4=5
Answer:
5
Step-by-step explanation:
PLEASE, WILL GIVE BRAINLIEST! THANKS! Hey guys LOL
Indicate in standard form the equation of the line through the given points, writing the answer in the equation box below.
P (0, -4), Q (5, 1)
Answer:
y=1x-4
Wait sorry I did it wrong the first time lol.
In standard Form, it should be 4x-4y=16
Step-by-step explanation:
yes yes hand me brain
Which function is graphed?
Answer:
I think that a Cube Root Function
Step-by-step explanation:
Volume How many fluid ounces are in each size?
1 cup = 8 oz. 1pint = 2 cups. 1 quart = 2 pints. 1 gallon = 4 quart
1 cup = _______fl oz.
Answer:
1 cup = 8 fl oz
Step-by-step explanation:
1 cup = 8 fl oz
Find: (6m5 + 3 – m3 – 4m) – (–m5 + 2m3 – 4m + 6)
Write subtraction of a polynomial expression as addition of the additive inverse.
(6m5 + 3 – m3 – 4m) + (m5 – 2m3 + 4m – 6)
Rewrite terms that are subtracted as addition of the opposite.
6m5 + 3 + (–m3) + (–4m) + m5 + (–2m3) + 4m + (–6)
Group like terms.
[6m5 + m5] + [3 + (–6)] + [(–m3) + (–2m3)] + [(–4m) + 4m]
Combine like terms.
Write the resulting polynomial in standard form.
Given:
The expression is:
[tex](6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)[/tex]
To find:
The resulting polynomial in standard form.
Solution:
We have,
[tex](6m^5+3-m^3-4m)-(-m^5+2m^3-4m+6)[/tex]
Write subtraction of a polynomial expression as addition of the additive inverse.
[tex](6m^5+3-m^3-4m)+(m^5-2m^3+4m-6)[/tex]
Rewrite terms that are subtracted as addition of the opposite.
[tex]6m^5+3+(-m^3)+(-4m)+m^5+(-2m^3)+4m+(-6)[/tex]
Group like terms.
[tex][6m^5+m^5]+[3+(-6)]+[(-m^3)+(-2m^3)]+[(-4m)+4m][/tex]
Combine like terms.
[tex]7m^5+(-3)+(-3m^3)+0[/tex]
On simplification, we get
[tex]7m^5-3-3m^3[/tex]
Write the polynomial in standard form.
[tex]7m^5-3m^3-3[/tex]
Therefore, the required polynomial in standard form is [tex]7m^5-3m^3-3[/tex].