Three less than 3 times a number, n, is
19 more than twice the number. What
is the number?
А
17
B
19
21
D 22
The equation is:
3n - 3 = 2n + 19
=> 3n - 2n = 19 + 3
=> n = 22
So, the answer is 22.
Add (1.3t3 + 0.4t2 – 24t) + (8 – 18t + 0.6t2) For each term in the second polynomial, enter the letter showing where that term should be placed to add the polynomials vertically.
Answer:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8[/tex]
Step-by-step explanation:
Given
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)[/tex]
Required
Solve
We have:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2)[/tex]
Collect like terms
[tex]1.3t^3 + 0.6t^2 + 0.4t^2 - 24t- 18t + 8[/tex]
[tex]1.3t^3 + t^2 -42t + 8[/tex]
So:
[tex](1.3t^3 + 0.4t^2 - 24t) + (8 - 18t + 0.6t^2) = 1.3t^3 + t^2 -42t + 8[/tex]
Answer:
look at pic
Step-by-step explanation:
The Fun Committee is hosting the Annual City Festival. Jennifer is in charge of the committee and is planning a race to raise money for the Festival. The runners will earn money from donors for the number of miles they run. If the runners start at the park, run to City hall, and then run back to the park, how many total miles will each runner run? Show your work and leave your answer in simplest radical form if necessary.
Answer: [tex]6\sqrt{5}[/tex] miles
This is the same as writing 6*sqrt(5) miles
==========================================================
Work Shown:
P = park
C = city hall
Point P is at the location (10,11)
Point C is at the location (7,5)
Apply the distance formula to find the length of segment PC
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\[/tex]
The exact distance between the park (P) and city hall (C) is [tex]3\sqrt{5}[/tex] miles.
This doubles to [tex]2*3\sqrt{5} = 6\sqrt{5}[/tex] miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.
Extra info:
[tex]6\sqrt{5} \approx 13.41641[/tex] so the runner travels a total distance of roughly 13.4 miles.
(17)^ 3 *(289)^ -6 =(17)^ 2m - 1
Answer:
m = -4
Step-by-step explanation:
The given expression is :
[tex](17)^{3}\cdot(289)^{-6}=(17)^{2m-1}[/tex]
We need to find the value of m
We know that, 17² = 289
So,
[tex](17)^{3}\cdot(17^2)^{-6}=(17)^{2m-1}\\\\(17)^{3}\cdot(17)^{-12}=(17)^{2m-1}[/tex]
Also,[tex]x^ax^b=x^{a+b}[/tex]
So,
[tex]17^{3-12}=17^{2m-1}\\\\17^{-9}=17^{2m-1}\\\\\implies -9=2m-1\\\\-9+1=2m\\\\-8=2m\\\\m=-4[/tex]
So, the value of m is equal to -4.
What is
4
7
as a decimal rounded to 3 decimal places?
Answer:
4/7 as a decimal is 0.57142857142857.
is (12, 4), (36, 12), (-6, -2), (21, 7) directly proportional?
Answer:
I think yes
Step-by-step explanation:
12/4=3
36/12=3
-6/-2=3
and so on
Daisy is trying to find the equation
of a linear function. Based on the
graph, she can tell the line goes
through (2, 20) and (3, 28). What is
the y-intercept?
Answer:
Your answer is (0,4)
Step-by-step explanation:
Una torre de 28.2 m de altura esta situada a la orilla de un rio, desde lo alto del edificio el ángulo de depresión a la orilla opuesta es de 25.2°. Calcular el ancho del río
Answer:
El ancho del río es 59.9 metros.
Step-by-step explanation:
El ancho del río lo podemos calcular con la siguiente relación trigonométrica asumiendo que la torre forma un triángulo rectángulo con el río:
[tex]tan(\theta) = \frac{CO}{CA}[/tex]
En donde:
CA: es el cateto adyacente = Altura de la torre = 28.2 m
CO: es el cateto opuesto = ancho del río =?
θ: es el ángulo adyacente a CA
Dado que el ángulo de depresión (25.2°) está ubicado fuera de la parte superior de la hipotenusa del triángulo que forma la torre con la orilla opuesta del río, debemos calcular el ángulo interno (θ) como sigue:
[tex]\theta = (90 - 25.2)^{\circ} = 64.8 ^{\circ}[/tex]
Ahora, el ancho del río es:
[tex]CO = tan(\alpha)*CA = tan(64.8)*28.2 = 59.9 m[/tex]
Por lo tanto, el ancho del río es 59.9 metros.
Espero que te sea de utilidad!
i13(12)-2give answer
What is the equation of the line that has a slope of 3 and passes through the point (1, -2)
Answer:
y= 3x -5
Step-by-step explanation:
The equation of a line can be written in the slope- intercept form, y= mx +c (where m is the slope and c is the y- intercept).
Given that the slope is 3, m= 3. Substitute m= 3 into the equation.
y= 3x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= 1, y= -2,
-2= 3(1) +c
-2= 3 +c
c= -2 -3
c= -5
Thus the equation if the line is y= 3x -5.
Four friends all give each other presents
The total costs of presents is £80.52
Work out the mean cost of presents in pounds
what is the answer to the problem
Out of the 30 days in June, you run 13 days and swim 6 days. You lift weights 7 days
and ride a bike 4 days. If you make a pie chart to show this data, how many degrees
of the circle should represent swimming?
9514 1404 393
Answer:
72°
Step-by-step explanation:
In a properly constructed pie chart, the proportion of the circle devoted to each section is the same as the proportion of that section to the the whole.
(6 swim days)/(30 days) = (swim pie angle)/(360°)
Multiply by 360° to find ...
swim pie angle = (360°)(6/30) = 72°
72° of the circle should represent swimming.
Given the roll of paper towels below how much plastic would be needed to cover the role so it can be sold given the diameter of the role is 10 inches and the height is 13 inches
Answer:
Amount of plastic need to cover paper role = 565.2 inches
Step-by-step explanation:
Given:
Diameter of paper role = 10 inch
Height of paper role = 13 inch
Find:
Amount of plastic need to cover paper role
Computation:
Radius of paper role = Diameter of paper role / 2
Radius of paper role = 10 / 2
Radius of paper role = 5 inch
Amount of plastic need to cover paper role = Total surface area of cylinder
Amount of plastic need to cover paper role = 2πr(h+r)
Amount of plastic need to cover paper role = 2(3.14)(5)(13+5)
Amount of plastic need to cover paper role = (3.14)(10)(18)
Amount of plastic need to cover paper role = 565.2 inches
(100 points)
1.One of the addends of 17,300 is 11,210. What is the other addend?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
2. If one of the factors of 954 is 318 , what is the other factor?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
3. HEector bought seven bokes of fruit. Each boc contained 24 fruit. How much fruit did Hector buy?
a. What are they asking for? __________________
b. identify all the necessary numbers. __________________
c. write the equation or problem in numeric form. ______________
d. solve the math. ______________________________
e.write the answer. ________________________________
Answer:
1a. The other addend of 17,300
1b. 17,300 and 11,210
1c. 17,300-11,210
1d. 17,300-11,210= 6090
1e. 6090
2a. The other factor of 954
2b. 954 and 318
2c. 954-318
2d. 954-318= 636
2e. 636
3a. The total amount of fruit Hector bought.
3b. 7 and 24
3c. 7 x 24
3d. 7 x 24 = 168
3e. 168 fruits
أريد أن أجد طريقة لإيجاد ارتفاع المخروط عن طريق معرفة قطره ومساحته . بليز أرجو الرد .
Answer:
سأعطي فقط مثالاً مقدمًا أدناه آمل أن يساعد
Step-by-step explanation:
الارتفاع = 24 سم
نصف القطر = 14 ÷ 2 = 7 سم
ارتفاع مائل = L =؟
L2 = R2 + H2
م 2 = 72 +242
م 2 = 49 + 576
م 2 = 625
L = 25
الحجم = 1 ÷ 3 × 22 ÷ 7 × 7 × 24
الحجم = 1232 سم
مساحة السطح المنحني = 22 × 7 × 7 × 25
مساحة السطح المنحني = 550
إجمالي مساحة السطح = 22 × 7 × 7 × 25 + 7
مساحة السطح الكلية = 704 سم
يرجى وضع علامة لي على أنه أذكى
What is the inverse of the function f(x) = x +3?
O h(x) = 5x + 3
O h(x) =
1x-3
Oh(x) = x-3
Oh(x) = x + 3
The value of the inverse of the function f(x) = x +3 is,
⇒ h (x) = x - 3
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
Function is,
f (x) = x + 3
Now, We can find the inverse of the function f(x) = x +3 as,
f (x) = x + 3
y = x + 3
x = y - 3
h (x) = x - 3
Thus, The value of the inverse of the function f(x) = x +3 is,
⇒ h (x) = x - 3
Learn more about the function visit:
https://brainly.com/question/11624077
#SPJ7
[tex]solve : - \\ \\ ( \sqrt{100 - 64)} [/tex]
Answer:
[tex] \sqrt{100 - 64} \\ = 36 \\ = {6}^{2} [/tex]
Solve the inequality
x^2+7x+10< 0
Answer: -5 < x < -2 or (-5, -2)
Step-by-step explanation:
Graph- (-5, -2)
Inequality- -5 < x < -2
Find the value of x. PLEASE HELP ASAPPPPPP
Answer:
5
Step-by-step explanation:
(38 + 6x - 6) ÷ 2 = 7x -4
multiply both sides by 2
(38 + 6x - 6 = 2( 7x - 4)
38 + 6x - 6 = 14x - 8
32 + 6x = 14x - 8
40 = 8x
x = 5
Midsegments are the average of both bases.
Determine the area of the triangle.
223.6 square units
248.7 square units
447.1 square units
458.4 square units
Answer:
223.6 square units. or 223.569 square units
Answer:A
Step-by-step explanation:I took the test
(a) Determine a cubic polynomial with integer coefficients which has $\sqrt[3]{2} + \sqrt[3]{4}$ as a root.
(b) Prove that $\sqrt[3]{2} + \sqrt[3]{4}$ is irrational.
Answer:
(a) [tex]x\³ - 6x - 6[/tex]
(b) Proved
Step-by-step explanation:
Given
[tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex] --- the root
Solving (a): The polynomial
A cubic function is represented as:
[tex]f = (a + b)^3[/tex]
Expand
[tex]f = a^3 + 3a^2b + 3ab^2 + b^3[/tex]
Rewrite as:
[tex]f = a^3 + 3ab(a + b) + b^3[/tex]
The root is represented as:
[tex]r=a+b[/tex]
By comparison:
[tex]a = $\sqrt[3]{2}[/tex]
[tex]b = \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = ($\sqrt[3]{2})^3 + 3*$\sqrt[3]{2}*\sqrt[3]{4}$*($\sqrt[3]{2} + \sqrt[3]{4}$) + (\sqrt[3]{4}$)^3[/tex]
Expand
[tex]f = 2 + 3*$\sqrt[3]{2*4}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*$\sqrt[3]{8}*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 3*2*($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
[tex]f = 2 + 6($\sqrt[3]{2} + \sqrt[3]{4}$) + 4[/tex]
Evaluate like terms
[tex]f = 6 + 6($\sqrt[3]{2} + \sqrt[3]{4}$)[/tex]
Recall that: [tex]r = $\sqrt[3]{2} + \sqrt[3]{4}$[/tex]
So, we have:
[tex]f = 6 + 6r[/tex]
Equate to 0
[tex]f - 6 - 6r = 0[/tex]
Rewrite as:
[tex]f - 6r - 6 = 0[/tex]
Express as a cubic function
[tex]x^3 - 6x - 6 = 0[/tex]
Hence, the cubic polynomial is:
[tex]f(x) = x^3 - 6x - 6[/tex]
Solving (b): Prove that r is irrational
The constant term of [tex]x^3 - 6x - 6 = 0[/tex] is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
[tex]f(-6) = (-6)^3 - 6*-6 - 6 = -186[/tex]
[tex]f(-3) = (-3)^3 - 6*-3 - 6 = -15[/tex]
[tex]f(-2) = (-2)^3 - 6*-2 - 6 = -2[/tex]
[tex]f(-1) = (-1)^3 - 6*-1 - 6 = -1[/tex]
[tex]f(1) = (1)^3 - 6*1 - 6 = -11[/tex]
[tex]f(2) = (2)^3 - 6*2 - 6 = -10[/tex]
[tex]f(3) = (3)^3 - 6*3 - 6 = 3[/tex]
[tex]f(6) = (6)^3 - 6*6 - 6 = 174[/tex]
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
Since none equals 0, then r is irrational
Rewrite the expression as a simplified expression containing one term.
Answer:
-(cos α)/(sin α)
= -cot α
Step-by-step explanation:
use trigonometric identities
On Monday, 405 students went on a trip to the zoo. All 7 buses were filled and 6 students had to travel in cars. How many students were in each bus
Answer:
57 students
Step-by-step explanation:
Since 6 students count not fit and they had to go in cars, there is a remainder of 6. Subtract that from the total, 405, and you get 399.
Then, divide that by 7, and you get the answer. 57.
Hope it helps!
Answer:
57 students
Step-by-step explanation:
405-6=399
399÷7=57
Graph the solution of the inequality 3/7(35x-14)<_ 21x/2+3
Answer:
You'll have a closed circle at x = 2, and shading to the left
See the diagram below
=========================================================
Explanation:
The fractions here are 3/7 and 21/2. The denominators of which are 7 and 2 respectively. The LCD is 7*2 = 14.
If we multiply both sides by 14, then this will clear out the denominators and make the fractions go away.
14*(3/7) = (14*3)/7 = 42/7 = 814*(21/2) = (14*21)/2 = 294/2 = 147So if we multiplied both sides by 14, then we have these steps
[tex]\frac{3}{7}(35x-14) \le \frac{21x}{2}+3\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}+3\right)\\\\14*\frac{3}{7}(35x-14) \le 14*\left(\frac{21x}{2}\right)+14*\left(3\right)\\\\6(35x-14) \le 147x+42\\\\[/tex]
--------------------------
Let's isolate x
[tex]6(35x-14) \le 147x+42\\\\6(35x)+6(-14) \le 147x+42\\\\210x-84 \le 147x+42\\\\210x-147x \le 42+84\\\\63x \le 126\\\\x \le 126/63\\\\x \le 2\\\\[/tex]
The graph of this will consist of a closed or filled in circle at x = 2. We shade to the left to represent numbers smaller than 2.
So either x = 2 or x < 2.
If we used an open hole at 2, then we wouldn't be including 2 (but we want to include this endpoint).
See the diagram below.
# If two vectors whose direction ratios are 1,2,3 and -k,2,1 are perpendicular to each other then, a) k=7 b) k=4 c) k=3 O d) k=6 me especially since we had be 1 poir 82) I don't know why he turned friends for so long.
Answer:
(a)k=7
Step-by-step explanation:
We are given that
Two vectors whose direction ratios are 1,2,3 and -k,2,1.
Let
[tex]a_1=1,b_1=2,c_1=3[/tex]
[tex]a_2=-k,b_2=2,c_2=1[/tex]
We have to find the value of k.
We are given that two vectors are perpendicular to each other.
We know that two vectors are perpendicular to each other then
[tex]a_1a_2+b_1b_2+c_1c_2=0[/tex]
Substitute the values
[tex]1(-k)+2(2)+3(1)=0[/tex]
[tex]-k+4+3=0[/tex]
[tex]-k+7=0[/tex]
[tex]\implies k=7[/tex]
Hence, option a is correct.
x/3 + 8 = 23 . Find the value of x
Answer:
45
Step-by-step explanation:
x/3 + 8 =23
=> x/3 = 23-8
=> x/3 = 15
=> x = 15 x 3
x = 45
Answer:
x=45
Step-by-step explanation:
To find x isolate the variables by using the properties of equality. First, subtract 8 from both sides, [tex]\frac{x}{3} = 15[/tex]. Then multiply both sides by 3, [tex]x=45[/tex]. Finally, to check you can plug 45 back into the equation, [tex]\frac{45}{3} +8=23[/tex]. Next, solve this equation and get 23=23, since this is a true statement 45 is correct.
A square has a perimeter of 36 cm.
What is the length of each side?
Answer:
Step-by-step explanation:
The perimeter of a square has a formula P = s + s + s + s or just P = 4s where s is the length of a side. If this perimeter has a number value, we can plug it in and solve for the length of each side, like this:
36 = 4s so
s = 9 cm. And there you go!
simplify (-9)×5×6(-3)
[tex]\bf \large \hookrightarrow \:( - 9) \: \times \: 5 \: \times \: 6 \: \times \: ( - 3) \\ \\ \bf \Large \hookrightarrow \: \: \: - 45 \: \times \: ( - 18) \\ \\ \bf \Large \hookrightarrow \: \: 810[/tex]
In which section of the number line is 32−−√?
where's the number line?
maybe u can attach it at the comments:)
Answer:
Section B
Step-by-step explanation:
