Answer:
6.25 kg cement, 7.5 L water
Step-by-step explanation:
2.5 kg cement / 4 kg sand = x kg cement / 10 kg sand
x = 6.25
3 L water / 4 kg sand = y L water / 10 kg sand
y = 7.5
evaluate arctan(tan(2pi/3))
Answer:
For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:
[tex] arctan(tan(\frac{2\pi}{3}))[/tex]
Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:
[tex] arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]
Step-by-step explanation:
For this case we know that [tex]\frac{2\pi}{3}= 120 degrees[/tex]. For this case we want to find:
[tex] arctan(tan(\frac{2\pi}{3}))[/tex]
Since the tan and arctan functions are inverse when we apply bth at the same time we got the identity function so then we got for this case:
[tex] arctan(tan(\frac{2\pi}{3})) = I(\frac{2\pi}{3}) = \frac{2\pi}{3}[/tex]
Help please! Thank you
Answer:
The rise is -6.
Step-by-step explanation:
For this problem, the direction of the vector gives the indication of a negative slope. We know that the equation to find slope = rise/run meaning y/x values. So for this, we can see the y-value of the blue triangle (the rise) to be 6, and the x-value of the blue triangle (the run) to be 3. And as stated before, this is a negative slope, in the y-direction. Hence, the rise is -6 for the blue triangle.
Answer this and I'll mark you the brainliest
if the polynomial x^4-3x^3-6x^2+kx-16 is exactly divisible by x^2+4x+3,find the value of k
Answer:
k = -18.
But See below.
Step-by-step explanation:
f(x) = x^4 - 3x^3 - 6x^2 + kx - 16
If x^2 + 3x + 2 is a factor then so is (x + 1) and (x + 2) as
x^2 + 3x + 2 = (x + 1)(x + 2)
So by the Factor Theorem f(-1) = 0:
f(-1) = (-1)^4 - 3(-1)^3 - 6(-1)^2 - 1k - 16 = 0
1 + 3 - 6 - k - 16 = 0
-18 - k = 0
k = -18.
Checking:
f(-2) = (-2)^4 - 3(-2)^3 - 6(-2)^2 - 18(-2) - 16
= 16 + 24 - 24 + 36 - 16 = 36 (NOT 0).
Answer:
k=11
explaination:
need help adding and subtracting functions
Answer:
Step-by-step explanation:
[x/2-2/1] × [2x^2 + x -3]
we can solve this very simply by multiplication
2x -2=10 solve for x
Answer:
x=6
Step-by-step explanation:
Take -2 and add it to 10 and get 12. So then the equation is 2x=12. Divide 2 by 12 and get x=6.
Write each of the following three statements in symbolic form and determine which pairs are logically equivalent. Include truth tables and a few words of explanation.
If it walks like a duck and it talks like a duck, then it is a duck.
Either it does not walk like a duck or it does not talk like a duck, or it is a duck.
If it does not walk like a duck and it does not talk like a duck, then it is not a duck.
Answer:
If it walks like a duck and it talks like a duck, then it is a duck.
and
Either it does not walk like a duck or it does not talk like a duck, or it is a duck.
are logically equivalent to each other.
but neither of the two is logically equivalent to
If it does not walk like a duck and it does not talk like a duck, then it is not a duck.
Step-by-step explanation:
Given statements:
Statemen 1:
If it walks like a duck and it talks like a duck, then it is a duck.
Statement 2:
Either it does not walk like a duck or it does not talk like a duck, or it is a duck.
Statement 3:
If it does not walk like a duck and it does not talk like a duck, then it is not a duck.
Let
p be the statement: it walks like a duck q be the statement: it talks like a duck r be the statement: it is a duckUsing p = it walks like a duck , q =it talks like a duck, r = it is a duck the given statements can be written in symbolic form as:
Statement 1:
p ∧ q → r
The ∧ symbol shows that if both p and q are true then, they imply r. This means both p and q together imply r
Statement 2:
~p ∨ ~q ∨ r
Here the statement p and q are negated and joined using or. So either negation p or negation of q or r (alternative)
Statement 3:
~p ∧ ~q → ~r
The ∧ symbol shows that if both negation of p and negation of q are true then, they imply r. This means both negated p and negated q together imply negated r
Statement 1:
p ∧ q → r ≡ ~(p∨q) ∨ r Using conditional equivalence p→q ≡ ~p ∨ q
≡ (~p ∧ ~q ) ∨ r
You can see it is equivalent to Statement 2 i.e. ~p ∧ ~q → ~r
Hence Statement 1 and Statement 2 are logically equivalent.
Now Statement 3:
~p ∧ ~q → ~r ≡ ~(~p ∧ ~q ) ∨ ~r Using conditional equivalence p→q ≡ ~p ∨ q
≡ ~(~p ) ∨ ~(~q ) ∨ ~r Using De Morgan's Law ~(p∧q) ≡ ~p ∨~q
≡ p ∨ q ∨ ~r Using Double Negation Law ~(~p)≡p
This shows that Statement 3 is neither logically equivalent to Statement 1 nor logically equivalent to Statement 2.
Proof by truth table is attached. The table shows that the columns for Statement 1 and Statement 2 have same truth values.
Hence
"If it walks like a duck, and it talks like a duck, then it is a duck,"
and
"If it does not walk like a duck, and does not talk like a duck, then it is not a duck,"
are logically equivalent.
The table also shows that column for Statement 3 does not match with either of the columns for Statement 1 and Statement 2. So
If it does not walk like a duck and it does not talk like a duck, then it is not a duck.
is not logically equivalent to Statement 1 and Statement 2.
Answer:
duck walk
Step-by-step explanation:
Translate the scenario below to a linear equation, then solve.
The second angle of a triangle is double the first angle. The third angle is 40 less than the first angle. Find the three angles.
First angle=
Second angle=
Third angle=
Answer: x + 2x + x-40 = 180
First angle= 55º
Second angle= 110º
Third angle= 15º
Step-by-step explanation: The sum of the angles of a triangle is 180º
Take the values given and use x as the unknown first angle. then create terms for the other two angles based on that:
The second angle of a triangle is double the first angle becomes 2x
The third angle is 40 less than the first angle becomes x-40
x + 2x + x-40 = 180 Solve by adding like terms . x + 2x + x = 4x
4x -40 = 180 Add 40 to both sides to "cancel" the -40 on the left
4x + 40 -40 = 180 + 40 becomes
4x = 220 Divide both sides by 4 to "cancel" the 4 on the left side
4x/4 = 220/4
x = 55 This is the first angle. Substitute 55 for the "x" in the original terms
2(55) = 110 The second angle
(55) -40 = 15 the third angle
Now use technology and use the cumulative probability 0.95, the mean muequals10.5, and the standard deviation sigmaequals4.10 to determine the value for x0, rounding to one decimal place.
Answer:
18.5
Step-by-step explanation:
In the above question, we are given the following values
Cumulative probability ( confidence interval) = 0.95 = 95%
Mean = 10.5
Standard deviation = 4.10
We are asked to find the value of x.
To solve for x , we would be using the z score formula.
z score = (x-μ)/σ,
where x is the raw score,
μ is the population mean
σ is the population standard deviation
z score was not given in the question, but we have our cumulative probability as 95%(0.95).
Using the appropriate table,
the z score for 95% confidence is z = 1.96.
Therefore,
z score = (x-μ)/σ,
1.96 = x - 10.5/4.10
Cross multiply
1.96×4.10 = x - 10.5
x = (1.96 × 4.10) + 10.5
x = 8.036 + 10.5
x = 18.536
Approximately to 1 decimal place
x = 18.5
solve it using quadratic formula.
grade 9
10 points
Answer:
{-1/4, 1}{3/4, 6}Step-by-step explanation:
1. We can clear fractions and solve the resulting quadratic. We clear fractions by multiplying the equation by the product of the denominators.
[tex]\dfrac{2x+1}{2x-1}-\dfrac{2x-1}{2x+1}=\dfrac{8}{3}\\\\3((2x+1)^2-(2x-1)^2)=8(2x-1)(2x+1)\\\\3(8x) = 8(4x^2 -1)\\\\4x^2 -3x -1 = 0\qquad\text{factor out 8, subtract 3x}\\\\x=\dfrac{-(-3)\pm\sqrt{(-3)^2-4(4)(-1)}}{2(4)}=\dfrac{3\pm\sqrt{25}}{8}\\\\x=\dfrac{3\pm5}{8}=\left\{-\dfrac{1}{4},1\right\}[/tex]
__
2. Using the same idea here, we get ...
[tex]\dfrac{2}{x-2}+\dfrac{3}{x}=\dfrac{9}{x+3}\\\\2(x)(x+3)+3(x-2)(x+3)=9(x-2)(x)\\\\2x^2+6x+3(x^2+x-6)=9x^2-18x\\\\4x^2-27x+18=0\\\\x=\dfrac{-(-27)\pm\sqrt{(-27)^2-4(4)(18)}}{2(4)}=\dfrac{27\pm\sqrt{441}}{8}\\\\x=\dfrac{27\pm21}{8}=\left\{\dfrac{3}{4},6\right\}[/tex]
What can each term of the equation be multiplied by to eliminate the fractions before solving? x – + 2x = StartFraction one-half EndFraction x minus StartFraction 5 Over 4 EndFraction plus 2 x equals StartFraction 5 Over 6 EndFraction plus x. + x 2 6 10 12
Answer: while solving an equation involving fractions we eliminate the fraction by multiplying the LCD of all the denominators present in the equation . LCD means Least common Denominator so for this question when we try to eliminate the denominator we first try to find the LCM (2,4,6) because that will give us the LCD.
2=2
4=2·2
6=2·3
LCM = 2·2·3
LCM = 12
It means we need to multiply the 12 to each term of equation to eliminate the fractions before solving.
12
To eliminate the fractions, multiply the equation by the 12
Equation
A equation is an expression that shows the relationship between two or more variables and numbers.
Given the equation:
[tex]x-\frac{5}{4}+2x=\frac{5}{6}+x[/tex]
To eliminate the fractions, multiply by the L.C.M of the denominator of the fraction i.e. 12 to get:
12x - 15 + 24x = 10 + 12x
Find out more on Equation at: https://brainly.com/question/2972832
please help :) Which number is less than 2.167 × 10 to the 4 power? A. 9,978 B. 1.1 x 10 to the 6 power C. 56,344,000 D. 2.468 × 10 to the 5 power
Answer: A
Step-by-step explanation
2.167x10^4 = 21,670
= 9,978
1.1x10^6 = 1100,000
= 56,344,000
2.468x10^5 = 246,800
Answer: A. 9,978
Based on the power, move the decimal point that many spaces to the right. (E.g., If it's 4.2 × 10^3, then move the decimal three spaces to the right, and you'd get 4200.)
2.167 × 10^4 = 21670
1.1 × 10^6 = 1100000
2.468 × 10^5 = 246800
Out of all the numbers mentioned in the question, 9,978 is the only one that's less than 2.167 × 10^4 = 21670.
Solve this problem, which steps would you take? Include any theorems, definitions, or reasons that explain the steps. Make sure you include all steps needed to solve for ∠A
Answer:
∠A=123°.
Step-by-step explanation:
From the given figure it is clear the CD and CE are two tangent lines on circle with center A.
Radius is perpendicular to the tangent at the point of tangency.
[tex]\angle ADC=90^{\circ}[/tex]
[tex]\angle AEC=90^{\circ}[/tex]
Smaller arc DE = (5x-2)°
It means central angle DAE is (5x-2)°.
[tex]\angle DAE=(5x-2)^{\circ}[/tex]
Now, ADCE is a quadrilateral and sum of all angles of a quadrilateral is 360 degrees.
[tex]\angle ADC+\angle DCE+\angle AEC+\angle DAE=360^{\circ}[/tex]
[tex]90^{\circ}+(2x+7)^{\circ}+90^{\circ}+(5x-2)^{\circ}=360^{\circ}[/tex]
[tex](7x+5)^{\circ}+180^{\circ}=360^{\circ}[/tex]
[tex](7x+5)^{\circ}=360^{\circ}-180^{\circ}[/tex]
[tex](7x+5)^{\circ}=180^{\circ}[/tex]
[tex]7x+5=180[/tex]
[tex]7x=175[/tex]
[tex]x=25[/tex]
The value of x is 25.
[tex]\angle A=5x-2=5(25)-2=125-2=123^{\circ}[/tex]
Therefore, the measure of ∠A is 123°.
What the answer now and answer fast correct answer
Answer:
[tex] f = 12.7 [/tex]
Step-by-step explanation:
Given:
<H = 94°
FG = h = 15
<F = 58°
GH = f = ?
Use the law of sines to find f:
[tex] \frac{f}{sin(F)} = \frac{h}{sin(H)} [/tex]
[tex] \frac{f}{sin(58)} = \frac{15}{sin(94)} [/tex]
[tex] \frac{f}{0.848} = \frac{15}{0.998} [/tex]
[tex] \frac{f}{0.848} = 15.03 [/tex]
Multiply both sides by 0.848
[tex] \frac{f}{0.848}*0.848 = 15.03*0.848 [/tex]
[tex] f = 15.03*0.848 [/tex]
[tex] f = 12.74544[/tex]
[tex] f = 12.7 [/tex] (nearest tenth)
plzzzz help! marking brainiest asap!
(-x^2+2x+3) + (-x^2-2x-1) = -2x^2 + 2
============================================
Explanation:
We have two large red tiles labeled with -x^2 on them. They add to -2x^2 which is found in every answer choice listed. This means that we must have a plus sign between the two parenthesis groups. If we had a subtraction sign, then -x^2 minus -x^2 would turn into 0x^2 or just 0, and the x^2 terms would go away entirely.
Because we must have a plus sign between the parenthesis, this means the answer is between C and D.
Now focus on the x terms. The slash marks mean that all of the x terms pair up and add to 0. They go away as there aren't any x terms that haven't been slashed. That explains why there are no x terms on the right hand side of any of the answer choices.
The question is: which of C or D has the x terms add to 0x? The answer would be choice D since 2x + (-2x) = 2x-2x = 0x. Choice C has 2x+2x = 4x which is what we don't want.
Lastly, choice D is further proven correct by noticing that the constants 3 and -1 add to 3+(-1) = 3-1 = 2. We have two small blue squares that add to 2 after the cancellations have happened.
Dyami planted a palm tree in the back yard of his house several years ago. Initially, it was 20 centimeters high and its height increased by 30 centimeters each year. Let H be the height of the tree in centimeters t years after it was planted. Which of the following best explains the relationship between t and H?
Answer:
when t is increased , h will increased too
Answer:
Th relationship is linear because H increases by 30 each time t increases by 1.
Step-by-step explanation:
H is linear if it changes at a constant rate per unit interval. In other words, constant differences in t should correspond to constant differences in H.
what is the mean deviation of the following numbers 2 4 6 8 10 12
Step-by-step explanation:
mean is always equal to additon of total no.s by total no.s
2 + 4 + 6 + 8 + 10 + 12
=42
total no.s = 6 no.s
42/6
=7
therefore 7 is the answer which is the mean deviation of the following no.s .
Ans with steps.. Tysm Plzz asap!!
Answer:
10x^2 + 8x
Step-by-step explanation:
Area of the outer rectangle = 5x(3x + 2) = 15x^2 + 10x
Area of the inner rectangle = x(5x - 2) = 5x^2 - 2x
Area of the shaded region = (15x^2 + 10x) - (5x^2 - 2x)
= 10x^2 + 8x
5x(3x + 2) - x(5x - 2) required expression.
Step-by-step explanation:
I get there are 2 rectangles in figure.
How can I get the area of shaded region? What if, I subtract the area of inner rectangle from outer rectangle. Ya It will surely work (⌒o⌒).
Now,
Area of outer rectangle = [tex]\sf length \times breadth[/tex]
[tex]5x \times (3x + 2)[/tex]
[tex]5x(3x + 2)[/tex]
Again,
Area of inner rectangle = [tex]\sf length \times breadth[/tex]
[tex]=x \times (5x - 2)[/tex]
[tex]=x(5x - 2)[/tex]
[tex] \sf Area \:of \:Shaded\: region = \: Area_{\:outer}-Area_{\:inner}[/tex]
[tex] \sf \: 5x(3x + 2) - x(5x - 2)[/tex]
If We simplify further then,
= 15x² + 10x - 5x² + 2x
= 10x² + 12x
Area of shaded region is 10x² + 12x in a simple way.
Ejenplo de numeros enteros de una cifra por extension
Answer:
Un número entero es un número entero que puede ser positivo, negativo o cero. Ejemplos de enteros son: -5, 1, 5, 8, 97 y 3,043. Ejemplos de números que no son enteros son: -1.43, 1 3/4, 3.14,. 09 y 5.643,1.
The Blank of the following set of data is 5. 13,7,9,5,2,3,5,4,10,12 A.Mean B.Range C.Median d.Mode
Answer:
d- Mode
Step-by-step explanation:
Mean is 7
Range is 11
Median is 2.5
Mode is the most repeated no... which is 5
What is the value of y in the solution to the system of equations? 1/3x+1/4y=2 2x – 3y = –30 –8 –3 3 8
Answer:
8 i'm pretty sure
Step-by-step explanation:
Answer:
y = 9 1/3 or 8 if the first equation is 1/3x + 1/4y = 1.
Step-by-step explanation:
1/3x + 1/4y = 2
2x - 3y = -30
Multiply the first equation by -6:
- 2x - 3/2y = -12
Adding the last 2 equations:
-9/2 y = -42
y = -42 * -2/9
y = 9 1/3.
If the first equation is 1/3x + 1/4 y = 1
then y = -36 * -2/9
= 8.
At the shop near the beach, ice cream is offered in a cone or in a cylindrical cup as shown
below. The ice cream fills the entire cone and has a hemisphere on top. The ice cream
levelly fills the cylindrical cup.
radius of cone= 3 cm
radius of cylinder= 4.5 cm
height of cone = 10 cm
height of cylinder = 5 cm
Determine how much more ice cream the larger option has. Show your work. ( 19)
Answer:
B
Step-by-step explanation:
The volume of a cone is 1540cm³. If its radius is 7cm, calculate the height of the cone. (Take pi = 22/7)
Answer:
30 cmGiven,
Volume of a cone = 1540 cm[tex] {}^{3} [/tex]
Radius ( r ) = 7 cm
π ( pi ) = [tex] \frac{22}{7} [/tex]
Height of cone ( h ) = ?
Now, let's find the height of cone:
Volume of cone = [tex]\pi \: {r}^{2} \frac{h}{3} [/tex]
plug the values
[tex]1540 = \frac{22}{7} \times {(7)}^{2} \times \frac{h}{3} [/tex]
Evaluate
[tex]1540 = \frac{22}{7} \times 49 \times \frac{h}{3} [/tex]
Calculate
[tex]1540 = \frac{154 \: h}{3} [/tex]
Apply cross product property
[tex]154 \: h = 1540 \times 3[/tex]
Calculate the product
[tex]154 \: h = 4620[/tex]
Divide both sides of the equation by 154
[tex] \frac{154 \: h}{154} = \frac{4620}{154} [/tex]
Calculate
[tex]h \: = 30 \: cm[/tex]
Hope this helps...
Best regards!!
Kellianne lined up the interior angles of the triangle along line p below. Which statements are true for line p? Check all that apply. It is a straight line with a measure of 360°. It stays the same even if the angles in the triangle change. The line will not be straight if one of the angles in the triangle is changed to an obtuse angle. The line is only straight when one of the angles is a right angle. It represents the sum of the measures of the interior angles of the triangle. The line will not be straight if all the angles in the triangle are acute. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.
Answer:
It stays the same even if the angles in the triangle change. It represents the sum of the measures of the interior angles of the triangle. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.Step-by-step explanation:
The sum of angles in a triangle is always 180°, even if all are acute or one is obtuse or a right angle. That means their sum will always produce a straight line. Thus, the following statements are true
It stays the same even if the angles in the triangle change. It represents the sum of the measures of the interior angles of the triangle. It combines the three interior angles of the triangle to form a straight line. It is a straight line with a measure of 180°.Answer:
B,E,G,H
Step-by-step explanation:
i got 100% on edge!
Factor this polynomial expression, and wrote it in its fully factored form 3x^3 + 3x^2 - 18x
Answer:
fourth option
Step-by-step explanation:
Given
3x³ + 3x² - 18x ← factor out 3x from each term
= 3x(x² + x - 6) ← factor the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, thus
x² + x - 6 = (x + 3)(x - 2) and
3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form
[tex]\sqrt[3]{x} =\sqrt[3]{512}[/tex]
Answer:512
Step-by-step explanation:
Let's solve your equation step-by-step.
3√x=3√512
3√x=67.882251
Step 1: Divide both sides by 3.
3√x
3
=
67.882251
3
√x=22.627417
Step 2: Solve Square Root.
√x=22.627417
x=22.6274172(Square both sides)
x=512
Check answers. (Plug them in to make sure they work.)
x=512(Works in original equation)
Answer:
x=512
Audrey charges a flat fee of $4 for each delivery plus a certain amount,in dollars per mile, for each mile she drives. For a distance of 30 miles, Curtis and Audrey charge the same amount
A cell phone company offers a plan that costs $35 per month plus an additional cost of $0.08 per text message.
Write an equation to represent this problem.
Answer:
C = 35 + 0.08t
Step-by-step explanation:
The equation is:
35 + 0.08t = C
C = Cost by month
t = cost for each additional message
What steps do you use to solve a system of two equations using elimination? For example:
7x +2y = -32
-3x+2y = -70
Answer:
Step-by-step explanation:
eliminate either vraible, here it is easy to eleimate y, by just subtacting, then solve for x. When you get the value of x, plug in one of the equation and find y. ther you go
Answer:
x= 3.8
y= -29.3
Step-by-step explanation:
mrs.gonzalez wants to buy 10 cans at the sale price which expression represents the number of cans by which she will exceed the limit
Davis decides to think about retirement and invests at the age of 30 . He invests $5,000 and hopes the investment will be worth $250,000 by the time he turns 70 . If the interest compounds continuously, approximately what rate of growth will he need to achieve his goal? Round to the nearest tenth of a percent.
Answer:
Rate of growth he will need to achieve his goal is 9.8%
Step-by-step explanation:
Principal=$5,000
Time(t)=70-30=40 years
Period (n)=12 months
Interest rate (r)=?
A=$250,000
r=n{(A/P)^1/nt - 1}
=12{(250,000/5000)^1/12*40 - 1}
=12{(50)^1/480 - 1}
=12{(50)^0.0021 - 1}
=12(1.0083 - 1)
=12(0.0082)
=0.0984
r=0.0984*100
=9.84%
To the nearest tenth=9.8%