Answer:
Base = 2 cm and height = 6 cm.
Step-by-step explanation:
Area = 1/2 * base + height
Let b be the base and h = height of the given triangle, then
6 = b/2 * h
6 = b/2(b/2 + 5)
b^2/4 + 5b/2 - 6 = 0
b^2 + 10b - 24 = 0
(b + 12)(b - 2) = 0
b = 2 (we neglect the negative b = -12)
So h = b/2 + 5 = 2/2 + 5 = 6.
Think of a value for a and a value for x so that the triangles are still similar.
Answer:
x=6
a=9
Step-by-step explanation:
Because 21 is 1.5 times 14, and 15 is 1.5 times 10, a has to be 1.5 times x. Also, x must be more than 4 in order for it to make a triangle. To make it simple, I'd use either 6 or 8. Just for ease, I'll use 6.
x=6
a=6*1.5=9
Two pipes A and B can fill an empty tank in 3hrs and 5hrs respectively. Pipe C can empty the full tank in 6 hours. If the three pipes A, B, and Care opened at the same time, find how long it will take for the tank to be full. *
Answer:
30/11 (hours)
Step-by-step explanation:
Pipe A can fill the tank until it is full in 3 hours.
=> In 1 hour, pipe A can fill 1/3 of tank
Pipe B can fill the tank until it is full in 5 hours.
=> In 1 hour, pipe A can fill 1/5 of tank
Pipe C can empty the full tank in 6 hours.
=> In 1 hour, pipe A can empty 1/6 of tank
Assume that we open 3 pipes A, B, and C at the same time.
Then, in 1 hour, the amount of water in tank is:
A = 1/3 + 1/5 - 1/6 = 10/30 + 6/30 - 5/30 = 11/30 (tank)
=> The time to fill up the tank is:
T = 1/A = 1/(11/30) = 30/11 (hours)
Answer:
30/11
Step-by-step explanation:
Imagine the tank can hold x litre of water
So,A can fill x/3 litre water per hour
And B can fill x/5 litre water per hour
And C can reduce x/6 litre of water per hour which is filled by A and B.
So the gross calculation per hour is:
(x/3+x/5)-x/6
=11x/30
Now suppose it tooks 'a' hour to fill the tank.
So, a(11x/30)=x
⇨ a= (30/11x)x
⇨a=30/11
Someone pls HELP MEEEE i’m giving the rest of my points away . i have like 20 mins to turn this in
Answer:
1) 27.89
2) 20
Step-by-step explanation:
#1)
9.5x + 75 --> 340
340 - 75 --> 265
265 / 9.5 = 27.89
#2)
120 / 6 =
20 minutes
the cube root of 2 to the seventh power
Answer:
4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal
Step-by-step explanation:
Simplify the following:
(2^(1/3))^7
Hint: | For all a>=0, (a^(1/3))^m = a^(m/3). Apply this to (2^(1/3))^7.
Multiply exponents. (2^(1/3))^7 = 2^(7/3):
2^(7/3)
Hint: | Separate the exponent of 2^(7/3) into integer and fractional parts.
2^(7/3) = 2^(6/3 + 1/3) = 2^(6/3)×2^(1/3):
2^(6/3) 2^(1/3)
Hint: | Divide 6 by 3.
6/3 = (3×2)/3 = 2:
2^2 2^(1/3)
Hint: | Evaluate 2^2.
2^2 = 4:
Answer: 4 2^(1/3) or 5.0396841995794926590688424291129134022810058588060319203279004486... decimal
what is mean absolute deviation (MAD) and how do I find it?
Steps to find MAD:
Step 1. Calculate mean([tex]\overline{x}[/tex]) of the data using formula: [tex]\overline{x}=\dfrac{\sum x}{n}[/tex] , where x denotes data points and n is the number of data points.
Step 2. Calculate distance of each data point from mean :
Distance = [tex]|x-\overline{x}|[/tex]
Step 3. Divide distance of each data point from mean by n:
MAD = [tex]\dfrac{\sum |x-\overline{x}|}{n}[/tex] , which is the final computation to find MAD.
Use the distributive property to rewrite the given expression without parentheses.
7(x+2)
7(x+2) =
Answer:
7x+14
Step-by-step explanation:
The distributive property is when you multiply the number on the outside of rhe parenthesis with the numbers on the inside.
In this case it will be 7×x and 7×2
7(x+2)=7x+14
Determine the intercepts of the line.
-6x + 3y = -7
z-intercept:
y-intercept:
Answer:
(7/6, 0) and (0,-7/3)
Step-by-step explanation:
I think you mean x-intercept and y-intercept not z-intercept and y-intercept. The first step is to convert the equation to slope intercept form:
-6x+3y=-7
3y=6x-7
y=6/3x-7/3
y=2x-7/3
Now, to find the x-intercept we find the value of x when y is 0.
0=2x-7/3
7/3=2x
7/6=x so the x-intercept is (7/6,0)
Now, to find the y-intercept we find the value of y when x is 0.
y=2(0)-7/3
y=0-7/3
y=-7/3 so the y-intercept is (0,-7/3)
A bank is offering 5.5% simple interest on a savings account. If you deposit $15000, how much interest will you earn in six year?
What is this question asking for?
What Kinda Interest?
Answer:
a. $4,950
b. The question is asking us to calculate the simple interest that would be earned on the deposited amount for the given number of years at the given interest rate
c. Simple interest
Step-by-step explanation:
a. We want to calculate the amount of interest to be earned in six years
To calculate this, we use the formula for simple interest.
Mathematically;
Simple interest I = PRT/100
Where P is the principal which is the amount deposited = $15,000
R is the rate which is 5.5%
T is the time which is 6 years
Substituting these values in the simple interest formula, we have
I = (15,000 * 5.5 * 6)/100 = $4,950
b. The question is asking us to calculate the simple interest that would be earned on the deposited amount for the given number of years at the given interest rate
c. Simple interest
(2x + 3y)² + 2(2x + 3y) + 1
Answer:
Here is your answer . hope this helps you.
If triangle ABC, m B = 90°, cos(9 = 17, and AB = 16 units.
Based on this information, m
Note that the angle measures are rounded to the nearest degree.
units.
Answer:
m∠A = 62°
m∠C = 28°
AC = 17 units
Step-by-step explanation:
In the given triangle ABC,
m∠B = 90°, Cos(C) = [tex]\frac{15}{17}[/tex] and AB = 16 units
Since, Cos(C) = [tex]\frac{\text{Corresponding side}}{\text{Hypotenuse}}[/tex]
Cos(C) = [tex]\frac{\text{Corresponding side}}{\text{Hypotenuse}}=\frac{15}{17}[/tex]
[tex]\text{C}=\text{Cos}^{-1}(\frac{15}{17})[/tex]
m∠C = 28.07°
m∠C ≈ 28°
Therefore, side BC = 15 units and AC = 17 units
Now we apply Sine rule in the given triangle.
Sin(A) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
= [tex]\frac{\text{BC}}{\text{AC}}[/tex]
= [tex]\frac{15}{17}[/tex]
A = [tex]\text{Sin}^{-1}(\frac{15}{17} )[/tex]
A = 61.93°
m∠A = 62°
Given \qquad m \angle LONm∠LONm, angle, L, O, N is a straight angle. \qquad m \angle MON = 8x - 13^\circm∠MON=8x−13 ∘ m, angle, M, O, N, equals, 8, x, minus, 13, degrees \qquad m \angle LOM = 7x - 17^\circm∠LOM=7x−17 ∘ m, angle, L, O, M, equals, 7, x, minus, 17, degrees Find m\angle MONm∠MONm, angle, M, O, N:
Answer:
[tex] \boxed{99°}[/tex]Step-by-step explanation:
m<MON = 8x - 13°
m<LOM = 7x - 17°
To find : m <MON
First, we have to find the value of x :
Create an equation
[tex] \mathrm{8x - 13 + 7x - 17 = 180}[/tex] ( sum of angle in straight line )
Collect like terms
[tex] \mathrm{15x - 13 - 17 = 180}[/tex]
Calculate
[tex] \mathrm{15x - 30 = 180}[/tex]
Move constant to R.H.S and change its sign
[tex] \mathrm{15x = 180 + 30}[/tex]
Calculate the sum
[tex] \mathrm{15x = 210}[/tex]
Divide both sides of the equation by 15
[tex] \mathrm{ \frac{15x}{15} = \frac{210}{15} }[/tex]
Calculate
[tex] \mathrm{x = 14}[/tex]
Now, let's find the value of m<MON
[tex] \mathrm{8x - 13}[/tex]
Plug the value of x
[tex] \mathrm{ = 8 \times 14 - 13}[/tex]
Calculate the product
[tex] \mathrm{ = 112 - 13}[/tex]
Calculate the difference
[tex] \mathrm{ = 99}[/tex] °
Hope I helped!
Best regards!
Answer:
48
Step-by-step explanation:
because i say so
what equation accurately represent this statement three less than 4 times a number is less than 12
Answer: 4t - 3 < 12
Step-by-step explanation:
What is the hundredth term in the sequence 15, 22, 29, 36, 43…?
A. 50
B. 78
C. 700
D. 708
Answer:
708
Step-by-step explanation:
We are adding 7 each time
15+7 = 22
22+7 = 29
29+7 = 36
So the common difference is 7
The first term is 15
The formula is
an = a1+d(n-1) where n is the term number
an = 15+7(n-1)
We want to find the 100th term
a100 = 15+7(100-1)
a100 = 15+7(99)
= 15+693
= 708
2x + 6 = 0
+2−5=1+5(−5)
Answer:
x=-3
Step-by-step explanation:
2x=-6
x=-3
your answer will be x=-3
The price of tiling a room varies directly as the size of the room. Sam is laying tile in his kitchen. If the tiling costs $4,224.00 for 264 square feet, what is the size of a kitchen that costs $3,824.00?
Answer:
239 ft².
Step-by-step explanation:
Let P represent the price for tiling.
Let S represent the size of the room.
From the question,
Price (P) varies directly as the size (S) i.e
P & S
P = KS
Where K is the constant of proportionality.
Next, we shall determine the value of K as follow
Price (P) = $ 4224
Size (S) = 264 ft²
Constant of proportionality (K) =?
P = KS
4224 = K × 264
Divide both side by 264
K = 4224/264
K = 16
Finally, we shall determine the size of the kitchen that will cost $ 3824 for tiling.
This is illustrated below:
Price (P) = $ 3824
Constant of proportionality (K) = 16
Size (S) =?
P = KS
3824 = 16 × S
Divide both side by 16
S = 3824/16
S = 239 ft²
Therefore, the size of the kitchen is 239 ft².
Use the parabola tool to graph the quadratic function
f(x)= -1/2x^2 + 7
Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.
Answer:
That's the graph for the function f(x)= -1/2 x^2 + 7
The vertex is f(0) = 7
Select the equivalent expression. (8^-5/2^-2)^-4 = ?
Choose 1 answer:
A. 1/8*2^2
B. 2^6/8^9
C. 8^20/2^8
Answer:
C. 8^20/2^8
Step-by-step explanation:
(8^5/2²)^4
8^20/2^8
5/8 divided by 11/9 divided by 1/4=
Answer:
45/22
Step-by-step explanation:
(a/b)/(c/d) = (a*d)/(b*c)
then
{(5/8)/(11/9)} / {1/4)}
= {(5*9)/(8*11)} / {1/4)
= {45/88} / {1/4}
= {45*4} / {88*1}
= 180/88
= 45 / 22
Please I Need Help :(
Answer:
D, 9^4 * 8^4
Step-by-step explanation:
The rule is whenever you have multiplication inside arentheses and it is raised to a power, you distribute the power to both the number s and solve.
I confirmed D is right on a calculator also.
Answer:
D
Step-by-step explanation:
19. If CD _|_ EF, M<ECH = x + 5 and m<HCD = 3x - 7 find each missing value.
G# F
a) x =
b) m<ECH=
c) m<HCD=
d) m<GCF =
e) m<ECG=
f) m<GCD =
[tex]a. $ x = 23^{\circ}\\b. $ m \angle ECH =28^{\circ}\\c. $ m\angle HCD = 62^{\circ}\\d. $ m \angle GCF = 28^{\circ}\\e. $ m \angle ECG = 152^{\circ}\\f. $ m \angle GCD = 118^{\circ}[/tex]
Given:
[tex]m \angle ECH = x + 5\\m \angle HCD = 3x - 7[/tex]
Note the following:
Since CD is perpendicular to EF, therefore:
[tex]m \angle ECD = 90^{\circ}\\m \angle FCD = 90^{\circ}[/tex]
Thus:
a. Find x
[tex]m \angle ECH + m \angle HCD = m \angle ECD[/tex]
Substitute
[tex](x + 5) + (3x - 7) = 90[/tex]
Add like terms
[tex]x + 5 +3x - 7 = 90\\4x -2 = 90\\4x = 90 + 2\\4x = 92[/tex]
Divide both sides by 4
[tex]x = 23[/tex]
b. Find [tex]m \angle ECH[/tex]
[tex]m \angle ECH = x + 5[/tex]
Plug in the value of x
[tex]m \angle ECH = 23+ 5\\m \angle ECH =28^{\circ}[/tex]
c. Find [tex]m \angle HCD[/tex]
[tex]m \angle HCD = 3x - 7\\m \angle HCD = 3(23) - 7\\m \angle HCD = 62^{\circ}[/tex]
d. Find [tex]m \angle GCF[/tex]
[tex]m \angle GCF = m \angle ECH[/tex] (vertical angles are congruent)
Substitute
[tex]m \angle GCF = 28^{\circ}[/tex]
e. Find [tex]m \angle ECG[/tex]
[tex]m \angle ECG = 180 - m \angle GCF[/tex] (angles on a straight line)
Substitute
[tex]m \angle ECG = 180 - 28\\m \angle ECG = 152^{\circ}[/tex]
f. Find [tex]m \angle GCD[/tex]
[tex]m \angle GCD = m\angle FCD + m \angle GCF[/tex]
Substitute
[tex]m \angle GCD = 90 + 28\\m \angle GCD = 118^{\circ}[/tex]
Therefore:
[tex]a. $ x = 23^{\circ}\\b. $ m \angle ECH =28^{\circ}\\c. $ m\angle HCD = 62^{\circ}\\d. $ m \angle GCF = 28^{\circ}\\e. $ m \angle ECG = 152^{\circ}\\f. $ m \angle GCD = 118^{\circ}[/tex]
Learn more here:
https://brainly.com/question/18292462
Patrick deposited $6,875 into a savings account 17 years ago. The account has an interest rate of 4.9% and the balance is currently $15,734.11. How often does the interest compound
Answer:
Quaterly
Step-by-step explanation:
HELP PLEASE !! REAL ANSWER ONLY
find the surface area of the cylinder round to the nearest tenth
Answer:
CSA is 12.57
TSA is 18.85 .. i dont know what the question is asking..
I will recommend you to use TSA
Answer:
19ft
Step-by-step explanation:
Formula for surface area of the cylinder=2πr(r+h)
We have,
h=2ft
d=2ft
r=d/2=2/2=1ft
Now,
2πr(r+h)=2π*1(1+2)=2π*1*3=6π=18.8495559215
Rounding to the nearest tenth,
We get Surface area of the cylinder=19 ft
what is the lcm of 7÷25 and 3÷25
Answer:
LCM of 7/25 and 3/25 is 25
Step-by-step explanation:
The full meaning of LCM is Lowest (Least) Common Multiple
Lowest (Least)Common Multiple can be defined as the lowest or least number that is the multiple of two or more number. Note that this least number is not zero
Lowest(Least) common Multiple when applied to fractions is the least number that is the multiple of the denominators of the fraction.
In the above question, we are asked stop find the LCM of 7÷25 and 3÷25
= LCM of 7/25 and 3/25
The two denominators are the same, hence, the LCM is 25.
Identify whether each phrase is an expression, equation, or inequality.
Term
Phrase
Expression
3 - 53 =y
Inequality
7-5 <2.9
2 + 0
Equation
24"
t
Answer:
The identities of the terms are;
3 - 53 = y is an equation
7.5 < 2.9 is an inequality
2 + 0 is an expression
t is a term
24" is a term
Step-by-step explanation:
An equation is an expression with the equal to sign
3 - 53 = y is an equation
An inequality is a mathematical expression that contains an inequality sign
7.5 < 2.9 is an inequality
A term is a sole number or variable or the product of variables and numbers that come before and after mathematical operators such as +, ×, -, or ÷
t and 24" are terms.
What is the only temperature that is the same in Fahrenheit and Celsius?
Answer: -40 °C and -40 °F.
Step-by-step explanation:
Answer:
-40
Step-by-step explanation:
Let the temperature be x which is the same in Fahrenheit and Celsius. Then it must satisfy the Fahrenheit and Celsius conversion formula which is (Fahrenheit-32)*(5/9)=Celsius
x=(x-32)*(5/9)
9x=5x-160, x=-40
this math question is about logarithm
Answer:
(k+2h)/(k+h)
Step-by-step explanation:
log 6 12 = (log a 12)/(log a 6) ( Log base change property)
log a 12 = log a (3*4) = log a 3 + 2*log a 2 = k+2h
log a 6 = log a (2*3) = log a 3 + log a 2 = k+h
log 6 12 = (k+2h)/(k+h)
Cindy and victor are playing a math game. The winner must get three in a row of the same type of real numbers and justify how do numbers are alike. Cindy said that Cindy and Victor are playing a math game. The winner must get three in a row of the same type of real numbers and justify how the numbers are alike. Cindy said she won because she was able to get three rational numbers on a diagonal. Victor said he won with three positive numbers in a column. Can both players say they won, for different reasons? Explain
Please see attachment for question
Answer:
Yes both players can say they won. Cindy and Victor won
Step-by-step explanation:
Both players can say they won because they both kept to the rules of the game. Cindy got rational real numbers on a diagonal while Victor got positive numbers on a column which are real numbers too. Pi on the last row on his column for the diagram on the right(see attachment) is 22/7 or 3.14159... is an irrational real number but is still a positive real number.
pls answer i will mark brainliest
Answer:
Part one:
In terms of price;
[tex]2x + \frac{5}{2} y = 19 \\ \\ 4x + 5y = 38 - - - (equation \: \: 1)[/tex]
In terms of people, each person will get one snack:
[tex]x + y = 8 - - - (equation \: \: 2)[/tex]
Part two:
[tex]in \: equation \: 2 : \\ x = 8 - y \\ substitute \: for \: x \: in \: 1 : \\ 4(8 - y) + 5y = 38 \\ 32 - 4y + 5y = 38 \\ y = 6 \\ \\ therefore : x = 2[/tex]
Sam bought 2 bags of chips
How to do this question plz answer me step by step plzz plz
Answer:
New depth of the milk will be 4 cm.
Step-by-step explanation:
If the carton (shaded side) is standing vertically, milk in the box will acquire the dimensions of the box.
Length of the cuboid formed by the the milk = 8 cm
Width = 5 cm
Height = 12 cm
Volume of the cuboid formed by the milk in the carton = Length × width × height
V = 8 × 5 × 12
= 480 cm³
If the carton is turned so that the carton stands on the shaded face,
Volume of the milk remains unchanged but the dimensions of the cuboid formed by the milk inside the carton will get changed.
Length = 15 cm
Width = 8 cm
Height = h cm
Then volume of the cuboid = Length × width × height
V = 15 × 8 × h
480 = 120h
h = [tex]\frac{480}{120}[/tex]
h = 4 cm
Therefore, new depth of the milk will be 4 cm.
In right triangle ΔABC (m∠C = 90°), point P is the intersection of the angle bisectors of the acute angles. The distance from P to the hypotenuse is equal to 2 in. Find the perimeter of △ABC if AB = 12 in. PLEASE HELP ILL AWARD MORE BRAINLY POINTS
Answer:
28 inches
Step-by-step explanation:
The point of intersection of the angle bisectors is the incenter. It is the center of a circle tangent to the three sides of the triangle. The circle has radius 2.
In the attached figure, we have labeled the points of tangency D, E, and F. We know that CE and CF are both of length 2, and we know that the points of tangency are the same distance from an external point where the tangents intersect. That means DA = FA and DB = EB.
The perimeter of the triangle is ...
P = DA +DB +FA +EB +CF +CE
Using the above relations, this can be written as ...
P = DA +DB +DA +DB +CF +CE = 2(DA +DB) +2(CE)
We are told that AB is 12 inches, so DA +DB = 12 inches. We also know that CE = 2 inches, so the perimeter is ...
P = 2(12 in) + 2(2 in) = 28 in
The perimeter of triangle ABC is 28 inches.