Answer:
x+y>1
Step-by-step explanation:
a pair of adjacent side of a rectangle are in the ratio 3 : 4 if its diagonal is 20 cm find the length of sides and hence the perimeter of the rectangle
Answer:
Step-by-step explanation:
Ratio=3:4
so,the pair of adjacent sides are 3x,4x
Pythagorean theorem,
[tex](3x)^{2}+(4x)^{2}=20^{2}\\9x^{2}+16x^{2}=400\\\\25x^{2}=400\\\\x^{2}=\frac{400}{25}\\\\ x^{2}=16\\\\x=\sqrt{16}\\\\x=4\\\\length=4x=4*4=16cm\\\\breadth=3x=3*4=12cm\\\\Perimeter=2*(l+b)\\\\=2*(16+12)=2*28\\\\=56cm[/tex]
y = 7x + 9
2y + 2x = -18
Answer:
Step-by-step explanation:
Just multiply the first equation by -1 and then add them together to find x. Should look something like
-2x - y = -7
5x + y = 9
--------------------
3x + 0 = 2
x = 2/3
Now back substitute using either equation to find y. I'll use the first:
2(2/3) + y = 7
4/3 + y = 7
y = 7 - 4/3 = 21/3 - 4/3 = 17/3
Answer:
x=2/3
y=17/3
Answer:
x=-9/4, y=-27/4. (-9/4, -27/4).
Step-by-step explanation:
y=7x+9
2y+2x=-18
----------------
simplify 2y+2x=-18 into y+x=-9
------------------
7x+9+x=-9
8x+9=-9
8x=-9-9
8x=-18
x=-18/8
simplify
x=-9/4
y=7(-9/4)+9=-63/4+9=-27/4
A mother is currently 7 times older than her son. In 2 years time, she will be 5 times older than her son.
Let x and y be the present ages of the son and mother respectively.
Use the fact that the mother is currently 7 times older than her son to set up an equation relating r and V (call this Equation 1).
Answer:
y=-x+7
Step-by-step explanation:
every year she goes down how many times she is younger than him by 1 so -x is actually -1x, and it starts at 7 years so we put that as our y intercept
The age of Noelle’s dad is 6 less than 3 times Noelle’s age. The sum of their ages is 74 . Find their ages.
Answer: Noelle's age is 20 years
Noelle's father is 54 years
Step-by-step explanation: First of all, let Noelle's age be represented by x. Given that her father's age is 6 less than three times her age, her father's age would be expressed as
3n - 6
Note also that their ages sum up to 74.
Therefore,
n + (3n - 6) = 74
n + 3n - 6 = 74
4n - 6 = 74
Add 6 to both sides of the equation
4n = 80
Divide both sides of the equation by 4
n = 20
Hence, Noelle's father's age is 54 (that is 3n - 6)
While Noelle's age is 20
Noelle’s age is 20
her dads age is 54
QUICK PLEASE
Select all that apply.
Which of the following are true?
A table can be used to show sample space.
Sample space is the probability of two events happening.
A tree diagram can be used to show sample space.
The counting principle can be used to find the number of outcomes in the sample space.
I think it might be D
The size of the sample space is the total number of possible outcomes. For example, when you roll 1 die, the sample space is 1, 2, 3, 4, 5, or 6. So the size of the sample space is 6. Then you need to determine the size of the event space.
Answer:
I think it's the last one
Step-by-step explanation:
Forty percent of students at pine crest middle school have a school sweatshirt. There are 560 students at the school.
How many students have a school sweatshirt.
Answer: 224 students own a school sweatshirt.
Step-by-step explanation:
40% of 560 means 60% do not have one
0.60 is 60% as a decimal
560 x 0.60 = 336 students without a sweatshirt
560 - 336 = 224
Is this the correct answer to this problem 5x(3x4) = 12x5=60
Answer:
Yes 60 is the answer
Step-by-step explanation:
Multiply the numbers in the bracket
Then multiply by 5
Answer:
Step-by-step explanation: 5×(3×4) =60
5×(12) =60
5×12 =60
determine whether a parallelogram with vertices A(-1, -2), B(-2, 0), C(0, 1), and D(1, -1) is a rectangle, rhombus, or square. Give all the names that
Answer:
Here, the coordinates aren't telling special characteristic of any shape, so it would be Paralleogram
In short, Your Answer would be Option B
Step-by-step explanation:
Whats the answer to. 4r + 8 + 5 = -15 - 3r
To solve the equation 4r + 8 + 5 = -15 - 3r, combine like terms and isolate the variable r leading to the solution r = -4.
Explanation:The student is asking how to solve the algebraic equation 4r + 8 + 5 = -15 - 3r. To solve for r, we must first simplify and combine like terms. This means we need to get all the terms with r on one side of the equation and the constant numbers on the other side.
Therefore, the solution to the equation is r = -4.
Final answer:
The solution to the equation 4r + 8 + 5 = -15 - 3r is r = -4.
Explanation:
The algebraic equation provided by the student is 4r + 8 + 5 = -15 - 3r.
To solve for r, we must first simplify and rearrange the equation by combining like terms and moving the variables to one side and the constants to the other.
By subtracting 3r from both sides and also subtracting 8 + 5 from both sides, we end up with 4r + 3r = -15 - 8 - 5. Simplifying further, we get 7r = -28.
Finally, dividing both sides by 7 yields r = -4.
How to solve 45degrees 45degrees 90degrees triangles
Answer: You're given one leg. Because you know both legs are equal, you know the length of both the legs.
Step-by-step explanation:
You're given the hypotenuse. Divide the hypotenuse by the square root of 2 to find the legs (which are equal).
Joe gave 1/4 of his total candies to his classmate then he gave 4/6 of when he had left to his brother when he went home then he realized that you didn’t give any to his sister he gave 25% of the remaining candies to her after all this he realized that he only had 21 candies left how many candies did he have In the beginning
Answer:
112
Step-by-step explanation:
Given: Joe gave 1/4 of his total candies to his classmate.
Then, he gave 4/6 of when he had left to his brother.
He gave 25% of the remaining candies to his sister.
Finally, he only had 21 candies left.
Lets assume the total number of candies at the beginning be "x".
First, finding the number candies left after giving candies to classmate.
∴ Remaining candies= [tex]x- x\times \frac{1}{4}[/tex]
Solving it to find remaining candies after giving candies to clasmate.
⇒ Remaining candies= [tex]x-\frac{x}{4}[/tex]
Taking LCD as 4
⇒ Remaining candies= [tex]\frac{4x-x}{4} = \frac{3x}{4}[/tex]
∴ Remaining candies after giving candies to clasmate= [tex]\frac{3x}{4}[/tex]
now, finding the candies left after giving candies to his brother.
∴ Remaining candies= [tex]\frac{3x}{4} - \frac{3x}{4} \times \frac{4}{6}[/tex]
Solving it to find the remaining candies after giving candies to his brother.
⇒ Remaining candies= [tex]\frac{3x}{4} - \frac{x}{2}[/tex]
Taking LCD 4
⇒ Remaining candies= [tex]\frac{3x-2x}{4} = \frac{x}{4}[/tex]
∴ Remaining candies after giving candies to his brother= [tex]\frac{x}{4}[/tex]
We know, Joe was left with only 21 candies after giving candies to his sister.
Therefore, putting an equation for remaining candies to find the number of candies at the beginning.
⇒[tex]\frac{x}{4} - 25\% \times \frac{x}{4} = 21[/tex]
⇒[tex]\frac{x}{4} - \frac{0.25x}{4} = 21[/tex]
Taking LCD 4
⇒ [tex]\frac{x-0.25x}{4} = 21[/tex]
⇒ [tex]\frac{0.75x}{4} = 21[/tex]
Multiplying both side by 4
⇒[tex]0.75x= 21\times 4[/tex]
dividing both side by 0.75
⇒[tex]x= \frac{21\times 4}{0.75}[/tex]
∴[tex]x= 112[/tex]
Hence, Joe had 112 candies at the beginning.
Please help I don't understand how to do this
Answer:
m<B=m<K=100
m<A=m<J=133
m<L=m<C=41
m<M=m<D=86
Step-by-step explanation:
Since [tex]ABCD\cong JKLM[/tex], the corresponding angles are congruent.
This implies that:
[tex]m\angle A=133=m\angle J[/tex]
m<L=41=m<C
m<M=86=m<D
The sum of angles in a quadrilateral is 360 degrees.
m<B+133+41+86=360
m<B+260=360
m<B=360-260
m<B=m<K=100
21. Higher Order Thinking Amil and Abe
rode in a bike-a-thon. Abe rode for 77 minutes
at a faster rate per mile than Amil. Find Amil's
unit rate. Then explain how you could use it to
find a possible unit rate for Abe.
Amil rode 15 miles
in 55 minutes.
Amil's unit rate is calculated by dividing the distance traveled (15 miles) by the time in hours (0.917 hours), resulting in approximately 16.36 mph. Abe's unit rate is faster but cannot be precisely determined without more information about his distance or time.
Explanation:Amil rode 15 miles in 55 minutes. To find Amil's unit rate, we divide the total distance by the total time. The unit rate is a measure of speed, indicating how many miles are traveled in one minute. To find this unit rate, we perform the following calculation:
Convert the time from minutes to hours to find the unit rate in miles per hour (mph), since speed is often expressed this way: 55 minutes × (1 hour/60 minutes) = 0.917 hours
Divide the distance by the time: 15 miles ÷ 0.917 hours = 16.36 mph (rounded to two decimal places).
Amil's unit rate is approximately 16.36 mph. This information can be used to estimate Abe's unit rate, knowing that Abe rode at a faster rate. If we knew how far Abe rode or his unit rate in miles per minute, we could compare the two directly. Without additional information about Abe's distance or time, we can only say that Abe's unit rate exceeds 16.36 mph.
Is 5/20 equal to 4/12
Answer:
No, it's not
Step-by-step explanation:
Lets simplify the two fractions to the lowest term
for 5/20 we'll divide the numerator and denominator by 5 (the HCF of the two)
it then becomes 1/4
For 4/12 we'll divide the numerator and denominator by 4 (the HCF of the two)
it then becomes 1/3
1/4 = 0.25
1/3 = 0.33
therefore 5/20 is not equal to 4/12
1.) Distance formula
FIND THE DISTANCE BETWEEN THE PAIR OF POINTS
Answer:
A(x1,y1) and B(x2,y2)
Step-by-step explanation:
you take two points your start and your stop and put them into the equations and solve
0.7(3x-5)+3.9=14.5
What is the value of x?
Answer:
srry that was my lil bro
Step-by-step explanation:
In circle C, r = 32 units.
What is the area of circle C?
32 units?
64Tt units
25611 units?
1024T1 units?
Answer:
the area of a circle is [tex]\pi[/tex]rsqr
32 x 32 =1024[tex]\pi[/tex]
Step-by-step explanation:
Answer:
A= 1024 x^{2}
Step-by-step explanation:
The dimensions of a 4-in. square are multiplied
by 3. How is the area affected?
Answer:
The area is multiplied by 9.
Step-by-step explanation:
The original square has an area of ...
A = (4 in)² = 16 in²
The larger square has an area of ...
A = (3·4 in)² = (3²)(4²) in² = 9·16 in² . . . . . 9 times the original area
The area is multiplied by the square of the scale factor: 9.
Which equation is parallel to the line LaTeX: y=\frac{1}{2}x+3y = 1 2 x + 3and passes through the point (10, -5)?
Group of answer choices
Plz help asap thank you!!
Answer:
[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]
Step-by-step explanation:
[tex]Let\ the\ required\ equation\ is\ y=mx+c\\\\where\ m\ is\ the\ slope\ of\ the\ equation\ and\ c\ is\ y-intercept\\\\It\ is\ parallel\ to\ the\ equation\ y=\frac{1}{2}x+3\\\\Hence\ slope\ of\ these\ two\ lines\ will\ be\ same.\\\\Slope\ of\ y=\frac{1}{2}x+3\ is\ \frac{1}{2}\\\\Hence\ slope\ of\ y=mx+c\ is\ \frac{1}{2}\Rightarrow m=\frac{1}{2}\\\\Equation:y=\frac{1}{2}x+c\\\\Line\ passes\ through\ (10,-5).\ Hence\ this\ point\ satisfies\ the\ equation\ of\ line.\\\\-5=\frac{1}{2}\times 10+c[/tex]
[tex]-5=-5+c\\\\c=-10[/tex]
[tex]Equation\ of\ line:\ y=\frac{1}{2}x-10[/tex]
In ΔXYZ, x = 5.9 meters, y = 8.9 meters, and z = 5.8 meters. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.
Answer:
Angles: 40.9°, 99.05°, 40.05°
Step-by-step explanation:
Triangles
When we are given the lengths of the 3 sides of a triangle, we can easily compute all the internal angles by using the cosine's law or formula. Being x,y and z the sides of a triangle, and \alpha, \beta , \gamma the three opposite angles respectively, then
[tex]x^2=y^2+z^2-2yzcos\alpha[/tex]
[tex]y^2=x^2+z^2-2xzcos\beta[/tex]
[tex]z^2=x^2+y^2-2xycos\gamma[/tex]
We have x=5.9, y=8.9, z=5.8, then from
[tex]x^2=y^2+z^2-2yzcos\alpha[/tex]
We solve for [tex]\alpha[/tex]
[tex]\displaystyle cos\alpha=\frac{y^2+z^2-x^2}{2yz}[/tex]
[tex]\displaystyle cos\alpha=\frac{8.9^2+5.8^2-5.9^2}{2\times 8.9\times 5.8}[/tex]
[tex]cos \alpha=0.756[/tex]
[tex]\alpha=40.9 ^o[/tex]
Similarly
[tex]\displaystyle cos\beta=\frac{x^2+z^2-y^2}{2xz}[/tex]
[tex]\displaystyle cos\beta=\frac{5.9^2+5.8^2-8.9^2}{2\times 5.9\times 5.8}[/tex]
[tex]cos\beta=-0.157[/tex]
[tex]\beta=99.05^o[/tex]
Finally
[tex]\displaystyle cos\gamma=\frac{5.9^2+8.9^2-5.8^2}{2\times 5.9\times 8.9}[/tex]
[tex]cos\gamma=0.765[/tex]
[tex]\gamma=40.05^o[/tex]
Answer:
Answer is D
Step-by-step explanation:
What is the solution to the equation 9(w – 4) – 7w = 5(3w – 2)?
Answer:
W= -2
Step-by-step explanation:
Simply the expression: 9(w – 4) – 7w = 5(3w – 2)
First step: 9w -36-7w = 15w-10
Second step: 2w-36=15w-10
Third step:-36+10=15w-2w
Fourth step:-26=13w
Fifth step: w=[tex]\frac{-26}{13}[/tex]
Six step: w=-2
Answer:
-2=w
Step-by-step explanation:
9(w-4) - 7w= 5(3w-2)
9w-36-7w= 15w - 10
2w-36=15w-10
- 2w -2w
-36=13w-10
+10 +10
-26= 13w
-2=w
]simplify \sqrt 5/16\
Answer:
(sqrt(5))/4
Step-by-step explanation:
Simplify the following:
sqrt(5/16)
sqrt(5/16) = (sqrt(5))/(sqrt(16)):
(sqrt(5))/(sqrt(16))
sqrt(16) = sqrt(2^4) = 2^2:
(sqrt(5))/(2^2)
2^2 = 4:
Answer: (sqrt(5))/4
Simplify: log81/8 + 2log2/3 - 3log 3/2 +log 3/4
Answer:
0.
Step-by-step explanation:
Using the laws of logarithms:
log81/8 + 2log2/3 - 3log 3/2 + log 3/4
= log 81/8 + log (2/3)^2 - log (3/2)^3 + log 3/4
= log 81/8 + log 4/9 - log 27/8 + log 3/4
= log 81/8 + log 4/9 - (log 27/8 - log 3/4)
= log (81/8 * 4/9) - log (27/8 * 4/3)
= log 9/2 - log 9/2
= 0.
2.) Midpoint formula
FIND THE MIDPOINT OF THE LINE SEGMENT
Answer:
The mid point of the line segment is [tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex].
Step-by-step explanation:
From the graph we can find the end points of the line segment. The end points are: [tex]$ (- 1, - 4) $[/tex] and [tex]$ (4, 1) $[/tex].
When the end points of a line segment are known, the mid point of the line segment is given by:
[tex]$ \bigg ( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \bigg ) $[/tex]
where [tex]$ (x_1, y_1) $[/tex] and [tex]$ (x_2, y_2) $[/tex] are the end points.
Here: [tex]$ (x_1, y_1) = (- 1, - 4) $[/tex] and [tex]$ (x_2, y_2) = (4, 1) $[/tex]
Therefore, the mid point of the line segment would be:
[tex]$ \bigg ( \frac{- 1 + 4}{2}, \frac{- 4 + 1}{2} \bigg) $[/tex]
[tex]$ \bigg(- \frac{3}{2}, -\frac{3}{2} \bigg ) $[/tex] is the required answer.
What is the area of cross section ADGF of this right rectangular prism?
A.
20 square units
B.
48 square units
C.
52 square units
D.
65 square units
Does 5 and 1 half equal 6
Answer: No
Step-by-step explanation:
5 + 1/2 = 5 1/2
A roller coaster starts with the cars being pulled up a ramp. The mass of the cars is estimated by the function m(p) = 175p + 1,180 where p is the number of passengers in the car. The potential energy of the car is calculated using the function E(m) = 9.8mh, where h is the height of the ramp.
If the top of the ramp is 30 meters, which function can be used to calculate the potential energy of a car in terms of the number of passengers?
Answer:
[tex]E(p)=51,450p+346,920[/tex]
Step-by-step explanation:
The function
[tex]m(p) = 175p + 1,180[/tex]
gives the mass of the car as a function of the number of passengers in it.
And the function
[tex]E(m) = 9.8m*h[/tex]
gives the potential energy of the car as a function of the car's mass.
Now if the height of the ramp is 30 meters, we have
[tex]E(m) =9.8m*(30)[/tex]
[tex]E(m) =294m[/tex]
And to find the potential energy as a function of the number of passengers, we just substitute [tex]m(p)[/tex] into [tex]E(m)[/tex] to get:
[tex]E(m(p))=294(175p+1180)[/tex]
[tex]\boxed{ E(p)=51,450p+346,920}[/tex]
which gives the potential energy as a function of the number of passengers.
Answer:
its A on edge2021
Step-by-step explanation:
ASAP I NEED THIS ANSWERED
The rectangle shown has a perimeter of 86 cm and the given area. Its length is 7 more than three times its width. Write and solve a system of equations to find the dimensions of the rectangle
The width of the rectangle is 9 cm.
The length of the rectangle is 34 cm.
Step-by-step explanation:
step 1 :
Let width of the rectangle be 'x'
The length of the rectangle = 7 + 3x
step 2 :
Perimeter of the rectangle = 2 (length + width)
⇒ 86 = 2 (7 + 3x + x)
⇒ 86 = 2 (7 + 4x)
⇒ 86 = 14 + 8x
⇒ 72 = 8x
x = 72/8
x = 9
∴ The width of the rectangle is 9 cm
step 3 :
The length of the rectangle = 7 + 3x
= 7 + 3(9)
= 7+27 = 34 cm
At the same time a 12 foot adult elephant cast a 4.8 foot shadow a baby elephant casts a 2 foot shadow how tall is the baby elephant?
Find the sum of the first 90 terms of the sequence -4,-1,2,5,8
Answer:
1655
Step-by-step explanation:
Note the common difference d between consecutive terms of the sequence
d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3
This indicates the sequence is arithmetic with sum to n terms
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
Here a₁ = - 4, d = 3 and n = 90, thus
[tex]S_{90}[/tex] = [tex]\frac{90}{2}[/tex] [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655
Answer:D
Step-by-step explanation: