Answer:
Step-by-step explanation:
9 * 44 =
9 (40 + 4) =
9(40) + 9(4) =
360 + 36 = 396
Final answer:
To mentally calculate 9 x 44, use the distributive property by multiplying 9 by 40 and 9 by 4, then adding the results to get 396.
Explanation:
The question asks how to mentally calculate 9 x 44 using the distributive property. To do this, you can break down the multiplication into simpler parts. First, use the distributive property to express 44 as the sum of 40 and 4. Multiply 9 by each part:
9 x 40 = 360
9 x 4 = 36
Then, add the two results together:
360 + 36 = 396
So, 9 x 44 equals 396.
what is the vertex of the quadratic function below y=3x^2-12x+17
Answer:
(2, 5 )
Step-by-step explanation:
Given a quadratic in standard form : y = ax² + bx + c : a ≠ 0
Then the x- coordinate of the vertex is
[tex]x_{vertex}[/tex] = - [tex]\frac{b}{2a}[/tex]
y = 3x² - 12x + 17 ← is in standard form
with a = 3 and b = - 12, thus
[tex]x_{vertex}[/tex] = - [tex]\frac{-12}{6}[/tex] = 2
Substitute x = 2 into the function for corresponding value of y
y = 3(2)² - 12(2) + 17 = 12 - 24 + 17 = 5
vertex = (2, 5 )
Given m angle A = 35°, and b = 4.2, find c. Show all work.
Answer:
[tex]c=5.1\ units[/tex]
Step-by-step explanation:
The picture of the question in the attached figure
step 1
Find the measure of angle B
we know that
In the right triangle ABC
[tex]m\angle A+m\angle B=90^o[/tex] ---> by complementary angles in a right triangle
we have
[tex]m\angle A=35^o[/tex]
substitute
[tex]35^o+m\angle B=90^o[/tex]
[tex]m\angle B=90^o-35^o=55^o[/tex]
step 2
Find the length side c
Applying the law of sines
[tex]\frac{c}{sin(C)}=\frac{b}{sin(B)}[/tex]
substitute the given values
[tex]\frac{c}{sin(90^o)}=\frac{4.2}{sin(55^o)}[/tex]
[tex]c=\frac{4.2}{sin(55^o)}=5.1\ units[/tex]
What is 9.7% expressed as a decimal
Answer:
0.097
move your decimal to the left twice
]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
Does 5 and 1 half equal 6
Answer: No
Step-by-step explanation:
5 + 1/2 = 5 1/2
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:
On a scale drawing the scale is 1/2 inch=1 foot what are the dimensions on the scale drawing for a room that is 22 feet by 17 feet
Hey there! I'm happy to help!
We have a room that is 22 by 17 feet. We know that for every foot, we draw a 1/2 inch. This means that we need multiply our dimensions by 1/2 to find the dimensions of the drawing.
22×1/2=11
17×1/2=8.5
Therefore, the dimensions of the room are 11 feet by 8.5 inches. These are the dimensions of a normal white paper!
Have a wonderful day! :D
To convert the actual room dimensions of 22 feet by 17 feet to a scale drawing with a scale of 1/2 inch equals 1 foot, the length becomes 11 inches, and the width becomes 8.5 inches in the drawing.
When creating a scale drawing, the dimensions of the actual room need to be converted into scale dimensions. According to the scale given, which is 1/2 inch equals 1 foot, the actual room dimensions of 22 feet by 17 feet should be converted using this scale ratio.
To do this conversion, each actual dimension must be divided by the scale factor. The scale factor is determined by the number of feet that are represented by 1/2 inch. Since 1/2 inch is equivalent to 1 foot, the scale factor is 1 foot per 1/2 inch. Therefore, we calculate the dimensions as follows:
Length: 22 feet / 1 foot per 1/2 inch = 22 x 1/2 inches = 11 inches
Width: 17 feet / 1 foot per 1/2 inch = 17 x 1/2 inches = 8.5 inches
Thus, the dimensions on the scale drawing for a room that is 22 feet by 17 feet would be 11 inches by 8.5 inches.
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The percent bar graph shows how students get home from school. if 80 students were surveyed, how many students take a car to school?
30
24
16
20
Step-by-step explanation:
Given, Total number of students is 80.
and 30% of the total students take a car to school
30% of 80
[tex]=\frac{30}{100}\times 80[/tex]
=24
Therefore 24 students take a car to school.
Answer:
24 students take a car to school
2y = 4
-x = -3
What is the solution to this system of equations?
Answer:
The solution to the system of equations given is (3, 2)
Step-by-step explanation:
Let's solve the system of equations given:
2y = 4
-x = -3
****************
2y = 4
y = 4/2
y = 2
____________________
-x = - 3
x = 3
The solution to the system of equations given is (3, 2)
The solution to the system of equations is x = 3 and y = 2.
Explanation:To solve this system of equations, we can use the method of substitution or elimination. Let's solve it using the substitution method.
From the first equation, we can solve for y:
2y = 4
y = 4/2
y = 2
Now, substitute this value of y into the second equation:
-x = -3
x = 3
So the solution to this system of equations is x = 3 and y = 2.
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.
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.
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.
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.
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
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
A box contains 5 blue pens and three black pens you chosse one pen at random do not replace it and then choose a second pen at random what is the probability that both pens are blue
Answer:
4
Step-by-step explanation:
U will add 5 plus 3 and then divide 8 by 2
Answer:4
Step-by-step explanation:
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:
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:
As the student council treasurer, you prepare the budget for your class rafting trip. Each large raft costs $100 to rent and each small raft costs $40 to rent. You have $1,600 to spend. Write and solve a linear equation to find the number of small rafts you can rent if you rent 12 large rafts.
Answer- You can get 10 Small rafts
12 x 100+ 1200
1600-1200=400
400/40 =10 Rafts
A linear equation representing the given situation and the number of small rafts is required.
The required equation is [tex]100x+40y=1600[/tex]
The number of small rafts will be [tex]10[/tex]
Cost of one large raft = $100
Cost of one small raft = $40
Total amount to spend = $1600
Let the number of large rafts be [tex]x[/tex]
and small rafts be [tex]y[/tex]
The equation will be
[tex]100x+40y=1600[/tex]
The number of large rafts [tex]x=12[/tex]
[tex]100\times 12+40y=1600\\\Rightarrow y=\dfrac{1600-100\times 12}{40}\\\Rightarrow y=10[/tex]
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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
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:
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]
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
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
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
___ are unique substances that form when two or more elements combine chemically ?
A compound is a unique substance that forms when two or more elements combine chemically. It always has the same elements in the same proportions.
A person paid $60 for a vase at an estate auction. She resold it to an antiques dealer for $40. What was her profit or loss?
Answer:loss 20
Step-by-step explanation:
She lost 20
Step-by-step explanation:
60 take away 40 is 20
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.
Solve for k.
6 1
2k - 6 - 3
Answer:
k = 6.
Step-by-step explanation:
k = 6
2k = 12
12 - 6 - 3 = 3
k = 1
2k = 2
2 - 6 - 3 = -7
So, the answer is k = 6 because it makes more sense.
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