Write an expression for each statement and then simplify it, if possible.
g
There are two numbers, that sum up to 53. Three times the smaller number is equal to 19 more than the larger number. What are the numbers ?
Answer:
If the smaller number is x, then the equation is
. The numbers are
,
.
Answer:
x = 18; y = 35
Step-by-step explanation:
This gives us the equation:
1. x+y=53
2. 3x=y+19
3. 3x-y=19
Add the first and last line together: x+y+3x-y=53+19
Simplifies to: 4x=72
Divide by 4 to get: x = 18
Plug your numbers into the first equation to get 18+y=53; y = 35.
Answer:
The numbers are 18 and 35.
Step-by-step explanation:
The smaller number is x.
Let the other number by y.
Three times the smaller number is equal to 19 more than the larger number.
3x = y + 19
The larger number is
y = 3x - 19
the numbers add up to 53
x + y = 53
x + 3x - 19 = 53
4x = 72
x = 18
y = 3x - 19 = 3(18) - 19 = 54 - 19 = 35
The numbers are 18 and 35.
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 6x3 − 9x2 − 216x + 3, [−4, 5]
Answer:
absolute minimum = -749 and
absolute maximum = 467
Step-by-step explanation:
To get the absolute maximum and minimum of the function, the following steps must be followed.
First, we need to find the values of the function at the given interval [-4, 5].
Given the function f(x) = 6x³ − 9x² − 216x + 3
at x = -4;
f(-4) = 6(-4)³ − 9(-4)² − 216(-4) + 3
f(-4) = 6(-64) - 9(16)+864+3
f(-4) = -256- 144+864+3
f(-4) = 467
at x = 5;
f(5) = 6(5)³ − 9(5)² − 216(5) + 3
f(5) = 6(125) - 9(25)-1080+3
f(5) = 750- 225-1080+3
f(5) = -552
Then we will get the values of the function at the crirical points.
The critical points are the value of x when df/dx = 0
df/dx = 18x²-18x-216 = 0
18x²-18x-216 = 0
Dividing through by 18 will give;
x²-x-12 = 0
On factorizing the resulting quadratic equation;
(x²-4x)+(3x-12) = 0
x(x-4)+3(x-4) = 0
(x+3)(x-4) = 0
x+3 = 0 and x-4 = 0
x = -3 and x = 4 (critical points)
at x = -3;
f(-3) = 6(-3)³ − 9(-3)² − 216(-3) + 3
f(-3) = 6(-27) - 9(9)+648+3
f(-3) = -162-81+648+3
f(-3) = 408
at x = 4
f(4) = 6(4)³ − 9(4)² − 216(4) + 3
f(4) = 6(64) - 9(16)-864+3
f(4) = 256- 144-864+3
f(4) = -749
Based on the values gotten, it can be seen that the absolute minimum and maximum are -749 and 467 respectively
A New York taxi service charges a $3.25 boarding rate in addition to its meter which is $2 for every mile. How much does it cost to ride in this cab for 1 mile? How much does it cost to ride in this cab for 20 miles?
Answer:
Hey there!
This can be modelled by an equation, y=2x+3.25
For one mile: y=2(1)+3.25, or y=5.25
For twenty miles: y=2(20)+3.25, or y=43.25
Hope this helps :)
Someone help me please
Answer:
3
Step-by-step explanation:
If the cube has 54 stickers across its six faces, and each face has the same number of stickers, first we can find the number of stickers in each face by dividing the number of stickers by the number of faces:
[tex]stickers\ per\ face = number\ of\ stickers / number\ of\ faces[/tex]
[tex]stickers\ per\ face = 54/6 = 9[/tex]
Each face has 9 stickers.
If each row and column has the same number of stickers, we can find the numbers of rows and columns by finding the square root of the number of stickers in the face:
[tex]\ number\ of\ rows = \sqrt{9} = 3[/tex]
If we have 3 rows, and each roll has the same number of stickers, the number of stickers per row or column is:
[tex]stickers\ per\ row = stickers\ per\ face / number\ of\ rows[/tex]
[tex]stickers\ per\ row = 9/3 = 3[/tex]
Let x represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: x 0 1 2 3 p(x) 0.17 0.33 0.32 0.18 Determine the probability the student visits the gym at most twice in a month. Report your answer to two decimal places.
Answer: Probability of visiting at most twice = 0.82
Step-by-step explanation: The probability distribution is of the form:
X 0 1 2 3
P(X) 0.17 0.33 0.32 0.18
It wants the probability of visiting the gym at most twice in a month, which means the probability of never going to the gym, P(X=0), or going once, P(X=1), or going twice, P(X=2).
Using the "OR" probability:
P(visiting at most twice) = P(X=0) + P(X=1) + P(X=2)
P(visiting at most twice) = 0.17 + 0.33 + 0.32
P(visiting at most twice) = 0.82
Therefore, the probability of visiting the gym at most twice in a month is 0.82 or 82%
Need answers!!!!! ASAPPP
Answer:
t
Step-by-step explanation:
Mary is 2 times older than Bob and Bob is 5 years older than Sally. Sally is 10 years old how old is Bob
Answer:
Bob is 15 years old.
Step-by-step explanation:
If Sally is 10 years old and Bob is five years older than Sally then we just need to add 10+5=15.
Hope this helps!!
find the coordinate of W' after a 90° rotation of the triangle about the origin and then a reflection about the line y= -3
Answer:
(4, -8).
Step-by-step explanation:
If point W were to be rotated 90 degrees, it would rotate 90 degrees clockwise. The current point of W is (-2, 4). After a 90 degree rotation about the origin, the point will be (4, 2).
y = -3 is a horizontal line where y = -3. The y-value of the newly rotated point is 2. That is five units above the line where y = -3. So, a reflection would result in a y-value of y = -3 - 5 = -8. The x-value does not change.
So, the coordinate of W' is (4, -8).
Hope this helps!
What is x? The degree of the angle of x
Answer:
x = 60°
Step-by-step explanation:
All the angles in a triangle add up to 180°. So, you have this equation.
87° + 33° + x = 180°
120° + x = 180°
x = 60°
The measure of angle x is 60°.
Hope that helps.
which statement is true about the radical expression square root of 25
Answer:
5
Step-by-step explanation:
The square Root of 25 in its simplest form means to get the number 25 inside the radical √ as low as possible.
25 is a perfect square, which means that you can simply calculate the square Root of 25 to get the answer. 5 times 5 equals 25. Thus, the square Root of 25 in simplest radical form is = 5
Find the value of x.
Answer:
[tex]\huge\boxed{y=\sqrt{55}}[/tex]
Step-by-step explanation:
ΔADC and ΔDBC are similar (AAA)
Therefore the cooresponging sides are in proportion:
[tex]\dfrac{AC}{CD}=\dfrac{CD}{BC}[/tex]
Substitute:
[tex]AC=6+5=11\\BC=5\\CD=y[/tex]
[tex]\dfrac{11}{y}=\dfrac{y}{5}[/tex] cross multiply
[tex](11)(5)=(y)(y)\\\\55=y^2\to y=\sqrt{55}[/tex]
During a camping trip, a group went one -third of the total distance by boat, 10km by foot and One – sixth of it by riding horses. Find the total distance of the trip.
Matrixes and Matrix Operations
Please help. I’ll mark you as brainliest if correct.
Answer:
3 × 7
Step-by-step explanation:
The order of a matrix is the number of rows and columns that it has. Rows are listed first and columns are listed second. The matrix has 3 rows going across horizontally and 7 columns going down vertically.
Therefore, the order of the matrix is 3 × 7.
Hope that helps.
Find the maximum and minimum values
Answer:
2 and 10 are the in and max
Answer:
Min = 2
Max = 10
Step-by-step explanation:
C = 2(x+y)
x ≥1
y ≥0
y ≤5 -x
The smallest y can be is zero
The smallest x can be is 1
The minimum is
C = 2 ( 0+1) = 2 ( 1) = 2
Looking for the max
y ≤5 -x
Add x to each side
x+y ≤5
The max is 5 for x+y
Substituting that into the equation for C
C = 2(5)
C = 10
Min = 2
Max = 10
 A central angle is best described as which of the following?
A.
It has a measure greater than 180 degrees.
B.
It is an angle that has its vertex on the circle.
C.
It is an angle that has its vertex at the center of a circle.
D.
It is part of the circumference of a circle.
Answer:
Answer C: It is an angle that has its vertex at the center of a circle.
Step-by-step explanation:
By definition of central angle, it is an angle whose vertex is at the geometric center of a circle.
Answer:
C.
It is an angle that has its vertex at the center of a circle.
rewrite (21+31).4 using the disbributive property of multiplication over addition
Answer: evaluate it is 52
Step-by-step explanation:
Matt has $3 left in his pocket. He spent $6
on lunch, $7 on a poster, and $10 on a
T-shirt. How much money did he have at
the beginning of the day?
Answer:
$26.
Step-by-step explanation:
Let's say that Matt started out with x dollars.
x - 6 - 7 - 10 = 3
x - 13 - 10 = 3
x -23 = 3
x = 26
He had $26 at the beginning of the day.
Hope this helps!
Suppose that the functions g and h are defined for all real numbers x as follows.
gx = x − 3x
hx = 5x + 2
Write the expressions for (g - h)(x) and (g * h)(x) and evaluate (g + h)(−2).
Answer:
Step-by-step explanation:
Given the functions g(x) = x − 3x and h(x) = 5x + 2, we are to calculatae for the expression;
a) (g - h)(x) an (g * h)(x)
(g - h)(x) = g(x) - h(x)
(g - h)(x) = x − 3x -(5x+2)
(g-h)(x) = x-3x-5x-2
(g-h)(x) =-7x-2
b) (g * h)(x) = g(x) * h(x)
(g * h)(x) = (x − 3x )(5x+2)
(g * h)(x) = 5x²+2x-15x²-6x
(g * h)(x) = 5x²-15x²+2x-6x
(g * h)(x) = -10x²-4x
c) To get (g + h)(−2), we need to first calculate (g + h)(x) as shown;
(g + h)(x) an (g * h)(x)
(g + h)(x) = g(x) +h(x)
(g + h)(x) = x − 3x + (5x+2)
(g+h)(x) = x-3x+5x+2
(g+h)(x) =3x+2
Substituting x = -2 into the resulting function;
(g+h)(-2) = 3(-2)+2
(g+h)(-2) = -6+2
(g+h)(-2) = -4
Which of the following equations is equivalent to 4/5a - 8 = 1/5?
Answer:
a = 10 1/4
Step-by-step explanation:
So with the following equation,
4/5a - 8 = 1/5,
we need to use the commutative property.
Which is the moving of whole numbers or variables.
So we add 8 to both sides.
4/5a = 41/5
Divide 4/5 by both sides
a = 10 1/4
So on of the equations could look like a = 10 1/4
Thus,
a = 10 1/4 could be one of the equations given which are equal to 4/5a - 8 = 1/5.
Hope this helps :)
Answer:
[tex]\huge\boxed{a=\dfrac{41}{4}=10\dfrac{1}{4}=10.25}[/tex]
Step-by-step explanation:
[tex]\dfrac{4}{5}a-8=\dfrac{1}{5}\qquad\text{multiply both sides by 5}\\\\5\!\!\!\!\diagup\cdot\dfrac{4}{5\!\!\!\!\diagup}a-(5)(8)=5\!\!\!\!\diagup\cdot\dfrac{1}{5\!\!\!\!\diagup}\\\\4a-40=1\qquad\text{add 40 to both sides}\\\\4a-40+40=1+40\\\\4a=41\qquad\text{divide both sides by 4}\\\\\dfrac{4a}{4}=\dfrac{41}{4}\\\\a=10.25[/tex]
Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.22.
Which of the following is a type I error?
A. Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29
B. Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually different from 0.29
C. Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29
D. Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29
Answer:
Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.
Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.
Step-by-step explanation:
We are given the following hypothesis below;
Let p = proportion of people who write with their left hand
So, Null Hypothesis, [tex]H_0[/tex] : p = 0.22 {means that the proportion of people who write with their left hand is equal to 0.22}
Alternate Hypothesis, [tex]H_A[/tex] : p [tex]\neq[/tex] 0.22 {means that the proportion of people who write with their left hand is different from 0.22}
Now, Type I error states that we conclude that the null hypothesis is rejected when in fact the null hypothesis was actually true. Or in other words, it is the probability of rejecting a true hypothesis.
So, in our question; Type I error is to Reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is actually 0.29.
Type II error states that we conclude that the null hypothesis is accepted when in fact the null hypothesis was actually false. Or in other words, it is the probability of accepting a false hypothesis.
So, in our question; Type II error is Fail to reject the claim that the proportion of people who write with their left hand is 0.29 when the proportion is different from 0.29.
Please help. I’ll mark you as brainliest if correct!
Answer:
Step-by-step explanation:
children=c
adults=a
c+a=359
a=359-c
2.75c+6a=1621
2.75 c+6(359-c)=1621
2.75 c+2154-6c=1621
-3.25 c=1621-2154
-3.25 c=-533
[tex]-\frac{325}{100} c=-533\\-\frac{13}{4} c=-533\\c=-533 \times \frac{-4}{13} =41 \times 4=164 \\children=164\\adults=359-164=195[/tex]
8. Let X be the number of cars per minute passing a certain point of some road between 8am and 10am on a Sunday. Assume that X has a Poisson distribution with mean 5. Find the probability of observing 3 or fewer cars during any given minute.
Answer:
P (3 or fewer) =0.2650
Step-by-step explanation:
Mean = x` = 5
The Poisson distribution formula is given by
P(X) = e-ˣ` x`ˣ/ x!
The mean is 5 and the X takes the values 0,1,2,and 3 which means 3 or fewer, so we add the probability of all the values of X to get the desired Value of X.
P(3 or fewer ) = e-⁵ (5)³/3!+ e-⁵ (5)²/2! +e-⁵ (5)/1!+e-⁵ (5)⁰/0!
Putting the Values
P (3 or fewer) = 0.006737 . 125 / 6 + 0.006737 . 25 / 2 +0.006737 . 5 / 1 + 0.006737 . 1 / 1
P (3 or fewer) = 0.140374 + 0.08422+ 0.03369 +0.006737
P (3 or fewer) =0.2650
if the discrimant of a equation is equal to -8, which statement describes the roots? A. there are two complex roots B. there are two real roots C. there is one real root D. there is one complex root
Answer:
Option A
Step-by-step explanation:
If Discriminant < 0 , (Just as -8) the roots are imaginary (Complex) and there are two complex roots.
Rachel's waist circumference is 37 inches and her hip circumference is 39 inches. Based on this information, what does her waist-to-hip ratio tell you?
Answer:
[tex]n = 0.949[/tex]. The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
Step-by-step explanation:
The waist-to-hip ratio of Rachel is:
[tex]n = \frac{37\,in}{39\,in}[/tex]
[tex]n = \frac{37}{39}[/tex]
[tex]n = 0.949[/tex]
The waist-to-hip ratio indicates that length of her waist circumference is equal to the 94.9 % of length of her hip circumference.
The length of her waist circumference is 94.9% the length of her hip circumference.
From the information given, Rachel's waist circumference is 37 inches and her hip circumference is 39 inches.
Therefore, her waist to hip ratio will be calculated thus:
n = 37/39
n = 0.949
This implies that the length of her waist circumference is 94.9% the length of her hip circumference.
Learn more about ratio on:
https://brainly.com/question/13763238
One number is 2 more than another. The difference between their squares is 52. What are the numbers?
Answer:
The aprox, numbers:
4.1633 and 8.3266
Step-by-step explanation:
a = 2b
a² - b² = 52
then:
(2b)² - b² = 52
4b² - b² = 52
3b² = 52
b² = 52/3
b² = 17.333
√b² = √17.333
b = 4.1633 aprox.
a = 2b
a = 2*4.1633
a = 8.3266
Check:
8.3266² - 4.1633² = 52
69.333 - 17.333 = 52
whats a significant figure
Answer:
Significant figures are any digits that contribute to the number: In 02.400, only 2 and 4 are significant digits. However, in 2.4001, 2, 4, 0, 0, and 1 are significant digits, because the number would not be the same without them.
Step-by-step explanation:
Hope it helps <3
I need help!!! If none Of these are correct say none.
side angle side
explanation
because in two similar triangles the SAS congruence rule be obeyed
Write an equation for the absolute value. PLEASE HELP I’m so confused on this!!!
Answer:
y = 3 |x − 8| + 1
Step-by-step explanation:
y = 3 |x|
Shift right 8 units:
y = 3 |x − 8|
Shift up 1 unit:
y = 3 |x − 8| + 1
trang can test message about 38 words per minute. if she types at this rate for 20 minutes about how many words will she type?
Answer:
760 words for 20 minutes.
Step-by-step explanation:
38 words = 1 minute
1 x 20 = 20
38 x 20 = 760 words
1. Identify the axis of symmetry for y = -3(x+3)^2-2. a. x = -2 b. x = 3 c. x = 2 d. x = -3 2. Choose the correct axis of symmetry for x = -4(y -4)^2+6 a. y = -6 b. y = -4 c. y =6 d. y = 4
Answer:
The answer is :
DDStep-by-step explanation:
Axis of symmetry is the equation where it cuts the middle of the quadratic graph.
For quadratic equation in the form of (x+a)² + b, the axis of symmetry will be (x+a) = 0 which is x = -a :
Question 1,
[tex](x + 3) = 0[/tex]
[tex]x = - 3[/tex]
Question 2,
[tex](y - 4 )= 0[/tex]
[tex]y = 4[/tex]
Answer:
[tex]\boxed{x=-3} \\ \boxed{y=4}[/tex]
Step-by-step explanation:
Axis of symmetry is a line that cuts the parabola in half touching the vertex.
Quadratic forms ⇒ y = ax² + bx + c or x = ay² + by + c
Axis of symmetry ⇒ x = [tex]\frac{-b}{2a}[/tex] or y = [tex]\frac{-b}{2a}[/tex]
First problem:
y = -3(x+3)²-2
Write in quadratic form ⇒ y = ax² + bx + c
y = -3(x² + 6x + 9) - 2
y = -3x² -18x - 27 - 2
y = -3x² -18x - 29
a = -3, b = -18
Find axis of symmetry.
[tex]x= \frac{-b}{2a}[/tex]
[tex]x=\frac{--18}{2(-3)}[/tex]
[tex]x=\frac{18}{-6}=-3[/tex]
Second problem:
x = -4(y -4)² +6
Write in quadratic form ⇒ x = ay² + by + c
x = -4(y² - 18y + 16) + 6
x = -4y² + 32y - 64 + 6
x = -4y² + 32y - 58
a = -4, b = 32
Find axis of symmetry.
[tex]y= \frac{-b}{2a}[/tex]
[tex]y=\frac{-32}{2(-4)}[/tex]
[tex]y=\frac{-32}{-8}=4[/tex]