Find the distance between the points (-4,7) and (-4,-5).
Answer: The distance between the points (-4,7) and (-4,-5) is 12.
Step-by-step explanation:
To calculate the distance between two points, we apply the following formula:
\(\huge \boxed{\sf{d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} }}\)
The points are:
x₁ = -4y₁ = 7x₂ = -4y₂ = -5To solve the process is:
First we solve what goes inside the parentheses.Then we calculate the result of the parentheses to the power of 2.We add the two results and then we calculate the square root.We substitute the points in the previous formula given, then
\(\huge \boxed{\sf{d=\sqrt{(-4-(-4))^2+(-5-7)^2 } }}\)
\(\huge \boxed{\sf{d=\sqrt{0^2+(-12)^2 }=\sqrt{0+144} }}\)
\(\huge \boxed{\sf{d=\sqrt{144}=12 }}\)
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Find intervals of concavity for f(x) = 3 cos x, with 0 < x < 21. Show your work for full credit.
The intervals of concavity for f(x) = 3 cos x, with 0 < x < 21, are (0, π/2) and (3π/2, 2π).
To find the intervals of concavity for f(x) = 3 cos x, we need to analyze the second derivative of the function.
First, let's find the second derivative of f(x):
f'(x) = -3 sin x (derivative of cos x)
f''(x) = -3 cos x (derivative of -3 sin x)
Now, we can analyze the concavity of f(x) by considering the sign of the second derivative:
When x ∈ (0, π/2): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.
When x ∈ (π/2, 3π/2): In this interval, cos x < 0, so f''(x) > 0. The second derivative is positive, indicating concavity upwards.
When x ∈ (3π/2, 2π): In this interval, cos x > 0, so f''(x) < 0. The second derivative is negative, indicating concavity downwards.
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In a statistics test, the class average is 76 with a standard deviation of 8. emmy is told that the z-score of her exam score is -1.50. what was emmy's actual score on the exam?
Emmy's actual score in the exam is 64.
What is the Z score of the population?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values. Standard deviations from the mean are used to measure Z-score. A Z-score of zero means the data point's score is the same as the mean score.
Given,
class average = 76
standard deviation = 8
Z- score = -1.50
The formula of Z-score is -
z = (x-μ)/σ
Where x is the actual score,
μ is the mean,
σ is the standard deviation.
Now putting the values in the formula we get,
-1.50 = (x- 76) / 8
⇒ on solving, we get x = 64
So the actual score of Emmy = 64
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4x+3=-5x+21 please help
Answer:
x=2
Step-by-step explanation:
Answer:
x=2
Step-by-step explanation
You deposit the same amount of money in a bank account each month. You deposit a total of $780 in 1 year. How many months does it take for
you to deposit $2275?
Answer:
35 months
Step-by-step explanation:
Given that,
You deposit a total of $780 in 1 year i.e. in 12 months
We need to find how many months does it take for you to deposit $2275.
$780 in 12 months
1$ in \(\dfrac{12}{780}\ \text{months}\)
$2275 in,
\(\dfrac{12}{780}\times 2275\ \text{months}\\\\=35\ \text{months}\)
Hence, it will take 35 months to deposit $2275.
A box of cereal states that there are
78 calories in a
3
4
-cup serving. What is the unit rate for calories per cup? How many calories are there in
4 cups of the cereal?
The unit rate for the cereal is 104 calories per cup and there are 416 calories in 4 cups
How to determine the unit rate for the cereal?From the question, the given parameters are
Calories = 78 calories
Size of cups = 3/4-cup
The unit rate of the calories per cup is calculated as
Unit rate = Number of Calories/Size of cup
Substitute the known values in the above equation
So, we have the following equation
Unit rate = 78/(3/4)
Evaluate the quotient
So, we have the following equation
Unit rate = 104
So, the unit rate is 104 calories per cup
For four cups of cereal, we have
Calories = 104 x 4
Evaluate
Calories = 416
So, the number of calories is 416 calories
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Which of the following is a zero for the function f(x) = (x + 3)(x - 7)(x + 5)?
Ox= -7
Ox= -3
Ox= 3
Ox=5
in
Answer:
x = - 3
Step-by-step explanation:
to find the zeros equate f(x) to zero , that is
(x + 3)(x - 7)(x + 5) = 0
equate each factor to zero and solve for x
x + 3 = 0 ⇒ x = - 3
x - 7 = 0 ⇒ x = 7
x + 5 = 0 ⇒ x = - 5
the zeros are x = - 3, x = 7, x = - 5
the one from the list is x = - 3
Lynn is a zoo kepper at matlock zoo.her hourly rate is $6.85.she earns $328.80 every week.how many hours does she works in a week?
Answer:
48 hours
Step-by-step explanation:
Answer:
48 hours
Step-by-step explanation:
328.80 a week, and a 6.85 hourly rate.
To find hours worked:
$328.80 (total earned) / $6.85 (earned hourly) = 48 hours
Breaking stress is-a.greater than the ultimate stressb.less than " " "c.equal to the " "d.none of these
Breaking stress is (b) less than the ultimate stress, because it is point at which material undergoes "plastic-deformation" but does not necessarily break.
The "Breaking-Stress", is also known as "fracture-stress", is the stress at which a material breaks or fractures under a given load or tension.
This means that the breaking stress is the "maximum-stress" that a material can withstand before it fractures or breaks apart.
The "Ultimate-Stress" is defined as the maximum stress that a material can withstand before it undergoes plastic deformation, such as permanent bending or stretching, but without necessarily breaking.
Since the breaking stress is the point at which the material breaks, it must be less than the ultimate stress, which is the point at which the material undergoes plastic deformation but does not necessarily break.
Therefore, the correct option is (b).
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The given question is incomplete, the complete question is
Breaking stress is -
(a) greater than the ultimate stress
(b) less than the ultimate stress
(c) equal to the the ultimate stress
(d) none of these
What is the base area.
Answer:
Area of the base is 10.5 cm².
Step-by-step explanation:
Formula for the volume of the given oblique prism = Area of the triangular base × Vertical height between two triangular bases
Vertical height = 6 cm
Volume = 63 cm³
From the formula,
63 = Area of the triangular base × 6
Area of the base = \(\frac{63}{6}\)
= 10.5 cm²
Therefore, area of the base is 10.5 cm².
Help is appreciated. Easy I just am always confused
Answer:
BA=BC
Step-by-step explanation:
The graph of a linear relationship passes through (0, 2), (1,5), and (3, 11) but not through (2,7). Which of the following is the equation for this linear relationship?A.O y = 2x + 3 B.O y = 3x + 2C. O y = 5xD. O y= 4x-1
There is a point that doesnt go in the curve.
So the procedure is to replace x by 2 ,and y by 7 in every option to see which doesnt belongs
So we see
Instructions: Find the length of the missing sides. Round your
answers to the nearest tenth. (Hint: Always make sure to label
your triangle first with your reference angle)
Degree 54
Hypotenuse 24
How do i find x and y?
The values of x and y are 19 and 14 respectively.
How to determine the lengthGiven the hypotenuse = 24
Opposite = x
Adjacent = y
Let's use the sine ratio to find the opposite side
sin of angle = opposite/hypotenuse
sin 54 = x/24
Cross multiplysin 54 × 24 ,= x
x = 19.42
x = 19
To find the adjacent side, we use cosine ratio
cos = adjacent/hypotenuse
cos 54 = y/25
Cross multiply
cos 54 × 24 = y
y = 14
Thus, the values of x and y are 19 and 14 respectively.
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Sketch the unique triangles that can be made with angle
measures 40° and 100° and side length 3. How do you know you have sketched all possibilities?
Please find attached the drawing of two triangles which are drawn with MS Word, based on the possible difference of two triangles having a ASA and a SAA configuration.
What are unique triangles?Unique triangles are triangles that are different based on their configuration, which derives from the positioning of the given parameters to correspond with different congruency requirement.
The conditions for the congruency of two triangles are;
SSS: The Side-Side-Side rule; two triangles are congruent if all three sides of one triangle are congruent to the three sides of the other triangle
SAS: The Side-Angle-Side rule; two triangles are congruent if two sides and the included angle of one are congruent to two sides and an included angle in the other triangle
ASA: The Angle-Side-Angle rule; two triangles are congruent if two angles and the included side of one triangle are congruent to two angles and an included side of the other triangle
SAA: The Side-Angle-Angle rule; Two triangles are congruent if two angles and an a non included side of one triangle are congruent to two angles and the non included side of the other triangle.
RHS: Right angle Hypotenuse Side: Two right triangles are congruent if the hypotenuse side and one leg of one triangle are congruent to the hypotenuse side and one leg of the other right triangle.
The configuration of the unique triangles can therefore, be ASA and SAA, which gives the triangles;
ΔABC; AB = 3, ∠CBA = 100°, ∠CAB = 40°ΔABC; AB = 3, ∠ABC = 100°, ∠BCA = 40°Please see attached drawings of the two unique triangles
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a brunette Hall is preparing to serve a party of 432 guests if each table seats 8 people how many tables are needed
Answer:
54
Step-by-step explanation:
432/8=54
How long would it take to make 100 shots when making 18 shots per minute at a steady rate
Answer:
5 minutes and 33 1/3 seconds.
Step-by-step explanation:
No. of shots made in 1 minute = 18
Let x be the no of minute to 100 shot
No. of shots made in 1*x minute = 18*x = 18x
Given total no of shots to be made = 100. Thus
18x = 100
x = 100/18 = 5 10/18
Thus, it will take 5 full minutes and 10/ 18 minutes to make 100 shots
we know that 1 minute is equal to 60 second
1 minute = 60 second
multiplying LHS and RHS by 10/18
1 * 10/18 minute = 60 *10 /18 seconds
10/18 minute = 100/3 seconds = 33 1/3 seconds
Thus, it will second 5 minutes and 33 1/3 seconds to make 100 shots.
A (tiny) library has 5 history texts, 3 sociology texts, 6 anthropology texts and 4 psychology texts. Find the number of ways a student can choose:
Thus, there are 18 ways to choose one book, 153 ways to choose two books, and 360 ways to choose three books, one from each category.
To find the number of ways a student can choose from the given library, we need to use the formula for combinations.
The formula for combinations is:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to be chosen, and ! denotes factorial.
Let's consider the different ways a student can choose:
1. Choosing one book from any category:
Total number of books = 5+3+6+4 = 18
n = 18, r = 1
Number of ways = 18C1 = 18! / 1!(18-1)! = 18
2. Choosing two books from any category:
n = 18, r = 2
Number of ways = 18C2 = 18! / 2!(18-2)! = 153
3. Choosing three books, one from each category:
For this, we need to choose one book from each category, and the order of selection does not matter.
n1 = 5, r1 = 1 (for history)
n2 = 3, r2 = 1 (for sociology)
n3 = 6, r3 = 1 (for anthropology)
n4 = 4, r4 = 1 (for psychology)
Number of ways = (5C1 x 3C1 x 6C1 x 4C1) = (5 x 3 x 6 x 4) = 360
Therefore, there are 18 ways to choose one book, 153 ways to choose two books, and 360 ways to choose three books, one from each category.
In summary, a student can choose:
- 18 ways to choose one book
- 153 ways to choose two books
- 360 ways to choose three books, one from each category
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Solve for x. Round your answer to the nearest whole number.
340 + 5x = 650 - 8x
a 30
b 20
c 24
d 23
Can someone help me out my grads are bad
Answer:
50 m^2
Step-by-step explanation:
3cm = 5 m
6 cm = 10 m
5 x 10 = 50 m^2
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Answer:
50 \(m^{2}\)
Step-by-step explanation:
3cm = 5m
6cm = 10m
5x10 = 50
f(x) = x3 -27
Find the zeros
Answer:
x=9
y=-27
Step-by-step explanation:
AC is a diameter of OE, the area of
the
circle is 2897 units², and AB = 16 units.
Find BC and mBC.
B
A
C
E
Given that AC is a diameter of the circle, we can conclude that triangle ABC is a right triangle, with AC being the hypotenuse. The area of the circle is not directly related to finding the lengths of BC or AB, so we will focus on the given information: AB = 16 units.
Using the Pythagorean theorem, we can find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (AC) is equal to the sum of the squares of the other two sides (AB and BC):
AC² = AB² + BC²
Substituting the given values, we have:
(AC)² = (AB)² + (BC)²
(AC)² = 16² + (BC)²
(AC)² = 256 + (BC)²
Now, we need to find the length of AC. Since AC is a diameter of the circle, the length of AC is equal to twice the radius of the circle.
AC = 2 * radius
To find the radius, we can use the formula for the area of a circle:
Area = π * radius²
Given that the area of the circle is 2897 units², we can solve for the radius:
2897 = π * radius²
radius² = 2897 / π
radius = √(2897 / π)
Now we have the length of AC, which is equal to twice the radius. We can substitute this value into the equation:
(2 * radius)² = 256 + (BC)²
4 * radius² = 256 + (BC)²
Substituting the value of radius, we have:
4 * (√(2897 / π))² = 256 + (BC)²
4 * (2897 / π) = 256 + (BC)²
Simplifying the equation gives:
(4 * 2897) / π = 256 + (BC)²
BC² = (4 * 2897) / π - 256
Now we can solve for BC by taking the square root of both sides:
BC = √((4 * 2897) / π - 256)
To find the measure of angle BC (mBC), we know that triangle ABC is a right triangle, so angle B will be 90 degrees.
In summary:
BC = √((4 * 2897) / π - 256)
mBC = 90 degrees
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The area between two negative scores can be found by
The area between two negative scores can be found by taking the absolute difference between the two scores.
The area between two negative scores can be found by taking the absolute difference between the two scores. This is because the absolute difference gives us the distance between the two scores without considering their signs.
To calculate the area between two negative scores, follow these steps:
1. Identify the two negative scores.
2. Subtract the smaller negative score from the larger negative score.
3. Take the absolute value of the result to remove the negative sign.
4. The absolute difference between the two negative scores represents the area between them.
For example, let's say we have two negative scores, -5 and -10. To find the area between them, we subtract -5 from -10, resulting in -10 - (-5) = -10 + 5 = -15. Since we are interested in the distance, we take the absolute value of -15, which gives us 15. Therefore, the area between -5 and -10 is 15.
The absolute difference between two negative scores gives us the area between them. This approach is applicable whenever we want to find the distance or area between any two numbers, not just negative scores.
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Please answer the given question
there are total 64 is the answer if she puts 2 cookies in each packet
hope this helps u :)
thompson and thompson is a steel bolts manufacturing company. their current steel bolts have a mean diameter of 140 millimeters, and a standard deviation of 8 millimeters. if a random sample of 49 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 1.8 millimeters? round your answer to four decimal places.
The probability that the sample mean differs from the population mean by 1.8mm and is rounded off to 4 decimal places is 0.8220
According to the given problem the mean diameter μ= 140 mm (population mean) and the standard deviation is σ=8mm
random sample size, n= 49 steel bolts is selected
Let the random variable that represents the diameter of steel bolts be denoted by x and from the problem we have x = 1.8mm
Let z = (x-μ) / (σ/√n ) (1)
using formula (1) and when the sample mean differs from the population mean by more than 1.8mm
z = 1.8/(8/√49 )
⇒z = 63/40 = 1.575
The probability that the sample mean will differ from the population mean by more than 1.8 mm
P( z > 1.575) = 1 - P(z< 1.575) = 1 - 0.178 = 0.822
The probability that the sample mean will differ from the population mean by more than 1.8 mm = 0.8220
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Please help! Use the Triangle Angle Bisector Theorem to find the value of x.
Do not round off at any point. I just need to know what x is.
By angle bisector theorem, the value of x is 5.625
What does the angle bisector theorem mean?
The angle bisector of a triangle divides the other side according to the Angle Bisector Theorem in a way that makes the ratio of the two line segments equal to the ratio of the other two sides.
According to angle bisector theorem
CB/DB = CA/DA
7.5/x = 4/3
x = 7.5•3/4
x = 22.5/4
x = 5.625
Hence, the value of x is 5.625
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if L is parallel to M, find the value of each missing variable(s)
Answer:
5. x = 13
6. x = 11; y = 3
Step-by-step explanation:
5. (9x + 2)° = 119° (alternate interior angles are congruent)
\( 9x + 2 = 119 \)
Subtract 2 from each side
\( 9x + 2 - 2 = 119 - 2 \)
\( 9x = 117 \)
Divide both sides by 9
\( \frac{9x}{9} = \frac{117}{9} \)
\( x = 13 \)
6. (9x + 25)° = (13x - 19)° (corresponding angles are congruent)
\( 9x + 25 = 13x - 19 \)
Collect like terms
\( 9x - 13x = - 25 - 19 \)
\( -4x = -44 \)
Divide both sides by -4
\( \frac{-4x}{-4} = \frac{-44}{-4} \)
\( x = 11 \)
(13x - 19)° + (17y + 5)° = 180° (linear pair)
\( 13x - 19 + 17y + 5 = 180 \)
Plug in the value of x and solve for y
\( 13(11) - 19 + 17y + 5 = 180 \)
\( 143 - 19 + 17y + 5 = 180 \)
Collect like terms
\( 129 + 17y = 180 \)
Subtract 129 from both sides
\( 129 + 17y - 129 = 180 - 129 \)
\( 17y = 51 \)
Divide both sides by 17
\( \frac{17y}{17} = \frac{51}{17} \)
\( y = 3 \)
A line contains the points (-26, -37) and (-32, -61)
What is the slop of the line in simplified form?
Answer:
The slope is 4
Step-by-step explanation:
We can find the slope by using
m = ( y2-y1)/(x2-x1)
= ( -61- -37)/( -32 - -26)
= ( -61+37)/( -32 +26)
= -24/-6
=4
Answer:
\( slope = 4 \)
Step-by-step explanation:
(-26, -37) and (-32, -61)
\( slope = \dfrac{y_2 - y_1}{x_2 - x_1} \)
\( slope = \dfrac{-61 - (-37)}{-32 - (-26)} \)
\( slope = \dfrac{-24}{-6} \)
\( slope = 4 \)
A map of the state of Michigan. The measured distance between Saginaw and Alpena is 2.2 centimeters. The map key reads 1 centimeter to 50 miles.
The actual distance between Saginaw and Alpena is
miles.
Answer:
110 miles
Step-by-step explanation:
Answer:110
Step-by-step explanation:
Show that the 9x^2-24xy+16y^2-12x+16y-12=0 represents a pair of parallel lines .Find the distance between the lines.
First of all u will 9x^2-24xy+16y^2-12×16y-12=0 u will add the 9x^ then u will subtract 2-24
i need help with this and if you don't know please don't answer
Answer:
18 ft
Step-by-step explanation: