Answer:
Step-by-step explanation:
Given g(x) = 8x2 − x + 5, find the following.
(a). g(0) = 5
(b). g(−1) = 14
(c). g(r) = ?
(d). g(x + h) = ?
An electrician leans an extension ladder against the outside wall of a house so that it reaches an electric box 29 feet up. The ladder makes an angle of 71 degrees with the ground. Find the length of the ladder. Round your answer to the nearest tenth of a foot if necessary.
Answer:
30.7
Step-by-step explanation:
sin(71) = 29/x
x = 29/sin71
≈ 30.7
please helppppp i’ll give brainlist
For problems 6 and 7 set up a proportion and solve.
6. The ratio of the birth weight to the adult weight of a male black bear is 3:1000.
7. The measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.
What is an angle?An angle is an abstract concept in geometry which is formed by two lines or rays that meet at a common point. An angle is measured in degrees and can be classified by its size as acute, right, obtuse, or reflex. An angle can also be formed by three points or two intersecting planes.
6. The average birth weight is 12 ounces. The average adult weight is 12 x 1000 = 12000 ounces. Since there are 16 ounces in 1 pound, the average adult weight of the male black bear is 12000/16 = 750 pounds.
7. The measures of the angles in a triangle are in the extended ratio 2:15:19.To find the measure of each angle, we can set up an equation using the extended ratio. Let x be the measure of the first angle, then 15x and 19x will be the measures of the other two angles. This can be written as: 2x + 15x + 19x = 360°. Solving this equation, we get x = 36°. Therefore, the measure of the angles in the triangle are 36°, 15 x 36° = 540°, and 19 x 36° = 684°.
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13) Two supplementary angles
are represented by 3y +10 and 2y+30 What are the measures of each angle?
Up to 180 degrees
Your Welcome
Please help me I will give brainlist if correct
Answer:
27/70
Step-by-step explanation:
To find an area you have to multiply [tex]length*width[/tex] In this problem, the length of the striped rectangle is 3/7 and the width is 9/10. So you would multiply them together. After multiplying you get the answer of 27/70, most likely Khan Academy will ask for a simple answer so the answer is 27/70 (it is already in its simplest form)
Evaluate
3x2−2xy+4y2
3
x
2
−
2
x
y
+
4
y
2
for
x=−1
x
=
−
1
and
y=−2
Answer:
3x² -2xy + 4y² at x = -1, y = -2 = 15
Step-by-step explanation:
Given function is
f(x, y) = 3x² -2xy + 4y²
To find At x = - 1 and y - 2 just plug these values for x and y into f(x, y)
f(-1, -2) = 3(-1)² - 2(-1)(-2) + 4(-2)²
(-1)² = 1 ==> 3x² = 3(-1)² = 3 x 1 = 3
(-1) (-2) = 2 ==> 2xy = 2(-1)(-2) = 2 x 2 = 4
(-2)² = 4 ==> 4y² = 4 (-2)² = 4 x 4 = 16
f(-1 1, - 2) = 3x² -2xy + 4y²
= 3 - 4 + 16
= 15
Figure ABCD is a parallelogram. Is it also a rhombus? Why or why not?
D
5m
B
5 m
C
OA. It cannot be determined, because a parallelogram with congruent
adjacent sides may or may not be a rhombus.
B. No, because all four sides are congruent.
C. Yes, because adjacent sides are congruent.
D. No, because adjacent sides are congruent.
The true statement about the parallelogram is (c) Yes, because adjacent sides are congruent.
How to determine the true statement about the parallelogramGiven that
Figure ABCD is a parallelogram
Such that
Side lengths = 5 cm
This means that
The figure is a square
As a general rule
All squares can be classified as rhombus
This is because a rhombus is a quadrilateral with all four sides of equal length and square is a type of rhombus in which all four sides are equal in length
Hence, the true statement is (c)
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Need help with number 10.
Prove the Converse of the Pythagorean Theorem
The Converse of the Pythagorean Theorem is proved below.
What is Pythagoras Theorem ?
Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
The converse of the Pythagorean theorem states that if a triangle has sides of length a, b, and c, where c is the longest side, and a² + b² = c², then the triangle is a right triangle.
To prove the converse of the Pythagorean theorem, we can use the fact that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides. That is, if a triangle has sides of length a, b, and c, where c is the longest side and c² = a² + b², then the triangle is a right triangle.
Proof:
Suppose we have a triangle ABC, with sides of length a, b, and c, where c is the longest side. Assume that a² + b² = c². We want to show that triangle ABC is a right triangle.
We will use the Law of Cosines to show that angle C is a right angle. The Law of Cosines states that for any triangle ABC with sides of length a, b, and c opposite angles A, B, and C, respectively:
c² = a² + b² - 2ab cos(C)
Substituting a² + b² = c² into this equation, we get:
c² = c² - 2ab cos(C)
2ab cos(C) = 0
cos(C) = 0
Since 0 is the cosine of 90 degrees, this implies that angle C is a right angle. Therefore, triangle ABC is a right triangle.
Thus, this completes the proof of the converse of the Pythagorean theorem.
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which graph of y = a•b^x has a>1 and 0
Answer: x=0
Step-by-step explanation:
Question content area top
Part 1
Assume the hold time of callers to a cable company is normally distributed with a mean of 3.7 minutes and a standard deviation of .6 minute. Determine the percent of callers who are on hold between 2.6 and 3.9 minutes.
Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
What Is a Normal Distribution?
A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
First, we standardize the value of 2.6 as follows:
z = (x - μ) / σ
where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (2.6 - 3.7) / 0.6 ≈ -1.83
z = (x - μ) / σ
where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (3.9 - 3.7) / 0.6 ≈ 0.33
We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:
P(-1.83 < Z < 0.33) ≈ 0.6068
Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
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Approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
What Is a Normal Distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
First, we standardize the value of 2.6 as follows:
z = (x - μ) / σ
where x is the value of 2.6, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (2.6 - 3.7) / 0.6 ≈ -1.83
z = (x - μ) / σ
where x is the value of 3.9, μ is the mean of 3.7 minutes, and σ is the standard deviation of 0.6 minutes:
z = (3.9 - 3.7) / 0.6 ≈ 0.33
We can use a standard normal distribution table or a calculator to find this area. Using a calculator, we can find the area as follows:
P(-1.83 < Z < 0.33) ≈ 0.6068
Therefore, approximately 60.68% of callers are on hold between 2.6 and 3.9 minutes.
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Suppose for a community the number of rows in gardens is normally distributed with a mean of 7 rows and standard deviation of 2 rows. Find the probability that a given garden has between 1 and 11 rows. Hint: use the 68 - 95 - 99.7 rule.
The given distribution is normal with mean μ = 7 and standard deviation σ = 2. So,The probability that a given garden has between 1 and 11 rows is approximately 0.9772 or 97.72%.
What is probability?Probability is a mathematical concept that is used to measure the likelihood of a particular event occurring. It is a way to quantify uncertainty, and it is expressed as a number between 0 and 1.
We need to find the probability that a given garden has between 1 and 11 rows.
First, we standardize the values using the formula z = (x - μ) / σ, where x is the number of rows.
For x = 1, z = (1 - 7) / 2 = -3. For x = 11, z = (11 - 7) / 2 = 2.
Using the 68 - 95 - 99.7 rule, we know that approximately 68% of the data falls within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Thus, the probability of a garden having between 1 and 11 rows can be calculated as:
P(1 ≤ x ≤ 11) = P(-3 ≤ z ≤ 2)
From the z-table, we can find that the probability of a standard normal distribution having a z-score between -3 and 2 is approximately 0.9772.
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If you were to travel 6 miles, and catch a train and traveled 8 miles, how many miles have you traveled?
Answer:
The answer would be 14 miles!
i need help with the question below
We use the arctangent function to find the angle [tex]theta[/tex]
[tex]\theta= 2(3 \sqrt{2},-3 \sqrt{2}) \approx 225.000^{\circ}[/tex]
How to find the values?Inverse tangent (notation: arctan or tan-1) is the inverse of the tangent. That is: Arctangent and tangent are inverse functions, so their composition is an identity.
To find [tex]z_{-} 1+z_{-} 2[/tex], we add the complex numbers in rectangular form:
[tex]$$z_1+z_2=6\left(\cos 55^{\circ}+i \sin 55^{\circ}\right)+6\left(\cos 135^{\circ}+i \sin 135^{\circ}\right)$$[/tex]
Simplifying, we get:
[tex]$$z_1+z_2=6\left(\cos 55^{\circ}+\cos 135^{\circ}+i \sin 55^{\circ}+\sin 135^{\circ}\right)$$[/tex]
Using the trigonometric identities [tex]\backslash \cos (\backslash p i-\backslash$ theta) =- $\backslash \cos \backslash$ theta\$ and $\$ \backslash \sin (\backslash p i-$ $\backslash$ theta) $=\backslash \sin \backslash$ theta[/tex], we can simplify this to:
[tex]$$z_1+z_2=6\left(-\frac{\sqrt{2}}{2}+i \frac{\sqrt{2}}{2}\right)=-3 \sqrt{2}+3 i \sqrt{2}$$[/tex]
Therefore, [tex]z_{-} 1+z_{-} 2=-3 \backslash s q r t\{2\}+3 i \backslash s q r t\{2\}[/tex]
To find [tex]r[/tex] and [tex]theta[/tex] such that [tex]z_{-} 1+z_{-} 2=$ rlangle $\backslash$ theta[/tex], we first calculate [tex]r[/tex] as the magnitude of [tex]z_{-} 1+z_{-} 2[/tex] :
[tex]$$|r+s i|=\left|z_1+z_2\right|=\sqrt{(-3 \sqrt{2})^2+(3 \sqrt{2})^2}=3 \sqrt{2} .$$[/tex]
Next, we use the arctangent function to find the angle [tex]theta[/tex]
[tex]\theta= 2(3 \sqrt{2},-3 \sqrt{2}) \approx 225.000^{\circ}[/tex]
Hence, we can say the values of both the z_{-} 1+z_{-} 2 and r is [tex]z_{-} 1+z_{-} 2=-3 \backslash s q r t\{2\}+3 i \backslash s q r t\{2\}[/tex] and [tex]\theta= 2(3 \sqrt{2},-3 \sqrt{2}) \approx 225.000^{\circ}[/tex] respectively.
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What is the measure of ∠b (messed up last)
Answer:
b=30
Step-by-step explanation:
The sum of the three angles of a triangle add to 180.
75+75+b = 180
150+b=180
Subtract 150 from each side.
b = 180-150
b=30
Answer:
b=30
Step-by-step explanation:
The sum of all the angles of a triangle add up to 180°
∠b = 75° + 75° = 150°
Now, we need to subtract 150° from 180° to see how much does angle b measure.
∠b = 150° - 180° = 30°
30° = ∠b
The angles of the triangle would be:
75°, 75°, and 30°
To prove this, we will sum all the angles again:
75° + 75° + 30° = 180°
75° + 75° = 150°
150° + 30° = 180°
Hence, the answer is ∠b = 30°
Dave bought a new game for $28. The tax rate was %7. How much was the tax and the total price?
The tοtal price οf the game including tax is $29.96.
What are the variοus types οf taxes?Physical assets such as prοperty and transactiοns such as the sale οf stοck οr a hοme are subject tο taxatiοn. Taxes include incοme, cοrpοrate, capital gains, prοperty, inheritance, and sales taxes.
Because the tax rate is 7%, the tax amοunt is 7% οf the purchase price. Tο calculate the tax, multiply the purchase price by the tax rate expressed as a decimal:
0.07 x $28 = $1.96 in taxes
As a result, the purchase tax is $1.96.
Tο calculate the tοtal price, add the purchase price and the tax:
Purchase price + Tax = Tοtal Price
Tοtal cοst: $28 + $1.96 = $29.96
As a result, the tοtal cοst οf the game, including tax, is $29.96.
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A company estimates that 2% of their products will fail after the original warranty period but within 2 years of the purchase, with a replacement cost of $450.
If they want to offer a 2 year extended warranty, what price should they charge so that they'll break even (in other words, so the expected value will be 0)
$
To break even, the company should charge a price that covers their expected loss. Therefore, the price that they should charge for the 2 year extended warranty is $9
What is expected value?
Expected value is a concept in probability theory that represents the average value of a random variable over a large number of trials. It is calculated by multiplying each possible outcome by its probability and adding up the products
Let x be the price that the company charges for the extended warranty. Then, the expected value of the extended warranty is:
E(x) = 0.98(0) + 0.02(-450) = -9
The negative expected value means that the company is expected to lose money on the extended warranty.
To break even, the company should charge a price that covers their expected loss. Therefore, the price that they should charge for the 2 year extended warranty is:
x = -$(-9) = $9
Therefore, the company should charge $9 for the 2 year extended warranty so that they break even.
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The sum of two numbers is 34 and the difference is 8 What is their product
Answer:
Step-by-step explanation:
[tex]x+y=34\\x-y=8\\2x=42\\x=21\\y=34-21\\y=13\\13(21)=273[/tex]
Find the area of this composite shape. Include correct units.
Show all your work.
The area of this composite shape is 273 m².
What is an area?
An area is a measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters, square feet, or square inches. The area of a shape or region is determined by multiplying the length of one side by the length of another side, such as the length and width of a rectangle or the radius of a circle. The concept of area is used in many areas of mathematics and science, including geometry, trigonometry, calculus, and physics.
first, refer figure that attached below:
The are a of "a"= area of ΔABC
AB = 20-14 = 6 m
BF = 18-11 = 7 m
Then, area of region "a" = 1/2*AB*BF = 1/2*6*7 = 21 m².
Now, area of region"b" = area of rectangle ABCD = ED*CD = 252 m².
Total area of this composite shape = a + b =21+252 = 273 m².
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Complete question is: The area of this composite shape is 273 m².
pls help quick. this was due a while ago. my math teacher doesnt teach and tells us to “read from the book.”
Answer:
183.3
Step-by-step explanation:
Since there were 1 angle and 2 sides, I used law of cosines
please help, thank you so much
a. The probability of rolling a number greater than 10 is 1/6.
b. The probability of rolling a number less than 5 is 1/3.
c. The expected number of times a 4, 6, or 9 will be rolled in 200 rolls is 50
How to calculate the probabilitya. The probability of rolling a number greater than 10 is equal to the number of faces with numbers greater than 10 (i.e., 11 and 12) divided by the total number of faces. Thus, P(number greater than 10) = 2/12 = 1/6.
b. The probability of rolling a number less than 5 is equal to the number of faces with numbers less than 5 (i.e., 1, 2, 3, and 4) divided by the total number of faces. Thus, P(number less than 5) = 4/12 = 1/3.
c. The probability of rolling a 4, 6, or 9 is equal to the number of faces with those numbers (i.e., 1 each) divided by the total number of faces. Thus, the probability of rolling a 4, 6, or 9 is 3/12 = 1/4.
Therefore, the expected number of times a 4, 6, or 9 will be rolled in 200 rolls is:
(expected number of times) = (probability of rolling a 4, 6, or 9) x (total number of rolls)
= (1/4) x (200)
= 50
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Each year, the school has a goal to have a third as many students in remedial mathematics courses as the year before. Currently the school has 1,200 students in remedial math. Approximately how many students will be enrolled in four years?
(a) 44 (b)15 (c) 32,400 (d) 1
Answer:
44 students
Step-by-step explanation:
1200 for the first year
a third of that is 400
400 for the second year
a third of that is 133.4
133.4 for the third year
a third of that is 44
One year, the population of a city was 137,000. Several years later it was 117,820. Find the percent decrease.
Group of answer choices
14%
15%
16%
19%
Answer:
The percent decrease in population can be calculated by dividing the difference between the two populations by the original population and then multiplying by 100. In this case, the percent decrease is ((137000-117820)/137000)*100 = 14%.
Step-by-step explanation:
Amy is making a cookie recipe which uses 1/2 teaspoon of sugar per batch. She wants to make 3 batches. How many teaspoons of sugar will she use?
I need help on this
Answer:
first name is pentagon
second is decagon
third is heptagon
Step-by-step explanation:
first is irregular
second is regular
third is irregular
the sonar system that detect a sunken ship 1500 m ahead with an angle of elevation of 90° to the highest part of the sunken ship. How many meter is Mr. submarine rise to pass over the sunken ship?
The value of tangent (90°) is 1, so the rise in distance for the submarine to pass over the sunken ship is 1500 m.
What is value?Value is the worth of something as measured by its usefulness, importance, or desirability. It is something that is sought after and appreciated by individuals and society. Value is subjective and can vary among people and cultures, but can be broadly defined as the quality of something that makes it worth having or doing.
To calculate the distance the submarine must rise to pass over the sunken ship, we must use the tangent function. The tangent of an angle is equal to the opposite side (in this case, the rise in distance for the submarine) divided by the adjacent side (in this case, the 1500 m distance to the sunken ship).
Therefore, the formula to calculate the rise in distance for the submarine is:
Tangent (90°) = Rise / 1500 m
Solving for the rise, we get:
Rise = 1500 m x Tangent (90°)
Using a calculator, the value of tangent (90°) is 1, so the rise in distance for the submarine to pass over the sunken ship is 1500 m.
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Because the tangent (90°) value is 1, the distance travelled by the submarine to cross over the sunken ship is increased by 1500 m.
What are trigonometric angles?Trigonometric angles are the angles in a right-angled triangle that can be used to illustrate various trigonometric functions. Standard angles in geometry include 0°, 30°, 45°, 60°, and 90°. The trigonometric functions are real functions that link the angle of a right-angled triangle to side length ratios. The sine, cosine, and tangent angles are the main classification of trigonometric functions. The primary functions can be used to determine the three functions cotangent, secant, and cosecant.
According to the question draw the graph we should solve the length of BC
tan A = BC/AC
tan90° = BC/1500
BC = 1500 tan90°
= 516.5 (m)
The value of BC is 516.5 m
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An isosceles triangle whose sides are 5cm, 5cm and 6cm is inscribed in a circle. Find the radius of the circle.
Answer:
To find the radius of the circle inscribed in an isosceles triangle, we can use the following formula:
r = (a/2) * cot(π/n)
where r is the radius of the inscribed circle, a is the length of one of the equal sides of the isosceles triangle, and n is the number of sides of the polygon inscribed in the circle.
In this case, we have an isosceles triangle with two sides of 5cm and one side of 6cm. Since the triangle is isosceles, the angle opposite the 6cm side is bisected by the altitude and therefore, the two smaller angles are congruent. Let x be the measure of one of these angles. Using the Law of Cosines, we can solve for x:
6^2 = 5^2 + 5^2 - 2(5)(5)cos(x)
36 = 50 - 50cos(x)
cos(x) = (50 - 36)/50
cos(x) = 0.28
x = cos^-1(0.28) ≈ 73.7°
Since the isosceles triangle has two equal sides of length 5cm, we can divide the triangle into two congruent right triangles by drawing an altitude from the vertex opposite the 6cm side to the midpoint of the 6cm side. The length of this altitude can be found using the Pythagorean theorem:
(5/2)^2 + h^2 = 5^2
25/4 + h^2 = 25
h^2 = 75/4
h = sqrt(75)/2 = (5/2)sqrt(3)
Now we can find the radius of the inscribed circle using the formula:
r = (a/2) * cot(π/n)
where a = 5cm and n = 3 (since the circle is inscribed in a triangle, which is a 3-sided polygon). We can also use the fact that the distance from the center of the circle to the midpoint of each side of the triangle is equal to the radius of the circle. Therefore, the radius of the circle is equal to the altitude of the triangle from the vertex opposite the 6cm side:
r = (5/2) * cot(π/3) = (5/2) * sqrt(3) ≈ 2.89 cm
Therefore, the radius of the circle inscribed in the isosceles triangle with sides 5cm, 5cm, and 6cm is approximately 2.89 cm.
11. At astronomy school, 30% of the students studying stars, 40% are studying black holes, 10% are studying planets, and 20% are studying comets. Use the random-number table to find the experimental probability that in a group of 4 students, at least 2 will be studying stars. Assign values from the table for each field of study: 11. A. Assign values for the number of stars. M. B. Assan values for the number of black holes. chshe 11. C Assign values for the number of planets. 11. D. Assign values for the number of comets. Use the table to simulate the probability that at least 2 will study stars. 3516 D 1388 5476 2802 11 E What is the simulated probability that at least 2 will be studying stars? 6035 5147 1264
D
L
F
DM = 8
M
K
FM = 2x
E
EM = 6
Answer: yes correct i love math
Step-by-step explanation:
The radius of a circle is 14 centimeters. What is the circle's circumference?
Use 3.14 for л.
The circumference of the circle who radius is 14 centimeters is approximately 87.92 centimeters.
What is circumference?
Circumference is distance around the edge of a circle. It can be thought as the perimeter of the circle. It is a measure of the total length of the circle, and is determined by the size of the circle's radius or diameter. The formula of circumference of circle is C = 2πr
What is radius ?
Radius is a term used in geometry to refer to the distance between the center of a circle or sphere and any point on its circumference or surface, respectively. It is typically denoted by the letter "r"
In the given question,
The circumference of circle is given by the formula:
C = 2πr
where r is the radius of circle and π (pi) is mathematical constant which is approximately equal to 3.14.
Substituting the given value of radius, we get:
C = 2 x 3.14 x 14
= 87.92 centimeters (rounded to two decimal places)
Therefore, the circumference of the circle is 87.92 centimeters.
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(HELP ME MY GRADES ARE DUE TMRO) Two friends, Arianna and Bo, had just bought their first cars. Bo uses 2
gallons of gas to drive 41.4 miles in his car. The table below represents
the number of miles, y, that Arianna can drive her car for every x
gallons of gas.
Answer:
Step-by-step explanation:
104.4 divided by 4 = 26.1