The inequality for this problem, along with it's solution, is given as follows:
A. x − 4 < 6; x < 10
What is the segment addition postulate?The segment addition postulate is a geometry axiom that states that when a line segment is divided into a number of smaller segments, the total length is given by the sum of the lengths of each of the smaller segments.
For this problem, we have that BD is a smaller segment of segment BC, hence the inequality is given as follows:
BD < BC.
Replacing with x, the solution is obtained as follows:
x - 4 < 6
x < 6 + 4
x < 10.
Meaning that option a is the correct option.
More can be learned about the segment addition postulate at https://brainly.com/question/2134445
#SPJ1
Can you please solve? TKSSSSS
Answer:
18π or
Step-by-step explanation:
To find the area of a semicircle, use the formula of the area of a semicircle.
Area = [tex]\frac{1}{2}[/tex] π r^2
Radius = 6
Area = [tex]\frac{1}{2}[/tex] π 6^2
Area = [tex]\frac{1}{2}[/tex] (36π)
Area = 18π (in terms of π)
Area = 56.52 (in terms of 3.14)
How many 3cm cubes can be placed inside the box?
Answer: 36 cubes
Step-by-step explanation:
Length x Width x Height
18 x 6 x 9 = 972
3 x 3 x 3 = 27
972 / 27 = 36
Help. Marked most brainlliest
Answer:
Incorrect
Step-by-step explanation:
In step one, when they multiplied exponents, they added them which is correct
Step two, they divided exponents, which means they should have subtracted. if they subtracted 6/5 and 2/5, it would have been
[tex]( {x}^{ \frac{4}{5} } )^{ \frac{1}{2} } [/tex]
Please help urgently! Find all the missing angles in the diagram below. Explain how you used two different angle theories to find at least two missing angles.
The requried measures of angles a, b, c, and d are 97°, 15°, 68°, and 68° respectively.
What is the angle?Orientation of the one line with respect to the horizontal or other respective line is known as a measure of orientation and this measure is known as the angle.
Here,
From the figure,
The calculation of the unknown angles is as follows,
112° and ∠d are supplementary angles.
So,
112 + ∠d = 180
∠d = 180 - 112
∠d = 68°
97° and angle a are corresponding angles, so
∠a = 97°.
112 and ∠c are also supplementary angles.
112 + ∠c = 180
∠c = 68°
Now,
∠a + ∠b = 112
∠a + 97 = 112
∠a = 15°
Thus, the requried measure of angles a, b, c, and d are 97°, 15°, 68° and 68°.
Learn more about Angles here:
https://brainly.com/question/13954458
#SPJ1
Sam wants to buy a video game that costs $125, He has already saved $50 so far. He tutors
a neighborhood kid to make extra money and earns $15 per session. Which inequality can
be used to determine the number of sessions, s, he needs to conduct to have enough money
to buy the video game?
A. 15x + 50 ≥ 125
B. 15x + 50 ≤ 125
C. 50x + 15 ≥ 125
D. 50x + 15 ≤ 125
Answer:
We can use inequality B to determine the number of sessions Sam needs to conduct. The reason is that he already has $50 and he wants to have enough money, so he needs to earn the remaining amount through tutoring. Thus, we can write the inequality as:
15s + 50 ≥ 125
where s is the number of tutoring sessions he needs to conduct. We can simplify and solve for s as follows:
15s ≥ 75
s ≥ 5
Therefore, Sam needs to conduct at least 5 tutoring sessions to have enough money to buy the video game.
come up with a model of your function. Explain your process
To model with mathematics is to test ideas using math and computer programs to simulate an object or action.
What do you mean by mathematical modeling?In order to understand a real-life problem, modelling entails developing a set of mathematical equations that accurately reflects a situation.
The model frequently needs to be modified because it does not adequately capture the situation.
By knowing how the system functions, which variables are significant in the system, and how they relate to one another, one can utilise a mathematical model to better understand a real-life situation. Moreover, models can be used to forecast and predict what a system will do in the future or for various parameter values. Finally, a model can be used to estimate variables that are challenging to precisely evaluate.
To know more about mathematical modeling, visit:
https://brainly.com/question/28028993
#SPJ1
Part 1 The height of a ball (in feet) after t seconds is given by the quadratic function h = -16(t-5)^2 + 119.
A. When does the ball reach its maximum height?
B. What is the maximum height?
The ball may rise height a maximum of [tex]119[/tex] feet.
How is height defined?Height, altitude, and elevation all refer to the vertical distance between something's top and bottom or its base but something above it. Anything that can be measured vertically, whether it is high or low, is referred to as having height.
As the ball hits the quadratic function's vertex, it has grown to its highest point. The position (b, c), wherein b is the vertex's x-coordinate, is where a quadratic function of the type is said to have its vertex.
As the quadratic function in this instance is, the point serves as the vertex (5, 119). The ball therefore reaches its highest point after 5 seconds.
[tex]h=-16(5-5)^{2}+119[/tex]
[tex]h=119[/tex]
Therefore, the maximum height of the ball is [tex]119[/tex] feet.
To know more about height visit:
https://brainly.com/question/19635695#SPJ1
#SPJ1
Which of the following would not be a possible function for f (x) and g(x)
The following function won't produce the intended composite function:
f(x) = 8/x + 4
g(x) = 1/x²
What are functions?A method or connection known as a function connects each element of a non-empty set A to at least one element of a second non-empty set B. A function in mathematics is a relation f between a set A (the function's domain) and a different set B (the function's co-domain).
In the given question,
When f(x) = 8/x + 4 and g(x) = 1/x²
Then (f o g(x)) = 8/1/x² + 4
= 8x² + 4
As a result, the following function would not produce the intended composite function:
f(x) = 8/x + 4
g(x) = 1/x²
To know more about functions, visit:
https://brainly.com/question/24909773
#SPJ1
Two families purchased lunch at a hotdog cart. The first family paid $18.00 for 4 hot dogs and 4 drinks. The second famliy paid $20.00 for 5 hot dogs and 3 drinks.
What is the price, in dollars, of a hot dog? Enter your answer as $0.00
one answer only
Answer:
The price of a hot dog is $2.00
express in exponential form (-2.5 + i4.2)
Answer:
The given complex number is (-2.5 + i4.2).
To express it in exponential form, we need to find the modulus (r) and argument (θ) of the complex number.
The modulus is given by:
|r| = √((-2.5)^2 + (4.2)^2) = √(6.25 + 17.64) = √23.89 ≈ 4.888
The argument is given by:
θ = tan⁻¹(4.2/(-2.5)) = tan⁻¹(-1.68) ≈ -1.03 radians
Therefore, the exponential form of the complex number is:
(-2.5 + i4.2) = 4.888e^(-i1.03)
What is the volume of this rectangular prism 2, 7/3, 2
Answer:
The volume V of a rectangular prism is given by the formula V = lwh, where l, w, and h are the length, width, and height, respectively.
In this case, we have l = 2, w = 7/3, and h = 2. Therefore, the volume is:
V = (2)(7/3)(2)
V = 28/3
V = 9.33 (rounded to two decimal places)
So the volume of the rectangular prism is approximately 9.33 cubic units.
Please help!!
Complete the identity
cos^2 θ/2=?
Answer:
cos^2 θ/2 = (cos θ + 1)/2.
Step-by-step explanation:
We can use the identity cos 2θ = 2cos^2 θ - 1 to derive an identity for cos^2 θ/2:
cos 2(θ/2) = cos θ
Replacing θ/2 with x:
cos 2x = cos 2(x/2)
Using the double angle formula for cosine:
cos 2x = 2cos^2 x - 1
Substituting θ/2 for x:
cos θ = 2cos^2 (θ/2) - 1
Rearranging this formula, we can solve for cos^2 θ/2:
2cos^2 (θ/2) = cos θ + 1
cos^2 (θ/2) = (cos θ + 1)/2
Therefore, cos^2 θ/2 = (cos θ + 1)/2.
What is 974.362 rounded to the nearest tenth
Answer:
974.4
Step-by-step explanation:
Answer:
974.4
Step-by-step explanation:
The tenth place is located the digit to the right of the decimal point, in this case, it will be three. When rounding, if it is four or below you keep it, or if it is five or above, you round up to the nearest ten.
974.362 - 6 is above 5, so you will make the three a four.
974.4
A decimal to the hundredths place is greater than 5.58 and less than 5.88.The digit in the tenths place is odd, and the digit in the hundredths place is even. What are all the possible decimals?
The pοssible decimals that satisfy the given cοnditiοns are:5.20, 5.22, 5.24, 5.26, 5.28, 5.60, 5.62, 5.64, 5.66, 5.68, 7.20, 7.22, 7.24, 7.26, 7.28, 7.60, 7.62, 7.64, 7.66, 7.68
What are decimals?Decimals are a way οf expressing numbers that fall between whοle numbers, using a decimal pοint tο separate the whοle number and the fractiοnal part. Each digit tο the right οf the decimal pοint represents a decreasing pοwer οf 10, starting frοm tenths, hundredths, thοusandths, and sο οn.
Since the digit in the tenths place is οdd, it can οnly be 5 οr 7. Similarly, since the digit in the hundredths place is even, it can οnly be 0, 2, 4, 6, οr 8.
Therefοre, the pοssible decimals that satisfy the given cοnditiοns are:
5.20
5.22
5.24
5.26
5.28
5.60
5.62
5.64
5.66
5.68
7.20
7.22
7.24
7.26
7.28
7.60
7.62
7.64
7.66
7.68
Nοte that these are the οnly pοssible decimals that satisfy all the given cοnditiοns.
To learn more about decimals from the given link:
https://brainly.com/question/29765582
#SPJ1
Which expression is equivalent to (5−4i)(3−2i)(5−4i)(3−2i)?
The given expression equivalent to (5−4i)(3−2i)(5−4i)(3−2i) is -231 + 372i.
What is expression ?
In mathematics, an expression is a combination of numbers, variables, and operations that represents a value or a quantity. It can be a simple expression consisting of only one number or variable, or a complex expression consisting of several numbers, variables, and operations.
We can use the distributive property of multiplication to expand the given expression as follows:
(5−4i)(3−2i)(5−4i)(3−2i)
= (5−4i)(5−4i)(3−2i)(3−2i)
= (25 - 40i + 16i²)(9 - 12i + 4i²)
= (25 - 40i - 16)(9 - 12i - 4)
= (-231 + 372i)
Therefore, the given expression equivalent to (5−4i)(3−2i)(5−4i)(3−2i) is -231 + 372i.
To know more about expression visit :
https://brainly.com/question/1859113
#SPJ1
Find volume in terms of pi
The volume of the figure is 93π
How to determine the volume of the figureFrom the question, we have the following parameters that can be used in our computation:
The composite figure
The volume is calculated as
Volume = Cone + Cylinder
Using the above as a guide, we have the following:
Volume = 1/3πr²(H - h) + πr²h
Substitute the known values in the above equation, so, we have the following representation
Volume = 1/3π * 3² * (15 - 8) + π * 3² * 8
Evaluate
Volume = 93π
Hence, the volume is 93π
Read more about volume at
https://brainly.com/question/463363
#SPJ1
Design n activity to teach Grade R learners about sharing with remainders. Indicate theme in which your activity will be based on
Use the cookies to teach basic fractions, such as one-half or one-third of a cookie.
What is Activity ?
An activity is a task, exercise, or action that is carried out for a specific purpose or goal. It can be an organized event or a spontaneous action that requires some level of effort or engagement from participants.
Begin by gathering the Grade R learners together and introduce the theme "Sharing Treats with Friends" and the concept of sharing with remainders. Explain to the learners that sometimes when we share treats with our friends, we might not have enough for everyone to have an equal amount.
Place the bag of cookies on the plate and ask the learners to estimate how many cookies are in the bag. Write their guesses on the board or chart paper.
Open the bag of cookies and count how many there are. Record the actual number of cookies on the board or chart paper.
Explain that the learners will be sharing the cookies with their friends, but they must make sure that everyone gets the same number of cookies. Divide the class into small groups of three or four learners.
Instruct each group to count the number of cookies in the bag and divide them equally among the members of the group. If there are any remaining cookies, they should be placed on the plate.
Ask the learners to share their results with the class. Some groups may have exactly the same number of cookies, while others may have remainders. Write their results on the board or chart paper.
Discuss with the learners how they can share the remaining cookies equally among their group members. For example, they could break the remaining cookies into smaller pieces or take turns sharing the last cookie.
Give the learners a chance to practice sharing with remainders by repeating the activity with different amounts of cookies and different group sizes.
As a conclusion, ask the learners to reflect on the activity and discuss how it felt to share with their friends. Encourage them to think about why sharing is important and how it can make everyone feel happy.
Optional extension activities:
Have the learners draw pictures or write stories about sharing treats with their friends.
Therefore, Use the cookies to teach basic fractions, such as one-half or one-third of a cookie.
To learn more about Activity from given link.
https://brainly.com/question/14805534
#SPJ1
How can you determine how many solutions a quadratic function has?
Determining how many x-intercepts the graph has
O Determining how many y-intercepts the graph has
Looking to see if the function opens downward
Looking to see if the function opens upward
Determing how many x intercepts the graph has, as those are the points when y = 0.
Simplify (6x2 − 3 − 5x3) − (4x3 + 2x2 − 8).
9x^3 + 4x^2 + 5
Explanation:
Let's simplify step-by-step.
6x^2−3−5x^3−(4x^3+2x^2−8)
Distribute the Negative Sign:
=6x^2−3−5x^3+−1(4x^3+2x^2−8)
=6x^2+−3+−5x^3+−1(4x^3)+−1(2x^2)+(−1)(−8)
=6x^2+−3+−5x^3+−4x^3+−2x^2+8
Combine Like Terms:
=6x^2+−3+−5x^3+−4x^3+−2x^2+8
=(−5x^3+−4x^3)+(6x^2+−2x^2)+(−3+8)
=−9x^3+4x^2+5
Ryan, a consumer electronics salesperson, earns a base salary of $1400 per month and a commission of 5% on the amount of sales he makes. One month Ryan received a $1710 paycheck. Find the amount
Answer:
Let x be the amount of sales Ryan made in that month.
Ryan's commission on the sales would be 5% of x, which is 0.05x.
Adding the commission to his base salary gives his total income for the month, which is $1400 + 0.05x.
Since his paycheck for the month was $1710, we can write the equation:
$1400 + 0.05x = $1710
To solve for x, we can first subtract $1400 from both sides:
0.05x = $310
Then divide both sides by 0.05:
x = $6200
Therefore, Ryan made $6200 in sales that month.
write the equation of a line parallel to 12x+8y=-40 through the point (6,-3)
Answer: To find the equation of a line parallel to 12x + 8y = -40, we need to first rearrange the equation into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
12x + 8y = -40
8y = -12x - 40
y = -1.5x - 5
So, the slope of the line is -1.5.
Since the line we want is parallel to this line, it will have the same slope, which is -1.5. Now we can use the point-slope form of a line to find the equation:
y - y1 = m(x - x1)
where (x1, y1) is the point through which the line passes, and m is the slope.
Substituting (6,-3) and -1.5 for x1, y1, and m respectively, we get:
y - (-3) = -1.5(x - 6)
y + 3 = -1.5x + 9
y = -1.5x + 6
So the equation of the line parallel to 12x + 8y = -40 through the point (6,-3) is y = -1.5x + 6.
Step-by-step explanation:
Emilia is designing a prize wheel for her school. 200 students will spin the wheel once each. Emilia wants the expected number of winners to be 90. If the wheel is split into 40 equal-sized sections, how many of the sections should be marked as "win"?
What transformation is happening? (x,y) —> (2x, 3y)
The scaling factors need not be the same, and this transformation scales the x-axis by a different factor than the y-axis, resulting in a non-uniform scaling.
What is Transformation axes ?
Transformation axes refer to the new coordinate axes after a transformation is applied to a given set of coordinates or points.
The transformation (x, y) → (2x, 3y) is a linear transformation that stretches the x-coordinate by a factor of 2 and the y-coordinate by a factor of 3, while keeping the origin fixed.
This transformation is an example of a scaling transformation, where the scale factor along the x-axis is 2 and along the y-axis is 3.
Visually, this transformation will stretch out the graph horizontally and vertically, making objects appear larger or smaller depending on their position relative to the x and y axes.
Therefore, The scaling factors need not be the same, and this transformation scales the x-axis by a different factor than the y-axis, resulting in a non-uniform scaling.
To learn more about Transformation axes from given link.
https://brainly.com/question/30553600
#SPJ1
The displacement (in meters) of a particle moving in a straight line is given by the equation of motion s = 2/ t^2 , where t is measured in seconds. Find the velocity (in m/s) of the particle at times t = a, t = 1, t = 2, and t = 3.
As a result, the particle's velocity changes as time passes. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3.
What about the equation's meaning?A mathematical equation, such as 6 x 4 = 12 x 2, states that two numbers or values are equivalent. a meaningful noun. When several or even more components need to be taken into account simultaneously in order to comprehend or describe the entire situation, an equation is used.
The derivatives of the displacing equation with time as a parameter is the particle's velocity.
v = ds/dt = d/dt (2/t²) = -4/t³
As a result, the particle's velocity at times t = a, t = 1, t = 2, and t = 3 is as follows:
v(a) = -4/a³
v(1) = -4/1³ = -4 m/s
v(2) = -4/2³ = -0.5 m/s
v(3) = -4/3³ = -0.15 m/s
The particle's velocity consequently varies over time. It is -4/a³ m/s at time t = a, -4 m/s at time t = 1, -0.5 m/s at time t = 2, and -0.15 m/s at time t = 3. Due to the fact also that velocity is negative for any and all values of t, the particle is travelling in the reverse way (i.e., to the left).
To know more about Equation visit:
https://brainly.com/question/649785
#SPJ1
Use Pattern blocks to represent each multiplication equation. recall that a hexagon represents 1 whole.
Pattern blocks are shapes that are used to illustrate math equations. They can be used to represent addition, subtraction, multiplication and division. If five hexagons are stacked on top of each other, then the equation can be read as 5 x 1.
What are pattern blocks?Pattern blocks are a great visual tool for teaching younger children basic multiplication. They can help children understand the concept of multiplication better, as well as help them to remember the equation. Pattern blocks are also a great way to show the relationship between addition and multiplication, since both equations can be represented using the same shapes. By using pattern blocks to illustrate multiplication equations, children can have a more concrete understanding of the concept.
For multiplication, there are two different ways to use pattern blocks. The first way is to use the number of sides on a pattern block to represent the multiplication equation. For example, if two hexagons are used to represent 2 x 2, then the equation can be read as two times two. The second way is to simply stack the pattern blocks in order to represent the equation. For example, if five hexagons are stacked on top of each other, then the equation can be read as 5 x 1.
For more questions related to shapes,
https://brainly.com/question/28756579
#SPJ1
9. Leroy received a stamp for his collection as a gift. When he received the stamp, it was worth $14.50.
The value of the stamp increases by 2% each year.
a. Write an equation for the value of the stamp V after t years.
b. Use the equation to predict the value of the stamp after 18 years.
Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.
What is equation ?A mathematical assertion that two expressions are equivalent is known as an equation. The equal symbol (=) separates the two sides, which are labeled as the left-hand side (LHS) and the right-hand side (RHS). The equation must have identical values on both sides, and it is frequently used to determine an unknown variable's value.
Numerous mathematical processes, such as addition, subtraction, multiplication, division, exponents, logarithms, and more, can be used in equations.
given
a. The formula for the stamp's worth V after t years is as follows:
[tex]V = 14.50(1 + 0.02)^t[/tex]
where t is the period of time since Leroy got the stamp, and 0.02 denotes a 2% annual increase in value.
b. We enter t = 18 into the equation to estimate the stamp's value after 18 years:
[tex]V = 14.50(1 + 0.02)^{18[/tex]
[tex]V = 14.50(1.02) (1.02)^{18[/tex]
V = 14.50(1.485) (1.485)
V = 21.54
Therefore, the stamp's estimated value is $21.54 considering that when he first got it, it was only worth $14.50.
To know more about equation visit:
brainly.com/question/649785
#SPJ1
Which equations can be used to find the lengths of the legs of the triangle? Select three options.
0.5(x)(x + 2) = 24
x(x + 2) = 24
x2 + 2x – 24 = 0
x2 + 2x – 48 = 0
x2 + (x + 2)2 = 100
Given : A = 24 sq feet
A = 0.5 base x height
base = x , height = x+2
A = 0.5 x(x+2) = 24 sq feet
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
To check the rest un-wrap the bracket:
x^2 + (x+2)^2 = 24
x^2 + x^2 + 4 + 4x = 24
2x^2 + 4x - 20 = 0
x^2 + 2x - 10= 0 (NO)
Likewise:
x^2 + (x+2)^2 = 100
x^2 + x^2 +4 + 4x = 100
2x^2 + 4x + 4 = 100
2x^2 + 4x - 96 = 0
3) x^2 + 2x - 48 = 0 (F)
To sum up: that's what apply:
1) 0.5 x(x+2) = 24 (A)
2) x^2 + 2x - 48 = 0 (D)
3) x^2 + 2x - 48 = 0 (F)
Everything step by stepped
The number of touchdowns scored by this professional football team could be: C. 10.
What is a percentage?In Mathematics, a percentage simply refers to any number that is expressed as a fraction of hundred (100). This ultimately implies that, a percentage indicates the hundredth parts of any given number.
In order to determine the number of points scored by the defense of this professional football team, we would use the following mathematical expression:
Number of points = 24/100 × 242
Number of points = 0.24 × 242
Number of points = 58.08
For the number of touchdowns, we have:
Number of touchdowns = 58.08/6
Number of touchdowns = 9.68 touchdowns.
Read more on percentage here: brainly.com/question/11360390
#SPJ1
Cómo convertir 3000m a km
Answer:
Step-by-step explanation:
1000m = 1km
So 3000m = 3km
why is it not possible to form a right triangle with the lengths 4, 8, and 10? please explain!
Answer:
It is not possible to form a right triangle with the lengths 4, 8, and 10 because the longest side of the triangle must be shorter than the sum of the other two sides. This is known as the Pythagorean Theorem, which states that in a right triangle, the square of the longest side (the hypotenuse) is equal to the sum of the squares of the other two sides. Since 8² + 10² = 164, and 10 is greater than the sum of 4 + 8, it is not possible to form a right triangle with those three lengths.
In this case, assuming that 10 is the hypotenuse, we have:
10² = 4² + 8²
100 = 16 + 64
This equation is not true, as 100 is not equal to 80. Therefore, we cannot form a right triangle