[tex]\bf \textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} a,b=&\stackrel{bases}{parallel}\\ &sides\\ h=&height\\ \cline{1-2} a=&2\\ b=&6\\ A=&24 \end{cases}\implies 24=\cfrac{h(2+6)}{2}\implies 24=\cfrac{h(8)}{2} \\\\\\ 24=4h\implies \cfrac{24}{4}=h\implies 6=h[/tex]
choose two correct answers
the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:
- Option C: [tex]\(\frac{1}{2}k\)[/tex]
- Option D: [tex]\(k + 2\)[/tex]
The correct option is (C) and (D).
the calculation step by step to find expressions equivalent to [tex]\(k - \frac{k}{2}\):[/tex]
1. Given Expression:
[tex]\[ k - \frac{k}{2} \][/tex]
2. Step 1: Find a Common Denominator:
To combine the fractions, we need a common denominator. The common denominator for \(2\) and \(1\) is \(2\). So, let's rewrite the expression:
[tex]\[ k - \frac{k}{2} = \frac{2k}{2} - \frac{k}{2} \][/tex]
3. Step 2: Subtract the Fractions:
Subtract the numerators while keeping the common denominator:
[tex]\[ \frac{2k - k}{2} = \frac{k}{2} \][/tex]
4. Step 3: Simplify:
Divide the numerator by (2):
[tex]\[ \frac{k}{2} = \frac{1}{2}k \][/tex]
Therefore, the expressions equivalent to [tex]\(k - \frac{k}{2}\)[/tex] are:
- Option C: [tex]\(\frac{1}{2}k\)[/tex]
- Option D: [tex]\(k + 2\)[/tex]
What’s the smallest zero for the function h(x)=4x^2-8x-60
Answer:
-3
Step-by-step explanation:
In order to find the smallest zero, we will have to find out all the zeros of the function.
In case you are wondering what a zero is, it is the x-value or the domain intersections. The points where the parabola intersects the x-axis.
4x² - 8x - 60 = 0
Why zero?
We know that the parabola intersects the x-axis and when it does, the y-value is 0. h(x) is nothing but 'y'.
4(x²-2x-15) = 0 → I took the gcd as 4 and did it accordingly.
x² - 2x - 15 = 0 → Divide on both sides with 4
Now, what multiples to -15 but adds up to -2?
-5 and 3
x² + 3x - 5x - 15 → Grouping the terms
x ( x + 3 ) - 5 ( x + 3 ) → Taking the GCD in both groups
( x - 5 ) ( x + 3 ) = 0
x = 5 , -3
The smallest one out of these zeros is -3.
Hope it helps! :)
How do I set up the equation for this?
If your average speed is 55 mph, how long will it take you to drive 248 miles?
Answer:
Speed = Distance ÷ Time
time = distance ÷ speed
Step-by-step explanation:
248 ÷ 55 * 60 = 270.54 minutes
a food truck sells tacos, burrito, and drinks.
Let event A = A customer buys a taco
Let event B = A customer buys a drink
What does P(A or B) = 0.60 mean in terms of this problem?
A) The probability that a customer buys both a taco and a drink is 60%.
B) Buying a taco and buying s drink are mutually exclusive events.
C) The probability that a customer buys either a taco or a drink is 60%.
D) The probability that a customer buys neither a taco nor a drink is 60%.
Answer:
Option C is correct.
Step-by-step explanation:
P(A or B) represents that event A has occurred or event B has occurred or both events A and B are happening.
We are given P(A or B) = 0.60 or 0.60/100 = 60%
So, Option C The probability that a customer buys either a taco or a drink is 60% is correct.
Answer: Option C
Step-by-step explanation:
For two events A and B, P(A or B) represents the probability that event A occurs, or event B occurs.
In this case, event A represents a customer buys a taco and event B represents a customer buys a drink. We know that
[tex]P (A\ or\ B) = 0.60[/tex]
So this means that the probability that a customer buys either a taco or a drink is 60%
The answer is the option C
i neeed helpppp can someone help me?
Answer:
-8/5
Step-by-step explanation:
The thing that makes lines different from other kinds of curves is their constant rate of change. We call this rate of change slope, and you usually see it represented with the letter m. We measure it as the rate our y-coordinate changes for some amount our x-coordinate changes.
We're given the two points (-1, 4), and (4, -4). From that first point to the second one, our x-coordinate increases by 5, while our y-coordinate decreases by 8, so our change in y is -8 for every 5 in the positive x direction, and we'd write our slope as
m = -8/5
50 points An unknown number x is at most 20. Which graph best represents all the values of x? (1 point) Number line graph with closed circle on 20 and shading to the right. Number line graph with open circle on 20 and shading to the right Number line graph with closed circle on 20 and shading to the left. Number line graph with open circle on 20 and shading to the left
At most means it can either equal 20 or be less than 20.
On a number line, there would be a closed circle on the number 20 and the area to the left of 20 would be shaded.
Number line graph with closed circle on 20 and shading to the left.
Please Help! Asap! I’m on a deadline!!
Answer:
the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and
Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂
so, the parallelogram is rhombus.
Step-by-step explanation:
A parallelogram is a rhombus if diagonals intersect each other at right angle and the diagonals intersect at mid point.
We are given vertices:
A(-3,2)
B(-2,6)
C(2,7)
D(1,3)
The diagonals of the parallelogram will be:
AC and BD.
Slope of AC = y₂ - y₁ / x₂- x₁ where A = (-3,2) and C = (2,7)
Putting values:
Slope of AC = 7-2/2-(-3) = 5/5
Slope of AC = 1
Slope of BD = y₂ - y₁ / x₂- x₁ where B = (-2,6) and D = (1,3)
Putting values:
Slope of BD = 3-(6) / 1-(-2) = -3/3
Slope of BD = -1
AS, Slope of AC = - 1/ Slope of BD
So, the diagonals intersect and right angle.
Now finding the mid point Z₁ of AC and Z₂ of BD:
Midpoint of AC = Z₁ = A+C/2
Putting values:
=(-3,2) + (2,7) / 2
= (-1,9)/2
= (-1/2, 9/2)
Mid point of BD = Z₂ = B+D / 2
Putting values:
=(-2,6) + (1,3) / 2
= (-1,9)/2
= (-1/2, 9/2)
Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂ i.e.
Z₁ = Z₂, the diagonals intersect at the same midpoint.
As,
the diagonals intersect at right angle i.e. slope of AC = - 1/ slope of BD and
Midpoint of AC = Z₁ is equal to Mid point of BD = Z₂
so, the parallelogram is rhombus.
What is the volume of a right circular cylinder with a radius of 3 in, and a height of 10 in?
Answer: 90[tex]\pi \\[/tex]
Step-by-step explanation:
Final answer:
The volume of a right circular cylinder with a radius of 3 inches and a height of 10 inches is calculated using the formula V = πr²h, which gives 282.74 cubic inches.
Explanation:
To calculate the volume of a right circular cylinder, you can use the formula V = πr²h, where 'V' is the volume, 'r' is the radius, and 'h' is the height of the cylinder. In this instance, the radius (r) is 3 inches, and the height (h) is 10 inches.
Using these values, you can plug them into the formula:
V = π × (3 in)² × 10 in
V = 3.14159 × 9 in² × 10 in
V = 3.14159 × 90 in³
V = 282.74 in³
Therefore, the volume of the cylinder is 282.74 cubic inches.
I need help please!!
Answer:
about 32.9
Step-by-step explanation:
By looking at the triangle, you can see that there is both an angle and a side provided. This allows you to use trigonometry (sin, cos, tan). You have to use tan to find the answer since it is used when you have either the opposite side or adjacent side and are solving for one of them. You take the tangent of the angle and set it equal to the opposite over the adjacent (see image attached).
I hope this helps.
Also sorry that the image is the wrong way, but it wouldn't let me attach it the right way.
QUESTION 1
Given a right triangle, the unknown side is opposite to the 35° angle.
The side adjacent to this angle is 47 units.
We use the tangent ratio to get:
[tex] \tan(35 \degree) = \frac{opposite}{adjacent} [/tex]
[tex] \tan(35 \degree) = \frac{x}{47} [/tex]
[tex] x = 47\tan(35 \degree)[/tex]
[tex]x = 32.9units[/tex]
to the nearest tenth.
QUESTION 2
The given angle is 47°
The opposite side is x units.
The adjacent side is 40 units.
We again use the tangent ratio to obtain:
[tex] \tan(47 \degree) = \frac{x}{40} [/tex]
[tex]x = 40\tan(47\degree) [/tex]
[tex]x = 42.9units \: to \: the \: nearest \: tenth[/tex]
Approximately how many accidents occurred between 1965 and 1970 inclusive?
Answer:
About 1,800 accidents
Step-by-step explanation:
Observing the attached figure
In 1965 ----> Approximately 260 accidents
In 1966 ----> Approximately 325 accidents
In 1967 ----> Approximately 300 accidents
In 1968 ----> Approximately 350 accidents
In 1969 ----> Approximately 360 accidents
In 1970 ----> Approximately 400 accidents
Total------> Approximately 1.920 accidents
which of the following is the best definition of a vertical asymptote
Answer:
Step-by-step explanation:
B
Answer: Option A: A vertical line that the line of the graph aproaches but never intecepts it.
Step-by-step explanation:
An asymptote is a graph line that aproaches infinitely to something (in this case a vertical line), but it does not touch it (so never intercepts the graph).
This means that the graph aproaches but never intercepts the line, so the correct answer is A.
The charge for a plumbing repair was $29.60 for parts, 1 1/4 hr. For labor at $56 per hr. And a $40 for the service call. What was the total cost (c) of the repair?
Answer: $139.60
Step-by-step explanation:
$40 for coming
$29.60 for parts
56 times 1.25 for labor = 70
70 + 29.6 + 40 = 139.6
The total cost (c) of the repair is given by the sum of the costs for parts, labor, and the service call that is [tex]\$139.60[/tex]
First, we calculate the labor cost. The plumber charged $56 per hour and worked for 1 1/4 hours. To find the total labor cost, we multiply the hourly rate by the time worked:
Labor cost = [tex]hourly \ rate \times \ time \ worked[/tex]
Labor cost =[tex]\$56 \times 1 1/4 hours[/tex]
Labor cost =[tex]\$56 \times (1 + 1/4) hours[/tex]
Labor cost = [tex]\$56 \times (5/4) hours[/tex]
Labor cost = [tex]\$56 \times 1.25 hours[/tex]
Labor cost = $70
Next, we add the cost for parts and the service call to the labor cost to find the total cost:
Total cost (c) = cost for parts + labor cost + service call cost
Total cost (c) = $29.60 + $70 + $40
Total cost (c) = $139.60
There were 442 students at Deerlake Middle School who voted on a theme for the spring carnival. Those who voted represent 76% of the entire student population. About how many students attend Deerlake Middle School?
A. 106
B.336
C.582
D.1842
Don't just guess. :p
Answer:
Option C is correct.
Step-by-step explanation:
Number of students of Deerlake middle school that voted = 442
Percentage of student that voted = 76%
Let x be the total number of student.
According to the Question,
[tex]\frac{76}{100}\times x=442[/tex]
[tex]x=442\times\frac{100}{76}[/tex]
[tex]x=582[/tex]
Therefore, Option C is correct.
What is the smallest two-digit prime number?
Answer: 11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
the prime numbers (1-15 is the furthes i will go for this) are 2,3,5,7,11,13
as you can see the smallest two didget prime number is 11------------
The formula for the perimeter of an equilateral triangle is p=3s. What is the perimeter?
In order to answer this, you have to have the unit of measurement and an illustration.
PLEASE HELP WILL MARK
Answer:
( 8.5 , 6.5 )
Step-by-step explanation:
Midpoint formula = ( x₁ + x₂ / 2 ) , ( y₁ + y₂ / 2 )
x₁ = 4
x₂ = 13
y₁ = 10
y₂ = 3
Midpoint = ( 4 + 13 / 2 ) , ( 10 + 3 / 2 )
Midpoint = ( 17 / 2 ) , ( 13 / 2 )
Midpoint = 8.5 , 6.5
When the point (-3,7) is dilated with the center of dilation at the origin, then the image of
the point is (-12.75, 29.75).
What is the scale factor of this dilation?
1) 4
2) 4.25
3) 9.75
4) 10
Answer:
4.25
Step-by-step explanation:
To find the scale factor divide the image coordinates by the original coordinates, that is
scale factor = [tex]\frac{-12.75}{-3}[/tex] = [tex]\frac{29.75}{7}[/tex] = 4.25
The answer would be 4.25
What is the circumference of a circle with a diameter of 7 inches? (use for pi) PLEASE HELP ASAP
Answer:
C = 7pi = 21.98 inches
Step-by-step explanation:
The circumference of a circle is given by
C = pi * d
where d is the diameter
C = pi * 7
If we use 3.14 as an approximation for pi
C = 3.14 * 7
C =21.98 in
Cara plants 5 seeds in 2 minutes, while Wade plants 3 times as many seeds in half the time. How many seeds can they both plant together in 10 minutes?
Answer:
together they can plant 175 seeds in 10 minutes
Answer with Step-by-step explanation:
Cara plants 5 seeds in 2 minutes.
⇒ Cara plants 5×5 seeds in 2×5 minutes
⇒ In 10 minutes Cara plant 25 seeds.
Wade plants 3 times as many seeds in half the time as Cara.
⇒ Wade plants 3×5 seeds in 2/2 minutes
i.e. Wade plants 15 seeds in 1 minute.
In 1×10 minutes Wade plants 15×10 seeds
i.e. In 10 minutes Wade plants 150 seeds.
150+25=175
Hence, they can together plant 175 seeds in 10 minutes.
A pencil manufacturer uses 5,376 grams of rubber to make 960 pencils. If they use 64,512 grams of rubber an hour, how many pencils are made per hour?
A) 11,420 pencils per hour
B) 11,480 pencils per hour
C) 11,520 pencils per hour
D) 11,580 pencils per hour
This answer would be C because I had worked out answer good
For this case, we look for the number of pencils per gram of rubber.
[tex]\frac {960} {5,376} = 0.178571428571[/tex]
0.178571428571 pencils per gram of rubber are made
We are looking for the number of pencils per hour.
[tex]0.178571428571 \frac {penc} {g} * 64,512 \frac {g} {h} = 11,520 \frac {pen} {h}[/tex]
Thus, 11,520 pencils per hour are made.
Answer:
Option C
What is the value of
x3 + 4, when x = 6?
I'm not sure if you meant to write 3x or [tex]x^{3}[/tex] instead of x3 but I will work out both versions just in case
In the equation 3x + 4 plug 6 in for x
3(6) + 4
Multiply 3 and 6 first
18 + 4
Add 18 and 4
22
OR
In the equation [tex]x^{3}[/tex] + 4 plug 6 in for x
[tex]6^{3}[/tex] + 4
Solve the exponent
(6*6*6) + 4
216 + 4
Add the numbers together
220
Hope this helped!
Answer:
220
Step-by-step explanation:
Im going to assume x3 equals x^3, so 6^3 is 216, add this to 4 and get 220
Two different functions are represented.
Function A:
X- 0,1,2,3,4
F(X)- 5,10,20,40,80
Function B- y=4/x
Which statement best compares the two functions?
Neither function A nor function B has an x-intercept.
Neither function A nor function B has a y-intercept.
The domain and range of both functions contain only positive numbers.
The domain and range of both functions contain only positive numbers and zero.
Answer:
Neither function A nor function B has an x-intercept.
Step-by-step explanation:
Function A has a y-intercept at (0, 5).
Function B is defined for negative numbers as well as positive numbers, but not for x=0.
These observations eliminate all answer choices but the first one.
The statement that best compares the two functions is; Neither function A nor function B has an x-intercept.
How to Interpret Functions?A y-intercept is the point where x = 0. Now, for function A we can see that when x = 0, y = 5. Thus, it has a y-intercept.
However, we are not given the point where y = 0 which is x-intercept. Thus, function A does not have an x-intercept.
Formula for Function B is y = 4/x.
This function does not have an x-intercept because at x = 0, the function is undefined.
Read more about Functions at;https://brainly.com/question/3951754
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what are the solutions to the equation x^2 + 4x+5=0
Help ASAP
Answer:
Let's solve your equation step-by-step.
x2+4x+5=0
Step 1: Use quadratic formula with a=1, b=4, c=5.
x=
−b±√b2−4ac
2a
x=
−(4)±√(4)2−4(1)(5)
2(1)
x=
−4±√−4
2
Answer:
No real solutions.
Answer:
x=-2+-i
Step-by-step explanation:
Solve the equation for x by finding a, b, c of the quadratic then applying the quadratic formula.
brainly what is the leanth of the line segment with endpoints (-6,-8) and (7,-8)
Answer:
The length of the line segment is 13 units
Step-by-step explanation:
The line segment joining the two points is horizontal since the y co-ordinate is the same.
For a horizontal line, the length of the line segment is simply the difference between the x co-ordinate values.
In this case we have;
7 - (-6) = 7 + 6 = 13
Therefore, the length of the line segment is 13 units
Answer:
13 units
Step-by-step explanation:
We want to find the length of the line segment with endpoints (-6,-8) and (7,-8).
Observe that, the y-coordinates are the same.
We can quickly use the absolute value method to find the required length.
According to this method the length of the line segment with endpoints (-6,-8) and (7,-8) is the absolute value of the difference between the x-values.
[tex]|7--6|=|7+6|=|13|=13[/tex]
The length of the line segment is 13 units.
60 points !!
Triangle QRS is shown on the coordinate grid. Triangle QRS is dilated with the origin as the center of dilation using the rule (x, y) → ( 1/4 x, 1/4 y) to create triangle Q'R'S'. Which statement is true? A) Triangle Q'R'S' is smaller than triangle QRS, because the scale factor is less than 1. B) Triangle Q'R'S' is larger than triangle QRS, because the scale factor is less than 1. C) Triangle Q'R'S' is larger than triangle QRS, because the scale factor is greater than 1. D) Triangle Q'R'S' is smaller than triangle QRS, because the scale factor is greater than 1.
https://lh3.googleusercontent.com/qPYvRzvroDEYvaSZbKCSiNmf-uxSPXZzCkwcqzIAnhtvrmk7zmrkSt5hQ-lftybdtUCa-A=s91
Answer:
A
Step-by-step explanation:
The triangle is being scaled down by a factor of 1/4. So Q'R'S is smaller than QRS because the scale factor is less than 1. Answer A.
Answer:\
The answer is A :) I took the assignment
(please hurry)Consider this composite figure.
Composite Figure
Apply the formula of each shape to determine the volumes.
What is the exact volume of the composite figure?
V =
π cm³
Answer:
39pi cm 3
Step-by-step explanation:
i just did the assingment
The composite figure is the combination of the two cones. The volume of the composite figure will be 39π cm³.
What is Geometry?It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
The volume of the composite figure.
The composite figure is the combination of the two cones.
[tex]V = \dfrac{1}{3} \times \pi \times 3^2 \times 5 + \dfrac{1}{3} \times \pi \times 3^2 \times 8\\[/tex]
On simplifying, we have
V = 15π + 24π
V = 39π cm³
More about the geometry link is given below.
https://brainly.com/question/7558603
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Please help. I don't understand it. HELP ASAP....
Answer:
[tex]\large\boxed{x\leq-27}[/tex]
Step-by-step explanation:
[tex]\dfrac{x}{-9}\geq3\qquad\text{change the signs}\\\\\dfrac{x}{9}\leq-3\qquad\text{multiply both sides by 9}\\\\9\!\!\!\!\diagup^1\cdot\dfrac{x}{9\!\!\!\!\diagup_1}\leq(-3)(9)\\\\x\leq-27[/tex]
Find the equation in standard form of the line parallel to y=-1/5x+7 and passing through the point (-10,-3)
Answer:
the desired equation is y = (-1/5)x - 5.
Step-by-step explanation:
Parallel lines have the same slope. Here that slope is -1/5.
Let's use the slope-intercept form of the equation of a straight line:
y = mx + b
We know this new line passes through (-10, -3). Substitute -3 for y in y = mx + b, as well as -10 for x and -1/5 for m:
-3 = (-1/5)(-10) + b and solve for b:
-3 = 2 + b. Then b = -5, and the desired equation is y = (-1/5)x - 5.
What’s the area of a 72 ft diameter circle?
Answer:
4069.44
Step-by-step explanation:
a=pie R squared
evaluate 9!/7! PLEASE I NEED HELP
Answer:
72
Step-by-step explanation:
Remember that 9! = 7! (8)(9)
write Substitute
7!(8)(9) for 9!
7!(8)(9)/ 7!= (8)(9)= 72
Answer: 72
Step-by-step explanation:
By definition, it is important to know that the factorial of a non-negative integer "n" is the product of all positive integers less than or equal to "n". This is expressed with an exclamation symbol (!):
[tex]n![/tex]
Then, the rule for this is the following:
[tex]n! = n *(n-1)![/tex]
Therefore, knowing this, you can evalute [tex]\frac{9!}{7!}[/tex] as following:
[tex]\frac{9*8*7*6*5*4*3*2*1}{7*6*5*4*3*2*1}=\frac{362,880}{5,040}=72[/tex]