Given data:
The upper end length of the trapezoid is: a=6 cm
The lower end length of the trapezoid is: b=10 cm
The height of the trapezoid is: h=15 cm
The expression to calculate the area of the trapezoid is,
[tex]A=\frac{1}{2}\times h\times(a+b)[/tex]Substitute vall known values in the above expression.
[tex]\begin{gathered} A=\frac{1}{2}\times15\times(6+10) \\ =\frac{1}{2}\times15\times16 \\ =\frac{240}{2} \\ =120cm^2 \end{gathered}[/tex]Thus, the area of the trapizoid is 120 square centi meter.
Match each exponential function with the graph that correctly models the function.
Answer:
Step-by-step explanation:
1) third graph -> the base is 3 so the graph increase
2) first graph -> if x = 0 ; y = -2
(1/3)^0 -3 = 1 - 3 = -2
3) second graph
A normal distribution has a mean of 75 and a standard deviation of 15.
Determine the z-score for the data value of 85.
0.67
1) Given that we've got the following data:
[tex]\mu=75,\sigma=15,X=85[/tex]We can plug them all together into the Z score formula:
[tex]Z=\frac{X-\mu}{\sigma}=\frac{85-75}{15}=\frac{10}{15}\approx0.67[/tex]Thus, the Z-score is 0.67
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2=1503\\\\t^2 =\frac{1503}{16}\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
does anyone know how to do simplifying expressions with Distributive property 8th grade math
One-fourth of the seventh-grade students
made honor roll in the first quarter. The
number of honor roll students increased by
18 in the second quarter. If 105 students
made honor roll in the second quarter, how
many total seventh graders are there?
There are 348 seventh-grader students in total.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
One-fourth of the students made the honor roll in the first quarter, and it grew by 18 in the second quarter, so add 18, and the total number of students who made the honor roll in the second quarter is 105.
Let the seventh-grade students would be x
As per the given condition, we can write the equation as:
⇒ 1/4 x + 18 = 105
Subtract 18 on both sides of the above equation,
⇒ 1/4 x = 87
Multiply by 4 both sides of the above equation,
⇒ x = 348
Therefore, there are 348 seventh-grader students in total.
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A 6-pack of magnets costs $6.06. What is the unit price?
Answer: $1.01
Step-by-step explanation: You just divide by 6
An empty bucket is being filled at a constant rate. after 4 minutes, the depth of the water is 12 inches. the water continues to be filled at that same rate. what is the relationship between the time in minutes, x, and the depth of the water, y?
Every 4 minutes, the depth of the water increases 12 inches. Like let's say after another 4 minutes it'll be 24 inches. I may be wrong but I may be right.
Answer:
See below
Step-by-step explanation:
Every minute 'x' produces 12/4 = 3 inches of 'y' water depth
y = 3 x
Please help now asap now !!!!!!!!!!!!
Answer: 771
Step-by-step explanation:
Reverse the equation for 96 x 8 + 3
96 x 8 = 768
768 + 3 = 771
You only add the 3 at the end since it was unable to be divided, you can't reverse and multiply it
24 divided by (-3/2)
Need help please:)
given the function y=3x + 5 find the range uf the domain is (-4,-1,2,5,)
The function we have is:
[tex]y=3x+5[/tex]We are given the domain of the function:
[tex]D=(-4,-1,2,5)[/tex]The domain of a function is the allowed values for x.
And we are asked to find the range, which is the values that the function returns for the x-values of the domain.
To find the range, we need to take the values of the domain, substitute them into the equation, and find the values that the function returns.
For the given domain, the allowed values for x are:
[tex]\begin{gathered} x=-4 \\ x=-1 \\ x=2 \\ x=5 \end{gathered}[/tex]For x=-4
We substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(-4)+5 \end{gathered}[/tex]And solve to find the first value of the range:
[tex]\begin{gathered} y=-12+5 \\ y=-7 \end{gathered}[/tex]For x=-1
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(-1)+5 \end{gathered}[/tex]Solve the operations:
[tex]\begin{gathered} y=-3+5 \\ y=2 \end{gathered}[/tex]For x=2
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(2)+5 \end{gathered}[/tex]And again, solve the operations:
[tex]\begin{gathered} y=6+5 \\ y=11 \end{gathered}[/tex]For x=5
Substitute this value into the function:
[tex]\begin{gathered} y=3x+5 \\ y=3(5)+5 \end{gathered}[/tex]Solve the operations:
[tex]\begin{gathered} y=15+5 \\ y=20 \end{gathered}[/tex]The values we have found for y are the range of the function:
[tex]R=(-7,2,11,20)[/tex]Answer:
The range of the function is (-7,2,11,20)
The average weight of a brown bear is 1000 about pounds. suppose a large stuffed animal weighs 6.9 pounds. write a percent to compare the weight of the stuffed animal to the weight of the brown bear.
Answer:
Step-by-step explanation:
0.69
What is the radian equivalent of 90 degrees?
Answer:
The Radiant Equivalent of 90 degrees, would be 1.57079633.
Look at the steps for constructing a perpendicular bisector of a line segment.
Which is an accurate description for step 2?
Draw arcs, using a compass, above and below line segment XY with X as the center with a width of less than half of line segment XY.
Draw arcs, using a compass, above and below line segment XY with X as the center with a width of more than half of line segment XY.
Draw arcs, using a compass, above line segment XY with X as the center and below line segment XY with Y as the center with a width of more than half of line segment XY
Draw arcs, using a compass, above line segment XY with X as the center and below line segment XY with Y as the center with a width equal to the half of the segment XY
The accurate description for step 2 is "Draw arcs, using a compass, above and below line segment XY with X as the center with a width of more than half of line segment XY."
What is Perpendicular Bisector?
A line that divides a line segment into two equal halves and forms a 90-degree angle at the point of intersection is called a perpendicular bisector. The word "bisect" refers to dividing equally.
By looking at the steps for constructing a perpendicular bisector of a line segment.
The accurate description for step 2 is below.
That is "Draw arcs, using a compass, above and below line segment XY with X as the center with a width of more than half of line segment XY."
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What is the image point of (6, -7) after the transformation D4 T3,5?
The final image of the given points after the given translation and dilation of D4, T3,5 is (27, -23).
What is meant by the term transformation?Image transformations usually involve the modification of various bands of data, such as a single multispectral image either from a number of images acquired at different times of the same area (i.e. multitemporal image data). Image transformations, in either case, generate "new" images from a variety of sources that highlight specific features or characteristics of interest more effectively than the original input images.For the given image point of (6, -7) .
First there is a dilation of 4.
Thus,
Image = (6×4 , -7×4)
Image = (24, -28)
Now, there is translation of 3 units right on x axis and 5 unit upward on y axis; T3,5.
Image = (24 + 3, -28 + 5)
Image = (27, -23)
Thus, the final image of the given points after the given translation and dilation is (27, -23).
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which is the correct way to model the equation 5x+6= 4x+(-3)
5 positive x-tiles and 6 positive unit tiles on the left side; 4 p
6 positive x-tiles and 5 positive unit tiles on the left side; 3 m
5 positive x-tiles and 6 negative unit tiles on the left side; 4 side
5 positive x-tiles and 6 positive unit tiles on the left side; 4
please help
The correct model the equation 5x+6= 4x+(-3) is 5 positive x-tiles and 6 positive unit tiles on the left side; 4 positive x-tiles and 3 negative unit tiles on the right side.
What is the model equation?
The model equation is a representation of an equation using tiles.
Given equation is 5x+6= 4x+(-3).
1 is represented by a positive tile.
-1 is represented by a negative tile.
We can rewrite the given equation as:
5×(x)+6× (1)= 4×(x)+(3×(-1))
The model of 5×(x)+6× (1) is 5 positive x-tiles and 6 positive unit tiles.
The model of 4×(x)+(3×(-1)) is 4 positive x-tiles and 3 negative unit tiles.
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what do you think the answer is? No it’s not the 3rd option or not that I think I just clicked a random answer on accident.
Answer
Option C is correct.
Sandra will be paid 72.30 dollars for babysitting for 12 hours.
Explanation
We are told that Sandra earned 60.25 dollars babysitting 10 hours.
If she babysits at the same rate, we are asked to calculate the amount she would earn if she babysits for 12 hours.
Let the amount Sandra is paid for babysitting for 12 hours be x dollars
10 hours = 60.25 dollars
12 hours = x dollars
We can write a mathematical relationship by cross multiplying
10 × x = 12 × 60.25
10x = 723
Divide both sides by 10
(10x/10) = (723/10)
x = 72.3 dollars
Hope this Helps!!!
The lines below are parallel. If the slope of the green line is -1/2,what is theslope of the red line?
When two lines are parallel they mean that both slopes are the same, this means that if the green line has a slope of -1/2, the slope of the red line is also -1/2.
help meeeeeeeeeeeeeee pleaseeeeeee
Answer: 9.7 seconds
Step-by-step explanation:
[tex]16t^2 =1503\\\\t^2 =1503/16\\\\t=\sqrt{1503/16} \text{ } (t > 0)\\\\t \approx 9.7[/tex]
Hey there Ms or Mr could you please help me out with this problem?just so you know, this is Pythagorean theorem & Simplifying Radicals My recent tutor said that this is the answer of course no I don't have any doubts I just want to know if this is correct.
When we have a radical, we can simplify it by the rule:
[tex]\sqrt[]{ab}=\sqrt[]{a}\sqrt[]{b}[/tex]So, we have to break down 500 into simpler radicals until we have a radical that can't be broken down. Let's simplify Root(500).
[tex]\sqrt[]{500}=\sqrt[]{50}\sqrt[]{10}[/tex]Now, we can break down Root(50) further.
[tex]\begin{gathered} \sqrt[]{50}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \end{gathered}[/tex]Now, let's break down Root(10) also, thus we have:
[tex]\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{10} \\ =\sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \end{gathered}[/tex]We can see:
• Root(25) is 5
,• Also Root(2)*Root(2) is 2 by using the rule:
[tex]\sqrt[]{a}\sqrt[]{a}=a[/tex]Thus, we finally have:
[tex]\begin{gathered} \sqrt[]{25}\sqrt[]{2}\sqrt[]{5}\sqrt[]{2} \\ =5(2)\sqrt[]{5} \\ =10\sqrt[]{5} \end{gathered}[/tex]the sum of 10 and 15 divide by the difference 8 and 3 how to translate
We have the following:
[tex]\frac{10-5}{8-3}=\frac{5}{5}=1[/tex]Solve the inequality for e:
negative 3 e greater than 21
Group of answer choices
e greater than negative 63
e less than negative 63
e less than negative 7
e greater than negative 7
The solution of the inequality negative 3 e greater than 21 is e less than negative 7.
Inequality:
If the two real numbers or algebraic expressions are related using the symbols >, <, ≥, ≤, then the expression is called an inequality.
Given,
Here we have the statement for the inequality.
"negative 3 e greater than 21".
Now, we have o solve it and then we have to find the value of e.
The given statement is rewritten as the following expression form,
That is,
-3e > 21
Here we need the value of e, so we have to divide both sides by 3, then we get,
=> -e > 7
To remove the negative sign, we have to reverse the inequality, then we get the value of e as
=> e < -7
Therefore, in statement it can be written as "e less than negative 7".
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I WILL GIVE LOTS OF POINTS
give me the answer for these algebra equations!
The slope intercept form of the required line is x + y = 5
What is equation of line in slope intercept form?
The most general form of equation of line in slope intercept form is given by y = mx + c
Where m is the slope of the line and c is the y intercept of the line.
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
The distance from the origin to the point where the line cuts the x axis is the x intercept of the line.
The distance from the origin to the point where the line cuts the y axis is the y intercept of the line.
The given line is
x + y = 4
y = -x + 4
Slope of the line = [tex]-1[/tex]
Slope of the line parallel to this line = [tex]-1[/tex]
The line passes through (2, 3)
Equation of the required line
y - 3= -1(x - 2)
y - 3 = -x + 2
x + y = 3 + 2
x + y = 5
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a food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. if the sample mean is 15.2 oz and the sample standard deviation is 0.70 oz, find the 95% confidence interval of the true mean.
95% confidence interval is (14.55, 15.85)
From the question, we have
Degrees of freedom = n - 1 = 7 - 1 = 6
For 6 degrees of freedom and 95% confidence interval:
Critical t value = 2.45
95% confidence interval is:
15.2 \pm 2.45*0.70/\sqrt{7}
15.2 \pm 0.65
(14.55, 15.85)
Multiplication:
Mathematicians use multiplication to calculate the product of two or more numbers. It is a fundamental operation in mathematics that is frequently utilized in everyday life. When we need to combine groups of similar sizes, we utilize multiplication. The fundamental concept of repeatedly adding the same number is represented by the process of multiplication. The results of multiplying two or more numbers are known as the product of those numbers, and the factors that are multiplied are referred to as the factors. Repeated addition of the same number is made easier by multiplying the numbers.
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What is the value of x in the equation 25x^2 = 16?O A ±5/4OB. ±4OC. ±4/5OD. ±16/25
Answer:
C. ±4/5
Explanation:
Given the equation
[tex]25x^2=16[/tex]The first step is to divide both sides by 25 to isolate the variable x.
[tex]\begin{gathered} \frac{25x^2}{25}=\frac{16}{25} \\ x^2=\frac{16}{25} \end{gathered}[/tex]Next, we take the square roots of both sides of the equation.
[tex]\begin{gathered} \sqrt{x^2}=\pm\sqrt{\frac{16}{25}} \\ x=\pm\frac{4}{5} \end{gathered}[/tex]The correct choice is C.
8. What is the solution to the following equation? (1 point)
x² - 10x + 24 = 0
Ox= 3 or x = 8
Ox= -3 or x = -8
Ox=4 or x =
Ox=-4 or x = -6
9. Ms. Ortiz sells tomatoes wholesale. The function p(x) = -80x² + 320x
The solution of the equation x² - 10x + 24 = 0 is x = 4 or x = 6. Option C is correct.
We are given a quadratic equation:
x² - 10x + 24 = 0
Let us split the middle term, we will get;
x² - 6x - 4x + 24 = 0
x (x - 6) - 4 (x - 6) = 0
(x - 4) (x - 6) = 0
equate each with zero, we will get;
x - 4 = 0 or x - 6 = 0
x = 4 or x = 6
So, the value of x is 4 or 6.
So, option C full fills the required criteria.
Thus, the solution of the equation x² - 10x + 24 = 0 is x = 4 or x = 6. Option C is correct.
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A rectangular prism gift box has dimensions of 2.5 inches, 7 inches, and 9 inches.How much wrapping paper will it take to cover the gift box? Round answer to the nearest tenth if necessary.
The question requires us to calculate the surface area of the rectangular prism.
The formula to calculate the surface area is given to be:
[tex]A=2\left(wl+hl+hw\right)[/tex]where l is the length, w is the width, and h is the height.
From the question, the following dimensions are provided:
[tex]\begin{gathered} l=2.5 \\ w=7 \\ h=9 \end{gathered}[/tex]Therefore, we can calculate the surface area to be:
[tex]\begin{gathered} A=2(7\cdot2.5+9\cdot2.5+9\cdot7) \\ A=206\text{ in}^2 \end{gathered}[/tex]OPTION C is correct.
20 POINTS! HURRY!!!!Which expressions are equivalent to 5(1/3x+7)-3(1/3x-4)? Select three options.5 1/3x-3 1/2x+35-121/6x+471 2/3x+36-1 1/2x+ 125(1/3x)+(5)(7)-(3)(1/2x)+(3)(4)1 1/3x+35-1 1/2x-12
The given expression is:
[tex]undefined[/tex]The lighthouse flashes every 10 seconds. how many times does it flash in one hour
Answer: It flashes 6 times per minute, so 360 times per hour.
Step-by-step explanation:
6*60
How do you think increased distance will affect travel time?
You can notice that travel time is afected by the traveled distance. That's because it is required more time to travel longer distances.
For instance, if Elena would live 6 miles to the school, she would take 30min to arrive to school. That is, for greater distances the travel time increases.
The expression on the left side of an equation is shown below.
3 (x + 1) + 9 = box
If the equation has no solution, which expression can be written in the box on the other side of the equation?
3 (x + 4)
2 (x + 6) + x
4(x – 3) – x
3 (x + 1) + 9 x
Answer:
C) 4(x – 3) – x
Step-by-step explanation: