Part A
GEOMETRY Consider a trapezoid that has one base that measures five feet greater than its height. The other base is one foot less than twice its height. Let x represent the height.
a. Write an expression for the area of the trapezoid.
A=(blank)x^2 +(blank)x ft^2
PART B Write an expression for the area of the trapezoid if its height is increased by 4 feet
A=(blank)x^2+(blank)x+(blank)ft^2
The area of the trapezoid is 1.5x² + 2x. If the height is increased by 4 feet, the new area would be 1.5x² + 8x
How to solve an equation?An equation is an expression that shows the relationship between two or more numbers.
Let x represent the height of the trapezoid.
a) One base of trapezoid measures five feet greater than its height. Hence:
First base = x + 5
The other base is one foot less than twice its height, hence:
Second base = 2x - 1
Area = (1/2)(sum of bases) * height = (1/2)(x + 5 + 2x - 1)(x) = 1.5x² + 2x
b) The height is increased by 4 feet. New height = x + 4
First base = (x + 4) + 5 = x + 9
Second base = 2(x + 4) - 1 = 2x + 7
Area = (1/2)(sum of bases) * height = (1/2)(x + 9 + 2x + 7)(x) = 1.5x² + 8x
The area of the trapezoid is 1.5x² + 2x.
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consider the trinomial 15x² - 34x - 16.
List all the factor pairs for -240.
Answer: To find the factor pairs for -240, we can use the following steps:
Find the prime factorization of -240: -240 = (-2) * (-2) * (-2) * (-3) * (-5)
For each prime factor, there are two possible factor pairs: (-1) and (1), and (-n) and (n). For example, for the factor -2, the possible factor pairs are (-1) and (1), and (-2) and (2).
The factor pairs for -240 are: (-1) and (1), (-2) and (2), (-3) and (3), (-5) and (5), (-6) and (6), (-10) and (10), (-15) and (15), (-30) and (30).
Thus, the factor pairs for -240 are: (-1, 1), (-2, 2), (-3, 3), (-5, 5), (-6, 6), (-10, 10), (-15, 15), and (-30, 30).
Step-by-step explanation:
Write a number sentence using multiplication ti show what fraction represented on the mumber line is equivalent to 3/4
The fraction that is equivalent to 3/4 is seen as; 6/8
How to represent fractions?A number sentence is defined as a mathematical sentence that is made up of numbers and symbols.
We want to write a number sentence using multiplication to show a fraction that is equivalent to 3/4.
Now, for us to find the final equivalent fraction, what we have to do is that we will divide or multiply by denominator and numerator by the same number that is equal to one e.g 3/3; 5/5; 6/6, etc.
Since we want to find equivalent fraction of 3/4, let us multiply both numerator and denominator by 2 to get;
(3 * 2)/(4 * 2) = 6/8
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Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
Someone pls help!!
Construct a circle through points
X, Y, and Z.
By drawing a side on any one of the points, points X, Y, and Z can be used to create the circle.
What is a circle?It is described as a collection of points, each of which is spaced uniformly apart from a fixed point (called the centre of a circle)
How can you create a circumcircle?First, draw three circles, each with the compass's drawing side on one of the points and the centre on another. The point of your compass should be on that point, and then you should place the drawing side on any one of the three points where they will all intersect in the middle.
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Write three ratios that are equivalent to 75% and three
ratios that are equivalent to 100%.
The three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4 and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.
What is ratio?
A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.
First we have to write the equivalent ratios for 75%.
Since, 75% can be written as,
75/100
Simplifying this, 15/20
Again simplifying this, 3/4
Hence, the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4.
Now to write the equivalent ratios for 100%.
Since, 100% can be written as,
100/100
Simplifying this, 20/20
Again simplifying this, 4/4
Hence, the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.
Therefore, the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4 and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.
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Anna wants to buy 4 sweaters. The sweater come at a discount rate. If you buy one sweater regular price the other sweater is 40% off. How much percent is off of each sweater?
Answer:
20%------------------------
If you buy a sweater, the second one is at 40% discount.
Divide the discount between the two to get:
40%/2 = 20%You get a discount of 20% for each sweater.
Answer:
Discount percentage = 20%
Step-by-step explanation:
Discount of the sweaters,
→ first sweater = 0%
→ other sweater = 40%
The average discount percent is,
→ (first sweater + other sweater)/2
→ (0% + 40%) ÷ 2
→ (0 + 40)/2
→ 40/2
→ 20% off
Hence, the answer is 20% off.
In a set of 100 ACT scores that are normally distributed and with a mean of 23 and standard
deviation of 4.69, (a) how many scores are expected to be lower than 18.31 (one standard
deviation below the mean)? (b) How many of the 100 scores are expected to be below 32.38 (two
standard deviations above the mean)?
a). The number of scores which are expected to be lower than 18.31 is; 16 scores.
b). The number of scorers that are expected to be below 32.38 is; 98 scores.
Calculations involving normal distribution.As evident in the task content; the 100 ACT scores in discuss are normally distributed, hence, all peculiar characteristics of a normal distribution apply.
First, since the mean is given as; 23 and the standard deviation is; 4.69.
By observation; 23 - 4.69 = 18.31 and
23 + 4.69 + 4.69 = 32.38.
a). Since the percentage of data values which fall below one standard deviation below the mean is; 15.9% which is approximately; 16%.
Therefore, the number of scores below the 18.31 score is; 16% of 100 = 16 scores.
b). Also, since the score; 32.38 is 2 standard deviations above the mean, and it follows from a normal distribution that the percentage of data values below such data value is; 97.7% which is approximately 98%.
Therefore, the number of scores which are expected to be below 32.38 is; 98% of 100 = 98.
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My new year's resolution using mathematics word essay 200 words
Use the image below to answer the questions that follow:
** I can't upload the image but the Whole Math problem is in the Link I added to make it easier! **
(The image is Half of a house on one side of the graph)
Question 1. What type of symmetry would be used to complete the image of the house?
Question 2. What is the equation of the line of symmetry (or the point of symmetry if there is one) for the image?
Question 3. Use the rules of symmetry to determine 13 ordered pairs that would need to be plotted so that they can be connected by lines to complete the image of the house
Question 4. Complete the image of the house by plotting the points from the previous question and connecting the dots. You may copy the image into a drawing program to complete this task electronically, or you may print the image and upload a hand-drawn image to this document. Be sure to label the points.
Answer:
I can't please the question is sooo hard but can you give steps
a) Find the total mass in kilograms of 3500 books, each with mass 800.
b) If the total mass of 8000 apples is 1.04 tonnes, what is the average mass of one apple?
A) Total mass of 3500 books is 2,800 kilograms.
B) The average mass of one apple is 130 grams.
A) To find the total mass of 3500 books, each with a mass of 800 grams, we can multiply the number of books by the mass of each book:
Total mass = (3500 books) * (800 grams/book)
= 2,800,000 grams
= 2,800 kilograms
Therefore, the Total mass of 3500 books is 2,800 kilograms.
B) To find the average mass of one apple, we can divide the total mass of the apples by the number of apples:
Average mass = (1.04 tonnes) / (8000 apples)
= 130 grams/apple
Therefore, the average mass of one apple is 130 grams.
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What is the circumference of this circle? Use π = 3.14
The circumference of this circle is equal to 50.24 centimeters.
What is a circle?In Mathematics, a circle can be defined as a closed, two-dimensional curved geometric shape with no edges or corners. Additionally, a circle simply refers to the set of all data points in a plane that are located at a fixed distance (radius) from a fixed point (central axis).
How to calculate the circumference of a circle?Mathematically, the circumference of a circle can be calculated by using this mathematical expression:
C = 2πr or C = πD
Where:
C represents the circumference of a circle.D represents the diameter of a circle.r represents the radius of a circle.Based on the image of this circle (See attachment), we can logically deduce that its radius is equal to 8 centimeters.
Substituting the given parameters into the circumference of a circle formula, we have;
Circumference of circle, C = 2 × 3.14 × 8
Circumference of circle, C = 50.24 centimeters.
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Complete the graph
Red Paint 4, 8, 12, 16
Blue Paint 6, _, _, _
Please help
Answer:
Step-by-step explanation:
10,14,18
A construction worker is making concrete by mixing sand, gravel, and cement in water. For each pound of sand, he uses 1 2/3 pounds of gravel. For each pound of gravel, he uses 2/5 pound of cement. He is making enough concrete that he needs to use 3 pounds of sand. How many pounds of cement does he use? PLEASE HELP DUE NOW !! TYYY
A. 1 pound
B. 1 4/15 pounds
C. 2 pounds
D. 2 1/15 pounds
Answer:
C
Step-by-step explanation:
1 pound sand for 1 2/3 pounds gravel.
1 pound gravel for 2/5 pound cement.
3 pounds sand = 3× 1 2/3 = 3 6/3 = 3+2 =
= 5 pounds gravel.
5 pounds gravel = 5 × 2/5 = 2 pounds of cement
PLS HELP ASAPPAPA
Type the correct answer in the box. If necessary, use / for the fraction bar.
If a rectangular prism has a length, width, and height of centimeter, centimeter, and centimeter, respectively, then the volume of the prism is
cubic centimeter.
Explanation:
Multiply out the fractions. This is because volume = length*width*height when it comes to rectangular prisms, aka blocks.
(3/8)*(5/8)*(7/8) = (3*5*7)/(8*8*8) = 105/512
This fraction cannot be reduced since 105 and 512 have no factors in common, other than 1. A clue of this is to notice how neither 3, nor 5, nor 7 share any common factors (other than 1) with 8 in the denominator.
Answer:
105/512
Step-by-step explanation:
hope this helps
The density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume. Express this density in pounds per cubic foot. Round your answer to the nearest whole number.
The density of the material is 1533.3 grams per quarts.
What is density?Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume.
Given that, the density of a certain material is such that it weighs 6900 grams for every 4.5 quarts of volume.
The formula to find the density is Density=Mass/Volume
Density =6900/4.5
Density= 1533.3 grams per quarts
Therefore, the density of the material is 1533.3 grams per quarts.
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3/8 = 8/X still not able to solve. Can you me how to solve by breaking down?
Answer: 21.3
Step-by-step explanation:
1. Cross multiply
8(8) = 3(x)
2. Simplify
64 = 3x
3. Divide by 3 on both sides to get the variable by itself
64/3 = 3x/3
4. Simplify
21.3333333333 = x
you can round the answer to the nearest tenth, which would be 21.3
jakie pole ma prostokąt o wymiarach 50cm x 16dm?
Solution
16 dm=160 cm
50 cm* 160 cm= 8000 cm²= 0,8 m²
odp C
Which equation is NOT true?
Parallelogram Q R S T with diagonal S Q. Angle R has measure (15 x + 55) degrees, angle R Q S is (6 x) degrees, angle S Q T is (4 x) degrees, and angle T is (26 x) degrees.
CLEAR CHECK
15+55=6+4
15
x
+
55
=
6
x
+
4
x
15+55=26
15
x
+
55
=
26
x
25+55=180
25
x
+
55
=
180
m∠=6+4
Answer: can you put them in order so i can read it better?
Step-by-step explanation:
Which graph is defined by the function given below?
y=(x + 2)(x+7)
10-
A.
-10
OA. Graph A
OB. Graph B
C. Graph C
OD. Graph D
10+
B.
10-
10
10-
D.
Graph A is defined by the function y=(x + 2)(x+7) as the graph at y=0 where the function crosses those two points .
what is function ?The study of mathematics comprises the study of quantities and their variations, equations and associated structures, shapes and their positions, and locations where they can be found. A combination of inputs and corresponding outputs are referred to as a "function," which describes the relationship between them. The term "function" refers to an association between inputs and outputs where each input produces a single, unique result. There are two domains, or scopes, assigned to each function. Usually, the symbol f is used to signify functions (x). input is an x. There are four basic categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
The function's zeros are
0=x+2 x=-2
and
0=x+7 x=-7
Consequently, the graph at y=0 where the function crosses those two points .
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two copies of one tenth
Answer:
0.2 or 1/5 or one fifth----------------------------------------
Two copies of one tenth translates as:
2*1/10 = 2*0.1 = 0.2 or 1/5Answer:
Two copies of 1/10 = 1/5
Step-by-step explanation:
Given statement,
→ two copies of one tenth.
Forming the expression,
→ 2 × (1/10)
Let's simplify the expression,
→ 2 × (1/10)
→ (2 × 1)/10
→ 2/10
→ 1/5
Hence, the answer is 1/5.
Use the picture below to answer the question.
6 ft
The angle of elevation from the swimmer to the lifeguard is 35*
Find the distance x from the swimmer to the base of the lifeguard chair.
Find the distance y from the swimmer to the lifeguard.
Round to the nearest tenth as needed.
Select the correct response
x=7.3ft, y= 3.4ft
x=8.6 ft y=10.5 ft
x=3.4ft, y=73 ft
x=10.5 ft, y= 8.6 ft
Answer: x = 8.6 y=10.5
Step-by-step explanation:
This is a question about trig identities, familiarize yourself with sin, cos, tanIn this problem, our value for degrees is 35 and our opposite side is 6ftOur variables to solve are x and y, x being the adjacent size and y being the hypothenusey has to be the longest size, it being the hypothenuse, so eliminate the first and last optionstan = opposite/adjacent so, tan(35)=6/x.solve this equation for x, yielding 8.6For y, using the fact that sin=opposite/hypothenusesubstitute and get the equation sin(35)=6/ysolve and get y =10.5x=8.6 and y= 10.5Select all the correct answers. The manufacturer of a popular brand of markers is planning to release a new color. To determine which color to add, it mailed out surveys to 5,000 of its customers regarding the general color family they prefer. The returned results are shown in this pie chart. A Pie Chart with four sections representing the color preferences Blues, Greens, Yellows, and Pinks Based on the results, one member of the management team says they should choose the new color from the blue family of colors since a majority of people prefer those colors. Another member doesn’t agree and thinks they should do more research. Which statements would support her request? The difference among the percentages is not statistically significant enough to make the claim of majority. A majority of the management team prefers the yellow family of colors. Not all color families were represented in the survey, which could cause a nonresponse bias. The mail-in survey may have resulted in an undercoverage bias. Since only existing customers were surveyed, the results were not random.
The statements that would support her request include:
The difference among the percentages is not statistically significant enough to make the claim of majority.Not all color families were represented in the survey, which could cause a nonresponse bias.The mail-in survey may have resulted in an undercoverage bias.Since only existing customers were surveyed, the results were not random.How to illustrate the information?A well-known marker brand's manufacturer intends to introduce a new shade. It mailed surveys to 5,000 of its customers asking them which general color family they preferred in order to decide which color to add.
The percentage difference is not statistically significant enough to support the majority claim. The survey did not include families of every color, which might have led to nonresponse bias.
It's possible that the mail-in survey had an undercoverage bias. Also, the results were not random because only current clients were polled.
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Answer: the other guy is correct except for the "since only existing customers...".
Step-by-step explanation:
Just took the test, the others he mentioned were right
let sets a and b defined as follows
A is c,d,e,f,g
b is the set of odd numbers greater than 5 and less than 13
Answer:
The set A is defined as the set containing the elements c, d, e, f, and g.
The set B is defined as the set of odd numbers greater than 5 and less than 13. This set includes the elements 7, 9, and 11.
Step-by-step explanation:
Whats the answer to this?
−0.7(−5b−5b+7)−0.9b
Answer: Simplify the expression.
6.1b − 4.9
The table shows the types and numbers of prizes at a carnival game what is the ratio of stuffed animals to posters
Answer:
Step-by-step explanation:
3
) For comparison with other years and with other countries, we prefer a histogram of the percentages in each age class rather than the countries. Explain why.
Therefore , the solution of the given question of percentage comes out to be It's because Different years and countries may have different overall numbers of newborns,.
What is percentage?A % is a number that indicates how many out of 100 it is, and it can also be expressed as a decimal or a fraction. Put the percentage value in the numerator and 100 in the denominator to convert a percentage to a fraction.
Here,
Given : we prefer a histogram of the percentages in each age class rather than the countries
It's because Different years and countries may have different overall numbers of newborns, making a comparison based on the absolute numbers difficult
If we insist on using the absolute numbers,
The group with the most population would definitely result in higher results, and make it impossible for us to see the changes in weight that happen to average inborns.
Therefore , the solution of the given question of percentage comes out to be It's because Different years and countries may have different overall numbers of newborns.
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[-12] + [4] find the absolute value of each integer then add them
Hello there!
Answer:
16
Step-by-step explanation:
[tex] |x| = x \: \: \: if \: \: x \: \geqslant 0 \\ |x| = - x \: \: \: if \: \: \: x \: \leqslant 0[/tex]
-12 < 0 so |-12| = -(-12) = 12
4 > 0 so |4| = 4
|-12| + |4| = 12 + 4 = 16
Answer:
16
Step-by-step explanation:
Hello! This question is looking for the absolute value of integers. The absolute value is the distance the number has from zero. For example, -12 as twelve numbers away from zero, twelve away in the negative direction. The absolute value of -12, then, is just twelve. An easy way to remember this is to take away the negative sign when taking the absolute value, since an absolute value can never be negative. The absolute value sign is represented by a squarish bracket [ and ].
This question says to find the absolute value of each integer and then add the two. First we have [-12]. This is 12 away from zero, and we can take away the - sign from the asked integer and we get 12.
The second integer given is 4, and when we take the absolute value of 4, [+4], we get positive four. This is because four is four spaces away from zero on the number line.
Thus, we have +12 and +4 as are values to add since they are the absolute values and we can form this equation
12+4=16
Thus, the answer is 16.
Hope this helps! Remember the hint, when something has brackets like that or asks for the absolute value, take away a negative sign and make it positive! Have a great day!
Scores on the Wechsler Adult Intelligence Scale (a standard IQ test) for the 20-to-34 age group are approximately normally distributed with μ = 110 and σ = 25. What percent of people aged 20 to 34 have IQs between 125 and 150?
The percentage of people aged 20 to 34 that have IQs between 125 and 150 of people aged 20 to 34 have IQs between 125 and 150 is 21.94%
What is percentage?Percentage simply means a proportion of the number as a fraction of 100
What percent of people aged 20 to 34 have IQs between 125 and 150?
Let X = Scores on the standard IQ test for the 20 to 34 age group
This implies that X ~ Normal(x=110, б² = 25)
The z-score probability distribution for the normal distribution is given by; Z = (x-ц)/б ~ N(0,1)
Recall that population mean = 110 and standard deviation = 25
Now, the percent of people aged 20 to 34 have IQs between 125 and 150 is given by = P(125 < X < 150) = P(X < 150) - P(X 125)
P(X < 150) = P( < ) = P(Z < 1.60) = 0.9452
P(X 125) = P( ) = P(Z 0.60) = 0.7258
The above probability is calculated by looking at the value of x = 1.60 and x = 0.60 which has an area of 0.9452 and 0.7258.
Therefore, P(125 < X < 150) = 0.9452 - 0.7258 = 0.2194 or 21.94%
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5432
-2
X
Which linear inequality is represented by the graph?
Oy< ²x + 3
Oy> ²x+3
Oy> ²x + 3
Oy< ²x + 3
Help please
The graph of an inequality in two variables is the set of points that represents all solutions to the inequality.
How do you find the linear inequality of a graph?The boundary line that separates the coordinate plane into two halves by a linear inequality represents the solutions to the inequality in one half. For > and, the border line is solid, and for and, it is dashed.
To determine the equation governing the inequality line, enter your slope and a point into the formula y = mx + B, where "m" denotes the slope, "x, y" denotes a point on the line, and "b" is the y-intercept. By inserting (0, 0), you get 0 = 0 + b, which equals 0.
When you rewrite the equation, you get y = x/2. The linear inequality x - 5 > 3x - 10 is an illustration. Due to the greater than symbol being utilised in this inequality, the LHS is clearly greater than the RHS.
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