Answer:
First angle: 52°
Second angle: 26°
Third angle: 102°
Step-by-step explanation:
Let the measure of the second angle = x.
Measure of the first angle: 2x
Measure of third angle: x + 76
2x + x + x + 76 = 180
4x + 76 = 180
4x = 104
x = 26 second angle
2x = 2 × 26 = 52 first angle
x + 76 = 26 + 76 = 102 third angle
Please help!
(02.01 HC)
Quadrilateral ABCD is located at A(−2, 2), B(−2, 4), C(2, 4), and D(2, 2). The quadrilateral is then transformed using the rule (x + 7, y − 1) to form the image A'B'C'D'. What are the new coordinates of A', B', C', and D'? Describe what characteristics you would find if the corresponding vertices were connected with line segments. (10 points)
Using translation concepts, it is found that:
The new coordinates of A' are: (5,0).The new coordinates of B' are: (5,2).The new coordinates of C' are: (9,2).The new coordinates of D' are: (9,0).Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule applied for each vertex of the rectangle is given as follows:
(x,y) -> (x + 7, y - 2).
The new coordinates of A' are given as follows:
(-2 + 7, 2 - 2) = (5,0).
The new coordinates of B' are given as follows:
(-2 + 7, 4 - 2) = (5,2).
The new coordinates of C' are given as follows:
(2 + 7, 4 - 2) = (9,2).
The new coordinates of D' are given as follows:
(2 + 7, 2 - 2) = (9,0).
Since there are only two values for the x-coordinates and two values for the y-coordinates, if the corresponding vertices were connected with line segments, a rectangle would be formed.
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Mitch throws a baseball straight up in the air from a cliff that is 95 ft high. The initial velocity is 95 /ftsec. The height (in feet) of the object after t sec is given by =ht+−19t2+95t95. Find the time at which the height of the object is 114 ft. Round your answers to two decimal places.
The time at which the height of the object is 114 ft rounded to two decimal places is; 5.85 seconds
How to find the height of a projectile?We are given;
Height of cliff = 95 ft
Initial velocity of throw = 95 ft/s
The height (in feet) of the object after t sec is given by;
h(t) = −19t² + 95t + 95.
Now, we want to find the time at which the height of the object is 114 ft. Thus, we will set h(t) = 114 ft to get;
114 = −19t² + 95t + 95.
Subtract 114 from both sides to get;
−19t² + 95t + 95 = 0
Using quadratic formula, we have;
t = [-95 ± √(95² - 4(-19 * 95))]/(2 * -19)
t = [-95 ± √(16245)]/-38
t = (-95 ± 127.4559)/(-38)
t = (-95 - 127.4559)/-38 or (-95 + 127.4559)/-38
t = 5.85 s or -0.85
Time cannot be negative and so t = 5.85 seconds
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Find the total surface area.
Answer: 1308m
Step-by-step explanation:
Top and Bottom: 19 x 16 x 2 = 608
Sides: 16 x 10 x 2 = 320
Front and Back: 19 x 10 x 2 = 380
608 + 320 + 380 = 1308
I, so confused please help me asap!
Quadrilaterals are plane shapes that are bounded by four straight sides. Thus, the required answers to the questions are:
46. True. Other examples include kites, rhombus, etc.
47. False.
46. When a plane shape is bounded by four straight sides of equal or different lengths, it is called a quadrilateral. Examples include trapezium, kite, rhombus, rectangle, square, etc. Each of these examples has individual properties.
Thus the required answer to question 46 is; True. It can be observed that with respect to their individual properties, other quadrilaterals which have a pair of opposite angles to be equal include: kite, rectangle, rhombus, etc.
47. A ray segment is a given line that points or heads in a specific direction. So that the direction in which the ray moves is very important.
Thus in the given question, the required answer is; False. This is because the two given rays are moving in opposite directions. Though the two rays may have the same length of the segment.
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Graph the line with a slope of −1 that contains the point (3,6).
Answer:
The equation of the line is y = -1.x + 9
Graph is provided in the attached figure
Step-by-step explanation:
The slope intercept equation of a line in 2D(x,y) coordinates is given by the equation
[tex]y = mx + c[/tex]
where m is the slope of the line and c the y-intercept i.e. where the line crosses the y axis at x = 0
Given slope = -1, we can find c and the equation of the line
Since (3,6) is a point on the graph, these coordinates must satisfy the above equation
Substitute for y = 6 and x = 3
[tex]6 = (-1)3 + c\\\\c = 9\\\\\textrm{Equation of line is }\\y = -1.x + 9 \\y = 9-x[/tex]
In the attached figure you can see that (3,6) is on the line
8v(v+3)(v+3) rewrite the expression factoring out (v+3)
If we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex]
Given an expression 8v(v+3)(v+3).
We are required to rewrite the given expression.
Expression is a combination of numbers, symbols, fraction , determinants,indeterminants, coefficients. They are not mostly found in equal to form. It expresses a relationship of a line or something else.
The expression is 8v(v+3)(v+3). There are three terms in which variable is v.
To rewrite the expression we have to multiply all the three terms with each other which can be done as under:
=8v(v+3)(v+3)
=[tex](8v^{2}+24v)(v+3)[/tex]
=[tex]8v^{3}+24v^{2}+24v^{2}+72v[/tex]
=[tex]8v^{3}+48v^{2} +72v[/tex]
Now divide it by 8.
=[tex]v^{3}+6v^{2} +9v[/tex]
Hence if we rewrite the expression 8v(v+3)(v+3) then we will get [tex]v^{3}+6v^{2} +9v[/tex] .
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Toenails grow at an average rate of about 0.05 mm per day, and the average toenail is about 3/4 inch long. About how many months does it take for a toenail to completely regenerate itself?
The number of months taken for the toenail to completely regenerate itself is 13 months
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
We have,
Toenail grows:
0.05 mm per day
0.05 mm = 1 day
[ 1 inch = 25.4 mm ]
So,
1 mm = 1/25.4 inch
0.05 x 1/25.4 inch = 1 day
0.0019 inch = 1 day
Divide both sides by 0.0019
1 inch = 1/0.0019 day
1 inch = 526.32 days
Multiply 3/4 on both sides.
3/4 inch = 3/4 x 526.32 days
3/4 inch = 395 days _____(1)
We can assume,
1 month = 30 days
Multiply 395/30 on both sides.
395/30 months = 395 days
13 months = 395 days _____(2)
From (1) and (2) we get,
3/4 inch = 13 months
Thus,
The number of months taken for the toenail to completely regenerate itself is 13 months.
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Find the savings plan balance after 18 months with an APR of 5% and monthly payments of $200.
The savings plan balance after 18 months is $3,730.38
What is an ordinary annuity?
An ordinary annuity means that periodic savings are made at the end of each period unlike an annuity due where payments are made at the beginning of each period.
To determine the savings plan balance after 18 months, we need to make use of the future value formula of an ordinary annuity provided below:
FV=monthly payment*(1+r)^N-1/r
FV=future value after 18 months=unknown
monthly payment=$200
r=monthly interest rate=5%/12=0.00416666666666667
N=number of monthly payments in 18 months=18
FV=$200*(1+0.00416666666666667)^18-1/0.00416666666666667
FV=$200*(1.00416666666666667)^18-1/0.00416666666666667
FV=$200*(1.07771621094479000-1)/0.00416666666666667
FV=$200*0.07771621094479000/0.00416666666666667
FV=$3,730.38
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ASAP help me with this PLEASE
Answer:
98 degrees
Step-by-step explanation:
In a quadrilateral, we have 4 angles whose sum is 360 degrees which can be derived using the Exterior Angle Sum Theorem which essentially states that any convex polynomial will have a sum of 360 degrees for it's exterior angles.
Since we know that two of the angles are equal, we can just represent angle A and D as "x", and since they're congruent, and there is two of them, the sum can be represented as "2x"
So using all the known values we can set up the following equation:
[tex]2x+64+100=360[/tex]
Simplify on the left side
[tex]2x+164=360[/tex]
Subtract 164 from both sides
[tex]2x=196[/tex]
Divide both sides by 2
[tex]x=98[/tex]
Since we know that "x" represents both angle A and B, then the angle A is 98 degrees.
Need help please...
Step-by-step explanation:
Here! ●□●□●□●□● THIS IS THE ANSWER BRO
Solve for exponential the value of X
[tex] {\qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
The two triangles are right angled Triangles and they have one common angle. so the two triangles are similar to each other.
By using similarity, ratio of their corresponding sides must be equal as well~
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{2 + 1} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: \cfrac{1}{3} = \cfrac{3}{x} [/tex]
[tex]\qquad \sf \dashrightarrow \: x = 3 \times 3[/tex]
[tex]\qquad \sf \dashrightarrow \: x = 9 \: \: units[/tex]
what is a1 of the arithmetic sequence for which a3=126 and a64= 3,725
If the third term of the aritmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
Given the third term of the aritmetic sequence is 126 and sixty fourth term is 3725.
We are required to find the first term of the arithmetic sequence.
Arithmetic sequence is a series in which all the terms have equal difference.
Nth term of an AP=a+(n-1)d
[tex]A_{3}[/tex]=a+(3-1)d
126=a+2d--------1
[tex]A_{64}[/tex]=a+(64-1)d
3725=a+63d------2
Subtract second equation from first equation.
a+2d-a-63d=126-3725
-61d=-3599
d=59
Put the value of d in 1 to get the value of a.
a+2d=126
a+2*59=126
a+118=126
a=126-118
a=8
[tex]A_{1}[/tex]=a+(1-1)d
=8+0*59
=8
Hence if the third term of the arithmetic sequence is 126 and sixty fourth term is 3725 then the first term is 8.
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Find the range for the set of data 24, 30, 17, 22, 22
Answer:
13
Step-by-step explanation:
The range of the data set can be defined as: max-min, and in a sorted data set, the min should be the first value, and the max should be the last value. We don't necessarily need to sort the data here, since we're just looking for two values which we can easily compare to other numbers without having them in order. Although it's important to note when looking for stuff like the median, first, and third quartile you should sort the data.
With that being said, let's look for the min and max! So by looking at the data set, you should be able to determine that the min (minimum) value is 17, and that the max (maximum) value is 30.
This means the range is defined as: 30 - 17 = 13
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Question reads....}[/tex]
[tex]\text{Find the range for the set of data 24, 30, 17, 22, 22}[/tex]
[tex]\huge\textbf{What does \boxed{range} mean in math?}[/tex]
[tex]\boxed{Range}\rightarrow\text{is the DIFFERENCE between the biggest number and the}\\\text{smallest number.}[/tex]
[tex]\huge\textbf{How do you find the \boxed{range}?}[/tex]
[tex]\text{You find the biggest number \& subtract it from the smallest number.}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\text{24, 30, 17, 22, 22}[/tex]
[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{biggest}}} number }\huge\boxed{\downarrow}[/tex]
[tex]\text{30}[/tex]
[tex]\huge\textbf{The \boxed{\mathsf{\mathsf{smallest}}} number }\huge\boxed{\downarrow}[/tex]
[tex]\text{17}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\rm{30 - 17}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\large\text{Start at 30 and go DOWN 17 spaces to the \boxed{left} and you will}\\\large\text{have your answer. }[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{13}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]i. 749x98+749 x2 ii. 62 x 999 +4795 iii. 736 x 97 iv. 258 x 1008
solve these using distributive property
pls help if u know
Step-by-step explanation:
I= 74810
II=66733
III=71392
iv=239904
In a mathematics class, half of the students scored 87 on an achievement test.
With the exception of a few students who scored 52, the remaining students
scored 71. Which of the following
statements is true about the distribution of
scores?
Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Therefore, the correct answer is option A. The mean is less than the median.
What are statistics?Statistics exist in the analysis of collection, analysis, interpretation, and presentation of data or into discipline to collect and summarize the data.
Half the students scored 87.
The next highest score exists at 71.
Then the median will be (71+ 87) / 2 = 79
A few students scored 52, so the mean exists a little lower than the mean of 71 and 87.
Therefore, the correct answer is option A. The mean is less than the median.
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The complete question is:
In a mathematics class, half of the students scored 87 on an achievement test. With the exception of a few students who scored 52, the remaining students scored 71. Which of the following statements is true about the distribution of scores?
A. The mean is less than the median.
B. The mean and the median is the same.
C. The mean is greater than the mode.
D. The mean is greater than the median.
how do i write 4x+5y=20 in slope intercept form
Answer:
Y=mx+b
Step-by-step explanation:
The answer is y = -4/5x + 4.
We know the general form for slope intercept form is :
y = mx + c
The given equation is in standard form.
4x + 5y = 20
Bring 4x to the other side by subtracting 4x on both sides.
4x + 5y - 4x = 20 - 4x
5y = -4x + 20
Divide 5 on both sides to isolate the variable y.
5y x 1/5 = 1/5 x (-4x + 20)
y = -4/5x + 4
laura spends 4 hours reading a book that is 76 pages long. what is the average number of pages she read per hour?
The average number of pages she reads per hour is 19 pages per hour
How to determine the average number of pages she read per hour?The given parameters are:
Number of pages = 76 pages
Number of hours = 4 hours
The average number of pages she reads per hour is calculated using the following formula
Average = Number of pages/Number of hours
Substitute the known values in the above equation
Average = 76 pages/4 hours
Evaluate the quotient
Average = 19 pages per hours
Hence, the average number of pages she reads per hour is 19 pages per hours
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Hi, please help me me by demonstrating how to solve these 2 questions step by step :)
The given height of the shape is calculated to be 1,895.04 inches.
How to solve for the heightWe have the following details required to solve this problem
The distance b1 = 800 m
The angle of elevation β1 = 50°
distance b2 = 1450 m
- The new angle of elevation α = 33°
We first have to find the height of h1
800 x tan 50 degrees
= 953.40
The height of h2
1450 x tan 33
= 941.641
The height of the shape is the sum of the heights of h1 and h2
953.40 + 941.641
= 1,895.04
Hence the height of the shape is given as 1,895.04 inches.
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If you borrow $100 for 5 years at an annual interest rate of 8%, how much will you pay all together
Answer:
$140
Step-by-step explanation:
interest = 8x5 = 40
total = time + interest
total = 100 + 40 = $140
A tower that is 114 feet tall casts a shadow 121 feet long. Find the angle of elevation of the sun to the
nearest degree
Answer:
43 degrees
Step-by-step explanation:
First, notice that we can draw a right triangle to represent this situation. The vertical leg of the triangle corresponds to the tower, and the horizontal leg corresponds to the shadow. The height of the tower, 114, is OPPOSITE, and the length of the shadow, 121, is ADJACENT to the angle of elevation to the top of the tower. Remember SOH CAH TOA, we can use TAN to find the angle since we know the values of O and A.
TAN(x) = O/A
TAN(x) = 114/121
x = ARCTAN(114/121)
x = 43
HELP NEED ANSWERS QIUCKLY! WILL GIVE BRAINLEST!
1. What is the difference between arithmetic and geometric?
2. Which formulas are used for each? Explain ratio and difference.
3. Given 4, 8, 16, 32 identify the next term and if its a ratio or difference
4. Explain the steps in using the sigma notation.
Answer:
Arithmetic => each new term differs from the previous term by a fixed amount
an = a1 + d (n − 1)
Geometric => each element after the first is obtained by multiplying the previous number by a constant factor
an = a1 (r)^(n − 1)
4,8,16,32 the difference is not fixed so it is a geometric so it is ratio
the ratio is 2 and n is 5 so 4*(2)^4 =4*16=64
To generate the terms of a series given in sigma notation, replace the index of summation with consecutive integers from the first value to the last value of the index.
if you also want the sum of them
arithmetic -> (n/2)(a1+an)
geometric -> (a1*(1-r^n))/(1-r) or
when the sequence is infinite you can use a1/(1-r)
Step-by-step explanation:
Arithmetic => 1,3,5,7,9,11,13,15....
Geometric => 1,2,4,8,16,32,64....
Joseph is planning dinners for the next 4 nights. There are 10 meals to choose from. If no meal is repeated, how many different meal arrangements are possible?
Considering the definition of combination, if no meal is repeated, 210 different meal arrangements are possible.
What is combinationCombinations of m elements taken from n to n (m≥n) are called all the possible groupings that can be made with the m elements in such a way that not all the elements enter; the order does not matter and the elements are not repeated.
To calculate the number of combinations, the following formula is applied:
[tex]C=\frac{m!}{n!(m-n)!}[/tex]
The term "n!" is called the "factorial of n" and is the multiplication of all numbers from "n" to 1.
Different meal arrangementsJoseph is planning dinners for the next 4 nights. There are 10 meals to choose from and no meal is repeated.
So, you know that:
m= 10n= 4Replacing in the definition of combination:
[tex]C=\frac{10!}{4!(10-4)!}[/tex]
Solving:
[tex]C=\frac{10!}{4!6!}[/tex]
[tex]C=\frac{3,628,800}{24x720}[/tex]
[tex]C=\frac{3,628,800}{17,280}[/tex]
C= 210
Finally, if no meal is repeated, 210 different meal arrangements are possible.
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5. Based on your data, what is the experimental probability that the family has two dogs or
two cats?
Answer:
2 dogs
Step-by-step explanation:
Suppose f(x) = x2. What is the graph of g(x) = f(4x)?
[tex]g(x)=f(4x)=(4x)^2 = 16x^2[/tex]
The graph is shown in the attached image.
If f ( x ) = 3x 2 - 6x + 2 and g ( x ) = 2x 2 + 2x - 11,
then find f ( x ) + g ( x ).
Answer:
[tex]5x^{2} -4x-9[/tex]
Step-by-step explanation:
f(x)+g(x)
[tex](3x^{2} -6x+2) + (2x^{2} +2x-11)\\3x^{2} -6x+2 + 2x^{2} +2x-11\\[/tex]
combine like terms --
[tex]5x^{2} -4x-9[/tex]
The sum of the given two functions f(x) = 3x² -6x + 2 and g(x) = 2x²+ 2x -1 is: f(x) + g(x) = 5x² - 4x - 9
Given that:
Functions, f ( x ) = 3x² - 6x + 2
And g ( x ) = 2x² + 2x - 11.
Then find f ( x ) + g ( x ).
To find the sum of two functions, f(x) + g(x), simply add the corresponding terms together.
To find f(x) + g(x), add the coefficients of the corresponding terms:
f(x) + g(x) = (3x² + 2x²) + (-6x + 2x) + (2 - 11)
Now, combine like terms:
f(x) + g(x) = 5x² - 4x - 9
So, the sum of the two functions is:
f(x) + g(x) = 5x² - 4x - 9
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Find the product. Write your answer in exponential form. 8^-2•8^-9
Answer:
8 ^-11
Step-by-step explanation:
It should be noted that in this case, since it's the product that we want to get, it's important to add the power together. This will be:
8^-2 × 8^-9
= 8^(-2 + -9)
= 8^-11
What is the common denominator of x+5/x+8=1+6/x+1?
Answer:
(x+8) (x+1)
Step-by-step explanation:
To find the common denominator, we need to find the least common multiple of the terms in the denominator
(x+8) from the first term
(1) from the second term
(x+1) from the third term
The least common denominator is
(x+8) (1)(x+1)
Simplifiying
(x+8) (x+1)
Useing graph paper draw a array for 237×43
The attached figure represents the array for 237 x 43
How to draw the array?The array is given as:
237 x 43
An array is represented as:
Row x Column
This means that:
Row = 237
Column = 43
i.e. the array has 237 rows and 43 columns
The numbers are large, so the cells would be small when the arrays are drawn
See attachment for the array
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Maria had a seven square-foot piece of construction paper. She used four square feet of the paper to make a large greeting card for a friend. Which operation would help to find the amount of paper she could use for another card? O division O addition subtraction multiplication
Answer:
subtraction
Step-by-step explanation:
If she had 7 sqft and used up 4 sqft, she no longer has that 4 sqft. It's used up, gone, taken away. We remove it from her total. That is "take away" this means subtraction.
7 - 4
= 3 she has 3sqft of construction paper left.
Consider the functions f(x) = (four-fifths) Superscript x and g(x) = (four-fifths) Superscript x + 6. What are the ranges of the two functions?
Let the two exponential functions be
[tex]$f(x) = (4/5)^x[/tex] and
[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]
Both of these exist exponential functions with positive bases, we end that the range for both exists: {y| y > 0}.
Therefore, the ranges of the two functions exists {y| y > 0}.
How to find the ranges of the two functions?Let the two exponential functions be
[tex]$f(x) = (4/5)^x[/tex] and
[tex]$g(x) = (4/5)^{(x + 6)}.[/tex]
Both of these exist exponential functions with positive bases, then neither of these can contain negative outcomes, while, as x increases, the outcome will also increase.
Then both the functions exist exponential growths, so the range for both of these exists the set of all real positive values, written in both cases as: {y| y > 0}.
Therefore, the ranges of the two functions exists {y| y > 0}.
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