Given :
ZC = 90°CD is the altitude to AB.\(\angle\)A = 65°.To find :
the angles in △CBD and △CAD if m∠A = 65°Solution :
In Right angle △ABC,
we have,
=> ACB = 90°
=> \(\angle\)CAB = 65°.
So,
=> \(\angle\)ACB + \(\angle\)CAB+\(\angle\)ZCBA = 180° (By angle sum Property.)
=> 90° + 65° + \(\angle\)CBA = 180°
=> 155° +\(\angle\)CBA = 180°
=> \(\angle\)CBA = 180° - 155°
=> \(\angle\)CBA = 25°.
In △CDB,
=> CD is the altitude to AB.
So,
=> \(\angle\) CDB = 90°
=> \(\angle\)CBD = \(\angle\)CBA = 25°.
So,
=> \(\angle\)CBD + \(\angle\)DCB = 180° (Angle sum Property.)
=> 90° +25° + \(\angle\)DCB = 180°
=> 115° + \(\angle\)DCB = 180°
=> \(\angle\)DCB = 180° - 115°
=> \(\angle\)DCB = 65°.
Now, in △ADC,
=> CD is the altitude to AB.
So,
=> \(\angle\)ADC = 90°
=>\(\angle\) CAD =\(\angle\) CAB = 65°.
So,
=> \(\angle\)ADC + \(\angle\)CAD +\(\angle\)DCA = 180° (Angle sum Property.)
=> 90° + 65° + \(\angle\)DCA = 180°
=> 155° +\(\angle\)DCA = 180°
=> \(\angle\)DCA = 180° - 155°
=> \(\angle\)DCA = 25°
Hence, we get,
\(\angle\)DCA = 25°\(\angle\)DCB = 65°\(\angle\)CDB = 90°\(\angle\)ACD = 25°\(\angle\)ADC = 90°.In a survey based on a random sample of high school seniors at Roosevelt High School,
60% of those surveyed said they do more than 2.5 hours of homework per day. Based on this
data which of the following conclusions are valid? (Choose 2)
A) Less than 60% of all seniors at Roosevelt do more than 2.5 hours of homework per day.
B) About 60% of seniors at Roosevelt do more than 2.5 hours of homework per day.
C) About 40% of all seniors at Roosevelt do less than 2.5 hours of homework per day.
D) 40% of seniors at Whitney do no homework.
A and B stand in a line at random with 10 other people. What is the probability that there are exactly 3 people between A and B?
Answer:
so no answer
Step-by-step explanation:
no answer
Find the surface area of the regular pyramid.
Answer:
195.6
Step-by-step explanation:
The general formula for the total surface area of a regular pyramid is T. S. A. =12pl+B where p represents the perimeter of the base, l the slant height and B the area of the base.
x^2+12x−7=(x+p)^2−q. find the value of p and the value of q
Answer:
p = 6 , q = 43
Step-by-step explanation:
x² + 12x - 7
using the method of completing the square
add/subtract ( half the coefficient of the x- term )² to x² + 12x
=x² + 2(6)x + 36 - 36 - 7
= (x + 6)² - 43 ← in the form (x + p)² - q
with p = 6 and q = 43
Find all solutions to the equation x3 + 16x – 3x2 = 48.
–4, –3, 4
–4, 3, 4
3, –4i, 4i
–3, –4i, 4i
The solutions of the quadratic equation x³+ 16x -3x² = 48 are 3, –4i, 4i
What is a quadratic equation?A quadratic equation is the second-order degree algebraic expression in a variable. the standard form of this expression is ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.
A mathematical statement with two expressions that have the same value and the sign "equal to" between them is called an equation.
We are given the quadratic equation as;
x³+ 16x -3x² = 48
Subtract 48 from both sides;
x³+ 16x -3x² - 48= 48 -48
x³+ 16x -3x² - 48= 0
Factor left side of equation.
(x - 3)( x² + 16) = 0
Therefore, the roots are 3, –4i, 4i
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awnser the qusetion 9iu523hb5hn33
The order of the matrices of each product is given as follows:
AB is nonexistent, BA is nonexistent.
How to apply multiplication of matrices?Multiplication of matrices is applied multiplying the rows of the first matrix by the columns of the second matrix, and hence the number of columns of the first matrix must be equal to the number of rows of the second matrix.
For the product AB, we have that:
A has four columns.B has two rows.Hence the product is nonexistent.
For the product BA, we have that:
B has four columns.A has two rows.Hence the product is nonexistent.
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Sandra spent $32 for a purse and buys aCD for $15. Write an expression to represent this problem
Answer:
x - ($32 + $15); or x - $32 + $15
Step-by-step explanation:
Spending on the purse and a CD means less cash then the starting amount, x.
Answer:
$32+ $15=$47
Step-by-step explanation:
What is the first step in evaluating the expression shown below?
12
÷
(
7
.
4
−
3
.
6
)
+
8
−
2
Answer:
Step-by-step explanation:
The first step in evaluating the expression is to perform the calculations inside the parentheses. This involves subtracting 3.6 from 7.4.
Step 1: Evaluate the expression inside the parentheses.
7.4 - 3.6 = 3.8
After evaluating the expression inside the parentheses, the expression becomes:
12 ÷ 3.8 + 8 - 2
Step 2: Perform the division.
12 ÷ 3.8 = 3.158
After performing the division, the expression becomes:
3.158 + 8 - 2
Step 3: Perform the addition and subtraction from left to right.
3.158 + 8 = 11.158
11.158 - 2 = 9.158
Therefore, the value of the given expression is approximately 9.158.
The first step is:
⇨ parenthesesWork/explanation:
The expression is:
12 ÷ (7.4 − 3.6) + 8 − 2
Let's recall the order of operations first:
order of operations = PEMDASPEMDASParenthesesExponentsMultiplicationDivisionAdditionSubtractionSo we evaluate
\(\sf{12\div(7.4-3.6)+8-2}\)
\(\sf{12\div3.8+8-2}\)
Next, division:
\(\sf{3.158+8-2}\)
Next, addition & subtraction:
\(\sf{9.158}\)
Hence, the first step is to evaluate the parentheses.Which one is it------------------
Answer:
you're right
Step-by-step explanation:
As the number of copies increases, the dimensions of the images continue to decrease but never reach 0. Option A is correct.
As of the given statement,
Both copy machines reduce the dimensions of images that run through the machines. which statment is true is to be justified.
In mathematics, dimensions are the measurements of the size or distance of an item, region, or space in one direction. In layman's words, it is the measurement of something's length, width, and height. Length is the most commonly used dimension.
here,
Both copy machines diminish the size of images that pass through them. Which statement is correct must be justified. So, As the number of copies increases, the image dimensions drop but never reach zero.
Thus, the image dimensions decrease as the number of copies grows, but never reaches zero.
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NO LINKS!! URGENT HELP PLEASE!!!
9. Find the equation of the PARABOLA with a vertex at (-2, 6) and passing through the point (1, -3)
Answer:
y= -x²-4x+2
Step-by-step explanation:
write in vertex form
a(x-h)²+k
in our case h = -2 and k= 6
y=a(x+2)²+6
now we just need to solve for a. we know that when x= 1 y = -3. plug these values in and solve for a
-3= a(1+2)²+6
-9=9a
a= -1
thus the formula is -(x+2)²+6
generally, teachers want things in standard form, so expand the exponent and simplify.
-(x²+4x+4)+6
y= -x²-4x+2
Answer:
\(y = -x^2 - 4x + 2\)
Step-by-step explanation:
The equation of a parabola in vertex form is:
\(y = a(x - h)^2 + k\)
where (h, k) is the vertex of the parabola.
In this case, the vertex is (-2, 6), so h = -2 and k = 6.
We also know that the parabola passes through the point (1, -3).
Plugging these values into the equation, we get:
\(-3 = a(1 - (-2))^2 + 6\)
\(-3 = a(3)^2 + 6\)
-9 = 9a
a = -1
Substituting a = -1 into the equation for a parabola in vertex form, we get the equation of the parabola:
\(y = -1(x + 2)^2 + 6\)
This equation can also be written as:
\(y = -x^2 - 4x -4+6\\y=x^2-4x+2\)
What is the value of x?
Answer:
12
Step-by-step explanation:
10x - 20 + 6x + 8 = 180
Supplementary angles
Answer:
x = 12
Step-by-step explanation:
The two given angles create a straight line (Definition of Straight Line). This means that:
\((10x - 20) + (6x + 8) = 180\)
First, combine like terms. Like terms are terms that share the same amount of the same variables:
\((10x + 6x) + (8 - 20) = 180\\(16x) + (-12) = 180\\16x - 12 = 180\\\)
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations and stands for:
Parenthesis
Exponents (& Roots)
Multiplications
Divisions
Additions
Subtractions
~
First, add 12 to both sides of the equation:
\(16x - 12 = 180\\16x - 12 (+12) = 180 (+12)\\16x = 180 + 12\\16x = 192\)
Next, divide 16 from both sides of the equation:
\(\frac{16x}{16} = \frac{192}{16} \\x = \frac{192}{16}\\ x = 12\)
12 is your answer.
~
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Suppose there is a simple index of two stocks, stock A and stock B. Stock A opens on Monday with 5000 shares at $2.75 per share. Stock B opens on Monday with 3000 shares at $4.30 per share. Stock A opens on Tuesday at $3.10 per share, and stock B opens on Tuesday at $4.85 per share. Both stocks have the same number of shares that they opened with on Monday. What is the rate of change of this simple index over 1 day?
The rate of change of the simple index over one day is approximately 12.78%.
To calculate the rate of change of the simple index over one day, we need to determine the percent change in the total value of the index between Monday's opening and Tuesday's opening.
On Monday, Stock A has 5000 shares at $2.75 per share, so its total value is:
Total value of Stock A on Monday = 5000 * $2.75 = $13,750
Similarly, on Monday, Stock B has 3000 shares at $4.30 per share, so its total value is:
Total value of Stock B on Monday = 3000 * $4.30 = $12,900
The total value of the index on Monday is the sum of the values of Stock A and Stock B:
Total value of the index on Monday = $13,750 + $12,900 = $26,650
On Tuesday, Stock A opens at $3.10 per share, and Stock B opens at $4.85 per share. Both stocks still have the same number of shares as on Monday.
The total value of Stock A on Tuesday is:
Total value of Stock A on Tuesday = 5000 * $3.10 = $15,500
The total value of Stock B on Tuesday is:
Total value of Stock B on Tuesday = 3000 * $4.85 = $14,550
The total value of the index on Tuesday is the sum of the values of Stock A and Stock B:
Total value of the index on Tuesday = $15,500 + $14,550 = $30,050
To calculate the percent change in the index, we use the formula:
Percent Change = ((New Value - Old Value) / Old Value) * 100
Percent Change = (($30,050 - $26,650) / $26,650) * 100 ≈ 12.78%
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Alice used a $250 cash advance from her credit card company to get cash while on a trip. The company charges a daily finance fee of 0.047%. She reported the advance plus the finance fee 40 days later. What amount did Alicia repay the company?
you do 0.047×40 and what ever that gives you you add it to 40 and it will give you the answer
The amount Alicia repaid to the company after 40 days is $254.7.
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
25% = 25/100 = 1/4
20% = 20/100 = 1/5
10% = 10/100 = 1/10
We have,
Advance cash = $250
Daily finance fee = 0.047%
The daily finance fee for 40 days.
= 40 x (0.047% x 250)
= 40 x 0.1175
= $4.7
The total amount paid after 40 days.
= 250 + 4.7
= $254.7
Thus,
The amount paid to the company is $254.7.
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-| 5 - 17| + (-2)^5 - 1
show work
Answer:the answer is 5 and a half (1/2)
Step-by-step explanation: I dont know how to explain this so sorry..
a student spends 18 out of 35 of his pocket money on transport and fruit what is the fraction left?
To find the fraction of pocket money left after spending on transport and fruit, we need to subtract the amount spent from the total pocket money and express it as a fraction.
The student spends 18 out of 35 of his pocket money, which means he has (35 - 18) = 17 units of his pocket money left.
Therefore, the fraction of pocket money left can be written as 17/35.
Pie chart values
20%. Rice
15%. Others
Pulses. 30%
maize 20%
wheat 15%
Percentage distribution of products in exports of the
given countries.
(a) What is the value (in $ billion) of pulses export
by US? on a billion
(6)
What is the ratio of wheat export of UK to
maize export of IND? 4:10
(e) By what percentage is the maize export of
JAP more than the rice export of AUS?
(d) If the export of AUS is doubled and that of US is
halved but percentage distribution of products of
export remains the same, then find the value of
Export of Rice by US
Export of Pulses by AUS
In USSR, find the ratio of maize export to the
rice export.
a.) The value of pulses exported by US in billion would be=30 billion.
b.) The ratio of wheat export of UK to maize export of IND would be= 6:5
How to calculate the value of pulses exported?For question a.)
To calculate the pulses, the following steps should be taken as follows:
From the bar chart, the value of pulses in billions = 30 billions.
For question b.)
The ratio of wheat export at UK and maize export at IND would be calculated as follows:
The quantity of wheat export at UK = 24
The quantity of maize export at IND = 20
Therefore, the ratio of wheat to maize = 24:20= 6:5
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Find the y intercept of the line on the graph
Answer: y = -1
Step-by-step explanation:
When x = 0, y = -1
Also, you can think about it as when the graph of the line passes the y axis
Brand A has a box of 25 forks for 1.99 and Brand B has a box of 42 totals for 3.89. What is the unit price for each brand and what brand is a better buy based on unit price
Answer:
Brand A
Step-by-step explanation:
Brand A has a box of 25 forks for 1.99
Take the price per fork
1.99 /25 = .0796
.08 per fork
Brand B has a box of 42 totals for 3.89
3.89 / 42
.092319048
.09 per fork
6.3 + 6.4 + 9.4
what is the sum of?
Answer:
22.1
You can search for any mathematical expression, using functions such as: sin, cos, sqrt, etc. You can find a complete list of functions here.
Rad
Deg
x!
Inv
sin
ln
π
cos
log
e
tan
√
Ans
EXP
xy
(
)
%
AC
7
8
9
÷
4
5
6
×
1
2
3
−
0
.
=
+
Answer:
22.1
Step-by-step explanation:
there is your answer have a great day
-4.5=a-8
Pleaseeee help
Answer:
A=3.5
Step-by-step explanation:
Add 8 to both sides to get A by itself and A=3.5
Answer:
a=3.5
Step-by-step explanation:
-4.5=a-8
-4.5+8=a
a=3.5
Does anyone have all the answers for the algebra 4 final exam on Edge?
An equation for a LINE that can be written in standard form, slope-intercept form, or point-slope form is Linear Equation.
Why is Linear Equation Important?Linear equations are useful in research and in many daily applications.
They let scientists to define physical relationships between two variables, make predictions, compute rates, and perform conversions, among other things.
Graphing linear equations aids in identifying trends.
Linear equations are particularly useful in mathematics because they may be used to simulate any real-world phenomenon in which one variable changes at a constant pace in relation to another variable.
As a result, they are extremely valuable for modeling, forecasting, and assessing real-world applications.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
an equation for a LINE that can be written in standard form, slope-intercept form, or point-slope form is ________ ?
please help me im on a timer
Answer:
11/8
Step-by-step explanation:
ILL GIVE U BRAINLIST OR WHATEVER
The nationwide percentage of Americans who invest in the stock market is usually taken to be 55%. Is this percentage different in Georgia? A survey and analysis among Georgia residents led to a test statistic of 1.75.
(b) What is the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average? (Use 4 decimals.)
Okay, here are the steps to find the p-value:
1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)
2) The test statistic for Georgia is 1.75
3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.
4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).
5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)
6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.
7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.
So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.
Let me know if you have any other questions!
Okay, here are the steps to find the p-value:
1) The nationwide proportion of Americans who invest in the stock market is 55% (0.55)
2) The test statistic for Georgia is 1.75
3) To calculate the p-value, we need to know the degrees of freedom (df) and the critical value of the test statistic.
4) The df = 1, since we're comparing a single proportion (Georgia) to a fixed value (national average).
5) The critical value at df = 1 and 95% confidence is 3.84 (for a two-tailed test)
6) Since the test statistic of 1.75 is less than 3.84, we look up 1.75 in tables to find the p-value.
7) For a test statistic of 1.75 and df = 1, the p-value is 0.1860.
So the p-value to test if the proportion of Georgians who invest in the stock market is different than the nationwide average is 0.1860.
Let me know if you have any other questions!
Tyler mows 7 lawns every week. He earns $10 for mowing each lawn. How much will he earn in 6 weeks?
Answer:
The Answer Would Be $420
Step-by-step explanation:
time 7 by 10 and get 70,
times 70 by 6 to get your final answer of $420
At Silver Gym, membership is $40 per month, and personal training sessions are $30 each. At Fit Factor, membershlp Is $60 per month, and personal training sessions are $20 each. In one month, how many personal training sessions would Sarah have to buy to make the total cost at the two gyms equal?
Answer:
3 training sessions
Step-by-Step Explanation:
What we are going to have are two equations set equal to each other. Our variable is going to be the letter x. X represents the number of personal training sessions we would have to have at their current costs for the two equations to equal each other. Because we are only doing one month, the membership costs will stay constant.
For Silver Gym, membership is $40 and training sessions are 25$ per session. That "per session" tells you that this is where the variable goes. Your equation for a month at Silver Gym is 25x + 40.
Do the same for Fit Factor; $70 membership, $15 per session: 15x + 70.
Now let's set them equal to each other:
25x + 40 = 15x + 70
Next, we want to get variables on one side and constants on the other. I like to do variables on the left and constants on the right but, this is just personal preference -- we'll end up with the same answer regardless. To do this, we are going to subtract 15x from both sides, subtract 40 from both sides, and then simplify. So the above equation becomes:
25x - 15x + 40 - 40 = 15x - 15x + 70 - 40
Simplify by combining like terms. The 15x and - 15x cancel each other out, same with the 40 and - 40. Leaving us with:
10x = 30
Divide both sides to isolate your variable x and satisfy the division property of equality.
x = 30/10
x = 3
You would have to do 3 training sessions for the two gyms to be equal in cost.
PLEASE..... Need help with questions 5 - 8....
5.
6.
7.
8.
Answer:
I'm sorry I only know 6 & 7 but... 6 is \(y=-\frac{2}{3} x-4\) and 7 is the slope is -5 and the y-intercept is (0,3) and the graph is blurry
Step-by-step explanation:
hope this helps sorry if it doesn't have a good rest of your day :) ❤
what is the perimeter of a rhombus when the diagonals are 42cm and 40cm
Answer:
Step-by-step explanation:
P = 4 a
a = √p^2 + q^2 / 2
P = 2√p^2 + q^2 = 2 x √42^2 + 40^2 = 116cm
∴ the perimeter of a rhombus when the diagonals are 42cm and 40cm is 116cm
a dot plot shows . the interquartile range the general shape of a distribution the relationship between two variables the mean, median, and mode
A dot plot can be used to display the relationship between two variables by grouping the dots in a particular way.
Finally, one should use the terms: a dot plot shows the general shape of a distribution, the mean, median, and mode, the interquartile range, and the relationship between two variables, in their answer.
A dot plot is a statistical graph in which data points are plotted on a line by a number scale.
It's a visual representation of data that allows us to see how the data is distributed.
A dot plot shows the general shape of a distribution, and it also shows the mean, median, and mode of a dataset. Furthermore, the interquartile range can be determined using the dot plot, which provides information on the distribution's dispersion.
In addition, a dot plot can be used to display the relationship between two variables by grouping the dots in a particular way.
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what is the value of x^2+4 for x=5
Answer:
25+4=29
thats your answer
PLEASE MARK AS THE BRAINLIEST
Answer:
29
Step-by-step explanation:
x^2+4
Let x= 5
5^2 +4
25+4
29
ITS DO TODAY HELPPPPPPP
The difference in the addition of both fractions is that they have different lowest common multiples.
How to solve Fraction Problems?We want to add the fraction expression given as:
¹/₂ + ¹/₄
Taking the Lowest common multiple of 8, we have:
(4 + 2)/8 = 6/8
However, for the second fraction expression, we have:
¹/₂ + ¹/₃
Taking the lowest common multiple which is 6, we have:
(3 + 2)/6 = 5/6
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