See below for the distance between the points and the lines
How to determine the distance between the lines and the points?Question 2
The line and the points are given as:
x = y
P = (4, -2)
Rewrite the equation as:
y = x
The slope of the above equation is
m = 1
The slope of a line perpendicular to it is
m = -1
A linear equation is represented as:
y = mx + b
Substitute m = -1
y = -x + b
Substitute (4, -2) in y = -x + b
-2 = -4 + b
Solve for b
b = 2
Substitute b = 2 in y = -x + b
y = -x + 2
So, we have:
x = y and y = -x + 2
Substitute x for y
x = -x + 2
Solve for x
x = 1
Substitute x = 1 in y = x
y = 1
So, we have the following points
(1, 1) and (4, -2)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(1 - 4)² + (1 + 2)²
Evaluate
d = 3√2
Hence, the distance between x = y and P = (4, -2) is 3√2 units
Question 3
The line and the points are given as:
y = 2x + 1
Q = (2, 10)
The slope of the above equation is
m = 2
The slope of a line perpendicular to it is
m = -1/2
A linear equation is represented as:
y = mx + b
Substitute m = -1/2
y = -1/2x + b
Substitute (2, 10) in y = -1/2x + b
10 = -1/2 * 2 + b
Solve for b
b = 11
Substitute b = 11 in y = -1/2x + b
y = -1/2x + 11
So, we have:
y = 2x + 1 and y = -1/2x + 11
Substitute 2x + 1 for y
2x + 1 = -1/2x + 11
Solve for x
x = 4
Substitute x = 4 in y = 2x + 1
y = 9
So, we have the following points
(4, 9) and (2, 10)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(4 - 2)² + (9 - 10)²
Evaluate
d = √5
Hence, the distance between the line and the point is √5 units
Question 4
The line and the points are given as:
y = -x + 3
R = (-5, 0)
The slope of the above equation is
m = -1
The slope of a line perpendicular to it is
m = 1
A linear equation is represented as:
y = mx + b
Substitute m = 1
y = x + b
Substitute (-5, 0) in y = x + b
0 = 5 + b
Solve for b
b = -5
Substitute b = 5 in y = x + b
y = x + 5
So, we have:
y = x + 5 and y = -x + 3
Substitute x + 5 for y
x + 5 = -x + 3
Solve for x
x = -1
Substitute x = -1 in y = x + 3
y = 2
So, we have the following points
(-1, 2) and (-5, 0)
The distance between the above points is
d = √(x2 - x1)² + (y2 - y1)²
So, we have:
d = √(-1 + 5)² + (2 - 0)²
Evaluate
d = 2√5
Hence, the distance between the line and the point is 2√5 units
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Use the distance formula to find the length of the segment C(2, 1) to
D(5,6). Round your answer to two decimal places.
Answer: 5.83
Step-by-step explanation:
\(\sqrt{(2-5)^2 + (1-6)^2}=\sqrt{34} \approx 5.83\)
Find each. a. za_2 for the 99% confidence interval b. za_2 for the 98% confidence interval c. za_2 for the 95% confidence interval d. za_2 for the 90% confidence interval e. za_2 for the 94% confidence interval
Answer:
a) Z = 2.575.
b) Z = 2.327.
c) Z = 1.96.
d) Z = 1.645.
e) Z = 1.88.
Step-by-step explanation:
Question a:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.99}{2} = 0.005\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.005 = 0.995\), so Z = 2.575.
Question b:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.98}{2} = 0.01\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.01 = 0.99\), so Z = 2.327.
Question c:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.95}{2} = 0.025\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.025 = 0.975\), so Z = 1.96.
Question d:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.9}{2} = 0.05\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.05 = 0.95\), so Z = 1.645.
Question e:
We have that to find our \(\alpha\) level, that is the subtraction of 1 by the confidence interval divided by 2. So:
\(\alpha = \frac{1 - 0.94}{2} = 0.03\)
Now, we have to find z in the Z-table as such z has a p-value of \(1 - \alpha\).
That is z with a pvalue of \(1 - 0.03 = 0.97\), so Z = 1.88.
Examine the diagram.
The mZ1 is
the 63° angle.
What is the measure of angle 1?
v degrees
1
63°
Answer:
1. the supplement of
2. 117
Step-by-step explanation:
got it right
Answer:
The m∠1 is
the supplement ofthe 63° angle.
What is the measure of angle 1?
117degrees
Solve for x.
5x + 6 > 2x – 9
Answer:
x>-5
Step-by-step explanation:
5x + 6 > 2x – 9
3x > -15
x>-5
Mrs. Hall bought a package of 8 pencils for $4.64. What is the unit price per pencil?
Answer:
$0.58
Step-by-step explanation:
There are 8 pencils per package. To find the value of each pencil, divide the cost by 8
4.64/8 = $0.58
Answer:
$0.58
Step-by-step explanation:
unit means one, or the rate or price of each pencil. so if the total was 4.64, youd divide 4.64 by 8, which comes out to $0.58 per pencil
Which expression is equivalent to 2−35,? Choose 1 answer:
Answer:
The answer is option A.
Step-by-step explanation:
2 - 35 can be written as 2 + (-35) since in 2+( -35) when the bracket is removed it becomes 2 - 35.
Hope this helps
Answer:
Your correct answer is option a. 2 + (-35)
Step-by-step explanation:
When you are finding which equation is equivalent to the one you have, the best thing to find is what your equation's answer is.
The area of the rectangular sheet is 500cm square. If the length of the sheet is 25cm, what is its width? Also find the perimeter of the rectangular sheet.
Answer:
20cm Perimeter: 90
Step-by-step explanation:
Hope this helps!(^-^)
Step-by-step explanation:
area of rectangular sheet is 500 CM square
length =25cm
area =l×b
500cm2=25cm×b
500cm2÷25cm=b
20cm=b
b=20cm
again,
perimeter =2(l+b)
perimeter =2(25cm+20)
perimeter =2×45
perimeter =90cm
Love is patient, love is kind. It does not envy, it does not boast, it is not proud. It does not dishonor others, it is not self-seeking, it is not easily angered, it keeps no record of wrongs. Love does not delight in evil but rejoices with the truth. It always protects, always trusts, always hopes, always perseveres. Love never fails. But where there are prophecies, they will cease; where there are tongues, they will be stilled; where there is knowledge, it will pass away. 1 Corinthians 13:4-8
Answer:
Ok
Explanation:
Thank you for sharing :)
Answer:
good job
Step-by-step explanation:
175
m/1 =
m/2=
160°
determine the requested value below
The measures of angle 1 and angle 2 are 12.5 degrees
We have to find the measures of angle 1 and angle 2
The circle will have 360 degrees
The unknown arc length be taken as x
175+160+x=360
Add the like terms
335+x=360
Subtract 335 from both sides
x=360-335
x=25
So angle m∠1 = 1/2(25)
m∠1 is 12.5
m∠1 = m∠2 as both are equal.
m∠2 = 12.5 degrees
Hence, the measures of angle 1 and angle 2 are 12.5 degrees
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If and is in , find cos
Answer:
9/41
Step-by-step explanation:
Draw a right triangle in quadrant 2 and label your opposite (40) and hypotenuse (41) sides then use the pythagorean theorem to find the missing side (the adjacent side) which is equal to 9. Then since cosine is adjacent/hypotenuse and you get 9/41.
what is the solution to this inequality?
3n > 45.
A. n>15
B. n>42
C. n>48
D. n>135
Answer:
the answer to your problem is c
Let's roll two dice and find the probability of rolling a certain sum. Is this a simple or compound event?
Two dice - Red and Blue
Recall that a simple event has one and only one outcome of interest. In this example, we are rolling two dice, but we are only interested in one outcome, the sum of the two dice. This is a simple event.
What is the probability of:
Rolling a sum of 1?
Rolling a sum of 3?
Rolling a sum of 12?
Rolling a sum of 7?
Since we are rolling a pair of dice and looking for the sum, the sample space is a little more complicated than rolling one die. The chart below will help us determine the possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.
# Rolled 1 2 3 4 5 6
1 1+1=2
1
+
1
=
2
1+2=3
1
+
2
=
3
1+3=4
1
+
3
=
4
1+4=5
1
+
4
=
5
1+5=6
1
+
5
=
6
1+6=7
1
+
6
=
7
2 2+1=3
2
+
1
=
3
2+2=4
2
+
2
=
4
2+3=5
2
+
3
=
5
2+4=6
2
+
4
=
6
2+5=7
2
+
5
=
7
2+6=8
2
+
6
=
8
3 3+1=4
3
+
1
=
4
3+2=5
3
+
2
=
5
3+3=6
3
+
3
=
6
3+4=7
3
+
4
=
7
3+5=8
3
+
5
=
8
3+6=9
3
+
6
=
9
4 4+1=5
4
+
1
=
5
4+2=6
4
+
2
=
6
4+3=7
4
+
3
=
7
4+4=8
4
+
4
=
8
4+5=9
4
+
5
=
9
4+6=10
4
+
6
=
10
5 5+1=6
5
+
1
=
6
5+2=7
5
+
2
=
7
5+3=8
5
+
3
=
8
5+4=9
5
+
4
=
9
5+5=10
5
+
5
=
10
5+6=11
5
+
6
=
11
6 6+1=7
6
+
1
=
7
6+2=8
6
+
2
=
8
6+3=9
6
+
3
=
9
6+4=10
6
+
4
=
10
6+5=11
6
+
5
=
11
6+6=12
6
+
6
=
12
How many outcomes are in the sample space? Answer
Answer:
the answer to your question how many outcomes is really gonn adepend on you you slove you problem but my amswer is gonna be 7.
What is the total measurements of this roof in square feet?
The total measurements of the roof in square feet as required to be determined in the task content is; 2649 ft².
What is the total area of the roof in square feet?It follows from the task content that the total area of the roof as given in the task content is to be determined.
On this note, the area of the roof is the total area of the 71ft by 39 ft rectangle minus the area of the shaded region with dimensions 15 ft by 8 ft.
Therefore;
Area = (71 × 39) - (15 × 8)
= 2649 ft².
Ultimately, the total area measure of the roof in square feet is; 2649 square feet.
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the sum of two numbers is 16 and their difference is 4. what are the two numbers? HELP! PLEASE! BRAINLIEST TO WHOEVER ANSWERS IN THE NEXT 2 MINUTES!
Answer 6 and 10
Step-by-step explanation:
Answer:
10+6 and 10-6
Step-by-step explanation:
10+6
16
10-6
4
You are playing in the NBA Playoffs and attempt a 3-point shot as the buzzer sounds for the end of the
game, if you make the shot your team wins! Your basketball is is traveling on a path described by the
following function: b(x) = -x2 +1.36x + 2. The net is on a level described by the following function:
n(x) = 3 between (8 < x < 8.5). Will you make the shot and win the playoffs?
You may work alone or in a group of up to 3 students total.
BONUS: How high in the air will the basketball be at its highest point?
UNITS: x is in meters, y is in meters.
The quadratic function for the path of the basketball as it is thrown indicates;
The path of the basketball will not make the shot
The height reached is about 5.24 meters
What is a quadratic function?A quadratic function is a function of the form; f(x) = a·x² + b·x + c, where a ≠ 0, and a, b, c, are numbers.
The function for the path of the basketball is; b(x) = (-1/7)·x² + 1.36·x + 2
The function for the location of the basketball net is; n(x) = 3 and (8 < x < 8.5), where;
n(x) = The vertical height of the basketball
Plugging in the value of the n(x) = b(x), to check if equations have a common solution, we get;
b(x) = n(x) = 3 = (-1/7)·x² + 1.36·x + 2
(-1/7)·x² + 1.36·x + 2 - 3 = 0
(-1/7)·x² + 1.36·x - 1 = 0
(1/7)·x² - 1.36·x + 1 = 0
Solving the above equation, we get;
x = (119 - √(9786))/(25) ≈ 0.803, and x = (119 + √(9786))/(25) ≈ 8.717
Therefore, the x-coordinates of the height of the path of the basketball when the height is 3 meters are 0.803 and 8.717, neither of which are within the range (8 < x < 8.5), therefore, the baseketball will not go through the net and the path will not make the shot.
Bonus; The x-coordinates of the highest point of a quadratic function, f(x) = a·x² + b·x + c is; -b/(2·a)
Therefore, the x-value at the highest point of the equation, b(x) = (-1/7)·x² + 1.36·x + 2 is; x = -1.36/(2 × (-1/7)) = 1.36 × 7/2 = 9.52/2 = 4.76
The height of the highest point is; b(9.52) = (-1/7)·(4.76)² + 1.36·(4.76) + 2 ≈ 5.24 meters
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Marbles, and 4 green marbles. The second bag contains 3 red marbles,2 blue marbles, and 4 green marbles. Aakesh will randomly select one marble from each bag. What is the probability that Aakesh will select a blue marble from each bag ?
The probability that Aakesh will select a blue marble from each bag is 4/45.
To find the probability that Aakesh will select a blue marble from each bag, we need to calculate the probability of selecting a blue marble from each bag and then multiply those probabilities together.
Let's start with the first bag, which contains 5 marbles: 2 red marbles, 2 blue marbles, and 1 green marble. The probability of selecting a blue marble from the first bag is:
P(Blue from first bag) = Number of blue marbles / Total number of marbles in the first bag
P(Blue from first bag) = 2 / 5
Now, let's move on to the second bag, which contains 9 marbles: 3 red marbles, 2 blue marbles, and 4 green marbles. The probability of selecting a blue marble from the second bag is:
P(Blue from second bag) = Number of blue marbles / Total number of marbles in the second bag
P(Blue from second bag) = 2 / 9
To find the probability of both events happening (selecting a blue marble from each bag), we multiply the individual probabilities together:
P(Blue from both bags) = P(Blue from first bag) * P(Blue from second bag)
P(Blue from both bags) = (2 / 5) * (2 / 9)
P(Blue from both bags) = 4 / 45.
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The digit 5 in which number represents a value of 0.5? The answers are 5.4, 0.059, and 8.513.
Answer:
8.513 is the answer
Step-by-step explanation:
The value of 5 in 0.5 is the tenths place, hence if we look at all other options, the values of 5 are 5(ones place), and 0.05(Hundredth), so the option of 8.513 suits the question's answer. Hope this helped, Thank you.
Solve for (A) current ratio, (B) acid test (quick), (C) average day's collection (D) asset turnover, and (E) profit margin on sales. Round to nearest hundredth or hundredth percent as needed. Current Assets $ 21,000 Accounts Receivable 4,200 Current Liabilities 16,000 Inventory 3,500 Net Sales 41,000 Total Assets 32,000 Net Income 6,000
From the calculation below, we have:
A) Current ratio = 1.31
(B) Acid test (quick) = 1.09
(C) Average day's collection = 37.39 days
(D) Asset turnover = 1.28 times
(E) Profit margin on sales = 14.63%
How we calculate current ratio and others?The requirements can be solved as follows:
A) Current ratio = Current Assets / Current Liabilities = $21,000 / $16,000 = 1.31
(B) Acid test (quick) = (Current Assets - Inventory) / Current Liabilities = ($21,000 - $3,500) / $16,000 = 1.09
(C) Average day's collection = (Accounts Receivable / Net Sales) * 365 = ($4,200 / $41,000) * 365 = 37.39 days
(D) Asset turnover = Net Sales / Total Assets = $41,000 / $32,000 = 1.28 times
(E) Profit margin on sales = Net Income / Net Sales = ($6,000 / $41,000) * 100 = 14.63%
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40= x²-y²
21= xy
find x and y
On solving the provided question, we can say that - the equation, 21 = xy; 40 = \(x^2-y^2\) x= 2 and y = 2
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here,
21 = xy;
40 = \(x^2-y^2\)
x= 2
and
y = 2
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97.16×10 to the power 3
Answer:
the answer is 97,160
Answer:
97160
Step-by-step explanation:
\(97160\)
solve for x in the simplest form
Answer:
x= 12/5
Step-by-step explanation:
Distribute the fraction and solve for x.
1 A boat travels at an average speed of 15 km/h for 1 hour.
a Calculate the distance it travels in one hour.
b At what average speed will the boat have to travel to cover the
same distance in 2 hours?
Answer: 15km, 7.5kmh
Step-by-step explanation:
a. Distance travelled = speed * time = 15* 1 =15km
b. Distance = 15
time = 2hrs
Speed = distance/time = 15/2 = 7.5kmh
in a recent survey 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen find the probability that 8 of them favor building the health center
The probability of those that favors building the health center is 0.196
What is probability?The probability is the measure of the likelihood of an event to happen. It measures the certainty of the event. The formula for probability is given by; P(E) = Number of Favorable Outcomes/Number of total outcomes.
In a recent survey, 70% of the community favored building a health center in their neighborhood. If 14 citizens are chosen, find the probability that exactly 8 of them favor the building of the health center.
According to the scenario, 70% of the community favoured in building a health centre.
Hence , p=0.7.
In order to find the probability, binomial theorem will be used as follows :
= 0.196
Hence, The probability is 0.196
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Jim saw that other bank offered the same rates but compounded the interest more often. Consider if he still put $15,000 into a saving account for 5 years that provided 2.8% annually but compounded it in each of the following ways match the following:
Weekly-
Daily-
Continuously-
Monthly-
Semi-annually-
Quarterly-
Answer:
See Picture. I made a 100.
Step-by-step explanation:
Weekly- $17253.46
Daily- $17254.01
Continuously- $17254.11
Monthly- $17251.29
Semi-annually- $17237.36
Quarterly- $17245.69
Compound interest is the addition of interest on the interest of the principal amount.
What is compound interest?Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,
\(A = P(1+ \dfrac{r}{n})^{nt}\)
As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.
A.) When the interest is charged weekly,
As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,
\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \$17,253.46\)
B.) When the interest is charged daily,
As we know that there are 365 days in a year, therefore, n = 365, substitute the values,
\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \$19,554.55\)
C.) When the interest is charged Continuously,
As we know that the formula for continuous compounding is given as,
\(A = Pe^{rt}\)
Substitute the values, we will get,
\(A = 15000 \times (e^{0.024 \times 5})\\\\A= \$16,912.45\)
D.) When the interest is charged Monthly,
As we know that there are 12 months in a year, therefore, n = 12, substitute the values,
\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \$15211.23\)
E.) When the interest is charged Semi-annually,
As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,
\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \$17,237.36\)
F.) When the interest is charged Quarterly,
As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,
\(A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \$17,245.7\)
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Points P, Q, and R are collinear and the ratio of PQ to PR is 3/4. Point P is located at (3, -5) and point R is located at (-4, 5). What is the y-coordinate of point Q?
Answer: 0
Step-by-step explanation:
To find the y-coordinate of point Q, we first need to find the coordinates of point Q. Since points P, Q, and R are collinear and the ratio of PQ to PR is 3/4, we know that the ratio of their x-coordinates and y-coordinates must also be 3/4.
Let's call the coordinates of point Q (x, y). We know that the x-coordinate of point Q is 3/4 of the way between the x-coordinates of points P and R. This means that the x-coordinate of point Q is (3/4) * (-4 - 3) + 3 = -1.
Similarly, the y-coordinate of point Q is (3/4) of the way between the y-coordinates of points P and R. This means that the y-coordinate of point Q is (3/4) * (5 - (-5)) - 5 = 0.
Therefore, the coordinates of point Q are (-1, 0). The y-coordinate of point Q is 0.
The coordinates of point Q are (3, -5), and the y-coordinate of point Q is -5.
What is Collinear Points?Collinear points are points that lie on the same straight line. In other words, if you can draw a straight line through two or more points, then those points are said to be collinear.
Given that the ratio of PQ to PR is 3/4.
Let's assume the coordinates of point Q are (x, y).
Using the midpoint formula, we can find the coordinates of the midpoint M of line segment PR:
M = ((x1 + x2)/2, (y1 + y2)/2)
Substituting the coordinates of points P (3, -5) and R (-4, 5), we have:
M = ((3 - 4)/2, (-5 + 5)/2) = (-1/2, 0)
and, M = ((x + (-4))/2, (y + 5)/2)
Equating the x-coordinates and y-coordinates, we get:
-1/2 = (x - 4)/2 => x - 4 = -1 => x = 3
0 = (y + 5)/2 => y + 5 = 0 => y = -5
Therefore, the coordinates of point Q are (3, -5), and the y-coordinate of point Q is -5.
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Determine whether each statement is always true, sometimes true, or
never true.
1. Every square is a rhombus.
2. Every rhombus is a parallelogram.
3. Every rectangle is a parallelogram.
4. The diagonals of a square are perpendicular.
5. If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a square.
6. If the diagonals of a quadrilateral are perpendicular, then the
quadrilateral is a rhombus.
7. The diagonals of a rectangle are congruent.
8. The diagonals of a rhombus bisect the vertex angles.
9. Some rectangles are rhombi.
10. Some rhombi are squares.
Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.
1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.
Learn more about Shapes:
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In ABC, the measure of the largest angle is 16 less than 4 times the smallest angle. The measure of the middle angle is 7 more than half the measure of the largest angle. What is the measure of the middle angle?
Answer:
Step-by-step explanation:
Let A ≤ B ≤ C
largest angle is 16 less than 4 times the smallest angle
C = 4A-16
middle angle is 7 more than half the measure of the largest angle
B = C/2 + 7
A+B+C = 180°
A = 28 ⅐°
B = 55 2/7°
C = 96 4/7°
The base of the mountain is 6,500 feet above sea level and AB measures 230 feet across. Given that the measurements for QAP is 20° and QBP is 35°, how far above sea level is peak P ? Express your answer to the nearest foot.
Height above sea level:
Answer:
6610
Step-by-step explanation:
We have tan(X) = opposite/ adjacent
tan(QBP) = PQ/BQ
tan(35) = PQ/BQ ---eq(1)
tan(QAP) = PQ/AQ
tan(20) = \(\frac{PQ}{AB +BQ}\)
\(=\frac{1}{\frac{AB+BQ}{PQ} } \\\\=\frac{1}{\frac{AB}{PQ} +\frac{BQ}{PQ} } \\\\= \frac{1}{\frac{230}{PQ} + tan(35)} \;\;\;(from\;eq(1))\\\\= \frac{1}{\frac{230 + PQ tan(35)}{PQ} } \\\\= \frac{PQ}{230+PQ tan(35)}\)
230*tan(20) + PQ*tan(20)*tan(35) = PQ
⇒ 230 tan(20) = PQ - PQ*tan(20)*tan(35)
⇒ 230 tan(20) = PQ[1 - tan(20)*tan(35)]
\(PQ = \frac{230 tan(20)}{1 - tan(20)tan(35)}\)
\(= \frac{230*0.36}{1 - 0.36*0.7}\\\\= \frac{82.8}{1-0.25} \\\\=\frac{82.8}{0.75} \\\\= 110.4\)
PQ = 110.4
≈110
Height above sea level = 6500 + PQ
6500 + 110
= 6610
A runner finishes a race in 2:27:15 Explain the meaning of the Digits?
Answer:
2 HOURS, 27 MINS,15 SECONDS IS HOW LONG THE RUNNER TOOK
Step-by-step explanation:
THE MEANING OF THE DIGETS STAND FOR THE TIME THE RUNNER FINISHED THE RACE SO 2:27:15
ANSWER: 2:27:15= 2 HOURS 27 MINS AND 15 SECONDS IT TOOK THE RUNNER TO FINISH THE RACE. THIS DIGET SHOWS THE TIME IT TOOK THE RUNNER TO COMPLETE THE RACE.
Please Help I forgot how to do this
Answer:
Here is your answer
Suffered:
I drawn it