Answer: x = 19
Step-by-step explanation:
Let's start with what we have, we'll let x = the number:
4x - 12 = 64
Then we add 12 to both sides:
4x = 76
Divide by 4 from both sides:
x = 19
From the observation deck of a skyscraper, Shaniece measures a 48^{\circ} ∘ angle of depression to a ship in the harbor below. If the observation deck is 1121 feet high, what is the horizontal distance from the base of the skyscraper out to the ship? Round your answer to the nearest hundredth of a foot if necessary.
By using trigonometry it can be calculated that-
Horizontal distance from the base of the skyscraper out to the ship is 1009.91 feet
What is trigonometry?
Trigonometry shows the relationship between sides and angles of a right angled triangle.
There are six trigonometrical functions. They are
[tex]sin\theta, cos\theta, tan\theta, cot\theta, sec\theta, cosec\theta[/tex]
[tex]sin\theta = \frac{perpendicular}{hypotenuse}\\\\cos\theta = \frac{base}{hypotenuse}\\\\tan\theta = \frac{perpendicular}{base}\\\\cot\theta = \frac{base}{perpendicular}\\\\sec\theta = \frac{hypotenuse}{base}\\\\cosec\theta = \frac{hypotenuse}{perpendicular}\\\\[/tex]
Trigonometry is a very important tool in mathematics.
Trigonometry is used here
Here, a diagram has been attached
Let AB be the skyscraper and C is the position of the boat
Let the horizontal distance from the base of the skyscraper be x feet
Angle of depression = 48°
Height of the observation deck = 1121 feet
[tex]tan 48 = \frac{1121}{x}\\1.11 = \frac{1121}{x}\\x = \frac{1121}{1.11}\\[/tex]
x = 1009.91 feet
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Answer: 1009.35
Step-by-step explanation:
need help struggling!
Answer:
Step-by-step explanation:
This is the same as before, two sides are the same length, so we know the angles are also the same. That is, D and C are equal
180= 106+2a
now algebra again
(180-106)/2 = a
74/2 = a
37 = a
find a so that the two points are 17 units aparts
(-5,8) and (3,a)
please tell me how you found it, i need the help!
Answer:
Therefore, the value of "a" could be 23 or -7 in order for the two points (-5,8) and (3,a) to be 17 units apart.
Step-by-step explanation:
To find the value of "a" such that the two points (-5,8) and (3,a) are 17 units apart, we can use the distance formula to calculate the distance between the two points.
The distance formula is:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values for x1, y1, x2, and y2, we get:
distance = sqrt((3 - (-5))^2 + (a - 8)^2)
Simplifying the expression, we get:
distance = sqrt((8)^2 + (a - 8)^2)
distance = sqrt(64 + (a - 8)^2)
Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":
sqrt(64 + (a - 8)^2) = 17
64 + (a - 8)^2 = 289
(a - 8)^2 = 225
a - 8 = 15 or a - 8 = -15
a = 23 or a = -7
Answer: 23 or -7
Step-by-step explanation:
The distance formula is:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the values for x1, y1, x2, and y2, we get:
distance = sqrt((3 - (-5))^2 + (a - 8)^2)
Simplifying the expression, we get:
distance = sqrt((8)^2 + (a - 8)^2)
distance = sqrt(64 + (a - 8)^2)
Since the distance between the two points is 17 units, we can set the expression equal to 17 and solve for "a":
sqrt(64 + (a - 8)^2) = 17
64 + (a - 8)^2 = 289
(a - 8)^2 = 225
a - 8 = 15 or a - 8 = -15
a = 23 or a = -7
determine if each set of equations is parallel perpendicular or neither place then in the correct category.
A. Perpendicular
B. Neither
C. Parallel
D. Parallel
E. Parallel
F. Perpendicular
G. Neither
H. Neither
I. Neither
Find equivalent expressions of 3 2x−9−4x 11 5x−x. choose three expressions.
Answer:
[tex]-(220x^2-5x+9)[/tex]
Step-by-step explanation:
[tex]3*2x-9-4x*11*5x-x\\\\-4*11*5xx+3*2x-x-9\\\\-4*11*5xx+6x-x-9\\\\-220x^2 +6x-x-9\\\\-44 5x^2 +6x-x-9\\\\-220x^2+6x-x-9\\\\-220x^2 +(6x-x)-9\\\\-220x^2+5x-9\\\\(-(220x^2-5x+9))[/tex]
Factor -1 out of -220x^2 +5x-9
What is the difference in elevation in meters between point x and point y on the map?.
The difference in elevation in meters between the points X and Y is 360.
Why are there contour lines?
A contour line is a line drawn on a topographic map to represent a dip or elevation in the ground.
The vertical separation or difference in elevation between contour lines is referred to as a contour interval. Every fifth contour line is a set of bold or thicker lines known as an index contour.
Which 3 types of contour lines are there?
There are three different types of contour lines that you might find on a map: supplemental, index, and intermediate. Index lines are the thickest contour lines, and they are frequently numbered at a specific location along the line. You can see the elevation above sea level from this.
Point X is marked on the contour line of 1,600 m. Point Y is marked on the second contour line between the 1,200 m and 1,300 m contour lines, thus:
2 x 20 = 40
So we have 1,240 m. Having the elevations of the two points, we only need to take the lower value from the larger value:
1,600 - 1,240 = 360 m
So we get a result of 360 m of difference in elevation between the points X and Y.
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When solved which system of equations will have exactly one point of intersection
Answer:
Step-by-step explanation:
d.) y=-x+2 and y=x+17
I graphed these system of equations on Desmos and the first 3 showed that the lines are parallel meaning they will never touch meaning that they won't have a solution or that they won't intercept. And for the last one, when I entered the equations it showed the interception, which is (-7.5, 9.5)
(Hopefully this is right)
Use £1 = 9.60 francs and £1 = 240 pesetas to work out how much 1 franc is in
pesetas.
Answer:
1 franc = 25 pesetas---------------------------------
Given:
£1 = 9.60 francs and £1 = 240 pesetasIt gives us:
9.60 francs = 240 pesetasDivide both sides by 9.60 to find the rate:
1 franc = 240/9.60 pesetas1 franc = 25 pesetasWhat is -1/4(-8.6) written as a decimal to the nearest hundredth
Answer:
2.15
Step-by-step explanation:
a sample of the paramedical fees charged by clinics revealed these amounts: $55, $49, $50, $45, $52, and $55. what is the median charge?
The median charge is $51. The median of a data set is also called the middle value.
How to find the median?Median is the value of the middle point in a data set. Here is how to find the median.
Sort the data from the smallest to the biggest.Separate the data into two. If the number of data is odd, the exactly middle part is the median. If the number of data is even, the median is the sum of left and right side divided by two.A sample of the paramedical fees: $55, $49, $50, $45, $52, and $55. Find the median!
The number of the data is 6.
Let's sort the data form the smallest!
$45, $49, $50, $52, $55, $55
The middle part of the data is $50 and $52. The median is
($50 + $52)/2 = $102/2 = $51
Hence, the median of the data is $51.
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a quadrilateral must be a parallelogram if one pair of opposite sides is a. congruent, only b. parallel, only c. congruent and parallel d. parallel and the other pair of opposite sides is
a quadrilateral must be a parallelogram if one pair of opposite sides is congruent and parallel
A quadrilateral with two sets of opposing parallel sides is referred to as a parallelogram.To be a parallelogram, one pair of opposite sides must be congruent and parallel. Congruent means that two sides have the same measurements or length while parallel means that two lines never intersect. For example, if one pair of opposite sides is congruent and parallel, and the other pair of opposite sides is parallel, then the quadrilateral is a parallelogram. This is because the two pairs of opposite sides form parallel lines and the respective pairs have the same length. Therefore, the answer is c. congruent and parallel.
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What was the equation of the graph below before it was shifted to the right 1
unit?
GX)=(x-1.6)-(x-1.5)
A. G(x) = (x)3
B. G(x) = (x-0.5) ³ - (x -0.5)
C. G(x) = (x-2)³ - (x-2)
D. G(x) = (x-.5)³
The equation before the transformation is g(x) = (x - 0.6) - (x - 0.5)
How to describe the equation before the transformation?From the question, we have the following function that can be used in our computation:
g(x) = (x - 1.6) - (x - 1.5)
Also, we have:
Transformation = shifted to the right 1 unit
This means that
g(x) = f(x - 1)
So, we have
f(x) = g(x + 1)
Substitute the known values in the above equation, so, we have the following representation
g(x + 1) = (x - 1.6 + 1) - (x - 1.5 + 1)
Rewrite properly
g(x + 1) = (x - 0.6) - (x - 0.5)
So, the equation is g(x) = (x - 0.6) - (x - 0.5)
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Please help me solve this algebraic expression
Answer:
Step-by-step explanation:
4+5(7)
4+ 35
39
I got this answer by simply plugging in the number that was given because it said a =7 I plugged in 7 instead of using a. The same goes to b it said that b=4 so then i plugged in 4 instead of using b.
Factorise this expression please help!!
Answer:
(a + 9)(a + 5)
Step-by-step explanation:
a² + 14a + 45
consider the factors of the constant term (+ 45) which sum to give the coefficient of the a- term (+ 14)
the factors are + 9 and + 5 , since
+ 9 × + 5 = = + 45 and + 9 + 5 = + 14 , then
a² + 14a + 45 = (a + 9)(a + 5)
20. Keith is offered an interest rate of 8.27% for a
loan with continuous compounding. Calculate
his equivalent rate with simple compounding.
[A] 0.0795 or 7.95%
[B] 0.0998 or 9.98%
[C] 0.0106 or 1.06%
[D] 0.0863 or 8.63%
[E] 0.1108 or 11.08%
Keith's equivalent rate with simple compounding is 0.0998 or 9.98%.
The Correct option is (B).
What is Compound Interest?The yearly interest rate is raised to the number of compound periods minus one, and the starting principal amount is multiplied by both of these factors. The resulting value is subsequently deducted from the loan's entire original amount.
Given:
Keith is offered an interest rate of 8.27% for a loan.
Now, using the following formula:
r = ([tex]e^{(i/n)[/tex] - 1) x n
where r is the equivalent rate with simple compounding, i is the interest rate with continuous compounding, and n is the number of compounding periods per year.
We have, i = 8.27%
Also assume that the number of compounding periods per year is 12, since many loans are compounded monthly.
Then,
r = ([tex]e^{(0.0827/12[/tex]) - 1) x 12
= (1.0082 - 1) x 12
= 0.0082 x 12
= 0.0984 or 9.84%
Hence, The equivalent rate is 0.0984 or 9.84%.
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Paul’s car is 17 ft long. He is making a Mindel of his car this 1/6 the actual size. What is the length of the model
Answer:2.8333…
Step-by-step explanation:
you just have to divide
solve for the matrix x if ax(d+bx)−1=c. assume that all matrices are n×n and invertible.
X = [tex](A - CB)^-^1[/tex]CD is the required matrix solution of the equation [tex]AX(D+BX)^-^1[/tex] = C
we are Given [tex]AX(D+BX)^-^1[/tex] = C:
Multiply both sides by (D+BX):
=> [tex]AX(D+BX)^-^1[/tex] * (D+BX) = C * (D+BX)
=> [tex]AX(D+BX)^-^1[/tex] (D+BX)) = C(D+BX)
=> AX * I = CD + CBX
where I is the identity Matrix of size n×n
=> AX = CD + CBX.
Subtract CBX on both sides and factor:
AX - CBX = (CD + CBX) - CBX
=> AX - CBX = CD + (CBX - CBX)
=> AX - CBX = CD + 0
=> (A - CB)X = CD.
Multiply both sides on the left by [tex](A - CB)^-^1[/tex]:
[tex](A - CB)^-^1[/tex] * (A - CB)X = (A - CB)^(-1) * CD
=> ([tex](A - CB)^-^1[/tex]* (A - CB)) X = [tex](A - CB)^-^1[/tex] CD
=> IX = [tex](A - CB)^-^1[/tex] CD
X = [tex](A - CB)^-^1[/tex]CD.
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I NEED HELP WITH #17
HELP PLEASEE
By complex and real number properties, the resulting electric resistance is equal to R' = 47 / 270 + i 4 / 45 ohms.
How to determine the total resistence of circuit by operation with complex numbers
Complex numbers are numbers of the form z = a + i b, where a, b are real numbers. The first component is the real component and the second one is the complex one. In this problem we find the case of a combination of two electric resistances described by two complex numbers. This expression must be simplified by means of real number and complex number properties:
R' = 1 / R₁ + 1 / R₂
If we know that R₁ = 4 + i 6 and R₂ = 2 - i 4, then the resulting electric resistance is:
1 / (4 + i 6) + 1 / (2 - i 4)
(4 - i 6) / [(4 + i 6) · (4 - i 6)] + (2 + i 4) / [(2 - i 4) · (2 + i 4)]
(4 - i 6) / (16 - i² 36) + (2 + i 4) / (4 - i² 16)
(4 - i 6) / (16 + 36) + (2 + i 4) / (4 + 16)
(4 - i 6) / 52 + (2 + i 4) / 20
(2 - i 3) / 27 + (1 + i 2) / 10
47 / 270 + i 4 / 45
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Abdullah and Amna bought a car for $9000. Abdullah paid 45% of the $9000 and Amna paid
the rest.
a) How much did Amna pay towards the cost of the car?
Answer:
$4950
Step-by-step explanation:
100-45 = 55
55% × 9000 = 4950
Ling bought d donut to hare with coworker. There were 6 donut in each box. Write an expreion that how how many boxe of donut Ling bought
The expression for the number of boxes of donuts bought by Ling is d/6.
We are given that -
Ling bought a ' d ' donut to share with a coworker.
There were 6 donuts in each box. This implies that 1 box contains 6 donuts.
Now, let us write the expression for the number of boxes of donuts bought by Ling as follows -
The number of boxes of donuts = the total number of donuts/donuts in 1 box.
Hence, the number of boxes of donuts = d/6
Thus, the expression for the number of boxes of donuts bought by Ling is d/6.
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The cost of a telephone call is made up of a fixed connection fee and an additional cost per minute, as shown on the graph below.
a) What is the cost of the connection fee?
b) What is the cost per minute?
If your answers are decimals, give them to 1 d.p.
Answer:
a) 80 pence
b) 6 pence
Step-by-step explanation:
The connection fee is the y intercept of the graph
The cost per minute is the slope of the graph
Select the graph for the solution of the open sentence. Click until the correct graph appears.
2|x| + 1 < 5
Answer:
graph C
Step-by-step explanation:
if x ≥ 0
2x + 1 < 5
2x < 5 - 1
2x < 4
2/2 x < 4/2
x < 2
0≤ x < 2
if x < 0
2 (-x) + 1 < 5
-2x < 5 - 1
-2x < 4
-2/-2 x > 4/-2
x > -2
-2 < x < 0
final solution
-2 < x < 2
5c=13
what does equal?
help please
The equal gives the solution for the variable 'c' in the given equation. I.e., c = 2.6.
What is a solution for an equation?A solution is the only value that satisfies the equation. It is also said to be the root of the equation.
Calculation:The given equation is
5c = 13
To solve the equation, divide both sides of the equation by 5.
So, we get
5c/5 = 13/5
⇒ c = 13/5
On converting the fraction into a decimal, we get c = 2.6.
To find whether the solution is correct or wrong, just substitute the value into the equation. If we get L.H.S = R.H.S, then that solution is the valid or correct one.
Substituting the value in L.H.S of the given equation, we get
5c = 5(2.6)
On multiplying,
5c = 13.0 ≈ 13
⇒ L.H.S = R.H.S
Hence, the solution is valid. The value of c is 2.6.
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Angles 3 and 6 are what type of angles?
A. Same side interior angles
B. Alternate exterior angles
C. Alternate interior angles
D. Corresponding angles
Help!!!
Answer:
A. Same-side interior angles
Step-by-step explanation:
Same-side interior angles are angles that has same-side interior angles sum up to 180 degrees. So, the answer is A.
Answer: A. Same side interior angles
Step-by-step explanation:
because they are inside the parralel lines and they are on the same side of the line going across them
a circle with a circumference of 396 cm is centered at the vertex of an angle, and the angle's rays subtend an arc that is 276.1 cm long. what is the measure of this angle in degrees?
1.1 cm is the 1/360th of the circumference. The circle's circumference is 69.72% of the arc that the angle's rays subtend.
We must comprehend and use the relationships between arc length and circumference in this question. By using geometry, we can determine that a circle's central angle is 360 degrees, and that the circle arc is directly proportional to the central angle.
The angle's rays' subtend an arc that is 69.72% the diameter of the circle.
The circumference's length is multiplied by 1/360 to get the 1/360th of the circumference, and the resulting measurement is
s= 1/360 x 396
= 1.1
the circumference is 1.1 cm.
By dividing the subtended arc by the arc length, one may determine the arc that the angle's subtend rays :
n = 276.1/396 x 100%
n= 69.72%
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Based on the given diagram, prove ABC is congruent to CDA by filling out the flowchart below.
The details of the angles in the diagram used to prove the congruency of the triangles ΔABC ≅ ΔCDA indicates;
Statements [tex]{}[/tex] Reasons
1. ∠D ≅ ∠B [tex]{}[/tex] 1. Given
∠ACB ≅ ∠CAD
2. Therefore; ∠ACD ≅ ∠CAB [tex]{}[/tex] 2. Angle sum property of a triangle
3. [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex] [tex]{}[/tex] 3. Reflexive property
4. ΔABC ≅ ΔCDA [tex]{}[/tex] 4. ASA congruency rule
Therefore, the completed flowchart is presented as follows;
∠D ≅ ∠B [tex]{}[/tex] ∠ACB ≅ ∠CAB [tex]{}[/tex][tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]
∠ACB ≅ ∠CAB Angle sum property Reflexive prop
Reason; Given
[tex]{}[/tex] ΔABC ≅ ΔCDA
[tex]{}[/tex]
What are congruent triangles?
Triangles are congruent if the three sides on both triangles are congruent or if two angles and a non included side in one triangle are congruent to two angles and a non included side of the other triangle
The details of the reasons used to prove the ΔABC ≅ ΔCDA are as follows;
Angle sum property of a triangle
The angle sum property of a triangle indicates that the sum of the three interior angles of a triangle is 180°
Reflexive property
Reflexive property of congruency states that a geometric figure is congruent to itself.
ASA congruency rule
The Angle-Side-Angle, ASA, congruency rule states that the if two angles and a non included side of one triangle are congruent to two angles and a non included side of the other triangle, then both triangles are congruent
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I’ve tried different methods to work it out but none of the answers are right
Answer:
maybe the first answer is 0.035 and the second answer is 0.045
Step-by-step explanation:
the population of men and women between the ages of 40-50 is approximately equal. the population of women is higher than men between the ages of 50-60. what does this likely result from?
The situation given in the question occurs due to the lower mortality rate which is seen in women of the age group 50-60.
Discrepancies between men and women's death rates and life expectancy. In general, women live longer than males. This means that, assuming everything else is equal, we should anticipate that women will make up somewhat more than half of the population.
Birth sex ratios are not equal. Males outnumber female births in every country. This means that, assuming everything else is equal, we should anticipate that men will make up somewhat more than half of the population.
The population's gender distribution can be impacted through migration. All other things being equal, we would anticipate that men would make up more than 50% of the population if some countries import a sizable amount of male-dominated labor.
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Pleaseeee helppppp meeeeee
Answer:
C
Step-by-step explanation:
You can do trial and error since it is a multiple ans question
Answer:
c
Step-by-step explanation:
do trial and error it's right the answer is c
A teacher recorded unit 4 test scores from her class.
58, 64, 66, 70, 71, 75, 77, 80,
84, 85, 87, 90, 93, 95, 96.
Find the percentile rank of a score of 71 on this street -
Victor is in the 60th percentile, what was his score?
The percentile score of 71 on test score is 27 and the score of victor is 71.
What is Statistics?Statistics is the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.
Given, the teacher recorded unit 4 test scores from class.
The scores are: 5,4,66,70,71,75,77,80,84,85,87,90,93,95 and 96.
A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it.
The percentile rank of a score of 71 on the test is find by formula
[tex]R_{100} =\frac{100(N < )+\frac{1}{2} }{N}[/tex]
=100×4+1/2(1)/15
=400+0.5/15
=400.5/15
=26.7=27th
Now we need to find the score of victor who has 60th percentile.
60=Score/15
score=71
Hence, the percentile score of 71 on this test score is 27 and the score of victor is 71.
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