P, Q & R form a right-angled triangle.
R, S & P lie on a straight line.
PS = SQ and ∠SQR = 36°.
Work out
∠RPQ
Answers
Answer:
∠RPQ = 27
Step-by-step explanation:
In ΔSRQ,
∠R = 90
∠SQR = 36°
∠R + ∠SQR + ∠RSQ = 180 {Angle sum property of triangle}
90 + 36 + ∠RSQ = 180
126 + ∠RSQ = 180
∠RSQ = 180 - 126
∠RSQ = 54°
∠PSQ +∠RSQ = 180 {Linear pair}
∠PSQ + 54 = 180
∠PSQ = 180 - 54
∠PSQ = 126
In ΔPSQ,
SQ = PS ,
So, ∠SQP = ∠SPQ {Angles opposite to equal sides are equal}
∠SQP = ∠SPQ =x
∠PSQ + x +x = 180 {Angle sum property of triangle}
126 + 2x = 180
2x = 180 - 126
2x = 54
x = 54/2
x = 27
∠RPQ = 27°
Related Questions
the square of the product of 4 and a number is the sum of the number and 15
Answers
Answer:
(4x)^2 = x + 15 or
16x^2 = x + 15
16x^2 - x - 15 = 0
or x =1 and x = -0.9375
Make sure next time that you ask a question..
Step-by-step explanation:
This shouldn't really be answered unless we are sure when the answer is there.
4x is the product of a number and 4
(4x)^2 = 16x^2
this will equal x + 15
16x^2 = x + 15
The question is that the answer? I suspect it is.
16x^2 - x - 15 = 0
This might be the answer. It's not clear.
"""""""""""""""""""""""""""""""""""""''''
Believe it or not, this factors without using the quadratic formula
(16x + 15) ( x - 1) = 0
16x + 15 = 0
x = - 15/16 = - 0.9575
x - 1 = 0
x = 1
help me with these asap
Answers
how to prove sinA+sin2A/1+cosA+cos2A=tanA
Answers
Answer:
my answer is in this picture. sorry about my handwriting.
In the following function defined by an equation in the form y = ax + bx+c, identify the values of a, b, and c.
y = 5x2 + 2x-1
a. d=-1, b = 2,0 = 5
b. a = -2, b = 5,0 = 1
C. a = 1, b = 5,0 = 2
d. a = 5,6 = 2,0 = -1
Answers
Answer:
d
Step-by-step explanation:
just compare,
y = aX^2+bX+C and
y = 5X^2 + 2X - 1
what is the value n ?
Answers
Answer:
nutella
Step-by-step explanation:
Solve the system of equations:
(1) x - y = 3
(2) 7x - y = -3
Answers
Answer:
x= 70
and y = 67 then
-70-67 =-3
Answer:
x=-1 y=-4
Step-by-step explanation:
answer is in the photo above
Help
Will
Give
Brainlist
:)))
Answers
Find the area of this circle. Use 3 for pi
Answers
Step-by-step explanation:
given pi value= 3
radius=7
we know,
area of a circle(A)= πr²
= 3×7²
=147cm²
Answer:
A = 147 cm²
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightGeometry
Area of a Circle Formula: A = πr²
r is radiusStep-by-step explanation:
Step 1: Define
Identify
r = 7 cm
Step 2: Find Area
Substitute in variables [Area of a Circle Formula]: A = 3(7 cm)²Evaluate exponents: A = 3(49 cm²)Multiply: A = 147 cm²The volume of water remaining in a tank after 10 of its original volume (x) is drained out
Answers
Answer:
x - 10
Step-by-step explanation:
The original volume is x, and 10 is removed.
In mathematical terms, this is expressed as x - 10.
Here is some information about a holiday.
7 night holiday
$340 per person
8% discount if you book before 31 March
On 15 February, Naseem books this holiday for 2 people.
Calculate the total cost of his holiday.
Answers
Answer:
$625.6
Step-by-step explanation:
Information about the holiday:
7 night holiday
$340 per person
8% discount if you book before 31 March
Number of people Naseem booked the holiday for = 2
Date of booking of the holiday = 15 February
Total cost of the holiday per person = cost per person - discount before March 31
= $340 - 8% of $340
= 340 - 8/100 * 340
= 340 - 0.08 * 340
= 340 - 27.2
= $312.8
Total cost of the holiday for 2 persons = 2 × Total cost of the holiday per person
= 2 * $312.8
= $625.6
A car dealership has seven cars in the lot unfortunately the keys to the cars of been mixed up the manager randomly grab the key and tries to start a car salesman also randomly picks a different key and tries to start another car what is the probability that both cars start
Answers
To determine The probability of both of these occurring, you would multiply the probability of each together. So, there is a 1/7 chance of the first salesman getting the right key, and 1/6 chance of the second salesman getting the right key. 1/7 x 1/6= 1/42 chance of both occurring.
the equation cos(x)( cos(x)-tan(x)sin(x)) simplifies to
Answers
In the diagram below of triangle PQS, S is the midpoint of PR and T is the midpoint of QR. If ST = 5x - 22, and PQ = 3x + 19, what is the measurement of PQ?
Answers
Answer:
PQ = 46
Step-by-step explanation:
The midsegment ST is half the length of the third side PQ , that is
ST = [tex]\frac{1}{2}[/tex] PQ , so
5x - 22 = [tex]\frac{1}{2}[/tex] (3x + 19) ← multiply both sides by 2 to clear the fraction
10x - 44 = 3x + 19 ( subtract 3x from both sides )
7x - 44 = 19 ( add 44 to both sides )
7x = 63 ( divide both sides by 7 )
x = 9
Then
PQ = 3x + 19 = 3(9) + 19 = 27 + 19 = 46
The graph shows the value of a certain model of car compared with its age.
Which statement is false?
Car's value ($)
Car's ago (years)
A. The correlation coefficient is close to -1,
B. The car's value is the explanatory variable.
O O Od
C. The car's age is strongly correlated to its value.
D. The data show a negative linear relationship.
Answers
Answer:
B. The car's age is the explanatory variable
Step-by-step explanation:
The graph shows a negative linear relationship between car's age and car's value because, as as one variable increases, the other decreases.
Also, data points are close to each other along the line of best fits, therefore, the correlation coefficient would be close to -1, showing a strong negative relationship.
An explanation variable is one that isn't affected or dependent on another variable. In this case, the car's age is the explanatory variable and not the car's value. The car's value is dependent on the car's age, therefore, the car's age is the explanatory variable.
The statement in option B is FALSE.
Dylan is saving money to buy a new bike that costs $195. He has $25 already saved and plans to save $40 each week. Which equation can be used to find the number of weeks he will need to save money to buy the bike?
Answers
Answer:
25+40x=195
Step-by-step explanation:
If he already has $25, you need to add that to 40x (40 times the amount of weeks it takes to get to 195, added with 25).
2/3 of a class are girls.
a) What is the ratio girls to boys in the class?
b) What is the ratio boys to girls in the class?
Answers
b) 1:3
2/3 of the class are girls, so 2:3. That leaves 1/3 of the class as boys, so 1:3 ratio.
9
Find the area of the triangle.
Please help
Answers
Answer:
[tex]6ft^2[/tex]
Step-by-step explanation:
The formula to find the area of a triangle: [tex]A=\frac{1}{2} bh[/tex]
The base is 4 because 2 + 2 = 4
[tex]A=\frac{1}{2}( 4)(3)[/tex]
[tex]A=\frac{1}{2} (12)[/tex]
[tex]A=6[/tex]
Hope this helps
Answer:
A) The first one for whole triangle = 6ft^2
or
B) The second one for blue = 3ft^2
Step-by-step explanation:
T1 Area = 1/2 x 3 x 4 = 6ft^2
T2 Area = 1/2 x 3 x 2 = 3ft^2
T3 Blue Area = 6-3 = 3ft^2
In a bowl of fruit, there are green grapes and black grapes in the ratio 3:4 If there are 24 green grapes, how many black grapes are there?
answer is 32
ask me more questions any time
Answers
Help me I have more pls
Answers
Answer:
y= 2/3x +4
Step-by-step explanation:
choose 2 points to find slope
I chose points of intersection
(-6,0) (0,4)
m=y2-y1/x2-x1
[tex]m = \frac{4 - 0}{0 - ( - 6)} = \frac{2}{3} [/tex]
then use slope point form rule
y-y1=m(x-x1)
[tex]y - 4 = \frac{2}{3} (x - 0) \\ \\ y = \frac{2}{3} x + 4[/tex]
Answer:
y = [tex]\frac{2}{3}[/tex] x + 4
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 6, 0) and (x₂, y₂ ) = (0, 4) ← 2 points on the line
m = [tex]\frac{4-0}{0-(-6)}[/tex] = [tex]\frac{4}{0+6}[/tex] = [tex]\frac{4}{6}[/tex] = [tex]\frac{2}{3}[/tex]
The line crosses the y- axis at (0, 4 ) ⇒ c = 4
y = [tex]\frac{2}{3}[/tex] x + 4 ← equation of line
2x-3 5x+6= Multiply and combine like terms
Answers
Answer:
10x^2 - 3x -18
Step-by-step explanation:
if you meant (2x-3)(5x+6), you just multiply out
Answer:
Step-by-step explanation:
Use FOIL method
(2x - 3)(5x + 6) = 2x*5x + 2x*6 + (-3)*5x + (-3) *6
= 10x² + 12x - 15x - 18 {Combine like terms}
= 10x² - 3x - 18
Like terms are terms that have same variable with same power.
SOMEONE PLS HELP ME!!!
Answers
The axis of symmetry is a line that splits a graph into two mirror images. For a parabola, the axis of symmetry goes through the vertex and is a vertical line.
The axis of symmetry for this graph is x = -1.
Hope this helps!! :)
Name a geometric figure that could be the height of a tree
Answers
Answer:
Triangle
Step-by-step explanation:
h = Tan A x d, where h is the tree height, d is the distance from tree, and A is the angle to the top of the tree.
Basically you want to solve for the hypotenuse by using basic trig
On a number line, a number, b, is located the same distance from 0 as another number, a, but in the opposite direction
The number b varies directly with the number a. For example b= 2 when a = -2
-2. Which equation represents this
direct variation between a and b?
Obra
O b = a
Ob-a= 0
Ob(-a) = 0
Answers
Answer:
b = -a
Step-by-step explanation:
We know that:
On a number line, the distance between 0 and b is the same distance that between 0 and a (but b and a are in opposite sides of zero).
And we know that, for example, when:
b = 2, a = -2
Remember that the distance between two values is given by:
|n - m|
Then the distance between 0 and b is:
|0 - b|
and the distance between 0 and a is:
|0 - a|
we have:
|-b| = |-a|
|b| = |a|
But the numbers are in opposite sides of the zero, so one must be positive and the other negative, then we can conclude that:
b = -a
or
-b = a
(these are equivalent)
Then the correct option is the first option:
b = -a
Select the correct answer from the drop-down menu. James is competing in the shot put event for his track team. His best attempt can be modeled using the quadratic function below, where x represents the horizontal distance, in feet, the shot traveled and h(x) represents the height, in feet, of the shot. h(x) = -0.05.12 + I +6 feet. It continues to increase until x= feet, and then In this situation, the height of the shot starts to increase when x = the height decreases until x= feet.
Answers
Answer:
What I did not understand the question properly.Is it a original question
Anita burger purchased 14 gallons of gas for $34.72. How much did she pay for each gallon
Answers
Step-by-step explanation:
14 gallons bought for $34.72
1 gallon bought for
[tex] \frac{34.72}{14} [/tex]
=$2.48
16. Solve y2 - 17x + 30 = 0 by factoring.
Answers
Answer:
x = 15 , x = 2
Step-by-step explanation:
[tex]x^2 -17x + 30 =0\\\\x^2 -2x-15x +30=0\\\\x(x-2)-15x(x-2) =0\\\\(x-15)(x-2)=0\\\\[/tex]
x = 15 , x = 2
the sum of three consecutive even intergers is 30. what are the intergers?
Answers
Answer:
8, 10, 12
Step-by-step explanation:
3 consecutive even integers are 8, 10, 12
8 + 10 + 12 = 30.
Answer:
8, 10 ,12
Step-by-step explanation:
Let x be the first integer
x+2 is the second
x+4 is the third
The sum is 30
x+ x+2 + x+4 = 30
Combine like terms
3x+6 = 30
Subtract 6 from each side
3x+6 -6 =30-6
3x = 24
Divide by 6
3x/6 = 24/6
x = 8
x, x+2, x+4 is 8, 8+2, 8+4,
8, 10 ,12
Express 60g as a percentage of 3kg?
Answers
Answer:
SOLUTION IS ON PICHOPE IT HELPS YOUMARK AS BRAINLIST ANSWERThe conditional relative frequency table was calculated by row using data from a survey of one station’s television programming. The survey compared the target audience with the type of show, either live or recorded, over a 24-hour time period.
A 4-column table with 3 rows titled television programming. The first column has no label with entries adult, children, total. The second column is labeled live with entries 0.625, 0.5, nearly equal to 0.583. The third column is labeled recorded with entries 0.375, 0.5, nearly equal to 0.417. The fourth column is labeled total with entries 1.0, 1.0, 1.0.
Which is the best description of the value 0.375 in the table?
Given that the program was targeted at adults, there is a 37.5% chance that it was recorded.
Given that the program was recorded, there is a 37.5% chance that it was targeted at adults.
37.5% of the programs are targeted at adults.
37.5% of the programs are recorded.
Answers
Answer:
37.5% of the programs are targeted at adults
Step-by-step explanation:
The following figure shows the given four column table for the target audience of television programming
[tex]\begin{array}{lllc}&Television \ Programming \\& Live&Recorded&Total\\Adult&0.625&0.375&1.0\\Children&0.5&0.5&1.0\\Total&\approx 0.583& \approx 0.417&1.0\end{array}[/tex]
From the table, we have that the best description of the value 0.375 in the table is that the percentage of television program targeted at adults is 37.5%
Answer:
The answer is a “Given that the program was targeted at adults, there is a 37.5% chance that it was recorded”
Step-by-step explanation:
i did the test
I’m doing algebra homework and I’m really stumped on this problem I could use the help
Answers
Step-by-step explanation:
Zeros : -2
axis of symmetry : x = -2
Max or Min : min
Vertex : (-2, 0)
