We have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.
A right angle triangle is given.
We have to prove that measure of the segment that joins the vertex of the right angle in a right triangle to the midpoint of the hypotenuse is one-half the measure of the hypotenuse.
What is a triangle ?
A triangle is a 3-sided shape. There are three sides and three angles in every triangle, some of which may be the same.
As per the question ;
Let's assume P is the midpoint of the hypotenuse of the right angle △ABC and it is right angled at B. Also , D is the midpoint of AB.
Now ;
Draw a line parallel to BC from P meeting B at O and join PB.
Here ;
In △PAD and △PBD
∠PDA =∠PDB = 90°
and
PD = PD common)
AD = DB (As D is mid point of AB)
So ;
△ PAD ≅ PBD
by SAS rule
and
PA = 1/2 PB
Thus , we have proved that PA = 1/2 PB using the SAS rule or Side Angle Side rule.
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Which function is the inverse of f (x) = 2 - 6?
O f¹(z) = +6
Of¹ (2)=+9
Of-¹ (z)=-6
Of¹ (2)=4-9
A student incorrectly claims that 2/3 divided by 5/9 = 5/6 find the correct quotation.What was the students error
Answer:
See explanation
Step-by-step explanation:
2/3 / 5/9=
2/3 * 9/5= ==> Dividing by a number is basically multiplying by its reciprocal.
(2*9)/(3*5)=
18/15=6/5 ==> The student just switched the numerator and denominator.
Answer:
6/5
Step-by-step explanation:
2/3÷5/9=2/3x9/5=2/1x3/5=6/5
In this problem, you will investigate the relationship between same-side exterior angles.
e. Write a proof of your conjecture.
Eight angles are formed when two parallel lines are intersected by a third line that intersects them at an acute angle, known as a transversal line. These angles interact in a number of ways, one of which is the same-side exterior. Both angles are on the same side of the transversal line, as indicated by the word "same-side," and both are "external," or "outside," of the parallel lines, as represented by the term "outside."
When a transversal crosses two parallel lines, it creates an angle between the lines and outside the lines on the same side. Because the alternate interior and alternate exterior angles are the same, and because linear pairs of angles are supplementary, the identical side angles are also supplementary.
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Click the pair of numbers that are relatively prime.
11 and 121
35 and 125
39 and 75
34 and 49
34 and 49 is pair of numbers that are relatively prime.
What is relatively prime example?
If there isn't an integer bigger than one that divides two integers, then those two numbers are substantially prime (or coprime) (that is, their greatest common divisor is one). For instance, 12 and 13 are not very prime numbers, whereas 12 and 14.What do you mean by relatively prime?
If there are no other positive factors (divisors) between two integers other than 1, they are considered to be relatively prime. Two integers and are said to be relatively prime if using the notation to represent the greatest common divisor.34 and 49 is the pair of numbers that are relatively prime.
The numbers have no common prime factors.
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Answer:
D
Step-by-step explanation:
Just did it on T4L
Find the slope of the line through each pair of points. (1,3) and (4,9)
The slope of the line passing through the pair of points, (1 , 3) and (4 , 9), is 2.
The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points. The formula for solving the slope is:
m = (y2 - y1)/(x2 - x1)
where m is the slope
x1 and y1 are the coordinates of one point
x2 and y2 are the coordinates of the 2nd point
Given two points in the line, (1 , 3) and (4 , 9), plug in the values to the formula for the slope.
m = (y2 - y1)/(x2 - x1)
m = (9 - 3)/(4 - 1)
m = 6/3
m = 2
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The perimeter of a rectangle is 398 meters.
The perimeter of a rectangle is 398 meters. The rectangle has a length of (12x-3) meters and a width of (8x+2) meters. What are the dimensions of the rectangle?
The value of perimeter of the rectangle is 398, So the length is 177m and breadth is 82m.
What is perimeter of rectangle?
The complete length of a rectangle's outside edge is known as its perimeter. The formula P=2l+2w, where l is the rectangle's length and w is its width, determines the perimeter P of a rectangle.
Given the perimeter of the rectangle = 398
perimeter of rectangle = 2 × (L + B)
Length of rectangle = (12x-3)
Breadth of rectangle = (8x+2)
⇒ perimeter of rectangle = 2 × (12x-3 + 8x+2)
⇒ 398 = 2 × (20x - 1)
⇒ 199 = 20x - 1
⇒ x = 200/20
⇒ x = 10
Length = 120 . 10 - 3
Length = 117
Breadth = 8.10+2
Breadth = 82
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Answer:
length = 117
width = 82
Simplify (2y-5)(2y+5)
Answer:-10
Step-by-step explanation:
Answer: 4y^2-25
Step-by-step explanation:
Name the geometric term modeled by a bridge support beam
Answer:
Line
Step-by-step explanation:
Extends in two directions
The geometric term modeled by a bridge support beam is "cylinder."
Given data:
A bridge support beam often takes the form of a cylindrical shape to provide structural integrity and distribute the weight of the bridge and its load evenly. Cylinders have circular cross-sections.
A bridge support beam is often modeled as a "cylindrical" structure in geometry. Cylinders are three-dimensional geometric shapes characterized by their curved lateral surface and two circular bases of the same size and shape. When designing bridge support systems, engineers often opt for cylindrical beams due to their inherent strength and ability to distribute weight efficiently.
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If x in {- 2, - 1, 0, 1, 2} find the solution set of x + 2 > 1
Answer:
if x is an element of that set therefore after solving the inequality we will determine the solutions according to the given set of numbers.x+2>1
x>1-2
x>-1
now from the set choose ot the numbers which are greater that -1
we find that x=0,1 and 2
Answer:
{0, 1, 2}.
Step-by-step explanation:
x + 2 > 1
x > 1 - 2
x > -1.
So, the solution set is:
{0, 1, 2}
Determine whether Δ P Q R ≅Δ X Y Z . (Lesson 4-4)
P(8,1), Q(-7,-15), R(9,-6), X(5,11), Y(-10,-5) , Z(6,4)
The measurement of triangle ΔPQR ≇ ΔXYZ.
What do we mean by the congruency of a triangle?Two triangles are said to be congruent if all three corresponding sides and angles are equal in size.To appear identical, these triangles can be moved, rotated, flipped, and turned.They will coincide if they are moved.Congruence exists when two triangles satisfy the five congruence conditions.They are the side-side-side (SSS), the side-angle-side (SAS), the angle-side-angle (ASA), the angle-angle-side (AAS), and the right angle-hypotenuse-side (RHS).So,
To prove: ΔPQR ≅ ΔXYZ
P(8,1) ≠ X(5,11)Q(-7,-15) ≠ Y(-10,-5)R(9,-6) ≠ Z(6,4)So, we can say that ΔPQR ≇ ΔXYZ.
Therefore, ΔPQR ≇ ΔXYZ.
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What is the answer to this problem?
Answer:
b = 8
........................
Solve the quadratic equation by compeleting the square. x^2 + 8x = 10
The value of x for the quadratic equation is 1.099 or -9.099 .
What is completing the square?
Completing the Square is a method used to solve a quadratic equation by changing the form of the equation so that the left side is a perfect square trinomial .
To solve ax²+bx+c=0 by completing the square:
1. Transform the equation so that the constant term, c , is alone on the right side.
2. If a , the leading coefficient (the coefficient of the x² term), is not equal to 1 , divide both sides by a .
3. Add the square of half the coefficient of the x -term, to both sides of the equation.
4. Factor the left side as the square of a binomial.
5. Take the square root of both sides. (Remember: (x+q)²=r is equivalent to x+q= ±√ r.)
6. Solve for x .
According to the question
Quadratic equation by completing the square
x² + 8x = 10
As we will try to make complete square of left side
for that
we have to add to both sides of the equation
As
a = 1
2ab = 8
b = 4
x² + 8x + 4² = 10 + 4²
By using the identity ( )
(x + 4)² = 10 + 16
(x + 4)² = 26
x + 4 = ±
x + 4 = ± 5.099
x = 5.099 - 4
x = 1.099
or
x = -5.099 - 4
x = -9.099
Hence, The value of x for the quadratic equation is 1.099 or -9.099 .
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HELP I WILL MAKE BRANLIEST CHECK SCREENSHOT FOR QUESTION
The following angles of the given triangles arranged from the smallest to the largest:
In triangle ΔXYZ: ∠X, ∠Z, and ∠Y
In triangle ΔXYW: ∠X, ∠Y, and ∠W
What is the Relationship between Angles and Sides of a Triangle?The size of the angles of a triangle are relative to the side lengths of each side opposite each of the angles in a tringle.
This implies that, a larger angle will face the longest side of the triangle, the mid-sized angle faces the mid-sized side, while the smallest angle is opposite to the shortest side of the triangle.
Based on the relationship between angles and sides of a triangle, we have the following angles of the given triangles arranged from the smallest to the largest:
In triangle ΔXYZ: ∠X, ∠Z, and ∠Y
In triangle ΔXYW: ∠X, ∠Y, and ∠W
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Determine whether each series is arithmetic or geometric. Then evaluate the finite series for the specified term number. 2+6+18+ . . . . . . ; n=6
The given series is a geometric series. The sum of its first 6 terms is 728.
To determine whether the series is an arithmetic or geometric one, we need to check how the consecutive terms relate to each other.
If it is an arithmetic series, then:
a(n) = a(n-1) + d
where d is the common difference.
If it is a geometric series, then:
a(n) = a(n-1) . r
where r is the common ratio.
The given series is:
2+6+18+ . . . .
and the number of terms is 6.
In the given series:
a(1) = 2
a(2) = 6
a(3) = 18
Notice that
a(2)/a(1) = 6/2 = 3
a(3)/a(2) = 18/6 = 3
Since the ratio of consecutive terms are constant, then the given series is a geometric series. Furthermore, its ratio, r = 3
Sum formula for the first n term of a geometric series is:
S(n) = a(1) . (rⁿ -1)/(r -1)
Substitute n = 6, a(1) = 2, and r = 3
S(6) = 2 . (3⁶ - 1)/(3 - 1)
S(6) = 2. 364
= 728
We can also evaluate the sum directly. Write all the terms until n = 6.
a(4) = 18 . 3 = 54
a(5) = 54 . 3 = 162
a(6) = 162 . 3 = 486
Hence, the series is:
2+6+18+54+162+486 = 728
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you earn $10 per hour babysitting and you babysit 25 hours each week. You also help your neighbor with household chores and are paid $8 per hour. If you spend 12 hours helping your neighbor, how much will you earn in one week?
Answer:
$346
Step-by-step explanation:
Babysitting = $250
($10 × 25 hrs)
Neighbour's Chores = $96
($8 x 12 hrs)
Total Earning = $346
($250 + $96)
Betsy has a bag with three mint sticks eight jelly treats and nine fruit tart chews if she eats one piece every three minutes what is the probability her first two pieces will be a fruit tart chew and a jelly treat
If Betsy has a bag with three mint sticks, eight jelly treats, and nine fruit tart chews and she eats one piece every three minutes, the probability her first two pieces will be a fruit tart chew and a jelly treat is 18.9%.
The probability of her first two pieces being a fruit tart chew and a jelly treat can be calculated as follows,
First, we divide the expected outcomes by the total possible outcomes.
Total possible outcomes = 3(mint sticks) + 8(jelly treats) + 9(fruit tart chews) = 20
Hence,
Probability for fruit tart chew: 9 ÷ 20
Probability for jelly treat: 8 ÷ 19 (as one possibility is considered to be fruit tart chew)
The probability of her first two pieces to be fruit tart chew and jelly treat can be determined by multiplying the probability for fruit tart chew with the probability for jelly treat,
Probability = (9/20)(8/19)
Probability = 72/380 = 0.189
Converting into percentage,
Probability = 0.189 × 100 = 18.9%
Hence, the probability that her first two pieces will be a fruit tart chew and a jelly treat is equal to 18.9%.
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Using the function you entered in Activity 1, set up the table as shown.
Scroll to x- values less than 3 . Do they make the inequality true?
Answer:
yes
yjnujhhhbhhhjhhbhhbhhhjj
Carla puts $625 into a savings account at an annual interest rate of 2.5%. If she does not withdraw or deposit any money, what is the interest that Carla will earn at the end of 6 months?
The formula is I=prt
Please dont put random answers
Ill give brainlyist to the correct answer
Answer: 7 81 cents
Step-by-step explanation:
yes
Evaluate the expression for the given values of the variables.
9t+6(2v-t)-7v;t=1 and v=5
The expression will give value 28
To evaluate the expression for the given value of variables, we will keep the value of each variable in the equation. The expression will be solved based on the arithmetic operators given in expression.
Rewriting the expression -
Value = 9t + 6 (2v - t) - 7v
Now keeping the value of v and t in expression to find the value.
Value = 9×1 + 6 (2×5 - 1) - 7×5
Firstly solving the bracket and performing multiplication of extreme left and right values of expression
Value = 9 + 6 (10 - 1) - 35
Value = 9 + 6 (9) - 35
Value = 9 + 54 - 35
Performing addition before subtracting the values
Value = 63 - 35
Performing subtraction
Value = 28
Hence, the expression according to given variables is equal to 28.
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Find each sum.
-1.95+10
Write an equation for each line in point-slope form and then convert it to standard form.
through (2,3) and (3,5)
The point-slope form is y - 3 = 2(x - 2) and 2x - y = 1 be the standard form.
How to find the equation in point-slope form?Given: (x1, y1) = (2, 3) and (x2, y2) = (3, 5)
The point-slope form is given by,
y - y1 = m(x - x1)
m = (y2 - y1)/(x2 - x1)
substitute the values in the above equation, we get
m = (5 - 3)/(3 - 2)
The value of m = 2.
Point-slope form is y - 3 = 2(x - 2)
Therefore, the point-slope form is y - 3 = 2(x - 2).
How to rewrite the equation in standard form?
The standard form is Ax + By = C
Since, slope-intercept form is y = 2x - 1
⇒ 2x - y = 1
Therefore, 2x - y = 1 is the standard form.
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Solve 5x - 2.5 = 17.5
X =
what si the answer for 2+2
Answer:
4
Step-by-step explanation:
2+2=4
Inverses from Algorithms
Suppose you were given the following algorithm:
Start with a number "n"
• Add 2
• Multiply the result by 3
• Subtract 10 from that result
• Square the final number
Use this algorithm to respond to the questions.
What is the correct order?
The steps to get the inverse of the given function are;
Take the square rootAdd 2Divide by 3Subtract 2How to find the inverse of a function?We are given the function;
Start with a number "n"
• Add 2
• Multiply the result by 3
• Subtract 10 from that result
• Square the final number
An inverse function is a function that undoes the action of the another function
Thus, the steps to get the inverse of the above function is as follows;
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Is it possible to find a value of $x$ so that the value of the surface area (in square inches) is equal to the value of the volume (in cubic inches)? a rectangular prism with length labeled 9 inches, width labeled 4 inches, and height labeled x inches.
A rectangular prism can have a surface area equal to its volume given the dimensions are 9 inches long, 4 inches wide and x inches high, where x is equal to 7.2 inches.
A rectangular prism is a three-dimensional figure with 8 vertices, 12 edges, and 6 rectangular faces.
If the dimensions of a rectangular prism is:
L = 9 inches
W = 4 inches
H = x inches
then the value of its surface area is equal to the value of its volume.
SA = V
2(lw + wh + lh) = lwh
Substitute the values and solve for x.
2(lw + wh + lh) = lwh
2[(9)(4) + 4x + 9x] = (9)(4)x
2(36 + 13x) = 36x
72 + 26x = 36x
10x = 72
x = 7.2 inches
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How many books does Jeff own if he has more than 14 books? Describe the number of books that Jeff owns if you add the constraint that he owns fewer than his sister, who owns 19 books.
Jeff can own 15,16,17 or 18 books as per the given question
The following question is based on inequality. Inequalities are mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. In this type of question, we will get a range of answers and not a specific answer.
No. of books owned by Jeff > 14
No. of books owned by his sister = 19 books
As per the question "He owns books fewer than his sister"
So, he owns >14 and <19 books
Therefore, he can own 15, 16, 17 or 18 books as per the given inequality.
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help please with all answers !☹️
Answer:
Here are the answers!
Step-by-step explanation:
When there are two angles on a line that are touching you can subtract what you know from 180° (Ex: 138° and angle 4)
The angles across from each other are the same.
The total of all three angles in a triangle should be 180°
Hannah is baking two cakes.
One cake needs 1 1/3 cup of milk han had 1 1/4 cup of milk how much does she need
Answer: 2 2/3
Step-by-step explanation:
Fred started a new e-Commerce business and borrowed $13,100 for 13 years to get the business up and running. The interest is $3916.90. Find the rate.
Round to two decimal places, if necessary.
Simple Interest
The rate of interest is 0.26%
Given,
The amount borrowed by Fred to start a new e-commerce business = $13100.
Time of investment = 13 years.
Interest for the money = $3916.90
We have to calculate the rate of interest.
For simple interest, equation is:
P = IRT
Where,
P = Principal amount
R = Rate of interest
I = Interest
T = Time period
Here,
P = 13100
I = 3916.90
T = 13
Then,
R = P / IT
R = 13100 / (3916.90 × 13)
R = 13100 / 50919.7
R = 0.26%
Therefore, the rate of interest is 0.26%
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-|10-7•5+8•-4+2•2| helppppppppp
Answer: -53
Step-by-step explanation:
-|10-7•5+8•-4+2•2|=
-|10-7•5+8•(-4)+2•2|=
-|10-35+(-32)+4|=
-|-25-32+4|=
-|-25-28|=
-|-53|=
-(53)=-53
