Answer:
The lengths are 5, 12, and 13.
Step-by-step explanation:
Let x represent the shorter leg of the triangle. Since the other leg is 7 cm more, the longer leg is x+7. Since the length of the hypotenuse is 3 cm more than double that of the shorter leg, the hypotenuse is 2x+3.
The Pythagorean Theorem may be used to find the lengths.
[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex] a, b are the short and long lengths and c is the hypotenuse
→ [tex]x^{2} + (x+7)^{2} = (2x+3)^{2}[/tex]
→ [tex]x^{2} + x^{2} + 14x + 49 = 4x^{2} + 12x + 9[/tex]
→ [tex]2x^{2} + 14x + 49 = 4x^{2} + 12x + 9[/tex]
→ [tex]2x^{2} - 2x - 40 = 0[/tex]
→ [tex]x^{2} - x - 20 = 0[/tex]
→ [tex](x-5)(x+4) = 0[/tex]
→ [tex]x = 5[/tex] (The length cannot be negative)
The shorter leg, x, is 5 cm. Since the longer leg is x+7, it is 12 cm. Since the length of the hypotenuse is 2x+3, the hypotenuse is 13 cm.
A triangle can have at most______right angle.
A. 4
B. 1
C. 0
D. 2
Answer:
B, 1 right angle
Step-by-step explanation:
Triangles don't have the same length of there sides. The sides are uneven which makes the triangle unique. Also, right triangles only have 1 right angle
Hope this helps
Mark brainliest pls
Answer:
B
Step-by-step explanation:
Another way you can think about it is by thinking about the total possible angle sum. The angles in a triangle must sum to 180, so if there are 2 or more right angles, then you either cant have a 3rd angle because thats already at or over 180 degrees. That is why it must be 1.
Jordan has some music books. He will buy 9 new music books each year. He will have 52 music books in 5 years. Rate of change per year = ____ Initial value = _____
Consider the line x-4y= -5.
Find the equation of the line that is parallel to this line and passes through the point (-7, -6).
Find the equation of the line that is perpendicular to this line and passes through the point (-7, -6).
Answer:
1) x-4y-22=-5
2) y=-4x-34
Step-by-step explanation:
write the formula of loss where cost price(CP) and
selling price(SP) are given
Answer:
CP - SP = LOSS when CP is more than SP
Triangles R S T and V U T are connected at point T. Angles R S T and V U T are right angles. The length of side R S is 12 and the length of side S T is 16. The length of side T U is 8 and the length of U V is 6. Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem? StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction and angle S is-congruent-to angle U StartFraction R S Over V U EndFraction = StartFraction S T Over U T EndFraction = StartFraction R T Over V T EndFraction StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction and angle S is-congruent-to angle U StartFraction R S Over V U EndFraction = StartFraction T U Over T S EndFraction = StartFraction R T Over V T EndFraction
Answer:
[tex]\dfrac{\overline{RS}}{\overline{VU}}=\dfrac{\overline{ST}}{\overline{UT}}\quad\text{and}\quad\angle S\cong\angle U[/tex]
Step-by-step explanation:
To use the SAS similarity theorem, you must show proportionality between corresponding sides, and congruence of the angle between them.
The answer shown above is the only answer choice that mentions an angle.
__
Comment on other choices
Choice B shows the three sides are proportional, so would be useful if the SSS similarity theorem were to be invoked. It isn't helpful for the using the SAS similarity theorem.
Choices C and D get the proportion statements wrong.
Answer:
RS/VU=ST/UT and Angle S congruent Angle U
five more than the quotient of a number x and six
Answer:[tex]\frac{x}{6}[/tex] + 5
Step-by-step explanation:
Answer:
x/6 + 5.
Step-by-step explanation:
The quotient of x and 5 is x/6.
Adding 5 we get:
x/6 + 5.
please help me!!!! (i only need question 1)
Answer:
28
Step-by-step explanation:
So I just figured out by counting. The top has 8, which means the bottom also has 8. The sides are 3, 2, 1, 1, 2, 3
The total is 8 + 8 + 3 + 2 + 1 + 1 + 2 + 3 = 28
Solve 18>12+x. Graph the solution.
The solution is ?
Answer:
x < 6.
Step-by-step explanation:
18 > 12+x
18 - 12 > x
x < 6.
The graph will be a vertical dotted line passing through the point (6, 0) and shaded to the left.
What is the sum? 8 + (negative 12)
Answer:
your answer is -4!
Step-by-step explanation:
plz mark me brainliest
Can someone help me with this homework?
Answer: (-4, -1)
Step-by-step explanation:
Starting at point (-4, -2) and translating 3 units up means we add 3 to -2.
So the new point is now (-4, 1).
Now we reflect over the x-axis which means the y-value of 1 becomes negative.
So the final point is (-4, -1)
Answer:
(-4,-1)
Step-by-step explanation:
when you translate it by 3 units up, it becomes (-4,-1). and when you reflect over the x axis, it becomes (-4,-1)
Write the coordinates of the image of Q(-3,-6) reflected in the line y=x
HELP PLEASE I RLY NEED HELP URGENT
Answer: (-6, -3)
Step-by-step explanation:
We have the point (-3, -6)
And we want to do a reflection over the line y = x.
When we do a reflection of the point (x, y) over the line y = x. the reflected point will be (y, x)
So if our original point is (-3, -6) then the reflected point is (-6, -3)
(2x + 5)(2x - 5)
find the product
Answer:
4x^2 -25
Step-by-step explanation:
(2x + 5)(2x - 5)
FOIL
first: 2x*2x = 4x^2
outer : 2x*-5 = -10x
inner : 5*2x = 10x
last: -5*5 = -25
Add them together
4x^2 -10x +10x -25
Combine terms
4x^2 -25
Answer:
4x²- 25
Step-by-step explanation:
Let's use the FOIL (First, Outer, Inner, Last) method to solve:
(2x + 5)(2x - 5)
FOIL
First:
(2x + 5)(2x - 5)
2x(2x)
= 4x²
FOIL
Outer:
(2x + 5)(2x - 5)
2x(-5)
= -10x
FOIL
Inner:
(2x + 5)(2x - 5)
5(2x)
= 10x
FOIL
Last:
(2x + 5)(2x - 5)
(5)(-5)
= -25
Let's put it all together:
4x² - 10x + 10x - 25
Combine like terms:
4x² - 10x + 10x - 25
4x²- 25
Therefore, the product is 4x²- 25.
What is the factors of 27
Answer:
1, 27, 3, 9,
Step-by-step explanation:
To find the factors of 27 you need to find which whole number times another whole number = 27
We know that 1*27 = 27
We also know that 3*9 = 27
The factors are all the numbers that are used in the multiplication.
In this example the numbers are: 1, 3, 9 and 27
Answer:
1,9,3,27
Step-by-step explanation:
if we break it down we can see:
1x27=27
9x3=27
The table represents function f,and the graph represents function
Answer:
The line of symmetry for function f is x = 2 and the line of symmetry for function g is x = 1.
The y-intercept of function f is greater than the y-intercept of function g.
Over the interval [2, 4], the average rate of change of function f is greater than the average rate of change of function g.
Berto has $12 and 3.75 per gallon how much gas can he get
Answer:
(3.2, 12)
Step-by-step explanation:
Total cost for gas = $12
Cost per gallon = $3.75
Letting total cost of gas be y and number of gallons be x, maximum number of gallons of gas he can buy would be ;
Total cost of gas/ cost per gallon = 12 / 3.75 = 3.2 gallons
Therefore , the coordinate pair (x, y) = (3.2, 12)
What answer is equivalent to -4(b + 2) - 36?
Answer:
− 4 b − 44
Step-by-step explanation:
Answer:
-4(b + 11)
Step-by-step explanation:
-4(b + 2) - 36 (multiply -4 into parentheses via distributive property)
= b(-4) + 2(-4) - 36
= -4b -8 - 36
= -4b - 44 (this could be an answer, but we can still simplify further by factoring out -4)
= -4(b + 11)
The perimeter of a figure is the total length of all of its sides.
False
True
Only answer if you know it’s a quiz
Answer:
True.
Step-by-step explanation:
That is exactly what a perimeter is. Hope this helps
If 15/50 = x/100, then x=
Answer:
30
Step-by-step explanation:
If 15/50 = x/100,
then 50x=1500,
and x-30
:-)
Find the surface area of the cylinder. Round to the nearest tenths.
Answer:
The surface area of the cylinder is 251.2cm²
Step-by-step explanation:
To solve this problem we have to calculate the circle area and the lateral area
radius = half of diameter
r = 10/2 = 5cm
To calculate the area of the circle we use the following formula
a = area
r = radius = 5cm
π = 3.14
a = π * r²
we replace with the known values
a = 3.14 * (5cm)²
a = 3.14 * 25cm²
a = 78.5cm²
The area of the circle is 78.5cm²
To calculate the lateral area of the cylinder we use the following formula
a = area =
h = heighti = 3cm
r = radius = 5cm
π = 3.14
a = 2 * π * r * h
we replace with the known values
a = 2 * 3.14 * 5cm * 3cm
a = 6.28 * 15cm²
a = 94.2cm²
The lateral area of the cylinder is 94.2cm²
Now we add the lateral area of the cylinder with 2 times the area of the circle and obtain the area of the cylinder
94.2cm² + (2 * 78.5cm²) = 251.2cm²
The surface area of the cylinder is 251.2cm²
A plane is descending onto the runway with an angle of depression of 55°. If it has 2.8 miles to go before landing (hypotenuse), what is the current altitude of the plane?
A. 4.9 miles
B. 3.4 miles
C. 4 miles
D. 1.6 miles
E. 2.3 miles
Answer:
Option C is correct
Step-by-step explanation:
Given: A plane is descending onto the runway with an angle of depression of 55°. Also, it has 2.8 miles to go before landing.
To find: current altitude of the plane
Solution:
Consider the attached image.
In ΔABC,
[tex]\angle ACB=55^{\circ}[/tex] (Alternate interior angles)
For any angle [tex]\theta[/tex],
[tex]tan \theta[/tex] = side opposite to angle/side adjacent to angle
[tex]\tan C=\frac{AB}{BC}[/tex]
Put [tex]\angle C=55^{\circ}\,,\,BC=2.8\,\,miles[/tex]
[tex]AB=2.8\,\tan 55^{\circ}=3.999\approx 4\,\,miles[/tex]
So, the current altitude of the plane is 4 miles.
plz help
solve for q
Answer: -3
Step-by-step explanation:
-3^2=-3*-3=-9
Because the square of q is equal to -9, the square root of -9 is equal to q.
Because of this fact, we can find the square root of -9 to get our answer.
[tex]\sqrt{-9}[/tex] = 3 i.
Therefore, q is equal to 3 i or [tex]\sqrt{-9}[/tex].
Hope this helped! :)
Order these fractions from least to greatest 7/8 4/6 3/4
Answer:
4/6 , 3/4, 7/8
Step-by-step explanation:
7/8 4/6 3/4
The common denominator is 24
7/8*3/3 = 21/24
4/6* 4/4 = 16/24
3/4 * 6/6 = 18/24
From smallest to largest
16/24, 18/24, 21/24
4/6 , 3/4, 7/8
Logan is reading about architecture and learns that trusses can be used to support roofs. He wants to find the measures of the angles on a truss. truss.
Answer:
It could help Logan to first study the constitution and shape of this type of armor in order to make a mental image of the positions of the angles as well as the size.
Step-by-step explanation:
A previous study allows Logan to understand that these types of trusses have a triangular shape and are widely used in the construction of roofs, therefore Logan could use to draw this type of trusses.
The box plot represents the number of minutes customers spend on hold when calling a company. A number line goes from 0 to 10. The whiskers range from 2 to 8, and the box ranges from 3 to 6. A line divides the box at 5. What is the upper quartile of the data?
Answer:
6
Step-by-step explanation:
The upper quartile (also known as Q3) is the right most side of the BOX (where the box ends). In the question, it says the box is from 3 to 6 meaning that the box ends at 6.
I hope this helps!
Answer:
6
Step-by-step explanation:
The upper quartile is 6 because the box ends at 6 and that is the upper quartile which is sometimes also known as Q3
Determine the nature of the roots: 2x2 + 8x + 3 = 0
Answer:
the nature of the roots of an equation is real, distinct and irrational
Step-by-step explanation:
Given Data provided in the question according to the question is as follows:
[tex]2x^2 + 8x + 3 = 0[/tex]
where
a = 2 , b = 8 , c = 3
As we know that
Quadratic expression
[tex]ax^2 + bx +c = 0[/tex]
Delta = [tex]b^2 - 4ac[/tex]
[tex]= (8)^2 - 4 (2) (3)[/tex]
= 64 - 24
= 40
Here,
Delta > 0, it does not contain perfect square
Therefore the nature of the roots of an equation is real, distinct and irrational
Evaluate:
a = -3, b = 1, and c= -4
-21 - C
Type the correct answer, then press Enter.
Ar
Answer:the answer is -17
Step-by-step explanation:
ttthhee maatthhhpleeaasss
A STORY OF UNITS
Lesson 23 Problem Set
3.7
Mischa makes a 4 foot by 6 foot rectangular banner. She puts ribbon around the outside edges. The
ribbon costs $2 per foot. What is the total cost of the ribbon?
к
W
What I know-
What I want to know-
Is there a Special condition?
Type here each banner is 4 by Type here how much it will cos Type here- $2 per ft
6 ft and its $2 per ft
for two
The ribbon will cost $ _40_
Math is
AWESOME!
Answer:
$40 will be the total cost of the ribbon.
Step-by-step explanation:
To find the cost of ribbon to be put on the edges of rectangular banner, we need to:
1. Find the perimeter of the rectangle.
2. Multiply the perimeter with the per foot cost to find the total cost.
Let us find the perimeter first:
Perimeter of a rectangle is given as:
[tex]P = 2 \times \text{(length+width)}[/tex]
Here, the dimensions of rectangle are 4ft by 6ft.
So, perimeter = [tex]2 \times (4+6) \Rightarrow 20\ ft[/tex]
It is given that per foot cost is $2.
Total cost of the ribbon = [tex]2 \times 20 \Rightarrow $40[/tex]
$40 will be the total cost of the ribbon.
question is attached
Answer:
7 and -5
Step-by-step explanation:
1. Factor: (x-7)(x+5)
2. Set both to zero and solve
What is the probability that the reader’s favorite is Rowling given that the reader is a teen?
Leave the answer in decimal form to 3 decimal places.
Answer:
Probability = 0.500
Step-by-step explanation:
If it is given that the reader is a teen, we have a total of 80 readers, where 40 of those readers have Rowling as their favorite.
So the probability that the reader's favorite is Rowling given that the reader is a teen is the number of teen readers that have Rowling as favorite (40) over the total number of teen readers (80)
Probability = 40 / 80 = 0.500