Answer:
The length of the hypotenuse is 14 ft[tex] \: [/tex]
Step-by-step explanation:
We'll solve this using the Pythagorean theorem, we know that,
[tex]\\ {\longrightarrow \pmb{\sf {\qquad (Hypotenuse {)}^{2}= (Base) {}^{2} + (Perpendicular {)}^{2} }}}[/tex]
So, As it is given in the question that, the length of one leg of a right triangle is 9 ft and the length of the hypotenuse is 3 feet longer than the other leg and we are to find the length of the hypotenuse and the other leg.
[tex] \: [/tex]
Let us assume the other leg as x ft and therefore the hypotenuse will be (x + 3) ft.
[tex] \: [/tex]
Now, substituting the values in the formula :
[tex] \\ {\longrightarrow \pmb{\sf {\qquad (x + 3 {)}^{2} = (9 {)}^{2} + (x) {}^{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad (x {)}^{2} + 2.x.3 + {(3)}^{2} =81 + (x) {}^{2} }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad \cancel{ (x {)}^{2}} + 2.x.3 +9 =81 + \cancel{(x) {}^{2} }}}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 6x + 9 =81 }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 6x =81 - 9 }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad 6x =72 }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\sf {\qquad x = \frac{72}{6} }}} \\ \\ [/tex]
[tex]{\longrightarrow \pmb{\frak {\qquad x =12 }}} \\ \\ [/tex]
Therefore,
The length of other leg is 12 ft . And the length of hypotenuse is (12 + 2) ft = 14 ft
LOCKS SOON WILL GIVE BRAINLEST! 50 POINTS!!! For triangle xyz , the measures of angles x,y, and Z are known. Which method should be used to start solving triangle xyz?
law of sines
law of cosines
neither law can be used
both laws can be used
If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.
What is the law of cosines and sines?The law of cosines can be used to determine the measures of the triangle if the angles are known. The law is given by:
a² = b² + c² - 2bc*cosA
a,b,c are the sides and A, B, C are the angles.
The law of sines are used to determine the measures of the triangle if the angles are known. The law is given by:
a/sinA = b/sinB = c/sinC
If the angles of measures of angles X, Y, and Z are neither law of sine and cosine can be used to solve the triangle.
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What is the y-value of the vertex of the function f(x)=−(x+8)(x−14)?
Answer:
f(x) = -(x + 8)(x -14)
= -(x2 - 112 - 6x)
= -x2 + 6x + 112 --- (1)
We know the graph of an equation y = ax2 + bx + c where a ≠ 0 is a parabola. The parabola opens upwards if a > 0 and opens downwards if a < 0. The vertex of the parabola is the point where the axis and parabola intersect. Its x coordinate x = -b/2a and its y coordinate is found out by substituting x = -b/2a in the parabola equation.
The parabola given in the problem statement has a negative coefficient of x2 and hence it is a parabola which opens downwards. Also for the equation
a = -1, b = 6 and c = 112. Therefor the x-coordinate of the vertex is
x = -b/2a
= -(6)/[2(-1)]
= 3
Substituting the value of x = 3 in equation (1) we get,
Now y = -(3)2 + 6(3) + 112
= -9 + 18 + 112 = 121
So the vertex point coordinates are (3, 121) and the y value is 121.
The graph below verifies the vertex point.
vertex of the graph
What is the y-value of the vertex of the function f(x) = -(x + 8)(x - 14)?
Summary:
The y-value of the vertex of the function f(x) = -(x +
Answer:
Step-by-step explanation:
D or 121 got it right on edgenuty
The perimeter of thr rectangle shown is 36 inches. Write and solve an equation to find the value of x.
Answer:
X = 3
Step-by-step explanation:
(4x-6)+(4x-6)+12+12=36
Line m is represented by the equation y +2 = (x + 4). Select all equations that represent lines perpendicular to line
Answer
y = x + 2
hope this helped
lol
Simplify the expression. Write your answer as a power.
(xy)^7
Answer:
[tex](xy)^{7}[/tex]
↓
[tex]x^{7} y^{7}[/tex]
So the answer is [tex]x^{7} y^{7}[/tex].
Does anyone know the answer for this?
Answer:
88
Step-by-step explanation:
Answer:
8(4+7)
Step-by-step explanation:
The GCF of 32 and 56 is 8. Then you divide by 8.
A taco shop sells tacos and fountain drinks.
Nash bought two tacos and three fountain drinks
for $13. Everly bought four tacos and two
fountain drinks for $14. Write and solve a
system of equations to determine the cost of a
taco and a fountain drink.
The cost of one taco is $2, while the cost of one fountain drink is $3.
What are the system of equations that represent the question?
2t + 3f = $13 equation 1
4t + 2f = $14 equation 2
Where:
t = number of tacos bought f = number of drinks boughtHow many drinks were bought?Multiply equation 1 by 2:
4t + 6f = 26 equation 3
Subreact equation 2 from equation 3
4f = 12
Divide both sides by 4
f = 12 / 4
f = $3
How many tacos were bought?
Subsistute for f in equation 1
2(t) + (3 x 3) = $13
2t + 9 = 13
2t = 13 - 9
2t = 4
t = 4/2
t = $2
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Can someone please help me it is due today! Thank you to whoever can help.
y = 0.6x + 3
How to determine the equation of the line?To determine the equation of the line, we need to determine the slope and the y-intercept. Then, we will substitute the slope and the y-intercept in the slope intercept form equation to obtain the equation in slope intercept form.
Slope of line:Two points that lie on line: (0, 3) and (-5, 0)
[tex]\implies \text{Slope} = \dfrac{\text{Rise}}{\text{Run}} = \dfrac{y_{2} - y_{1}}{x_{2} - x_{1}}[/tex]
[tex]\implies \text{Slope} = \dfrac{3 - 0 }{0- (-5)}\\[/tex]
[tex]\implies \text{Slope} = \dfrac{3 }{0+5}\\[/tex]
[tex]\implies \text{Slope} = \dfrac{3 }{5} = 0.6[/tex]
Y-intercept of line:[tex]\implies \text{Intersection of line on y-axis: 3}[/tex]
[tex]\implies \text{y-intercept: 3}[/tex]
Equation of line:Slope intercept form:
y = mx + b[Where "m" is the slope and "b" is the y-intercept]
Substitute the slope (m) and the y-intercept (b) in the formula;
[tex]\implies \text{Slope intercept form: y = (m)x + (b)}[/tex]
[tex]\implies \text{Equation of line in slope intercept form: y = (0.6)x + (3)}[/tex]
Open the parenthesis in the equation;
[tex]\implies\text{Equation of line in slope intercept form: \boxed{\text{y = 0.6x + 3}}}[/tex]
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I’ll give you brainliest for the first person with an answer
Answer:
1296mm^2
Step-by-step explanation:
Surface Area of the Rectangular Prism to the left on top of the box:
Area of square = lw, 9mm * 9mm = 81mm, then multiply by 2 because 2 of the squares are a part of the surface, giving 162mm^2
Area of a rectangle =lw, 9mm * 9mm = 81mm, then multiply by 2 again, because 2 rectangles are a part of the surface, giving 162mm^2
So, the total surface area of the rectangular prism to the left on top, is 324mm^2
Surface Area of the Triangular Prism:
Area of a triangle: 1/2bh, and our base length would be 12, because we have to subtract 9 from 21 since the base length of the triangle isn't stated. Anyways, A = 1/2bh, so A = 1/2(12)(9) = 54mm^2, but multiply by two, so we get 108mm^2.
Area of the rectangle: lw, so 15mm * 9mm = 135mm^2
So, the total surface area of the triangular prism is 243mm^2
Surface Area of the Rectangular Prism at the bottom:
Area of the long rectangles in front = lw, 21mm * 9mm = 189mm^2, multiply by 2, 378mm^2
Area of the rectangles to the side = lw, 9mm * 9mm = 81mm^2, multiply by 2, 162mm^2
Area of the rectangle at the very bottom = lw, 21mm * 9mm = 189mm^2
So, the total surface area of the rectangular prism at the bottom is 729mm^2
Add all the total surface areas of each shape to get the total surface area of the figure:
324mm^2 + 243mm^2 + 729mm^2 = 1296mm^2
The surface area of the figure above is 1296mm^2
montreal canadiens memorabilia is on sale for 40% off due to their disappointing season how much would a jersey that cost $80 be after sales and tax
what is 40$ of 80?
Answer:
nothing much just got home
The volume of a box is 124.4 in3. Find the volume of a larger, similarly shaped box that has a scale factor of 4. Round your answer to the nearest tenth.
Using the scale factor, the volume of the larger similar shaped box is 497.6in³.
What is a Scale Factor?A scale factor is simply the ratio of the corresponding sides of two similar objects. A scale factor of 4 simply means that the new shape is multiply four times the size of the original shape.
Given the data in the question;
Volume of original box V° = 124.4in³Scale factor SF = 4Volume of the larger box V = ?Since scale factor of 4 means that the new shape is multiply four times the size of the original shape.
Volume of the larger box V = V° × SF
V = 124.4in³ × 4
V = 497.6in³
Therefore, using the scale factor, the volume of the larger similar shaped box is 497.6in³.
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MAn article is
bought and sold at a profit of one fourth of selling
price. Find the profit percent.
Answer:
25% profit
Step-by-step explanation:
Statement
An article is bought and sold at a profit of one fourth of selling price.
⇒ Buying price = x
⇒ Selling price = Buying price (1 + 1/4) = 5x/4
Profit %
Selling price - Buying price / Buying price(5x/4 - x) / x(x/4) / x⇒ 1/4⇒ 0.25⇒ 25% profitValue (in billions) 2017 2018
Total assets $16. 20 $16. 80
Total liabilities $14. 60 $14. 80
Deposits $11. 90 $12. 20
From 2017 to 2018, borrowings by commercial banks changed by $ _ billion (round your answer to two decimal places).
From 2017 to 2018, owner’s equity for commercial banks changed by $_ billion (round your answer to two decimal places)
Answer:
Borrowings = $0.10 Billion
Owner's Equity = $0.40 Billion
Step-by-step explanation:
Total liabilities = deposits + borrowings
Borrowings = total liabilities - deposits
Borrowings in 2017 = $14.60 - 11.90 = $2.70 billion
Borrowings in 2018 = $14.80 - $12.20 = $2.60 billion
Borrowings from 2017-2018= 2.60 - 2.70 = $0.10 billion
Owner's Equity= total assets - total liabilities
Owner’s equity in 2017 = $16.2 - $14.6 = $1.6 billion
Owner’s equity in 2018 = $16.8 - $14.8 = $2 billion
Owner's Equity from 2017-2018= 2 - 1.6 = $0.4 billion
Hope this helps!
The Owner's Equity for commercial banks in 2017-2018 is $0.4 billion.
The given is,
Borrowings = $0.10 Billion
Owner's Equity = $0.40 Billion
What is the formula for the total liabilities?Total liabilities = deposits + borrowings
So we have Borrowings = total liabilities - deposits
Borrowings in 2017
= $14.60 - 11.90
= $2.70 billion
Borrowings in 2018
= $14.80 - $12.20
= $2.60 billion
Borrowings from 2017-2018
= 2.60 - 2.70
= $0.10 billion
Owner's Equity= total assets - total liabilities
Owner’s equity in 2017
= $16.2 - $14.6
= $1.6 billion
Owner’s equity in 2018
= $16.8 - $14.8
= $2 billion
Owner's Equity from 2017-2018
= 2 - 1.6
= $0.4 billion
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Two consecutive positive integers have a product of 156. Find the integers.
The integers are ___
So here this question is of concept linear equations. As in linear equations we assumes the unknown number as an variable after that an equation would be formed which we would solve and get the answer. Here also we would be doing same.!!
So let us assume the unknown positive integers as a and (a + 1).
★ Product of both integers :-
a (a + 1) = 156 [Equation formed]★ Solving the equation :-
[tex]: \longrightarrow \: \sf{a \: (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a \times (a + 1) \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: = \: 156} \\ \\ : \longrightarrow \: \sf{a {}^{2} \: + \: a \: - \: 156 = 0} \\ \\: \longrightarrow \: \sf{a {}^{2} \: - \: 12a + 13a\: - \: 156 = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{a(a \: - \: 12) + 13(a\: - \: 12) = 0} \\ \\ : \longrightarrow \: \sf{(a \: - \: 12) (a\: + \: 13) = 0} \\ \\ : \longrightarrow \: \red{\bf{a \: = \: 12 }}[/tex]
Therefore,
First positive integer is 12★ Second positive integer :-
2nd positive integer = a + 1 2nd positive integer = 12 + 1 2nd positive integer = 13Evaluate the expression:
Will mark brainlyest!!
Answer:
6
Step-by-step explanation:
pemdas=parenthesis, exponents, multiplication, division, addition, subtraction. with this, we multiply 2 x the absolute value of -3, which is just 3. therefore, 6. now we see we need to subtract the absolute value of 6 from the absolute value of 8, which gives us 2. and 2+4 is 6.
Answer: 6
Step-by-step explanation:
8-2 x 3+4
2x3=6
8-6+4
2+4
=6
hope this helps
Line segment A' B' is the result after line segment AB goes through a single transformation. In which transformation would the measure of line segment A'B' be different than the measure of line segment AB?
[tex]\color{indigo}\rule{1pt}{1000000pt}[/tex]
Find the missing measurement for x.
Answer:
EASYYY 90°
Step-by-step explanation:
30 + 60 = 90
180-90=90
also
thats a right angle which is always 90°
ALSO
the angle opposite another angle is always the same measurement.
Find the perimeter of the parallelogram.
Will mark brainlyest!!
Answer:
58cm
Step-by-step explanation:
Answer:
58
Step-by-step explanation:
16 +16=32
13+13=26
32+26=58
Hope it Helps
Find, from first principle the derivative of 1/x^2+1 with respect to x.
Answer:
d/dx = -2/x^3
Step-by-step explanation:
1/x^2 + 1
We can solve for the derivative using the power rule
d/dx = -2/x^3 + 0
d/dx = -2/x^3
*URGENT*
If you were at the Market Square and you wanted to get to the Doctor’s Office, according to the map, how would you get there? (Write your answer according to units.)
Answer: (2,-5) X:2. Y:-5
Move accross 2 units to the right and then 5 units down from 2
Find the surface area of the right triangular prism (above) using its net (below).
Answer:
The Answer is 96 units squared
Step-by-step explanation:
First, you find the area of all the sides:
Triangle 1: 6
Triangle 2: 6
Rectangle 1: 21
Rectangle 2: 28
Rectangle 3: 35
Then you add all of the numbers together.
6+6+21+28+35 = 96 units squared
I hope this helps :)
Find the solution(s) to 2x2 - 5x – 3 = 0. Check all that apply.
A. x = }
B. x= -1
0 C. x= -3
D. x= 2
E. x = 3
Answer:
E. x = 3
Step-by-step explanation:
The equation can be factored by considering the factors of the product of the first and last coefficients. Those factors must have a sum equal to the middle coefficient.
(2)(-3) = -6 = (-6)(1) = (-3)(2) = ... other factors with positive sums
The sums of the factor pairs shown are -5 and -1. We're interested in the factor pair {-6, 1}. Replacing the middle term coefficient with the sum of these, we can write the equation in a way that lets us factor pairs of terms.
2x² -6x +x -3 = 0 . . . . . . . . replace -5x with -6x+1x
2x(x -3) +1(x -3) = 0 . . . . . . factor pairs of terms
(2x +1)(x -3) = 0 . . . . . . . . . complete the factoring
Solutions are the values of x that make these factors zero:
2x +1 = 0 ⇒ x = -1/2
x -3 = 0 ⇒ x = 3
_____
Additional comment
A number of methods are used to find the factors of a quadratic with a leading coefficient other than 1. When the coefficients are small integers, this is one of the more straightforward methods: actually listing and examining the pairs of factors of "ac." If "ac" has a large number of divisors, other methods may be more practical.
Answer:
x = 3 AND x = -1/2
Step-by-step explanation:
its right
A rectangle has vertices at coordinates 0,0 3,0 0,6 what is the area of the rectangle
Answer:
18
Step-by-step explanation:
6th grade math!!
Please help me I have a unit test tomorrow, and I’m having a hard time figuring this out. So please be quick! I think we’re supposed to use a formula for rectangles but im not sure
dont mind my answers thanks for helping me out have a good day
Answer:
ACD and DCB are supplementary and others are correctly chosen ...
The price of an item has been reduced by 55%. The original price was $51
Answer:$22.95
Step-by-step explanation: The original price is 51%
Discount is 55% of $51= 55/100×51=$28.05
Deduct the discount from the original price. $51-$28.05=$22.95
The figure is made up of a semi circle and triangle find the area of the figure use 3.14
Help pleaseee points=13
Answer:
63.25
Step-by-step:
39.25 + 24 = 63.25 ft squared
Answer:
Step-by-step explanation:Does anyone know what this would be?
Henry calculated the mean absolute deviation of the points he earned throughout the year health and music
history: MAD 3.5
English: MAD: 2.65
health: MAD of 2.5
music: MAD of 3.28
in which class were his scores the closest together
health
English
music
History
Answer:
health class
Step-by-step explanation:
when the mean absolute deviation (M.A.D) is lower, that means the data is closer together. When it is higher that means the data is more spread out.
Answer:
its health
Step-by-step explanation:
i took the k12 test and got it wrong and it showed this one was correct
It took an airplane 3 hours to go 1725 miles.
How many miles per hour
Answer:
575 mph
Step-by-step explanation:
The plane is traveling at 575 mph.
1725/3
575
Circle A has center of (2, 3) and a radius of 5, and circle B has a center of (1, 4) and a radius of 10. What steps will help show that circle A is similar to circle B?
Dilate circle A by a scale factor of 2.
Translate circle A using the rule (x + 1, y − 1).
Rotate circle A 180° about the center.
Reflect circle A over the y-axis.
Answer:
A
Step-by-step explanation:
To show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.
What is a circle?It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have two circles:
Circle A has a center of (2, 3) and a radius of 5
Circle B has a center of (1, 4) and a radius of 10
The standard circle's equation can be written as:
(x - h)² + (y - k)² = r²
The equation for circle A:
(x - 2)² + (y - 3)² = 5²
The equation for circle B:
(x - 1)² + (y - 4)² = 10²
To show that circle A is similar to circle B:
It is required to perform the geometric transformation:
Dilate circle A by a scale factor of 2.
The radius of circle A is 5 units and after dilation by a scale factor of 2, the radius of the circle becomes 10 which is the radius of circle B.
Thus, to show that circle A is similar to circle B the step required is Dilate circle A by a scale factor of 2 option (A) is correct.
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