Length of the missing leg is:
Pythagorean theorem - Integers -
Find the missing leg
PLEASE HELP
(need to show work)
Im so confused!!
Answers
The lengths of the legs of each triangle are:
1) Leg = √19
2) Leg = √105
3) Leg = √60
How to use Pythagoras Theorem?
Pythagoras Theorem is defined as the way in which you can find the missing length of a right angled triangle.
The triangle has three sides, the hypotenuse (which is always the longest), Opposite (which doesn't touch the hypotenuse) and the adjacent (which is between the opposite and the hypotenuse).
Pythagoras is in the form of;
a² + b² = c²
a = √(c² - b²)
1) We are given that:
Hypotenuse = 10
Opposite side = 9
Thus, using Pythagoras Theorem, we have:
Leg = √(10²- 9²)
Leg = √19
2) We are given that:
Hypotenuse = 19
Opposite side = 16
Thus, using Pythagoras Theorem, we have:
Leg = √(19²- 16²)
Leg = √105
3) We are given that:
Hypotenuse = 8
Opposite side = 2
Using Pythagoras Theorem, we have:
Leg = √(8²- 2²)
Leg = √60
Related Questions
Lisa’s test grades are 79, 89, and 90.
What is Lisa’s test average?
Answers
Answer: 86
Step-by-step explanation: You would add up all the numbers, then divide by the amount of numbers there are.
For example
79+89+90=258
Since there are three numbers(79,89,90) you would divide 258 by 3 and would get 86.
Hopes this helps
Add the numbers together. 79 + 89 + 90
Then divided by 3.
86.
Mark launches a toy rocket with an initial vertical velocity of 25ft/s from a platform that is at ground level. how long will the toy rocket be in the air?
Answers
Answer:
A
Step-by-step explanation:
First: C is incorrect. It is using the value of acceleration due to gravity in the metric system.
Second: the 16 must be opposite in sign from the 25. That makes B and D incorrect.
Answer: A
If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle? A) (x + 6)2 + (y + 10)2 = 20 B) (x − 6)2 + (y − 10)2 = 20 C) (x + 6)2 + (y + 10)2 = 2 5 D) (x − 6)2 + (y − 10)2 = 2 5
Answers
Answer:
[tex]\large\boxed{A.\ (x+6)^2+(y+10)^2=20}[/tex]
Step-by-step explanation:
The standard form of an equation of a circle:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
(h, k) - center
r - radius
We have the endpoints of the diameter of a circle (-8, -6) and (-4, -14).
The midpoint of a diameter is a center of a circle.
The formula of a midpoint:
[tex]\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)[/tex]
Substitute:
[tex]x=\dfrac{-8+(-4)}{2}=\dfrac{-12}{2}=-6\\\\y=\dfrac{-6+(-14)}{2}=\dfrac{-20}{2}=-10[/tex]
We have h = -6 and k = -10.
The radius is the distance between a center and the point on a circumference of a circle.
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Substitute (-6, -10) and (-8, -6):
[tex]r=\sqrt{(-8-(-6))^2+(-6-(-10))^2}=\sqrt{(-2)^2+4^2}=\sqrt{4+16}=\sqrt{20}[/tex]
Finally we have
[tex](x-(-6))^2+(y-(-10))^2=(\sqrt{20})^2\\\\(x+6)^2+(y+10)^2=20[/tex]
Answer:
It's A...Just had it but i Chose B but it's A
Step-by-step explanation:
fine the value of m-8 when m=15
Answers
Answer:
23
Step-by-step explanation:
15+8=23
Answer:
7
Step-by-step explanation:
um thats just 15-8
Determine the factors of 3x2 + 10x − 8. (Which is the right answer?)
A. (3x − 8)(x + 1)
B. (3x − 1)(x + 8)
C. (3x − 4)(x + 2)
D. (3x − 2)(x + 4)
Answers
ANSWER
[tex](3x - 2)(x + 4)[/tex]
EXPLANATION
The given quadratic trinomial is
[tex]3 {x}^{2} + 10x - 8[/tex]
Comparing to the general quadratic trinomial:
[tex]a{x}^{2} + bx + c[/tex]
We have a=1, b=10 and c=-8
[tex]ac = 3 \times - 8 = - 24[/tex]
The factors of -24 that adds up to 10 are -2 and 12.
We split the middle term to obtain;
[tex]3 {x}^{2} + 12x - 2x- 8[/tex]
Factor;
[tex]3x(x+ 4) - 2(x + 4)[/tex]
Factor further;
[tex](3x - 2)(x + 4)[/tex]
The last option is correct.
A simple random sample of ten people is taken from the set of all registered voters in a given district to determine their average age. Which of the following is a reason why you can not make a statistical inference on the population?
Answers
Answer:
The sample size is not appropriate.
The population isn’t given to be approximately normal. And for the following question, "A convenience sample of forty people is taken from a population. Which of the following is a reason why you can not make a statistical inference on the population?" The answer is The wrong sampling method was used.
Answer:
Answers are : (1st & 2nd choices)
• The sample size is not appropriate.
• The population isn't given to be approximately normal.
What is 2f + 4f + 2 – 3 evaluated at f = 3?
Answers
Answer:
17
Step-by-step explanation:
given
2f + 4f + 2 - 3 ← simplify by collecting like terms
= 6f - 1 ← substitute f = 3 into the expression
= (6 × 3) - 1 = 18 - 1 = 17
Answer:
17
2(f) + 4(f) + 2 - 3 | (f) = 3
2(3) + 4(f) + 2 - 3
(6 + 12) + (2 - 3)
(18) - (1)
Step-by-step explanation:
All perfect squares are divisible by two
Answers
Answer:
No
Step-by-step explanation:
No, because think of 9, its not divisible by two and for the second one yes, a perfect square always has a positive and negative
The height of one right circular cylinder is 7 centimeters and it’s radius is 2 centimeters. The height of the second right circular cylinder is 28 centimeters and it’s radius is also 2 centimeters. What is the ratio of the volume of the larger cylinder to the volume of the smaller cylinder? Please Explain!!
Answers
Volume of a cylinder
[tex]\pi \times {r}^{2} \times h[/tex]
larger cylinder: r=2, h=28
volume of larger cylinder lets say (V) :
[tex]\pi \times {2}^{2} \times28 \\ = 4 \times 28\pi =112\pi[/tex]
vokume of smaller cylinder lets say (v): r=2, h=7
[tex]\pi \times {2}^{2} \times 7 \\ = 4 \times 7\pi = 28\pi[/tex]
so the ratio= volume of largercylinder/ volume of smaller
[tex]ratio = \frac{112\pi}{28\pi} \\ = \frac{4}{1} [/tex]
so in ratio terms the
Ans: 4:1
The ratio of the volume of the larger cylinder to the smaller cylinder is 4:1, calculated using the volume formula for cylinders, V = πr²h.
To calculate the ratio of the volumes of two cylinders, we need to use the formula for the volume of a cylinder, V = (πh), where r is the radius and h is the height.
For the first cylinder with a height of 7 cm and a radius of 2 cm, the volume is V₁ = 3.14 (2 cm) (7 cm) = 88.36 cm³.
For the second cylinder with a height of 28 cm and the same radius, the volume is V₂ = 3.14 (2 cm) (28 cm) = 353.44 cm³.
The ratio of V2 to V1 is then 353.44 cm³ / 88.36 cm³, which simplifies to 4:1.
Emma’s total bill for dinner was $20. The cost of her dessert was 30% of the total bill. What was the cost of her dessert?
Answers
$6 was her dessert. you do 20x0.3=6
Data was collected of students’ hair color and gender. The results are in the table below.
Answers
Answer:
Step-by-step explanation:
Part One
Number of girls with blonde hair = 6
Total number of students = 40
% = 6/40 * 100% = 15%
Part Two
Number of Red Headed boys = 2
Just read the chart.
Part Three
The Chance that black hair is 4/40 = 0.1 or 1 in 10
9.
The original cost of a lamp is $18.95. The lamp is on sale for 25% off. How much will you pay
Answers
Answer:
$14.21
Step-by-step explanation:
To find 25% of 18.95, you can multiply 18.95×0.25, which approximately equals $4.74. Then subtract $4.74 from $18.95 to get $14.21
Answer:
$14.2125
Step-by-step explanation:
We have been given that the original cost of a lamp is $18.95. The lamp is on sale for 25% off.
Since the lamp is on a 25% sale, then the cost of the lamp would be 75% (100%-25%) of the original price.
[tex]\text{Cost of lamp after sale}=\$18.95\times \frac{75}{100}[/tex]
[tex]\text{Cost of lamp after sale}=\$18.95\times 0.75[/tex]
[tex]\text{Cost of lamp after sale}=\$14.2125[/tex]
Therefore, you will have to pay $14.2125 for the lamp.
nine stores is 3% put of 100. of how many stores are a hundred percent ? use proportions or multiplication please!!
Answers
Answer:
30,000 stores
Step-by-step explanation:
setting up a proportion is proably the easiest way to solve this equation..
9/ x = 3%/100%
0.03x = 9(100)
0.03x = 900
/0.03 /0.03
x = 30,000 stores
hope this helps!!
Which expression is equivalent to (3^2)^-2
Answers
Answer: 1/81
First you simplify it to 3^-4
Then express it with a positive exponent which goes to 1/3^4
Then evaluate it to 1/81
Answer:
The expression which is equivalent to the given expression is given by :
[tex]\bf\frac{1}{81}[/tex]
Step-by-step explanation:
The expression is given to be :
[tex](3^{2})^{-2}[/tex]
Now, we need to find a expression which is equivalent to this given expression.
[tex](3^{2})^{-2}\\\\\implies (3\times 3)^{-2}\\\\\implies (9)^{-2}\\\\\implies\frac{1}{(9)^2}\\\\ \implies \frac{1}{81}[/tex]
Hence, The expression which is equivalent to the given expression is given by :
[tex]\bf\frac{1}{81}[/tex]
A concession stand sells apple cider for $3.35 a cup and donuts for $2.45 each, on Saturday the stand sold 126 items and made $362.70 how many cups of apple cider did the stand sell
Answers
52 cups.
3.35 times 52 equals 174.20
2.45 times 77 equals 188.60
So 52 cups of apple cider were sold in total.
Answer:
The number of cups of apple cider sold was 60 cups
Step-by-step explanation:
We will develop equations to solve this problem.
Let a= price for a cup of apple cider in dollars
Let b= price for a donut in dollars
Let x = number for cups of apple cider sold
Let y= number of donuts sold
Let z = number of items sold on the day = 126 items
Let v = total money made = $362.70
Lets write two equations. One in terms of the amount of items sold of cups of apple cider and donuts, and one in terms of how much money was made for selling cups of apple cider and donuts.
z = x + y
x = z- y (1)
v = ax + by (2)
we substitute equation 1 in to equation 2
v = a(z-y) +by = az -ay +by = az +y(b-a)
solve for y
y = (v-az)/(b-a) = (362.70 - 3.35×126)/(2.45-3.35) = 66 donuts were sold
therefore x = z-y = 126-66 = 60 cups of apple cider were sold
If point S is reflected across the y-axis, what are the coordinates of its reflection image.
A. (2,-3)
B.(-2,3)
C.(3,-2)
D.(-3,2)
Answers
Answer:
D) coordinates of its reflection image is ( -3 , 2) .
Step-by-step explanation:
Given : S ( 3 ,2) If point S is reflected across the y-axis,
To find : what are the coordinates of its reflection image.
Solution : We have given S ( 3 ,2).
By the reflection rule over y -axis : (x ,y) →→ ( -x , y) .
Then x = 3 , y = 2
Then coordinates of its reflection image is
(3 , 2 ) →→ ( -3 , 2) .
Therefore, D) coordinates of its reflection image is ( -3 , 2) .
EMERGENCY
The graph represents function 1, and the equation represents function 2.
Function:
y = 8x + 12
How much more is the rate of change of function 2 than the rate of change of function 1?
Answers
Answer:
The rate of change is 8 more for function 2 than it is for function 1.
Step-by-step explanation:
Function 1 is a horizontal line, which has a slope of 0. Slope is the same as rate of change.
Function 2 has a slope of 8 (since it is the coefficient of x.
As a result, we know that function 2's rate of change is 8 higher than that of function 1.
A kayak rental company charges a $15 fee to rent a kayak plus $3.50 per hour. Which equation represents the function for the total cost, c, to rent a kayak for h hours?
A. c=3.5x+15
B. c=3.5x-15
C. c=-3.5x+15
D. c=-3.5x-15
Answers
Final answer:
The correct equation is c=3.5h+15, where c is the total rental cost and h is the number of hours the kayak is rented. The equation includes a fixed fee of $15 and a variable hourly rate of $3.50. The correct answer is option (A).
Explanation:
The equation representing the function for the total cost c, to rent a kayak for h hours, is A. c=3.5h+15. This equation consists of a fixed cost and a variable cost.
The fixed cost, or y-intercept, is the initial $15 fee required to rent the kayak, which is represented when h=0. The variable cost, or slope, is $3.50 per hour of rental, indicating that for each additional hour h, the cost increases by this amount.
Find the value of y.
Answer options: 62, 66, 70, 74
Answers
Answer:
The value of y = 70°
Step-by-step explanation:
∵ The measure of the major arc = 160 + 60 = 220°
∵ The measure of the circle is 360°
∴ The measure of the minor arc = 360 - 220 = 140°
∵ y is the angle between a chord and a tangent
∵ The chord subtended by the arc of measure 140°
∵ y is subtended by the arc of measure 140°
∵ Angle of tangent subtended by an arc,
its measure = half the measure of the subtended arc
∴ The measure of y = 1/2 the measure of the subtended arc
∴ y = 1/2 × 140 = 70°
Answer:
70
Step-by-step explanation:
The equation yˆ=−2.58x+566.67 models the distance a driver can see in feet, where x is the age of the driver in years. According to the regression equation, how far can a 30 year old driver see in feet?
Answers
Answer:
489 to the nearest foot.
Step-by-step explanation:
y = -2.58x + 566.67
x = 30:
y = -2.58*30 + 566.67
= 489 to nearest foot.
Answer:
A 30 year old driver can see 489.27 feet
Step-by-step explanation:
The equation yˆ=−2.58x+566.67 models the distance a driver can see in feet, where x is the age of the driver in years.
WE need to find out the height when x is 30
Plug in 30 for x and find out y
y=−2.58x+566.67
Replace x with 30
y=−2.58(30)+566.67 = 489.27
A 30 year old driver can see 489.27 feet
18% of 120 to 12% of 120
Answers
Answer: 18% of 120 is 21.6
And, 12% of 120 is 14.4
* Both of their work is below:)
* Hopefully this helps:)!! Mark me the brainliest:)!!
∞ 234483279c20∞
Answer:
18% of 120 to 12% of 12021.6 to 14.4Step-by-step explanation:
18% of 120
Convert 18% to a decimal by dividing by 100:
18 / 100 = 0.18
120 * 0.18 = 21.6
12% of 120
Convert 12% to a decimal by dividing by 100:
18 / 100 = 0.12
120 * 0.12 = 14.4
18% of 120 to 12% of 12021.6 to 14.4Which phrase could the expression x-4 represent? a number less than 4 the difference of a number and 4 the sum of a number and 4 four less a number
Answers
Answer:
Four less a number
Step-by-step explanation:
x-4 is literally subtracting 4 and 4 less a number is basically also subtracting 4 from an equation.
Answer:
The difference of a number and 4.Step-by-step explanation:
The sentence that represents better the given expression is "The difference of a number and 4".
Mainly because states the difference in the right order, first the unknown number, which is called "a number", and in second place the number 4, referring to the difference is the subtract of 4 units from the number, not in the opposite way.
On the other hand, "a number less than 4" specifies that the unknown number is minor than 4, which is not true. "the sum of a number and 4" is completely wrong, because there's no sum at all. "Four less a number" refers to a difference but in the opposite way 4-x.
Therefore, the right answer is
The difference of a number and 4.in the equation y=4x-7, what is the value of y when x=2?
Answers
Answer:
-56Step-by-step explanation:
y=4x-7= x=2y=4(2)-7
y=(4)(2)(−7)
Answer:
y=−56
Value of y when x = 2 is 1.
What is an equation?
An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.
Given equation
y = 4x-7
Value of y when x = 2
Substitute x = 2 in above equation
[tex]y = 4 \times 2 -7[/tex]
[tex]y=8-7[/tex]
y = 1
Value of y when x = 2 is 1.
Find out more information about equation here
brainly.com/question/2263981
#SPJ2
what is 3 1/8 - 1/2
Answers
Answer:
[tex]\frac{21}{8}[/tex]
Step-by-step explanation:
Given: [tex]3\frac{1}{8} - \frac{1}{2}[/tex]
Let's changed that mixed number to an improper fraction. Now we get:
[tex]\frac{25}{8} - \frac{1}{2}[/tex]
Let's find out least common denominator. This one is easy, the LCD is 8. Now that we know the LCD, let's convert both our fractions:
[tex]\frac{25}{8} - \frac{4}{8}[/tex]
We can use [tex]\frac{4}{8}[/tex] because it is equal to [tex]\frac{1}{2}[/tex]. Now, all we need to do is subtract the numerators:
[tex]\frac{25}{8} - \frac{4}{8}=\frac{21}{8}[/tex]
Answer:
[tex]\frac{21}{8}[/tex]Step-by-step explanation:
Which method is the most efficient method to use to solve x^2+4x+3=0
Answers
Answer:
Factoring
Step-by-step explanation:
To solve the equation [tex]x ^ 2 + 4x + 3 = 0[/tex], you must apply the factoring method.
You must find two real numbers b and c such that:
[tex]b + c = 4[/tex]
and
[tex]b(c) = 3[/tex]
Then the expression:
[tex]x ^ 2 + 4x + 3 = 0 = (x + b)(x + c)[/tex]
You can prove that:
[tex]b = 3\\c = 1[/tex]
So
[tex]x ^ 2 + 4x + 3 = 0 = (x + 3)(x + 1)[/tex]
[tex](x + 3)(x + 1) = 0[/tex]
[tex]x +3 = 0[/tex] or [tex]x + 1 = 0[/tex]
[tex]x = -3[/tex] or [tex]x = -1[/tex]
X will be -1 and -3!
Identify if each of triangles below is congruent or not. Remember that the diagram may not be drawn to scale. Justify your conclusion.
Answers
Answer: ¨A¨ is congruent due to SSS. ¨B¨ is not because corresponding sides are not congruent. ¨D¨ is congruent due to AA. Can´t see all of ¨C¨
Step-by-step explanation:
Solve the exponential equation. Write the exact answer with natural logarithms and then approximate the result correct to three decimal places.
[tex]5^{1-x} =2^{x}[/tex]
I was able to start it, but I somehow got [tex]log_{5}2=0[/tex], and I don't think that's right.
Answers
Answer:
Fraction form: x = ln(5)/ln(10)
Decimal form: 0.69897000
please mark brainliest
10.5 Tangents. Hw 20
Answers
Answer:
Refer to step-by-step.
Step-by-step explanation:
1. x = 4
x + 3 = 7
x = 7-3
x = 4
2. x = 25
We need to use the Pythagorean theorem to find x.
a² + b² = c²
15² + 20² = x²
225 + 400 = x²
652 = x²
√652 = √x²
x = 25
3. x = 12
Line NP and Line QP will have the same measurement.
x = 12
4. x = 29.41
We need to use the Pythagorean theorem to find x.
a² + b² = c²
24² + 17² = x²
576 + 289 = x²
865 = x²
√865 = √x²
x = 29.41
5. NO
We apply the Pythagorean theorem to find if they are tangent.
a² + b² = c²
9² + 40² = 41²
81 + 1600 = 2500
1681 = 2500 NO
6. NO
a² + b² = c²
4² + 12² = 13²
16 + 144 = 169
160 = 169 NO
7. NO
a² + b² = c²
20² + 21² = 28²
400 + 441 = 784
841 = 784 NO
8. YES
a² + b² = c²
14² + 48² = 50²
196 + 2304 = 2500
2500 = 2500 YES
Plz help me!!!!!!!!!!
Answers
Answer:
a = ( 5 +/- sqrt(57) )/2
Step-by-step explanation:
Uh...well just multiply by a and move the 4, setting the equation to 0.
a, b, and c are 2, -5, -4
Plug that into the QuadF.
Answer: [tex]\bold{\dfrac{5\pm \sqrt{57}}{4}}[/tex]
Step-by-step explanation:[tex]2a-5=\dfrac{4}{a}\\\\\text{Multiply by the LCD (a) to clear the denominator:}\\\\\\2a(a)-5(a)=\dfrac{4}{a}(a)\\\\2a^2-5a=4\\\\2a^2-5a-4=0\quad \rightarrow \quad a=2,\ b=-5,\ c=-4\\\\\\\text{Quadratic formula is: }x=\dfrac{-b\pm \sqrt{b^2-4ac}}{2a}\\\\\\x=\dfrac{-(-5)\pm \sqrt{(-5)^2-4(2)(-4)}}{2(2)}\\\\\\.\ =\dfrac{5\pm \sqrt{25+32}}{4}\\\\\\.\ =\dfrac{5\pm \sqrt{57}}{4}[/tex]
HELP ASAP PLS!!
Which triangle is a translation of triangle ABC?
A) DEF
B) GHI
C) JKL
D) MNO
Answers
Answer:
the answer would be JKL
Step-by-step explanation: