9514 1404 393
Answer:
4
Step-by-step explanation:
If the unknown leg is represented by x, then the Pythagorean theorem tells you ...
x² + 3² = 5²
The sum of the squares of the legs equals the square of the hypotenuse.
Solving for x, we have ...
x² = 5² -3² = 25 -9 = 16
x = √16 = 4 . . . . . . . only the positive root is of interest
The missing leg length is 4 units.
_____
Additional comment
This exercise shows you that the triple (3, 4, 5) will form a right triangle. It is the smallest integer "Pythagorean triple", and the only one that is an arithmetic sequence (the differences between the numbers are the same). You will see this a lot, sometimes multiplied by various factors: 6, 8, 10, for example. It is worth remembering.
Answer:
4
Step-by-step explanation:
Correct answers:
$4$
Let a represent the length of the leg and label a on the figure.
The figure shows a right triangle with legs marked a and 3. The hypotenuse is marked 5.
The figure shows a right triangle with legs marked a and 3. The hypotenuse is marked 5.
Using the Pythagorean Theorem with b=3, c=5, and solving for a, we have
a2+b2a2a2a2a2aa=c2=c2−b2=52−32=25−9=16=16−−√=4
The length of the leg is 4.
Given the definitions of f(x) and g(x) below, find the value of g(f(-1)).
f(x) = -4x – 7
g(x) = x² + 7x – 2
Answer:
-14
Step-by-step explanation:
[tex]f(x) = -4x – 7 \\ plug \: x = - 1 \\ f( - 1) = - 4( - 1) - 7 = 4 - 7 = - 3 \\g(x) = x² + 7x – 2 \\g(f( - 1)) = {( - 3)}^{2} + 7( - 3) - 2 \\ = 9 - 21 - 2 \\= - 14[/tex]
A new pair of shoes is advertised for $110. The sales tax is 7.5%. What is the total cost of the shoes?
Answer:
118.25
Step-by-step explanation
If the tax is in percent, divide the tax rate by 100. You do this by moving the decimal point two spaces to the left. In this, there's 7.5/100 = 0.0
Find the tax value by multiplying tax rate by the item value:
tax = 110 × 0.075
tax = 8.25
Which of the following points satisfies the linear inequality below? Select all correct answers.
5x + 2y 26
Select all that apply:
(0,5)
(3,1)
(3,-4)
(-4,1)
Answer:
All points satisfy the inequality
Step-by-step explanation:
Given
[tex]5x + 2y \le 26[/tex]
Required
Select all points that satisfy the above inequality
[tex](a)\ (0,5)[/tex]
This implies that
[tex]x = 0; y = 5[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 0 + 2 * 5 \le 26[/tex]
[tex]0 + 10 \le 26[/tex]
[tex]10 \le 26[/tex]
This satisfy the inequality
[tex](b)\ (3,1)[/tex]
This implies that
[tex]x = 3;\ y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * 1 \le 26[/tex]
[tex]15 + 2 \le 26[/tex]
[tex]17 \le 26[/tex]
This satisfy the inequality
[tex](c)\ (3,-4)[/tex]
This implies that:
[tex]x = 3; y-4[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * 3 + 2 * -4 \le 26[/tex]
[tex]15 -8 \le 26[/tex]
[tex]7 \le 26[/tex]
This satisfy the inequality
[tex](d)\ (-4,1)[/tex]
This implies that:
[tex]x = -4; y =1[/tex]
So, we have:
[tex]5x + 2y \le 26[/tex]
[tex]5 * -4 + 2 *1 \le 26[/tex]
[tex]-20 + 2 \le 26[/tex]
[tex]-18 \le 26[/tex]
This satisfy the inequality
A grocer wants to mix two kinds of coffee. One kind sells for $0.85 per pound, and the other sells for $2.70
per pound. He wants to mix a total of 21 pounds and sell it for $0.95 per pound. How many pounds of
each kind should he use in the new mix? (Round off the answers to the nearest hundredth.)
Answer:
x = $0.85 per pound = 19.85 pounds
y = $2.70 per pound = 1.14 pounds
Step-by-step explanation:
Let
x = $0.85 per pound
y = $2.70 per pound
x + y = 21 (1)
0.85x + 2.70y = 19.95 (2)
From (1)
x = 21 - y
Substitute x = 21 - y into (2)
0.85x + 2.70y = 19.95 (2)
0.85(21 - y) + 2.70y = 19.95
17.85 - 0.85y + 2.70y = 19.95
- 0.85y + 2.70y = 19.95 - 17.85
1.85y = 2.1
y = 2.1 / 1.85
y = 1.14
Substitute y = 1.14 into (2)
0.85x + 2.70y = 19.95
0.85x + 2.70(1.14) = 19.95
0.85x + 3.078 = 19.95
0.85x = 19.95 - 3.078
0.85x = 16.872
x = 16.872 / 0.85
x = 19.85
x = $0.85 per pound = 19.85 pounds
y = $2.70 per pound = 1.14 pounds
PLS HELP WITH NUMBER 6
Answer: The answer to this question is A
Melanie invested $9,800 in an account paying an interest rate of 4 1 2 4 2 1 % compounded quarterly. Amelia invested $9,800 in an account paying an interest rate of 4 3 4 4 4 3 % compounded continuously. After 20 years, how much more money would Amelia have in her account than Melanie, to the nearest dollar?
After 20 years, the amount of Money Amelia would have more than Melanie would be $181,551.37.
What is the future value of Melanie's account?The formula for calculating future value:
FV = P (1 + r) nm
FV = Future value P = Present value R = interest rate = 4 1/2 ÷ 4 = 1.125%m = number of compounding = 4N = number of years9800(1 + 0.0125)^80 = 23,983.29
What is the future value of the amount in Amelia's account?the formula for calculating future value when there is continuous compounding is : A x e^r x N
Where:
A= amount e = 2.7182818 N = number of years r = interest rate9800 e^0.0475 x 20 = 205,534.66
Difference = 205,534.66 - 23,983.29 = $181,551.37
To learn more about future value, please check: https://brainly.com/question/18760477
Find the area
10 yd
12 yd
13 yd
Answer:
138
Step-by-step explanation:
a+b/2xh
The volume of a cuboid is 176cm
The length is 11 cm and the width is 20mm
Work out the height of the cuboid in cm.
Answer:
.08cm or 0.08cm
Step-by-step explanation:
First of all, we can see that 20mm is in millimeters, not centimeters.
If we convert the ones in centimeters to millimeters, it will result in decimals, which I want to avoid, but you could also do it that way.
There are 10 mm in 1 cm, so I multiply all of the values in cm by 10.
So now, we have that the volume is 1760mm, the length is 110mm, and the width is 20mm.
The formula for the volume of a cuboid is: [tex]w*l*h = volume[/tex]
We have the width, length, and volume, so let's plug it in.
[tex]20*110*h=1760[/tex]
To solve for h:
1. Multiply 20 and 100
[tex]2200*h=1760[/tex]
2. Divide both sides by 2200
[tex]h = 1760/2200[/tex]
3. Divide right side
h = 0.8
Keep in mind that this is in millimeters. In centimeters, it would be .08
What is c? This is pythgreomthryrom a=8 b=6 c=?
Answer:
4
Step-by-step explanation:
How many cities could have an annual rainfall of 28.5 in 32.5 in
Answer:
A) 6
Step-by-step explanation:
Answer:
2. A) 6
Step-by-step explanation:
#CarryOnLearning
The data below are the ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults. Age 38 41 45 48 51 53 57 61 65 Pressure 116 120 123 131 142 145 148 150 152 What is the best predicted value for blood pressure of an individual who is 64 years old
Answer:
156
Step-by-step explanation:
Given the data:
Age (X) :
38
41
45
48
51
53
57
61
65
Pressure(Y) :
116
120
123
131
142
145
148
150
152
From the data, we could obtain a regression equation to mod the data Given using a linear regression calculator :
The regression equation obtained is :
y = 1.48769X + 60.46103
Using the model, the predicted blood pressure for a person aged 64 will be :
y = 1.48769(64) + 60.46103
y = 95.21216 + 60.46103
y = 155.67319
y = 156 (nearest whole number)
Find the exact value for the expression under the given conditions.
cos(α+β), sin α= -8/17 for α in Quadrant lll and cosβ= -8/15 for β in Quadrant ll.
Answer:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
Step-by-step explanation:
We are given the conditions:
[tex]\displaystyle \sin(\alpha)=-\frac{8}{17}\text{ and } \cos(\beta)=-\frac{8}{15}[/tex]
Where α is in QIII and β is in QII and we want to find the exact value of cos(α + β).
The first ratio gives us the opposite side and the hypotenuse with respect to α . Then the adjacent side is (we can ignore negatives):
[tex]a=\sqrt{(17)^2-(8)^2}=15[/tex]
The second ratio gives us the adjacent side and the hypotenuse with respect to β. Then the opposite side is:
[tex]o=\sqrt{(15)^2-(8)^2}=\sqrt{161}[/tex]
Therefore, for α, ignoring negatives, the adjacent side is 15, the opposite side is 8, and the hypotenuse is 17.
And for β, ignoring negatives, the adjacent side is 8, the opposite side is √(161), and the hypotenuse is 15.
We can rewrite our expression as:
[tex]\displaystyle \cos(\alpha+\beta)=\cos(\alpha)\cos(\beta)-\sin(\alpha)\sin(\beta)[/tex]
Since α is in QIII, sin(α), cos(α) < 0, and tan(α) > 0.
And since β is in QII, cos(β), tan(β) < 0, and sin(β) > 0.
Using this information, substitute:
[tex]\displaystyle \cos(\alpha+\beta)=\left(-\frac{15}{17}\right)\left(-\frac{8}{15}\right)-\left(-\frac{8}{17}\right)\left(\frac{\sqrt{161}}{15}\right)[/tex]
Therefore:
[tex]\displaystyle \cos(\alpha+\beta)=\frac{120+8\sqrt{161}}{255}[/tex]
Guys please last one ok
Answer:
last one, 4th
i really hope it helps.
The perimeter of a triangle is 29. One side of a triangle is 5 less than twice the side of the shortest length. The third side is 6 more than the shortest side. What are the lengths of the triangle?
Answer:
7, 9, 13Step-by-step explanation:
Let the sides of the triangle be a, b and c.
We have:
P = a + b + c = 29a = 2b - 5c = b + 6Substitute values and solve for b:
2b - 5 + b + b + 6 = 294b + 1 = 294b = 28b = 7Find a and c:
a = 2*7 - 5 = 14 - 5 = 9c = 7 + 6 = 13The sides are: 7, 9, 13
How many odd numbers are between 10 and 50?
Answer:
There are 20 odd numbers between 10 and 50
Step-by-step explanation:
Here are all the odd numbers! Hope this helps!
11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49
Jessica's bedroom is 17 feet long and 9 1/2 feet wide. What is the area of the bedroom?
Find the area of a circle with diameter 16 yd.
Use the value 3.14 for it, and do not round your answer.
Be sure to include the correct unit in your answer.
Answer:
200.96
Step-by-step explanation:
pi*r^2
need you to check if answer is correct
It's Pythagorean theorem
Answer:
6root3
Step-by-step explanation:
Answer:
6 radical 3
Step-by-step explanation:
The coordinates of D are
Answer:
The coordinates of D are -1,0
Step-by-step explanation:
I believe
Answer and explainaction please. End of course test is next week and I want to make sure I can work out answers on my own! :)
Answer: This is what I get.
Step-by-step explanation:
A solid figure is composed of a cube and a pyramid as shown. What is the volume
Answer:
288 in^3
Step-by-step explanation:
1) find the volume of the cube
V = side^3 = 6^3 = 216 in^3
2) find the base surface of the pyramid:
base surface = side^2 = 6^2 = 36 in^2
3) find the height of the pyramid:
height of the solid - height of the cube = 12 - 6 = 6 in
4) find the volume of the pyramid:
V = (base area x height) / 3 = (36 x 6)/3 = 72 in^3
5) add up the two volumes
V = 216 + 72 = 288 in^3
A company produces remote-controlled helicopters. The company’s profit, in thousands of dollars, as a function of the number of helicopters produced per week can be modeled by a quadratic function. When 1 helicopter is produced per week, the company’s profit is 4 thousand dollars. The maximum profit, 22 thousand dollars, occurs when 4 helicopters are produced per week.
The function that models the scenario, where h is the number of helicopters produced per week, is
f(h) = –2(h – 4)2 + 22.
When 6 helicopters are produced weekly, the company’s profit is (blank)
thousand dollars.
Answer:
the answer is B
Step-by-step explanation:
Help me with 6 and 7
Answer:
6 b 7 d give me brainlest
Step-by-step explanation:
A block of wood has the shape of a triangular prism. The bases
are right triangles. Find its surface area.
Answer:
287.25 sq in
Step-by-step explanation:
Approximately what is the sale price of a skateboard listed at $159.69 with a 25% discount?
Answer:
159.69*0.75 = 119.76
Step-by-step explanation:
Cause we have a 25% discount, that means that the skatebord costs 75% of its original price.
The 75% of the original price is the 75/100 part (0.75)
Natasha goes bowling she pays $5.75 for an admission ticket and $9.25 for each round of bowling she plays the total amount of Tasha pays for admission and the number of rounds who plays is $33.50 which equation can be used to determine the number of rounds X that Natasha bowled
a.) 5.75 x + 9.25=33.50
b.) 9.25 X - 5.75= 33.50
c.) 5.75 + 9.25 X= 33.50
d.) 5.75 x - 9.25=33.50.
Which side lengths form a right triangle?
What is the surface area of the right cone below?
Answer:
176π [tex]units^{2}[/tex]
Step-by-step explanation:
SA = B + LA where B is the area of the base (circle) and LA is the lateral area
LA = radius of the circle times the slant height
= 8π(14) = 112π
B = [tex]8^{2} \pi[/tex] = 64π
SA = 112π + 64π = 176π
The surface area of the right cone is 176π square units.
How to calculate the surface area of a composite figure?
Surface area are derived for some standard shapes like circle, triangle, parallelogram, rectangle, trapezoid, cone etc.
When some shape comes which isn't standard figure, then we find its area by slicing it (virtually, like by drawing lines) in standard shapes. Then we calculate those composing shapes' area and sum them all.
Thus, we have:
[tex]\text{Area of composite figure} = \sum (\text{Area of composing figures})[/tex]
That ∑ sign shows "sum"
We are given that;
The surface area of a right cone is given by the formula:
Surface area=πr(r+l)
where r is the radius of the base and l is the slant height of the cone12.
In this case, r=8 and l=14, so we can plug these values into the formula and simplify:
Surface area=π×8(8+14)
Surface area=π×8×22
Surface area=176π
Therefore, the surface area will be 176π square units.
Learn more about area of a composite figure here:
https://brainly.com/question/10254615
#SPJ7
what is the measure of angle 2
Answer:
45
Step-by-step explanation:
180 - 135 = 45
The measure of angle 2 is 45.