Answer:
a) The radius of the lake to be r=10 units.
b) [tex]14\sqrt{5}[/tex] units
Step-by-step explanation:
The lake has equation: [tex]x^2+y^2=100[/tex]
We can rewrite this as [tex]x^2+y^2=10^2[/tex]
Comparing this to [tex]x^2+y^2=r^2[/tex]
We have the radius of the lake to be r=10 units.
b) The bridge is represented by the function y −x = 2
This is the same as y=x+2
We substitute this into the equation of the circle to get:
[tex]x^2+(x+2)^2=100[/tex]
[tex]x^2+x^2+4x+4-100=0[/tex]
[tex]2x^2+4x-96=0[/tex]
[tex]x^2+2x-48=0[/tex]
[tex](x+8)(x-6)=0[/tex]
[tex]x=-8,x=6[/tex]
When x=8, y=2(8)+2=18
When x=-6, y=2(-6)+2=-10
The length of the bridge is the distance between the points (8,18) and (-6,-10)
[tex]=\sqrt{(8--6)^2+(18--10)^2}[/tex]
[tex]=\sqrt{196+784}[/tex]
[tex]=\sqrt{196+784}[/tex]
[tex]=\sqrt{980}[/tex]
[tex]=14\sqrt{5}[/tex]
Select the correct product.
(5m 2 - 2m + 1)(3m - 4)
15m3 - 26m2 + 5m - 4
15m3 - 26m2 + 11m - 4
15m3 - 14m2 + 11m + 4
15m3 - 14m2 - 5m - 4
Answer: 15m3 - 26m2 + 11m - 4
A math teacher assigns three projects. She gives the students five project options to choose from. How many different groups of projects can students choose from?
Answer:
15
Step-by-step explanation:
3 options x 5 options = 15 total options
5. Solve the equation. 8/x+3 = 1/x+1
Answer:
x = -5/7
Step-by-step explanation:
8 1
---------- = ----------
x+3 x+1
Using cross products
8 (x+1) = 1 (x+3)
Distribute
8x+8 = x+3
Subtract x from each side
8x-x +8 = x-x+3
7x+8 =3
Subtract 8 from each side
7x +8-8 =3-8
7x = -5
Divide each side by 7
7x/7 = -5/7
x = -5/7
Diego's family car holds 18 gallons of fuel. Each day the car uses .8 gallons of fuel. A warning light comes on if the remaining fuel is 1.2 or less.
a. starting from full tank, can Diego's car go 15 days without the warning light turning on?
b. starting from a full tank, can Diego's car drive 20 days without the light coming on?
c. Deigo says that the expression 18-.8t helps him understand, what does T stand for?
d. write and solve an equation to determine the number of days his car can go before the warning light turns on.
e. write and solve an inequality that represents this situation. Explain clearly what the solution to the inequality means in the context of this situation.
Answer:
a) yes
b) yes
c) days
d) equation: 18 - 0.8x =1.2
solution: 21
e)inequality: equation: 18 - 0.8x [tex]\geq[/tex]1.2
solution: x < 21. This means that if he drives for less than 21 days the warning sign won't turn on.
Step-by-step explanation:
a) 18 - 15*0.8 = 6 so yes
b) 18 - 20*0.8 = 18 - 16 = 2
d) 18 - 0.8x =1.2
0.8x = 16.8
x = 16.8/0.8 = 21
Final answer:
a. No, the car cannot go 15 days without the warning light turning on. b. No, the car cannot drive 20 days without the light coming on. c. 'T' in the expression 18 - 0.8t stands for the number of days of fuel usage. d. Diego's car can go 21 days before the warning light turns on. e. The inequality 18 - 0.8t > 1.2 represents the situation.
Explanation:
a. To determine if Diego's car can go 15 days without the warning light turning on, we need to find out how much fuel will be left after 15 days of usage. Each day the car uses 0.8 gallons of fuel, so after 15 days, the car will have used 15 * 0.8 = 12 gallons of fuel. Starting from a full tank of 18 gallons, the remaining fuel after 15 days will be 18 - 12 = 6 gallons. Since the warning light comes on if the remaining fuel is 1.2 gallons or less, Diego's car will not be able to go 15 days without the warning light turning on.
b. To determine if Diego's car can drive 20 days without the light coming on, we follow the same steps as in part a. After 20 days, the car will have used 20 * 0.8 = 16 gallons of fuel. Starting from a full tank of 18 gallons, the remaining fuel after 20 days will be 18 - 16 = 2 gallons. Since the remaining fuel is less than 1.2 gallons, the warning light will turn on before 20 days.
c. In the expression 18 - 0.8t, 't' represents the number of days of fuel usage.
d. To determine the number of days Diego's car can go before the warning light turns on, we need to solve the equation 18 - 0.8t = 1.2. Rearranging the equation, we have 0.8t = 18 - 1.2, which simplifies to 0.8t = 16.8. Dividing both sides by 0.8, we get t = 21. So Diego's car can go 21 days before the warning light turns on.
e. To write an inequality that represents this situation, we can say that the remaining fuel after t days should be greater than 1.2 gallons. This can be expressed as 18 - 0.8t > 1.2. Solving this inequality, we get t < 21. This means that Diego's car can go up to 20 days before the warning light turns on, but on the 21st day, the warning light will turn on.
Which is equivalent to (9y2-4x)(9y2+4x) , and what type of special product is it?
Answer:
81y^4 - 16x^2, difference of squares.
Step-by-step explanation:
So we need to expand the following product:
(9y2-4x)(9y2+4x) = 9y2*9y2 + 4x*9y2 - 4x*9y2 -4x*4x = 81y^4 - 16x^2
And this type of product is the difference of squares.
Answer:
Step-by-step explanation:
The given expression is ( 9y² - 4x) (9y² + 4x)
We will simplify the given expression
(9y² - 4x) (9y² + 4x) = 9y² (9y² + 4x) - 4x (9y² + 4x) [Distributive property]
= 81y⁴ + 36xy² - 36xy² - 16x²
= (81y⁴ - 16x²)
This simplified form is the difference of squares of terms (9y²) and (4x)
Evaluate 3a2 + 2b when a = -4 and b = 6.
156
48
36
144
60
156
Explanation:
3 x -4 =-12
-12 x -12 = 144
2 x 6 = 12
12 + 144 =156
Answer:
60
E
Step-by-step explanation:
Givens
a = - 4
b = 6
Formula
3a^2 + 2b
Solution
3(-4)^2 + 2*6
3(16) + 12
48 + 12
Answer: 60
What’s the answe please
Answer:
C - a line segment and a ray are both two-dimensional. Already has one endpoint and extends and One Direction indefinitely.
Step-by-step explanation:
Well, A ray is and endpoint with an indefinite line coming out of it.
(·--------------------->)
A line segment ends like this:
(·---------------------·)
They are both 2-dimensional. :)
Which represents the solution set of the inequality 5x-9521?
Answer:
thats just things u needto remember.
Step-by-step explanation:
The expression is not factorable with rational numbers.
5
x
−
9521
The solution of the inequality {5x < 9521} is given by the inequality → x < 1904.2.
What is inequality?An inequality is used to compare two or more expressions or numbers.
For example -
2x > 4y + 3
x + y > 3
x - y < 6
Given is to find the solution set of the inequality →
5x < 9521
The given inequality is -
5x < 9521
Dividing by {5} on both sides, we get -
(5x/5) < (9521/5)
x < 1904.2
Therefore, the solution of the inequality {5x < 9521} is given by the inequality → x < 1904.2.
To solve more questions on inequality, visit the link-
https://brainly.com/question/11897796
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Sam has 2/3 of a piece of poster board. He cuts the poster board into 6 equal size pieces. What part of the whole poster board is each smaller piece?
2/3 divided by 6
2/3 times 1/6
1/9
A bag of flour weigh 3 lb. If a chef needs 15 lb. of flour, how
many bags of flour should he buy?
Answer:
The chef would need 5 bags
Step-by-step explanation:
Because 3 times 5 equals 15
To determine the number of bags of flour the chef should buy, divide the total weight required (15 lb) by the weight of one bag (3 lb), resulting in the need to purchase 5 bags.
To find out how many bags of flour the chef should buy, we need to divide the total weight of flour needed by the weight of one bag. If a bag weighs 3 lb, and the chef needs 15 lb, we calculate it as follows:
Determine the total weight needed: 15 lb.
Determine the weight of one bag: 3 lb.
Divide the total weight by the weight of one bag: 15 lb \/ 3 lb = 5 bags.
Therefore, the chef should buy 5 bags of flour to have a total of 15 lb.
Y= 10x - 32 what is the x and y value of this equation
Answer:
[tex]y=10x-32 \\ \\ x=\frac{y}{10}+3.2[/tex]
Step-by-step explanation:
[tex]y=10x-32[/tex]
Because that's the equation given.
To solve for x, isolate the variable and then divide by the coefficient.
[tex]y=10x-32 \\ \\ 10x=y+32 \\ \\ x=\frac{y}{10}+\frac{32}{10} \\ \\ x=\frac{y}{10}+3.2[/tex]
The length of GJ is 18 inches.
What is the length of GL?
A. 6 in.
B. 9 in.
C. 18 in.
D. 36 in.
It would B. 9.
Reason to this is because the radius is outlined by line GL. GL is half of the diameter which is GJ.
The answer is B. 9 because GJ is the circumference of the circle and they’re basically asking you to find the radius and the radius is half the circumference and half of 18 is 9 so the answer would be B.
Use the substitution method to solve the system of equations 3x+2y=13 y=x-1
Answer:
b
Step-by-step explanation:
The solution of the equations 3x + 2y = 13 y = x - 1 will be (3, 2). Then the correct option is B.
What is the linear system?A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.
The equations are given below.
3x + 2y = 13 ...1
y = x - 1 ...2
Then from the equations 1 and 2, we have
3x + 2(x - 1) = 13
5x - 2 = 13
5x = 15
x = 3
Then the value of y will be
y = x - 1
y = 3 - 1
y = 2
More about the linear system link is given below.
https://brainly.com/question/20379472
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A restaurant used 15 pounds of ground beef to make hamburgers for the day. How many burgers did they make if each burger is 6 ounces? (16 ounces = 1 pound) Explain your answer and show all conversions.NEED ANSWERS TODAY BECAUSE IT DUE TOMORROW!!
They were able to make 40 burgers with it
Answer: 40 hamburgers
Step-by-step explanation:
15 pounds x 16 ounces=240 ounces of hamburger meat
Each burger is 6 ounces 240 divided by 6= 40 hamburgers
if f(x)=4x+7, which if the following is the inverse of f(x)?
Answer:f
1/4y +-7/4 is your answer hope this help if it did mark me brainliest
Step-by-step explanation:
Greatest Common Factor 1
Find the Greatest Common Factor for each pair of numbers and order then from least (top) to greatest (bottom).
8 & 12
6 & 2
18 & 6
21 & 9
Answer:
6 & 2
21 & 9
8 & 12
18 & 6
Step-by-step explanation:
in a 30-60-90 triangle, the length of the side opposite the 30 angle is 8. find the length of the side opposite the 60 angle
Answer:
[tex]8\sqrt{3}\ units[/tex]
Step-by-step explanation:
Let
x----> the side opposite the 60 angle
Applying the law of sines
[tex]\frac{8}{sin(30)}=\frac{x}{sin(60)}\\ \\x=8*sin(60)/sin(30)\\ \\x=8\sqrt{3}\ units[/tex]
x>y, and the difference between x and y is 5. The number x is 1 more than twice the number y.
Answer:
the answer is d
Step-by-step explanation:
Answer:
A
Step-by-step explanation:
What is the product of 2x + y and 5x – y + 3? x2 + xy + x + y2 + y
Answer: [tex]10x^2+3xy+6x-y^2+3y[/tex]
Step-by-step explanation:
You need to remember the Product of powers property:
[tex](a^m)(a^n)=a^{(m+n)}[/tex]
Then, knowing this property, now you have to apply the Distributive property. So:
[tex](2x+y)(5x-y+3)=\\\\=(2x)(5x)-(2x)(y)+(2x)(3)+(y)(5x)-(y)(y)+(y)(3)\\\\=10x^2-2xy+6x+5xy-y^2+3y[/tex]
Finally, to simplify this expression, you need to add the like terms.
Therefore, you get that the product is:
[tex]=10x^2+3xy+6x-y^2+3y[/tex]
Answer:
10 3 6 -1 3
Step-by-step explanation:
Sally’s dog boarding service currently has 2 Great Danes, 8 golden retrievers, 22 mastiffs, and 12 Doberman pinschers. What is that ratio of Doberman pinschers to the total number of dogs at Sally’s boarding service?
Answer:
3/11
Step-by-step explanation:
First, determine how many dogs are at the boarding service:
2+8+22+12 = 44
Then:
# of Dobermans 12
-------------------------- = ------- = 6/22 or 3/ 11
total # of dogs 44
The desired ratio is 3/11.
identify the domain and range of the function graphed below
Answer:
Part 1) The domain is
[tex]x\leq 4[/tex]
All real numbers less than or equal to 4
Part 2) The range is
[tex]y\geq 0[/tex]
All real numbers greater than or equal to 0
Step-by-step explanation:
Part 1) Find the domain
Observing the graph
we know that
The domain is the interval for x ------> (-∞,4]
so
[tex]x\leq 4[/tex]
All real numbers less than or equal to 4
Part 2) Find the range
Observing the graph
we know that
The range is the interval for y ------> [0,∞)
[tex]y\geq 0[/tex]
All real numbers greater than or equal to 0
How do I solve using quadratic formula?
Answer:
Step-by-step explanation:
In elementary algebra, the quadratic formula is the solution of the quadratic equation. There are other ways to solve the quadratic equation instead of using the quadratic formula, such as factoring, completing the square, or graphing.
My bro is right good job
A store donated cases of crayons to a daycare center. Each case holds 24 boxes of crayons; each box holds 8 crayons. How many crayons did the center receive?
In order to find out the total number of crayons, you multiply the number of cases by the number of boxes per case, and then by the number of crayons per box. Assuming the store donated 5 cases, the daycare center received a total of 960 crayons.
To determine how many crayons the daycare center received from the store, we need to multiply the number of cases the store donated by the number of boxes in each case, and then multiply that by the number of crayons in each box. Let's break it down step by step:
Find the total number of boxes by multiplying the number of cases by the number of boxes in each case.Find the total number of crayons by multiplying the total number of boxes by the number of crayons in each box.Assuming the store donated 5 cases (the number of cases was not specified in the question, so we need to assume a number for this example), here's how you would calculate it:
Total number of boxes = 5 cases * 24 boxes/case = 120 boxesTotal number of crayons = 120 boxes * 8 crayons/box = 960 crayonsTherefore, the daycare center received a total of 960 crayons.
from a balloon 1127 feet high, the angle of depression to the ranger headquarters is 79° 56'. how far is the headquarters from a point on the ground directly below the balloon?
Check the picture below.
make sure your calculator is in Degree mode.
graph the following inequality x≥2
Answer:
The graph is as attached.
Step-by-step explanation:
Simply draw a line of x = 2 on your graph paper.
That line should be a complete line not dotted line.
Since x is greater than 2, shade the left side of the line because we are interested in the right side (where x is greater and equal to 2)
Answer:
Here, the given inequality,
[tex]x\geq 2[/tex]
Related equation is,
x = 2
Which is the equation parallel to y-axis and passes through (2,0),
Also, 0 ≥ 2 ( False )
The shaded region of the inequality will not contain the origin,
Now, '≥' shows the solid line.
Thus, by the above explanation,
We can graph the given inequality ( shown below )
identify the frequency of the graph
ANSWER
[tex] \frac{1}{2} [/tex]
EXPLANATION
The frequency of a wave function refers to the number of times the graph repeats its cycle within the interval [0,2π]
We can observe explicitly from the graph that the frequency is half.
The period of the given function is 4π
[tex] \frac{2\pi}{b} = 4\pi[/tex]
[tex]b = \frac{2\pi}{4\pi} = \frac{1}{2} [/tex]
Hence the frequency is half.
If cos0= -5/13 and sin 0<0, what is tan 0
Answer:
12/5
Step-by-step explanation:
I doubt that you actually meant If cos0= -5/13 and sin 0<0. Please use a Greek letter, such as Ф, to represent the angle.
If you'd do this, you'd have:
If cosФ= -5/13 and sin Ф<0
cos Ф and sin Ф are both negative in Quadrant III.
Recall that cos Ф = adj / hyp, and that hyp is always +. Thus, adj = -5 and hyp = +13. Using the Pythagorean Theorem to find opp:
opp² + adj² = hyp², or:
opp² = hyp² - adj². Applying this, we find that opp = -12.
Recall that tan Ф = opp / adj.
Here,
tan Ф = -12 / (-5) = +12/5
Identify the terms, coefficients, and constants in the expression 3x+10.
Answer:
Terms (in BOLD) : 3x+10
two terms
Coefficients (in BOLD) : 3x+10
one coefficient
Constants (in BOLD) : 3x+10
one constant
Step-by-step explanation:
Terms are the contents in the equation of such. For example, 10+4n. There are two terms. Coefficients are the number next to a variable. For example, 9x. 9 is the coefficient. Constants are numbers without a variable. Numbers like 7, 8, 9, 10-- they don't have variables so they are constants in an equation. Now, knowing this information lets get to work!
The equation: 3x+10
Terms (in BOLD) : 3x+10
two terms
Coefficients (in BOLD) : 3x+10
one coefficient
Constants (in BOLD) : 3x+10
one constant
Hope this helps!!
-Ketifa
Final answer:
The expression 3x+10 consists of two terms: 3x (with the coefficient 3) and 10 (the constant).
Explanation:
In the expression 3x+10, there are two terms: 3x and 10. The term 3x consists of a variable (x) and a coefficient (3), which is the number multiplying the variable.
The term 10 is a constant because it does not contain any variables and its value does not change. The coefficients in this expression are therefore the number 3, and the constant is 10.
What is the circumference of a circle having a radius of 6cm?
Answer:
12cm.
Step-by-step explanation:
The radius is half of a circe.
6 * 2 = 12.
Answer:
37.68 cm
Step-by-step explanation:
the circumference of a circle is : P = 2π r
P= 2×3.14×6 =37.68 cm
What is the sum of the first 10 terms of the sequence defined by an=4n-3
A. 37
B. 190
C. 380
D. 384
The answer to this is:
B. 190
The sum of the first 10 terms of the sequence an=4n-3 is 190.
The question is asking for the sum of the first 10 terms of the sequence defined by an=4n-3. To find the sum, we first list the first 10 terms by substituting values of n from 1 to 10 into the formula. Thus, for n=1, a1=1(4)-3=4-3=1; for n=2, a2=2(4)-3=8-3=5; and so on until n=10, a10=10(4)-3=40-3=37.
The first ten terms of the sequence are: 1, 5, 9, 13, 17, 21, 25, 29, 33, and 37. The sum of these terms can be calculated as 1+5+9+13+17+21+25+29+33+37 = 190.