Final answer:
To find the value of x, set the two expressions for the lengths of the sides of the rectangle equal to each other and solve. The value of x is 2. To find the length of each diagonal, use the Pythagorean Theorem with the lengths of the sides of the rectangle. The length of each diagonal is 13 * sqrt(2).
Explanation:
To find the value of x, we can set the two expressions for the lengths of the sides of the rectangle equal to each other, since opposite sides of a rectangle are congruent. So, we have:
6x + 1 = 9x - 5
To solve for x, we can subtract 9x from both sides and add 5 to both sides:
1 + 5 = 9x - 6x
6 = 3x
x = 2
Therefore, the value of x is 2. To find the length of each diagonal, we can use the Pythagorean Theorem. The diagonal of a rectangle acts as the hypotenuse of a right triangle formed by the sides of the rectangle. In this case, the length of one side is 6x + 1, and the length of the other side is 9x - 5. So, the length of each diagonal is:
d = sqrt((6x + 1)^2 + (9x - 5)^2)
d = sqrt((6(2) + 1)^2 + (9(2) - 5)^2)
d = sqrt(13^2 + 13^2)
d = sqrt(2 * 13^2)
d = 13 * sqrt(2)
what is the y-intercept of y=3x - 8
Answer:
(0, -8)
Step-by-step explanation:
y is defined as x=0,
therefore y = 3*0 - 8= -8
Answer:
-8 or (0, -8)
Step-by-step explanation:
The point slope form: y = mx + b
m is the slope
b is the y-int
Step 1: Identify the y-int
y = 3x - 8
-8 is the y-int
(0, -8)
Answer: -8 or (0, -8)
How do you put y+2x=5 into slope-intercept form?
Answer: y=-2x+5
Step-by-step explanation:
Y+2x=5
y-2x=5-2x
y=-2x+5
then graph
Answer:
y=-2 x +5
Step-by-step explanation:
Write in slope-intercept form, y=m x+b
write an equation of the circle with center 6.-9) and radius 10!
The equation of the given circle is [tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
Step-by-step explanation:
Step 1:
The equation of a circle with its center at (h, k) and a radius of r is given by
[tex](x-h)^{2}+(y-k)^{2}=r^{2}.[/tex]
The h value is the x coordinate and the k value is the y coordinates, so (h, k) is (6, -9).
The radius is given as 10 so [tex]r =10[/tex] and [tex]r^{2} = 100.[/tex]
Step 2:
By substituting the values we know, we get
[tex](x-h)^{2}+(y-k)^{2}=r^{2} = (x-6)^{2}+(y-(-9))^{2}=10^{2}.[/tex]
So the equation of the given circle is
[tex](x-6)^{2}+(y+9)^{2}=100.[/tex]
The solution set for -18 < 5x - 3 is _____.
3 > x
-3 > x
3 < x
-3 < x
Answer:
-3 < x
Step-by-step explanation:
add the negative 3 to the other side
you get: -15 < 5x
divide by 5 on both sides
you get: -3 < x
that's the answer
What is the length of D.
8ft
Answer:
96 inches
Step-by-step explanation:
8 ft is 8(12) inches, which is 96 inches
Use the system of equations to answer the questions.
2x + 3y = 3
y = 8 - 3r
The value of y from the second equation is substituted back into the first equation. What is the resulting equation?
What is the value of x?
What is the value of y?
Answer:
the value of x and y is 3 and -1 respectively.
Step-by-step explanation:
from the question
let
2x + 3y = 3........................ equation 1
y = 8 - 3x.............................. equation 2
put y = 8 - 3x in equation 1
2x + 3y = 3........................ equation 1
2x + 3 ( 8 - 3x) = 3
2x + 24 - 9x = 3
24 - 7x = 3
24 = 3 + 7x
24 -3 = 7x
21 = 7x
divide both sides by 7
x = 3
put x = 3 in equation 2
y = 8 - 3x.............................. equation 2
y = 8 - 3 ( 3)
y = 8 -9
y = -1
therefore the value of x and y is 3 and -1 respectively.
If 3x + 8 = -4, then
evaluate x3 + 5
Answer:
-59
Step-by-step explanation:
x3 is meaningless; I assume you meant x^3.
If that's the case, then:
3x + 8 = -4 is equivalent to 3x = -12, so that x = -4.
Then (-4)^3 + 5 = -64 + 5 = -59
Answer:
-59
Step-by-step explanation:
the question can be solved by some simple mathematical steps.
If 3x + 8 = -4
then, x3 + 5 =?
from 3x + 8 = -4
collect the like terms
3x = -4 - 8
3x = -12
divide both sides by 3
3x/3 = -12/3
x = -4
if x = -4 then to find x3 + 5 will imply that we will insert the value of x = -4 into the x3 + 5
-4 ³ + 5
-64 + 5
= -59
therefore the value of x3 + 5 is solved to be -59
identify the numerical coefficient of the term 5xy
x∙5∙25∙4÷5, if x=813
Final answer:
When x equals 813, the algebraic expression x⋅5⋅25⋅4÷5 simplifies to 81300 by substituting x with 813 and following the order of operations through multiplication and division.
Explanation:
The question asks for the calculation of an algebraic expression with the substitution of x=813. The expression is x⋅5⋅25⋅4÷5. To solve this, we first substitute x with 813, and then we follow the order of operations.
Substitute x with 813: 813⋅5⋅25⋅4÷5.Multiply the numbers together: 813⋅5 equals 4065, 4065⋅25 equals 101625, and 101625⋅4 equals 406500.Finally, divide by 5: 406500÷5 equals 81300.Therefore, when x=813, the solution to the expression is 81300.
Jason went to the post office and bought both 41-cent stamps and 26-cent postcards and spent $10.28. The number of stamps was 4 more than twice the number of postcards. How many of each did he buy?
Solution:
Let stamps be s and postcards be p
Given that,
The number of stamps was 4 more than twice the number of postcards
s = 4 + 2p -------- eqn 1
Jason bought both 41-cent stamps and 26-cent postcards and spent $10.28
41 cent = $ 0.41
26 cent = $ 0.26
Therefore,
[tex]s \times 0.41 + p \times 0.26 = 10.28[/tex]
0.41s + 0.26p = 10.28 --------- eqn 2
Substitute eqn 1 in eqn 2
0.41(4 + 2p) + 0.26p = 10.28
1.64 + 0.82p + 0.26p = 10.28
1.08p = 10.28 - 1.64
1.08p = 8.64
Divide both sides by 1.08
p = 8
Substitute p = 8 in eqn 1
s = 4 + 2(8)
s = 4 + 16
s = 20
Thus Jason bought 20 stamps and 8 post cards
Factor the quadratic expression completely.
-7x^2-24x-9=
Answer:
[tex] - 7 {x}^{2} - 24 - 9 \\ - 7 {x}^{2} - 21x - 3x - 9 \\ - 7x(x + 3) - 3(x + 3) \\ ( - 7x - 3)(x + 3)[/tex]
Two number cubes are rolled for two separate events:
Event A is the event that the sum of numbers on both cubes is less than 10.
Event B is the event that the sum of numbers on both cubes is a multiple of 3.
Complete the conditional-probability formula for event B given that event A occurs first by writing A and B in the blanks:
Answer:
11/30
Step-by-step explanation:
P(B/A) = P(B^A)/P(A)
P(A) = 30/36 = 5/6
P(B^A) = (2+5+4)/36 = 11/36
11/36 ÷ 30/36
11/30 or 0.3667
Which figure has only one line of symmetry? A. rhombus B. square C. circle D. isosceles triangle
Answer:
D. isosceles triangle
Step-by-step explanation:
Answer:
D. Isosceles Triangle
Step-by-step explanation:
An Isoceles triangle can only be folded once, it has one line of symetry. A square has 4, a circle has infinete and a rhombus has 2 so it has to be an isoceles triangle.
what is the answer to 6 more than the product of five and a number decreased by one
Find the surface area of number 1. Will give Brainliest
Answer:
142 in^2
Step-by-step explanation:
Base: 7 × 3 = 21 (×2 = 42)
Small faces: 5 × 3 = 15 (×2 = 30)
Larger faces: 5 × 7 = 35 (×2 = 70)
Add: 21 + 30 + 70 = 142
Factor out the greatest common monomial factor from the polynomial. (If the polynomial has no common monomial factor, enter NCF.)
8x + 8
Answer:
Step-by-step explanation:
8x = 8 * x
8 = 8 * 1
Greatest common factor = 8
8x + 8 = 8(x+ 1)
The mass of an empty container is 3/10kg. When the container is half filled with water, the mass becomes 1 1/10kg. What is the mass of the container when it is completely filled with water
Answer:
1.9 kg
Step-by-step explanation:
Empty container: 3/10 kg = 0.3 kg
Container half filled: 1 1/10 kg = 1.1 kg
Mass of water that fills it halfway: 1.1 kg - 0.3 kg = 0.8 kg
Mass of water that fills it completely: 2 * 0.8 kg = 1.6 kg
Mass of container completely filled with water: 0.3 kg + 1.6 kg = 1.9 kg
if f(x) = 3x - 12, what is f(2)?
-6
-18
18
6
Answer: -6
Explanation: In this problem, we're given the function f(x) = 3x - 12 and we're asked to find f(2).
To find f(2) or the value of the function when x equals 0, we simply substitute 2 in for x in our function. So we have f(x) = 3(2) - 12 or 6 - 12 which equals -6.
So f(2) or the value of the function when x equals 2 is -6.
plz help me asap will give brainliest and 100 points.
3. A new ice cream shop is opening up and the owners are making a large ice cream cone for display (see
picture below). What is the volume of the ice cream cone? Round your answer to the nearest hundredth of a
cubic inch. Use 3.14 to approximate pi. Show your work and explain your steps.
Answer:
167.47 cubic metres
Step-by-step explanation:
Volume of a cone is given by [tex]\frac {\pi r^{2}h}{3}[/tex] where r is radius and h is the height of the cone. Assuming a radius of 4m and height of 10 m then the volume, using 3.14 for [tex]\pi[/tex] will be
V=[tex]\frac {3.14\times 4^{2}\times 10}{3}\approx 167.47 m^{3}[/tex]
-4 1/4 divided by 1/2
Answer:
-8.5, or -8 1/2
Step-by-step explanation:
Put it into an improper fraction: -17/4
Multiply: -17/4 * 2/1 (To divide, multiply by reciprocal)
= -34/4
Simplify: -17/2, or -8 1/2
Answer:
-34/4 or -8 1/2
Step-by-step explanation:
First we want to put -4 1/4 so its all a fraction we do this by multiplying 4 to 4 and adding it to the 1 already in the fraction (We can ignore the sign and just add it to the fraction because the entire fraction is negative not just the 4). So we have -17/4
To divide fractions we use keep change flip it is an easier way to divide fractions with out making decimals. We keep the first fraction change the division into multiplication and flip the last fraction, in this case 1/2 becomes 2/1. Now we have
-17/4 * 2/1
Our next step is to multiply the numerators together and the denominators together and then put it back in fraction form.
-17 * 2 = -34
4 * 1 = 4
Our final result is
-34/4
Or if you need it as a mixed number you just divide the 34 into 4 as many times as you can and make that the whole number. 34 doesn't completely fit into 4 but 32 does so we have
-8 2/4 or simplified further
-8 1/2
The lines kx + 2y = -7 and y = 2x - 5 are perpendicular to each other. Find the value of k.
Answer:
k=1
Step-by-step explanation:
1. find the negative reciprocal of the slope of y=2x-5 because that is the slope perpendicular to it.
m=2 ; negative reciprocal is 1/-2
2. isolate y in the first equation
y= kx/-2 + 7/-2
3. the only value for k that would make their slopes the same would be 1
Skylar got a manicure for $28 and pedicure for $35
salon. If she plans to tip 15%, how much will she pay?
Answer:
$72.45
Step-by-step explanation:
Add the amounts of the manicure and pedicure together: 28 + 35 = 63
Then find 15% of $63. You will need to find the decimal equivalent of 15%. To do this, divide 15 by 100 or move it two decimal places to the right: 15/100 = 0.15
Now, multiply total of the manicure and pedicure, 63, by 0.15: 63 x 0.15 = 9.45
$9.45 will be her tip. To find the total amount Skylar payed, add the tip to the amount spent on the mani/pedi: 63 + 9.45 = 72.45
Skylar will pay $72.45
Hope this helps!
Final answer:
To calculate Skylar's total payment including a 15% tip for her manicure and pedicure, add the cost of both services ($63) and then calculate the tip ($9.45). The total payment is $72.45.
Explanation:
The student's question involves calculating the total cost of a service which includes both a tip and the original prices of the services purchased - in this case, a manicure and a pedicure. To find how much Skylar will pay after tipping 15%, we first need to calculate the total cost of the services before the tip.
Firstly, we add the cost of the manicure ($28) and the pedicure ($35) to get the total cost before the tip:
Manicure = $28Pedicure = $35Total cost before tip = Manicure + Pedicure = $28 + $35 = $63Next, we calculate the amount of the tip by multiplying the total cost by the tip percentage (which we convert from 15% to a decimal by dividing by 100):
Tip percentage = 15%Tip as a decimal = 15% / 100 = 0.15Tip amount = Total cost before tip × Tip as a decimal = $63 × 0.15 = $9.45Finally, we add the original total cost to the tip to find the final amount Skylar will pay:
Final total cost = Total cost before tip + Tip amount = $63 + $9.45 = $72.45So, Skylar will pay $72.45 in total for her manicure and pedicure including a 15% tip.
Mai spends 7 3/5 hours in school each day. Her lunch period is 30 minutes long, and she spends a total of 42 minutes switching rooms between classes. The rest of her day is spent in 6 classes that are all the same length. How long is each class?
The each class is 64 minutes or 1 hour 4 minutes long.
Step-by-step explanation:
1 hour = 60 minutes.
Total time spent in school = 7 hours+3/5 hour = 7(60) + (3/5)(60) minutes.Total time = 420+36 = 456 minutes.Lunch period = 30 minutes.Time for switching classrooms = 42 minutes.Time spent in 6 classes :
Time spent in 6 classes = Total time - (lunch period + switching classes)
⇒ 456 - (30+42)
⇒ 456 - 72
⇒ 384 minutes.
The Time for each of 6 classes :
Time for each class = Time spent for all 6 classes / 6
⇒ 384/6
⇒ 64 minutes.
⇒ 1 hour 4 minutes.
Stop 1: first, let's pay the bills.
1) Henna's cell phone company has a basic monthly plan of $60 plus $0.12
per minute. At the end of the month she was charged with a total of
$123.00. How many minutes has she used this month?
Answer:
525 Minutes
Step-by-step explanation:
The equation would be...
$60 + $0.12m = $123
Now we can simplify
($60 - $60) + $0.12m = ($123 - $60)
$0.12m = $63
($0.12m/$0.12) = ($63/$0.12)
M = 525
Simplify the expression -23 + 6
Answer:
−23+6
=−23+6
=−17
Step-by-step explanation: Mark brainliest please!
Melinda has a scrap piece of fabric with one angle
measuring 52°. If she needs to find a complementary
angle, what angle measure does she need to cut the
next piece?
Melinda should cut the piece of fabric at an angle of______
Answer:
38
Step-by-step explanation:
Answer:
38
A right angle. A line comes out of the angle to split the angle into 52 degrees and blank.
Melinda has a scrap piece of fabric with one angle measuring 52°. If she needs to find a complementary angle, what angle measure does she need to cut the next piece?
Melinda should cut the piece of fabric at an angle of
38
°.
Step-by-step explanation:
Which of the following describes a pattern in the table
Im not sure it depends on the pattern? lol
The pattern described in the table is the value of b is 5 times the value of a.
What is a pattern?A pattern is defined as a sequence of repeating objects, shapes or numbers. We can relate a pattern to any type of event or object. A pattern has a rule that tells us which objects belong to the pattern and which objects do not belong to the pattern.
Given is a table,
a - 0 1 2 3 4
b - 0 5 10 15 20,
We can see, that the values in the b row are 5, 10, 15, 20 they are the multiple of 5
And values in row a, are 1, 2, 3, 4, we can see they are the numbers which are related to row b, in a way that, values in b are 5 times the value of a,
1 × 5 = 5
2 × 5 = 10
3 × 5 = 15
4 × 5 = 20
5 × 5 = 25
Therefore, we can say that the numbers in b are 5 times the corresponding value of the a,
Hence, the pattern described in the table is the value of b is 5 times the value of a.
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The complete question is :
Which rule describes the pattern in the table?
a 0 1 2 3 4
b 0 5 10 15 20
The value of b is 5 times the value of a.
The value of b is 5 less than the value of a.
The value of b is 5 more than the value of a.
The value of a is 5 times the value of b.
Solve for all solutions x2=29
Answer:
x=14.5
PLEASE MARK BRAINLIST!!
Step-by-step explanation:
2x=29
Divide by 2 on both sides:
x=14.5
Answer: it should be x=14.5
25% of the students attended the school dance. if 32 attended the dance, how many students are there in all?
Answer:
128 students in total
Step-by-step explanation:
25/100 = 1/4
1/4 = 32/ x
1 x 32
Answer:
your answer is A
Step-by-step explanation:
32 *4=128
4*25=100%
1/10(x+50)=-3x-13+4x
The question is about solving the linear equation 1/10(x+50)=-3x-13+4x. This process involves simplifying the equation, combining like terms, and isolating x to find the solution.
Explanation:This question involves algebra, specifically the solving of linear equations. To start, your equation is
1/10(x+50)=-3x-13+4x
. First step is to simplify the equation: both sides of the equation need to be simplified and rearranged. After simplifying, we can combine the x terms and constants together. You will then isolate x on one side of the equation by adding or subtracting terms as needed. This will give you the solution to the equation. It's important to remember that the solution to the equation is the value of x that makes both sides of the equation equal. Note that one might end up with no solution if the equation is not consistent after simplifying.
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