Does a translation produce congruent figures?
What is the value of y? 3(y 5)=–2y3(y 5)=–2y
a. –5
b. –5
c. –3
d. –335?
18 + x > 40
a. x > 58
b. x > 22
c. x > -58
d. x > -22
Trip walks a total of 12 miles to and from school each week. Lindsey rides her bike a total of 56 miles to and from school each week.
Use the greatest common factor and the distributive property to complete the equation, and find the total number of miles Trip and Lindsey travel to and from school each week.
(3 + ) =
Final answer:
The total number of miles Trip and Lindsey travel to and from school each week is 68 miles, determined by using the greatest common factor of 12 and 56, which is 4, and the distributive property to group and multiply the sum of the unit contributions by 4.
Explanation:
To find the total number of miles Trip and Lindsey travel to and from school each week using the greatest common factor (GCF) and the distributive property, we first identify the GCF of the two numbers. The GCF of 12 and 56 is 4. We can then apply the distributive property to factor out the GCF and write the equation as follows:
(3 + 14) × 4 = total number of miles traveled to and from school each week.
Trip contributes '3' units of the GCF and Lindsey contributes '14' units of the GCF. To find the total, we add 3 and 14 to get 17, and then multiply by the GCF:
17 × 4 = 68
Therefore, Trip and Lindsey travel a total of 68 miles to and from school each week.
Which is the only fraction that must be represented by a non terminating decimal?
a. 7/5
b. 7/4
c. 7/3
d. 7/2
Answer:
The correct option is C) 7/3.
Step-by-step explanation:
Consider the provided numbers.
If the rational number can be written in the form of [tex]\frac{p}{2^n\times 5^m}[/tex] then the rational number will be a terminating decimal.
Now consider the provided options:
Option A) 7/5 can be written as: [tex]\frac{7}{2^0\times 5^1}[/tex]
Thus it is a terminating decimal.
Option B) 7/4 can be written as: [tex]\frac{7}{2^2\times 5^0}[/tex]
Thus it is a terminating decimal.
Option C) 7/3 can be written as: [tex]\frac{7}{2^0\times 5^0\times 3^1}[/tex]
Thus it is not a terminating decimal.
Option D) 7/2 can be written as: [tex]\frac{7}{2^1\times 5^0}[/tex]
Thus it is a terminating decimal.
Hence the only fraction that must be represented by a non terminating decimal is 7/3.
The correct option is C) 7/3.
Convert 2/5 to a percent
2/5 to a percent would be 40%.
The work is attached in the image provided.
Which equations represent the line that is parallel to 3x − 4y = 7 and passes through the point (−4, −2)? Check all that apply.
y = –x + 1
3x − 4y = −4
4x − 3y = −3
y – 2 = –(x – 4)
y + 2 = (x + 4)
To find a line parallel to a given line and passing through a certain point, determine the slope of the given line, rearrange it to slope-intercept form, then substitute the point's coordinates to find the y-intercept of the parallel line.
To find a line parallel to the given line, we need the same slope of 3. Start by rearranging the given equation 3x - 4y = 7 to slope-intercept form: y = (3/4)x - 7/4. Since the parallel line passes through (-4,-2), substitute these values into the slope-intercept form to find the y-intercept. The equation of the line parallel to 3x - 4y = 7 that passes through (-4,-2) is y = (3/4)x + 2.
For which values of x and y is line p parallel to line q?
X=5,y=3
x=1, y=5
x=3, y=5
x=3, y=6
Step 1
Find the value of x
we know that
If lines p and q are parallel
then
[tex](45x-5)+(16x+2)=180\°[/tex] ------> by consecutive interior angles
Solve for x
[tex](45x-5)+(16x+2)=180\° \\61x=180+3 \\x=3\°[/tex]
Step 2
Find the value of y
we know that
If lines p and q are parallel
then
[tex](26y)=(45x-5)[/tex] ------> by corresponding angles
substitute the value of x and solve for y
[tex](26y)=(45*3-5)[/tex]
[tex](26y)=130[/tex]
[tex]y=5\°[/tex]
therefore
the answer is the option
[tex]x=3\°[/tex] , [tex]y=5\°[/tex]
Given f(x) = the quantity of 4x plus 1, divided by 3, solve for f−1(3).
2
4
6
8
Answer:
2
Step-by-step explanation:
Here, the given function is,
f(x) = The quantity of 4x plus 1, divided by 3
[tex]\implies f(x)=\frac{4x+1}{3}[/tex]
The steps that involve in finding the inverse of f(x) are as follows,
Step 1 : Replace f(x) by y,
[tex]y=\frac{4x+1}{3}[/tex]
Step 2 : Switch x and y,
[tex]x=\frac{4y+1}{3}[/tex]
Step 3 : Isolate y in the left side of the equation,
[tex]3x=4y+1[/tex]
[tex]-4y=1-3x[/tex]
[tex]y=\frac{1-3x}{-4}[/tex]
[tex]y=\frac{3x-1}{4}[/tex]
Step 4 : Replace y by [tex]f^{-1}(x)[/tex],
[tex]f^{-1}(x)=\frac{3x-1}{4}[/tex]
For x = 3,
[tex]f^{-1}(3)=\frac{3\times 3-1}{4}=\frac{9-1}{4}=\frac{8}{4}=2[/tex]
Hence, First option is correct.
Triangle ABC is similar to triangle DEF. The scale factor from triangle ABC to triangle DEF is 1/3. If DE = 6 m, find the length of AB.
1
18
2
3
The sum of the angle measures of any triangle is
180
degrees. Suppose that one angle in a triangle has a degree measure of
7x+3
and another has a degree measure of
3x-6
. Write an expression for the degree measure of the third angle in the triangle.
Ariane gets paid $0.50 for the first 100 craft kits that she assembles. She earns $0.75 for each kit over 100. This week she assembled 135 kits. How much did she earn?
A. $67.50
B. $72.50
C. $76.25
D. $101.25
Final answer:
Ariane earned $50 for the first 100 kits at $0.50 per kit, and for the additional 35 kits at $0.75 per kit, she earned $26.25. Adding these amounts, her total earnings are $76.25.
Explanation:
To calculate Ariane's earnings for assembling 135 craft kits, we need to consider two different pay rates: one rate for the first 100 kits and a higher rate for each kit above 100.
For the first 100 kits, she earns $0.50 per kit, which is 100 kits × $0.50/kit = $50. For the remaining 35 kits (135 total - 100), she earns a higher rate of $0.75 per kit, which is 35 kits × $0.75/kit = $26.25.
Now, we add both amounts to find the total earnings:
$50 (first 100 kits) + $26.25 (kits over 100) = $76.25 total earnings
Thus, Ariane earned $76.25 for assembling 135 craft kits this week.
A sector of a circle is shown. Find its area, rounded to the nearest tenth.
a)9.8 cm^2
b)10.5 cm^2
c)11.2 cm^2
d)12.3 cm^2 ...?
The area of the sector of the circle whose radius is 4.2 cm while the angle made at the center is 68° is 10.5 cm².
What is a circle?A circle can be defined as a shape that consists of all points in a plane that are at equal distance from a given point, therefore, the center.
As it is given that the length of the radius of the circle is 4.2 cm, while the angle made by the sector at the center of the circle is 68°. Therefore, the area of the sector of the circle can be written as,
[tex]\text{Area of the sector of the circle} = \pi r^2\times \dfrac{\theta}{360^o}[/tex]
Substituting the value, we will get,
[tex]\text{Area of the sector of the circle} = \pi \times(4.2^2)\times \dfrac{68^o}{360^o}[/tex]
[tex]= 10.472 \approx 10.5\rm\ cm^2[/tex]
Hence, the area of the sector of the circle whose radius is 4.2 cm while the angle made at the center is 68° is 10.5 cm².
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What is the next number in the sequence?
1,4,13,40,121,...
The formula for the volume of a cube is V(s) = s³ where s is the side length of the cube. What is the domain and range of this function?
s < 0, V(s) < 0
s > 0, V(s) < 0
s < 0, V(s) > 0
s > 0, V(s) > 0
An airplane takes off with a full tank of 40,000 gallons of fuel and flies at an average speed of 550 miles per hour. After 8 hours in flight, there are 14,000 gallons of fuel left. It will take another 3.5 hours for the plane to reach its destination. How much fuel will be left in the tank when the plane lands? What is the total distance of the flight?
1. The quantity of fuel left in the tank when the plane lands will be 3,375 gallons.
2. The total distance of the flight is 6,325 miles.
How are the quantities determined?The quantities are computed using basic mathematical operations, including subtraction, division, addition, and multiplication.
Full tank of the airplane = 40,000 gallons
Average speed = 550 miles per hour
Number of hours on first flight = 8 hours
The quantity of fuel left = 14,000
The quantity of fuel consumed in 8 hours = 26,000 (40,000 - 14,000)
The quantity of fuel consumed per hour or per 550 miles = 3,250 miles (26,000 ÷ 8)
Additional hours on the final flight = 3.5 hours
The quantity of fuel consumed during the final flight = 11,375 gallons (3.5 x 3,250)
The total quantity of fuel consumed for the flight = 37,375 gallons (26,000 + 11,375)
The quantity of fuel left after the flight = 2,625 gallons (40,000 - 37,375)
The total hours for the flight = 11.5 hours (8 + 3.5)
The total distance of the flight = 6,325 miles (550 x 11.5)
Mathematically, after flying 11.5 hours or 6,325 miles, the airplane consumed 37,375 gallons of fuel, leaving only 2,625 gallons in its tank.
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How do I find the 25th term of the arithmetic sequence -39, -31, -23, -15,...
Frank had $25 in his checking account he withdrew $15 cash and $9 to pay his bill what is the expression
Let f(x) = -4x + 7 and g(x) = 2x - 6. Find (f.g)(1)
Answer:
The answer would be 23
Step-by-step explanation:
I think this is a composite function, so it would be
f(g(1))
you must first replace all the "x" in f(x) with g(x)
f(g(x) = -4(g(x))+7
f(g(x)) = -4(2x-6)+7
f(g(x)) = -8x+24+7
f(g(x)) = -8x+31
If x=1
f(g(1)) = -8*1+31
f(g(1)) = -8+31
f(g(1)) = 23
If a fish weighs 8 times as much as her parakeet if they both weigh 63 ounces together how much does the fish weigh alone
One angle is twice another angle. The sum of the angles is 90 degrees. How many degrees are in each angle. Please explain.
A father is 1 year older than 3 times the age of his son. The son is 20 years old.
Let F = the age of the father.
Which formula would calculate the father's age?
1. F=3(20-1)
2. F + 1 = 3(20)
3. F - 1 = 3(20)
Marcie wants to enclose her yard with a fence. Her yard is in the shape of a rectangle attached to a triangle. The formula for the area of the enclosed space is A = lw + 0.5bh. Solve for b.
A. b = A divided by the quantity l times w plus 0.5 times h
B. b = The quantity A minus l times w all divided by 0.5 times h
C. b = A – lw – 0.5h
D. b = A + lw + 0.5h
No Idea :o
Johann maintains a$75,000 insurance policy on his boat. He pays $50 per month in premium and his deductible is $2,500 if he is involved in a accident and make a claim of 15,000 on the policy, how much will his insurance company pay ?
A. $2,500
B.$12,500
C.$15,000
D.$17,500
Answer:
B) 12,500
Step-by-step explanation:
Just took the quiz :)
Loren puts £600 in a bank account.
The account pays 3% compound interest each year after ONE year she withdraws £200.
How much will she have in the account after 2 years?
To solve the problem we will first calculate the remaining balance in Loren's Account after a year.
The balance in Loren's account after two years is £430.54.
Given to us
Loren puts £600 in a bank account,the account pays 3% compound interest each year,after ONE year Loren withdraws £200Principal Amount that Loren put in her account, P = £600Rate of interest that bank pays, r = 3% = 0.03Balance of Loren after one yearUsing the compound interest formula,
Balance of Loren after one year = [tex]P(1+r)^t[/tex]
Substituting values,
[tex]=600(1+0.03)^1\\= 600(1.03)\\= 618[/tex]
Remaining Balance of Loren after one yearNow, as Loren takes £200 out of the account, the remaining balance would be,
= Balance of Loren after one year - £200
= £618 - £200
= £418
Balance in Loren's account after two yearsIn the second year, the balance will be paid on the remaining balance, therefore, applying the formula of compound interest,
P = £418
r = 0.03
t = 1
[tex]=P(1+r)^t\\=418(1+0.03)^1\\=418(1.03)\\= 430.54[/tex]
Hence, the balance in Loren's account after two years is £430.54.
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Parallelograms can be used to prove statements about triangles.
True False
Answer:
it's true
Step-by-step explanation:
The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram.
A parallelogram's facing or opposing sides are of equal length, and its opposing angles are of similar size.
As per the parallelogram drawn.
ΔABC ≅ ΔADC (By SAS postulute of congruency)
So we can make the statement that the two triangles made by the diagonal of a parallelogram will be congruent.
Hence "The triangles made by diagonal parallelograms will be congruent so we can prove statements so will be True".
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What is 3x-5y=12 with a substitution of X=3y
Please help me . factor. X^2-13x+40
Factoring x2-13x+40
The first term is, x2 its coefficient is 1 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is +40
Step-1 : Multiply the coefficient of the first term by the constant 1 • 40 = 40
Step-2 : Find two factors of 40 whose sum equals the coefficient of the middle term, which is -13 .
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -8 and -5
x2 - 8x - 5x - 40
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-8)
Add up the last 2 terms, pulling out common factors :
5 • (x-8)
Step-5 : Add up the four terms of step 4 :
(x-5) • (x-8)
Which is the desired factorization
Find the half-life of an element which decays by 3.401% each day?
The half life of an element which decays 3.401% is 20 days.
What is Half Life?The time required for a radioactive substance (or one-half of its atoms) to decay or change into a new substance is commonly characterised as its half-life. Ernest Rutherford discovered the idea for the first time in 1907. It is commonly denoted by the symbols Ug or t1/2.
To help you comprehend the notion, consider a radioactive element with a half-life of one hour. In this example, one half would decay in an hour and the other half would decay in another hour.
We are given;
y = a[tex]b^{(t)}[/tex]
Where t is the half life
y = a/2 is the amount of substance remaining after decay
So, b = 100% - 3.401%
b = 96.599%
b = 0.96599
Now, a/2 = a[tex](0.96599)^t[/tex]
and, 0.5= [tex](0.96599)^t[/tex]
Now, taking log on both side we get
ln (0.5) = t(ln 0.96599)
t = ln(0.5)/ln(0.96589)
t = 20.032 days
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What is 4.75 as an improper fraction in simplest form
The solution is : 4.75 as an improper fraction in simplest form is 19/4.
Here, we have,
given that,
4.75 as an improper fraction
we need to find the simplest form
we have,
4.75
= 4 75/100
= 475/100
= ( we can divide numerator and denominator by 25 )
=475/25 /100/ 25
= 19/4
[ in simplest form]
Answer:
4.75 as an improper fraction in simplest form is 19/4.
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