Answer:
(fg)'(10)= 3 and the other one is 1.5
Step-by-step explanation:
fg and 10 with the 4x- 10 as the fraction of values of the followings of G-9 so its (fg)'(10)= 3 and the other one is 1.5
I6
Jim began a 270-mile bicycle trip to build up stamina for a triathlete competition. Unfortunately, his bicycle chain broke, so he finished the trip
walking. The whole trip took 9 hours. If Jim walks at a rate of 4 miles per hour and rides at 40 miles per hour, find the amount of time he
spent on the bicycle.
Jim rode for hours.
The amount of time spent on bicycle by Jim =6.5 hours
The amount of time spent on walking by Jim =2.5 hours
What is the distance, speed and time equation?To calculate speed, divide the distance travelled by the time it took to complete the voyage, so speed = distance divided by time. These equations can be reduced as s=d/t, where s represents speed, d represents distance, and t represents time.
Distance divided by time equals speed. Distance = time * speed
To solve for speed or rate, utilize the speed formula, s = d/t, which implies speed equals distance divided by time. To solve for time, utilize the time formula, t = d/s, which implies time equals distance divided by speed.
Given,
Distance=270miles
Time=9 hours
Speed by walk=4 miles/hour
Speed by cycle=40 miles/ hour
t= time for riding a bicycle
9-t= time for walking
Distance= Speed ×Time
270=40t+4(9-t)
40t+36-4t=270
36t=234
t=6.5
Time spent on bicycle = 6.5 hours
Time spent on walking = 9-6.5
=2.5 hours
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The legs of a right triangle are 18 centimeters and 80 centimeters long. What is the length of the hypotenus: 82 or 85 or 89 or 98
Answer:
82
Step-by-step explanation:
1.) Recognize that this is the Pythagorean Triple 9, 40, 41, just multiplied by two (9*2 = 18, 40*2 = 80).
2.) Now, to find the third number, we just multiply 41 by 2 to get 82.
Answer:
The hypotenuse is equal to 82 centimeters.
Step-by-step explanation:
Using the Pythagorean theorem (a^2 + b^2 = c^2), which states that the legs of a right triangle (a and b) squared, equal the hypotenuse squared, we can plug in the values of the legs of the right triangle into spots a and b. This gets us the equation 80^2 + 18^2 = c^2. We can then square the values to get 6400 + 324 = c^2. We then get 6724 = c^2, and then take the square root of both sides to get the value of c, the hypotenuse. This gets us c = 82, so the hypotenuse is equal to 82 centimeters.
What is the equation of the line in slope-intercept form?
Enter your answer in the boxes.
Y=___x + ___
Answer:
y=0.6x+3
Step-by-step explanation:
Slope intercept form: y=mx+b
m- slope
b- y intercept
to find slope with y2-y1/x2-x1
3-0/0-(-5)
3/5
0.6is the slope
y intercept is 3 since it intersects at 3 on the y axis
Hopes this helps please mark brainliest
help. 20 points. this is a proportion question.
what does x = ?
Answer:
x = 7
Step-by-step explanation:
[tex]\frac{3}{x}=\frac{x-4}{7}[/tex]
==> cross multiply
[tex]3*7=x*(x-4)[/tex]
==> simplify
21 = x² - 4x
==> subtract 21 from both sides
0 = x² - 4x - 21
==> factorize by finding two numbers that multiply to -21 and add up to equal -4
0 = (x - 7)(x + 4)
==> set each factor to 0 and solve for x
0 = (x - 7) 0 = (x + 4)
7 = x -4 = x
We can now plug in the values of x into the proportion to see which are true.
[tex]\frac{3}{x}=\frac{x-4}{7}[/tex] [tex]\frac{3}{x}=\frac{x-4}{7}[/tex]
x = 7 x = - 4
[tex]\frac{3}{7}=\frac{7-4}{7}[/tex] [tex]\frac{3}{-4}=\frac{-4-4}{7}[/tex]
==> subtract 4 from 7 ==> subtract -4 from -4
[tex]\frac{3}{7}=\frac{3}{7}[/tex] [tex]-\frac{3}{4}=-\frac{8}{7}[/tex]
The only true answer is x = 7
A rancher has 444 feet of fencing to enclose two adjacent rectangular corrals. The wall separating the two
corrals consists of a single fence. What dimensions for one of the individual corrals will produce the largest
total area?
Answer:
2 lengths and 3 widths
444 = 2*L + 3*w --> L = (444 - 3w)/2 = 222 - (3/2)w
Area = length x width
Area (w) == (222 - (3/2)w ) w
The max occurs at the average of the zeros.
The zeros are 222 - (3/2)w = 0 or w=0
222 = (3/2)w or w=0
w = 444/3=148 or w=0
The average is (444/3 +0)/2 = 222/3=74
width is 74 and length is 222 - (3/2)(74) = 222 - 111 = 111
The max area is 74 * 111 = 8214
Z varies jointly as the square root of the product of X and Y. IF z=3 when X=3 and Y=12 find X when Z=6 and Y=64
When Z=6 and Y=64 the given proportionality value of x = 1/2.
What is proportionality?
The concept of proportionality in mathematics denotes the linear relationship between two quantities or variables. The size of one item increases by twofold, whereas the size of the other quantity decreases by one-tenth of the earlier amount. Two integers that each represent a component of a whole are compared to determine their proportion. In essence, a percentage declares that two fractions are the same even if the amounts are different. For instance, half of 10 marbles is equal to half of 50 marbles in terms of proportion.
Here Z varies jointly as the square root of the product of X and Y.
Then,
=> Z∝[tex]\sqrt{XY}[/tex]
=>Z=k[tex]\sqrt{XY}[/tex]
Where k is constant . Now put X=3 , Y = 12, Z=3.
=> 3=k*[tex]\sqrt{12*3}[/tex]
=> k = 6/3 = 2 .
Then the equation is ,
=> Z==3[tex]\sqrt{XY}[/tex]
Now put Z=6 and Y=64
=> 6 = 3[tex]\sqrt{x*64}[/tex]
=> 2/8 =[tex]\sqrt{x}[/tex]
=>[tex]\sqrt{x}[/tex] = 1/4
=> x = 1/2.
Hence the value of x is 1/2.
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4) Employees
at The Shoe Shack get a
25% discount when they buy a pair
of shoes at the store.
Theo wants to buy a pair of shoes with a regular price of $48.
What is the discount on a pair of shoes with a regular price of $48?
Answer: 12
Step-by-step explanation: 25% is always 25/100 or 1/4. To get this you have to multiply 48 by 1/4 with is 48/4 = 12$.
Hoped This Helped!
The trail is 2448 miles long. It begins in city a and ends in city be man Fred has hiked three eights of the trail before how many miles has he hiked
The number of miles which Fred has hiked according to the task content is; 918 miles.
How many miles has Fred hiked?It follows from the task content that the given trail in discuss is 2448 miles long and the actual number of miles hiked by Fred is to be determined.
Given; Trail distance = 2448 miles.
However, Fred has hiked three eights of the trail before;
It therefore follows from proportion that;
If; 1 trail = 2448 miles;
Then; 3 / 8 trail = 3 / 8 × 2448 miles.
= 918 miles.
On this note, the number of miles hiked by Fred is; 918 miles.
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the equation of line g is y = 3/4x + 3/4. line h is perpendicular to g. what is the slope of line h
The slope of line h that is perpendicular to line g is: -4/3.
What is the Slopes of Lines that are Perpendicular?The slope values of any two lines that are perpendicular to each other are values that are negative reciprocals to each other.
The equation of of line g is given as y = 3/4x + 3/4, it is expressed in slope-intercept form as y = mx + b. This means that the value of the slope of line g is 3/4.
The negative reciprocal of 3/4 is -4/3. Therefore, the slope of line h that is perpendicular to line g would be -4/3.
The slope of line h is: -4/3.
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Which graph could be used to find the distance between the points (-3, -13) and (11, 9)?
We can use the graph of the line y = 11/7(x) - 58/7 to find the distance between the points
How to determine the graph for finding the distance between the points?
The slope-point equation of a line is given as:
y-y1 = m(x−x1)
where m is the slope of the line, and slope (m) = y2−y1 / x2−x1
Given: the points (-3, -13) and (11, 9)
x1 = -3, y1 = -13 and x2 = 11, y2 = 9
slope(m) = 9-(-13) / 11-(-3) = 22/14 = 11/7
Using y-y1 = m(x−x1), put m = 11/7 and make y the subject:
y-y1 = m(x−x1)
y-(-13) = 11/7(x-(-3))
y + 13 = 11/7(x+3)
y + 13 = 11/7(x) + 33/7
y = 11/7(x) + 33/7 - 13
y = 11/7(x) - 58/7
Therefore, the graph of the line y = 11/7(x) - 58/7 could be used to find the distance between the points
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Answer: The answer is A
Step-by-step explanation:
6 boxes each containing 40 oranges were repacked into 8 smaller boxes. How many oranges were in each of the 8 boxes?
Answer:
53 oranges.
Step-by-step explanation:
To find this, we must set up a proportionality formula.
6 8
- = -
40 x
Our goal is to find x.
First we cross multiply and get:
6x=320
Now we can divide each side by 6 to get x by itself.
x=53.33,
however, because you cannot have less than a whole orange in a box, each box contained 53.
Trying to see how smart you'll are
Answer: M = -11/3
Step-by-step explanation:
The length of a rectangle is four more than twice its width. If the perimeter of the rectangle is 56 cm, what is the width of the rectangle?
The rectangle has its width to be 8 cm
How to determine the width the rectangle?From the question, we have the following parameters that can be used in our computation:
The length of a rectangle is four more than twice its width
The perimeter of the rectangle is 56 cm.
The above parameters imply that
L = 2W + 4
P = 2(L + W)
Where L represents the Length and W represents the width
The perimeter is given as 56
So, we have
2(L + W) = 56
So, we have
L + W = 28
Substitute L = 2W + 4 in L + W = 28
2W + 4 + W = 28
Evaluate
3W = 24
Divide by 3
W = 8
This means that the width of the rectangle is 8 cm a
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Using the graph below, determine the employee's hourly wage.
By using the graph, the employee's hourly wages is calculated as $10.6
Graph:
Basically, a graph is a collection of points, called vertices, and lines between those points, called edges.
Given,
Here we have the graph with straight line.
And we need to determine the employee's hourly wage.
While we looking into the graph we have identified that the x axis refers the number of hours the employ is working and the y axis refers the money earned by them.
In order to find the wages for one hour, we need to select one point from the graph.
Here we have take the point (5,53)
The first point refers the number of hours that is 5.
And the second one refers the wages for 5 hours that is 53.
So, the one hour wages is calculated as,
=> 53/5
=> 10.6
Therefore, the employee's hourly wage is $10.6.
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A woman has a total of $11,000 to invest. She invests part of the money in an account that pays 7% per year and the rest in an account that pays 8% per year. If the interest earned in the first year is $
810, how much did she invest in each account?
If a woman has a total of $11,000 to invest. The she invested in each account is: 4000 at 8%, 7000 at 7 %.
Total amount of money invested = $11000
x+y=11000,
Total interest for the year= $760
0.07×x+0.08×y=810
x=11000-y
We substitute for x
0.07×(11000-y)+0.08×y=810
We multiply out
770-0.07y+0.08×y=810
We combine like terms.
0.01×y=40
Divide both side by 0.01y
y = 40 /0.01
y= 4000 at 8%
x=11000-y
Calculate x
x = 11,000 - 4,000
x=7000 at 7 %
Therefore she invested 4000 at 8%, 7000 at 7 %.
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Which descriptions from the list below accurately describe the relationship
between AQRS and ATUV? Check all that apply.
4
76°
4
Q2S
76
12
28
76
T 6
12
76
A. Congruent
B. Similar
c. Same size
D. Same sides
The given two triangles ΔQRS and ΔTUV are similar.
What is similar figures?
The same shape between two figures is referred to as similarity. If two figures have congruent corresponding angles and equivalent length ratios on their corresponding sides, they are said to be similar mathematically. The scale factor is the name of this often used ratio.
Given: Two triangles ΔQRS and ΔTUV.
The angles of ΔQRS are 28°, 76° and 76°.
The angles of ΔTUV are 28°, 76° and 76°.
So, the angles of given two triangles are congruent.
Now consider, the sides of the triangle.
The sides of ΔQRS are, 4, 4, 2 and
The sides of ΔTUV are 12, 12, 6.
It seems that the sides of the triangle are in proportion.
Therefore, the given two triangles ΔQRS and ΔTUV are similar.
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7) Keith had 100 dollars to spend on 7 books. After
buying them he had 16 dollars. How much did each book cost?
8) Sally spent half of her allowance going to the movies. She washed the family
car and earned nine dollars. What is her weekly allowance if she ended with
sixteen dollars ?
9) Oceanside Bike Rental Shop charges 15 dollars plus 6 dollars an
hour for renting a bike. Joan paid 57 dollars to rent a bike. How many
hours did she pay to have the bike checked out ?
10) On Monday, one hundred sixty-nine students went on a trip to the zoo. All four
buses were filled and nine students had to travel in cars. How many students were
in each bus?
Answer:
7)
so
100-16=84
then
84÷7=12
each book costs 12 dollars
Are there any values of x for which the areas of the figures are the same? Explain.
The area of the triangle is x + 1 cm², while the area of the rectangle is x cm². Therefore, there is no value of x that makes the areas of both figure equal, because there is no solution to the equation.
How to Find the Areas of Rectangle and Triangle?A triangle's area = 1/2(base)(height)
A rectangle's area = length × width.
Area of the green triangle = 1/2(x + 1)(2)
Area of the green triangle = x + 1 cm²
Area of the rectangle = x × 1
Area of the rectangle = x cm²
Setting both areas equal, we have:
x + 1 = x
x - x = -1
0 = -1 [not true]
There's no solution or the values of x.
Therefore, we can conclude that there are no values of x for which the areas of both shapes are equal, because there is no solution to the equation.
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Calculate the radius of the circle if its area is 110 mm².
The radius of the circle is 5.91mm
What is the area of the circle?
The area of the circle is the product of mathematical constant pi and square of the radius. radius is the distance of a point on the circle from the center of the circle.
The area of the circle is 110 mm^2
We have to find the radius to do that we first substitute the value of area in the area of circle formula and then compute the value of the radius
We know that,
The area of the circle
= π·r^2
110=22/7*r^2
35 = r^2
r= 5.91mm
Hence The radius of the circle is 5.91 mm
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Measure of ∡5
(Hint: What theorem lets you compare ∡3 and ∡5?)
Answer:
mAngle5 = 52° by
Alternate Interior angles
Step-by-step explanation:
When you have a pair of parallel lines and a transversal (the line that crosses them both)
this set up makes 8 angles....ALL the angles are either the same measure or they add up to 180°. Literally, if you know the measure of ONE angle, you can find the measure of all 8 angles. Its only two different numbers for all 8.
So, for your problem the two angles are in between the parallel lines (interior) and on different sides of the tranversal (alternate). By the Alternate Interior Angle Theorem they are congruent. One of them is 52° so the other one is also 52°
The function f(x)
o 95 miles; f(3) represents the total distance remaining after 3 hours.
represents the total distance traveled after 3 hours.
O 95 miles; f(3)
O 165 miles; f(3)
represents the total distance remaining after 3 hours.
O 165 miles; f(3)
represents the total distance traveled after 3 hours.
= 260 - 551
represents the distance, in miles, remaining on a trip z hours into the trip. What is the value of f(3), and what does it represent?
f(x) represents the distance, in miles, remaining on a trip z hours into the trip. The value of f(3) is 95 miles and it represents the total distance remaining after 3 hours.
Define function.A function is a relationship between a number of inputs where each input has exactly one output, according to one definition. f is typically used to represent a function (x). A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.
Given,
Function:
f(x) = 260 -55x
When f(3)
f(3) = 250 - 55(3)
f(3) = 250 - 165
f(x) = 95
95 miles; f(3) represents the total distance remaining after 3 hours.
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Assume the hypothesis is false. What is the
truth value of the conditional? Assume
the hypothesis is true. What would be
a counterexample?
The conditional statement has a true truth value if neither the hypothesis nor the conclusion is true.
A conditional statement is phrased as follows if we have the two propositions P and Q:
Q if P is true.
where P denotes the premise and Q denotes the result
The following are conditional statements' truth values:
The conditional statement is true if P and Q are true.
The conditional statement is false if P is false and Q is true.
The Conditional statement is false if P is true and Q is false.
The conditional statement is true if P and Q are both false.
Therefore, the conditional statement's truth value is true if both the hypothesis and the conclusion are false.
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Several years ago, Annie bought a computer for her small business. For tax purposes, Annie declares a constant rate of depreciation, or loss of value, for the computer. The graph shows the linear relationship between the value of the computer and the number of years Annie has owned it.
The line is:
y = 400*x + 2000
And the statements are:
The original purchase price of the computer is given by the y-intercept, which is $2,000
The change in the price of the computer is the slope, which is 400.
How to write the linear equation?
A general linear equation is written as:
y = a*x + b
Where a is the slope and b is the y-intercept.
If the line passes through two points (x1, y1) and (x2, y2), then the slope is:
slope = (y2 - y1)/(x2 - x1)
Using the graph we can identify two points like:
(1, 1600) and (5, 0)
Then the slope is:
a = (0 - 1,600)/(5 - 1) = 400
And the y-intercept is 2,000, as we can see on the graph.
Then the line is:
y = 400*x + 2,000
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Ayuda, por favor. Amir condujo desde Jerusalén hasta el lugar más bajo de la Tierra, el Mar Muerto, descendiendo a una velocidad de 12 metros por minuto. Estaba al nivel del mar después de 30 minutos de conducción. Representa gráficamente la relación entre la altitud de Amir relativa al nivel del mar (en metros) y el tiempo (en minutos).
The linear function y = -12x + 360, representing Amir's height at a time of x minutes, is graphed at the end of the answer.
What is a linear function?The slope-intercept representation of a linear function is given by the rule shown as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the change in the output variable y when the input variable x is increased by one.b is the y-intercept of the function, which is the numeric value of the function when the input x is of zero.From the test, his rate is of -12 m/s, hence the slope of the function is given as follows:
m = -12.
When x = 30, y = 0, hence the intercept b of the linear function can be obtained as follows:
0 = -12(30) + b
b = 30 x 12
b = 360.
Thus the equation is:
y = -12x + 360.
The domain in which the function is graphed is:
x ≥ 0.
As time cannot assume negative values.
TranslationThe problem asks for the graph of the linear function, considering that:
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if 1,2 and 3 are the eigen values of A=[2 0 1; 0 2 0; a 0 2], find the value of a?
The value of ''a'' will be 1
What is Matrix?
A set of numbers arranged in rows and columns so as to form a rectangular array, is called Matrix.
Given that;
1,2 and 3 are the eigen values of matrix A.
Now,
We know that;
The product of eigen values of a matrix is equal to the determinant of that matrix.
So, We find the determinant of matrix as;
[tex]A = \left[\begin{array}{ccc}2&0&1\\0&2&0\\a&0&2\end{array}\right][/tex]
Hence, We get;
| A | = 2 (4 - 0) - 0 (0 - 0) + 1 (0 - 2a)
| A | = 8 - 2a
And, The product of eigen values = 1 x 2 x 3 = 6
Hence, We get;
| A | = 8 - 2a
6 = 8 - 2a
2a = 8 - 6
2a = 2
a = 1
Thus, The value of ''a'' will be 1
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Consider the frequency distribution to the right. Complete parts (a)
through (c) below.
Value
624
541
606
577
586
610
Frequency
12
8
10
15
5
6
Find the mean of the frequency distribution
The mean of the frequency distribution is 591.446.
Let the values be 'x' and frequency be 'f'
To find the mean of the frequency distribution use formula,
[tex]Mean=\frac{Sum of values}{Total number of values}[/tex]
where, sum of the values = ∑fx
Total number of values=∑f
From table,
First find fx,
[tex]f1x1=624*12=7488\\\\f2x2=541*8=4328\\\\f3x3=606*10=6060\\\\f4x4=577*15=8655\\\\f5x5=586*5=2930\\\\f6x6=610*6=3660[/tex]
Now,
∑fx=[tex]7488+4328+6060+8655+2930+3660=33121[/tex]
Now , the total number of values,
∑f=[tex]12+8+10+15+5+6=56[/tex]
Now,
[tex]Mean=\frac{33121}{56} =591.446[/tex]
Thus, the mean of the frequency distribution is 591.446.
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What is the value of X
Answer:
x=4
Step-by-step explanation:
Jack is now seven times as old as James. In 5 years, Jack will be five times as old as James. How old is
James now?
70
10
55
Answer:10
Step-by-step explanation:Step-by-step explanation:
James's age = x
Jack's age = y
y = 7x
y + 5 = 5(x + 5)
y = 7x
y + 5 = 5x + 25
7x - y = 0
5x - y = -20
7x - y = 0
-5x + y = 20
2x = 20
x = 10
James's age: x = 10
Jaxson has a collection of 200 coins. How many coins represent 5% of his collection?
Answer: 13 coins
Step-by-step explanation:
100% --> 260
1% --> 2.6
5% --> 13
Answer:
10 coins
Step-by-step explanation:
Jaxson has a collection of 200 coins. How many coins represent 5% of his collection?
5% = 0.05
200 * 0.05 = 10 coins
in chemistry class, Pavel combined 80ml of a solution that was 30% saline with 20ml of a solution that was 90% saline. What is the concentration of saline in the mixture? Build a table to solve this problem.
help pls
The saline concentration of the mixture expressed as a percentage is 42%
What is a percentage?A percentage is the expression of a quantity as a fraction that has a denominator of 100.
The volume of the solution that is 30% saline = 80 ml
The volume of the solution that is 90% saline = 20 ml
The concentration of the saline in the mixture; Required;
The table of values can be presented as follows;
Component [tex]{}[/tex] Unit Value [tex]{}[/tex] Amounts (ml) [tex]{}[/tex] Value
30% saline [tex]{}[/tex] 0.3 [tex]{}[/tex] 80 [tex]{}[/tex] 0.3×80
Solution
70% saline [tex]{}[/tex] 0.7 [tex]{}[/tex] 20 [tex]{}[/tex] 0.7×20 [tex]{}[/tex]
solution
Mixture [tex]{}[/tex]x [tex]{}[/tex] 100 [tex]{}[/tex] 100 × x
0.3 × 80 + 0.9 × 20 = (80 + 20) × x
42 = 100·x
The concentration of the saline mixture is x = 42/100 = 0.42
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