Answer:
Area = 40
Step-by-step explanation:
The area of a rhombus is
Area = a*b/2
Where a and b are the lengths of the diagonals.
Area = 8 * 10/2
Area = 40
Answer:
40
Step-by-step explanation:
In a rhombus the two diagonals intersect perpendicularly. So you can see a rhombus as the union of two triangles whose base is one of the diagonals of the rhombus and whose height is the half of the other diagonal.
Therfor you can calculate the area of the rhombus calculating the area of the two triangles that are the same.
In this case the area of each triangle must be [tex]\frac{4\times 10}{2}= 20[/tex] (if you take the 10-lenght-side as the basis of the triangles).
Hence the area of the rhombus is 40 because is the double of the area of each triangle.
Please help ASAP!!!!
Answer:
A. [tex]x=6[/tex] or [tex]x=1[/tex]
Step-by-step explanation:
The given function is:
[tex]y=x^2-7x+6[/tex]
When y=0; we have:
[tex]x^2-7x+6=0[/tex]
[tex]x^2-6x-x+6=0[/tex]
Factor by grouping:
[tex]x(x-6)-1(x-6)=0[/tex]
[tex](x-6)(x-1)=0[/tex]
Either [tex](x-6)=0[/tex] or [tex](x-1)=0[/tex]
Either [tex]x=6[/tex] or [tex]x=1[/tex]
6. I need help with question in the attached picture!
ANSWER
[tex]log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) =\log 7[/tex]
EXPLANATION
The given logarithmic expression is:
[tex] log( \frac{14}{3} ) + log( \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]
We apply the product rule to the first two terms to get:
[tex]log( \frac{14}{3} \times \frac{11}{5} ) - log( \frac{22}{15} ) [/tex]
We the apply the quotient rule:
[tex]log( \frac{14}{3} \times \frac{11}{5} \div \frac{22}{15} ) [/tex]
[tex]log( \frac{14}{3} \times \frac{11}{5} \times \frac{15}{22} ) [/tex]
We cancel out the common factors and simplify to obtain:
[tex]log( 7 ) [/tex]
Required Knowledge.
log(ab) =log(a) + log(b)
log(a/b) = log(a) -log(b)
SOLUTION
log(14/3) +log(11/5) -log(22/15)
=log((14/3)×(11/5)) -log(22/15)
=log(154/15) -log(22/15
=log( (154/15) ÷ (22/15) )
=log( (154/15) × (15/22) )
=log(154/22)
=log(77/11)
=log(7)
Hence 7 is your answer...
Hope it helps...
Regards;
Leukonov/Olegion.
Write parametric equations of the line y=4x-5
Answer:
A set of parametric equations for the line y = 4x - 5 is;
x = t
y = 4t - 5
Step-by-step explanation:
To find a set of parametric equations for the line y = 4x - 5;
We can assign either variable x or y equal to the parameter t, in this case we can easily let x = t
We then substitute x = t in the original equation;
y = 4t - 5
Therefore, a set of parametric equations for the line y = 4x - 5 is;
x = t
y = 4t - 5
3. Let's assume you purchase 100 shares of XYZ Company for $1 per share. After three months, the share price increases to $5. This means the value of the investment has increased from $100 to $500, for a capital gain of $____
Answer:
400
Step-by-step explanation:
The initial value of the investment is 100 *1 = $100
The final value of the investment after three months is 100 * 5 = $500
This means the value of the investment has increased from $100 to $500. The capital gain is the increase in the value of an investment;
500 - 100 = $400
Javier has been saving for a digital camera. He finds one on sale for $67.50. It usually costs $90.00. What is the percent of the discount?
A: 20%
B: 25%
C: 30%
D: 35%
Answer:
B: 25%
Step-by-step explanation:
$90.00 - $67.50 = $22.5
$22.5 / $90 = 0.25 = 25%
Answer:
B: 25%
Answer:
25%
Step-by-step explanation:
What is the slope and y-intercept of this line?
y = –3x + 9
slope: 9, y-intercept: –3
slope: 3, y-intercept: –9
slope: –3, y-intercept: 9
slope: 1, y-intercept: –3
Answer:
C
Step-by-step explanation:
y=mx+b
b= y-intercept
m=slope
m=-3
b=9
[tex]\huge\boxed{Slope=-3,\;Y\;intercept=9.}[/tex]
___________________________________________________________
[tex]\boxed{Explanation}[/tex]
y=mx+b.
m is always where the slope is located.
b is always where the y intercept is located.
Therefore, since -3 is located at m that is the slope and 9 is located at b so that is the y intercept.
Which of the following is equal to the rational expression when x doesn’t equal 1 or -1? 5(x-1)/(x+1)(x-1) please help
Answer:
Final answer is [tex]\frac{5}{(x+1)}[/tex].
Step-by-step explanation:
Given expression is [tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex] where x doesn’t equal 1 or -1. Now we need to find about which of the given choices is equal to the given rational expression. Choices are missing but we can still solve this problem.
[tex]\frac{5\left(x-1\right)}{(x+1)(x-1)}[/tex]
cancel out common factors from top and bottom.
[tex]=\frac{5}{(x+1)}[/tex]
Hence final answer is [tex]\frac{5}{(x+1)}[/tex].
Answer:
5/x+1
Step-by-step explanation:
A van travels 320 miles on 16 gallons of gas. Find how many gallons the van needs to travel 420 miles
The van needs 21 gallons of gas. Take 16/(320/420)
The van will need 21 gallons of gas to travel 420 miles, based on its fuel efficiency of 20 miles per gallon.
The student is asking how many gallons of gas a van needs to travel 420 miles, given that it travels 320 miles on 16 gallons of gas.
First, we calculate the van's fuel efficiency which is found by diving the miles traveled by the gallons of gas used. For the van in the question:
Fuel efficiency: 320 miles / 16 gallons = 20 miles per gallon (MPG)
Next, we can use this fuel efficiency to find out how many gallons will be needed for 420 miles. We divide the total miles by the MPG:
Gallons needed: 420 miles / 20 MPG = 21 gallons
Therefore, the van will need 21 gallons of gas to travel 420 miles.
It will take Adam four hours to drive to Disney Park, and 2.5 times less time if driving 45 mph faster. What is the distance Adam should cover to get to the park?
Answer:
120 miles
Step-by-step explanation:
we know that
The speed is equal to the distance divided by the time
Let
s------> the speed in mph
d-----> the distance in miles
t -----> the time in hours
s=d/t
solve for the distance
d=s*t
It will take Adam four hours to drive to Disney Park
s=x mph
t=4 h
substitute
d=4x -----> equation A
It will take Adam 2.5 times less time if driving 45 mph faster
so
s=(x+45) mph
t=4/2.5=1.6 h
substitute
d=1.6(x+45) -----> equation B
equate equation A and equation B
4x=1.6(x+45)
Solve for x
4x=1.6x+72
4x-1.6x=72
2.4x=72
x=30 mph
Find the distance d
d=4x -----> d=4(30)=120 miles
Answer:
120 miles
Step-by-step explanation:
Find the value of x in the figure. Please Explain
A)34.9
B)55.1
C)90
D)124.9
Answer:
90 because it’s a right angle and a right angle it 90 degrees
The two angles make up a right angle.
This means the two angles are complementary and need to equal 90 degrees.
X = 90 - 55.1 = 34.9
11. The slope of a linear function h(x) is 2. Suppose the function is translated 8 units up to get d(x). How can h(x) be
translated to the left or right to represent the same function d(x)? Explain your answer.
Answer:
See below.
Step-by-step explanation:
If we translate h(x) to the left it will override line d(x) because the slope of both lines is the same. H(x) will need to move 4 units to the left to do this (because the slope = 2 = 8/4).
To represent the same function as d(x), the linear function h(x) with a slope of 2 should be translated 4 units to the left, resulting in the function h(x+4). This horizontal shift increases the value of y by 8 units, which equates to the vertical shift applied to create d(x).
To translate the linear function h(x) to result in the same function as d(x), which is h(x) translated 8 units up, we need to consider the properties of linear functions and translations. Since h(x) has a slope of 2, we can denote it as h(x) = 2x + b, where b is the y-intercept. When h(x) is translated 8 units up to become d(x), the new function is d(x) = h(x) + 8 = 2x + b + 8. To counteract this vertical shift with a horizontal translation and maintain the same function as d(x), we must shift h(x) in such a way that every x value for h(x) yields the same y-value for d(x) after the translation.
To achieve this, we would have to shift h(x) to the left by 4 units, resulting in the function h(x+4). This is because for every 1 unit increase in x, the value of h(x) increases by 2 units (the slope), so a shift of 4 units left would increase y by 8 units, which is the same effect as the vertical translation applied to obtain d(x). Thus, h(x+4) = 2(x+4) + b = 2x + 8 + b, which aligns with d(x). This explanation confirms that the properties of linear functions and translation mechanics allow us to equate d(x) with a horizontally translated version of h(x).
I will mark brainliest
Solve 2sin2(x) – 5sin(x) – 3 = 0. Let u = sin(x). Which of the following is equivalent to the given equation?
Answer:
(2u + 1)(u – 3) = 0 is equivalent to the given equation
For the second part of the question, the solutions to the equation are C and D, 7π/6 +2kπ and 11π/6 + 2kπ
Step-by-step explanation:
Write a function rule for the table.
f(x) = x + 1
f(x) = x
f(x) = –1 – x
f(x) = x –1
I assume one of the four options is the correct answer...
Remember that in order to determine if a function rule is correct, you should be able to plug an x value into the equation and get the corresponding y value as the answer.
The first option, f(x) = x + 1, is correct!
Answer: The correct option is (A) f(x) = x + 1.
Step-by-step explanation: We are given to write a function rule for the following table :
x -1 0 1 2
f(x) 0 1 2 3
From the given table, we see that
[tex]f(-1)=0=-1+1,\\\\f(0)=1=0+1,\\\\f(1)=2=1+1,\\\\f(2)=3=2+1.[/tex]
Therefore, the required function rule is given by
[tex]f(x)=x+1.[/tex]
Thus, option (A) is CORRECT.
Find the value of x. Round to the nearest tenth
Answer:
16.2
Step-by-step explanation:
A trick to remember for right triangles is SOH-CAH-TOA:
Sine = Opposite / Hypotenuse
Cosine = Adjacent / Hypotenuse
Tangent = Opposite / Adjacent
Here, we have the side adjacent to the angle and the hypotenuse. So we should use cosine.
cos 22° = 15 / x
x = 15 / cos 22°
x ≈ 16.2
Share £35 in ratio 2:3
7. The coordinates of the vertices of a rectangle are go
I by
R(-3,-4), E(3, 4), C(4,4), and T(4-4). Plot these points
on the coordinate plane at the right and connect them to
draw the rectangle. Then connect points E and T to form
diagonal ET.
a. Use the Pythagorean Theorem to find the exact
length of ET.
b. How can you use the Distance Formula to find the
length of ET? Show that the Distance Formula gives
the same answer
Answer:
a. By Pythagorean Theorem: [tex]ET=\sqrt{113}[/tex]
b. By Distance Formula: [tex]ET=\sqrt{113}[/tex]
Step-by-step explanation:
The given rectangle has vertices R(-3,-4), E(-3, 4), C(4,4), and T(4-4).
The points have been plotted on the coordinate plane as shown in the attachment.
a. Using the Pythagoras Theorem;
[tex]ET^2=EC^2+CT^2[/tex]
We substitute the side lengths to obtain:
[tex]ET^2=7^2+8^2[/tex]
[tex]ET^2=49+64[/tex]
[tex]ET^2=113[/tex]
Take positive square root to obtain:
[tex]ET=\sqrt{113}[/tex]
b. The distance formula is given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The endpoints of ET are at E(-3,4) and T(4,-4).
Using the distance formula;
[tex]ET=\sqrt{(4--3)^2+(-4-4)^2}[/tex]
[tex]ET=\sqrt{(7)^2+(-8)^2}[/tex]
[tex]ET=\sqrt{49+64}[/tex]
[tex]ET=\sqrt{113}[/tex]
help me im timed i cant figure it out
For this case we have to find the inverse of a function, follow the steps below:
Replace f (x) with y.We exchange the variables.We solve for "y".Finally we change y by [tex]f ^ {- 1} (x)[/tex]Then, it is observed that of option 3:
[tex]f (x) = 4x[/tex]
Replace [tex]f (x)[/tex]with y:
[tex]y = 4x[/tex]
We exchange the variables:
[tex]x = 4y[/tex]
We solve for "y":
[tex]4y = x\\y = \frac {x} {4}[/tex]
Finally we change y by [tex]f ^ {- 1} (x):[/tex]
[tex]f ^ {- 1} (x) = \frac {x} {4}[/tex]
Answer:
The correct option is C
Answer:
It's the third choice.
Step-by-step explanation:
f(x) = y = 4x
x = 1/4 y
Change the y to x:
so the inverse g(x) = 1/4 x.
Find the length of AC if AB is 8, BC is 13, and B is between A and C?
Answer:
21
Step-by-step explanation:
Since B is between A and C, we can simply add 8 and 13 to get the length of AC becauswe B is on line AC. This gives us 8+13 or 21 as the distance between A and C.
A and C is 6 because 2 sides have to be bigger than the other
who do I write the fraction 2/5 as an equivalent fraction with denominator 15x
Answer:
Step-by-step explanation:
multiply the top and bottom of the fraction by 15x
2*15x
=======
5*15x
30x
====
75x
Look at the figure. Classify the pair of angles: <4 and <5.
Answer:
Option B
same-side interior angles
Step-by-step explanation:
Given in the question, two non parallel lines a and b.
The area between lines a and b is called the interior of the two lines.
Angles 4 and 5 are same-side interior angles.
Other options are wrong because:
A)The area which not between lines a and b is called the exterior
C)Corresponding angles are on same side of the traversal line.
Example
Angles 1 and 5
D)Alternate interior angles are in interior region but in opposite side of traversal line.
Example
Angles 3 and 5
how many yards can fit in 5 miles
Answer:
8800 yards
Step-by-step explanation:
1760 feet * 5 = 8800 yards
Answer:
8800
Step-by-step explanation:
I googled it
Three families are sharing the cost of renting a canoe for 7 days. The cost for each family is $14 per day. What is the total cost of renting the canoe for 7 days from the rental shop?
Answer:
294
Step-by-step explanation:
so three family's and 14$ a day so
14*3=42
then take 42 and times it by how many days so 7
so 42*7=294
1. If tan θ= -8/15 and if the terminal point determined by θ is in quadrant II, find cscθ sinθ+ tan θ.
Since
[tex]\csc(x)=\dfrac{1}{\sin(x)}[/tex]
we have
[tex]\csc(x)\sin(x)+\tan(x) = \dfrac{1}{\sin(x)}\cdot \sin(x)+\tan(x)=1+\tan(x)[/tex]
And since
[tex]\tan(x)=\dfrac{8}{15}[/tex]
we have
[tex]1+\tan(x) = 1-\dfrac{8}{15}=\dfrac{15}{15}-\dfrac{8}{15}=\dfrac{7}{15}[/tex]
The value of cscθ sinθ + tan θ is 7/15.
What is the relationship between cscθ and sinθ?cscθ is the reciprocal of sinθ.
We can find the value of the given expression below:The expression is given by cscθ sinθ + tan θ.
We can simplify this expression before solving it.
Let the expression be y = cscθ sinθ + tan θ.
cscθ = 1/sinθ
y = sinθ * 1/sinθ + tan θ
y = 1 + tan θ
The value of tan θ is given as -8/15.
We can substitute this above:
y = 1 + tan θ
= 1 - 8/15
= (15-8)/15
= 7/15
The value of the expression cscθ sinθ+ tan θ is found to be 7/15.
Therefore, the value of cscθ sinθ + tan θ is 7/15.
Learn more about trigonometric ratios here: https://brainly.com/question/24349828
#SPJ2
A survey was taken of 49 people to see if they watch basketball and/or soccer games on television. The results are shown in the Venn diagram.
Enter your answers in the boxes to complete the two-way table based on the given data.
Can someone help me please
Answer:
[tex]\begin{array}{cccc}&\text{Watch basketball}&\text{Don't watch basketball}&\text{Total}\\\text{Watch soccer}&7&12&19\\\text{Don't watch soccer}&17&13&30\\\text{Total}&24&25&49\end{array}[/tex]
Step-by-step explanation:
From the diagram you can see that
17 people watch only basketball;7 people watch both basketball and soccer;12 people watch only soccer;in total, 17+7+12=36 people watch some sports;so, 49-36=13 people do not watch sports.So, you can fill the table in following way
[tex]\begin{array}{cccc}&\text{Watch basketball}&\text{Don't watch basketball}&\text{Total}\\\text{Watch soccer}&7&12&19\\\text{Don't watch soccer}&17&13&30\\\text{Total}&24&25&49\end{array}[/tex]
Answer:
dude was right but heres photo proof
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Consider the equation.

The value of x in terms of p is .
The value of x when p is −5 is .
Answer:
15/p and -3
Step-by-step explanation:
4(px+1)=64
Distribute 4: 4px + 4=64
Subtract 4 from both sides : 4px+4-4=64-4
Divide by 4p: 4px/4p=60/4p
x=15/p
A classroom is 24 metres long and 21 metres wide. Find the area of the classroom
Answer:
504 m²
Step-by-step explanation:
21 m * 24 m = 504 m²
So, the answer is 504 m²
The formula for the area of a rectangle is:
Length × Width
OR
L × W
In this case...
L = 24 m
W = 21
^^^Plug these numbers into the formula for the area of a rectangle
24 × 21
504
The area of this class room is 504 [tex]m^{2}[/tex]
Hope this helped!
~Just a girl in love with Shawn Mendes
What is the value of a in the equation 3a+b=54 , when b=9 ?
Use substitution method
3a+9=54
3a+9-9=54-9
3a= 45
divide by 3
3a/3= 45/3
a= 15
Answer is a= 15
Answer:
a = 15
Step-by-step explanation:
3a + b = 54
3a + 9 = 54
3a + 9 - 9 = 54 - 9
3a = 45
3a divided by 3 = 45 divided by 3
a = 15
3 x 15 + 9 = 54
45 + 9 = 54
54 = 54
During the past seven weeks Diego spent between $11 and $17 for lunch each week
Answer:
c
Step-by-step explanation:
11+17 x 7=130
x=130
130 is bigger than 120 but smaller than 180
Kiran bought 6 yards of ribbion for $3.90 . which ratio is proportional to 6 yards at $3.90 ?
The lowest proportion would be 1 yard at .65¢
We can get this by dividing $3.90 by 6, since we divided 6 by 6 to get 1.
Answer:
any option which has 0.65 as a unit rate
Step-by-step explanation:
since 3.90/6=0.65
divide the $ by the amount of fabric and you should get 0.65, if u get 0.65 thats ur answer
hope this helps!