Answer: [tex]864\ m^2,\ 24\ m[/tex]
Step-by-step explanation:
Given
Perimeter of the rhombus is [tex]120\ m[/tex]
Length of one of the diagonal is [tex]d_1=36\ m[/tex]
All the sides of the rhombus are equal
[tex]\Rightarrow 4a=120\\\Rightarrow a=30\ m[/tex]
Area of the rhombus with side and one diagonal is
[tex]\Rightarrow \text{Area=}\dfrac{1}{2}d\sqrt{4a^2-d^2}[/tex]
Insert the values
[tex]\Rightarrow \text{Area=}\dfrac{1}{2}\times 36\times \sqrt{4\cdot 30^2-36^2}\\\\\Rightarrow \text{Area= }18\sqrt{3600-1296}\\\Rightarrow \text{Area= }18\times 48\\\Rightarrow \text{Area= }864\ m^2[/tex]
Area with two diagonals length can be given by
[tex]\Rightarrow \text{Area =}0.5\times d_1\times d_2 \\\text{Insert the values}\\\Rightarrow 864=36\times d_2\\\Rightarrow d_2=24\ m[/tex]
Thus, the area of the rhombus is [tex]864\ m^2[/tex] and the length of the other diagonal is [tex]24\ m[/tex]
The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Answer:
59.04°
58.31 inches
Step-by-step explanation:
The solution triangle is attached below :
Since we have a right angled triangle, we can apply trigonometry to obtain the angle ladder makes with the ground;
Let the angle = θ
Tanθ = opposite / Adjacent
Tanθ = 50/30
θ = tan^-1(50/30)
θ = 59.036°
θ = 59.04°
The length of ladder can be obtained using Pythagoras :
Length of ladder is the hypotenus :
Hence,
Hypotenus = √(adjacent² + opposite²)
Hypotenus = √(50² + 30²)
Hypotenus = √(2500 + 900)
Hypotenus = 58.309
Length of ladder = 58.31 inches
Answer:
59°
58.3 inches
Step-by-step explanation:
Here is the full question :
A ladder is placed 30 inches from a wall. It touches the wall at a height of 50 inches from the ground. The angle made by the ladder with the ground is degrees, and the length of the ladder is inches.
Please check the attached image for a diagram explaining this question
The angle the ladder makes with the ground is labelled x in the diagram
To find the value of x given the opposite and adjacent lengths, use tan
tan⁻¹ (opposite / adjacent)
tan⁻¹ (50 / 30)
tan⁻¹ 1.667
= 59°
the length of the ladder can be determined using Pythagoras theorem
The Pythagoras theorem : a² + b² = c²
where a = length
b = base
c = hypotenuse
√(50² + 30²)
√(2500 + 900)
√3400
= 58.3 inches
Charlene is a salesperson. Let y represent her total pay (in dollars). Let x represent the number of
items she sells. Suppose that x and y are related by the equation y=32x + 1900.
What is Charlene's total pay if she doesn't sell any items?
A. $32
B. $1,900
C. $3,200
D. $19
two triangles are similar what is x
Answer:
x = 10
Step-by-step explanation:
smaller triangle / bigger triangle = 20 / 28
hence,
3x / (4x+2) = 20/28
28(3x) = 20(4x+2)
84x = 80x + 40
4x = 40
x = 10
the product of 7 and the quotient of 40 divided by 5 is
The quotient of 40 and 5
40÷5=8
=> Product of that number with 7 and 8
So number to find is : 7x8=56
The product of 7 and the quotient of 40 divided by 5 is 56.
What is the quotient?The quotient is the result which is derived by the division of two numbers.
For example, the quotient of 30 divided by 3 is 10.
What is the product of two numbers?The product is the multiplication of two numbers which is written as a*b.
For example, the product of 8 and 9 is 72.
Here given we have to calculate the product of 7 and the quotient of 40 divided by 5.
The quotient of 40 divided by 5 is 40/5= 8
The product of 7 and The quotient of 40 divided by 5= 7*8= 56
Therefore the product of 7 and the quotient of 40 divided by 5 is 56.
Learn more about quotient
here: https://brainly.com/question/673545
#SPJ2
y= -(x+3)^2 -5
What is the leading coefficient?
How do you find the vertex?
Answer:
To find the leading coefficient, first expand the function:
[tex]y= -(x+3)^{2} -5\\\\y=-(x^{2} +6x+9)-5\\\\y=-x^{2} -6x-9-5\\\\y=-x^{2} -6x-14[/tex]
The leading coefficient is the coefficient of the highest-order term, which, in this case, would be the -1 from -x².
To find the vertex: see image below
Vertex = (-3, -5)
5. Which pair of equations represents parallel lines?
A. y =2x+7
Y=2x-7
B. Y=7
X=7
C. Y=2x-7
Y=-1/2-7
D. Y=2x+7
Y=x+7
Answer:
C
Step-by-step explanation:
Find the square roots of these numbers by division method.
a-6090
Reflect Triangle ABC in BC. What kind of figure will result? How would your answer change if ABC is isosceles? a right triangle with right angle at A? a right isosceles trianglewith right angle at A?
9514 1404 393
Answer:
a kitea kite or rhombus, dependinga kitea squareStep-by-step explanation:
The reflections are illustrated in the attached.
A1, A1' are opposite vertices of the reflected original triangle. They are part of a kite figure.
A2, A2' are opposite vertices of a reflected isosceles triangle, where BA=BC. Figure A2BA2'C is a kite.
A2a, A2a' are opposite vertices of a reflected isosceles triangle with AB=AC. Figure A2aBA2a'C is a rhombus.
A3, A3' are opposite vertices of a right triangle with the right angle at A3. Figure A3BA3'C is a kite figure.
A4, A4' are opposite vertices of a reflected right isosceles triangle with AB=AC and the right angle at A4. Figure A4BA4'C is a square.
***CAN SOMEONE HELP ME PLEASE!!***
The polygon in each pair are similar. Find the missing side length
Answer:
45 / 27 = 30 / 18 = x / 24
x = 40
Step-by-step explanation:
Hi there!
The question here states that the two polygons are similar
Polygons that are similar have similar side length ratios.
If we want to find a side length we must create a proportional relationship
We are already given a partial proportional relationship.
Which is...
45 / __ = __ / 18 = x / __
First let's fill in the blanks
The side that is corresponding to the side with a length of 45 has a length of 27. So it would be 45/27
The side that is corresponding to the side with a length of 18 has a length of 30. So it would be 30/18
The side corresponding to side labeled "x" has a length of 24. so it would be x/24
So we would have
45 / 27 = 30 / 18 = x / 24
Now let's find x
We only need 2 ratios ( the one including x of course, and the other one can either be 30/18 or 45/27)
30 / 18 = x / 24
Now let's solve for x
Cross multiply
30*24=720
18*x=18x
We now have 18x = 720
Divide both sides by 18
18x / 18 = x
720 / 18 = 40
x = 40
To check our answers we can see if the ratios are similar
If they are then we are correct
45/27 = 1.66
30/18 =1.66
40/24 = 1.66
They are all equivalent meaning that our answers are correct
one class collects 8 1/4 pounds of recyclable materials. Another class collects 1 1/2
Step-by-step explanation:
what to find then??.........
For the triangle shown, what are the values of x and y?
60°
30°
6
Select the correct answer.
O x = 2V3, y = 473
O x= 3V3, y = 6/3
O x = 6/3, y = 12
O x = 6V3, y = 1273
Answer:
x = 6/√3 = 2√3
y = 2×2√3 = 4√3
So, 1st option is correct
please help me i will give 20 points for this question
Answer:
1. a. 2
b. -½
c. y - 3 = -½(x - 8) => point-slope form
y = -½x + 7 => slope-intercept form
2. a. -1
b. 1
c. y - 5 = 1(x - 3) => point-slope form
y = x + 2 => slope-intercept form
Step-by-step explanation:
1. (8, 3) and (10, 7):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (8, 3) = (x_1, y_1) [/tex]
[tex] (10, 7) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{7 - 3}{10 - 8} [/tex]
Gradient = [tex] \frac{4}{2} [/tex]
Gradient = 2
b. The gradient of the line perpendicular to this line = the negative reciprocal of 2
Negative reciprocal of 2 = -½
c. The equation of perpendicular line if it passes through the first point, (8, 3):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (8, 3)
Slope (m) = -½
Substitute (a, b) = (8, 3), and m = -½ into the point-slope equation, y - b = m(x - a).
Thus:
y - 3 = -½(x - 8) => point-slope form
We cam also express the equation of the perpendicular line in slope-intercept form by rewriting y - 3 = -½(x - 8) in the form of y = mx + b:
Thus:
y - 3 = -½(x - 8)
y - 3 = -½x + 4
y - 3 + 3 = -½x + 4 + 3
y = -½x + 7
2. (3, 5) and (4, 4):
a. The gradient for the line joining the points:
Gradient = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Let,
[tex] (3, 5) = (x_1, y_1) [/tex]
[tex] (4, 4) = (x_2, y_2) [/tex]
Plug in the values
Gradient = [tex] \frac{4 - 5}{4 - 3} [/tex]
Gradient = [tex] \frac{-1}{1} [/tex]
Gradient = -1
b. The gradient of the line perpendicular to this line = the negative reciprocal of -1
Negative reciprocal of -1 = 1
c. The equation of perpendicular line if it passes through the first point, (3, 5):
Equation of the perpendicular line in point-slope form can be expressed as y - b = m(x - a).
Where,
(a, b) = (3, 5)
Slope (m) = 1
Substitute (a, b) = (3, 5), and m = 1 into the point-slope equation, y - b = m(x - a).
Thus:
y - 5 = 1(x - 3) => point-slope form
We can also express the equation of the perpendicular line in slope-intercept form by rewriting y - 5 = 1(x - 3) in the form of y = mx + b:
Thus:
y - 5 = 1(x - 3)
y - 5 = x - 3
y - 5 + 5 = x - 3 + 5
y = x + 2
Write an equation in standard form of the line that passes through the given point and has the given slope (-8,0); m= -4 PLEASE HELP NEED DONE ASAP WILL GIVE BRAINLIEST
Answer:
4x+y=-32
Step-by-step explanation:
given,
slope (m) = -4
point: (-8,0)
as we know the slope intercept form of the line is, y=mx+b, b=y-mx, now we put x=-8, y=0 to find b [because the point is given (-8,0) so it must satisfy the equation]
so,
b = 0-(-4)×(-8) = -32
y=mx+b
or, y=-4x-32
or, 4x+y=-32
(this is the standard form of the line)
Using the equation y - y1 = m(x - x1)
y - 0 = -4(x - (-8))
y = -4(x + 8)
y = -4x - 32
PLS HELP ME ON THIS QUESTION I WILL MARK YOU AS BRAINLIEST IF YOU KNOW THE ANSWER PLS GIVE ME A STEP BY STEP EXPLANATION!!
A sample of 500 U.S. teachers are asked to express their opinions on standardized testing for their students. The population in this study is _______________.
A. all U.S. students
B. standardized tests
C. all U.S. teachers
D. the 500 U.S. teachers
Answer:
Option A
Step-by-step explanation:
Dont let the sample of 500 teachers fool you the 500 teachers opinion is on their students standardized testing experience. In this case the students are the test subjects(population).
Write the sum using the summation notation assuming the suggested pattern continues 2, -10, 50, -250, +…
Is this sequence arithmetic or geometric? How do you know?
Answer:
geometric
x=number of terms
∑ 2(-5)^(k-1)
k=1
Step-by-step explanation:
the sequence has a ratio of -5 (2*-5=-10, -10*-5=50)
x=number of terms
∑ 2(-5)^(k-1)
k=1
for this i don't know what the last term is since it doesn't show in the question but just find 2(-5)^x and x will be the top term
Please help explanation if possible
Answer:
y = | x-5|
Step-by-step explanation:
y = |x-h| +k where (h,k) is the center of the "v"
The "v" is located at (5,) so h=5 and k = 0
y = | x-5| +0
Three is subtracted from a number, and then the difference is divided by eleven. The result is twelve. What is the
number?
Answer:
The number is 135.
Step-by-step explanation:
1) Form an equation
Three is subtracted from a number
⇒ [tex]x-3[/tex] (where x is "the number")
The difference is divided by 11
⇒ [tex]\displaystyle \frac{x-3}{11}[/tex]
The result is 12
⇒ [tex]\displaystyle \frac{x-3}{11}=12[/tex]
2) Solve the equation
[tex]\displaystyle \frac{x-3}{11}=12[/tex]
Multiply both sides by 11
[tex]\displaystyle \frac{x-3}{11}*11=12*11\\\\x-3=132[/tex]
Add 3 to both sides
[tex]x-3+3=132+3\\x=135[/tex]
Therefore, the number is 135.
I hope this helps!
help me please brainliest for the best answer!!
Answer:
The volume of the irregular figure would be 102 [tex]cm^3[/tex].
Step-by-step explanation:
If you wish to make the process of calculating the volume easier, you can picture the irregular figure as two rectangular prisms: the large one on the bottom, and the smaller one appearing to protrude from the prism below it. Using this method, you only need to find the volumes of the two rectangular prisms and add the values together to get the volume for the irregular figure. The formula used to find the volume of a rectangular prism is [tex]l*w*h[/tex], where [tex]l[/tex], [tex]w[/tex], and [tex]h[/tex], represents the length, width, and height of the rectangular prism respectively. Using the formula above, the volume of the larger rectangular prism would be [tex]6*3*5=30*3=90 cm^3[/tex], and the volume of the smaller rectangular prism would be [tex]3*2*2=6*2=12 cm^3[/tex]. So the volume of the entire irregular figure would be [tex]90+12=102 cm^3[/tex].
Answer:
102
Step-by-step explanation:
Large rectangle:
6 × 3 × 5 = 18 × 5 = 90
Small rectangle:
7 - 5 = 2
3 × 2 × 2 = 6 × 2 = 12
90 + 12 = 102
Hope this helped.
Which functions have a maximum value greater than the maximum of the function g(x) = -(x + 3)2 - 4?
Answer:
max: -4
Step-by-step explanation:
(x+3)^2 》0 mọi x
<=> -(x+3)^2 《0
<=> -(x+3)^2 -4 《 -4
Convert 75 mg into gram
Answer:
[tex]{ \tt{1 \: mg = 1 \times {10}^{ - 3} \: g}} \\ { \tt{75 \: mg = (75 \times 1 \times {10}^{ - 3} ) \: g}} \\ { \bf{ = 75 \times 10 {}^{ - 3} \: grams}} \\ { \bf{ = 0.075 \: grams}}[/tex]
Let A represent the average value of the function f(x) on the interval [0,6]. Is there a value of c for which the average value of f(x) on the interval [0,c] is greater than A?
Answer:
The average value of the Function f(x) by squeeze theorem states that no extreme or greater value will exist within the designated area for f(x)
Can anyone plz solve this question step by step ASAP!
Answer:
40√3 cm²Step-by-step explanation:
Step 1
Find the height:
h² = 8² - (12 - 8)²h² = 64 - 16 = 48h = √48 = 4√3Step 2
Find the area:
A = 1/2(a + b)hA = 1/2(12 + 8)(4√3) = 40√3 cm²HELP PLEASE ASAP!!!!! Alex can cut a cord into 7 pieces in 36 seconds. How long will it take him to cut the cord into 12 pieces?
Answer:
GIVE ME BRAINLIEST
Step-by-step explanation:
What is the volume of the rectangular prism?
Answer:
94.5 yd^3
Step-by-step explanation:
The volume of a rectangular prism is given by the formula:
A = lwh
Where:
l = length
w = width
h = height
Volume is how much space a 3d figure occupies.
USE THE FORMULA WITH THE GIVEN DIMENSIONS:
A = (7)(4.5)(3)
= (31.5)(3)
= 94.5
Volume is measured in cubic yards, in this case.
Therefore your answer is 94.5 yd^3
I hope I helped!
Answer:
Step-by-step explanation:
length = 7 yd
Width = 4.5 yd
height = 3 yd
Volume of rectangular prism = length * width * height
= 7 * 4.5 * 3 = 94.5 yd³
If Tan A=5/12 then find cot A, cos A and Sin A
Cot A=1/tan A=12/5
cos A= 12/13
sin A=5/13
Draw a right angled triangle
the hypotenuse is the longest side which is 13 using Pythagoras theorem
the side opposite the angle A is 5
the side closest to the angle A which is called the adjacent is 12
sinA =opp/hyp
cos A= adj/hyp
cotA =1/tanA=cos A/sinA
Note: Pythagoras theorem is
hyp²=opp²+adj²
Answer:
Step-by-step explanation:
[tex]tan \ A = \frac{5}{12}=\frac{opposite \ site}{adjacent \ side}[/tex]
hypotenuse² = (opposite side)² + (adjacent side)²
= 5² + 12²
= 25 + 144
= 169
hypotenuse = √169 = √13*13 = 13
[tex]Cot \ A = \frac{adjacent \ side}{opposite \ side}=\frac{12}{5}\\\\Cos \ A = \frac{adjacent \ side}{hypotenuse}=\frac{12}{13}\\\\Sin \ A = \frac{opposite \ side}{hypotenuse}=\frac{5}{13}[/tex]
In Exercises 1-4, determine whether the dilated figure or the original figure is closer to the center of dilation. Use the given location of the center of dilation and scale factor k.
1. Center of dilation inside the figure; k = 3
Center of ditation inside the figure, k = 1/2
3. Center of dilation outside the figure: = 120%
4. Center of dilation outside the figure; k = 0.1
When the Center of dilation is inside the figure
The original figure is closer to the center of dilationThe dilated figure is closer to the the center of dilationWhen the Center of dilation is outside the figure
3. The original figure is closer to the the center of dilation
4. The dilated figure is closer to the center of dilation
The center of dilation is the fixed point from which the distances in a dilation are measured
The scale factor is ratio of the side lengths of an original figure or preimage to the side lengths of the newly formed image
Center of dilation is inside the figure
Where the center of dilation is inside the figure, and the scale factor is larger than 1, k = 3 > 1, we have;The distance of a point on the dilated figure, including the distances from the center of dilation is 3 times the distances of points on the original image from the center of dilation
Therefore, the original figure has a shorter distance to and is therefore closer to the the center of dilation than the dilated figure
2. Where the center of dilation is inside the figure, and the scale factor is a fraction between 0 and 1 k = 1/2, we have;
The distance of a point on the dilated figure, including the distances from the center of dilation is 1/2 times the distances of points on the original image from the center of dilation
Therefore, the dilated figure has a shorter distance to and is therefore closer to the the center of dilation than the original figure
Center of dilation outside the figure
3. Given that the center of dilation is outside the figure and the scale factor is larger than 1, k = 120% = 120/100 = 1.2 > 1, we have;
The distance of the dilated figure from the center of dilation is 120% of the distance of the original figure from the center of dilation, therefore, the original figure is closer to the the center of dilation than the dilated figure
4. Where the center of dilation is outside the figure and the scale factor is a fraction between 0 and 1, k = 0.1 < 1
The distance of the dilated figure from the center of dilation is only 0.1 times the distance of the original figure from the center of dilation, and therefore, the dilated figure is closer to the center of dilation
Learn more about scale factors and center of dilation here;
https://brainly.com/question/12162455
I'LL GIVE BRAINLIEST !!! FASTERR !
Answer:
Option A, 86°
Step-by-step explanation:
each diagonals of a rhombus divides the angles at half, so a+b+c+d = 360°/2 = 180°
now, a+b+c+d-94° = 180°-94° = 86°
Answer:
D 266°
Step-by-step explanation:
a+b+c+d-94°
90°+ 90°+ 90°+ 90° -94°
360°-94°
266°
f(x) = Square root of quantity x plus seven. ; g(x) = 8x - 11 Find f(g(x)). (1 point)
f(g(x)) = 2 Square root of quantity two x plus one
f(g(x)) = 8 Square root of quantity x plus seven - 11
f(g(x)) = 8 Square root of quantity x plus four
f(g(x)) = 2 Square root of quantity two x minus one
Answer:
2 sqrt(2x-1)
Step-by-step explanation:
f(x) = sqrt(x+7)
g(x) = 8x-11
f(g(x))=
Place g(x) in for x in the function f(x)
f(g(x)) = sqrt( 8x-11 +7)
= sqrt( 8x -4)
Factor out 4
= sqrt( 4(2x-1)
= 2 sqrt(2x-1)
[tex]\\ \sf\longmapsto f(x)=\sqrt{x+7}[/tex]
[tex]\\ \sf\longmapsto g(x)=8x-11[/tex]
g(x) will be put on the place of x[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-11+7}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{8x-4}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=\sqrt{4(2x-1)}[/tex]
[tex]\\ \sf\longmapsto f(g(x))=2\sqrt{2x-1}[/tex]
Helpppppppppppppppppppppppp im not smart pls don't just say some bull i need help ill just get it deleted
Answer:
a. 6m
b. m-2
c. 5(m-2)
d. 6m +5m -10= 56
E. 11m=66
divide by 6: m=6
Maple Granola= 6$
Apple Granola= 4$
help! please!!!!!! look at photo :))
Hey there!
We know that Danielle earns $10 per hour, so muliply that by 3 and get 30.
Because Danielle works an extra half an hour, divide 10 by 2 and get 5.
Danielle earns $35 in 3 hours and a half.
Hope this helps! Please mark me as brainliest!
Have a wonderful day :)
