Answers
Answer:
Adjacent, x = 60°
Step-by-step explanation:
Adjacent angles are pairs of angles next to each other. Vertical angles make an x shape, are across from each other, and have the same measure. These are adjacent angles.
This is a 90° angles, which is signified by the little red box. To solve for x, make an equation by adding the two angles together and set them equal to 90.
x - 30 + x = 90
2x - 30 = 90
2x - 30 + 30 = 90 + 30
2x = 120
2x/2 = 120/2
x = 60°
Here, the angles x° and (x - 30)° both are complementary angles, so they will add upto 90°, thus we can obtain a equation as ;
[tex]{:\implies \quad \sf x^{\circ}+(x-30)^{\circ}=90^{\circ}}[/tex]
[tex]{:\implies \quad \sf 2x^{\circ}-30^{\circ}=90^{\circ}}[/tex]
[tex]{:\implies \quad \sf 2x^{\circ}=120^{\circ}}[/tex]
[tex]{:\implies \quad \sf x^{\circ}=\dfrac{120^{\circ}}{2}=\bf \boxed{60^{\circ}}}[/tex]
Hence, the required value of x is 60
Related Questions
If 3x - 5y = 11 and 2x + 3y = 5, then what is the ratio of x to y?
Answers
Answer:
-58/7
Step-by-step explanation:
Alright so this is a system of equations. First we'll solve the system, and then find the ratio afterwards.
[tex]3x-5y = 11\\2x+3y =5\\[/tex]
Isolate for y on both.
[tex]2x + 3y = 5\\3y = 5-2x\\y = \frac{5-2x}{3}[/tex]
and
[tex]3x - 5y = 11\\-5y = 11-3x\\y = \frac{11-3x}{-5}[/tex]
Set both equations equal to each other:
[tex]\frac{11-3x}{-5} = \frac{5-2x}{3}\\ \\\frac{3(11-3x)}{-5} = 5-2x\\ \\3(11-3x) = -5(5-2x)\\\\33 - 9x = -25 + 10x\\33 = -25 + 19x\\58 = 19x\\\frac{58}{19} = x[/tex]
We've got x, now let's solve for y:
[tex]y = \frac{11-3x}{-5} = \frac{11-3(\frac{58}{19}) }{-5}[/tex]
Now we got both x and y, and what they equal.
[tex]y = \frac{-7}{19}\\[/tex]
[tex]x = \frac{58}{19}[/tex]
The ratio of x to y, is essentially [tex]\frac{x}{y}[/tex]. So we will calculate that.
[tex]\frac{\frac{58}{19} }{\frac{-7}{19} } = \frac{58}{19} * \frac{19}{-7} = \frac{-58}{7}[/tex]
round to the nearest hundredth
(please help picture inculded)
Answers
Answer:
AB ≈ 6.53
Step-by-step explanation:
using the cosine ratio in the right triangle
cos40° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{AC}{AB}[/tex] = [tex]\frac{5}{AB}[/tex] ( multiply both sides by AB )
AB × cos40° = 5 ( divide both sides by cos40° )
AB = [tex]\frac{5}{cos40}[/tex] ≈ 6.53 ( to the nearest hundredth )
Given the function h of x equals negative 2 times the square root of x, which statement is true about h(x)?
The function is decreasing on the interval (0, ∞).
The function is decreasing on the interval (–∞, 0).
The function is increasing on the interval (0, ∞).
The function is increasing on the interval (–∞, 0).
Answers
Using translation concepts, it is found that the correct statement about h(x) is:
The function is decreasing on the interval (0, ∞).
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
In this problem, the parent function is:
[tex]f(x) = \sqrt{x}[/tex]
Which is increasing on (0, ∞).
After the translation, the function is:
[tex]h(x) = -2\sqrt{x}[/tex]
It was multiplied by a negative number, which means that it was reflected over the x-axis, and it will be decreasing on the interval (0, ∞).
More can be learned about translation concepts at https://brainly.com/question/4521517
What is the slop of the line?
5(y+2)=4(x-3)
A. 3/2
B. 2/3
C. 4/5
D. 5/4
Answers
Answer:
c. 4/5
Step-by-step explanation:
Write the following series in sigma notation.
7 + 16 + 25 +34 +43 +52 + 61
Answers
The series 7 + 16 + 25 +34 +43 +52 + 61 is an illusration of arithmetic series
The sigma notation of the series is: [tex]\sum\limits^7_{n=1} {9n - 2}[/tex]
How to write the series in sigma notation?The series is given as:
7 + 16 + 25 +34 +43 +52 + 61
The above series is an arithmetic series, with the following parameters
First term, a = 7Common difference, d = 9Number of terms, n = 7Start by calculating the nth term using:
a(n) = a + (n - 1) * d
This gives
a(n) = 7 + (n - 1) * 9
Evaluate the product
a(n) = 7 - 9 + 9n
Evaluate the difference
a(n) = 9n - 2
So, the sigma notation is:
[tex]\sum\limits^7_{n=1} {9n - 2}[/tex]
Read more about arithmetic series at:
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-2x^2+bx -5 Determine the b-value that would ensure the function has two real root.
Answers
Answer:
No solutionStep-by-step explanation:
Given is the quadratic function
y = -2x² + bx - 5In order to have two real roots the discriminant should be posivive
D = - b² - 4acD = - b² - 4(-2)(-5) = - b² - 40We need D > 0
-b² - 40 > 0b² + 40 < 0b² < - 40There is no solution as b² is never negative
Consider the function defined by f(x) lnx/x^4 for x > 0 and its graph y = f(x).
The graph of f has a horizontal tangent at point P. Find the coordinates of P.
Answers
Answer:
[tex]\sqrt[4]{e};\frac1{4e}[/tex]
Step-by-step explanation:
The first derivative of [tex]f(x)[/tex] will give, for each x, the slope of the tangent at that specific x. Let's calculate the derivative, applying the quotient rule.
[tex]D(\frac AB) = \frac{A'B-AB'}{B^2}\\f'(x)= \frac1{x^8}[(\frac1x)x^4-(lnx)(4x^3)]=\frac1{x^8}[x^3(1-4lnx)]=\frac{1-4lnx}{x^5}[/tex]
Now, to find the point with an horizontal tangent (called "stationary points"), we set the first derivative equal to 0. Considering that we're working with [tex]x > 0[/tex] we deal only with the numerator.
[tex]1-4lnx = 0 \rightarrow lnx= \frac14\\x=e^\frac14 =\sqrt[4]{e}[/tex]
At this point we Replace the value we found in the equation to find it's y coordinate
[tex]f(\sqrt[4]e) = \frac{ln\sqrt[4]e}{\sqrt[4]e^4}= \frac{\frac14}{e} = \frac1{4e}[/tex]
Hazel and 4 of her friends bought tickets for a baseball game. They received a $30 group discount. If the total cost was under $125, how much could each ticket have been?
Answers
Each ticket could have cost up to $31.
What is the discount?
A discount is a reduction in the price of an item or service. It is often offered as an incentive to encourage customers to purchase or use a particular product or service. The discount amount may be a percentage of the total price, a fixed dollar amount, or a combination of both.
Let the cost of each ticket be $x. Then the total cost for 5 tickets would be 5x. After applying the $30 group discount, the total cost would be 5x - $30.
We know that the total cost was under $125, so we can set up the inequality:
5x - $30 < $125
Simplifying this inequality, we get:
5x < $155
Dividing both sides by 5, we get:
x < $31
Hence, each ticket could have cost up to $31.
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PLS HELP I am giving 25 points here is the question
A shopkeeper sold 12 bags of potatoes for $2.99 each. He bought the potatoes for $1.90 for each bag what was his total profit
Answers
Find theFind tha amount of profit per bag by subtracting:
2.99 - 1.90 = 1.09
He made $1.09 profit per bag.
Now multiply the profit per bag by the number of bags:
1.09 x 12 = 13.08
Total profit = $13.08 amount of profit per bag by subtracting:
2.99 - 1.90 = 1.09
He made $1.09 profit per bag.
Now multiply the profit per bag by the number of bags:
1.09 x 12 = 13.08
Total profit = $13.08
Shopkeeper makes $1.09 profit for each bag
1.09 x 12 = 13.08
The shopkeeper makes $13.08 profit.
Is (-7, -3) a solution to this system of equations?
x = -7
y = -x - 10
Yes or no
Answers
===========================================================
Explanation:
The point (-7,-3) means x = -7 and x = -3
Right off the bat, the first equation x = -7 is proven true based on the first coordinate.
Let's now plug the coordinates into the second equation.
y = -x-10
-3 = -(-7)-10
-3 = 7-10
-3 = -3
Which is a true statement.
Both equations are true when (x,y) = (-7,-3)
This is why it is a solution to the system. It turns out it's the only solution to this system. This system is consistent and independent.
You can use a graphing tool like Desmos to plot the two equations, and you should see them crossing at the point (-7,-3)
Answer:
The answer is yes
*View the attached graph to check your answer graphically.*
Step-by-step explanation:
x = -7
y = -x - 10
For this problem, I will be using substitution, since the second equation is already in the slope-intercept form.
First, I will substitute the first equation, for x, into the first equation:
x = -7
y = -x - 10
y = -(-7) - 10 <== multiplying two negatives, makes a positive
y = 7 - 10
y = - 3 <== the value of y
Now, we find the value of x by substituting - 3 for y:
y = -x - 10
- 3 = -x - 10
+10 +10
7 = -x <== you can't have a negative variable
/-1 /-1
-7 = x <== the value of x
(x, y) ==> (-7, -3)
Therefore, yes (-7,-3) is a solution to this system of equations.
*View the attached graph to check your answer graphically.*
Hope this helps!
you buy a sandwich for $6.965, a salad for $3.25, and a drink for $1.79. if sales tax is 7%, how much change do you receive from $20 bill, rounded to the nearest cent?
Answers
6.965 + 3.25 + 1.79 = 12.005, now, let's apply a 7% taxation on that
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{7\% of 12.005}}{\left( \cfrac{7}{100} \right)12.005}\implies 0.84035~\hfill \underset{total~bill}{\stackrel{12.005~~ + ~~0.8435}{12.84535}} \\\\\\ 20~~ - ~~12.84535\implies 7.15465~~\approx ~~ \$7.15[/tex]
In ΔWXY, y = 8.6 cm, x = 8.5 cm and ∠X=100°. Find all possible values of ∠Y, to the nearest 10th of a degree.
Answers
The possible value of ∠Y to the nearest tenth of a degrees in triangle WXY is 85.1 degrees.
How to find angle of a triangle using sine rule
Let's find angle Y using sine rule,
Hence,
x / sin X = y / sin Y
where
x = 8.5 cmy = 8.6 cm∠X = 100°8.5 / sin 100° = 8.6 / sin Y
cross multiply
8.5 sin Y = 8.6 sin 100°
sin Y = 8.6 sin 100° / 8.5
sin Y = 8.4693466759 / 8.5
Y = sin ⁻¹ 0.99639372657
Y = 85.1325941735
∠Y = 85.1°
learn more on triangle here: https://brainly.com/question/23998296
Lita must find the area of the sector enclosed by central angle QCR in circle C.
Points Q and R lie on circle C. The measure of angle Q C R is 74 degrees and the radius of circle C is 1 foot.
What steps should Lita take to correctly solve this problem?
A: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so the portion of the area she wants to find is 74∘360∘. Therefore, she must multiply 74∘360∘ times the area, which is πr2.Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360 degrees textsf comma so the portion of the area she wants to find is 74∘360∘. Therefore, she must multiply 74∘360∘ times the area, which is πr2.
B: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so the portion of the area she wants to find is 74∘360∘, so she must multiply 74∘360∘ times the area, which is 2πr.Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360 degrees textsf comma so the portion of the area she wants to find is 74∘360∘, so she must multiply 74∘360∘ times the area, which is 2πr.
C: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so she should subtract 74∘ from 360∘. The portion of the area she wants to find is 286∘360∘, so she must multiply 286∘360∘ times the area, which is 2πr.Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360 degrees textsf comma so she should subtract 74 degrees from The portion of the area she wants to find is 286∘360∘, so she must multiply 286∘360∘ times the area, which is 2πr.
D: Lita knows that m∠QCR=74∘ and that the whole circle has a measure of 360∘, so she should subtract 74∘ from 360∘. The portion of the area she wants to find is 286∘360∘, so she must multiply 286∘360∘ times the area, which is πr2.
Answers
To find the area of the sector, Lita must multiply 74°/360° times the area of the circle, which is πr² (Option A).
What is the Area of the Sector of a Circle?Area of sector = ∅/360 × πr², where ∅ = central angle, and r = radius of the circle.
Given the following:
∅ = m∠QCR = 74°r = 1 ft.The area of the circle she wants to find is: 74°/360°.
Since the area of the whole circle is, πr², therefore, to find the area of the sector, Lita must multiply 74°/360° times the area of the circle, which is πr² (Option A).
Learn more about area of sector on:
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Find the distance between the two points
☟ ︎Photo down below ☟
Answers
[tex]\qquad\qquad\huge\underline{\boxed{\sf Answer☂}}[/tex]
Let's use distance formula ~
[tex]\qquad \sf \dashrightarrow \: d = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: d = \sqrt{(2 - ( - 4)) {}^{2} + (0 - 1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: d = \sqrt{(2 + 4) {}^{2} + ( - 1) {}^{2} } [/tex]
[tex]\qquad \sf \dashrightarrow \: d = \sqrt{ {}^{} 36+ 1{}^{} } [/tex]
[tex]\qquad \sf \dashrightarrow \: d = \sqrt{ {}^{} 37{}^{} } [/tex]
Therefore, the required distance is [tex]\sf \sqrt{37}[/tex] units
I don't know how to solve this
Answers
Answer:
7
Step-by-step explanation:
List out possible numbers that would add to the answer choices and see which has most possibilities
7
3 + 4
5 + 2
1 + 6
10
5 + 5
4 + 6
11
5 + 6
12
6 + 6
On Saturday, the temperature was
75.5°F. The temperature rose by
6°F on Sunday, then dropped by
3.5°F on Monday. Write an expression
to represent how the temperature
changed. What was the temperature
on Monday?
Answers
Answer:
78°F
Step-by-step explanation:
75.5°F on Saturday...
75.5 + 6 = 81.5 on Sunday
81.5 - 3.5 = 78°F on Monday
The expression that represents the temperature change is
N = L + 6°F + 3.5°F
The temperature on Monday is 85°F.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Temperature:
Saturday = L= 75.5°F ______(1)
Sunday = M = Rose by 6°F
M = L + 6 _____(2)
Monday = N = Dropped by 3.5°F
N = L + 6 - 3.5 _____(3)
The expression that represents the temperature change:
From (1), (2), and (3) we get
N = L + 6°F + 3.5°F
The temperature on Monday:
N = 75.5 + 6 + 3.5
N = 85°F
Thus,
The expression that represents the temperature change is
N = L + 6°F + 3.5°F
The temperature on Monday is 85°F.
Learn more about expressions here:
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Can anyone solve this?
Answers
Answer:
54 cubic inches
Step-by-step explanation:
Just as the area of a triangle is half the area of a rectangle with the same dimensions, the volume of a triangular prism is half the volume of a rectangular prism with the same dimensions:
V = 1/2(LWH)
V = (1/2)(9 in)(4 in)(3 in) = 54 in³
The volume of Phil's block of cheese is 54 in³.
Put the equation below into vertex form.
y=(x+9)(x+25)
Answers
Explanation: y= x^2+34x+225
a=1, b=34
X= - 34/2+1
x = -17
Y= (x+9)(x+25), x=-17
Y=-64
So vertex is (-17,-64)
standard form:
y = ax^2 + bx + c
y = x^2 + 34x + 225
a=1 b=34 c=225
point of symmetry formula:
x = -b/2a
x = -34/2
x = -14
plug in x to find the vertex
y = (-14+9)(-14+25)
y = (-5)(11)
y = -55
vertex = (-14,-55)
vertex form
y = a(x-h)^2 + k [where (h,k) is the vertex]
so your answer is:
y = 1(x-(-14))^2 + (-55)
or
y = (x+14)^2 - 55
I hope this helps and is the BRAINLIEST!!
Good luck with your studies!
Which of the following notes is G?
Answers
How do you multiplying or dividing a fractions to obtain equivalent
Answers
To obtain an equivalent fraction by dividing, look at the top number and the bottom number. If they both can be divided by a number without it being a decimal, it’s an equivalent fraction. Example: 8/10, both of those numbers can be divided by 2 that isn’t a decimal, 4/5. 4/5 and 8/10 are equivalent
Sammy’s dad drove their car 150 miles in three hours. At this rate, how far would he drive in nine hours?
Answers
Answer:
distance in 3 hours = 150 miles
distance in 1 hour = 150/3 = 50 miles
distance in 9 hours = 50 × 9 = 450 miles
Answer:
Sammy's dad traveled 450 miles in 9 hours.
Step-by-step explanation:
mph = [tex]\frac{Miles}{Hours}[/tex]
Miles = 150
Hours = 3
Plug into the formula of distance/time
[tex]\frac{150}{3} = 50mph[/tex]
Sammy's dad is driving at 50mph
In three hours you can use this formula: [tex]50mph=\frac{miles}{9}[/tex]
Multiply both sides by 9: [tex]50mph * 9 =\frac{miles}{9} *9[/tex]
Solve:
[tex]50mph * 9 =miles[/tex]
[tex]450 =miles[/tex]
Sammy's dad traveled 450 miles in 9 hours.
Hope this helped! :)
Which graph matches? I'll give brainliest. and 100pts
Answers
Function:
[tex]\sf 2\left(3\right)^{x}+2[/tex]
Find y-intercept:
[tex]y=2\left(3\right)^{0}+2[/tex]
[tex]y=\sf 4[/tex]
option B is correct as it cuts y-intercept at 4
Answer:
This is a positive exponential graph with a y-intercept of 4 (when x is 0, y is 4)
Hope this helps!
Y+1.27=7.23 solve for y
Answers
Answer:
y=5.96
Step-by-step explanation:
You can do a reverse equation and do 7.23 - 1.27 = 5.96
PLSS help important
(will gibe brainliest)!
I dont understand this
Answers
To form the vector notation for the translation:
--> must find how much the new graph moved horizontally from the old
graph
--> the graph moved 8 units horizontally
--> must find how much the new graph moved vertically from the old
graph
--> the graph moved 4 units vertically
In vector notation, that would be (8,4)
Hope that helps!
please help, what would the answer be?
Answers
3 x 2 = 6
Scale is 1:2 ratio
9 x 2 = 18ft
18 x 6 = 108ft
The answer is probably 108ft, there are no given scale ¯\_(ツ)_/¯
HELP ME PLEASE
PRETTY PLEASEEEEEEEEEEE
Answers
Answer:
93
Step-by-step explanation:
19x-2 = 18x+3
x=5
15(5) -2=93
18(5)+3=93
Constants are numbers without letters attached.
What is the constant in the equation x/2 - 3?
answers:
2
-3
Answers
Answer:
constant = - 3
Step-by-step explanation:
[tex]\frac{x}{2}[/tex] - 3 = [tex]\frac{1}{2}[/tex] x - 3
the number without letters attached is the constant - 3
Answer:
-3
Step-by-step explanation:
The answer is -3 because 2 has a letter attached to it which is x/2 -3 is without a letter.
hope dis helps):
Solve for x: √(32^0 + 2/3)=(0.6)^2-3x
Answers
Step-by-step explanation:
Given: √{32⁰ + (2/3)} = (0.6)²⁻³ˣ
Asked: Find the value of x = ?
Solution: Given that √{32⁰ + (2/3)} = (0.6)²⁻³ˣ
⇛√{1 + (2/3)} = (0.6)²⁻³ˣ
⇛√{(1/1) + (2/3) = (0.6)²⁻³ˣ
⇛√{(1*3 + 2*1)/3} = (0.6)²⁻³ˣ
⇛√{(3 + 2)/3} = (0.6)²⁻³ˣ
⇛√(5/3) = (0.6)²⁻³ˣ
Squaring on both sides then
⇛{√(5/3)}² = {(0.6)²⁻³ˣ}²
⇛√(5²/3²) = {0.6}(²⁻³ˣ)²
⇛√{(5*5)/(3*3)} = {0.6}(²⁻³ˣ)²
⇛5/3 = {0.6}(²⁻³ˣ)²
[[tex]\mathsf{\because}[/tex] (aᵐ)ⁿ = aᵐⁿ]
⇛5/3 = (0.6)²*²⁻³ˣ*²
⇛5/3 = (0.6)⁴⁻⁶ˣ
⇛5/3 = (6/10)⁴⁻⁶ˣ
⇛5/3 = {(6÷2)/(10÷2)})⁴⁻⁶ˣ
⇛5/3 = (3/5)⁴⁻⁶ˣ
⇛(3/5))⁻¹ = (3/5)⁴⁻⁶ˣ
[[tex]\mathsf{\because}[/tex] a⁻ⁿ = 1/aⁿ]
Base are the same, so the exponents must be equal.
[tex]\mathsf{\therefore}[/tex] -1 = 4 - 6x
Shift the number 4 from RHS to LHS, changing it's sign.
⇛-1 - 4 = -6x
⇛-5 = -6x
⇛x = {(-5)/(-6)}
[tex]\mathsf{\therefore}[/tex] x = 5/6
Answer: Hence, the value of x for the given problem is 5/6.
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(3^-2 × 4^-2)^-3 = 12^x In the given expression find the value of x. https://brainly.com/question/25746273?referrer
What is the number with the mark
Answers
[tex]\huge\mathsf\blue{♧ANSWER♧}[/tex]
[tex]\huge \mathfrak \blue{\frac{ - 7}{8} }[/tex]
how to multiply and divide decimals with whole numbers