Using relations in a right triangle, the area of the triangle is given by:
B. 9tan(65º)/2.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.In this problem, we have one leg(length 3) and the angle with the hypotenuse(65º), hence the other leg can be found as follows:
[tex]\tan{65^\circ} = \frac{x}{3}[/tex]
x = 3tan(65º).
What is the area of a right triangle?The area of a right triangle is half the multiplication of it's legs, hence in this problem:
A = 1/2 x 3 x 3tan(65º) = 9tan(65º)/2.
Which means that option B is correct.
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If m(arc BY)= 44, enter the
mZY AC.
(The figure is not drawn to scale.)
Answer: [tex]68^{\circ}[/tex]
Step-by-step explanation:
Assuming AC is a tangent, this means [tex]m\angle BAC=90^{\circ}[/tex].
Since arc BY measures 44 degrees, by the inscribed angle theorem, [tex]m\angle BAY=22^{\circ}[/tex].
This means [tex]m\angle YAC=90^{\circ}-22^{\circ}=68^{\circ}[/tex]
Solve each of the following by using the general quadratic formula: (2 decimal places)
The solutions to the given quadratic equation [2x² - 3x - 4 = 0] are x = 2.35, -8.85.
The solutions to the given quadratic equation [x² + 2x + 2 = 0] are x = -1+i, -1-i.
What are the solutions to the quadratic equation?Given the equation for the general quadratic formular;
[ -b±√( b² - 4(ac)) ]/2a
a) 2x² - 3x - 4 = 0
a = 2b = -3c = -4We substitute into the equation.
x = [ -(-3)±√(-3)² - 4( 2 × -4 )) ] / 2×2
x = [ 3±√9 + 32 ] / 4
x = [ 3±√41 ] / 4
x = [ 3+√41 ] / 4, [ 3-√41 ] / 4
x = 2.35, -8.85
The solutions to the given quadratic equation [2x² - 3x - 4 = 0] are x = 2.35, -8.85
b) x² + 2x + 2 = 0
a = 1b = 2c = 2We substitute into the equation.
x = [ -2±√( 2² - 4( 1×2 )) ] / 2×1
x = [ -2±√( 4 - 8) ] / 2
x = [ -2±√(-4) ] / 2
Lets re-write -4 as -1( 4 )
x = [ -2±√( -1 × 4) ] / 2
x = [ -2±√4 × √-1 ] / 2
Write √-1 as i
x = [ -2±√4 × i] / 2
x = [ -2± 2 × i] / 2
x = 2[ -1 ± i] / 2
x = (-1 ± i)
x = -1+i, -1-i
The solutions to the given quadratic equation [x² + 2x + 2 = 0] are x = -1+i, -1-i.
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Given that ΔJKL ≅ ΔUVW and ΔUVW ≅ ΔABC, complete the following statements.
Triangle JKL is congruent to triangle
.
Side LK corresponds to sides
.
Angle JLK corresponds to angles
.
Step-by-step explanation:
JKL is congruent to ABC
side LK corresponds to WV and CB
angle JLK corresponds to angle UWV and angle ACB
MATH HELP!!! 100PTS!!!
Suppose that u=log10(3) and v=log10(5). Find possible formulas for the following expressions in terms of u and/or v. Your answers should NOT involve any log 's.
a) log10(0.6)=
u-v
b) log10(0.25)=
c) log10(27000)=
3+3u
d) log10(sqrt10)=
Answer:
a) u - v
b) 2v - 2
c) 3u + 3
d) ¹/₂
Step-by-step explanation:
Given:
[tex]u=\log_{10}3[/tex]
[tex]v=\log_{10}5[/tex]
Part (a)
Rewrite 0.6 as a fraction:
[tex]\implies \log_{10}(0.6)=\log_{10}\left(\dfrac{3}{5}\right)[/tex]
[tex]\textsf{Apply the quotient log law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay:[/tex]
[tex]\implies \log_{10}\left(\dfrac{3}{5}\right)=\log_{10}3-\log_{10}5[/tex]
Substitute the values of u and v:
[tex]\implies \log_{10}3-\log_{10}5=u-v[/tex]
Part (b)
Rewrite 0.25 as 25/100:
[tex]\implies \log_{10}(0.25)=\log_{10}\left(\dfrac{25}{100}\right)[/tex]
[tex]\textsf{Apply the quotient log law}: \quad \log_a\frac{x}{y}=\log_ax - \log_ay[/tex]
[tex]\implies \log_{10}\left(\dfrac{25}{100}\right)=\log_{10}(25)-\log_{10}(100)[/tex]
Rewrite 25 as 5² and 100 as 10²:
[tex]\implies \log_{10}(25)-\log_{10}(100)=\log_{10}(5^2)-\log_{10}(10^2)[/tex]
[tex]\textsf{Appy the Power log law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \log_{10}(5^2)-\log_{10}(10^2)=2\log_{10}5-2\log_{10}10[/tex]
[tex]\textsf{Apply the log law}: \quad \log_aa=1[/tex]
[tex]\implies 2\log_{10}5-2\log_{10}10=2\log_{10}5-2(1)[/tex]
Substitute the value of v:
[tex]\implies 2\log_{10}5-2(1)=2v-2[/tex]
Part (c)
Rewrite 27000 as 30³:
[tex]\implies \log_{10}(27000)=\log_{10}(30^3)[/tex]
[tex]\textsf{Appy the Power log law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \log_{10}(30^3)=3\log_{10}(30)[/tex]
[tex]\textsf{Apply the log product law}: \quad \log_axy=\log_ax + \log_ay[/tex]
[tex]\implies 3\log_{10}(30)=3\log_{10}(3)+3\log_{10}(10)[/tex]
[tex]\textsf{Apply the log law}: \quad \log_aa=1[/tex]
[tex]\implies 3\log_{10}(3)+3\log_{10}(10)=3\log_{10}(3)+3(1)[/tex]
Substitute the value of u:
[tex]\implies 3\log_{10}(3)+3(1)=3u+3[/tex]
Part (d)
Rewrite √10 as [tex]10^{\frac{1}{2}}[/tex] :
[tex]\implies \log_{10}(\sqrt{10})=\log_{10}(10^{\frac{1}{2}})[/tex]
[tex]\textsf{Appy the Power log law}: \quad \log_ax^n=n\log_ax[/tex]
[tex]\implies \log_{10}(10^{\frac{1}{2}})=\dfrac{1}{2}\log_{10}(10)[/tex]
[tex]\textsf{Apply the log law}: \quad \log_aa=1[/tex]
[tex]\implies \dfrac{1}{2}\log_{10}(10)=\dfrac{1}{2}(1)=\dfrac{1}{2}[/tex]
what is the negative-2y+13 answer?
The negative of the expression -2y+13 is 2y-13.
Given Expression:-2y+13
We know that an expression is a combination of numbers, variables, symbols, indeterminants, etc. It is not expressed in equal to form. It expresses a relationship but we cannot find the value of variable because it is usually not present in equal to form.
We have to find the negative of the expression -2y+13 and to find out that we need to just put a negative mark in front of the expression and then adjust the expression for finding the negative of that expression.
Negative of -2y+13=-(-2y+13)
=2y-13.
Negative of an expression expresses opposite thing.
Hence the negative of -2y+13 is 2y-13.
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i am not able to solve this problem
The length of the board is 0.665 meters wide. When the boarder is added in all 4 edges, the length decrease by 0.05 meters on both side. So, the remaining length across is 0.665 - 0.5 x 2 = 0.565, so b.
*but maybe it's not a rectangle*
does this table represent a function ? why or why not
Answer:
yes
Step-by-step explanation:
every hours of training has mapped to monthly pays and each element in hour of training has mapped to unique element in monthly pay.
A line passes through the point (8, -9) and had a slope of -5/4. Write an equation in slope-intercept form for this line.
Answer:
y = -5/4x +1
Step-by-step explanation:
The slope-intercept form of a line is given by
y = mx + b where m is the slope and b is the y intercept
We are given the slope and a point on the line
y = -5/4 x + b
We can substitute the point for x and y and solve for b
-9 = -5/4(8)+b
-9 = -10+b
Add 10 to each side
-9+10=-10+10+b
1 = b
The slope intercept form of the equation is
y = -5/4x +1
A company makes 352 boxes of cereal each day. how many boxes are made in 7 days?
Answer: 2,464 boxes are made in 7 days.
Step-by-step explanation:
1 day = 352 boxes
7 days = ?
To solve this word problem, you can multiply 352 and 7.
352*7= 2464
# [4-5{1-(4-3+1)}] of 100% equals
a) 50%
b)-1%
c)zero
d)100%
Answer:
To solve this, we need to first evaluate the given expression. We can do that by simplifying the contents of each bracket, starting with the innermost one:
[4-5{1-(4-3+1)}]
⇒ [4 - 5{1 - (2)}]
⇒ [4 - 5{-1}]
⇒ 4 - (-5)
⇒ 4 + 5
⇒ 9
Now we can calculate what 9 out of 100 is:
9 of 100 = [tex]\frac{9}{100}[/tex]
⇒ 9%
Pls see below very short question
Answer:
[tex]f(x)=2(2)^{0.5x}-3[/tex]
Step-by-step explanation:
Parent function:
[tex]g(x)=2^x[/tex]
Properties of the given parent function:
y-intercept at (0, 1)horizontal asymptote at y = 0As x → -∞, y → 0As x → ∞, y → ∞Given form of function f(x):
[tex]f(x)=a(b)^{kx}+c[/tex]
If the parent function is [tex]g(x)=2^x[/tex] then b = 2:
[tex]\implies f(x)=a(2)^{kx}+c[/tex]
From inspection of the graphed function f(x):
y-intercept at (0, -1)horizontal asymptote at y = -3Therefore, the y-intercept has shifted 2 units down, yet the asymptote has shifted 3 units down. This implies that there has been a vertical shift of 3 units down and a vertical stretch.
The vertical shift is denoted by the variable "c" so c = -3:
[tex]\implies f(x)=a(2)^{kx}-3[/tex]
The vertical stretch is denoted by the variable "a". To find value of a, substitute the point of the y-intercept into the equation:
[tex]\begin{aligned}f(0) & = -1\\\implies a(2)^{k \times 0}-3 & =-1\\a-3 & = -1\\a-3+3 & = -1+3\\a & = 2\end{aligned}[/tex]
Therefore, as a = 2:
[tex]\implies f(x)=2(2)^{kx}-3[/tex]
From inspection of the given graph, the curve passes through point (4, 5). Substitute this point into the equation to find the value of k:
[tex]\begin{aligned}f(4) & = 5\\\implies 2(2)^{4k}-3 & =5\\2(2)^{4k}& =8\\(2)^{4k}& =4\\(2)^{4k}& =2^2\\4k & = 2\\k & = 0.5\end{aligned}[/tex]
Therefore, the equation of the function f(x) is:
[tex]\implies f(x)=2(2)^{0.5x}-3[/tex]
5. 61°N, 150°W 5. 61 ° N , 150 ° W
Based on the coordinates given, the location that is being described is Cook Inlet, in the Gulf of Alaska.
Where do the given coordinate lead to?The coordinates of 61°N, 150°W means that the place is located in the Northern and Eastern hemisphere.
When a map is used, it points to an area in the Gulf of Alaska that is very close to the Cook Inlet which is close to Anchorage.
Question is:
Determine what country or place is located on the given approximate coordinates.
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The slope of the line below is 3. Use the coordinates of the labeled point to
find a point-slope equation of the line.
A. y-6-3(x-8)
B. y-8--3(x-6)
C. y-6--3(x-8)
D. y-8-3(x-6)
10
(6,8)
10
The point-slope equation of the line is y - 8 = 3(x - 6)
How to determine the equation?The points are given as:
(x1, y1) = (6, 8)
The slope is given as:
m= 3
The equation is then calculated as:
y - y1 = m(x - x1)
This gives
y - 8 = 3(x - 6)
Hence, the point-slope equation of the line is y - 8 = 3(x - 6)
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Juma spent half of his July
The total salary juma receives for the month of July before the deductions is sh. 12,800
Amount of earningsLet
Total salary = xAmount spent on school fees = 1/2xAmount spent on farming = 1/8xSchool fees + farming = 1/2x + 1/8x
= 4x+x/8
= 5/8x
Amount remaining = x - 5/8x
=8x-5x /8
= 3/8x
Amount spent on food = 2/3 × 3/8x
= 6/24x
= 1/4x
So,
1/4x = sh.3200
x = 3200 ÷ 1/4
x = 3200 × 4
x = sh. 12,800
Complete question:
Juma spent half of his salary on school fees one-eighth on farming and two thirds of the reminder on food . Calculate his July salary if he spent sh.3200 on food
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Will give 15 points. Rewrite each expression using the property indicated.
I. commutative: 4 x 5
2. associative: (12 x 7) x 8
3. identity: 32 x1
4.distributive: 6 x (8-5)
5.associative: (3+4) + 5
6.zero: 0 x 4
write an equation for the graph below in terms of x
The linear equation for the graph in terms of x is given by: y = -0.5x - 3.
What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Looking at the graph, when x = 0, y = -3, hence the y-intercept is of b = -3. The graph also passes through point (2,-4), hence the slope is given by:
m = (-4 - (-3))/(2 - 0) = -1/2 = -0.5.
Hence the equation is:
y = -0.5x - 3.
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helllppppppppppp please
Answer:
4
Step-by-step explanation:
to find the x intercept of a line in standard form we can simply set y as 0 and find x
4x - 7(0) = 16
4x = 16
x = 4
the answer is 4
A square piece of card has a square of side 2 cm cut out from
each of its corners. The remaining card is then folded along
the dotted lines shown to form an open box whose total
internal surface area is 180 cm².
What is the volume of the open box in cm³?
A 100 B 128 C 162 D 180 E 200
Answer:
E) 200
Step-by-step explanation:
Let the length of the side after cutting the corners =x cm
Length of the side before cutting the corners = x + 4 cm
Area of square before cutting = (x + 4)² square cm
Area of that square that was cut = 2*2 = 4 cm²
Area of 4 squares cut from all 4 corners = 4 * 4 = 16 cm²
Area of internal surface area = 180 square cm
(x + 4)² - 4*4 = 180
x² + 2*4*x + 4² - 16 = 180
{expand using the identity (a + b)² = a² + 2ab + b²) }
x² + 8x + 16 -16 = 180
x² + 8x - 180 = 0
x² + 18x - 10x - 180 = 0
x( x + 18) - 10(x + 18) = 0
(x + 18) (x - 10) = 0
x - 10 = 0 {Ignore x +18 = 0}
x = 10
Open box:length = x = 10 cm
breadth = x = 10 cm
height = 2 cm
Volume of open box = length * breadth * height
= 10 * 10 * 2
= 200 cm³
Joan draws a bar chart to show the temperatures at midday on March 1st in five cities.
Joan has made four mistakes in her diagram.
Write down any three of them.
The mistakes that Joan made are:
The y-axis does not start from zero.The width of the bars are not equal.The space between the bars are not equal.What is a bar chart?A bar chart is a graph that shows the numerical values of variables represented by the height rectangles of equal width.
In a bar graph, the rectangles must be of equal width and the space between each bars must be equal.
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Find a number between 2- and 2.1251:
8
Uh
What is the quotient of startfraction negative 8 x superscript 6 baseline over 4 x superscript negative 3 baseline endfraction?
The fractional number given has a quotient of -2x⁹.
Given that (-8x⁶)÷(4x⁻³) is the fractional number.
The resultant number obtained by dividing two numbers is known as the quotient. Let's divide number a by number b. Then, q=a÷b will be these two numbers' quotient.
Here are the actual numbers (a,b).
In this case,the fraction is (-8x⁶)÷(4x⁻³).
Assume that q=(-8x⁶)÷(4x⁻³)
If you write the denominator variable as x⁻¹=1÷x, you obtain
[tex]\begin{aligned}q&=\frac{-8x^6}{4\frac{1}{x^3}}\\ &=\frac{-8x^6\times x^3}{4}\end[/tex]
As we are aware, if two numbers are multiplied together and their bases are the same, their powers can be represented as sums, such as
q=(-8x⁶⁺³)÷(4)
q=(-8x⁹)÷(4)
By dividing the numerator by the denominator, we get
q=-2x⁹
Hence,the given fraction (-8x⁶)÷(4x⁻³) has a quotient of -2x⁹.
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Answer: option D -2x^9 on edge 2023
Step-by-step explanation:
In a study to add a new feature to a software program, the programmer introduced two categories, men and women, in the survey she conducted. Is the study observational or experimental? if it is an experiment, what is the controlled factor?.
The is an observational study.
What is an observational study?
In an observational study, researchers examine the effects of a particular intervention, risk, diagnostic test, or treatment without trying to control who is exposed to it.
By having a control group, or those who are not exposed, and an experimental group, or those who are subjected to the intervention, treatment, etc., an observational study contrasts from an experimental research, where the scientists are controlling who gets exposed to the treatment, intervention, etc. The groups are randomly assigned or picked in the best studies.
Reason Behind it Being an Observational Study
Since, in this case also, the two categories of men and women, the candidates are randomly picked for the survey of the new software programmer feature. Hence, it is a scenario of observational study.
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A LANE IN THE MIDDLE OF A TWO-WAY ROAD THAT HAS DASHED LINES ON BOTH SIDES AND TWO LARGE CURVED ARROWS FACING EACH OTHER MAY BE USED FOR:
This lane symbol is used for marking the beginning and ending of a left turn to the drivers.
What are lane symbols?
A permitted lane usage is denoted by a lane symbol. For example, a lane marked with a diamond is one that is designated for high-occupancy cars. A lane symbol of a bicycle marks that the lane is designated for cyclists. At crossings, arrows indicate movements that are necessary or allowed. The user of the roadway must yield when there is a row of solid triangles. Likewise, two large curved arrows facing each other on a lane in the middle of a two way road with dashed lines on either sides indicate the beginning and ending of a left turn.
A Lane symbol or marking are also utilized to warn drivers of potentially dangerous situations that may be coming up. For instance, a triangle with no filling indicates a yield ahead. A speed hump is indicated by a succession of lines across a lane that get bigger and wider.
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Type the correct answer in each box. Round your answers to the nearest integer.
-10
10
-10
In the figure, the perimeter of hexagon ABCDEF is approximately
Reset
A
10
B
15 20
Next
D
units, and its area is
C
square units.
Answer:
500 is your answer.
Step-by-step explanation:
First solve the length of side BC, CD, EF and FA Since BC = CD = sqrt( 10^2 + 10^2) BC = CD = 14.1421
FA = EF = sqrt(10^2 + 20^2) = 23.3607
So the perimeter = 10 + 10 + 14.1421 + 14.1421 + 23.3607 = 93
The area is made up be triangle FAE, rectangle ABDE and triangle BCD
A = 0.5(20)(20) + (10)(20) + 0.5(20)(10)
A = 500 sq units
Find the tangent of angle Θ in the triangle below.
A. 12/13
B. 12/5
C. 5/12
D. 13/12
E. 5/13
Answer:
tanΘ = [tex]\frac{5}{12}[/tex]
Step-by-step explanation:
tanΘ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{5}{12}[/tex]
Find the surface area of the regular pyramid.
Answer:
384mmStep-by-step explanation:
The surface area of a square pyramid is 1/2 the product of its base perimeter & slant height.
SA = area of base + 1/2 (perimeter of base * slant height)
So, we can substitute 12 and 10 into this equation.
The area of the base is 12*12 (144). The perimeter of the base is 48mm.
144 + 1/2(48*10) = Surface Area.
144 + 240 = Surface Area.
384mm = Surface Area.
Hope that helps :)
Determine the equation, in both factored and standard forms of the following parabola
The standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)² and The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).
How to derive the two forms of the equation of the parabola
Mathematically speaking, parabolae are defined by second order polynomials. The standard form of the equation of the parabola is defined by:
y - k = C · (x - h)² (1)
Where C is the vertex constant.
And the factored form has this form:
y = k · (x - r₁) · (x - r₂) (2)
First, we determine the standard form of the equation of the parabola: (h, k) = (3, - 3) and (x, y) = (0, 0)
0 - (- 3) = C · (0 - 3)²
3 = 9 · C
C = 1/3
Then, the standard form of the equation of the parabola is y + 3 = (1/3) · (x - 3)². Now we proceed to determine the factored form of the parabola: (r₁ = 0, r₂ = 6), (h, k) = (3, - 3)
- 3 = k · (3 - 0) · (3 - 6)
- 3 = k · 3 · (- 3)
- 3 = - 9 · k
k = 1/3
The factored form of the equation of the parabola is y = (1/3) · x · (x - 6).
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Can you answer my question please and thank you
Answer:
b = 12
Step-by-step explanation:
since a² + b² = c²
we can find b by pythagorean theorem.
sqrt(13² - 5²) = b
hence,
b = 12
Answer: 12
Step-by-step explanation:
To find a length of a right triangle, we can use Pythagorean theory:
leg² + leg² = hypotenuse²
5² + b² = 13²
25 + b² = 169
b² = 144
b = [tex]\sqrt{144}[/tex]
b = 12
cals 1/2
10. MA bisects segment CB at midpoint M. Based on the definition of angle bisector and midpoint, find the value
of x and the following measures.
Middle
x =
MB.=
CM =
CB =
x+6
(92)
M
2r-4
B
Answer:
x = 10MB = 16CM = 16CB = 32Step-by-step explanation:
There are two different relations here that can be used to write equations for the value of x:
a perpendicular to a line creates a linear pair of right anglesa midpoint divides a segment into two congruent segmentsValue of xUsing the angle relation, we have ...
∠CMA ≅ ∠BMA
(9x)° = 90°
x = 90/9 = 10
Segment lengthsUsing the found value of x in the expressions for the segment lengths, we find ...
MB = 2x -4 = 2(10) -4 = 16
CM = x +6 = 10 +6 = 16 . . . . . . . congruent to MB, as it should be
CB = CM +MB = 16 +16 = 32
HELP HELP HELP
If you know algebra 1 then you can do these 5 quick algebra 1 questions for 50 points!
Only answer if you know the answer to all questions please! ;)
1. x = a
2. y = b
3. A vertical line has an undefined slope.
4. rise/run or Change in y/change in x (m) = y2 - y1 / x2 - x1
5. Rewrite the equation in slope-intercept form to determine the y-intercept.
What is the Equation of a Line?In slope-intercept form, the equation of a line in slope-intercept form is, y = mx + b, where m is the slope and the y-intercept = b.
1. The slope of a vertical line is undefined, therefore, the equation for a vertical line is given as: x = a, where a is the value of the x-intercept.
A vertical line that contains (a, b) will have the equation, x = a.
2. The slope of a horizontal line is 0, therefore, the equation of the horizontal line is, y = b, where b is the y-intercept.
A horizontal line that contains (a, b) will therefore have the equation, y = b.
3. A vertical line has an undefined slope.
4. For example, if we have the two points (3, 3) and (0, 5), two methods to find the slope are:
rise/run
or
Change in y/change in x (m) = y2 - y1 / x2 - x1 = 5 - 3 / 0 - 3 = 2/-3 = -2/3.
5. If we have an equation in point-slope form, for example, y - 3 = 2(x - 4), to find the coordinates of its y-intercept, rewrite the equation in slope-intercept form to determine the y-intercept:
y - 3 = 2x - 8
y = 2x - 8 + 3
y = 2x - 5
The y-intercept is -5, thus, the coordinates would be: (0, -5).
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