Based on the amount of cash that Elias Rubio brings, we can calculate that his total cash deposit is $1,323
How much did Elias deposit in cash?This can be found as:
= (75 x 1) + (78 x 5) + (83 x 10) + (80 x 0.25) + (32 x 0.10 or 10 cents) + (95 x 0.05 or 5 cents) + (5 x 0.01 or 1 cent)
Solving gives:
= 75 + 390 + 830 + 20 + 3.20 + 4.75 + 0.05
= $1,323
Remaining part of the question:
How much did he deposit in cash?
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pe-intercept Equatic
Question 4 of 10
If f(x) = 5x - 12, what is f(2)?
Answer:
f(2) = 2
Step-by-step explanation:
Given function:
f(x) = 5x - 12
To Find:
f(2)
Solution:
Well,it is absolutely clear from the problem,that x = 2.So just substitute 2 in x's place on the function,then simplify using PEMDAS.
[tex]f(x) = 5x - 12[/tex]
[tex]f(2) = 5(2)- 12[/tex]
[tex]f(2) = 10 - 12[/tex]
[tex]\boxed{f(2) = - 2}[/tex]
Hence,f(2) is equal to -2.
How many solutions are there to the system of equations graphed below if
the lines are parallel?
O A. Zero
O B. Two
C. Infinitely many
O D. One
Solve for x. Round to the nearest hundredth sin x ≈ 0.965926
how do u do a problem like this?
In the given equation, the value of x is approximately 75°
TrigonometryFrom the question, we are to determine the value of x
The given equation is
sin x ≈ 0.965926
If sin x ≈ 0.965926
Then,
x ≈ sin⁻¹(0.965926)
∴ x ≈ 75.0°
Hence, the value of x is approximately 75°
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could someone please help me with this
Answer:
ia) center: (0, 0), the origin
ib) angle: 90°
ic) direction: CCW
ii) LM ≅ L'M', ∠L ≅ ∠L'
iii) (2, 1)
Step-by-step explanation:
A rigid transformation preserves size and shape of a figure, so the image is congruent to the original. The rigid transformations are rotation, reflection, and translation. Each has characteristics that allow one to determine the nature of the transformation(s) involved.
__
rotationangle and direction
One way to determine the angle and direction of rotation of a figure is to compare a horizontal segment on the original with the corresponding segment on the image. Here, a convenient segment is NM, which is horizontal and points to the right. Its angle relative to the direction of the +x axis is 0°.
The transformed segment N'M' points upward, at an angle relative to the +x axis of 90°. This tells you the figure was rotated 90° in the CCW direction. (This is fully equivalent to a rotation of 270° in the CW direction.)
center
Points in a rotated image always remain at the same distance from the center of rotation as the original points. In most cases, the center of rotation is the origin. We can check to see if that is the case by looking at the distances of a couple of points from the origin.
N is at coordinates (1, 1), so is √(1² +1²) = √2 from the origin
N' is at coordinates (-1, 1), so is √((-1)² +1²) = √2 from the origin
L is at coordinates (1, 3), so is √(1² +3²) = √10 from the origin
L' is at coordinates (-3, 1) so is √((-3)² +1²) = √10 from the origin
This confirms that the origin is the center of rotation.
__
Since each point and its image are on a circle centered at the center of rotation, the line between them is a chord of that circle. The perpendicular bisector of that chord goes through the center of rotation. Here, we observe that the perpendicular bisector of NN' is the y-axis. The perpendicular bisector of LL' is a line with slope -2 through (-1, 2). It will intersect the y-axis at the origin, confirming the origin as the center of rotation.
__
geometric relationshipsA rigid transformation preserves lengths and angles, so any length or angle on the rotated figure is congruent to the original:
LM ≅ L'M', MN ≅ M'N', NL ≅ N'L'
∠L ≡ ∠L', ∠M ≡ ∠M', ∠N ≡ ∠N'
__
translationThe components of a translation vector add to the corresponding coordinates of a point.
L +v = L'
(1, 3) +(1, -2) = (2, 1) . . . image of point L
Can someone help me?
Answer:
A. 7 and 3D. 1 and 5Select all the functions that show an inverse variation...
a) y=6x
b) y=3/x
c) y=1/3x
d) y= -.07x
e) y= 2/x+4
f) xy=-3
PLEASE HELP ILL MARK BRAINLEST
The sum of the reciprocals of the first four consecutive positive integers is greater than two. What is the least number of consecutive positive integers necessary to make the sum of the reciprocals greater than three?
The least number of consecutive positive integer that is required to make the sum of the reciprocals greater than three is 7.
What is an integer?An integer is simply a number that is not a fraction.
The first four consecutive positive integers are:
1, 2, 3 , 4.
Their reciprocals are:
1/1, 1/2, 1/3, 1/4; and
The sum of them are greater than 2; that is
1/1 + 1/2 + 1/3 + 1/4 = 2.08333333333 > 2
to make the expression >3
We would require the following integers
1/1 + 1/2 + 1/3 + 1/4+ (1/5) + (1/6) + (1/7) + (1/8)+ (1/9) + (1/10) + (1/11) = 3.01987734488
Thus, the additional consecutive reciprocal integers that is required to make the sum of the reciprocal of the fist four greater than 3 is 7.
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Is in between 2 number on the number line
Answer:
D
Step-by-step explanation:
Answer:
between 3 and 4
Step-by-step explanation:
3 squared is 9 and 4 squared is 16 so something in between 3 and 4 can be squared to equal 10 (since a square root is the opposite of squaring)
what is the factored form of x^3 - 729
Answer:
(x - 9)(x^2 + 18x + 81).
Step-by-step explanation:
Use the difference of cubes factorization, which claims that a^3 - b^3 = (a - b)(a^2 + ab + b^2)
x^3 - 729 = (x - 9)(x^2 + 18x + 81)
Answer:[tex](x-9) (x^{2} +9x + 81)[/tex]
Step-by-step explanation:
find the length of AD
The length of AD is 5 units. so, option A is the correct answer.
What is the Pythagoras theorem?The Pythagoras theorem states that the square of the longest side must be equal to the sum of the square of the other two sides in a right-angle triangle.
The length of DC is given as 13 units.
The length of AC is given as 12 units. We can see that angle D is a right angle, so the triangle will be a right-angle triangle.
by Pythagoras theorem;
[tex]DC ^2 = AD^2 + AC^2\\\\13^2 = AD^2 + 12^2\\\\AD^2 = 169 - 144\\\\AD^2 = 25\\\\AD = 5[/tex]
Hence, the length of AD is 5 units. so, option A is the correct answer.
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Identify the geometric mean of 9 and 9/4.
The geometric mean of 9 and 9/4 will be 9/2 or 4 1/2.
How to calculate the mean?It should be noted that in order to find the geometric mean of the numbers given, give to find the square root and then multiply.
This will be:
= ✓9 × ✓9/4
= 3 × 3/2
= 9/2 = 4 1/2
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Hey, any help would be very needed thanks so much!!
Let's take this problem step by step:
To find the ordered pair of the system:
⇒ must set both equations equal to each other
⇒ must solve for 'x'
Let's solve:
[tex]x^2-2x+3=-2x+28\\x^2-2x+3+2x-28=0\\x^2-25=0\\(x-5)(x+5)=0[/tex]
Let's find the x-values:
[tex](x-5)=0\\x=5\\\\(x+5)=0\\x=-5[/tex]
Let's find f(x)'s value for each of the 'x':
[tex]x=5\\f(5)=-2(5)+28=18\\\\x=-5\\f(-5)=-2(-5)+28=38[/tex]
Answer: (5, 18), (-5,38)
Hope that helps!
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3. (3, 5) and (k, 9), slope = 1/2
Linear relationships unit 3 lesson 10 grade 8 openuprespurces
Answer:
k = 11, if I understand the question.
Step-by-step explanation:
Please rephrase the question if my interpretation is incorrect. (BTW, isn't (k,9) a dog?)
======================
I'll assume that we want to find the value of k as given by the equation of a line that has a slope of (1/2).
Let's determine if we can establish an equation with what we know:
1. It goes through point (3,5), and
2. It has a slope of (1/2)
We'll look for a line with the form y=mx+b, where m is the slope and b is the y-intercept (the value of y when x=0).
From (2) we know y = (1/2)x + b.
We can find b by using the one known point that lies on the line (3,5). Use y = (1/2)x + b, insert the point (3,5), and solve for b:
y = (1/2)x + b
5 = (1/2)(3) + b
5 = 1.5 + b
b = 3.5
The line is y = (1/2)x + 3.5.
Now use the point (k,9):
y = (1/2)x + 3.5
9 = (1/2)k + 3.5
(1/2)k = 5.5
k = 11
The point is (11,9) so k = 9
See the attached graph.
Multiplying Monomials and Binomials:16x(x+24)
Claire and jane did an examination together. jane scored 9 more marks than claire and her marks were 60% of the sum of their scores. what are the scores of each student?
The score of Jane is 27 and the score of Claire is 18.
A linear equation is an equation where highest degree of variables is 1.
Let the score of Jane's mark is x
Given, that score Jane is 9 more than the score of Claire.
So, the score of Claire= x-9
Given, the score of Jane is 60% of the sum of their scores.
the sum of their scores is = x+x-9= 2x-9
from the above it is clear that
the linear equation will be
x=60%(2x-9)
⇒x=0.6(2x-9)
⇒x= 1.2x -5.4
⇒1.2x-x= 5.4
⇒0.2x= 5.4
⇒x= 5.4/0.2
⇒x= 27
So the score of Jane is 27.
As score Jane is 9 more than the score of Claire.
the score of Claire is = x-9= 27-9=18
Therefore the score of Jane is 27 and the score of Claire is 18.
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Line A and Line B are perpendicular. The slope of line A is -0.5. What is
the gradient of line B? Give reasons.
Answer:
Step-by-step explanation:
When 2 lines are perpendicular, their slopes are negative reciprocals of one another. Here, if the slope of A is -1/2, the slope of B is +2/1, or just 2.
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Using the properties of integer exponents, match each expression with its equivalent expression.
From the power rules, the matching of each expression with its equivalent expression is:
[tex]5^{-3}=\frac{1}{125}[/tex]
[tex]-5^{-3}=-\frac{1}{125}[/tex]
[tex](-5^{-3})^{-1}=-125[/tex]
[tex](-5^{-3})^{0}=1[/tex]
Power RulesThere are different power rules, see some them:
1. Negative exponent. For this rule when you have a negative exponent, you need to invert the number, i.e, the power base is converted to the denominator. After that, you should solve the power with a positive exponent. See the examples:
[tex]4^{-3}=\frac{1}{4^3} =\frac{1}{64} \\ \\ {\frac{4}{6} }^{-2}=( {\frac{6}{4} })^{2}=\frac{36}{16}[/tex]
2. Power. For this rule, you should repeat the base and multiply the exponents. See the example, [tex](2^{2})^3=2^6=64[/tex].
3. Zero Exponent. When you have an exponent equals to zero, the result must be 1. See the example, [tex]2^0=1[/tex].
From this for your question, you have:
[tex]5^{-3}=\frac{1}{5^3}=\frac{1}{125}[/tex][tex]-5^{-3}=-\frac{1}{5^3}=-\frac{1}{125}[/tex][tex](-5^{-3})^{-1}=(-5)^{3}=-125[/tex][tex](-5^{-3})^{0}=(-5)^{0}=1[/tex]Read more about power rules here:
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Given: ∠CBA ≅ ∠FBA; ∠CAB ≅ ∠FAB
Prove: ΔBCA Is-congruent-to ΔBFA
The proof is shown below
What is congruency?Two figures or objects are congruent if they have the same shape and size, or if one has the same shape and size as the mirror image of the other.
Given:
∠CBA ≅ ∠FBA; ∠CAB ≅ ∠FAB
Now, ∠BCA is congruent to ∠BFA [reflexive property of congruence]
Also, AB= AB (common)
Thus, we can conclude that Δ BCA≅ Δ BFA by ASA criteria.
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What is the measure of
Find the vertex and focus of the
parabola:
y²-10y + 4x + 21 = 0
Vertex = ([?],
[]
Focus=([], [])
Answer:
Vertex: (1, 5)
Focus: (0, 5)
Step-by-step explanation:
Given that the parabola's equation is y² - 10y + 4x + 21 = 0, solve for the vertex and the focus.
Vertex:
Step 1: Isolate x to the left side of the equation; we get x = - (y² / 4) + (5y / 2) - (21 / 4).
Step 2: Complete the square of the previous equation; here we get - (1 / 4) * (y - 5)² + 1. x is squal to this.
Step 3: Use the vertex form, x = a(y - k)² + 1. a is - 1 / 4, h is 1, and k is 5.
Step 4: Fill in (h, k). We get the answer (1, 5) as the vertex.
Focus:
Step 1: Find p, and distance from the vertex to the focus. We can find p by using 1 / (4a).
Step 2: Simplify. This gives us -1 as p.
Step 3: We plug in the values we just got earlier to get the vertex. The focus of a parabola can be found by using: (h + p, k).
Step 4: Substitude the values. We have (1 + -1, 5).
Step 5: Simplify. Therefore, the answer is (0, 5).
This took me a long time to calculate. Please mark me as Brainliest!!!This uservabove me did it all for you. I don't have much to say...
Consider the table below.
x y
-1 -5
0 5
1 11
2 13
3 11
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and c are constants.
The standard equation is: y = (-2)x² + 8x + 5
What is Quadratic Equation?A quadratic equation is a second-order polynomial equation in a single variable x ax²+bx+c=0, with a ≠ 0 .
We know,
y = ax² + bx + c
For (-1, -5)
-5 = a - b + c..................(1)
For (0, 5)
5 = c
For (1, 11)
11 = a + b + c.....................(2)
From (1) and (2), we get
a=-2
and b= 8
Hence, the standard equation is:
y = (-2)x² + 8x + 5
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Is LMN OPQ If so name the congruence postulate that applies
The triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement Hence, Option D is correct.
What is SSS congruency?If the corresponding two sides of two triangles are of the same measurement, then the considered pair of triangles are congruent.
We have given two triangles that are congruent to each other;
LMN is congruent to OPQ
Given;
LM = OP
MN = PQ
LN = OQ
Thus, the triangle is congruent by SSS congruency because the corresponding two sides of two triangles are of the same measurement
Hence, Option D is correct.
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What is the value of f^-1 (-3)
According to the plot of [tex]f(x)[/tex], whose curve passes through the point (-5, -3), we have
[tex]f(-5) = -3 \implies f^{-1}(-3) = \boxed{-5}[/tex]
??????????????????????????????????????????????????
Answer:
x=20
Step-by-step explanation:
The angles are 'Co-interior Angles', they make a C shape and add up to 180 degrees
so 4x +5x =9x
9x=180
x=20
4x=80
5x=100
If f(x) = 2x² - 5 and g(x) = 3x + 3, find (f- g)(x).
OA. 3x-2x2 - 2
OB. 2x²-3x-8
OC.-²2²-8
OD. 2x²-3x-2
(f- g)(x) = 2x²-3x -8 , Option B is the correct answer.
What is a Function ?A function is a mathematical statement that derives relation between two variables.
Two functions are given in the question
f(x) = 2x² - 5
g(x) = 3x + 3
(f- g)(x) = ?
(f- g)(x) = (2x² - 5 - (3x + 3))
(f- g)(x) = 2x²-3x -8
Therefore Option B is the correct answer.
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Which equation represents the line that passes through the point (-2.4, -7.1) and has a slope of -5.3
Please help me with this question
I tried to use the law of cosine but the numbers I get are in decimal places and are too small for the angles.
Answer:
y = √119 ≈ 10.909θ ≈ 65.376°α ≈ 24.624°sin(θ) = (√119)/12 ≈ 0.909059cos(θ) = 5/12 ≈ 0.416667tan(θ) = (√119)/5 ≈ 2.181742csc(θ) = (12√119)/119 ≈ 1.100038sec(θ) = 2.4cot(θ) = (5√119)/119 ≈ 0.458349Step-by-step explanation:
You can use the Law of Cosines after you find y or θ. Using the given information, you can apply the Pythagorean theorem, the Law of Sines, or the definition of the cosine trig function.
The mnemonic SOH CAH TOA is intended to remind you of the relations between sides and angles in a right triangle. It tells you ...
Sin = Opposite/Hypotenuse
Cos = Adjacent/Hypotenuse
Find yThe Pythagorean theorem relates the measures of the sides. It tells you ...
y² +5² = 12²
y = √(144 -25) = √119
Find anglesThe trig relations above tell you ...
sin(α) = 5/12 ⇒ α = arcsin(5/12) ≈ 24.624°
cos(θ) = 5/12 ⇒ θ = arccos(5/12) ≈ 65.376°
Of course, once you find one of the angles, you can find the other. The sum of the two acute angles in a right triangle is 90°.
Find trig functionsUsing the definitions above for the trig functions, you have ...
sin(θ) = y/12 = (√119)/12
cos(θ) = 5/12
tan(θ) = y/5 = (√119)/5
Using trig identities, you have ...
csc(θ) = 1/sin(θ) = 12/√119 = (12√119)/119
sec(θ) = 1/cos(θ) = 12/5 = 2.4
cot(θ) = 1/tan(θ) = 5/√119 = (5√119)/119
_____
Additional comment
The attached calculator screen shot shows you the angle θ on the first line, and the value of y on the second line. The csc, sec, and cot are shown on the third line. You will notice the angle mode (DEG) is seen in the lower left corner. If the calculator angle mode is set to radians, you will see the angles as relatively small radian values: θ ≈ 1.141, α ≈ 0.4298.
We have shown both exact values and decimal values you can round to the desired precision.
Which triangles in the diagram are congruent?
70°
triangle 1
70°
triangle 3
OA triangle 1 and triangle 2
OB. triangle 1, triangle 2, and triangle 3
OC. triangle 1 and triangle 3
OD. triangle 1, triangle 3, and triangle 4
70°
triangle 2
#
triangle 4
Submit Test
Rea
Answer:
its e
Step-by-step explanation:
because e is is referring to savvy
Which method is better to solve the following equation?
²-25=0
Your answer:
O Quadratic Formula
O Square Rooting
Clear answer
Next
Please answer this thanks
Answer: down below
Step-by-step explanation:
1. How many hay bales did the farmer sell?
To do that, you need to divide the weight of a hay bale by the total weight of the hay bales that the farmer sold.
That will be 24,300 / 75 = 324 bales
2. Divide the new number (26,700) by the same number 75.
26,700 / 75 = 356 hay bales
Subtract the bales from last year to the bales from this year:
356 bales - 324 bales = 32 bales
