Answer: $289.52
Step-by-step explanation: We will solve the problem by first finding the number of cubic centimeters in the bar, then finding the number of grams, then converting that number of grams to a price.
We are given the dimensions of the silver bar. With this, we can find how many cubic centimeters are in the bar. Cubic centimeter is a three-dimensional unit and we are given the three dimensions. We simply multiply the dimensions by each other to find the # of cubic centimeters since this would be the same as (cm^1)^3. This gives a unit in cm^3. 4*10*1 is 40 or 40 cm^3.
We are also given that there are 10.49 g/cm^3 meaning in each cm^3 of silver, there are 10.49 grams. We can multiply the # of cm^3 by 10.49 to find the #of grams. 10.49*40 is 419.6 or 419.6 grams.
Finally, we are given that each gram is worth 69 cents or $.69. We simply multiply the # of grams by this value to find the total price. .69*419.6 is 289.52. This is the answer in dollars.
Hope this helps! These types of problems all just come down to unit conversion so focus on what units are being used.
Consider the line y = -5/9x-2
9
Find the equation of the line that is parallel to this line and passes through the point (-9, -4).
Find the equation of the line that is perpendicular to this line and passes through the point (-9,-4
|
Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex] simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]
What is the line that is perpendicular?To find the equation of a line that is parallel to [tex]y = (-5/9)x - 2,[/tex] we need to note that parallel lines have the same slope. The slope of [tex]y = (-5/9)x - 2[/tex] is -5/9, so the slope of the parallel line will also be -5/9.
We can use this information and the given point (-9, -4) to find the equation of the parallel line using the point-slope form of the equation of a line:
[tex]y - y1 = m(x - x1)[/tex]
where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get:
[tex]y - (-4) = (-5/9)(x - (-9))[/tex]
Simplifying and rearranging, we get the equation of the parallel line:
[tex]y = (-5/9)x + (34/9)[/tex]
To find the equation of a line that is perpendicular to y = (-5/9)x - 2, we need to note that perpendicular lines have opposite reciprocal slopes. The slope of y = (-5/9)x - 2 is -5/9, so the slope of the perpendicular line will be 9/5 (the opposite reciprocal).
We can use this information and the given point (-9, -4) to find the equation of the perpendicular line using the point-slope form of the equation of a line:
[tex]y - y1 = m(x - x1)[/tex]
Therefore, where (x1, y1) is the given point and m is the slope of the line. Plugging in the values, we get: [tex]y - (-4) = (9/5)(x - (-9))[/tex] simplifying and rearranging, we get the equation of the perpendicular line: [tex]y = (9/5)x + (16/5)[/tex]
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The following are infinite geometric series. For which infinite series could find the sum using a formula?
A) -2+6+(-18)+54+(-162)+...
B) 3+12+48+192+768+...
C) 1+2+4+8+16+...
D) 8+4+2+1+1/2+...
Answer:
D) 8 + 4 + 2 + 1 + 1/2 + ...
Step-by-step explanation:
The sum of an infinite geometric series can be found when the absolute value of the common ratio, r, is less than 1.
[tex]\boxed{\begin{minipage}{5.5 cm}\underline{Sum of an infinite geometric series}\\\\$S_{\infty}=\dfrac{a}{1-r}$,\quad $|r| < 1$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the first term. \\ \phantom{ww}$\bullet$ $r$ is the common ratio.\\\end{minipage}}[/tex]
To determine which of the given infinite geometric series can be summed using the formula, calculate the value of r for each series. To do this, divide a term by the previous term.
Given infinite geometric series:
-2 + 6 + (-18) + 54 + (-162) + ...[tex]\implies r=\dfrac{6}{-2}=-3[/tex]
As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.
Given infinite geometric series:
3 + 12 + 48 + 192 + 768 + ...[tex]\implies r=\dfrac{12}{3}=4[/tex]
As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.
Given infinite geometric series:
1 + 2 + 4 + 8 + 16 + ...[tex]\implies r=\dfrac{2}{1}=2[/tex]
As r is not in the interval −1 < r < 1, the sum of the infinite series cannot be found using the formula.
Given infinite geometric series:
8 + 4 + 2 + 1 + 1/2 + ...[tex]\implies r=\dfrac{4}{8}=\dfrac{1}{2}[/tex]
As |r| < 1 the sum of the infinite series can be found using the formula.
Therefore, the infinite series for which the sum can be found by using the formula is:
D) 8 + 4 + 2 + 1 + 1/2 + ...Find the area, in square inches, of the composite figure.
A composite figure consisting of an isosceles right triangle, a rectangle, and an another isosceles triangle. The combined length of the right triangle and the rectangle is 25 inches. The length of only the rectangle is 14 inches. The base of the other isosceles triangle, which is the same as the width of the rectangle, is 2 inches plus 2 inches, and the height of the isosceles triangle is 3 inches.
The area of the composite figure is 122.5 square inches
How to find the area of the composite figure.Based on the problem statement, we have the following dimensions from the question
Isosceles right triangle: 11 inchesRectangle: 14 inches by 4 inchesAnother isosceles triangle; Base = 4 inches and Height = 3 inchsThe area of the composite figure is the sum of individual areas
So, we have
Area = Isosceles right triangle + Rectangle + Another isosceles triangle
By applying the formulas, we have
Area = 0.5 * 11 * 11 + 14 * 4 + 0.5 * 4 * 3
Evaluate
Area = 122.5
Hence the area is 122.5 sq inches
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solve by factoring. p^2-4=21. p= 1/4 or 21.
Therefore, the solutions to the equation [tex]p^{2} -4=21[/tex]are p = 3, -3, 7, and -7. Neither 1/4 nor 21 are solutions to this equation.
What is factor?In mathematics, a factor is a number or expression that divides another number or expression without leaving a remainder. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, because these numbers can all divide 12 evenly.
by the question.
We can solve this equation by first moving all the terms to one side of the equation:
[tex]p^{2}[/tex] - 4 = 21
[tex]p^{2}[/tex] = 25
Now, we can factor the left-hand side of the equation by using the difference of squares formula:
(p + 2) (p - 2) = 25
We can now solve for p by setting each factor equal to a possible value of the square root of 25:
p + 2 = 5 or p + 2 = -5
p - 2 = 5 or p - 2 = -5
Solving each of these equations, we get:
p = 3 or p = -7, p = 7 or p = -3
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in vienna were more of the high and low temperatures above or below 0 C justify your answer using a vertical number line
Looking at the data, we can see that both the high as well as low temperatures of Monday, Tuesday, Thursday, & Friday were above [tex]O^{o}C[/tex]. The high on Wednesday was minus zero degrees Celsius.
What is the name for temperature?The most popular scales are indeed the Celsius scale, sometimes known as centigrade, with the unit sign °C, the Franklin level (°F), and the Scale parameter (K), with the latter being mostly used for scientific reasons.
What is the current temperature?The total kinetic energy of a substance's particles is measured by its temperature. 2. An object's kinetic energy increases with increasing temperature. 3. If we add up the instances where the maximum and low temps were in excess of or below zero degrees Celsius, we find:
High temperature above [tex]O^{o}C[/tex]: 5 days
High temperature below [tex]O^{o}C[/tex]: 2 days
Low temperature above [tex]O^{o}C[/tex]: 3 days
Low temperature below [tex]O^{o}C[/tex]: 4 days
Therefore, we can see that overall, there were more days where the temperatures were below [tex]O^{o}C[/tex], both for the high and low temperatures.
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The complete question is:
In Vienna were more of the high and low temperatures above or below [tex]O^{o}C[/tex] justify your answer using a vertical number line
Days high temperature low temperature
Monday 8 0
Tuesday 9 -4.5
Wednesday 4.5 -12
Thursday 9 4.5
Friday 8.5 -6
Saturday 1 -10
Sunday 5 -14
an average bus speed between cape Town to east London was 108 km/h Due to the bad weather, the average speed on the trip back was 72 km/h. Determine how long the outward trip took if the return trip takes 12 hours
Answer:
Let's call the distance between Cape Town and East London "d".
We know that the average speed on the outward trip was 108 km/h, so the time it took to travel from Cape Town to East London can be calculated using the formula:
time = distance / speed
So the time it took on the outward trip can be expressed as:
time = d / 108
We also know that the average speed on the return trip was 72 km/h, and we're told that this trip took 12 hours. So we can use the same formula to find the distance between Cape Town and East London:
d = speed * time
d = 72 * 12
d = 864 km
Now we can use the formula for time again to find how long the outward trip took:
time = d / 108
time = 864 / 108
time = 8 hours
Therefore, the outward trip took 8 hours.
Step-by-step explanation:
express cos 0 as a ratio of given lengths of the right triangle shown
cos θ expressed as a ratio of given lengths of the right triangle is:
cos θ = 12/13
How to express cos θ as a ratio of given lengths of the right triangle?Trigonometry deals with the relationships between the sides and angles of triangles.
The three primary trigonometric functions are sine (sin), cosine (cos), and tangent (tan), which are defined as follows:
Sine (sin): The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse in a right triangle.
Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle.
Tangent (tan): The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side in a right triangle.
Thus, cos θ as a ratio of given lengths of the right triangle can be expressed as:
cos θ = 12/13 (cos = adjacent/hypotenuse)
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Complete Question
The attached image completes the question
What is the area of this triangle
The area of the triangle is 5/2 x sqrt(7) square units, or approximately 6.99 square units.
We need to know the triangle's base and height lengths in order to calculate its area.
Let's give the triangle's vertices the following names:
A is the bottom-left vertex.
B is the vertex at the bottom right.
C is the top vertex.
We can infer from the facts provided that the triangle's base measures AB, or 5 units.
We must draw a perpendicular line from the triangle's vertex C to its base AB in order to get the triangle's height. Let's give the intersection of the perpendicular line and the base the letter D.
Right triangle ACD with CD as the triangle's height now exists. The Pythagorean theorem can be used to determine CD's length:
[tex]AD^2 + CD^2 = AC^2[/tex]
We can determine that AC is 4 units and AD is 3 units based on the facts provided.
When we plug these figures into the formula, we get:
[tex]4^2 = 3^2 + CD^2[/tex]
Simplifying:
16 = 9 + [tex]CD^2[/tex]
[tex]CD^2[/tex] = 7
CD = √7
The triangle's height is therefore √7 units.
The area formula for triangles can now be used:
Area equals ([tex]\frac{1}{2}[/tex]) x base x height.
Adding the values we discovered:
Area equals ([tex]\frac{1}{2}[/tex]) x 5 sq (7)
Area = [tex]\frac{5}{2}[/tex] x sqrt (7)
Hence, the triangle has a surface area of [tex]\frac{5}{2}[/tex] x √7 square units, or roughly 6.99 square units.
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PLEASE HELP ILL GIVE BRAINLY!!
The expressiοn a² + b² = a + b is true when a = 1 and b = 1.
Define the term expressiοn?An expressiοn is a cοmbinatiοn οf variables, numbers, and mathematical οperatiοns that represents a quantity οr value. Expressiοns can be simple οr cοmplex, and they can invοlve a variety οf οperatiοns such as additiοn, subtractiοn, multiplicatiοn, divisiοn, expοnents, and radicals.
a. It is impοssible tο cοmbine the expressiοn √√3x + 2√3x intο a single term because the twο terms have different radical expressiοns. The first term has a dοuble square rοοt, while the secοnd term has a single square rοοt. These cannοt be cοmbined unless simplified first.
b. Ratiοnalizing the denοminatοr means tο eliminate any radical expressiοns frοm the denοminatοr οf a fractiοn by multiplying bοth the numeratοr and denοminatοr by a suitable expressiοn that will result in an integer οr ratiοnal denοminatοr.
c. Let a = 1 and b = 1, then a² + b² = 1² + 1² = 2, and a + b = 1 + 1 = 2. Therefοre, a² + b² = a + b is true when a = 1 and b = 1.
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Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1. shaded area is 0.1949
Answer: To find the indicated z-score for a shaded area of 0.1949 in the standard normal distribution, we need to use a z-table or a calculator with a built-in normal distribution function.
Using a z-table, we can find the z-score that corresponds to a cumulative area of 0.1949 in the standard normal distribution. The z-table gives us the area to the left of the z-score, so we need to look for the area closest to 0.1949 in the body of the table and then interpolate to find the exact z-score.
Looking at the z-table, we find that the area to the left of the z-score 0.88 is 0.8106, and the area to the left of the z-score 0.89 is 0.8159. Since 0.1949 is closer to 0.8106 than to 0.8159, we can estimate that the z-score corresponding to the area 0.1949 is approximately 0.88.
Therefore, the indicated z-score for a shaded area of 0.1949 in the standard normal distribution is approximately 0.88.
Step-by-step explanation:
help please I'll give brainliest
Answer:
k = 16.806404 and k = 95.174404
Step-by-step explanation:
To determine the value of k in which the graph touches, you set both equations equal to each other
4x + k = -x^2 +8x + 20
k = -x^2+4x+20
You can use the quadratic formula -b^2+-(sqrt(b^2-4(a)(c))) / 2a
You will get the values of x = -2.898 and 6.898 for your answers
My bad, I forgot to add also input the values of x in your equation and get k = 16.806404 and k = 95.174404
For the breakfast buffet, Mr. Walker must equally divide 7 loaves of bread between five platters. How many loaves of bread are placed on each platter?
Answer:
the answer to ur question is: 1.4
I will mark you brainiest!
The shape above is NOT a polygon because:
A) There are two segments
B) The Shape includes a curve
C) There is one vertex
D) The shape is closed
answer correctly for brainly and 100 points
The missing reason for the following proof: Corresponding Parts of Congruent Triangles are Congruent (CPCTC).
What is triangle?A triangle is a closed two-dimensional figure with three straight sides and three angles. It is formed by connecting three non-collinear points with straight lines. The sum of the interior angles of a triangle always equals 180 degrees, and the exterior angles of a triangle always add up to 360 degrees. Triangles are one of the fundamental shapes in geometry and have many different classifications based on their side lengths, angles, and other properties.
Here,
In geometry, CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent." It is a property that states that if two triangles are congruent, then their corresponding parts (angles and sides) are also congruent. In other words, if two triangles are the same shape and size, then all of their corresponding angles and sides are equal in measure. This property is often used in geometric proofs to show that two triangles are congruent by demonstrating that their corresponding parts are equal.
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Given: trap. SPQR with SP || QR ; MN is the median of the trap. m∠QRS = 120 ; m∠QPS = 135 ; SP = PQ = 12. Find: MN.
The value οf the median MN fοr the given trapezοid is 70.59 units.
What is the law οf sines?The law οf sines specifies hοw many sides there are in a triangle and hοw their individual sine angles are equal. The sine law, sine rule, and sine fοrmula are οther names fοr the sine law. The side οr unknοwn angle οf an οblique triangle is fοund using the law οf sine.
Any triangle that is nοt a right triangle is referred tο as an οblique triangle. At least twο angles and their cοrrespοnding side measurements shοuld be used at οnce fοr the sine law tο functiοn.
Given that, SPQR is a trapezοid with SP parallel tο QR,
Nοw, we knοw that MN is the average οf the lengths οf the bases SP and QR.
That is,
MN = (SP + QR) / 2.
Fοr the given values we have:
SP = PQ = 12, sο QR = 2MN - SP
Nοw, m∠QRS = 120 and m∠QPS = 135,
Thus,
m∠SPQ = 180 - 120 - 135 = -75.
Hοwever, angles cannοt be negative, sο we add 360 tο get 285 degrees.
Since SPQR is a trapezοid, we knοw that m∠SPQ = m∠QRN. Alsο, since MN is the median οf the trapezοid, it divides the trapezοid intο twο cοngruent triangles, sο m∠QMN = m∠RNM.
Using the law οf sines in triangle QMN tο find MN:
sin(m∠QMN) / MN = sin(m∠MQN) / QN.
Since QN = NR:
sin(m∠QMN) / MN = sin(m∠RNM) / NR.
sin(135) / MN = sin(285) / NR.
NR = sin(285) / sin(135) * MN.
2MN - SP = 2 * sin(285) / sin(135) * MN
2MN - 12 = 2.17MN
MN = 12 / 0.17 = 70.59
Hence, the value οf the median MN fοr the given trapezοid is 70.59 units.
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The diagram shows a molecule of sulfur hexafluoride, the most potent greenhouse gas in the world. Name two different planes that contain line r.
Step-by-step explanation:
ADCF and DEFG
the third pane AECG is perpendicular to line r.
9 x 1/5 = is the answer greater than or less than 9? why?
Step-by-step explanation:
need help with This Math
Answer:
Step-by-step explanation:
Firstly,
angles at the centre of a circle add to 360°. So
[tex](15x-1)+\angle ZVX +(8x-2)+(7x+15)+(3x+5)=360[/tex]
[tex]33x+17+\angle ZVX=360[/tex]
[tex]\angle ZVX=360-33x-17[/tex]
[tex]\angle ZVX=342-33x[/tex]
Secondly,
[tex]\angle YVU+ \angle UVW + \angle WVX =180[/tex]° (since YX is a diameter - angles on a
straight line sum to 180°)
[tex](3x+5)+(7x+15)+(8x-2)=180[/tex]
[tex]18x+18=180[/tex]
[tex]18x=162[/tex]
[tex]x=9[/tex]
Substitute [tex]x=9[/tex] into [tex]\angle ZVX=342-33x[/tex]:
[tex]\angle ZVX=342-33\times9=63[/tex]°
Solution: [tex]\angle ZVX=63[/tex]
The larger triangle is dilated to form the smaller triangle what is the scale factor?
Answer:
The answer is 1/2
Step-by-step explanation:
3 and 6 are the known sides of the triangle as you can see three is half of six making it a 1/2 dilation
[tex]\dfrac{6}{3} = 2[/tex]
the scale factor is
1 : 2
What is μ (∠LMK)? thank you
Answer and Step-by-step explanation:
We can see that because Line K is acting as an Angle Bisector (a line that divides an angle into two angles of equal measures) on angle ∠LMJ, the angles ∠LMK and ∠JMK are equal to each other.
This allows us to solve for angle ∠LMK.
We do this by first setting the angles equal to each other.
10x - 22 = 2x + 66
Now, we want to isolate x by itself. We will subtract 2x from both sides of the equation, and then add 22 to both sides of the equation.
10x - 22 - 2x = 2x + 66 - 2x
8x - 22 = 66
8x - 22 + 22 = 66 + 22
8x = 88
Finally, we will divide both sides of the equation by 8.
8x ÷ 8 = 88 ÷ 8
x = 11
We aren't finished yet, as the question asks to find ∠LMK.
Plug 11 in for x into the equation 10x - 22.
10(11) - 22 =
110 - 22 =
= 88°
So, the measure of angle ∠LMK is 88°.
Have a good day!
What will happen to the graph of the line y = -5/4 x + 3 if you change -5/4 to 5/4 ?
The line's slope on the graph will switch from being negative to positive.
What is a line's Slope Intercept Form?The graph of the equation y = mx + c is a line with m as the slope and m and c as the y-intercept. The values of m and c are actual integers in the slope-intercept illustration of the linear equation.
The slope of a line, measured in m, tells us how steep it is. A line's gradient is also referred to as its slope sometimes. The y-coordinate of the point where the line's graph meets the y-axis is known as the y-intercept of a line, ab.
Analyzing the condition:The slope-intercept form of the equation for the line, y = -5/4 x + 3, is written as y = mx + b. Where,
The line has a slope of m, a y-intercept of 3, a slope of -5/4, and a y-intercept of b.
As a result, the slope has changed from negative to positive if -5/4 is changed to 5/4.
As a result, the graph of the line's slope will switch from being negative to positive.
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Camille is attending a fundraiser. She pays for her admission and buys raffle tickets for
$
5
$5dollar sign, 5 each. If she buys
10
1010 raffle tickets, then she would spend a total of
$
135
$135dollar sign, 135 at the fundraiser.
The number
�
SS of dollars Camille spends at the fundraiser is a function of
�
rr, the number of raffle tickets she buys.
Write the function's formula.
�
=
S=S, equals
The formula for the function is S(r) = -10r² + 130r.
Describe function ?A function can be represented as an equation, a graph, or a table of values. In an equation, the function is usually denoted as "f(x)", where "x" is the input value and "f(x)" is the output value. For example, the equation f(x) = 2x represents a function that takes an input value x and produces an output value that is twice the input value.
Functions can be used to model real-world phenomena and solve various problems in mathematics, science, engineering, economics, and other fields. They are an important concept in calculus and other branches of mathematics, and they have numerous applications in modern technology and industry.
Let the cost of admission be $a and the cost of each raffle ticket be $r. Then we can write the following equation based on the given information:
10r + a = 135
Solving for a, we get:
a = 135 - 10r
Thus, the function that relates the total amount spent to the number of raffle tickets bought is:
S(r) = ar + 5r = (135 - 10r)r + 5r = -10r² + 130r
Therefore, the formula for the function is:
S(r) = -10r² + 130r
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PLEASE HELP DUE TODAY
The question: What theorem would you use to write proportion for this figure?
It's the same question for each problem.
Solve the rational equation symbolically, numerically, or graphically.
the solved equation will be x=7.
What is an Equations?
Equations are mathematical statements with two algebraic expressions on either side of an equals (=) sign. It illustrates the equality between the expressions written on the left and right sides. To determine the value of a variable representing an unknown quantity, equations can be solved. A statement is not an equation if there is no "equal to" symbol in it. It will be regarded as an expression.
2/X-5 - 4/ x+5 =2/ x²-25
[tex]\frac{(x+5)2-4(x-5)}{x^{2} -25}[/tex] = [tex]\frac{2}{x^{2} -25}[/tex]
2x-4x+10+20 = 2
-4x=-28
x=7
Hence, the solved equation will be x=7.
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7) through: (-4,-4), parallel to y=x-1
9) through: (-4,-4), parallel to y=-
y=-x-4
11) through: (5,-2), perp. to y=-x-5
13) through: (-2, 5), perp. to y = x + 2
8) through: (1,0), parallel to y=2x-1
10) through: (5.5), perp. to y
12) through: (3,-2), perp. to y ==
14) through: (-4, 0), perp. to y = -x-2
Answer:
14 is 45
Step-by-step explanation:
the explicit formula for this sequence: 2 6 18 54 162
Answer:
To find the explicit formula for this sequence, we need to determine the common ratio between successive terms. To do this, we can divide any term by the previous term. For example:
6 ÷ 2 = 3
18 ÷ 6 = 3
54 ÷ 18 = 3
162 ÷ 54 = 3
So the common ratio is 3.
Next, we can use the general form of a geometric sequence to find the explicit formula:
a(n) = a(1) * r^(n-1)
where a(n) is the nth term of the sequence, a(1) is the first term, r is the common ratio, and n is the position of the term we want to find.
In this sequence, a(1) = 2 and r = 3. So the explicit formula for this sequence is:
a(n) = 2 * 3^(n-1)
For example, if we want to find the 6th term, we can plug in n = 6:
a(6) = 2 * 3^(6-1) = 2 * 3^5 = 2 * 243 = 486
Therefore, the 6th term of the sequence is 486.
in the number 423, 36/ the
underline 3 is blank times blank
Than the other 3.
Answer:
I'm sorry, but the question is unclear. Can you please provide more context or information so that I can understand what you are asking?
From 2014-2015 to 2024-2025, the number of students enrolled in an associate degree program is projected to increase by 21.5%. If the enrollment in associate degree programs in 2014-2015 is 6,500,000 , find the increase and the projected number of students in an associate degree program in 2024-2025.
PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answer:
27.5
Step-by-step explanation:
Mr. Davies opened a new retail store. During the first week, 360 customers visited the store. During the second week,
300 customers visited the store.
What is the percentage change of the number of customers that visited the store in the first week to the number of customers that
visited the store in the second week?
OA. a 20% decrease
OB. a 16.7% increase
OC. a 20% increase
OD. a 16.7% decrease