3 combinations:
3 quarters and 6 dimes
5 quarters and 1 dime
1 quarter and 11 dimes
1) Remember that a dime corresponds to $0.10 and a quarter to $0.25. And the value we want to find is $1.35
2) As we can see the last digit on $1.35 is 5 then we can infer that we're going to need an odd number of quarters ($0.25). Also, notice that we need whole numbers for the quantities of each coin. In other words, multiples of 0.10 and 0.25 whose sum yields to $1.35. So let's do it step by step:
So, we can write out the following list of combinations:
q (quarter) 3 q = 3 x 0.25 = $ 0.75
d (dimes) 6 d = 6 x 0.10 = $ 0.60
0.60 + 0.75 = 1.35
2.2) Another possible combination:
q (quarter) 5 q = 5 x 0.25 = $ 1.25
d (dimes) 1 d = 1 x 0.10 = $ 0.10
0.10+1.25= 1.35
2.3)
q (quarter) 1 q = 1 x 0.25 = $ 0.25
d (dimes) 11 d = 11x 0.10 = $ 1.10
0.25+1.10 = 1.35
3) Hence, considering that we need to combine dimes and quarters and their sum must be lesser than $1.35 We have three combinations with whole numbers of dimes and quarters:
3 quarters and 6 dimes
5 quarters and 1 dime
1 quarter and 11 dimes
Rewrite the function by completing the square. f (x)= x^2 - 9x + 14
f (x) = _ ( x + _ )^2 + _
Answer:
f(x) = 1(x - 4.5)² - 6.25
Step-by-step explanation:
Hello!
Let's find the Vertex Form of the quadratic by Completing the Square.
f(x) = x² - 9x + 14x² - 9x + 14 = 0x² - 9x = -14The formula for a Perfect Square Trinomial is (a+b)² = a² + 2ab + b².
To find b², we need to divide -9 by 2 and square it.
-9-4.520.25Add this number to both sides and factor. Remember, the b term here is simply half of the b term in the equation (-4.5).
x² - 9x + 20.25 = -14 + 20.25(x - 4.5)² = 6.25(x - 4.5)²- 6.25 = 0Convert this back to function form:
f(x) = 1(x - 4.5)² - 6.25The equation is f(x) = 1(x - 4.5)² - 6.25.
6. sin D - Ог F 25 ot E 7. cos F. 24 8. sin F Nodule 13
In the given triangle :
FD = 25, FE = 7, DE = 24
SinD
From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,
So, the SinD is express as :
[tex]\begin{gathered} \sin D=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin D=\frac{FE}{DF} \\ \sin D=\frac{7}{25} \end{gathered}[/tex]sin D = 7/25
cos F
From the trignometric ratio of cos : It expresses as the ratio of measurement of the side adjacent to the angle and to the hypotenuse of the triangle
So, the Cos F is express as :
[tex]\begin{gathered} \cos F=\frac{Adjacent\text{ side}}{Hypotenuse} \\ \cos F=\frac{FE}{DF} \\ \cos F=\frac{7}{25} \end{gathered}[/tex]cos F = 7/25
Sin F
From the trignometric ratio of sin: It express as the ratio of measurement of the side opposite to the angle to the measurement of hypotenuse of triangle DEF,
so, Sin F is express as :
[tex]\begin{gathered} \sin F=\frac{Opposite\text{ side}}{Hypotenuse} \\ \sin F=\frac{DE}{DF} \\ \sin F=\frac{24}{25} \end{gathered}[/tex]sin F = 24/25
Answer :
sin D = 7/25
cos F = 7/25
sin F = 24/25
URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS!!!!!!!!
Answer:
Option 2
Step-by-step explanation:
hope this helps
Find the Value of interval [0,2pie] such as that tan s= -radical3/3
The values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
What is trigonometry and how is it assessed?
Simply put, trigonometric functions—also referred to as circular functions: are the functions of a triangle's angle. This means that these trig functions provide the relationship between the angles and sides of a triangle. Sine, cosine, tangent, cotangent, secant, and cosecant are the fundamental trigonometric functions. Numerous trigonometric identities and formulas indicate the relationship between the functions and aid in determining the triangle's angles.
The quadrants determine the values of the trigonometric functions.
Given, tan s = -(√3)/3 ⇒ tan s = -(√3)/(√3)² ⇒ tan s = (-1)/(√3)
Therefore, the simplified value of tangent of s is tan s = (-1)/(√3)
Again the interval of the function is [0, 2π), so only the second and fourth quadrants can contain the given value of tangent being negative.
For the value of s in second quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (π - (π/6)) ⇒ tan s = tan (5π/6) ⇒ s = 5π/6
For the value of s in the fourth quadrant, we have:
tan s = (-1)/(√3) ⇒ tan s = tan (2π - (π/6)) ⇒ tan s = tan (11π/6) ⇒ s = 11π/6
Thus, the values of s in the interval [0, 2π) such that tan s = -(√3)/3 are 5π/6 and 11π/6.
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Given f(x), find g(x) and h(x) such that f(x)= g(h(x)) and neither g(x) nor h(x) is solely x.
Given:
[tex]\begin{gathered} f(x)=g(h(x)) \\ f(x)=\sqrt[]{-4x^2-3}+2 \end{gathered}[/tex]Solve :
[tex]g(h(x)=\sqrt[]{-4x^2-3}+2[/tex]The function g(x) convert then x is equal to h(x) then:
[tex]\begin{gathered} h(x)=-4x^2 \\ g(x)=\sqrt[]{x-3}+2 \end{gathered}[/tex]Fastex Shoes claims that it has designed a new range of lightweight shoes that allow athletes to run faster than they can using any other shoes.SportsPlus, a rival shoe manufacturer, then came up with a design that it claims performs even better than Fastex's design. A sports magazinedecided to test the claims. It created two groups of 15 randomly selected athletes each. Members of both groups were pretested anddetermined to have equal athletic ability. Additionally, they followed the same nutrition plan and training program during the study.The athletes did a 1-mile run to test the shoes. The magazine found that the athletes who used Fastex shoes had reduced their 1-mile run timeby an average of 396, and athletes who used Sports Plus shoes had reduced their 1-mile run time by an average of 2%.Given the magazine's data collection method and findings, what conclusion can be made?OA. The data collection method used was fair since both shoe designs were tested on identical parameters.OB. The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.OC. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than theathletes given SportsPlus shoes.OD. The data collection method used was random since the athletes in the two groups used two different shoe designs.
B: The data collection method used was nonrandom since the athletes using Fastex shoes may have trained better.
This is false because they followed the same nutrition plan and training program during the study.
C. The data collection method used was unfair since the athletes given Fastex shoes may have been better runners than the athletes given SportsPlus shoes.
This is also false because members of both groups were pretested and determined to have equal athletic ability
D. Each group used one shoe design.
So, the correct option is A
Part A. 150% of what number is 156 Part B. 4.4 is 5.5% of what number
EXPLANATION
Since 150% represents a percentage bigger than 156, the appropiate relationship would be as follows:
[tex]Part\text{=}\frac{\text{Percentage}}{100}\cdot\text{Whole}[/tex]Where the whole number is 156 and the percentage is 150%:
[tex]\text{Part}=\frac{150}{100}\cdot156[/tex][tex]\text{Part}=1.5\cdot156=234[/tex]In conclusion, the solution is 234
A pianist plans to play 4 pieces at a recital from her repertoire of 25 pieces, and is carefully consideringwhich song to play first, second, etc. to create a good flow. How many different recital programs arepossible?
Given 25 pieces of repertoire, if a pianist plans to play 4 pieces at a recital and is considering playing which song to play first, second, etc, the possible ways is,
[tex]^{25}P_4=\frac{25!}{(25-4)!}=\frac{25!}{21!}=303600\text{ possible recital programs}[/tex]Hence, the different recital programs possible is 303600
Find the measure of the arc or central angle indicated. Assume that lines which appear to bediameters are actual diameters.
From the given circle, the measure of the arc or the central angle indicated is as shown at the center of the circle is subtended by the arc
Hence, the measure of the arc or central angle indicated is 65° ,Option B
Find R on line segment NM that is 1/4 the distance from N(-3,-3) toM(2, 3).R(x, y) =
The distance on the x-coordinate from N to M is:
distance = 2 - (-3) = 2 + 3 = 5
Because 2 is the x-coordinate of M and -3 is the x-coordinate of N
Then, 1/4 of the distance is:
1/4*distance = (1/4)*5 = 5/4 = 1.25
So, the x-coordinate of R is:
(x-coordinate of N) + (1/4*distance) = -3 + 1.25 = -7/4 = -1.75
At the same way, the distance on the y-coordinae from N to M is:
distance = 3 - (-3) = 3 + 3 = 6
Then, 1/4 of the distance is:
1/4*distance = (1/4)*6 = 6/4 = 1.5
So, the y-coordinate of R is:
(y-coordinate of N) + (1/4*distance) = -3 + 1.5 = -1.5
Answer: R(x, y) = (-1.75, -1.5)
simplify 3^5×3^4.a. 3×20b. 3^9c. 6^9d. 3^20I think its b but I am unsure.
Recalling the laws of exponents:
[tex]a^m\cdot a^n=a^{m+n}[/tex]So, for the number 3^5 times 3^4, we have:
[tex]3^5\cdot3^4=3^{5+4}=3^9[/tex]Therefore, the answer is the option b) 3^9.
Miles east of 100 80 60 40 20 1 2 3 4 5 6 7 8 9 10 Time (hours) Where were the two cars in relation to each other when they began traveling? O A. Car B was 5 miles east of car A. O B. Car B was 20 miles east of car A. O C. Car Awas 15 miles east of car B. D. Car A was 5 miles east of car B. < PREVIOUS
Car B was 5 miles east of car A, Option A
Please help me step by step
The value of the function f(x) at x = 0 is found as -1.
What is meant by the term function?A function is described as the connection between such a set of inputs that each have one output. A function is a relationship between inputs in which each input is linked to exactly one output. Every function does have a domain and a codomain, as well as a range. In general, a function is denoted by f(x), where x would be the input. A function's general representation is y = f(x). In mathematics, a function is a special relationship between inputs (the domain) and outputs (the codomain), where each input has precisely one output and the output could be traced all the way back to its input.For the given question,
The graph of the function f(x) = -x² + 4x - 1 is given.
For finding the value of f(x) at x = 0, check the y-coordinate of the graph when x = 0.
Put x = 0 in the given function.
f(0) = -0² + 40 - 1
f(0) = - 1
Thus, the value of the function f(x) at x = 0 is found as -1.
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The formula k=5/9(f-32)+273.15 converts temperature of the object in a laboratory is cooled to 1.5 kelvin. What is the temperature of the object in degrees fahrenheit?
The temperature of the object is -456.97 degrees
i need help, im confused
Answer:
2
Step-by-step explanation:
can someone please help!!!
The simplified expression is as follows:
[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]
How to simplify expression?The expression can be simplified as follows:
To simplify an expression means to write an equivalent expression which contains no similar terms.
This means that we will rewrite the expression with the fewest terms possible.
Therefore,
[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } }[/tex]
The expression can be represented as follows:
3x⁶ / 14y⁹ ÷ 33x⁴ / 10y²
3x⁶ / 14y⁹ × 10y² / 33x⁴
Hence,
3x⁶ / 14y⁹ × 10y² / 33x⁴ = 30x⁶y² / 462x⁴y⁹
Therefore,
30x⁶y² / 462x⁴y⁹ = 10x² / 154y⁷ = 5x² / 77y⁷
Hence,
[tex]\frac{\frac{3x^{6} }{14y^{9} } }{\frac{33x^{4} }{10y^{2} } } = \frac{5x^{2} }{77y^{7} }[/tex]
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12.Work backwards to write a quadratic equation that will have solutions of x = -1/2 and x = 4. (Your equation must only have integer coefficients, meaning no fractions or decimals.)
In general, a quadratic equation can be written in terms of its solutions:
[tex]y=(x-a)(x-b).[/tex]Now, notice that:
[tex]x+\frac{1}{2}=0\text{ }[/tex]when x= -1/2, and it is equivalent to:
[tex]2x+1=0.[/tex]Therefore, you can write the quadratic equation as:
[tex]y=(2x+1)(x-4).[/tex]Computing the above multiplication, you get:
[tex]y=2x^2-8x+x-4.[/tex]Simplifying the above equation you get:
[tex]y=2x^2-7x-4.[/tex]Answer: [tex]y=2x^{2}-7x-4[/tex]You need 30 ounces of chocolate chips to bake some cooldes. You already have 8 ounces of chocolate chips at home. Write an inequality that could beused to find how many ounces of chocolate chips you need to buy.whats the inequality:
Given:
Amount of chocolate chips needed = 30 ounces
Amount of chocolate you have already = 8 ounces
Let's find the inequality that can be used to find the ounces of chocolate chips you need to buy.
To write the inequality, we have:
8 + x ≥ 30
Where x represents the ounces of chocolate chips you need to buy.
Therefore, the inequality that could be used to fid how many ounces of chocolate chips needed is:
8 + x ≥ 30
ANSWER:
8 + x ≥ 30
and In an experiment, the probability that event A occurs is 3/5 the probability that event B occurs is 3/4 and the probability that events A and B occur is 3/7what is the probability that A occurs given that B occurs
So ABC and DEF are the same triangle, this question is asking me to write an equation between the relationships of DEF. How do I write that?
Explanation
The first step is to draw a representation of the given parameters.
Since this is a right-angle triangle, the Pythagorean theorem applies. This can be seen below;
[tex]\text{Longest Leg}^2=sum\text{ of the square of the short legs}[/tex]We can then apply it to the sides of the triangle.
DF is the longest side. Therefore,
Answer
[tex]DF^2=DE^2+EF^2[/tex]пеу Fabric Sale At a fabric store, fabrics are sold by the yard. A dressmaker spent $46 on 5 yards of silk and cotton fabrics for a dress. 1 x + y = 5 117x + 4y = 46) Silk is $17 per yard and cotton is $4 per yard. Here is a system of equations that represent the constraints in the situation. What does the solution to the system represent?
It is said that the dressmaker bought 5 yards of cotton and silk. Let's see the first equation of the system:
[tex]x+y=5[/tex]And that he spent $46 on those 5 yards. Also, it is said that silk costs $17 per yard and cotton $4 per yard. Let's see the second equation of the system:
[tex]17x+4y=46[/tex]If 46 is how much the dressmaker spent, and 17 and 4 represent how much silk and cotton cost PER YARD then we know that x and y represent how much of each fabric did the dressmaker bought. Also, in the first equation you see that the total is 5 yards. So, if you solve this system you will find that 'x' is how many yards of silk the dressmaker bought and 'y' is how many yards of cotton he bought.
In summary, the solution of this system represents how may yards of silk (x) and cotton (y) the dressmaker bought.
10) f(x) = x5 - 10x4 + 42x3 -124 x2 + 297x - 306; zero: 3i ? A) 2, -3i, -4 - i, -4 + i C) 2, -3i, 4 - i, 4 + i B) -2, -3i, -4 -i, -4 + i D) -2, -3i, 4-i, 4 + i
Answer
Option C is correct.
The roots of the given function include
2, -3i, (4 + i), (4 - i)
Explanation
To solve this, we would put the given roots of the solution into the place of x. The ones that give 0 are the roots of the expression
The expression is
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
Starting with 2
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(2) = 2⁵ - 10(2)⁴ + 42(2)³ - 124(2)² + 297(2) - 306
= 32 - 160 + 336 - 496 + 594 - 306
= 0
So, 2 is a root
-3i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(-3i) = (-3i)⁵ - 10(-3i)⁴ + 42(-3i)³ - 124(-3i)² + 297(-3i) - 306
= -243i - 810 + 1134i - 1116 - 891i - 306
= 0
So, -3i is also a root
4 + i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(4 + i) = (4 + i)⁵ - 10(4 + i)⁴ + 42(4 + i)³ - 124(4 + i)² + 297(4 + i) - 306
= 0
So, we know that the right root, when inserted and expanded will reduce the expression to 0.
4 - i
f(x) = x⁵ - 10x⁴ + 42x³ - 124x² + 297x - 306
f(4 - i) = (4 - i)⁵ - 10(4 - i)⁴ + 42(4 - i)³ - 124(4 - i)² + 297(4 - i) - 306
= 0
Inserting any of the other answers will result in answers other than 0 and show that they aren't roots/zeros for this expression.
Hope this Helps!!!
Solve the inequalities|4x + 5| + 2 > 10
We have to solve this inequality:
[tex]\begin{gathered} |4x+5|+2>10 \\ |4x+5|>10-2 \\ |4x+5|>8 \end{gathered}[/tex]We now use the properties of the absolute value. We will have two boundaries: one corresponding to when 4x+5 is negative and the other is when 4x+5 is positive.
When 4x+5 is negative, the absolute value function will change the sign of the expression, so we will have:
[tex]\begin{gathered} -(4x+5)>8 \\ -4x-5>8 \\ -4x>8+5 \\ -4x>13 \\ x<\frac{13}{-4} \\ x<-3.25 \end{gathered}[/tex]The other interval will be defined when 4x+5 is positive. In this case, the absolute function does not change the sign and we get:
[tex]\begin{gathered} 4x+5>8 \\ 4x>8-5 \\ 4x>3 \\ x>\frac{3}{4} \\ x>0.75 \end{gathered}[/tex]Then, the solution set is the union of the intervals x < -3.25 and x > 0.75.
We can express the interval as (-∞, -3.25) ∪ (0.75, ∞).
Answer: (-∞, -3.25) ∪ (0.75, ∞)
Classify each set of measures as AAS, ASA, SSA, SAS, or SSS. Then find the indicated length or angle measure (to the nearest tenth).
Hello there. To solve this question, we'll have to remember some properties about triangles.
Given the triangle:
Notice in this case we have two consecutive angles and a side between them. This is a case of ASA (angle-side-angle).
With respect to the side with measure x, we have two consecutive angles then the side, hence AAS.
To find x, we'll have to apply the law of sines:
[tex]\dfrac{A}{\sin(\alpha)}=\dfrac{B}{\sin(\beta)}=\dfrac{C}{\sin(\gamma)}=2R[/tex]In this case, the angle opposite to x measures 73º and the angle opposite to 4 measures 85º, hence:
[tex]\dfrac{x}{\sin(73^{\circ})}=\dfrac{4}{\sin(85^{\circ})}[/tex]Multiply both sides by a factor of sin(73º)
[tex]x=\dfrac{4\sin(73^{\circ})}{\sin(85^{\circ})}[/tex]Using a calculator, we get the following approximation (rounding to the nearest tenth):
[tex]x\approx3.8[/tex]This is the measure of x we're looking for.
3: Select the correct equation for the given situation. Then, select the solution for that equation. Two research submarines start to rise vertically toward the ocean surface. The Tri-I sub is at 4,863 feet below sea level (or -4,863 feet) and is ascending 81.1 feet per minute. The Quad-II sub is at 3,645 feet below sea level (or -3,645 feet) and is ascending 76.9 feet per minute. If the ocean surface is at 0 feet, how many minutes (m) must elapse for the two submarines to reach the same depth? m = 290 minutes m = 145 minutes m = 53.8 minutes 4,863 - 76.9m = 3,645 - 81.1m O -4,863 + 81.1m = - 3,645 + 76.9m 0 - 4, 863 + 76.9m = -3, 645 + 81.1m – 4, 863 – 81.2m 2 – 3, 645 + 76.9m Om < 53.8 minutes
Unknown, the correct equation is:
- 4,863 + 81.1m = - 3,645 + 76.9m
And to solve for m, you use the standard form:
Like terms:
81.1m - 76.9m = -3,645 + 4,863
4.2m = 1,218
Answer:Nuts
Step-by-step explanation:
green on green
A person standing 306 feet from the base of a church observed the angle of elevation to the church’s steeple to be 20°. How tall is the church. Give answer to the nearest whole number
Solution
- The solution steps are given below:
[tex]\begin{gathered} \text{ Applying SOHCAHTOA, we have:} \\ \frac{h}{306}=\tan20 \\ h=306\tan20 \\ \\ h=111.374...ft\approx111ft\text{ \lparen To the nearest whole number\rparen} \end{gathered}[/tex]Final Answer
111 ft
Set up the equation for the following word problem and solve the equation. Let y be the unknown number.81 times a number minus 77 is equal to - 77 less than the number.Step 1 of 2: Write out the equation,
The equation of the word is,
[tex]undefined[/tex]Which is the upper left quadrant on the coordinate plane?A coordinate plane.Quadrant IQuadrant IIQuadrant IIIQuadrant IV
The quadrants on the coordinate plane are the following:
then, we have that the upper left quadrant is quadrant II
As a town gets smaller, the population of its high school decreases 6% each year. The senior class has 320 students now. In how many years will the high school have 100 students?
From the details provided, we know that the population of the town gets smaller, that is, a decline and not a growth. The annual rate of decline (or decay) is 6% (or 0.06). The formula for this is given as shown below;
[tex]y=a(1-r)^x_{}[/tex]The variables here are;
[tex]\begin{gathered} a=\text{initial value} \\ r=\text{rate of decline} \\ x=\text{period (in years)} \end{gathered}[/tex]The equation to represent the decline of this town's student population shall be;
[tex]\begin{gathered} y=320(1-0.06)^n \\ Simplified,\text{ we now have;} \\ y=320(0.94)^n \end{gathered}[/tex]When the population ofnthe town becomes 100, then we can replace variable y with 100. Since the formula is used to find the current population, and we have been given the population after a certain number of years, then our y is now 100.
We can now determine the number of years (variable n) that it takes before the population declines to 100 as shown below;
then our y is now 100.
We can now
how many inches are in 20 centimeters?
We know that an inch is equivalent to 2.54 centimeters, then if we want to know how many inches are in a centimeters we do this:
[tex]a\times\frac{1inch}{2.54\operatorname{cm}}[/tex]In this case, we have 20 centimeters, then replacing a by 20 we find the equivalent inches to 20 like this:
[tex]20\text{cm}\times\frac{1inch}{2.54\operatorname{cm}}\approx7.87\text{inches}[/tex]