The original price of the dress purchased by Suzie is given by the equation A = $ 32
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the original price of the dress be A
Now , the equation will be
The cost of the purchase = $ 27.20
The percentage of the cost of purchase = 85 %
So ,
The original price of the dress x percentage of the cost of purchase = cost of the purchase
Substituting the values in the equation , we get
A x ( 85/100 ) = 27.20
On simplifying the equation , we get
Multiply by 100 on both sides of the equation , we get
85A = 2720
Divide by 85 on both sides of the equation , we get
A = 2720/85
A = $ 32
Therefore , the value of A is $ 32
Hence , the original price of the dress is $ 32
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Kaitlin is on her way home in her car. She has driven 30 miles so far, which is two-thirds of the way home. What is the total length of her drive?
Graph 24x+25=−6y+7 .
After 2 1/4 h, a chainsaw has used 2 13/16 gal of fuel. How many gallons of fuel did the chainsaw use each hour? Enter your answer as a mixed number in simplest form in the box.
Answer:
1 1/4 or 5/4 gallon per hour.
Step-by-step explanation:
Fuel used in 2 1/4 hour = 2 13/16 gallon
Fuel used in 9/4 hour = 45 / 16 gallon
Fuel used in one hour = [tex]\frac{\frac{45}{16}}{\frac{9}{4}}[/tex]
= 5 / 4 gallon per hour = 1 1 /4 gallon per hour
Thus, teh fuel used in each hour is 1 1/4 gallon or 5 / 4 gallon.
(HURRY!!!)
What is the slope of a line that is perpendicular to the line shown on the graph?
A)-2
B)-1/2
C)1/2
D)2
Answer:
slope of perpendicular line = [tex]-\frac{1}{2}[/tex]
Step-by-step explanation:
Find the slope of a line that is perpendicular to the line shown on the graph
To find slope of the given line , we pick two points from the graph
(0,1) and (1,3)
[tex]slope = \frac{y_2-y_1}{x_2-x_1} =\frac{3-1}{1-0} = 2[/tex]
Slope of given line = 2
slope of perpendicular line = negative reciprocal of slope of given line
slope of perpendicular line = [tex]-\frac{1}{2}[/tex]
What is 27 divided by 735
A flowchart proof presents a logical argument using blank_____.
Answer: A flowchart proof presents a logical argument using boxes and arrows.
Step-by-step explanation:
We know that a flowchart proof is a way of representation of a mathematical proof that includes a logical series of statements ( or can say arguments) in boxes with connecting arrows.
i.e. we use boxes and arrows in a flow chart proof.
By the definition of flowchart proof, the complete sentence will be : A flowchart proof presents a logical argument using boxes and arrows.
Use the unit circle to find tan sin 90
a.1
b.0
c.-1
d.undefined
To evaluate tan(sin(90°)), first determine sin(90°) which equals 1. However, tan(1) is not a standard unit circle value, and if the question intended to find tan(90°), this would be undefined.
The correct option is (d).
The question is asking to use the unit circle to find the value of tan(sin(90°)).
Firstly, the sin(90°) on the unit circle is 1, as the sine function corresponds to the y-coordinate of the unit circle at that angle. Therefore, sin(90°) = 1.
Now, we need to find the tangent of this value, which is tan(1). However, tan(1) is not solvable by standard unit circle values, so it seems we may have a misunderstanding in the question. If the intention was to find tan(90°) instead, then the answer would be undefined as the tangent function at 90 degrees is undefined due to division by zero.
Find the first six terms of the sequence.
a1 = 4, an = 2 • an-1
The 24 students in Mr. Brown’s homeroom sold 72 magazine subscriptions. The 28 students in Mrs. Garcia‘s homeroom sold 98 magazine subscriptions. Whose homeroom sold more magazine subscriptions per student? Explain your reasoning.
If BC = 7 and CD = 24, find AC.
Answer:
2√42 ≈ 12.961
Step-by-step explanation:
All of the right triangles are similar, so ...
short leg/long leg = BC/AC = AC/CD
AC² = BC·CD = 7·24 = 168
AC = √168 = 2√42
What is the area of a triangle whose vertices are J(−2, 1) , K(4, 3) , and L(−2, −5) ?
Enter your answer in the box.
we know that
The Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides. The formula is equal to
[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
where
a,b,c -----> are the lengths of the sides of a triangle
p ----> is half the perimeter
we have
[tex]J(-2,1)\ K(4,3)\ L(-2,-5)[/tex]
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step 1
Find the distance JK
[tex]J(-2,1)\ K(4,3)[/tex]
Substitute the values in the formula of distance
[tex]d=\sqrt{(3-1)^{2}+(4+2)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(6)^{2}}[/tex]
[tex]dJK=\sqrt{40}\ units[/tex]
Step 2
Find the distance KL
[tex]K(4,3)\ L(-2,-5)[/tex]
Substitute the values in the formula of distance
[tex]d=\sqrt{(-5-3)^{2}+(-2-4)^{2}}[/tex]
[tex]d=\sqrt{(-8)^{2}+(-6)^{2}}[/tex]
[tex]dKL=10\ units[/tex]
Step 3
Find the distance JL
[tex]J(-2,1)\ L(-2,-5)[/tex]
Substitute the values in the formula of distance
[tex]d=\sqrt{(-5-1)^{2}+(-2+2)^{2}}[/tex]
[tex]d=\sqrt{(-6)^{2}+(0)^{2}}[/tex]
[tex]dJL=6\ units[/tex]
Step 4
Find the perimeter of the triangle
we know that
the perimeter of a triangle is the sum of the length sides of the triangle
so
[tex]P=dJK+dKL+dJL[/tex]
substitute the values
[tex]P=\sqrt{40}\ units+10\ units+6\ units=22.32\ units[/tex]
Find half the perimeter
[tex]p=22.32/2=11.16\ units[/tex]
Step 5
Find the area of the triangle
Applying the Heron's Formula
[tex]Area=\sqrt{p(p-a)(p-b)(p-c)}[/tex]
we have
[tex]p=11.16\ units[/tex]
[tex]a=dJK=\sqrt{40}\ units=6.32\ units[/tex]
[tex]b=dKL=10\ units[/tex]
[tex]c=dJL=6\ units[/tex]
substitute the values
[tex]Area=\sqrt{11.16(11.16-6.32)(11.16-10)(11.16-6)}[/tex]
[tex]Area=\sqrt{11.16(4.84)(1.16)(5.16)}[/tex]
[tex]Area=17.98\ units^{2}[/tex]
[tex]Area=18\ units^{2}[/tex]
therefore
the answer is
The area of the triangle is [tex]18\ units^{2}[/tex]
The area of the triangle with given vertices is 18 units squared.
Explanation:To find the area of a triangle with given vertices, we can use the formula:
Area = 1/2 * |(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2))|
Plugging in the coordinates of the vertices:
A = 1/2 * |(-2 * (3 - (-5)) + 4 * (-5 - 1) + (-2) * (1 - 3))|
Simplifying the expression:
A = 1/2 * |(-2 * 8 + 4 * (-6) + (-2) * (-2))|
A = 1/2 * |(-16 - 24 + 4)|
A = 1/2 * |-36|
A = 1/2 * 36
A = 18
Therefore, the area of the triangle is 18 units squared.
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Paulo scored "x" on his first math test, then scored 10 points higher on his second, scored 5 points lower on the third than the second, and scored half as well on the fourth test as the second. if his average for the four tests is 75 points, what did he score on the second test?
HELP!!
A vendor has 14 balloons for sale: 7 are yellow, 3 are red, and 4 are green. A balloon is selected at random and sold. If the balloon sold is yellow, what is the probability that the next balloon selected at random is also yellow?
7 over 14
7 over 13
6 over 14
6 over 13
Answer:
6 over 13
Step-by-step explanation:
its right i took the test
How many real solutions does the equation have?
r2 – 94 = 0
The quadratic equation r² – 94 = 0 has two real solutions, as the discriminant is positive when applying the quadratic formula.
Explanation:The question deals with the quadratic equation r2 – 94 = 0. To determine how many real solutions this equation has, we can rearrange it into the standard quadratic form ar2 + br + c = 0, where a = 1, b = 0, and c = -94. The real solutions of a quadratic equation are found using the quadratic formula, which is r = −b ± √(b2 - 4ac) / (2a). In this case, the discriminant (b2 – 4ac) becomes (02 – 4(1)(-94)) which simplifies to 376. This expression is a quadratic equation of the form at² + bt + c = 0, where the constants are a = 1, b = 0, and c = -94. To find the number of real solutions, we need to determine the discriminant, which is given by the formula: discriminant = b² - 4ac. If the discriminant is greater than zero, the equation has two real solutions. If the discriminant is equal to zero, the equation has one real solution. If the discriminant is less than zero, the equation has no real solutions. In this case, the discriminant is: 0 - 4(1)(-94) = 376. Since the discriminant is greater than zero, the equation r² - 94 = 0 has two real solutions. Since the discriminant is positive, this equation has two real solutions.
The equation has two real solutions.
Explanation:This expression is a quadratic equation of the form where the constants are To find the number of real solutions, we can use the discriminant, which is given by . If Δ > 0, there are two real solutions. If Δ = 0, there is one real solution. If Δ < 0, there are no real solutions. Let's calculate the discriminant:
Δ = 0² - 4(1)(-94) = 376
Since Δ > 0, the equation has
Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. the students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. researchers found that visually impaired students averaged 8.14 hours of sleep, with a standard deviation of 1.78 hours. assume that the number of hours of sleep for these visually impaired students is normally distributed.
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23: keith is driving from reno to kansas city to meet his girlfriend. the distance between the two cities is 1,650 miles. if keith can average 50 miles per hour, how many hours will it take him to complete his trip?
divide total miles by speed
1650 / 50 = 33
it will take 33 hours
With nothing but nick and pennies in his pocket , Rupert can afford 77 cents worth of candy. If he has 21 coins in his pocket how many coins does he have of each type
Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle. if the measure of the vertex angle is 18, find the measure of each base angle.
The measure of each base angle is 81.
What is Triangle?A triangle is a three-sided polygon that consists of three edges and three vertices.
Given,
Sports a pennant for the sports teams at lincoln high school is in the shape of an isosceles triangle.
An isosceles triangle is a triangle in which two sides are equal.
Given that the measure of the vertex angle is 18
We need to find the measure of each base angle.
By angle sum property the sum of three angles is 180 degrees.
x+x+18=180
2x+18=180
Subtract 18 from both sides
2x=180-18
2x=162
Divide both sides by 2
x=81
Hence, the measure of each base angle is 81.
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Is this the correct way to fill out this deposit slip? (For an assignment) I have yet to put my name and date
If two chords are the same distance from the center of a circle then they are
If two chords are the same distance from the center of a circle then they are congruent.
Given that, two chords are the same distance from the center of a circle.
What is the chord on a circle?The chord of a circle is a line that connects two points that are located on the circumference of the circle. These two points can be located anywhere on the same circumference.
Chords are equidistant from the center if and only if their lengths are equal. Equal chords are subtended by equal angles from the center of the circle.
Hence, if two chords are the same distance from the center of a circle then they are congruent.
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Which expression is equal to 3√54−4√24 ?
Final answer:
The expression 3√54−4√24 simplifies to √6 after factoring out the perfect squares under the radicals and combining like terms.
Explanation:
The student's question requires simplifying the expression 3√54−4√24. To simplify a square root, we look for perfect squares that are factors of the number under the root. For √54, we can notice that 54 = 9 * 6, and since √9 is a perfect square, we have 3√54 = 3*√9*√6 = 3*3*√6 = 9√6. Similarly, for √24, it is 24 = 4 * 6, so √24 = √4*√6 = 2*√6, and thus -4√24 = -4*2*√6 = -8√6. Combining these two results, we have 9√6− 8√6, which simplifies to √6. Therefore, the simplified expression is √6.
What is the measure of angle a
Answer:
m∠A = 70°
Step-by-step explanation:
The given figure is nothing but parallel lines cut by a transversal.
We use property of transversal to find the value of angle A.
Here ∠A and 110° are pair of interior angles on the same side.
The pair of interior angles on the same side add upto 180 degrees.
Therefore, ∠A + 110 = 180
Subtract 110 from both sides, we get
∠A + 110 - 110 = 180 -110
∠A = 70°
m∠A = 70°
Mary made $126 for 7 hours of work
At the same rate, how much would she make for 18 hours of work?
what is 13n-6p-11n=2p solve for n
Lisa and Bart spin this spinner 60 times the result are below/ black=17 blue=15 orange=21 purple=7 a. What is the experimental probability of a spin of orange? B which color had an experimental probability that matched its theoretical probability
[tex]\text{Answer: a) }P(\text{ getting an orange )}=\frac{7}{20}[/tex]
b) Blue color had an experimental probability that matched its theoretical probability.
Explanation:
Since we have given that
Number of times this spinner is spinned = 60
Number of times black occur = 17
Number of times blue occur = 15
Number of times orange occur = 21
Number of times purple occur = 7
a) So, Experimental probability of a spin of orange is given by
[tex]P(\text{ getting an orange }=\frac{\text{ Number of times orange occur}}{\text{total number of times the spinner spins}}\\\\P(\text{ getting an orange})}=\frac{21}{60}=\frac{7}{20}[/tex]
b) which color had an experimental probability that matched its theoretical probability.
According to theoretical probability ,
Every event must have equal probability, i.e. [tex]\frac{1}{4}[/tex]
And,
[tex]P(\text{ getting blue color)}=\frac{15}{60}=\frac{1}{4}[/tex]
So, Blue color had an experimental probability that matched its theoretical probability.
PQ and RS are two lines that intersect at point T, as shown below: Two lines PQ and RS intersect at point T. Angles PTR and STQ are shown congruent. Which statement is used to prove that angle PTR is always equal to angle STQ?
Lines PQ and RS do not have a fixed length.
Angle PTR and angle PTS are supplementary angles.
Lines PQ and RS intersect at an angle less than a right angle.
Angle PTR and angle PTS are complementary angles.
Answer:
B. Angle PTR and angle PTS are supplementary angles.
Step-by-step explanation:
As R, T, S are collinear and PQ intersects RS at T, so ∠RTP and ∠STP are supplementary angles.
[tex]\Rightarrow m\angle RTP+m\angle PTS=180^{\circ}[/tex] -------1
As P, T, Q are collinear and RQ intersects PQ at T, so ∠PTS and ∠QTS are supplementary angles.
[tex]\Rightarrow m\angle PTS+m\angle QTS=180^{\circ}[/tex] ------2
Subtracting equation 1 and 2,
[tex]\Rightarrow m\angle RTP+m\angle PTS-m\angle PTS-m\angle QTS=180^{\circ}-180^{\circ}[/tex]
[tex]\Rightarrow m\angle RTP-m\angle QTS=0[/tex]
[tex]\Rightarrow m\angle RTP=m\angle QTS[/tex]
[tex]\Rightarrow m\angle PTR=m\angle STQ[/tex]
Therefore, to prove that angle PTR is always equal to angle STQ the statement needed is angle PTR and angle PTS are supplementary angles.
If the temperature is 64.4 degrees Fahrenheit, what is the temperature in degrees Celsius?
18
3.8
53.6
58.3
Answer:
[tex]18^{\circ}C[/tex]
Step-by-step explanation:
Given :The temperature is 64.4 degrees Fahrenheit
To Find : What is the temperature in degrees Celsius?
Solution:
The temperature is 64.4 degrees Fahrenheit
To convert in into Celsius
Formula : [tex]T(^{\circ}C) =(T(^{\circ}F)-32) \times \frac{5}{9}[/tex]
Substitute the vale
[tex]T(^{\circ}C) =(64.4-32) \times \frac{5}{9}[/tex]
[tex]T(^{\circ}C) =(32.4) \times \frac{5}{9}[/tex]
[tex]T(^{\circ}C) =18^{\circ}C[/tex]
So, Option A is true
Hence the temperature in degrees Celsius is [tex]18^{\circ}C[/tex]
A line contains the points (34, 12) and (32, 48) .
What is the slope of the line in simplified form?
Answer:
-18
Step-by-step explanation:
Which expression is equivalent to 5 . 4 × 0 . 18 5.4×0.18?
A. ( 54 × 18 ) × ( 1 10 × 1 100 ) (54×18)×(110×1100)
B. ( 54 × 18 ) × ( 1 10 × 1 10 ) (54×18)×(110×110)
C. ( 5 . 4 × 0 . 18 ) × ( 1 10 × 1 10 ) (5.4×0.18)×(110×110)
D. ( 5 . 4 × 0 . 18 ) × ( 1 10 × 1 100 )
5.4 x 0.18 can be expressed as [tex](54 * 18) * (1/10 * 1/10)[/tex], where each 1/10 returns the decimal point stripped from 5.4 and 0.18 initially. So the correct answer is option B.
Explanation:The appropriate approach to solving this question is by acknowledging how numbers with decimal points function on multiplication. To express 5.4 x 0.18 in another form, we can take the decimal points away and multiply the resultant figures, 54 and 18. Then, we introduce the decimal points back using fractions equivalent to 0.1 and 0.01 (that is, 1/10 and 1/100, respectively). Hence, the correct equivalent is option B: [tex](54 * 18) * (1/10 * 1/10).[/tex] The 1/10 accounts for the decimal in 5.4, and the other 1/10 accounts for the decimal in 0.18.
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