I need help please and thank you
(A AND B ARE NOT ANSWERS THEY ARE SEPARATE PROBLEMS)
Answers
Answer:
Part a) Wayne's savings before he spent $28 was $31.08
Part b) Stef's savings after she spent $28 was $9.29
Step-by-step explanation:
Part a)
Let
x ----> original amount of Wayne's savings
y ----> original amount of Stef's savings
we know that
Original ratio
[tex]\frac{x}{y}=\frac{5}{6}[/tex]
[tex]x=\frac{5}{6}y[/tex] ----> equation A
After spending $28 each
[tex]\frac{x-28}{y-28}=\frac{1}{4}[/tex]
Multiply in cross
[tex]4x-112=y-25\\y=4x-112+25[/tex]
[tex]y=4x-87[/tex] ----> equation B
substitute equation A in equation B
[tex]y=4(\frac{5}{6}y)-87[/tex]
solve for y
[tex]\frac{20}{6}y-y=87[/tex]
[tex]\frac{7}{3}y=87[/tex]
[tex]y=37.29[/tex]
Find the value of x
[tex]x=\frac{5}{6}(37.29)=31.08[/tex]
so
The original amount of Wayne's savings was $31.08 and the original amount of Stef's savings was $37.29
therefore
Wayne's savings before he spent $28 was $31.08
Part b) Find Stef's savings after she spent $28
Subtract $28 from the original savings
so
$37.29-$28=$9.29
therefore
Stef's savings after she spent $28 was $9.29
Related Questions
What is the area of the shaded region?
Answers
Answer:
[tex]\large \boxed{\text{21.86 ft}^{2}}[/tex]
Step-by-step explanation:
Area of shaded region = area of square - area of semicircle
1. Area of square
A = s² = (6 ft)² = 36 ft²
2. Area of semicircle
Area of circle = πr²
Area of semicircle = ½πr²
r = 3 ft, so
A = ½π(3 ft)² = ⁹/₂π ft³
3. Area of shaded region
A = area of square - area of semicircle
[tex]\begin{array}{rcl}A & = & \mathbf{\left(36 - \dfrac{9}{2} \pi \right )} \textbf{ ft}^{\mathbf{2}}\\\\ &\approx & \left (36 - 14.1372\right)\text{ ft}^{2}\\ & \approx & \mathbf{21.86}\textbf{ ft}^{\mathbf{2}} \\\end{array}\\\text{The area of the shaded figure is approximately $\large \boxed{\textbf{21.86 ft}^{\mathbf{2}}}$}[/tex]
What are all possible functions from 1 to 9
Answers
Answer:
In mathematics, a function (f) is a relationship between a given set X (called domain) and another set of elements Y (called codomain) so that each element x of the domain corresponds to a single element f (x) of the domain (the that form the route, also called scope ranking).
See: Relations and functions
In everyday or simpler language, we will say that mathematical functions are equivalent to the common logical process that is expressed as "dependent on."
Mathematical functions can refer to everyday situations, such as: the cost of a phone call that depends on its duration, or the cost of sending a parcel that depends on its weight.
As an example, what would be the rule that relates the numbers on the right with those on the left in the following list ?:
1 --------> 1
2 --------> 4
3 --------> 9
4 --------> 16
The numbers on the right are the squares of those on the left.
The rule is then to "square":
1 --------> 1
2 --------> 4
3 --------> 9
4 --------> 16
x --------> x 2.
To refer to this rule we can use a name, which is usually the letter f (of function). So, f is the rule "square the number".
Usually two notations are used:
x --------> x 2 or f (x) = x 2.
Thus, f (3) means applying the rule f to 3. Doing so results in 3 2 = 9.
Then f (3) = 9. Similarly f (2) = 4, f (4) = 16, f (a) = a 2, etc.
Equivalent expressions 3.7r - 1.5r =
Answers
Answer:
2.2r
Step-by-step explanation:
3.7r - 1.5r =
= r(3.7 - 1.5)
= r×2.2
= 2.2r
Yo sup??
given expression: 3.7r-1.5r
3.7r-1.5r
=3.7r+(-1.5r)
=2.2r
Hope this helps.
Which of the following sets of numbers could be the side lengths of a right triangle? 5, 12, 13 5, 5, 9 14, 14, 14 2, 3, 5
Answers
Answer:
5,12,13
Step-by-step explanation:
i think thats what the other person meant to say, either way, these numbers are correct
Answer: 5, 12, 13
Step-by-step explanation:
Louise completed the work shown below.
(5x3 + 3)2 = (5x3)2 + (3)2 = 25x6 + 9
Determine if Louise’s answer is correct. Explain.
Answers
Louise’s answer is not correct
Step-by-step explanation:
Let us revise how to solve (ax + b)²
Square the 1st term ⇒ (ax)²Multiply the 1st term, the 2nd term and 2 ⇒ 2(ax)(b)Square the 2nd term ⇒ (b)²(ax + b)² = (ax)² + 2(ax)(b) + (b)²The answer of square a binomial contains three terms: (1st)² + 2(1st)(2nd) + (2nd)²
∵ The bracket is (5x³ + 3)²
- Square the first term
∴ The first term of the answer = (5x³)² = (5)²(x³)² = [tex]25x^{6}[/tex]
- Multiply the 1st , the 2nd term and 2
∴ The second term of the answer = 2(5x³)(3) = 2(5)(3)x³ = 30x³
- Square the 2nd term
∴ The third term of the answer = (3)² = 9
∴ (5x³ + 3)² = [tex]25x^{6}[/tex] + 30x³ + 9
∵ Louise’s answer is (5x³)² + (3)² = [tex]25x^{6}[/tex] + 9
- By comparing the his answer with the answer above, he did
not find the middle term
∴ Louise’s answer is not correct
Learn more:
You can learn more about expand a binomial in brainly.com/question/2334388
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Answer:
Sample Response: Louise’s answer is not correct. She is missing the term 30x3. When squaring a binomial, it is best to write the product of the binomial times itself. Then you can use the distributive property to multiply each term in the first binomial by each term in the second binomial. Louise also could have used the formula for a perfect square trinomial, which is found by squaring a binomial.
Step-by-step explanation:
Sample Response ^^^
2 adjacent angles of a parallelogram are (2x+45°) and (4x-15°) . What is the value of x?
Answers
Value of x is 25°
Step-by-step explanation:
Step 1: Adjacent angles of a parallelogram are supplementary. Therefore their sum is equal to 180°⇒ (2x + 45°) + (4x - 15°) = 180°
⇒ 6x + 30° = 180°
⇒ 6x = 150°
⇒ x = 25°
Step-by-step explanation:
Adjacent angles of a parallelogram are Supplementary.
[tex] \therefore \: (2x + 45 \degree) + (4x - 15 \degree) = 180 \degree \\ \\ \therefore \: 6x + 30 \degree = 180 \degree \\ \\ \therefore \: 6x = 180 \degree - 30 \degree \\ \\ \therefore \: 6x = 150 \degree \\ \\ \therefore \: x = \frac{150 \degree }{6} \\ \\ \huge \red{ \boxed{\therefore \: x = 25 \degree }}[/tex]
Gabbys age is two times mikhails age.the sum of their ages is 75. What is mikhails age
Answers
Answer:
Mikhail's age is 25 years old
Step-by-step explanation:
Let's make an equation: Say Mikhail is x, so Gabby would be 2*x=2x
If the sum of their ages equals 75, then x+2x=75, and x=2x=3x, so 3x=75.
75/3=25
Final answer:
Gabby's age is twice Mikhail's age, and the sum of their ages is 75. By setting up and solving a system of equations, we can determine that Mikhail's age is 25.
Explanation:
To solve this problem, we can set up a system of equations using the information given. Let's say Gabby's age is represented by 'G' and Mikhail's age is represented by 'M'. We know that G = 2M and the sum of their ages is 75, so we can write the equation G + M = 75. Now we have a system of equations:
G = 2M and G + M = 75.
To solve this system, we can substitute the value of G from the first equation into the second equation: 2M + M = 75. Combine like terms: 3M = 75. Divide both sides by 3: M = 25. So Mikhail's age is 25 years old.
Find x, y, and z. For number 24
Answers
x = 32, y = 11.31, z = 33.94
Step-by-step explanation:
Step 1: Let the triangle be ΔABC with B as the right angle. Let the hypotenuse be intersected by the altitude drawn from B at D. So there are 3 triangles, ΔABC, ΔADB and ΔBDC.
Step 2: To find x, y and z, use Pythagoras theorem where square of hypotenuse is equal to sum of squares of the other two sides of the right triangle.
Step 3: Make equations based on the theorem for all 3 triangles.
In ΔABC, (4+x)² = 12² + z²
⇒ 16 + 8x + x² = 144 + z²
⇒ x² + 8x - z² = 128 --------- (1)
In ΔADB, 12² = 4² + y²
⇒ 144 = 16 + y²
⇒ y² = 128 ------- (2)
In ΔBDC, z² = x² + y²
⇒ z² = 128 + x² ------ (3)
Substituting (3) in (1) ⇒ x² + 8x - (128 + x²) = 128
⇒ x² + 8x - 128 - x² = 128
⇒ 8x = 256
⇒ x = 32
From (3), z² = 128 + 32² = 128 + 1024 = 1152
⇒ z = 33.94
From (2), y² = 128
⇒ y = 11.31
Help ASAP..........
John and Mary went to the airport last Sunday. John took a bus first, and it took him 30 min to reach the train station. Then he got on a train and it took him 55 min to reach the airport. Mary left home 25 min later than John. She took a taxi and she reached the airport 20 min earlier than John. How long did it take Mary to get to the airport
Answer with full steps
Answers
Answer:
Mary reached the airport in 40 minutes
Step-by-step explanation:
1. Let's review the information given to us to answer the question correctly:
Time it takes John to go from home to the train station = 30 minutes
Time it takes John to go from the train station to the airport = 55 minutes
Mary left 25 minutes later and reached the airport 20 minutes earlier than John
2. How long did it take Mary to get to the airport?
Total time it takes John to reach the airport = Time it takes John to go from home to the train station + Time it takes John to go from the train station to the airport
Total time it takes John to reach the airport = 30 + 55
Total time it takes John to reach the airport = 85 minutes
Now, let's calculate the time it takes Mary to reach the airport, this way:
Total time it takes John to reach the airport - minutes Mary left later - minutes Mary got to the airport earlier than John
85 - 25 - 20 = 85 - 45 = 40
Mary reached the airport in 40 minutes
Answer: Mary got to the airport in 40 Minutes.
Simplify the expression (9 + 21)(9 – 21).
Answers
Answer:
-360
Step-by-step explanation:
1. Add 9 + 21 and subtract 9 - 21
2. That would be (30)(-12)
3. Then multiply 30 x -12
4. You get -360
What does x equal in
-0.4 (x+3)=4
Answers
Answer:
x=-13
Step-by-step explanation:
1. Divide both sides by -0.4
2. Subtract -3 on both sides.
3. -10-3=-13
Solve for X: 5 - (x+5) > -2(x+4)
Answers
Answer:
value of x is greater than -8.
Step-by-step explanation:
5-(x+5)>-2(x+4)
we need to find value of x.
consider
5-(x+5)>-2(x+4)
using distributive property, we get
5-x-5>-2x-2×4
5-x-5>-2x-8
nowsimplify both side
-x+2x>-8
transfer -2x form RHS To LHS
-x+2x-8
x>-8
therefor, value of x is greater than-8.
IM KINDA SLOWWWWW sorry
Answers
For the square root of 48, you can simplify it by finding two numbers; one of them having a perfect square and whatever number you choose for the second one, you find numbers there with one number having a perfect square. So for example, I would do 4*12 since it’s the easiest one I know. 4 has a square root of 2. However, with twelve, you can find two numbers that multiply to it with one of them with a perfect square, which would be 4*3,(again 4 having a perfect square root). So you would multiply 2 from the first 4(when you square rooted it), and the second 2( from 4*3). You should get 4 √ 3. The little sign means square root by the way. And if u wanna make sure they are equivalent, you can find the square root of 48 and find the product of 4 times the square root of 3. They should give the same answer.
You cannot simplify the square root of 15 as there are no two numbers with one of them having a perfect square.
You can simplify the square root of 100, that gives you 10.
This may not have helped, but I tired to explain it the best I could. Let me know if u want another explanation :)
You run around a park 18 times. Each lap is 1/6 mile. How many miles do you run
Answers
Answer:3
Step-by-step explanation:
Divide 18 by 6
Answer:
3 miles
Step-by-step explanation:
If each lap is one mile, 18 times = 1/6 + 1/6 + ... + 1/6. This is equal to 18*1/6 by definition of multiplication, and 18*1/6 = 18 divided by 6 because fractions are just big division symbols. This gives 3 or 3 miles.
What is 8x to the second power plus 10x
Answers
hope this helps!
The expression [tex]8x^2 + 10x[/tex] factors to [tex]2x(4x + 5)[/tex] and has solutions x = 0 and x = -5/4.
We first need to understand what it represents. In this expression, [tex]x[/tex] is the variable, and the terms [tex]8x^2[/tex] and [tex]10x[/tex] are polynomial terms where:
[tex]8x^2[/tex] indicates that the variable [tex]x[/tex] is raised to the power of 2, meaning it is multiplied by itself ([tex]x \times x[/tex]) and then scaled by a factor of 8.
[tex]10x[/tex] means that the variable [tex]x[/tex] is multiplied by 10.
The first term is [tex]8x^2[/tex].
The second term is [tex]10x[/tex].
In this case, the terms are not like terms because one is [tex]x^2[/tex] and the other is [tex]x[/tex]. Therefore, they cannot be combined further. The expression is simplest as it stands, which is: [tex]8x^2 + 10x[/tex]
Factoring out [tex]2x[/tex] gives us:
[tex]2x(4x + 5)[/tex]
Thus, [tex]8x^2 + 10x[/tex] can also be expressed as [tex]2x(4x + 5)[/tex]. This is useful if you are trying to find the roots of the equation (setting it equal to zero) since it can help identify the values of [tex]x[/tex] that satisfy the equation [tex]8x^2 + 10x = 0[/tex].
This gives two possible solutions for x:
2 * x = 0 which leads to x = 0
4 * x + 5 = 0 which leads to x = -5/4
Walter struggles to write legibly and has a difficult time putting his thoughts on paper. Which learning disability does he have?
Answers
Dysgraphia learning disability . Dysgraphia is a neurological disease in which a person struggles to express their ideas in writing form appropriate to their age and mental capacity .
What is meant by dysgraphia?Children who have dysgraphia typically have confusing, uneven handwriting that varies in slant, form, upper- and lower-case letters, as well as cursive and print styles. They also have a tendency to copy or write things slowly.
Dysgraphia is a neurological disease in which a person struggles to express their ideas in writing form appropriate to their age and mental capacity even after receiving proper instruction and schooling. Various signs of dysgraphia might appear at various ages. It is regarded as a learning disability.
The disorder's origin is uncertain, however in adulthood, parietal lobe injury is frequently a contributing factor. Treatment for motor abnormalities to help control writing movements may be part of dysgraphia treatment, which varies. Other therapies could deal with memory loss or other neurological issues.
To learn more about Dysgraphia refer to:
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help asap please!!!!!!!
Answers
Answer:
VW=30, WX=20, YW=30,ZX=20
Step-by-step explanation:
20 PPOINTS SOMEONE PLEASE HELP ME ON #11 pleaseeee
Answers
Answer:
Set #9 are congruent triangles.
Step-by-step explanation:
They are the same shape and size. If I were to flip them over, they would mach up.
Answer:
cap its only 10
Step-by-step explanation:
how do you do number 5 please.
Answers
Answer:
2.4 kg
Step-by-step explanation:
Given
dog eats 0.3 kg of dog food each day
hence we can say that the unit rate is 0.3 kg per day
1 day ------> eats 0.3 kg
8 days -------> eats 0.3 kg x 8 = 2.4 kg
Answer:
2.4 kilogram
Step-by-step explanation:
If
1 day = 0.3kg
8day =
0.3 multiply by number of days
0.3kg * 8= 2.4kg
what is the answer to 10+7x
Answers
Answer:if u I simplified then 17x
Step-by-step explanation:
Like terms are 10+7=17+x=17x
For all values of x, which expression is equivalent to x + 1 − x + 2x + x + 1?
Answers
Answer:
3x+2
Step-by-step explanation:
We want to find an expression that is equivalent to:
[tex]x+1-x+2x+x+1[/tex]
We regroup similar terms to get:
[tex]x-x+2x+x+1+1[/tex]
We now combine the similar terms to obtain:
[tex]3x+2[/tex]
Therefore the expression that is equivalent to: x + 1 − x + 2x + x + 1 is [tex]3x+2[/tex]
Answer:
3x + 2
Step-by-step explanation:
3x + 2
Solve by simplifying the given expression OR substitute 1 for x in each expression.
x + 1 − x + 2x + x + 1 → x − x + 2x + x + 2 → 3x + 2
OR
x + 1 − x + 2x + x + 1 → 1 + 1 − 1 + 2(1) + 1 + 1 = 5
3x + 2 → 3(1) + 2 = 5
write a number with two decimal places that are bigger than 4 1/5 but smaller than 4.25
Answers
Answer:4.21,4.22,4.23, 4.24
Step-by-step explanation:
4 1/5 is 4.2 as a decimal and the numbers between 4.2 and 4.5 as numbers with 2 places past the decimal place are the ones above.
The number with two decimal places that are bigger than 4(1/5) and smaller than 4.25 is 4.22.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
4(1/5)
= 21/5
= 4.2
Now,
Two decimal numbers between 4.2 and 4.25.
4.21, 4.22, 4.23, and 4,24.
Thus,
The number is 4.22.
Learn more about expressions here:
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Three plants grew 3/4 feet. How much did they grow in all
Answers
Answer:
2 and 1/4
Step-by-step explanation:
If Greg but 10 pieces of candy for $5.20 How much will it be for one piece of
Answers
Answer:
One piece of candy costs $0.52.
Step-by-step explanation:
5.2/10=0.52
what is the solution ? Please help with this !!
Answers
Answer:
the answer is c
Step-by-step explanation:
see picture
write the ratio 2/7 to 4 as a fraction in simplest form
Answers
Answer:
1/14
Step-by-step explanation:
2/7 to 4 means 2/7 to 4/1
This gives
2/7
4/1
rearranging, we have;
2/7 * 1/4
2 * 1
7 * 4
= 2/28
to reduce to the simplest form, we'll divide the numerator and denominator by 2 ( the HCF of both)
1/14
To write the ratio 2/7 to 4 as a fraction in simplest form, multiply both the numerator and denominator of 2/7 by 4. Simplify the resulting fraction by dividing both the numerator and denominator by their common factor, which is 4. The simplest form of the ratio is 2/7.
Explanation:To write the ratio 2/7 to 4 as a fraction in simplest form, we need to multiply both the numerator and denominator of 2/7 by 4. This gives us (2 * 4) / (7 * 4) = 8/28. Since both 8 and 28 have a common factor of 4, we can simplify the fraction further.
Dividing both the numerator and denominator by 4, we get 8/28 = 2/7.
Therefore, the ratio 2/7 to 4 as a fraction in simplest form is 2/7.
Learn more about Simplifying fractions here:https://brainly.com/question/26436699
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I don’t understand how to get the answer
Answers
x = –5 or x = 3
Solution:
Given expression:
[tex]|-1-x|=4[/tex]
[tex]\Rightarrow |-x-1|=4[/tex]
⇒ –x – 1 = 4 or –x – 1 = 4
First take –x – 1 = 4.
Add 1 on both side of the equation.
⇒ –x – 1 + 1 = 4 + 1
⇒ –x = 5
Divide by –1 on both side of the equation, we get
⇒ x = –5
Now take –x – 1 = –4.
Add 1 on both side of the equation.
⇒ –x – 1 + 1 = –4 + 1
⇒ –x = –3
Divide by –1 on both side of the equation, we get
⇒ x = 3
x = –5 or x = 3
Hence the two values of x are –5 or 3.
Set up and solve a proportion 6/100=s/12
Answers
Amount of tax on the book (s) is $0.72
Step-by-step explanation:
Step 1: Given 6/100 = s/12Step 2: Cross multiply to solve for s⇒ 6 × 12 = 100 × s
⇒ 72 = 100s
⇒ s = 72/100 = 0.72
If PQR measures 75°, what is the measure of SQR?
Answers
Answer: the measure of SQR is 53°
solve for x.
Brainlest for anyone who helps!!
thanks you
Answers
================================================
Explanation:
If points F and E are the midpoints of segment VU and segment ST respectively, then segment FE is the midsegment of the trapezoid. The midsegment is parallel to the bases, and the midsegment's length is found by adding up the bases VS and UT, then dividing by 2.
(VS + UT)/2 = FE
(29 + x+17)/2 = 23 ... plug in given info; isolate x
(x+46)/2 = 23
x+46 = 23*2 ... multiply both sides by 2
x+46 = 46
x = 46-46 ... subtract 46 from both sides
x = 0