Yolanda's was 25 years old when they were married.
Step-by-step explanation:
Let,
Age of Xavier = x
Age of Yolanda = x + 4
Combined age = 126
According to given statement;
Xavier's age + Yolanda's age = 126
[tex]x+(x+4)=126\\x+x+4=126\\2x=126-4\\2x=122\\[/tex]
Dividing both sides by 2
[tex]\frac{2x}{2}=\frac{122}{2}\\x=61[/tex]
Yolanda's age = x+4 = 61+4 = 65
Age when married = 65 - 40 = 25
Yolanda's was 25 years old when they were married.
Keywords: word problems, addition
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John is driving around town. When he reaches the gas station, he notes that he has traveled 20 miles. He reaches home 2 hours later and notes that he has traveled 30 miles.
If d represents the distance and t represents the time, in hours, John has traveled since the gas station, which of the following equations can be used to model this situation?
Answer:
[tex]d=5t+20[/tex]
Step-by-step explanation:
The equation that will model this situation will be of the form
[tex]d=mt+b[/tex]
where [tex]t[/tex] is the time in hours john has traveled since the gas station, and [tex]d[/tex] is the distance.
Now we know that John has already traveled 20 miles when he is at the gas station, this means at [tex]t=0[/tex], [tex]d=20[/tex]; or
[tex]20=m(0)+b[/tex]
[tex]\boxed{b=20}[/tex]
Thus we have
[tex]d=mt+20[/tex].
Now we need to figure out [tex]m.[/tex]
When John reaches home 2 hours later he notes that he has traveled 30 miles, which means he has traveled 30 - 20 = 10 miles; thus we have
[tex]m= \frac{\Delta d}{\Delta t} =\frac{10 miles}{2hours} =5[/tex]
[tex]\boxed{m=5}[/tex]
Now we have the full equation:
[tex]\boxed{d=5t+20}[/tex]
The equation A = x(x-4) describes the area, A, of a rectangular flower garden, where x is the width in feet.
What would be the width in feet of the flower garden if the area is 12 square feet?
A.2
B.6
C.4
D.7
Answer:
The flower garden width would be 6 ft
Step-by-step explanation:
A = 12 ft^2 = x(x + 4) becomes:
x^2 + 4x - 12 = 0, or (by completing the square) x^2 + 4x + 4 - 4 - 12 = 0
Thus, we have (x + 2)^2 - 16 = 0, or (x + 2)^2 = 16
Taking the square root of both sides yields x + 2 = ±4.
In this context only a positive x value makes sense: x = 2 + 4 => x = 6.
The flower garden width would be 6 ft. The other dimension would be 6 - 4, or 2, ft.
To find the width of the flower garden when the area is 12 square feet, the equation A = x(x-4) is used. Solving for x, the width of the flower garden is 6 feet.
To find the width of the flower garden when the area is 12 square feet:
Plug in A=12 into the equation: 12 = x(x-4)
Solve the equation for x by factoring or using the quadratic formula
The possible values for x are 6 and -2, but since width can't be negative, the width of the flower garden is 6 feet (B)
Delia is hosting a BBQ. She buys a total of 50 burgers and Hot Dogs for $90. Delia pays $2 per burger and $1.50 per Hot Dog. Write a system of linear equations to find the number x of burgers and the number y of Hot Dogs Delia buys. Solve the linear system by substitution. Please help-
A wire 18 ft long is cut into two pieces. Each piece is bent into the shape of a square. The perimeter of the larger square is twice the perimeter of the smaller square. Find the perimeter of the larger square.
Answer:
12
Step-by-step explanation:
18/3=6
If one piece is twice as large as the other, than 18 needs to be divided by 3, making it exact.
Answer:12
Step-by-step explanation:
Perimeter of a square =4L
Perimeter of larger square is twice the perimeter of square =2x4L=8L
Wire length =18ft
Wire length =sum of the two perimeterr
18=4L+8L
18=12L
L=18/12
L=1.5
Perimeter of larger square=8L
Replace Lwith 5
Perimeter of larger square =8x1.5
Perimeter of larger square =12ft
Find the perimeter of a rectangle whose dimensions are 15 inch times 8 inches
What is the radius of a circle with the equation x2 + y2 – 14x + 10y = 250?
Answer:
18
Step-by-step explanation:
x^2 + y^2 – 14x + 10y = 250
x^2 -14x + y^2 + 10y = 250
x^2 - 14x + (-7)^2 + y^2 + 10y + (5)^2 = 250 + (-7)^2 + (5)^2
(x-7)^2 + (y + 5)^2 = 250 + 49 + 25
(x-7)^2 + (y + 5)^2 = 324
Comparing with the general circle (x - b)^2 + (y - a)^2 = r^2
we have; r^2 = 324
r = square root(324)
r = 18
Help me please I really don’t get this
Answer:
y equals 45, because you substitute the x in the bigger equation with -2, and then solve for y
One gallon of paint usually covers about 350 square feet. How many square feet will 2.5 gallons cover? Show your
work, including labeling your answer with the appropriate units of measure.
Answer:875 feet
350÷2=175
350+350+175=875
Step-by-step explanation:
A sky jump makes an angle of 27° with respect to the water as shown below. How are the 27° angle and the unknown angle related? What is the value of X?
Answer:
153
Step-by-step explanation:
The figure shows a right triangle with acute angle of 27°, this angle is the angle between the water level and the ski ramp.
It is also shown the suplementary angle 27° marked as X°, which is the angle that you must determine.
In the figure is clear that x is the exterior angle of the corner with the angle of 27° and that X° + 27° = 180°.
Then you can solve for X.
X = 180° - 27° = 153°.
Answer: 153°
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At time t = 0, a football player kicks a ball from the point A with position vector (2i + j) m on a horizontal football field. The motion of the ball is modelled as that of a particle moving horizontally with constant velocity (5i + 8j) m s–1.
Find
(a) the speed of the ball,
(b) the position vector of the ball after t seconds.
The point B on the field has position vector (10i + 7j) m.
(c) Find the time when the ball is due north of B.
At time t = 0, another player starts running due north from B and moves with constant speed v m s–1. Given that he intercepts the ball,
(d) find the value of v.
(e) State one physical factor, other than air resistance, which would be needed in a refinement of the model of the ball’s motion to make the model more realistic.
Final answer:
To solve these physics problems, we used vector mathematics to find the speed of the ball, its position after a certain time, the time it aligns with a certain point, and the speed of a player to intercept it. Additionally, we considered gravity as a factor for a more realistic model of the ball's motion.
Explanation:
Speed of the ball: To find the speed of the ball, we calculate the magnitude of the velocity vector (5i + 8j) m/s using the Pythagorean theorem, which results in \(\sqrt{5^2 + 8^2} = \sqrt{89}\) m/s.
Position vector after t seconds: We calculate the position vector at time t by using the initial position vector (2i + j) m and adding the product of the velocity vector and time t. This yields the formula (2i + j) + t(5i + 8j).
Time when the ball is due north of B: For the ball to be due north of B, their i-components must be equal. Given B's position vector is (10i + 7j), we set the i-component equal to 10 and solve for t, getting t = (10 - 2)/5 = 1.6 seconds.
Value of v for the running player: Since the player intercepts the ball after 1.6 seconds, and the ball's j-component of the velocity is 8 m/s, the player's velocity v must be the distance covered in the j direction divided by time, which is (8j - 7j)/1.6 = 0.625 m/s.
Physical factor for a more realistic model: One physical factor to make the model more realistic could be the effect of gravity on the ball's trajectory, which would cause the ball to follow a parabolic path rather than a straight line.
Find the common difference for the given sequence. Type a numerical answer in the space provided. Do not include
spaces in your answer. If necessary, use the key to represent a fraction bar
105, 110, 115, 120.
Answer: -5
Step-by-step explanation:
Answer: 5
Step-by-step explanation:
The formula for calculating common difference is given by :
[tex]t_{2}[/tex] - [tex]t_{1}[/tex] = [tex]t_{3}[/tex] - [tex]t_{2}[/tex] = [tex]t_{4}[/tex] - [tex]t_{3}[/tex]
Where [tex]t_{1},t_{2}[/tex] are the terms given .
from the sequence given :
[tex]t_{1}[/tex] = 105
[tex]t_{2}[/tex] = 110
[tex]t_{3}[/tex] = 115
[tex]t_{4}[/tex] = 120
Therefore : common difference will be
110 - 105 = 5
115 - 110 = 5
120 - 115 = 5
Therefore , 5 is the common difference
Liam wants to buy a car. He has $100. The car that he wants costs $120,000. His parents is willing to give him $1,300. How long will it take him to get enough money to buy the car?
one fourth of the students in Mrs. Bennett's class have blue eyes. Two eighths of the students have green eyes. Does the class have an equal number of students with blue and green eyes.
Yes
No
Answer:
Yes
Step-by-step explanation: 2/8 is eq equivalent to 1/4 when reduced to the lowest term(i.e form)
Yes, this is because 2/8 is equivalent to one fourth, this is because eighths are fourths cut in half, so, you only need two of them to make a one right.
Hope this helps, if not, comment below please!!!
Holly spilled 1/4 of her 2-liter bottle of soda How much soda does she have left?
Answer:
3/4
Step-by-step explanation:
im a big brain so yea
A test is worth 50 points. Multiple-choice are worth 1 point and short answer questions are worth 3 points. If a test has 20 questions how many multiple choice questions are there
Answer:
5 multiple choice questions
Step-by-step explanation:
Write equations to represent the situation.
let "x" be the number of multiple choice questions
let "y" be the number of short answer questions
Equation for the total number of questions:
x + y = 20 # of multiple choice questions + # of short answer questions
Equation for the total points: (Multiply the type of question with how many points you get.)
x + 3y = 50 You don't need to write '1' beside 'x' for multiplying by 1.
The system of equations we need to solve is:
x + y = 20 and x + 3y = 50
We can solve using the substitution method.
Rearrange x + y = 20 to isolate one variable.
Isolate 'y'.
x + y = 20
x - x + y = 20 - x Subtract 'x' from both sides
y = 20 - x
Take the other equation x + 3y = 50. You can replace 'y' with the equation that equals 'y' that we got when rearranging.
Substitute y for 20 - x
x + 3y = 50
x + 3(20 - x) = 50 Use distributive property. Multiply the 3 outside the bracket by each number inside the bracket.
x + 60 - 3x = 50 Combine like terms. 'x' and '-3x' are alike because they both have 'x'.
60 - 2x = 50 Start isolating 'x'.
60 - 60 - 2x = 50 - 60 Subtract 60 from both sides.
-2x = 50 - 60 60-60 cancels out on the left side.
-2x = -10
-2x/-2 = -10/-2 Divide both sides by -2 to isolate 'x'.
x = -10/-2 -2x/-2 becomes 'x'. -2/-2 cancels out.
x = 5 Number of multiple choice questions
Therefore there are 5 multiple choice questions.
If you needed the number of short answer questions too, you would substitute x for 5 in any of the other equations.
select the correct answer
Answer:
???
Step-by-step explanation:
Where's the problem/question?
I NEED THE ANSWER ASAP PLEASE
Answer:
720$
Step-by-step explanation:
(1000+(230*24))-5800=720
The director of a production company constructed the Venn diagram shown to display the types of employees in the company. How many of the employees are both actors and dancers?
Answer:
9
Step-by-step explanation:
The way to find the answer is by finding the point we're the two circles intersect and adding the number in that space to the number in the middle as the people in the middle are shown to be capable of both things as well
Toms garden is 8 acres. Two fifths is corn. Of that, three tenths is early corn and one tenth is late corn. How many acres of early corn does he have ?
Answer:
He have 0.96 acres of early corn.
Step-by-step explanation:
Given:
Toms garden is 8 acres. Two fifths is corn.
Of that, three tenths is early corn and one tenth is late corn.
Now, to find the acres of early corn.
Total garden = 8 acres.
Total Corn in garden = [tex]\frac{2}{5}\ of\ 8=\frac{2}{5} \times 8=\frac{16}{5}[/tex] acres.
As, given of the total corn in garden, three tenths is early corn.
Now, to get the early corn he have:
= [tex]\frac{3}{10} of \frac{16}{5}[/tex]
= [tex]\frac{3}{10} \times \frac{16}{5}[/tex]
= [tex]\frac{48}{50}[/tex]
= [tex]0.96\ acres.[/tex]
Therefore, he have 0.96 acres of early corn.
Question 4
Two spinners are spun +
and the scores are added
together. The results are
shown in the diagram
opposite.
2
a) Write down the
probability that the || 3
score is 3
b) Write down the
probability that the
score is an even
number.
c) If the two spinners
are spun 200 times,
how many times
would you expect
the score to be 2.
Answer:
a is 7/25
b is 14/25
c is 24
Step-by-step explanation:
a) because there are 25 possible outcomes and 7 of them are 3 it is 7/25
b) using the same logic 14 possible outcomes are even
c) because the probability of it being 2 is 3/25, which can be made into ?/200 by multiplying the 25 by 8, which means we have to do the same to the 3, making it 24
Match each picture to its name.
Answer:
line PQline PQ+ lineQR= line PRPQ moves in opposite directions point PP and Q moves in the same directionData;
PQMatching the Line or Points1) Line P to Q can be represented as
[tex]--\\PQ[/tex]
2)
The Line P, Q and R will be represented as
[tex]PQ + QR = PR[/tex]
3)
The point P and Q will be represented as
[tex]< \to \\PQ[/tex]
With the sign above it's head
4)
point P will be represented as
[tex].P[/tex]
5)
The point PQ moving towards in the right hand side can be represented as
[tex]\to\\PQ[/tex]
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-(2)negative negative two quotation to the zero power equals
Answer:
1
Step-by-step explanation:
While I am not 100% sure what you are putting (I'm assuming it's -2^0), anything to the power of 0 will equal a positive 1 as your answer.
What is 16 2/3% of 96 lamps
Answer:
16 lamps
Step-by-step explanation:
we know that
96 lamps represent the 100%
so
using proportion
Find out how many lamps represent 16 2/3%
but first convert to an improper fraction
[tex]16\frac{2}{3}\%=\frac{16*3+2}{3}=\frac{50}{3}\%[/tex]
Apply proportion
[tex]\frac{96}{100\%}=\frac{x}{\frac{50}{3}\%} \\\\x= (\frac{50}{3})(96)/100\\\\x=16[/tex]
Answer:
16 lamps
Step-by-step explanation:
Eva was playing a game with a friend and had 100 points.
Then, she drew a bad card and lost 120 points.
What was her new score?
She had 100 points then lost 12-0 points.
Subtract 120 from 100.
100 - 120 = -20
Answer:20
Step-by-step explanation:
Sarah bought two t-shirts and one sweatshirt. The t-shirts cost $15.22 each. If Sarah spent a total of $67.94,how many dollars did the sweatshirt cost? Express your answer as a decimal to the nearest hundredth.
Answer:
111
Step-by-step explanation:
So firstly, you have two t-shirts, so you do 15.22*2=30.44. Then you use 67.94, and subtract 30.44, which is 37.5
Simple as that!!
- 1\2[p+2]= -3 -p
Can somebody solve this for me ! plz
Answer:
-4
Step-by-step explanation:
-1(p+2)/2=-3-p
Multiplying both sides by 2
-p-2=2(-3-p)
-p-2=-6-2p
Combining similar terms
-p+2p=-6+2
p=-4
Find x.
pleaaaaase help
Answer:
x = 12
Step-by-step explanation:
1. Set up a proportion:
32 (32 + x)
------ = ------------
24 (24 + 9)
2. Cross-multiply & solve for x:
32*(24 + 9) = 24*(32 + x)
1056 = 768 + 24x
288 = 24x
12 = x
x = 12
How does adding or subtracting polynomials compare to adding or subtracting integers?
Answer:
Subtracting Polynomials is very similar to adding polynomials. In fact, we will be changing the subtraction problem to an addition problem. In the Pre-Algebra section of the website, we started out by reviewing integers. We said, " When you subtract integers, you must add the opposite. We also talked about the Keep - Change- Change Rule.
Step-by-step explanation:
The explanation regarding the adding or subtracting polynomials compare to adding or subtracting integers is explained below:
The following information should be considered:
Subtracting Polynomials is same to adding polynomials. It should be changed the subtraction problem to an addition problem. In the Pre-Algebra section of the website, here we begins with reviewing integers. We said that at the time when you subtract integers, you must add the opposite. Also, Keep - Change- Change Rule should be considered.
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Write an equivalent expression for -3t+4q+5t-7q
Answer:
The equivalent expression can be given as:
⇒ [tex]2t-3q[/tex]
Step-by-step explanation:
Given expression:
[tex]-3t+4q+5t-7q[/tex]
To write an equivalent expression:
Solution:
In order to write an equivalent expression, we will combine the like terms. By like terms, we mean the terms with the same variable constant.
For example : [tex]5x[/tex] and [tex]-3x[/tex] are like terms.
We have:
[tex]-3t+4q+5t-7q[/tex]
Combining like terms :
⇒ [tex]-3t+5t+4q-7q[/tex]
⇒ [tex]2t-3q[/tex]
Thus, the equivalent expression can be given as:
⇒ [tex]2t-3q[/tex]
Write 15/45 as unit rate
Answer:
Step-by-step explanation:
15/45 = 1/3 {giving by 15th table}
= 0.33