Answer:
[tex]\sqrt{97}[/tex] units
Step-by-step explanation:
Calculate the distance using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A(- 5, 3) and (x₂, y₂ ) = B(4, - 1)
d= [tex]\sqrt{(4+5)^2+(-1-3)^2}[/tex]
= [tex]\sqrt{9^2+(-4)^2}[/tex]
= [tex]\sqrt{81+16}[/tex]
= [tex]\sqrt{97}[/tex] ≈ 9.85 ( to 2 dec. places )
What is between 49 and 50
Identify the values of variables x, y, and z based on the image given of the angles formed by a transversal and parallel lines
Answer:
[tex]x=62\\y=94\\z=94[/tex]
Step-by-step explanation:
Let's start by identifying relevant angle theorems for two parallel lines cut by a transversal.
Alternate Interior Angles Theorem
Two angles that are on different sides of the transversal and inside of the two parallel lines are congruent (=).
Alternate Exterior Angles Theorem
Two angles that are on different sides of the transversal and outside of the two parallel lines are congruent (=).
Same-side Interior Angles Theorem
Two angles that are on the same side of the transversal and inside of the two parallel lines are supplementary (= 180).
Same-side Exterior Angles Theorem
Two angles that are on the same side of the transversal and outside of the two parallel lines are supplementary (=180).
Corresponding Angles Theorem
Two angles on a figure that correspond are congruent (=).
_
Now, let's look at the figure and apply these theorems.
[tex]z[/tex] and [tex]86[/tex] are same-side exterior angles, meaning they're supplementary:
[tex]z+86=180[/tex]
Subtract [tex]86[/tex] from both sides of the equation:
[tex]z=94[/tex]
Now that we know our [tex]z[/tex] value, let's recognize that [tex]z[/tex] ([tex]94[/tex])corresponds to [tex]x+32[/tex], meaning they're congruent:
[tex]x+32=94[/tex]
Subtract [tex]32[/tex] from both sides of the equation:
[tex]x=62[/tex]
Let's find the value of the angle:
[tex](62)+32[/tex]
Add:
[tex]94[/tex]
Since the corresponding angles are of the same value, they're congruent, proving our [tex]x[/tex] & [tex]z[/tex] values correct.
_
Since [tex]y[/tex] and the angle represented by the expression [tex]x+32[/tex] ([tex]94[/tex]°) are alternate-interior angles, they are congruent:
[tex]y=94[/tex]
What is the equation of the line that passes through the point (1,7) and has a slope of −1?
Answer:
y = -x+8
Step-by-step explanation:
which pair of ratios forms a proportion? hint: check for cross products. a. 6/9=9/12 b. 8/16=10/21 c. 6/15=10/25 d. 4/14=6/27
Answer:
c. 6/15 = 10/25
Step-by-step explanation:
Using the hint, we can form the cross products of the offered choices:
a. 6(12) vs 9(9) ⇒ 72 vs 81 . . . not a proportion
b. 8(21) vs 16(10) ⇒ 168 vs 160 . . . not a proportion
c. 6(25) vs 15(10) ⇒ 150 vs 150 . . . IS A PROPORTION
d. 4(27) vs 14(6) ⇒ 108 vs 84 . . . not a proportion
__
The cross products are the same for choice C, so that is a pair of ratios that form a proportion:
6/15 = 10/25
Given a∥b and m∠5=77° .
What is m∠2 ?
Enter your answer in the box.
Answer:
Step-by-step explanation:
m<5 and m<4 are supplementary angles => m<5 + m< 4 = 180
m<4 = 180 -77 = 103
m<4 and m<2 are corresponding angles => m<4 = m<2 = 103
The measure of the angle m∠2 is 103.
What are supplementary angles?The supplementary angles are defined as the angles having a sum of 180 degrees. The angle is defined as the span between two intersecting lines or surfaces at or close to the point where they meet.
In the given image the given angle is m∠5=77°. The measure of the angle m∠2 will be calculated by using some of the angle properties.
m∠5 and m∠4 are supplementary angles:-
m∠5 + m∠4 = 180
m∠4 = 180 -77 = 103
m∠4 and m∠2 are corresponding angles => m∠4 = m∠2 = 103
Therefore, the measure of the angle m∠2 is 103.
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During her first year of college, Sara put $2000 in the bank to save for a trip to Italy after graduation. The money earned 3% simple annual interest. After 4 years, how much money did she have in the bank for her trip?
a lotStep-by-step explanation:
Answer:
2,240
Step-by-step explanation:
Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy.
Step-by-step explanation:
1. Let's review the data given to us for solving the question:
Investment of Sara during her 1st year of college = US$ 2,000
Duration of the investment = 4 years
Annual interest rate = 3%
2. Let's find the future value of this investment after 4 years, using the following formula:
FV = PV * (1 + r) ⁿ
PV = Investment of Sara during her 1st year of college = US$ 2,000
number of periods (n) = 4
rate (r) = 3% = 0.03
Replacing with the real values, we have:
FV = 2,000 * (1 + 0.03) ⁴
FV = 2,000 * (1.03) ⁴
FV = 2,000 * 1.12550881
FV = 2,251.02
Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy. Later you round the answer and that gives you 2,240
plz mark me brainliest
Help me solve this problem please
[tex]5x - (x - 2) \geq 2x - 4(x - 8)\\5x - x + 2 \geq 2x - 4x + 32\\5x - x - 2x + 4x \geq 32 - 2\\6x \geq 30\\x \geq 5\\[/tex]
Interval notation: [tex]x \in \lbrack 5, \infty \rangle[/tex]
A bakery charges $14.00 for 4 croissant sandwiches. What is the unit rate, in dollars per sandwich?
Answer:
3.5 per
Step-by-step explanation:
14/4=3.5
what is the solution for this? Y = 3bx - 7x
Answer:
[tex]x=\frac{y}{3b-7}[/tex]
Step-by-step explanation:
Rewrite the equation as [tex]3bx-7x=y[/tex].
Factor x out of 3 b x
[tex]x(3b)-7x=y[/tex]
Factor [tex]x[/tex] out of [tex]x(3b)+x*-7[/tex]
[tex]x(3b-7)=y[/tex]
Divide each term by [tex]3b-7[/tex] and simplify.
Divide each term in [tex]x(3b-7)=y[/tex] by [tex]3b-7[/tex].
[tex]\frac{x(3b-7) }{3b-7} =\frac{y}{3b-7}[/tex]
Cancel the common factor of [tex]3b-7[/tex]
Which is a correct verbal expression for
8n?
F n more than 8
G the quotient of 8 and n
H the product of 8 and n
J 8 increased by n
The correct verbal expression for 8n is "the product of 8 and n". therefore, option H is the correct choice.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
Here,
The correct verbal expression for 8n is "the product of 8 and n". Therefore, option H is the correct choice.
Option F "n more than 8" would be written as "n + 8".
Option G "the quotient of 8 and n" would be written as "8/n".
Option J "8 increased by n" would be written as "8 + n".
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Express your answer in scient 9.3.107 - 3.4.106 Stuck? Watch a video
Answer:
o resultado coreto é 59.001
i am trying to find a no solution problem with this as the set up of the problem
__x+__=__x+__
Plz help me!!!!!i need to get this correct plz help!!!
Answer:
yes
Step-by-step explanation:
if you divide 18 by 3 you get six and if you divide 15 by 3 you get 5, so it simplifies to 6:3 which is the same as the ratio for rings
I have a polygon 4 angles angle A is 3x angle B is 4x angle C is 2x and angle D is just x please help
Answer:
36 degrees =x
Step-by-step explanation:
If the polygon has 4 angles then it is a quadrilateral and must have 360 degrees. you can see that all angles in that polygon added up are 10x. If 10x=360 then x= 36 degrees, 2x=72 degrees, 3x=108 degrees, 4x=144 degrees
Answer:
36 degrees =x
Step-by-step explanation:
Math
this goes to the question i just posted someone please help me please
Answer:
Ok only if yo help me with my last question
Step-by-step explanation:
can someone tell me how to do this I am so confused
Answer:
I think it is D.
Step-by-step explanation:
Wilma estimates that she'll drive about 18,000 miles during the year. The car she wants to purchase gets an
average of 24
miles per gallon, and the average cost per gallon of gas in her neighborhood is $2.72. Locate the error in her calculations,
and select the correction.
Step 1
18,000 miles/year
18.000 miles = 1,500 miles/month
12 months
Step 2
1.500 miles/month
125 gallons/month
12 miles/gallon
Step 3
(125 gallons/month) x ($2.72/gallons) = $340 cost/month
Given parameters:
Distance in a year = 18000miles
Car mileage = 24miles/gallon
Average cost per gallon = $2.72 per gallon
Problem;
Find the error in her calculation;
Step 1
18,000 miles/year
18, 000 miles = 1,500 miles/month -- Since there are 12months in a year
12 months
Step 2
1500 miles/month
Car mileage = 24miles/gallon
Gallons per month; [tex]\frac{1500}{24}[/tex] = 62.5gallons/month
125 gallons/month this is an error and should be 62.5gallons/month
12 miles/gallon should be 24miles per gallon
Step 3
(125 gallons/month) x ($2.72/gallons) = $340 cost/month
Correct
Step 2 is wrong because it uses wrong values.
Answer:
Option 1
Step-by-step explanation:
Wilma made a mistake is step 2. Instead of dividing by 12, she should have divided by 24. She should budget $170 per month for fuel expenses.
Find the y-intercept of the line on the graph.
Answer:
2
Step-by-step explanation:
Answer:
(0,3)
Step-by-step explanation:
(0,3) is where the line intersects the y- intercept.
How to measure 1 cup of milk
Answer:
you get a one cup measurments and pour milk to the 1
Step-by-step explanation:
ive done it before
What is the domain of the function f(x) = x+ 2?
Answer: Choice D) [tex]x \ge -6[/tex]
=========================================================
Explanation:
Taking the square root of a negative number leads to a nonreal result.
So we want the radicand to be 0 or positive
Set the stuff under the square root to be 0 or larger. Solve for x.
[tex]\frac{1}{3}x+2 \ge 0\\\\\frac{1}{3}x \ge 0-2\\\\\frac{1}{3}x \ge -2\\\\x \ge 3(-2)\\\\x \ge -6[/tex]
If x is -6 or larger, then [tex]\frac{1}{3}x+2[/tex] is 0 or larger leading to some real number for f(x).
The inequality sign does not flip because we multiplied both sides by a positive number. The inequality sign only flips when we multiply both sides by a negative number.
What percent of 106 is 67?
Answer:
~63%
Step-by-step explanation:
67/106
=0.63207 × 100
= 63.207% or just 63%
Step 1: y minus (negative 2) = three-fourths (x minus 3). Step 2: y + 2 = three-fourths x minus StartFraction 9 Over 4 EndFraction. Step 3: y + 2 + 2 = three-fourths x minus StartFraction 9 Over 4 EndFraction + StartFraction 8 Over 4 EndFraction. Step 4: y = three-fourths x minus one-fourth.
A student used the point-slope form to write the equation of a line that has a slope of Three-fourths and passes through the point (3, –2). The student’s work is shown to the left.
Examine the steps to determine whether the student made an error.
The student made
Answer:
The student made an error in step 3
Step-by-step explanation:
I did it on edge 2020 and have a cat witness
Answer:
he made an mistake in problem 3
Step-by-step explanation:
have a good day
did it on edge
A car travels 196 miles in 3.5 hours. Which of the following is NOT an equivalent number of miles per hour?
Answer:
56mph
Step-by-step explanation:
Rudy took a test and earned a 92%. If Rudy answered 46 questions correctly, how many questions were on the test?
How many questions did he answer incorrectly?
How many questions would have to be correct if he made an 88%?
Answer:
50
4 were incorrect
44/50 would make it 88%
Step-by-step explanation:
Answer:
1. There are 50 questions on the test.
2. He answered 4 questions incorrectly.
3. To make an 88 he would have gotten 44/50 questions right.
given m ll n find the value of x.
Answer:
45 degrees
Step-by-step explanation:
Since the angle x and angle 135 degrees are supplementary, you just have to minus 135 from 180 which the answer is 45 degrees.
The value of the angle x will be equal to 45 degrees.
What are lines and angles?An endlessly long row of evenly spaced dots that spans in both directions makes up a line. Its length is the only dimension it has. A geometry called an angle is created when two line segments, lines, or rays intersect.
Given that the line is crossing the two parallel lines making an angle of 135 degrees with one line. The value of x will be calculated by using the supplementary angle property.
x + 135 = 180
x = 180 - 135
x = 45
Therefore, the value of the angle x will be equal to 45 degrees.
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21. 3a + 5b = -27
4a + 10b = -46
how to solve with substitution
Answer:
a = -4 and b = -3
Step-by-step explanation:
Step 1: Solve 3a + 5b = -27 for a
3a + 5b = -27
3a + 5b + -5b = -27 + -5b
(Add -5b go both sides)
3a = -5b- 27
3a = -5b - 27
3 3
(Divide both sides by 3)
a = -5 b - 9
3
Step 2: Substitute -5 b - 9 for a in 4a + 10b = -46
3
4a + 10b = -46
4(-5 b - 9) + 10b = -46
3
10 b - 36 = -46
3
(Simplify both sodes of the equation)
10 b - 36 + 36 = -46 + 36
3
(Add 36 to both sides)
10 b = -10
3
10/3 b = -10
10/3 10/3
(Divide both sides by 10/3)
b = -3
Step 3: Substitute -3 for b in a = -5/3 b - 9
a = -5/3 (-3) - 9
a = -4
(Simplify both sides of the equation)
Evelyn can run 3 miles in 40 minutes. Which equation can be solved to find m, the number of miles Evelyn can run in 60 minutes? ___1 4 and ____ 4 10 ___3 40 5 _1 m __1 2 and __6 12 ___3 40 5 __ 60 m __ 3 8 and __9 16 ___3 40 5 __ m 1 __ 2 6 and ___3 12 ___3 40 5 ___ m 60
Answer:
Step-by-step explanation:
Let m be the number of miles that evelyn can run in 60 minutes.
If evelyn can run 3 miles in 40 minutes, to calculate the number of miles she can run in 60 minutes, we will apply the equality postulate as shown;
3 miles = 40 minutes
m miles = 60 minutes
Cross multiply
40* m = 3* 60
40m = 180
Divide both sides by 40
40m/40 = 180/40
m = 180/40
m = 4.5 miles
The equation that can be used to find m is 40m = 180 and the value of m is 4.5miles
I need help forming an equation
Answer:
21=1/2n+5
There were 32 volunteers on the first day
Step-by-step explanation:
number of volunteers on the first day=n
21=number of volunteers on the second day
21=1/2n+5
-3y > 9 or 2y – 6 > 2
Pls solve with steps and explain
Answer:
[tex]y<-3\quad \mathrm{or}\quad \:y>4[/tex]
Step-by-step explanation:
so first lets solve -3y>9
[tex]-3y>9\\[/tex]
div both side by -3( rember to switch sign)
[tex]y<-3[/tex]
thats the first answer
2nd, lets solve 2y-6>2
[tex]2y-6>2[/tex]
add 6 to both side
[tex]2y>8[/tex]
div both side by 2(no switch sign)
[tex]y>4[/tex]
The price of a video game was reduced from $60 to $45. By what percentage was the price of the video game reduced? GIVE ME THE ANSWER THE CORRECT ANSWER!!!!
Answer: 25% decrease
Step-by-step explanation: