The algebraic expression 15(2 + r) by the distributive property can be written as 30 + 15r.
What is distributive property?This property states that multiplying the sum of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the algebraic expression is 15(2 + r). The expression by using the distributive property can be written as:-
E = 15(2 + r)
E = 30 + 15r
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Two cars start at the same time, but travel in opposite directions. One car's average speed is 80 miles per hour (mph). At the end of 2 hours, the two cars are 220 miles apart. Find the average speed in mph of the other car.
The speed of an object is the relationship between the distance covered by the object and the time taken. Thus, the average speed of the other car is 30 mph.
The speed of an object is the relationship between the distance covered by the object and the time taken. The expression for speed is given as;
speed = [tex]\frac{distance covered}{time taken}[/tex]
⇒ distance = speed x time taken
In the given question, the distance of the first car after 2 hours can be determined as:
distance = 80 mph x 2 h
= 160 miles
The distance covered by the first car after 2 hours is 160 miles.
Thus, since the total distance between the two cars after 2 hours is 220 miles, then;
distance covered by the second car = 220 miles - 160 miles
= 60 miles
The distance covered by the second car is 60 miles.
So that the average speed of the other car is;
speed = [tex]\frac{60}{2}[/tex]
= 30 mph
The average speed is 30 miles per hour (mph).
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If DAB = 80°, then DAC =
Answer:
80
Step-by-step explanation:
DAB =DAC...........
Question
The epicenter of an earthquake is the point on Earth's surface directly above the earthquake's origin. A seismograph can be used to determine the distance to the epicenter of an earthquake. Seismographs are needed in three different places to locate an earthquake's epicenter. Find the location of the earthquake's epicenter if it is 2 miles away from A(−2,5), 4 miles away from B(2,3), and 7 miles away from C(−2,−4).
Answer:
The epicenter is ( - 2, 3)Step-by-step explanation:
Let the epicenter be E(x, y).
Use the distance formula for each given distance:
AE² = (x + 2)² + (y - 5)² = 2²BE² = (x - 2)² + (y - 3)² = 4²CE² = (x + 2)² + (y + 4)² = 7²Use the first and third equations, considering both have same term for x, and solve for y:
(y - 5)² - 4 = (y + 4)² - 49y² - 10y + 25 - 4 = y² + 8y + 16 - 4918y = 54y = 3Substitute y into one of equations and solve for x:
(x + 2)² + (3 - 5)² = 4(x + 2)² + 4 = 4(x + 2)² = 0x + 2 = 0x = - 2The epicenter is E( - 2, 3)
Answer:
(-2, 3)
Step-by-step explanation:
Given:
A = (-2, 5) → 2 miles awayB = (2, 3) → 4 miles awayC = (-2, -4) → 7 miles awayModel each given point as the center of a circle and the distance the epicenter is away from the point as the circle's radius.
The epicenter's location will be the point of intersection of the three circles.
Equation of a circle
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where (a, b) is the center and r is the radius
Circle A
center = (-2, 5)radius = 2 miles[tex]\implies (x+2)^2+(y-5)^2=4[/tex]
[tex]\implies x^2+4x+4+y^2-10y+25=4[/tex]
[tex]\implies x^2+4x+y^2-10y+25=0[/tex]
Circle B
center = (2, 3)radius = 4 miles[tex]\implies (x-2)^2+(y-3)^2=16[/tex]
[tex]\implies x^2-4x+4+y^2-6y+9=16[/tex]
[tex]\implies x^2-4x+y^2-6y-3=0[/tex]
Circle C
center = (-2, -4)radius = 7 miles[tex]\implies (x+2)^2+(y+4)^2=49[/tex]
[tex]\implies x^2+4x+4+y^2+8y+16=49[/tex]
[tex]\implies x^2+4x+y^2+8y-29=0[/tex]
To find the point of intersection of the three circles, solve simultaneously.
Substitute equation B into equation A to eliminate x² and y²:
[tex]\implies x^2-4x+y^2-6y-3=x^2+4x+y^2-10y+25[/tex]
[tex]\implies -4x-6y-3=4x-10y+25[/tex]
Rearrange to isolate y:
[tex]\implies -6y-3=8x-10y+25[/tex]
[tex]\implies 4y-3=8x+25[/tex]
[tex]\implies 4y=8x+28[/tex]
[tex]\implies y=2x+7[/tex]
Substitute the expression for y into equation C and simplify:
[tex]\implies x^2+4x+(2x+7)^2+8(2x+7)-29=0[/tex]
[tex]\implies x^2+4x+4x^2+28x+49+16x+56-29=0[/tex]
[tex]\implies 5x^2+48x+76=0[/tex]
Substitute the expression for y into equation B and simplify:
[tex]\implies x^2-4x+(2x+7)^2-6(2x+7)-3=0[/tex]
[tex]\implies x^2-4x+4x^2+28x+49-12x-42-3=0[/tex]
[tex]\implies 5x^2+12x+4=0[/tex]
Equate the equations to eliminate 5x² and solve for x:
[tex]\implies 5x^2+48x+76=5x^2+12x+4[/tex]
[tex]\implies 48x+76=12x+4[/tex]
[tex]\implies 36x+76=4[/tex]
[tex]\implies 36x=-72[/tex]
[tex]\implies x=-2[/tex]
Substitute the found value of x into the found expression for y:
[tex]\implies y=2(-2)+7[/tex]
[tex]\implies y=-4+7[/tex]
[tex]\implies y=3[/tex]
Therefore, the point of intersection of the three circles if (-2, 3) and hence the location of the earthquake's epicenter is (-2, 3).
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A file that is 273 megabytes is being downloaded. If the download is 18.9 complete, how many megabytes have been downloaded? Round your answer to the nearest tenth.
Answer:
51.6 megabytes
Step-by-step explanation:
It is asking you what 18.9 percent of 273 is. To find this you multiply 18.9 x 273 and then divide it by 100 which equals 51.597.
You then round it to the nearest tenths which gives you 51.6
a. If you wanted to draw a circle around this triangle that passed through points A, B, and C as shown by circle P, what steps would you take to do that? b. What steps would you take to draw a circle within the triangle such that each side of the triangle became a tangent line to the circle as shown by circle R? c. If a line drawn from point B to point P measures 2 inches, what is the diameter, circumference, and area of circle P in terms of I? d. Describe how you would find the area of the region bounded by segment BC and arc BDC in terms of a if the arc measure of arc BDC is 60°
The circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
Steps involved in inscribing a triangleThe steps involved in inscribing a triangle;
Construct two chords on the circle.Then , draw a perpendicular bisector to the chords with the compass which must meet at the center of the circle. Make a line from the center to one of the farthest points of the chords.Draw two lines to form a 30 degree with the radius on the opposite side.Stretch out these two lines to make two chords on the circle. The two chords should make angle of 60 degrees to each other.Then connect the other extreme of the two chords this makes an equilateral triangle.If the line drawn from point B to point P measures 2 inches, then the diameter is
= 2 × 2
= 4 inches.
The formula for calculating the circumference of a circle is given as;
Circumference = 2 π r
Radius = diameter/ 2
Radius = 4/2 = 2 Inches
Substitute the values
Circumference = 2 × 3. 142 × 2
Circumference = 12. 57 inches
Area = π r²
Area = 3. 142 × 2²
Area = 3. 142 × 4
Area = 12. 57 square inches
Thus, the circumference and area of the circle is 12. 57 inches and 12. 57 inches square respectively.
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find x and y
can someone pls solve
Answer:
x = 65°y = 105°
Step-by-step explanation:
According to the picture, the angles with measure of 65° and x are included between two parallel pairs of lines.
It makes them equal:
x = 65°y is the exterior angle of the triangle with two remote interior angles with measure of 40° and 65°.
As per definition of the exterior angle its measure is same as the sum of remote interior angles:
y = 65° + 40° = 105°WILL GIVE BRAINLIEST
given: RTSU is a rectangle with vertices R (0,0), S (0, a), T(a,a) and U, (a,0) where a ≠ 0
Prove: RTSU is a square
look at image
The missing parts of the proof are: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
What is a Square?A square is a special type of rectangle whose consecutive sides are congruent. All four sides of a square are congruent.
In the proof given, the distance formula [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex] was used to find ST = a units in step 2.
By the definition of congruence, RS = ST in step 4.
Finally, RSTU is stated to be a square because if two consecutive sides of a rectangle are congruent, then it is a square.
The option that completes the proof in the right order is: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
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Answer:
distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it’s a square
Step-by-step explanation:
so its c for me
Graph line y=-1/4x+3
Answer:
connect the points (0, 3) and (4, 2)
Tina puts the letters of the word RADAR on pieces of paper and puts the pieces in a bag. She
draws two letters without looking. The first piece of paper is not replaced before the second
piece is drawn. What is the probability that Tina draws an R twice?
Answer:
1/10
Step-by-step explanation:
the probability of drawing r the first time is 2/5, if tina had gotten the r the first time, the probability of drawing r on the second time is 1/4, so the probability tina draws an r twice is 2/5 * 1/4, or 2/20, or 1/10
A 8 gram sample of a substance that's a by-product of fireworks has a k-value of 0.1027. Find the substance's half-life, in days. Round your answer to the nearest tenth
The substance's half - life is 7 days
How to determine the half-life
The formula for finding the half - life is given as;
Half - life = [tex]\frac{0. 693}{k}[/tex]
The k value given is 0.1027
Half - life = [tex]\frac{0. 693}{0.1027}[/tex]
Half - life = 6. 75
Half - life = 7 days in the nearest tenth
Thus, the substance's half - life is 7 days
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What is the solution (1/4)x+1=32
[tex] \frac{1}{4} x + 1 = 32 \\ \frac{1}{4} x = 32 - 1 \\ \frac{1}{4} x = 31 \\ x = 31 \times 4 = 124[/tex]
The answer is 124.
(1/4)x + 1 = 32(1/4)x = 31x = 31(4)x = 124solve asap please!!!
find the outer perimeter of this figure
Answer:
41.12 ft
Step-by-step explanation:
10 + 6 = 16
2 x pi x r = 25.12
16 + 25.12 = 41.12
Answer:
Step-by-step explanation:
find the outer perimeter of this figure
we find the perimeter of the semicircleThe perimeter of circle formula = 2πr unitsr = diameter : 2 = 8 : 2 = 4
2π4 =
8π=
8 × 3.14 = 25.12 ft
find figure perimeter
25.12 + 6 + 10 =
41.12 ft
In ΔABC, BC = 13, CA = 20 and AB = 19. Which statement about the angles of ΔABC must be true?
m∠B > m∠ A > m∠C
m∠C > m∠B > m∠A
m∠A > m∠B > m∠C
m∠C > m∠A > m∠B
m∠B > m∠C > m∠A
m∠A > m∠C > m∠B
Answer:
m∠B > m∠C > m∠A
Step-by-step explanation:
The angle opposite the largest side in a triangle is the largest, and the angle opposite the shortest side is the smallest.
Solve.
Three times the sum of some number plus 3 is equal to 7 times the number minus 23.
The unknown number of the given expression is 8
Linear equationsLet the unknown number be x such that three times the sum of some number plus 3 is equal to 7 times the number minus 23 is expressed as;
3(x + 3) = 7x - 23
Expand
3x + 9= 7x - 23
Collect the like terms
3x-7x = -23 - 9
-4x = -32
x = 8
Hence the unknown number of the given expression is 8
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1
Select the correct answer from each drop-down menu.
Ray and Terry work in the same office. They sit across from each other at fixed desks that are separated by a partition, or a short dividing wall,
exactly halfway between them. The distance between the end of each desk and the partition is 35 inches. For both Ray and Terry, the top of the
partition is at an angle of elevation of 30° with respect to the end of the desk. This scenario can be modeled by the given diagram.
Ray has the incorrect reasoning because he incorrectly select the sine function when he should have utilized the tangent.
How to find the height of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees.
The height of the ray can be found using trigonometric ratios.
Therefore,
tan 30 = opposite / adjacent
where
opposite side = height
adjacent side = 35 inches
Therefore,
tan 30° = height / 35
cross multiply
height = 35 tan 30°
height = 20.2072594216
height = 20.21 inches
Therefore, Ray has the incorrect reasoning because he incorrectly select the sine function when he should have utilized the tangent.
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Answer:
1. Ray
2. Sine
3. Tangent
Step-by-step explanation:
Plato/Edmentum
Does this represent a proportional relationship
Answer:
D.
Step-by-step explanation:
the suggested relation can be described as y=15x. Then the correct answer is D) Yes, the points are on the line that passes through the origin.
Match the expressions to their solutions or equivalents. (-3/8) + (-1/8)
Answer:
-1/2
Step-by-step explanation:
-3/8+-1/8=-4/8 which is equal to -1/2
Answer:
1/4
Step-by-step explanation:
(3/8)+(-1/8)
= (3/8) - (1/8)
= 2/8
= 1/4
The function f(x)=−4x+1 has a horizontal asymptote at?
The function has a horizontal asymptote at y = 1
How to determine the horizontal asymptote?The function is given as:
f(x) = -4/x + 1
Set the radicand to 0.
So, we have:
y = 0 + 1
Evaluate
y = 1
Hence, the function has a horizontal asymptote at y = 1
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120 increased by d percent and increased by 25 percent. what is the result?
Using proportions, the expression for the final amount is:
150(1+d).
What is a proportion?A proportion is a fraction of a total amount, and the measures are related using a rule of three.
For this problem, we have that:
The increase of d% is equivalent to a multiplication by (1 + d).The increase of 25% is equivalent to a multiplication by 1.25.Hence the equivalent expression is:
120 x 1.25 x (1 + d) = 150(1+d).
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they’re 25 student’s 14 female and 11 male two students are selected at random to participate in a probability experiment. compute that
b) a male is selected then a female
c) a female selected then a male
d) two females are selected
e) no males are selected
The probabilities in each of the given categories are; A) 51.33%; B) 51.33% C) 30.33% D) 30.33%
How to find the Probability of Selection?The number of ways to select 2 out of 25 is; 25C2 = 25! / (23! * 2!)
= 25*24/2
= 300
(A) Probability of selecting 1 male and 1 female:
[(11C1) * (14C1)]/300 = [11!/(10! * 1!)] * [(14!/(12! * 2!))
= 51.33%
(B) Probability of selecting 1 female and 1 male:
[(14C1) * (11C1)]/300 = 51.33%
(C) Probability that 2 females are selected is;
(14C2)/300 = 30.33%
D) Probability that no males are selected is;
P(no males) = (11C0 * 14C2 )/300 = 30.33%
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Consider the following graph
a) What is the equation of the axis?
b) What is the period?
c) What is the amplitude?
d) Is this a sine graph or a cosine graph? Explain
a) The equation of axis is the middle y-coordinate, which is y = -1.5.
b) The period is the amount of time it takes for the graph to repeat, which is 6.
c) The amplitude is the vertical distance from an extreme point to the midpoint, which is 3.
d) This is a cosine graph since when x=0, y is not equal to 0.
For csc 330:
a) state value of the ratio exactly
b) find one equivalent expression
c) draw a diagram to illustarte.
The value of the ratio based on the angle illustrated is 1:12.
How to illustrate the information?From the information given, it should be noted that the angle in a circle is 360°. Therefore, the value of theta will be:
= 360° - 330°
= 30°
The equivalent expression based on the angle will be:
= 30/360
= 1/12
= 1:12
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11. What effect size do you use for parametric t-tests?
12. What effect size do you use for non-parametric t-tests?
13. What effect size would you use for chi-square tests?
The effective sizes for parametric tests, non parametric tests and chi square tests are as detailed below.
How to interpret the size of statistics test?
11) Parametric t-tests are statistical tests that assume the data approximately follows a normal distribution. Now, when trying to check for parametric t-tests, the effective size we use is Cohen's d which is an appropriate effect size for the comparison between two means.
12) Nonparametric t-tests are those statistical tests that don’t assume anything about the distribution followed by the data, and hence are also known as distribution free tests.
In non - parametric t - tests, we calculate effect size by using the formula;
r = z/√N
where;
r is effect size
z is z value
N is Observation number.
13) In the chi-square test, the effect size index (w) is calculated by dividing the chi-square value by the number of scores and taking the square root.
The effective size is considered small if w = 0.10, Considered medium if w = 0.30, and large if w = 0.50.
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John is twice as old as Peter. In 8 years, John's age will be 2 more than the sum of their present ages. How old is John now?
Answer:12
Step-by-step explanation:
Peter's age = x
John's age = y
y=2x
after 8 years = y+8=y+x+2
=(y-y)+8-2=x
=6=x
y=2(6)=12
Which of the following rational functions is graphed below?
Answer:
A
Step-by-step explanation:
If you were to substitute 2 or -3 into equation A, the denominator would be zero and you would have to divide by zero. Thus there are asymptotes for this function at -3 and 2, matching the graph
equivalent expressions to 7^3*7^x
Kylie has a modern quarter with a mass of 5.623 g and an older silver quarter with a mass of 6.24 g What is the combined mass of the quarters?
Answer:
11.863 g
Step-by-step explanation:
5.623 g + 6.24 g = 11.863 g
Find the critical value (t-value) that form the boundaries of the critical region for a two-tailed test with a = 0.05 for a sample size of n1 =11 & n2 =8
Using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df is of Tc = 2.1098.
How to find the critical value of the t-distribution?It is found using a calculator, with two inputs, which are given by:
The confidence level.The number of degrees of freedom, which is one less than the sample size.In this problem, the inputs are given as follows:
Confidence level of 95%, as 1 - 0.05 = 0.95.17 degrees of freedom, as there are two samples, one with 11 - 1 = 10 df, and the other with 8 - 1 = 7 df, hence the total df is 10 + 7 = 17.Hence, using a calculator, the critical value for the t-distribution with a confidence level of 95% and 17 df, using the stated two-tailed test, is of Tc = 2.1098.
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To find the quotient of two fractions, you first need to rewrite the division problem as an equivalent multiplication problem. Find this quotient using multiplication.
The divisor of the expression 2/3 ÷ 6/5 is 9.
We have,
Expression:
2/3 ÷ 6/5
The concept used.
a/b ÷ c/d = ad / bc
Now,
2/3 ÷ 6/5
This can be written as,
= 2/3 x 5/6
= (2 x 5) / (3 x 6)
= 10 / 18
= 2 x 5 / 2 x 9
Cancel the common factor.
= 5 / 9
This can be read as,
Dividend = 5
Divisor = 9
Thus,
The divisor of the expression is 9.
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