Answer:
Base = 10 cm
Height = 6 cm
Step-by-step explanation:
Here is the formula for the area of a triangle.
[tex]A=\frac{bh}{2}[/tex]
We are given
[tex]A=30[/tex]
[tex]b=h+4[/tex]
Replace all occurrences of [tex]b[/tex] with [tex]h+4[/tex] in each equation.
[tex](h+4)*\frac{h}{2} =30[/tex]
Apply the distributive property.
[tex]h(\frac{h}{2})+4(\frac{h}{2})=30[/tex]
[tex]\frac{h*h}{2}+4(\frac{h}{2})=30[/tex]
Use the power rule to combine exponents.
[tex]\frac{h^2}{2}+4(\frac{h}{2})=30[/tex]
Factor 2 out of 4 .
[tex]\frac{h^2}{2}+2(2)(\frac{h}{2})=30[/tex]
Cancel the common factor.
[tex]\frac{h^2}{2}+2h=30[/tex]
Solve for h.
Multiply each term in [tex]\frac{h^2}{2}+2h=30[/tex] by 2 to eliminate the fractions.
[tex]\frac{h^2}{2}*2+2h*2=30*2[/tex]
Simplify each term.
Cancel the common factor of 2.
[tex]h^2+2h*2=30*2[/tex]
[tex]h^2+4h=60[/tex]
Subtract 60 from both sides of the equation.
[tex]h^2+4h-60=0[/tex]
Factor using the AC method.
Consider the form [tex]x^2+bx+c[/tex] . Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]b[/tex] . In this case, whose product is − 60 and whose sum is 4 .
−6, 10
Write the factored form using these integers.
[tex](h-6)(h+10)=0[/tex]
Set [tex]h-6[/tex] equal to 0 and solve for h.
Then add 6 to both sides of the equation.
[tex]h-6=0\\h=6[/tex]
Set [tex]h+10[/tex] equal to 0 and solve for h.
Then subtract 10 from both sides of the equation.
[tex]h+10=0\\h=-10[/tex]
The final solution is all the values that make [tex](h-6)(h+10)=0[/tex] true.
[tex]h=6,-10[/tex]
Given [tex]b=h+4[/tex]
Replace all occurrences of h with 6 in each equation.
[tex]b=6+4\\b=10\\h=6[/tex]
The cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet. It costs $3,000 to paint a room with a surface area of 1,500 square feet. Determine an equation that gives the relationship between c and a.
The equation that gives the relationship between cost (c) and area (a) is c = 2a
How to determine an equation that gives the relationship between cost and area?A variation is a relation between a set of values of one variable and a set of values of other variables
Given that: the cost (c) to paint a building varies directly with the area of the surface being painted (a) in square feet
We can write:
c α a
c = ka
where k is the constant of proportionality
since c = $3,000 and a = 1500
c = ka
3000 = 1500k
k = 3000/1500
k = 2
Thus, the equation of the relationship is c = 2a
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50 POINTS!!! Which graph represents this system? y = 3. x + y = 4. Which graph represents this system? y = 3. x + y = 4. On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (3, 7). On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (2, 6). On a coordinate plane, a vertical line is at x = 3 and another line goes through (0, 4) and (4, 0). On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0).
For a system with equations y = f(x) and y = g(x), the graph of the system will be just a coordinate plane with the two functions graphed on it.
What is functions graphed?
What Does Graphing Functions Mean? Drawing the curve that represents a function on a coordinate plane is known as graphing a function. Every point on the curve will satisfy the function equation if the curve (or graph) represents the function. As an illustration, the graph below depicts the linear function f(x) = -x+ 2.
From this, we can see that the correct option is the first one:
"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."
Also a graph of the system can be seen at the end of this answer.
Here our system is:
y = 3
x + y = 4
The first one is a horizontal line at y = 3.
The second can be rewritten as:
y = -x + 4
So this is a line with a negative slope, that passes through the points (0, 4) (when you evaluate in x = 0, you get y = 4) and (4, 0) (when you evaluate in x = 4, you get y = 0)
Then the correct option is the first one:
"On a coordinate plane, a horizontal line is at y = 3 and another line goes through (0, 4) and (4, 0)."
The graph can be seen below
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A tutor guarantees that 10% of her students will obtain A on every test they write. For the last test, the mean mark is 68 and the standard deviation is 6.
What mark is required to receive an A on the test?
The mark that is required to receive an A on the test is; 75.68
How to find sample mean?The formula for z-score here with the parameters given is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
p-value = 10% = 0.1
μ = 68
σ = 6
Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;
1.28 = (x' - 68)/6
x' = 68 + (1.28 * 6)
x' = 75.68
We conclude that this value is the mark required to receive an A on the test.
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Find the values of x and z !!
The value of x and z are [tex]4^\circ, 96^\circ[/tex].
Now from the picture I can say that, [tex]\angleAOB[/tex][tex]\angle AOB[/tex] and [tex]\angleCOD[/tex][tex]\angle COD[/tex] are opposite angles.
We know the measure of the triangle are equal in Pair.
So we have got the equation as -
[tex]10x+44=13x+32[/tex]
⇒[tex]13x-10x=44-32[/tex]
⇒3x=12
⇒x=4.
We have got that the measure of [tex]\angle AOB, \angle COD[/tex] are both [tex]84^\circ[/tex].
Now angles around a point add to [tex]360^\circ[/tex].
So, [tex]\angle AOD[/tex] and [tex]\angle BOC[/tex] are equal since they are pairwaite wisw.
Now, [tex]z+z= 360^\circ - (84^\circ+84^\circ)[/tex]
⇒[tex]2z=192^\circ[/tex]
⇒ [tex]z=96^\circ[/tex],
Hence we have got the value of x and z i.e. 4 and 96.
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Please help meee !!!!???
Answer: 19 feet
Step-by-step explanation:
The area, 266, divided by the width, 14, equals to 19 feet.
The original selling price was $171.59. The sale proteas $148.37. What is the first step in finding the percent markdown? Find the percent markdown
The original price is $171.59 and the price during sales is $148.37 then the percent markdown will be 13.53%.
What is the Percentage?The Latin phrase "per centum," which means "by the hundred," is where the English word "percentage" comes from. Percentage segments are those with a numerator of 100. In other words, it is a connection where the whole is always deemed to be valued 100.
As per the given information in the question,
Original selling price = $171.59
Price during sales = $148.37
Then, the percentage markdown will be,
% markdown = (171.59 - 148.37)/171.59 × 100
= 23.22/171.59 × 100
% markdown = 13.53%
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What is the quotient of 535 ÷ 30? Enter your answer in the boxes.
Select the correct answer.
Which graph represents function g?
g(x) = (-x)1/2
Answer:
Step-by-step explanation:
g(x) = (-x)1/2
Solve by factoring
X^2+x=63
Answer:
x = 3[tex]\sqrt{7- x}[/tex]
Step-by-step explanation:
so what you do here is move the x to the other side.
X^2 = 63 - x
then you square root both sides
so [tex]\sqrt{x^{2} }[/tex] and [tex]\sqrt{63 - x}[/tex]
so you end up with
x = [tex]\sqrt{63 - x}[/tex]
so now we ask what can we take out? 9 times 7 is 63 and 9 is a perfect square so when we take the square root of that, we end up with
x = 3[tex]\sqrt{7- x}[/tex]
have a good day :)
according to the information that comes with a certain prescription drug, when taking this drug, there is a 20% chance of experiencing nausea (n) and a 45% chance of experiencing decreased sexual drive (d). the information also states that there is a 14% chance of experiencing both side effects. what is the probability of experiencing only nausea?
The probability of experiencing only nausea is 0.06.
Using Venn Probabilities, it is found that there is a 0.45 = 45% probability of experiencing neither of the side effects.
What is a Venn probability?
In a Venn probability, two non-independent events are related with each other, as are their probabilities.
The "or probability" is given by:
P(N∪D) = P(N) + P(D) - P(N∩D)
In this problem, the probabilities given are:
P(N)= 0.2 , P(D)= 0.45 , P(N∩D) = 0.14
The "at least one" probability is:
P(N∪D) = 0.20 + 0.45 - 0.14 = 0.51
Hence, the "neither" probability is:
1 - P(N∩D) = 1 - 0.51 = 0.49
The probability of experiencing only nausea = P(nausea) - P(both side effects)
=0.20 - 0.14
=0.06
0.49 = 49% probability of experiencing neither of the side effects.
The probability of experiencing only nausea is 0.06.
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it is known that pre-schoolers, on average, spend three hours a week on tablets. i believe that this is no longer true, and that the average time that pre-schoolers spend on tablets differs in either direction from the previously given average. i calculate a z-test statistic of 1.74. what is my statistical decision?
Retain the null because 1.74 is greater than 1.645.
What is z - test statistic?
Any statistical test for which the test statistic's distribution under the null hypothesis can be roughly represented by a normal distribution is known as a Z-test.
Z-tests examine a distribution's mean.
Let X be the average time that prescholars spend on tablets.
X ~ N(μ, α^2)
To test H0: μ = 3 hours Vs H1: μ ≠ 3 hours.
The z - test statistic is obtained as 1.74.
Taking level of significance α = 0.05
Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex]
Since the observed z - statistic is 1.74 which is less than Zα/2 = [tex]Z_0_._0_2_5 = 1.96[/tex],
so we retain the null hypothesis.
Hence, retain the null because 1.74 is greater than 1.645.
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Complete question:
Complete question is attached below.
what is the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order?
The final answer is that the probability of rolling a six sided die six times and having all numbers from 1 through 6 appear once in any order is 1.54.
This is calculated by probability of independent events.
We know that any die can get any of the six sides and all the throws are independent, so their intersection is given by the product.
So, P(A and B occurring together )= P(A)P(B) if A and B are independent.
And the probability of the throws i.e. the no. of ways every throw gets a unique number is (6/6) x (5/6) x (4/6) x (3/6) x (2/6) x (1/6)
This is because, being the probability of independent events , they are multiplied.
so, the total probability is 6.5.4.3.2.1/6^6 = 1.54
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A football team has four different jerseys that players wear throughout the season: school colors, white, throwback, and pink (for breast cancer awareness). The tree diagram shows the conditional probabilities of the outcome of their games when players wear each type of jersey.
For a randomly selected game, determine the probability that players wore their white jerseys, given that they won.
0.34
0.41
0.42
0.80
Answer:0.41
Step-by-step explanation:
consider the following: the mayor of a town has proposed a plan for the annexation of a new community. a political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation. using the data, a political strategist wants to test the claim that the percentage of residents who favor annexation is above 65%. what is the alternative hypothesis? group of answer choices
We can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.
What do you mean by Annexation?
International law defines annexation as the forcible acquisition of one state's territory by another state, typically after the possession of the region by an occupying military force. In most cases, it is considered to be unlawful.
According to the question,
We have the given data:
A political study took a sample of 1,600 voters in the town and found that 69% of the residents favored annexation.
The conclusion of the hypothesis test is that we reject the null hypothesis that the percentage of residents who favor annexation is 65% or lower. The sample data suggests that 69% of residents favor annexation and the p-value associated with the test statistic is 0.07, which is less than the significance level of 0.05.
This indicates that the data is significantly different from the null hypothesis and that the true percentage of residents who favor annexation is likely greater than 65%.
Therefore, we can conclude that the mayor's plan for annexation is likely to be supported by the town's residents.
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Steven is a waiter. He earns $3.45 an hour plus 20% tips. One day he worked 7 hours and served meals costing $497 what were his earring? Round you answer to the nearest cent.
A shipping container will be used to transport several 50-kilogram
crates across the country by rail. The greatest weight that can be
loaded into the container is 27500 kilograms. Other shipments
weighing 9500 kilograms have already been loaded into the container.
Write and solve an inequality which can be used to determine x, the
number of 50-kilogram crates that can be loaded into the shipping
container.
Answer:
50x + 9500 ≤ 27500
x ≤ 360
Step-by-step explanation:
50x + 9500 ≤ 27500 Subtract 9500 from both sides
50x + 9500 - 9500 ≤ 27500 - 9500
50x ≤ 18000 Divide both sides by 50
[tex]\frac{50x}{50}[/tex] ≤ [tex]\frac{18000}{50}[/tex]
x ≤ 360
what is the answer to this question?
−6(4y + 4y + (−4))
Answer:
-48y+24
Step-by-step explanation:
−6(4y + 4y + (−4))
=-6(8y+-4)
=-48y+24
Answer:
-48y + 24
Step-by-step explanation:
−6(4y + 4y + (−4)) =
= −6(8y - 4)
= -48y + 24
Angie is determining the volume of a box in the shape of a rectangular prism. She finds the length is 2cm more than the width and 3 cm less than the depth. Which equation can Angie use to get the volume of the box, in cubic centimeters?
A. V = w(w+2)(w+3)
B. V = w(w+2)(w+5)
C. V = w(w-2)(w-3)
D. V = (w+2)(w+5)
The volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.
What is a rectangular Prism ?
A polyhedron with two congruent and parallel bases is known as a rectangular prism. It's also known as a cuboid.
A rectangular prism has six faces, each of which is in the shape of a rectangle and has twelve edges. It's called a prism because of its cross-section along its length.
It is given that length of the rectangular prism has length of 2 cm more than the width and 3 cm less than the depth
Let the depth be x cm
and width be y cm
Then the length will be y+2 cm and x-3 cm
y+2 = x- 3
x = y+5
A rectangular prism is a cuboid with six faces
Volume of a rectangular prism can be written as
length * width * depth
= (y+2) *x*y
= (y+2)* (y+5)*y
= (y²+2y)(y+5)
= y³ +5y²+2y²+10y
= y³ +7y² +10y cm³
Therefore the volume of a box in the shape of a rectangular prism is y³ +7y² +10y cm³.
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7. Olivia purchases gifts for her mom and
grandma
for Mother's Day. The first is a pair of
sunglasses for $16.35 and the second is a
bracelet. Her total is $39.75. How much did she
spend on the bracelet?
Answer: $23.40
Step-by-step explanation:
To find out how much Olivia spent on the bracelet, we need to subtract the cost of the sunglasses from the total amount spent. In this case, that would be $39.75 - $16.35 = $<<39.75-16.35=23.40>>23.40. Therefore, Olivia spent $23.40 on the bracelet.
Number of nickels in $4.20
Answer:4
Step-by-step explanation:
One group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house. At which house will they first meet?
The house that they will first meet if a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house is the 24th house.
How to calculate the multiple?The smallest positive integer that is divisible by both a and b is known as the least common multiple, lowest common multiple, or smallest common multiple of two integers, or lcm(a, b), in mathematics and number theory. Since the result of dividing an integer by zero is undefinable, this definition only applies if both a and b are not equal to zero.
Before fractions can be added, subtracted, or compared, the "lowest common denominator" can be employed.
From the information, a group of carolers goes to every 6th house in a neighborhood, another goes to every 8th house.
It should be noted that this will be illustrated through tye lowest common multiple.
Multiples of 6 = 6, 12, 18, 24
Multiples of 8 = 8, 16, 24
Therefore, they'll meet at the 24th house.
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Need help
What criteria are necessary to prove that two triangles are congruent to one another?
Answer:
SSS, SAS, ASA, AAS
Step-by-step explanation:
s = sides
a = angle
Given the function f(x)=7(3-x)+5 what is the answer
The answer of the function f(x)=7(3-x)+5 is -7x + 26.
What is a function?A function is a relationship between a number of inputs and outputs. A function is an association of inputs where each input is coupled with exactly one output. There is a range, co-domain, and domain for every function.
Given the function;
f(x)=7(3-x)+5
To simplify the function:
First, solve parenthesis,
f(x)=21 - 7x +5
Taking, constant with constant term,
f(x) = -7x + 26
Therefore, the answer is -7x + 26.
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Consider the line -8x -6y = -4.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Slope of the line is .[tex]\frac{-4}{3}[/tex]
Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]
What is the slope of a line?A line's steepness and direction are measured by the line's slope. Without actually using a compass, determining the slope of lines in a coordinate plane can assist in forecasting whether the lines are parallel, perpendicular, or none at all.
Any two different points on a line can be used to calculate the slope of any line. The ratio of "vertical change" to "horizontal change" between two different locations on a line is calculated using the slope of a line formula.
A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. As opposed to the net change in the x coordinate, the net change in the y coordinate is y.
y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,
A line's slope is a measurement of how steep it is or the direction it is going in relation to a coordinate system.
where m is the slope and m = y/x
Take notice that tanФ = y/x.
This tanФ is often referred to as the line's slope.
Calculation:The given equation is of the form [tex]ax+by=c[/tex]
On comparing we can say that a is -8 and b is -6
So using the slope formula [tex]\frac{-A}{B}[/tex] we get slope as [tex]\frac{4}{-3}[/tex]
The perpendicular line slope can be found out by equation [tex]m1.m2=-1[/tex]
Therefore substituting slope from the above as m1 we get m2 = [tex]\frac{3}{4}[/tex]
Slope of the line is .[tex]\frac{-4}{3}[/tex]
Slope of the line perpendicular to the given line is [tex]\frac{3}{4}[/tex]
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Divide. Check your solutions by multiplying.
1. 409÷5
Answer:
Step-by-step explanation:
409/5 is 1/8. then 81.8 and then check by multiplying 81.8 by 5 and that equals 409.
Help me answer this question for a 10 on my homework
Answer:
1. 4
2. rise = 2; run = 1; slope = 2
3. y = 2x + 4
Step-by-step explanation:
1. Look at the graph. On the y-axis, the line passes through 4. The line crosses the y-axis at 4, so 4 is the y-intercept, and b = 4 in the equation y = mx + b.
2. Choose any two points on the line. I choose the y-intercept, (0, 4) and point (-1, 2).
slope = rise/run
We need to go from point (-1, 2) to point (0, 4) by only moving vertically and horizontally. Start at (-1, 2). Go up 2 units. That is a ris of 2. Now go right 1 unit to arrive at point (0, 4). that is a run of 1.
slope = rise/run = 2
3. We have b = 4, and m = 2.
y = mx + b
y = 2x + 4
due today pls help me
Answer: B
Step-by-step explanation:
A - Nope.
B - Possibility.
C. Nope. (2.23606797)
D. Nope.
When facing questions like this, it can be easier to use the process of elimination.
PLEASE HELP!!!!! I WILL MARK BRAINIEST
Answer:
Step-by-step explanation:
7/8
------
3/10
use the fraction rule: 7x10/8x3- 35/12
try that, im not sure if its fully correct
4. If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).
The proof that AB = CD in the concentric circles is shown below
How to prove the equation AB = CDFrom the question, we have the following parameters that can be used in our computation:
The concentric circles
This means that the circles have the same center
From the circles, we have the following congruent lines
AC = BD
Subtract BC from both sides of the equation
So, we have the following representation
AC - BC = BD - BC
Evaluate the difference
This gives
AB = CD
Hence, it is true that AB = CD
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Answer:
Hope it will help you...
(Find LCM of) :
ax² - (a² + ab)x+ a²b,
bx² - (b² + bc)x+ b²c and
cx² - (c² + ac)x + c²a
Answer:
Here is answer
Step-by-step explanation:
To find the least common multiple (LCM) of three polynomials, we need to find the smallest polynomial that is divisible by all three of them.
Let's start by factoring each of the given polynomials:
ax² - (a² + ab)x+ a²b = a(x - b)x
bx² - (b² + bc)x+ b²c = b(x - c)x
cx² - (c² + ac)x + c²a = c(x - a)x
The LCM of these three polynomials is the smallest polynomial that is divisible by all three of them. In this case, the smallest such polynomial is (x - a)(x - b)(x - c)x. This is because it is divisible by each of the given polynomials and no smaller polynomial is divisible by all three of them.
Therefore, the LCM of the given polynomials is (x - a)(x - b)(x - c)x.
